EQP_problems.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-06-02T17:51:27.472413",
     "start_time": "2017-06-02T17:51:27.268040Z"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pycutestmgr as cute\n",
    "import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.sparse import csc_matrix\n",
    "from ipsolver import eqp_kktfact, projections, projected_cg\n",
    "from numpy.testing import (TestCase, assert_array_almost_equal,\n",
    "                           assert_array_equal, assert_array_less,\n",
    "                           assert_raises, assert_equal, assert_,\n",
    "                           run_module_suite, assert_allclose, assert_warns,\n",
    "                           dec)\n",
    "cute.clearCache('HS71')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-06-02T17:55:34.686537",
     "start_time": "2017-06-02T17:51:27.473843Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CVXQP1_S\n",
      "CVXQP2_S\n",
      "CVXQP3_S\n",
      "CVXQP1_M\n",
      "CVXQP2_M\n",
      "CVXQP3_M\n",
      "CVXQP1_L\n",
      "CVXQP2_L\n",
      "CVXQP3_L\n",
      "CONT-050\n",
      "CONT-100\n",
      "DPKLO1\n",
      "MOSARQP1\n",
      "DUAL1\n",
      "DUAL2\n",
      "DUAL3\n",
      "DUAL4\n",
      "PRIMAL1\n",
      "PRIMAL2\n",
      "LASER\n"
     ]
    }
   ],
   "source": [
    "list_names = (\"CVXQP1_S\",\n",
    "              \"CVXQP2_S\",\n",
    "              \"CVXQP3_S\", \n",
    "              \"CVXQP1_M\",\n",
    "              \"CVXQP2_M\",\n",
    "              \"CVXQP3_M\",\n",
    "              \"CVXQP1_L\",\n",
    "              \"CVXQP2_L\",\n",
    "              \"CVXQP3_L\",\n",
    "              \"CONT-050\",\n",
    "              \"CONT-100\",\n",
    "              \"DPKLO1\",\n",
    "              \"MOSARQP1\",\n",
    "              \"DUAL1\",\n",
    "              \"DUAL2\",\n",
    "              \"DUAL3\",\n",
    "              \"DUAL4\",\n",
    "              \"PRIMAL1\",\n",
    "              \"PRIMAL2\",\n",
    "              \"LASER\")\n",
    "n = len(list_names)\n",
    "\n",
    "kkt_time = np.zeros(n)\n",
    "factorization_time_ne = np.zeros(n)\n",
    "cg_time_ne = np.zeros(n)\n",
    "factorization_time_as = np.zeros(n)\n",
    "cg_time_as = np.zeros(n)\n",
    "constr_ne = np.zeros(n)\n",
    "constr_as = np.zeros(n)\n",
    "constr_kkt = np.zeros(n)\n",
    "opt_ne = np.zeros(n)\n",
    "opt_as = np.zeros(n)\n",
    "opt_kkt = np.zeros(n)\n",
    "niter_ne = np.zeros(n)\n",
    "niter_as = np.zeros(n)\n",
    "\n",
    "k = 0\n",
    "for name in list_names:\n",
    "    print(name)\n",
    "    cute.prepareProblem(name)\n",
    "    problem=cute.importProblem(name)\n",
    "    info = problem.getinfo()\n",
    "    x0 = info[\"x\"]\n",
    "    G = problem.ihess(x0)\n",
    "    f, c = problem.obj(x0, True) \n",
    "    b, A = problem.cons(x0, True)\n",
    "\n",
    "    G = csc_matrix(G)\n",
    "    A = csc_matrix(A)\n",
    "\n",
    "    start_time = time.time()\n",
    "    x, lambd = eqp_kktfact(G, c, A, b)\n",
    "    kkt_time[k] = time.time() - start_time\n",
    "\n",
    "    start_time = time.time()\n",
    "    Z, _, Y = projections(A, method='NormalEquation')\n",
    "    factorization_time_ne[k] =  time.time() - start_time\n",
    "\n",
    "    start_time = time.time()\n",
    "    x_ne, info_ne = projected_cg(G, c, Z, Y, b, tol=1e-20)\n",
    "    cg_time_ne[k] = time.time() - start_time\n",
    "\n",
    "    start_time = time.time()\n",
    "    Z, _, Y = projections(A, method='AugmentedSystem')\n",
    "    factorization_time_as[k] = time.time() - start_time\n",
    "\n",
    "    start_time = time.time()\n",
    "    x_as, info_as = projected_cg(G, c, Z, Y, b, tol=1e-20)\n",
    "    cg_time_as[k] = time.time() - start_time\n",
    "\n",
    "    \n",
    "    constr_kkt[k] =  np.linalg.norm(A*x -b)\n",
    "    constr_ne[k] =  np.linalg.norm(A*x_ne -b)\n",
    "    constr_as[k] = np.linalg.norm(A*x_as-b)\n",
    "\n",
    "    opt_kkt[k] =  np.linalg.norm(G*x-A.T*lambd+c)\n",
    "    opt_as[k] =  np.linalg.norm(G*x_as-A.T*lambd+c)\n",
    "    opt_ne[k] = np.linalg.norm(G*x_ne-A.T*lambd+c)\n",
    "    \n",
    "    niter_as[k] = info_as['niter']\n",
    "    niter_ne[k] = info_ne['niter']\n",
    "    \n",
    "    k += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-06-02T18:00:08.452541",
     "start_time": "2017-06-02T18:00:07.946129Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3369ed7a50>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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vmU6TySRpt5Nz55LhMNnYWHZ1AMBRVmqty66h8c6cOVPPnz+/7DJYQZvPbab3TC/TOs3k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\nSVKlWMRIkiRJqhSLGEmSJEmV8v9LmsySEADM/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f336a00ccd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "ax = plt.gca()\n",
    "ax.scatter(constr_ne, opt_ne, s=50, color='blue', label='Normal Equation')\n",
    "ax.scatter(constr_as, opt_as, s=50, color='green', label='Augmented System')\n",
    "ax.scatter(constr_kkt, opt_kkt, s=50, color='black', label='Direct Factorization')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim([1e-20, 1e10])\n",
    "ax.set_ylim([1e-20, 1e10])\n",
    "ax.set_xlabel(r\"$\\||A x^*-b\\||$\", fontsize=30)\n",
    "ax.set_ylabel(r\"$\\|\\|\\nabla_x \\mathcal{L}\\|\\|$\", fontsize=30)\n",
    "ax.legend(fontsize=30, loc=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-06-02T18:01:15.543577",
