node2vec.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# node2vec\n",
    "---\n",
    "[node2vec](http://snap.stanford.edu/node2vec/) for link prediction:\n",
    "1. Perform train-test split\n",
    "1. Train skip-gram model on random walks within training graph\n",
    "2. Get node embeddings from skip-gram model\n",
    "3. Create bootstrapped edge embeddings by taking the Hadamard product of node embeddings\n",
    "4. Train a logistic regression classifier on these edge embeddings (possible edge --> edge score between 0-1)\n",
    "5. Evaluate these edge embeddings on the validation and test edge sets\n",
    "\n",
    "node2vec source code: https://github.com/aditya-grover/node2vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Read in Graph Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy.sparse as sp\n",
    "import numpy as np\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sklearn.metrics import average_precision_score\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "EGO_USER = 0 # which ego network to look at\n",
    "\n",
    "# Load pickled (adj, feat) tuple\n",
    "network_dir = './fb-processed/{0}-adj-feat.pkl'.format(EGO_USER)\n",
    "with open(network_dir, 'rb') as f:\n",
    "    adj, features = pickle.load(f)\n",
    "    \n",
    "g = nx.Graph(adj) # re-create graph using node indices (0 to num_nodes-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CpyGXoyfDQC6XQ6FQYOrUqVAqlfD29oavry+GDx8OuVzOt9XFxYUfKL516xa6\ndOkCb29vEBGSiZDPMIC1PXkch0dE+HLiRPj7+8NgMICIoNPpsLxbN0u0TDm/d94XXyAoKAibN2/G\nyZMn4ejoCIPBgA0bNsDNzQ0//PADlnfrVnaGKccJDpzmSSToK5PBy8sLBw8efHzRbYQ4ZmZmonr1\n6hg0aJAlkqkkQZy1jQV2Qk6f5agYIZ6ouBNRCyL6mSwLzIwUKJNARCeJ6AwRHaysTlHcn3OE4pCX\nLhW0aE0KBeZHRSEqKqrsgKYNvvnmGxgMBqzq2bNC6J5Zo8Hc9HRER0fjRP/+go/xOQyD38aNg8Fg\nsPm0kJeXh6igIBQKzbCsJOWBvS2DCB9UspBFBllyw8tkMowfPx4KhQJubm4IDg5G69at4eXlBcDi\nRmIYpszTDACkp6dDTcJJurKIYLDmdy8ZY2jevDnmT52KrA8/xO0ePXBu2DBsXrUKTZo0QVhYGLp3\n7w6VSgWO4+Du7s6HX/q6uv7pkMdZCgV69+4NX19fNG/eHOeWLasQ4ljg4IAUJyesX7++zLltWb0a\ng9RqHI6Ph6l5c/vHqiyevSox808RT0zcyZLj5xciqk6WZR5PEVFouTLORHSWiHysrw2V1SuK+3OM\nQByy+dAhfL5li2D2xCyGwZ5NmzB//nzodDp8/PHHdg/z87Fjgm4Es0aDEf37Iz4yEoUCg4p5Uina\nNWuGzz77DNWqVSuTb+XxqXyDNK3WsrqT9XxyWBY5EgmW6/W89VjB8mZZy0CxjfeyGQaD1GoMdXLi\nJyuV34oVCnQngpeTE3qxLL6uXx99JBJ4OTkhMjIStWvX5lMGfPfdd2AYpoJ7ycPDw25Kg2yGwRsc\nB47jULt2bRgMBrAsC47joFar4enpieDgYNSoUQMymQxNmzaFj48PHBwcUKdOHeh0OsTHx6Nv3754\no9S4QVW2bCLsbNcOqampUKvVqOXrK/hdFqtUvGslKysLr732GoKCgvDDDz+goKAAn7VuXemCI3/2\nt/o0++qrKu5VmS9dj4guAbgMoJCINpBlcfbSdCGirQB+t856vV3FCbIizxtGI1GrVpa/JWuR5uQQ\nGY2Um5hII995h74fP55QauHqkox/l2bPpt5Dh9LZs2dp+/btNGHCBOrZsyfl5ubaPFTg8ePEMrYn\nrTNmM2VERFBkfDy95e1NxRIJWSfIUzYRZTMMfdqrF2WZzXTgwAHq2bMnpaenU1G5bJSxsbHk2akT\nDezYkWghcf96AAAgAElEQVT2bKKRI+nasGEU5eZGFzt1orz8fJvHzzebqUigbSzH0WaOo7VFRWSy\nGEMVAMPQdYahs48e0QyzmRK+/56mFxfT2UePqEFxMd28eZOCgoKIiGjHjh2k1WqJKXU8o9FIN2/e\npBCJhIRyKKoACiIirVZLUqmUjEYj1alTh9q0aUOpqamUlJREdevWpRs3btALL7xAEomEbt++TVqt\nlsxmMxkMBmrSpAmtXr2aAgDB49hCrlBQypo1tGPHDrpz5w5tbN+epBLbq6lyREQbN9KRI0coIiKC\npFIpnThxgmQyGdWvX5/WFBSQQmhBblsLeD++SIK/VWrVis+0+cxSmfoTUUciWlbq9StENK9cmVlE\nNJ+IDhDRcSJ6VaCuXkR0jIiO+fj4/D/0cSL/79iJLimUy2FassRSTiA87cGDB+jcuTNCQkLwzTff\noGvXrggNDcVPP/1U4VC/vvSSfQtx5EiYDx1CnlTKh0EWEKGAZTGndWtUq1YNq1atQlBQEJYsWYKW\nLVvirbfeqnCcR48ewcvLC19//TW/Ly0tDVOmTMHc9HQYWZa3WnOt6QLauLqib+3aKJDLeevcSIRc\niQTfZGSAs8aAd/L0RL5MViZaxsiyOPzuu4JujhyOgyPL8rnT4+Pj0ahRozJtfv/990FEGKnTCS58\nUaxQYLBGA6PRiGXLliEuLq6C9d+rVy/06NEDly5dgqOjI3Q6HaZMmYKwsDA8evQItWrVAsuy+DQ1\nVfAppnSCsFyOQ55MVtEyriTE8ZvYWBgMBmzZsgWFhYWYOHEidDodVqxYYWlzeQtcJrMknBs+XNjN\n8lfWDXgKoCfolqmKuM8joiNEpCIiHRFdJKIa9uoV3TLPKU8on8fatWt5IVm+fDl0Oh2WLl1aRnyW\nN2xof3r5vHmCIZhZRDi4axf0ej3WrVsHg8GAHTt2oHr16hX8uwDw2WefITAwkM8Ief78eWi1Wty+\nfRtv9+2LQWo1pkkkGKRW443OncGyLKRSKX4+fhy3Jk9GBhH6OzhA5+CAH3/8EQzDgIggl8uxZfVq\nvMGymEyEfnI5avn54dvXXxd0c+RyHN7gOD5NsZubG4YMGVKmvZ6enmAYBhoS9rnnSiT4YPx4GI1G\neHp64vvvvy9Tx549e+Dr64s7d+4gIiICTk5OmDVrFvR6PS5cuIAOHTqAYRh07NgRd69cgVHA3ZYn\nleI9Dw98l5CA96tXtyy0XY78efMEB5dzWBbTQ0Jw7do1nD59GlFRUWjevDl+//33spUYjcCIERZh\nL4nKsuNmKRwy5In8Vv+/eZLi3pCI9pV6/Q4RvVOuzEgimlDq9XIietFevaK4P6fYGTDNl0qRv2BB\nlau6cuUK4uLikJCQgC+//BK1atXCSy+9hEePHiE7OxteTk6CYXGFDg7A3LmClpmRLNPjd+/eDTc3\nN6xYsQLu7u7YuXNnhaXiSujUqRNGlrrh+/Xrh4EDB/IDkUSEhIQELFiwADqdDkSEM2fOALAIMMdx\n8PDwQLNmzaDVaqFUKmEwGLB+/XooFAoQEby8vKDT6fBDUpJd4ZnGcTh58iTMZjM4jsP+/fv5dmVn\nZ4PIsr4Hx3HYM3p0hXj7YpUKqc7OyMrKwvjx49G5c+cy53r//n14eXlh//79GDJkCHQ6HQYPHoxq\n1aph+/btmDBhAogIkZGRePDgARo2bIgZ7dohq9RxjEQoVCjQ0d0d8+fPh8FgwK+//lrhumZmZsJT\noxEOC5XLUXDvHiZNmmSzk+epLDXBjRuWfPPDhuHrl1/GKCcnu+kZ/guWu4SILhORPz0eUA0rVyaE\niL60llUS0U9EVMtevaK4P5/cunRJ0ILLlUhQ08sL69evt31z2qC4uBjvv/8+9Ho91qxZg969eyMw\nMBATJkxASkpKhcfxYoUCj4jQmAiH4+LsCuQUhsGvv/6KJUuWICAgAJMnT0aYdc3QoKAgPHz4sExb\n/vjjDxgMBn7i0K1bt/hUBTNnzoRWq4VWq0VQUBB69+4NIkKzZs0AAP379wfLsnBwcEBwcDDCwsKg\n0Wig0+kwd+5cSCQSEFnSDcjlcmxLSUG2gDsll2XRk2Hw8OFDnD9/HkTEJzsrKipCw4YNQURgWRZ9\n+/ZFcHAw3NVq9GQYFAwZAixbhm4vvoj3338fN27cgKurK65cuVLmXF955RUMGDAAe/bsgaOjIxo2\nbIjY2FiMGzcOW7Zs4VMf3LlzB8nJyXj55Zeh0+mgJsLuDh2QQYT9XbogY/RotG7dGn5+fti2bVuF\n73fu3LngOA7x8fEo+PJLy8C71b2TwzAoVipxec0aPo7/9zNnhCNb7LlZHBxgdnDg89vkcpwlz7yA\nK+lpjo9/YuJuqYtaEdEFskTNjLbu60NEfUqVeZssETM/EdHgyuoUxf05oFwI2U/WmaEvODhYwgdt\nRCAcPHgQERERaNy4MY4dO1blQx09ehQ1atTAK6+8gpUrV0IqleL111+3dBLl/PebV62Cq6srehIJ\nZmXMYVm8YzDA19cXubm5GD16NOrVq4cePXogNTUV/fr1Q5s2bSpkkFy5ciWioqJQVFQEwOLb7tCh\nA/r164dx48ZBLpdDqVSiTp06cHNzA8Mw2LNnDzIzM8FxHLRaLUaNGgVnZ2fIZDIoFAr06dMHvr6+\nvKVNROjdpYugJZvNsnCVyQAAU6ZMgaOjIwDg5s2baNKkCd9RSKVS+Pv78wt6p6SkALC4lHQ6HR49\neoSePXvi7bffLnOOW7duRWBgIC5dugQXFxdotVr07NkTrVq1QmZmJliWhVKpxJUrV9CpUye0bt2a\nP9cJEybAxcUF7u7u+PXXX/nZxgMHDixzDJPJhLZt24JlWYwbN47f/+3evXjb1RV7IyORO3cuPhg/\nHlqtFosXL4b50CG7kS1FQ4fa7cxtbgoFUCoS6nmKlqmSuP8TmyjuzzjlLOYiuRxZRGjl6Ii1a9fa\nzedRXFyMpUuXws3NDd27d7cZgmiL7Oxs9O7dG97e3lCr1YiKikJaWlqZlYdKGDNmDOoGB9sdlIyL\njIRMJkNycjIKCgrQtWtXpKWloUmTJhgyZAgaNWqESZMmlanXbDbjhRdewLRp0wAAOTk58PLyQkxM\nDHbv3o3XX38dPj4+ICK8//77cHR0hJOTE86dOweNRgOO45Ceno60tDTeddKwYUPerVMi8B4eHkiS\nycq4U4xkGSvo7O2NatWqAQBatWqFiIgIHDhwAJ6enkhPTwcRgWEYyGQyjBkzBv7+/mBL5ZHp2rUr\n3nvvPZw+fRoGg6FMvp7bt2/D3d0dhw4dQlxcHDQaDUaMGIGAgABcvHgRCoUCEokEx44dQ+/evREf\nH8/790eNGgWDwYCuXbtixIgRSE9PR4sWLRBdbmLajRs3+JDKr776CoAlhfCYMWPg5uaG7du34+zZ\ns6hXrx6SkpIsTxV2XC5mjQafrl2Ld/R6QTeL3UlO8+Y9U7lnRHEX+eewc6MVyOVVvjkePnyIYcOG\nQavVYurUqZWv12l9UtgRFoa+UineHTIEgwYNgo+PT4VJSCWW4aj4eGTR4+n3hXI5jAyDVo6OaN68\nOdzd3REYGIj09HTk5uYiMTERvXr1QkBAAGbOnAlPT0/s3bu3TN2//PILtFotLl68CABYtWoV5HI5\nLl68iPPnz8PR0REsy6JOnTpwcHBAaGgoAgMDkZaWxueKuXr1Ki/mSqUSb775Jm+1E1nWVI2MjIRW\nLkd3IkwmwiC1Gn46Hdzd3VGvXj0AgI+PD2JiYuDm5oYFCxbwvnuO4zBp0iS89tprCAwM5Bfx+Pnn\nn6HT6fDw4UO0aNECs2fP5s/LbDajQ4cOePvttzF93Di8qVBgd3g4BqvVOHHwIDw9PcGyLLZt24ZR\no0YhKiqKnwU7dOhQGAwG/PDDD/Dz88OyZcvg7u4OnU6HS5cu8cfYvXs35HI5AgICcOfOHQDAxYsX\nUa9ePTRv3hzXrl3DtGnToNVqsWDBgsdPTnZcLrksi3HVquHLTz+tUg6jCttTOnAqhCjuIv8cTziE\n7MKFC2jdujUCAgLw6aef2vbHl0vxWySXI4fj8EZICBYtWgSDwYDJkyeXcaMYjUbUrl0bU8eOxUCV\nChlEuDt1Kjo0b47u3btDp9OhUaNGkEgkaNSoEbp374579+4hNDQUI0aMgN6amsDNza2CT/qDDz5A\nUlISzGYzsrOzwTAMNmzYAAAICgpCUFAQnwdGLpejb9++qFOnDhiGgZOTE44ePQqDwQCGYaBSqTBu\n3DioVCpe3BmGQaNGjcrs02q1MBgM0Gg06Ny5Mx48eACGYRAYGIh9+/ZBr9fzUTgODg64evUqnJyc\nwHEcllm/k1dffRUTJkzAvn37EBgYiIKCAv6c1q1bh9DQUJyYMwdZVtdVSYeYzbKIJUJGRgZmzJiB\n4OBg+Pn5gYjQv39/uLu7IzMzE0eOHEGNGjVQq1YtuLm5YWOpzJtvv/02GIZBly5dYDabYTabsWLF\nCuh0OsyePRtnz55Fw4YNkZCQgMuXL5f9/iuJwjINHw4AOLdsGXI4jh+vMJIlRUSR0Gzip3jgVAhR\n3EX+OSq50QqHDftL1e7btw+hoaFo2rRp2WiVSp4UfFxdMWXKFMTGxiI5ORl/WFPuAsDly5fh7u6O\nuXPnwsHBwTJYuW0bnyNdr9fD3d0dvr6+iImJwaBBg/Drr7+iWrVqGDVqFDw8PDB27FhERUWVWRi7\nqKgIdevWxfLly3HmzBl4eXkhICAABQUFCAgIgFarhaOjI5KSksBxHCZMmIDWrVvzIZITJ05Ejx49\nwDAMlEolxo4dC7lczoszx3GIiIiARqPhxd3V1RXu7u5w5jisTUjAAkdH9CDC/z7/HFqtlnf7MAyD\n1NRULF68GDVq1IBCoUBRUREuXrwIrVaLu3fvIjw8HFu3buXP5/r16zAYDDi4cyeyhAZyJRKsWbAA\n3t7eCAwMBBGhR48e8PT05OchDB48GK1atYJer0evXr0AALm5uahXrx44jsPy5csBWDJ5duzYEbVq\n1UJmZiZmzJgBrVaLuXPnVhjn+OGHHzDc1VV4BqxKhesTJ6J9+/bw9PTEO2++iekhIZjv6IgFdeti\nYKdOFt+6rc8qFE+9G6Y8oriL/HPYe0TmOAzWaDBhwgTcvXv3T1ddWFiIOXPmQK/Xo1+/fpY6KnlS\nuDZhAurUqYM2bdpgyJAh8PT0LBMaeODAAbi4uCA4OBgpKSngOA6vvvoqEhMT8f3338PV1RUSiQSN\nGzdGeHg4xo0bhxMnTkCn02HgwIGoXbs2OnTogG7dupV5qjh58iT0ej1WrFiB1NRUtGjRAuPHj+cH\nERMSEjBy5Eio1WrI5XLcunULarUaDMMgMjIS+/fv54W7fv36vJ+cZVmwLAt/f384OTnxZZydndHG\nmsOlvB++mUKB8PBwvhP4+OOPERMTA5VKhW7dugEAXn/9dbz77rtYvnw5Ykut4GQ2m5GSkoKxY8di\nTni4oIgWyeUY7OiIGjVqgIjw8ssvw8vLC+fPnwdgGUtxd3eHSqVCUFAQcnNzcfr0aTg7O8PFxQVn\nz54FAHz11Vfw8vLCoEGD8OOPP6Jx48aIi4sr474BLG675ORkMAyDF+rXt7j8BDodP50OAwYMQNOm\nTeHr64slS5agoKAAV69ehY+LC8xC4q5UWsT9GcovI4p7aZ6hL+6ZwE6OdGg0OPvDD+jRowdcXFzQ\nv39//PLLL3/6EHfv3kX//v2h1+txtGlT28cq5TPNz8/HsGHD4OnpicmTJ8PDwwNjxozho1rGjBkD\nuVyOhw8fYvDgwSAieHp6YuXKlcjMzISDgwO8vLzQpEkTBAUFYfr06dizZw8MBgM6duyIlJQUhIWF\nYdGiRWXaOWrUKNSuXRtvvfUWfvzxR6jVarRr1w4HDhyAn58ftFotpk+fDolEgvr162POnDko8anf\nvXuXt9SlUik4a54XrVYLIoJKpSoj7u4qleAAcZFCAYNSybtkjhw5AldXV7Asi5s3b+LSpUvQarW4\nevUqPD09ceTIEf4cli9fjoiICMyZMwfTheK+rdtsq5uoY8eO8PX1tQiy9f76rXNnvKlQQCeX49y5\nc1iyZAk4jkPDhg2Rn5+PgoICDB8+HB4eHti1axdmzZoFrVaLWbNmlbHWzWYzxowZA4lEAjc3N8yc\nORNRUVHoHRaGYqWyzEpdWUSYkprK571ZvHhxGVcTAEwNCuIXE7Hplhkx4pnKLyOKewnPYGKgZ4El\nr75qWYnIzpJoN27cwDvvvAOtVosXX3wRP/zwQ+UVl+uIzxw5ghkhIYJT6POl0scpDQB8+eWX8PLy\nQo8ePZCUlIS4uDhcvXoVmZmZ0Gq1aNGiBYqLizF37lxeCG/fvo2dO3eCZVlERUWhSZMm8PHxwaJF\ni7B06VJUr14dDRs2RK9evaDX68sIY15eHhwdHdG7d28AgL+/P1q0aAGz2YxGjRohOjoaH374IeRy\nOXx8fNC8eXNe0KdPn17G7eLh4QEiQmhoKN8BqNVq/v2eJJwELF8qxSDrU0FqaioGDx4MNzc3REVF\nAQC6d++OsWPHYsKECXjppZf49v/666/QarXo27cvGIZBb46zm2isu7VdCoUCGRkZeLhzZ4XFSgrk\ncoxNTATDMHjnnXcAAOfOnUNUVBRat26NI0eOIC4uDo0bN66Q/XPXrl3Q6XSQSqUYPHgw2rVrB19f\nX2zYsAFmsxl3rlzBxuRkzHRwwJL69dEqPl5Q1Es4kZxs3zgQ8sc/pbHuorgDVV5MV6QSygnu/ClT\nLAtOX75cpRCyrKwsfPjhh/Dx8UF8fDx27txZwa8KQDib5N69gml3HxGhppcXP7EIsPhzX3zxRYSG\nhuLNN9+Em5sbZs+ejfDwcCQlJWGYdUxg9+7dYBgGBoMBJpMJbdq0gaOjI6Kjo/kQv7Vr12LMmDGI\nioqCn58f3nrrLXh7e+NWqRWcIiIioNVqce/ePTg7O8PZ2RlXrlzBjh07EBAQgBo1aqBTp06Qy+VI\nS0uDo6Mjb607ODjwbpgSiz00NBSMNZe7TCbjO4Mp9gSKHqcIXrNmDbRaLViWxZ49e3D58mW4urri\nzJkzcHV15QcrL1y4AG9vbygUCigUCiiVSkQEBAhm7XxEhNSEBAQGBmLx4sV4pW1bwVj8R0T48rPP\nYDabsWjRImi1WsyfPx+zZ8+GVqvFjBkzUFxczF/Dq1evIiYmBgzDoHnz5ujfvz+0Wi0yMjKQl5eH\nhw8fYuzYsXB1dUWHDh2QmJgIb29vLFq0CAUlrrtyT+ZFRUXYtGkT3vf3F/bXy+WWdAVCVv1TONgq\nijvwzCYGeqooJ7gloYR/CCwwbY/CwkJ8/PHHiIiIQGhoKJYvX/44/LGyjnjfPpg1Gj6OOV8qhVmt\nxm8ffww/Pz/IZDL07dsX2dnZACyP9qtXr4ZOp0P//v3h5uYGvV6PGzduICAgAKtWrQIAfP/992AY\nBu7u7jh+/DhcXFzg7e2NiIgIxMXFwWAwYNu2bXjllVeQlJQEvV6P119/HQkJCbzLx9PTE126dEHb\ntm0RFhaGcePG8REh4eHhCAgIwAcffACVSoVFixYhIiKCt8arVasGlmWhUCh4K97b2xtKq4ul9GbP\ncs+xWtVyuRxr1qyBu3W5QrPZjJ49e2L06NF44403MHToUOzevRutWrWCWq2Gh4cH0tLS4ODggLi4\nOMuTi3Uxj5LZnDnW1Zz616mD0NBQ3Lhxw/KdVZKbP+vDD9GmTRtERERg3759aNKkCRo0aMD76AGg\noKAAPXv2BMuyqF69OoYPH84Pxv7xxx/Izs7GlClToNfrkZKSghaNG+NtFxecSE5G4YIFljVXyxkE\nJrUaa/v0gY+PDxo3boytq1cjRyj+vbKc/E9hmKQo7kClUR2/d+0Ko2i9C/MPPfmYzWZ88cUXSE5O\nhoeHBzIyMpAze3blHbHRiP+98QY2BwVhZWws/PV6LFmyBHl5eRg4cCAUCgUMBgN2797NH+vy5cto\n1KgRoqKioFarERMTg71790Kv1+N///sfAODjjz8Gx3FwdnZGWloa3n77bVSvXh21a9dGbGwsdDod\ndu/ejcTERKSmpsLDwwNNmjTBsGHDYDQaoVAocP/+fWg0GnTq1AlGoxEeHh44evQo1q1bhxo1aiAp\nKQm+vr6oVasWpk+fzgt2UlISSqJjEhMTQURwdHSEq6srX6bEcre38IaRZaEiQkpKCpKTkyGTyTB6\n9GhcuXIFrq6u2L17N1QqFapXr47IyEhkZGRAq9Vi5syZUCgUaNKkCQIDAyGVSkFEyBg9GqPc3LBU\np0N3IiTUrYvw8HDcvn378RdZyf01lWXRqlUrTJ06lR97KG2tr1ixAmq1GkqlEgMGDEBwcDCaNWuG\n06dPIz8/H3PnzoWHhweaNm2K+Ph4tNPrUSCXP+5QhFIHkGWQ9cShQ/yx9owebRH4kjQVDg7IlUox\nSy5/5vLLiOIO2LXcS5Y6IyJUr14d6enpmDJlCvbt21f2B/xf5p9+8snKwu/jxmFHWBg+r2RVopI4\n5j179qB58+YAgOPHjyM2Npafofn1119Db118umPHjvzM16KiIvTt2xccx+H111+HTqfD8OHD4enp\niatXrwIAOnbsyPt6XVxccO7cOQQFBSEkJAQNGzaETqfD3r17ERYWhtatW6NWrVrw9fXFtGnTUKtW\nLQBAzZo1Ua1aNeTl5WHx4sVISEhAYWEhqlevDp1Oh2HDhkEikcDDwwNeXl4o7V8nIrRq1Qosy6Ik\nL4xcLuf/LynTmCwLTJdMyjIplcgiQpJMBrlcjvnz5/MrJWVnZ6NDhw6IiIiARCJBdHQ0vvvuOxQV\nFaFx48YYO3YslEolgoKCoNVq+eN17doVkZGRCAkJQUlysOjo6ArRTzcmThTMf5NNhDVNmkCr1YLj\nODRt2hTr16+H0WjEqVOnEBQUBJZl0aZNGyQkJKBmzZrYtWsXCgsLsWLFCvj6+qJx48aIjY2Fl5cX\nlsyYITyIX4XfZ1ZWFtzVamxLTcUiFxeMcnPDjAkTcOPnn585160o7oBdy/MRWRYpLv3YGx4ejtjY\nWDg7O6NatWpITU3F2LFjsXXrVly5cqXKya6eGyqxzI4nJ//1jrCcu8ckkwlOEc9lWYw0GLBq1Soc\nPnwYMTExfDVmsxkbNmyAj48POnbsiMzMTLRt2xZ6vR4uLi5YsmQJTCYTTpw4gRo1aiAwMBCpqanw\n9/dH/fr1ERERgZycHNy8eRM6nQ5xcXFgGAadO3fGzZs3ERISgho1aqBBgwbQ6/XYtWsXPD09kZCQ\ngMTERGg0Grzwwgt48OABHykzatQoFBUVISQkBNu3b8fixYsRHByMevXqgYjwyiuvYPz48SAiODk5\n8T54vV7PC7lCoUBUVBTKu2aICPFRUXhTpcKG6tWxPS0Nr7ZvjxIf/ujRo6HRaBAeHs6HV6anp8PX\n15cfcJw+fTri4uIQGhoKlUoFnU7Ht6F+/fqIi4vjwx1r1aqFBg0alElRAADbt2+Ht7Oz4JNEvlwO\nX60WU6ZMwe3bt7Fy5Uo0a9aMz3vj5eWFDh06wGAwYN68ecjPz8eGDRsQHByMqKgoNGrUCF5eXpg/\nf77Fdbd0qWC+eMHNGkX1ySefoGXLlpBKpYiLi8N3331X9l4uP9ajVFp88V26PJXRdaK4lyAwSHd9\n40Y0aNCAf+QtvanVavTp0wcfffQRxowZg5SUFHh6esLFxQWJiYkYMmQIPvroI/z000+83/W5xI7l\nXiSXY1FMDJycnJCcnIzly5fjvo083Tax5+6xsZk1GhzavZuPYjEYDHwWxBJyc3MxceJEuLq6YtSo\nUZg3bx5cXFzg5+eHxo0bY/PmzYiIiIDRaESPHj3g5+eHpKQkODs7o2XLljCbzVi8eDEaNGiAl19+\nGUSEd999F7dv3+b95iXT/Ddv3gydTofw8HAEBwfD1dUVa9asQfPmzXHz5k3o9XqcPHkSO3fuRM2a\nNZGdnQ0nJycwDIPY2FhoNBo+/QDHcfwU/tIby7Jo2bKlTXGvX78+HBwcMHnyZPj6+qJdu3YocfGU\n+O2jo6PRrFkzDBkyBOHh4dhsHSM5c+YMdDodXnvtNchkMgQFBcHT05MX3I7Nm2OkTocMIowyGJDc\nsCGySomb2WzGe++9B2dnZxBZ4uvNajWfV79AKkU+w2C3qyuujR8PZGXBZDJh0qRJkMlkcHR0RP36\n9SGVSiGTydCuXTu88847qF27NkJDQ9GgQQN4enpi3rx5yMvLA2CZp7DK3f1PCXuxQoG1SUnQ6XRI\nSkrCRx99hHXr1iExMdH2b7IkF9LLLwMODk91dJ0o7qURSGJlNpuxceNG6PX6MvHEpTe9Xo93330X\n2dnZuHXrFvbu3YuMjAx06tQJQUFBUCqVqFevHnr37o1Fixbh+++/LzOT8ZmmCj737OxsbNy4Ee3b\nt4ejoyNat26NtWvXlhGECthz9xDxCy3kchyyiPBaQAA++ugjFBYW4rPPPoNEIkH16tWxfPnyCiL/\n+++/o0uXLqhWrRqmTp3Krzfq6OgINzc3XjC2bt0Kg8GAli1bQiKRoH379jCZTGjcuDHmz5+PyMhI\nEBG6deuGe/fuITo6Gn5+foiOjka1atWwcuVK6PV6KJVKhISEwM/PDzNmzABgiRuvW7cuCgsLkZiY\niO7du8PR0RE+Pj549dVX4eDggO3bt0On04HjOAwcONDmb6+kDeV97yWunKVLlyIyMpLvOBwcHCCV\nSuHh4YHff/8dLi4umD17Nho3bgyz2YzCwkLUrVsXAwcOhEwmQ61atfgkZ0qlEmMTE2EstRZqLsta\n1o61CpvRaET79u35qB6NRoMff/wR7Zo1w0RfX5wKD0eeVeBLhLFIoUAb6ySxlJQU+Pj4oEOHDrh0\n6RK2bt2K6tWrQ6FQgOM4KBQKvPHGG3jw4AFycnIwbdo0uLm5gYjQXy7/U2u0GhkG77/zTpm0EXl5\neUXuwyQAACAASURBVHB2dsb169f/8u/9aUAU9z/BgwcP0LdvX2i1WgQEBJRJ4FR68/LywqRJk5CT\nk8N/NisrC9988w3mzJmDbt26ISIiAgqFAmFhYejatStmzJiBr776qupW7dPGn5gn8OjRI3z00UdI\nSUmBo6MjOnTogE2bNpW5XgAqX62pZUtg5Eg8nDEDXs7OWL9+PR/6Nn36dHAch6+//hpNmzaFv78/\nli5dWiHG+fDhw6hbty5iYmLQtWtXuLq6QqVSoUaNGvxyedevX0ezZs0QEhICjuOQkJCAo0ePQqfT\nYf/+/XB2dgbHcWjSpAnu37+PBg0awNvbG3Xq1IG/vz+mTZsGmUwGtVoNqVTKL9FnNpuRlJSEGTNm\nICMjAyzL4quvvoKLiwtcXFzg4eGB2NhY9O3bF0TE+7pL4u5LLPeS/8tvjo6OYBgG0dHRvO+eZVmk\npKSAZVksXLgQ/fr14xfXKInLnzhxIpo0aQKNRoNq1arxaXo5jkOvzp0F0w5Ao8Hl06cREhICR0dH\nSKVSODk5Yfr06XB3d8eAAQOQlpQkGEKZzbJoXKcOoqOjcfDgQRw5cgRNmzaFl5cXoqKi4OHhgUmT\nJmH27NmIiYmBVCoFwzBgWZY3uuwNJpuJkGcdFM2TSFCkVMJ08KDNn3PvLl3weXq6YD54oeifp2lw\nVRT3v8B3332HWrVqoV69ehXyepTf/P39MXny5IrCBUt414kTJ7B8+XIMGDDg/9i77vCoyvR77vSa\nZNJ7AukNkhBCSagSSgApAhFFpUgvArpEFFDQpQkCgiBlEUUUEHUFLPhTXAVU1EVXWYqgolJcpaX3\nOb8/Zu5lksydSZDmbs7zfA9k5ra55Xzvfct5mZWVRZPJxMjISA4YMIDz5s3jrl27ePr06T+HH9+F\nfK8cLly4wA0bNjAnJ4eenp686667+Oabb0r+UznLvRjg671788dvviHXr+c7LVvyzb59ycJCfvHF\nF8zLy6MgCJwyZQrPnDnD/fv3MycnhxEREfUKWWpqarhp0yYGBwczMzOTKpWK/fr1Y2hoKEeMGMHz\n58+z5vJl/l9eHp/WaDhGoWBiWBhHjx7NgQMHcvDgwXzwwQdpMBgYFRXFs2fPMjs7myEhIUxOTmZ8\nfDz1ej1DQ0OpUCjo5+cnyR6cPHmSJpNJ0lGfPXs2H3vsMYaHh3PAgAFUqVTs27evRNZiAZN4zwmC\nIPnB6w5BECgIAlUqFYcOHUrRJaPVaqnVannq1ClaLBbOmDGDeXl5JG3djnx9fSWlSlG5UhAE3nff\nfZxqMsnLDuh0nKTXU61WMyQkhHFxcezYsSPDwsKYn59PX19f7uzXT5YYiwWBn4waxa+++oq33347\nAwIC2LJlSwYFBXHFihUsKCiQRMvEKl1Hd6kYA/n9jTdqGRrlajULBYEzYmN5vF07VmVkkPfea+u4\n5Az79rFKr7/Szs9uqJS//z7feecd7klLc2103CJpkU3kfpWorKzkwoUL6ePjw5EjR7JVq1YMDg6u\nZV3VHTExMVy4cKH0yu8MNTU1PH78OLdu3cr8/Hx2796dfn5+9PPzY/fu3Zmfn8+tW7fy+PHjzgt8\n/sT4z3/+w9WrV7Njx460WCwcd/fdrJIpSioE+Ejr1iwEpBS1YqCWeyA8PJz33HMPLRYLhw8fzsOH\nD/PAgQPs3r07w8PDuWbNmlrywYWFhRwxYgSVSiUTEhKYnJzMYcOGsa/FwkqdTiKlYns+d0+Tif7+\n/ly+fDkDAgL4ww8/0N/fn97e3jx27Bi7du3KoKAgKeMjNTWVXl5ejI2NZUBAAH/66Sf+/e9/p8lk\nYmZmppSO+O2339JsNks+7sTEROr1eioUCnbr1o0AJDcJgFqKkCaAo2ArVBqjUDAuOJgjR45kVFQU\nFQoFR40aRa1Wy2HDhnHSpEkcN26cVLBUXl7OlJQU9u/fnyqVStLSAcDBgwfTYrFwgStSg01yODEx\nkVlZWfTw8GCfPn2Yk5PD1NRUfv31127fxnbHxdHHx4fJyckMDAzk8uXLefToUU6bNk1yywiCQJPJ\nRJVKJU1UPXv25FNPPcV27drR29ubt7Vpw0cCAviM0cgdvXrxpw0bGvZm6cLlUgiwe/v2fHvgQFt3\npibL/b+T3EV8//337NGjh5SXnJ6ezoSEBKljjjNrCgDj4uK4ePFil0Qvwmq18vTp09y1axfnzZvH\nAQMGMDIykmazmVlZWZw0aRL/9re/8dChQ7Kl1X82nD59msuWLeOiyEhacaWJgvj/V9u1k23TV2M0\nkkVFzMjI4MGDB3n+/HkumjWL08xmbm/enMceeoif/d//sWfPngwLC+Pq1aslkv/nP//JpKQkDhgw\ngD4+PgwymVgmU5lYADAqIIB6vZ69evXikiVLWFZWxqSkJOp0On788cfs2bMnLRYLNRoNvby8GB8f\nz7i4OLZo0YLR0dH09/fnZ599xvT0dG7atIn5+fkcOXIk+/XrR0EQGBISQj8/PykYOmTIEIpZMnWD\n/Fn2Y6orFvavZ5+V3CrNmzenIAg8dOgQLRYLhw0bxgcffJAkOXPmTHbo0EFKwxQ137t06SK9HYzX\naGQt9yKAB2JiuMbTk6MAeqvV1Gq17NOnD48dO8bvvvuOD3p6yq5vBVgmCOxrsfDpp5/mtm3bmJaW\nJrk/dTodLRYL9Xo9dTodb7vtNlosFm7evJnV1dV87733OHToUCkLKDY2lr6+vpw8fLiskVDXR161\nZg0rZa631WCwEXdhoXzuvCgwdgugidyvAcQ0u6CgII4dO5abN29mSkoK09PT2atXr1r5x44kL36e\nmJjIJUuWuG9CUQcXL17k3r17uXTpUg4bNoxJSUnU6/VMTU3liBEj+Mwzz3Dfvn2ug5a3MlxYUWWA\n7ENYDHBxXBxTUlK4c+fOehrvxYLAIoWCrz7wAF988UVmZWXRz8+PEydO5KJFixgZGclNmzZx6tSp\nLt0QJQoFx2k0tFgsNBgM9PHxYUlJCWtqapibm0ulUsmXXnqJafZOToIgMCsri3FxcfTz86NSqWS/\nfv1IkocOHaK/vz+PHDlCg8FAX19f6nQ6tmjRgmq1mmvXriUApqSk1DISHC12OV9zpU5HI2zZM1qt\nli1atOCUKVN477330s/PjxcvXuRnn31GPz8/enl50dvbW3L7JCYmSro1SqWSZhf7scIWXBXPTZFC\nwY0jR3Lo0KHSG62HIMj77O2jVKWin33yEnuwGo1GmkwmBgYGcsmSJZwzZw5DQkK4Y8cOzpo1i2Fh\nYUxPT+fKlStr5dn/8MMPfOeOO664WOoOo5G/L1zIKVOmsFmzZm6lG/jww7b78k8gDdxE7tcQly5d\n4rhx4xgUFMSXX36ZW7duZUJCAtu3b88HH3xQSgurO0SlPwBMSkrismXLrtoCLy0t5cGDB/ncc89x\n7NixzMzMlApQhgwZwgULFvDdd9+tpXlyy8KFz73CzUO4yq5Z7oqMCgB6qVQMDQ21FRt5e3OsUsmn\nlEquy8zk5OHD+V56usv9rPX2ZlJSEhUKheQfF91lU6ZMoSAIUpBXqVRKwUHRVx4SEsL169eTJCdN\nmkR/f3/Gxsayc+fOHDVqFM1mMy0WC3Nzc6lSqSQfet37ZxRcSA4oFBwFm79dEAS+8MILtFgsvO22\n27hs2TKWlJQwJiaGSUlJVKvVkpvHz89Pst5NAEcLApdptdwSFsZihULaX4kgyNYeVOh0tNirWX19\nfenj48Ph0dEshXxLuyKAY5RKRkdHU6vVUqfTMSsri2+//TaLi4s5ZMgQRkZGsk2bNvTz8+PUqVP5\nr3/9q97tU1NTwwMHDvD9jAyX13C+/bfeeeedPPnww6zS6WQnAm7Y4PK+rNFoyJ49b4m89yZyvw44\ncOAAk5OT2bNnT544cYIvvfQSY2Ji2LlzZ65Zs8Zp0YloiRkMBikLIDk5mStWrPjDrpaqqioePnyY\nmzdv5vTp09mlSxd6eXkxODiYvXv35qxZs/jaa6/xhx9+uLUCt+6afbgghwctFqakpHBjVhbLXXTX\nOTlzJgcMGMDenp4s12ikPOxi2FQLK6dPd1m9vDYzk/7+/lLVqFKpZE5OjlS0JapKisFVo9FIhULB\ntm3b0tPTUyLvdevWSTUS27dvZ3R0NDdu3Eij0cjk5GSqVCopz13MjhHvGUEQ3PrCFwBS/vgDDzzA\nAQMGSE1Dpk6dKrk/xG3rdDqJ2EV3j1hlWiwILLST4rtpaTwQEyNVwjo7R/fb31K9vLwkLZwlbo53\nsT3lcfLw4fz1ySdpnTGD/xw/nhHe3lSr1czNzeXrr79e79moqqri+++/zwkTJjAoKIjJycl8s29f\nVssQdrlazcJly6T1Txw65DIb6Ox33/FI374uj12aCG5y3nsTuV8nVFZWSrocixYtYmlpKZ9//nk2\na9aMOTk53LVrlxS8k3PZWCwWiehTUlK4cuXKevnaVwur1coff/yRr7/+OmfPns0+ffowJCSEXl5e\n7Ny5M6dNm8YXX3yR33777c0rwHKTLVMq82AVAOzdqROTk5O5xI1cgfiaXS2zn0I7yTslLoWCQWaz\n1Nw6PT2dOp2O3t7eDAoK4j/+8Q+StnZ6ABgVFUWdTkeDwUA/Pz/m5ubSbDZLio8vv/yy1KDixRdf\nZIsWLdipUyfJfRcXF0cAUrm/aMErlUpOhLwlbAX4uL8/lUolx48fT4vFwsTERL766qv8xz/+QV9f\nX6pUKol4xWYgosUup+hYrFDQS6Vy68p4SqVicHAw1Wo1DQYDtVqtS3dXMcAP7rqLJXv2sMZolCbc\nItgalv/+xhu1bpPy8nLu3r2bI0aMoI+PD1u3bs0FCxZw586dHDFiBGMCA2Xf3ip0OlvWzPr1LJ86\nlbMCA7lz0iQWCgJr7K6XSq2WpSoVBwcH09vbmytbtpSOye24iXnvTeR+nSEGXFNSUvjJJ5+wsrKS\na9euZVhYGHNzc7l//36uWLGCFoulHsmLmQE6nY6BgYFUq9VSQ+Vnn332mhG9I3777Tfu2bOHCxcu\nZF5eHmNjY2kwGNi6dWuOGTOGa9as4WeffeY0tfOaw02xyOnnn2e5VitZlCUKBQsFgVm4YtWOUSpl\nNd6LAOb7+vKDoUOv6M3XGZVaLV+LiWGhIEg50mLRVDZsyoyi3oper6fJZKLRaGSIhwenGAzc1749\nJ+l09LNbxMHBwRwxYgRNJhMtFgub+fpytCBwuU7Hp+LiWH3pEocPH86uXbvSZDLRy8uLGo2GQUFB\nUjBUtK5FAlar1ZzghtxnenlRoVBw0qRJ7NatG9u3b8+CggJGRETQ09OzVoDWMUY0zWyW9VcXwZaZ\n48olVK5Wc6qHB4ODg+np6SmlcnrYM46cHq/JxDdWr5ZVaKTZzOJff+WOHTs4dOhQenl5sUOHDly6\ndClXrFjBLl260Gg0UhAEhoaGcvTo0fzhxRdrZcuIbx+PWiwsU6uleEyZUskytZr9TSZO9fDgKrOZ\na9u04fply3j48GGby62wkOUNJfebmD3TRO43AFarla+88gqDgoI4fvx4Xrp0ieXl5Vy1ahWDg4PZ\nr18/fvXVV9yzZw9TU1OdSh2IxO7j4yNJ14rpdc8999x1ta6Lioq4f/9+rly5kiNHjmRaWhr1ej0T\nExN59913c8mSJfzggw+uTwGWPRgqEmu91117bv2eVq2Y7+vLfrfdJp2/1q1bMzMhQbZopkihYFJE\nBBe5eUBfCA7mygUL+ESzZlwA8JmWLRnq5UV/f38pE6Zly5bSZNxNp2OZWl2r+XIBwL3z5kmpkv36\n9WO2/XORPIths4b7eHlRq9VywoQJDA4OZseOHSXr3pkEgUqlapBbpm3btlJx1MH33+eLHTvyWbOZ\nowWBHjLyGkvdSN0ugOtgbqEgMNBkkqpVxd6wvr6+7GSfJMvsb1fVej3L1Gr2Mpu5NCFBkhKuO0qV\nSk7U6ZiTk8PFixdz8uTJjIuLk7bdqlUrLl26VJJ1driRpTqM4zNmMN7LS/atpESp5Ibly7l27VrO\nnz+f06dP57333svevXszOjqaHRUKFrqY1GqNm5T33kTuNxAXL17k2LFjGRwczG3bttFqtbK0tJTL\nli1jYGAgBw0axMOHD/P48eO888476wXOxAdZqVRKvTPj4+OlgGxaWhrXrVt3Q9woFRUV/Oqrr7hx\n40ZOnjxZ0kKJiIhg//79OXfuXO7cuZO//PLLH/fjFxVxY3Y2v+rZU7Y4ymq18p577uHtt9/O48eP\nS9kpKpWKiyIinKZTTrIHQV3qnysUfKlrV2ZkZDAoKIje3t6Mjo6m3t6L1MfHh3fccYeUzeGj0bhs\ncVf2++8MCQmhyU7kzpar0Gr595deYnx8PAcOHMgxY8bQYDBQr9fTz8+PYmzG0Y3nynouhk3Z9J57\n7mGbNm04u0sXVun1tVImCwB2cELwYxwCp/UmR4Cj7Va+OFGJRC1uM8futxdTMcV71cPDg126dOHd\n/fpxdnAwn1KpOEapZJjFQh8fHy52k1HzUni4NGFYLBb269ePe/bscXmvXbp0ibt372Z+fj5bt27N\n0Q4SCs6u+8rUVI4aNYoTJ07k8OHDefvttzM+Pp6ArYisV4cO3JGby3NpabTKWfJaLblq1R+7/68S\nTeR+E7B//34mJSUxNzdX0rQoLi7m4sWL6e/vz7vuuovHjh3jpUuXOG/ePKlKsO6DJwbnNBoN09PT\npbQ5pVLJ9PR0btiw4Yb6y2tqavjdd99x27ZtfPjhh9mjRw/6+/vT19eXOTk5nDFjBl955RUeO3as\nfgGWm/6106dP51NPPeVy/xUVFczJyeGYMWP4wQcfEAC9lEpWygTTihUKmgBmxMXJEm0hbB2cRDE4\no9FIjUbDkSNHUqPR0Gg00svLS9KQecjLyyUZPmAy0dvbmw9ZLC6XO/vEExw4cCAnTJhAb3tGjmOB\nnNForFWwNBGus4IifX3p5eXFUE9PW39RmeWMsL0lpqenU2E/P662Kyqm6vV6eiqVHAVboHUk6qup\nimmNgwcPZl5enpS627lzZy5ZsoRvvPEGZ8yYwejoaJcTrijDrVAoGBERwbvvvpuvvvoqL1++XOt+\nOHPmDLdu3crRo0ezWbNmUjtCUYt+sVx6pH1si4piYGAgfX19pa5PFouFf/vb32pPIu4E7hwK624k\nmsj9JqGiokIKuC5evFjynxcWFvLJJ5+UFPlOnjzJqqoqbtu2jfHx8bLWvMlkolKppKenJ3v06MGM\njAyJ6DMyMrhx48abEhi1Wq08c+YMd+/ezSfshNWsWTOaTCa2b9+eEydO5K78fFYbDFfK0p1kGsyd\nO5ePPvqo2/0VFhYyLS2NTzzxBLOysjgKkNUSLwK4KDaWRqORE1u2ZCEgZX04WrOi1emYnRIXFyeV\n2YvNKx566CFu9Pd3SRgv2onQHbE86+nJ48eP09fXl8OGDWNOTo50vc1ms9OCpWL7qGuRZ8HWi8DP\nz4/zIiJcng+RNB3vrS5qdb19idtVqVQMDw+n3i47IBKnGBtQKpU0GAycMmUKP/jgA06bNo3+/v7M\nzs7m3/72Nx45coRLly5lamqqNFEKgsA2iYmyPvdyjYYJYWGMjIxkRkYGw8PDpeuj1+vpZXdriemp\nYr58QEAAe/TowaVLl/Knn37iL489JjuBlCqV/HL8eJ46dYpWq5UFBQVMTk7mMofMmlrYt89G4nLX\n9CYEVpvI/Sbj5MmT7N69O1u0aCF1/CHJy5cv87HHHqOPjw/vv/9+njp1iiT5+eefs2/fvlIWTV3L\nSLyxVSoVIyMjOWzYMGZmZlKtVlOlUrF169Z84YUXbrp0waVLl/jhhx9y5fz5LJXJaKkyGFhgV+Zb\nvWgRt3TpImvZO+LcuXNs1qwZ58yZ49YX/WHbtlIv0q6ZmZwdHMyF9lZ0ouWp0+nYvHnzWg0yDAZD\nLcEuUX9ltEODDKekgSsSAS7dHfa3r3vuuYchISFUKpWSS87bTrbO1i0EOB7gErWaIwGaHe4RlUrF\nZTJ+bHHMd7ifvLy8pPvMbHf9zIcttdEISDnojnUajnUbzZo14zPPPMPly5dLKpmPPPIIP/74Yz79\n9NNMTU2lwWCgt7c3PTw8mJCQUCtrp6/FwlKV6kqpv8OkX1FRwSVLlrB58+aSm9JZDYn4ttCvXz9O\nnz6dU6ZMYW5uLgMCAuilVLJIZqIrA7gvM5M1a9ey6uJF9urVi2PHjnXq9hENmGOTJ7PqFurW1ETu\ntwAcA64TJkyo9Xp54cIFPvLII/T29ub48eN5+vRpkrZXzoceeohGo7GeNS/6mgMDA6lSqahSqdim\nTRs+8MADbNu2rUT0bdq04ebNm28u0btIdyxRKDheo2FeSAiLFQop66XGYHCbQ3zs2DH6+/vzfri2\n3CdotUxISGD//v1pMBhoNptrkbhoiUZGRtLX17fWZxqNRiI10eI0QT5F09E6dufuMNn336pVK3p7\ne1Oj0TA4ONimD+NmYhgJMC8vT7ofxEnIy8uLY5RKt+uKbhbxt3nYiX2BfVIyOdxndYW7xG5KK1as\n4JAhQ+jp6cm8vDxu2bKFTz/9NFu2bEk/nY6TdDou1+n41+bNmRwRIW0nJiaGc+fO5YULF2wX0h4E\nLZkyhe/fdRcHdu8uqVSKE4kgCDQajdTpdIyKiuKjjz7Kbdu2cfLkyUxOTpbiL+LxabVa+vr6MiYm\nhp8tWcIqg0GakMXiqhr7JChmz+SnpbFo2TKevfdefjpqFJ/Mz+edd97JtLQ0muwaQy+FhrqcOG90\nYLWJ3G8hXLx4kWPGjGFwcDC3b99ey0r47bff+Je//IUWi4VTpkyRWsOVlpZy7dq1jIiIoFarrWfN\ni5kJ/v7+ktDSwIED+dhjj7FNmzYS+bdt25Yvv/zyjSd6N4VKH6SmyqadlSiVnPuXv3DHjh38/vvv\n61lVn3zyics8bdEX/eGHH3Lu3Lls2bKlRILiuQNsFqpSqWR6TAwnAHwH4NsAp6pU9LRPBI4Bzs2u\nHnBcsY6duVYc3R1KpZIajYZmey69mE7oLrtnPiBJBoiTkCgn0JBJxfH+cXWMdQ2K8PBwtm7dWsqj\nf/zxx7lo0SKmpqZSq9XSaDSyt6cnixSKWu6vQoDDo6MlQi8pKeE777zDMWPGSDo94puHRqORMmJm\nzZrFl19+ma+88grnzJnDXr16SW8barWamZmZfOaZZyTXym+//cY33niDHTp0kAwcs9lML5WK4zUa\nrlCpWC5jCFhxxWVXplSyXKPhu7Nm8fPPP7/Sfep6t5tsJJrI/RaEs4CriHPnznHq1Km2oNxDD0mV\nkGIz6U6dOkn+xro582q1mjExMTSbzdRoNPTx8eG0adO4dOlSiejVajXbt2/PV1555cYQvSuJAY2G\n36SnSxkY9chdoeCy5GR2796doaGh9PT0ZKdOnTh16lS+8MIL/Oabb+jj48POKhVL1WqJoCpgs9By\n7Odl8ODB0uEEBQVJVrhIWlqtlh3s7hZrnQe+xAnRubOsJzhcH0d3x9zwcHrapWzFayZOMg8//DBT\nUlIYEhLSIMtdPBZPT09aLBZJYdIVYXey709882tIMDUyMpL33XcfW7ZsSQ8PD7Zq1YoJCQm1XFZq\ntdpGokqlfLs9jYY9srJosVgkK1t0L/r6+nLw4MGcP38+V6xYwdmzZ7N3794MDAykj48Pu3fvzkce\neYSvvfaaROTff/898/Pz6e/vz65du3L79u2sqKjgxx9/TH9/f3788cd8++23OW3aNLZr145ms9nl\neXU66vrRb7EmHk3kfouioqKC8+fPl7rB1y1YOn36tJRJMXPmzCuvsbS5JEaPHi2p59UlelFdLz4+\nXrKEYmNjuXz5cq5Zs0bSNFer1czKyuL27duvH9G76V/7QcuWLh8w0QoWX83Dw8OZkZHB7OxsxsTE\nUBAEent7Mwc2P6qoSVPXAr3//vtZXl5OrVbL9957TzpnWq3WZcENYbM8HTND3JGij520HN+yAgMD\nbb5tgJN0Oi5EbRdIVFQUo6KiGkS6nnX832KNRK1MK9j8+o6ZLWJltEiu41Qql5PI3PBwenp6smfP\nnhwzZgxTUlKk+8lisdDb25uixR0SEsInIiJcFpSNs1vTycnJHDNmDGfOnMkHH3ywHpHPnDmzFpHL\n4fLly9y/fz8nTpwovdmK2WU+Pj5MSEhg69at2aZNG4aFhXGRm/TLesOZNS42rREzktRqWzu+PXuu\nz/PjAk3kfovj5MmTzMnJYcuWLaVOOY746aefOHr0aPr4+HDOnDm1GhRfvHiRixYtop+fX610Skd/\npVqtZnJyMps1ayb93alTJ7722mtcv349MzIyJKs/OzubO3bsuPJAuUlfdAnHdWfMsGUa1MmW2ZWf\nzzFKpazPvEypZM26dTx69CgffvhhZmZm0mKx1CMyf73erQWq1WqZmppKjUbDVq1aSeuKOeRlLh7y\nMtiCjI5BRafyu4LA27Ramkwm6Ro4Tr459uOUc4GIsRW1Wu3SXSKmTIrbdVb97CzwKC4vuqPcBaOf\nsvu7xXVNJpPknvL29uaAAQO4detWPvvss2zVqpXbDKHdLVowNze3UUReUVHBo0eP8u9//zsXL17M\nUaNGsUOHDpLoWUREBJOSkpicnFwr8KvX69m8eXO2b99e0p53JYkgO5z50ffsseW3i2+cDYgRXQ80\nkfufAFarlS+//DIDAwM5ceLEevm8pE3mYPjw4fT19eUTTzxRS+a3qqqK27dvZ3p6Os1mM1UqVT0C\nNJlM9PDwYPv27enn5ydpoAwbNoz79u3jhg0b2KpVK8kPPLFlS1bq9S7TF2XhrCWfyUTm59fr4vTL\nkSOyGQ0FANNiYlhQUFBvF7/++iu3bt3KkJAQTjObXVqgz6N+sNBxuCM5onaWiaN1PBK1877F8+54\nDTQaDUM8PBqUTy764uW27zh5A1c6Nl3NaIz7R5xMEhMTOXHiRHbo0EESHnOcJF2lHu7IzXVKELla\nIAAAIABJREFU5Farlb/88gs/+OADrl69mlOnTmWvXr0YERFBtVpNf39/RkVFMTo6miEhIdTpdDQa\njWzWrBlTUlIkl5HBYKBGo6G/vz+bN28uSRt3796der2ehz76iNVusokcR6VGQ6td0VPCLeSaaSL3\nPxEuXrzI0aNHMyQkhK+++qpTS+b48eO8++676e/vz0WLFtUrwT548CAHDx5MvV5Ps9ksWWmObgi9\nXs/k5GRmZWVJlZH+/v589NFHefz4cT7/zDOyRT9ub+CruPlrPvqIZQ4+c6vBwEqdjncEBEhNyw8f\nPux0d/fffz8P9ejh8iGVc9WIY4JG49Zyr0t0cpaxY+GR42TSGCIVXSdXS9oNHX46nUvt9t4aDTMz\nM9mjRw+GhYU5PSZvb2+2a9eOUVFRNEM+uE2zmZdPn+bBgwe5efNmzp49m4MGDZL892JAOTQ0lN7e\n3lKVa3h4OGNjYxllLzgSybtNmzbMy8tjfn4++/fvz5iYGH711Vf1NJH++c9/SgHWu/r2ZZmbtwvH\nUaxQsEdWFvfu3ctPPvmEO3fu5L7hw+VFxW5wULWh5C7Ylr3xyMjI4JdffnlT9n2rYv/+/Rg7diya\nNWuGVatWITIyst4yR44cweOPP459+/ZhxowZGDduHPR6vfT96dOn8eyzz2LNmjXQarW4ePEiampq\nAACCIIAkPD09UVlZifbt2+P8+fM4cuQIBEFAvo8PZp0/D3VlZb39lgoCdnXrhvP9+qGkpARFRUUo\nLi6W/m135AjG/Pvf0FutTtddGR2NQ2lpCAsLQ7NmzRATE4P4+HgEe3hgsr8/ogD8qFDg9i1b8Mb/\n/R9+++03/PLLLzj51Vd4b9QotPbyAmJigLw8VGq1uP/++5Hx9de4//BhGBp4DxcCiAUwCEBvAAoA\nnQDoZJYvAhAiCCgiIQgCPD09cfny5XrLZQN4y749E4BiAFYAuQD6Ash3cUwLADzi8Ld4jRxhApAH\nIBrASQA7FAoUODnP7qBUKmE0GlFZWYns8nK8B0BwslwhgGAAJQ7HZDaboVarUVBQgOrqagiCAKVS\nCb1ej5UrV+LO0FCo+vUDq6uhqqhAuVIJwWrF35VKfEjiHQ8PlCgUKCsrQ1lZGcxmM0wmExQKBcrL\ny1FQUAAPDw80b94czZs3R2RkZK0RbrHAsGsXcOIEEBODdz09MWrqVBw8eBChoaFOf2/Xrl0xcuRI\nnF+4EPf/+98wOVmGAKoUCmis1lrX7aBKBavVivDwcCQmJmLCzz+j9+HD8if34YeBBQsafC3+CARB\n+CfJDLcLNmQGuB6jyXJ3joqKCv71r3+VAq5y1af/+te/2L9/fwYHB3PlypX1uj2VlJRw7dq1jI6O\npp+fH7VabS21QbHS0MPDgzExMezfvz9Xe3i4tGhEF4VOp2NkZCSzsrKYm5vLYcOGuW1+8UJwMBMT\nExkUFMQgk4ljFIpaVq5Op5N8zz4+PvTw8OCEFi1qNY8oV6lYrFSym07HgIAApkZFue3+4zhKAZaj\nfmaM1clnxaitySK+Aen1erZv3176210QdEIjLHdno6Epi+6GoysF9vPuSqt9rL3oyMvLS/KRb9++\nnQcOHOCSJUskd4jjNj2VSo5Tq/mS/VzXPeaeZjNTU1M5ZMgQ5ufnc82aNXznnXd49OhR12qkdTpu\nVel0LAT4txEjuHDhQk6aNImDBg1ip06dmJmQwL9YLHxao5HuLXfut0NBQXwjPp7jNBru3bmTX331\nFfPy8ujt7c3Q0FB26tSJvy9YcMukQ6LJLfPnxokTJ6SA68GDB2WX+/LLL9m7d2+GhYXxueeeq9fk\nwGq1cs+ePezevTvNZjN9fX2lvHmxAlAQBPr6+nK8RiM1pa47qrRanpo9m1OnTmVkZKSUVte8eXP2\n79+ff2vXTnZdsbGDxWLhyLg4lqhUUhqk2MH+0U6dOGTIEMbGxkrZJe7ytgVBYBf7+o7pkA0l+7rE\n/w7A3bBVgtbVT3E2TAA3udhnEWzkLkeixW7201D9l4YOx8CwO8I70KkTn3rqKU6cOJGdOnWSqmkd\ng/dKe+MNR20cV8dc1z1XVlbGX375hZ9++im3bNnCBQsWcNKkSbzjjjvYsWNHJicnMz4kxGU9Q5C9\n4Xh8fDzHJiXVurdK7PK/xwcMsBXIObsG9piBKKkQHR3N5cuXc//+/fziiy84ePBgGo1GBhgMrJRT\n0rzBLfiayP2/AFarlVu2bGFgYCAnTZrkNOAq4rPPPmP37t0ZGRkpqzdz9OhRjhs3jiaTiREREdRo\nNJI1L6YGyj1IhQBjgoI4d+5cnjp1imVlZVyxYgWTk5OpUCjoq9XKaobUmEz8ev9+zrQ3S3BKhILA\ncLvPVaVSufVVT9dqOdreqWiKUsmpajXnwxZEddWoWY7MRP+6nO9czqJ2N5k8hasn98YGPhsz3G37\nfvtbi5hRJQgCPRUKjlOpuDkkhC907MgnZszgwoULuXTpUs6fP5/33nsvZwUGutzuGId8f8ehUqlo\nNBrp5+fH5s2bMyMjg3369OELHTuywkXHLclidhXzMZlk9WFKlEpGBQSwRYsWDDKZOF6t5tstWvCJ\niAj66XRMSUnhgAEDbCJ0ctf5BjfPvqbkDqAngOOwufwedrFcawDVAAa522YTuTccFy5ckAKutVIW\nnWDfvn3s3Lkzo6Ojpe7xzra3cOFCBgUFMSIiQmpEAYCdVar6qX4AR8TEMDk5WcqxT09P5/r163n5\n8mWWlZVx2bJlHBYZWW/dGkflvPXrr2Th1H3IBIGbO3fmqlWruGPHDh7r398laZY77KcYtsnhtgbk\nrrsaL8K5C6Szgy6KW+u0Dpk9/wcIeqmb7TvL5GnIcKcKWaRQsHNGBrOystiqVSuGhYWxo0LRIPeQ\nuzeCzWFh7Nq1K7t27crOnTuzbdu2bNmypZQR4+3tTZPJJPU1cLe9Zz08mJiYyCcjI6Um3nVHjcHA\nC2PGsNpolPRsqnQ6lmk07KRU0s/Pj9mwpbSK6bnlajXLNBrOzclh586d+UhAgHw65Z/VLQNACeB7\nAM0BaAD8C0CizHJ7AbzdRO7XB/v27WNiYiL79OkjCY7JYe/evczKymJ8fDy3bt3qtFipsrKSW7du\nZWZmJn19fRkaGkqDwUAPu87JYpWK9wsCfe3+cL1ezxEjRvD++++nr68vPTw8qNVq2bdvX+7atYuV\nlZUs/e03vjt4MNf6+HAkbI2qe/bsyb1799LqRpJge1QU77rrLg4YMIBLExJkC2PkLPBCu/CVMz+1\n6G93NVnIWeF1XSANrXgsB/juVRJ0FuC22XRjLHfxjWQRwHEqFX3t1bkNIWyXE4EgMDU6momJiYyO\njuaDnp4u9eene3oyJCSEYWFh0ggNDWVISAiDgoIYGBhIPz8/enl5Ua/Xu9RmdzwH7iaB1Z6ezIiP\n5+Ph4XwhOJiL4+LY77bb2K5dO9cVtlotVy9e7DYz60bqy1xLcm8HYI/D3zMBzHSy3FQAEwFsaiL3\n64eKigo++eST9PHx4ZIlS1zK/Yr+9szMTCYnJ/O1116Ttfo//fRT5uXl0Ww2S2lqojUvyg4DV8re\nMzMz+dBDD/GOO+6Q5Fg9PDw4YcIEfvHFF7RarXzhhRcYGxvL+Ph4mgFuVipZ6UbsKyQkhJmZmQw2\nm1ks4+ZpCOHVzRUPgE1SQO7hrBtUrXdsuOKuecsNkThuq6yBx9tQMhVHY3zuroKycjn1V+secte9\nKS4khM2bN2d8fDxbtmzJzMxMZmdns1u3buzRowdbtWolpT7Gx8fznv79ZTWIqgwGHtizh59//jl/\nmj1btll2jV7P/8yfzxMnTvC7777j8ePHeezYMR49epRHjhzhJyNHurfKbyF9mWtJ7oMAbHD4+x4A\nq+osEwLgI9iywWTJHcAYAF8C+DI8PPwGnYr/Tpw4cYLdunVjamqqy4AraSP53bt3Mz09nWlpady5\nc6csyf/888/Mz8+nxWJhQkICLRYLvex9OsXSeoVCQaPRyOjoaHp4ePCee+7h7Nmz2a5dOynPPiIi\ngnPmzKHJZOKlXbtoNZnkfaewWYAWeyWtqOK45u67WaXXs9oeICuDa+ubAJfAuc/cBHnftytfvDgc\n3UCuCLsh23JH0K7I1AqbRd/QbJlrEZR1ZxUvViqp0+mo1Wqp1WqduvbqvhEoFAoq7f53R019UZ3T\nYDDQZDLZipEMhlqt70RXYR97S8SAgAA28/V1+XaRFBHB5s2bS0VRMTExjI2NZVxcHNf7+Li+Vr16\nkWfO/PcVMTWQ3F8F0Nb+/ybL/QbBarXypZdeYmBgICdPnuy0orPu8q+//jpTUlKYmZnJd999V5bk\ni4uLuWbNGsbGxjIiIkISJhMzIwwGg6Q8GRERwaCgIMbHx3PWrFmcOXMmw8LC6OnpSU+FQrYS1fHB\n72PverRp0yb26dOnVuMKkdDL7EPOAi+xf1/XHbMZtqyWqwm0NpawXZG+WDDlLp3RrTyAk3VEsqxb\npexWX96hcKpuBWxsbCyzsrJclu9X6XQ8OXMmv/nmG548eZLnzp1jUVERB3bvzoNjxrBmxgzWrFvH\nmoIC6V6rrKzkW2+9xbvvvpuenp7Mycnhxo0ba0ls1INDn9S6LRkLCwuZlZXFRbffTmvdCumGVFe7\nssoBm+SA2Uw++2z9CuxbWH7AbRGTIAjtADxOsof975kAQHKBwzI/4ko9hC+AUgBjSP5dbrtNRUzX\nDhcvXkR+fj7effddrFixAgMGDIAgOCtPscFqtWLHjh14/PHH4e3tjXnz5qFr166yy7733ntYvnw5\nvvjiC0RERODYsWMoLy8HSRiNRngIAm4vK0OsQoECPz+sLyxEu+7dkZ2dDeu6dRh77JjTApJKAFsV\nCky0F5CIUCqV8NFocKKsDB5O1iOcF9/IfS7uSyN7RlzD1f6qAahhK1xSA9C62M5bAL6BLSthG64U\nCdXFKADLAafnrBjAAwA22v9WKBQAbNfJGRYAeNjFMS3VaLApNhYhISH45ptvEBgYiHHjxqGmpgY7\nd+7E3r17YbRacZqEwV4M54gShQJd4uJwoaICpaWlKC0tRUlJCWpqamAymWAymWAwGKDX62G1WlFQ\nUIDz58/DbDYjKioKCQkJ8PX1hcFggNFohMFgkB11v9dqtSguLkavXr2QlJSENWvWQFFaCmzbBpw8\nCURHA3l5gMnZmXRAUREQEmL71xXMZuC774C33mrc9q8xGlrE1BByVwH4DsBtAM4A+ALAXST/LbP8\nJgC7Se5wtd0mcr/22LdvH8aOHYvo6GisWrUK4eHhLpevqanB1q1bMXfuXISEhGDevHno0KGD7PJH\njhzBihUrsHXrVoSGhuLo0aPobjBge0lJverM0cHBOGQw4IFz5zCpRI7GgIUA9uXm4uOPP8bIkSMB\nAG+++SZyfvoJy+Cc4MpxhUQF2EgWACogX216NXAkbzlUA6gB8AEAFYCOMsdQDlu2weuwEXuxk2VE\nmGB70JxNbHWrR53BscrV1URRKgjY0aEDVhQX45tvvoHBYEBJSQnMZjNKS0uhUqkgCALuvvtu9DKb\n0Xv1aigAKMvKQKMRgkIBvP02kJ1da7vnzp1DcnIyTpw4gc8//xyvvvoqdu/eDQ8PD3Tu3Blt27aF\nyWSSJgO5UVJS4vL7iooKKBQKaDQa+Pv7SxNJYyYIcQSePImU/HwIVVVQVFU5P7FGI7BiBTBqlIuz\nf/1xzcjdvrFc2O4RJYCNJP8qCMI4ACD5XJ1lN6GJ3G8aKisrsXjxYixfvhyPPPIIpkyZApVK5XKd\n6upqvPTSS5g3bx6io6Mxb948tG3bVnb5CxcuYN26dVi7ZAm+uXhRloRCBQF5pCxJO1qh4ptGREQE\nzGYzxp06hQnuLKnrjGoAr8EmVeDONhOte3dvFY4l7gdQX1pAJP4s2NLOnEkaHKizbbltCIKATunp\nePubb6B3QliFACJUKmg1GizOyECKXo+PTp/G6gsXoPb2hkKhwPDhw1FUVISzZ8/i4s8/I+XoUVgu\nXMDhsjJ84OsLr9BQBAcHIzg4GBHe3sg6cwbl336L90+dwh4vL5QoFBg6dCiGDh2KpKQkN2ex4Sgq\nKkKPHj2QkJCAJ598EuXl5Y2eHOouw6IizD9xAh1LS+V3fANlBuRwTcn9eqCJ3K8vTpw4gfHjx0tE\n3Lp1a7frVFVV4fnnn8eTTz6JlJQUzJs3D61atZJdvnrtWtRMngytE+IQiXs75K3QYkFAio8PTp0/\nD0EQYCIxBEAMgCAAdwAwOlnvatwyV4ti+zE0drvuyL4Qtt/3GuQJ3Ij6pF3XYnc3CWi1WmQD+Htl\nJUDCBKBaq0VZRQUG6nQoLy93qoszxGiEuVcvtGjRAklJSUhKSkJUVJRkKFRXV+M///kPzp49i7Nn\nz6LgrbcwaONGWGtqpO0QQB+FAicDA6UJIDg4GEFBQbX+Dg4Ohq+vr+RicoeioiL07NkTKSkpWL16\ndYPXaxA2bACmTgWcvW3+N1ru1wNN5H79QRJbtmzBQw89hCFDhuDJJ5+Eh4czmq2NiooKbNiwAfPn\nz0fr1q0xd+5ctGzZsv6C+fnA4sWy2xFFsVwR0GFPTxQVFaGjQoGd1dUQHJa5GlJ1h6udAAib+8X1\nO9AVlMPmy4yFczdNMWyvwXon3zXE9QI0zn1jBHCXUomWBgO+KS3FNgBajQY/19RA60QorghAnNkM\nvZ8fFAoFCgsLUVBQgNjYWCQnJyMpKQmhoaH48ccfceDdd/H6wYMwOzkOms048/nnOFNQgLNnz+Lc\nuXPShCCOc+fOoaCgAAEBAW4nAY1Gg169el0fYgdc+9/NZuDs2RvuY6+LJnJvgoQLFy4gPz8fe/bs\nwTPPPIP+/fu7DLiKKCsrw9q1a7Fo0SJkZ2fj8ccfr/1q7cLKcbTc8wAkAPABcAHAEdS2Ql2RFO3L\niYSvhi0w6uzoS+2f10DejfJHrPtq2Ai5oet/AqC9i+/lgrx1g6ZyaEzgtbHr02jEpccew/64OHz1\n1Vc4dOgQDh06hEuXLsHDwwMlJSUoLi6GVqvFPRUVWEY6V+dsoLVbUVGBX3/9tRbh150Ezp49i8uX\nL8NoNCIpKQkhISGyE4HFYmnQPe4U+/cDubmA1Wq7t41GoG58oajIFri1q1QiL89G/jcADSX3hhoi\nTfgTw8fHBxs2bMDHH3+MsWPHYtOmTVi5cqXbgKter8fUqVMxevRorF69Gl27dkW3bt0wZ84cxMXF\n2W7o6dOdrqvV6TD6kUew4vHHAau1nsXuOB3kwWbVO0MJgL8D8IaNWDtBnlyrAaQCeMK+TWc39x95\nE2jMw1IMm+XeAs7J01X2jgk2V4w7RMtsu6HbcLW+UFIC74sXcfvtt6N79+7YvXs3ampq8OGHH0Kv\n18PLy0vKfGlmtcIgt5OSEltmiRtotVpEREQgIiLC6feFhYXo1asXEhMT8fDDD0sTgTgJHD16tNbE\nUFZW5tTyr/uZp6dn/UkgO9tmoctl3Tgj/+nTnQaXbyaayP1/CB07dsTXX3+Np556Cunp6Xj00Ucx\nefJktwFXo9GIv/zlLxg3bhyeeeYZZGdno3fv3pg9ezai3n4bld26wVpTA111NcqVSlTW1CCvshJv\nzp8PjUOKnkgkb8PmrugDG8HIEaC4zmAAVfb/y71nEsBOAF/DRppyv+ha+OWJK5k5ctuzwpaCOFBm\nGzWwTQByVrd7OrQt05BtONOIFwQBJ0nZ9Ss1Gjz/wQdY2KwZfvnlFwC2yT4pKQkJCQlQKBT44Ycf\nUFhYCCEiAhWnTjmNvZSrVNj344/QfPQRUlNT4enp2YBfVhuFZ85gdadOmGM2I6d1ayj8/REVFeVy\nndLS0lrWv/j/b7/9ttZnVVVV8pNAs2YIzspCcHAwzEaj7ToXFdmI3dFtI7655ubeEm4bEU1umf9R\nnDhxAuPGjcOlS5ewbt06ZGS41/4XUVBQgGXLlmHVqlUYMGAASv7zH4z38UGHwEBUR0Yi/rHHcNvv\nv2Op3WKvizL7v6L7RExt/KNB0gq4zjO/lhBz1gFgElArVuAY0JSLN4jB1KtNdwT+eMqkhyDgF1J2\n/TCFAs1btMDEiRNxxx134LvvvsPLL7+Mbdu2ISIiAnfddReGDBmCIJNJ1k9dqdPh4XvuwWeHD0t5\n9GlpaUhLS0N6ejrS0tIQEBAge4wle/YAublQKhTQVVc7d5H8ARQXFzudBOoOAAgKCsJoQcCUH36A\nzknO/40KuDY162iCW1itVr744osMCAjglClT3Fa41sWFCxf4yCOPUKlUcvDgwTx9+jRJ8sCBA1zq\nQmqgMaOh1aFi9eq12Ke7UYHaeipy+iyiWNcS2NQhn6rz/bVoxFF3G8VutlFX0rhbA45BlATw8fHh\n5MmT+d1339W/GewNNSRNfyfVm9XV1Txy5Ai3bNnChx56iF27dqXFYmFQUBB79+7NWbNm8bXXXuOP\nP/5Iq9XKgtOnr77t4zVGYWEhjx07xlN33un6/rgBAmJo0nNvQkNx/vx5jhw5kqGhoXz99dcbtW5J\nSQn1ej2nT59Oi8XCKVOm8Ny5c3w3NbXR+iuOJfoVAKsaQbiNkQj4o6MU7jVZGkrcDRHucjcct3G/\nINAs04dV7pi6OTkGQRCk4UjyOp2OMTExfPzxx3n48OHa8hVFRZzu6clL48bVkwiQg9Vq5alTp/j6\n669z9uzZ7NOnD4ODg+nl5cVJOp2sMuiNFuuScAsIiDWRexMajX/84x+Mj49nv379+PPPPzdonU8/\n/ZTitTx37hynTp3KcIuFZVdpuVfiivSuK4Gum0XwVoB93ZDtte6gJBIrAKm5St3h6+sr/d9ZQ2t3\n+u1G1O7UJDZY9/Pzk3T8zWaztG2NRiOJx82aNYtff/01z549S29vb5f9BhqCgoICZmRk8KXQUNfX\n4wbK7Eq4ikbw1xoNJfdrnCTahD8zOnXqhK+//hqtWrVCWloali9fjurqapfrHDp0CGlpaQCAwMBA\nLFu2DF/PnGm73Z2AsGWKyH0npjoCtoBlY4Kf1zon3hHirykD8BJsvnQTbOmEC+z/ivEFV9k/Cvv3\njYWoHVPpJCcdAM6fP3/lWO3nXqe7kmHv6phgtWKoIMDkEAisqqqCVqtFSUmJ1EA9ISEBoaGh8PPz\ng1qtRmlpKU6ePImnn34aHTt2RFpaGjw8PHDo0CHpGBoKkvjhhx+wcuVKREVF4fDhw/j099/lZRqM\nRlsWy42G2Wzz95vNtmMQj0X8/BYJpgJN2TJNqAOtVovZs2cjLy8P48ePx+bNm7Fu3TrZStVDhw7V\n+85y/jwgMyk4asE0FETjiLuxyzdkPfFzMeVvD2yBUcdA6tOwBVLdpSjeAVsVrqNUwPVAZWWllOYX\nTbo8puYkioqKMHToUGzbtg1WqxVqtRrFxcVQKpVo0aIFjh8/joKCAiQkJCA8PBz79u2Dj48Pfv31\nV5SVlaGwsBAajQY9e/aE0WjE4MGDMWjQIGRmZjrNOT99+jT27t2LDz/8EHv37kVlZSXKysqgVquh\n0Wjged99MGzc6LxaVKGwpSfeDLhLlbxV0BDz/nqMJrfMrQ+x4UZAQAAfeOABFhYWXvmysJBcv54b\n/f35/cyZtr9FrF/PGns7s3ouANjax5U6uF+K4F6n/VYbci6gAtgae7iSF26o9K/jEJuGjwL4tEYj\nadXXDZB6OPQ+VSqVjImJYWpqaoM7GonbW6pWc4a3N032balUKqrVanbt2pVJSUkUBIEBAQG84447\nmJmZSR8fHxoMhloNtP38/BgUFMTQ0FBOnTqVb775Jrds2cIxY8YwOjqaPj4+HDRoEFesWME5c+ZI\nTV9WrlzJItG9YQ/U3myZ3VsJaPK5N+Fa4ffff+eIESMYFhbGN954Q3rgxH6oVocH7v3332ebxERZ\n/66YzSESTYWd6J9xQZiN9aVXoWHBWHG7JXDdiakxowzgNDSsx6rjhHA1Adpi+6gbIN0+ZQpVKpXk\nn1coFPTT6WR19cX9O9tHkULB/nZ/vsViodlsplKpZOfOnXn77bdTq9VSrVYzJyeHRqORPj4+jI+P\nZ/PmzWv5/sVGL1qtltnZ2dywYQN//vlnzpkzR2qr17t3b+edxVxouf8voqHk3pTn3oQG46OPPsL0\n0aOx78cfYXDidimCTfCrQqVCB0HAm1VVtdwWhM3v60wMrBI2f3tjct3lPnf3neMyn8NWROVM4+Vq\nUQFgGmxyxmJ+exVsPlBnx+ROKsBVPrsziDnqhVYrfLVaDKqpQVtfX5z//XeMqampl5M/QKPB55WV\nsvsoEgRE6XT4vcxWoeDr6wtBEHDhwgWkpaWhY8eO2LZtG86ePStJAnz33XcoKCiQipaKiopgtVqh\nVCoRFBSEgoICFBcXIzY2FtXV1ejdsSOWtW0Lxfff3/By/j8bmrRlmnBdULVmDawPPOBSCVIkKS+V\nCncplYgWBBypqICHRoO5FRXOtUzgmowr7MvoYCt6qgLwJmzVq+LnzuBuu1X2bV9rb2kZgPWw+d9v\ng006wVWASxRZcwZXGjDOUAxgmiDgV09PbLl8uVYBFQFs0GpRXlFRS2lyvFqNxVVVstWu0wQBh9LS\n8P3336OqqgqlpaXQ6/VQq9UoLCyESqVCTU0NPD09UVBQAIPBgDvvvBPNmjXDSy+9hLKyMphMJhw/\nflwK0qvVaqjVanRUKLC9uBhqlQq66mrnWvE3UcvlVkOTtkwTrgvUp04BMs0MRD0TpVJp68JjNuMf\nHh742ssLxcXFGPvjjzBVVDhd1xUBi4JgjssQwHMAxgFYBeAuONdqcSW7K37fENJsyJuAI3QApjRw\nPXdyA64CtM5gAhBHYunly7UscXEboyoq0MLHBz9duCB9Fy5D7I7b46FDyANwzmTCJwkJ+OLYMZTZ\nrXmr1QrRUFy0aBFOnz6NTZs2oaioCM2aNUNxcTHKy8uh0WjQpk0bqFQq7Nu3D7qqKmyavGO4AAAg\nAElEQVQDbIqSdtIX7AHUqu7dYf3lF2iPHv1TaLncamgi9yY0DjExtofLSQZDCYBTSiVqampQUFCA\ngoICCIIgybIeqqmR1TJxBT1qE6TOPt6GrcT+V7huoeeKXFWwWe9y3ZbEt4R9ALq52Y+zfTZkQrDC\nZkHLNd1wpSHjDMWw9bp0lY5524ULtdxArvZRCmAirshFFBcXw3r0KCZGRqI4KgqRBw8ioLgYPyqV\neLW4GDNmzIAgCDCbzVAqlTh9+jQqKyvh4eGB9u3bQ61W4/333wcATPDxgdJhknFEVUUF5oSF4Ymq\nKugd3YC3qJbLrYYmt0wTGgc3etflP/yA/V9/jV27duHNN9/EmTNnoNPpUFVVBXVFRaN8x5WwEQoB\np6qDohtIQOPcFo4Q7345n/5HsPm7owG0uYrtu0IlbJNHrv1vOc37f6HxPvf1AB50sUxdN5A72WVn\n56cE9dNBrbB1rtrvsJyXUol7tVqEVVTgWE1NrU5R80mXPV7/LQiIJJ3GaW6V5hk3Gg11yzQVMTWh\ncXBSxFGj16NCq8W0uDj4NWuG2bNnw9PTE5s3b0ZpaSmKiopQXl6OXy5dQp7ZjCqdDuV2JUo500Js\nnr0azokduOIG2oarL2Byt15n2Fw+bSB/rFeDagDHAMwE8D1sxO6BKxOUyf732/b95sJG2mJOfDFs\n5FpS57NCAKsBJMI2cTiDMzdQscw+ynBF6K0uDLC5U+oe81u4EjTvIAj4qaYGfy0txUM1NVgO2ySS\nBYCk9MYghzg5YgdsFvyOHe4bW/+Poslyb0Kjg1VnzpzBh7t2oXTTJpR9+y1+NZlQfvvt6Jibiy5d\nusDLy0t23RkzZoBFRXgqIwP497+BNWuA8vo0JKoa3gebT13Osp4IYDNsrhlZEnBY/npWsTZmH+Jy\nYkcmwHnGjmOQ2lnbPTh8BtRWqJQ7FleKkXX3kQpgcgN+j7NjdtViUTwGwcUyDQE1Ggha7f+U/71J\nFbIJDUMDikSKioq4e/duTpkyhQkJCfT29uagQYO4du1a/vDDD43a3ZkzZ2ixWHj+/Hmn+y9RKFii\nUnFlXh4tFgunaTQu89/Hw1Z0I1egc6NH5XXY5nzU1pdxNlxpx4jnT07xUW6bWbDVIFxN/v9bcF3M\n5Vg4JebX/xFVz0q9nhUXLlzLJ+OWBRqY594UUP1fhovGAzU9emDJ9Ol4++OP8c9//hOtW7dGTk4O\nXnjhBaSnp0OpVMps1DWCg4MxcOBArFq1Co899li9Um51RATGffghdu3dC41Gg5CiIpeZLmFoeMbL\n9QZhC9A6Wszie/HVvjE4ulCsDo1P6sKVdkw1gJ9g84M/DOA/Dt/JbdMEm0vIVf6/q7eUrrClgMrp\n6zt2ijoAmxW/HVfiD41FRVkZHgoIwK+9e2Py5Mno3LnzVd+j/zVoyAxwPUaT5X4LwIV8aYkg8JVu\n3fjWW29dKQW/Rjh27Bj9/PxYXFxc77vq6mred999DAgIoFKp5HQPD7fW37W23N1ZqjdLXtiZ2qM4\nFjRgW42RO3B1Tq2wvaE0RDJC7lyVwWbZN3SfDRnvtWpFb29varVamkwm3nPPPfz000//sErlrQY0\nqUI2wS1OnHAuygTAQOLOjAzk5ubWUgu8FoiLi0N2djY2bqxdk1ldXY1hw4Zh//79KCsrg0ajwbrC\nQsjZq0YAv8Pme5a3aeuDbr5zZ2U31gp3tT932IErvnHbc+0c7gKTQO0grbv4hMv+qrCljoqZTHIq\nn66gha2CN8vhs8Zex1owGpEzfjzOnz+Pjz/+GAMHDsTrr7+OLl26wNfXF5MnT8Y333zj8hz+16Eh\nM8D1GE2W+y2Am9h44LPPPmNCaCirnnuOnDGDVWvW8I7u3enl5UWdTlfLostxYQFaYWs24WqZazVu\npMUuWtqOHZ9cDVc+98ZsV6FQUBCERlnR7uIM5S7OXV1dnfGorfPT4HPuREu9qqqKe/bsYd++fanV\naqnVahkcHMxHH32UJ0+evG739vUGmoTDmuAWN7PxwL59LFYqWanVkrAFUuu6DLp27coff/yRr/bo\n4ZJoSuE6eHezR4n9GMXjcySvokYQn9wQ3TV1hb9cjfluttmYyaIS8kJtRQA3Qz5YWleRsjGCa9K5\n1GrJu+6yGSuO6qQOKC0t5fbt29mpUyeq1WpqtVpGRUVx0aJFUnvIes/G+vXkjBkut3sz0ETuTWgY\nboakqotJpQDgX2fOZE1NDUmb7PBai8XlA14BW3bGzSZxuVEA0B9XWtmNBzjVfsxvwSaBLNeSz8vL\nqxbparVaGo1Gp+QO2CaD0Uol3wJYIaMCWQTbZOgoFWxCfYJvzGTh6rcvcbOMONG48/PLfV6tUjXq\n3r106RLXrVvH1NRUajQaajQatmjRgs8++6wti8vZM2Ey2Yj+FiD7JnJvQsNxoyVVXbiDqvV6Vq9d\nKy26YcMGTtRqJe13ufH2HyShPzLqSgeLbgq5AKYzad1CO8mJfUyDPTwI2LTUxZZ3arWaSqVSttVe\nQy3vYvv+xP2Xq9UsAJiNK+31xElD7M/6FhqXquj4212RtqPlvvlaXZNGvHWeOXOGixcvZlRUFLVa\nLb3Vavmm3OK4yZryTeTehFsXM2a4fHgWK5VMSUlhZGQk1Wo1e2Zl2V69XRDEBBdk5oqU/0hutTgO\nAHwRNtdLsf0zUae+WyNI15kbpkWLFrXIPDExkYGBgTSZTATA7Oxs6nS6epk0giAwC7VJvAhXdOCd\n7b9UpWJCWBjvvfdeim8JXbp0oUajodm+rYacjwqAGx1+S6D9XLj6zSYXy4jXqsHX5CrjRcePH+dr\nvXrJnp8/MolcSzSU3JuyZZpw4yGKjzlBuUqF7wUBR44cgdG+zKkLF5BbVSWbdWIF8AKulM/Lld2L\nEGV+l8Gmr+Jcp7JhKAawBUA/2HLCxV+lsf/9GmpnpjS2v+q3336L8PBwqU1daGgomjdvjq+//hqC\nIODLL79EaGgo4uPjAUDK7dZoNDgAm77+NEHAAvu/DwOy51EA0KOgAFu3boVSqURFRQX279+Pu+++\nG4lt2uBuiwVlKpXbrBwNbBXDJbBlwxx32Kf4byls1yrXvlwebNk31wQlJbb2d41EbGwsBqakuM0k\nkmC12uozblE0kXsTbjzy8mw9MJ2gqqYG8Y89hh07dsBoNIIkvL29UWS1ogy1iYmwEcMgAHcC6KdQ\n4BG4JmzCRiJaAGMAPA5bYw1HTZVK+/qlDp+5mliAhhO2u/6q0Q7/HwVgPolOJ0/CR6OBTqfDhx9+\niIMHD8LDwwN6vR5GoxHTpk3D8ePHIQgCrFYrFAoFKioqkJ+fjyqNBps1GjwqCNhAIszF/nXV1Vgy\ndiyys7Mxfvx4dO/eHTU1NXj11VcRHx+PL3U6BNTU4AHY0inlzrFYeCUWQnngij6Qo1pmDGwFTO7O\ni7i8eL0B2wQud03+UPNsF4ZHPVzlJHLD0BDz/nqMJrfM/zjsQSux12oxwHKtlqXvvSctkp2dzdWr\nV9PTnknj7NW4bts+0dc73snnrrJS+qB+X9cCXPGDz3fi4hB9yu4KiBwzUxrif3bmkxf3dd999xEA\ndTod/7+9Mw+Posra+Ht7X7N2dghJIAQjqwQSIlFkEUEFUcYojKCEsIkCAiKugw6KOKjI4kJUZHQ0\nyowoqB+izoiCDIrDoqiAyiIBBFmyr/1+f/RClq5OJ2Tn/p6nnk533ao6t6py6tS5557TuXNnCiFY\nVlbG66+/nj179qzimtHpdDQajYyNjaXFYqEQghO9HL9IreaB+fP5+++/s1OnTszKyuLAgQPdfv/4\n8HD+NSaGTwBcHB2t6KZxuVp89bXXdl4qb7MhNJRr4+M512RioWsgtSHdJd4iyKovjRwurASkz13S\nktm3bx8z0tM5w2LhliuuYNHy5VX+IX/66SeGhIQwJiaGmUIwXyHyQ0lhu+qyroYjWuPVWhRNbT5h\nAAxz7meL8zPM+fssq9Xn4tPToDyz85xzn7745NVqtVsxPvnkk1yxYgV79epFq9XqVuqAY4BUpVIx\nMDCQgMP/Xeyllqq/U5HHxsZSo9HQYrHQz8+PV6rVzBOC5QaDu1+uGq4Fzv25HkJDnMd+1tnW20PP\nldvG1zDIF4KCOGTIEO7evbvxIr2q71dpaeE+d6ncJU3KgQMHOH78eNpsNj722GM8d+5c1QbO+OJ/\nJyfzwfBwWgAudVr3dVmqJ8uqLRJDKRrHNU3emzUdoFbXqpCrb1891t3XyJKXkpMJOAZMXYOoGo2G\nYWFhFEK4JyHZbDaq1WpqNBr3Q+BKp5xFTmXsOn6pRsNzAIeazRwzZgwTEhKo0WjckTPBOp3X/t2l\nVnOxWs0MVH34ZArhtS8TK/UBzv57m/BUIAR33X131XQCjRXpVWm/Z6dMcbz5NWW4sBekcpe0KH75\n5RdOmDCBwcHB/Mtf/sIzZ87UbOS0mFz/RC6l97ROx8LawtNqWYoAlup0Xh8ESksxlCNMlJR3ZYXt\nzSothsOF5FKKtbl4zkydyvT0dCYnJ9cIiQwPD2dISEiNTI9CCK8yFAnBS202t1J+/vnnWVRURJJ8\n7LHHeI+fHwsUzn8ewMdiYhgXF8fIyEjeeuut7uN6O2apXs/t48dzc2oqH+3QgYEaDf2E8BqRU6zV\nstiVTbQJWbx4MafffnvThgt7QSp3SYvg0KFDnDRpEoOCgvjQQw/x9OnTnht68XXmAYrKxdcQuXyA\npV4eEPVNFpYH8C7npCIzwOlGoztW3exUrL76ni1wuJGU3iLy4JigZDab6e/vz/bt21dR4pUXC6pO\nUrqzFhmm6fXUaDRUqVTMyMhwXxa73c6PevTwem4edz4UXFa4yWRyyzFIr2epwVDlgZ0PsEynY4XJ\nRAIsMxhYYjBww6WXKj5E7QD/HhXFTp06ccOGDU109zro3bs3P/nkkyY9pjekcpc0K0eOHOHUqVMZ\nFBTE+fPnn8/froSXiU2FKhU3dOvGYp3Ona7AbjKRFgsrlAbVPCz/Vam8znT0dT/Vl3WXXMIuXbrU\nULBCCBqNRp8GXH2ZDXrOqbSDg4PdfnGXLz06OpqV3RvV3yJqy+D49ZAhDAoKohCCarWaq1at4osv\nvsg5c+bwoYgIrw+GTKf/Pzo6mlOnTmVoaCiTk5MZFBREAPRTqfi32Fhutlj4b61WcXyjVGEswLUs\nt1o5cOBAxsXF8brrruP+/fsb/T7ev38/w8LCWFZW1ujH8hVflbvM5y5pUHJycvDEE0/gH//4ByZO\nnIgff/wRISEhtW/oJUOl0W6Hv78//vfBB+jzyy/Ar79CkMCKFaAzpJI4Hy7nKWtjoRD4w273mhu+\nAuerIvlKPoAP9+3DfgAqlapKfnSSqKio8Fp8Oh/AbzgfMqh0DFc91UKVCvl//AEhBPr06YPD33+P\nS8+cQecjR7APjhJ31fflOq7iuVGpsPXECWi1WrfMd955J3r37o19+/ah9I8/MFdBNjsceditVity\ncnKQlZWFlJQUJCUl4dprr8U777wDvz17MOnXX2EyGqH2Ml9Bq9UCQgAlNYMsizUajHn4YRz6/Xfs\n3r0bGo0GKSkpmDJlCubPn++eE9HQZGdnY/To0dBoWqGq9OUJAOAaOOYiHABwn4f1YwHsBrAHwFYA\nPWrbp7TcWykKCZWOHTvGGTNmMDAwkLNnz+aJEyfqtl8vlnuZwcDsoUPZo0cP+vv7M334cJYozFj1\nFj0z24tlnAdwv81Gex2jclw+9+HDh9fwd6tUKup0Oq++50KAs7zIVX22Z+WluoWeD8fYQoHCvrz1\nwQLQarW6rW0A9FepOEml4jsdO/IJD28D5wBuf/ppnjt3junp6QwPD2d0dDSPHDlS5X4pUhjr8Lgo\ntC3UahkfEcF169Zxz549TEtLY/fu3Tl06FBGR0fz7bffbpS87d26dePmzZsbfL8XAhrKLQOHMfMz\ngDg4Jp/tApBYrU0qgEDn38MA/Le2/Url3grxEHpWYbG4S+LNnDmTx44dq9++fcxQeeLECf43M5NF\nCu4YVwZGl4JzKbRCOOLUvfl0C724BVz7rRwHn4vzeWPMZjMvueSSKsrXYrG40xe7FHF1uQpQu8vk\ncdT0oYej7ukW6DyWa/yi0Bk9M8xqpcFg4LRp07hx40YmJSW55S13Riq5+vukEHxSpeLuGTN4/913\ns0ePHuzYsSMnTZrEwsJCPvXUU+zYsSMPHz7suK7e0kpXWyqMRnLePMXwxv/85z/s1KkT//SnP/HY\nsWNcvXo1w8LCOHLkSCYmJnLgwIH87rvvGuhmJ/fu3cuoqCh3EruWQkMq934ANlb6Ph/AfC/tAwEc\nrW2/Urm3Mrwo3yKtljn79l34MXyNW64lN83LJhNLFAZPXUmzXPHaNJm8+tvz4AjBK8B5q7UEjljx\nEUZjlVC+yrHnwTodM5zK0JV10VuOFW8Dtk+qVMytFFboisuvq4VerNVyKsApOh1fCAxkBsAAjYah\noaE0GAzs1q0bDQaD1zeNcrOZy554gt26deMzzzxDvV7P3r17V/FJP/3004yLi+PBgwdrvVaVl1yA\n/1qzxmt4Y2FhIefNm8eQkBCuXr2ap06d4uTJkxkWFsbbbruNNpuNs2bN4tmzZy/4dnzkkUc4c+bM\nC95PQ9OQyn00gKxK328DsNxL+zmV2ystUrm3MpqqsIcPcctb7rhD0QIv0en47w4dFCc95QGcodFw\nohBc6e/Pz6KjWazwFlACR3x8bTHslZW6y0ovUKtruDCegLL7xZty9zVhV21LnkrFMLOZFoD3BgXx\nbxoNpxuNtKJqNkivqXfNZhY89xxjY2Pp5+fHXbt2cfDgwZw8eXIVt8izzz7LmJgYnnziCcX7xtVn\n1yzjmUlJjImJ4axZs1haWur1NtmxYwd79erFq6++mr/++iu3bdvGXr16MTU1lTfddBMjIiK4evXq\nelvddrudCQkJ3LZtW722b0yaRbkDuArADwCCFdZPAvANgG+io6Ob5ERIGojaLLD77mt0EYqLizll\nyhReFh/PcqUHjdVKzprlVdbCmTO5ceNGdu7cma9FRHht+5EXRecKY1SpVExISCDgPba7trTFxajp\n016i1dZ5dm6REFWKg7j2dYPNxh+yshzuIec+84VgvkrFK50PKCFErdE9i4Rg+/btGRkZyWHDhnHT\npk3s2rUrH3300SrXa9myZUxs354VSlFQAJdqNHw4Kor3TJpElUrFuXPn8tprr2VqampV370HSktL\nuWjRIgYHB/OZZ55hcXExn3vuOdpsNo4bN469e/dmSkoKv/nmmzrfazt37mRMTEyLrL/a5G4ZAN2d\nvvnOvhxYWu6tjGYsyUc6QiuTk5M5atQox6xWLy6csuefV4yLryxrUVERXx8wQFF5Fmk0LB082Kui\nqx7j7c3qLYJyiuEKk4mzjUbODgioEie/qBZF62k5BzDGaOREIbhICD7aoYM7ra63txCrD33IB/jR\nn/7Ed999lw888AAtFgtjY2NpNpupVquZkJDAqVOn8rnnnuOmTZu4cOFC3hgaygqzuUqsey7AEc7B\nW6vVypiYGD711FNUqVRcvXo1H3/8cYaHh/PjSrmGlPjpp594xRVXMDk5mXv27GFOTg7HjBnD6Oho\nTp8+nWFhYZw8eTJP/fqrz9WV5s+fz3vvvbehbt8GpSGVuwbALwBiKw2oXlqtTbQzkibVl4NSKvfW\nRzOW5Pv0008ZHh7ORYsW+TT1fPakSSzwNalUbi5LFXKg2C0WctkyxYeay3Lv06eP2zVTW5oDpcHT\nMpOJidHR7N69O4UQ1Gq1tSb6KgBYqlZXGfSsXhxEq9Vy/vz5HDVqFKd7Ob6rLxqNhgP79PHqc698\n/vbs2cOQkBBu3bqVn3/+OQMCAjhp0iROnTqVAwYMYFhYGA0GAwO1Wi7r2ZOvhIXxHn9/3nj11bz0\n0ksZHBxMOI+blZXFiRMnUqPR8PPPP+dnn33GiIgILliwwOFe8VL6rqKigi+88AJtNhsfeeQRFhcX\n85NPPmFCQgKvueYaLhw2jLlCsMQVjeMlhYDdbmdcXBx37NjR8DdzA9Bgyt2xLwwHsM9pmT/g/G0K\ngCnOv7MAnAGw07nUenCp3FshTVySz263c/HixQwPD/d5huDf//53durUiafff58FajWL1OpaZS3Y\nuNERSVMpAVa5yeRoW0tJwMo+9zCTyWvxj3w4LP1z1Y51DuBHDzzALl26sHfv3jSZTFSpVDx06BA7\nR0R4tbbj/fx4b3AwF2s0zADYKz6e1Qd3VSoV777sslqjchZrNFyzZg0BcMGQIaTV6o5KclnbFZ9/\nXuP8rV+/npGRkTx06BC3bdtGm81WxVd9+vRpzps3j4GBgbziiisYEBDgTp1QudIUAK5bt479+vWj\nwWDgTz/9xJycHF5xxRW8p29fVlgstd57v/32G0eMGMHExER+9dVXLC4u5uKHHlIet/BgmGzfvp3x\n8fEt0iVDNrByb4xFKvdWShOV5Dt37hxvvPFG9unTh4cOHfJpm127dtFms3HHjh0cOXIkb73+epa9\n+GKtsi5YsIATbr6ZRcuXc6nJxBkWC3dv3Xq+QbWHWh7AXGelI5fyBMDpBoNj5qyCIikCGBca6g5r\nfBzgA+HhtBkMHDRoEBMTE5mSkkKbzUaz2ew+/N9uuMFjjPkVKhWzsrIYFhbmluGLL77go48+WiVh\nmC8ZF/MAvjVkCE0mEwMCAnjdddfx5aVLOU2v50p/f87y86MZ4JgxYzyew6eeeoo9e/Zkfn4+169f\nz7CwMP70009V2rzyyisMDw+nn58f4+PjuWLFCgohmJSUxD59+rjl1Wg0bqWfmZnJVU8/Xaf0vna7\nndnZ2QwPD+fdd9/NomXL3Kmlqy8VJlMNl+Ls2bP54IMP+nTPNQdSuUtaLXv37mWXLl04efJkFhcX\n+7TNmTNn2LFjR65evZo33XQTr7/+epaUlNS63alTpxgUFMT9+/fz0Ucf5aBBg/j666/TZrPxxRdf\nPG+9OR9qq0JCmKlWM0inY5jJVCX2fHktk3X+DrB9+/bu3CsqlYrp6emcNGkS9Xo9O3fuzNTUVLZr\n147h4eHMy8vjQw89xKCgIM6cOPF8gW2dzj2pKSEhgcXFxZw7ZQoz4PDRr0pO5sL77mNcXByt8J6v\npvJbgKtI9sKFC2k2mxkTE8OVK1eyf//+jIiIcFvY//vf/2qcR7vdzjvuuIOjRo1iRUUFV61axdjY\n2BrzHlavXk21Ws2MjAyOHDmSarWaoaGhHDZsGFevXu0eu5g2bRpNJhODgoK4KjnZpzEUT9d23Lhx\nXOnn57XvX111lfteqaioYPv27blnzx6f7rvmQCp3Savk7bffps1m4yuvvOLzNhUVFbz++us5bdo0\n3nzzzRw+fLjPD4W5c+dy8uTJ/OqrrxgaGsrffvuNJPnjjz+yW7duHDNmDPOclmFFRQXNZjODgoLY\nH2C+SlUj9rxUwcJ0+bSFEOwRF+d+KKzs3Zu5R48SAIOCgpiamspOnToxNDSUkZGRHDt2rPvNJd7p\ncgHgztcOgFdptSw3m2tY9vcYDDzng2IvhyMqx1LpLSQhIYFdunThjh07mJiYyE6dOvHhhx+mEIJ+\nfn4eQwyLi4t5+eWX84EHHiDpeCPq1atXjbTOAwcOpMViYUBAAIOCgjhy5EhqtVqWlJSwe/fuDAgI\nIAAOHjyYer2eayIjvcpfW6TWnhkzFAfNK4xGPt21K7t06cKPP/6YW7ZsYWJiok/3TnMhlbukVVFW\nVsbZs2czNja2zgNZCxcuZEpKCm+++WZeffXV7nS1tXH06FEGBQXxxx9/ZFxcHP/1r39VWV9QUMCM\njAwmJCRw9+7dfP3112m1WhniVJqelIVivLoQ7BYbWzNlgBAs1us52FnkOjExkXq9nmazmf/973+r\nyJOWlkYhBPXODI5CCEZarXWWxVMb1wNhgNMlEhAQQIvFwrvvvpt+fn5uV0VKSgoB8I477vB4Tk+c\nOMEOHTrwjTfeoN1u56RJkzh48OAqb1HvvPMOe/bsSbPZzICAAH755ZfU6XRcuHAh3377bfbt25ep\nqakEwHbt2nGKRnN+7KQOlruLM4cPM1/J8rdaac/N5XvvvcfY2Fh27NiR99xzj2NDLwO4zYlU7pJW\nw/Hjx3nllVdy6NChtWePrMbGjRsZERHBm266iYMGDWJhYaHP206dOpVz5szh+PHjOXHiRMV2a9as\noc1mo81mY58uXby6OVzFJuyVlKcd4KPh4Vz55JPM81IFKQzgJLWaz/v7c1F8fA1lcu211zIgIIA2\nm43r169nQECA12ia+mS6PAdwwdy5NJlMDA0NpRCCGo2G2dnZ7N69O3/77Te3e+bbb7/1eL5cYx/b\ntm1jWVkZR4wYwbFjx7qt/ZMnT9LPz49Lly4lAC5ZsoRjxoyh2WzmoUOHmJCQwE8++YR33nmn441G\nq1UeM6glUis3N5cpKSl8dvRo2q1W98zkQrXaEX/vGjRftYols2bxTr2eUX5+fGXCBEe0VAsp0FEZ\nqdwlrYKtW7eyXbt2fOihh1heXl6nbQ8ePMiwsDAOHTqUAwYMYEFBgc/b/vzzzwwODuZLL73E+Ph4\nt+tFifvvv59DjEbm+uDmUFKaT0ZHew1rrDzxqFCtrqFMbrnlFsbFxTEgIIAPPvggn3rqKb4SGlpn\nWby+YcDhPgoMDOTAgQOp0+mo0WgYFBREi8XCAwcO8Pnnn6cQggEBAYoRJe+99x4jIyN55MgRFhQU\nsF+/fpw7d657fY8ePbh161babDbq9XouX76cHTp04KBBg/jqq69ywIABJB0+esBR0MTuSe4VKxSv\nWUFBAa+88kpmZmY65HSOm5TNmcN111/PDsHBXDdnDu2VBssLhGCFyaT8ptBMpfUqI5W7pOXg4fXW\nbrdzxYoVDAkJ4fr16+u8y6KiIiYlJbFv375MS0tjfn5+nba/7bbbOGvWLIaEhKIdyqMAABuNSURB\nVHD79u1e2+bl5bFjaCjLvETC+KI0P/cxgZaSMsnMzHSHSvbo0YNr167l8p49z+fJ8XEpr2V95YLe\nNmeFpg4dOjA4OJgxMTHcsWMHe/To4VC6f/6zouti0aJFvOyyy5ifn89Tp06xS5cufPbZZ0mSs2bN\n4l//+lfeeuutNJvNtNlsNBqNTElJ4ZNPPsmYmBh++eWXJMndW7bU2XIvLi7m1VdfzT//+c+KRsP3\n27Ypu2uUlmYqil0ZqdwlLQMPsfF2i4WPDR3K7t2717vgQmZmJuPi4piamsrcOvpCv/vuO4aGhvLy\nyy/nE088UWv7BQsWcFVysrtQSH2XM+3bK1r9ii6USspk9uzZ7NevH/v160e9Xs9PP/2U/bp2Jeuo\n3MugPFO2cmWoynHyrhDFwMBA2mw23n777UwTokrmyOquC7vdznHjxnH06NGsqKjgwYMHGRUVxezs\nbK5fv54DBw7k4sWLGRkZyblz51Kr1fLBBx+kzWbjAw88wGHDhjkuwKpVyiGmHpRtaWkpR4wYwdGj\nR3svsrFq1fm6qHVZmiDVhjd8Ve6OSgcSSWOQlwcMH+74dBXiKCiAyM/H7E8/xVebNqFTp0513u3L\nL7+MtWvXIjg4GB999BGsVmudtn/wwQeRlJQEjUaDuXOVylA4OHnyJJ555hm0Ky6G1kMRCRelAIoA\nFCqsJwDjkSPQKaxXKiKCggLgwAEAjoIYarUa8fHxMBqNOHz4MPYeOQLceKPXPpRWkoFwTDnXK7S1\nA8iu/puzAEl5eTnOnDmDP/74A198+CE2kPADoC4qOi+r65rn50MIgRdffBFHjx7FggUL0KFDB3zw\nwQeYPn06AGD79u0IDAxEx44dsWXLFqSnp2PJkiW488478c9//hM7d+7Et99+C+zfD1GocGYrnR+X\njGPHjgVJvPHGG96LbOzfD6FQIEYRsxmoxz3bHEjlLmk8srOBSpWJKmPQ62Fav963/eTlAVlZwLx5\nOPjQQ5g/fTqioqKwadMm+Pkp1S/yzPbt27F161Zs374df//736FWe669lJ+fj9WrV6Nnz54oLS3F\nflJRcZcC+AeArlBW0gKeFWoBgGIAxUJhy0rKxGq1QqVSwd/fH6Wlpdi0aRPsdjsK+vYFTCbP/YCj\nUlKJUwbXUVyfdH4WCoFcANcJAZe602g0UKlqqgiSGPD778rKo7QUeO01AIDBYMC7776L1157DdnZ\n2ejRowfeeustTJgwAXFxcTh9+jS0Wi2OHj2Kq666CmFhYVixYgXat2+Pjh07YuHChUB8PKhQaclu\nNAI5OcC8ebC/9BKm3XYbzp49i7fffhs6ndKj1El8vOP81gWVCkhPr9s2zYUv5n1jLNItcxHQEJkk\nPcwOzROCuR9+WC+RrrrqKoaGhjI7O7vGOrvdzq1btzIjI4MBAQEcNGgQrVYrDx8+zInR0V4rGQ2G\n52IcxVB2udg1GnL8eI5KSfHJp/zSSy8xLS2N48eP54gRIxgUFMRu3bpxp+scedg+X6XigpAQr8nM\nPoQjSic+IoIqlYpCiCp56j0ttWWOpFZbZTB4586dtNls7vGNN998k1arlenp6ezWrRuXLFnC9PR0\nBgQE8PXXX2dwcDDDwsLo7+/Pb/79b8VcQXbA7bIp0miYr1azaNMm324Gb/mSjEaylUfLSMtd0nh4\ns4x8eb314NaxALCQsKanA/n5tctQyer/YfZs/Pj11xg6dChuvvlmd5MTJ07gqaeeQmJiIm6//XbE\nx8fj+++/R2RkJO655x7s+M9/8Mxvv3m0yglHDux/wlG31GU/u9qq4cWaLy8HIiLwh06Huzt2RJFG\n47aaS3U6wGoFPvwQsDiqoFqtVlRUVOD06dOYMGECCgoKEBISgp9//93Rzmo9f77NZtBqxcNJSUgK\nD/dYvxUADAD2qFR4GcCxvDyoVCqQhHC+SVSuTWowGAA4rkEEzrt7PFJW5nbPAECPHj3w0ksvYdSo\nUTh69ChuueUWjB07Fu+99x6OHz+OjIwMfPzxx+jbty+EEHjjjTdQXFyMkpIS3HDDDfh3ly4oV6lQ\n5nrTMpncNWFdLhtDeTnMFRUw3Hijb/eG6/xWO2+wWoGPPwaOHQOWLgXuu8/xmZMD9O9f+35bCr48\nARpjkZb7RcCFZpK80DTD1az+fCGYKwQLNm5kaWkp33vvPY4cOZIBAQG84447+MUXX7hD+3bt2sWw\nsDCePXuWD0dGKs5wLNZq+Sq8p/lVSthld/YhJiaGcXFx3Lt9O48vXMilZjNnBwbyi48+qtKdDz74\ngH379mX//v1ZWFhIrVbL1NRULlmyxNHAQ96fvLw8PtahA4u1Wo8yuAZQjUYjzWYzrVYrrVZrFSvd\nZcWrVCoOdk7gUiqWUts1WrhwIZOSklhQUODuAwDm5eVxxowZHDx4sHuCVFZWFvs734hcEUEVOh2p\n1bJ8yBDlKKG6RrQ0Ub6khgIyWkbSIriQTJIX4tbxVhZQp2NcaChTU1P58ssve4y2ufbaa7l06VKu\nXbuWz9YSjfJVLUpOKUKmQK1m3rFj1Ol0tFqtPHPmDEnyuuuu47333st27dpx3LhxPH78OEly8+bN\n7NWrl3t6fEpKCiMjIzl9+nSvp/H3n39WnDyVC0dmS4vFQovFwqioKKrV6io56l25cHxJQFbbNbLb\n7Rw7dizT09Npt9t51VVXUaPR8JprruG+ffsYEBDAqKgofvrpp4y12RSLa9eW4bK5I1oaE1+Vu3TL\nSBqX/v0dr7P1eb29ELeOl8FcQeLLu+7Cli1bMGHChBrRNl988QW+//57ZGZmYubMmTik1ULpJd9u\nMuFHQHF9PoDlWi0K1GqU6fXu30r1evxt4EAMvuEG+Pn5oby8HP7+/o71+fkYOnQo9u7di9DQUHTt\n2hUrV66EyWRCcXExzpw5AwCYMGECjh8/jl9++UX5PAAIiYvDubfeQp4Qbhlc7gfL5s24/c47UVZW\nhoKCApw9exaRkZEwm83w8/ODEAKaoiJkwBFFU8sQZVU8XCMhBLKysnDw4EE89thjuObyyzFNp8Mt\nO3fiv5mZuObyy3H69GncfPPN+GDcOOgUol10Oh2gV4j5aUURLY2KL0+Axlik5S6plQtx69TT6rfb\n7ezXrx/XrFnDp59+mhqNhh1DQxXzgeer1QyDIwWwp/XnAIYYjVy5eDEXxsVxlc3GTLWaHYKDuXv3\nbo4aNYpGo5ExMTFuGXr37l1lYtWePXuYlpbGrl27MiIignq93nl6cqlSqehrycqdX37JGRYLD44Z\nU8X9UFxcTJvNxn/84x/s3r272wVjMpk4QKOpkn++TouXa3Ts2DHeGBrKYp3O7dIqcJb8GwLwlcsv\n577gYO/7V8rC2QJmkTYmkG4ZSZugvm6devrr161bx27duvHUqVPU6/VMTEykTqfjf/76V4851V05\n3fsDLNRo3L7oPDgKUqcJQYPBwGXLlrFDhw7UaDTs3r07X3vtNXbq1ImrVq1i+/btaTQa3RkpO3fu\nzB9++KGKXHa7ncuWLaMQgiqVyt22W0wMM4Wg3cfkVp9++ilDQkK4a9euKr/PmDHDnc1x3759vPLK\nK+vuhnFN8vLlGuXmOgqieNiPvdJ59jq5a968Ji0e01KQyl3SdqjPgFc9rP7y8nImJiZy/fr1vPzy\ny2mxWCiE4Ouvv85HH32UFoATheBrUVHMgMNX7aooBIDbP/uMa668ko8729kMBlosFgLgsGHDOGvW\nLBoMBt52220kyZkzZ7Jz584cNmwYu3XrxtjYWB44cMCdk6U6RUVF1Gq1NJlMDAkJ4Yb77mNRJcvX\nV+X21ltvMSoqir/++qv7t927dzMyMrLKjM78Z5915LjxRbFbLOTy5b5fI28P37q8FbSywdCGQCp3\niaSOVv+rr77KtLQ0Llu2jHq9nmq1mhMnTuSJEyeo1+sJOIptpKWlETg/0OiK+AgKCuLUqVMJgF26\ndKFWq6VarWZISAi1Wi2XL19OlUrltpDLysrYrl07durUiTNnzuQLL7zAqKgomkwmnj17toZ8drud\nGo2Gl1xyCde++qrXNLa1KbmlS5cyISGBJ0+edP+WnJzMDRs2nG9Um2vrQqxlX/bdkMdrQ/iq3OWA\nqqTtUofB3OLiYjzyyCMYP3487r//fpSVlaFjx4548MEHkZKSgrKyMgQGBiIyMhLff/89hBCw2+1Q\nqVQoKyuDSqWCWq3GW2+9BQAIDQ2FzWaD2WzG8OHDUVFRgbVr18JqtboHQDUaDS699FLk5OTg999/\nx+TJk7F48WIUFhZi7969NWQUQsBqtcLPzw/d9u6FyWj03G+73TGg7IW7774bo0aNwnXXXYcC5xyC\njIwMZGVlnW/kZUC7BED51VfXP/67PrNDU1JaZ7x5c+HLE6AxFmm5S1oSS5Ys4bBhwxgdHU2NRkOd\nTseNGzcyOjqaQ4cOpRCCN9xwA5OTk93Wusv/rdfrqdPpOG3aNHeFJJ1Ox+nTp1Ov13PBggUMDw+n\nWq2mxWKhzWZzFxTp2bMn+/XrR6vVym+//ZZ5eXnU6XQMCQnhZ599VkPO6OhoDho0iD+NGuXdwvUh\nFNBut3P8+PEcPnw4S0tLmZubS39///Ol8by4tgo0Gi5ZsKD+J9yb20zJYm/mbIwtBUjLXSLxjXPn\nzmHRokXIz89HvjPh1eTJkzF+/HgsWLAAu3btgkajQfv27bFnzx4IIWAwGEASdrsdEydORGlpKQIC\nAhAUFAQAKC0tRXZ2NlQqFY4fPw673Q673Y6SkhIkJSXhzTffBAAcPnwYQgjMnDkTo0aNwsGDBxEQ\nEIB33nkH6enpeP/996vIarVaYTKZcNLf/8Jm/8LxJrBq1SoAQGZmJiwWC2666SasWbPGdTDFGZwn\nV6/GE8uWucMy64ynfSvkxwHQunK6tBR8eQI0xiItd0lLYcGcOXw0OprP6PWcqtWyU1gYQ0JC+O67\n73L//v0UQvDWW29lTEwMExISqNfrGRgYSCEEAwMD2bVrV2q1WoaFhVGr1TIoKIgAOGfOHOp0Ovr7\n+9NgMBBwzAS9//772aNHD+bm5tJgMDA+Pp4//PAD58+fz+TkZMbFxZEkv/76a4aFhfH11193y+oq\nJ/jcwoUXNvu3Evn5+UxOTub8+fO5ZcsWxsfHVy3CoTBoOXHiRN57770XdvKr73vjxosyAqYuwEfL\n3Us+TImkjZKX5/BJ79+PvPx8zFq5EgKOnCn5AHjiBPY9+yx633ADMjMzQRKXXHIJ/u///g9DU1Nx\n5YEDiDtzBgcAbPPzg9lsRqTViuvOnkX7sjIUGY14r2NHPP/880hLS8P/Nm/GeLsdsQA0HTpg5apV\nEH5+ePfddxEdHY2cnBxERkbisccew+bNm5GbmwsASEpKwmeffYahQ4fi3LlzmDZtGvz8/KDX6/F7\nUZHD8h0+3OFjLyhwWMAqVZV8NL5gNpuxYcMG9O/fH+Hh4fATAvvnzUNnIRy+8fR0ICOjxnZ/+ctf\n0L17d9x1111o165d/a6FxVJz3zk5jutz4IDjDSQ9vU79kTgQjgdB05OUlMRvvvmmWY4tuYj58ssq\nCpFQSOxltQI5OTCHhSEwMBAlJSX4U0QEntq7F6yogAVAgRAggG9vvhk9s7OhAty/a3Q6jAsOxpkz\nZ/CvkhLAbocFQJFKBaHRYEr79tgXGgq9Xo/t27e73UEffPABRo8ejZUrV+KOO+4AAPz6668YMmQI\nMjIy8P22bRj8xx+ILCjA1XfeCVx7rUOZN4AiPHjwIGb16YN/nD0LAUcirioPDA+DmPfddx/++OMP\nt3tH0vgIIXaQTKq1oS/mfWMs0i0jaXLqMIhXqlbzx7g4ZgCMtdn42vLliqGHShNtcgEWKSXsUqkY\nrdXymUsv5QsBAe4JSBs2bGBaWhpDQkK4bds2t+g5OTn8c0wM81QqFrnS3za0y8LLxCIlV8/p06dp\ns9lqTLqSNB6QA6oSSTW85JupjraiAgm//IJnAew8dQrHp08HfdzWhV4IqMrLPa7TkPixrAyZe/di\n8tmzwMyZQFQU9F9/jYiICGRlZWH06NE4duwYACDCYsFrp07BYrc7LGqgRuWjCyY7G2qloiEK4ZWB\ngYGYO3cu7r///gs/vqRBkcpdcvGwf//5cn8+YoEjT/tMIRRzoivla9eR0Cm4PQ0kjADMrvVORX3F\nk08iWK/HiBEjkJmZiZtuugklJSVAdjZUSi5UH+LafcLb+alWzq4yd911F77++mts//RTd+58ZGU5\nHjySZkMOqEouHlwTZ+paNxOAnUQxHMUtqqPkty+Gcnk9RV+/3Y60nBwAjlqvO3fuxF133YUXAwOV\n6316Ubx1wtv58RJeaTQasXLMGFw6dChoMDjkNJuBe+5R9NVLGh9puUsuHtLTHYODHqgtrMCAultC\nKo2mzgWxdaWliHIWnFapVHjttdewdetWfH706AXHtdeKl/PjNc48Lw/XPf88zBUV5x9ADe0yktQZ\nqdwlFw9Kk3IsFoh581A+ZAjKFQpmEw7lTpx/ENhNJpQZDHjBaKzyu+tvrVqtWJqvXKv1eJwSrRYF\nERGVRLZi3bp1mLBxI8qVfP4NNcHHW9k5b+GV2dkQSrI1lMtIUmekW0ZyceHKN+MhjlqTlwdERXn0\nFYtqnyUA7iksxGabDdvOnKmixF1/s6TEowhF8OyqAQA7gCOpqVV+69SpE9687z6UzplTsyar0Vjn\nuHaveDk/itTTVy9pXKRyl1x8eJo4A5y3UH2Jg9dq0aNXLwQdPgxWVHg8jJLrxQTgR7MZcWfPQqPV\nQlVWBrvJBKFSYXFKCuJCQqpukJeH5AULPO9MrQZ69lQ4Uj1ROj9K1NNXL2lcpFtGIqlM5UySycmK\nClpfVgbx88+4VK9XjKJRggBizp6FDkBZWRlKAawAEG634y+ffIKJEyciNDQUcXFx6NatGx7v2RNF\nSpYx2fxuj/r66iWNirTcJZLquCxXEvjuO48Wqd1oRNItt+DYsWMoPnr0fOx5JZSsfoHzUTcu98xd\najXuysnBVddfj9mzZ6NPnz4oKChAfn4+ghYvhlGpTmpLcHt4eOOpbyoEScMhlbtEokR6uiOczwMq\njQa9Fi1CL1LRT18sBMqdMwXNcIRG6qEcAonsbOTn5yMkJARhYWHn1w0YAKxb17LdHvXx1UsaFanc\nJRIlfLVIFdoYP/wQm06exGeTJyMpIAADAgJg+Pprz8dyWuD5+fmwWq1V13l5yLQot0ddffWSRkUq\nd4nEG75YpF7aDAGQNmwYFi1ahC/+9jcs1umgKy2teRynBZ6Xl1dTuUu3h6QeyKyQEkkTceB//0Nk\nnz4weYqucWah9I+KwsGDBxEYGFizTX6+dHtIfM4K6VO0jBDiGiHET0KIA0KI+zysF0KI55zrdwsh\nLquP0BJJW6ZTr14w/vvfKDMY4PKe200mh2JfuxZ8803cn5sLv7ff9pyXxeX2eOIJx6dU7BIv1Krc\nhRBqOCK1hgFIBHCrECKxWrNhAOKdyyQAzzewnBJJm0CkpUF78iRUy5bhk6Qk3KNSYcOECeDo0cCs\nWZgHQD17tmOQ9ssvm1tcSSvGF597XwAHSP4CAEKItwCMBFC5PPtIAGucuYa3CSEChBARJI81uMQS\nSWvHYoFx+nQMnj4doVu2oOMVV1Sdvu+Kihk+3OHLlxa6pB744paJAnCk0vffnL/VtY1EIqlG9x9+\ngMlo9LxS5mWRXABNOkNVCDFJCPGNEOKbkydPNuWhJZKWyf79jZ/KV3JR4otyPwqgfaXv7Zy/1bUN\nSL5EMolkUkj1/BkSycWIKy+LJ1rKBCVJq8QX5f41gHghRKwQQgfgFgDvV2vzPoBxzqiZFADnpL9d\nIvEBmZdF0kjUqtxJlgOYDmAjgB8AvE3yeyHEFCHEFGezDwH8AuAAgFUApjWSvBJJ26K+OdQlklqQ\nk5gkkpaAnKAk8RFfJzHJ9AMSSUtA5mWRNDAyn7tEIpG0QaRyl0gkkjaIVO4SiUTSBpHKXSKRSNog\nUrlLJBJJG0Qqd4lEImmDSOUukUgkbRCp3CUSiaQNIpW7RCKRtEGkcpdIJJI2iFTuEolE0gaRyl0i\nkUjaIFK5SyQSSRuk2VL+CiFOAjjUxIe1ATjVxMdsStpy/2TfWi9tuX/N0bcOJGstZddsyr05EEJ8\n40se5NZKW+6f7FvrpS33ryX3TbplJBKJpA0ilbtEIpG0QS425f5ScwvQyLTl/sm+tV7acv9abN8u\nKp+7RCKRXCxcbJa7RCKRXBS0SeUuhLhGCPGTEOKAEOI+D+uFEOI55/rdQojLmkPO+uBD38Y6+7RH\nCLFVCNGjOeSsL7X1r1K7PkKIciHE6KaU70LwpW9CiAFCiJ1CiO+FEJ83tYz1xYf70l8IsV4IscvZ\ntzuaQ876IIR4RQjxuxDiO4X1LVOfkGxTCwA1gJ8BxAHQAdgFILFam+EAPgIgAKQA+G9zy92AfUsF\nEOj8e1hr6Zuv/avU7jMAHwIY3dxyN+C1CwCwF0C083toc8vdgH27H8CTzr9DAJwGoGtu2X3s3xUA\nLgPwncL6FqlP2qLl3hfAAZK/kCwF8BaAkdXajASwhg62AQgQQkQ0taD1oNa+kdxK8ozz6zYA7ZpY\nxgvBl2sHAHcB+CeA35tSuAvEl76NAfAvkocBgGRr6Z8vfSMAqxBCALDAodzLm1bM+kFyMxzyKtEi\n9UlbVO5RAI5U+v6b87e6tmmJ1FXuDDgsitZCrf0TQkQBGAXg+SaUqyHw5dp1BhAohPiPEGKHEGJc\nk0l3YfjSt+UALgGQA2APgBkk7U0jXqPTIvWJprkFkDQOQoir4FDu/ZtblgbmWQDzSNodRmCbQgOg\nN4BBAIwAvhJCbCO5r3nFahCGAtgJYCCAjgA2CSG+IJnbvGK1Xdqicj8KoH2l7+2cv9W1TUvEJ7mF\nEN0BZAEYRvKPJpKtIfClf0kA3nIqdhuA4UKIcpLrmkbEeuNL334D8AfJAgAFQojNAHoAaOnK3Ze+\n3QFgER1O6gNCiF8BdAGwvWlEbFRapD5pi26ZrwHECyFihRA6ALcAeL9am/cBjHOOcqcAOEfyWFML\nWg9q7ZsQIhrAvwDc1gotvlr7RzKWZAzJGABrAUxrBYod8O2+fA9AfyGERghhApAM4IcmlrM++NK3\nw3C8kUAIEQYgAcAvTSpl49Ei9Umbs9xJlgshpgPYCMco/iskvxdCTHGufwGOKIvhAA4AKITDqmjx\n+Ni3hwEEA1jptG7L2UITG1XHx/61SnzpG8kfhBD/B2A3ADuALJIew+9aEj5et8cArBZC7IEjqmQe\nyVaRKVII8SaAAQBsQojfADwCQAu0bH0iZ6hKJBJJG6QtumUkEonkokcqd4lEImmDSOUukUgkbRCp\n3CUSiaQNIpW7RCKRtEGkcpdIJJI2iFTuEolE0gaRyl0ikUjaIP8P4vTPgneL+4wAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117a45490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# draw network\n",
