cascade_generation_playground.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "from cascade import generate_cascade_old\n",
    "from simulations import simulate_IC\n",
    "from ic import sample_graph_from_infection, make_partial_cascade, make_full_cascade\n",
    "from graph_generator import grid_2d, add_p_and_delta\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "g = grid_2d(10)\n",
    "g = add_p_and_delta(g, p=0.7, d=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "induced_g = sample_graph_from_infection(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7444444444444445"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "induced_g.number_of_edges() / g.number_of_edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "es1 = set(map(lambda e: tuple(sorted(e)), g.edges()))\n",
    "es2 = set(map(lambda e: tuple(sorted(e)), induced_g.edges()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "assert es2.issubset(es1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEACAYAAACnJV25AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXdYFNf3uN+hl6WLCmIHjBVL7A1777F3jb3Hkq4pJmqM\nGo0aS+wNNTZsUdGYiCVixwoqCooUQXpZdvf+/iD6SxRYZAaTr595n2cfdfe67y7Mnr1z59xzJCEE\nKioqKipvDyb/9gtQUVFRUVEWNbCrqKiovGWogV1FRUXlLUMN7CoqKipvGWpgV1FRUXnLUAO7ioqK\nyltGvgO7JElrJEmKliTp2t/uc5Ik6agkSXckSToiSZJD4bxMFRUVFZX88joz9nVAm5fu+wgIEEJU\nAE4AHyv1wlRUVFRUCob0OhuUJEkqDewXQlT769+3gaZCiGhJkooDJ4UQ7xTOS1VRUVFRyQ9y19iL\nCiGiAYQQUYCr/JekoqKioiIH9eKpioqKyluGmcz/Hy1JUrG/LcXE5DZQkiS1KI2KiopKARBCSK8z\n/nVn7NJft+f4A0P++vtgYF9e/1kI8dbeZs2a9a+/BvX9qe9NfX9v360gvE6641bgDOAtSVK4JElD\ngblAK0mS7gAt//q3ioqKisq/SL6XYoQQ/XJ5qKVCr0VFRUVFRQHUi6cK4evr+2+/hELlbX5/b/N7\nA/X9/S/yWnnsskSSJN6US0VFReVtQZIkRCFfPFVRUVFR+Y+jBnYVFRWVtww1sKuoqKi8ZaiBXUVF\nReUtQw3sKioqKm8ZamBXUVFRectQA7uKyhvg6tWrjBoxnHfKl6GMhxuN677LmjVrSEtLU9wlhODs\n2bMM6t8X73KlKVuqBC19G+Pn54dWqy0UX0BAAD27d8WzbCnKlS5Jx3at2b9/P3q9XnGfXq/H39+f\nju3bUK5MSTzLlaZnj64cP368wFvw3zbUPHYVlUJEp9MxbswoDuzZzYhGnnTzKYWtpTk3nzxj1Zkw\nLj9OYN+BQ7z77ruK+NLT0xnYrw+Xg84xpk012tUqj4WZKZfvR7Hy2HXCn2Vy8NejeHt7K+JLSEig\ne5dOxEaGM6ZLbZrX9MLEROLM9Qf8tO88WSbWHDh8BHd3d0V8kZGRdGzfFnMyGdOzIQ18PDEYDJw4\nf5ufdp7G1a0ku/f64+joqIjvv0BB8tjVwC6Dmzdv8sOiRZz78xxOTk4M6D+AIUOHYm5uXii+oKAg\nFi/+gatXr1K8WHGGDhtGnz59MDEpnBOv3377jaU//khIaAilS5Vm1OjRdOzYEUl6rWMsXwgh2L9/\nP6tWruRh+EO8vbwZP2ECzZo1U9wFYDAY8PPzY93atURFR+Hj48OkSZOpXbu2op6xo0dyK/Aoe0Y2\nxc7K4pXH915+wNgdF/njzFkqVKggyyWEoEfXzpgmPGTjpPZYmr9aMWT10St8s/sif164hJubmyyf\nVqulhW8TqrpZsHhiZ0xN/3kcCiGYvSGAnWfuc+ZcEPb29rJ8SUlJ1K9bm94tKvHpiPavHId6vYGJ\n87ZzPSKN47/9joXFqz/vghIWFsbiH37g5O8nsbG2oVevXowcNQobGxvFHLmhblB6gxw/fhxf36aU\n9ijKhlVLmDF5DFu3bKJrly5kZWUp7tvu50fnzp1416cSm9csY/TwASxa+D3Dhw8rlNPPJYsXM2TI\nYNq0aMTmNcvo815HZkyfxqeffKK4C+DTTz7hwxnT6fNeRzavWUabFo0YMmQwSxYvVtwlhGD48GEs\nWvg9o4cPYPOaZbzrU4lOnTqy3c9PMc/t27fZtWM7u0fkHNQButYow6SmXnw181PZvj/++INbVy+y\naVKHHIM6wIjW1en6bhkWfD9ftm/Xrl1IGQksmfRqUIfsgPTZ4Ja846Zh9erVsn2rVq2iUmknPhvZ\nIcfJhampCT9+1BtJm8Tu3btl+55z+fJl6tWrh7WFxM/LFvDV59P57cQxmjdvRmpqqmIeJVFn7AXA\nYDDg7e3FskVzadOq+Yv7dTodzdp0ZcSoMQwaNEgxX1paGqVKlSLg4C9U96n6j/trNWjJkh+X0qpV\nK8V8UVFRVKxYkSvnfqN06ZIv7o+Li6fKu40JCDhO5cqVFfNdv36dVq1acv3CKVxcnF/c//BhBNXr\nNeP27dsUK1ZMMd+xY8eYOGE8F88E/GPGdeVqMC07vEd4eLgiM7FJE8ZhE3aO2Z1r5jnuWWomXrN2\nc+fufYoWLVpgX+/3utG4SAZjO9TKc9y9J89o8PFWwh9FYm1tXWBf4wZ1mdShIt2bVstz3NnrDxjy\nnT937t4v8NmlwWDA27McG7/qS71q5fMcuyvgIkt+ucypM+cK5HqZhg0bMGJIP4YM7PviPiEE7/Ud\nSu26Dfjo48Jt9azO2N8QQUFBWFla0rrlP5cJzMzMmDh2BNu2blXUd+TIEWr4VP1HUAewsbFh9PuD\n8du2TVHfrl276NyhzT+COoCLizOD+/dW/P35bdvGkAF9/hHUAUqXLkmn9m3YtWuXor5tW7cyZsSQ\nV4J3dZ+qVK9WhaNHjyriOf37STpV9TA6zsnWkjrl3Tl//rws36lTgXSs42l0XHk3J9yc7bh161aB\nXQaDgbPnL9KxQSWjY+tVLk1CQgLR0dEF9kVHR5OUlEjdquWMju3U1Iez5y9gMBgK7HtOeHg4oaGh\nDOjb8x/3S5LElAmj8duu3BmekqiBvQAkJyfjWsQlx9NBV1cXzp49iyRJit26d++OVS6n8q5FXNj5\ny05FfePHj8fRIef1UNciLsz/fr6ivvnfz8e1iEuOPkcHO8aNG6eo75ddv+Tqs7KypFu3bop4QkND\nsTIzzdcxlZmWQqdOnWT5nj17hlUuSzAvk5GWSq1atQrsMjU1RRgMmOfj/UmShF6nxd3dvcA+d3d3\n9LosJMn4xNXcLPu1mZqayv4dli5dGjNTU8zMXv25urq6kJycnK+f95tGDewFoGbNmly5dp2YmNhX\nHvM/cITRo0cr2kElNDSUc+cvkp6e/qrv4BG+/uprRX2nTp3i8NETr8x4hBDsO/ArmzdvUdS3efMW\n9h349ZX3ZjAY+PXYbwQGBirq+/qrr3P0paen82fQRe7evauIp6mvL8GP440eTwaD4FGKjosXL8ry\nVa5UkeCHuXan/P/vMzOLuNQsHj9+LMtXrGgRbj0wPguPeZaMHhPS0tIK7EpLS0NnkIiJSzLqu3X/\nCcWLuyryO8zMzMQg4NbtkFc8/gd+pWHDhkZfz7+BGtgLgLOzM8OHDaP3wBFERj4BsnNrN2/bwZbt\nuxg3fryiPk9PT1q1asXAYWOJi8sOFFlZWSxeupIzfwYxZOhQRX0NGzakhIcHYyfNICkpe0aSnp7O\n51/OIT4hka5duyrq69q1K3HPEvj8yzkvvrySkpIZM3E6JTw8aNCggaK+wUOGcObPIBYvXfniQvfT\np3EMHDaW1q1bU7583mu4+WXoyDGsPPvA6LiA24/RODpTo0YNeb4Ro1l57LrRcTsCb1G3Tm3ZKYhD\nhw1n1f4go+PWHgyiR48estbzra2t6d69G+v2nTE6duUvgQwd9n6BXX/HwsKC6dOm0W/IKO7dDwOy\nJzgHDh3hu0XLmDZtuiIepVEDewGZ99131KvfkMq1GlO7USuKlqzA4uVrOHz4MCVLljT+BK/J2rXr\ncC3mjmeVOtRt0oYiJbzZc+AIx4+fwMHBQVGXJEns3buPpNQMyrxTk7pN2uDqUYErwbc5dixA8XRO\nc3Nzjh0L4PK1W5T08qFCtbqUeacmyWmZ7N27L1+n36+Do6Mjx4+fYM+BIy98XlXr4lrMnTVr1irm\n6dSpE3FaiVV/3M51THxqBtN2X2bqR5/Kfp8DBw7kzO0n7D13J9cxEbFJzPI7wwcz5F/wGz1mLH4n\nrhJ47X6uY26ERbH4lzNMmvyBbN/kKVP5YcsJbtx9nOuYwEuhbD96gdGjx8j2PeeDqVPp27c/9Zq2\no2b95hQrXZEPP5/N9u3bqVYt7wvH/xZqVoxMkpKSuHnzJvXr1+dNvL/4+HhCQkLemC8qKoqwsDAa\nNGjwRnwRERGUKlWKqKgoRTNhcuP+/fuUL1+euLg4nJ2djf+H1yQ0NJQWTRvTs5obE5tVxMPJFgC9\nwcCh4Ag+9r9K5z4DmDd/gSK+Cxcu0KFta8a382Fkm+q4OmT7tFl69py7w0ebTjF5+kdM+WCqIr6j\nR4/Sv29vPh3gy+B27+KgyZ6Vp2Vo2RZwmc/XHGPh4qX065dbZ83XY8uWLUydMpGvx3akb7s62Fhb\nApCYnMYG/7N88/OvbPXboWiW2HPS09MJDg6mbt26GAwGxSccuSFJr58Vo+jaZV63bNXby5t+f2+z\n7217b48ePRLjRo8STvYaUbdCaVGrVBHh4eok6tb0EX5+for7QkJCxJBBA4SjvUY0quYlapYvLoq5\nOIrmTRqKw4cPK+67cuWK6P1ed+ForxFN360kqnu5Cxcne9GxXWsRGBiouO/UqVOiY/s2wsXJQfjW\nrSp8vD2Eo4Od6N2zu7hy5Yrivpf5l47P14q36oxdIf76VlV9/8dcb9KXnJzM5cuXadq0KTdv3qRi\nxYqF6ouPjyc4OBhfX1/u3r2r2LWD3IiOjubmzZs0b96c8PDwQlmS/DsRERGEhITQsmXLN3aGB//a\n8amWFPg3eFuD0b/he5vfm+pTfQX0qRuUVFRUVP6XUQO7ioqKyluGGthVVFRU3jLUwK6ioqLylpG/\nwhIquXLr1i0iIiKA7KwHOzu7QnMJIbh27RpRUVEAZGRkYGVlVWg+g8HApUuXiIuLA7J3uxZWrfnn\nz3/x4kUgOx+7Zs2ahVZr/t/geVYMZB83byIr5tq1awDcu3fvjWTF3LhxA8jOWHkTWTF37tx54S7s\nrJh79+5x/372Zqz4+PhC2fegGK+bH1nQG29ZHrufn594t0pl4W5vJxq5FxOe1ubC0dZGjB3xvnj8\n+LGiLr1eL1asWCEqlS8ryrg4iqZlSohyGitRxMFeTP9gioiPj1fUp9VqxffffSfKuBUXXi5OopF7\nMeFhaSbcXJzFFzM/F6mpqYr6UlNTxRczZwq3Ii6iSnFX4eNoK7yLuoiyJdzE9/O/E1qtVlHfyxT2\nsfno0SMxdtQI4WSnEfU8S4pa7k7Cw8VR1PGpWnh57AP6CUc7W9GoUllRs5SLKObsIJo1qi8OHTqk\nuO/y5cuiV4+u2Xns1b1FjXLFhIujvejQpqU4deqU4r5Tp06JDm1bCRcne9GsdmXh4+kuHO01oleP\nboWSx37o0CHh26ShKObqLJrXryaqepUQjg52YsjggSI0NFRx38vwb+WxS5I0BRgOGIBgYKgQQvvS\nGKGE67/AjA8+YO/6tUxztaGJow2mf+1Ai8rUseFpCkcyJU6cPo2Xl5dsl8FgYEj/vtz4/QSfeBaj\ngav9ix1vYSnpLLsfwwWdOSfPnKV48eKyfVqtli7t2pJ8/SqTXW2oZmv5wncnLZPlT9N46lqCgFOn\nZHfEgeydu62aNqFYYgxTyhel4l87JYUQXH6Wwry7Mdh6V2bvocOKdsR5zhvZedqkMe95OTO+Tlk8\nHLJLBesNgl9Dn/DJb6F07juQed8ruPO0TWvGNfZkZGNvXO2yd4JqdXr2XXnIh/uuMPnDT5Tdedqn\nF5/2qMvgFlVxsM0+g0zLzMLvjxt8tvU0Cxb/SP/+AxTxbdmyhamTJzD7/Vb0aVEDm7+qniampLPh\n8AW+2XxS0Z2nixYt5IcF85g3qStdm9fA4q/qmbHxyaza9QdLt5/i4KFfFWttmBP/Sh67JEnuQCDw\njhBCK0nSduCgEGLjS+PeisC+adMmZk+awOZyzjjmUrLULzaZzXpLbty9l2O5z9dh3rffsmfZYrbV\nKYu1ac6+7+9E8qd1Ef7487zsbc6Txo7l9p4d/FDKEbMcnksIwazIJHQ16rLTf78sF0CvLp2xun2F\neVU8cnztOoNg5OUHeLfvxg/Llsn2PSc0NJT33x/OnTt3cLC3IyY2jt69evHD4sWKLW/pdDoqe3sy\nsWoRRrxbNscx8Wlamm88y8dzFzBw4EBZvqSkJN7xKs+yHjXoXL10jmMi4lNosvAIa7fuoGXLlrJ8\nERER1PSpyq4Pu9CoUs7LLjfCY2k5cwdHT5zEx8dHlu/q1au0btGMgEXvU7lszpOYwGv3eW/mVi5d\nuYaHh/Fa+HkREBDAsMH9ObVuKiWL5/ylv/fEZSZ8t4vbd0ILbRn238xjNwVsJUkyA2yASIWe9z+F\nEILvvvqSj4vZ5hrUAfq42mGXnsqBAwdk+bKysli8cAFzK7nlGtQBPvB2I+LeXYKCjFfay4uEhAQ2\nbFjPLDe7HIM6ZB9kHxe34/jx4zx48ECWLywsjOMnjvNFRfdcv5DMTCTmVi7Bhg3rSUxMlOV7TkJC\nAi1aNKd7p7ZEhF7lzrU/uXv9PE9jnjB8+DBFHAD79+/HxVSfa1AHcLaxYH7LCiyYM1v2ppdNmzbR\noEyRXIM6QElnDV92qMrCed/KcgGs+Gk5fZtUzDWoA1Qu5cqkjjVZvEj+GckPixYw+b0GuQZ1gEbV\nytG7eTVW/LRctm/Bd3P5amyHXIM6QNfmNahXtTSbNm2S7VMS2YFdCBEJLADCgcdAghAiQO7z/he5\nfPkyKU+fUt/eePnRXhpTfl76oyzfkSNHKG1twTt/LU/khokkMaCEI2tW/CTLt2PHDho6aXC1yPss\nw9rUhM7OGtavXSPLt2HdOnp4FMHGSLOGolYWNCnuzI4dO2T5XnjXr6dB3dpMGj/qxcVgFxdnNq1d\nztGjR7l3754inrUrljOimvGG0S3KFSMlPu7FhdWCsm7lT4xskPuXyHN61irHn+eDePw49yqJ+fKt\n+ZmRrYxXNxzWshq7du3OsZ9AfklPT2f37t0M7WC82fioTnVYJ/PYfPz4MeeDgujZyvgSy6geDVn7\n8wpZPqWRHdglSXIEugClAXdAI0mSMqXc/mM8ePAAb40VJvlY7qhgY8mDsDDZvgqa/K0rV7SzJuxu\nqDxfWBjekj5fY73NJcJCXm0+8Fq+0BAq2uYvy6aCpUTY/dzLw74Op0+fpkvHtq/cb21tTctmTTlz\nxnjN7/zw8EEYVYsbL6lsYiJRqbij7DOgBxERVC1h/DqBtYUZ5Yo7v8jmKgharZbY+GdULFnE6Nii\njrbY21oRE2O8CUhuxMTE4KCxoaiT8eWOimWKER0bJ6upfEREBJ6l3bDOpXPZ36nm5cHD8EcFdhUG\nSqQ7tgTuCyHiASRJ2g00AF5pjPnFF1+8+Luvry++vr4K6N8cFhYWZObzbFlrEDx8+FD2mnfnEjm3\ncHuZDIOBc+fPyfaNcnfM17hMg4HtO3aycXvBZ9FWJia8Uy33ZYO/k64zsHTuXObMnVtg33Osra1p\nWDfnphb37ocxaNAgRZqR21uakZFVKl9jo+Oe0aNHD1k+a3NTMnT5+2KOeRpP/fr1ZfkkCbJ0BizM\n8z7jEkKQkJhEmTJlZPk01pbZGR9GjvEsnR6DwSD7YnsZ93x+9rRZWCiYBnzy5ElOnjwp6zmUWGMP\nB+pJkmQlZf/EWwA5dsn94osvXtz+rwV1gDp16nAlPomkfHx4TiRnMkxmi7wbN25wPllLVj6a8h6L\nS+XTr2fL8gUEBPB7Zv4KHP2mlfh540ZZvlXr13P0WaZRlxCC4wkZBAQEKJJ6u2/fPlb8vIG0tLR/\neK5cDeb+g3BSU1MV8Qx5fyQHQo3PUp+lawlJyCA6OlqWr1PHjhy4Fm7Udy82iTRhKqtVnRCChnVr\ncyDI+FniuTuPKe7mhl6vL7BLr9dTrFgx/rxp/P3tP32ThvVqy3pvaWlppGQauP/o1faXr/hOXqNR\no0ZGx+UXX1/ff8TKgqDEGvt54BfgMnAVkIBVcp/3v0jRokVp27YNfrF5N7BN0Rn4JT6NsRMmyvJV\nqlSJChUrsjfiaZ7jotK1HImMZ/j78tqBNW/eHL2thjNJea+FhqRlcis1k/fee0+Wr2fPngQnpHA7\nMTXPcadiEtFb29K8eXNZvue0bNmSevXr07R1F3bt2c/Va9dZtOQn2nXtw7KlS7GxsVHEM3bCRNZd\nCScpI+8lgZ8vhNG+XVuKFi0qzzdpCssD76E1MvFYevI2g4cMldWqDmDsxCksOXQFgyH3iYAQgkX7\nLzF63ERZm81MTEwYPW4Ci3aeznOcwWBgya6zjJs4pcAuyD6rGzRoMD9u+y3PcZnaLJbt+INxEybJ\n8imNIlkxQogvhRAVhRDVhBCDhRAFX9z6j/PlnLlsSNRyLD4lx8dTdAbGRTyjZ98+VKhQQbZv3uIl\nfBUSzdnYnDNCnmZoGXQxjKnTZ1CkiPH1zryQJIlFy3/io8dJ3ErNeSYdkZHFuPAE5i5YIDst0MrK\nirnfL2DopQeEp2bkOOZGQiqTgiNYuGy5Yh1rJElizZq1TPlgGivWbKZJy05cCr6Nv/9+evfpo4gD\noEKFCvTo1Zuev1zMNbjvu/mYJRcjmPm1/CyVJk2aULH6uwzacJrMrJyD+8+Bd9h3M4ap02fI9vXo\n0QNh68LEnwPQ6189qxRCMHvHGW7HZjJixAjZvpEjR3LzcRKzNwTkeFap1xuY8IM/WDvRvXt32b5p\n02ew57frrN51KsfHM7VZDPpsA5Wq1qBx48ayfUqi1mMvABcuXKBz27ZUtDCht50Z5a0tSDcYOJaY\nwY5n6XTp2ZOlK1fJzmF/TkBAAH3f60HDIvb0c7OntK0VSTod+54k4hf+lDETJvDVN98qFvj8/PwY\n8/5wWjja0t3eguIWZsTr9OxLyuRAXApffTuHCZOUm6H8uHgxMz/9hG4eRejp7oCLpTmR6Vq2RyZy\n5Ek8y1f/TB8FA+7LFGZ9bZ1Ox/gxo9m/+xeGVy9J14pu2Jibcis2idVXI7kak8K+g4cV2+CSnp7O\nwL69uXz+LKMaetK+SgkszEy5HP6UFWfCeJSi5+CRY3h7eyviS0hIoHuXjsQ8esCY1tVo4VMaSZI4\nc+sRPx0NRmeu4cDhI7IbZz8nMjKSju3aYKZPZ0yX2jSoUgYh4PjFUH7yP09R99Ls3rcfR8f8XSsy\nRkhICB3ataFkUQ2jejSkZsVSaLP0HDoVzIpfAqlRqw6btmyTffaTF2prvDdIamqqWLNmjWhYs4Yo\nVayosDWRxKihQ8TVq1cLxZeQkCAWL14s6lStIkoVKyo0Zqbig0kTRUhISKH4YmJixJxvvxE+3l6i\npGsRYWsiic8/+UREREQUii88PFx89vHHoopnOWFjaiKqv+Mt5nz7rYiJiSkU3995E8fm1atXxaj3\nh4kKZUsJWwtT0bhOLbFmzRrFyzMIIYTBYBBnz54Vg/r1Ed5lSwmNpZlo2aSR8PPzE5mZmYXiCwgI\nEO917Sw8y5QUGitz0bFtK7F//36h0+kU9+l0OuHv7y86tmstypUuKTTWluK9bl3E8ePHhcFgUNyX\nmZkptm3bJlo2ayLKlvYQdjZWYtCAfuLcuXOF4nsZ1NZ4/x7/I11c3jqX6lN9/0d8agclFRUVlf9l\n1MCuoqKi8pahBnYVFRWVtww1sKuoqKi8ZaiBXUVFReUtQw3sMrhy5QoTx4yhW5s2WEuwevVqUlPz\n3kVZUIQQnDlzhlHDhtGlVSssga1bt5KZaXxLfkEwGAwcO3aM4QMH0LV1aywl2LdvH3p9/mqRvC46\nnY59+/YxuG8fbE0khg8cSEBAAIZ8lFMoCJmZmWzdupWBvXqiMTNlzPvvc+bMmULLdkhNTWX16tX0\n69EdO3NTJo0bx9WrVwvFBdn55T/8sIi+3btiZ2HGjGlTCZFZtC0vYmJimDPnW/p074KdlTkzP/+M\n8HDj2/8LSnh4ODM//4xe3btgZ23BnDnfyioyZoyQkBBmTJ9Gz+5d0FhbsHjxYhISEgrNJxc13bEA\nREdH07trF0KuX6eTuUQZE0gXglOSOVczspi3YAEjRo1SzHfv3j16duxI3KMIWqSnU0wI0gSc0Wh4\nKEmsXL+ebt26Kea7cuUKvbt0QUpKpD06XE0lEgyCo5I5T03N2bxzJ02bNlXMd/LkSQb17k1R9HSy\nMcHZzJToLB27U/ToNfZs37uX6tWrK+bbs2cPo4cPo6K9NZ1cbLA3N+VhmpZtkYk4ubmzfe8+RfuD\nrl61io+mT6OBuwsdPOyxMTPjdkIqG0Oi8K5YmW27divWr1MIwZxvZjN/3jzaeLvRtqwTFqYmXIlO\nZsPVCBo2asz6LdsU6X4FoNfr+XD6VNb8/DM9apalmacrkgTnHsSz5fw9unTtyk+rfsbS0lIRX0ZG\nBmNHj2Tf3r30961MPa/iCAEnbjxi95nbDH//feZ99z2mefQveB0SExMZOmgAp08HMrTdu1T3ckOb\npefw+bv8eu4WMz78kI8+/kSxzYE58a90UMq36C0J7HFxcdSvWYOmKYkMtTF7pSHFgyw901Ky+PDb\nOYybMEG2Lzw8nLo1atAtKZH2BsMrJYPvCMEcKyuWb9gou3YLQHBwMM0aNmSyBbSyNn/lgD2XoeWr\nNAO7Dh5UJLj//vvvvNexA9+VcKCR4z9rtAghOBifyrcxqZwIPE3VqlVl+3755RcmDB/G2lplqOH8\nzxKwBiHYEBbD0keJnL1wkVKl8leZMS+WLf2RhV/NYkfrang7a/7xmM5gYN7FMPZGZ3A66AIuLvmr\nJpgXn378IYe2bmBXz1ov2vA9J1OnZ+rRm1zTWnPi1GnZNXGEEAwfMoiwi4FsH9YIF80/S0ykZGQx\nbPNZMp1Ls/fAIdk7sXU6HV07dcAyJZJ1E9qhsf5n9ca4pDR6fb+fsj71WbNug+xgm5aWRvOmjale\n0oZF4zth+VKfgkcxCXT5ZCPtu/flm2/nyHLlhRrY3wATRo/myY6tzMijTvpjnZ6hCRncCXsgeybW\no0MHbI8epY/IfUkiVAi+srHlUUyM7K3N9WtUp0X4PTrb5j7DOp2u5UcLDXcjHskq7GQwGPAqVZKP\nNAJfx9ybieyITeKggztnLslrRJGWlkZpdze21CpDNSdNruMW3okkrGwV2a3/oqKiqOhZnt971KWs\nQ+5BdMriCjtJAAAgAElEQVSp29jUb82S5fK6/ty4cYOWjRtwYWRTXHP5/Qkh6PXLRer3HclHH38s\nyxcQEMD4of35c3o7NFY5l63N0htovvgYoz+ZLbsU8saNG1k5/0tOfNUL81yas6Ska6kzYzNLf94o\nu/Xf3LlzOPfrDnZ9PSDXL4nYZylUH76YgN/+oHLlyrJ8uaFuUCpkUlNT2bJ5M4Os8j7NK2FmSnMb\nK35eJa/IZWRkJMdPnKCzIe91bS9JwluC7du3y/JdvXqVB3fv0t4m7zrWDazMsUpP49ixY7J8R48e\nxVabQdM8gh5A9yJ2PLh7l2vXrsnybd++nRpOmjyDOsCIckUJOHGCJ0+eyPL9vHoVXb3c8wzqAFN8\nSrFly2bZ12eW/7iY92uUyjWoQ3aQ+LBBOVYtXyr7esnyxYuY1NQ716AOYG5qwowW7/DTkkWyXADL\nlyxiRtdauQZ1AI21BRPbV+enHxfLcun1elb+tIxPBvjmOfN3ddIwomNtflq+VJZPadTA/hoEBgbi\naW1JcSOt3ABamhjw3yEv0B45coRaZmbY5OOUslFKKnu2bJHlO3jwIM3NpFz7nT5HkiRaiiz8d+2S\n5du/ezftrSWjp8xmkkRbe0vZPWT379xOV9e82wwC2Jmb0czNhSNHjsjyHdj1Cz3LGq+4Wcrehkqu\nDpw+nXdJWqM+f396VylhdNy7JZwx1Wm5efNmgV1CCA4eOUqf2uWMjm1ftSQ3b9/h6dO8y0/nxdOn\nT7kdEkr7Wp5Gx/ZrWpkDh4/IuhB+8+ZNzCXBu+/k3s/1OX1bVufAfv8CuwoDZcoP/o+QnJyMvUn+\nzogcTCRu3Lgpe52vFYCp8e9fOyn71FiOTwJGOeRvKcdBkvj+59UsX726wD5rE4mZZVzzNdZREnz2\n6ad8+umnBfbZmZnyXt38VTW0zMpk6NChDB06tOA+czOcKuWvS5FpZjpt2rQpsAvA0tQEZ+v8dQ0y\n1WVSrZrxfqV5YSJJ2OfDZ2pighkGXF3z97vODWc7a0zz81mwtkCn08laJgSoUCp/9fGd7WxITi6c\nbLiCos7YX4OiRYvyJJ+tx6L0BmrVqiWrIua2bdtIsTfe4xEgVkCnLl1k+b5fsIBo0/y1+IpCYuzE\nSbJ8YydM5HFW/tIZIzFlwcKFsnwdOnfmUVr+0kPjTczZtm2bLF+td2sRkZy/Bs6Jkjm///67LF+Z\nUh6EJ6YZdekNgmSDCaGhoQV2GQwGbG2siUwwHtDStDq0QiIxMbHAvsTERLR6SMs03urhSXwKGlsb\nWT/LkJAQkjP0+Uq3DY95hmsR471m3yRqYH8NGjRoQIJkSohWZ3TsAWFKf5nNBTp06MDNLB1PhfFT\nyuMaDQNl+nr27MmJdC1peXTEAdALwaEs6C/zYljfgQPZm5SJ3sj7S9UbOBKfQs+ePWX5+g8dxvbo