     "start_time": "2017-06-02T18:01:14.977401Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.text.Text at 0x7f3369a2e550>,\n",
       " <matplotlib.text.Text at 0x7f3369c41910>,\n",
       " <matplotlib.text.Text at 0x7f33699fb6d0>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QYgEAABgMJRYAAIDBUGIBAAAYDCUWAACAwVBiAQAAGAwl9ghV1ddV1bSqfqDrLAAAAMeB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\nAABAzyCIBQAAAAD0DIJYAAAAAEDP+P/uz/mLf0ByIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3369a57b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "ax = plt.gca()\n",
    "ax.scatter(np.ones(n), factorization_time_ne+cg_time_ne, s=20, color='blue', label='Normal Equation')\n",
    "ax.scatter(2*np.ones(n), factorization_time_as+ cg_time_as, s=20, color='green', label='Augmented System')\n",
    "ax.scatter(3*np.ones(n), kkt_time, s=20, color='black', label='Direct Factorization')\n",
    "ax.set_ylabel(r\"Total Time\", fontsize=30)\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim([1e-4, 1e4])\n",
    "ax.set_xticks([1, 2, 3])\n",
    "ax.set_xticklabels(['Normal Equation', 'Augmented System', 'Direct Factorization'], fontsize=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-06-02T18:00:29.921009",
     "start_time": "2017-06-02T18:00:29.273881Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.text.Text at 0x7f3369e78a50>,\n",
       " <matplotlib.text.Text at 0x7f3369e21310>,\n",
       " <matplotlib.text.Text at 0x7f3369dea410>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sj61c/BlJjkw/qyT/OckXdPcf7n9aAAAAZmUsM7Hp7q0kz6+qz0vy15J8UZKVJLck+ZMk\n9yb52SQ/1N0/N1ROAAAAZmc0Jfai7n5rkrdefF9VH9fdDwwYCQAAgH0yituJH4wCCwAAcOMYfYkF\nAADgxqHEAgAAD9vW1lbOnDmTra2toaNwwI3mmdiquinJ85M8L8nTk3xikkfs4NLu7s+aZTYAALiR\nbWxsZG1tLYcPH8758+ezvr6eEydODB2LA6q6+6HPGlhVPTPJv0/ymbu9NJMSe9Pep9p7q6urffbs\n2aFjAADAjm1tbWV5eTnnzp376NjCwkLuvvvuLC0tDZKpqu7s7tVBfjkzN/czsVW1kuRNSR6VSSlN\nkgeS/GGSDw+Tam9V1fEkx2+99dahowAAwK5sbm7m8OHDl5XYQ4cOZXNzc7ASy8E29yU2yT9JciRJ\nZ7IP7HckeWt3/8mgqfZQd59Ocnp1dfUlQ2cBAIDdWFlZyfnz5y8bu3DhQlZWVoYJxIE3hoWdvjyT\nAvtLSb6su990kAosAACM2dLSUtbX17OwsJAjR45kYWEh6+vrZmGZmTHMxD5meny1PWEBAGD+nDhx\nIkePHs3m5mZWVlYUWGZqDCX2d5M8MckfDB0EAAC4uqWlJeWVfTGG24nvnB6tegQAAHCDG0OJ/f5M\nViX+hqoaw8wxAAAAMzL3Jba735zknyd5apJ/V1WPGDYRAAAAQxnFzGZ3//2q2s5ku53Pr6pXJ3lb\nkvdnsmfsQ13/ttkmBAAAYD+MosRO/UySFyX5s0n+0S6u64zr3wkAAMA1zP3txElSVX8/yc8neUYm\npbR2+QIAAOAAmPsZyqr68iTfc8nQ3Ul+IcnvJfnwIKEAAAAYxNyX2CR/b3q8P8lLu/sHhwwDAADA\ncMZwO/FnZ3IL8asUWAAAgBvbGErsLdPjm4cMAQAAwPDGUGLfOz3eNGgKAAAABjeGEntHJisMf/7Q\nQQAAABjWGErsy5N8MMmLq+qpQ4cBAABgOHNfYrv7niRfncl2Om+qquMDRwIAAGAgc7/FTlW9cvrj\n2SRHk/xYVb03yZkk70/ywEN8RXf3N88wIgAAAPtk7ktskpdlssVOpsdK8oTpa6eUWAAAgANgDCU2\nmRTXB3v/YPqhTwEAAGAMxlBinzZ0AAAAAObD3JfY7r5r6AzXq6o+Pck/TLLY3V8zdB4AAICxm/vV\niedNVb2qqt5XVe+4Yvy2qrqrqt5dVd+aJN39nu5eGyYpAADAwaPE7t6rk9x26UBV3ZTkFUmen+Tp\nSU5U1dP3PxoAAMDBpsTuUne/JckHrhh+TpJ3T2dezyd5bZLbd/J9VXWyqs5W1dmtra09TgsAAHCw\nzM0zsVX1nIs/d/fbrjZ+vS79vhl5XJL3XvL+niTPrarHJPmuJM+sqm/r7u++SrZTSU4lyerqqpWU\nAQAAHsTclNgkv5jJdjidy3NdHL9eV37fvunu92eyzy0AAAB7YJ5KbHLt/V93sy/sEO5N8oRL3j9+\nOgYAAMAemqcS+727HJ8nZ5I8paqelEl5/bokf2WnF1fV8STHb7311hnFAwAAOBiq22OYu1FVG0m+\nNMknJ/m9JP9nd69X1V9M8vIkNyV5VXd/126/e3V1tc+ePbuXcQEA4IZTVXd29+rQOZiNeZqJHYXu\nPnGN8TuS3LHPcQAAAG4oc7XFTlXdMX09d+gsAAAAzJ+5KrFJbkvyvCSfMnQQAAAA5s+8ldgbUlUd\nr6pT29vbQ0cBAACYa0rsHOju0919cnFxcegoAAAAc02JBQAAYDSUWAAAAEZDiQUAAGA05rXE9tAB\n9pOFnQAAAHamuuenL1bVA5kU2AtJHtijr+3uvmWPvmumVldX++zZs0PHAACAUauqO7t7degczMbN\nQwe4hsN78B2dpHKDzeoCAAAcZPN6O/FeqKEDAAAAsLfmdSb2Lyf5iaFDAAAAMF/mtcRe6O4PDx0C\nAACA+XKQbyceDasTAwAA7IwSOwe6+3R3n1xcXBw6CgAAwFxTYgEAABgNJRYAAIDRUGIBAAAYjXlb\nnfhtSTrJB4YOAgAAwPyZqxLb3Z87dAYAAADml9uJ54AtdgAAAHZGiZ0DttgBAADYGSUWAACA0VBi\nAQAAGA0lFgAAgNFQYgEAABgNJRYAAIDRUGIBAAAYDSV2DtgnFgAAYGeU2Dlgn1gAAICduXnoALtV\nVY9J8vQkn5jkETu5prtfN9NQAAAA7IvRlNiq+rokfy/JM3d5aSdRYgEAAA6AUZTYqvqBJCcvvh0y\nCwAAAMOZ+xJbVV+T5KWXDN2Z5GeS3Jvkw4OEAgAAYBBzX2LzsRnY+5N8Q3e/dsgwAAAADGcMqxM/\nK5PnWl+twAIAANzYxlBib5ke3zxkCAAAAIY3hhL729NjD5oCAACAwY2hxL5pevzsQVMAAAAwuDGU\n2H+Z5EKStap69NBhZqGqjlfVqe3t7aGjAAAAzLW5L7Hd/fYk/2uSxyT5yar6tIEj7bnuPt3dJxcX\nF4eOAgAAMNfmfoudqnpRkg8meV2Sr03yrqr60SS/mOT3kzzwUN/R3a+baUgAAAD2xdyX2CSvzccW\ndeokC0lOTF870ZkUYAAAAEZuDCU2Seoh3gMAAHADGEOJ/aahAwAAADAf5r7Edve/HToDAAAA82Hu\nVycGAACAi5RYAAAARmPubye+lqo6nOTPJHlUkj9K8r7uPj9sKgAAAGZpVCW2qj4pycuSvDDJZye5\n6ZKPP1JVv5Lk9UlOdfcHBogIAADADI3mduKqemGSdyX5Z0memUkBr0teN0/HvyvJu6rqLw0UFQAA\ngBkZxUxsVX1tkh/OxwprkvzPJL+R5ENJHpnkKUk+ffrZJyb5j1V1orv/4z7HBQAAYEbmvsRW1Z9J\nciqTWeNOsp7ke7v73Vc598lJ/kGSten5/09Vvbm7t/YxMgAAADMyhtuJvzmTxZs6yTd190uuVmCT\npLt/s7tPJjk5HXrk9HoAAAAOgDGU2NsyKbA/3d2ndnJBd68neWMmtx4/f4bZAAAA2EdjKLEXn3P9\n0V1e92PT45P3MMtMVNXxqjq1vb09dBQAAIC5NoYS+6jpcbdb5lw8/5F7mGUmuvt0d59cXFwcOgoA\nAMBcG0OJff/0+OkPetafdvF8+8UCAAAcEGMosb+SybOtf72qdrSa8vS8b8jkWdr/McNsAAAA7KMx\nlNiLz7Y+Ncl6VR16sJOr6qYk/3eSp02HdvssLQAAAHNqDCX2VUl+c/rzX03y9qp6aVVddntxVT2p\nqk5mMnN7cRb2N6fXAwAAcADs6PbcIXX3haq6PcnPJfnEJE9J8sokqaoHkvxxkk/I5YW8kvxBktu7\n+/79TQwAAMCsjGEmNt39a0lWk/xsJgX14uumTFYvvumK8TcleVZ3v3OQwAAAAMzE3M/EXtTd/zPJ\nn6+qZyd5YZLnJHlsJiX2j5L8TpK3Jfl/u/vsYEEBAACYmdGU2Iu6+0ySM0PnAAAAYP+N4nZiAAAA\nSJRYAAAARkSJBQAAYDTm5pnYqnrl9Mfu7m++yvj1uuz7AAAAGK+5KbFJXpakpz9/8zXGr5cSCwAA\ncADMU4lNJnu8Xq2w1sP4zodbgAEAAJgT81Rin7bLcQAAAG4wc1Niu/uu3YwDAABw47E6MQAAAKMx\nNzOx11JVz5n+eFd3b+/iukdleityd79tFtkAAADYX2OYif3FJG9N8iW7vO7zp9f+wp4nAgAAYBBj\nKLEP18NZ2RgAAIA5cpBL7MXyaosdAACAA2Lun4l9GB4zPd43xC+vqluSvDLJ+SRv7u4fHiIHAADA\nQXIgZ2