Optimization with constraints.ipynb

{
 "cells": [
  {
   "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": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def constraint1(x1):\n",
    "    return (-1)*x1 + 1\n",
    "def constraint2(x2):\n",
    "    return (-1)*x2 + 1\n",
    "def constraint3(x1, x2, a):\n",
    "    return np.sqrt(x1**2 + x2**2) - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x6572e30>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x6545050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def function(x1, x2):\n",
    "    return np.sin(np.pi*(np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)))\\\n",
    "            /(np.pi*np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2))\n",
    "    \n",
    "x1 = np.linspace(-5,5)\n",
    "x2 = np.linspace(-5,5)\n",
    "\n",
    "x1v, x2v = np.meshgrid(x1,x2)\n",
    "z = 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 0x6650350>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cWxYHG6Heje7UqVObWr470TqtjP5/qNVbiGwRLoSQ8wKBRBqegxv9IM0kIlaA\nOMiiQNoqQnHgzY3tiHzd7XccqIJ8NIp4rgg6iOL6hVLDGycyEAfXAHM93WG6iBy49ydRwgVU07Mu\nDZlFJKAgIFIl9ve/wMj1H9zUbFHf5NLKZ+ggy9522l+nRWuntumdBqj6RkzFYpG1tTVmZmb2HBRw\nFBwKm+XYC3IjSClrE5x1Xeeee+7ZZOziR7atCnKjVRY7CbFPu+qZd6Pen3lwcHBbE6ROmAuFX/oY\nwi0je2MoouSlJwRghOBBy4tg59cTxQkQjkRgwzC4qThi3EHYlY3oGJD9cUTJQCkW4QGgDPin0wYu\ngoysL/rZIO9JIl7NIUMKXFRhHkTJQqYURM7FHUwgsiUUadK/8OfE/5dfgFC01mxRLBZZWlqiWCxi\n2zbhcHhTRNdojrTTZW+H5fS2n8aTnYyYtg4K8M3pb9++zXPPPYfjOLz88svce++9+xoAsZc5PcAf\n/dEf8dGPfhQhBA899NBdrdWtcCIEebt6Wdg8ODQajXLjxo27OpigvR12u22nXojPnDmzY464HSVr\nPltvg6WUzM/PMzk5SV9f367+zAcdIauj/w119S0IOyiUkFUFgQungVPrKQsngli3Bar9HsACBQN5\nCc99/iU2cs7xkledgTdFRAyyKZ8sNQ2RMvDdhkQ+h4yCuO5COYvsCiHylmeAgYGoOgjHxY2mUIw8\n+t9/GPNbfnPbZgspJdVqtbaYtbq6uqmG14+mt7v17nQO+Tg7ve00KOD8+fNomsZLL73Epz71Kd58\n801++Id/mPe///0NHdte5vQjIyN87GMf4ytf+Qrd3d0sLS21/FrqORGCvBW/SmF8fJx4PM7999+/\n67DDg2553irETz311K4fynZFyP6Fyv97aWmJ8fFxuru7d51Y4nPQE0P0kU955kGhMFSrUInAxRIy\nlUAsFb1Eb85b0ZMREMX1Y1FA5rxAWgCkgcdAviqgCiJbd3EWeGmPJRDrb7G4YEMUWFz/fwXkg0mw\nCggJchAv35w1PKHOlqEbRNmAsk1o5IuYz6xAZKNGt7Y7IYhEIkQikbtqeOtvvX0PZL80LJFIUC6X\nOzqf7zDK7BzHaWhAaTMIIRgcHOSZZ57hC1/4Ar/7u7+7r+c3Yk7/W7/1W3zoQx+qLVS2w+GtnhMh\nyL7gSClZXFxkYmKCrq4uHnzwwbvMwbejXYK8Nf9n2zbT09PMz883JMQ+rdpvbt3O6uoqo6OjpFKp\nfc3wO8iYHzJRAAAgAElEQVSUhTr9WZTMFHJYR0yXkBrIixLhANV1EY5qCN9EqFuH4vqiWzeIumoL\nSoAD8hENpyQJzdW9l0M6uCbOIzraC+vPDwNFkKdjiDte9Cp7BGIFL8pecyAMogrOgIY6ZeMmoihO\nGTfSBYZF5CsfpvIt/7Xh17uTx0R9aVg2m6VarbKwsLDJWvOgRj8dRsrCtu2GvpOt0KyxUCPm9G+9\n9RYAzzzzDI7j8NGPfpRv//Zvb+2A6zgRgiyl5M6dO00PDm33GKd6IR4eHm5YiH3aFSE7jsOLL75I\nIpHgoYce2vcX4SBTFvrkpyAeRWhrYLu4N1KoczmkAhR9QY4g8JyDHD2MhieobkRFyXnnx02Dsu6e\nqlQt7HsFMqfVFvHc3jBqyUStmrhnQBghhGF5kXOP5aUydBBKHs4DYyAsF854/1ayLvJxEFoFNBBx\nG5lTUWf+AaoZCDdfJgmbS8OklGiaxtDQUK3iwM+R+hUHWxcRW4k2j3PKYjeanRbSCLZtMzIywpe/\n/GVmZ2f5pm/6Jl599dW27e9ECPLIyAi2bTd0G74d7RJk27apVqvcvHmzKSH2aTUSWltbY3R0lGq1\nykMPPdR0bXUzEbLvdbG6urrpdtz/o2kaysqXUMwxRKiKrCRRruURyrrYxqOoC57CKvaGjZswNv7t\nyBDK+iqd7APm644ZcB/QUV+wwQZHK6PiWXS6Z8C1BFrJ36aFPKMhkjYCkFJBCNdLlZQAFZz7wmg9\nZViRuLE4omgg+gRSptBf/j8wn/zV/Z3UXfDTS/UGTPXWmvUdcSsrKzXHtu18pxuJfA8rZXFUp4U0\nYk5/5swZnnzySUKhEBcvXuTatWuMjIzwxBNPtHzccEIE+Z577mkpotQ0bccJzY1g23ZtbBPQ1Nim\ndpDL5RgdHUVRFK5fv87Y2FhTFyifnRZLt8OyLMbHx2st1pcvX0ZKSbFYrEV5Y2NjOI7D485HcBMC\nrSqR4RJEQGQ8EXbVKiqeibwUMZQLJex0F1IWkAmBWFJQcxvvldQUWF/okxqoBYlwSriPJpG3DEJ1\nvsmqAdYlE97aOG6Z1iEuEI6FqLi452Mok+uLgk+CJsobFRpuyRNuASJsopX/HNP9ZVCaP8f17CWQ\n23XEbZ0oMjMzUxsCu9V3emvtdKfamOvp1LSQgzKn/87v/E4++9nP8oEPfICVlRXeeuutWs65HZwI\nQW6VUChU+xDvh3oh9qsmXnzxxQM4wt3Zag7v588OelEONi9Y+nP7hBCYpomiKHdXIZRfJP76DMKQ\nONEwqlvFRdTqiEVFYl3TsU5JYqvroWyqQGhVQgSqV8K4hiA8baDMAcUwXl0bOAMCbd3VTXELGE/p\nxEc3vEVkFNQQyJDipSUAM60huy2i61G2nTTRAetUEnXIQVlcF+ckKAWJ26MgiipESihRG23i/8S+\n/PNtOZfNNIbsNFGk3ghoq1H9YS0iwv7L3pohl8vdZQfbCI2Y07/73e/mr/7qr7hx4waqqvJLv/RL\nTe1rx2No25YOkU532DmOw/T0NHNzcwwPD/P000/Xrvr1k6cPmnpz+CtXrtxlpnKQguy6LjMzM8zM\nzNy1YLlbVB3O/yxKogIrFgzHYbGKUCRCgj2oILpdNMfEimzkRmVI4OURoBoXdJUNuADW5SjyrY2+\naplkUz2y0iexsiqhlfV88ylQXTCu9hF/wytXsgckaoRa2kNftameVxFnXUSlhJkMoRcsryqjAGiu\nZ17UJZBE0Yt/gu3+R1Baj/ramUKob7SoN2q3bbu2iJjL5TBNk8XFxU3+x/4i4kGkMzoRlRcKhaaj\n1r3M6YUQfPzjH+fjH/94S8e4EydCkFul0UGnuwmxTzubOnaKmEqlEmNjY5RKpW3N4X0OQpD9OuaJ\niQkGBwd3HOa63XFLZwStfAvpROB0GGmtf+EtgXMxCWfzqOvCKN2651s6G0XDdT/uUdEeMimP6EQX\nTYTcEG4AzXGQFwQyA8IFK9aNWl0jzApWXEWtOESEgVZ2qfZphFe8i7JzUSVmrZvh9wn0Akhj3QVu\nVSJ1gSMTqLki6Cah/C9jpX+y6XNaOz8daJ3WNK1Wv+s3sQwODtZqp4vFIsvLy7X5fNvZarZyjEc5\nh3wUOBGC3I4IeTcRrfd58BfrdoqA27VA6Itp/Ye3EXP4etrdYLK8vMzY2Bjd3d27NpTsRNj831HI\nUtFSRBOrmDMaCpAfTpJS8lhiQ1DV8sZx1+qPAb28ceG0wy6xkoNzxaXQFSWW38gtV5I6EctLV5Tv\njRF+s4xqe7VymnQxLndDoUzc9YTe6VVgxXuu1u1gFwRaWRIu2khFIGyHykAXkfk8TlqiLheQPTpg\nElr7w7YI8mG1Tu9WO+3npuvblkOhUNPDazs1Ty8Q5GPMThHyfoTYp51jnPxoollz+HbVM2cyGUZG\nRojH4zz88MNEo9E9n3NXh6C7hGK+hlRAi2WpuiHCFYu1exKkC15rtFPtJkQGV4C+vhhXjupEC56w\n2pogXNzICWu2916oSLRLOsXlLlKzXrdHpTdMxPUeq4fKLF/rZdBZqT03amcxTkVqHX3RkonVpeIm\nE4TJUR7U0SZNVNOlfDpKdLYMskL5Qh/6uTXEvQ6VkCC0GkEpLqGW/wAn+q+aPcW1c9bpTr3d9qco\nyrZty/WLiPsZXtspjqsXMpwQQW53hOwL8dzc3F2GO41sq11df/5A1WbN4VtNWeRyOQzDYHp6mvvu\nu2/btvNG0Zyfoeq42Oke0mtLFCwd82KKUNJAFLyoWJa8i6IZ0YhkvXNYiYVrglxJRUjk1qsxBIRL\nG37HuXiEPn0FoxolvlyGsPTX+lCR2JeVTdUVCIE8JWBs/b+ANaShdHnHELJtr5pCgrLuPGcPq4R6\nK6hVB0eLEqKKOlTFrmiECp9qWZA7XYbWbGNIM8Nr/Wi6EwQR8jHHL+/aKsTNlK+1I0L2jVNefvll\nLl26tG9zeJ9mBdkwjFptdyQS4eGHH973NupxqWJpLxN2TGR0vUStK0pXbIV8uQcoUxUa0fJ6pKyk\n2JjFtPG6XT2Cr7L5rgTp+jpl1UGzHdxLLpWqTsTefMeTiJXJnRokNe9F0EZ/jIRexIyG0cteqsNS\ndSLhKtigmS7FgT4SiyuEcxbFG4Mkehcxwt2Eq1BWoySqZaqRGKJXw7GXkc5XEOozTZ+nTttvtrMx\nZK/htb4BU7lc5vnnn6/VTtdPu27XxahQKBxLc3oIBBnwPjSmafLcc881LcQ+rUwNqe/wC4VCXL9+\nvaUr/X4FuVKpMDo6imEYtcXCr371q00Lhf+8Cp9CSgP6I0SXqxixCNF4GVxQyt6XsKKkCbNCORwm\nn+7D7LZRIjaIBPMDOhiCiBnCL6OoxCOQ2xDkxLo466JK/oEk0Tvl2u/MkEZSFij3O7iLAsWVOKkk\nCkWWT6cZHvNEunQ6Qika4dTysrePmEMCKCaSuOe8iFu380ggXM3hIpCuhVqxcHqrKMbHkbHmBbnT\nOeROtE7X1077FR6PPvoopmnWFhG3GjDVV3uEw+F9nxPXdQ+lD6AdHM+j3kKzH2LHcZidnWV2dhYp\nZVsaOpoZdLqdOfzt27db9pFodFHPNE3Gx8fJZDJcuXKF/v7+2jmtNyhqFL/bTEqJRFIO/yW6ZSIj\nRTTTZfl8gtPZVaSEcNkblleJxCndgJ7eVWKleVJOHleCdCp0hx3ogUooxvJgH+GJMkLZODdGJErc\n2RDgalcXuXiCs7e8ko18d5I+sUZclMidP0VqYh4l6rneD4SWKYfDREyTrlQBV1WQeJ7MvcYaxXiS\n6lWVmFbABUKOQyGSIlnJkY30kSytQUzimglKiVvo9gyqsuGHsB8OI4fcycYQvxy0vnZ6q0m9b8CU\ny+WYm5urGTBtbRnf6Xvqe9ocV06EIMP+usr8GtrZ2VmGhoZ48skneeGFF9ryZdjPoNPdzOHbkfpQ\nFGXXcr76SSUXLlzgnnvuuUt4WzUYyqmfR9HmCWk2GAmWTsURjgasUnW7CDt5Fk8NInvz9DtrmG6E\nlOOJZVntIe54M5eKWoyELBFJl3AfhlwxgZNVUKWLEU8SZ0OQrbDC2dAc8wMDnFpawo1vvK+RrjXu\nDAxwWnh1yCHhsnS6m3DRoU/1IuNMaoCe3BICyJ3tZTg2CS6sxAfpMxZRQhGo5FCRqNKhKHtxq2WU\niMudykdwlj7aVIR3GCmLTuesd7sA7GbA5Kc9/Nl8juMQiUQ2iXQsFqt9Vo/C9O5mODGC3Aj1AugL\nsS+A/mJcq9aAjaQsGjGHb0fJ2k4pC9d1mZ6eZnZ2dluD/Hp8g6FmI6l86P8lTJykkmEpdJVEZA4n\n67X+rtCHek8crStPfL16IkeK2HrNcUF0E18fgldW+0g40wBYaojhoUXuxIfofi0HoeimuXtx1RPn\nrnMFytkIMW3jl2FRoXhtCDayHfRFVllJ1nW5JS3IeQ3ZyvkiTlGgIhGa19UWsVawVJ14NUNFC+G4\nLslKmXJCEu15Hasg74rwfOFIJpPEYrFtz+dxWdRrZX/NfI528j6uVCq1tMfS0hJf+tKX+OxnP0ul\nUuETn/gEDzzwAI8//njDab9GzOkBPv/5z/Pd3/3dvPDCCzz++OP7fj27cWIEebcIeasQv+Md77ir\nZbSdgrxTZLsfc/h2Rcj1glx/IRgaGmqoeqSVCDmnvADqDAZJwsRxda/ZIm5lKCoplgZ1zilLVJ0k\n3SwAUHU23peCcBla/3dRUelfPx0FtZtelhhOLpB9rAv3jqwJsqFF6RJeeVtcLTNz7ynOlurch4Bw\nX4ViNUbC8vKWmnCwhlTPAxnoFWuUIl0UExpdsQzL9DFUXCZtz1NRdCKuyXz8FGfys+RiQyBKCLUf\nt+oSCRu4Z/6Ey9aP1fbnW2wWi0VmZ2fvGuqZTCZJJBInfoSTbdtty+0KIYhGo0Sj0ZoB0/333897\n3/tePvzhD9PT08Nf/uVfAvCt3/qte26vEXN68BYMP/nJT/Lkk0+25XVs5cQI8nbUC/Hg4OC2QuwT\nCoXaUq62Xdmbbw7vN1U0ag7fqiD7UbbvEz0+Pk5vb+++mjpaseC8E/7vKMQI22uMyMtcDY9h2jpJ\nWWW05wJJxcsfrzlJBtcFOeRsRLNJZyOM1etSEkWRohcv5RDXSxTvDZN/JU1XNctyvI8LYsOxy+1J\nMKVd5nzeq2+rKDo98WUW+0+RWPdCXk72EE6XcfMKCi5CQDE9iBzwGknciA5FUHFYjPdxurBIWEhe\nP38ZLaWjCskd9zQxM0+Ps4Kt/zXS+jBiva1wu+nLvtdEoVAgm80yOztLPp/n1VdfrQn0fpzbmuEw\nhqoe9AXAsizOnDnD+973vn09rxFzeoCPfOQj/ORP/iS/9Eu/1LZjrudECvJ+hNinleqIrdvxhdQf\nITU2NkYymeTRRx9t2Ke5XRGyYRjcvHlz3/uv30YzgrxamqISncQVDpoGjqWhICk6CTLpboRmk8IT\nPOFuROApyyt9M9Hot7zSNwn02pnaY6q6W+uQXtZ6SUTz5O7vRXnFwoxsfp+zUY1kKov1hkZI2iwk\nBugXd+hLL1Bc9qLkYqqPXn2K8fglrhijAFSSFsmkd3wJZQlDTRB3isSESUXRWRlK4kRsYmQpyyRh\nkaMakUzZl+mSa6xof0q//Z27nlffa8LnxRdf5MaNG7WFrZmZGUqlUi2a3m38UzN0WpA75fR2UOb0\nX//615mZmeG9731vIMh74Udyc3NzTE9PNyzEPu2MkOundMRisYYnl9SjqmpD/ho7kc1muXXrFqZp\n8sQTTzQ9pWG/KYtischbb73F2oX/juUohO0wuXAXSb2A5WoshvsZYIUSEZR1VfUj4aJMkXY9EVxS\n+zhje1HzmjZAj9yYXdbPRsddVe0mRp5EfJWF+3uJrmxE0gCxSJFuPcvMwDUuLb5BNbG+ZqC4TPdd\n4Nr8m0TS3vbstAPrpn/LXQnWxEWuyLdQcRjvOsUDayN0OXlePXMP4YhBgR6SGGRJMSDmKcgeHCXM\njNDp4U92FeTtcF2XcDhMJBK5y7ltu8nLfgtzJ6LpdtApH4uDqEF2XZcf+7Ef4zOf+Uzbt13PiRHk\npaUlbt26xcDAwL6E2KddHXaFQoG1tTU0Tdtzlt9uNBshF4tFRkZGcF2XixcvsrS01NLInEZTFn4N\nc6lU4vLVi8z3LZBUCuStODFRJUGRW/Z1YqIEYsMjyJYK/c4KLoJb6kX64rCmSYpqjEx1ENWsUhVh\nekxPkDNqmm6Zre23oKn4iYB0IsuEuMjZZS9nbCgxekKe2CZOzZLNdJGMF2rPHeoe5Y3Kdc7okwAM\nRhdY0s+StJdJJrOU3XTNCzkV8vb5ZuJh5qNpLjBKTJZBQIocUkpUqaOJVUySZIRJQblN0r1n3+d7\nKztVH9TX8tb7IMdiMZLJZC0/fVAz7PbLQc7T8zkoc/pCocBrr73Gu971LgAWFhZ49tln+cIXvtDW\nhb0TI8iJRKIpIfZp1PFtJ3xzeL/G8qGHHmp6W7B/QS6VSoyOjlKpVLh69Srd3d0YhsHCwkJLx7FX\nyqLemN6vYX6FvyBrCXQthK7Y2K7CdPUiTgRibglU0G0LNFiVvdxy7sNKKeSUNGHG0YAqaYiv4gDj\n8jTCiDJYmCYfitHNhiAntA2/zSxDJBN5Xig/zBPFl1kOnyG1nk8OqRYLFy5xNvxm7fG6YrN8posz\nda8nl+piqRonruQIKassu330yxV6WeW1xFUqqQoJkcVBEBVlMjJNj8iyRB9J8phCgpugIlTGQn/E\nw9WPNHyu95s+0HWdnp6eXaPp6elpLMsiFAptyk3HYrGOl4YdZae3vczpU6kUKysbd2bvete7+OVf\n/uWgymIn4vF4SxFus1NDCoUCo6OjuK5bM4f/6le/2vRx+DS6qFetVhkbGyOXy3HlypVNDnDtKp3b\nLmXhW5HeuXOnZkzv3y6/VLlJVLOZNM9zf+wN5sUgiYhBWUTRVe+ilyLLba4yaV/gbPccYRy0igPr\nKe6EW651TcdEBRI5FmIpZs0zDJfnSUiDokjRo9YJsuwnIe4Q7i0wUz1NORyn/uZ1NZnCsi5ySU7U\nfuZqgpKMExNedJlOTjIRvYh/X7OkDNC/bko01XWa08oScUrMc5ozzFGW/SCyWITQxRpF9wwhYRJB\nsKAtUakWiLDZnOcg2S2aLhQKGIbB1NQUpVIJwzB444037spNHxSdEuT6XHCjNGJO3wlOjCB32qTe\nMAxGR0cxTXNbc/hW2StCtiyLyclJlpeXuXjxIvfee++2TR2tCvLWlEX9QFm/maX+S/al5duUu3Mo\nIooSlpiuzqrbR1fIwDF10GHZ7eF1ea/XzOFufAS7Q97CXVWGSAivBs1B0CszXppDATui8aL2IMPF\nZSpKhLO+OxCwKiIk8CLf2YEBku7mKTAVmSCvhbhkeYK8Qi8ppcgtrvIoLwOQU9LkQ4P0r3tpdClF\nLEdjjUE01cVEQ8emsn7liClL2FKljwwOgpJQSLNEhR4kBi+H/oynrNZMh9qBruv09vbWOuNc1+Wl\nl17i7NmztfblqampTTP62u0z0c6yt51oxVhoL3P6er785S83tY+9ODGC3CqNCnKj5vCtspMg10em\n586d46mnntrxy9KO0jk/QvYrRkZHR3f0Q7Zs+Jvq33Iu5FJFIyENRpXLXnoiBKptkdG7+SfjMa4l\nRwCIqp5oFuw4pzUvvbJkDXBB95pAMvTQIzZSFF3k0TWT+VQ3i87gJkGO1z0urhcZlxcYZiMvKESJ\nblHklriH6/I2C8p5FCro0sQmhCYsRuQNQGKjouEQVqrcEvdTUHvQMViUw5wVU/SzQlWGiIky0+Is\nl5hkRF5BEGOFMBYqYWAudAvXclHYW9A62fLrR6tb7TX9GX3b+UzUty8nk8l9pwc7ESHn8/lj6/QG\ngSDX2EuQfXP4fD5/V2pgO1otKdqabqivIDl9+nRDE63bFSEXCgXGx8cJh8O7+iH/X3+Woes7lsnL\nNIPhZapGDDcm6Y94QqtEHN6S1zxrTMByVbrXc8AFJwXrgpyzUrCu9SW7mx7NE9ol+kjgN3O4ZLU0\nr7pP8YDyHBm66WOjNG5eniJMlVn7PGe0Ke4wREx41RwrWh9Yt7FEnDAVIqLKm+7jPCC+RkUopMlz\ni+vcz+sArGpdRNZTGjmSnAV0LO6IYS4yiUGM5+Q3s0Y3EbFGhm66XIs+sYAiVnhB+weetN/Z0vvQ\nbnZqCtnNZ8JvX66PpsPhcK3CI5lM7jr6qVOCfFyd3uAECfJBpSyaMYdvx1w9P7qVUrKwsMDExAT9\n/f37Wrjcj7/HdhiGwdLSEoqicP/992+adryVl0cFt0//Dx7WTSQKJipEBZYZQg9bLFX7scNe1BnX\nPVFdkz30K15qwAlvfImV+MZFJGdFOLN+GldlPwkxVftdmix5ofCcfJqIKHGKjY48wxkkqS1wm2uc\nZpoZzpFer3tOKQVesx9FaPna4yvCZoZh0uvteiU2LjpLyhAxDAZY4bSYY4Vu+lhDl2Hy9DEvTnvR\ntMjgyBCasHEVkzF5iW5ZYTz0YkOCfJSd3rYzq6+PpguFQi2aFkJsiqYTiUStrLQTOeTjak4PJ0iQ\nW2WrIJumyeTkJCsrK/s2h2+XIFcqFZ577jnS6XRD3X1bafYL7i8U+rd/fX19u4qxZcMv/oFLz79d\npeAkGdbusFQ6zanYHUxToRiOMyYuc4kJpJT0Ck+EK+pGk0qoZMN6dZ4vnABRpa6u2ErUIudVerwc\ntPBK58Y5v0mQs1IjCaS0DC/Ib6As1E3b/WftHh5SXqn9v1tk+Gf7Uc5oXoqjX64wL4ZIyRwhLGbF\nGQZYQUEyyUX6WEMReV6QjxOlQIZu+llmXvTTL1cpEcUmwiJddIsCr6lvcL+zuetrK51MWbSjbXqn\naLreA3l5eZmJiQls26ZcLjM1NVWr9jiISo/jbE4PJ0iQW31jfRGtd0A7f/78rjnavbbVLGtra7z1\n1luYpsljjz3WUh3xfvBf+9LSUm2hcHJycs+0xy/+PypzV7/K6UQVK6JhWAkKToxTgJnQebn6IJgq\n6GCIeG3BTKtzBErqeVbNbnJ6F8n17gxHKpzSNsr2qu7G41dkH4Prjm2KkKzSyyTnuMA0rhR0qxvp\nC+nZBG065pxI84r1IA/r/1z7WUEZgvWcsxAwxXmEkGg4dFHAkQJVSJJ4tcz/xMOs0sdlCoTXK6s1\nbISQuG6CmMhTEhGmRC+u/gL3l3cW5JPk9FbvgewjpeTmzZuk0+lNg1R3iqabpR1+NIfJiRFkaO0W\n3XEcqtUqN2/e3NMBbS+abTIpFAq89dZbKIrCfffdxyuvvNIRMfZbzaenpzl79uymi9Beeeg3RuGX\nf0/h3X88h2mHUA2X2fgwA+ElHFdhRekjFS5gq942SkYMv6ZMAP+Ye4ZsNMWwfgeAZXo5xRKvWzfI\nVHsZFEs8EXseXVicCt2p7Vd14rVPryMVuskzJy/R7WbJ2ykSkY3xTobsYsk8x6nwRrefJmyKbDTt\nZGQ3mljjDkOcXvfVSMkscwyTFAZJioyLS1xljH5W+Jr9DYQ1i7DwSiUjZDFljF6xSlXGsYVDXJRY\nk12AYF5YLIgMQ3KjZriew/CV6GRXnxACRVHo6+vbNEh1p2jaz037DS6NRNPH2QfZ50QJcjPUm8MD\nDS2W7UUzTR0jIyOYpsnVq1c7dstVbzrU39+/rfvbbhc5x4Ef+ukQT/zAW8R6DUIRk7yVJIZBHyv8\ns/MgZ5U5AAbWo1lTRMhW07wevpcuWUBNuVSsjdRFtRiDBOghG8NMIOKLfKXyjZSdCE9Hv1Z7XMlw\n8IuMF60hdL0KAr5aeoa0m+VMZLb22IXiGULJNaYq5zkfmcJwukhraygC3rJvcE17gwkuoQqXtep5\nToc9QV6snmLavsh9idcAqFT7IDyGJUOMaee5xBS9ZMg5PaTUDHP2EOe0cfKyiz5libzsASQJTDIi\nzp/rX+cHq9s7j510pzfY/i52p2i6Wq1ustb0o+n6SDqRSGybFjyuXsjwNhbk7czhn3/++baZ1DcS\nIfuVG4VCoVa50SlWV1cZGRmhq6tr1/z0bqVzn/gdlZdeU3jnL05gVeNU9QpRvYRtq0xXzlGKe9F9\n0YlxVp3BlYLl8iBGOkbRSNAd93K6jrshDI698ZF08X4ejlSZKZ7j7+13cp1bDIdm6Y0s1x5XcPro\nxRP+nkSGsbXLnGFDkDNmjFMix4RzkfNMMVW9hBrzIuiM9BaAioU0qa4MWihL3uqiK5RnyTqPpW4c\nTzo0R9FJ8s/lB4lHTRxFQRUueaWXFBk0zct3x6Tn7ZwhQb/MUBAmqgzzOjmWCqv0xbvv+pwdtYnT\n7WY/0asQgkgkQiQS2TaaLhQKLC0tMT4+Xpv7uLi4yPT0NJFIpKnXtpcX8sc//nF++7d/G03T6O/v\n53d+53c4f/78vvbRCCdKkBtJWbiuW/Mk3mpA5JeaHXSEXN9u3GjlRivU3w77aRFVVXnggQf29NpQ\nFGXbi8vtEcGXviRIP7NEtL+E1G2WK0OcT0xghUIsKgO19mjT0SkR5XnrHQylF9BUh3JpI3URrZqw\nfj2IKxuWm1F1I+1QzevETxtM2Oe5tXidJ4ZeqP2ulA/RW1eJVw2HmS+f51TUq8iIRL3t9MZXedV4\nkIybYmi9fK4rtMZY4UFica+6QlUcXi/cxzu6buJGLHpDBvOVU5yKzKMrFv9UeBgnqqCrZRZLlzkd\nGyFGDlcKBsUyebeXhLLKknOFghpDc8OAiyNCqIrJ59zXeOol70Ll5059v4mTbE7fjgvATtF0pVKh\nVCrx+uuvc+fOHR577DGi0Sgf+9jHeOc7965uacQL+ZFHHuHFF18kFovxG7/xG/zET/wEn/vc51p6\nPdtxogR5N+rLx3byBPb9LNohyNuJmG3bTE1NsbCwcFe78W7H3YpY+40dlUqFkZERKpUK165dazgt\nshisvQIAACAASURBVJ25kOvCv/4xjedeVHj6r6coRuKk9AKWauNKQabSQ1e0SMwogQZ2McILiSew\nXZ2Q6p0Xzd64YHXpXp2x7Sr0xbw2ZVdCn7rhHaBHvKhT01ymQ0P8w/I38T/1/z0A4bp8ccmOko5m\nGc1doD98B8OK1SJxgJyaJKVu7uAbNa8wmNxop45EyrxZvIGW9PZ5xxrmVMSr4FiVvfRrXvolL8Oc\nBmKiQM4cplufJSOHecl9gIrbR0JdYkl0U5EhzopFImqJyVOSf5N6HOnKTbnTfD6PYRi88sorm5ov\nIpHIgVysD2Oe3kHszzeqf+qpp0in0+TzeT73uc9RLBb3fvI6jXghf/M3f3Pt30899RS///u/374X\nUceJEuTtPri+Ofz4+Pie5WPtcnzbOui0fobf8PBwwwuG7SifA7h9+zbZbLahhpatbOdl8bu/p/Dc\niwqhiwbmYIkuxWXF7mPQWmDMuEh/zyquK+gOZ1gxe5kPD9KjZyitxWulbYmEV6lgGDH64p7wruX7\nOJX2hG+t0ENv10alRE9849+Wq6H3V/m7sXfy1Pnn6ElsCPeKcYpQqkIsbfDK0lOEtCzJ8MaXU7gq\no2sXeGB4o+Rt3knjGqc5FfcWDZPhIv9cepDzeN2CyWgWyw0hhIsV0ciZg6T0RXqj85TtGFGtRKGa\npuoIxsPDhFQDHO8ioUhBSDEYZwidKlGR5QvaEv/CHqzV9Z46dYpyuczIyAhXr16t5U4XFhaoVCq1\njrp6m81Wxa3TKYtOtU37TSFbvTx2oxEv5Ho+/elP8x3f8R3NH+gunChBrmerOfwjjzyypzl7OwXZ\nNM1Nvg87zc7bjVbMgRzHYWpqikKhwNDQ0L7qqOvZWmVx65bgxz+s8Y3vcBj/t/M4XRqmEkLXTGRe\nJav1MKQuU16NkgunGZWXGIx6EaUW9c6tZav0rotwPp+qCXKxlID1wL2YTdcEecXoJRbfqEfWQ17k\nGrlc4W9H/2eeuPJ87XdrS0kGUt5MPru3QjHz/7P3nrGWZdd952+fdHN6Odd79VLVqxy7wmuxuxlE\nibAMj6Thl5E4A9kgCNADfRBFwQojC9a46aEHA42BgYbSWIIkmxI51lAMbrK7q0NVdeXYFV/O+d0c\nT9rz4dyXih0qdYsscwGFuu+ec0/c+7/X/u+1/quJCCPr22fSzZgRDdtR0dTqoBlySNvNNOMBsuOq\nlNSNbK+AVmE+34sUCr6QyWK+iZixiKY4rBS7aA/fxlEr3FG70ZUyZStGWM9QMuMoagEFBdMNYIkI\nUjq8ps/wT+3GLc95zWN9sCwRbC0BNTs7u6UE1GagfpRwr6cx0D+KfRxZeul0+iNfEP/rv/5rLl++\nzFtvvfWRHP+ZBOTHFYd/WoCsKAqZTIbz58+/r+7Dw9jjxDNLKZmdnWVycpKWlhZqampobGx87Gnv\nZsrCceBf/AuNcllw9jr0nSwRCFRw8hqudJjytWGkLEhAsRhiLBTGKRhoEe8ewtXKotlCjJqYR1NY\n9qaY0039tbJpcS+TqiEYmq1eg0J0EwWRJsHFxec42uh5NGJTi1ZVSVK00OaOoiiel18hQDCa4/bs\nbva13mAp30AgXMZ1KxTKCUL+FMur2/DX51hKNtBQ4w0mq0UD24gCFUJaBsdVURUHV7OxXY0h0UWl\nHCVhLGIVQvjjGSQ+fGqafLkJXS8BCssijkOFt5UcP+duzXp7v3f0fiWgisXieobcg6nMa0AdCATe\n87jPCmWx2T4qLeQ1e+211/jjP/5j3nrrrUdO0npYe6YAOZfLcfv2bQzDYNeuXY80bYGnA8hr0QtS\nyvXFhce1RxEHklKyvLzMyMgItbW164uVmUzmifQsNnvIL7+s4vNJQBL6vSS2lKSSNbQ2zLIyWUtk\nW46QVaRU8rMSqKXOv0Il7U2LHVvQUOWHTdNH2fQxs9zOaqWG1FQC11GwVI3sfIy4lUbbVCm6bG8M\nZqlUDb66DZlUR1eQDZI747vYse0OkYaNdGjT1DETRd6d3Mu+Li8BxB/1jmvFNWxHJ1tugbCDokju\nz23n4PYrTOXrMeorLOaa1gHZVnXyqp8gFfz+EqsrnTTUjRL1L3IneQytxsFxPMDRQxkcV2AoGVwJ\njgtRNUvOqcXnKsy7tfwndWkLID8qhfBeMpubw8VyuRyLi4uUSiVUVd3CS4dCoX8UyuInFZA/TAsZ\n4Nq1a3zxi1/klVdeoaGh4Wld8o/ZMwXIiqKwY8eOLfn2j2JPAsiZTIbh4WE0TaOnp4elpaUnAmN4\neA85nU4zNDREIBDgwIEDW877pJrIa5Erly8L/u2/VbFtwYnnbYZ+oYTuupiuTqEYQtR4inCRQIaR\nXC+JkCcapFez8YrpEFrdArOzrUyVW1muqUW0CtyswIiauI7EcCwqhsEiDeQzQRbGWugNDWMYG+Cc\nW43iq9sIefNFygghyLRFuD22h7qeDT55ab4RZZuk2OAjVwhj2QZKlc7whUxGx3aR1f34q5mBgbYi\n+WIIUS1v7W8qUK748fvKzBTbKBaD9FTr7BWlR3+tpOuYKLdTxyRGMIlpGRh6mWSyjvqaZcqFWoKB\nFcq2H93WSUsLVbMYdgPclBX2Cs/TehqJIe8XLmbb9o9RHqVSiWw2Sz6f3xLp8VHZx0GRZLNZmpqa\nPnzHB+xhtJC/8pWvkM/n+dVf/VUAOjo6+Id/+IenfQvPFiBHIpEnqvrxOFVD8vk8IyMj2LZNb28v\nsViMQqHA/Pz8h//4Q+zDAHlzuaadO3e+50D0pIpvXqFUyde/buK6GiA4t9+hPiEpEiCupJnNNdNR\nP42b1xgvdGHFNAIBj/MN+zyPNZ+LcLH4HHaHCvMSoQrMskYsWhXzWQ0Tr1Z5LqSD+OMV7JjCHbcf\n675OIpEkGChiOhsUR6nkJxgvAAJVlwzTjT9fIhz2ADZbiBGggB5yuDWxmxhZ1NjGgJuJ6eiBjfet\nGA5Xxg4R2+Fdk+5zmJjqpLd1BKdOoLkmrqOgqC7BmmXyxRDDpV5ErIIrQVFcikt1GE1zGIrXtZyy\njj9kUyrGcNQcMb9CxtJIEeP/EAX+n2q830fpsWqaRjwe3+I93r17l5qaGqSUWyqLGIbxkVQW+Umm\nLODDtZBfe+21J7q2h7VnCpCf1DRNo1QqffiOQKlUYnR0lEKhQG9v75YyOg9GWTyuvR8gryWU5PP5\nHzv3g/akmsiKovC1r9Xyve+Z7NtX5MbNWnz/XQlbKpjNGpWUH8oCoUjS8wl8fRWYAjrANhXqojnu\nT/WTsSLUdqVwLEG03uOSzZQfmj3wq+T8sAbImRC+uEdLFFZDGDttrmb20zS9hBHeoCtSczX4ujf+\nrogg787u4rneSyiKxPFvAInWYbJ0vYbmzo306XSuBjcdorV7eP27pFpL2M6jat4gpkRhaaULtdFF\nxaWw0kykbhZVdZlbHUC2CxTKrCw20NC4hKJ5zzoYTmLZKkY4zdR8O8KoIStsEpaNq2pERYVbMsqU\n49ChqR976rSUcj0OevN3m9XblpeXKRaL6/TIZqB+VHD9ODzkn3ZhIXjGAPnjqBpimiZjY2OkUim6\nu7upr6//sfO+Xxzyo9qDdINt24yPj7O8vPzQCSVP6iF/5zs2p055FMiNGxrbfrvEaoeDa2uwZJKL\nhQnlimRnopSEHx8V9IJ37/mpENdD+7E6dIKL3kBnzhsoHd4Cm70INFfv1dwIrbPTAqpJUMVkGKM+\njRKD+VAjzl2NWjeJUCTFYggfG4AsdBulW3D72m527b2Fr7G8sU0RzKttNLMByJliDLdF0GhpaLp3\nzWq9TnqqjdrtXsibES9z53oXsUZv4FjKBIhU2YAVGqGqwew63sKxrzZFPhMiHCuwPNnNVH2CrIhi\nJMrYlp+Fso+IVSTsS6LoJf7YDPGn2sefOv1eiSEfpN62RnnMz8+Tz+dxXZdgMLgFqA3DeN97WMuo\n+yCbygjao5LHfQw/A+RnzD4IkDerwHV1ddHf3/++je9J1d7WbM273RzH/KD4z8Mc43EAWUrJuXPL\nfPnLFk1NNqurteRygsWTKqoqMWpMyjNhAk1Fr2pGsI3mgKcBEQoVyC5EGU93Eu/J4lbAX+cBspvb\n8Kw0dQOEVZ+16ftNMdzWxn3mFqKoe1wu3TjEwR3XQdnYzyppGC1eOFx+V5Chm/34DmwAcnE5iL7P\nZvJ2J9t2TQBgR1WMuMXC7Vbadk2Snk1gtroUMiHW4KiUCZDUa4lVdZJ9nQUqmTCpVJh0p0RMx4m1\npzFq89iWiqY7pJMJVtP1zGodqMEi4bKLpYCeVKnUV1ggRHg1gc+X4bzrkLXVf5TU6Yf1clVVJRaL\nbRF+l1KuF1NNp9NMT09jmuaWYqqbBesfpCzSJTg3qXJ9TuHMksa7Syq/tsfij1989LqWa/bTroUM\nPwPkLfZegLwmPrQWPP4wSR1Py9NRFIVkMsn4+DhNTU2PHMcMj7eol81muXbtPn/wB7WUywEmJgwG\nBkqs9IZJ1lm4szquq6EEbdyyZN6uAxeMOgvX9lKlxyPbCES9zuXOaCjdsno9G9cSrPOSJ6QrCTfn\n1r8PtW7QRoqy8T5Kyz7CbSXsfQYX7x2hJTa7vi01XoNSTaxSDBg1O+mrDKH5vPMlZ2qhHlK1cVpN\nFbusojebgCBTG6LZUliab4BW0LdZLI000tCzyMJMC0q/QyXtxxcvo6iQWW5k1q16YmYYSCN8Not3\nmmgdmEXT/Ey21iOoYGdVtFgJSgZK2ARNEE4qpF2FSrqFpkCWP0gF+Fc/ZWpva7KZoVCIxsaNmOq1\nYqqbyz8JITAtm5tzAa4tuQwnA7w2o2M6gsP9DpcXFF7sdPjXn3h8MIaf/vJN8IwB8pM26LWqBuB5\nEHNzc0xOTtLc3PxYYPgkthZb6vP5HjuOGR6NQy6XywwNDVEuV/iTP6lneNimp0cyMiIYGrLx/5aG\nKEuMuE06WUvdvnmKt4OIneAbK0EdZIdjLPQ0ga7ga/A8VLGBtQSiHthaOY1IlQYozISJd1Q/Lwbw\nNW50zOAmcMbeAJBKrZ97Kzs5UL6G5ncoZLfSF0UZZvRiP/3P3wWg5ATQsVCbXMbPdeHTTMQRr73o\nTQ7TVzsohgOoeAC+atbQwCLlSBBFg6XJBtrjHo2xqhqYnRoK4DaXsU0FzXBRgirZhQhD9c1oKxo0\nVCgvBQj35DGnDYy+EvZyEAMLrd7FXDVIrtbwqs/mf7ZctJ9QD/lRbHMxVdOCt++o/H8XVK6Ol7mT\niyKBzrYCYcWlr75IIe2jVRp8/eeyqEIHHr8Pm6b5obTIT7o9U4AMT6aJvJZht7CwwNjY2JZ43o/L\nstksQ0ND6LrOtm3bcBznicKRHoaysG2bsbExVlZW6Onp4VvfUvj+9z0Redct0NamoO3TmUjoCJ+K\nVnBR/TbWioFV0TGw8DkVCmMhFkvNRPQsMgl6jUdD6Ir3v1MWRBvySAfSownMgIZr6hQXA+i6Tai5\nSGEhjK/R42Xz0yGM9g0qQ2wKIilO+3EPaty4tI8DB67h+B4Al1YoNPlJjcRI9GSQdRuDUmFHiNKt\nIP5NAJ6NRaB1o91o/SbLd+op7VA9iGhVkLZAaJJMoQFzyo9/exoRdEjfr6eufxFfa553x3dBk0Lx\nvo9oQ4VwwjtvIGHhAFFTUGiuoBVChC0HS4VyzuBlq4bfDy0+1Dt9GvZRLSLaNrx1Q+Vbb+ncmRHc\nXPKGuK5tNq0Rh4F2yfhqAM0U3EkZZCsK/+snJiguznBpqoKu61tiph+24vWzoIUMzyAgP4klk0kK\nhQLJZJKDBw8+8Wj7KI1+syZyX18fsViM5eVl0un0h//4A+yDPOTNwvRrFaz/y39J81u/NcbgYIwz\nZ1zSaZfduxUufaIBTAXpKJQSEWKFFdL3a/E3VoV6Mhqjeidh17teddmBavCHP1HAKarMX2hkKtZO\noSuMY6v4+z3O18rrzDW3oqRt1BWH0iWdpn3LFGfDGO1V4aGyQmD7hoiQmfeh4VA54ufmuQHiXRsJ\nIZVlA63du+dJpwNjfhijc2NQUhOShUoz25hY/y6fjlBaMmg47g0GQhUMT/cSGKh66HUuK1caSOxY\nZaEjhjbrw493bZriDQbpsWbyZpwwWXzdJo4poNZEXfRBYwVzIYAvXkZIhWAGSqEKaQzUXIjT5SCl\n4MfnIcPTo9akhPM3Ff7uRzqX7qrcWVGwHcHevQ61IcnB7Q53ZwQlR+GcKciWBZ/cZ1GpCHY22nz5\nM7VQZe03V7yenJx8zxp9kUjkfWerP81ayPAMAvLjeMjpdJrh4WEMwyAQCGxReXpce1hhINM0GR0d\nJZ1O09vbS21t7XqjetKQtbVjPBhbvTmrb7Mw/fnzGb761SmkhDNnMgwORlldVXknncet8aMEBe6U\nDXUGxdUITq2O2mFhT2jMJlpx/Rp6yDuXL+XRFeaSSma8lWVZh6bY+PZ728UmtTel+hs3rlGOa0we\n6mF6qYvwYoFIKYsacMmNRdEGNn4joxsdL91RQ+l+hG1NHqWQHY3AmhREv8bQ93tJfG5DYKg87yN9\nIkTjoo6/0Tt3qlhDpUml3k0iqriYrE/QmDHRYt5581oI67aGPKpgBizMVR9GbQW5vUT6boKR1hbU\nXPW6wi6lO0HCAwVyMwaRxgpGTiCbHJz7frTmCnbUIJi3qQibZF7n31Ua+LOOx37VH7u9e0/h776n\nc+q8ykhKoVQWHDlqo6zCC/stMkUFMy24Mq6yktN54ZCFbQoMXfL6DZ36iMtf/U/lLcc0DIOampot\noZyO46yniW+uKuL3+4lEIpTLZWzbfuyZ7IdpIVcqFX7913+dK1euUFtby9/+7d/S2dn5WOf6MHvm\nAPlRLJfLMTzsxaCuZfi98847T+XYHwbIjuMwMTHBwsLC+xZRfRrRGg8u6mUyGYaGhvD7/VtmAbdv\n5/ln/+w24bBGa6vB7KzN+HiJ3t4Kd/cMgC1w8xKiGgzbWO0BtFQZsoLS9QjuMRUlY6Hu8QZDxe+y\n+no9y4ValMHqAKls8lKr4W7SlWidm6ItOgQgcRtUlrbVkV6M0LUyiVsRaHjPQjqgbrdY4xvLkz4y\ng3GCl0vUH17GtrZ6mov+ZnxTUwQ7PIoiM6IjnleYvdRKd+ME0oVSnwGNCskLCWqfS1Ge92Hu10md\nraH+eS8zUN1jMX3NywQTOqRGYjTWLiFUmJ/vQvYrOGGX0u0AgV0lgpp3HcHuCq4NoqCRulhPMR2g\ntKAStYsQchExEyXo4/RyiGzFJPrRyCRssced4g8NC7719zr/9VWNmYJCMuNlbpbmBfv7bHQTImXJ\nxLzKxKLC4BGbSgk6g0nevlpLyA+RBsmhFpuvfM6kNvzh17GmdvdgxetyuUw+n+fq1at84xvfYHR0\nlBdeeIH9+/fzxS9+kZ07d37osR9GC/nP//zPSSQSjIyM8M1vfpOvfvWrH4kWMvw3CsjFYpGRkRHK\n5TK9vb0/FirzNPi19wNT13WZnZ1lamrqQ6U4nwYgr3nZpVKJoaEhLMuiv79/XeRbSsnoaIHf//1h\nUimHVMqhsdFl9+4g+XyKN6eDKJ8L4ZpAQYE2CfcVaAfVLlK4UgPVJAptxaMg7DGFuZUuKh1BlJsV\nlCpXqzZXF0xTYGzz7sudAG17NS55VqBVeVzXldApsOM+hjv70L+9Qm9pATUgKY0HUHo23o9l6ghV\nMNXdQnAqixVXtzTsSpvG7FIDvR2egExRePeePx6mOBnAKQnY4b2DZCBELSnSI2FEs6DQ6aPO9kSL\niveDpFdriFdD4CrNGq4L5QmD6USCqJNHUcHJ+4ASVlcFZVXFCErmX9lOtiMGMyC6JDIJdiFKwRYE\n5iuYTZBVBb/x/RS/1z21PjX/KDWRH9bu3BH8/d/r/OAHGqsFwdy8wuAnbZJzgtZmF9WE3qCDawne\nuaxy4rjNxLLCSwMWN++oJHOClq4AzTHJ7i6HK6MqrQ2SX9z/+G17TQc5EAjwy7/8y+zZs4eXX36Z\nP/3TP13XlH4Yexgt5O985zv84R/+IQC/8iu/wpe//OWPjIN/5gD5gx7SWnn7TCbzvtrAa6FvT7qQ\n92AI3Zou8+joKHV1dQ+1WPikOhTgDQArKyusrq7S09OzLusopcR1XSYmCvzCL1xjerrCyZMJzp0r\nUSg4tLSkiMclHBrANVVQhPfvvguaDa6BsxjA6dRB86adhrAxz2mkJ5rgULVIasR7BjIvUbfZgECO\nq2uUIe68AK8v4EyraK3e/vakQOna8J5Wetop34mzs2WY0ryEnk03We89I5nQGZ7rpKZ9I6zDToPb\no1NQa0ldXiFxuIS53ZsVCEMwMx3HZ5VgR/V69gbJ3gyQDldjbts10uciJI7nWJlJUOoLEi1kUUKg\ndUhSVyIkU43IPRqVSwaBYyay38YtCpSgpHg9zLxdh5v3Ekd0RWKpgmjOJVcvkBnQSgbudYnTILjp\nttDYEUC1c1s0kTVN2xLf+7CLXe9lH+Ydl0qSixfhu99V+eEPBYriY3xc5fjzNu+OqITDEtuCo9ts\ntBCcflNj336HG8MKB3pszBwsjAlaahRWMgovHbWYXbIRmuTV6xqNMcnXv/BkIW4PWjabJRqNUlNT\nwwsvvPDQv3sYLeTN+2iaRiwWY3V19SMpufbMAfJ7mWVZjI+Ps7Kysl7e/v2A+2kB8mbvNpVKMTQ0\nRCgUeqTFwifxkNeSSSYnJ/H7/Rw5cmSdX3ddF9d1GRsr8PnPX6auzs/0NJw9m+LYsRiVSplr15Zh\n13aUuhCupkCdAgslaAtCvQpnbOy9frBc6FTBAWtcJ99dC+Uy4N2jss0CFJSpCqLNe+ZqMcd607Mr\n659Vu7z+2ZlzUbu8XZysRGxTKaoJbqzsork4uaZzj1uRuN3aerBUyfYzexG2faYqgD8E4qgHXDMN\nrWh3x2DnRrMvHa+hcKG8WfmThUIN5tHA+jHzoSCxSo5Udw1EFYoXdcIvetxzJpMgucubYVUyKgFA\nRAXFswFCR4ukZ6NUdocgLiENdjuQl1TiAqkJwnmXnCqQYYExKynGFX7/nRjf+Jz/xzSR1+J7H1zs\nWvOkHzal+cEkFMuSXL1q8e67ku9+V3LunEt7e5jhYYWjRwUXL6pousS2YfCIja5L3nhdp6PLZTYr\niIYkDbUuHSuCUADOvKuxq9/GkLCn0eHKfY1sMcrgYZtYSPI/fNKiKfF0oyI+Di3kj8OeOUDeDLSO\n4zA1NcXc3Nx6FMGHeRVPU6Q+l8sxPu6VBnocOdDH1UNe88QbGhrYvXs3c3NV4XXHQUpPle3u3Qz/\n/J/f4N69PKpa4OTJOm7eLJPPpygWS7R3+pneuwPXEagpGyeqQyAAaRvVkjhF3Ws9sy50AN+HSn+V\n46tSGKxU1qkAtbixsCiNjc6oxDfehxtwWGuS0tp4B9ZQBdHn0Qx2XYjR4W66b4wS3KdSGXYRuzdA\nqLTkkt/XR+LiFaJHwSxvKqDaEWb8u/X4NlGLMidZTcVpwFz/Llv0odw30Qe8QcXZG2DueyGcEx65\nW4gECFdV7PJpA5YdaNSQuw2c5TJqvcQJQvJ79VR6EjBiQY8Ot1zkEQVu2FQOa3BPUjQkblRBH7MR\ntoA5eNWncm/Opa+J9faq6/p7Lna9V0rz5lp9kUhki3NRLrvcv1/gtdcMvvWtZfJ5hW9/26JUgp6e\nKCMjcOiQwZUrCiBRFMHJkzkCAZXXXgsSjUmovrL+fofWtAAdXn1dp67eZXxeYbDPZsUUvHNJ5cSg\nTVfRwVef4vSleo7vsvn1zzx5/3rQPkot5LV92trasG2bTCazJbX8adozB8iwtaJ0S0sLx44de+gg\n+KcByOVymZWVFRzHYffu3Y+dzvmoURbpdJr79+9v8cTz+TyO46yDsRCCs2dX+Pznz6LrCgMDEe7c\nKXDvXprjx3289dYqlYqLuucAij+AtFwcvwp3LDjmgwnhVYnWKoAP8ib8yADTBl+1OTV7ACCWShuA\nHPD2lzkX1ZDYExYI0Foc1nq4tn3TO9rkQbnpTbRN0cbprGPEjtF78zKysJXSUYLeuSfi/exevYPd\nEN2yPafUos4U0No8cK3crlDaOYB19yb6Tu+7shWBKUlsYOMakoWNzu5uD1O5kUJrEhRaW+BaDuWz\ngCEoX7UJ/byKnZbkq1y1knZw0aHG8p7ZmpxusYy7LQD3LKyKi6VrlEsSMWbxqa/l+SXrBvG4QXNz\nkETCIB73UVvrJxDQCQY1AgEVrwvHCYUSKIpDPm+ztFTi8uUsCwurLC6azM66WJbK/fsGs7MuR47E\nuHAhgKqmaWmJUSrB4cMBLl8GRZGEwzA4mMXnE7z+uoZhQE2NV5H2wEEby5QoQvLaDwwUFdp2STpb\nHfp6XN4+q9F2BIYmFY7vtlieVlhKCYjFONZr8ydfLj+2VsUH2UephfxLv/RL/OVf/iXHjx/n29/+\nNi+99NJHxuk/c4CczWa5fv069fX1j5XU8SSAvJkaiUQixOPxJ8qtf696du9lxWKRoaEhHMdhYGBg\nfTVaSomqqmSzWa5cuUI0GuVHP8rzF38xRzisMjtbJpezeOGFBsbGVvnRjxbp7o5g4We6oxdpu2D7\nEKaN1FUouSgFE7cuACEJORux4CK7VZgu4AG0A9u9ZqXIAjITwL1SoJRVKS6HcRwdGtshD8xmoDWM\n7+Iq/sIq8R4HJ6wghcDXH2RtKNrWG2Ws+nkgYHClqOLqKrPKMT7XP8fZqrcqJKg9XhqvGQujllpx\n+jaSaoSUaN0d9Bp5xqsiQ/t2dfBqEur9zaRJopkSs6MFR1GoWxjBajIga1No3IZvKYNs8LzmUkpB\nTkpoU6HJQFoOQlewakPIZIFCtgkmctBUg9ulQcmFbT4YMaHHQIzZyB1+KLhQtqHLD0sS0g5S1SjI\nBH/9mgkLo5w82cjZs17SyPHjTZw752k+HzxYz9WraVRV0NFRw/h4kcZGP9msSqnkcuRIgkuXQwn3\nGQAAIABJREFUvLZ85EiM6ekyoZDg9m0XEAwMCG7fttm2zSYahUOH8vh8Gm+95YFmZ6c3oBw+7KNQ\nKNPfb3L9apBMRnDwkIKUgk+8YJNcFaQzcOptDVWFYEDSqkkKFYWxaYWXTlZ4dwgGByT9HR9NAkcm\nk1lfmHsUexgt5N/4jd/g137t1+jp6aGmpoZvfvObH8EdVK/nIzvyP5IFg8EPLGT6YfY4gOy6LlNT\nU8zOzq5TI3Nzc09FYOiDbLPyXF9f3/o0ajNPrGkax48fp1Sq8G/+zVX+4i+myWQcwmGFvj4fUrpc\nuzZMT0+cQsFgdDRH9OTzCMOHLAvwOcigjqixkZcruAMBqDiIFhV5zkJu8wBPRBwkwEoGemoQIxnc\nSYljRaAUgDZPMS44t0qxygDv6/BxQ6hUEg3sb6nlQk6l/rrFyY4sd+uLpLwjUkxsCO5HnQ0vOu9q\nXBtpoW3HLDOqTaurcnFTkzb1VgZyOW7GPDqiqehwwzV4c6WGweAS02G4k/U8vxuynpfsPH40RjVv\nEO/zNXKbFPvVKPMBH8ciYc5RjRTpb0Ter15LfRDt+hzOkRhym5/Mt3PI7T5oA0wXQhrKvRTu/gRK\npoSLgZzPo0zpuOMOBIKok2VcR0XEQIQlMqugHDxB7/gPuXDBGzwGBhKcP78GxnVcveolphw92sC5\nc17kx7ZtUS5ezKFpgsVF7/lt3x7gypUy0ajgueeipNMmtp0HIvj9C8TjPk6dMhBC0tLiDeb79wtK\npTKDgzZTUzZTU5ITJ8JkMoKdOyV+v6Svt8KtGzpLSwrHXrJpdR2MsOSNUzqHj9roChzZ7vD6BR/t\nDWV++wuPr1X+YfZRaiH7/X6+9a1vPdH1Paw9c4D8tKMjPsiklMzPz6+L/2ymRtbSsD8K2zwAdHZ2\nrivPbQZi8Ph0IQTz80W+9KWzvPrqHI2NAdrbo9y6laW+XsNxyszMOFy5skw0qrLjUCf3nDiYEpo1\nRNpExlXkkgmOBj4FZSmPe0H1ahOFqs+73QNZNVNAecXG0utQW0I4msaBdsG16iM9tDvO6WrCXSik\nQ/Xz2ltbLuksTcWZvxvnxN40s9HyphKlULI2ALlJkQzlddrvNlMzMEutvTXFXM9avDNeQ+eheVZ0\nQbOMcqO6LbnSSrM2y3l7Y4E1NR8mom8MoqdXovTGMqwsedz/jUU/wc48RWA/BsQDnK4yJnt6GrhO\nhcZ0BVtGWQaI+1DuL+PuqUcaHi3jdgbhtRUwY7iuAn4bwhrOiAlhgUwDAQdCCqghZvUeYrFzNDeH\niUQkR4+G8ft1VFXw/POxantzOXkyiN+vU6mUOXlSIxr1sbpaJJFwCIVUVlZy+P0qZ8/mKRZdDhwI\nce1aEVWFZDII2Bw9Gsa2oa0tzcKCweSkYN8+wdSUj7o6l+Vlk6NHsxSLcd45qzE4KFhelnzyUxWu\nXtFRdTCDgmN7bFaWBSMTCoc+4XCkq8IXfmkKv6/lodv4o9qzICwE6/T8s2MfhybyWqbb+fPnyWQy\nHDlyhO7u7i089dPSRH7wvPPz85w7dw7HcTh27Nj6AsQaT7ymq6soCkIIfvCDaZ577h+4dSvF7t1x\nFhdLzMxk+MVfTHDlygznzy8Si2kcO1ZHf3+Ue6lDoOkolo2YLiMbDVgsgQih+ItQsXHHchAOoLle\n9pueyyNCGj3TSXY3NGP5G+itA6eaFBP2bbyT3KYZ67Kz8X3K3vTeXMiaKq9criV+s47+TftNlDcG\n3I6qENB0wYc70kzF3DoryhQ0iq5BZMYLT8rkN8D3TjFCQ2br4s0Nq47V9IbEZEUq1MxoXFnyPPS0\npbC3OiCsTBncXVIwhHdD14sqrY6gYTVMNpGgplpUdc9ubxFObo9hTKfRL2RQpiUEdZhPQ70PFnJQ\np0JUQxRtmFARUzZKWCUf6Gc1DYGAj3Pn5rlwYZ5y2ebUqSlOn54mmy3z5ptTXLw4x8REmjNnZhge\nTnLmzDIXL66gaSrvvJMim7Xp6opRLLqEwwqjowrNzYKXXgrT0VFiYCDP3FyGK1eWUVUfk5OCaFSQ\nz8c4ebLEjh0Ww8MFcjmXW7c0GhvzFAppSqUyU5OCbBYOHXGIuRJNh6Ulhc+8aHPvXZXGhM3xAw9X\n+OFxLZPJbJEH/Wm1Z85DflLTdZ1CofC+29cy3Xw+H/v27XvfitZPSxN5zdZC5yKRCIcPH16nZKSU\nWxbs1lbls1mTr3zlPD/84TTbtkW5ejXJ0lKZz3ymkZGRZX7wg1FaWkK0tUUol02mppbJiZMo8QSu\nlKAJpO2AZSFKJlIJI6MKytUMWlMQE2jb4WMC2F1rkhz3M7aUIFhVYmyISIar3m92HYQl46Z3fX5F\nMl6phsFJyVh5A3SXzI3PMq9x+60og4cLTERtxjdRFvqm8e5WKkCdyXpMsg/JeMl7NxfmQ3y2rsjZ\nzNYah8nZIMG4pFgNcNspJGrSB5vCS+1sHWEka0oZ96dhW3OFu4sev/qcanPB1nAR7MjovDrhDRhH\nVIczrsrNgkJDsEJaNXjJCPOKobF9h8VYBXyNBhVAESZuPIKYzCIDAkIGMmUg58oQ8xPd+98D/5WT\nJ+uJRv2kUib79yeorQ0xMpKjvt7Hrl21XL6cJBBQ6emp4f79LK2tPjRNYf/+ILGYhm1X2Lu3TChk\ncPv2KrkcXL1qsrpqc+JELXfuWASDglQKTpywCQZ1Tp1aRkofk5MhQNLcHMTvXyIYDHP2bJgDB2yg\nxI6dDq++kiCeMKkUK0SEn0t3NHZ1OfyrL618LOWbftq1kOEZBOSn4SG/V129tYUz27a3ZLp90HGe\nhofsui5Xr14FtobOvR89AfD970/ye793ibo6P8vLZZaXywwONqGqNq+/fo+6ugAnTjRy61YSXXdY\nWspT29DF3MoOb86k6biujRqxcceAzhCaU6Zd0cgkYqSqM8OUP8gBJ4c7pzGZ12gPF5i2PU7WxAFU\nBJKxigfCnX7JhON97va73Da9TrrdJxkuVtOMhWS8tPEOsyZYrsIbFyN8enuFpaikUAXQ1U0gXoPN\nm0MBjhlZLsZUehHclBsTwNmhBIGQYC1lxC8kl6cVjgQdThvedSSKkjMLGnsbHG66VcGgZY29YThT\npSYWnRA7FwRrRZ8WFspQ572TuVsWPqFSkQqjKw4i6i1Q9vk07BWXc3dUAppkrKCzo9bhHhF2xRzu\nkcDIlZEBGytaA1N5lIqNMFRE2iWrxbh0p4UT++Z55ZUhpIQDB5p4++0FLMtl//5GTp8ew3Ekzz3X\nzDvveCTP4GAHZ85MVhf94oyPl9m2LcidOxVsWzI42MKZM3kaGjSEcDlxwsHv93Pq1CJNTQapVBjX\nhZYWP01NJQxD5dSpLO3tGvm8yvPPF5iejjAxobD/ABx7zsJFcP58lMFPZlmcVzixa4ZMaoqSYazX\n6wuFQk9djP9ngPwTbE8qwbkZSNey+7LZ7Lr4z8PYk3rIa6JD5XKZ/v7+H8uwey8gnpzM8tWvvkMq\nZTIxkWNoKMPBg3Woqsvs7CLJZJkTJ1q5cWOJctmkvd0AXMJhH3enjyNqFKRuoRYKOJF6QjJPuNHP\nvM/gU+0Or9zxc6CvRNIN0B6u0FjUuHwjQnuPdy3tDT6mq67kdMV7/s1aiblqeaN63WbC8njeuAZr\nob/1qlwHuG7D5d2SB4aKlIwUNjpucUmjbUGy0g9FCSPFjW3t0iSJxsXbYfYdKxGxt3b4mC0IrEqW\nqn12h+Jy3VG5MqTSsEeyJAWzi95vnAWgAZoVlzvzCnEfhDokBVcQUiSZKR9rmSST5TADuoNuudyY\nD7K3LstNosxbBv1OjvtaBLlqcuW6H0sKTjQ4vLOskqgyLyEDHBRO9OicmUzQgImTsEj5gjgZBSoW\nLFrorSeZmPpbDh1qoqYmSKXisHdvLY4DuZyNolBdG/Cqfe/ZU88773gLgLt3h7l3r0Jzs05PT4zm\nZpNQSCWbLdDSUqSrK87Zs3O0tARIpbz3tmNHHMsyCQQEp06tEggIgsEampsd+voEFy+u4LpxZmbg\nxRdN7t/XqamFVFbj05+yeP10hKOHHf71H7QyOWmtU2rT09PrM9AHk1qeRG+8XC4/cZX3nwR7JgH5\nSWwNkG8vOizPz0Bulv6eD87ue7/jPA4gb05m6erqolAoEI1GPxCIczmTf//vr/Hmm7PMzuaZmyvS\n2RklkfARCFhcvTrPgQMN2LbD8HCKgYEErivx+32kUiWWVl/EdnWEWSFgCAJNIXZ2W5wdamDvEYft\npstKqpq0EXBow2WHrfLqDZWGmMt0vgpkmnc9NX7JguNRKl0xnZBjEbRsAskSe4SCVABb0hCIsCS1\nLYNnbBOOdvskw5sAOVmE+0mV9opL/y6Ld+QGZxxRqtWbpcLE9QC9HVtnJ9kM3FxQOXTE4YpUCVVF\nxoq2YF/WxR+VjKc9lL29pLK/0SFswjwK6QoMCoczqOzF5dy0yq4Bl9vVASFSgsyMd++pvA7V/J8A\nfjpVi0tnfPQnctwqRZlZqQBBri4J4n6Xa6sKdX7JUFYh5oN9tQr39RhqGsKBIkvFCsUcOCnIyH/C\nrsRr3L27zPR0jr6+GlKpMsvLRerrg2iag2FYdHSEKJdLxONl6up0RkdTVCoW3d3tvP66F0C4e3cr\nt27l6OuLcu5cBp9PsGdPjELBQtMU3n7bSybq6moEbAYHIywvF3EchddfV6ivV1AUh5aWFe7dq6Nc\ndqitURkZEczVCgaP2Hz931XWY44jkQgNDWsB2N7Mr1AokMvlWFxcZHR0FMdxfqxO38NES621n592\n6U34GSD/mCmKQj6fZ/zWVf5qcR+rVjfKXcHRJpdtEcnPbZfs6fjwQoyPuqi3OWJjczLL4uIipmmi\nqhuVidcaXqVi841v3OE//se7RCI6ly4tEQrpDA424bo29+4t0dERpa8vwZUrCxw92kQ2W0bXFYpF\ni1gswORkM8lcLdFml46BAKYdwt8iEdVLNyyHN97WifRWKYVAgOJZQbrPu4bORslS1SueLHrf7Qo7\nIATLU+DOKwzPqoBOb7OP4ZR3nMagw1JRJR6yMJuy7GjQGPFFyBZNwPN0NnvOfkUynPZ+O72qUH8p\nT0ePypTrNeHF3MYLKZQFlSEVrVFiIwgIyb0l77ez9wThHZL51Y39z48qfLrXYWrT+ygvQHkTc3V/\nRuBrkWSrVaMCBble3CK7bLI0KwCN6XKAvfUON0sqd7MaA3mXCVvBlh5KT5WC9NdVuJ/3sVPLcNOM\nsoMV5sbDtNpw5pwfvwV7Ox1sxU90IMCcT1KcKlGecLl8Yy8R/xu88EIHqVSZuroEu3bVoigaMzM5\nfD6B40iGh9OEwxqlkk4+n6ezM8rVqykSCZ39+xvIZl0GB0MYhgqUiET8/PCH0yiKoKenBdeVvPhi\nbbUKh8Vbb+UxTcnevbUMDpq4bpDTp0u88EIU2y6iKAZvv+3jxZdM3r2p84v/Y4XubhPL8maZoVBo\n3ZlQFAVFUd5TwW2tTl8qlWJqamq9CshmkA4EAu8Jvj8D5J9QexzKQkq5PlLbts0//cQBflnTeGvS\n4f++rHJ9WXBzXuE/XQQ3Dy/1uHxiwOWFfRLfexT0eBTKIplMMjQ0RCwW21KuSUqJYRjcu3ePRCJB\nLBYjEolQqcBf/dUQX//6Tbq6wszN5clmLY4caUAIh4WFNOWyzc6dtdy4scSOHTX09cWwbYdo1MAw\nFITQmZuLkC8eoLMzStINUMhJtu92uXZJRe2RHG7NcerNCH1dJkOmwfE2h4s/UrBscKvAqvmBLLSE\nXLZpkti8g8wIzkx73mZnm9cJQ4ZkLO11mKaQy0LB2y5tjaujNchRQSzkEu62iQRtcmhk0znAI6y7\nfDZ33Y0IC+nGKV8VtB92ybiCkcxGZ+wLSm7cVhmsdTijqfTrLternPBCTuGFrMOb6Y1FJolAbmTP\nApDNClrcjTa0XFT4FDavTXld5vKkQkefzZSpocxLBgI6Z6qLmL4qFXNEd5FV0vreisLOVoe7GZW4\nUU2c0cP0Lbjcm60lWxS4CZOSKehrTnHxfgStDH0NJgNBgXo0QK7dYPScQHKA1dUh6utDCCEZH08z\nNpamri5AJKIwNLRELGbQ01PDxESGtjYdv19SLmdoaopx4cIsxaLN88+3cerUHMGgRiLho6FBZ//+\nGnK5Cn19FlevZshkHA4fbqKnx6a93c8bbyTp6QkxN+fyyU9KrlzxuOXt