\nnBuk/J3ItEyCYhPo0KGDLF+fwUPZeNd4a7WrsYnEaQ00bNhQnm/gYNZdfWx03NG7Ubh7eODpaXxZ\nIzckSaJP796sO3vX6Nht5+/SrEkTWSmW9vb2+DZpzLbfbxgduzbgGn369C6wC8DT0xM3d3eOnL9j\ndOyagxfoO0B+j1wlUQP7a2BmZsa4yZP5KVOgyyMYXcrI4nqWnv79+8vy2dnZ0X/AADZbZjfxzY1T\nAtI1Gtq2bSvLV7JkSZr5+rIuPe8vrl3pWXiUK0fNmjVl+WrVqkWJsuXYEpt3sP0pJplmvr54eHjI\n8rVr145nkhkHHsflOkYIwbzQKPr3H4CdXf7OlnKjf//+nI9KIDAPn85g4MsLDxg9YYLs3OuRo0bz\ny41HXI/OudsWZM+evzp1j/EfTJflAhg/aTLL/wghPJduYgBxKRl8F3Cb8VOmyvZNmDKVeXuDiEvK\n/awkPDaR5b9ekd2qTpIkJkyeyhfrTpCWoc11XPC9J+z87RojRoyU5VMaNbC/JtM//BC76jX4JFVP\n1EvLMjohOJqWyWdpevx278HW1viFOmPMW7iQ+HLl+dHSkoSXgnuWEBwSsNrGht0HDyqyKWPVho2c\nsXVgSaqW5JdOQ9MNgg2pWrZijt/evbJdAFt37WZtso6VUYmkvdReLUmnZ15kIr9hxcr1G2S7TE1N\n2bX/AB/fesKGsGgyX/I9zdDyQXAEYbYuzF2wQLZPo9Gw7ZddDD5+g19CItG99POMSE5nQMANzEp7\nM33Gh7J97u7uLF2xig5b/+TXkCev9CINeZpMJ78gqjZsJjv1EKBatWp8/PksWiw+RuDdqFcmH1ci\n4mj143HeGzCE1q1by/a1bt2aHn0G0nLWTq7cj/rHY0IIAm9G0Pzz7Xz8+UzZ1w8ABg0aRKWa9Wg/\nYx0h4f888zIYDBw+d4t2M9aydPkKxTpEKYacdajXufEWdVDKzMwUUydOFE62tqKJi5MY6KgRnW0t\nhZvGVtSpWlWcOXNGUV9ycrJ4f9AgYW9lJZpqNOI9MzPRAoSztbVoWqeOuH79uqK+2NhY0btrV2Fv\nZSXauziKQY4a0crGQjhaW4kOLVuIBw8eKOp78OCB6NiqpXCysRY9PVzFsOIOoksJV+FgbS36dOsm\nYmNjFfUFBweL5g3qi6L2GjHIu6QY5eUmOpX3EI62NmLk0CEiOTlZUd+ZM2dEvRrVhYezoxhRw1OM\nr15WtKtQWjjba8S0KZMV72p06NAhUe0db+HlVkSMb/iOmFDfUzR/p5Qo6uwoZn/1pdDr9Yr6tmzZ\nLDxLlxQ+Zd3F5NY+YnzzSqJehVLCo3hRsXTpEkW7DBkMBrF06Y/Cw62YqF+lnPigW30xrkMt4eNV\nUniWLSW2bt2imEsIIfR6vZj99VeiaBFn0aJuZTGtX3MxumsD4V3GXVSr/I44fPiwor6coAAdlNTA\nLoPk5GSxadMmMWfOHAGIS5cuFaovPj5erFmzRnz77bcCELdv3y5U35MnT8SKFSvEN998IwDFA/rL\nPHjwQCxdulQAYsWKFSIqKqpQfbdu3RKLFy8WgFizZo2Ij48vVN+lS5fEwoULBSA2bdokUlJSCs1l\nMBhEYGCgWLBggQDEjh07REZGRqH59Hq9OHr0qJg/f74AhL+/v8jKyio0X1ZWlvD39xfz5s0TgDh6\n9KjiX1h/JyMjQ+zYsUPMnTtXACIwMPCNtMUTomCBXd15qhD/I+253jqX6lN9/0d86s5TFRUVlf9l\n1MCuoqKi8pahBnYVFRWVtww1sKuoqKi8ZaiBXSY6nY64uNw3oChNVlaWrGJKr4tWq32jvucdobTa\n3DeFKEl6evaW/6ws41vVleB5BUedzvjuZbkIIUhOTgYotM5XL/sSE7M3RxVW56u/YzAYePbs2Qt3\nYaPX64mPj39jPjmogb2A3Lx5kzHvD8fZ3h7PkiUxk6BW5UqsW7euUNrVXbhwgQG9euGg0VDOwwMT\noGGtWuzYsaNQPrQnT56kR8cOOGg0eJUqhSnQrpkvBw8eVPygFkJw8OBB2vo2xUGjwVICe40t3Tu0\n5+TJk4q6IPsDumPHDprWq4OTgwPWZiY42dsxuF9fLly4oLgvMzOTdevWUdunCkWcnbA2N8XF0YEx\nI9+XVWExN1JSUli6dClVKnhSvKgrVuamFCvizLQPphAWFqa4Lz4+nnnz5lK+TEk83N2wMjelpHtx\nZs38XHbp45x48uQJs2bNpGQJN8qUKomluSnly5Zi3rx5LwKvkoSFhTFt6gcUK1qEcmVLY25mSpVK\nFVi6dCkpKcZLVPwbqOmOBWDL5s1MHjOavs429HSxpbiFGXoh+CMhjfUJmeBRhkPHj+Po6KiIb9GC\nBXwzcybNMjJoYDBgB+iAK8AJW1s869Vj94EDWFlZGXkm4wgh+Hj6NLb+vJqhTlZ0dbFDY2ZChsHA\nobgU1iZkUr9tB9Zs3KjITle9Xs/wgQMJPHSAfqYGWlpbYmUikWIwcDhNi59Oot+Ikcz9/ntF2o9l\nZGTwXpfORN8KZkJldzqWK4a5qQlx6Vo2337MsuuP+PDzWUz+4APZLsjuPdqhdUssk2KY+G4p2ngV\nx9RE4nFSOmsvPWTlpYcsWrqc/v0HKOKLjIykdXNfymtgYlMvmnq7IUkS92KTWBUYyoZz99iyfaci\nO0EB7ty5Q5uWzWlcoRjj21entlf2DszrD2P46der7D1/D/+Dh6ldu7YivqCgIDp1aEe3xpUY06Uu\nVcq5Zd9/K5yle85x6vojjgacwNs7f1U8jXHkyBEG9O/LkM71GNmjEeVLFkUIwe8XQli87ST3IpM5\nGnCiUHee/msdlCRJcgB+BqoABmCYEOLPl8a8FYH95MmT9OrUkfVlnfGyebWhgUEIvopMJKq0NwGn\nAmUHox07djBx6FCmpKWRU+M0HbDO2hrPDh3YsnOnLBfA4oULWfnNV6wv44yT+auBO01vYNTDZzQZ\nMITvFi6U7ZsxZQon169lvq0Z1jmURE7QG5iQomPsrC+YpECwHdS3N8lX/2RNs0qY51ACNiI5nfb7\nL/Hd8pX06tVLlksIQWvfppTLimFxmyqY5PD+bsYk0nbzn2zf6y+71WBWVha1a1Sjm6cdn7arluOx\nd/puFD1W/8Fvp05TpUoVWb7ExESqV63Mx12q837rnHvS7jt3hzGrTnDh8lXZtX4iIiKoXasGKz7o\nTOdGOb/21f7nmLv9LFeuXcfBwUGW7/r16zRr2pjdC0fRsMarBdOEEHyz+hB7Tt3l/IVLmJvnrzLq\n6/JvBvb1wO9CiHWSJJkBNkKIpJfGvBWBvXmD+rSPCaNLkdwLROmFoH3oUzbtPyirYp8QggplytAp\nPJyKeYzLBD6zsuLC9euymjBnZmZSqngx1pdywDOPOttPs3S0vRVN2KNHODsXvFxpfHw8ZUuUwM/Z\nGpc86mzfz9IxMR0excRgYZG/euM5cffuXRrUqkFwv0bY5PCl9ZyTEU/5+HoswSF3ZX0xBwYGMrRn\nN66NboppHnX8t1x5yJanFgT8HlhgF8DOnTtZ8sV0fpvYMs/XPf9IMLesyrJhyzZZvh9++IGz+9az\n7YOOeY6bsuYEVt4NmffdfFm+GdOnoY24yMLxnfIc1+fLbTTsOIBJk+QVAhs0oB9VimYxbUjudfKF\nEPgOX8Skj75SpOdwTvwrG5QkSbIDGgsh1gEIIXQvB/W3hbt37xJ8LZh2znm3VjOVJPo4WPDTDz/I\n8gUGBpIZH887RsZZAvX0en5aKq891969e/G0Ms8zqAMUMTejmbOGjRvkFebasH49jW2t8gzqAOXM\nzShrJrFXZuGxlcuX0a+Ce55BHaCphwu6lCTZHY1W/riEUTU88gzqAO9V8SD42jXu3jVeAjcvVvz4\nA+Maljf6ZTSsoRf7/PfLXo9euexHxrYxXmxrTFsf1q9bK+sCdVZWFuvXrWVMl3pGx47tUoeVMlvV\nxcfH479/P0O75j0xkySJsb0as2LZj7J8SqPExdNywFNJktZJknRJkqRVkiTJ66j8H+X69etUd9Jg\nkY8uSnU0lgRfkdd8+fr165TX68nPV7VnVhZXg4Jk+YKDg6lllr9shnct4JrMC43XLgRRzZC/D7uP\nTktwcLAs3/XLl2hQzHhNcEmSaFDcUbYv+NoVGpfOaQHtn1iamVK7VFFu3DBeazwvrt+8RSOv4kbH\nuWis8HRz5t69ewV26XQ6Qu4/oGFF463jvEu4YCZBdHR0gX1RUVGYm5rgVdJ4F6ZG1coSci9MVubR\n3bt38Szlhotj3pM4gCa1vAiW+btTGiVa45kBNYFxQogLkiT9AHwEzHp54BdffPHi776+vvj6+iqg\n/+9yP+y+7DV24/OT/8/p06dl+8aXcMr32G3btrFu69YCu6wkmOKYv9LGQghmz57N7NmzC+yztzBj\naC5rwS+Tlp7G2LFjGTt2bMF9lmbgWypfYxMTE+natWuBXQDWRs5E/k5CQiJ16tSR5XudQy0tLZWS\nJY1/CeSFoyb/yQEGg0H2mrdnyfy1xlOakydPys4GU2LG/giIEEI8n779Qnagf4Uvvvjixe3/YlCv\nUqUKV56loDXSYQjgfEomXbr3kFUR848//iBSoyE/VybumpszdvJkWT4/Pz8u6fMXHC5oYc6CBbJ8\n336/gGsm+fvwXTO3ZPv27bJ8I8eN50y08VVCIQRXErWcOnVKlq9zl26cemh8j0OmTk9IYqasVnVC\nCOrXq0tgaJRRX1xKBk/Ts3Oy5fgqlC/H6VsRRn0hj+OwsLZFq9UW2KXVajG3tCY0wnhHqsBrYbzj\nVV7We4uLiyM2MY24BOPpjH9cDKVq5cpGx+UXX1/ff8TKgiA7sAshooEISZKe5xe1AJRPzv0P4Onp\nSdVqVTmcR8cYyL546peoZcykybJ8jRo1wtLZmdtGxmUC50xNGTN+vCxf165duZuRxd30vDcHPc3S\n8Vt8CoMGD5blGzxkCKdSM4jT5738cz9LR5hOyJ7Rjho7jq13IknLyjvv//dHcZhp7GW3qhs1YSIr\nLz9Cb2Qi8Mv1R1StVk1WqzqA0RMms+z0PYTI27f2dChdOnfCySn/Z2c5MWrcBJYfuWZ03E+/XmXI\n0GGyZtDm5uYMGTqMn/adMzp2+b7zjBor77Pg7OxM506dWLc37+ssQgiW7zjF6HETZPmURqkNShOB\nLZIkXQF8gG8Vet7/HDO/ncN30SmE5tIU2SAEX0cmUrZSZRo0aCDLJUkSs+fPZ4uNDbnN+3TARmtr\n2nfsKCsjBsDS0pJPPp/J1EeJxOcS/NL0BqZEJDJq9GhZGTGQ/eEZNXo0s9L0pOcS/BL0BmalGfh0\n5kxZGTGQ/cXctn17Rv9+i6xcvkwiktOZcOoOM7+ZI3tZq2HDhpTxrsjkI9df6Wb0nJsxiXx84g6f\nf/WNLBdkfzEnS9Z8c/harsH99N0oFpy4xfSPP5XtGzp0KOfvPWX1kdyvJe07d4ftp+8wYaK8DBWA\nCRMn4XciGP/A67mOWe1/jqCQKIYMGSLbN+OjT5i/IYDTl3O+qC2EYPaqQ6RkmdKlSxfZPiVRNygV\ngK1btjBp9Cj6ONvQ6w1uUPLNyKDh3zYoXQZ+K4QNSp/MmM6W1asY6mxNV2fNiw1KB+NSWJegpX7b\n9oWyQamviYFWNn/foJSFnw76jxzFnPnzFd2gFHXrGhMqu9OpXPEXG5Q23XrE8huPFd+g1LF1KyyS\nol/ZoLTm0kNWXXrID8t+ol8/ef1xn/P3DUoTmnrh+7cNSisDQ9n05302++1QfINSowrFGN/Oh9pe\n7kiSxPWHMSw/fJV9QcpvUOrcsT1dG1V8sUFJCEHQrQiW7jnH6ZuPOXLsuGIblI4ePUr/fn0Y3Kku\no95r/GKD0smgOyzx+537T1I4cuz4f26Dkqx1qNe58ZZ1ULpx44YY8/5wYWdtLRysrYSZhKhVuZJY\nt25doXSqCQoKEgN69RLWFhbCztJSmIBoWKuW2L59u9DpdIr7Tp48KXp07CCszM2Fo7W1MAXRrpmv\nOHDggOKdYwwGgzhw4IBo27SpsDQzE5YSwsrcTPTo0EGcPHlSUZcQQuh0OrF9+3bRtF4dYWFmJqzN\nTIStlZUY3K+vCAoKUtyXkZEh1q1bJ2r7VBFWFubC2sxU2NvaiDEj3xc3btxQ3JecnCyWLl0qKnuX\nFzZWlsLK3FQUcXIQ0z6YIu7fv6+4Ly4uTsybN1eULVVCaGyshaW5qXAv5ipmzfxcREZGKu6LjIwU\ns2bNFO7Fiwo7jY2wNDcVZUt7iHnz5om4uDjFfffv3xfTpn4girg4CQd7jTA3MxWVK3qLpUuXKt5G\nMSdQOyi9efR6PYmJibi4uBhd21SCrKwskpKSKFKkyBvxabVakpKScHV1fSO+zMxMrKysyMzMlL30\nkh/S09OxsbHJvjhXSDsH/05qaioajQadTqfIGU9eCCFITU3Fzs4OvV6PiUnhloYSIrvomIODwxvx\nGQwGkpKScHJywmAwKHJGZ8yXmJiIs7PzG/E951/beZov0Vsa2J/zP9Ke661zqT7V93/Ep7bGU1FR\nUflfRg3sKioqKm8ZamBXUVFRectQA/v/QVJTU5GAtLS0f/ulqKio/AdRA7sMUlJS2Lx5M3PmzAHg\n8mV5Rb/yy6+//or468/CJCoqipUrV/Ltt9n7zR4+fFiovocPH7Js2TIAVq5cKatoVH64ffs2ixcv\nBmDt2rUv2qwVFpcvX2bRokUAbN68uVC77wghCAwMZMGCBUB2Sd/C6Oz1HIPBwLFjx5g/P7s0r7+/\nf6G2/9PpdPj7+zNv3jwAjh07Vqjt+DIyMti5cydz584Fsusy/aeTQV43P7KgN96iPPbMzEwxbfIk\n4WynEW3KlhDjK5YU/csUFSUc7UVdn2rizJkzherv0bmzcAPxXpcuhfL8MTExoleXLsLO0lI0srER\n7UxMRB0Q9lZWol3z5uLBgweK+h48eCDaN28uHKysRFsba9EdREtbG2FvZSV6d+kiYmNjFfUFBweL\nZvXriaL2GjHIu6QY7eUuOpf3EI62NmLk0CGK5yafPn1a1K3hIzycHcTImp5iQo2yov07pYWznUZM\nmzxJZGZmKuo7dOiQqFrBS3i5FRETGr4jJtb3Ei0qlhZFnR3F119+IfR6vaK+LVs2C8/SJUX1cu5i\ncmsfMaF5ZVH/ndLCo3hRsfTHJYruezAYDGLp0iXCw62YaFClvJjavYEY3+Fd4eNVUniWLSW2bt2i\nmEsIIfR6vfj6669EUVcX0aJRLTFtRDcxpn9b4V2ulKhWpZI4dOiQor6cQM1jL3yysrLo3LYN3L/N\n7IrulPhbFyWdQXDgcRyf336C3+49tGjRQnF/ZmYmrk5O9EtPZ6u1NbHPnmFp+Wonp4ISGxtLvZo1\n8Y6Opl1WFjZ/dwMnTE057eDAmaAgypUrJ9t3//59GtauTdukJDoZ9Fj9LTc4RQh2mJlzpWhRzl66\nhKur8ZKtxrh06RJtmjdjenlX+pR2xeJvudZPM7R8ExLFPRtnTgSeRqMxXrLVGMePH6dvj27Mq+dJ\nN0+3f9Rmf5SczrSzdzF4eOJ/+FdF8ui3bdvG1PFjWNG+Cm28iv8j1zo0LpnRB69Tvk4T1m3eokge\n9uIfFrF43jesG1ifhuWL/eM5r0TEMWzzWdr1HMBcmU02nvPh9Gn8umc76ya0oXq5/1+iWAjB6VuP\nGLLkMJNmfMykSVNku4QQDBk0kLCQa6z+djReZdz/8divf1xixCcrWLBoCX379pXtyw01j/0N8O3s\n2QSsXsrGWuUwy6Uu+5nYREZde8SDR4+xtc1fWdr8cuDAAab270/fpCS22tuzaOtWOnTooNjzd2nX\nDt3x43TLoynCCRMTQitXJuia8QJQxqhTrRo1b92kcx7HxgYzM7TNmrPn8GFZLr1ej1fpUnxS0o6O\nJXKuky6EYPK1cIq26MiPK1bI8qWkpFCupAcbmlekUS4+ncFAryPBNBsyik8+/UyWLzIykqoVK3Bs\nYH2qFMu5LVyaVkfLzeeY8MVcBsss4nbt2jVaN2vC2entKJVL85n41Azqz/+V5eu3yC5jcPToUcYO\nH8i5eQNwtsu55UN4bCL1Zmzm6InfqVbNeBOQvNiwYQNLF87hty1fYmOd8+Qp+M5Dmg+YRfD1m4VW\nVkAN7IWMTqejjLsb66uVoIqROuJDLz2g20ezGDlyZIFc9+7dw9/f/5X7d+/ciebsWeoC54C0Bg3o\nlkNLrs6dO792UbCIiAiqeHvzTUYGeVWdMQCf29hw+NQpatbMsUJzvrh48SKdmjZhZXo6pnnMHtOF\nYJiFJTdCQ2X1zTxw4ACzRg3nYP28qyg+Sc+kxR+3eRj5BDu73FsgGmPlypXs/2EO21rl3Vv0amwi\n/X4LIexxpKzdqF/MmsmTYzv5sV3evsMhT5h9LYGgq7kX08oPI4cPwyP+Op+288lz3JrA2xyItcb/\n8FFZvk7t2tDZ05zhRmrqz95+msfW5Vi5ek2BXUII3q1Zna8mdKZd01p5jh07czVu3rWZNeuLAvvy\nQt2gVMicOXOGImYmRoM6QN/i9mxbW/AD6+nTp8z67DM+nzqVnR99xK6/btKFCzyfh/gABAW9eGzn\nRx/x+dSpzPrsM54+ffrazp07d1JTiDyDOmQfNPUyMtiyceNrO/7O1o0baZaRmWdQB7CWJBpJ2a9P\nDlvWraV3MePLK27WltR2deTgwYOyfH4b1jHI0/jykY+rAy4WJrJb8flt2sBQnxJGx7X2LE7ko0ey\nWvEJIfDbvp2hRr4kAfrW8eS3P06RlFTwjplJSUmc/OMUfZsar3s+rGU1/Py2F9gF2R2UoqKe0KZx\nDaNjh/dqzrYtm2X5lEYN7K9BTEwMHrb5W8/2sLUkNtZ4U4DcqFu3LsE3b1LJx4d4MzPqabW01Gpp\nnpXF85NQa6B5VhYttVrqarU8MzOjko8PwTdvUrdu3dd2xkRF4ZjPzAlng4GoR49e2/F3oh89omg+\nMxlcMjKJiTLeRCIvYqOi8LDJ3+/P3dJU1u8Pso+XkrksGbxMSXsb2b7YuGeUcrAxOs7URMLDyU6W\nT6vVkp6RiXs+Jjk2FmY429nK6rEaFxeHs70tNpbGr0O4OWtIy8hAq827r0BexMbGUtLNNV/1bkq5\nFSH2qfGGKm8SJVrj/c9gZ2fHM23+UrieZeoIDw9X5AKVCbAU6AF45fB4KLAL0KalIa5coUyZMgV2\nNc/nuGRg365dbJXx/syBQfn8/8+EYNN33zH3u+8K7NOYmdC9Rv6Wpx4nJLN+4kQmTpxYYJ+dhRnP\nqhXL19gH0bGyu9zbmJsSn66lSD4mHw+jY2X3CzCVJJLStdgbaX6uNxiIiU+gbNmysnxWFmbo9QZM\njTQ/T07XIgwG2UkFxV3z14gkPjEFOzv5F9qVRJ2xvwaNGjXi9rNkHuXSZOPv7IlO4sOZsxRJFdUL\nwaHjx/GTJF6+pJkF+EkSh44fxyDTc+XKFa7Z2JB3fyEQwGWNhgO//irL53/4MKc0GqP5wDohOG9j\nw3EhK5UAACAASURBVNWrV2X5lqz6mb2xqUZ/d8lZOoKSM4mMjJTlm/HZ5+wMM74kFp6UxmNt9sVW\nOb4hw4ax/fpjo74Lj+OxcXRBp9PJ8nXu0A6/oPtGfYeCI6herarsz4FP1Socumh8+Wjr7zfo0rGD\nLJdOp8PKRkPQtVCjvm37A+nYqZPRcW8SNbC/Bra2tvQfMIAf7+W9ceZhSgYHH8fxfgEvnOaEiYkJ\nHhoNL5+ImgMeGo0iJWB9fHwo5+nJGSPjrgN6jYZWrVrJ8rVu3RqtrS0XjIw7DpT18pKd5dC7d28u\nP0vh6rO8Nwatvh9Dy+bNcXNzk+UbMXIUe0MjCUvMe4fwoqvh9O8/QHYG1dgJk/j5cjixqblPPIQQ\nzD19n5Fjx8s+ZsZOmsLi30NIycg9gypLb2De8duMmSg//XDsxCl8t/ciWbrcpx4p6VqWHLrCmAny\nOjaZmpoyavRY5qzYm+fEIyYugdXbAxgrsxWf0qiB/TX5YvY3nNOaMv9OJLoc2p2FJqXRJ+ges+fM\npVix/J2G54ftW7fimZqKAK5IEgv++lMA5VNT2b51qyKenzdv5oBGw5+QYxPtG8AmGxs2+PnJrrdt\nYmLCej8/llhZcymHD48QgpNCsMXGltWbNslyAdjY2PDTz2sYciGMy/HJrzxuEIK196PZEp3CgqXL\nZPuKFSvG7Llz6XroCiE59MnVGQx8E3SPwEQ9X8yeLdtXuXJlho0aTYdt53mUw5dJpk7PhMPXibV0\nYuIk+a3qWrRoQYPmremy8iRxKRmvPJ6SkUX/dYEUKVuRfv36yfb169cPJw9P+i08QEoOfXnjktLo\nMmcPDXxbKbKHZOLEiUQnZjFu1moyM1/98oqIfEq7Yd8w7P0RVKpUSbZPSdR0xwIQHR1N3+7duHPz\nBv08nPGytSBdZ+BwfBpBT5OY+/33jBg5SjGfwWCguIsLnRMSuGRtTWqxYoQ8eIBX6dJoYmKomZ7O\nficnnjx9qkhzgytXrtCzc2f0z55RJyUFR7LX1C/a2ZFsacnWX36hadOmsj3POXnyJAN69sQxM5Mm\nKSk4SBBHdts/ydGJHf7+VK+ed4rb67Bnzx5GDx/GO3bWdC5ig725KQ/TtGyL/H/snXV0VFfbR/fE\nXYkAMYK7uwUpUtzd3QsUKtBC+xZaqljx4JDg7tIAQYMESYAECTEiRIhnMjPn+4PCR0uSCbmTFujd\na80qC05nR2aeOffcc57fc2yLl2D7vv06OXz1ktWrVvH5jE9pWMKOji7WmBrocz85k40hTylXsTI+\nu3brbBIghOCH+fP48YcfaFOuOO1L2WKop0dgXCobb0bQpEkz1m3ZipWVlU58arWaz2ZMx3vNGrrX\nKkWLMsXQUyi4GJbI1isP6dK1K8tXrdHZIbqsrCzGjx3Nvr176d+8Mg3LOaMRgtN3othz8R4jRo5k\nwY8/6yzEJCUlhWFDBuHv78/QHi2oUcmDnBwVh88EcuzsDWZ+9hmff/5FkYZuyNF4/zCBgYFiyoTx\nolv7dsJMX0+sXr1apKWl6dxz4cIFYayvLxzMzMTIoUNFenq6AER6eroYOXSocDQzE8b6+uLixYs6\nc2o0GnHixAkxbOBA0bF1a2EEYt++fUUSwyfEi7i6ffv2iUG9ewszEMMHDhQnT57UeQzfS7KyssTW\nrVvFwF49hYWBnhg3cqS4cOFCkfnS0tLE6tWrRf+e3YWlob6YMnGCCAwMLBKXEEIkJSWJhQsXin7d\nuwpLIwMx89PpIiQkpMh8sbGxYv78eaJv967C0thQfP3VbBEeHl5kvvDwcPH1V7NFr26dhaWpkZg/\nf56IjY0tMt/9+/fFzJkzRM/uXYSFmYlYuHChSE5OLjLf6yC3FPj3KMpUlc8/+4zlS5eyfvNmunXr\n9oZv9+7dDB00iPETJ/LDn02RdI2coCT7ZN+/6pNPnv4bFOUvOyQkBDMzs7+cuvy7LzIykoyMDJ2l\ns/8dubDLPtn3r/rkwv5v8B95cX1wLtkn+94Tn9xSQEZGRua/jFzYZWRkZD4w5MIuIyMj84EhF/ZC\nkpGRgbe3N41r1cTdyRFzPQVjhg3j5s2bReJLTk5m0aJF1KlUCVcHB8wUMHXSJEJDtR95LgxxcXF8\nP28e1cqUwaVYMUyB2V98QaTExl95ERERwewvPqeyZylMFFC9bFm+nzePuLi4IvGFhoYydfIkKni4\nY6qnoG6VyixevJjnz58Xie/mzZuMGT6M8u5umOnr0aR2Lby9vYskt1YIwcWLFxnUtw9l3V0xN9Sn\nVZNG+Pr6SmqMlZ/v5MmT9OrSiTJuLpgb6dPho1YcOHAAtVpbg4q3R61Ws3//fjq2b4OnuysWpsb0\n6t6VU6dOFcnat1KpxMfHh9YtmlHK3RVLM2MGD+zPpUuX/tG19rdBvnlaCK5evUrndu2oaKSgj6Uh\nZUyNyNRoOP48i+1JmXTu2ZPfV63GwEA3PdZOnDhBvx7dqW1kQCc9NS4G+qRqBCdzBIeyVIydPIn/\nzf9eZ4ckfH19GTt8OA0U0CorC3vgOXDGyBg/4H8//MAkHZxcfMmSRYv46osvaGtqSDsDsNXXI06t\n4ZBawdnMHJZ7e9O3b1+duIQQfP3llyxfspge9uZ8bGWCpb4e4dk57ErN4WJqFj47d0lul/ASlUrF\nhNGjOLB7FwNd7fnY2RozA31CUjLY9DSF26nZ7D9ylDp16ujEl5mZycA+vblx6QIjKzjTxq0Yhvp6\n3IpPwTs0jiilgkMnTups91RycjLdO3UgLuwBY2u64FXKAT2FgksRCawIjEJlZsPBYyd0FkIRHR1N\nx/ZtMdRkMq5LPRpV8UCjEZy+HsryfQE4lHBj974D2NjY6MQXEhJCh/ZtcXO0ZEzPxtSs4IoyR82R\nc7dZvtOfmrXrsWmLD6amBeviWRj+1V0xCoVCD7gKRAohOufy7x9EYb9//z5N69djrqMZH+WSGpOm\n0jAhIokanbuzbPUayb7Lly/ToVUr5pnpU9PkzZaliWoN09LV9J86ldk6aPR/6NAhhvXuzZysTErl\n8kERIwRfm5jyzaJFjBg5UrJvzerVfDt9GostDChh8OZpwRCliulpKtZu26aTpKjvvpnLtiWLWO1u\ng73hmx+8ASmZTIl8zsETJwvV+vjvjB81ittH97OuViksDN/8/g5HJfD5vRjOXbpM+fLlJbmEEHTv\n1BHFoyBWtaiIcS6nL9cHR/BTUAyXrwdK7oWjVCpp1awJlfVS+K1tlb/E/r38euafDWFXRCYXAq5J\nPu2akpJCw/p16NOkDLMGt3pjIqNWa5i8aD93YpSc8juLkVH+XSe18fTpU+rXrc2sER8xqkfTN/49\nW5nD4NkbUJs4smvPviI7ffpvF/apQG3A6kMu7H27d8P1mj+ji+c9I0hTaWhzLxb/a9ckv1mb1a1L\ny0f3+DifVqzxag0DkjJ5EB5BsWLFCu0SQlDW1YVhT59SM58XaZgQfG1uQWRcHCYm2mI58iYrKwsX\nR0eWmOlR2ijvq5srWUoWG1tzX2Ib5GfPnlHG3Y2D5Z1wyse3Jz6Fww7u+F26UmgXwL1792hWry7n\nW1TCMpcPkZcsCYnmcdmabN21W5LvzJkzjOnbk/Pd62KUT2vbmefvY96sAz//tlCSz8fHh2VzZnJi\nQH308oiJFELQf/cNGg0ax/Tpn0ry/fzzz1w+6su2uXn3ndFoNLT8ZA3jZ86VfJU3fdpUVPFB/Daj\nd55jlDkqavSex6p1W2jWrJkkX178a9sdFQqFC/AxIH2K+g4TFxfH0aPH6OuQf1yahYEePe3MWLZk\nsSRfcHAw9+8G08Ys/5mHg74ezcyM8V69WpLv9OnTKJ6noK0ri4dCgSewc+dOSb4dO3ZQ3sgg36IO\nUNfYENJSOH36tCSf95rVtLa1yLeoA3Swt+Re8F2Cg4Ml+ZYvWUx/N/t8izrAIA9Hjhw9Jvl+wu+/\n/cqo8s75FnWAsVVc2LBuHZmZmZJ8y377hUm1XfMs6vCiKE2p686KxYvQFDBUJTc0Gg0rfl/C1F6N\n8x2np6fHpO4N+H3xb4V2wYslrY0bNzCpX4t8xxkZGjChdzN+X7JIkk/X6Orm6W/ADHJvCPjBcOXK\nFWrYWWGVy5LB32lpacy5kycl+fz9/WlgaoRBAWapjVFz9vgxSb5z585ROyOjQLPiOmlp+B2XlmF5\n9sQJGqu138xTKBQ0FirOnTsnyXfu+HFamGn/3RnpKWhqYyY5qs7/j9O0cdS+/GBjZEAtJ1uuXJF2\nheDv70/7Uo5ax3lam+NsYcrdu3cL7dJoNFy8foOPy2lfzqnvakdycjKxsfm3u86P2NhYUlJSqF/J\nTevYTo0rcfHKNUkfJHfv3qWEgw2eLtqjDTt5VcPf37/QrqJA8t09hULRAYgVQgQqFAovIM+qMHfu\n3Fd/9vLywsvLS6r+H0WpVGJcwAsiIz0FofdDJa+7dTQzBlPt6SxGCgVnzpyV7BukUEABnsMQWLtp\nE94S2umaKGB6AaLVAIyE4NtvvuGbb74ptM9CX0HXMs4FGqvJzGT06NGFDiMHsDTQx7hE/sHSL8lK\nTaWTxLAGY309TLTM1l/50tOoXTv/kGZt6CnAUF/7a0WhUKBWZku+gWpnZVag17ehgT5Co5Hc4bGc\ne8E6bpoYGaLMybsn/dvi5+eHn5+fpOfQxYy9MdBZoVA8AnyAFgqFIteU47lz5756vG9FHcDDw4OQ\ntCw0BbhXcD8jm+ZeLSR1xDxw4ADRptozLAEeqgX9Bw+S5Fu5ciXh5gXzhRsZ8dns2ZJ8n82azSNF\nwV6Cjw2NWblqlSRf34GDuJ9ZsGjDcH1jDhw4IMnXzMuL4OfaE5s0QvBU6HPt2jVJvsoVyhOU8Gaf\n+b+TqVKTqIKoqChJPqdi9tyL1+6LS8tCrW9IRkZGoV0ZGRmohIK4JO2+u2GxODs5SPreIiMjefY8\nk8ws7VeUt0IjcXdz0TquoHh5ef2lVhYGyYVdCPGlEMJNCOEJ9AVOCyEGS33ed5GaNWtiUawYF1O0\nr01uT1MzcuIkSb62bdsSrYGHWnJWNUKwTwUjx0+Q5Ovduzc3VGoSRf4fXFlC8IdCwbARIyT5ho4Y\nwdFMFVm5BJa8ToJaw5WMbHr3zvsmVkEYOW48O1KytX4w38/IJipHQ9u2bSX5RoyfwOan2gvR2bjn\nWNoXo2bNmpJ8w8dNYG2I9uWO3aFPqVevruQZ9LARI1l9I0LruPU3ntCje3dJWwJNTU3p3r076w4F\naB278sAVhg2X9tosWbIk9erWZccJbflesHLXeYaPHCvJp2vkA0pvgUKhYObXc/g+Np3kfOK5fONT\nSTU1p2PHjpJ8hoaGfDJ9Oj9li3yL39oMFW7lylG3bl1JPhsbG4YMHcoKE1PUeRQ/IQTeRsa0btVK\nUmg2vLgCatWqFYsyX2Rv5oZKCH7K1DBk6BCsra0l+erVq0fJ0mX4PTbvYpup1vBNTBqffPophoZv\nbi99Gzp16kSSgTEbH+d9UzRJmcPc+0/5dPZX0pfRBg3iclwqBx/G5DkmMjWTedefMP2LWZJcAGPH\nT2B7UDTnn+Sd6xoc95wlAU+YInFHDMAnU6ezcOcFgh7n/f3533rEttO3GDtuvGTf9Jmf8/WyQ0TE\nJOY5Zu/pG1y6/YRBgwZJ9ukS+YBSIZg5bRp7169luoMZzW3M0P/zDRmTrWLDszSOZSs4ff48ZcuW\nlezSaDQM6deXm8eOMdYIahsbvCoAETlqNmerCbay5cylyzg7F2z9OD+USiWd27ThWUAA/bMyKQ+v\nfI+FYJuxCZmlS3P6wgUsLfPfHVQQUlJSaN2kCdaRTxhmpKDMnztWhBDcUapYowSbmrXYd/SY5H3J\nADExMXg1bED1nHRGFTPD3cTole9SSia/Pcukaus2rN+yVSdpVKGhobRs2oROtsaMLOVICbMX21bV\nQnDqaRLfhcbSbfBQFvzyq2QXvDg816HNR4yu4Mzwyi4UM33hU6o1HHgYw9dXHzP1i9lMnT5dJ77j\nx48zoHdPPm9cmsE13LH+86xFhlLFttsRzDkbyq9Ll9G//wCd+LZs2cL0TybxvxEf0a91Tcz+/P09\nT8tkw5GrzNvsx1bf7To7YPbbb7+y8JcF/DC5K91a1cTozx1O8YmprNx5lt+3n+PQYd0dMMsNOUHp\nH8TX11fUrVpFlLCyFI1LOInSJobCxtxMTBg9SkRFRenUpVarxcqVK0XFUh7C1cpSNHCwF64GesLe\n0lJ8OvUTkZiYqFOfUqkUP//4o/BwdhYelhairo2NcALhbGsr5nz1lUhPT9epLz09Xcz96itR3M5O\nVLC1ERUN9YWnjbUoVby4+PnHH4VSqdSpLzExUcyYOlUUs7IS1R2LiSrmxsLdxlpU8iwlVq5cqfMU\npcjISDFh9Ghha2Eu6rg4i2o25qKEjZWoV62q8PX11alLCCFCQkLE0IH9hY2FmWjk6SJqOFgJJ2tL\n0aJRQ3HkyBGd+wIDA0Wfbl2EjYWZaFbBXVR3thb2VhaiY5vWwt/fX+e+c+fOiY7t2wh7WyvhVaeS\nqF6mhLCxshB9enYvklSqI0eOiBbNmggnBzvRsmE1UaVMSWFjbSmGDR0sQkNDde77OxQiQUku7BIJ\nDg4Wx48fF4BISUkpUpdGoxGBgYHi2LFjAhCZmZlF6lOr1SIgIEAcPXpUACInJ6dIfUqlUly8eFEA\nIiAgQKjV6iL1ZWZmCn9/fwGIwMDAIovFe0lKSoo4c+aMAERwcHCRuoQQIiEhQfj5+QlAPHjwoMh9\nMTEx4vTp0wIo0li8l4SHh4uTJ08KQMTExBS578GDB+LEiRMCEAkJCUXue0lhCru8FKMj/iPN/j84\nl+yTfe+JTw7akHl/uXv3Loo//ysjI1M45MIu807xzawvcTcx5NvZ0ndtyMj8V5ELu8w7w927dzl5\n/DibK5bk5PHj3Lt379/+kmRk3kvkwi7zzvDNrC8ZVswcRyMDhtqb8c2sL//tL0lG5r1EN0kQ/2Hu\n3r1LRMSL03epqak62dudF0IIbt26RUzMiwMaWVlZktrmakOj0XD9+nUSEhIAyMnJkXxoJy9eztZP\nVHyxF7+/gyVt/py1V6hQoUicWVlZXL364mThzZs3qVatWpH11IYXr48bN24AL77fihUrFpkLIDEx\nkVu3bgHw8OFDSpcuXaS+2NhYgoKCgBeJWK6urkXqi4iI4P79+6/cTk4F6+1SWB4+fMijR4+AFz9b\nOzu7IvVJ4m230RT2wQe23fHVPnYbK9Hco6QoZ2kqbC3MxfhRRbOPfcWKFaJiKQ/hbmMlmpRwEh4m\nhqKYlZWYMXVqke5jL21jLRo62IsS+nrC2dZWzC2CfexCCNGnW1fxqbuDCKlf5tXjU3cH0bd7N527\nEhISxKfTpgoHW2tR27OkqF3CVng62Ysq5cqIlStX6nybZWRkpBg/epSwtbQQ9UuVFDUdrUVJO2tR\ntyj3sQ/oJ2wszEWTcm6iZnEb4WRjJVo0biAOHz6sc9+NGzdE725dhI2luWhWxVPUdLUX9tYWokOb\n1uLcuXM69507d050aNta2NtYiRa1yovqpRyFjZWF6N2ja5HsYz98+LDwatpIOBWzFS3rVRZVSxcX\nNlaWYuiQQe/sPnZ5u2Mh+Gz6NPZuXM/sck60dLZ9dfI0OiObNY/jOJCUzelz/jo8edqPO6dPMK2Y\nKfWtTF/NKp9kKVn9LIObhub4Xbyks5OnXdq1JenGdUYbQWWj/z/p+kCpYp1S8NzFnZP+/pITcV5y\n9+5dmtatw4mKzli81p0wTf0isORcwFWdzdpjYmJo0aQRjewNmN6wNGXsX3TOFEJw5nE8s8+EUqmh\nF2s3bdbZydNWzZrQraQ146q5UtLiRb8UtUZw/Ekcc64+pvOAISz4+RfJLvjz5Gnbjxhf04WRdUrh\n8GdAi1KlYf+9KL44HcInn8/S7cnTPr34sm1lhjQsi7Xpi5OgGUoV2wIeMvvgLX5ZvJQBAwbqxLdl\ny2amT5nEd/0b07dZZcyMX1xBPk/PYsOp28zbdZmt23bo8OTpLyz8aQELxraja9Mq/3/yNCmNVfsv\nsXTvZQ4dOfbOnTyVC/tbsmnTJuZNn8KeBmWwNcp9WWLj4zi8E3MICn0gOfd0wfz57Fr4M94etpjk\nUWiWxKRw3cGVc1cCJC8lTBk/jtu+Pnxnrp9rH3ghBD9mqNBr1IwdBw5Icr2kb/duuF4/z2jnN3vB\nrIp5TmTtJvhITBeCF197swb18LLI4iuv3D8oMpQqOvoG0HnkBGZ+9oUkn0qlonLZMoz3tGJ45dz7\niCdmKWl/4AZf/Pir5H4jKSkpVCjjyeLW5elcMfcGXxHPM2ix4QJrfXbQunVrSb6IiAhqVa/KzpFN\naZJHO+Sg6CQ+WnyS43+coXr16pJ8N2/epE1LL05+25vKbrn3SfcPjqDnj/u5fvM2Li7SOi6ePHmS\n4YP7c27JGFydbHMds/fsbSYtOcy9kAdFtgwr72MvYoQQ/PS/b/mmfPE8izrA4FKOWOdkcfDgQUm+\nnJwcFv3yC3OcLfIs6gATnCyJCA0lIEB757v8SE5OZsP6Dcww1csz3EOhUDDF1ICTp04SFhYmyQf/\nv7beP49Uqv4OljrbIXPlyhWinzxiVrO84wrNjAxY3LYSi375lRyJPbYPHDiAHTl5FnUAOxMj5tf3\n5Of530k+9LJp0yYalrTJs6gDuFqbMadpGX75YZ4kF8CK5b/Tr7ZHnkUdoHIJWyZ7lWfRrz9L9i38\n9Wc+6Vgrz6IO0KSSK32aVGDF8mWSfb/8+D3fDm+dZ1EH6NqsKg0qubJJQi5BUSAX9rfgxo0bpCUm\n0NRRe5fBgcUtWfP7Ukm+Y8eO4WKoRzmzvPNOAfQUCnpbG7NG4ot5+/bt1DMzxl5LWIOJnoJ2pkas\n9/aW5IP/3wljkYfTQl9PZztkvFeuYER1l3yj3ACqOFnjYW3CsWPSEqnWLl/GsLLaE3hauBYjLfHZ\nqxurhWXdimWMqq69FW/PKq5cuRJAVFSUNN+aNYxqXEbruOGNyrJr925JUXyZmZns3r2HYa2raR07\npk011nlLS+mMioriSkAAvVpov8oY06kOa1evkOTTNXJhfwvCwsKoaGOBXgGWOypZm/Mk7LFkXzmj\ngl2BlTM1ICw0VJrv8WM8c7ILNLa0UPMoJESST9ts/SW6mrU/efSQKo4Fu1yu4mDBkydPJPnCwh5T\nxV77fQg9hYJKxawlXwGFRURSxUn7pMPUUB9PB5tXu7kKg1KpJD4xmYr5hLq/xNHKFCtTY0mZrnFx\ncVhbmOJYgMStiq7FiH2WIOmKKyIigjKuzpgaa98FVq10cZ6EF/5nWRTI2x3fAiMjI7K1hEK8JFut\n4UnYE8lr3h/bWQDa36zZGsHFSxcl+4ZYFmz7ZLZ4McPftH17oV0megrGlrDNc7b+Egt9PQbaGFOz\nciWtoRz5YWVswMjiBetZn5iSxsSJE5k4cWLhfUYGZNUo2Ba82MQkevToUWgXvCjYWaqC5XzGJSTR\nsGFDST6FAnLUGoy0ZAALIUhOSZXcv9/CxOjFjg8tr/EclQaNRiO5zbOHc95LMK+TpVTppKW0LpFn\n7G9BvXr1uBabwHMtiUYAx+NSGD5mrKQtokFBQVzLEeQUoJj9kalm9nfzJPlOnjzJRX3jAq31XtA3\nYs2mTZK+N3NTUwY7a5/xAQx2tsHc1JTg4OBCO7+c+z8OPsw7FOIlSpUG/+gUSS4hBENHjuZIeIJW\nX1JWDqGpSmJjYyX5OnXowKGQp1p9DxPTyFAYSIqqE0LQuF4dDt0K1+q79CgOZ+fiqNXqQrvUajVO\nzk5cvh+t1XcgIJTG9etK+t4yMjJIUwoeRWv//R3wD6JJ48Zax/2TyIX9LXB0dKRdu3ZsCsv/kjI1\nR4VPRALjJkmLxqtUqRLlK1bikJYcy1ililOJaYwYOUqSr2XLlggLSwKy87+EfahUcT9HRc+ePQvt\n0ra2/ncs9PUYVsxc0lr7iJEj2X83mmgt0Ybb70RQsVIlyQeIxk+ezMa7UaQo8/95rgsKp337djg6\nOkrzfTKN5dcjUWqZtf9+JYwhw4ZLiqoDGD9lGovOPkCTz8RDCMFCvxDGTpoiafuonp4eYydM5reD\n1/Idp9EIFh8KZMKUaYV2wYsovsFDhrJk1/l8x2UrVfy+7woTJn8iyadr5ML+lsyd/z2rIpI4EpX7\nJ3lqjorh18Po2acv5cvnvfuioPy4eAk/xmUQkEcxSshRMS48mU9nfkaxYsUkuRQKBb+tWMH/MjSE\n5HFVEq1S81mGmgW//FroU6/BwcGcOnFC69r633m51l7Yzo/FihVj+owZdNt+lbi0rFzHnAuL5/PT\n9/n+l4WFcrxO+fLl6dGnL/2P38mzuB94GMOyuzHM+W6+ZF+zZs2oVKsuQ/fdIDuP6Ebva4858DiJ\n6TNmSvb16NEDrB2ZsuMKas2bHyZCCL47cot7zzWMGiVt0gEwevRogmOz+G7b+VyvKtVqDZNWnwQL\ne7p37y7Z9+mMmew5H8Lq/Zdy/fdspYrB87dRqWpNmjZtKtmnS+R97IXg6tWrdG7fjioWxgwqYUU5\nSzMy1GoOxzxnS0QCnXv2YumKlZL3sL/k5MmT9O3RnQaWJvS0NMTV2JA0tYZDKVnsTkhn3KTJfDt/\nvs6Ow/v6+jJuxAiamhjSwUDgpK9HklrDEZWC45lK/vf990yaMqXQz9+nW1fcblzIdd+6NlbFPCei\nVmN8d+8plFsIwdezZ7Fi6RKG1HSjd6XiWBkb8jgpnbW3ovF7/AyfHTsl7/F+iUqlYuLYMezfvZOh\n5UvQuZQDZoYG3EtMZV1oHLcSM9h3+IjODrhkZmYyqG9vbly+wKiarrQv64SRvh6B0cmsuhlNZJbg\n0PGTlCtXTie+5ORkunfuQFz4I8Y1Lk3LCiVQABcfxbLs/GPUJlYcPHpccnD2S6Kjo+nYvi0GuXqL\nKQAAIABJREFUOWmMa1OVRhVdEEJw6uYTlh+/haOLB7v3HcTGpmBLfNoICQmhQ/u2uNqbMaZTHWqV\nK4kyR83hi/dYceAKNWvXY9NWX8lXP/khR+P9g6Snpwtvb2/RpHYt4e7sJMwN9MSY4cPEzZs3i8SX\nnJwsFi1aJOpWqSzcHB2EuZ5CTJs8SYSEhBSJLy4uTnw/b56oVraMcClWTJgpEF99+YWIiIiQ9LxB\nQUHC3txMXK/j+Zf2AQV9XK/jKezNzSQnEIWEhIhpn0wWlUqXEuaG+qJ+japi8eLFIjk5WdLz5sXN\nmzfFmBHDRTkPN2FuqC+a1K0tvL29i6Q9g0ajERcvXhSD+/UR5TxchbmRvmjVtLHw9fUV2dnZReI7\nefKk6Nmlkyjj7iIsjA1Ex7atxYEDB4RKpdK5T6VSif3794uO7T4Snm4uwsLESPTs2lmcOnWqSFKw\nsrOzhY+Pj2jdopko5eYiLM2MxeAB/cSlS5eKPHVLCCG3FPg3+Y+kuEh+Himz9ZdInbX/nff1Zyn7\n/lM++eSpzLtJYdfW/47UtXYZmQ8dubDL/GO87U6YvNDFDhkZmQ8ZubDL/CPoarb+EnnWLiOTN3Jh\nl/lH0NVs/SXyrF1GJm/km6c64j9yA6dQ/++zZ89wdHTEw8YKEy3HzwGeP0/B2lp7j5UslZqw5BTi\n4uIk7eF/n36Wsu8/63urm6dyrxgJBAYGsm71aiLDHmFuoM/q1avp378/5ubaGxW9LUIILl68yKa1\na4mJisRMX4+tW7fSo0cPjI3z7/5YGDQaDadOncJ340YS4+MwUSjYt28fHTt2RF9fe3F+nWLFinH3\n7l2ys/NuMKZSqTh37hx/HDvKqRMnaNCgEW07dqJevXr5nlg0NjYuVFHPzs5m165dHNm3F0tDfcaN\nGsmgYcNp2LBhkcTjpaens3XrVvyOH8HS2IApEycwfNRoyT3K8yI5OZn169dz+dwZLE0MmfnpdEaO\nHqOz/esy7zbyjL0QxMbG0q9Hd0LvBjO4nDPlbczIUKk4GPmci9GJ/PDTz4waPVpnvocPH9KnaxeS\nY6LpW9wadzMjUnLUHEjI4G5KJiu819KtWzed+QIDA+nTtQv6aal0t9DHydCARJWaAxka4tBn0/bt\nNG/eXGc+Pz8/Bvfrg7O+gh4O5tgbG/A0K4dtMamozCzw3b2HGjVq6My3Z88exo0cQSU7C7q72WBl\nZEhYaiYbQ2OxdSqB7569Os0HXb1qFZ/P+JTGHg50Lm2HuaEBd5+lse5mJOUqVmLrzt06y+sUQvD9\n/Hn8tOAH2lVxo30FR4wM9LkRlcz6iw9o3LgJ67f46CT9ys7OjqSkpAKPt7W1JTEx8YP0SXXlx7+S\noKRQKFyAjYAzoAZWCyEW5zLugyjsCQkJNK5bh65OJnxWuxQGf5tNhiSm0evYLabP+YYJE6X1igEI\nDw+nYZ3aTHSxZkgpxzdaBt9ITGX4tTCWeK+V1LvlJbdv36Zlk8Z86WhOBzvzN2av/skZzIxKYefB\ngzop7mfOnKFn544sqeaGl9NfTwsKIdgXlcBX92I4fc6fqlWrSvbt3LmTSaNGsPWjqtT5WwMyjRCs\nuRPBb8ExXAi4iptb3gEZBeX3pUv47bu57O5dhwoOfy2mKrWG+edC2RmWyvkrV7G3t5fsm/XF5xzZ\nvok9o5vjYvvXK8fsHDXTdl0lMMWA02f9MTMzk+RSKBSITO1N1V6NNy0maQlDoVCgSbpf4PF6tuUl\n+wr6/Un93rR+Hf9CYXcGnIUQgQqFwgK4BnQRQtz727gPorBPHj+ejAvH+K1Z3g2iHj/PoPmuy9x7\n+EjyTKxX506UenyHaeXzPpJ9MymNgdfCCH8aI/loc6NaNen4PJpeDnnP6PyS0/khTUFoeISkxk4a\njYay7m5862ZFq+J5t0jdEhbLbqw5fzX/BlDayMjIwL1kcXa3rUaNfMJSFlx9yH3HsuzYu1+SLyYm\nhoply3BxZFM87SzyHDfx8C1MarVi8e/SglKCgoJo3awxN77siINl7q8DIQQ9V5+lQc9hfP65tOg/\nubC/NvYdK+yStygIIWKEEIF//jkNuAuUlPq87yLp6els2bKZaTU98h1XytqMLmWLs2b1Kkm+6Oho\nTp4+zSjP/Lv+Vbe1oIatBdu2bZPku3nzJk8ePqBbsfy3JDa3NsMsO4sTJ05I8h0/fhxLtZKWWlr3\n9nFzJOzBA27duiXJt23bNuo42eRb1AHGVXPj1KnTPH2qvQVufqxZvYruVVzyLeoAMxqVZsvmzaSn\np0vyLVuymFGNy+ZZ1OFFkfi8TSVWLVuKWp17ozCZ9x+dbndUKBQeQA3gsi6f913B39+fyg42uObz\nxnlJr1LFOLhrpyTfsWPHaFnCHktD7fe4uzqYs3+7ryTfoUOHaGdpnGfe6UsUCgUdzPQ4sHuXJN+B\nPbvpWsxM681KAz0FHZ2tJGfIHti5nZ7udlrHWRkZ0srDSXI03qE9u+hbUfsVm7uNOZWL23L+fP4t\nYrVx8MA++tUtpXVcXQ8H9NU5BAcHS/LJvLvobFfMn8swO4Epf87c32Du3Lmv/uzl5YWXl5eu9P8I\nqamp2Jhoj8qCFyHFQcHXJO+w6OdesB7dtkYGnDxxUpJPAXzior3wAdgY6LF4zRp+X7W60D4zfT3m\n1dBeiABsDfSYPWsWs2bNKrTPysiAge1qFmisiVrJsGHDGDZsWKF9lsYG2DX0KtBYA2Umbdu2LbQL\nwNhAHzvzgu2Q0lcrqVZNe36orimKHUfvkk8X+Pn54efnJ+k5dDJjVygUBrwo6puEEPvyGjd37txX\nj/etqMOLoI2IlIwCjY1IzaR27dqSOmL6+PiQoFewD5LIjGw6dukiyffzL78QLQq2lTE6R8P4yZMl\n+cZNmkRkVsFyKaNyBL/8+qskX4dOnYlILVigcoIwwMfHR5KvTu3aPEku2OslWRhy5swZST4PNxee\nJOQ6p/oLao2GVLWC0NBQSb7C8KH7dIGXl9dfamVh0NVSzFogWAixSEfP907SqFEjnmWruRX/XOvY\njQ/i6Td0uCRfhw4dCIhP5mmm9oBp39g0BgyT5uvVqxfHktJIV+efwKMWgt3Ps+k/aLAkX7+Bg9ge\n/Ry1ljdRukrNwagEevXqJcnXf+gwNj/UHnUWlZbJpahndOjQQZKvz+BhrL+jfZ0+8GkSz7JUNJYY\nr9Z34GDWXXqkddyxoChKlHShTJkyknwy7y6SC7tCoWgMDABaKhSKGwqF4rpCoWgn/Ut79zAwMGDc\n5MnMvRqGKpfEmJf4RyVwJSaZAQMGSPJZWloyYMBAfgiJyXcGcSAqged6hrRrJ+3H7urqSgsvL5bH\n5h/FtyU+DRdPT2rVqiXJV7t2bUp6lGLd4/yjBheGxtDSywsXFxdJvvbt25Oo0WPvg7yLrRCCb68+\nZsCAAVhaSutrM2DAAC5FJHH2cXyeY1RqDbP9Qhk7cdJbH/z6O6PHjGX7tcfcjsp7P3WGUsU3R24z\nceqnklwy7zbyAaW3JCcnh87t26EX+YCfGpb5y41UlUbD3gcxfHbpAT679tCqVSvJvrS0NFo2aUzp\njERmlXOmmMn/p6FnqzX4hsfz88N4jv/hR82aBVs/zo/4+Hga16lNM5HFOEcLrF5rAZCh1rApPhWf\ndA3+VwIoVapg6+P58ejRI5o2qM8QZ0tGejpi9prvuVLFwgcxnMqA8wFXcXBwkOy7ceMGbVu24Mua\nbgysWBLj14ppfEY2cwIecV/Pgj/8L+jkBPGpU6fo17M7v35Uke6VSmLwWq+c8OQMph4PRu3syb7D\nRzE0LNiyW374+PgwbeI4Vg9oQNtKLujp/f8ac0jsc0b7XKZ0rcas27RF8vqzvN3xtbHv2HZHubAX\nAqVSyazPZrJ2rTf1i9tT3tKIxIwsTsek4uLuwa+/L6Nhw4Y686WlpTF98iS2b99OU2c73AwVxGdk\n8UdSJlWrVmXxqtVUrlxZZ75nz54xafRojhw9ipedBU4KDVEZ2VzIUtO4cWOWrl6Du7u7znxPnjxh\n0uhR+J8/T7uS9lgLNfFCn1PRz2jfrh2LV66SnOf6Onfu3GHKuDEE3b5Nh1JOmKEmUgl+4XH07t2L\nXxYtwcIi/y2Kb8PFixeZPmk8kU/C6FDOCWOhITRVxaXwZwwfMYJ5PyzAyMhI+xMVkCNHjvD59E/I\nSkmmXcXiKISa23EZ3IlOYvInn/DFl7MlnT94iVzYXxv7jhV2STcX3vJGhPjQSE1NFZs2bRLff/+9\nAMT169eL1JeYmCi8vb3F/PnzBSDu3btXpL6nT5+KFStWiHnz5glAhIWFFakvLCxMLF26VABixYoV\nIiYmpkh9d+/eFYsWLRKA8Pb2FomJiUXqu379uvj1118FIDZt2iTS0tKKzKXRaIS/v7/45ZdfBCC2\nb98usrKydOqwtbUVQIEftra2H6xPqis/kKPx/j3+Ix3mPjiX7JN974lPjsaTkZGR+S8jF3YZGRmZ\nDwy5sMvIyMh8YMiFXUZGRuYDQy7sElGpVCQkaD/NqCtycnJ49qzgW8ykolQq/1Hfy5QlpVL5j/gy\nM1+0GMjJKVhrA6m87OCoUqmK3CWEIDX1xWGzf6KToxCC589fnMrW5HOAT1doNJpXQRgf8saMwiAX\n9kISHBzMuNEjsbexpqyHGwZ6CupWr8K6devyjYArLFevXmVI/37YWllSzsMdfYWC5g3qs3379iJ5\n0/r5+dGzU0esLSwo6+6GvgI+btWCQ4cO6fxNJITg0KFDfNy6JdaWlpga6GFtaUHPzp0kN0PKDbVa\nzfbt2/FqWB9ba2tMDfWxtbZi6IB+XL16Vee+7Oxs1q1bR90aVSlmb4uZkT72ttaMGzOqSDospqWl\nsXTpUqpUKIezkwMmRgY4Odjz6fRpPH78WOe+xMREFixYQGlPD1xKlsDE2BBXlxLMmfO15NbHufH0\n6VPmzJmDq0tJPDzcMDYypLRnKRYsWKDTFCM7OzsUCsUbD+CNv7OzK1jzvH8KebtjIdiyZTNTJ45n\nTC13htdyp6SVKWqN4FhoDIsCwsmxduLg8RPY2OTfZ7ygLPz1Vxb87xsmVHFhYIWS2JsakaPWcPBR\nLIuDoiheqTo79u7DxMREsksIwRczZ+DjvYax7vb0dCuGpaEBmWo1+yMSWB6eSMM27VizYaPkI/Dw\nosiOHDqEyyePMblKCbqXLYGpgT4pyhx870WzJCiKvkOH8/2PP+mkU19WVha9unYmNuQOU+u607li\nCQz19XiWns2GwHCWBIQxc9bXfDJtmmQXvMge7dC2NcYZCXziVY52lV3Q19MjKimdNedDWeEfwm9L\nfmfAgIE68UVHR9OmVQtK2xkypUNNmldxQ6FQ8PBpEquO32T96Tts8d1OmzZtdOK7f/8+bdu0pmnt\n8kwc1Ja61coCcCfkCcu3HGfvyQD2HzhE3bp1deILCAigU8cOdGvfjPFDu1KlgueLvw+8y9K1uzh7\n+Q7HT5zUSbbr2xyIknoYStvX8bbbHeXC/pb4+fnRt1sXjg6sT6VcAhs0GsGUY3d4ZOjIcb8zkovR\n9u3bmTl+DIc71cq1D3yOWsPw08FY1ajPRh9pQRsAi377ldU/zGd7PU/sjN884p6hUjPo6mOa9BnA\ngl9+lez77NPpXNzty/a2VTHPpe98QqaSTocDGfnpF0yZOlWyb0j/vqQFB7Cxaw0M9d+8YA1PzuCj\nTRdZsHQFvXv3luQSQtCmRXPK6CWzuHe9vxzvf0lQdBJtlpxk2+59kqMGc3JyqFurBt2rOzKrd6Nc\nX3vngyPovmAff5z1p0qVKpJ8z58/p0b1qnwxuhMj+3yU65h9Jy4zbs4arl67IbnXT0REBHXr1Gbl\nj9Pp3LZprmNWb97P90t9CLx5C2vr/ANVtCEX9oKIPpDC3rppYwY65dC/et5H6tUaQbUVZ1i/c6+k\njn1CCKqULc2Cqo40d837SH1GjpoqW/y5dCNQUghzdnY2bsWd2VHHg3JWeedhxmcpafpHEI8iIiVd\ngiYmJuLp5sq1vo1wNMu7j/i9xFQ6HblN+NMYSUfvHzx4QKM6tQiZ1Aozo7yjCE4/jOXTC9Hcvh8q\n6YPZ39+f4X27c2d2J/TzOcK/+VIomx+pOeF3rtAugB07drDkuy/543+98/26f9p9ieAcRzZs3irJ\nt3DhQi6e2ovPwk/yHTf1u3WYOJZnwYIfJflmzpyB8nkkv32Tf5Zw3zFzadSyA1OmTJHke58Lu7zG\n/hY8ePCA23du06Ny/jMPfT0Fo2uWZOWSNzK93wp/f3806ak0c8k/5NjMUJ/+5Uuwctnvknx79+6l\nvKVpvkUdwMHEiNYl7Nm4YYMk34YN62nv6ZxvUQeoYGdJeVtz9u7dK8m3cvkyBlV3zbeoA7TwdESV\nniI50Wjl74sZ27hMvkUdoFdtT27dusWDBw8k+VYsXcT4dlW1fhgNb12Nffv3S16PXrn8d8YP0L6k\nM25AG9avWyvpBnVOTg7r161j/JCuWseOH9qVlSuk5ce+78iF/S24c+cOdd0cMTbQvrbczL0Yt28F\nSvY1dLYp0KyxsbMVd25cl+S7ffs29S0KFqrVwMqY29ekhUvfvn6NRsUK1kGxcTEzbt++Lcl3J/A6\nTVy13/dQKBQ0cbOT7Lt98yZNy2qPxjM21Kde6eIEBQVJ8t0JCqZpJVet4+ytzChT0oGHDx8W2qVS\nqQh58IjGtStoHVuu1IuulrGxsYX2xcTEYGhoQFlP7d9fk/rVCAl9+I/sPHpXkQt7EfLo0aNc76oX\n9DF+/HgyMguWwANw/vx5Sb558+a91eWkj6+PJJ+vb8EzWoUQfPfdd5J8F95iBp6Zkcn48eMl+d5m\nB8rz58/p2rWrJN/LrY0F9dWrV6/QLkNDw7d6rWSkZ+Dq6lpon5ubGxlvEfat0WgwNDSU9PN8n5EL\n+1tQpUoVAsLjyFZp31549skzunTrLqkj5tmzZ7n5XFmgN9D5mBTGTJwkyefr68uV9IJtnbyUks38\nn36W5Jv3409ceFawN+uFhEy2bdsmyTd6wiT8I5K1uoQQXHuWyblz5yT5OnftyrlQ7bPU7Bw1959l\nSI6qa9igPueCI7T6ElIyiE9TkpiYKMlXvmxpzl+7p9UX8jgKIxMTlEploV1KpRJDI2NCH2n//vwv\n36JC+bKSvreCvOfeZeTC/haUKVOGqlWqsisoMt9xao1g1Y0oxkycLMnXpEkT9MwtORuZ/wGojBw1\nW+9HM2b8BEm+rl27cj81kxAtua7xWUpORicweMgQSb4hQ4Zy5FEMcRn57/u/l5jK/aR0unbVvr6a\nH2PGjWfTzQgylPlfov/xKA4DcyvJUXVjJkxmxfkHqLUc1tlx7RHVqlWTHFU3duIUlh29rbUorT15\niy6dO2NrayvJN2bcBJZtOa513PItxxk6bLikIBFDQ0OGDhvGsg3a77MsW7+XMWPHF9r1ISAX9rdk\n9v/m8fmp+wTH5Z57qtEIPjl2B49yFWnUqJEkl0KhYM78H5h47n6eIcxKtYYxfndp36GDpB0xAMbG\nxnz51VeMvxlBQnbuN7oyVGrGBoYzZuxYyYcy7OzsGDN2LMNOB5Oek3uxTchUMvyPu3wx+yvJYRRl\nypSh/ccfM+LALXLyyHUNT85g3OE7fP3dfMmX440bN8a9TAWmbA9Ao8m92AZFJ/HZvkBmf/OdJBe8\n+GBO0Rgxb/uFPIv7+eAIft53lRmffynZN2zYMK7cfsRq37yL+74Tl9l2+AKTJkmb5ABMmjQZ372n\n2H8s791Dqzfv58rN+wwdOlSy731G3u5YCLZu3cInE8YxupY7I147oHQ09CmLAyKK7IDS+MolGVTR\nBXtTI5RqDQcfxbAkKFrnB5S+nDmTrd6rGethT0/X/z+gtC/iGSvCk4rsgNKkyiXoUe7/Dyj53Itm\naVAU/YaNYP6CH3Wy7vnygFJMyB2m1nWjS8WSrw4orQ98wtKAJzo/oNSx3UcYpT9744DS6vMhrPQP\nZeHSZfTvLy0f9yWvH1Ca/HENvKq6o1C8OKC08vhNNv4RxGafbTo/oNSkVrlXB5QUCgV3Qp6wbPNx\n9p3S/QGlzp060rVd01cHlIQQfx5Q2o1/QBDHjp/4zx9QkrwO9RbrVeJDIigoSIwbPVJYmZsJGwsz\nYaCnEHWrVxHr1q3TeVKNEEIEBASIIf37CXMTE2Fjbib0FQrRvEF9sW3bNqFSqXTu8/PzEz07dRQm\nRobCxsxU6CsQH7dsIQ4ePCg0Go1OXRqNRhw8eFB83LqlMDY0FKYGesLEyFD07NJJ+Pn56dQlhBAq\nlUps27ZNeDWsL4wMDYSpgb4wNzURQwf0EwEBATr3ZWVliXXr1om6NaoKE2MjYWqoL6wszMS4MaNE\nUFCQzn2pqali6dKlonL5ssLM1FiYGBmIYnY24tPp08SjR4907ktISBALFiwQpTzchIW5mTA2MhQl\nijuJOXO+FtHR0Tr3RUdHizlz5ogSxZ2FpaWFMDYyFKU83MWCBQtEQkKCzjyA0CTdL9CjKOsbcoLS\nP49areb58+fY29v/IzdccnJySElJoVixostYfB2lUklKSgoODg7/iC87OxsTExOys7N1mgOaF5mZ\nmZiZmb24OaeDMGltpKenY2FhgUql0skVT34IIUhPT8fS0hK1Wq2TnFNtvtTUVKytrf8Rn0ajISUl\nBVtbWzQajc53stjZ2b1qMqYNW1tbnfapeZ3CzNjlwq4j/vzhy773zCX7ZN974pNPnsrIyMj8l5EL\nu4yMjMwHhlzYZWRkZD4w5MIuIyMj84FRsI5PMrmSlpbG3r17iYh4ccz5xo0b1KxZs8h8SUlJ7Nmz\nh5iYGADu3btHhQramzAVlpiYGPbt2/cq+u/Jkye4u+fdrlgqT5484eDBgwCsXLmSrl274uSkvYlW\nYbl37x7Hjh0DYO3atXTr1k3yacz8uHHjxqtEqM2bN9O1a1csLCyKxCWE4Pz581y+fBl40dK3c+fO\nGBvn30mzsGg0Gk6dOkVg4IvGd/v37+fjjz/GwKBoSoxKpeLw4cPcvXsXgBMnTtCqVasi34nz3vC2\n+yML++AD2seenZ0tPp32ibCzthQda5cVM9rVECOalBeuDraiQe0a4sKFCzr1paamilHDhgobC3PR\no2Zp8WmzimJgDXfhZGMlWjVtJO7cuaNTX1xcnOjfu4ewsTQXAxpXEjPa1RB96noKOysL0bl9WxEW\nFqZTX1hYmOjcro2wszQXQ+uVE1MblRX965QVNhZmon+v7iI+Pl6nvtu3b4uWTRsJJ1srMdqrqpj2\nURXRs34FYWNpLkaPGCZSU1N16jt//rxoUKemcHWyFxM61RfTutYXHRtWFnY2VuLTaVNFdna2Tn2H\nDx8WVSuVF+U8SogpfbzEJ72biVb1KwvHYnbif99+I9RqtU59W7ZsEWU83UWNSp5i6uC2YvKAVqJR\nrQrCpYSzWLp0iU7PPWg0GrF06VLhUrK4aFSnipg+spuYOOhjUb1SGVGmtIfYunWrzly2tjYCKNDD\n1tZGZ96/w7+1j12hULQDFvJiacdbCLEglzFCF65/m5ycHLp0aIdBYjiLe9bB1e7/Z1wqtYZd1x/z\nya5r+OzYTatWrST70tLSaNWsCRUNMviuRXkcLf7/dKlSpWFDYBjfnHvIsVN/6ORqIT4+niYN6tGx\nnA1ftq2KzWu90tOzc1jyx12WXwjj7IWLeHp6SvY9evSIZo0aMLZ6cSbU88T8tV7pyZlKfjgfyqGI\nDPwvB+Dg4CDZd/36ddp91Ipv2ldhaKOyGL3WgjkuJZMv9wcSnG7AqTP+OplNnzp1in69e7BweAt6\nNa6I/mupTRHxKUxacwqVZQn2HTysk330Pj4+TP9kIqtndKdd/Qp/2dsdGhHPqJ9241mlLus2bNLJ\nvu9Fixay6JcFrP92MI1rlvnLcwbeC2fYnE2079yLHySGbLzks89mcPTAHtYtmECNSqVe/b0QgvPX\n7jJ05u9MmTZTcsgG/Hny9GnBOoLqFW/8Tp08lVzYFQqFHhACtAKigQCgrxDi3t/GfRCFff68eZzZ\n7s3+sS0wyCVaDeBMyFP6rjvP4/BIzM0L1m88LyaNH0vylVOs6Vw9zzfi7qAoZl+M4P6jMMmHXnp2\n6YRnTjTfd62V55glfwSz/UEWFwKk9WMHaFSnFj2dYWL9vPvczDp1l8dWHuzcf1CSS61WU87Tg+/b\nladH7VK5jhFCMHzTBayrNWfJsuWSfGlpaXh6uLFtegeaV8l9CUul1tBp3m6adxvEl1/OkuSLjo6m\nauWKnF44mqqli+c6JiNLSYspq5k482uGSGziduvWLdq0bsGlTTNxK557GEzi83QaDPqRZavWSW5j\ncPz4ccaPGcGlnfOxs7HMdUx4dDwNenzB8ZOnqVatmiTf+1zYdbEgVQ8IFUI8EULkAL5AFx087zuH\nSqVi+dLFzO9cI8+iDtC8XHEalHJgy5Ytknypqals2byFb1uUz3d21b1ySWz1NRw9elSSLyIigj/8\n/JjVrmq+48Y3r0BUeBjXr0sL9rh27RrR4WGMq5v/zP+LJmU57edHZGT+XTW1ceTIEeyNFXkWdXjx\nJvquUw22bNn8Vv3Nc2PLli00LF8yz6IOYKCvx/wBTVjx+1LU6oK1TM6LVatW0rtl9TyLOoCZiRFz\nhrZk6SLpebVLlyxiQp/meRZ1ADtrc2YObc3Sxb9J9i1Z9Bufje6SZ1EHcCvhwPgBbfn99yWSfe8z\nuijsJYHXmyRH/vl3HxwXLlzA0dyIGq75R9UBDK/vge/GdZJ8hw4doqGHAyWt3gyx/jtDqzjjs0Ga\nb8eOHXSv6YGFSf5LAvp6egypX4qtWzZL8vls2cygKiXQzyXk+XUsjA3oVqkkO3bskObbuJ5h9dy0\njitpa06jsiU4dOiQJN+2zRsY3rKi1nE1SzvjYGksOYrPd8smhn9cW+u4tvXKEx0VJSlI//27AAAL\n+ElEQVSKTwiBr+82hnXR3sG0f/t6/OF3lpSUlEL7UlJS8Dtzln6dcg+xfp3hvVq9VYjLh4guCntu\n78r3f80lF+Li4nCzL9i6q7u9BfHx8ZJ88fHxuFkWbBeDm40ZcRKixwDi4mJxsymYz93WnGcxTyX5\n4p9G42at/UMLwN3CUPL3Fx8Xg5tdwX5/btYmkn9/cfHxuDtYF8znaC399fIsEXcn7bt69PX1cHW2\nk+RTKpVkZmVRwlF7B1MzU2PsbCwl9VJJSEjAztYKM1Ptr8/ijrZkZGShVCoL7Xvf0cVepEjg9WmQ\nCy/W2t9g7ty5r/7s5eWFl5eXDvT/HJaWliRqCYV4SUJ6NuER4ZJvUHUon/dl9eskZii5eOm6ZN/E\nFpULNO5ZWhY++7ezYWvhZ0ZG+npUal2lQGNj07JYtmABPyx44758gbE0MWRwmYKFZ4THJ7F88mQm\nTy58H3ErM2MS07IKNPZxZAw9e/YstAvA3MSIxJRMitlo//B6EhkjOS9AX09BSlomVhb5fzir1Rri\n4hMpVSrvJbCCYGJshFqt1nofKTUtE6HRFNnWzqLGz8/v1bbYwqKLGXsAUEahULgrFAojoC+wP7eB\nc+fOffV434o6vEg0uhPxjPDENK1jfa+FM/PLryVtEY2KiuJCdAopWdrT3bfdi2PJytWSfIGBgey5\nHY0qjxCKlwgh8A2MZP/Bw5J8+w4ewvdenNabTjlqDfsePOPmzZuSfIuWrcTnRpTWn2VKppILTxKJ\njo6W5JvxxSx8/LX3834S95yIpCzS0tIk+YYMG4bPqRtafQF3wzG1sEalUknyde7UAZ8jV7T6Dp27\nRY0a1SS5hBBUr1aVw37a7+tsPXCWLp07Svb9W3h5ef2lVhYGyYVdCKEGJgLHgSDAVwhxV+rzvouY\nm5szYOBAFhy7k++4R/Ep7Lr+mJGjRknylShRgtYtW7L0cv5p8tejkwiISqJPnz6SfNWrV8fD05ON\nF0PzHXfkTiSpan0++ugjSb42bdqQKgw4GhqT77hNgU/w8CwjeZdDnz59uPI4jmtPnuU7bvEfd2nd\nshXFixfsaikvRo0azc7zd3kUk3/r1wW7LzNg4EDJO6jGT5jEqgMBxCflPfEQQjB/sx+jx42XvINq\n/MQpLNrqR1pG3lclOTkqflx/knETpCcojZ84mR9X7SMnj7QtgLT0TBZvOMK4CZMk+95ndHJMSwhx\nVAhRXghRVgjxgy6e811l7rff4ReRztyDgbnObO/FJNNu6Sm++/57nZya/HnxUtbciWXZlUe5xqsF\nRCbSfdtVlq9eg6lpwdar82P5mnXMOnQb3ysPc521HA+OZMSWi3hv2CT5lJ+enh7eGzcz6uBtTjx4\ns7gLIdh2K4Kvzz5gube0G8MAZmZmLF+1hq4r/bjyOO6Nf9doBL//cZfVl57w8yLpuyqcnJz4bv73\ntP1mJ/ci3/wwUak1zPXxxy8kgbnf/E+yr3LlygwfOZp2M9YSGfdmaHe2UsWE3/YSl2nA5MnS93m3\natWKRs1a0mXKChKS3/wwScvIov+X67AvXor+/ftL9vXv3x9bJ1f6T11EWvqbUZEJSSl0GbOARs1a\n6OQMyfuM3I+9EMTGxtK/Vw9C7gUzvGFpKjpZkaFUsefOUy48iOGHH39m1OjROvM9fPiQvt27khz3\nlGFVS1DK1pzn2TnsuB9PUHwqy1d7061bN535AgMD6derB0bqTIbUcaekrRnxqVlsvh7J01QlG7f6\n0rx5c535/Pz8GNK/H8XN9Olf0REHM2OiUjLZGBxDjqEZPjt3U6NGDZ359uzZw7jRI6lc3IY+NUpg\nbWrEo2dprL30GBsHZ7bt3quTw1cvWb1qFZ9/NoPGldzoWtcDM2ND7kUm4n3qDuXKV2Tr9p06a50g\nhOCH7+fz44IFtG1QgY/rlcXQQI/ABzGsP3KVJk2asm7jZqysrHTiU6vVfDZzBt7ea+jeuhYt6pRF\nT6Hg4q0wth6+TJeuXVm+YpXO1ruzsrIYP24s+/btpX/nZjSsWRaNRnD6UhB7jl1ixIgRLPjxJ52E\nmLzP+9jlwi6Bmzdvss57NZFhjzExNcXro3b069dP8iV1bgghuHTpEpvWryU2Ogpzcwvad+lGjx49\niiRpSAjBqVOn2LZ1M4nxcVjZ2NCtV186dOhQJMk/arWaQ4cOsWe7L8+Tk7B3cKLvwEG0bNlS58k4\n8CKpaffu3RzZv5eM9DQcS5Rk0JBhNGjQoEh86enp+Pj44HfyGFlZmbi4l2LY8JFUr15d5y54kbW6\nYcMGLl84R05ODp5lyjFy1GjKli1bJL64uDi8vb25deMqarWGilWqMnLkKFxdXYvEFxERwZo1q7kb\ndAd9fT2q1ajNiBEjcHR01JnDzs6WpKQ3r3xyw9bWhsTEgqUtvS1yYZeRkZH5wJATlGRkZGRk5MIu\nIyMj86EhF3YZGRmZDwy5sMvIyMh8YMiFXUZGRuYDQy7sMjIyMh8YcmGXkZGR+cCQC7uMjIzMB4Zc\n2GVkZGQ+MOTCLiMjI/OBIRd2GRkZmf9r795CrCoDKI7/l1lkaRZRhg4aEt2EEh+6SRFWJEbaS2AF\nWT700EUp6KYPvUYQIdWLZGKhBE5BBl1UxIce7EKKllaCkJo00Y2IILRWD2cPHGqYo3P2zPZ8rh8M\nc86ePXvW5sys+fblmylMij0iojAp9oiIwqTYIyIKk2KPiChMij0iojAp9oiIwqTYIyIKk2KPiChM\nij0iojAp9oiIwqTYIyIKk2KPiChMij0iojAp9oiIwnRV7JJekLRP0i5Jb0s6p65gERExMt2O2DcD\ns2zPBvYDz3YfqTdt37696QijquT9K3nfIPt3Kuqq2G1vtf1P9XQH0Nd9pN5U+jdXyftX8r5B9u9U\nVOc59qXABzVuLyIiRmB8pxUkbQGmtC8CDKy0/V61zkrgqO0No5IyIiKOm2x3twFpCfAQMM/2X8Os\n190Xiog4RdnWiazfccQ+HEnzgaeAm4Yr9ZEEi4iIkelqxC5pP3AG8HO1aIfth+sIFhERI9P1qZiI\niDi5jOnM0xInNEmaL+lrSd9KerrpPHWS1Cdpm6S9kvZIWtZ0ptEgaZykLyRtajpL3SRNlrSx+rn7\nStK1TWeqi6THJX0pabek9ZLOaDpTtyStkTQgaXfbsvMkbZb0jaSPJE3utJ2x/pMCRU1okjQOeAW4\nHZgF3CPp8mZT1eoY8ITtK4HrgUcK279By4G9TYcYJauA921fAVwN7Gs4Ty0kTQUeA+bYvorW9cLF\nzaaqxVpafdLuGWCr7cuAbRxHb45psRc4oekaYL/t72wfBd4CFjWcqTa2f7C9q3r8B61SmNZsqnpJ\n6gMWAK81naVukiYBN9peC2D7mO3fG45Vp9OAsyWNB84CjjScp2u2PwZ+/c/iRcC66vE64K5O22ny\nj4CVMKFpGnCo7flhCiu+QZIuBmYDnzSbpHYvAU/SmptRmpnAT5LWVqeaVkua0HSoOtg+ArwIHAS+\nB36zvbXZVKPmQtsD0BpsARd0+oTai13Sluqc1+Dbnur9nW3rlDKhaahbOIsrCEkTgX5geTVyL4Kk\nO4CB6qhEDP169rLxwBzgVdtzgD9pHdb3PEnn0hrJzgCmAhMl3dtsqpNHV/exD8X2bcN9vJrQtACY\nV/fXbsBhYHrb8z4KOBxsVx3m9gNv2n636Tw1mwsslLQAmABMkvSG7fsbzlWXw8Ah259Xz/uBUi7w\n3wocsP0LgKR3gBuAXh8sDmVA0hTbA5IuAn7s9AljfVfM4ISmhZ0mNPWIz4BLJM2orsgvBkq7s+J1\nYK/tVU0HqZvtFban255J67XbVlCpUx2+H5J0abXoFsq5SHwQuE7SmZJEa9+KuDDM/48eNwEPVI+X\nAB0HWLWP2Dt4mdaEpi2t16K3JzTZ/lvSo7Tu9hkHrLFdyjcXkuYC9wF7JO2kdZpphe0Pm00WJ2AZ\nsF7S6cAB4MGG89TC9qeS+oGdwNHq/epmU3VP0gbgZuB8SQeB54DngY2SltL6hXZ3x+1kglJERFny\nr/EiIgqTYo+IKEyKPSKiMCn2iIjCpNgjIgqTYo+IKEyKPSKiMCn2iIjC/Au5xJJWgZF4FgAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6d63ae6320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import infeciton_time2weight\n",
    "from plot_utils import plot_snapshot\n",
    "pos = {n: np.array(n) for n in g.nodes()}\n",
    "\n",
    "source, obs_nodes, infection_times, tree = make_partial_cascade(g, 0.05, sampling_method='late_nodes')\n",
    "\n",
    "node2weight = infeciton_time2weight(infection_times)\n",
    "\n",
    "plot_snapshot(g, pos, node2weight, \n",
    "              query_node=(3, 3),\n",
    "              source_node=source,\n",
    "              queried_nodes=obs_nodes, \n",
    "              max_node_size=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "infection_times =  make_full_cascade(g, source=(5, 5))\n",
    "assert infection_times[(5, 5)] == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "infection_times = make_full_cascade(induced_g, source=(5, 5), is_sampled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "expected = nx.shortest_path_length(induced_g, source=(5, 5), weight='d')\n",
    "actual = infection_times\n",
    "for n, t in expected.items():\n",
    "    assert t == actual[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 1.09 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "make_full_cascade(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 4.01 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "generate_cascade_old(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 2.16 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "simulate_IC(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 1.38 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "make_partial_cascade(g, 0.05, 'late_nodes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nx.shortest_path_length(induced_g)[(0, 1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.stats import hmean\n",
    "from collections import defaultdict\n",
    "from joblib import Parallel, delayed\n",
    "def infection_time_estimation(g, n_rounds, mean_method='harmonic'):\n",
    "    \"\"\"\n",
    "    estimate the harmonic mean of infection times given each node as source\n",
    "\n",
    "    Returns:\n",
    "    dict source to nodes' infection time:\n",
    "    for each node as source, return the estimated infection times of all nodes\n",
    "    \"\"\"\n",
    "    sampled_graphs = [sample_graph_from_infection(g)\n",
    "                      for i in range(n_rounds)]\n",
    "    s2t_len_list = Parallel(n_jobs=-1)(\n",
    "        delayed(nx.shortest_path_length)(g, weight='d')\n",
    "        for g in sampled_graphs)\n",
    "    # 3D array\n",
    "    s2n_times = defaultdict(lambda: defaultdict(list))\n",
    "\n",
    "    for g, s2t_len in tqdm(zip(sampled_graphs, s2t_len_list)):\n",
    "        for s in s2t_len:\n",
    "            for n in g.nodes_iter():\n",
    "                s2n_times[s][n].append(s2t_len[s].get(n, float('inf')))\n",
    "\n",
    "    est = defaultdict(dict)\n",
    "    if mean_method == 'harmonic':\n",
    "        def mean_func(times):\n",
    "            times = np.array(times)\n",
    "            times = times[np.nonzero(times)]\n",
    "            if times.shape[0] >\t0:\n",
    "                return hmean(times)\n",
    "            else:\n",
    "                return 0\n",
    "    else:\n",
    "        raise ValueError('{\"harmoic\"} accepted')\n",
    "\n",
    "    for s, n2times in tqdm(s2n_times.items()):\n",
    "        for n, times in n2times.items():\n",
    "            est[s][n] = mean_func(times)\n",
    "    return est, s2n_times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 3.18 s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "est, s2n_times = infection_time_estimation(g, n_rounds=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from synthetic_data import gen_kronecker\n",
    "from graph_generator import P_hier\n",
    "g = gen_kronecker(P_hier, k=10, n_edges=2048)\n",
    "g = add_p_and_delta(g, 0.7, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "956\n",
      "1968\n"
     ]
    }
   ],
   "source": [
    "print(g.number_of_nodes())\n",
    "print(g.number_of_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100it [01:10,  1.58it/s]\n",
      "100%|██████████| 956/956 [00:42<00:00, 22.38it/s]\n",
      "100it [01:11,  1.43it/s]\n",
      "100%|██████████| 956/956 [00:42<00:00, 17.37it/s]\n",
      "100it [01:10,  1.57it/s]\n",
      "100%|██████████| 956/956 [00:41<00:00, 23.04it/s]\n",
      "100it [01:10,  1.43it/s]\n",
      "100%|██████████| 956/956 [00:44<00:00, 21.68it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 2min 36s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "est, s2n_times = infection_time_estimation(g, n_rounds=100)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}