{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "\n",
    "<h1 style=\"font-size: 2em;\">An Introduction to Relations using Sage&nbsp;</h1>\n",
    "<p><strong><em><a title=\"Applied Discrete Structures\" href=\"http://faculty.uml.edu/klevasseur/ads2\" target=\"_blank\">Applied Discrete Structures</a>&nbsp;</em>by Alan Doerr &amp; Kenneth Levasseur is licensed under a Creative Commons Attribution - Noncommercial - ShareAlike &nbsp;3.0 United States License.</strong></p>\n",
    "<p>This document describes the basic ways in which a relation can be represented with Sage. &nbsp;These topics are introduced in chapter 6 of&nbsp;<em><a href=\"http://faculty.uml.edu/klevasseur/ads2\">Applied Discrete Structures</a></em>.</p>\n",
    "\n",
    "<p><strong>Example 1.</strong> &nbsp;Consider the \"random relation\" the set of digits, 0 through 9, which each pair of digits is related with probablity 0.25. &nbsp;The list of digits, which we call A, is created using <span style=\"font-family: 'courier new', courier;\"><strong>range</strong></span>. &nbsp;In Python, the default first number in range is 0 and the list specification is \"open on the right\" so that the upper limit is not included. &nbsp; &nbsp;Therefore <span style=\"font-family: 'courier new', courier;\"><strong>range(10)</strong></span> produces the digits 0 through 9.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 10)"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=range(10)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>Here is the complete list of pairs from which we draw approximately 25% for our relation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0),\n",
       " (0, 1),\n",
       " (0, 2),\n",
       " (0, 3),\n",
       " (0, 4),\n",
       " (0, 5),\n",
       " (0, 6),\n",
       " (0, 7),\n",
       " (0, 8),\n",
       " (0, 9),\n",
       " (1, 0),\n",
       " (1, 1),\n",
       " (1, 2),\n",
       " (1, 3),\n",
       " (1, 4),\n",
       " (1, 5),\n",
       " (1, 6),\n",
       " (1, 7),\n",
       " (1, 8),\n",
       " (1, 9),\n",
       " (2, 0),\n",
       " (2, 1),\n",
       " (2, 2),\n",
       " (2, 3),\n",
       " (2, 4),\n",
       " (2, 5),\n",
       " (2, 6),\n",
       " (2, 7),\n",
       " (2, 8),\n",
       " (2, 9),\n",
       " (3, 0),\n",
       " (3, 1),\n",
       " (3, 2),\n",
       " (3, 3),\n",
       " (3, 4),\n",
       " (3, 5),\n",
       " (3, 6),\n",
       " (3, 7),\n",
       " (3, 8),\n",
       " (3, 9),\n",
       " (4, 0),\n",
       " (4, 1),\n",
       " (4, 2),\n",
       " (4, 3),\n",
       " (4, 4),\n",
       " (4, 5),\n",
       " (4, 6),\n",
       " (4, 7),\n",
       " (4, 8),\n",
       " (4, 9),\n",
       " (5, 0),\n",
       " (5, 1),\n",
       " (5, 2),\n",
       " (5, 3),\n",
       " (5, 4),\n",
       " (5, 5),\n",
       " (5, 6),\n",
       " (5, 7),\n",
       " (5, 8),\n",
       " (5, 9),\n",
       " (6, 0),\n",
       " (6, 1),\n",
       " (6, 2),\n",
       " (6, 3),\n",
       " (6, 4),\n",
       " (6, 5),\n",
       " (6, 6),\n",
       " (6, 7),\n",
       " (6, 8),\n",
       " (6, 9),\n",
       " (7, 0),\n",
       " (7, 1),\n",
       " (7, 2),\n",
       " (7, 3),\n",
       " (7, 4),\n",
       " (7, 5),\n",
       " (7, 6),\n",
       " (7, 7),\n",
       " (7, 8),\n",
       " (7, 9),\n",
       " (8, 0),\n",
       " (8, 1),\n",
       " (8, 2),\n",
       " (8, 3),\n",
       " (8, 4),\n",
       " (8, 5),\n",
       " (8, 6),\n",
       " (8, 7),\n",
       " (8, 8),\n",
       " (8, 9),\n",
       " (9, 0),\n",
       " (9, 1),\n",
       " (9, 2),\n",
       " (9, 3),\n",
       " (9, 4),\n",
       " (9, 5),\n",
       " (9, 6),\n",
       " (9, 7),\n",
       " (9, 8),\n",
       " (9, 9)]"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuples(A,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>The result of the next expression is random. &nbsp;The output represents a fundamental way to represent any relation as a set of ordered pairs.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 7),\n",
       " (0, 8),\n",
       " (1, 6),\n",
       " (2, 0),\n",
       " (2, 1),\n",
       " (2, 9),\n",
       " (3, 3),\n",
       " (3, 5),\n",
       " (3, 9),\n",
       " (4, 6),\n",
       " (5, 5),\n",
       " (5, 9),\n",
       " (6, 1),\n",
       " (6, 8),\n",
       " (6, 9),\n",
       " (7, 1),\n",
       " (7, 5),\n",
       " (8, 6),\n",
       " (9, 4),\n",
       " (9, 5)]"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r=random_sublist(tuples(A,2),0.25)\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>\n",
    "    Next, we'll be creating a dictionary and will need to extract the entries of pairs.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pair=(4,5)\n",
    "pair[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>There are several wasy to create a directed graph (<span style=\"font-family: 'courier new', courier;\"><strong>DiGraph</strong></span>) in Sage. &nbsp;The most basic as a dictionary. &nbsp;The following code creates a dictionary corresponding to the relation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "rd={}\n",
    "for p in r:\n",
    "    if p[0] in rd:\n",
    "        rd[p[0]].append(p[1])\n",
    "    else:\n",
    "        rd[p[0]]=[p[1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>To recover the information defined within a (small) dictionary, use the <c>keys</c>, <c>values</c> or <c>items</c> methods. &nbsp;With <c>items</c>, the result is a list of pairs where the first entry is related to all values in the list that makes up the second entry.  You can recover just the first entries, with <c>keys</c>, or the second entries of items with <c>values</c>.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_items([(0, [7, 8]), (1, [6]), (2, [0, 1, 9]), (3, [3, 5, 9]), (4, [6]), (5, [5, 9]), (6, [1, 8, 9]), (7, [1, 5]), (8, [6]), (9, [4, 5])])"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rd.items()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys([0, 1, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rd.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_values([[0, 3, 4, 5, 7], [5, 6, 8], [0, 3, 9], [6, 9], [0], [0, 2, 9], [9], [2, 3, 5, 7], [0, 1, 6, 8]])"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rd.values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Now we can create a digraph using the dictionary <c>rd</c>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Looped digraph on 10 vertices"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g=DiGraph(rd)\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>We can plot the graph. For larger relations, the information you get may not be very easy to read, but here it is clear.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UVAdLxw7D0M62kCthLDo2IREn7z3BjgvXQThcHDh4ECNGjBC6Tkq1hZoxJQ8+n4/z589j+fLliIqKYs6rqalh06ZNmDJlSqWPCxdHp06d8OLFCwBASEgIDA0NWVZEESeEEHz//l1gSVVxEdvyUVVVZTbCaN++PaytraGgoMC87+7uXmpktzFjxuD48eNCbaCRnp6OwYMGwc3dHascRmHFhBGQEWEJV2xCImbvPICrbq+wdu1arF27lo4p12yoGVMAT09PzJ8/H15eXsw5aWlpzJ07F6tXr5aoKEuJiYlQU1NDbm4u9PT08OXLF3oTqwHEx8cL7PHs7e1d4h7PMjIysLS0ZFrOHh4e2LZtW6n1tG7dGjdv3iyxGzwnJwcD+vfHy5cvcGvrWnS1Ni/TZwKALWcuw+nQSWzevBkrVqwoczmUKg8145pMREQEli1bxuwFnE///v2xY8cOGBgYsKSseK5cucJ0682dO1dgQg6l5pCdnY13794JTAyLjY0VS9kNGjTArVu3YGlpWeT7zs7OWLNmDR7s3oTurS3KXd/aY2ex6eQFvHz5ktmBjFLjoGZcE0lPT8f27duxdetWZGRkMOeNjIywe/fuIuNGSwoTJkzAmTNnAACPHj2SaK2UyoMQgi9fvggsqQoNDS1zeQoKCjh9+jSGDRsmcP79+/ewsLDAwpGD4DJzUnllA8hbBmU3cyli0jIRGBQERUVFsZRLqVJQM65JEEJw6dIlLFu2DL9+/WLO161bFxs2bICjo6NEhy7k8/nQ1NREbGwslJSU8PfvX8jJybEtiyKhxMbG4u3bt3B1dWUe4ERlzZo1WLt2LTM5bMjgwQj280HQ2YPFTtRad/wsNvx7XuCcRl1V/L53sdh6Qn/+Qssx07F3717MmjWrTFopVZpSzZjGF6wm+Pj4wNbWFqNHj2aMWEpKCnPnzsWXL18wa9YsiTZiIO8z5HdFdu/enRoxpUTq168Pe3t7tG7dusxlbNiwAaampsjOzkZERARu3b6N+SMGljhjGgCMdRsj6u4F5gg6d6jE9IaNG2GQXTsc+OefEtdgU2oukn13ppRKVFQUVqxYUahl0KtXL+zatQstWrRgSZno3Lt3j3ndt29fFpVQqhKvX78uV/4PHz5g//794PF4kJeVxdiepS/vk5aSgma9uiLV4ziwD7rPXQEfH59yPUBQqie0ZVxFycjIgLOzMwwMDASMuHnz5rh//z4ePHhQpYwYEDTjPn36sKiEUpV48+ZNufJLSUmhW7du8PLygo2xIVSUSh/T/fIrEg36j4bu4AkYtdoFYZG/S83ToVVLyMrIwNvbu1x6KdUT2jKuYhBCcO3aNSxZsgQ/f/5kztepUwfr1q3DzJkzISMjw6LCsvH792+8e/cOAGBubg5tbW2WFVGqAuHh4QLzI4RBUVERbdu2RceOHZmwnIqKivDz9cXwjjal5rcxbo7Ta5bAoFED/IlPgPOpi2g/bSHeXziCerWLD9sqKyMDE/2mhaKEUSgANeMqhb+/P+bNm4dXr14x57hcLqZPn47169dX6Xi49+/fZ17TLmqKsAjTKlZVVUWHDh2Yw8LCosgH1sioKOhqlxyGk8/nQ7+hNgK/hMHrYwhyeLkY3tUOK4+cwj9Xb2HtlHEl5tfV0kBkKRtrUGom1IyrANHR0Vi5ciVOnjwpMPmje/fu2LVrF1q2bMmiOvFAx4spZSExMbHQOW1tbXTs2BEdOnRAx44dYWRkVOpe2IQQ5ObmQlq6cLq0jExcePwMl5+8gG/IZySn/S/OtrSUFHj/H4Jz/b/ncezWQ7Q1aYGJ/XqgVxurQvXKSEsjJzOnDJ+UUt2hZizBZGVlYc+ePXB2dkZKSgpzvlmzZti5cyf69etXLaJTZWVl4fHjxwDywnNaW1uzrIhSVRg3bhw+fvyIjIwM2NraomPHjmjatKnIvwsOhwMFBQUBo/0d9xdbzl7BmftPkZyWjp42llg6djgsm+vDwlAfanVqg8PhID0jE/pDJ6KjuQmaamvikacf+i1ag6bampg5pD9mD+3PzM5OSk2DsmrFbOtIqdpQM5ZACCG4efMmFi9ejLCwMOZ8rVq1sGbNGsyZM6dabZz+8uVLZju63r17S0yMbIrko6ysjP3794ulLGMjIwR9+Q5CCM49dMO83YchxeVixuB+mDawN5poaQIAFu87BnlZWehoqiMmIRHOJy8iLTMLW2dNRmMtDWyeMRHeH0Nx6PpdOB06iZN3H+HkqkWwNjJE4LcfGD2hk1j0UqoX1IwljMDAQCxYsADPnj1jznG5XEydOhUbNmyAuro6i+oqBtpFTZEErKyt4X7/HgYtW4/brzwxukdn7F04o9CkrMjYOIxeuwVxicmoX6c22rRsDo/ju9FYK2+7RA6HAxvj5rAxbo5Fo4dg4qadaDdtAeYMs0fEnxhYWVmx8fEoEg6NwCUhxMTEYPXq1Th+/Dj4fD5zvnPnztizZw9MTU1ZVFexNGvWDF+/foWUlBTi4uIkauMKSs3h1KlTmDhxImopKeLU6sUYaNdOLOXm8HhwOX0Z64+fBTgcREZGlmm/ZkqVhkbgknSys7Oxc+dONGvWDEePHmWMWFdXF66urnBzc6vWRvz582d8/foVAGBra0uNmMIKSUlJ2Lt3L7hcLrq1thCbEQN5k7ZWTRwF9f8PErJ69WoahYtSCNpNzRKEENy5cweLFi1izAgAVFRUsGrVKsybN69GhIOkXdQUtiGEwMHBAT9//sTs2bNx8OBBBH4Jg1kzXbHVcfjGPfz5G4/Vq1dj48aN8PLywuDBg1GvXj0oKioWeSgoKBT6f2mzwilVF9pNzQLv37/HggUL8PTpU+Ych8PBpEmTsGnTJmhqarKornLp1q0b3NzcAOSFJTQyMmJZEaWmcf78eYwdOxaurq7o06cPrCwtIZ2TBc/juyErhgA636OiYTp2BsaOH481a9agQYMGZS5LXl4eysrKGD9+PHbu3FlubZRKg+7aJAqEEPj5+cHb2xt+fn6IiopCLo8HZRUVGBsbw8rKCh07doSqqmqZyo+Li8PatWtx+PBhgXHhDh06YM+ePbCwKP/eqVWJlJQU1KtXDzk5OWjSpAnCwsKqxVItStUhOjoaRkZG6NmzJy5ezNt1yc/PD23btsXQzu1xZs2Scs3uj0tMQqdZS5HB5yAwKAh8Ph+qqqpi6aZOTU2FkpJSucuhVAp0zFgY0tPT8c8//8DYyAjW1taYN28u/N+8gnx6MmrnZiI18ieOHjyAgQMHQltbGxMnTkRAQIDQ5efk5GDv3r1o1qwZDh48yBhxkyZNcPXqVbx48aLGGTEAPHnyBDk5eQEQ+vbtS42YUuls27YNAASWR1laWuLChQu44vYKI1ZtRlJqWpnK/hweAbuZS/E3NQMPHz2CiooKateujX379pVbd8eOHakRVzNqfMv45cuXmDRxIn78/IlBdu0wzb43OrRqWWgLNUIIfv2JxflH7jhy8wF+/YnBwoULsXHjRigoKBRb/v3797Fw4UKBjdCVlJTg5OSEhQsXQl5evsI+m6QzefJknDhxAkDe99S7d2+WFVFqEunp6WjQoAGmTp3KmHJBbt26hXHjxqK2ogKOLJuLXm2shHpgzOHxsO/KLaw+egaNGjXCvfv30axZM+Z9QghGjBiBq1evllm7l5cX3fmpakG7qYuDEIKNGzdi7dq1aG9mjH+dFsBAp6FQeXm8XOy+5Io1x85CV1cXDx4+ROPGjQXSfPr0CQsXLsTDhw8Fzk+YMAGbN2+u8Rsh8Pl8NGjQANHR0VBQUMDfv39LfKihUMTNyZMnMXnyZHz9+hW6ukVP1goPD8eUyZPx5OlTtDLQx4zBfdGrjRUaqqsJGHNubi5CwyNwxe0lDrneRVxiMubNmwdnZ2coKhbeBerv37/Q09NDUlKSyLqHDx+Oy5cvi5yPwirUjIvDyckJLi4uWDdlHFY6jCzTuNCnH+Hov3gdeFwpvHr9Gjo6OoiPj8f69etx4MAB5P5/zFoAaNeuHfbu3UsX/P8/fn5+zHfRr18/3Llzh2VFlJpGz549QQhhQrEWhY+PD7S0tBAcHIxDBw/i7r17IIRAva4qmjXShqy0DFIzMvDxezjSMjLA5XLB5/MxZ86cUrujb968iUGDBomkWUZGBiEhIcU+PFAkllLNuEYubTp79ixcXFywfc5ULBo9pMzltGiigxcHt6HDjMXo368fJk6ahI0bNyI+Pp5J06hRI2zbtg0jRoygY6IFoEuaKGxCCIGvry/mzZtX5PtJSUmwt7fHixcvICUlhd+/f+P2nTuIjo6Gt7c3fH198fPnT2RnZ6OpoiKGOUxGw4YNMXr0aACAm5sbCCEl/ubz56BERUUJrXvGjBnUiKspNa5lHBUVBWNjI/RrY4Uza5eIpcyAz99gPWkOcnP/N0NaUVERy5Ytw+LFi4vspqrp2NjYMJus//z5Ezo6OiwrotQkfvz4gaZNm+Lu3buFHgZfvnyJcePGITw8nDnn5uaGLl26lFqura0ts61jQEAAzMzMSkw/b948HDx4EDweTyjdurq62L59OwYNGkQf7qsWdDb1f1myZAnkpaWwZ/50sZXZykAPKx1GMT+OMWPGIDQ0FGvWrKFGXAR//vxhjNjU1JQaMaXSyV8NYW5uzpzLysrCsmXL0KlTJwEjBiD02v8xY8Ywr8+fP19qehsbG/B4PKGNNSwsDEOGDEGHDh3g4eEhVB5K1aBGmfHv379x5coVLB83HHVrq5Sa/uD1O9AdPAEKdv1h5TAbrwLeF5t22djhqK2shNGjR+PcuXNo2FC4yWA1kQcPHjCvaRc1hQ3y90GuXz9vO8P379/DxsYG27ZtK3INsLCTC4cNGwZp6bzRv4sXLwrEEygKNTU1AMDs2bNLTKepqQlbW1vm/2/evEG7du0wdOhQfPnyRShtFMmmRpnxiRMnICsjjfG9u5Wa9vLTF1iw5wicHEbi3ekDsDVriT4LVyE8OqbI9ArycpjcvycePniArKwscUuvVtDxYgrb5K9v53K52LVrFywtLREYGFhsemGXIKqpqaFnz54AgIiICLx69arE9PnGPXPmzBJjDWzbtg0vX77E7du30bx5c+b89evXYWRkhLlz5yI2NlYojRTJpEaZsdvTp+hhbYE6Ksqlpt190RWT+vfElAG90aKJDvYsmI5G6vVxyPVusXmGd+2I+ISEEn/UNZ2cnBxm9mrdunXRpk0blhVRaiL55tqlSxcsWrQI2dnZJaYXZdld/iQuALhw4UKJafMf3FVUVHD27Nki49Gbm5tjzJgx4HA46N+/P4KDg3H48GFoaORt2cjj8bB//37o6+vDxcUF6enpQmulSA41xoz5fD7e+b+DZYtmpabNzsmBX+gX9Ggt+KTa3cYCHsGfis1notcU0tJS8PPzK7fe6srr16+RnJwMAOjVq1e5Qg1SKGWBEIJPn/J+xy9fvhQqjyhmbG9vz0THunr1aolG//PnT0hLS6NevXowMjLCli1bCqXZvn27wAYR0tLScHR0xNevX7F27VpmXkpycjKcnJxgYGCAU6dOCSytpEg+NcaMo6OjkZSUDBO9JqWmjUtMRm4uHxp1BWNQa6iqIrrAsqX/Ii8nC8PGOvj48WN55VZbaBc1hU3i4+MxatQouLi4CJ2Hw+FA9j8R+UpCSUkJAwYMAAAkJCTg7du3xab19fWFsbEx01KfO3euwKztXr16oWvXrkXmVVZWxrp16/D161dMmzaNMezIyEhMnDgRFhYWePTokdC6KexSY8w4v+tGRYTZzf+d4EhAwCllhrqygjztJiqBfDPmcrno1asXy2ooNYn8vcFFjV6loKAg8jKiPn36MK9LCiri5+cHS0tL5v9cLhenTp1Cy5YtoaurK1Qcay0tLRw5cgTv379H//79mfNBQUHo1asXevToIVIsfQo71Bgzlvn/rdCy/3/iRkmo1akFKSkuov8mCJyPSUgs1Fr+Lzk8nkhP0TWJsLAwhISEAADatm2LunXrsqyIUlP4/v07+vTpg8jISJHzliVMa/fu3ZnXxZlxZGQkgoOD0bZtW4HzjRo1QnBwML59+yYQ07o0WrRogdu3b+P58+ewtrZmzj958gQWFhaYMGFCoSVbFMmhxpixpqYmZGRk8DWi9Gg3sjIysDRshic+/gLnn3r7o61Ji2Lz8fl8fI2IKve62fT09Go5M5J2UVPYIjc3t9RlRsVRFjPW0NBAq1atAADv3r0r8vd87NgxyMvLY/jw4WXSVRx2dnbw9PTExYsX0bRpUwB54+RnzpyBgYEBli1bxiztokgONcaM5eTkYNKyJfxCvgqVfsGowfj39kOcuPMIn36EY8GeIwj/E4Ppg4o3kW+Rv5GcmlZi/Onc3FxERETg7du3uHz5MrZv3445c+bA3t4eFhYWUFNTg5KSEtTV1YsN1VdVoWZMYQt9fX08fPgQLVu2FDlvWTcw6dGjB4A8I3z69KnAezk5OTh69CjGjRuHWrVqlan8kuByuRg5ciQ+ffqEXbt2MXuwZ2VlYdu2bdDX18fevXtLnUVOqTxqVDjM2bNn49a1qwi7dhLS0qXP4j14/Q62n7uK338T0FK3MXbNc0RHc5Ni0++/eguL9h3Dnz9/8O7dOzx48ABcLhdRUVEIDw9HeHg4IiMjhZ7laGFhUW1mZqelpaFevXrIyspCo0aN8PPnTxrOj1Lp5Obm4syZM1i9erXQXdampqZlWq7o5uaGbt3yYho4ODjg5MmTzHt79uzBggULEBQUBBOT4u8p4iIhIQEuLi7Yt2+fQBwEXV1duLi4YNiwYfT3WLHQXZsK8u7dO1haWuLmtrUY0KFt6RlEgBCClmOmo6WVNRYsWIh27dqVu8zly5eLNOtTkrl9+zbs7e0BANOnT8ehQ4dYVkSpyWRkZGDv3r1wcXFhltoVR+vWreHl5SVyHVlZWVBVVUVGRga0tbUREREBDoeDL1++wMzMDFOnTsXevXvL+hHKxM+fP7Fq1SqcO3dO4Hzr1q2xY8cOdOjQoVL11CBobOqCWFhYwKZ1a2w5c0Xsa/BuvfTAp+8/MWPGTGRmZoqlzHHjxomlHEmAdlFTJAkFBQUsX74cHz9+LHXCZVm7qeXk5NCpUycAeRvUfPjwATk5OZg4cSK0tbWxefPmMpVbHho3boyzZ8/Cz89PYAmVt7c3OnbsiIEDBzKTLCmVS40yYwDYtn07PN9/wv6rt8VWZnxSCmbu+Ad9+/RBp06d0LlzZ8yZM6dcZZqbm8PIyEhMCtmFEMKYsby8vFC731AolYG7u7tYo2/9l/xxYwB4+PAhJk2aBC8vL5w8eZIJDMIGFhYWePr0Ke7fvy8wjn7r1i20bNkSM2bMQHR0NGv6aiI1zow7duyIuXPnwunwKXi+Lz6alrDweLmY5LwTmbxcHD12jBl32bdvH9atW1fmcqtTqzgwMJAZn+vcuTPdyYoiMRw4cIB5nb8toaGhoUAaZeXSw+cWR0Ez3rVrF86fP49z585JRHcwh8NB7969ERAQgH///Rfa2toA8sbVDx8+DH19fWzYsAFpaWksK60Z1DgzBoAtW7bAysoKfRaugUdw2aNlZefkYOy6rbjv4Yvz5y8wF3M+a9aswaJFi0QuN38mZHWBdlFTJBE/Pz9mLNjU1BRXr17F7NmzERoaip49e6JVq1ZQUVHBxIkTy1xHixYtmBjSv3//xunTpzFixAix6BcXUlJSmDRpEr58+YJNmzZBRSVvR7u0tDSsXbsW+vr6OHbsmNB7LlPKRo00YwUFBdy9dw8mZmboNGspnE9dBI8n2hhywOdvsJk8HzdfeeLKlSsCEXfy4XA42L59O6ZNmyZS2Xw+H506dcLGjRvx/ft3kfJKItSMKZJIwVbxrFmzICUlhb179+Lo0aN4+/Yt4uLicP78efTu3btM5WdnZ2PXrl2Ii4tjzgm7LzIbKCoqYuXKlfj69StmzZrF7CgVHR2NadOmwczMDHfv3i1yi0mKGCCECHtUOzIyMsjy5csJl8slJvpNyb8rF5K0Z7cI3+NhsYf/mYNkqn1vIi0tTUxatiR+fn6l1sPj8cjo0aMJ8maki3zY2tqSI0eOkPj4+Er4VsRLbGws4XA4BAAxMjJiWw6FQggh5O/fv0ReXp4AILVr1yapqakC7//8+ZN0796dACAtW7YkBw8eJMnJyUKV/fPnT7Jy5Uqirq5OOBwO6d27N/NbXrx4cUV8nAohNDSUDB48uND9qFOnTsTHx4dteVWNUj22RptxPl5eXqR3r16Ew+EQZUUF0tPGkqx0GEWOrZhPTqxaSHbPn04c+vYgLfWaEgBEW0uLbN68mWRlZQldR3Z2NrG3ty/VeOXk5EiHDh2KfE9WVpYMGTKE3Lx5U6S62eTs2bOM/iVLlrAth0IhhBCyY8cO5rqcN29ekWn4fD558uQJGTRoEOFyuUReXp60adOGzJo1i5w4cYLcuXOHPHz4kNy8eZPs27ePjB8/nhgbGxMOh0NUVFTI7NmzycePH0lcXBzzQGpiYlK5H1QMvH79mrRt27bQ/WjUqFEkLCyMbXlVBWrGotC/f38CgHA4HFKvbl3mopORkSEW5uZk6tSp5Pr16yQ7O7tM5WdmZjJP28UdEyZMIITkPV1v3ryZtGjRosh09erVIzNnziRv374lfD5fjN+CeBk5ciSj+fnz52zLoVBIbm4u0dPTY67LkJCQUvOEh4eTXbt2kdGjRxNDQ0PGXAs+KFtZWRFHR0dy6tQpkpKSIpDf2tqaSRsVFVVRH63C4PP55Nq1a0RfX7/Q5164cCH5+/cv2xIlHWrGwpKbm0vU1dUJAKKsrEyys7MJj8cjWVlZYjW71NRUYmtrW6wZP336VCA9n88nfn5+ZP78+Yy+/x76+vpk3bp15OvXr2LTKQ5ycnJInTp1mK7Asj7EUCji5OHDh8xvp1u3bmUqIy0tjURHR5Pw8HASExNT6rW9cuVKps5Tp06VqU5JIDs7m+zfv5+oqakJ3IPq1KlDtm/fTjIyMtiWKKlQMxaWwMBA5sLq169fhdaVmJhILCwsCplqgwYNCI/HKzZfTk4OuX//Phk1ahRRUFAo0pjbtWtHDh06JBFPqi9fvmR0jRgxgm05FAohhJBp06Yx1+W1a9cqpU43NzemztmzZ1dKnRVJYmIicXJyYsbd84/GjRuTc+fOkdzcXLYlShrUjIWl4BjS3r17K7y+2NhYYmRkJHAhizKmmpSURE6ePEm6dOlSqMssv/to0KBBxNXVlWRmZlbgJymeZcuWMXrOnDnDigYKpSB8Pp80aNCAmZ/x34lbFUVMTAzzW+jcuXOl1FkZ/Pr1izg4OBS6B1lYWBA3Nze25UkS1IyFpVevXsyF9OHDh0qpMzIyUmDsKjg4uEzl/Pr1i2zdupW0bNmyyNayqqoqmT59Onnz5k2lji/n6+FwOCQmJqbS6qVQisPf35/5XfTu3btS665fvz4BQDQ0NCq13sogMDBQ4B6af/Tp04e8f/+ebXmSADVjYcjMzGS6fbW1tSvVsH79+kVmz54tlpYjn88n/v7+ZOHChURTU7NIY9bV1SVr1qwhX758EYP64vn58ydTZ5s2bSq0LgpFWDZt2sRcl//880+l1t2pUyem7ri4uEqtu7J48uQJadWqlcA9h8vlksmTJ5PIyEi25bEJNWNhePbsWaHZzFWdnJwc8vDhQzJmzBiiqKhYpDG3adOGHDhwoEJuDAcPHmTq2bhxo9jLp1DKQsElOt+/f6/UumfNmsXU/eLFi0qtuzLJzc0lZ86cIY0aNRK43ygoKJBVq1YJvV67mlGqx9bICFz/5cmTJ8zr/P1HqzrS0tLo2bMnzp07hz9//uD06dPo1q2bwJ6lnp6emDVrFrS0tDBw4EBcv35dYK/T8nD37l3mNY26RZEEYmNj4enpCQAwNjZGkyZNKrX+ghu/fPxY9jC8kg6Xy8W4ceMQGhqKrVu3onbt2gDytq3ctGkT9PT0cPDgQeTk5LCsVMIQxrFJNW8Zt27dmnl6+/37N9tyKpSIiAiybds2YmJiUmRruU6dOmTatGnk1atXZe6uT0tLY2ZZVna3P4VSHGfOnGGu86VLl1Z6/c+fP69WM6qFJTY2lsybN4/IyMgI3GsMDAzIjRs3asr9gXZTl0Z8fDzhcrkEyAt7