2xUOHsxx8UKEEyccfud3\nvKKmY2Nj5PN5Ojo61vvD2iL0GjAD61FBD9bpk1JSqVTI5/Pr3nSpVELTNMLhMKVSiUKh8MTl1ZLJ\nJJ///OeZmJigs7OTv/u7v/sxTvr69et86UtfIpvNoqoqv/u7v8vnP//5JzrvgyYeEbh+KuqkWJb1\nSCppyWSS4eFhwuEwPT09XLlyhRMnTqxvr9jw8psqb40qiJIkqsHCkkApSuIqdNdLXtwr+fnnXYKb\naKx33nlny3EetHw+z9DQEEII+vr6CIW8BbHN9ISUklKpRC6X4913F/n+92f5z/95CcNQaG0NcOtW\njoYGPzt2hMjlity5s8LBg40sLhZQVYVw2FOMi0QMdH0tCkOhWKwln99Lc3sDFU3FH4QzN1Va2iRq\n0ELES4RdnUtzIQZPOuCCzMDZaZXeDpdh1+tIvTtcGoREX5G8Oex1ioE+lztLCjUhSbLqtextdriZ\n8kDwaLPDxXnv88FGh6uL3ufWsMvsikI0KNl7xGVBwkjR27bHXeXdrMffK0iCKZe8rdJc49J7SPL2\nxAbAPh9wOH1XBST7n3cJ23BmeGP7iYjDql9wv+TdQ0yT5G/CvsMuV6vnG/Q5LEwJRmMCWXWFPxm0\neXtGxXK9v/c0ZchFw0y8rRA2QGmArC1QhGSg3WXitAIuiCjkLMFz7Q4XUiq6Ijnc5HL7DYX+BpdL\noyon+hzeGVLZ1+4wsajg5GB3W4WJCZX0nEKcCm1dJSo5H0auSDB4G0WZw7IsRkaW2b49TDpdJBoN\n4fPpBIM+pqay5HIm27bVcPduClUVtLfXkMlY1NX50TQdISShUICbNzMIoZDJ6BQKDs89187ysklP\nT4B790yKRYlpRolEoK8vzIULJfr7GzBNh5oaP6dPw6c/HWR+XvIf/oOkpyfF/fv3aWlpob29HSHE\nep9ca9dr/2+2tRng5oih9zLLssjn81y4cIE/+7M/48qVK3R3d7Nnzx5+8zd/k927d7/vb9/Lfvu3\nf5uamhp+53d+h5dffplUKsXXvva1Lfus9dXe3l7m5uY4dOgQd+/efdj454dy359ZD/lhLJfLMTQ0\nhKIo7N69ex0QHzSfBv/Lpxzu7HH5399QGJ8X+HySWADsAgwvCW79vwov/6lKf5Pkn7zkMnji/QeE\ntYXCXC5HX1/f+kj8XjzxykqF7353lu99b5rp6Tx372Y4eLCeyck0t27lOHEiQqlU4O23l2hvDzIw\nEGNyMk1HR5jFxQI+X4hg0At/Mk0XXfcjZQ3RaA+BYJTUqkagBpYycKSvzJu3Agw+X+bC2Rh9JyVC\nSHxFyetvaBx+3vNwGhslw/NwpMlh4V3B2VmVEweqteMMyXCVDthe75Jc8QAuFgC89Sb0TRFQwU15\nPO0hyewKZIuCOxcUQj6X3r4CwzKEamxEtXQFHUaXvaY7n1RoubhCrDFGRnoHS2fW9hTMXFdoad36\nLqwcsChRGyWOFOwwXC64KskJ4dEcUrA6DyPzCs+1OVzIqShIbt1S2NtS4kpVSvP+cpRjwmECQd6E\nwYDDmZyKKwVtKZdb1cXJkzUOZxdVrs4qNNS4NAUk+n1JNifIVyufzKU9YX4UyBQFgzscbtzzIUw4\nuN/BLfqoJH1EpYUbDSCcbqSs4Dgz1Nb6WFgo0dgYQdcVVldLnD49QyCgMTBQx9mz42iawp49TVy9\nOkki4adSCTMzU+DgwWbOnFkA4MSJNmzbIpHwcffuCsmkRalUx8KCyc//fD3LyxWCwRBvvFHk5MkQ\nhUIBv99gbEzy2c8q/PCHLv/yXzqEQvcZHy+zb9++LQttm73hzfYgQK+1/82e9IMgres6iUSCz372\ns/T29vJHf/RH/M3f/A23bt16LFnM73znO7z55psAfOELX+CFF174MUDu6+tb/9zS0kJDQwPLy8tP\nNSHlmQTkD7NSqcTIyAilUom+vr6HfqADjZL/61cdXn5F5dKYwC0CBrglgc+QRFvh9qTgwv+m4jNV\nWhsH2LlT5dgxk717BZ2dLrOzkywsLNDd3b2+ULgZiOfmyty7l+Ptt1eYny/wzW+OsmdPjNnZHJmM\nyeCgp2vw3HMJjhyRvPbaOIoiOH68heXlPLouKBbLLC871NToCGGSz1uEQmE0LYSu1+K6bRSLUWw7\nQDQuGRmGWGOR1QAMdGncuxElGoXRBcHPtTucelNF0yT3FrzOIFTJYc1BmYHp2SqvW6UjelvddU94\ns8pobhOdvro5rG2TLO7mSNW2QJmb8wFYDDJ4wmGksClDzycY3bRvMZ+g0ZRU2l1cCffmN7aZJRcx\nbkOkmkEpJPfHFbJlwcl2h7MVlbVYuIklhZPbHMYcwd0p774WJwRqnWSX3+ZmUgdbRav1QDukApMb\n9zI0J9Cjkq6w5PRpjXhcki4Lxhc8r9lyBXsjDhdeVVEkhHySu7MKu9sdbk2rHN7ucHlMpa/VZXhJ\noWzBsQGXkVGF1KygPSJR0AloCrpRj2V14/erhMNZbDtPsVhkYSHH6GieXbti+HwaiiJ5/vk2QiGD\nTMbiueeaSCSC5HI2vb0RHEdh716Durowp06NE4/7MIwEy8sVPvOZVvJ5m+5ug1deWaG11Ud7e5Aj\nRyyGhmwcR7J3r5+ZmSKzswk+/ekMn/3sXeLxDpqbmx/aMVoD2c2xyh8E0pt/J4RYTwoJBAIcOXLk\noc75oC0uLtLc7JWxaWpqYnHxgwvOXrx4EdM06e7ufqzzvZ89k4D8fg3BsizGxsZIJpN0d3dTX1//\nvosDruu+55RJV+H3P+dwZVLwf/5IYXZRoPk8HjmzIgjq0NYvmZ0SjE6GsCzB6dM+JidztLWt4vP5\niMc76OmRLCyM09oK9+/nCQQcbt7MEo9LhoezHDgQ4fz5VY4fb+batUXCYY29e0NIaXLsWJhMJsP5\n8yu0tUXo6IigaZKVlSKlksauXQ0EgxqVyhpn55LPe1KKuZyCrlsoSplMxmDiRpDenSnu3Kil/xOS\nQAHupAQnP+FQSINZEEgp2Nnv8G5W5eQ2h5uvqWTyghPHvOM3JVymq5xyLMy6J5ysxgkLIRmtLsj5\nVcloqpoQIiQjqY1nvLBpYU5flxYSzN4WxDSJ6HKZL///7L15cCTpWe77y8zaV9WirbSvrZbULanV\n6m61NDNesccOcGBjDpvtuGwnAmxDXHMiHEEEcCHw5XCOHYaA4ARMgG2Og7lgggvXNmY8np6ZVm+j\n3ltLa5eqtFVJte9VmfndP7K61WOwZ8XGY95/lKr6KjMrK/PJN5/veZ9XRn2kDZvTLFjeldF0iXG3\nhhaC2+Lowu62V7h9z87JUynuynV0KgVWS8aT0N0bMqFTOouLR/uwuCBzckBjr3ZpbB7IjDZkUfd0\nwEs0Y2WyV+NKQmHIqnP9uoy/TZAoS8TyMpMtGsU9yJdkHvNrXNxV2E3LnOnXWErLRF6S0KuQLUtM\nDWtcWlWw1p4SSlXj+9e5BNGkxNuHNfJ5iQa3oH9MJ52UOIhISCkJmy1HY6Mdq7UPqzWGrsdxuQp4\nPCX8/gKapqIokMkUyWQKLC0Z/hYDAwGuXdvH6TTT3BxgdTXN4GCAe/eSDA97aG2t4/CwSHe3nWee\n2cXtNtPaWs/0tIli0cLVq3He9rYmjh2rAi5u3y5z6pSDS5ey/Nqv7TE5eeoNdUl/EK8GpB8sf/3r\nX2dnZ+cV1/mud72L/f39f/X67//+77/s/0cnzv+t2Nvb4yMf+Qhf/OIX33Q99VsSkL89HpWSdXR0\n0N/f/10P+APp23c7scY7BH/yEY3f+n8UIjGJdAxkk6A+JIiGZXQVnA4NRSljthRoanKwu1tPb2+J\n/f0yN2+mOXHCxDe+kebUKRNXr2YZHLRz716aU6f8XL16yPR0PXfuJJiergfKXL68w8mTATY20kSj\nBc6da8XhgHv3oqTTFQYGAjQ2OtB1KBSq2Gw2CgWdYNCLLDvRNDflsgtVdWDUvmTo6sqyONfI8ZNZ\nlmdcHJ/SCNRJqAdw+6bC+NsMYAwGBWNVjcwGpHM13XPC+NsREuzXrod0LRO2mwWpEvR4dZqcOkld\npmQTBB06L+0bp12vT2cpYVxwHovOeuIRpYR2VAEZcgguLSr4DwUnJzXWY49M4Hl0bm0b67hxT+FJ\nc5Xbj+TaDmH8hstzXjrP6tRr5ofeGNmSRO96gt3ikbY8kZew7L78t07uWkkeHnErkU0Ja51gbU6i\nUJE4ZdeYKde2mRXcuVeTz23J2O2CoiqRy0j0FnVurClMndS4tKywviNhkgU3N2S66nXmtyXe1a8S\nXZTw7wju3pNJxiQmRnXmXlQINmi0BJNoHgWT7gXKQIJKxYMsG5IQTRPkciVaW91Iks7GRo6DgwId\nHR4aGx1kMmVOnHBjMsmkUhkGBsykUnkODkr09jr5xjfC+HxWOjoaOX/ehdls5cUXd5mcbCWTqfKe\n97h44YUEx4658Xiq9PUJFheL/MZvSPz0Tw98x+vlzYhvB+lYLManPvUpZFnmj/7oj17x888+++x3\nfK+xsZG9vT2am5vZ29t7mUTv0chkMrz//e/n93//9zl37tzr+BbfPZQHvaJeZbymwd+vePQuuru7\ny9zcHG63m6GhIerq6l7xUSoWi+H3+1/RqMhigveMCkwKLO9L2MyQzUuICgTrqhzGVeIxBZNsIRTS\nCQRU7Haw2zWCQQsrK0VGRhxcu1bk7FkXm5slxscdqKpgeNjCwUGaQAAikRTz8ykmJhqgxaVHAAAg\nAElEQVS5efMAl8vE1FQ9+/tpZmf3cLksnD0bwuOxkE5XKJc1PB4HBglgRQg71aqDatWBplmIxaqs\nr5vp6fGimFzY7QrVkonDQwWTv4opWWZ524LJrHOoS5zsqHK4JjM/p9A/KAgfyrQ26ezUNMLtrYJ4\nXmKkScetCVwJQaggWJ5VSK5ItJsENy8by12SILsqMeDW6arTwQzxskyHJUu8ZHAcDpPgIC2hC+N3\nClkFO0mZYlnCmoTOBsF2ydh2r1MQPjjKUixJ6G8WRGrVgdqBAbyqJtEgCUoViXj2aHyPxUrApbFf\nM7IPmMssXlEINpUp1FQdx52CZjOEa3rrTFHi3a0at+eNzyTSEvY6KOsS3qigq06wk5UpViXOdemE\nszL9Lp1CGGIZmUpFogqkCzJn+nS2kzKnOjWcB1CKSNy9pdDXrbO8ojA5oXP9pozdouJ159jd8nKw\nJ9HcXKZalchkJDStiMkE1ape68Yskc2WKZU0dnczvP3tHbhclhqgSQQCbmKxMkJIBIN1yLKgs9NO\npVKlrk7g9dq4dy9Ffb2VpaUi4+N1JJMq0WieQsHB0JCJ7W2Z7e0Cfr8Zn8/E//pf9cjy90Z2JoTg\n7//+7/n4xz/OJz/5SX7rt37rZd1VXk+Ew2GWl5eZnp7mT//0T+no6ODd7373y8ZUKhV+9Ed/lJ/8\nyZ/k53/+51/rJv6vVzPoLWcu9CAemP/kcjkmJibo6ur6dzOp/+A5nf/xf6j4/AKbU8PqzHCQKmI2\nyXR2mQgEzMTjJiRJYXdXZ2GhgBAFHI4K6+sHTEzozM5u0dur8uKLYWS5yIULO+g6HByUicdVzpxp\nIJ0uMDFRR0+PncuXwywtxTl3LsToaCOZTIWtrTQOhwWTyYSuS+zslLDZ7CiKFU2TyOczJJMFqlUP\nZ87YuPC8itmsoGklFhctnD6rk1620druQNVkhk5oDPlKRGYFKzUVw9aBkYmFmqvIkmC8XUOOCqQ7\nUF6Ci/9iYuGuguMR/rjyiPovW4RkSuL2DYXIbY3lryqE1ir02+z4bcaMe59PR9UfMRR6BHDb3IIr\n31CY9horjSeP1u22CpYiMleflxmp02h36ew+Qomk4xIN3+Zxs7EhcbCk4DAZ2+4wV9A0hZZHzI4O\n14rcvqHhNB2dE9kVHUvtM7myxEmnzkhQY/6ewuF+bYIO2NiVaPPq3P6mDDUKJ5qUON1lcKIHSYmx\nVo1b/6iQ2pa4vaAwfFzj+l2ZY30a95YkFEUl1FZh8X4ddrvM4KCZgwMTu7sZII3bbSMet1AqWTGb\nbVitdgIBJ4GAg6YmJ+l0mUpFp1hU2dvL8dxzG6RSBcxmE1evRigUKqyslLh1K01jYz2SZGZ62kOh\nUCKfT7O5mSeTyTIwYGNvL0EupxMIpOno8KJpZp56yofJ9L0B42g0ys/93M/xzDPPcOHCBT74wQ++\nKfrjT3/603zzm9+kr6+PZ599lk9/+tMAXL9+nV/8xV8E4G//9m958cUX+cIXvsDo6Cijo6Pcvn37\nDW/70XhLyt5SqRQrKyv09fW9rnLKxcVFGhsbX9Yu55VCVVVW1jb543+wsbXXhJy3Uoxl0UoO8mkT\n6EVCoSpCqCSTOltbGfr7BcvLGTyeChaLIBpN0tpqZWsrSX29FSFK1NcreL0Sd+/uY7EoNDXZmJ3d\no7nZwdCQj3xeJRrNIUkSXq+daLTAsWP1lEo64MBms7G+XiaftzEw0Eil4kSSJDY2AvT0wNWrJs6e\ntVFVJTRV4vp1E6Pv0MgVJZodgouXFabeqXFpXqGhXiemyLjsGqNtae7fdSDrEKsY6Dt5usKVRYMi\nGBrQmd+SQRL4/JDMSZgUgcUEhbIBWB67RqZo0BdDrTrrUYlTUzpWn+C5VeP1do9OOHwEqmdDGtcW\njJvDE2/XuBSWUWtucKebNa7fMt6rcwtOT2o8e/OIlTsf0rg6I3P87YL5uEyfT2flJWPdZ84UeKno\noD9XZnnDqA4beUzjoCSxe0kCIXH+XIXLhxZanGV2XrByYjTJvZShkHHbdLqsOnfnje1NnNKY3TX2\n5Z2NVb71gpFtnzihcS+i0Fqvs5uTmOjQ0Tdg9o7CuXGNq3cUho/pzM3LHO/Js3jfyfnxCleumOlv\n17FZYP6uTGdniaamCpVKnlIpjcmUxe8HWVaJRhNUKnkCAYlIJE5/vwshdL71rU3sdjOnTjWiqjqa\nBm63hUJBJ5Mp09Tk4YUXotjtJhoa6hFCp7+/nrW1Ag0NbtbWKrS3w/y8lYEBG4WCmY98ROLDH/Y8\nLNp4sznVB6HrOl/5ylf47Gc/y+/93u/xgQ984AetEORV7exbkrKwWq0Eg8HX7Y2cSqWwWCzfUQb3\naAgh2NnZYX5+noDfx0+/r5X6gIn5sEQ+X0WUwO2QcToUYjGBrquYTCUqlTxer0ZLi4zTCT6foL7e\nhMej43KBx1NlZeWQUMjOiy/uEAgYbXwODgqMjPipq7OQTJZYXY3T1VXH3NwBhUKVnp4ghYKKLNvI\nZCrk8xUsFg+9vQFu3qzgdFowmx34/WWyWTsHB9DZJbN0v8DmpoM6P7R2ClZnZQ6SEuWyhL9dEI3L\njI3otPsEhzdkolE7yYSZkVGI1DJYq6NMMmfGZlU5yBuUQ1ezyl7aAKaBVo3dGmfc1agSTRm/j8Mq\nOEhJlCsSkQ0ZX1bQ2yqIViQGfILI4dFFXs5INUCHIIJO9xE90eUSRGpKkFJFokPSOdAlqjXAbhSC\nnT0ZW0Wg1UGfQxCOGOP39kyMHdeYu2PmwbXjlqDdJwhvGGMODmSCLYJuk0xkQ0Yr25A8UNUkujxF\nLHtF9ovGzcmsVUlLChMtKluzCnkVhJBoqhNE8zKZgsSTJ1Re/FsFiwLpPOzuS3S2CZY3ZPo6Miyt\nuxke0FhYNtEeErS1aVRLMHCsjNcjs7YmUamoBAISJpNMOl0mnS6i60UcDh2bDTKZEna7mbm5GD6f\njYmJJjRNoKoCEJTLBhj7/XZUFTo67LS1+YlE0rS313H1aprubjv5fJlyuQL4GB52c/eumZ/4CS+/\n+qs+SqUSsViMzc1NdnZ2yGQylEolhBCYzeY3DNL7+/v88i//Mru7uzz99NOcOnXqBw2M4Yedsngj\nYTabXxVl8YAWyefznDlzho6ODmRZ5kfO6HzmVyt095uR3VWK5TSH8RxCFLBay5hMEsGgl+Vlnd3d\nKvm84OrVJKqq88ILB5hMMpcvpxgba2Z29pDh4SCdnQ6q1SKKUkVVddbXU1gsCjabmdu3o5w+HcJu\nt7K2lsRisVCtFtjcVGlsrKdQ0EildEZHXayullHVMrGYSiQieOc7yzx/ocjAgA2vVzAxXubi1xT6\nB3TSGQm3WxDel3lsWKMchpl/UGht1UnXFBGVGrXgcgq2ar7BA10Sas3Vzes84ghk8VAgTChwdOr1\nh3SqNYrAZhHMrchc/EeFxg2B65Fque6gzuEjFXk2CS49pzDlMeiLnf2j96wmwdUrCoOSbmipTYLF\npZpEb0fmhFkjsnnUQEDXJXyxl18Qq1sy8t7R9ktliR6z4F4tq44nJU41GtSDLWlled1LwGWM34pZ\nGQvmWb2oE9mTGWox6svvLisMtqgMturc/5aCLMFGWObcqI6uSzgshvGObHbidQtagzptnhJBW5Hn\nvp7DoqS5fSvJnTs7dHbuI0SMUimN263S2GiiqcmFrrtIJk1omhWLxYrJpDA0VE9zs5N8vsreXg5F\nkbh374DZ2V1cLjPXr+9z+XIYsLC7m2N4uA5d1/D7K2xsFBBCp6XFz/5+Hl03MTkJv/M7Tfh8Ptrb\n2xkeHubs2bOcPn2alpYWJElid3eXGzducPXqVebm5tja2iKZTL5qOlDXdZ5++mk+8IEP8Au/8At8\n6Utf+ndrLvofJd6SGTLwhpzWcrkcqqp+R32yUTV3j0KhwNDQEE1NTQ+9JnRdR9M0vC7Be6ckknkr\n6bwdi2zF6TCTz+sUi0U0LYXFUsLtVjGbq7S2OshkqgwPe8jligwPu5CkKi6XhM2mMzMTwem00NTk\npFJR0XXY2cnS2Ojk+PEA2WyFQMDO4aFKLlelvt5PW5uX27fz9PT4iERKmExWenvNzMxUOX3aw+Hh\nAYWCl3gcenstRKOHqKqHw0OZjl5B9EDisfNV9hYVtu5LHKYkqqpE/7AgvCdjMgtSVYlKVWJ4QGcn\nUZto6zyaaGtulNiv6ZLr6xQO0sYjvdOc5TBrZJPtwRI7cSNbHm7T2dkzPptOS2TDEqO9OrGqxLHg\nUQYMYCpBKmNk1W8/rnJ762iO4ERIZ3tLZndHZvqkjtcpiKwffbaUrBB0QjR39BRlTwj62gSRtDHu\neLPOyhUZZyMUax7NbVbD5yNRuyGlEhLD/Tq3nlOoqhKnenQiGePzwz6ZxQUj45aEhbJkAH+TK8v2\nNZn9XTOjw3n2DixUKyrlqkQsbmWgV6feLaiXVS48I9Hfq3P1qsTYGCwtCaxWlfZ2M9evV2htlVAU\nwb17KYrFAg5HlXK5QLFYxO02FBeSpHP/foJQyEU+X8FslrlxI4rPZ2NqqpV4vIjDoTA62szMzA42\nm8LhoUCIMsGgg0RCo7U1iMkkcLncFItV/vIve/H7//UTqCzL2Gw2PB4P9fX1tLS0EAqFcDgcVKtV\nEokEW1tbRCIREokEhULhYauxR+d49vb2+KVf+iVisRhPP/00o6OjP4hZ8aPxqjLktyQgS5L0hgC5\nUChQLpf/FYdcKpVYXFxkb2+P/v5+Ojo6MJvNLwPiR43iFUVi8pTA5RGshCVEVQGh4PFIOBxWFMXG\n7m6FXK6EohRYW0shRIbt7RxQZW4uSUeHm9nZA06cqKe11UY0mmd+/hCfz8bgYBCn00yxWEVRNPL5\nCvX1Tg4ODB2lxWKlocHJ3FyRwUEPd++myGZdnDkDFy4UaW93srdn44knyjz7bJ7GRjOrq27MFkFb\nh4pezqMIC2srCiOndMK1IhCzB5JpiaFBne24jN8rONam0+gRdLgF5pIgIGv4tAIUKnQFZHrqBXaL\ngskMmSKoupVSDeTsJo1EzgDqRluGaMIA6s5GlZ19hciaTKdd4A0ItmpA3+gVbG8dAWzIIujwC8I1\n5UePVxDZrmXEGxIn23TWdo7Gj7bCxl0LjiYDbEN1Ouu3FZL7Ev42Qa4sccyls7IoM9avE6kpMxwJ\ngUWDWE3lUa5IjLh0Vmv7Ej2QaAoJPE7B4jdlzpzU2T6UyRUkJkd09hISgZyZgFNm/1CmXJYRsk46\nY2aoP0VVU2ixZ7j8rJVy2TCxSiZl7HadSkUmn1fp6TFz40aFyUkzm5uCdLrM4KCD/f0qqVSF5mY7\n8XiFalXgdtvJZAqcOBHAYpG4eXOPdLrMyZMNdHXVUSyq2O0mmps9lMs6XV0eNA3C4RRtbQGqVRPH\njgW4fj1FV5ePclnjf/7PLgYHX5nOexCSJGG1WvF4PASDQVpaWmhpacHtdqNpGqlUinA4zObmJp/4\nxCf42te+xh/8wR/w8Y9/nN/+7d/+jk0gfsDihxeQgdfkZfHtUSqVyOfzD0swVVVlbW2NtbU12tvb\n6evrw2azfUcg/vY7eW8njJ3UmV+RKORkZElQKgk0rYzbrdHcbENRZFpbXSQSGn19ThKJIj09JorF\nDC6Xjs2mc+uW4Wk8NdVGfb2dw8MCGxtJ7HZBPG5I3ZxOJx6PiUjkaNImEDDz4ot53va2IIeHCex2\nD+GwzqlTLvb2YjgcNnZ2YHi4DqdTYmQkzfPfqqBrgr09J6oq0dkj2N6VaQ7ppEoSI8c0mj2C8o7E\n/j2ZShLmrigU4rB4T2Z3Q8HngMV5FzurCh5ZMHvBkL4d9+rUOwSdbQIhw86h6aHErc5iJl7LUDsb\nsuwfGuCcSUF+TXB8WGMvo3CyVWf7EYBtsgmuPq8wPaERzsrIaR7SKggJbauCxa+SrxjA760KtjZl\nBlt19ioyI4064TWZSlXiWEgnoUkkFgwOPRKWOH5CEHQJlq4pxGIyZ09r7MRlOht17j4j09YhSOUl\nNF1iqF3HrUF4RaZaktDNoGoSxYLEqU6d688qOO2CVEGiWFSYGFPZ3ldoD5mpxirM37UwMlJkfd3K\nwECarS07AwMlVlZMTEzASy/pTE7KxOM6LS1VurtlqtUKHR0Cn89QZTQ0yOh6GZ8Plpbi+P02lpcT\nlEo6U1MtmExGifX+fhav18HCQpxSSUVRBJKkMzDQzOJillDIQ7UK3d11rK2V+W//rZ0f+ZE3ThsY\nCYNhWB8IBAiFQkiSxLPPPouu6zz22GNcuHCB559/nh/7sR97w9v7DxD/ySG/3ngge3vQTPTatWtY\nrVbOnTv3UDD+AIi/vYfdd4rONvgfv6sx9QTIJjuybMLttuB0Otja0kgmNSoVlVyuQqGgUihoVCoW\nFhcrBIMB1tYKdHV5GRmp4+AgwbVrEba3k9hsMjduJLHZLCwv57l/P47LZaevz0ylIrh7N4EQMufP\nS8zMHKIoJjIZlcceq/DMMzEkSXDzpqCtDTQtw+LiBomEwYMODVkplSRkRRDZlZg8U2HkWJnCZpWX\nnhEs3FAIr8l0dukPJ8eaGjOIGrg2Nh0pHLxHLov4vXDzRYUrf6fQHBOMuXSG23Q8dsFq5OiUVGTX\nw+W+UJWDAxM3/l8zJ11JsvHcw/fMinhYbTfzjwrvalfZegSs2/x5NtdteJNm7BZBvUcwv2C8f+Oa\nUX0Ye6QE+saswtvbNNLpRwB9H/zaEZ+8tSBhtwhCiqBSkfDJR+9lkhKZDWM5GpM43WckB01+gV6r\nyF1bUzg1ZPDrd++ZOTemcv+lAu01d7y9PQtut87CgpeeHo07dxwMDpbJ57NMTKyzsrJCPr/Gzs4e\nV66EKZezPPPMLqVSiTt3Euzu5slkdDY3CwSDRi+9ri4vo6NBcrkKa2tJ8vkqIDMzE8ZkEmSzVa5f\nT+D3+yiVVM6cCXL3bhpNEyQSVT72sQY+/OHG73iOv97QdZ2//uu/5id+4if4lV/5Ff7pn/6Jz372\ns/zzP/8zTz311Ju+vf/I8ZYF5DfCNymKQi6X4+rVq5RKJc6ePUt7ezuyLD/sYfeAEnklIH40LBb4\nPz+u8Uu/pOEPODCZHBSLJurqZEIhOzabwokTPsplieHhBjQNnniiBadTweu14nI5KJcVNjcLdHW5\nAYVKRXDuXD2pVAFZrmCzKTz77CYmk422NjPDw24uXw6jqg5CIZneXjOLizuoqg1dh5Mn3UxMlGhu\nznDlSoZAQOH2beP7qKqFkZEq735XmoPtFFdeyLEdllGrEp2dgs3NGk8cOpqksTmOHmUPkkfHZS96\ntJx+ZGLOaobZbynM/YPMuEVjrNsAJJMiuL9xdHoG3Uf84tyLdXizDuwWY2xnfZ5c/hF/jPkqpzuP\nTDLafYYUb+W+wohXp79BRzyic47OS1QyvCyyyxIB7xHIRncllMTR//v7MpPdGrPPG/t467bCWLdx\nTigJgVw60iLfuiHT0qCTWha8dE2isdHYt61VO067oKNVx1TKkcvClSuCY8d0YjGJkREdVZVwuyWm\npvJI0j4bG7tsb0tomowsW0gmderrLdy8mWNoyM6VK1l6epysrVVpbnYQCjk4dsxJJBJnby+PLMus\nr6dob/dycFBAVTUmJgJYrQqKIvH4461cuBChXNYoFHRGR+solRTe+94Av/Ebb65vA8DOzg4f/vCH\nmZ2d5cUXX+R973vfDzpX/IbiLQvIrzfS6TTz8/MUCgVOnTpFf38/JpPpIRCrqvqvjOJfa7z7nYI/\n+L+N6iiPx0Ug4KFQkCmXTRwe6iSTFYrFKpubWXI5lRdf3MPjsVMoFJGkCnV1dlTVxPHjQYaHG1EU\nG93dfsbGmvD5ZCYnA8zMREgmM1y7dsjEhItC4RCzuchzz6VobrZxcFBherrM3bsxLl+OUqpVyQ0M\nOAkE4G1vK7G7u8udO5tkMirlEtTXSywsGN+5tfWRpqQHBsAoJsFyTT/s9wuW14wxDUGdtRq4ul2C\n+6uPFH08kpmWkxLXv6IwZNZ4fFgj/4gJUewRQD/eI7j0L2Y6KoKAR9DofrnWPL6ncev/M9NXb6g6\nImtH8wlXLyg4Mi+ns5qdAnMCLGYDQBt8Ole+JdPtORo33KZz4zmFlsaj19SoRCh4BNLJbYnxYxr3\nrioszMtMnjTG5vISfZ4M2xsKlYpMa4txjA4PJSZPqeysZpi5qDMyItA0kCQNSdK5ckXwxBNFEokN\nYJ/5+QLHjzvZ21Pp6LCzva3R3+9mbQ1Onw4SjZp4xztcqGqREydUrl5d4/Awzq1be1SrEo2NDoTQ\nURSJzc00bW0OWlrMKIqF5mY3J040Eo+XGBur5/BQrbkN6oyMOPn0p/t4M0PXdb74xS/yoQ99iF/7\ntV/jL/7iL95U17Qf1PhPQK5FsVjk7t27LC8vc+zYMRwOx0Oe+AEQv1p64tVEKAT//b9LPPmkDbPZ\nhcPhRpJMeDxmBgZ8mM0mTp9uxGpVOHGiDqu1wtZWlo2NIq2tboJBG4WCysxMhJ2dDJubWb71rTBO\np4tMRvD44/W4XHZ8PpWtrQpzcxnKZRPHjlVobS2ztrZDtSo4PFTp7nawsKBx+rSMEGkODlaoVgvs\n7law2STm5ozTpL/fgl7LLKNRA2zcHo3NLYNaGDyuk6nxtn39+sOxPV1HoHWsV6daM9HpbNPZ2T06\nBddWjOX5WYXKssTZFo2A1wDdlY2j4+1zGuu7f1vBFhYUEkfH1e2osrHmRNNkdi57ONdXJbx5VDbo\ndVe48LTCsdYjOd7mgsTKvMyZTuM79TcJdE1i9qLC2UENSRJE5iQKeYl6xdi2xyW49YKMR4EHmfBW\nRMJXPAL/5XkZt1Onqy3Hi9+UGBoyblw3biiMjWn4/YKVxQTBgLHdRELDZhPcvw9TU4LJyTzb21vE\nYgWuXi0yNGThpZdKTE25uH27xPS0h1hM5X3vsxGP79HdXeSFF7YBWFkp095eT7VqoVKRGRlxc3iY\n4vLlbSRJJRgEhwNU1USxqOFy2SgWq7S2uslkBHa7CUky8653+fmTPxl7U7PW7e1tPvShD3H79m0u\nXrzIe9/73h/qrPjReMtO6j1wg3qlMAy+V9nY2KCjo4Pe3l5sNhvhcJhQKPSKE3ZvJCQJTp2S6ekx\nMT8vUakYYv5otFzLTgpsb6cQQkbXTciywuhoEEWRuXFjn42NNOPjzUSjedLpIpOTLczMhFFVlVxO\nYXExydhYS22izsf6egqr1cT8PCiKRLFow+erEAqVyOUSWCx5bt1SEQIUxUUqJRgfd7G+bmR0dXU2\nFEWnszOBw1Ghs7NMX18BoRewWXK0hkpkEgVctiKhBhWXpUJXq0qgTqeuTkKSIOg/suwcHjjinvu6\ndcKbj0jaZJibVbDk4Pw5leWNI8rCVIVkjQ4JeATR+xKNnUVSOTOj/Trb60rtt5Xo8QkkqyGPAxg/\nDlv3FfSMjDuk0egrsTVnVOaF1yROjFc4WJZJ10qu83GJ8XGducu1jiM7MuemNZrrBKt3ZWJRifPn\ndCJRmXNjGi/NVAmFJNJpmWJBYrAvRTknkYxLuFwa+bzZ0BvbobExyf37ZRoaBKmUQiolce6cRDwu\nUV9/wM5Ogo0NlTNn7GxtqbUGA4JwWGNqykQulyIYzPHcczscP+7iypVDTpzwsb6eweu1EQgo+P0S\nTU0WNjbSbG5mOHbMSyBgQlUVdneLFAplhBBEImmcTjPlMvh8NgoFicnJIJ/5zKk3zaNC13W+8IUv\n8OlPf5rf+Z3f4ZOf/CS2Rz1a39rxnyqL7wbIDybsFhcXCQaDHD9+HJfLyPSEEGxublIul9F1HbPZ\n/IZbxHy3aG6Wefe7zWxvm9nZ0ZFllWIxjRAqzc1OPB4r+Xy5dkFK3Lq1R3u7h74+o1lpU5OT3l4/\npZJGR4eHtrY6LBaNwUE/MzO7VKsa6+sVUqkqbW0NuN0wMeEin09TLpdYX4dcTqe52UMsBt3dEhsb\nVmw2QUcHhEJVOjrSLC3FiMfjdHcLZmfLbG8XcbsVFuZVslmdclnh8ECgaYL9PZmdiM5hVCOyAZvL\nVbIHZVy2Mv3dOo2NBmDu1XTFQ7064Zp0rK1FZ6sGzuWiRJ0FmnwC1SRR5xGEV46Au7ejwNp9K9Wk\nwuApHbkisbt99L5NCPIHEq4GQa4g4RGCgz2ZUkGmLQDNjcbEpBESQWuZxIFEsWY2VCpK9Nbn2dw8\nquArp0EvCOK1CsJMUsLfIMgfVEjEDeOfw0NjfF+voFqpcHAgk0rB+fM64bCZwcE0FkuGcFgmHhdM\nT8uEwzLFomB4OMrlywnq62UKBdjYUDl71ujcMTVlxeVKsrq6hxDVWpMCP5cvxzl3zrDRnJwM4POp\nzM5u09zsYHU1xf5+gTNnfLjdFvb3VZaXUwwNNRCJ5NnfLzA+3k4mo+NwmNjZKTEyYuIjH3GQy2Wp\nVCpIkoTZbH7dCUk4HOZjH/sY1WqVp59