    "nx.draw_networkx(g, with_labels=False, node_size=50, node_color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Preprocessing/Train-Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from gae.preprocessing import mask_test_edges\n",
    "np.random.seed(0) # make sure train-test split is consistent between notebooks\n",
    "adj_sparse = nx.to_scipy_sparse_matrix(g)\n",
    "\n",
    "# Perform train-test split\n",
    "adj_train, train_edges, train_edges_false, val_edges, val_edges_false, \\\n",
    "    test_edges, test_edges_false = mask_test_edges(adj_sparse, test_frac=.3, val_frac=.1)\n",
    "g_train = nx.from_scipy_sparse_matrix(adj_train) # new graph object with only non-hidden edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total nodes: 348\n",
      "Total edges: 2866\n",
      "Training edges (positive): 1721\n",
      "Training edges (negative): 1721\n",
      "Validation edges (positive): 286\n",
      "Validation edges (negative): 286\n",
      "Test edges (positive): 859\n",
      "Test edges (negative): 859\n"
     ]
    }
   ],
   "source": [
    "# Inspect train/test split\n",
    "print \"Total nodes:\", adj_sparse.shape[0]\n",
    "print \"Total edges:\", int(adj_sparse.nnz/2) # adj is symmetric, so nnz (num non-zero) = 2*num_edges\n",
    "print \"Training edges (positive):\", len(train_edges)\n",
    "print \"Training edges (negative):\", len(train_edges_false)\n",
    "print \"Validation edges (positive):\", len(val_edges)\n",
    "print \"Validation edges (negative):\", len(val_edges_false)\n",
    "print \"Test edges (positive):\", len(test_edges)\n",
    "print \"Test edges (negative):\", len(test_edges_false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Train node2vec (Learn Node Embeddings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import node2vec\n",
    "from gensim.models import Word2Vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# node2vec settings\n",
    "# NOTE: When p = q = 1, this is equivalent to DeepWalk\n",
    "\n",
    "P = 1 # Return hyperparameter\n",
    "Q = 1 # In-out hyperparameter\n",
    "WINDOW_SIZE = 10 # Context size for optimization\n",
    "NUM_WALKS = 10 # Number of walks per source\n",
    "WALK_LENGTH = 80 # Length of walk per source\n",
    "DIMENSIONS = 128 # Embedding dimension\n",
    "DIRECTED = False # Graph directed/undirected\n",
    "WORKERS = 8 # Num. parallel workers\n",
    "ITER = 1 # SGD epochs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Walk iteration:\n",
      "1 / 10\n",
      "2 / 10\n",
      "3 / 10\n",
      "4 / 10\n",
      "5 / 10\n",
      "6 / 10\n",
      "7 / 10\n",
      "8 / 10\n",
      "9 / 10\n",
      "10 / 10\n"
     ]
    }
   ],
   "source": [
    "# Preprocessing, generate walks\n",
    "g_n2v = node2vec.Graph(g_train, DIRECTED, P, Q) # create node2vec graph instance\n",
    "g_n2v.preprocess_transition_probs()\n",
    "walks = g_n2v.simulate_walks(NUM_WALKS, WALK_LENGTH)\n",
    "walks = [map(str, walk) for walk in walks]\n",
    "\n",
    "# Train skip-gram model\n",
    "model = Word2Vec(walks, size=DIMENSIONS, window=WINDOW_SIZE, min_count=0, sg=1, workers=WORKERS, iter=ITER)\n",
    "\n",
    "# Store embeddings mapping\n",
    "emb_mappings = model.wv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Create Edge Embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create node embeddings matrix (rows = nodes, columns = embedding features)\n",
    "emb_list = []\n",
    "for node_index in range(0, adj_sparse.shape[0]):\n",
    "    node_str = str(node_index)\n",
    "    node_emb = emb_mappings[node_str]\n",
    "    emb_list.append(node_emb)\n",
    "emb_matrix = np.vstack(emb_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Generate bootstrapped edge embeddings (as is done in node2vec paper)\n",
    "    # Edge embedding for (v1, v2) = hadamard product of node embeddings for v1, v2\n",
    "def get_edge_embeddings(edge_list):\n",
    "    embs = []\n",
    "    for edge in edge_list:\n",
    "        node1 = edge[0]\n",
    "        node2 = edge[1]\n",
    "        emb1 = emb_matrix[node1]\n",
    "        emb2 = emb_matrix[node2]\n",
    "        edge_emb = np.multiply(emb1, emb2)\n",
    "        embs.append(edge_emb)\n",
    "    embs = np.array(embs)\n",
    "    return embs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Train-set edge embeddings\n",
    "pos_train_edge_embs = get_edge_embeddings(train_edges)\n",
    "neg_train_edge_embs = get_edge_embeddings(train_edges_false)\n",
    "train_edge_embs = np.concatenate([pos_train_edge_embs, neg_train_edge_embs])\n",
    "\n",
    "# Create train-set edge labels: 1 = real edge, 0 = false edge\n",
    "train_edge_labels = np.concatenate([np.ones(len(train_edges)), np.zeros(len(train_edges_false))])\n",
    "\n",
    "# Val-set edge embeddings, labels\n",
    "pos_val_edge_embs = get_edge_embeddings(val_edges)\n",
    "neg_val_edge_embs = get_edge_embeddings(val_edges_false)\n",
    "val_edge_embs = np.concatenate([pos_val_edge_embs, neg_val_edge_embs])\n",
    "val_edge_labels = np.concatenate([np.ones(len(val_edges)), np.zeros(len(val_edges_false))])\n",
    "\n",
    "# Test-set edge embeddings, labels\n",
    "pos_test_edge_embs = get_edge_embeddings(test_edges)\n",
    "neg_test_edge_embs = get_edge_embeddings(test_edges_false)\n",
    "test_edge_embs = np.concatenate([pos_test_edge_embs, neg_test_edge_embs])\n",
    "\n",
    "# Create val-set edge labels: 1 = real edge, 0 = false edge\n",
    "test_edge_labels = np.concatenate([np.ones(len(test_edges)), np.zeros(len(test_edges_false))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Evaluate Edge Embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=0, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train logistic regression classifier on train-set edge embeddings\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "edge_classifier = LogisticRegression(random_state=0)\n",
    "edge_classifier.fit(train_edge_embs, train_edge_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Predicted edge scores: probability of being of class \"1\" (real edge)\n",
    "val_preds = edge_classifier.predict_proba(val_edge_embs)[:, 1]\n",
    "val_roc = roc_auc_score(val_edge_labels, val_preds)\n",
    "val_ap = average_precision_score(val_edge_labels, val_preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Predicted edge scores: probability of being of class \"1\" (real edge)\n",
    "test_preds = edge_classifier.predict_proba(test_edge_embs)[:, 1]\n",
    "test_roc = roc_auc_score(test_edge_labels, test_preds)\n",
    "test_ap = average_precision_score(test_edge_labels, test_preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "node2vec Validation ROC score:  0.893906792508\n",
      "node2vec Validation AP score:  0.872970914172\n",
      "node2vec Test ROC score:  0.884371599215\n",
      "node2vec Test AP score:  0.839029679154\n"
     ]
    }
   ],
   "source": [
    "print 'node2vec Validation ROC score: ', str(val_roc)\n",
    "print 'node2vec Validation AP score: ', str(val_ap)\n",
    "print 'node2vec Test ROC score: ', str(test_roc)\n",
    "print 'node2vec Test AP score: ', str(test_ap)"
   ]
  }
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