V5MIDAwkixcvJlpaWkUac5MmTciqVatIaGioSOXevXuXKWPKlCkVpJ5CEY0RI0aw2k0cGxtbLWdUC8vXr1/J8OHDC91nbG1tiYeHB9vyKhpqxqVx/fp15qJYsGAB23JYgcfjkcePH5Nx48YRJSWlIo25devWZP/+/SQ2NrbU8mbMmMHku3HjRsV/AAqlFLKzs0nt2rWZ3p+cnBxWdOQH7qmOM6qFxdPTs8iQv0OHDq3wiaUsQs24NKZPn85cDPfu3WNbDuukpqaSs2fPkh49ejA9BgUPaWlp0r9/f3LlypUio+3w+Xyio6PDrHX+b1hACoUNCnYRjxw5kjUdNWFGtTDw+Xxy69Yt0rx580L3lzlz5gj10F/FoBO4SuPp06cAABkZGXTs2JFlNeyjpKSEsWPH4tGjR4iIiMDOnTvRqlUr5n0ej4c7d+5g+PDh0NTUxNSpU/Hy5Uvw+XwAwIcPHxAeHg4AsLOzK9fG7BSKuJCUbTyNjY2Z1x8+fGBNB9twOBwMGDAAwcHBOHToENTV1QHk3V/2798PPT09uLi4ICMjg2WllUeNNuMfP37g69evAIC2bdtS4/gPWlpaWLhwIfz9/REcHIylS5eiQYMGzPtJSUk4fvw47OzsoKuri5UrV+LkyZPM+/369WNDNoVSiHwz5nK56NWrF2s6CppxdZ5RLSzS0tKYPn06vn79irVr10JRUREAkJycDCcnJxgYGOD06dPIzRVtv/nS4PP5yMzMFHu55UKY5jOppt3Ux44do2thRYTH45GnT5+SCRMmEGVl5SLHl/MPLy8vtuVSKCQsLIy5Jtu1a8eqlhcvXtTIGdXCEhUVRaZOnVpoiMzMzIw8evSozOWmpKSQY8eO5e26ZWAgEL6zUcOGZODAgWTbtm0kOjpajJ9GANpNXRLVcX1xRSMlJYWuXbvi1KlT+PPnD86fP49evXqByy18KbVr1w79+vXD5cuXa1R3E0WykJQuaoB2U5eGlpYWjh49iuDgYIGetcDAQPTs2RM9e/ZEYGCg0OUlJCRg/vz5aNBAG46OjvgW9A5dTQxxYPFsnFq9GEdXzMMIuzZIjviBtWtWo1GjRhg1ahTCwsIq4uOVCIcQImxaoRNWBfh8PtTV1fH371/Url0bcXFxkJaWZltWlSU6OhpLly7F2bNni3y/Vq1aGDp0KMaOHQs7O7sizZtCqQj69OmDBw8eAAACAgJgZmbGqh4NDQ3ExMRAQ0MD0dHRrGqRdJ4/f47FixfDz8+POcfhcDBu3Dhs2rQJjRo1KjbvvXv3MG3qVKSmJGPWkP6YZt8bjbU0ik2fkJyC0/efYs/lm4hLTsHWrVsxc+ZMcd2rOKUlqLF3xICAAPz9+xcA0LlzZ2rE5URTUxMFH+xGjhwp8ENJTk7GiRMn0KVLFzRp0gQrVqygY2aUCocQAh8fHwCAuro6TE1NWVb0v9bxnz9/mHsQpWg6deoEb29vXLx4kYmYRgjBmTNnYGBggBUrViApKalQvm3btqFfv34wbdwA788fhvN0hxKNGABUa6lg/shBeH/+MCb06oI5c+ZgwoQJ4PF4FfHRClFjzTh/FjUAdO/enUUl1YPc3Fym9aGiooLTp0/jx48fcHd3x8SJE6GiosKk/fXrF7Zs2QJjY2NYWlpiz549+PPnD1vSKdWYmJgYxMXFAQBMTU0FwsGyhY6ODvM6JiaGRSVVAy6Xi5EjRyIkJAQ7d+6EqqoqACAzMxNbtmyBnp4e9u3bh+zsbADA7t27sWzZMqx0GIV7uzaioXp9kepTVlTAgSWzcXHjCly6dAkTJ06ECD3IZabGmjEdLxYvXl5ezFN+jx49ICsrCy6Xi86dO+PEiROIjo7GxYsX0bdvX0hJSTH53r17hwULFqBBgwbo06cPLl68iPT0dLY+BqWaERwczLw2MTFhUcn/qFWrFvM6OTmZRSVVCzk5OSxcuBDfvn3D4sWLISsrCwD4+/cv5s2bByMjIzg7O2Px4sVYMnYYNjpOKNfD14hudji9ehHOnTuHo0ePiutjFEuNNOOMjAy8evUKQN5TarNmzVhWVPUpbZKMoqIiRo4cibt37yIqKgp79+6FlZUV835+y3r06NHQ0NCAg4MD3NzcJGvpAaXK8f79e+Z1y5YtWVTyP/I3TgCoGZcFVVVVbN++HaGhoRgzZgxz/tu3b1i7dg0sDPXh7OgglrpG9eiMyQN6YfHixfjx44dYyiyOGmnGb968YXYn6t69u0R0XVV1Cppx7969S0yrrq6OuXPnwsfHBx8/foSTk5NA111qaiqzy1Tjxo2xbNkygZsqhSIskt4yLmq8kyIcTZo0wblz5+Dr64vOnTsDyBtPPrV6EaSlpYrMc8j1LszGTkftroNRu+tgtJs6Hw88fEqsZ+fcqailII/169eL/TMUpEaaMe2iFi8RERHMcgMrKytoamoKnbdFixZwdnbG9+/f8fz5c0yePFngZhUZGYlt27bBxMQE5ubm2LVrF37//i32z0CpnuQ/xHE4HIEtDNmEdlOLF0tLSzx9+hSNdRphkF17GDVtXGzahvXV4DJzEnxO7oPPyX3obNkKA5eux4ewH8XmqaWkhFlD+uHSpUuIj4+vgE+QR40044KTt7p27cqikurB/fv3mddlXcfJ5XJhZ2eH48ePIzo6GleuXEH//v0FZrkHBARg0aJFaNiwIXr16oVz584hLS2t3Pop1RM+n8+s5dXV1YWSkhLLivKg3dTix9vbGz/Df2HG4JKj/vXv0AZ92rWGgU5DGOg0hPN0BygryMPzfUiJ+Sb374XcXB4uXbokTtkC1DgzjouLg7+/PwCgVatWqF9ftJl2lMKIO6iCgoIChg0bhtu3byMqKgr79+9H69atmff5fD4ePXqEcePGQUNDA+PHj8eTJ09YG1+Oj4+Hn58fPD09ERAQgNTUVFZ0UAT58eMH87AmKePFAO2mrgg8PDwgLyeHjq2EH4rIzc3FpSfPkZaZhbYmLUpMq163DswN9OHh4VFeqcVS48zY3d2dmaZOlzSVn8zMTKanQUNDA5aWlmItv379+pg9eza8vLwQEhKCVatWMesNASAtLQ1nz55Fjx49oKOjgyVLliAoKEisGv4LIQTPnz/H2LFjodu0KerVqwcrKyu0bdsW5ubmqFWrFoxatMDMmTMrXAuleCRxvBigLeOKwM/PD60MdIsdKy5I8NfvUOkyEPJ2/TFj2364blldYtd2PpaG+vDz9RWH3CKpcWZMx4vFy4sXL5ilSH369KnQyFqGhobYuHEjvn37hpcvX2Lq1KkCN7aoqCjs2LEDZmZmMDMzw44dOxAVFSVWDY8fP0ZLY2N07twZfm9eYWBbC5xbtww+J/cj6NxheBzfg2Mr5qNjCz3cunYVZmZm6NihAzVlFpDEmdQAHTOuCMJ//oR+A61S06VnZiIhJQXbZk3B+qnj0cXSDGPWboVHUOkBiJo1aoDwX7/EIbdIalTYKUIIY8ZycnLo0KEDy4qqPmzE/eVyuejQoQM6dOiAffv24d69ezh79izu37+PnJwcAEBQUBCWLFmCpUuXomvXrhg3bhwGDx5c5p250tLSMH/+fBw/fhydLVth/z9b0cmi6CASNsbNMal/T+xbOAO3X3li3fFzsLKywurVq+Hk5CSwzppScUhqy5h2U4ufnJwcyEgrFjpPCMHboI84ee8xvD6E4NOPX8x2rwVp77gQTbU1Yd3CACO7d0K/9jaFWtky0lLM/aUiqFGxqb9+/cqsKe7SpQvc3NxYVlS1IYRAX18fYWFhkJGRQVxcnMCNprL5+/cvLl++jLNnz8LT07PQ+4qKihg0aBDGjRuHrl27Ch0CNTExEb179UJwUBB2zJmCaQP7iLQcLis7GxtPXsCWM1cwfPgwnD17joZfrQRatmyJDx8+QEZGBmlpaZCRkWFbEoC86yk/ilTPnj3x8OFDlhVVfbp26YJ6HB4uO68EAPB4uTh57zEOXLuNoK/foddAC91aW8CyuT4sDZtBR1MdstLSyOHlou+i1ZCVloaVkQFe+gfDL+QLGqqrYdrAPpg73B61/n/i39azV7Dl/DUkJpbpAYrGpi4IDYEpXkJDQ5ndTTp06MCqEQNAvXr1MHPmTHh4eODz589Ys2YNdHV1mffT09OZXaYaNWqERYsWISAgoMRQd1lZWejXty9CP33EswNb4Tior8jr0uVkZbHJ0QFXnJ1w7dp1TJ06tVLC69VksrOzERoaCiBv+ZykGDEAgdCwtGUsHloYGSE47CcA4EPYD7SbNh8ztu1HU21NPNzjjNAr/+LQ0jkIi4xGakYmUtLT8eP3H+y8eB0+nz5j1aTR2Dl3GnxO7ofvqf3o2cYKLqcvw2TMdDz2ytukIvjrdxi1qLjlcTXKjOl4sXi5e/cu85rtren+S7NmzbB+/Xp8/foVr1+/xvTp05nWCJC3y9SuXbtgbm4OU1NTbNu2DREREYXK2bhxI7y8vXF3x3pYtTAol6bBnWzxr9N8nDp1CpcvXy5XWZSSCQ0NZQL8S9J4MZC3DWn+Mis6ZiweLC0tEfIjHJtOnIelwxykpmfizdFduLF1LXrYWDJzWf7EJ2D8+m1oPmIqus1dDu8PIXiwexO6t7ZgyrIwbIZjK+bj48WjMGjUAL3mr8S0LXvhHfIFlgWiBoqbGtNNnZubCzU1NSQmJqJu3bqIiYmhY3flpHPnznj+/DkAICQkBIaGhuwKKoWsrCzcv38fZ8+exd27dwuN/3A4HHTu3Bnjxo3DkCFD8PnzZ9jY2GD1xNFYM3lMMaWKzshVm/HUPxgfP36ChkbJO8lQysaFCxeYUIkuLi5Yvnw5y4oEadCgAaKiotCwYUP8qsBJQTWFsLAw6OnpAQAWjxmKDVPHQ15OttzlEkJw9OZ9zN99GFk5OTh//jxGjx5dlqJoN3U+fn5+SExMBJA3XkyNuHwkJSXh9evXAAA9PT0YGJSv1VgZyMnJYdCgQXB1dUV0dDQOHTqEdu3aMe8TQphdpjQ0NDBo4EAYNGqAFRNGFFumy+lLaD1pDmp1HQSNPiMwaNl6hP4s+ea6f9FM5GRl4Z9//hHbZ6MIEh4ezryWxNjz+UM6tJu6/BBCsHv3bgBAY00NbJs9RSxGDOQ9oDsO6ovurS3A4XBw/PhxZGZmiqXs/1JjzJiOF4uXx48fM92AffuKPo7KNnXr1sX06dPx5s0bfP36FevWrWOerIG8zUQiIiIwZ5g9ZEqYbPXSPxgzh/SHx7HdeLzXBTxeLnrOX4m0jOJ/sPVV62Bcr644dvQos+0bRbwUNLk6deqwJ6QYFBQUAIDuUCYGDh8+jH/++Qdz5szBz+g/uPL0pVjL/xD2A4+932HSpEnw8PDA7NmzxVp+PjXGjAuOF1MzLj9sLGmqKPT09LB27Vp8+fIFHh4emDlzJhQUFCArK4MxPTuXmPfBHmc49O0BY90mMGumixOrFiI8OgZ+IV9KzOc4sA/+xMTQGf0VRMGx2IJr0SWF/ChtBSdzUUTn+/fvWLJkCRwcHBAdHQ0OgOnb9iEmPlEs5fN4uZi4aRf09PTwzz//YO/evfj3338rZAZ8jTDjtLQ0vH37FkBejNqmTZuyrKhqw+fz8eDBAwCAkpIS7OzsWFYkHjgcDtq0aYMDBw6gb9++sDYyhIpS4bWLJZGUmtfSqVur5JtsS70mUK2lAt8KjOhTkynYMpZEM85/WGB7BUJVhs/nY9KkSVBRUcHTp09x9epVEAApaekYuHw9UtMzyl2+49a98P/8DSdPnYK8vDymTp2K7t27Y+rUqWIfYqgRZvzq1SumO5C2isuPr68vYmJiAOR9n3JyciwrEj/+797B0lC0sUZCCBbtOwJbM2O01GtSYloOhwPL5vrw86NmXBFIuhnn65NEbVWFO3fu4Pnz5/jz5w+zEqJOnTrY5OyMDz9+oef8lfgd97dMZadnZmLixp04de8JTp06BRsbGwBgxo3j4+OxZ88ecX0UADXEjAuOF9MlTeWnOnVRF0dMbAx0NETbRGT2jgMI+vodFzYIN3O3kXp9/In+UxZ5lFIo2E0taa3P7OxsZhIQNeOy8ePHDzg4OAAAs2a/Y8eOCAoKwvLly+Hu/gxhf+LQcsx0nHvoJtK6/lcB79Fq/Cxcff4GFy5cwNixYwXe19HRwdixY3H06FGxRuSqEWacP17M4XDQpUsXltVUDeLj4/H3b9FPlQXNuE+fPpUlqVLJzeWLNCltzs6DuPPaE+4HtqGhunAmzuVyWdtpqrqT3/KUlZWFvLw8y2oEkeQHharApUuXYGJiwqyOkZKSwsaNG+Hu7o5GjRoByNtX/cPHj+jVty/Gr98O07EzcPD6nWLHkpPT0nDV7SU6z1oKuxmLod5QBwEBARg5cmSR6WfMmIGoqCjcuXNHbJ+r2sfk+/PnDxOk39LSEnXr1mVZkeTj6+uLDh06IDMzE9bW1ujbty/69u0LCwsL/PnzB35+eRFpzM3Noa2tzbLaiqGWigoSUkrfCpEQgjk7D+Lmi7d4dnAbmmprCl1HQnIKatWmN+OKQJK7gSW9C11SSUlJwZw5c3D69GnmnI6ODi5duoS2bdsWSl+vXj1cuHAR06Y5Yv++fZi3+zBm7ziAhhrqaNlUB0oK8sjKzsHniCh8/v/liB07dMClS5cwdOjQEpe/tmrVCjY2Njh//jwGDx4sls9X7c244GxVOl4sHD4+Pkw3mo+PD3x8fLBu3TpoamoKLP+prl3UQN7GAgGfv5WabtaOA7j4+Blubl0LFUUFRP+NBwDUVlKCgnzJY+n+X8IwcHjRT96U8iHJE6Roy1h0vL29MXr0aHz79r/fpKamJoKCgkp9oOnUqRM6deqE379/4/Xr1/Dz80NISAhS0tMhq1QHPS1aw8nSEm3bthUpXkLHjh3FGkmv2psxHS8WneIuyOjoaERHRzP/f/DgAVRVVdGvX78qEfRDFEzNzHDu1Enw+fwSt4U87JoXErTzrKUC50+sWgiHvj2KzRebkIjvkb9hVYHh9WoqhBDaMq4m8Pl8bNu2DatXr2biGigrK0NWVhYTJkwQ6fvT0tLCsGHDMGzYMLFos7S0xPbt2xEbG4v69UWbX1IU1dqMC26ZqKCgIBBtiVI8pqamQqXz8/ODn58fFi1aBH19ffTt2xeDBw9Gx44dK1hhxRESEoJDhw7h+PHjSE9Px1Mff/SwsSw2Pd+jbOsNzz50g4yMDH1ArADS09OZsXhJNDtqxsIRGRmJ8ePHw93dnTnXunVrHDhwANbW1rCwsCghd8VjaZl3X/D390ePHsU/eAtLtZ7A9fnzZ2bKe4cOHSRuIoekUr9+fWhqCj/2CeRtT7l3717Y2dnhxIkTFaSsYuDxeLh+/Tq6du2KFi1aYN++fUhPT4eUFBf7r9wSe325ubk4fOM+hg0bBnV1dbGXX9OR9G5gSdcnCdy8eROmpqaMEXM4HDg5OeH169fMAwzbcd3zf7sJCQliKa9amzGNulV2hG0dF0VkZKQYlVQcv3//xoYNG9CkSRMMHTpU4AlcQUEB7dvb4t5bbzzw8BFrvXsu38TXX5FQVVVlut4o4kPSW56Sro9N0tPTMWPGDAwaNAjx8XnzLxo0aAB3d3c4OztDRkaGiRnB9raYsrJ58a/FFdK2WpsxHS8uO2ZmZmXKZ2Vlhfnz54tXjBghhODFixcYMWIEdHR0sHbtWoGHB319fezatQuRkZF4/vw5enTvjmlb9iEhOUUs9X/6EY6Vh04CAA4cOIB27drhw4cPYimbkoekm52k62OLoKAgWFtb4/Dhw8y5QYMGITAwEJ06dWLO5QcZYjuue1ZWFgCILehRtTVjHo+HZ8+eAcjrdi1PS68mUpbvq3nz5njw4IFExttNTk7GwYMHYWJigk6dOuHKlStMq5TL5cLe3h6PHj1CaGgoFixYAFVVVXA4HBw7fhzpOTnov2QdUtLKF9Q/PDoGfRetQe06dZg1zD4+PrCwsICLiwttJYsJSY9LTbupBSGEYN++fWjdujU+fvwIIK9n6siRI7h+/Trq1asnkD5/shTbW0/m1y+uoaZqa8be3t7MRd+1a9cSZ8RSCiOqGevo6ODJkydQU1OrIEVl4/3795g5cyYaNGiAWbNmCbRC69evDycnJ3z//h03b95Ejx49Cl0nOjo6ePjwEd7/CEfXOcvxLSKqTDo8339ChxmLARk5+L17h7dv3zL7P2dnZ8PJyQlt27alrWQxkJaWxrxWVBQttnhlQFvG/yMmJgb9+vXDvHnzmJammZkZ/Pz8MG3atCID79SuXRv6+vpMvAO2KBhvQRxUW4eiWyaWj+bNm0O6hK0DC6Kuro4nT56gYcOGFaxKOLKzs3H58mXY2dnBxMQEhw4dYnbJAQBbW1tcuHABv379grOzM3R0dEosr3Xr1nj27Dni0rNgNn4m9l25iSwhu8iSUtOw9J/jsHVcBM2GOnj95g0aNWqENm3awN/fH0uXLmUeAHx9fWkrWQwoKSkxryVxi8KCE35qcsv40aNHMDU1xf3795lz8+fPh6enJ1q0aFFiXktLS4kwYwMDA/E9UBFChD2qFLa2tgQAAUB+/vzJtpwqiYmJCfMdFnfUqlWL+Pv7sy2VEELIr1+/yOrVq4mmpmYhnUpKSsTR0ZEEBASUufyUlBQyY8YMAoCoqdYhS8cNJy8O7SDJbjcI3+Mhc8Q+vEIe7nEmU+17E0UFeSIrK0tcXFxITk5OkeV6eHiQ5s2bC+i1srIiwcHBZdZak/H09GS+xzlz5rAtpxBmZmYEAJGSkiKZmZlsy6l0MjMzycKFCwWud3V1dXL//n2hy9i9ezeRk5Mjf//+rUClxcPn80mLFi3IuHHjhM1SqsdWSzNOTk4m0tLSBAAxMDBgW06VZcyYMSUasYKCAnn16hWrGvl8Pnn69CkZNGgQkZKSKqSxefPmZN++fSQxMVFsdX769InMmzeP1K5diwAgHA6HNNRQJ3qNGhCt+mpM3dpaWmT9+vUkMjKy1DIzMjLI0qVLCZfLZfLLysoSZ2fnYk2cUjSfPn1ivsMJEyawLUeA7OxsIisrSwAQIyMjtuVUOp8+fSKtWrUS+I326tWLREdHi1ROdHQ0kZGRIbt27aogpSXz/PlzAoC4u7sLm6VmmvGdO3eYP/SsWbPYllNl2bp1a7FGLC0tTe7duydymTwej5w8eZJcuHChXNoSEhLI3r17iaGhYSFtUlJSZMiQIcTNzY3w+fxy1VMS2dnZJDAwkJw4cYKsWrWKLFu2jKxdu5ZcuHCBhIaGktzcXJHL9PT0LNRKtrS0pK1kEYiMjGS+u4EDB7ItR4CPHz8y2oYPH862nEqDz+eTY8eOEUVFRYGHzd27d5fpd0IIIaNGjSLNmjUrc/7yMHz4cNK8eXNR7i8104znzZvH/MFv3LjBtpwqy8OHD4s0Yg6HUyYz5fP5ZNasWUw5rq6uIpcREBBApk6dKvCjzj80NTXJmjVrSEREhMjlShIZGRlk2bJlAq1kGRkZsmnTJtpKFoKUlBTme+vSpQvbcgS4fPkyo23jxo1sy6kU/v79S4YMGVKox6q8w1uvX78mAMiZM2fEI1RI/P39iZSUFNm3b58o2WqmGRsZGREAhMvlirV7sqYRFRVVpBkfPHiwTOXt2rVLoJyOHTsKlS8zM5OcO3eOtGvXrkg9dnZ25MqVKyQ7O7tMuiQVT09P0qJFi0Kt5KCgILalSTR8Pp95kLGysmJbjgCrVq2qUQ2F58+fk4YNGwpcw46OjiQtLU0s5Y8ePZqoqqqSqKgosZRXGllZWcTMzIyYmJiQrKwsUbLWPDMu2EXVpk0btuVUafh8fqEWqLOzc5nKcnV1JRwOp5CRltT9+uPHD7JixQpSv379QvlUVFTIrFmzyPv378v68aoEGRkZZPny5UW2kqvbw4c4qVOnDgFAmjVrxrYUAQYOHMj8Hb9+/cq2nAojOzubrFq1SuA3X7du3TL1hpVEXFwc0dDQIP3796/QIal81qxZQ6SkpIifn5+oWWueGZ8+fZr5469evZptOVUebW1t5vucOnVqmS54Ly8voqCgUGSrdsaMGQJpc3NzycOHD0n//v0FDCj/MDY2JgcOHCDJycni+ohVAi8vL6bHJ/+wsLCgreRiaNy4MQFANDQ02JYigJ6eHgFAFBUVWRnrrAy+fftG2rRpI3CtdurUifz69atC6rt16xYBQBYvXlyhhnzu3DkCgKxbt64s2WueGY8bN465AF68eMG2nCrPqVOnSK1atUjv3r3LdKGHhYURdXX1YieCKSsrk6SkJPL371+yY8cO5mb138liI0aMIC9evKiUp19JpbhW8saNG2kr+T/kL8uTl5dnWwpDamoq01K0trZmW06FcP78eaKioiIwmXLz5s2Ex+NVaL179+6tUEM+ffo0kZKSIhMnTizrQ1TNMmM+n0+0tLQIkLeuVMQ+/RpJbm4u8fDwIHv37iXjx48n3bt1I106dyYDBgwgTk5O5Pr162VeyxcfH19oZnBRR5s2bYi8vHyh8w0bNiQbN24kv3//FvOnrtp4e3sX2UoODAxkW5rE0L59e+a7kZT7gLe3N6Np0qRJbMsRK0lJSQINIQBEV1eXeHp6VpqGfEMeMGCA2MaQ09LSyPz58wkAMmXKlPI8VNQsM37//j1zIfTp04dtORJNSkoK2b17NzFo1owAILIyMsTayJAM69KBjOxuR3q1sSKaavUIACInJ0cmTJgg0jhJVlYW6dSpU6lGXNTRtWtX4urqSmcOl0BmZiZZsWJFoVbyhg0baCuZENKnTx/me4mNjWVbDiGEkBMnTjCa2FofWxF4enoSXV1dgd/w+PHjSVJSUqVruXnzJlFXVyeqqqrk7Nmz5Wolv3z5kujr6xN5eXmyc+fO8ra4a5YZ7969m7kYdu/ezbYcicXNzY00adyYyMhIk5HdOxH3A1tJ5ss7AlGk8o/wW2eJy8xJpLGWJuFwOGThwoWlzoTk8/mFnpJLO5SUlMi8efPIp0+fKulbqB54e3sTY2Njge/S3Ny8xreSR44cyXwf3759Y1sOIYSQBQsWMJqePHnCtpxyw+PxyObNm5kAS0BeRL7z58+zqisuLo6MGjWKACCGhoZkz549JCEhQai8mZmZ5Pz580zPStu2bUlISIg4ZNUsM+7bty9zUdAgCYXh8/nM0opOFmbk67WTRRpwUUfO63tk+5ypRF5OjjQ3NCQ/fvwotp61a9eK3BoePHhwJX4T1YvMzEzi5OQkEIGspreSHR0dme9CUsK1duvWjdFU1Ydefv36Vajnq02bNiQsLIxtaQwvXrwgI0aMINLS0kRBQYHY2dmRhQsXkvPnz5NXr14Rb29v8vr1a+Lq6kpWrVpFevfuTerWrUuAvPXpV69eFedYd6keyyGEQEiETsgG2dnZqFu3LtLS0qClpYXIyMgid/yoqRBCsGTJEuzcuRObZ0zE0rHDyrSTVciPX+i3eC1yOFy8fvOm0CYLp0+fhoODg8jlSktLIzw8HFpaWiLnpeTh6+sLBwcHgZ2fzM3NcfLkyTLvT11VWbp0KbZv3w4AeP78Oezs7FhWBGhpaSE6OhpqamqIiYmpsvcnV1dXTJkyhdnwgsvlYuXKlVi9ejVkZGRYVleY6OhonD9/Hp6envD19cWPHz8KpVFXV4eVlRWsrKwwcuTIUjeqKAOl/rGrza5NXl5ezNZp3bp1q7IXekVx4sQJ7Ny5E3sXzsDy8SPKvKVk8yaN8OLgNkjxeejfr5/ABt/u7u6YMmVKmcrl8Xg4duxYmfJS8rCysoKfnx+cnJwgJSUFAPD394eVlRU2bNiAnJwclhVWHgV30im4ZSFbxMXFITo6GgDQsmXLKnl/Sk9Ph6OjI4YMGcIYccOGDfHs2TNs2LBBIo0YADQ1NbFo0SJcvXoV379/R1xcHD59+gR/f398+PABkZGRiI6Oxr1797B+/fqKMGKhqDZm/OTJE+Z1t27dWFQieYSHh2PBgvlw6NsDc4bZl7u8BupqcHVZjY+fPsHZ2RlA3sNQjx49yrX135EjR2qUYVQEcnJycHZ2hqenJ1q2bAkg70Fn7dq1aN26NQIDA1lWWDloaGgwr4tqCVU2Bb93ExMTFpWUjYCAAFhaWuLo0aPMuaFDhyIoKAgdO3ZkUZno1KtXD82bN0erVq1gZGQEbW1tiXg4qjZmXHD/YmrGgixetAi1FBSwa940sZXZykAPK8aPwObNm/Ht2zesXr0aubm55SozKioKt2/fFpPCmo2VlRV8fX2xcuVKppUcEBAAKysrrF+/vto/9BgZGTGvP378yKKSPB49esS8bt26NYtKRIPP52PPnj2wsbFBSEgIAEBRURHHjx/HlStXoKqqyrLC6kO1MOOkpCR4e3sDAPOkQ8kjIiICrjduwGnCCNRRUS423Uv/YAxYvBYN+o8Gt20v3HzxttSyl40bBhVFBRw5cgSzZs2CnJxcufU+fPiw3GVQ8pCTk8OmTZvg5eUl0Epet24dWrdujYCAAHYFViAFzbjgGDpb3Lt3DwDA4XDQq1cvltUIx58/f9C3b18sWLCAGY4yNzfHu3fvMHnyZIloTVYnpNkWIA6ePXvGtMq6d+/OshrJ4vjx41CQk8PYnl1KTJeWmQnTZk3h0K87hq7YJFTZivLycOjbHf8eP45NmzYhMzMTOTk5SEhIQHx8POLj4wVel3QkJCRAWVkZffv2FcfHphTA0tISvr6+2LRpE1xcXJCbm4uAgABYW1tj1apVWLFiBWRlZdmWKVbq1KmDBg0aIDIyEh8+fMibrcqSeXz//p1pnbdt2xZqamqs6BCFhw8fYsKECYiJiWHOLVq0CM7OzmJ56KYUplqYMe2iLh53Nzf0srGAipJiiel6t7VG77bWIpc/vGtH7L7oiqCgIFhZWUFGRgbq6upQV1cXqRw+nw8+nw9p6WpxSUoccnJy2LhxIwYOHIiJEyciODiYaSXfuHEDp06dQqtWrdiWKVaMjIwQGRmJhIQE/PnzB5qamqzoyG8VA5D4h82srCwsX74ce/bsYc5paGjgzJkz6NGjB3vCagDVops6f/KWtLS0RCxhkBT4fD78A/xh2cKgwuow1WsKKSkp+Pr6lqscLpdLjbgSyG8lr1q1ihlLDgwMhLW1NdatWycwO76qY2xszLxms6u6qpjxp0+fYGNjI2DEffv2RVBQEDXiSqDKm3F4eDg+f/4MAGjTpg1UVFRYViQ5REZGIjU1DSZ6TSqsDgV5OTRr1ACfPn2qsDoo4kVWVhYbN26Et7c3M7OXx+Nh/fr11WosWRLMOC0tDc+ePQOQtwzI1NSUFR0lQQjB0aNHYWlpycz6lpOTw759+3Dnzh2Re7koZaPKm3HBLmo6XixIeno6AEBJXr5C61FWVEBGRkaF1kERPxYWFvD19cXq1asLtZLXrl1b5VvJBc2YrRnV7u7uyMrKAgD06dNH4iY9/f37F0OGDIGjoyPzGzYyMoK3tzfmzJkjcXqrM9XKjOl4sSD5i/BzyrH2Vxiyc3gSu+CfUjKysrLYsGEDvL29mVYbj8fDhg0bYG1tDX9/f5YVlp2CwRvYahnfvXuXed2vXz9WNBTHs2fPYGZmhhs3bjDnZsyYAV9fX4lswVd3qrQZ8/l8xoxVVFSq1Pq9ykBbWxvS0tL4EhFVYXXk5ubiW0QUGjduXGF1UCoeCwsL+Pj4YM2aNczYfVBQEFq3bo01a9ZUyVZy/oxqAMyM6sqEEIL79+8DyOv27dKl5BUNlUVOTg6cnJzQtWtXREZGAsgLhHHr1i0cPHgQCgoKLCusmVRpMw4ODkZsbCwAoHPnznQC0H+Ql5eHsZER/EK+lJo2NT0DAZ+/IeDzNwDA96hoBHz+hvDomBLzff4VibSMDFhZWYlFM4U9ZGVlsX79+kKt5I0bN8LKygrv3r1jWaHo5HdVJyQkMOEoK4ugoCBEREQAyLs/KSkpVWr9RfHt2zfY2trCxcWFeTjp0qULAgMDMWDAAJbV1WyqtBkXDIFJx4uLpm27dnji419qdCzfkM+wmDALFhNmAQAW7TsKiwmzsPbYmRLzPfTwhYyMDCwtLcWmmcIu5ubmhVrJwcHBVbKVzOa4saTNoj579ixatWrFBEiSlpbG1q1b8eTJE6YHgcIeVdqM6Xhx6UyePBm/omNw/61Piek6WZiB7/Gw0HFy9eJi8/D5fBy+eR9DhgwRCMxPqfoUbCXn7/iUm5tb5VrJbEbiKjhezKYZJyUlYezYsRg/fjxSU1MBAPr6+nj79i2WLl1a5k1jKOKlyv4VMjMz8fLlSwB5SwYMDQ1ZViSZWFlZwdrKClvOXil37Oj/cs39Nb6ER2DGjBliLZciOZibm8Pb2xtr164t1EpevXo1M1NYUmFreVNcXBw8PT0B5D0QNG3atNLqLoinpyfMzc1x/vx55tzEiRPh7+8Pa2vRg/xQKo4qa8YeHh7MVHy6ZWLJbN+xAx7BH7H/qvg2YYhLTMKMbfvA5XLh5eUFPp8vtrIpkoWsrCzWrVsHHx8fgVbypk2bmG0bJRW2Nox4+PAhMybLRqs4/+9ja2uL79+/AwBq1aqFixcv4sSJE1BWLj5OPYUdqqwZ0/Fi4bGzs8OcOXPgdPgUPN+XPzhHDo+H8eu3IzktHXw+H0uXLkXfvn0F4thSqh/5443r1q1jWsnv37+HjY0NVq1aJZGt5Nq1a6Nhw4YA8lr04u4dKg5XV1fmdWWb8a9fv9ClSxeBndTatWuHwMBAjBw5slK1UISnWphx165dWVRSNdiyZQusrKzQe+FqvA0qewshMysbI1e5wM0vEEOHDWN6JB4+fAgzMzO4ubmJSzJFApGVlcXatWvh6+vLxLLOzc2Fs7OzxLaSbWxsAOSNnVbGWHdERASzFaimpibatWtX4XXmc+3aNZiamjJDeFwuF2vXrsWLFy/QpEmTStNBEZ0qacbx8fHMj97U1FRgI3FK0SgqKuLe/fswa2WOzrOXYtPJCyIHA/H99BmtJ8/DAy8/uLq64tKlS3j06BHz/UdHR6N79+5YtWoVeBUcaITCLmZmZvD29sb69eslvpVcMK7y48ePK7y+I0eOMC1SR0fHSgmIk5aWhqlTp2LYsGFITEwEAOjo6ODFixcCPRkUCYYQIuwhMVy9epUAIADIokWL2JZTpcjMzCQrV64kUlJSpKVeU3JsxXyS+uwm4Xs8LPbwObmfOPTtQaSkpIiFuTkJDAwUKDM6Opr06NGD+ZsAILa2tuTPnz8sfUpKZRIQEEBatWol8Pdv2bIl8fHxYVsaIYSQ79+/M7o6dOhQoXVlZWURDQ0NAoBISUmRiIiICq2PEELevXtHDA0NBb7/4cOHk4SEhAqvmyI0pXpslTRjR0dH5qJ78OAB23KqJD4+PqRvnz6Ew+GQWspKpIeNJVk+fgQ5vGwuOe60gOyYO5WM69WVGDZuRAAQnUaNyI4dO0h2dnaR5eXm5pKtW7cSaWlp5m/TtGlT8unTp0r+ZBQ2yM7OJhs2bCAyMjLM319KSoo4OTmRzMxMtuURAwMDAoBIS0uTpKSkCqvn4sWLzOcfOnRohdVDSN5vbufOnQLfuZKSEjlx4gTh8/kVWjdFZKqnGevq6hIARFZWlqSmprItp0oTFhZGNm7cSPr370e0tbQIh8MhAIiCggJpbW1NZsyYQW7dukV4PJ5Q5Xl4eJAGDRowN4c6deqQZ8+eVeyHoEgMgYGBxNzcXKCVZmxszHorefbs2YyeW7dulassPp9PEhMTi3zP1taWqacir/vfv38X6o2ytLQkoaGhFVYnpVxUPzP+9u0bc/F16tSJbTnVDj6fL7TxFsevX7+ImZkZ83eSkZEhp06dEpNCiqRTXCt5xYoVrLWSb9++zWiZOXNmucoaOXIkAUC6du1K/Pz8mPOBgYECDyAV1Tq9e/cuqV+/voARL1myhGRlZVVIfRSxUP3M+MiRI8wF6OzszLacasesWbOItLQ0sbe3L1c5ycnJpE+fPgI3jDVr1tDusxpEUa1kIyMj4u3tXelaUlJSmIcDfX39MpeTk5Mj8HkAkNGjR5OwsDAybdo05tyBAwfEqD6PjIwMMnfuXIG6tbS0yJMnT8ReF0XsVD8zHjZsGHMhenl5sS2nWvH371/C5XKZ7zcoKKhc5eXk5JBZs2YVunFJwhgipXLIzs4mGzduFGglc7lcsnz58kq/Duzs7BgN3759K1MZycnJhcw4f8gsf76EiooKSU5OFqv29+/fExMTE4E6+/fvT2JiYsRaD6XCqF5mzOPxSN26dZmxyPJ2p1IEWb9+faEfe3nh8/lk165dzFh0/ozWuLg4MSimVBUCAwOJhYVFoVZyZT5QOzs7M3UfOnSoTGXExMQUacYFjzZt2pD09HSxaObz+eTgwYNEXl6eKV9eXp4cOHCA9jJVLaqXGfv6+jIX5ODBg9mWU61ISUlhHnQKHm/fvhVL+Tdu3CAKCgpMuc2aNSNfvnwRS9mUqkF2djbZtGlTka3kjIyMCq+/4P1j0KBBZSrj58+fpZoxANKgQQNy4sSJcjUYYmNjib29vUC5LVu2JMHBwWUuk8Ia1cuMXVxcyv1kSymaXbt2FXlT6dSpk9iewH18fJg1mABIvXr1yKtXr8RSNqXqEBQUxEorOTc3l9SrV48AILVq1Sp2mV5JhISECGXGBc3z7t27Iv+G3NzciLa2tkBZs2fPFluLm1LpVC8z7tKlC3Nh0laV+MjMzBRYjvTf4/Hjx2Kr68ePH8TY2FhgrO3ChQtiK59SNSiulbxs2bIKbSXnz4QGQF6/fi1yfn9/f5HMOP/Q0NAg9+/fL7X8rKwssmzZMoFhHTU1NXLnzp2yfFyK5FB9zDgtLY3IysoSAKRJkyZ0vESMHDt2rMQbiZWVlVi/78TERNK9e3eBOmhPR80kODiYWFpaClwLLVq0IJ6enkLlX7t2LdHU1CTHjx8XKv3JkyeZetasWSOy3rdv35bJjIG8JX7FrU8mhJAvX74