++jU3DX4LxKsC5LeklwXwkGb49hBCEIvFWFtbo6Ghgc7O\nzodg+4CeEEJQqVTIZDJkMhnS6TSVSgWHw4HH43nY2+71lmZ/p6hWq3zxi5v8/d8XUBQVu13l8DCL\n1wuRSJKODgeqWmFvL4XVquB0msnlKphMMtev7+PxWGht9bGwEGdwsIG1tQo2m8zERAvFYhWPx8KN\nG2mKRQ2LxUM8XmFqKsSlSzna2x0cHtro7RW0tjrZ3CySzebY3bWiaTA8LDE3Z9ywOjpsbG1J+P0y\nmYwVVYWhISPLBzh92sT16w+WZa5frxVaHBcsLhqP9B4PmMxw/ISdeNaCXJVYqCkfpiY1Ll18YHIv\nkGUoFCT8QcG5d2p8/etHN8fuxhLrq0aWVecTDIypXJ01fpe2Fp3IfWOd3cd0lAZYqflSAFgsgrPn\nS1y8esRBnxsvk00LljatqKpEqKnK3laVkycL3JkzZJCnRjNUShXm5vw8YP3e+7FWFlcAACAASURB\nVGSJb/zz0eUxOSkRDluIx3dpaJA5OHBSLEpYrTA1pfDcc2EkCU6ccHH3roTFAgMDNvL53ZrsUiKV\n0jl/3snlyxV8PpnxcY0LF9Y4e9bH5csJGhos2GwKkUiR6ek6NK2KrmeJRDLs7xeYnGzk7t0ofr+J\n+nqBpplZWUkiyzKDg0HW11M13wrjnDl9uhVVlfngBzv5r/91EFVVyWazZLNZMpkMuVwOWZZxuVx4\nPB48Hs8r+lfous5f/dVf8dRTT/HZz36Wd77znT9sQPwgfni9LODIgvPRSKVS3Lt3j2q1ytDQEA0N\nDQ+VEw9kbMDDbMDpdOL3+wmFQrS2tj4UsieTyYfVRqlUilLJcEy3WCyv62TTdZ3t7W3u37/PxEQ9\nP/7jHWxtmdnbq2KxQC5XJZerYLXK3L8fx2y20NBgw2KRmJ3dZ3s7y/BwPX6/nWKxyuCgn0ymTD6f\nZ2ysnuefj5DPl9nd1Tk8LHPmTAtLS3laWqw4nSa6uqChQWJzcx8hyszNFYhGCwwOeolEdCQJZLmO\nXE7Q02Nio0Yf9PZW2d83Hvc7OwW7NT64vd3EtkFl0t6uPFweGBCEwwZojY1JrKxAZFNFUks47EW6\nOk3s7cvUeQTRqLGu0VGdrVrmXCxIWKU0oeY88bSNhqAgsnZ0UxwZUZm9UuTcpMz2rsLIoE64Vp2X\njEuMH6+wv6c85LBPndK4cqnMY49LhLcVvF7B9nqFvV04f14Q3lE4OagR3hQk4mb6+iGVkkHPs7Ym\nMzKSIRp1YbNpRKO79PZmicXctXNNMDCQZWNDJZ0WnD0LkYiJpiaBJG2RTEpomoQkaSiKGbMZ2tqi\nrKzkSSQ0jh+3Eo2qRCJV3vlOO5oWY3v7EJdLYWEhx/S0n8XFHC6XifFxB0tLe/h8cOdOjFJJY2Ki\nkaWlOO3tEh6PiWxWcO/eISMjjdjtJioVnc7OOhTFxN5ejrGxFnRd5hOfGOKnf9qYwJNlGbvdjtfr\npaGhgdbWVpqamrBarQ/9KzY2Nh76V5TL5Zf5V2xtbfHRj34UgL/5m79hYGDghxWM4Yc9Q9Z1narh\nwk6hUGBlZQVVVenv73/Yevzf6mH3Wk4YXdfJ5/Ok02nS6TS5nOG65na78Xq9eDwenE7nd11nPB5n\ndXWVQCDwsmwd4B/+IcNXvrJDOp3CYilTrRapVMpomkqpVObOnT26urz09Pgol1UKBRWQyGZV4vEi\nPT0BtrdL2GwyPT1BstkqDodCKqWxs5OloyPI1atJ2tud7O4ahjMPMmaLBWw2N5mMxKlTbm7eNPZp\nasrNpUvGk8fJk07m5nRA4Pcrhp+yScdqNZHPK5jNApvNRLY20dfSovKgscP4uMSNG6K2To1Ll4wJ\nr6FhCx63h6tXrQghMTmpceWKcQPw+8ukUjl0XaL/uImOLjvf/PoRII+PF7hxQwUJpt9hYz9iYnX5\nKHvr6krg9SosLHqoVCTGRgvcumWMnzjvwGoRzFw4eqqaepuZezcrZGr8c1sbtHfJXHrR8JuwWKCt\nzY7Tmebu3RI2m8Dvd7G762JwME2lcsDmphdVlZEkGBtzUCodsLCQqh1HY73nz9tIp1PMz8eZmHAz\nO1sFJB57zEU2q7O9HaatzcqtW2na2uyUShoHBxWefDLA8vI+sViOwUEf167FaG934fVKmM0FDg/z\ntLbWcf9+EkmCgYEA+XwVu92E220ll1MRQkIIGzabwmc+c46Rkdde9KFp2ssy6c997nPMzs6STqf5\n2Z/9WX7qp36K06dP/7vSfj8A8Z8ZcrlcZmVl5WFr797eXqxW66uusHuleLQk9NEMwmw2UywW2d/f\nZ3Nzk/39/Yf+GIqiYDKZKBQKzM/Pk8/nOX78OI2Njf/q0e/4cStPPOFle1siFlOxWIxOIB6PBUWB\nlhYnHo+FfL7K4mKcUMjN9et7xGI5hofruX07RjKZZ2gowHPPbRGNZhHCxNxcgu7uOm7cMIorjh0L\nEomU8Pks7O8L6upUxsYcBIMKHR0qXq+Ex1MiEMiRSGTR9SQtLXmWlqIIccjJkyV2dg6pq8ty5oyK\n1Vqmo6NMd3cBgHJZoampzHats4fLBfv78KC63eOpcnBQ80Lu1bhyJU5/f5mODisrKyZKNR/hwcHU\nwyw8fqhT584QClnZ26tlt9slHjwUWZQqzU0a4bCldiw1VlZy7O+rjI8LBGZWV456QaXiVYIBwc72\n0TnQ1V6qPREZQJLNCvp6E2xsmAAJTQOfL0cyWSGfB1WVaGwU6LoNVT0gHFYZHa2wt2dQKm1tMSKR\nDMWiRCRS4exZG3t70NCQwu0uEQ6r7O5WmJ52EQ5rtLeDyXTI0lKOVKrK0JCb5eU8XV0OhobMPPvs\nCp2dTrLZKqurGc6fb8Bur7C5eYDTacHttvPSS3uMjzdhs5kwmWTcbgt2u2G56XJZSaUELS0Onnrq\n7XR1HTWSfS3xwL/C6/WSz+f5u7/7O86dO8fv/u7vIoTga1/7Gm9/+9t/mCbw/q344c6Qs9kss7Oz\ndHZ2PizLfLQP1xvVEr+WeJSPTqVSZDIZhBA0NDTQ2NiIx+N5xT5kzz+f5n//7wiJRJJUKk2lUqZY\nLNLUZEMIjY2NFEJAU5MTv99OPq9SLqu4XFYODsqoqqCjo469vRIWi4TP56ZYVGsZs0oymcflUrh9\nu4yiyDQ11bG9XaSnx836uqG8OH8+yOXLRnY4NeXn0iWjO+jEhJfZWeP1U6c83LxZrL3uYHbWAOV3\nvMNLNmulWLShKII7dww+OhhUicfLD6v7TpxQuXfPeLIZHTVKl5PJEPv7doaGUszPG4jb3q4TDhs3\nlOnpIEJYuHTpCGCnp8vMzKSYnm7g0iUPk5MFLl8+qu57//vNfP3rJh6c/qOjOpHIAQ5HC5GIYdjT\n2LgHaFQqzRwemjh9usr165ucPevg2jV/bTsFyuUUs7NOHiRB73+/xNe+duRsNzHhpVhUWFhYpbvb\nTCSiUC5L2O2CkZEqV6+mkCSYmPDx0kslJAmefNLJ17++jizD2bNBrlxJ4XAonDnjYXl5l3K5Slub\nk9u34zQ22unuthOLHRKLlThxooGVlSROp5mGBitCgM1mQlEkQEZVNWw2B8lklQ9/uJePf/zkG74O\nNE3jqaee4ktf+hKf//znefzxx7+n9ISmaQ+d5r761a9+z7b7GuKHO0M2m800NTXh9XofgvFrKXV+\nM0NRFGw2G7lcjmQySU9PD319fSiKQjqdJhwOP7QmLBaLCCGwWCwvy5g7O228//1BikULOzsaiiLQ\nNB1Fkbl37xC/3053txeLRebatV1WVhJ0d3u5eDFMLJZlYMDPhQtbRKMZOjp8vPDCNtFojnJZZ2Eh\nicOhsL6uo+swOdnE/LwBXn19fnZ2aoUfioVUSsPlUohGNSoVw8N5Y8Nwn2tqMrO2ZoC3368QDlfR\ndTCZIJVSWV3NEYulaWtTCYU0QiETwWCV7VpW6vdXCIeNx3Xj/wyLixqVSoonnjAxNydqvQDh5Mkq\n4bBBL4TDBQYGCiQSNkolMJshk0lRLArC4TzT0xILC2VqVH9tfw4ZGVHY3jZuhC0tOdbWitTVlTCZ\nXAwPq9y/nyKbFXR2lshmnVgsMRKJKru7FcbHLUiSmdXVMOFwhcceMxMOm+julrl5c5PJSTuRyINf\nT8XrTbG7WyGR0Dl92s7Ojs7ZsxY2NvZwOEzk84JYrERnp0xnZ5XLl8OcPu1lZ6fC7m6ByUk/oZCZ\na9fWGR6uY2kpRTRa5PHHm3C7K1y/vkNjo5OGBhd37sQYG6sHdBwOQxnhclnIZsuAjM3mxGYz85nP\nTPKBD3S/4etgfX2dj370o9hsNr785S/T19f3PeeKP//5z1OtVimXy/zMz/zM93TbrzJ+uDPkB0qJ\nN8oTvxlxeHjI6uoq9fX1dHZ2/putpIQQ5PP5h6qObDaLEAKXy/WQj34wo314WOEv/3KLl16KUqlk\nUdUSxWIJSRIsLh7Q0uLG47GiaTo2mwmn00IiUaJY1GhocLG0lKVU0ujpcTE3l0OSZAYHG1laymC1\nKtTVuUinqwSDVtJpBU0TdHe7WF6uUq0KTp70cvGikRFPT9cxM2OA92OPebl40ciIp6acXLpkjHk0\nUw6FzOzvVx9SC8PDFrzeOvb3HTQ368zMGKjpdGpUKuWHE3BnzlTZ3oaGhg5u35Zpa8sRidRKpzsF\nm5tJWlrsOBwh6uoEs7MHD4/t5KRCtaozN+emVIKJCZidjdb2s4HtbTtbW0edTQcGnJhMOnNzR8Uj\njz0GMzNlhJBr+ydx5oyDCxcOAUNTfuZMkEIhx717SRQFRkYC3LwpOHu2SjgcRwg7+/sGT/Pkkx6e\neWYVTRO0t9spFMzE4yqPP27n4CDFwkKupsKws7Ki0d1dxW6He/eylMuC0dEAul4lHo9TKmkcOxbk\n7t0D2tvdWK0SNpsJWTa030IIikUVr9eNriu8611t/OqvnsBqfWOcrqZp/Pmf/zlf/vKXH2bF34/Y\n3t7mYx/7GL/5m7/J5z73uR/oDPkty7Jns1nS6fTDpqbfDyDO5XKsrKxgMpkYHR39rhyakcW4cLlc\nhEIhwJg0fDBREg6HyeVyKIqC2+3mIx/x8oEP+Hj66Sh37kSx220IUaWzs1rLsGVyOQ1V1fmXf1kH\nYGqqleefX0fXBUNDHmZndxACpqbauHRpDYDp6VZmZjYBaGtrYWEhUZuo9HF4mMVikVlbS2MylQgG\nrSSTRU6elGudSDKcO6eQSsnE40eTY0Z3CiN6eqzs7hpp7uCglbm5HGAAt9drYmDAw9KSnZERM5cv\nV2rHRrC1VSEa1dndXWJiwsbSko8HkrPW1iqbm7CzU8Rm26C72/eyYxuP51heLjI8rBKJ+CiVjqiL\nS5divP/9Tra2BA+uGbu9RLWawOHwUCgYxRhbWwkmJ21cvmypHRuFubkN2tu9hMM6QoDZnAGMG4+m\nwdJSkne/28c3v2mAfWenjN9vweMxcenSfc6f93HxYoZwuEhvr8zQkJUXXtjEYpE5ezbItWsJEgmY\nmjIxMxOjVNJpa7MjBGhakvX1DP39XqLRCrduRTlzprHWbVwhn68SDDrY389jtSoEAn7q6x38+q+P\nMDT0xt3aVldX+cQnPsH4+DgzMzPfV4vMX//1X+cP//APyWaz37d9eLPiLQvI9+/f51Of+hTpdJqB\ngQHGx8eZmJhgZGTkdfXZey1RqVRYX18nm83S19f3umv0ZVnG6/Xi9Xppa2sDDCvQB1l0qRTjR36k\nwPi4nQsXFFZXi9TVebFadWQZFhfjJBIlTp5soKHBQT5f5vhxFzabha2tMkLAiRMNXLsWA2BkpIFL\nl/YBOHOmmZdeMmqSJycbuXw5Xnu9npkZY7m318vMjDHm/PkAzz1n6NvGxuq4cydNd3cdnZ0eSqUC\nzc0S0SgsLx/xvF7v0Xft6VFr3HOW7m4PLpcPRTGAbWRE4fbtIwmjJKkoSoTR0Sbm5szcvZvhATj7\n/Rrf/OYKU1MhZmfN9PYqLCwYme7cXJpz53S2to5okWBQ5lvf2mJy0su1a3Z0XaJcTrOwkKO/v8TW\nVpCTJ03MzpYIh0tMT/u5dMmELKc5OKgSCmVo6ApQ8LmYlSuoHXW4xz1k8xIVu4lLqSSeJ8fILB+y\nGU0y1q9TLh2yuVnh4sUo09ONXLqUobERVle36etzsbKS46WXYrznPY3cvLnJs88WaW934/HYiUZz\n+HwVJMlMa6ubW7eSHDvmoq7OSiqVRtclJMmgKWKxPPX1Xux2K//lv/Tz4z/+xukJTdP4sz/7M55+\n+mn++I//mOnp6Te0vjcaX/3qV2loaGB8fJznn3/++7ovb0a8ZSmLB1GtVpmfn+fq1avMzs5y+/Zt\nZFlmbGyMU6dOMTExQX9//6vuSP3d4oGeeGdnh87OTpqamr4nWXm5XCaTybC6esA//uMOt26lKJcr\nSJKOySShKDKxWJZIJMfISCPXru2j64KxsUZyuSpWq0Iw6KyVaFPTHVtIJCqUywJNM7G2VsDlMmE2\nG687HCbsdivxeAWTCRobbezsGGA7OOhhYcGwT5uaCnDpkgHgb3tbA9WqQjZrZXtbJp831g8Pikmy\ntc/bWFhI0t7upqUlhK6rXLtmZLUNDQrJZJ5q1fjce94T4NYtQcy4pzA+XuTGDQOAOzutBAJ2btw4\n8pc4cwY2NlIEAo3cvy8zPS0zM/PgJuRF07zcuBF+OH5szM3/396ZB1dVn///dc5dc9fseyAmIRAi\naxJURPsDtS5ja5XvqLWOdhxrx6q40RG1Rdt+xdFqB1q1bjO21dbO1G/VWh20Wq2gkMWAJEAgC4Hs\n683dl7P9/rjmllSrgEluAuc1wx9JyD1PyOV9nvN8nuf9+P0KbW2hxOfO/3YO7+5VIT8D7GbMmRas\nBvAFBTBbEUfHsFhNqAaIhhVEBdSUdBjzYddiiP5hUsZ6GeyI38AuvTSTd989TCSikpJiYMmSHDRN\nZvfuboqKnFitBpqbR6isdCCKMcBEU9MwNpuRs84qJBqVUVWNcFgiNdXC8HAIs9mAzWamqsrJ//xP\nMVlZqTidTpxO5wnvuDt48CDr1q1jxYoV/OIXv5jyxOZYuPfee3nxxRcxGo1EIhF8Ph9XXHEFL730\nUrJD+0+OSQhOekH+TzRNIxAIJHZ91dfXc/DgQTIzM6murqaqqooVK1aQk5NzXGJ6LHXi6SIclvi/\n/2vnnXcOceSIB0kKYTTCkSNhHA4TWVk2HA4r/f1B2to8pKWlYDKZ6OqKlyTKy9Npbo7XRmtqCqmv\nH0AUBc49t4De3hAul4WcHBdjYwqRiIDbbeGDDzyoKixZ4ubTT+MdBjk5FsbGJKLReHZbVuagrS3w\n2eumEImoqGoGHo+RgYFAog1uxQoLdXVjABQUWLBYNLKy0qit1TjnHCvbto0lftZ58xQGB6NUVubS\n3GxElscIheLXKyw0EA57yM3NYO9eK7m5CgMDI591HQgsX57Lnj1+AoHxgSCorg7T0mJN9E6vWpXC\n4NAIA9E8vCkZCAVZiMYoKS4jgVEFTDawWDH7BjAgEDa7QBBwayGCERuypEJwFMFsBXs62ugAKDYw\nOnBK/bjEAD37d1JcKGEymWht9bFqVRqRSJTRUYmODh9Go0B1dQo+n8KBA3F/4lWrCjEYBGRZIxZT\ncLtTCIVkzGYT+flprFqVx5VXlmE2CwQCgUSXz3iv/PFM28myzFNPPcVf/vIXfvOb37By5crJeqtO\nKh988AGPPfbYrK4hn3KC/EVomkZfXx91dXUJkR4cHKSsrIyqqiqqq6tZtmwZDofjcyIdCAQ4ePAg\nZrM5YUw0ExgdHaW1tRWPx0pTk0pdXR+hUBhZjiBJEi0tHrxemUWLUolENJxOC3a7FYfDzKFDPnp7\nAyxenMv27X0AVFfn0NAQPwgrK0vjyJEgsZhKeroFQRAIBCTmznUyZ04qkQgMD2tkZdnYtm30s+9P\no6HBA8RdxoxGFZ8vLoRr1mQRixno7BTRNJH+fj+KMj404kpk2AsXukhLs/HRR+NtcRZ27/734d3F\nF2fQ1KTQ3R0X5LPOEtixYxhBgLPPzkNVLXz88WDi7y9dGkVVobnZjaoKLFwos2/fCHPn2lBJxSek\nEbLZkdz5mIxhsFlJQcIXMIHZgV0bRYqpxLCDIQUxNIpZA4MRgpoA4RAGQyaKYsIpePCPRLBnWwn6\noyC7EQ0WHIzgG0oDqQ+D3McZK7zs39+ExxNFFAVqatJRFIlduzwoikZRkZMFCzKIRBQURcVoNGAy\nGTEaTSxdmsPq1XNYterLn8z+c5Dj6IGmcZG22WwYDAZaWlpYt24dZ599Nj/72c9mzPv7i9AF+SRG\nURQOHDhAbW0ttbW17Nq1C0mSWLx4MVVVVZSUlPDqq69y9dVXU1lZifvogmgSiUQiHDx4EFVVKS8v\nTxy2qKrGBx/08OGHPezZM4iqygwN+TCbxc/c4aKEQjLd3fHH/RUrsjl0yE9OjoPcXAeKAl6vxPBw\nBLPZQltbvCRxxhk51NbGhXrVqryEgJeUuBgaClNc7CY11QYY2bEjgCwLnH22m48+imfgBQUpDA3F\nxV0Q4JvfzMfjgcbGCOnpJrzeSCLDXrXKxfbtA5x+ehqa5kIUFZqa4nG4XCKCEH+dqqo8jhwx0Ns7\nlDhQPO00C1arTDTqoKNDIj/fyMjIENGoSmmpBZ8vAw0fw2E3pM6FtEJczjA+bBDwg2QCowuHbZRA\nFIiKYEgHQcMq9xKJiWDLx6CGceDHO+IGYQQMCmZDJrGoFaK9EHFiNAu4M32MDJgBByZtFCmYR0rK\nMOGwgCBIZGT0YzYP4vH0Eg57cDg0Vq7MIRxWiEZBVUUUxUhenpWLLprL2rUlpKZaTvh9My7S45n0\nAw88QHt7O2NjY/zwhz/kyiuvpLKy8oTLHTq6IE86oVCIuro6Nm/ezLZt21iwYAEA1dXVVFdXU1NT\nQ2FhYVLetIqicPjwYQYHB5k3b96XrksPhyX+8Y9u6ur6aWkZQpYVdu3qQVE0lizJQhBUBgeD9PYG\ncblMeDwxfL64/eOiRdm0tIxQVOSmpCQdv1/C65UJhTT6+8MEgxKCABUVaezbF8+Iq6pS+eSTMWw2\nI8uX52AwGDh4MEZfX4wzz0xj5854lltSYufw4fgjeXa2lZqaPOrrgwwOyrhcBkQxytjYeHbswmBQ\n8XqttLXFWLXKlqgFA5x/fgb9/VqidW35cjONjSNYrQaqq/OJxWLU1cUzbyzZFC5YwEAgB0kNgDsL\nq+oj4glhNDqRhQhYnJiio0ghFwajEcXgxeUQ8Y3YQLBjNgRQQh6wuFA0BzZhmIjHiSqngKkDg2hC\nUeeA0otZdBKLpOBw9hGNahhEFU1TiUZzcbkG8Pls2O2DBIMCoujBZDJitYZQlChms0x2NixZYmPd\nunKWLs2c9PfS/v37ue2221i5ciUXX3wxTU1NNDY28vzzz3/lAJPOf0UX5Klg//79vPLKK6xfvx6r\n1crIyAh1dXXU1tZSV1dHV1cXc+bMoaamhqqqKqqqqhKtd1OBpmkMDQ3R0dFBXl4eRUVFx3VDiEYl\ntm3ro66ujz17BvF4QsRiMsPDIfLyHHR2jpGTY8dqBVHU2LvXg8cjUVnp4sABP7Ks4XKZycmxE40q\n5OW5yMiw097up63NT2amCa9XIRKJZ7lVVRl88kk8oz733AI0zUhPj0xHR5ilS13s3h0XyXnznHR0\njCGKAsuWZZOebmPr1rhwGwxxA6NDh/wIApx7bj79/VEOHIgfvJ1+upPm5nhp4swzcxFFEx9//G+x\nrqiw4fHbCckL8IVysabFiIhZIPlwGqKE/AKkWFBEJ0QGsSgCJrNIQLWCKkM4ALEcjBYfsjEMYQPE\nchFFGaNpkJgkA6nYbDE0xUg4lAr0AUHc7vjqLL/fBKg4HB4CAQsu1xjBoILZHEGSFGRZwelUMJk0\nRDFCaamJc85J54YbSpg796gFhZOILMts2bKFv/3tbzz11FPU1NRMyXX+k66uLq677joGBgYQBIGb\nbrqJ22+/fVquPY3ogpwMVFWlo6MjUepoaGggGAyycOHCRCa9ePFiLJYTf7wcJxgMcuDAASwWS8Kn\n4+vS0jLKxx/3smNHD11dPmw2I6qq0tvrY+/eYSwWAytXFuL1hjEaIRCIAgr79sUP65Yty2T37mE0\nDdLSTFRU5GAwGPF6FVwuU6Kk4XAYSU210t0d/741awqJxVQGBlTa2oIsWOBk//54hl1W5uTIkWHm\nznWTmZmK0Whk27Z/C2x1tYvGxkFqanIZGhIQRSVRUnE4jOTmimRludm1y4UkFaEJeaiWMJjzMBqi\nWAQvQW8ExBwQLJiMEVLMY/h8UVDngKCB1o8txUw0FkNRczAIAygSQBYmUz9ms0owmAnYsdn6kOUI\nsVgMMH42KerG5RqOvyZgNHpxOMyoKkiSjCxLGAwKqhrGaJQoKhKZO9fMeedlcMMN87HZJtfq9T/Z\nt28ft912G2vWrGHjxo2T8l46Vvr6+ujr62P58uX4/X6qqqp47bXXWLhw4bTFMA3ogjxTiMVi7Nmz\nJyHSTU1NmM1mli1blhDpsrKyY85sZVmmo6ODsbEx5s+fP2X1a1lW2b17iMbGAZqbBxkZidDb68di\nMRAKxTCbBdraxhgaClFY6GD+/DRGR/14PFFGRqJkZaXQ0REf+li8OJPOTh9z56bidlux2y28+27P\nZ1OALvr7fYRC8XLE+ecXE4lo9PdLHD4cpLjYTGtrvLOipMRFKBShtDSD3l6F7OwUamt7EjGfe24W\n4bBMMGhk3z6VkpIKOjrSgXxEgwdVLQDCoI2AIYrIHFTFFN9jJ3bjdIt4RwsAEYMhiDt1iNFRE2gF\nQASLpR+TSSYSMSPLdmAAQbCjaWC3+wgGNSAH6MdsVpAkCykpI0QiMqpqwWiMAhYcjjCRiIzBEMZg\niJKaqlFensJFF+Vz9dVlpKVNz+GZJEls3ryZN998k6eeeorq6uppue6Xcdlll3HrrbdywQUXJDuU\nyUQX5JmKpmn4fD7q6+sTpY729nby8vISXR3V1dVkZWVNKHWMd4McPnyYOXPmJEyTppOODi979w7x\n6adDNDUNEQzGMBoFJEmiq8tDX1+E8vJ0/P4YoiiQnm5GFKGry093dwhRhMWL09m9exSHw8SyZblY\nrSba2rwcOuSlpiaXhob+hOnPeecVEY0qDA7G6O0NkplpprMz3lZXUuIiNdWMxWJlzx4vxcVZ7N0r\nA3OBQiAVhyNAIFAIjOFyBfD5xoAiwIogqGjaYUAFsgATgiBjMg0Ti4lAKiBgNI7gcCj4fFZU1QoM\nARGsVjMWixmfL4imxTeEuN1BJEnGaBSJxWRU1UQsFkAUo1itKkZjFLM5Rn6+kbIygdWrM1m7dgku\nl2vaf5fNzc2sW7eOb37zm9x///3TmhX/Nzo7Ozn33HNpbm7G5Tox97kZMoiaHAAAD+FJREFUii7I\nswlN0+ju7mbnzp3U1dVRV1fH6Ogo5eXlVFdXY7fb+eijj7jnnnsoLS2d9G0lJ0o4HObDDz/l8OEw\niuLi0CEfra1eYjEZUDCZjNTX9zA2FmX58lxsNgOSJOPzRYjFZDyeGKOj8cx45co8VFVAFA0cOeKn\nuNjJ9u1xhx6Hw8TixfGFAj6fRF+fiiQ5GBszA05sthxCofGDTD8Wi51o1AdEEQQVqzWTcDgFCAPD\nuN1WvF4r8ZKCjNMZxO9X0DQ7YMBuD2Eyyfh8oKopmExhBMGLySSiKE5EMYYsBz8T7gBpaRZUNd7N\nomlRBEHBapWxWhXKyx0sXpzOWWdl841v5DI42MPg4CD5+flIkoTP5yMSiWCxWBK+JS6Xa8oEUpIk\nfvWrX7F161Z++9vfsnz58im5zvESCAT4xje+wf33388VV1yR7HAmG12QZzuyLLN9+3Z+8pOf0N3d\nTVFREeFwmCVLliSy6Pnz5yfF+FtVVTo7OxkcHKS8vJz09PQJX5ckhcbGQZqbR+jq8jM4GKavL4jP\nF8PrjWIwGGhv9+BwGCksdKJpCqOjYYaGYhiNBlyuFHw+DbfbjsFgIRw2MzgoAQYgGxCw2WLIsgNR\nVInF/KiqAhgxGMyoqobdrhIK2bDbo5/5HGhA3APDYomgKEFkWQTiVqA2WwizWUCWRQIBAxBAFCO4\nXFaiUQGjUUVVoyiKgiDE98xlZ5uwWkVcLpH8fDPLlmWwbFkmK1bk4HRO7Ejwer20tLSQnZ3N3Llz\nJ5Soxv27x8fifT4fsVgssbFjXKS/7o24qamJdevWcfHFF3PffffNmK4JSZK49NJLufDCC7nrrruS\nHc5UoAvyycCHH37IyMgI3/nOd4D4Qd4nn3ySyKIPHDhAWlpaotRRU1Mz5aWMkZERWltbyc3NZc6c\nOcfd5qdpGq2tYxw44KWz009PT5Du7hCjo1FCIYGhoRixmIIsi0gShMMysixgMhkSE5AGg0ggICAI\nGrIcRRCsOBwigiChKPHvkyQBi0VFUQTMZiMmk4osyyiKQjRqID75G7cLNZvjK5VMJgVVlTCZICvL\njtksYrFoZGcbKS93k5lpJTs7hdNPT+f004+t5UxRFNrb2/H5fFRUVGC324/53ykcDk8QaVmWsdvt\nCYF2uVzHdEOOxWI89thjvPvuuzz99NMsXbr0mGKYDjRN4/rrryc9PZ3NmzcnO5ypQhfkU4Hxpa3j\nB4b19fX09fVx2mmnJQyVli1bNik1yvGhE03TmD9//rRNbUWjMh5PhMFBL93doxw6NExvb4BgUEWS\nTBgMZhQlhiRJOJ3pn3lyaEiSiqoKpKaaycgwYzSKRCIKqqqQkWEjPd1KRoaFtDQzWVkp5OTYMJkm\nd+R9/OZVUFBAYWHh1/4dHG3TOv5HVdUJo9BOp3PC6P6nn37K7bffzqWXXsqGDRtmTFY8zvbt2znn\nnHNYtGhR4ua+adMmLrnkkiRHNqnognyqoqoqra2tiXp0Y2MjkUiE008/PSHSlZWVx/wfU1VVjhw5\nQn9/P2VlZWRmTv4wwokgSRK9vb0cPnwYo9GYWKk1/ojvdruTJj6SJHHw4EFisRgVFRVTevNSVXWC\nX4Xf76e1tZW33noLQRBob2/nhRdeoKqqaspi0PlKdEHW+TfRaJTdu3cnvDqam5ux2WwsX748UY8u\nLi7+XPlh3BNj3DRppozOSpJEa2srkUiEBQsWJEbExx2/jq7D2my2CXXYqa65DwwM0NHRwWmnnXbc\nJlWTRW1tLQ888ADp6ek4nU727dvHNddcw9133z3tsegAuiDrfBmapuHxeKivr0+IdGdnJ4WFhVRX\nV1NaWsprr73GLbfcQlVV1YywWoR43AMDAxw6dOiYLE41TSMUCk0QaVVVJxjpfB1LyqOJRqO0tLRg\nMBgoLy9PSnYejUZ55JFH2LZtG08//TSLFi1KfG18j+RUsXXrVm6//XYUReHGG29kw4YNU3atWYgu\nyDrHh6qqtLe389BDD/HWW29RWVnJ6OjoBIP/xYsXJ02cQ6EQLS0tWK1W5s2bd8IdB+OP+OMC7ff7\nEUUxIdButxubzXbM4qVpGj09PXR1dTFv3ryklXQaGxu54447WLt2LevXr5/W1khFUSgvL+cf//gH\nhYWF1NTU8PLLL59s03Zfh1N7hZPO8SOKIhkZGZSWltLZ2YnNZkOSJJqbm9m5cyd/+MMf2LNnDwaD\nYYLB//jC1qlCVdWEcdL8+fNPeAPLOEeL7ziyLCfWfrW3txMMBjGbzRNE2mKxfE6kQ6EQ+/fvx263\nU1NTk5QWxEgkwsMPP8yOHTv4/e9/T2Vl5bTHUFdXR1lZGSUlJQBcffXVvP7667ogHyd6hnyMPP74\n46xfv56hoaEZc6iVDDRNw+/3TzD4H68xH916N1m107GxMQ4cOPCFvbtTTSwWS2TR48MbKSkpiTKH\nz+djeHh4Um4SJ0pDQwN33nknV111FXfddVdSbggAr7zyClu3buX5558H4MUXX6S2tpYnnngiKfHM\nQPQMebLo6urinXfeYc6cOckOJekIgoDL5WL16tWsXr0aiIt0b29vwuD/mWeeYWhoiHnz5iUc75Yv\nX47dbj9mkT760G7RokVJWaJpNpvJysoiKysLiP+ckUiEgYEB9u3bhyiKGI1Gurq68Hq9uN3uz7Wc\nTRWRSIRNmzZRW1vLSy+9REVFxZRfU2fq0QX5GLjzzjt59NFHueyyy5IdyoxEEAQKCgq4/PLLufzy\ny4F4TbGlpYXa2lpee+01Nm7ciKIoCYP/6upqFi5c+LmMTtM0+vv76ezsTGqXwhehqio9PT14PB6q\nqqpwOByJvmCv10tfX1+iT3v80NDtdmO32yc1s6+rq+Puu+/mu9/9Lu+//37SsuKjKSgooKurK/Fx\nd3c3BQUFSYxodqKXLL6C119/nX/+859s2bKF4uJiGhoaTumSxdchFArR2NiYmDLcv38/LpcrIdDp\n6em89dZbfP/73/9ah3ZTgcfj4cCBA+Tl5TFnzpxjWpF09B47g8EwoR6dkpJy3DeacDjM//7v/9LY\n2MgzzzyTWJAwE5BlmfLyct577z0KCgqoqanhT3/6U1Lq2TMUvWRxrJx//vn09/d/7vMPPfQQmzZt\n4p133klCVCcfNpuNVatWJVbHa5rG8PAwH330Eb/+9a9pamqirKyMQ4cOJXqjq6qqcLvdScuSZVmm\ntbU14SFyLB0mBoOB1NTUCXXlcRMhn8/H4OAgoVAIi8WSEOivMhPauXMn69ev59prr+Wxxx5L6hLd\nL8JoNPLEE09w4YUXoigKN9xwgy7GJ4CeIX8JTU1NnHfeeYn6ZXd3N/n5+dTV1ZGbm5vk6E4e3n77\nbXbt2pU4lGpvb0/YkjY0NBAKhSYY/C9atGharCKHhoZoa2tj7ty55OXlTfpNYXyIZbxH+ughFovF\ngsViwWq18otf/ILdu3fz3HPPUV5ePqkx6Ewbeh/yZDMdJYsf//jHvPHGG5jNZkpLS3nhhReSdoI/\nU4jFYnz66acJv47m5mYsFssEg//S0tJJq9PGYjFaWloAmD9//rT5BB89xLJnzx7uv/9+hoaGKC4u\n5rrrrmPNmjV61jl70QV5spkOQX7nnXdYs2YNRqORe+65B4BHHnlkyq43G9E0Da/XO8Hgv6Ojg/z8\n/ERvdHV1NZmZmceV1R69AKC0tJTs7Owp/Cn+O8FgkJ///Oc0Nzfz5JNPEolEqK+vx263c+211yYl\nJp2vjS7Is51XX32VV155hT/+8Y/JDmXGo2kaR44cSQh0fX09Ho8nYfBfXV3N0qVL/+thWjgcpqWl\nBYvFkrQDRU3TEksIbrjhBn70ox8lrVasP6lNOrogz3a+9a1vcdVVV+lZ0QkiyzJ79+5N2JLu2rUL\nQRAmGPyXlZXx8ssvU15ezvz58z9ntD9dBINBHnzwQVpaWnj22WcpLS1NShzj6E9qk44uyDOVL+vq\nGO91fuihh2hoaOCvf/3rjOnDne2M9ww3NDRQV1fHe++9R319PQsWLOCss85KTBlOxQHel8W0bds2\nNmzYwA9+8ANuvvnmGeOoN47+pDYp6II8W/nd737HM888w3vvvZeUCbVTga6uLq666iqeeOIJ8vPz\nJxj89/f3U1JSMsHg3+l0TrpIBwIBNm7cSFtbG8899xynnXbapL7+ZKE/qU0KuiDPRrZu3cpdd93F\nv/71r8TI7lRd51S3SlRV9QuzUVVVOXjw4ASD/1gs9jmD/xOtM2uaxocffsiGDRu4+eabuemmm5KS\nFetPatOKLsizkbKyMqLRKBkZ8Q3KZ555Jk8//fSkXkO3Sjx+IpHIBIP/vXv3YrfbJxj8H4v5kd/v\n56c//SmdnZ08++yzFBcXT88PcALoT2qTii7IOl/Mjh07ePDBB3n77bcBePjhhwG49957kxnWrELT\nNEZHRycY/B8+fJiioqIJU4ZpaWkIgoCmaXzwwQfcd9993HLLLdx4440zrlZ8NNP1pHYKoY9O63wx\nPT09FBUVJT4uLCyktrY2iRHNPgRBICMjg4suuoiLLroIiJc6Ojs72blzJ++//z6//OUv8fv9lJeX\nMzg4SEpKCm+88cascA289dZbiUajXHDBBcDUPKnpfB5dkHV0JglRFCkpKaGkpIRrrrkGiHtY7Nmz\nhzfeeIONGzfO6Kz4aNra2pIdwimJLsinILpV4vRhMpkSntA6Ol/F7Lhd60wqNTU1tLa2cujQIWKx\nGH/+85/59re/PWXX6+rqYvXq1SxcuJDKykq2bNkyZdfS0ZnN6IJ8CnK0VWJFRQVXXnnllJrWGI1G\nHn/8cfbt28fOnTt58skn2bdv35RdT2cijz/+OIIgMDw8nOxQdL4CvWRxinLJJZdwySWXTMu18vLy\nyMvLA8DpdFJRUUFPT4/eZjcN6OvHZhd6hqwzrXR2drJr1y7OOOOMZIdySjC+fkwf6pgd6IKsM20E\nAgHWrl3L5s2bcblcyQ7npOf111+noKCAJUuWJDsUnWNEL1noTAuSJLF27Vq+973vccUVVyQ7nJMG\nff3YyYU+qacz5WiaxvXXX096ejqbN29OdjinBPr6sRmHPjqtMzPYvn0755xzDosWLUoMRmzatGla\nDhUVRaG6upqCggL+/ve/T/n1Zir6xvSko49O68wMVq1axXHe+CeNLVu2UFFRgc/nS8r1dXSOB/1Q\nT+ekpbu7mzfffJMbb7wx2aEknc7OTj07ngXogqxz0nLHHXfw6KOPzhr/CB2d460h6+jMCgRBuBS4\nRNO0HwmC8P+A9ZqmXZrksHR0vhQ9ddA5WTkb+LYgCJ3An4E1giC8lNyQdHS+HD1D1jnp0TNkndmC\nniHr6OjozBD0DFlHR0dnhqBnyDo6OjozBF2QdXR0dGYIuiDr6OjozBB0QdbR0dGZIeiCrKOjozND\n0AVZR0dHZ4bw/wEunXnRF+U/2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6543a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm \n",