Kr6uYkXz99+1t7+L2vqqr3VdU7rhi/raruqqp3V9W3TodfmOT13f2SJF+5VxkAAABuZHM1\nE1tVX5+Plc8r/ZOqetlDfUWSW5J8VpJHZ3Ir8c/sXcK8Osn3J3nNR39h1U1JXpHkWJJ7kpypqjck\neXySt09P+8geZgAAALhhzVWJTXJrktvyp59jrSTP3MX3XHwe9gNJ/vke5EqSdPdbqmrliuHnJHl3\nd78nSarqtUluz6TQPj7Jf8+DzHhX1ckkJ5PkiU984l5FBQAAOJDm9XbiuuR1tbEHe92f5DeS/ECS\nP9fd751x1sclufR33DMd+09JvrqqfiDJ6Wtd3N2nunu1u1eXlpZmmxQAAGDk5m0m9juTfM8l7yvJ\nH2cyM/uiJD/xENc/0N0XZpRtV7r7viTfOHQOAACAg2SuSmx3fyRXPD9aVcmkzF7o7g8Pkesh3Jvk\nCZe8f/x0DAAAgD02VyX2Ghamx/ODpri2M0meUlVPyqS8fl2SvzJsJAAAgINpXp+J/aju/vD0deVi\nT/uuqjaSvDXJU6vqnqpa6+77k3xLkjcmeWeS13X3r+7ye49X1ant7e29Dw0AAPtga2srZ86cydbW\n1tBROOBqDrohU6urq3327NmhYwAAwK5sbGxkbW0thw8fzvnz57O+vp4TJ04Mlqeq7uzu1cECMFOj\nK7FV9clJnp3Js6dHktz0UNd09/8161x7QYkFAGBstra2sry8nHPnzn10bGFhIXfffXeG2n1DiT3Y\nxvBMbJKkqj47yXcneV4u33pnJ0ZRYgEAYGw2Nzdz+PDhy0rsoUOHsrm5OViJ5WAbRYmtqhck+Y9J\nPj4PXWD7inPmfqq5qo4nOX7rrbcOHQUAAHZlZWUl589fvgbrhQsXsrKyMkwgDry5X9ipqpaS/EiS\nRyT5cCazql81/biTfHuSr0nyd5P81CXjr0ny/CR/cT/zXo/uPt3dJxcXF4eOAsCD2LpvK2fuPZOt\n+yxaAnDR0tJS1tfXs7CwkCNHjmRhYSHr6+tmYZmZMczE/s0kj8qkmH5Vd/9U8tH9Y5Pkv3X3G6Y/\n/4uq+rwkr0vy15L8Snd/3z7nBeAA2nj7RtbesJbDNx3O+Y+cz/rt6znxjOEWLQGYJydOnMjRo0ez\nubmZlZUVBZaZmvuZ2CRfPj2+5WKBfTDd/dbpNeeTfE9VPWuW4QA4+Lbu28raG9Zy7v5z2f7wds7d\nfy5rP75mRhbgEktLS3n2s5+twDJzYyixn5HJLOwbr/H5oSsHuvudSX44k5nml84uGgA3gs0Pbubw\nTYcvGzt006FsfnBzmEAAcAMbQ4m9+KDob10xfvHp8Vuucd3PTY9futeB9lpVHa+qU9vb20NHAeAq\nVh69kvMfuWLRko9cyMqjV4YJBAA3sDGU2D+ZHu+/YvwPp8cnXOO6i+d/2p4n2mMWdgKYb0u3LGX9\n9vUs3LyQIx9/JAs3L2T99vUs3eKWOQDYb2NY2Om3kjwtyZV/Kbw7yWOSfO41rnvGLEMBcGM58YwT\nOfqko9n84GZWHr2iwALAQMYwE/s/psfPumL8v2ayH+zzquqyz6rqcUlelsmztO+aeUIAbghLtyzl\n2Y97tgILAAMaQ4l9cyZl9S9cMf5DmZTUm5K8paq+vaq+oaq+Pcl/y8eepX39fgUFAABgtsZQYn88\nyQNJnlJVz7442N3vSPKvMym4j07yj5L84PT4mOlpv57k5fuaFgAAgJmZ+xLb3e9L8meTPCvJ5hUf\n/50k35XJSsV1xeuOJH++u/9438JeJ6sTAwAA7Ex199AZHraqelSSL0zyKUn+OMnZ7n7PsKl2b3V1\ntc+ePTt0DAAAGLWqurO7V4fOwWyMYXXih9Tdf5TkJ4fOAQAAwGzN/e3EAAAAcNHcz8RW1SunP34w\nyT/r7nM7vO6zM91mp7u/eVb5AAAA2D9zX2Lzsf1ek8mesF/Z3ffu4LonXXKtEgsAAHAAjOl24kry\nOUnOXLrVDgAAADeOMZXYX86kyH5qkjdX1dcOnGfP2GIHAABgZ8ZUYr8jyd9Kcn+ShSQ/UlX/dNBE\ne6S7T3f3ycXFxaGjAAAAzLUxldh09yuSvCCTRZ4qyT+uqtdW1SOGTQYAAMB+GFWJTZLu/ukkn5/k\nNzMpsn85yc9W1WMHDQYAAMDMja7EJkl3/3qS5yT52UyK7GqSX6qqZw4aDAAAgJkaZYlNku7+gyTH\nkqxnUmQfn+TnquqFgwYDAABgZkZbYpOku+/v7pck+XtJHkjyCUleV1X/cNhkAAAAzMLNQwfYC939\nfVV1V5IfSfKoTFYy/o1hUwEAALDXRj0Te6nu/s9JviDJb2Vye/FnDJsIAACAvXZgSmySdPc7Mlnk\n6RcyKbL83onLAAAgAElEQVSjUFXHq+rU9vb20FEAAADm2hhuJ37a9HjPTk7u7t+vqr+Q5H9Psjiz\nVHuou08nOb26uvqSobMAAADMs7kvsd1913Vccz7J98wgDgAAAAM6ULcTAwAAcLApsQAAAIzG3NxO\nXFUvuvhzd7/uauPX69LvAwAAYLzmpsQmeW2Snr5ed5Xx63Xl9wEAADBS81Rik2tvizOa7XIAAACY\nnXkqsd+0y3EAAABuMHNTYrv73+5mHAAAgBuP1YkBAAAYjbmZib2Wqnrl9Md3dPcrH/Tkkaqq40mO\n33rrrUNHAQAAmGtjmIl9WZKXJjk8dJBZ6e7T3X1ycXFx6CgAAABzbQwl9gPT4z2DpgAAAGBwYyix\nm9PjY4YMAQAAwPDGUGJ/LJN9Yp83dBAAAODqtra2cubMmWxtbQ0dhQNuDCX2lUl+J8ntVfUVQ4cB\nAAAut7GxkeXl5Rw7dizLy8vZ2NgYOhIH2NyX2O7+QJK/lOT3kry+qv5ZVX3qwLEAAIBMZmDX1tZy\n7ty5bG9v59y5c1lbWzMjy8yMYYudO6Y//m6ST03yfyT5tqp6T5J7k5x7iK/o7n7BDCMCAMANa3Nz\nM4cPH865cx/7s/zQoUPZ3NzM0tLSgMk4qOa+xCa5LUlPf754/LgkT56+AACAgaysrOT8+fOXjV24\ncCErKyvDBOLAm/vbiafqitfVxq71AgAAZmRpaSnr6+tZWFjIkSNHsrCwkPX1dbOwzMwYZmIXhg4A\nAABc24kTJ/I5n/M5edvb3pbnPOc5edrTnjZ0JA6wuS+x3f3hoTPcSLa2ks3NZGUl8T/PAADYiY2N\njaytreXw4cM5f/581tfXc+LEiaFjcUCN5XZi9sHGRrK8nBw7NjlaGR0AgIdidWL2mxJLkskM7Npa\ncu5csr09Oa6tTcYBAOBaLq5OfKmLqxPDLMz97cRXU1XPSPLcJI9N8qgkf5Tkt5O8rbvfMWS2sdrc\nTA4fnpTXiw4dmoy7rRgAgGuxOjH7bVQltqq+Mck/SPKUBznnXUm+p7tfvV+5Hq6qOp7k+K233jpY\nhpWV5Ir/9uTChck4AABcy8XVidfW1nLo0KFcuHDB6sTMVHX3Q581sKo6nOQ/JPnKi0MPcvrFf9Ab\nkryouy/MMtteWl1d7bNnzw72+zc2JrcQHzo0KbDr64nn8QEA2Imtra1sbm5mZWVl8AJbVXd29+qg\nIZiZsZTY1yT5q5cM/dckP5XkN5J8KMkjM5md/fIkXzg9p5P8cHd/wz5GfViGLrGJ1YkBABg/JfZg\nm/vbiavqizIpsJ3kniRf390/f43Tv7OqviDJv0+ynOTrq+rUg5zPFZaWlFcAAGB+jWF14hdPj/cl\n+dKHKqTd/V+TfFkmM7RJ8jdmFw0AAID9NIYS+8WZzMK+qrv/504u6O73JHlVJs/OftEMswEAALCP\nxlBiHzs9vm2X1108/1P3MAsAAAADGkOJvbjy1G6zPtgKxgAAAIzQGErs70yPz93ldZ97xfUAAACM\n3BhK7M9mMqv64qp68k4umJ734kxmcd8yu2gAAADspzGU2B+cHj8hyZuq6osf7OSq+sIk/1+SW6ZD\n6zPMBgAAwD6a+31iu/sXquo1Sb4hyeMyKbJnkvxUkt/IZOudW5I8JcmxfOy2407ymu5+6/6nBgAA\nYBbmvsROvSTJkSRfNX3/7Onrai4u6PSj0+sAAAA4IMZwO3G6+0J3vzDJNyb5tUyK6rVev5bkr3f3\nV3f3/QNFBgAAYAbGMhObJOnuH0ryQ1X11CTPyWQP2Ucl+aNMViF+W3ffNWBEAAAAZmhUJfaiaVFV\nVgEAAG4wc19iq+rPTH/8g+6+sIvrbk7ySUnS3e+bRTYAAAD21xieif3dJL+d5Pm7vO7LLrkWAACA\nA2AMJTb52IrD+30tAAAAc2QsJRYAAAAOdIldnB7/eNAUABwYW/dt5cy9Z7J139bQUQDghnWQS+zt\n0+O9g6YA4EDYePtGll++nGP/7liWX76cjXdsDB0JAG5Ic7U6cVW9IMkLrvHxy6rqtof6iiS3JHlm\nkqcn6SQ/v3cJAbgRbd23lbU3rOXc/edy7v5zSZK1H1/L0ScdzdItSwOnA4Aby1yV2CSrSV56lfFK\n8rxdflcl+ZMk3/dwQwFwY9v84GYO33T4owU2SQ7ddCibH9xUYgFgn83j7cR1xeta4w/2+pMkP5nk\nS7r71/Yt+RWq6tOrar2qXj9UBgAevpVHr+T8R85fNnbhIxey8uiVYQIBwA1s3krs9yd52iWvp0/H\nO8k3X/HZ1V5PTfK4JI/q7hd095nrDVJVr6qq91XVO64Yv62q7qqqd1fVtz7Yd3T3e7p77XozADAf\nlm5Zyvrt61m4eSFHPv5IFm5eyPrt62ZhAWAAc3U7cXe/P8n7Lx2r+uhk7L3dfdc+xnl1JqX6NZdk\nuSnJK5IcS3JPkjNV9YYkNyX57iuu/xvd/b79iQrArJ14xokcfdLRbH5wMyuPXlFgAWAgc1Vir+Fp\n0+M9+/lLu/stVbVyxfBzkry7u9+TJFX12iS3d/d3J/mK6/k9VXUyyckkeeITn3jdeQGYvaVblpRX\nABjYvN1O/Kd0913T131DZ8nkVuX3XvL+nunYVVXVY6rq3yR5ZlV929XO6e5T3b3a3atLS/4wAgAA\neDBjmIlNVT07kwWb3tvdv7OD8x+b5AlJHujus7POdy3T26NfNtTvBwAAOGjmfia2qr4kyS8leWse\nZNbzCp+W5BeT/GJVfe4exrk3k3J80eOnYwAAAOyDuS+xSb56enz7TmdVu/vOJP8tk9nbF+1hljNJ\nnlJVT6qqw0m+LskbHu6XVtXxqjq1vb39sAMCAAAcZGMosZ+fyRY7/2WX170xkxL7BdfzS6tqI5PZ\n36dW1T1Vtdbd9yf5lul3vzPJ67r7V6/n+y/V3ae7++Ti4uLD/SoAAIADbQzPxD55evy1XV7369Pj\nrdfzS7v7xDXG70hyx/V8JwAAAA/