QKysrgTzdu3cnUVFRIuukSBzVx4wfPXrEXKBTpkxhW061gcfjkWbNmpV6I7l27ZpY683OziZTpkxhyudwOOTixYtirYNSNcjJySHOzs6FWslLly4tsZV89+5dJr2cnBz5/v17qXVFREQweWxsbETW6ubmVmYzBkBGjhxZ6MGWz+eTU6dOEWVlZQHj3r59O8nNzRVZI0UiqT5mvGTJEuZCvXz5Mttyqg2XL18W6ibSvHlzkpOTI9a6+Xw+Wbp0KVOHtLQ0uXfvnljroFQdgoODC7UMmzdvXmQrOT4+vtCY6rBhw4SqJ3+YhMvlkr9//4qkseADQFmPggFwEhISBLrOgbzJjb6+viLpokg81ceM8wPRczgcEhsby7acagGfzxeIlFXacfLkyQrRMHXqVKYOBQUFOqmrBpOTk0M2b97MDEnlm+aSJUsEWskTJkwo8hp9+fJlqXUsXLiQSX/+/HmR9BXcpKash5KSEvny5Qt58+YNady4scB7kydPJikpKSJ/bxSJp3qYccG1fRYWFmxKqVbcv39fpJuIjo5OhQRq4PF4AsFcateuTfz9/cVeD6XqUFwr2cPDo8TWqYWFRaldu8+ePWPS9+vXTyRdZ86cKbcZAyDa2toCk7Rq165Ne/yqN9XDjAvuhLJ06VI2pVQrCga1F/bYu3dvhWjJysoSCHyvrq5OPn/+XCF1UaoGRbWSORyOwNhqUceJEydKLDc3N5dZPSAtLS1SAJqjR4+W+huRk5MjTZo0Efo3ZWtrS378+FHer4si2ZTqsVxUAZ4+fcq87t69O4tKqg+vX7/G69evRc63adMmpKamil2PrKwsXF1d0bZtWwBATEwMunfvjoiICLHXRakaSEtLY8WKFXj37h2sra0B5DUeSrv+nJyckJKSUuz7XC4Xo0aNAgDweDxcvXpVaE0ZGRklvm9hYYFdu3bhx48fQpXn4OCAZ8+eoXHjxkJroFRPJN6MCSF48uQJAEBeXh62trYsK6oeuLi4lClfbGws9u7dK2Y1eSgpKeHevXswMTEBAPz8+RM9evRAXFxchdRHqRoYGxvj7du3cHBwECp9dHQ0Nm/eXGKaMWPGMK8vXLggtJbizJjL5WLlypV48+YNDh8+LHR5jx8/RmJiotDpKdUYYZrPhMVu6s+fPzPdOd26dWNLRrUiICCgXONdtWrVqtAg/1FRUcye1UDeOmdxB96nVC0SEhIKzZ4u6ZCVlSVhYWHFlsfn80mLFi2Y9D9//hRKR8HJX/mHrq4uefPmDSGEkAsXLoj8e7K3t6dxE6o/Vb+bOr9VDNAuanHh6elZrvyZmZkV0lWdj5aWFp48eQItLS0AgK+vL+zt7ZGZmVlhdVIkmwULFiAqKkro9NnZ2ViyZEmx73M4HIHW8cWLF4Uq9/379wL/nzJlCgICAtCuXTvk5ORg9erVQmvM59atWzhy5IjI+SjVCw4hRNi0QicUJ4MGDcLNmzcBAH5+frCwsGBDRrXi79+/cHBwQFhYGGRlZSEjI8McsrKyCA8PR2hoKACgffv20NfXZ9LJysqiX79+6Nq1a4XrfP/+PTp27IiEhAQAgL29Pa5fvw4pKakKr5siOdy/fx99+/YtU97nz5/Dzs6uyPfCwsKgp6cHAGjWrBkWLFgAPz8//AoPB4/Hg5KyMoyMjGBpaQk7Ozuoq6vjyJEjmD59OqSkpHDy5EmMGzeOKe/o0aNwdHQsk055eXn4+fnByMioTPkpEg+n1BTCNJ8JS93UOTk5pHbt2gTI21SARqOpHAoGAnFxcWFVi4eHB1FSUmL0ODs7s6qHUrmI2j3936NVq1bF7pyUkZFBmjZtSqSkuP8/s1qKtDLQJ0M625IR3exIn3atSUMNdQLkRcQaOXIkefv2LYmJiSm0YUN6enqJ8d2FOQYOHFgZXymFHUr1WOlyun2F4uvri6SkJABA165dweVKfK96tUBXV5d5HRYWxqISoE2bNnB1dUWvXr1ACMGaNWvQqVMntGvXjlVdlMrhn3/+Eal7+r8EBATg1KlTmDx5ssB5Ly8vOEyYgJ8/f6JPO2vMGtIfduamkJeTLVRG9N94XHryAodu3EO7S5cwZcoU7Ny5EwoKCkyavXv3IjIyssw6AaBOnTrlyk+p2ki0u9ElTewgSWYMAD169MCqVasAALm5uRg9ejSdgVpDKGh4ZWXu3LkC18uuXbvQrl07KHMJAs8exO3t69GzjVWRRgwAmvXqYv7IQfh08SgOLpmDSxcuwNTEBCEhIQCApKQkkceK5eTkYGJighEjRmDdunVwdXXFsWPHyvwZKVUfiR4ztrOzw8uXLwEA379/R5MmTSpbQo2EEAJVVVUkJSWhadOmEmHIPB4PnTp1wps3bwAAw4YNw+XLl8HhlD4UQ6m6EELw+PFjBAYG4sePH/jx4wd+/vyJHz9+ID09XehyJkyYgFOnTmHLli1YsWIFlowdBmdHB0hLiz7/4MfvaAxYsh5/klLw6vVrhISEYODAgUWmVf7/cecWLVowh5GREZo2bUrnPtQsSr1RSawZp6amom7dusjJyYG+vj6+fPlSmdXXeCwsLODv7w8pKSlkZGRARkaGbUn4+fMnWrVqxbRyjh07hilTprArisIKhBDExcUxBl3QpPOPtLQ0Jv3GjRvRsmVLDBo0CGsmj8G6KeNKKL10/iYlo9PMpcggHLzz90fPnj3x8+dPdOzYEe3atWMMuEGDBvSBkQJIuhmnpqbi3r170NHRgbW1NaSl/zeEXXAG5fTp03Ho0CFxV08pgaFDh+L69esAgC9fvkBfX59lRXlcv34dQ4cOBZDXhenn54cWLVqwrIoiaRBC8PfvXwQFBYHL5cLExATGRkawMdTFja1rxWKQ3yKiYDZ+JiZOmox//vlHDKop1ZhSLzhWx4ynT5+OkSNHol27dqhXrx4GDhyIAwcOIDQ0lK4vZpmWLVsyr9++fcuiEkGGDBnCLB/JyMjAyJEj6fpjSiE4HA7U1NTQpUsXdOrUCatWrUJ2ZgYOLZ0jtpaqXkNtbJ7ugAMHDsDf318sZVJqLqya8Z8/f5jXycnJuHXrFmbPno3mzZvjwIEDAPJ+VAWNgVI5dOnShXnt7u7OopLC7N69G8bGxgCAoKCgEoM7UCiJiYk4c+YM5o8YCC21eiWmTUlLx/zdh9Fk0Hgo2g1A+6kL4PMxtNj0s4b0h46mBm0ZU8oNq2ZcUgCPnJwcAHndTYaGhmjVqhUWL16MR48eiTRxg1I2bGxsmJms7u7uEGE4o8JRUFDApUuXIC8vDyBv+cutW7dYVkWRVM6ePYvs7GxMGdCr1LRTXfbgqc87nFmzBEHnDqO7jQW6z12ByJii46NLSUlhmn1vXLx4kVmGSaGUBVbN2MrKSui0gYGB2LlzJ3r16gVVVVWMGjVKYIIGRbzIycmhffv2AIBfv37h27dvLCsSpGXLlti9ezfz/0mTJtEdnihF4u7ujg5mxqW2ijMys3D9+WtsnTUZHc1NoN9IG+umjENTbU0cunG32HzDu3ZERkZGucPMUmo2rJpx/rZoopKdnY1Lly7hxYsXYlZEKUjBrupnz56xqKRoHB0dMWjQIABAfHw8xo4di9zcXJZVUSQNP19fWDZvVmo6Xm4ucnP5kJcVXG+sICeLN4Efis2n11ALtVWU4efnV26tlJoLq2bcuHFj1KtX8tNqcWhra9MoTBWMJI8bA3nzCY4fP45GjRoBAF68eCHS9nWU6k9aWhp+RUTARK9JqWlVlBTRtmULbDp5AVGxf5Gbm4tzD93g9SEUv//GF5uPw+GgpW5jfPr0SYzKKTUNVs2Yw+GUqXWsoqKC+/fv0/BxFYylpSVUVFQASN64cT5169bFuXPnmP+vX78eycnJLCqiSBL5+w8rKcgLlf7M2iUgBGg4YAzk7fpj/5VbGN2jE6S4JQfoUFaQp3NZKOWC9XCYoowbA4C0tDRcXV1hZmZWQYoo+UhLS6Njx44AgJiYGHz8+JFlRUXTsWNHjBgxAgAQGxuLrVu3sqyIIinkB6vJ4Qk3fKHXUBvPD21HivtNhN88C68T+5DDy0VTbY0S82Xn5EJWtuhwmhSKMLBuxqK2jE+ePIlu3bpVkBrKf5H0ceN8Nm/ezNx4d+3aRSdzUQAAtWrVQp06tfHll2ibOCgpyENLrR4SklPwyMsPAzq0LTH9l4goNG7cuDxSKTUc1s1YlJaxi4sLxo4dW4FqKP9F0seN89HV1cXs2bMBAJmZmWXa5J1S/eBwOLAwt8C7kK9CpX/k6YuHHr74HhWNJ97v0GX2MhjqNMTEfj2KzRMTn4iIPzGwtLQUl2xKDYR1M9bW1oa2tnap6WbOnIlly5ZVgiJKQUxNTVG3bl0AeRu1S/Js5VWrVjHzCE6fPo3AwEB2BVEkgrbt2uFFQDAyMrNKTZuUmo7ZOw+gxcipmLBhO9qbGuPR3s2QkS5+t9mHnr4A8tbmUyhlhXUzBkpvHQ8cOBD79u2jAddZgMvlonPnzgCAhIQEiTa4unXrMlstEkJoZC4KAGDixIlISE7BZbfSl0IO79YRX6+dRObLO4i6exH/LJ6F2spKJeY5fOMeenTvDh0dHXFJptRAJN6M27ZtiwsXLtDtxlgk34wBye6qBoDZs2czW20+efIEjx49YlcQhXX09PTQq2dP7LhwHdn/H9lPXLj7BsDz/SfMmDlTrOVSah4SsYXiw4cP0bt370LnDQwM8Pbt2zKvRaaIh5CQEGZnJGtra3h7e7OsqGQuXryI0aNHAwBMTEyYrSApVRMej4ekpCTmSE5OFvh/UecTEhLw/ft3JCUlYeDAgVi2bBmsra2xfNxwbJg2Xiy6UtMzYDpuBhrrG8D92TNwuRLRtqFIJpK9hWI+cXFxqF+/vsA5DQ0NeHh4oGnTphVVLUUE8vc3BgB/f3+0atWKXUElwOfzYWNjA1/fvLG8EydOYOLEiSyroohKVlYWevXqhefPn5erHC6Xi9zcXKxfvx4bN27E/V0b0b118XHxhYHP52P8+u24+doLwcHB0NXVLVd5lGqPZG+hmI+amhpq1arF/F9eXh737t2jRixBTJs2jXl97NgxFpWUDpfLxY4dO5j/r1q1igZkqIIEBweX24gBoE2bNgAAJycn9OzRAwOXrcej/590VRZ4vFxM2bwHF588x6lTp6gRU8SCRJgxAIHJD+fPn6fLBCSM0aNHQ1FREUDe30fSzc3Ozg4DBgwAAERFRWHXrl0sK6KIipmZGQwMDMpVhoaGBu7fvw8gLwDItevX0blzF/RdtAbLD55AZla2SOV9/P4TttMX4exDN5w9exbDhg0rlz4KJR+JMeM7d+6gT58+OH78OAYPHsy2HMp/qFWrFhPlKikpCVevXmVZUels3bqVGSvevn073eWriiEjI4OdO3eWq4yTJ0+idu3azP8VFBRw6/ZtbNq0CXsu34TZ+Jk4eP0Okku5Nj6E/cDsHQdgMWE2knL4eP36NcaMGVMubRRKQSptzDg3NxcPHjzAs2fP4Ofri9DQUGRkZkBGWgZNmzaFpZUV2rVrh8GDB0NJqeSlBBR28PDwYDbnaNeuHd68ecOyotKZOHEiTp06BSDvxuzg4MCqHopoEELQq1cvPH78WOS8Dg4OOHnyZLHvv3//HmvXrMGt27chLysLG2NDWBjqQ6+BFmSkpZGclo6gr9/hF/oVwV/DoKGujpmzZmHJkiXMXt8UipCwP4ErMzMTe/fuxcEDBxD+6xcaa2nCurk+jHQbQ0leHtk8Hr6ER8Lv81d8DPuJWrVUMHHiJDg5ORWa1EVhF0IITE1N8f79ewB5NzNjY2OWVZWMp6cn2rbNC2XYtm1bvH37lmVFFFH5+PEjTE1NRQo4o62tjffv30NVVbXUtBERETh37hzu378Pz7dvkfP/9cjKysLYyAiWVlbo3r07Bg4cSONPU8pK6UEyCCHCHiLj5eVFWjRvTmRkpMnEfj2I94l9hO/xsNjj2/VTZNm44US1lgpRq1ePXLlypSzVFktSUhK5c+cOiY+PF2u5NYm9e/cS5D2Ykfnz57Mtp1T4fD4xMTFhNL9//55tSZQyMGXKFOZvKMxx9+5dkeu4cuUKk9/FxaUCPgWlBlOqx1bYmPGZM2fQrl07KHEI/E7+g39XLoRVi5InYzTV1oTLzEn4dPEY7ExbYPjw4Vi4cGG5t+4jhODixYswNDRE//790b1793KVV5MZO3Ys5OTkAOT9jTMzM1lWVDIcDgdTp05l/i/pM8EpgvB4PPzzzz+4du2a0HnGjx+Pvn37ilxXTEwM81pLS0vk/BRKeagQMz537hwmTJiAif164O3RXWgpxMbeBVGvWwdXnFdi38KZ2L17d7kMOTQ0FN27d8fo0aMRHR0NAPDz85N4E5FU6tati6FDhwIA4uPj4erqyrKi0hk7dizk5fP2s60KDxCUPB4/fgwzMzPMmTMHiYmJQuXR0tLCnj17ylTfnz9/mNcaGiVvmUihiBuxm/H79+8xadIkOPTtgSPL5kJaumyRjzgcDmYPG4D9i2Ziz549uHz5skj5MzIysGrVKpiYmMDNza3Q+7GxsWXSRalaa44BQFVVlXmASEhIwPXr11lWRCmJz58/o3///ujZs6fAHtpjxoxBs2bNSsx7+PBhocaJi6KgGaurq5epDAqlrIjVjHk8HiY6OKBZI20cXDJbLBs7zBo6AMO6dsDsWbMEfiwlce/ePRgbG8PZ2Rk5xcSipWZcdjp06ABDQ0MAeTs5ff78mWVFpVPVHiBqIomJiVi0aBFatmyJu3fvMufbtGkDT09PnDt3Dvv37y82/5gxY5i15WWBtowpbCJWMz579iz83r3DCaeFkJcretYhj5eLVUdOQXfwBCjaDYDeEAds+Pc8+Hx+seX+s2gWwM/Fhg0bSqw/PDwcgwcPRr9+/fD9+/cS0xYcH6KIBofDwZQpU5j/HzhwgEU1wmFra4vmzZsDAF68eIHQ0FCWFVHyyc3NxZEjR9CsWTPs2rWLeYBu0KABzp07hzdv3jDbE/bs2bPI8WANDQ3s3bu3XDoK3hNoy5hS2YjVjA8eOIBebazQ2tiw2DRbz13BkRv3sX/RTHy8dBRbZ03GjgvXsP/q7WLz1FetgxmD+uLMmdNISUkp9H5OTg62b9+OFi1a4MaNG0JppWZcPiZMmMCstTx8+HCpDz9s898HiOPHj7OohpLPs2fPYGFhgenTpyMuLg5AXjjcNWvWIDQ0FGPGjCm0AcPOnTsh/Z/9hQ8fPlzuDWXyW8Z169aFjIxMucqiUERFbGYcEBAAXz8/TB9U8ixGz+BPGNChDfq2t0ETLU0M7dIBPVpbwC+k5K7OaQN7IyMjs9DY8cuXL2Fubo6lS5eKFKKRmnH5qF+/PhYsWAAAyM7OhpOTE8uKSmfChAnMOtFTp04hK6v0zeYpFUNYWBgGDx6MLl26ICgoiDk/YsQIhISEYP369cUG/zE0NMScOXOY/48aNQoDBw4st6Z8M6Zd1BQ2EFvQjwMHDmDBgvlIfuoKuRIWxm85cxlHbtzDo72bYaDTEIFfwtBznhN2z3fEqB6di80HANaT5sLEph1OnjyJiIgIODg4FDk5SxhUVVWhoaEBLpcLLpcLDofDvC7u/9LS0qhfvz60tbWhra2NBg0aCPyroqJSJi1VleTkZOjr6zPj715eXmjdujXLqkpm5MiRzAPd5cuXMXz4cJYV1SxSUlKwefNm7Nq1C9nZ/4sLbWlpiT179sDW1laoclJTUzFr1izk5OTgwIEDZZ60lU9aWhqUlZUB5MU1F8cGFRRKAUqdQCVdWgJh8fPzg4le0xKNGACWjRuOpNQ0tBg5FVJcLnL5fGxynFCqEQOAhYEePP9/WzxDQ8NybVaQkJCAhISEMucvCmVlZcaYC5p0wddaWlrMOt2qTq1atbB27VrMnj0bALB48WK8ePFCLBP3KoqpU6cyZnzs2DFqxpUEn8/H6dOn4eTkxCwxBABNTU1s3rwZEyZMEGk/YGVlZZw+fVps+ujkLQrbiM2Mw759g2GjBqWmu/z0Bc4/csf59ctg3LQxAr58w4I9R6CtVg8T+pYcjKN540a48PQl+Hx+ubsYpaWloaSkBD6fzxyEEIH/lzSprChSU1MRGhpa6uQgNTU1NGvWDFZWVrCysoK1tTUMDAyYTQ2qEtOmTcO+ffvw+fNnvHr1Crdv34a9vT3bsoqlc+fO0NXVRVhYGNzc3JCQkFDuVhWlZF6/fo158+bh3bt3zDlZWVksXLgQTk5OEtGjVHDYipoxhQ3EZsbZ2dmQU6lVarql/xzHsnHDMbJ7JwCAiX5T/IyOwZYzl0s1YzlZGWRnZ4PL5eLOnTtwcnJCcHCwSDFr82nVqhV8fHxKTZcfqozP5yMnJwd//vxBVFQUIiMjERUVVeTr1NTUEsuMi4tDXFwcPDw8mHPKysqwsLAQMGg9PT2JbmUCeTvrbN26FYMGDQIALFu2DH369JHYCTBcLhcDBgzAnj17QAjBixcvxDLeSClMeHg4li5dWmiex+DBg7F9+3aJ2geYtowpbCM2M5aXl0eGEK3V9MysQt1RUlwu+EKMXadnZkFePq+Lt3fv3ujduzdiY2Nx+vRpHD16FF++fBFar7DrjDkcDjN+LC0tjSZNmqBJkyYl5klJSSnRsH/9+oVfv34J5ElNTcXLly/x8uVL5lydOnVgaWnJmLOVlRV0dHQkzqDt7e1ha2uL169fIzQ0FMePH8eMGTPYllUsXbp0YaI0ubu7UzMWM2lpadi6dSu2b98uEO3M1NQUe/bsQefOpQ9JVTY04AeFbcRmxgaGhnjztPRtzvrb2mDzqUvQ0agPY93G8A/9ht2XbmBivx6l5v34/ScMmgnGt65fvz4WL16MRYsW4cWLFzh69CiuX78uMDmkKGJiYkAIqRBjU1FRgaGhIRMYoygSEhLg5+cHX19f+Pr6wsfHB+Hh4QJpEhMT4ebmJjBJTU1NTaD1bGtri7p164r9M4gCh8PBjh070KZNGwDA2rVrMWbMGNSqVXpPCRt07NgRXC4XfD4fz549Y1tOtYHP5+PChQtYvnw5IiMjmfNqampwdnbG5MmTJXYohraMKWwjttnUx44dw/Tp05H01BVKCvLFpktJS8fqo2dw8+VbxMQnQrt+PYzsboc1k8ZAtpSuTdOxM9Cua3ccOXKkxHRxcXE4c+YMjh49WuL4bUpKCjODUhKIiYkpZNC/f/8uMY+UlBQ6dOgAe3t72Nvbo2nTppWktjAFZyqvXLkSmzZtYk1LadjY2MDb2xsAEB0dTW/A5cTLywvz5s2Dl5cXc05aWhpz587F6tWrUadOHfbECcHs2bOZ4DWenp5MkBEKRUxU3n7Gnz9/hqGhIc6vXybUzGhRCf35Cy1GTsX58+cxevRoofIQQvDq1SscPXoU165dKzTp68ePH2jcuLHYtYqTqKgoxpzzDTo/OEJRmJqawt7eHgMHDoS5uXmldmmHhYWhefPmyMnJgYKCAr58+YIGDUqf1McGK1aswJYtWwAAly5dwogRI1hWVDWJjIzE8uXLce7cOYHz/fr1w86dO2FgUPJObZLC8OHDcfXqVQDA9+/fSx2KolBEpPLMGAC6dO6MnIQ4vDy8Q9gyhWbBniM4//QlfkVEMDvwiMLfv39x9uxZHD16FJ8+fYKenh5CQkIKRfKRdAghCA8Ph6+vL96+fYvbt2/j69evRaZt1KgRBgwYAHt7e9jZ2VXKxugLFy7E7t27AQATJ07EiRMnKrzOsvD48WP07NkTQN6M8NJ6WyiCZGRkYMeOHdiyZYvAEkMjIyPs3r0bPXqUPuwkSdjZ2THzNdLS0qCoqMiyIko1o3LN2NXVFUOGDMH9XZvQq62VsOWWyo/f0TAZMwNz5s2Di4tLucoihCAsLAzq6uoSsaSivBBC8OnTJ9y6dQu3bt0S6CYsSO3atdGnTx/Y29ujd+/eFTaeGx8fDz09PSQmJoLD4eDFixfo0KFDhdRVHtLS0qCqqoqcnBzo6+uLNPmvJkMIwdWrV7F06VL8/PmTOa+qqooNGzZg+vTpVe4BFwCaN2+O0NBQKCsrFxlyl0IpJ5VrxoQQ9OrZEx+DAhB87jBqKxcdzk4U+Hw+us5eBr/PYQh+/552H5VCVFQU7ty5g1u3bsHNza3IiWwyMjLo0qUL7O3tMWDAALF3Je/atQuLFi0CkNc6DwgIYH2SWVF07NgRr169ApC3DKdRo0YsK5Js/Pz8MH/+fLx+/Zo5JyUlhZkzZ2LdunUS+TcWFlVVVSQmJkJPT6/YniYKpRyUasZi3SiCw+Hg2PHjSErPxOg1W5BdzPaFwkIIgdPhU3jhH4zUtDTY2dkxk24oRaOtrQ1HR0fcv38fcXFxuHLlCsaMGSMwgSYnJwePHj3CzJkz0bBhQ7Rp0wYnTpxARkaGWDTMmzcPdnZ2AIBfv35hypQpEOGhr9Lo0qUL85rOqi6e6OhoTJ48GdbW1gJG3LNnTwQFBWHfvn1V2oizs7ORmJgIgM6kprCHWM0YAHR0dODq6go3v0AMWrYByWlpZSqHx8vFkv3Hse3sFSZgfHh4OGxtbbFv3z6JvLlLGioqKhg2bBjOnTuHmJgYPH36FHPmzIGOjo5AOi8vL0yePBkNGzbE0qVLy70Dk5SUFM6dO8fcoG/cuCGRY7IFzdjd3Z1FJZJJVlYWtm7dCgMDA5w4cYL5zRkYGODu3bt48OABjIyMWFZZfujWiRSJID/ClBCHSDx+/JgoKyuTRprq5NHezYTv8VDo4/2FI6S1cXPC5XLJnj17yK9fv0j79u0J8rrKCQAydOhQkpiYKKosCiGEz+eTd+/ekbVr1xJTU1OB7xUA4XA4pF+/fuThw4ckNze3zPXcvHmTKVNeXp4EBweL8VOUn8zMTKKgoEAAkEaNGhE+n8+2JImAz+cTV1dXoqurK3Bd1K5dm+zcuZNkZWWxLVGs+Pr6Mp/R0dGRbTmU6kmpHlthZkwIId+/fyddOncmAEgXq1bk6uZVJPPlnSINmPfmPnl+cDsZ2b0TkZGRJoYGBuTt27dMWdnZ2WTJkiUCNwd9fX3i7+9ftq+GwuDl5UXGjRtHZGVlCxlzs2bNyJ49e0hCQkKZyp49ezZTlrGxMUlLSxOv+HLSrVs3Rt+XL1/YlsM6gYGBpPP//2bzDy6XSxwdHUlMTAzb8iqEe/fuMZ91zZo1bMuhVE/YNWNC8p6yL168SNq3a0cAEFkZGWLVwpA49O1OZg7pT6bY9yYdzU2IipIiAUAMmjUju3fvJunp6UWWd+vWLVKnTh3mxyMnJ0eOHj1KWzVi4M+fP8TZ2Zk0bNiwkCkrKioSR0dHEhQUJFKZGRkZAq3v6dOnV5D6srF582ZG27Fjx9iWwxoxMTHE0dGRcLlcgb97586dSWBgINvyKpQTJ04wn/fAgQNsy6FUT9g344IEBQWRffv2kQkTJhCb1q2JmakJsbK0JMOGDSNbtmwhL168EKpbNCwsjFhZWQncNIYNG0b+/PkjDpk1npycHOLq6kq6dOlSyJQBEDs7O3L16lWSnZ0tVHkfP35kuoMBkGvXrlXwJxCeJ0+eMLqWLFnCtpxKJysri+zcuZPUrl1b4G+sq6tLXF1da8RD7pYtWyTy2qRUKyTLjMVJZmYmmTVrlsANRE1NjVy6dKlG3EAqiw8fPpCZM2cSZWXlQqasra1NNmzYQH7//l1qOceOHWPy1alTh/z8+bMS1JdOWFgYo2vIkCFsy6k0+Hw+uXPnDjEwMBD4myorKxMXFxeSkZHBtsRKY8GCBcznf/nyJdtyKNWT6mvG+Vy+fJnUrVtX4IYyePBgEh0dzba0akVSUhLZv38/MTQ0LGTKMjIyZMyYMSQ0NLTY/Hw+nwwfPpzJ0759e5KTk1OJn6BocnJyiJSUFAFAzM3N2ZZTKXz48IH07Nmz0KS9SZMmCfVgVd0YPXo08z2UdA1TKOWg+psxIYRER0eTwYMHC9xc6tatS86fP09byWKGz+eTJ0+eEHt7+0Lji1JSUmT69OkkKiqqyLwJCQmkcePGEjdZJn/WcK1atar19fL3718yZ84c5uEj/7C1tSW+vr5sy2ONrl27Mt8FXaFBqSBqhhkTkmcSly9fJmpqagI3mgEDBhRrDpTy8ePHD7J8+XJSr169QpO9Vq5cWeSN7e3bt4wZcLlccvv2bRaUC1JwRvXfv3/ZliN2cnJyyP79+wv1IOno6NBhHUKIiYkJMxm0pn8XlAqj5phxPjExMQLdofljlKdPn6Y/tAoiJSWFbNy4kaioqAh87/Xq1SO7d+8mmZmZAumdnZ0FZsM/e/aMHeH/z7Rp0xg9Pj4+zHk+n0+ysrJIamoqSUhIqJLXz6NHj4iRkVGhh6UNGzYUu2KhpqGurk7y15pTKBVEzTPjfK5du8b8yPKPvn37koiICLalVVtiYmLIvHnziIyMjMD33rhxY3LmzBnC4/EIIYTk5uaSMWPGMO+rqKhUSjcpj8cjc+bMIdbW1sTMzIwYGRkRfX19gaVyioqKREFBgUhLSxcaGzcwMCDx8fEVrlMchIaGkn79+hX6DGPHjqW/gQLweDxmuMXKyoptOZTqS801Y0IIiY2NFZicAeRFETpx4kSVbOVUFcLCwsiYMWMIh8MR+O5NTU3J/fv3CZ/PJ9nZ2aRv374CM+E/ffpUobqePXtW5FItUY5Xr15VqMbykpCQQBYuXFjogcjGxoZ4eHiwLU/iiI6OFnhYp1AqiJptxvncvHmTaGpqCtycevbsScLDw9mWVq3x9/cnvXr1KmRonTp1Il5eXiQ9PZ107NiROd+wYcMKXfIUExMjsN5Z1KNBgwYSGwqSx+ORw4cPk/r16wto1tbWJmfPni1XWNPqTGBgIPNdTZo0iW05lOoLNeN8/v79S8aPHy9wo1JRUaHRuyoBNze3QkFagLx1vT4+PsTc3FygK7gig7csX768zGa8e/fuCtNVHtzd3QvFGJeXlyerV68mqampbMuTaAoGfVm+fDnbcijVF2rG/+Xu3btEW1tb4MbVrVs38u3bN7alVWv4fD65cuUKadasmcB3LyUlRcaPHy+wKYG5uXmFLTGJj48vFG1KmKNevXoSZ2zfvn0rtKQPABkxYgT58eMH2/KqBOfOnZP4hy1KtaBUjxX7FoqSTt++ffHhwwdMmjSJOff06VO0aNEC8+fPR2xsLIvqqi8cDgfDhg3Dhw8fcOjQIWbf2NzcXJw5cwZRUVGoVasWAMDf3x/9+/cX2/7KBVFVVcXSpUtFzjd37lxmK0+2SUlJwYoVK9CiRQu4uroy5y0sLPDq1StcunQJjRs3ZlFh1eHPnz/Ma7qXMYVVhHFsUo1axgV58OBBoU0RVFRUyMaNGyWuFVTdSE1NJZs2bSq0HKpgQIq+ffsKHf9a1Lo1NDSEbhUrKytLxPrj3NxccuLEiULzHzQ0NMi///5Lx4XLwNKlS5nv0c3NjW05lOoL7aYujaSkJLJy5cpCE3s0NDTIwYMHK8QMKP8jNjaWzJs3r8ilRADI6NGjK8Rk9u/fL7QZL168WOz1i8qrV6+IpaWlgC5ZWVmyfPlykpyczLa8KouDgwPzfUraftuUagU1Y2GJjIwkjo6OhUIFNmvWjFy5coVO8qpg/P39iZmZWZFm6OjoyKxRFhdZWVmkSZMmpRqxrKwsqxHcfv78SUaMGFFI16BBg+g8BzHQu3dv5jutrvs1UyQCasaiEhISQoYOHVro5mdtbU3c3d3Zlletyc7OJuvXry+0RhYA6d+/v9iHDk6dOlWqGTs6Ooq1TmFJTU0lq1evJvLy8gJ6TE1N6XUoRiwsLJjhEdrNT6lAqBmXFU9PT2JnZ1fo5tyzZ0/i7+/PtrxqTVBQEHOTLHg0b95crLsK8Xi8QqEiCx5cLpd8/fpVbPUJQ25uLjl79ixp0KCBgBY1NTVy+PBhsfcQ1HTyv2dNTU22pVCqN9SMywOfzyf3798vtIYTABkzZgwJCwtjW2K1JTs7mzg7OxdqJauoqAjEjy4vrq6uxZrx6NGjxVaPMHh5eZE2bdoIaJCWliYLFy4kCQkJlaqlJsDn85nry9TUlG05lOoNNWNxkN9aKbj9H5C3j++8efPoWFMF8v79e9KyZctCLVZxrQnl8/mkdevWRZpxUFCQWOoojYiICDJu3LhC9ffr14/ur1uBxMfHM9919+7d2ZZDqd5QMxYnmZmZZPfu3YW2DFRRUSHr1q0jsbGxbEusluTk5JCVK1cWinXdtWtXkpaWVu7ynz59WqQRVjTp6elk48aNRFFRUaBuIyMj8ujRowqvv6bz6dMn5jsfO3Ys23Io1RtqxhVBYmJikcuh5OTkiIODg1i7USn/w8/Pj6iqqgp853Xq1BHLFoz/7R5++/Zt+QUXQ/7e2//taVFVVSX79++ny+kqiefPnzPf/aJFi9iWQ6neUDOuSKKiosj06dMLLYcC8nbJOXv2bKG9fCnlIysrS2Bzifxj+vTpJCUlpczlFmwda2tri1GxIH5+fqRDhw4C2qWkpMicOXMkIrBITeLy5cvM32Dbtm1sy6FUb6gZVwZfv34lCxcuFNgXN/+oX78+WblyJd0hSsysXr260HfdpEkT4ufnV+Yyp02bRvT19cmbN2/EqDSP379/k0mTJhXqau/Rowf58OGD2OujlE7BwC+nTp1iWw6lekPNuDJJTU0lR48eLXL2tZSUFBkyZAhxd3enAUTExO3bt4msrKzA9ywrK0sOHz4s8neclJREfHx8yKtXr4inp6fYllBlZmaSLVu2FAr72axZM3Lnzh16LbDIqlWrmL/HgwcP2JZDqd5QM2YDPp9PXr16RUaMGFFkmEcjIyNy8ODBcnWrUvLw9/cn6urqRS5LKu379ff3J46OjsTgPztJMd3VWlpk6NAh5MGDByIHhODz+eTGjRsCu1EBILVr1yY7d+6U2H2RaxJTp05l/i7v3r1jWw6lelOqx3IIIRASoRNS/kdUVBSOHj2KI0eOIDo6WuC9WrVqwcHBATNnzoShoSFLCqs+ERER6NOnD4KDgwXOGxoa4vr16zA2NhY4HxQUhFkzZ+L1mzdooF4fAzu2hWVzfbTUbQIlBXlk5/Dw5Vck/EK+4KGnHwK/fIOeri527toFe3v7UvUEBwdj/vz5cHd3Z85xuVxMnToVGzduRP369cXzwSnlwt7eHrdv3wYAREZGQltbm2VFlGoMp9QUwjg2oS3jcpOVlUUuXbpEbG1ti2yFde/enbi6upL09HS2pVZJkpOTyZAhQwp9r/Ly8uT06dOEkLz14hs3biQyMjLEWLcJue6ymmS/ukf4Hg+LPXLfPiBvju4ifdrlrUUeM2ZMsXstx8TEkOnTpxMulyugoXPnziQwMLAyvw6KENjY2DB/IzqDnVLB0JaxJBIQEIADBw7g/PnzhfbsVVRURM+ePWFvb49+/fqhXr16LKmsehBCcOTIEcybNw/Z2dkC702cOBHpaWm4eu0alo8fjtUTR0NOVlakss89dMPc3YfRVFcPT54+hZqaGgAgOzsbBw4cwPr165GUlMTk0dXVxY4dOzBw4EBwOKU/GFMqF11dXXz//h1169bF379/2ZZDqd6UegOgZswi8fHxOHnyJA4ePIiwsLBC73O5XHTo0AH29vawt7eHrq4uCyqrHsHBwRg2bBhCQ0MFznO5XFzcsBzDunYse9lfv6Pb3BXQaaqLl69e4fnz51iwYAE+f/7MpFFWVsaqVaswf/58yMnJlbkuSsWipKSE9PR0tGjRAh8/fmRbDqV6Q824KsDn8/H48WNcvXoVd+7cQWxsbJHpTExMGGO2tLSkra0SSEtLw7x58/Dvv/8y5/5duRAT+/Uod9kBn7+h3bQF0NDUws+fP5nzHA4HEydOhLOzMzQ1NctdD6XiSE1NhYqKCgCgU6dOePbsGcuKKNUcasZVjdzcXHh6euLmzZu4desWvnz5UmS6hg0bYsCAAbC3t0enTp0gK0KXa03iyJEjmD1rFvq1b43rW9aI7QFm54XrWLL/GPN/W1tb7NmzB5aWlmIpn1KxfPv2Dfr6+gCA4cOH4/LlyywrolRzSr3xcCtDBUV4pKSk0L59e2zfvh2hoaH4+PEjXFxcYGNjI5AuIiICBw8eRM+ePVG/fn2MGjUKly5dEhizrKp4eXlhzpw5uHTpErKysspV1p8/fyArI4NDy+aWaMSRMXEYt24r1HoOg1Ine5iPnwm/kKIfhABg/oiBMNFrCkUFBVy6dAkvX76kRlyFiImJYV5raGiwqIRCyYO2jKsQv3//xp07d3Dz5k24ubkVmqQEANLS0mjVqhWsrKyYw9jYGNLS0iwoLhstWrRASEgIAKBevXpwcHDA1KlTRV7+lZOTgyaNG6Nv61Y4snxesekSklNgMWEWOluaYfqgflCvWxvfIn6jiZYG9BoWv9zl9L0nmLhpJ758+cK0sihVg5s3b2LQoEEAgE2bNmHlypUsK6JUc2g3dXUlJSUFjx49ws2bN3Hv3j0kJiYWm1ZeXh7m5uYCBm1oaAgpKanKEywCOjo6+PXrV6HzdnZ2mDZtGgYPHgx5eflSy3F3d0fXrl3hc3I/LJs3Kzbd8oMn8DboA14e3imSzozMLGgPGINFS5Zi9erVIuWlsMuRI0cwffp0AMCxY8cwZcoUlhVRqjmlmnHVaS5RBFBRUcHQoUMxdOhQ5OTk4NWrV7h16xYeP36M0NBQFHzIyszMhIeHBzw8PJhzysrKsLCwEDBofX19iZgUpq6uXqQZv3jxAi9evEDdunUxfvx4TJ06FUZGRsWW4+PjAxUlRZgb6JVY351XnuhhY4nhTpvwIiAYDdTUMGNIP0y1711iPgV5ObRuYQBfXx/hPhhFYvjz5w/zWl1dnUUlFEoe1IyrATIyMujSpQu6dOkCIK/V/O7dO/j6+jLH169fBfKkpqbi5cuXePnyJXOuTp06sLS0hJWVFSwsLKCjowNtbW1oaWlBRkam0j5PaTfH+Ph47NmzB3v27IGtrS2mTZuGoUOHQkFBQSDdu3fvYG6gBy635KkRYVG/cfjGXSwYORgrJoyE98dQzNt1CHIyMhjfp1uJeS0M9XHO7bVwH4wiMRQ0YzpmTJEEqBlXQ1RUVGBnZwc7OzvmXEJCAvz8/AQMuuCyHABITEyEm5sb3NzcBM5zOBzUr18fDRo0gLa2NrS1tYt8raamVqrxCYMoLZXXr1/j9evXmDt3LtNabtmyJQDgT3Q0GqmrlVoGn09g1bwZNs+YCAAwN9THh+8/cfjG3VLNuJFGfcTGxQmtlyIZ0AlcFEmDmnENQVVVFd26dUO3bv8zl5iYGAGD9vHxwe/fvwvlJYQgJiYGMTEx8Pf3L7YOaWlpaGlpCRi1trY25OXlweVyweFwwOVymeO//88/V9w665JITEzEvn37sG/fPujo6CAkJAR8Ph8cTumXuJZaXbRoqiNwrkUTHbg+e1NqXi6Hi9zcXJH1UtiFtowpkgY14xqMuro6evfujd69/zc2GhUVBV9fX3z48AFRUVGIiopCZGQkoqKi8Pv3b/B4vGLL4/F4+PXrV5HjvZVJeHg4Hj9+jFq1ayE+ofRWa3sTI3wOjxA49zk8Eo01S2+h/1979x4VVdnvAfw7iDMIgnJXE0aPyPCmeEGMUDENtXwxj2malgheI0MFCc3M5TVLvCAY0koN006nReax3hTLS16gVORuAuprRmrgmGI4wIwwc/7wdRKFYWYYmD3y/fyj7Hn2nh9rufyu/dvPfp5bf1XA4T+LR5DleBDG9vb2jz3eIDIHhjHV0aVLF4wdOxZjx4597DO1Wg25XF4noB/98/r160bd2ZpS9+7dERISgtOnT2Pn9k8aHR81+WUMnrMQa3d+iUnBQ3HmfDG2fXNA5+tQD+RcuIQ+ffqYomxqQQ/CmJO3SCj4ahOZnFKpRGlpKa5du4bS0lLU1NRArVZDrVZDo9Fo/97QzwUFBUhOTjb4ezt37ozNmzdj4sSJEIlE2Lt3LyZMmIDf9u2Gh7vubQu/Sz+Nd5NTcPHqNXTv3AnRU8Y3Optao9Gg2/gwTHo9FBs2bDC4XjIPpVKpfTVu0KBByMho/HEEURPx1SZqeRKJBFKpFFKp1Kjzz549a1AYW1lZYf78+Vi5ciUcHBy0x59//nm0a9cOu9IOY2n4FJ3XGDMkAGOGBOgc86hj2fn4vfQGQkJCDDqPzIuTt0iIuBwmCY4hrcPAwEBkZWUhPj6+ThAD91/VmjJlCj75Jg33dDzrNlbSnm/xDx8fDBs2zOTXpubDyVskRAxjEhxXV90tZQBwcnLC9u3bkZ6ejn79+jU4LioqCtflf+LDXabdCODwmWzsPZaBmLffxr1793D16lVUV1eb9DuoeXDBDxIitqlJcNq1awd7e3tUVFTU+/nMmTPx4YcfwsWl8XeIfX198c4772BN3Dq8NORZ9GtkNS59lFfcxawPEvD88OEYN24cHBwctBta2NnZwcXFBc7OznBxcdHr7/os7UmmwzY1CRHDmATJ1dX1sTD29fVFcnIyBg8ebNC1li1bhgP792PM28txLCkOXh4Nb/7QmLuVVRgbuwJ/VVdjx6ef4uLFi3V2llIoFFAoFI8tqKKLvb09YmJisHz5cqPrIv2xTU1CxDY1CVKXLn8HZvv27bFp0yZkZ2cbHMTA/QllB9LSYO/ohKFz38bx7Hyjarp87Q8Ez3sHeZev4MCBNHTr1g0BAQHaFb+MVVFRgY0bN8KANxuoCRjGJEQMYxKk2NhYdO/eHa+99hoKCwsRHR3dpG0gO3XqhBMnT6Knz9MY/tYizNu4FTfL9dv7uVqpQmLqPvQJfRM37lbhxx+PITAwEMD9pUL3798POzs7o2sDgPHjxwtik47WgGFMQsT3jKlVUavV2LJlC5YsWQJ1bS1eDR6KV54PwgAfL3R2cdaOu3NXgZwLl5D281mk7D+Em7fLERERgbi4ONjXs+JWYmIiFixofJGQ+jg4OODChQsMhhYSHByMo0ePAri/jGqHDh3MXBG1AtzPmKg+crkcKSkp+Dg5Gb9euQIAcO7YAXbtbKC6V4PSm38CADp27IDp02cgIiIC3t7eDV6vtrYWgwcPxunTpw2uJSEhAfPnzzfq9yDD+fr64ty5c5BIJKiqqmJHgloCw5hIF41Gg5KSEmRlZaGwsBBVVVUQi8Xo1q0bBgwYAB8fH7Rp00avaxUUFMDPz0/n+t2P6tOnD7KysprUgifDuLm5QS6Xw9PT06CJdkRNwDAmaklLly7F2rVr9R5//PhxDB06tBkroofV1NRALBZDo9Fg4MCBOHPmjLlLotah0TDmBC4iE1q2bBl69uyp9/j33nsPBQUFzVgRPezmzZvaWet8Rk9CwjAmMiEbGxt88knjO0U9cPLkSfTv3x/R0dG4c0e/2d1kvIcX/ODqWyQkDGMiExs2bBhmzpypc8ycOXPg5eUF4P7kr82bN0Mmk+Hzzz/n+8bNiK81kVAxjImawfr16xv8z97X1xdJSUkoKCjAmjVrtJvbl5WVITQ0FM899xzy841bmIR0YxiTUDGMiZqBo6MjEhMT6/0sKSkJ1tbWsLGxwdKlS1FYWIiXX35Z+/nJkyfh5+eHqKgotq5NjGFMQsUwJmomEydOxJgxY+ocCw0NRVBQUJ1jUqkUe/fuRVpaWp3WdUJCAmQyGXbv3s3WtYnwmTEJFcOYqJmIRCJs3boV7du3B3B/pa24uLgGx7/44os4d+7cY63radOmYejQoWxdmwDvjEmoGMZEzcjDwwPffvstJkyYgH379qFTp046x0skknpb1+np6fDz88OCBQvYum4ChjEJFRf9IBKwgwcPYt68ebh06ZL2mLu7O+Li4hAaGsqlHA3k5+eHnJwctGnTBiqVClZWvB+hFsFFP4gs2YPW9fvvv1+ndR0WFsbWtREePDN2c3NjEJOg8F8jkcBJJBK8++67KCwsxPjx47XH2bo2jEajqRPGRELCMCayEFKpFF9//TUOHjyoXXKztrYWiYmJkMlk2LVrF2dd63D79m3cu3cPAJ8Xk/AwjIkszAsvvICCggKsXbu23tZ1Xl6emSsUJk7eIiFjGBNZIIlEgiVLlqCoqAgTJkzQHn+4dV1eXm6+AgWIYUxCxjAmsmCenp7Ys2dPnda1Wq1m67oeXPCDhIxhTPQEqK91fePGDYSFhSEoKIita/DOmISNYUz0hGiodZ2RkQE/Pz/Mnz+/VbeuGcYkZAxjoifMg9b1999/D29vbwD3W9dbtmyBTCbDZ599BrVabeYqWx7DmISMYUz0hBo1ahTy8/Oxdu1a2NraArjfug4PD2+Vs64ffmbMMCahYRgTPcEetK4LCwtbfev64TtjFxcXM1ZC9DiGMVErwNb132Hs7OyMtm3bmrkaoroYxkStSGttXWs0Gm0Ys0VNQsQwJmplHm5dv/LKK9rjT3LrWqFQoKqqCgDDmISJYUzUSnl6euKrr77CDz/88MS0ri9evIjU1FQcOXIE586dg1wuR21tLWdSk+BxP2MiglKpRHx8PFavXo3Kykrt8UGDBiEpKQn9+vUzX3F6Kisrg5eXF+7evVvnuJWVFTp27Ihbt24BAGQyGUJCQuDu7g53d3e4ubnB3d0dPj4+2tY9kYk1up8xw5iItEpKShATE4M9e/Zoj1lZWWHu3LlYvXo1OnbsaL7iGnHt2jV07drV6POdnZ2Rm5vbpGsQNaDRMGabmoi0Gmpdf/TRR/D29sbOnTsF27p+6qmnEBQUZPT5f/75J86fP2/Cioj0xzAmoseMHDkS+fn5+OCDD7StW7lcjunTpyMoKAi5ubnmLbABs2bNMvrcXr16Yfjw4Sashkh/bFMTkU6///47Fi5caBGt68rKSnTp0gV37twx+NwTJ0406c6aSAe2qYmoaTw8PLSta5lMBkC4rWtbW1tMnTrV4PNmzJjBICaz4p0xEelNpVIhPj4eq1atqjPrOjAwEElJSejfv78Zq7svLy/PoNnfTk5OKC4u5hKZ1Jx4Z0xEpiMWi7F48WIUFRVh4sSJ2uM///wz/P39ERkZidu3b5uxQqBv377w9/fXe/z69esZxGR2DGMiMpiHhwdSU1Mfa10nJSVBJpMhJSXFrK3r2bNn6zVuyJAhCA8Pb95iiPTANjURNYkQW9cVFRXo3LkzFApFg2Osra2Rk5OD3r17t2Bl1EqxTU1EzUuIrWt7e3tMnjxZ55iYmBgGMQkG74yJyKQOHz6MyMhIFBcXa4+5urpi3bp1CAsLg5VVy9wDnDp1CoGBgfV+JpVK8csvv8DOzq5FaqFWj3fGRNSyRowYgfz8fKxbt04bdnK5HDNmzMCQIUOQk5PTInUEBAQ0eOe7ZcsWBjEJCsOYiExOLBZj0aJFKCoqwqRJk7THW7J1LRKJ6p3INW7cOLz00kvN+t1EhmKbmoianbla17du3YK7uztqamoAADY2NiguLoanp2ezfB9RA9imJiLz09W6Hjx4MLKzs5vle52cnNCrVy/tzxEREQxiEiTeGRNRi7p69SpiYmKQmpqqPWZlZYWIiAisWbMGjo6OJv2+zMxMhISEoGvXrjh16hTEYrFJr0+kB+5nTETCdPjwYcybNw9FRUXaYy4uLli3bh3Cw8Ob3LqurKxESUkJVCoVbGxsIJVKIZFImlo2kTEYxkQkXCqVCps3b8aqVavqLNDx7LPPIikpCX5+fgZdLysrC9u2bUNGejrOFxbWWQWsbdu28O3dG8OGD8ecOXO0K4cRtQCGMREJX32ta5FIhDfffFOv1vVPP/2E6KgonMnMhEcnN4x+1h8DfHpC5tkVNmIxKpXV+OXyb8gquojvfsrEzdvlGDliBDYnJODpp59u7l+PiGFMRJbjyJEjiIyM1Lt1rVQqsXTpUmzatAkDn5bh3bBXETLoGbRp06bB71CqVPj6xwysTvkCv/5RhlWrViE2NrbFFiOhVolhTESWRaVSISEhAStXrqzTug4ICMDWrVu1rWuFQoH/HjsW6enpWDU7FAunjNcZwo+qVqqwfPtubPifPXj99deRkpICa2trk/8+RGAYE5Gl0tW6XrFiBUKnTkX6yZP4bsNKPOfXx+jvST18Aq+vuP++8/bt2yESNfr/JpGhGMZEZNnqa13b2tqiuroaB+PXYMQzhk3yqs9n+w9h+pqN+OKLLzBlypQmX4/oEVz0g4gsW3BwMPLy8hAXF6ddMKS6qgoLp4w3SRADQFjISEwMDkJk5FsoKyszyTWJDMEwJiLBE4vFiI2NRVFREaRSKZ5yc8Gq2dP0Pv+Dz76EVeCLiIr/uMExH8W8hZr/PK8mamkMYyKyGGKxGNevX8eCV8fBRqLfSlqZ54ux7Zs09PHqrnOcq2NHTBsdjO3btkGpVJqiXCK9MYyJyGKkpqZCBCD8n6P0Gn+3sgpTV8Thk3cWwNG+faPjI14OgfzmTRw6dKiJlRIZhmFMRBYjMzMTfXv+F5w62Os1PnJDEv456Bm9ny3/o5sn3JwckZmZ2ZQyiQzGl+qIyGJknT2LITIvvcZ+eegYsosv4cyniXpfXyQSYYDMC2cZxtTCeGdMRBajtLQUnu6ujY77vUyOqPiPsXvFIr2fLT/g4e6K0tJSY0skMgrvjInIYtTW1uq1ylZW0UXcuF0O/+mRD52rxoncc0j6+ltUH/9Xg9dpY2WF2toak9VMpA+GMRFZDHt7e5RX3G10XLB/P+R/Xvc1phnvb4SP1AOLpk7SGeh37ipgb+/Q5FqJDMEwJiKL0bt3b+RdvNzoOHs7W/Tu0a3OMTsbGzg5ODx2/FG5l37Fcy+MbkKVRIbjM2Mishj+AwfibNHFOvsUm9JfCgWKrpTA39+/Wa5P1BCGMRFZjNGjR0N+uxw/nM42+Nwft67H5ugInWO++P4YAGDkyJHGlEdkNG4UQUQWQ6PRwK9/fzzV3gb/2rDS5NfuN+0t9Ojli//bt8+k16ZWjxtFENGTQyQSYWFMDPZnnMbBn8+a9NrbvklDwaXLiIqONul1ifTBO2MisigajQYvjBqFwoI85O3aCkcH/Vbj0uXKH6XoM3UuJk2ejB07dpigSqI6uJ8xET15SkpK0LdvH/SWeuDAptVob9vO6GvduFWOYW8tQrVGhNy8PHTo0MGElRIBYJuaiJ5Enp6eOHAgDbn/voKRC5bgtz+M24O44NKvGDo3FuVVSvxw6BCDmMyGYUxEFikwMBBHjx7FtdsV8J36Jj7eux/3avRbOauqWon3d/4v/GfMg7Vte6RnZKBnz57NXDFRw9imJiKLdufOHcTExGDHjh3o7OqM2WNfxJjBAfDt0Q0S8d/rUiuqqpF74d/YezwDO/cfwp27CixevBjLly+HRCIx429ArQCfGRNR65Cfn4/k5GTs3r0bCoUCbdtao3uXzpC0bYtKpRK/XvsDarUaTo6OmDlrFt544w306NHD3GVT68AwJqLWpaqqCvn5+cjKysLly5ehUqlgY2MDb29vDBgwAL169YJYbNhOTkRNxDAmIiIyM86mJiIiEjqGMRERkZkxjImIiMyMYUxERGRmDGMiIiIzszZgbKOzwYiIiMhwvDMmIiIyM4YxERGRmTGMiYiIzIxhTEREZGYMYyIiIjNjGBMREZkZw5iIiMjMGMZERERmxjAmIiIys/8HYAP58EZDtjkAAAAASUVORK5CYII=",
      "text/plain": [
       "Graphics object consisting of 40 graphics primitives"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13/50"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.density()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0\n",
      "1 2\n",
      "2 +Infinity\n",
      "3 +Infinity\n",
      "4 4\n",
      "5 2\n",
      "6 2\n",
      "7 1\n",
      "8 1\n",
      "9 3\n"
     ]
    }
   ],
   "source": [
    "for k in range(10):\n",
    "    print(k, g.distance(0,k))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "+Infinity"
      ]
     },
     "execution_count": 14,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.distance(9,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>Here is the adjacency matrix of the graph. &nbsp;Row <span style=\"font-family: 'courier new', courier;\">i</span> column <span style=\"font-family: 'courier new', courier;\">j</span> is 1 if the edge <span style=\"font-family: 'courier new', courier;\">[i,j]</span> is part of the relation. &nbsp;Recall that in Python, indexing of matrices starts at 0 just as with lists; so the first row is row 0, corresponding to the digit 0. &nbsp;This is why we used the digits as our vertex set.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0 0 0 0 0 0 0 1 1 0]\n",
       "[0 0 0 0 0 0 1 0 0 0]\n",
       "[1 1 0 0 0 0 0 0 0 1]\n",
       "[0 0 0 1 0 1 0 0 0 1]\n",
       "[0 0 0 0 0 0 1 0 0 0]\n",
       "[0 0 0 0 0 1 0 0 0 1]\n",
       "[0 1 0 0 0 0 0 0 1 1]\n",
       "[0 1 0 0 0 1 0 0 0 0]\n",
       "[0 0 0 0 0 0 1 0 0 0]\n",
       "[0 0 0 0 1 1 0 0 0 0]"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R=g.adjacency_matrix()\n",
    "R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>The square of this matrix gives us information on the number of paths of length 2 between any two vertices.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0 1 0 0 0 1 1 0 0 0]\n",
       "[0 1 0 0 0 0 0 0 1 1]\n",
       "[0 0 0 0 1 1 1 1 1 0]\n",
       "[0 0 0 1 1 3 0 0 0 2]\n",
       "[0 1 0 0 0 0 0 0 1 1]\n",
       "[0 0 0 0 1 2 0 0 0 1]\n",
       "[0 0 0 0 1 1 2 0 0 0]\n",
       "[0 0 0 0 0 1 1 0 0 1]\n",
       "[0 1 0 0 0 0 0 0 1 1]\n",
       "[0 0 0 0 0 1 1 0 0 1]"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R*R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>The cube gives us information on paths of length 3.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0 1 0 0 0 1 1 0 1 2]\n",
       "[0 0 0 0 1 1 2 0 0 0]\n",
       "[0 2 0 0 0 2 2 0 1 2]\n",
       "[0 0 0 1 2 6 1 0 0 4]\n",
       "[0 0 0 0 1 1 2 0 0 0]\n",
       "[0 0 0 0 1 3 1 0 0 2]\n",
       "[0 2 0 0 0 1 1 0 2 3]\n",
       "[0 1 0 0 1 2 0 0 1 2]\n",
       "[0 0 0 0 1 1 2 0 0 0]\n",
       "[0 1 0 0 1 2 0 0 1 2]"
      ]
     },
     "execution_count": 24,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R*R*R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>The matrices above are technically not adjacencly matrices since they are not 0-1 matrices. &nbsp;See Example 3, below, for how to remedy this situation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "g.transitive_closure().adjacency_matrix()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<h5>Example 2 - Prime Steps</h5> <p>\n",
    "     We define $r$ on the divisors of 60 by $ a r b  \\Leftrightarrow  \\frac{b}{a}$ is a prime.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D=60.divisors();D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: [2, 3, 5],\n",
       " 2: [4, 5, 6, 10, 15],\n",
       " 3: [6, 10, 15],\n",
       " 4: [10, 12, 15, 20, 30],\n",
       " 5: [10, 12, 15],\n",
       " 6: [12, 15, 20, 30],\n",
       " 10: [20, 30],\n",
       " 12: [30, 60],\n",
       " 15: [30],\n",
       " 20: [60],\n",
       " 30: [60]}"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r={};\n",
    "for p in tuples(D,2):\n",
    "    if (p[1]//p[0]).is_prime():\n",
    "        if p[0] in r:\n",
    "            r[p[0]]=r[p[0]]+[p[1]]\n",
    "        else:\n",
    "            r[p[0]]=[p[1]]\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "6f5b9eeca810673c4f2aa96c8596aee79de89141",
      "text/plain": [
       "Graphics object consisting of 43 graphics primitives"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DiGraph(r).plot(tree_root=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p><h5>Example 3.</h5><p>\n",
    "\n",
    "</p> This short example illustrates the transitive closure of a relation. &nbsp; We start by defining a relation directly as a simple dictionary. &nbsp;The graph is a \"chain\" of length 4.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "s={}\n",
    "s[0]=[1]\n",
    "s[1]=[2]\n",
    "s[2]=[3]\n",
    "s[3]=[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "DiGraph(s).plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>The transitive closure of a relation is the smallest <em>transitive relation</em> containing that relation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "DiGraph(s).transitive_closure().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p><strong>Example 3. &nbsp;</strong>This next example is of a relation that is defined in terms of a boolean function. &nbsp;It is based on mod 17 arithmetic, where $a\\cdot b (mod 17)$ &nbsp;is defined to be the remainder when 17 is divided into $a\\cdot b$. &nbsp;For example $5\\cdot 10 (mod 17) = 16$ &nbsp;since $5\\cdot 10 = 50 = 17\\cdot 2 + 16$</p>\n",
    "\n",
    "<p>The set of remainders when you divide by 17 is $\\{0, 1, 2, \\ldots , 16\\}$ but since 17 is prime and we start with the positive remainders, products will never equal 0 mod 17.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]"
      ]
     },
     "execution_count": 9,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B=range(1,17)\n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>We define the relation $m$ on $B$ by &nbsp;$(a, b)\\in m$ &nbsp;if $3\\cdot x (mod 17) = y$ &nbsp;or&nbsp;$5\\cdot x (mod 17) = y$. &nbsp;In Sage, this translates to the following function.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def m(x,y):\n",
    "    return (3*x).mod(17)==y or (5*x).mod(17)==y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>Changing the number 3 and 5 in the definition above to 3 and 6 creates an interesting alternative relation. &nbsp;Also changing the modulus can be interesting, but if you use a non-prime modulus, you have to include 0 as a possible remainder.</p>\n",
    "<p>Again, we build a dictionary based on the boolean function.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "md={}\n",
    "for k in B:\n",
    "    for j in B:\n",
    "        if m(k,j):\n",
    "            if k in md:\n",
    "                md[k].append(j)\n",
    "            else:\n",
    "                md[k]=[j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "aaa1798907679c3acbfd5f35b229506dd093edfe",
      "text/plain": [
       "Graphics object consisting of 49 graphics primitives"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g=DiGraph(md)\n",
    "g.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]\n",
       "[0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0]\n",
       "[0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0]\n",
       "[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0]\n",
       "[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0]\n",
       "[1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]\n",
       "[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n",
       "[0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]\n",
       "[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]\n",
       "[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]\n",
       "[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1]\n",
       "[0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n",
       "[0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0]\n",
       "[0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0]\n",
       "[0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0]\n",
       "[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G=g.adjacency_matrix()\n",
    "G"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>The square of relation m can be determined by squaring the adjacency matrix of m. Thanks to&nbsp;Jason Grout, who pointed out how to turn all nonzero entries in the product to a 1. By doing that you lose the information about the number of paths of length two between any pair of vertices, but the plot of the graph is much nicer.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0]\n",
       "[1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1]\n",
       "[0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0]\n",
       "[0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0]\n",
       "[0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0]\n",
       "[0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0]\n",
       "[0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0]\n",
       "[1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0]\n",
       "[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1]\n",
       "[0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0]\n",
       "[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0]\n",
       "[0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0]\n",
       "[0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0]\n",
       "[0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0]\n",
       "[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1]\n",
       "[0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0]"
      ]
     },
     "execution_count": 14,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H=(G*G).apply_map(lambda x: 1 if x!=0 else 0)\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<p>Here is the graph of the square of m, but with multiple edges.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "7083039f15d58083d6bc388722afee4ed523e585",
      "text/plain": [
       "Graphics object consisting of 80 graphics primitives"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DiGraph(H).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
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