    "c1 = constraint1(x1v)\n",
    "c2 = constraint2(x2v)\n",
    "c3 = constraint3(x1v, x2v, 5)\n",
    "plt.figure()\n",
    "ax = plt.subplot(111, projection='3d')\n",
    "ax.plot_surface(x1v,x2v,z, cmap=cm.jet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x67fc3d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YVVwdezUOmvpx2GR8fTSz8k0uW+qgqSmHTcIOHO9ruVlzOGTqzRMEzCqsDkNoDplmcM+m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\nCTNPJAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x66688d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def constrained_function(x1, x2, c):\n",
    "    return np.sin(np.pi*(np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)))\\\n",
    "            /(np.pi*np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)) + \\\n",
    "            c*np.maximum(0, constraint1(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint2(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint3(x1,x2, 5))**2\n",
    "\n",
    "x1 = np.linspace(-10,10)\n",
    "x2 = np.linspace(-10,10)\n",
    "\n",
    "x1v, x2v = np.meshgrid(x1,x2)\n",
    "\n",
    "z = constrained_function(x1v, x2v, 1)\n",
    "plt.contourf(x1v,x2v,z)\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x67dda30>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zM0Ntbe0dDX9WY6MFWWvNxMQEfX19WJbFiZY6/D/6Mub/+0eolicyG4VuRwa3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\nieXJccG2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x65436b0>"
      ]
     },
     "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": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def create_new_base(direction, lam):\n",
    "    new_base = np.zeros(direction.shape)\n",
    "    D = direction.transpose()\n",
    "    M = lam.transpose()\n",
    "    Q = np.dot(D, M) #is really matrix multiplication for 2D arrays\n",
    "    v = np.zeros(direction.shape)\n",
    "    v[0] = Q[:,0] \n",
    "    #as in classical method, first vector is unchanged, only normalized\n",
    "    new_base[0] = v[0]/np.sqrt(np.dot(v[0].transpose(), v[0]))\n",
    "    for j in range(1, len(direction)):\n",
    "        scalar_dir = np.zeros(len(Q[0,:]))\n",
    "        for k in range(0, j): #here happens the summation of vectors\n",
    "            p = np.dot(Q[:,j].transpose(), new_base[k, :])\n",
    "            p = np.multiply(p, new_base[k, :])\n",
    "            scalar_dir = np.add(scalar_dir,p)\n",
    "        v[j] = np.subtract(Q[:,j] ,scalar_dir)\n",
    "        new_base[j] = v[j]/np.sqrt(np.dot(v[j].transpose(), v[j]))\n",
    "    return new_base\n",
    "\n",
    "def rosenbrock_method(function, x0, direction, s, alpha, beta, N, verbose, c):\n",
    "    #alpha - expansion coefficient\n",
    "    #beta - contraction coefficient\n",
    "    lam = [0 for i in range(len(direction))] #success list for each direction\n",
    "    p = [0 for i in range(len(direction))] #failure list for each direction\n",
    "    i = 0\n",
    "    x_base = x0\n",
    "    x_list = []\n",
    "    while i <= N:\n",
    "        if verbose: \n",
    "            print(\"ITERATION NUMBER : {}\".format(i))\n",
    "            print(\"CURRENT MINUMUM : {}\".format(x_base))\n",
    "        for j in range(len(direction)):\n",
    "            if verbose:\n",
    "                print(\"\\nCurrent value {}\".format(function(x_base, c)))\n",
    "                print(\"Value of next_step {}\".format(function\\\n",
    "                                                     (np.add(x_base,np.multiply\\\n",
    "                                                             (direction[j],s[j])), c)))\n",
    "            if function(np.add(x_base,np.multiply(direction[j],s[j])),c) \\\n",
    "                < function(x_base, c):\n",
    "                #successful step\n",
    "                if verbose: print(\"\\nSuccess\")\n",
    "                x_base = np.add(x_base,np.multiply(direction[j],s[j]))\n",
    "                x_list.append(x_base)\n",
    "                lam[j] = np.add(lam[j],s[j])\n",
    "                s[j] = np.multiply(alpha,s[j])\n",
    "            elif function(np.add(x_base,np.multiply(direction[j],s[j])), c) \\\n",
    "                >= function(x_base, c):\n",
    "                if verbose: print(\"Failure\\n\")\n",
    "                #failed step\n",
    "                s[j] = (-1)*s[j]*beta\n",
    "                p[j] = np.add(p[j],1)\n",
    "            if verbose: print(\"State of success: {} \\nState of failure: {} \\nStep is: {}\"\\\n",
    "                              .format(lam, p, s))\n",
    "        for_all = 0\n",
    "        if verbose: print(\"\\nInvestigating failures and successes\")\n",
    "        for j in range(len(direction)):\n",
    "            if verbose: print(\"Failure [{}] : {}, Success[{}] : {}\"\\\n",
    "                              .format(j, p[j], j, lam[j]))\n",
    "            if p[j] !=0 and lam[j]!=0:\n",
    "                for_all += 1\n",
    "        if verbose: print(\"Directions for which there was a success and a failure : {}\"\\\n",
    "                          .format(for_all))\n",
    "        if for_all == len(direction):\n",
    "            if verbose: print(\"Change of base\\n\")\n",
    "            l = np.zeros((2,2))\n",
    "            l[0,0] = lam[0]\n",
    "            l[1,0] = lam[1]\n",
    "            l[1,1] = lam[1]\n",
    "            if verbose: print(\"Triangular matrix: \\n{}\".format(l))\n",
    "            direction = create_new_base(direction, l.transpose())  \n",
    "            if verbose: print(\"New base is {}\\n\".format(direction))\n",
    "            lam = [0 for i in range(len(direction))] #clear\n",
    "            p = [0 for i in range(len(direction))] #clear\n",
    "        i = i+1\n",
    "        if verbose: print(\"####################################################\")\n",
    "    return x_base, x_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def target_function(x, c):\n",
    "    x1 = x[0]\n",
    "    x2 = x[1]\n",
    "    return np.sin(np.pi*(np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)))\\\n",
    "            /(np.pi*np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)) + \\\n",
    "            c*np.maximum(0, constraint1(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint2(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint3(x1,x2, 5.0))**2    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def optimization_with_constraints(function, x0, direction, s, alpha, beta, N, \\\n",
    "                                  verbose, N2, error):\n",
    "    j = 0\n",
    "    x_min = np.array([0.0,0.0])\n",
    "    x_min[0] = 2*np.random.random() - 1\n",
    "    x_min[1] = 2*np.random.random() - 1\n",
    "    c = 0.5\n",
    "    while j<N2:\n",
    "        c = 2*c\n",
    "        minimum, _ = rosenbrock_method(function, x0, direction, s, alpha, \\\n",
    "                                       beta, N, verbose, c)\n",
    "        if np.sqrt((x_min[0]-minimum[0])**2 + (x_min[1]-minimum[1])**2) < error:    \n",
    "            x_min[0] = minimum[0]\n",
    "            x_min[1] = minimum[1]\n",
    "            return x_min\n",
    "        else:\n",
    "            j += 1\n",
    "            x_min[0] = minimum[0]\n",
    "            x_min[1] = minimum[1]\n",
    "    return x_min    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "x_init = 100*np.random.random((100,2))-50 #draw x's in the specified interval\n",
    "s = np.array([0.1,0.1])\n",
    "direction = np.array([[1.0,0.0], [0.0,1.0]])\n",
    "minima = []\n",
    "for xpair in x_init:\n",
    "    p = optimization_with_constraints(target_function, xpair, direction, \\\n",
    "                                      s, 3, 0.5, 30, 0, 100, 1e-3)\n",
    "    minima.append(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x68fb510>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xln3oJ0ErhQsbweVTj2Fpz8NMzfZyafqkihxLyULGSglDpMa0MMBWmrlh8pv5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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6838fb0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(-10,10)\n",
    "x2 = np.linspace(-5,5)\n",
    "x1v, x2v = np.meshgrid(x1, x2)\n",
    "z = constrained_function(x1v, x2v, 5)\n",
    "plt.contourf(x1v,x2v,z)\n",
    "x1s = [point[0] for point in minima]\n",
    "x2s = [point[1] for point in minima]\n",
    "\n",
    "plt.plot(x1s, x2s, 'r*')\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.title('Value of a = 5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def target_function(x, c):\n",
    "    x1 = x[0]\n",
    "    x2 = x[1]\n",
    "    return np.sin(np.pi*(np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)))\\\n",
    "            /(np.pi*np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)) + \\\n",
    "            c*np.maximum(0, constraint1(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint2(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint3(x1,x2, 4.4934))**2    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "x_init = 100*np.random.random((100,2))-50 #draw x's in the specified interval\n",
    "s = np.array([0.1,0.1])\n",
    "direction = np.array([[1.0,0.0], [0.0,1.0]])\n",
    "minima_2 = []\n",
    "for xpair in x_init:\n",
    "    p = optimization_with_constraints(target_function, xpair, direction, s, \\\n",
    "                                      3, 0.5, 30, 0, 100, 1e-3)\n",
    "    minima_2.append(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x805c170>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NvWxd28Fvbf4AP/39m3OP3oZwIsETOfmh86Z1HZUuJLaEYWatwPnAi3HFIFIN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\nRg+6WwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6816590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(-10,10)\n",
    "x2 = np.linspace(-5,5)\n",
    "x1v, x2v = np.meshgrid(x1, x2)\n",
    "z = constrained_function(x1v, x2v, 4.4934)\n",
    "plt.contourf(x1v,x2v,z)\n",
    "x1s_2 = [point[0] for point in minima_2]\n",
    "x2s_2 = [point[1] for point in minima_2]\n",
    "plt.plot(x1s_2, x2s_2, 'g*')\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.title('Value of a = 4.4934')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def target_function(x, c):\n",
    "    x1 = x[0]\n",
    "    x2 = x[1]\n",
    "    return np.sin(np.pi*(np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)))\\\n",
    "            /(np.pi*np.sqrt((x1/np.pi)**2 + (x2/np.pi)**2)) + \\\n",
    "            c*np.maximum(0, constraint1(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint2(x1))**2 + \\\n",
    "            c*np.maximum(0, constraint3(x1,x2, 4.0))**2    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "x_init = 100*np.random.random((100,2))-50 #draw x's in the specified interval\n",
    "s = np.array([0.1,0.1])\n",
    "direction = np.array([[1.0,0.0], [0.0,1.0]])\n",
    "minima_3 = []\n",
    "for xpair in x_init:\n",
    "    p = optimization_with_constraints(target_function, xpair, direction, s, \\\n",
    "                                      3, 0.5, 30, 0, 100, 1e-3)\n",
    "    minima_3.append(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x8049030>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qEkS6tR81UWEhGdkzdVhor6UWhkiMKCQkSgoMkRhQUEg2wmxdAJi7h/qC+WRm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80076d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(-10,10)\n",
    "x2 = np.linspace(-5,5)\n",
    "x1v, x2v = np.meshgrid(x1, x2)\n",
    "z = constrained_function(x1v, x2v, 4)\n",
    "plt.contourf(x1v,x2v,z)\n",
    "x1s_3 = [point[0] for point in minima_3]\n",
    "x2s_3 = [point[1] for point in minima_3]\n",
    "plt.plot(x1s_3, x2s_3, 'y*')\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.title('Value of a = 4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class ListTable(list):\n",
    "  \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": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "table = ListTable()\n",
    "table.append(['#','Value of a', 'Minimum x1', 'Minimum x2', 'Distance form zero'])\n",
    "count = 1\n",
    "a= 5\n",
    "for x1m, x2m in zip(x1s, x2s):    \n",
    "    table.append([count, a, np.around(x1m, decimals=3), np.around(x2m, decimals=4), \\\n",
    "                  np.around(np.sqrt(x1m**2 + x2m**2), decimals=3)])\n",
    "    count+= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "table2 = ListTable()\n",
    "table2.append(['#','a', 'Minimum x1', 'Minimum x2', 'Distance form zero'])\n",
    "count = 1\n",
    "a= 4.4934\n",
    "for x1m, x2m in zip(x1s_2, x2s_2):    \n",
    "    table2.append([count, a, np.around(x1m, decimals=3), np.around(x2m, decimals=4), \\\n",
    "                  np.around(np.sqrt(x1m**2 + x2m**2), decimals=4)])    \n",
    "    count+= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "table3 = ListTable()\n",
    "table3.append(['#','a', 'Minimum x1', 'Minimum x2', 'Distance form zero'])\n",
    "count = 1\n",
    "a= 4.0\n",
    "for x1m, x2m in zip(x1s_3, x2s_3):    \n",
    "    table3.append([count, a, np.around(x1m, decimals=3), np.around(x2m, decimals=3), \\\n",
    "                  np.around(np.sqrt(x1m**2 + x2m**2), decimals=3)])    \n",