PGGZib5ked7s68cXzH7WHWQAAABjQGErsB6fH3e4/c/H8D+1h\nlpnwTCwAAMDOjKHE/tb0+CW7vO5Lp8d79i7KbHgmFgAAYGfGUGLflMkCTS+sqs/YyQVV9ZlJXpjJ\nglA/M8NsAAAA7KMxlNj1JA9ksgjVT1TVgy7UVFVPyWTbm5szKbHrM08IAADAvpj7Etvdv57k32Yy\nG/vkJP+9qr6/qp5XVU+sqk+aHp9XVa/IZH/YJ2daYLv77cOlBwAAYC+NYYudJPnbmRTTL0+ykOSb\npq+rqenxvyT55tlHe/iq6niS47feel27AQEAANww5n4mNkm6+/4kfzHJP81kteF6kNcfJvknSb5i\net3cs7ATAADAzoxlJjbd/UCS76iqf5nkeJIvTPL4JEcyKa73JPm5JKe7+w8HCwoAAMDMjKbEXtTd\n20n+/fQFAADADWQUtxMDAABAosQCAAAwIkrsHKiq41V1ant7e+goAAAAc21Uz8RW1WOTnEjy3Hxs\nUaebHuKy7u7PmnW2h6O7Tyc5vbq6+pKhswAAAMyzUZTYqvq4JN+Z5O/m8swX94Ttq4zlKp8BAAAw\nYqMosUl+IMn/ko8V1A8meXQmBXU7k3/HIy85v5P8fpIH9jEjAAAAMzb3z8RW1ecluXib7S8leVp3\nf9Ilp7y4u48k+eQkX5/kVzIpu2eTfGZ3P3Y/8wIAADA7c19iM5mBTZJzSY53911XO6m7P9DdG0lW\nk2wkuS3Jf9qfiAAAAOyHMZTYL8jk9uAf6e7ff6iTu/v+JN+YZDPJl1bVX5ttPAAAAPbLGErsxduB\n336Nzx9x5UB3n0/y6kxuK/762cTaO7bYAQAA2JkxlNiF6fG3rxi/b3r8xGtc9xvT41xvr5NMttjp\n7pOLi4tDRwHgQWzdt5Uz957J1n1bQ0cBgBvWGErsB6fHK2dc3z89PuUa110st0t7ngiAG87G2zey\n/PLlHPt3x7L88uVsvGNj6EgAcEMaQ4m9OKO6fMX4OzK5Xfh517ju6PT4h7MIBcCNY+u+ray9YS3n\n7j+X7Q9v59z957L242tmZAFgAGMosW/LpKw+64rxO6bHp1fVt136QVW9NMkLM1kQ6szMEwJwoG1+\ncHNX4wDA7IyhxP709PhlVXX4kvEfTvK+6c/fWVWbVfUzVXV3kldect4r9iMkAAfXIw8/MufuP3fZ\n2Ln7z+WRhx85UCIAuHGNpcT+UiZb5nzRxcHu3k7yDUnOZzJT+8QkX5Lk8dP3SfIvuvuOAMDD8KHz\nH8rCTQuXjT3ipkfkQ+c/NFAiALhx3Tx0gIcy3ff1867x2U9V1bOS/OMkX5bkk5N8OJNbiP91d79+\n34ICcGCtPHrlY/97dKqqJuMAwL4aw0zsg+rud3b3X+nuT0lyqLs/obu/RIEFYK8s3bKU9dvXs3Dz\nQo58/JEs3LyQ9dvXs3SLBfABYL9Vdw+d4YZXVceTHL/11ltf8q53vWvoOABcw9Z9W9n84GZWHr2i\nwALMsaq6s7tXh87BbCixc2R1dbXPnj07aIatrWRzM1lZSZb8fQYAwAgpsQfbXN1OXFXfN3191tBZ\nbkQbG8nycnLs2OS4sTF0IgAAgMvNVYlN8r8l+dtJnnytE6rqVdPX5+xfrINvaytZW0vOnUu2tyfH\ntbXJOAAAwLyYtxK7Ey9O8tcz2VKHPbK5mRw+fPnYoUOTcQAAgHkxxhLLDKysJOfPXz524cJkHAAA\nYF4osSSZLOK0vp4sLCRHjkyO6+sWdwIAAObLzUMHYH6cOJEcPWp1YgAAdm9rayubm5tZWVnJkj8k\nmSEzsVxmaSl59rMVWAAAdm5jYyPLy8s5duxYlpeXs2GbC2ZIiQUAAK7b1tZW1tbWcu7cuWxvb+fc\nuXNZW1vLlm0umBElFgAAuG6bm5s5fMU2F4cOHcqmbS6YkXktsb1H54xCVR2vqlPb29tDRwEAgF1Z\nWVnJ+Su2ubhw4UJWbHPBjMxrif2xqvrI1V7Tz+vBzrnidf+Q/5Cd6O7T3X1ycXFx6CgAALArS0tL\nWV9fz8LCQo4cOZKFhYWsr69b3ImZmefViesa472DcwAAgH1y4sSJHD161OrE7It5LLEPVUwVVwAA\nmDNLS0vKK/tirkpsd8/r7c0AAADMAaURAACA0VBiAQAAGA0lFgAAgNFQYgEAABgNJRYAAHjYtra2\ncubMmWxtbQ0dhQNOiQUAAB6WjY2NLC8v59ixY1leXs7GxsbQkTjAqruHzsDU6upqnz17dugYAACw\nY1tbW1leXs65c+c+OrawsJC77757sH1jq+rO7l4d5Jczc2ZiAQCA67a5uZnDhw9fNnbo0KFsbm4O\nE4gDT4kFAACu28rKSs6fP3/Z2IULF7KysjJMIA48JRYAALhuS0tLWV9fz8LCQo4cOZKFhYWsr68P\ndisxB9/NQwcAAADG7cSJEzl69Gg2NzezsrKiwDJTSuwcqKrjSY7feuutQ0cBAIDrsrS0pLyyL9xO\nPAe6+3R3n1xcXBw6CgAAwFxTYgEAABgNJZbLbG0lZ85MjgAAAPNGieWjNjaS5eXk2LHJcWNj6EQA\nAACXU2JJMpl5XVtLzp1Ltrcnx7U1M7IAAMB8UWJJkmxu/umx7quPAwAADEWJJUnyyEdOZl8v9Sd/\nMhkHAACYF0osSZIPfShZWLh8bGFhMg4AADAvlFiSJCsruxsHAIBLbW1t5cyZM9myqAozpsSSJFla\nStbXJ7OvR45Mjuvrk3EAJrbu28qZe89k6z5/oAFcamNjI8vLyzl27FiWl5ezYZsLZqi6e+gMTK2u\nrvbZs2cHzbC1NVnMaWVFgQW41MbbN7L2hrUcvulwzn/kfNZvX8+JZ5wYOhbA4La2trK8vJxzlyyw\nsrCwkLvvvjtLA/1BWVV3dvfqIL+cmTMT+/+3d+dxjlVl/se/j91VEhqrmyU4CJIg4MLgglajDoqo\nXQpii+JGOSINpa2O6zguOPpTnHEZt7FFUUDDNKAGxRUUFVtpFddqaBFUNiEl4BaQLqBJU9XN8/vj\n3HRuUslNqiupJNWf9+tVr0puTk5Obu5ynnvOPQdV0mlp+XICWACIK24uauyiMZW2ljR536RKW0sa\n+9YYLbIAIKlQKGhwcLBq2cDAgApMc4EOIYgFAKCJwqaCBhfVVNAWDaiwqdCdAgFAD8lms5qamqpa\nNj09rSyDq6BDCGIBAGgiuyyrqW01FbRt08ouy3anQADQQ9LptHK5nFKplIaGhpRKpZTL5brWlRgL\nH0EsAABNpJeklTsup9TilIYeOKTU4pRyx+WUXkIFDQAkaXR0VBMTE1q3bp0mJiY0OsqYAegcBnbq\nIb0wsBMAoLHi5qIKmwrKLssSwAJAD2Ngp4WNllgAAAAAQN8giAUAoAX5q/PKrMlo5PwRZdZklL+G\nORABAOgGglgAAJpgih0AAHoHQSwAAE0wxQ4ANFcsFjU+Pq5ikQt86CyCWAAAmmCKHQBIls/nlclk\nNDIyokwmo3yeWy7QOQSxAAA0wRQ7ANBYsVjU2NiYSqWSJicnVSqVNDY2RossOmZxtwuwkJnZ8yUd\nK2lIUs7dL+1ykQAAO2j00FGtOGAFU+wAQI1CoaDBwUGVSqXtywYGBlQoFJROc6xE+9ES24CZnWNm\nfzeza2qWH21m15nZjWZ2alIe7v5Nd3+VpNdIemknywsA6Lz0krSW77ucABYAYrLZrKamam65mJ5W\nNpvtToGw4BHENrZW0tHxBWa2SNIZko6RdIikUTM7xMwebWbfrvnbO/bWd0fvAwD0seLmosZvG2dU\nYgCISafTyuVySqVSGhoaUiqVUi6XoxUWHWPu3u0y9Cwzy0r6trsfGj1/sqTT3P3Z0fN3SpK7f6jB\n+03S/0j6gbuva5BmtaTVkrT//vs/YWJios3fAgDQDvmr8xq7aEyDiwY1tW1KueNyGj10tNvFAoCe\nUSwWVSgUlM1mux7AmtkV7j7c1UKgY2iJnZ19Jd0Se35rtKyRN0haIelFZvaaegnc/Wx3H3b34W7v\n7ACA+pgnFgCaS6fTWr58edcDWCx8DOzUQe5+uqTTu10OAMDclOeJLW2NDVoSzRPL/bEAAMwvWmJn\n5zZJD4093y9aBgBYwJgnFgCA3kEQOzvjkg42swPMbFDSCZIummumZrbSzM6enJyccwEBAO3HPLEA\n0FyxWNT4+Djzw6LjGNipATPLSzpK0l6S/ibpve6eM7PnSFojaZGkc9z9A+36zOHhYd+wYUO7sgMA\ntFlxc5F5YgGgjnw+r7GxMQ0ODmpqakq5XE6jo90b/I6BnRY2gtgeQhALAL2NIBYAZioWi8pkMiqV\nKuMGpFIpTUxMdG2QJ4LYhY3uxAAAtCB/dV6ZNRmNnD+izJqM8tfku10kAOgJhUJBg4ODVcsGBgZU\nKBS6UyAseASxAAA0wRQ7ANBYNpvV1FTN4HfT08pms90pEBY8gtgewMBOANDbylPsxJWn2AGAnV06\nnVYul1MqldLQ0JBSqZRyuRzzxaJjuCe2h3BPLAD0puLmojJrMlXzxKYWpzTx5gnujQWASLFYVKFQ\nUDab7XoAyz2xCxstsQAANMEUOwDQXDqd1vLly7sewGLhW9ztAgAA0A9GDx3VigNWMDoxAABdRkss\nAAAAAKBvEMT2AAZ2AoDexxQ7AAD0BgZ26iEM7AQAvYmBnQCgvzCw08JGSywAAE0wxQ4AAL2DIBYA\ngCayy7Ka2jZVtWx627Syy7LdKRAAADsxglgAAJpgih0AaK5YLGp8fFzFYrHbRcECxxQ7AAC0gCl2\nAKCxfD6vsbExDQ4OampqSrlcTqOjo90uFhYoBnbqAWa2UtLKgw466FU33HBDt4sDAAAAtKxYLCqT\nyahUig1+l0ppYmJC6XR3LvgxsNPCRnfiHuDuF7v76qVLl3a7KAAAAMCsFAoFDQ7WDH43MKBCodCd\nAmHBI4gFAAAAsMOy2aympmoGv5ueVjab7U6BsOARxAIAAADYYel0WrlcTqlUSkNDQ0qlUsrlcl3r\nSoyFj4GdAAAAAMzJ6OioVqxYoUKhoGw2SwCLjiKIBQAAADBn6XSa4BXzgu7EAAAAAIC+QRDbA8xs\npZmdPTk52e2iAAAAAEBPI4jtAb00xU6xKI2Ph/8AAAAA0GsIYrFdPi9lMtLISPifz3e7RAAAAOgX\nxWJR4+PjKtIagg4jiIWk0PI6NiaVStLkZPg/NkaLLAAAAJrL5/PKZDIaGRlRJpNRntYQdBBBLCRJ\nhYI0OFi9bGAgLAcAAAAaKRaLGhsbU6lU0uTkpEqlksbGxmiRRccQxEKSlM1KU1PVy6anw3IAQFDc\nXNT4beMqbqZiBgBlhUJBgzWtIQMDAyrQGoIOIYiFJCmdlnI5