    "    count+= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>#</td><td>Value of a</td><td>Minimum x1</td><td>Minimum x2</td><td>Distance form zero</td></tr><tr><td>1</td><td>5</td><td>1.383</td><td>-4.2741</td><td>4.492</td></tr><tr><td>2</td><td>5</td><td>3.499</td><td>2.8194</td><td>4.494</td></tr><tr><td>3</td><td>5</td><td>3.336</td><td>3.0071</td><td>4.491</td></tr><tr><td>4</td><td>5</td><td>4.344</td><td>-1.1422</td><td>4.492</td></tr><tr><td>5</td><td>5</td><td>3.808</td><td>2.3858</td><td>4.493</td></tr><tr><td>6</td><td>5</td><td>3.316</td><td>3.032</td><td>4.493</td></tr><tr><td>7</td><td>5</td><td>4.408</td><td>0.7546</td><td>4.472</td></tr><tr><td>8</td><td>5</td><td>3.143</td><td>-3.2114</td><td>4.493</td></tr><tr><td>9</td><td>5</td><td>1.589</td><td>4.2028</td><td>4.493</td></tr><tr><td>10</td><td>5</td><td>4.074</td><td>-1.9723</td><td>4.526</td></tr><tr><td>11</td><td>5</td><td>3.86</td><td>2.4367</td><td>4.565</td></tr><tr><td>12</td><td>5</td><td>3.258</td><td>-3.0883</td><td>4.489</td></tr><tr><td>13</td><td>5</td><td>4.465</td><td>0.5254</td><td>4.496</td></tr><tr><td>14</td><td>5</td><td>4.383</td><td>0.9924</td><td>4.494</td></tr><tr><td>15</td><td>5</td><td>4.496</td><td>0.0534</td><td>4.496</td></tr><tr><td>16</td><td>5</td><td>2.646</td><td>3.5822</td><td>4.453</td></tr><tr><td>17</td><td>5</td><td>2.066</td><td>3.9902</td><td>4.493</td></tr><tr><td>18</td><td>5</td><td>4.349</td><td>1.1322</td><td>4.494</td></tr><tr><td>19</td><td>5</td><td>1.349</td><td>4.2894</td><td>4.497</td></tr><tr><td>20</td><td>5</td><td>2.91</td><td>3.433</td><td>4.5</td></tr><tr><td>21</td><td>5</td><td>4.032</td><td>2.0069</td><td>4.504</td></tr><tr><td>22</td><td>5</td><td>4.164</td><td>-1.6917</td><td>4.494</td></tr><tr><td>23</td><td>5</td><td>4.34</td><td>-1.171</td><td>4.495</td></tr><tr><td>24</td><td>5</td><td>3.262</td><td>-3.0916</td><td>4.494</td></tr><tr><td>25</td><td>5</td><td>1.248</td><td>-4.3166</td><td>4.493</td></tr><tr><td>26</td><td>5</td><td>3.683</td><td>2.5742</td><td>4.494</td></tr><tr><td>27</td><td>5</td><td>1.698</td><td>4.1602</td><td>4.493</td></tr><tr><td>28</td><td>5</td><td>2.283</td><td>3.87</td><td>4.493</td></tr><tr><td>29</td><td>5</td><td>3.75</td><td>-2.4765</td><td>4.494</td></tr><tr><td>30</td><td>5</td><td>2.427</td><td>-3.7809</td><td>4.493</td></tr><tr><td>31</td><td>5</td><td>4.472</td><td>0.4806</td><td>4.498</td></tr><tr><td>32</td><td>5</td><td>4.305</td><td>-1.2943</td><td>4.495</td></tr><tr><td>33</td><td>5</td><td>4.562</td><td>-0.5341</td><td>4.593</td></tr><tr><td>34</td><td>5</td><td>4.414</td><td>-0.8424</td><td>4.493</td></tr><tr><td>35</td><td>5</td><td>3.701</td><td>2.5481</td><td>4.494</td></tr><tr><td>36</td><td>5</td><td>3.935</td><td>2.1086</td><td>4.464</td></tr><tr><td>37</td><td>5</td><td>3.539</td><td>-2.7747</td><td>4.497</td></tr><tr><td>38</td><td>5</td><td>4.479</td><td>0.3751</td><td>4.495</td></tr><tr><td>39</td><td>5</td><td>1.775</td><td>4.1257</td><td>4.491</td></tr><tr><td>40</td><td>5</td><td>3.361</td><td>2.9788</td><td>4.491</td></tr><tr><td>41</td><td>5</td><td>1.392</td><td>-4.2723</td><td>4.493</td></tr><tr><td>42</td><td>5</td><td>4.227</td><td>1.5236</td><td>4.493</td></tr><tr><td>43</td><td>5</td><td>2.91</td><td>3.4209</td><td>4.491</td></tr><tr><td>44</td><td>5</td><td>4.479</td><td>0.3229</td><td>4.49</td></tr><tr><td>45</td><td>5</td><td>3.895</td><td>-2.2409</td><td>4.493</td></tr><tr><td>46</td><td>5</td><td>2.789</td><td>-3.5217</td><td>4.492</td></tr><tr><td>47</td><td>5</td><td>3.564</td><td>-2.7353</td><td>4.493</td></tr><tr><td>48</td><td>5</td><td>1.685</td><td>4.166</td><td>4.494</td></tr><tr><td>49</td><td>5</td><td>3.952</td><td>-2.1494</td><td>4.499</td></tr><tr><td>50</td><td>5</td><td>2.758</td><td>-3.5493</td><td>4.495</td></tr><tr><td>51</td><td>5</td><td>4.104</td><td>1.8573</td><td>4.505</td></tr><tr><td>52</td><td>5</td><td>1.246</td><td>-4.3324</td><td>4.508</td></tr><tr><td>53</td><td>5</td><td>1.475</td><td>4.2446</td><td>4.494</td></tr><tr><td>54</td><td>5</td><td>2.348</td><td>3.8315</td><td>4.494</td></tr><tr><td>55</td><td>5</td><td>4.428</td><td>-0.7702</td><td>4.495</td></tr><tr><td>56</td><td>5</td><td>2.02</td><td>3.9931</td><td>4.475</td></tr><tr><td>57</td><td>5</td><td>2.152</td><td>3.9444</td><td>4.493</td></tr><tr><td>58</td><td>5</td><td>1.575</td><td>-4.2098</td><td>4.495</td></tr><tr><td>59</td><td>5</td><td>4.477</td><td>-0.3874</td><td>4.494</td></tr><tr><td>60</td><td>5</td><td>1.979</td><td>-4.0349</td><td>4.494</td></tr><tr><td>61</td><td>5</td><td>1.983</td><td>-4.0203</td><td>4.483</td></tr><tr><td>62</td><td>5</td><td>3.817</td><td>2.4032</td><td>4.511</td></tr><tr><td>63</td><td>5</td><td>2.981</td><td>3.3652</td><td>4.495</td></tr><tr><td>64</td><td>5</td><td>3.19</td><td>3.1651</td><td>4.494</td></tr><tr><td>65</td><td>5</td><td>1.215</td><td>-4.326</td><td>4.493</td></tr><tr><td>66</td><td>5</td><td>4.424</td><td>0.7982</td><td>4.496</td></tr><tr><td>67</td><td>5</td><td>1.881</td><td>4.0804</td><td>4.493</td></tr><tr><td>68</td><td>5</td><td>4.408</td><td>0.874</td><td>4.493</td></tr><tr><td>69</td><td>5</td><td>4.118</td><td>-1.7989</td><td>4.493</td></tr><tr><td>70</td><td>5</td><td>3.292</td><td>3.0763</td><td>4.505</td></tr><tr><td>71</td><td>5</td><td>2.188</td><td>3.9246</td><td>4.493</td></tr><tr><td>72</td><td>5</td><td>3.401</td><td>2.937</td><td>4.494</td></tr><tr><td>73</td><td>5</td><td>3.347</td><td>2.998</td><td>4.494</td></tr><tr><td>74</td><td>5</td><td>2.759</td><td>-3.5469</td><td>4.493</td></tr><tr><td>75</td><td>5</td><td>1.464</td><td>-4.2483</td><td>4.493</td></tr><tr><td>76</td><td>5</td><td>1.857</td><td>-4.0913</td><td>4.493</td></tr><tr><td>77</td><td>5</td><td>1.807</td><td>-4.114</td><td>4.493</td></tr><tr><td>78</td><td>5</td><td>4.36</td><td>-1.0843</td><td>4.493</td></tr><tr><td>79</td><td>5</td><td>4.432</td><td>0.7379</td><td>4.493</td></tr><tr><td>80</td><td>5</td><td>4.463</td><td>-0.5301</td><td>4.494</td></tr><tr><td>81</td><td>5</td><td>3.654</td><td>-2.6039</td><td>4.486</td></tr><tr><td>82</td><td>5</td><td>3.932</td><td>2.1774</td><td>4.494</td></tr><tr><td>83</td><td>5</td><td>2.888</td><td>3.4389</td><td>4.491</td></tr><tr><td>84</td><td>5</td><td>4.099</td><td>-1.8409</td><td>4.493</td></tr><tr><td>85</td><td>5</td><td>4.499</td><td>0.7064</td><td>4.555</td></tr><tr><td>86</td><td>5</td><td>4.021</td><td>-1.988</td><td>4.485</td></tr><tr><td>87</td><td>5</td><td>4.065</td><td>1.9132</td><td>4.493</td></tr><tr><td>88</td><td>5</td><td>3.372</td><td>-2.9693</td><td>4.493</td></tr><tr><td>89</td><td>5</td><td>4.491</td><td>0.1127</td><td>4.492</td></tr><tr><td>90</td><td>5</td><td>4.308</td><td>1.2697</td><td>4.491</td></tr><tr><td>91</td><td>5</td><td>2.314</td><td>-3.8516</td><td>4.493</td></tr><tr><td>92</td><td>5</td><td>1.739</td><td>-4.1364</td><td>4.487</td></tr><tr><td>93</td><td>5</td><td>4.126</td><td>-1.7552</td><td>4.484</td></tr><tr><td>94</td><td>5</td><td>1.078</td><td>4.3594</td><td>4.491</td></tr><tr><td>95</td><td>5</td><td>4.404</td><td>0.8964</td><td>4.494</td></tr><tr><td>96</td><td>5</td><td>3.493</td><td>-2.8272</td><td>4.494</td></tr><tr><td>97</td><td>5</td><td>4.139</td><td>1.7415</td><td>4.49</td></tr><tr><td>98</td><td>5</td><td>3.736</td><td>-2.4914</td><td>4.491</td></tr><tr><td>99</td><td>5</td><td>2.779</td><td>-3.5233</td><td>4.487</td></tr><tr><td>100</td><td>5</td><td>4.3</td><td>-1.3051</td><td>4.494</td></tr></table>"
      ],
      "text/plain": [
       "[['#', 'Value of a', 'Minimum x1', 'Minimum x2', 'Distance form zero'],\n",
       " [1, 5, 1.383, -4.2740999999999998, 4.492],\n",
       " [2, 5, 3.4990000000000001, 2.8193999999999999, 4.4939999999999998],\n",
       " [3, 5, 3.3359999999999999, 3.0070999999999999, 4.4909999999999997],\n",
       " [4, 5, 4.3440000000000003, -1.1422000000000001, 4.492],\n",
       " [5, 5, 3.8079999999999998, 2.3858000000000001, 4.4930000000000003],\n",
       " [6, 5, 3.3159999999999998, 3.032, 4.4930000000000003],\n",
       " [7, 5, 4.4080000000000004, 0.75460000000000005, 4.4720000000000004],\n",
       " [8, 5, 3.1429999999999998, -3.2113999999999998, 4.4930000000000003],\n",
       " [9, 5, 1.589, 4.2027999999999999, 4.4930000000000003],\n",
       " [10, 5, 4.0739999999999998, -1.9722999999999999, 4.5259999999999998],\n",
       " [11, 5, 3.8599999999999999, 2.4367000000000001, 4.5650000000000004],\n",
       " [12, 5, 3.258, -3.0882999999999998, 4.4889999999999999],\n",
       " [13, 5, 4.4649999999999999, 0.52539999999999998, 4.4960000000000004],\n",
       " [14, 5, 4.383, 0.99239999999999995, 4.4939999999999998],\n",
       " [15, 5, 4.4960000000000004, 0.053400000000000003, 4.4960000000000004],\n",
       " [16, 5, 2.6459999999999999, 3.5821999999999998, 4.4530000000000003],\n",
       " [17, 5, 2.0659999999999998, 3.9902000000000002, 4.4930000000000003],\n",
       " [18, 5, 4.3490000000000002, 1.1322000000000001, 4.4939999999999998],\n",
       " [19, 5, 1.349, 4.2893999999999997, 4.4969999999999999],\n",
       " [20, 5, 2.9100000000000001, 3.4329999999999998, 4.5],\n",
       " [21, 5, 4.032, 2.0068999999999999, 4.5039999999999996],\n",
       " [22, 5, 4.1639999999999997, -1.6917, 4.4939999999999998],\n",
       " [23, 5, 4.3399999999999999, -1.171, 4.4950000000000001],\n",
       " [24, 5, 3.262, -3.0916000000000001, 4.4939999999999998],\n",
       " [25, 5, 1.248, -4.3166000000000002, 4.4930000000000003],\n",
       " [26, 5, 3.6829999999999998, 2.5741999999999998, 4.4939999999999998],\n",
       " [27, 5, 1.698, 4.1601999999999997, 4.4930000000000003],\n",
       " [28, 5, 2.2829999999999999, 3.8700000000000001, 4.4930000000000003],\n",
       " [29, 5, 3.75, -2.4765000000000001, 4.4939999999999998],\n",
       " [30, 5, 2.427, -3.7808999999999999, 4.4930000000000003],\n",
       " [31, 5, 4.4720000000000004, 0.48060000000000003, 4.4980000000000002],\n",
       " [32, 5, 4.3049999999999997, -1.2943, 4.4950000000000001],\n",
       " [33, 5, 4.5620000000000003, -0.53410000000000002, 4.593],\n",
       " [34, 5, 4.4139999999999997, -0.84240000000000004, 4.4930000000000003],\n",
       " [35, 5, 3.7010000000000001, 2.5480999999999998, 4.4939999999999998],\n",
       " [36, 5, 3.9350000000000001, 2.1086, 4.4640000000000004],\n",
       " [37, 5, 3.5390000000000001, -2.7747000000000002, 4.4969999999999999],\n",
       " [38, 5, 4.4790000000000001, 0.37509999999999999, 4.4950000000000001],\n",
       " [39, 5, 1.7749999999999999, 4.1257000000000001, 4.4909999999999997],\n",
       " [40, 5, 3.3610000000000002, 2.9788000000000001, 4.4909999999999997],\n",
       " [41, 5, 1.3919999999999999, -4.2723000000000004, 4.4930000000000003],\n",
       " [42, 5, 4.2270000000000003, 1.5236000000000001, 4.4930000000000003],\n",
       " [43, 5, 2.9100000000000001, 3.4209000000000001, 4.4909999999999997],\n",
       " [44, 5, 4.4790000000000001, 0.32290000000000002, 4.4900000000000002],\n",
       " [45, 5, 3.895, -2.2408999999999999, 4.4930000000000003],\n",
       " [46, 5, 2.7890000000000001, -3.5217000000000001, 4.492],\n",
       " [47, 5, 3.5640000000000001, -2.7353000000000001, 4.4930000000000003],\n",
       " [48, 5, 1.6850000000000001, 4.1660000000000004, 4.4939999999999998],\n",
       " [49, 5, 3.952, -2.1494, 4.4989999999999997],\n",
       " [50, 5, 2.758, -3.5493000000000001, 4.4950000000000001],\n",
       " [51, 5, 4.1040000000000001, 1.8573, 4.5049999999999999],\n",
       " [52, 5, 1.246, -4.3323999999999998, 4.508],\n",
       " [53, 5, 1.4750000000000001, 4.2446000000000002, 4.4939999999999998],\n",
       " [54, 5, 2.3479999999999999, 3.8315000000000001, 4.4939999999999998],\n",
       " [55, 5, 4.4279999999999999, -0.7702, 4.4950000000000001],\n",
       " [56, 5, 2.02, 3.9931000000000001, 4.4749999999999996],\n",
       " [57, 5, 2.1520000000000001, 3.9443999999999999, 4.4930000000000003],\n",
       " [58, 5, 1.575, -4.2098000000000004, 4.4950000000000001],\n",
       " [59, 5, 4.4770000000000003, -0.38740000000000002, 4.4939999999999998],\n",
       " [60, 5, 1.9790000000000001, -4.0349000000000004, 4.4939999999999998],\n",
       " [61, 5, 1.9830000000000001, -4.0202999999999998, 4.4829999999999997],\n",
       " [62, 5, 3.8170000000000002, 2.4032, 4.5110000000000001],\n",
       " [63, 5, 2.9809999999999999, 3.3652000000000002, 4.4950000000000001],\n",
       " [64, 5, 3.1899999999999999, 3.1650999999999998, 4.4939999999999998],\n",
       " [65, 5, 1.2150000000000001, -4.3259999999999996, 4.4930000000000003],\n",
       " [66, 5, 4.4240000000000004, 0.79820000000000002, 4.4960000000000004],\n",
       " [67, 5, 1.881, 4.0804, 4.4930000000000003],\n",
       " [68, 5, 4.4080000000000004, 0.874, 4.4930000000000003],\n",
       " [69, 5, 4.1180000000000003, -1.7988999999999999, 4.4930000000000003],\n",
       " [70, 5, 3.2919999999999998, 3.0762999999999998, 4.5049999999999999],\n",
       " [71, 5, 2.1880000000000002, 3.9245999999999999, 4.4930000000000003],\n",
       " [72, 5, 3.4009999999999998, 2.9369999999999998, 4.4939999999999998],\n",
       " [73, 5, 3.347, 2.9980000000000002, 4.4939999999999998],\n",
       " [74, 5, 2.7589999999999999, -3.5468999999999999, 4.4930000000000003],\n",
       " [75, 5, 1.464, -4.2483000000000004, 4.4930000000000003],\n",
       " [76, 5, 1.857, -4.0913000000000004, 4.4930000000000003],\n",
       " [77, 5, 1.8069999999999999, -4.1139999999999999, 4.4930000000000003],\n",
       " [78, 5, 4.3600000000000003, -1.0843, 4.4930000000000003],\n",
       " [79, 5, 4.4320000000000004, 0.7379, 4.4930000000000003],\n",
       " [80, 5, 4.4630000000000001, -0.53010000000000002, 4.4939999999999998],\n",
       " [81, 5, 3.6539999999999999, -2.6038999999999999, 4.4859999999999998],\n",
       " [82, 5, 3.9319999999999999, 2.1774, 4.4939999999999998],\n",
       " [83, 5, 2.8879999999999999, 3.4388999999999998, 4.4909999999999997],\n",
       " [84, 5, 4.0990000000000002, -1.8409, 4.4930000000000003],\n",
       " [85, 5, 4.4989999999999997, 0.70640000000000003, 4.5549999999999997],\n",
       " [86, 5, 4.0209999999999999, -1.988, 4.4850000000000003],\n",
       " [87, 5, 4.0650000000000004, 1.9132, 4.4930000000000003],\n",
       " [88, 5, 3.3719999999999999, -2.9693000000000001, 4.4930000000000003],\n",
       " [89, 5, 4.4909999999999997, 0.11269999999999999, 4.492],\n",
       " [90, 5, 4.3079999999999998, 1.2697000000000001, 4.4909999999999997],\n",
       " [91, 5, 2.3140000000000001, -3.8515999999999999, 4.4930000000000003],\n",
       " [92, 5, 1.7390000000000001, -4.1364000000000001, 4.4870000000000001],\n",
       " [93, 5, 4.1260000000000003, -1.7552000000000001, 4.484],\n",
       " [94, 5, 1.0780000000000001, 4.3593999999999999, 4.4909999999999997],\n",
       " [95, 5, 4.4039999999999999, 0.89639999999999997, 4.4939999999999998],\n",
       " [96, 5, 3.4929999999999999, -2.8271999999999999, 4.4939999999999998],\n",
       " [97, 5, 4.1390000000000002, 1.7415, 4.4900000000000002],\n",
       " [98, 5, 3.7360000000000002, -2.4914000000000001, 4.4909999999999997],\n",
       " [99, 5, 2.7789999999999999, -3.5232999999999999, 4.4870000000000001],\n",
       " [100, 5, 4.2999999999999998, -1.3050999999999999, 4.4939999999999998]]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>#</td><td>a</td><td>Minimum x1</td><td>Minimum x2</td><td>Distance form zero</td></tr><tr><td>1</td><td>4.4934</td><td>3.863</td><td>-2.2798</td><td>4.4857</td></tr><tr><td>2</td><td>4.4934</td><td>4.142</td><td>1.7039</td><td>4.4788</td></tr><tr><td>3</td><td>4.4934</td><td>2.318</td><td>-3.8371</td><td>4.4827</td></tr><tr><td>4</td><td>4.4934</td><td>2.672</td><td>3.6105</td><td>4.4914</td></tr><tr><td>5</td><td>4.4934</td><td>3.05</td><td>-3.2952</td><td>4.4902</td></tr><tr><td>6</td><td>4.4934</td><td>4.162</td><td>-1.6868</td><td>4.4904</td></tr><tr><td>7</td><td>4.4934</td><td>4.427</td><td>0.6314</td><td>4.4723</td></tr><tr><td>8</td><td>4.4934</td><td>2.29</td><td>3.8659</td><td>4.4933</td></tr><tr><td>9</td><td>4.4934</td><td>3.273</td><td>-3.078</td><td>4.493</td></tr><tr><td>10</td><td>4.4934</td><td>1.05</td><td>4.3688</td><td>4.4932</td></tr><tr><td>11</td><td>4.4934</td><td>3.148</td><td>-3.2001</td><td>4.489</td></tr><tr><td>12</td><td>4.4934</td><td>3.731</td><td>2.4714</td><td>4.4753</td></tr><tr><td>13</td><td>4.4934</td><td>3.96</td><td>-2.1194</td><td>4.4916</td></tr><tr><td>14</td><td>4.4934</td><td>3.907</td><td>-2.2138</td><td>4.4907</td></tr><tr><td>15</td><td>4.4934</td><td>2.377</td><td>-3.8062</td><td>4.4872</td></tr><tr><td>16</td><td>4.4934</td><td>2.198</td><td>3.919</td><td>4.4932</td></tr><tr><td>17</td><td>4.4934</td><td>4.134</td><td>-1.7253</td><td>4.4799</td></tr><tr><td>18</td><td>4.4934</td><td>3.271</td><td>3.0787</td><td>4.492</td></tr><tr><td>19</td><td>4.4934</td><td>3.246</td><td>-3.0996</td><td>4.4884</td></tr><tr><td>20</td><td>4.4934</td><td>4.441</td><td>0.2134</td><td>4.4461</td></tr><tr><td>21</td><td>4.4934</td><td>3.318</td><td>-3.0262</td><td>4.4905</td></tr><tr><td>22</td><td>4.4934</td><td>3.862</td><td>-2.2952</td><td>4.4925</td></tr><tr><td>23</td><td>4.4934</td><td>3.807</td><td>2.3521</td><td>4.4748</td></tr><tr><td>24</td><td>4.4934</td><td>3.104</td><td>-3.2476</td><td>4.4921</td></tr><tr><td>25</td><td>4.4934</td><td>4.382</td><td>0.984</td><td>4.4911</td></tr><tr><td>26</td><td>4.4934</td><td>1.096</td><td>4.356</td><td>4.4917</td></tr><tr><td>27</td><td>4.4934</td><td>4.158</td><td>-1.6574</td><td>4.4757</td></tr><tr><td>28</td><td>4.4934</td><td>4.351</td><td>-1.1017</td><td>4.4882</td></tr><tr><td>29</td><td>4.4934</td><td>2.948</td><td>-3.3907</td><td>4.4933</td></tr><tr><td>30</td><td>4.4934</td><td>4.139</td><td>1.7259</td><td>4.4846</td></tr><tr><td>31</td><td>4.4934</td><td>3.579</td><td>2.709</td><td>4.4886</td></tr><tr><td>32</td><td>4.4934</td><td>4.465</td><td>-0.4869</td><td>4.4918</td></tr><tr><td>33</td><td>4.4934</td><td>2.507</td><td>-3.7171</td><td>4.4837</td></tr><tr><td>34</td><td>4.4934</td><td>3.448</td><td>2.8675</td><td>4.4849</td></tr><tr><td>35</td><td>4.4934</td><td>4.039</td><td>-1.968</td><td>4.493</td></tr><tr><td>36</td><td>4.4934</td><td>4.072</td><td>-1.8998</td><td>4.4929</td></tr><tr><td>37</td><td>4.4934</td><td>4.229</td><td>-0.0743</td><td>4.2293</td></tr><tr><td>38</td><td>4.4934</td><td>4.188</td><td>1.6209</td><td>4.491</td></tr><tr><td>39</td><td>4.4934</td><td>2.061</td><td>-3.985</td><td>4.4866</td></tr><tr><td>40</td><td>4.4934</td><td>3.016</td><td>3.3194</td><td>4.485</td></tr><tr><td>41</td><td>4.4934</td><td>4.12</td><td>-1.7937</td><td>4.4934</td></tr><tr><td>42</td><td>4.4934</td><td>3.03</td><td>-3.312</td><td>4.4891</td></tr><tr><td>43</td><td>4.4934</td><td>4.43</td><td>0.7492</td><td>4.493</td></tr><tr><td>44</td><td>4.4934</td><td>3.473</td><td>2.8363</td><td>4.4841</td></tr><tr><td>45</td><td>4.4934</td><td>4.448</td><td>0.0091</td><td>4.4485</td></tr><tr><td>46</td><td>4.4934</td><td>2.869</td><td>-3.4306</td><td>4.4724</td></tr><tr><td>47</td><td>4.4934</td><td>3.881</td><td>-2.2641</td><td>4.493</td></tr><tr><td>48</td><td>4.4934</td><td>1.437</td><td>4.2572</td><td>4.4933</td></tr><tr><td>49</td><td>4.4934</td><td>4.199</td><td>1.5993</td><td>4.4931</td></tr><tr><td>50</td><td>4.4934</td><td>4.247</td><td>-1.4188</td><td>4.4782</td></tr><tr><td>51</td><td>4.4934</td><td>4.336</td><td>0.4472</td><td>4.3586</td></tr><tr><td>52</td><td>4.4934</td><td>1.406</td><td>-4.2636</td><td>4.4895</td></tr><tr><td>53</td><td>4.4934</td><td>4.354</td><td>0.977</td><td>4.4627</td></tr><tr><td>54</td><td>4.4934</td><td>2.14</td><td>-3.9404</td><td>4.4838</td></tr><tr><td>55</td><td>4.4934</td><td>4.211</td><td>-1.52</td><td>4.4772</td></tr><tr><td>56</td><td>4.4934</td><td>1.326</td><td>4.2878</td><td>4.4882</td></tr><tr><td>57</td><td>4.4934</td><td>2.728</td><td>3.5707</td><td>4.4933</td></tr><tr><td>58</td><td>4.4934</td><td>4.484</td><td>-0.2918</td><td>4.493</td></tr><tr><td>59</td><td>4.4934</td><td>1.463</td><td>-4.2469</td><td>4.4918</td></tr><tr><td>60</td><td>4.4934</td><td>3.613</td><td>-2.6689</td><td>4.4921</td></tr><tr><td>61</td><td>4.4934</td><td>2.448</td><td>3.7679</td><td>4.4934</td></tr><tr><td>62</td><td>4.4934</td><td>4.47</td><td>-0.4573</td><td>4.4934</td></tr><tr><td>63</td><td>4.4934</td><td>3.72</td><td>-2.4711</td><td>4.4656</td></tr><tr><td>64</td><td>4.4934</td><td>3.276</td><td>-3.0509</td><td>4.4769</td></tr><tr><td>65</td><td>4.4934</td><td>2.535</td><td>-3.6885</td><td>4.4755</td></tr><tr><td>66</td><td>4.4934</td><td>2.693</td><td>3.5298</td><td>4.4395</td></tr><tr><td>67</td><td>4.4934</td><td>4.008</td><td>-2.0081</td><td>4.4828</td></tr><tr><td>68</td><td>4.4934</td><td>4.475</td><td>0.3962</td><td>4.493</td></tr><tr><td>69</td><td>4.4934</td><td>4.487</td><td>-0.1714</td><td>4.4906</td></tr><tr><td>70</td><td>4.4934</td><td>3.997</td><td>2.0527</td><td>4.4933</td></tr><tr><td>71</td><td>4.4934</td><td>1.271</td><td>-4.3098</td><td>4.4934</td></tr><tr><td>72</td><td>4.4934</td><td>4.182</td><td>-1.6376</td><td>4.4913</td></tr><tr><td>73</td><td>4.4934</td><td>4.009</td><td>-2.0285</td><td>4.4932</td></tr><tr><td>74</td><td>4.4934</td><td>4.388</td><td>0.9415</td><td>4.4878</td></tr><tr><td>75</td><td>4.4934</td><td>4.305</td><td>1.2869</td><td>4.4934</td></tr><tr><td>76</td><td>4.4934</td><td>4.1</td><td>-1.8341</td><td>4.4913</td></tr><tr><td>77</td><td>4.4934</td><td>2.568</td><td>-3.6874</td><td>4.4934</td></tr><tr><td>78</td><td>4.4934</td><td>4.397</td><td>0.9237</td><td>4.4929</td></tr><tr><td>79</td><td>4.4934</td><td>1.385</td><td>4.2724</td><td>4.4913</td></tr><tr><td>80</td><td>4.4934</td><td>4.456</td><td>-0.5605</td><td>4.4909</td></tr><tr><td>81</td><td>4.4934</td><td>2.213</td><td>-3.9102</td><td>4.493</td></tr><tr><td>82</td><td>4.4934</td><td>2.236</td><td>-3.8921</td><td>4.4888</td></tr><tr><td>83</td><td>4.4934</td><td>4.077</td><td>1.8869</td><td>4.4926</td></tr><tr><td>84</td><td>4.4934</td><td>4.409</td><td>-0.8415</td><td>4.4889</td></tr><tr><td>85</td><td>4.4934</td><td>4.48</td><td>0.3404</td><td>4.4934</td></tr><tr><td>86</td><td>4.4934</td><td>4.095</td><td>1.8494</td><td>4.4928</td></tr><tr><td>87</td><td>4.4934</td><td>2.547</td><td>3.6819</td><td>4.4769</td></tr><tr><td>88</td><td>4.4934</td><td>3.586</td><td>2.6751</td><td>4.474</td></tr><tr><td>89</td><td>4.4934</td><td>4.169</td><td>-1.638</td><td>4.4792</td></tr><tr><td>90</td><td>4.4934</td><td>2.878</td><td>-2.7812</td><td>4.0021</td></tr><tr><td>91</td><td>4.4934</td><td>2.397</td><td>3.8</td><td>4.4928</td></tr><tr><td>92</td><td>4.4934</td><td>3.459</td><td>-2.8568</td><td>4.4865</td></tr><tr><td>93</td><td>4.4934</td><td>1.98</td><td>4.0219</td><td>4.4827</td></tr><tr><td>94</td><td>4.4934</td><td>3.439</td><td>-2.8756</td><td>4.4825</td></tr><tr><td>95</td><td>4.4934</td><td>4.461</td><td>-0.5083</td><td>4.4903</td></tr><tr><td>96</td><td>4.4934</td><td>4.05</td><td>-1.8878</td><td>4.4685</td></tr><tr><td>97</td><td>4.4934</td><td>4.149</td><td>1.7236</td><td>4.4927</td></tr><tr><td>98</td><td>4.4934</td><td>4.415</td><td>-0.8322</td><td>4.4928</td></tr><tr><td>99</td><td>4.4934</td><td>1.907</td><td>-4.0086</td><td>4.4388</td></tr><tr><td>100</td><td>4.4934</td><td>1.93</td><td>4.042</td><td>4.4792</td></tr></table>"
      ],
      "text/plain": [
       "[['#', 'a', 'Minimum x1', 'Minimum x2', 'Distance form zero'],\n",
       " [1, 4.4934, 3.863, -2.2797999999999998, 4.4856999999999996],\n",
       " [2, 4.4934, 4.1420000000000003, 1.7039, 4.4787999999999997],\n",
       " [3, 4.4934, 2.3180000000000001, -3.8371, 4.4827000000000004],\n",
       " [4, 4.4934, 2.6720000000000002, 3.6105, 4.4913999999999996],\n",
       " [5, 4.4934, 3.0499999999999998, -3.2951999999999999, 4.4901999999999997],\n",
       " [6, 4.4934, 4.1619999999999999, -1.6868000000000001, 4.4904000000000002],\n",
       " [7, 4.4934, 4.4269999999999996, 0.63139999999999996, 4.4722999999999997],\n",
       " [8, 4.4934, 2.29, 3.8658999999999999, 4.4932999999999996],\n",
       " [9, 4.4934, 3.2730000000000001, -3.0779999999999998, 4.4930000000000003],\n",
       " [10, 4.4934, 1.05, 4.3688000000000002, 4.4931999999999999],\n",
       " [11, 4.4934, 3.1480000000000001, -3.2000999999999999, 4.4889999999999999],\n",
       " [12, 4.4934, 3.7309999999999999, 2.4714, 4.4752999999999998],\n",
       " [13, 4.4934, 3.96, -2.1194000000000002, 4.4916],\n",
       " [14, 4.4934, 3.907, -2.2138, 4.4907000000000004],\n",
       " [15, 4.4934, 2.3769999999999998, -3.8062, 4.4871999999999996],\n",
       " [16, 4.4934, 2.198, 3.919, 4.4931999999999999],\n",
       " [17, 4.4934, 4.1340000000000003, -1.7253000000000001, 4.4798999999999998],\n",
       " [18, 4.4934, 3.2709999999999999, 3.0787, 4.492],\n",
       " [19, 4.4934, 3.246, -3.0996000000000001, 4.4884000000000004],\n",
       " [20, 4.4934, 4.4409999999999998, 0.21340000000000001, 4.4461000000000004],\n",
       " [21, 4.4934, 3.3180000000000001, -3.0261999999999998, 4.4904999999999999],\n",
       " [22, 4.4934, 3.8620000000000001, -2.2951999999999999, 4.4924999999999997],\n",
       " [23, 4.4934, 3.8069999999999999, 2.3521000000000001, 4.4748000000000001],\n",
       " [24, 4.4934, 3.1040000000000001, -3.2475999999999998, 4.4920999999999998],\n",
       " [25, 4.4934, 4.3819999999999997, 0.98399999999999999, 4.4911000000000003],\n",
       " [26, 4.4934, 1.0960000000000001, 4.3559999999999999, 4.4916999999999998],\n",
       " [27, 4.4934, 4.1580000000000004, -1.6574, 4.4756999999999998],\n",
       " [28, 4.4934, 4.351, -1.1016999999999999, 4.4882],\n",
       " [29, 4.4934, 2.948, -3.3906999999999998, 4.4932999999999996],\n",
       " [30, 4.4934, 4.1390000000000002, 1.7259, 4.4846000000000004],\n",
       " [31, 4.4934, 3.5790000000000002, 2.7090000000000001, 4.4885999999999999],\n",
       " [32, 4.4934, 4.4649999999999999, -0.4869, 4.4917999999999996],\n",
       " [33, 4.4934, 2.5070000000000001, -3.7170999999999998, 4.4836999999999998],\n",
       " [34, 4.4934, 3.448, 2.8675000000000002, 4.4848999999999997],\n",
       " [35, 4.4934, 4.0389999999999997, -1.968, 4.4930000000000003],\n",
       " [36, 4.4934, 4.0720000000000001, -1.8997999999999999, 4.4928999999999997],\n",
       " [37, 4.4934, 4.2290000000000001, -0.074300000000000005, 4.2293000000000003],\n",
       " [38, 4.4934, 4.1879999999999997, 1.6209, 4.4909999999999997],\n",
       " [39, 4.4934, 2.0609999999999999, -3.9849999999999999, 4.4866000000000001],\n",
       " [40, 4.4934, 3.016, 3.3193999999999999, 4.4850000000000003],\n",
       " [41, 4.4934, 4.1200000000000001, -1.7937000000000001, 4.4934000000000003],\n",
       " [42, 4.4934, 3.0299999999999998, -3.3119999999999998, 4.4890999999999996],\n",
       " [43, 4.4934, 4.4299999999999997, 0.74919999999999998, 4.4930000000000003],\n",
       " [44, 4.4934, 3.4729999999999999, 2.8363, 4.4840999999999998],\n",
       " [45, 4.4934, 4.4480000000000004, 0.0091000000000000004, 4.4485000000000001],\n",
       " [46, 4.4934, 2.8690000000000002, -3.4306000000000001, 4.4724000000000004],\n",
       " [47, 4.4934, 3.8809999999999998, -2.2641, 4.4930000000000003],\n",
       " [48, 4.4934, 1.4370000000000001, 4.2572000000000001, 4.4932999999999996],\n",
       " [49, 4.4934, 4.1989999999999998, 1.5992999999999999, 4.4931000000000001],\n",
       " [50, 4.4934, 4.2469999999999999, -1.4188000000000001, 4.4782000000000002],\n",
       " [51, 4.4934, 4.3360000000000003, 0.44719999999999999, 4.3586],\n",
       " [52, 4.4934, 1.4059999999999999, -4.2636000000000003, 4.4894999999999996],\n",
       " [53, 4.4934, 4.3540000000000001, 0.97699999999999998, 4.4626999999999999],\n",
       " [54, 4.4934, 2.1400000000000001, -3.9403999999999999, 4.4837999999999996],\n",
       " [55, 4.4934, 4.2110000000000003, -1.52, 4.4771999999999998],\n",
       " [56, 4.4934, 1.3260000000000001, 4.2877999999999998, 4.4882],\n",
       " [57, 4.4934, 2.7280000000000002, 3.5707, 4.4932999999999996],\n",
       " [58, 4.4934, 4.484, -0.2918, 4.4930000000000003],\n",
       " [59, 4.4934, 1.4630000000000001, -4.2469000000000001, 4.4917999999999996],\n",
       " [60, 4.4934, 3.613, -2.6688999999999998, 4.4920999999999998],\n",
       " [61, 4.4934, 2.448, 3.7679, 4.4934000000000003],\n",
       " [62, 4.4934, 4.4699999999999998, -0.45729999999999998, 4.4934000000000003],\n",
       " [63, 4.4934, 3.7200000000000002, -2.4710999999999999, 4.4656000000000002],\n",
       " [64, 4.4934, 3.2759999999999998, -3.0508999999999999, 4.4768999999999997],\n",
       " [65, 4.4934, 2.5350000000000001, -3.6884999999999999, 4.4755000000000003],\n",
       " [66, 4.4934, 2.6930000000000001, 3.5297999999999998, 4.4394999999999998],\n",
       " [67, 4.4934, 4.008, -2.0081000000000002, 4.4828000000000001],\n",
       " [68, 4.4934, 4.4749999999999996, 0.3962, 4.4930000000000003],\n",
       " [69, 4.4934, 4.4870000000000001, -0.1714, 4.4905999999999997],\n",
       " [70, 4.4934, 3.9969999999999999, 2.0527000000000002, 4.4932999999999996],\n",
       " [71, 4.4934, 1.2709999999999999, -4.3098000000000001, 4.4934000000000003],\n",
       " [72, 4.4934, 4.1820000000000004, -1.6375999999999999, 4.4912999999999998],\n",
       " [73, 4.4934, 4.0090000000000003, -2.0285000000000002, 4.4931999999999999],\n",
       " [74, 4.4934, 4.3879999999999999, 0.9415, 4.4878],\n",
       " [75, 4.4934, 4.3049999999999997, 1.2868999999999999, 4.4934000000000003],\n",
       " [76, 4.4934, 4.0999999999999996, -1.8341000000000001, 4.4912999999999998],\n",
       " [77, 4.4934, 2.5680000000000001, -3.6873999999999998, 4.4934000000000003],\n",
       " [78, 4.4934, 4.3970000000000002, 0.92369999999999997, 4.4928999999999997],\n",
       " [79, 4.4934, 1.385, 4.2724000000000002, 4.4912999999999998],\n",
       " [80, 4.4934, 4.4560000000000004, -0.5605, 4.4908999999999999],\n",
       " [81, 4.4934, 2.2130000000000001, -3.9102000000000001, 4.4930000000000003],\n",
       " [82, 4.4934, 2.2360000000000002, -3.8921000000000001, 4.4888000000000003],\n",
       " [83, 4.4934, 4.077, 1.8869, 4.4926000000000004],\n",
       " [84, 4.4934, 4.4089999999999998, -0.84150000000000003, 4.4889000000000001],\n",
       " [85, 4.4934, 4.4800000000000004, 0.34039999999999998, 4.4934000000000003],\n",
       " [86, 4.4934, 4.0949999999999998, 1.8493999999999999, 4.4927999999999999],\n",
       " [87, 4.4934, 2.5470000000000002, 3.6819000000000002, 4.4768999999999997],\n",
       " [88, 4.4934, 3.5859999999999999, 2.6751, 4.4740000000000002],\n",
       " [89, 4.4934, 4.1689999999999996, -1.6379999999999999, 4.4791999999999996],\n",
       " [90, 4.4934, 2.8780000000000001, -2.7812000000000001, 4.0021000000000004],\n",
       " [91, 4.4934, 2.3969999999999998, 3.7999999999999998, 4.4927999999999999],\n",
       " [92, 4.4934, 3.4590000000000001, -2.8567999999999998, 4.4865000000000004],\n",
       " [93, 4.4934, 1.98, 4.0218999999999996, 4.4827000000000004],\n",
       " [94, 4.4934, 3.4390000000000001, -2.8755999999999999, 4.4824999999999999],\n",
       " [95, 4.4934, 4.4610000000000003, -0.50829999999999997, 4.4903000000000004],\n",
       " [96, 4.4934, 4.0499999999999998, -1.8877999999999999, 4.4684999999999997],\n",
       " [97, 4.4934, 4.149, 1.7236, 4.4927000000000001],\n",
       " [98, 4.4934, 4.415, -0.83220000000000005, 4.4927999999999999],\n",
       " [99, 4.4934, 1.907, -4.0086000000000004, 4.4387999999999996],\n",