KZWShobC/1wuLAcASPmr88qsyWjk\n/BFl1mSUv4aucgAgSdlsVlM1rSHT09PK0hqCDiGIxXajo9LEhLRuXfg/OtrtEgFAbyhuLmrsojGV\ntpY0ed+kSltLGvvWGC2yACApnU4rl8splUppyZIlSqVSyuVyStMagg4hiO0BvTRPbDotLV9OCywA\nxBU2FTS4qKar3KIBFTYVulMgAOhB7l71H+gUgtge0EvzxAIAZsouy6q0tVS1bMvWLcouy3anQADQ\nQ8oDO23ZskWbN2/Wli1bGNgJHUUQCwBAC/x+T3wOADsrBnbCfCOIBQCgicKmgnYd3LVqWWowRXdi\nABADO2H+EcQCANBEdllWU9tqKmjbpulODACqHthpaGiIgZ3QcQSxAAA0kV6SVu64nFKLUxp64JBS\ni1PKHZdTegkVNACQpNHRUU1MTGjdunWamJjQKNNcoIOM0cN6x/DwsG/YsKHbxQAANFDcXFRhU0HZ\nZVkCWADoYWZ2hbsPd7sc6IzF3S4AAAD9Ir0kTfAKAA0Ui0UVCgVls1m6EqOj6E4MAECLipuLGr9t\nXMXNTBsBAHH5fF6ZTEYjIyPKZDLK5/PdLhIWMLoT95Be6E5cLEqFgpTNSlxAA4CK/NV5jV00psFF\ng5raNqXccTmNHso9XwBQLBaVyWRUKlXm006lUpqYmOhaiyzdiRc2WmKxXT4vZTLSyEj4zwU0AAiK\nm4sau2hMpa0lTd43qdLWksa+NUaLLACIeWIx/whie4CZrTSzsycnJ7tWhmJRGhuTSiVpcjL8HxsL\nywFgZ1fYVNDgopoK2qIB5okFAIV5Yu+9996qZaVSiXli0TEEsT3A3S9299VLly7tWhkKBanmApoG\nBsJyANjZMU8sACQzs8TnQDsRxEJSuAd2qrp+punpsBwAdnbMEwsAjRUKBaVSqaplu+yyC92J0TFM\nsQNJYRCnXC50IR4YCAFsLsfgTgBQNnroqFYcsIJ5YgGgBt2JMd8IYrHd6Ki0YgWjEwNAI8wTCwD1\n0Z0Y84kgFlXSaYJXAAAAtK7cnXgqdm9auTtxt6bYwcLGPbGoUixK4+OMSgwAAIDWZLPZqgBWkqan\np+lOjI4hiMV2+by0//7S058e/jNPLAAAAJpJp9PK5XJKpVIaGhpSKpVSLpejFRYdY+7e7TIgMjw8\n7Bs2bOjKZxeL0r77hgGdygYGpNtuo3sxAAAAmisWiyoUCspms10PYM3sCncf7moh0DHcEwtJ0saN\n1QGsFJ5v3Cg961ndKRMAAAD6Rzqd7nrwip0D3YkhSdq0aXbLAQAAAKAbCGIhSVq2bHbLAQAAAKAb\nCGIhSTrssHAPbNzAQFgOAAAAAL2CIBaSwuBN554r7bKLtGRJ+H/uuQzqBAAAAKC3MLATthsdlVas\nkAoFKZslgAUAAADQe2iJBQAAAAD0DYLYHmBmK83s7MnJya6WI5+XMhlpZCT8z+e7WhwAAAAAmMHc\nvdtlQGR4eNg3bNjQlc8uFkPgWipVlqVS0sQE3YoBAADQX8zsCncf7nY50Bm0xEJSuA92cLB62cBA\nWA4AAAAAvYIgFpLCQE5TU9XLpqfDcgAAAADoFQSxkBS6DOdyoQvx0FD4n8vRlRgAAABAb2GKHWzH\nFDsAkKy4uajCpoKyy7JKL+EgCQBANxDEoko6TfAKAPXkr85r7KIxDS4a1NS2KeWOy2n00NFuFwsA\ngJ0O3YkBAGiiuLmosYvGVNpa0uR9kyptLWnsW2Mqbi52u2gAAOx0CGIBAGiisKkg1cxI5+5hOQAA\nmFcEsahSLErj4+E/ACDYbXA3lbaVqpZt2bZFuw3u1qUSAQCw8yKIxXb5vJTJSCMj4X8+3+0SAUBv\nuGXyllktBwAAnUMQC0mh5XVsTCqVpMnJ8H9sjBZZAJCkTVs2zWo5AOyMisWixsfHVaQCiQ4jiIWk\nMK3O4GD1soGBsBwAAABIks/ntf/+++vpT3+69t9/f+Xp0ocOIoiFpDAv7NRU9bLp6bAcAHZ2y3ZZ\nNqvlALAzKRaLOumkk7RlyxZt3rxZW7Zs0UknnUSLLDqGIBaSwtywuZyUSklLloT/uRxzxgKAJB22\nz2EaXFTdXWVw0aAO2+ewLpUIAHrHxo0bNT09XbVsenpaGzdu7FKJsNARxKKKe/V/AICUXpLW2uev\nVWpxSksGlii1OKW1z1+r9BKu9AEAMN/MiVZ6xvDwsG/YsKErn10shhGJS7EZJFIpaWKC1lgAKCtu\nLqqwqaDssiwBLABEisWi9ttvP03F7k0bHBzUrbfeqnSXKpJmdoW7D3flw9FxtMRCEgM7AUAr0kvS\nWr7vcgJYAIhJp9Nau3atUqmUlixZolQqpbVr13YtgMXCt7jbBUBvYGAnAAAA7KjR0VGtWLFChUJB\n2WyWABYdRUssJFUP7DQ0xMBOAAAAAHoTQSy2Gx0N98CuWxf+j452u0QAAADoB/l8XplMRiMjI8pk\nMswTi45iYKce0s2BnQAAAIAdUSwWlclkVIqNEJpKpTQxMcHATugIWmIBAGhRcXNR47eNq7i52O2i\nAEDPKBQKGqwZIXRgYEAFRghFhxDEdpCZPcrMzjSzr5rZa7tdnlYUi9L4ePgPAKjIX51XZk1GI+eP\nKCj2hrAAACAASURBVLMmo/w1dJUDAEnKZrNV0+tI0vT0tLKMEIoOIYhtwMzOMbO/m9k1NcuPNrPr\nzOxGMzs1KQ93/4O7v0bSSyQd0cnytkM+H+aKHRkJ/7mVAQCC4uaixi4aU2lrSZP3Taq0taSxb43R\nIgsAClPs5HI5pVIpDQ0NKZVKKZfLMUIxOoYpdhpbK+nTks4rLzCzRZLOkDQi6VZJ42Z2kaRFkj5U\n8/5T3P3vZvY8Sa+VdP58FHpHFYvS2JhUKoU/KTxfsYIRigGgsKnQcDlzxgIAU+xgfhHENuDuPzGz\nbM3iwyXd6O43SZKZXSDpOHf/kKTnNsjnIkkXmdl3JH2p9nUzWy1ptSTtv//+bSv/bBUK0uBgJYCV\npIGBsJxjEICd3W6Du6m0tVS1rLS1pN0Gd+tSiQCg96TTaYJXzAu6E8/OvpJuiT2/NVpWl5kdZWan\nm9lZki6pl8bdz3b3YXcf7uZOn81KNbcyaHo6LAeAnd09U/cotShVtWyXRbvonql7ulQiAAB2XrTE\ndpC7r5e0vsvFaEk6HboPf/rTlWVjY7TCAoAkZZdlJateZmZhOQAAmFe0xM7ObZIeGnu+X7Ss7xWL\n0llnVS876yxGKQYASUovSSt3XE6pxSkNPXBIqcUp5Y7LcT8sAABdQEvs7IxLOtjMDlAIXk+Q9LLu\nFqk9Nm4M3YfjpqfD8mc9qztlAoBeMnroqFYcsEKFTQVll2UJYAEA6BKC2AbMLC/pKEl7mdmtkt7r\n7jkze72k7yuMSHyOu/+uDZ+1UtLKgw46aK5ZAQA6KL0kTfAKAECXmbt3uwyIDA8P+4YNG7ry2X/4\ng3TIITOX//730qMeNf/lAYBeVNxcpCUWAPqAmV3h7sPdLgc6g3tiIUm65x4pVT3wpnbZJSwHAEj5\nq/PKrMlo5PwRZdZklL8m3+0iAQCwUyKIhaT6U+mYMcUOAEihBXbsojGVtpY0ed+kSltLGvvWmIqb\nGf0OAID5RhDbA8xspZmdPTk52bUypNNSLhdaY4eGwv9cjil2AECSCpsKGlw0WLVsYNGACpsK3SkQ\nAAA7MYLYHuDuF7v76qVLl3a1HKOj0sSEtG5d+D862tXiAEDPyC7LamrbVNWy6W3TzBMLAEAXEMSi\nSjotLV9OCywAxDFPLAAAvYMpdgAAaAHzxAIA0BsIYgEAaBHzxAIA0H10J+4BvTCwEwAAAAD0A4LY\nHtArAzsBAAAAQK8jiAUAAAAA9A2CWAAAAABA3yCIBQAAAAD0DYJYVCkWpfHx8B8AAAAAeg1BbA/o\nldGJ83kpk5FGRsL/fL6rxQEAAACAGczdu10GRIaHh33Dhg1d+exiMQSupVJlWSolTUxIaaZEBAAA\nQB8xsyvcfbjb5UBn0BILSVKhIA0OVi8bGAjLAQAAAKBXEMRCkpTNVrfCStKWLWE5AAAAAPQKglhs\nt3Vr8nMAAAAA6DaCWEiSNm6U7r+/etn994flAAAAANArCGIBAAAAAH2DILYH9MIUO4cdNnNgp8HB\nsBwAAAAAegVBbA9w94vdffXSpUu7VoZ0Wlq9unrZ6tVMrwMAAACgtxDEQlKYJzaXq16Wy4XlAAAA\nANArCGIhiXliAQAAAPQHglhICvPBTk1VL5ueZp5YAAAAAL2FIBaSwr2vuZyUSklDQ+F/Lsc9sQAA\nAAB6y+JuFwC9Y3RUWrEidCHOZglgAQAAAPQeglhUSacJXgEAAAD0LroTAwAAAAD6BkFsDzCzlWZ2\n9uTkZLeLAgAAAAA9jSC2B7j7xe6+eunSpd0uCgAAAAD0NIJYAAAAAEDfIIgFAAAAAPQNglgAAAAA\nQN8giAUAAAAA9A2CWAAAAABA3yCIBQAAAAD0DYJYAAAAAEDfIIgFAAAAAPQNglgAAAAAQN8giO0B\nZrbSzM6enJzsdlEAAAAAoKcRxPYAd7/Y3VcvXbq020UBAAAAgJ5GEAsAAAAA6BsEsQAAAACAvkEQ\nCwAAAADoGwSxAAAAAIC+QRALAAAAAOgbBLEAAAAAgL5BEAsAAAAA6BsEsQAAAACAvkEQCwAAAADo\nGwSxAAAAAIC+QRALAAAAAOgbBLEAAAAAgL5BEAsAAAAA6BsEsT3AzFaa2dmTk5PdLgoAAAAA9DSC\n2B7g7he7++qlS5d2uygAAAAA0NMIYgEAAAAAfYMgFgAAAADQNwhiAQAAAAB9gyAWAAAAANA3CGIB\nAAAAAH2DIBYAAAAA0DcIYgEAAAAAfYMgFgAAAADQNwhiAQAAAAB9gyAWAAAAANA3CGIBAAAAAH2D\nIBYAAAAA0DcIYgEAAAAAfYMgFgAAAADQNwhiAQAAAAB9gyAWAAAAANA3CGIBAAAAAH2DIBYAAAAA\n0DcIYgEAAAAAfYMgFgAAAADQNwhiAQAAAAB9gyAWAAAAANA3CGI7zMyWmNkGM3tut8sCAAAAAP2O\nILYBMzvHzP5uZtfULD/azK4zsxvN7NQWsnqHpK90ppQAAAAAsHNZ3O0C9LC1kj4t6bzyAjNbJOkM\nSSOSbpU0bmYXSVok6UM17z9F0mMl/V7SLvNQXgAAAABY8AhiG3D3n5hZtmbx4ZJudPebJMnMLpB0\nnLt/SNKM7sJmdpSkJZIOkVQys0vc/f6aNKslrY6e3mNm17Xze+ygvSTd3u1CAECP4hgJAI31yjEy\n0+0CoHMIYmdnX0m3xJ7fKumJjRK7+7skycxWSbq9NoCN0pwt6ez2FnNuzGyDuw93uxwA0Is4RgJA\nYxwjMR8IYueBu6/tdhkAAAAAYCFgYKfZuU3SQ2PP94uWAQAAAADmAUHs7IxLOtjMDjCzQUknSLqo\ny2XqhJ7q3gwAPYZjJAA0xjESHWfu3u0y9CQzy0s6SuHm9L9Jeq+758zsOZLWKIxIfI67f6B7pQQA\nAACAnQtBLAAAAACgb9CdGAAAAADQNwhi+5SZZc3Mo7+13S4P6jOzQvQbFbpdFgC9y8zWl4/p3S4L\n0Cmxesv6bpcFSGJmu8S21+91uzztZGa/jL7Xlm6XZS5anmKnzon1Se7+qybvOUFSPnr6Pnc/bXbF\nw3zYwUrTVe7+uLYXpsdFc/5mJYnteeEws5ykU6KnLulAd7+5i0VCG5nZmyUtk7TJ3dd0uzzzwcyy\nklZJerqkRyp8f5c0KWlC0jUKgxWuc/cbulLIFpjZ8yWVzzVr3H1TN8uzM0ioE0xJukuVbehKSb+S\n9B13L81T8XqWmS2T9Obo6W/c/ZttynetpJNm8ZZJd1/Wjs/uBDN7pcLsHlvd/f3dLs9CYGYvknRo\n9PRj7n5PN8szX+YyT+wHJT2zXQUB+sQqSU+LHp/WvWKgXcxsiaSXxBcp/M7v7UqB0AlvlpRRqHgv\n6CDWzEzSeyS9S9JAnSR7R3/LJZ0cvec57v7deSvk7DxflQr8WkkEsd0zqDDY5V6SDpT0jGj5JjM7\nV2EAzMluFa4HLFPlvHGupLYEsQvQKyU9UdJ9kghi2+NFkl4aPT5TEkFsE88wsxXuvq5tpUEveEGL\n6XbmE1XL3D3b7TKgqRdJ2q1m2Ulmdpoz8h36z8ckvSX2/HJJ35N0s6RpSXsqXLE/UtKjozSL5rOA\n6CvxOoFJWippd4XW8SMVeiYtk/QmSS80s1F3v7xRZu5unSvqTuFTkn7UJM30fBRkoXP3LQrb/ILj\n7k/qdhnaYUeC2Hsl7Ro9/qAkgtgFpF3dX4A+cnL0f1rSVyT9q0Kr3TMk/bBbhQJmy8weL+nfo6f3\nSXqpu38rIf1BCq0itG6irqQ6QdTqf4xC74aDFbqIftvMjnD3381TEXc2V1JPA4IdGdjpFknfiB4v\nN7Pj21geAJg3ZvYwhdYEKbRW/W/s5ZNnvgPoaaOqtBysSQpgJcndb3T3U5NazoBGPLhE0rBCi78U\nWmovNDMGDgXQUTt6kHm3pPujx+83szl3RTKzxWb2SjO7xMz+bGb3mdkdZrbBzN5vZvs0ef+q2Chi\nq6Jlw2b2eTO70cw2R68dFXtP1cix0UhkbzazX0WffZeZXWFmrzezwZrPe5iZfdLM/hDl/Q8z+76Z\nrWjhuz7SzN5mZheZ2U1mdm/0ff9iZt8zs38zs112YDX2DDN7rpldbGZ/NbMt0br+opk9OXp9xu9V\n8/7E12eb1sxSZvYCMzsj9vtOm9mkmf3OzD5rZo9N+Iz10WAXT4st8zp/p9W8r+XRic3sWWZ2fmyb\nuNvMrjWzM83sCU3eO2O0ajPby8xOM7Oro7zuNrMrzeydZrZrUn47kVWqVPrPc/crJZVbEI43s6Fm\nGdgsRttsNa2ZPdjMPmJmv48dX35tZv9R/u2abVtmtjb2edlo2QvN7LvRMbYUbV8fNbN0zXuXRseo\nK8zsTjO7x8zGzew11mLlNNr+3mVmP42OA1NmVoyev93Martw176/9vi82MxWm9nlZnZ7VP4bzOzT\nZrZfUh4KLeuSlGmw365q8P5BMxuzcKy+JTqWbTKz35rZx8vrtYV1scTM/jPa/+6Kjju/NbP3mdle\nreTRokfGHv94RzMxswti6+bxLaQfjH5bN7PbrKZOYGaLzOxEC+eE8nosRY+vNLMvmNlJFu5PL79n\nbfTbxQe0ubnOb7c2oVxHR/ncEB3/7jWzP0bLntLkOzWqU5xrZjdH5Z8ws7yZHVrz3kVm9jIz+5GF\n8/oWM7vezP7HWjim9Bt3v0thXIFyi/6jVLk/r4o1OQY2OG4dH+2Df4qOI3Vv82jX/hrl9XALx+Dx\naNsu1xeutFCPeKaZWZQ2G5UpPhjgSQ2ONS2Xod3M7BAze4eZfTvahu+N1tGfLdS9X21mD5xFfkvM\n7A3Re2+N7dd/NLOvRr/Fg2LpfxmtpydGix7YYB2d2uDz0mb23iif261Sb77UQr05sexWfVz7p2jZ\nS6L1cUv0G2+JpU8cndgqI/y2+jdjJGAzGzCz55jZJ8zsZ7Ft7S4zu87MzjGzf2n2nVS9v/2lzmef\n2aDsTUcnNrMjLMRSN1ioC2y2EFedY2ZHNnnvjHVoZg+KtsMro/1zs4V66vvNbGmz8lRx95b+FEY1\ndEnXRs/XxpatavCeE2JpTkvI++GSro2lrfd3j6RXJOSxKl4eSadK2lonn6Ni7ylEywqS9lEYaa/R\n539P0gOj9x0XladR2tcnlPOkJt+z/HejpEcl5JONpV3b6u/Y5Lf1ueQT5bWoZtuo/dsm6e21v1ez\n37PJZzZNq3ByaWW9f7DB+9e3+P7Tat63fRtLKP9uki5qku/9kj4p6QGtbA8KV8ZvTchvo6Q95vp7\n9/OfwkW8iWh93Bnbv98RW0+rZ7H/rG9HWoXRZP+R8Nv9VtJDm21bNfvhgZK+kJBnQVImet8jFI4/\njdJ+RZK1sE/e1WSb/qukJyfkUYiVbS+Flp5Gef1D0hMS8mj2N+O4Ee1DNzV5332SXt1kXRzcJJ9b\nFO4vXF9eNodt+pJYvg3Ply3k8/RYPp9pIf1LY+n/u+a1vST9usXf4fkNtt+kv7V1ypNWuBWg2Xs/\nL2kgYRvevn1Ier3CLQf18tki6dnR+x5U8zvU/v1BUrpdx7FO/MXLO8v3fTj23h80yXt9g9fjv/sj\nJH293nrs4P66WNInVL/+WPv3tOg92Ra3VZeU3YHfI75OVu3gb7q6xfJdJ+ngFvJ7nqS/t5DfZ2Pv\n+WWLZTi1zue9WGEslqT33STp0QllviCW9gBJF9fJY0ss/S6x5d+rk1+r32dG3rE8ftHie8+WtLjJ\nd0r6O7NB2WeUKZZmUK0dh89XVH+qk0fVOlSI965LyOtGSQ9tdbuey8BOpyl0XRqUdJqZfcndp2ab\niYUr6JcrnHQUfYG10f/dFXaUYyQtkbTWzLa5+xebZPtSSUcrbPDnSrpCIXh6rOoPSDQg6WuSDlM4\n+VysUCl6pKQ3KJyEny3pP83sEklflVRSCCo2RHkco0pXrv81sx+6+x/qfFZK4Ye6QtJPFH7MOyUN\nKbQWvFThRz5Q0nfN7HHeX1MKnK7KlfMphfV/uUIQdrikMYUT3Xzf05FS+E1/oBDA3aZQIdlX0uMV\nriIPSHqnmf3dZ07D8W6F7eD9kv45WlZvEKxrZ1MoCy0W35VUbhXYJOkchQsqi6Plr1DYz94YfY/V\nTbJ9qKTvSNpD0hclXaZw0eUQSa9TGNjlcQr3Mb1iNuVdYJ4haf/o8YXufl/0+AsK9/s/QKFL8dnz\nVSAzO0TSt1UZd2BjVJ5bJT1Y4fhwhKQva3ZjGvyPwgBWv43ym5D0T5JepTDIT0bSeWZ2nMI+sm/0\nGesk3a2wj7xO4Tj8YkmXKgQA9b7Dm1QZAfhehePlzyXdobAPHa1wXH+wpHVmttzdf59Q9sUKx+cj\nFLblb0r6S1TGVyrsj7tLusDM/rnmPLRaYV2erXCOKar+/nNlzXd4cvTdd1U4Xn8/+s63KeyDT5Z0\nYvT6mWZ2n7uvrbMu9lAYhKXcUnyzwv59g8L+ebykFQoV9XYMlvfH2OPXROflrbPNxN0vM7PrFIKI\nl5nZW9393oS3vKr8Vkm5mtc+pzASshTO63lJ1yucQ4eizzhSldaZstMVfus3KgTVkvRqhYpz3J/i\nT6J1/guFc6gkXaWwfm9UOA8dqhCU7qtwPlocPU/yXIXfqqiw3V+jsB0cL+lYSQ+U9GUzO0DhnHeM\npJ9JulBhW80o7D8ZhXrFJyS9vMln9qMvKVyklqR/MbMBd5/LIEOfUFiXf1SoKF+nsM89LZ6ojfur\nKRxrnhct2qawDV6msN3tqtDK/GyFc2i5F8/fFeoDe0s6K1p2mcI2XKt2+50vuyps/xsk/VRhXW5S\n6P6dUai/HqhQ/7zEzB7v7nfXy8jMTlTYzsvff6PCPla+iLC/Qt1lJJZGCtvGHgp1wIcr1MHiMwOU\nVd1PbWYvUAjWyr2AfhR9XlEhGH2FQv3mAEk/MbNhd48fC+s5Q2Hbul7hnHiDwvmtYatnHeXvk+QI\nSW+NHtery6cULvj+UOE8NKFwUewhCgPvvSxK8yqFOmxtK/XHFNbNf6hSjzy5zmfd3KSc9VygSj33\nXoXY7Feq1OdPUVhnL1c4lh/XJL/dFWKshyn8fpcqxD8HSfo3hWPygQrnkGe1VMJZXMUpR8nXxpad\nHlv+xjrvadoSq1CBL6e5UHWieYUTzLYozV2S9mmQJh7N/0HSQ5p8p0Is/f2SXl4nzcGSNkdpNils\n6DeozpUCSf8vll/dq9cKFa4DEsr0AIUNvpzPexuky8bSrG31d2zy2/oc83lqLK87Vb9l5BEKJ/X4\nb7Wqye854/XZplWoOM+4ihV7PRNtM+Vt7EEN0q2fzbpS89ayeKvftfW2WYWLK3fE0h3bZHsor/8n\n1kl3QPSaK1xpTtxHFvKfQoBfXl9PqXltXey1RzbJp5xufQufmZhWoXJRTnOG6rS8K1xAjP/Wjbat\ntTXpzqzNT+HkeFUszQaFk9Uz6uR3pMJx0iX9vsFnDqvSWrVR0v4N0j1X4SKXS/plgzSFmvLPaBVX\nuMobvxr+kiZ51V1XNWkfpBAYlfejpzVId5AqLfn3SNqrTprPx8r2PUm71knzpprv6XPYpo+oyWuj\nQkVjxjmzhbzeEstnVUK6h8W2i+/XvLZ37LVxSUsS8sko6g2QsB1nWyj3N1Q5p7+pQZrdFAKdcr5H\n10mzqmZd/krS7nXSnV2z/7jqtyTtLenPqhx7Z/2bzNffjm6LCj2x4r3UHpuQ9/oGecR/b1fo+TGY\n8Jnt3F/fHvvcCSW36j2hdntVG+tlCetk1Q7m8eh6+1fNb/eu2Oe8o0G6RyicI8rb8WsT8txT0pF1\nljdtBYyl3UPV9Z/X1UkzULOOftogr9pWyy+oQU+MKH1iS2wLZc+q0lo9JenpddKMSNolIY+9Y+tr\nWtK+LXy3f2qhbIm/gap7jd4q6eF10hwY2/dc0liTdegKFy+f1eB73hJL95iW1vEsfoxyxvEg9sGq\nHLD+Jmm3mvckBrGSHhN7/WZJqYTP/3Qs7fvrvL4q9vr9qnPwrPOeQuw9ZyakO6vmRzg8YYMvd6H7\n42w3+Jq8fhzlc2PCztGWg2XNd2v1b1WdfL4Ze/2khM87toW8ViW9vqNpm+QT70I344JGlGZ9OU2L\neZa3sUKd1wYVulSWD05JJ8wXxcp2eZPtwSWdmJDX+1tJt5D/FK4+l0/EN6mme6zCld3yOvpwk7zK\n6da38LkN0yoEgOXXr5a0KCGf9bG0M7atKM3amvzqXsRRuAIf33benvC5l8bS1buQV+4Wf5canGxj\naf8rlte/1Hm9EHs9l5DPimbpkvbDOmnjwdvKJmmfEUv7nzWv7a3QfdEl3a6E7vsKF3C3/wZz3Lbj\nF5fjf+VBGU9VuGJf99aEWD57KFQ46h5zYuk+EPuMF9W89qTYa/++g98nvh1nm6R9fCztx5uk3V3h\nwrRLurTO66tied2nBgGAQuvB/bG0lyR85n/G0vXssXcu26Kqbw1bkZD3+hZ+71uUcOEjSt+u/XU3\nVYKl+5RwPk7IPxvLf20bf4/4Omn6N8fP+lWUzzUNXj8v9lnv2cHPmE0QG7+wcG5CugFVGiJcNRem\nozTxQO8mJQSPUfodDmIVLq5cE3t/01uTEvJ6VCyftzZI0+4g9nex/GYE37F08car6zWzLlUbxL4t\nIa/Xt5Iu/jen0ePc/W+qdBvbW2FC+dmIj2z8KXcvJaT9iMIXq31fPT9196tmWZZPJ7z2s9jjDe7+\n63qJPMwpVe5efIDNbXCmn0f/D7T2DvzREdEN9cdET/+mcIWrLnf/jsLBptf8PPa4tmtbJ/yLwoUg\nSfquu1/dKKG7f1WhO5wkHWFmeyfkW1To1tVIfI65Q1op6AJ0gkIrpCR9waMjaMzXFHpgSNKJ1obB\n61oQ74pzhrtvS0j7yVnmfZY37lYaP75tU6U7XD3xUWyrth0z213hApUk5d39tiZlih8jmnUdSvq+\nP1FoEZhRph10YvT/ene/OCmhu/9IoXVNmvkdjlW4UCWFCu0/ErL66KxL2bhMb5T0GoXjcNx+kp4v\n6UMKLf63mtmpjc5TUXkvjJ4eYWaPqk1jZotVGcX775JqR0OOd0H+Z3Ve+bdzSR9PSujudyp0bZOk\nI5sMCnOxu080yOc2hYskZWck5NNw/1lA7ow93nOOeZ3j7pubpGnX/nqMKl1Dv5R0Pl7gyvWgR8UH\nZZLCwFkKF9Sl8Du37biVIF7f/3CjRB66rcf3+WZxwueiOnvbWRj88AJVjnmfdPcdvi3Jw62J5e7B\nHa+bmtkjVTk+jbv7ZQll+6kqdYiDVZl7vJ4pSZ9NeH3WddO53BNb9lFJr1XY+d9qZp9pcrKOOzz2\n+NKkhO7+JzO7VuGKxCPNbMjDiHj1/LTFzy/brJo++DXilYG6AWydtKYwAfhf6yWyMIrxCQr3Cu2v\ncNWmUUV5X4Ur+fOh3n2e9VxZ8/yxqlTYftykAi6F/v8zKkWdFAV+r1A4eR2icCW+0Si9dUc7bbOW\nt//IDxS6REnhQNbohL2hyfqPBxe7t/C5C9Epscfn177o7pvN7BsK93rso1DB+XaHyzQce9zwpBFZ\nP8u8f5XwWvz4dp27J92bGU9bu+0coco9S9vM7PlNyjQQe5x0LLhXoSW5LnefMrPbFe7xndP2HI2M\n+Jjo6d9a+A5S6I0kzfwOy2OPm803PK5w7/GDmqRribufZWHU3ucoBNNHKHQDjN+fto9CQPsSMzva\n3evdq3eWKkHCqxRaveKOjfKRQqBee//j7xSChodIGovuOfycpF+7+/1qv6dG/zdJOjx8XKIHxv4/\nTI0vribtP1LYLw6IHifVEZL2n4Ui3jhSe3FwthLrcm3eX+OjVV/UWvG64lOqruzPipkdrXAf6rDC\n+BmN6p4PUNhvr4ste4IqF39/0KThac6ii2SHRU9v8+SxE6TqelSzYG+2ccJsfFzh2CuFWyb/Iymx\nmS1TmJ/+OQr37O+pcK9pPb1YN71U4RwjhfX+2wbpfufu9zR4TdqBuumcg1h3nzSzDytcIVmq0FXp\n7cnv2i4+bc71LaS/XuHAYwoVlkZBbLMWgFr/qNMSE3df7PEdTfKKp51xhTs66H5Frd60HMzbkPy+\n45NoPyT2+MaGqWaXpm3M7KUKFbJWh++ej3W+I9t/vffWanbBI3EbXeiiwZPKB+lfuvsNDZKep8rg\nKyer80FsfB+6KSmhu99pZpsULpS1ouFxy93vi1X253J8y8Yevzb6a1XSCeuOJsfneLnmuj0/VJVK\n+FNVCYpaUfsdWj4murub2R8VBotpCw8DlX0j+lPUqjKscNvEy1UJug5T6LkxY3o4d/+ZmV2jULE6\n0cxO9eqBs14ZezxjoC9332Zmr1bo2TCocPHoFEmbzOwXCi2T33f3K+byXWOy0f/dVZnPvlWJ22CT\n97ZaR9gZjr3xY1KrDRqNNKvLtXN/jQcHvdhTrOzKHamnRQOefVWVQdJaUVsPmu91tKcqjSNN60hR\nY9cWhX0rcVpOzT5OaImZvUqVXqm/k3RCUqOCmT1L4UJ6Uu+6OOqmMe1oiZXClaE3KZy0X29ma9z9\nz03eI1WuOm/11kY2jkfwSVesZ3t1aDZXhOd69firqlQW7lZoTfuNwmBH98byP0GVeZ/moyvjXMXn\nfEwaxbKsWRehtonmsfqSKie7KxUG7vmjwoig8R2nXPGZj3Ue34ZbWR+tbv+daOFYSE6OPZ7RChvz\nQ4UT3b6SVprZXu7eyR4R5SuvW+u0aNWzWa0Hsa1uE3PZdmY3v1u1wYTX5nN7nst3GKh53lPHRA8j\njV4m6TIz+y9J/6sw+r4kPdPMnuLul9d561kK5/i9FHrqfFmSzGxfVW4hWd/oYpC7f9vMDlcYkOxY\nhfW0LHrvMZI+EAXKb3P3GXMxzlLXt8EOtTD3hei2i3igU5xjls3qcu3cX+PBQVJrUd+JekB8U5Ug\n/y6F1uarFOqeJVW28RNV6YpbWw+a73U02zpSOd0uat6rpe2tyGZ2lCq3E9yucI92o8a28gX1i6kW\n/gAAEHlJREFUi1TpEfJ7hQHnblDorh3v7vx/CsdN6qYxbQli3b1kZv+t0Nc5Jek9CvfkNFMevnux\nmQ22EMjGKwV1h/7uZVEwVQ5gr5I04u51D/JmdkS95T0svhE36qIb16irxI5odm/3abE0q939c/US\nmVk7y9SK+Dbcymf39fbfC6LuSSfGFp1hZkn3sJUNKHT3me29qPHPbradlk8Wi1ucmmK+t9dm4seA\nU9z9/7pWkh0X/w7nuftJbcprvo+Jidx9q5m9RWGgm/J9W89U9T2bZecrTNG0RKFL8Zej5aeoUqGq\ne0yNfd5Vkl4QtQYfoTAewJHR/wGFlt5LzOxEbz6FXpJ7FCp6f3L3zBzywY55tCrberPbtNqhnftr\nPNjYrWGq/jSiSgA7rjAad91WcjN7ZkI+872OZltHiqeb1zqSmR2k0ONkQOHez+Pd/eYmb3u3KgHs\n/3P39yfkn3TBvd36pm46p4GdauRUmaNuLPpBm/lL7PHBLaQvp3E1uNe0x8W7a72rUQAb6bcTcLzl\nvZXfvlmaeOto0hVyKbQQ1BUNRFA+eG9oFMBG5nud7+j2L1Wvb7TuGFUG05qtkxssL1982+HtNBL/\nTR+WlDAaRKnVVtj5Eu+eNR/37XRCO79Dy8fEqKUk8Tdvt2igrx/HFj2kQbpJhUFKJOkZZvawqLzl\n+8rvUKi8tfKZd7v799z9Pe5+lELXs09EL5fnWJ9LS0P599vbzGpb2tB5L4s9/nnCYHLt0s799dbY\n43kdr2MexOue72wybk1SPWi+19Edqpxfm9aRzOyhqnRDnbc6UnRP67dVGRjs1dGAR82Uf5dbFEZ5\nb5T/nprfCyt9UzdtWxAbtRq8J3q6WGH6hGbiAyCMJCWMNs5HRk+vTWqi72HxynPDiZijwGs29y30\ngqtUOdg8rYWKSNLVPql6oua6lauYpBv491Slx0Gzya+f3eR1KdYdwloYNaSJlrf/OmmaDTCG+uKB\n6LmS3tfCX7mb5GPN7DDNVN5W57KdSpWRzaXm+/9RTV7vhp+oMpDLbO75nw/l/TZxn426i5cHD3mS\nmc3l/qP4PvqMJmmXax7HPoiJ935K6h5YHrHaJI0pHIuy0bLzo/tvZ83d73D3t6iy7e+tmZWmeBe0\nZsfcclC+i0JLL+aJme2j0FJfluv0Z7Z5f40HHc/bwTxms63Op1brnrsq+b7iK1TphjtiZqmEtEla\nPR5vVZjrWpL2i0bNTRI/78xLHSnq3XWhwsB5kvRRd1/bwvsWqXJh+6Ym4z60cj5t57Y327rpvK/3\nsna2xEpSXpVRqU5QGLE2yddjj9/QZEqat6lS3pau+vag+H1RByake62at9r0lKgSU56u4MGqviJb\nxcyOUfOrePFR6BpWAM3sAEkrE/JpaZ1H3dz+vUmZpOqK3ly7//1clR4Fx0b3R9RlZserUrm7vMFI\nokhgZmlJz42e3qUwSftpzf5UPWVGvdbY8raaMbOk1rQ3NilifHqS1zW5EPSmJnnNu2ibLN/T+JRo\nwIpeUd5vW9lnz43+76owUOGO+o4qQeKqqPW8kcTRK1tlZi33MogqX8fEFjUc+dPdx1UZkX6Vqm8X\nSuxK3KJC7HHtbU6zOeaeF3v83nmaGmunF50/v6JK75A/qDI9U6e1a3/9rioDUb3MzJKmCmmknfWD\ndmq17vkGJfTwiW75+0r0dHeFevmOKK+nwRZ6TMTr+w0/L8onPnr6fMUJn1SlRfVitbgNRoM9lS/+\nJdVNB1rMs23bnrtfq8r54InRrZB1Rbc+lkf2vkEJMwl0QluD2OhKwruip6bKoBGN0v9W4cAhha5U\n/xe1QlYxsxMlvS56erekz7SlwPNvPPb4PfXmpTOzlQr3H/Wj+BxdnzSzGSNtmtnBauEKbTQnX3n0\nu6dG66U2r7TCQFkND4JRV7hyS9qwmc2YQsjMdlM44T60Wbkkxe9xeHwL6RuKTgjlrnSLJV0YXc2u\nLd9jVD13Z79uH932r6psK1+fxfQAeVXmIX1ZnWNUfDCaD9droY8G0pkx+mucu29Q5Z7EQyWdXu8+\nWjM7TdLTWiv6vHu3pPK9vBdE0zk0ZGYZM/uYJc973A7l/XZPM9u/SdozJJXnBD3VzN6WdD+zmS01\nszdamDZtu+h2kXJQtZekL9ZruTCz1ytMedEOa8zsUjM7NgpSG5V5V4Xgs9x6cLdmzvFa68zo/0NU\nmYrt50nTXpjZs83sTdGo/I3SHKTK1f57NLOlqOVjrrv/SpXK61MV1nnD1jkzW2xmx5vZ6xqlQWMW\nHKPQkl6uyN4l6cXzOMBVu/bXzaqcWwclXZwUyJrZ48ysqutt1E23PEXZ49rQW6td4nXP0+oFjmb2\nQrXWg/KDqrTGvsfMGo5Cb2Z7mFm9lt34Pl2vd1Pc51W5uHCyhdHOaz9nsUIdqdwQcLm7/6w2XbtF\nx+5/i57+VtLLZrndl3+X/eqtxyhGWKvKNFJJ2lY3jcTn5P1CvVtEo4v28TEMPtzCTAJt1a7RibeL\nRiL8ucKADa1cDVitcIU3rdB6+3gzO1dhSoJlCt06jo2lf627/2VGLv3hG6qMdnq4pN+bWU5hOo1l\nCnNErVQYEOFrkl443wW01uZZK/tOfPAZd7/czD6jsFPvLumX0W95uUJXh8MVuqItURgpr9lnfUyV\ngPdrZnaOQpdFUzjwnayw3i6U9OKEfD4l6fTo8VfN7ItRme5WCBZWKVTMzlOYRzbJD1VpUcuZ2ScU\nTqDlIdRvdPfZTB/0cYXf/CkKB+DfRd/zSoX98whJJ6ly8//n3P07s8gfFa2OSlzF3f9uZpcq7J97\nKhyTvhpLco7CtGJ7KEwE/9NoG7tdYQ7oExSmNrkgepzk1Qontl0V9qMnm9kXFO5FerDCiOVHSPpF\nlPe+6qHRqN39yuhk/DmFY8B3zexnChcrb1YIcPdQuDXkKarMjbumw0X7oSpdBL9uZp9VuO+nvO6u\ndvfbou+wOToO/lihi+9HJL3azL6mcHX6nmj5wxSOaUcpVHrjA4aVvUPS0Qr36x0j6Zpo/75RYf0c\nrxDA3axQ+Z3rFDsW5Tci6XYzW6+wPZVHv989+owXKkxTV/aWFkbeziscr+KjT57d5D37KPy2HzGz\nyxTmW70pKsteCt2oX6JKXWFNnYtL8Tl2PxJdvLxOlQtLt7l7/Or/KZIerjDI0EslPdvMvqIQaN2p\nMPjkvgrnkBGFddLxrq/9qqZOYAq//x4K29GRqkzVJIXj1Ki7d3pAp+3avL9+TOG49DyFe0M3Wpgv\nfL2kvytsO49Q6D5Znq5qoiaPHylc5DlQ0pfN7Ouqvj3qx52eX7WOryjMCb23wvcr1zMKCtv/SoXj\n090KPeoa1s3c/fookDxXYWC3z1iYVubrChegXOF4d4TCse9czZyT9YcKdX9JOtfMPinpT6ocj68r\nD4oUTSf3SoVz7gMknWlmL1KoT9+ucFvDK1QZoG6TQp2uo8xsP1XOW/crHENWNLlusc3dL449/5Qq\n3bc/E11YWadwnHq4Qt3vYQoXyp+gECc1Ej9OfsLMHqJwnikfJ//Uwjy727n7edF+9QKFBp7fWJh7\n/JcKv/HhCsfa8r26F7v7/B9H3b2lv6jQrnA/arO0R8bSl/9OS0j/cEnX1nlP/G+zpFck5LEqlnZV\ni9+pEKUvNEl3VCvfI0q7NpY2W+f1JylcVWr0Pe9UqCyfFlt2VJ18srHX17b6Ozb5bWf7t6xOXosU\ngsFG79mm0CWk6e+lcMJcm5DXfQrzFCbmFeXzhSbf5ZsKJ6jy8/UNyrRI4YDcKJ/TatI33cYUDgIX\nNynf/QqB+AMa5NHy9tDObadf/hSuTJa/8y2N1mPC+0+Ivf87dV5/jsJw+I1+v4tb2b6ivJ6ucBxo\nlNfVCieVW6PnVzXIJ77vZJt8v6blitI13W+jdCsVusq3chy5XdJedfJouu+0mjbax65LKMOM76JQ\nWb2yxe+wRWHEz3qf/XCFILXRe29RuPVmfXnZHLbz9zbZDuut+xNnkf9nYu/dJGnXJulParEc9ytU\nCBsd376U8N61ddIPKVw0anU9/NeObutR2pZ+O/XJsXcW6638d6dCt8oZdYKEvNc3eH1tLE12FmVu\n1/46oNC6u62FfI6s8/7HKVykafSelr9Tg3WSuC0m5PFUhQtljcp1h8JFnf+JLXtSQn7HR+9pto4+\n02Ad/yrhPafWec+LFVr5kz7rJkmPTihz/JjwTy2ss11i6b9X89ojZ7mPuKQtdT7jf5u8Z73ChYby\n+bRhDKZwIaFRPmfWpP1lozLF0gwqXIRo9r2+KOmBs12Hc0lb/mv3PbGSJHf/iaq72DVLf73CVdNX\nRe/7q8IV+zsVDkoflHSwu5/XMJM+4e6/VKiwfFrhqtWUwoHlGoXm+8e6+yWNc+ht7r7N3V+hUIn9\njsI8cfcpXGXLS3qKu3+0xbxcofVsVOHq5p1RXgWF1q9hd/98K/m4+8sV7tO9TKHyNaUQBHxb0kvd\n/fnewtVRD/cxjCjco/CLqEwNJ7Juhbvf4+4rFa5afknhyu4WhQs31yu0dix39zf6TjwH4RzFW2Hz\nO7Aev6XK9ALPjq5ybhfts49VmMvtTwrbV1FheztR0vNa2b6ivC5TOEF+TCHwKilssxskvVVhgKhb\nVRkJMWmkya7wcLX5AIV7Jy9SCNRKqqyXXyhchV4p6SHe2fl35e73KFxA/IDCOWVSTVqw3f06havf\nxymcyK9X2Aa2KfweVylcsFslaR9vMMdpdH47VOFWm98otAzdrXDM/29Jh3mYgmbO3P19Cq0tL1QI\nKn6s0PunFJV7UmGbulDhAuCB7j6bqRvWxR5/0d2bzX97nsL2+i6FCzk3KhzXymX5jcK58Anu/uaE\n/fJEhbEi1isE3omj3rr7Xe5+gsLFqzUKg8PcEb3vHoVbTL6pcA/dge7+nkZ5ocq0wnq8WeHY9nGF\nlvSHuPub3H1T0ps7qY3767S7v07heP5JhYuGm2L5XKFw7DoyquvWvv83UTk+r7CvtTJHdMd5GC33\nsQpTYd6scCzepNAN9oOSHuPuP5hFfl9XaCV8m8K28DeF7aOksJ9/ReEi1lvrvHda4WLtuxSC2fL6\nTfq8CxVat9+n0LvkH9Hn/U3huPQ6SY/y6l4ZPc/DwHYrFWKfOxS+058l/UCh3vIMd7+zxexeonAb\n509UOd7NpWxTHqateopC3eaPCtvzvQoXDM6V9DR3/1ffwcH95sqi6BeYV2a2SmGnkKSTvYXR3AAE\n0b1a5UH0Tnf3nhvoCQtP1LX9X6Onh0UVdgAA5l1HWmIBAB31+tjjy7pWCuw0ontRXxQ9/TUBLACg\nmwhiAaCHmNlTm4yu+TpVBsW4TaFLPNBp71RlgLnTkxICANBpbR+dGAAwJ/8naRcz+67CvXxFhYEw\nDlQYKTA+JcFrPEwID7SVme2rMFbFrpKeqXBPqhQGYbygW+UCAEAiiAWAXrSvwsA7jZQkvcrdaYVF\np4yoMm5B2X2STokGuAMAoGsIYgGgt7xcYXTZJykEs3sqtIbdqTDi5jpJn3X3v3WthNjZ/FXSryW9\nl3thAQC9gNGJAQAAAAB9g4GdAAAAAAB9gyAWAAAAANA3CGIBAAAAAH2DIBYAAAAA0DcIYgEAAAAA\nfeP/A8WSc50yWGJKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3369e55fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "ax = plt.gca()\n",
    "ax.scatter(np.ones(n), factorization_time_ne, s=20, color='blue', label='Normal Equation')\n",
    "ax.scatter(2*np.ones(n), factorization_time_as, s=20, color='green', label='Augmented System')\n",
    "ax.scatter(3*np.ones(n), kkt_time, s=20, color='black', label='Direct Factorization')\n",
    "ax.set_ylabel(r\"Factorization Time\", fontsize=30)\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim([1e-4, 1e4])\n",
    "ax.set_xticks([1, 2, 3])\n",
    "ax.set_xticklabels(['Normal Equation', 'Augmented System', 'Direct Factorization'], fontsize=30)\n",
    "plt.savefig(\"FactorizationTime.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-06-02T18:00:43.773304",
     "start_time": "2017-06-02T18:00:43.217810Z"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.text.Text at 0x7f3369df4310>,\n",
       " <matplotlib.text.Text at 0x7f3369d45490>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mS4ndnFcleeb5E1W1I8krkjwryZOSHK2qJ533lu8cvz4VWls/AgDAlSy/Yzlzt87l0GsP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\ntHdE3NLzEgEAAAAAKtPvQay0YnDayVO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JL5G0paQ3SXp1lmbSeBYQ5YwkiH1M0hrZ/Bcl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\nqA2CWAAAAABAbRDEAgAAAABq4/8DG8teWtsrBakAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3369f90250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13, 13))\n",
    "ax = plt.gca()\n",
    "ax.scatter(np.ones(n), niter_ne, s=20, color='blue', label='Normal Equation')\n",
    "ax.scatter(2*np.ones(n), niter_as, s=20, color='green', label='Augmented System')\n",
    "ax.set_ylabel(r\"Number of Iterations\", fontsize=30)\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim([1e-4, 1e4])\n",
    "ax.set_xticks([1, 2])\n",
    "ax.set_xticklabels(['Normal Equation', 'Augmented System'], fontsize=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "cutest",
   "language": "python",
   "name": "cutest"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "toc": {
   "nav_menu": {
    "height": "12px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}