       " [100, 4.4934, 1.9299999999999999, 4.0419999999999998, 4.4791999999999996]]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>#</td><td>a</td><td>Minimum x1</td><td>Minimum x2</td><td>Distance form zero</td></tr><tr><td>1</td><td>4.0</td><td>1.88</td><td>3.524</td><td>3.995</td></tr><tr><td>2</td><td>4.0</td><td>3.372</td><td>2.074</td><td>3.959</td></tr><tr><td>3</td><td>4.0</td><td>3.922</td><td>0.243</td><td>3.93</td></tr><tr><td>4</td><td>4.0</td><td>3.965</td><td>-0.506</td><td>3.997</td></tr><tr><td>5</td><td>4.0</td><td>2.275</td><td>3.273</td><td>3.986</td></tr><tr><td>6</td><td>4.0</td><td>3.653</td><td>-1.626</td><td>3.999</td></tr><tr><td>7</td><td>4.0</td><td>3.14</td><td>-2.472</td><td>3.996</td></tr><tr><td>8</td><td>4.0</td><td>2.665</td><td>-2.982</td><td>3.999</td></tr><tr><td>9</td><td>4.0</td><td>2.601</td><td>-3.026</td><td>3.99</td></tr><tr><td>10</td><td>4.0</td><td>2.025</td><td>3.444</td><td>3.995</td></tr><tr><td>11</td><td>4.0</td><td>2.213</td><td>-3.332</td><td>4.0</td></tr><tr><td>12</td><td>4.0</td><td>1.864</td><td>3.531</td><td>3.992</td></tr><tr><td>13</td><td>4.0</td><td>3.863</td><td>0.925</td><td>3.972</td></tr><tr><td>14</td><td>4.0</td><td>3.003</td><td>2.639</td><td>3.998</td></tr><tr><td>15</td><td>4.0</td><td>1.07</td><td>3.854</td><td>4.0</td></tr><tr><td>16</td><td>4.0</td><td>3.629</td><td>1.68</td><td>3.999</td></tr><tr><td>17</td><td>4.0</td><td>1.946</td><td>-3.494</td><td>4.0</td></tr><tr><td>18</td><td>4.0</td><td>3.445</td><td>2.026</td><td>3.997</td></tr><tr><td>19</td><td>4.0</td><td>2.168</td><td>-3.361</td><td>3.999</td></tr><tr><td>20</td><td>4.0</td><td>2.066</td><td>-3.425</td><td>4.0</td></tr><tr><td>21</td><td>4.0</td><td>3.942</td><td>-0.637</td><td>3.993</td></tr><tr><td>22</td><td>4.0</td><td>2.262</td><td>3.242</td><td>3.953</td></tr><tr><td>23</td><td>4.0</td><td>3.808</td><td>-1.215</td><td>3.997</td></tr><tr><td>24</td><td>4.0</td><td>2.386</td><td>-3.201</td><td>3.992</td></tr><tr><td>25</td><td>4.0</td><td>2.718</td><td>-2.935</td><td>4.0</td></tr><tr><td>26</td><td>4.0</td><td>3.584</td><td>-1.769</td><td>3.997</td></tr><tr><td>27</td><td>4.0</td><td>3.524</td><td>1.888</td><td>3.998</td></tr><tr><td>28</td><td>4.0</td><td>3.046</td><td>-2.59</td><td>3.999</td></tr><tr><td>29</td><td>4.0</td><td>2.591</td><td>-3.046</td><td>3.999</td></tr><tr><td>30</td><td>4.0</td><td>2.571</td><td>-3.059</td><td>3.996</td></tr><tr><td>31</td><td>4.0</td><td>3.835</td><td>1.112</td><td>3.993</td></tr><tr><td>32</td><td>4.0</td><td>2.429</td><td>3.174</td><td>3.997</td></tr><tr><td>33</td><td>4.0</td><td>3.891</td><td>0.881</td><td>3.989</td></tr><tr><td>34</td><td>4.0</td><td>3.465</td><td>-1.984</td><td>3.993</td></tr><tr><td>35</td><td>4.0</td><td>3.959</td><td>-0.284</td><td>3.969</td></tr><tr><td>36</td><td>4.0</td><td>1.932</td><td>-3.465</td><td>3.967</td></tr><tr><td>37</td><td>4.0</td><td>1.881</td><td>3.528</td><td>3.998</td></tr><tr><td>38</td><td>4.0</td><td>3.107</td><td>-2.511</td><td>3.995</td></tr><tr><td>39</td><td>4.0</td><td>2.753</td><td>2.483</td><td>3.707</td></tr><tr><td>40</td><td>4.0</td><td>2.904</td><td>-2.693</td><td>3.961</td></tr><tr><td>41</td><td>4.0</td><td>3.054</td><td>-2.536</td><td>3.97</td></tr><tr><td>42</td><td>4.0</td><td>3.949</td><td>-0.636</td><td>4.0</td></tr><tr><td>43</td><td>4.0</td><td>2.083</td><td>-3.401</td><td>3.988</td></tr><tr><td>44</td><td>4.0</td><td>3.237</td><td>2.308</td><td>3.975</td></tr><tr><td>45</td><td>4.0</td><td>3.048</td><td>-2.591</td><td>4.0</td></tr><tr><td>46</td><td>4.0</td><td>2.846</td><td>2.806</td><td>3.997</td></tr><tr><td>47</td><td>4.0</td><td>2.936</td><td>2.716</td><td>4.0</td></tr><tr><td>48</td><td>4.0</td><td>3.857</td><td>1.055</td><td>3.998</td></tr><tr><td>49</td><td>4.0</td><td>2.249</td><td>-3.304</td><td>3.997</td></tr><tr><td>50</td><td>4.0</td><td>2.419</td><td>-3.184</td><td>3.999</td></tr><tr><td>51</td><td>4.0</td><td>3.939</td><td>0.365</td><td>3.955</td></tr><tr><td>52</td><td>4.0</td><td>3.386</td><td>-1.998</td><td>3.931</td></tr><tr><td>53</td><td>4.0</td><td>3.521</td><td>-1.893</td><td>3.998</td></tr><tr><td>54</td><td>4.0</td><td>3.981</td><td>-0.389</td><td>4.0</td></tr><tr><td>55</td><td>4.0</td><td>3.066</td><td>2.559</td><td>3.994</td></tr><tr><td>56</td><td>4.0</td><td>1.534</td><td>3.652</td><td>3.961</td></tr><tr><td>57</td><td>4.0</td><td>3.871</td><td>-0.994</td><td>3.997</td></tr><tr><td>58</td><td>4.0</td><td>3.97</td><td>0.433</td><td>3.994</td></tr><tr><td>59</td><td>4.0</td><td>3.723</td><td>-1.449</td><td>3.995</td></tr><tr><td>60</td><td>4.0</td><td>3.06</td><td>-2.555</td><td>3.987</td></tr><tr><td>61</td><td>4.0</td><td>3.841</td><td>-1.117</td><td>4.0</td></tr><tr><td>62</td><td>4.0</td><td>3.303</td><td>2.25</td><td>3.997</td></tr><tr><td>63</td><td>4.0</td><td>3.285</td><td>2.254</td><td>3.984</td></tr><tr><td>64</td><td>4.0</td><td>3.851</td><td>-1.061</td><td>3.995</td></tr><tr><td>65</td><td>4.0</td><td>3.351</td><td>-2.181</td><td>3.998</td></tr><tr><td>66</td><td>4.0</td><td>3.929</td><td>0.637</td><td>3.981</td></tr><tr><td>67</td><td>4.0</td><td>3.51</td><td>1.917</td><td>4.0</td></tr><tr><td>68</td><td>4.0</td><td>3.73</td><td>1.438</td><td>3.997</td></tr><tr><td>69</td><td>4.0</td><td>3.719</td><td>1.468</td><td>3.999</td></tr><tr><td>70</td><td>4.0</td><td>3.777</td><td>-1.289</td><td>3.99</td></tr><tr><td>71</td><td>4.0</td><td>3.747</td><td>-1.4</td><td>4.0</td></tr><tr><td>72</td><td>4.0</td><td>3.926</td><td>-0.513</td><td>3.96</td></tr><tr><td>73</td><td>4.0</td><td>1.487</td><td>3.712</td><td>3.999</td></tr><tr><td>74</td><td>4.0</td><td>3.946</td><td>-0.618</td><td>3.994</td></tr><tr><td>75</td><td>4.0</td><td>3.675</td><td>1.577</td><td>3.999</td></tr><tr><td>76</td><td>4.0</td><td>3.677</td><td>1.573</td><td>4.0</td></tr><tr><td>77</td><td>4.0</td><td>3.258</td><td>2.312</td><td>3.995</td></tr><tr><td>78</td><td>4.0</td><td>1.66</td><td>-3.638</td><td>3.999</td></tr><tr><td>79</td><td>4.0</td><td>2.887</td><td>-2.767</td><td>4.0</td></tr><tr><td>80</td><td>4.0</td><td>2.493</td><td>3.016</td><td>3.913</td></tr><tr><td>81</td><td>4.0</td><td>2.326</td><td>-3.253</td><td>3.999</td></tr><tr><td>82</td><td>4.0</td><td>3.976</td><td>0.376</td><td>3.994</td></tr><tr><td>83</td><td>4.0</td><td>3.927</td><td>-0.745</td><td>3.997</td></tr><tr><td>84</td><td>4.0</td><td>3.876</td><td>0.957</td><td>3.993</td></tr><tr><td>85</td><td>4.0</td><td>1.546</td><td>3.68</td><td>3.991</td></tr><tr><td>86</td><td>4.0</td><td>3.663</td><td>-1.602</td><td>3.998</td></tr><tr><td>87</td><td>4.0</td><td>3.804</td><td>-1.225</td><td>3.997</td></tr><tr><td>88</td><td>4.0</td><td>2.884</td><td>2.675</td><td>3.933</td></tr><tr><td>89</td><td>4.0</td><td>3.766</td><td>-1.343</td><td>3.998</td></tr><tr><td>90</td><td>4.0</td><td>3.942</td><td>0.317</td><td>3.955</td></tr><tr><td>91</td><td>4.0</td><td>3.992</td><td>0.016</td><td>3.993</td></tr><tr><td>92</td><td>4.0</td><td>3.992</td><td>-0.242</td><td>3.999</td></tr><tr><td>93</td><td>4.0</td><td>1.849</td><td>3.527</td><td>3.982</td></tr><tr><td>94</td><td>4.0</td><td>2.251</td><td>3.299</td><td>3.993</td></tr><tr><td>95</td><td>4.0</td><td>3.733</td><td>-1.421</td><td>3.994</td></tr><tr><td>96</td><td>4.0</td><td>3.843</td><td>1.043</td><td>3.982</td></tr><tr><td>97</td><td>4.0</td><td>1.666</td><td>-3.615</td><td>3.981</td></tr><tr><td>98</td><td>4.0</td><td>3.922</td><td>0.784</td><td>3.999</td></tr><tr><td>99</td><td>4.0</td><td>3.572</td><td>-1.795</td><td>3.998</td></tr><tr><td>100</td><td>4.0</td><td>3.147</td><td>-2.467</td><td>3.999</td></tr></table>"
      ],
      "text/plain": [
       "[['#', 'a', 'Minimum x1', 'Minimum x2', 'Distance form zero'],\n",
       " [1, 4.0, 1.8799999999999999, 3.524, 3.9950000000000001],\n",
       " [2, 4.0, 3.3719999999999999, 2.0739999999999998, 3.9590000000000001],\n",
       " [3, 4.0, 3.9220000000000002, 0.24299999999999999, 3.9300000000000002],\n",
       " [4, 4.0, 3.9649999999999999, -0.50600000000000001, 3.9969999999999999],\n",
       " [5, 4.0, 2.2749999999999999, 3.2730000000000001, 3.9860000000000002],\n",
       " [6, 4.0, 3.653, -1.6259999999999999, 3.9990000000000001],\n",
       " [7, 4.0, 3.1400000000000001, -2.472, 3.996],\n",
       " [8, 4.0, 2.665, -2.9820000000000002, 3.9990000000000001],\n",
       " [9, 4.0, 2.601, -3.0259999999999998, 3.9900000000000002],\n",
       " [10, 4.0, 2.0249999999999999, 3.444, 3.9950000000000001],\n",
       " [11, 4.0, 2.2130000000000001, -3.3319999999999999, 4.0],\n",
       " [12, 4.0, 1.8640000000000001, 3.5310000000000001, 3.992],\n",
       " [13, 4.0, 3.863, 0.92500000000000004, 3.972],\n",
       " [14, 4.0, 3.0030000000000001, 2.6389999999999998, 3.9980000000000002],\n",
       " [15, 4.0, 1.0700000000000001, 3.8540000000000001, 4.0],\n",
       " [16, 4.0, 3.629, 1.6799999999999999, 3.9990000000000001],\n",
       " [17, 4.0, 1.946, -3.4940000000000002, 4.0],\n",
       " [18, 4.0, 3.4449999999999998, 2.0259999999999998, 3.9969999999999999],\n",
       " [19, 4.0, 2.1680000000000001, -3.3610000000000002, 3.9990000000000001],\n",
       " [20, 4.0, 2.0659999999999998, -3.4249999999999998, 4.0],\n",
       " [21, 4.0, 3.9420000000000002, -0.63700000000000001, 3.9929999999999999],\n",
       " [22, 4.0, 2.262, 3.242, 3.9529999999999998],\n",
       " [23, 4.0, 3.8079999999999998, -1.2150000000000001, 3.9969999999999999],\n",
       " [24, 4.0, 2.3860000000000001, -3.2010000000000001, 3.992],\n",
       " [25, 4.0, 2.718, -2.9350000000000001, 4.0],\n",
       " [26, 4.0, 3.5840000000000001, -1.7689999999999999, 3.9969999999999999],\n",
       " [27, 4.0, 3.524, 1.8879999999999999, 3.9980000000000002],\n",
       " [28, 4.0, 3.0459999999999998, -2.5899999999999999, 3.9990000000000001],\n",
       " [29, 4.0, 2.5910000000000002, -3.0459999999999998, 3.9990000000000001],\n",
       " [30, 4.0, 2.5710000000000002, -3.0590000000000002, 3.996],\n",
       " [31, 4.0, 3.835, 1.1120000000000001, 3.9929999999999999],\n",
       " [32, 4.0, 2.4289999999999998, 3.1739999999999999, 3.9969999999999999],\n",
       " [33, 4.0, 3.891, 0.88100000000000001, 3.9889999999999999],\n",
       " [34, 4.0, 3.4649999999999999, -1.984, 3.9929999999999999],\n",
       " [35, 4.0, 3.9590000000000001, -0.28399999999999997, 3.9689999999999999],\n",
       " [36, 4.0, 1.9319999999999999, -3.4649999999999999, 3.9670000000000001],\n",
       " [37, 4.0, 1.881, 3.528, 3.9980000000000002],\n",
       " [38, 4.0, 3.1070000000000002, -2.5110000000000001, 3.9950000000000001],\n",
       " [39, 4.0, 2.7530000000000001, 2.4830000000000001, 3.7069999999999999],\n",
       " [40, 4.0, 2.9039999999999999, -2.6930000000000001, 3.9609999999999999],\n",
       " [41, 4.0, 3.0539999999999998, -2.536, 3.9700000000000002],\n",
       " [42, 4.0, 3.9489999999999998, -0.63600000000000001, 4.0],\n",
       " [43, 4.0, 2.0830000000000002, -3.4009999999999998, 3.988],\n",
       " [44, 4.0, 3.2370000000000001, 2.3079999999999998, 3.9750000000000001],\n",
       " [45, 4.0, 3.048, -2.5910000000000002, 4.0],\n",
       " [46, 4.0, 2.8460000000000001, 2.806, 3.9969999999999999],\n",
       " [47, 4.0, 2.9359999999999999, 2.7160000000000002, 4.0],\n",
       " [48, 4.0, 3.8570000000000002, 1.0549999999999999, 3.9980000000000002],\n",
       " [49, 4.0, 2.2490000000000001, -3.3039999999999998, 3.9969999999999999],\n",
       " [50, 4.0, 2.419, -3.1840000000000002, 3.9990000000000001],\n",
       " [51, 4.0, 3.9390000000000001, 0.36499999999999999, 3.9550000000000001],\n",
       " [52, 4.0, 3.3860000000000001, -1.998, 3.931],\n",
       " [53, 4.0, 3.5209999999999999, -1.893, 3.9980000000000002],\n",
       " [54, 4.0, 3.9809999999999999, -0.38900000000000001, 4.0],\n",
       " [55, 4.0, 3.0659999999999998, 2.5590000000000002, 3.9940000000000002],\n",
       " [56, 4.0, 1.534, 3.6520000000000001, 3.9609999999999999],\n",
       " [57, 4.0, 3.871, -0.99399999999999999, 3.9969999999999999],\n",
       " [58, 4.0, 3.9700000000000002, 0.433, 3.9940000000000002],\n",
       " [59, 4.0, 3.7229999999999999, -1.4490000000000001, 3.9950000000000001],\n",
       " [60, 4.0, 3.0600000000000001, -2.5550000000000002, 3.9870000000000001],\n",
       " [61, 4.0, 3.8410000000000002, -1.117, 4.0],\n",
       " [62, 4.0, 3.3029999999999999, 2.25, 3.9969999999999999],\n",
       " [63, 4.0, 3.2850000000000001, 2.254, 3.984],\n",
       " [64, 4.0, 3.851, -1.0609999999999999, 3.9950000000000001],\n",
       " [65, 4.0, 3.351, -2.181, 3.9980000000000002],\n",
       " [66, 4.0, 3.9289999999999998, 0.63700000000000001, 3.9809999999999999],\n",
       " [67, 4.0, 3.5099999999999998, 1.917, 4.0],\n",
       " [68, 4.0, 3.73, 1.4379999999999999, 3.9969999999999999],\n",
       " [69, 4.0, 3.7189999999999999, 1.468, 3.9990000000000001],\n",
       " [70, 4.0, 3.7770000000000001, -1.2889999999999999, 3.9900000000000002],\n",
       " [71, 4.0, 3.7469999999999999, -1.3999999999999999, 4.0],\n",
       " [72, 4.0, 3.9260000000000002, -0.51300000000000001, 3.96],\n",
       " [73, 4.0, 1.4870000000000001, 3.7120000000000002, 3.9990000000000001],\n",
       " [74, 4.0, 3.9460000000000002, -0.61799999999999999, 3.9940000000000002],\n",
       " [75, 4.0, 3.6749999999999998, 1.577, 3.9990000000000001],\n",
       " [76, 4.0, 3.677, 1.573, 4.0],\n",
       " [77, 4.0, 3.258, 2.3119999999999998, 3.9950000000000001],\n",
       " [78, 4.0, 1.6599999999999999, -3.6379999999999999, 3.9990000000000001],\n",
       " [79, 4.0, 2.887, -2.7669999999999999, 4.0],\n",
       " [80, 4.0, 2.4929999999999999, 3.016, 3.9129999999999998],\n",
       " [81, 4.0, 2.3260000000000001, -3.2530000000000001, 3.9990000000000001],\n",
       " [82, 4.0, 3.976, 0.376, 3.9940000000000002],\n",
       " [83, 4.0, 3.927, -0.745, 3.9969999999999999],\n",
       " [84, 4.0, 3.8759999999999999, 0.95699999999999996, 3.9929999999999999],\n",
       " [85, 4.0, 1.546, 3.6800000000000002, 3.9910000000000001],\n",
       " [86, 4.0, 3.6629999999999998, -1.6020000000000001, 3.9980000000000002],\n",
       " [87, 4.0, 3.8039999999999998, -1.2250000000000001, 3.9969999999999999],\n",
       " [88, 4.0, 2.8839999999999999, 2.6749999999999998, 3.9329999999999998],\n",
       " [89, 4.0, 3.766, -1.343, 3.9980000000000002],\n",
       " [90, 4.0, 3.9420000000000002, 0.317, 3.9550000000000001],\n",
       " [91, 4.0, 3.992, 0.016, 3.9929999999999999],\n",
       " [92, 4.0, 3.992, -0.24199999999999999, 3.9990000000000001],\n",
       " [93, 4.0, 1.849, 3.5270000000000001, 3.9820000000000002],\n",
       " [94, 4.0, 2.2509999999999999, 3.2989999999999999, 3.9929999999999999],\n",
       " [95, 4.0, 3.7330000000000001, -1.421, 3.9940000000000002],\n",
       " [96, 4.0, 3.843, 1.0429999999999999, 3.9820000000000002],\n",
       " [97, 4.0, 1.6659999999999999, -3.6150000000000002, 3.9809999999999999],\n",
       " [98, 4.0, 3.9220000000000002, 0.78400000000000003, 3.9990000000000001],\n",
       " [99, 4.0, 3.5720000000000001, -1.7949999999999999, 3.9980000000000002],\n",
       " [100, 4.0, 3.1469999999999998, -2.4670000000000001, 3.9990000000000001]]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Conclusions:\n",
    "    1. It is visible that the value of a determines the distance form point of origin. \n",
    "        The constraint pushes the minimum inwards this point\n",
    "    2. The optimization with constraints is very effective, since the constraints might \n",
    "        push the minimum in the correct direction very quickly, not distrubing the result \n",
    "        at the same time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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