Prefix_trees.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tries, a.k.a. Prefix Trees\n",
    "\n",
    "Jacob L. Fine\n",
    "\n",
    "June 25th, 2024\n",
    "\n",
    "Since many strings may have the same prefix, we may desire to come up with some way to store them that reduces redundnancy. For instance, since the strings 'computation', 'computer', and 'compute' all share the prefix 'comput', there may be some method that stores 'comput' and then the remaining characters, 'ation', 'er' and 'e'. \n",
    "\n",
    "This leads to the concept of a 'prefix tree', also referred to as a 'trie'. Tries group strings based on their prefix, such that each node corresponds to one letter in a given word, and paths from the root node to each leaf node constitute a complete word. To insert a new string into the trie, or to check if an existing string is preset, we keep checking if the prefix (which is dynamic in length) of the query word, or the word we would like to insert, is present in the graph. We can determine whether a query string is present in our trie using depth-first search (DFS), since we keep following a path from the root node to the leaf node(s) until we find our string. \n",
    "\n",
    "Tries may also be used in autocomplete, for instance, if we type 'comput' into our phone keyboard, we may be recommended possible words such as 'computer', 'compute' and 'computation', or more. Combining tries with probablistic modelling and/or machine learning can be used to make even more powerful recommendations, for instance, if we know which terms the user prefers. \n",
    "\n",
    "In bioinformatics, tries can be used to group DNA or RNA sequences with common prefixes, which can be relevant in genome and/or transcriptome assembly, given that both cases require the efficient storage and retrieval of large sets of sequences.\n",
    "\n",
    "We will implement a trie below, for an arbitrary list of RNA sequences, and display the results as a graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UCmIAAAAAAADwKRTEAAAAAAAA4FMshmEYZocAAACoS9++ffXll1+qoqJCLpdLfn5+slgsGjt2rJKTk82OBwAAAC9ChxgAAPAKnTt3Vnl5uVwulyTp7NmzKi8vV2hoqMnJAAAA4G3oEAMAAF5h48aNGjVqVJXH7Ha7Dhw4oKuuusqkVAAAAPBGdIgBAACvMHLkSN1yyy2yWs8NX2w2m2bNmkUxDAAAAA1GhxgAAPAa53eJ0R0GAACAS0WHGAAA8BojR45U//79JUlTp06lGAYAAIBLQkEMAAB4DYvFomeffVZt2rTRT3/6U7PjAAAAwEsxZRIAALR4RUVFKioqUmlpqcrKylReXq42bdrI399fAQEBCg4OVnBwsNkxAQAA4CXsZgcAAAA4X2FhobKyspSVlaXt27dr27ZtOnz4cJ2vCwsLU0xMjAYPHqzo6GhFR0erc+fOzZAYAAAA3oYOMQAAYCqXy6WVK1dq+fLl+vjjj1VQUCDp3F0kDcNQRUVFvfdltVplsVjkdrslSeHh4RoyZIimTp2qCRMmyG7nWiAAAAAoiAEAAJMUFBRo8eLFWrBggY4ePSqbzeYpZDWmyv2GhobqkUce0axZsxQWFtboxwEAAID3oCAGAACajWEYSk9P14IFC+R0OiWpSYpgtansIHM4HEpKSlJcXJwsFkuzHR8AAAAtAwUxAADQLNLT0zV79mzl5ubKbrfL5XKZlqXy+H379tXChQsVFxdnWhYAAAA0P6vZAQAAQOtWXFysuXPnasSIEdq3b58kmVoMO//4+/bt04gRI/Too4+quLjY1EwAAABoPnSIAQCAJpOenq7p06crLy+vQYvjNzer1arIyEgtWbKEbjEAAAAfQIcYAABodOd3heXn57foYpgkVVRUKD8/n24xAAAAH0GHGAAAaFS7du3SxIkTW3xXWG0qu8VSUlIUFRVldhwAAAA0AQpiAACg0WzdulUJCQkqLS1t1rtHNjabzaaAgAClpqYqNjbW7DgAAABoZEyZBAAAjSI1NVWjRo1SSUmJVxfDJMntdqukpESjRo1SWlqa2XEAAADQyOgQAwAAly0tLU3jxo1TRUWFV06TrI3VapXVatXq1asVHx9vdhwAAAA0EgpiAADgsnz44YcaPXq0zp4926qKYZWsVqv8/Py0YcMGpk8CAAC0EhTEAADAJdu1a5eGDRumkpKSVlkMq2S1WtWuXTtlZGSw0D4AAEArQEEMAABckuLiYg0YMED5+flev2ZYfdhsNkVERCg7O1uBgYFmxwEAAMBlYFF9AABwSZ588knl5eX5RDFMOrfQfl5enp566imzowAAAOAy0SEGAAAaLD09XSNGjDA7hmk2b96suLg4s2MAAADgElEQAwAADeJrUyUvxNRJAAAA78eUSQAA0CC+NlXyQkydBAAA8H50iAEAgHrz9amSF2LqJAAAgHeiIAYAAOrFMAz1799f+/bt89nusPPZbDb17t1bOTk5slgsZscBAABAAzBlEgAA1Et6erpyc3Mphv2H2+1Wbm6utmzZYnYUAAAANBAFMQAAUC8LFiyQ3W43O0aLYrfbtWDBArNjAAAAoIGYMgkAAOpUUFCgbt260R1WA5vNpkOHDiksLMzsKAAAAKgnOsQAAECdFi9eLK6h1cwwDC1evNjsGAAAAGgAOsQAAMBFnT17VpGRkTp69KjZUVqs0NBQ5eXlMaUUAADAS9AhBgAALmrVqlUUw+pw5MgRrVq1yuwYAAAAqCcKYgAA4KKWL18um81mdowWzWazadmyZWbHAAAAQD0xZRIAAFxURESECgoKzI7R4kVERCgvL8/sGAAAAKgHCmIAAKBWhYWF6tKli9kxvEZhYaFCQkLMjgEAAIA6MGUSAADUKisry+wIXoXzBQAA4B0oiAEAgFplZWWxflg92Ww2CmIAAABegoIYAACo1Y4dO9SSVleYMWOGDMOQYRhyuVyKjIw0O5KHYRjasWOH2TEAAABQDxTEAABArTIzM1VRUWF2DI+ZM2d6/myz2TRjxgzzwlygoqJCmZmZZscAAABAPbCoPgAAqFFRUZE6depkdgyPHj16aP/+/bJardq+fbtuvPFG7d27V9dcc43Z0ao4fvy4goODzY4BAACAi6BDDAAA1KioqMjsCFXMmDFDVqtVhw8f1qxZsyRJffr0UWxsrMnJqjpx4oTZEQAAAFAHCmIAAKBGpaWlZkeoYvr06ZKk5cuXa/fu3dq9e7ekqtMoW4KWdt4AAABQHQUxAABQo7KyMrMjeMTFxenqq6+WJC1durTK/++8804FBASYlu1CLem8AQAAoGZ2swMAAICWqby83OwIHud3gW3evFmSZLefG8Z07NhRiYmJWrZsmQnJqjtz5ozZEQAAAFAHOsQAAECN2rRpY3YESVJgYKAmT57s+XtQUJCCgoLUvn17z2Mtadpk27ZtzY4AAACAOlAQAwAANfL39zc7giRp8uTJnuLXwIEDZbFYPP899thjkqSRI0cqMjLSzJgeLeW8AQAAoHYUxAAAQI1ayrpcld1fubm5ys7OrvJccnKyJMlms2nGjBnNHa1GLeW8AQAAoHYWwzAMs0MAAICWp6ioSJ06dTI7htc5fvy4goODzY4BAACAi6BDDAAA1Cg4OFhhYWFmx/Aq4eHhFMMAAAC8AAUxAABQq5iYGFmtDBfqw2azKSYmxuwYAAAAqAdGuAAAoFaDBw+WxWIxO4bXGDx4sNkRAAAAUA8UxAAAQK2io6PldrvNjuEV3G63oqOjzY4BAACAemBRfQAAUKvCwkJ16dLF7Bheo7CwUCEhIWbHAAAAQB3oEAMAALXq3LmzwsPDzY7hFSIiIiiGAQAAeAkKYgAA4KKGDBkim81mdowWjQX1AQAAvAsFMQAAcFFTp05lHbE6uN1uTZs2zewYAAAAqCfWEAMAABflcrkUERGho0ePmh2lxQoNDVVeXp7sdrvZUQAAAFAPdIgBAICLstvtSkpKktXKsKEmVqtVSUlJFMMAAAC8CB1iAACgTgUFBerWrRtTJ2tgs9l06NAhhYWFmR0FAAAA9cSlXgAAUKfw8HA5HA66oC5gt9uVmJhIMQwAAMDLUBADAAD1kpSUJJfLZXaMFsXlcikpKcnsGAAAAGggpkwCAIB6MQxD/fv31759+5g6qXNTJfv06aPs7GxZLBaz4wAAAKAB6BADAAD1YrFYtHDhQoph/+F2u7Vw4UKKYQAAAF6IghgAAKi3uLg4zZkzx+fvOGm1WjV37lwNHz7c7CgAAAC4BEyZBAAADVJcXKwBAwYoPz/fJ7vFbDabIiMjtWfPHgUGBpodBwAAAJfAty/vAgCABgsMDNSSJUt8shgmnZsquWTJEophAAAAXoyCGAAAaDBfnTrJVEkAAIDWgSmTAADgkvja1EmmSgIAALQevnVZFwAANJrAwEClpKQoICCg1XeKWa1WBQQEaMWKFRTDAAAAWoHWPXoFAABNKioqSqmpqfLz82u1RTGr1ao2bdooNTVVUVFRZscBAABAI2idI1cAANBsYmNjlZKSIqvV2uqKYpXvKSUlRbGxsWbHAQAAQCNpXaNWAABgivj4eK1evbpVdYpVdoatXr1aY8aMMTsOAAAAGhGL6gMAgEazdetWJSQkqLS01KsX2rfZbAoICFBaWppuueUWs+MAAACgkbWOS7gAAKBFiI2NVUZGhiIiIry2U8xqtSoiIkIZGRkUwwAAAFop7xypAgCAFisqKkrZ2dlKSkqSdK7byhtU5pwzZ46ys7NZQB8AAKAVY8okAABoMunp6Zo+fbry8vJUUVFhdpxaWa1WRUZGaunSpRo+fLjZcQAAANDE6BADAABNJi4urkV3i13YFUYxDAAAwDfQIQYAAJpFenq6Zs+erdzcXNntdrlcLtOyVB6/b9++WrRoEYUwAAAAH0OHGAAAaBZxcXHKycnR5s2b5XA4ZLPZmn3hfavVKpvNJofDoc2bNysnJ4diGAAAgA+iQwwAAJji8OHDWrx4sRYsWKAjR47IZrPJ7XY3+nEq9xsaGqqkpCQ9+OCDCgsLa/TjAAAAwHtQEAMAAKZyuVxatWqVli1bpszMTOXn50s6V8gyDKNBi/FbrVZZLBZPYS0iIkIxMTGaNm2axo8fL7vd3iTvAQAAAN6FghgAAGhRCgsLtXPnTmVlZWn79u3atm2bCgoK6nxdeHi4YmJiNHjwYEVHRys6OlohISHNkBgAAADehoIYAABo8YqKinTixAmVlpZq48aNmjt3rj744AN1795dAQEBCgoKUnBwsNkxAQAA4CWYNwAAAFq84OBgT8Hr4MGDkqRBgwYpMjLSzFgAAADwUtxlEgAAAAAAAD6FghgAAAAAAAB8CgUxAAAAAAAA+BQKYgAAAAAAAPApFMQAAAAAAADgUyiIAQAAAAAAwKdQEAMAAAAAAIBPsZsdAAAAoD7eeecdHTx4UPv375ckvfLKK+rQoYNuvPFGTZgwweR0AAAA8CYWwzAMs0MAAADUJSQkREVFRbLZbHK5XPLz89PZs2c1fPhwpaenmx0PAAAAXoQpkwAAwCt8//vfl8VikcvlkiSdPXvW8zgAAADQEHSIAQAAr3Dq1CldddVVOnXqlCTJarVqwIAB+uSTT2SxWExOBwAAAG9ChxgAAPAKHTp00I9//GNP8auiokIvvvgixTAAAAA0GB1iAADAa5w6dUphYWEqKSlR3759lZOTQ0EMAAAADUaHGAAA8BodOnTQlClTJElPPvkkxTAAAABcErvZAQAAAOpSVFSkoqIilZaW6oEHHpCfn5+uvfZa7dmzRwEBAQoODlZwcLDZMQEAAOAlmDIJAABalMLCQmVlZSkrK0vbt2/Xtm3bdPjw4TpfFxYWppiYGA0ePFjR0dGKjo5W586dmyExAAAAvA0FMQAAYCqXy6WVK1dq+fLl+vjjj1VQUCBJstlsMgxDFRUV9d6X1WqVxWKR2+2WJIWHh2vIkCGaOnWqJkyYILud5ngAAABQEAMAACYpKCjQ4sWLtWDBAh09elQ2m81TyGpMlfsNDQ3VI488olmzZiksLKzRjwMAAADvQUEMAAA0G8MwlJ6ergULFsjpdEpSkxTBalPZQeZwOJSUlKS4uDgW5gcAAPBBFMQAAECzSE9P1+zZs5Wbmyu73S6Xy2Valsrj9+3bVwsXLlRcXJxpWQAAAND8rGYHAAAArVtxcbHmzp2rESNGaN++fZJkajHs/OPv27dPI0aM0KOPPqri4mJTMwEAAKD50CEGAACaTHp6uqZPn668vLwGLY7f3KxWqyIjI7VkyRK6xQAAAHwAHWIAAKDRnd8Vlp+f36KLYZJUUVGh/Px8usUAAAB8BB1iAACgUe3atUsTJ05s8V1htansFktJSVFUVJTZcQAAANAEKIgBAIBGs3XrViUkJKi0tLRZ7x7Z2Gw2mwICApSamqrY2Fiz4wAAAKCRMWUSAAA0itTUVI0aNUolJSVeXQyTJLfbrZKSEo0aNUppaWlmxwEAAEAjo0MMAABctrS0NI0bN04VFRVeOU2yNlarVVarVatXr1Z8fLzZcQAAANBIKIgBAIDL8uGHH2r06NE6e/ZsqyqGVbJarfLz89OGDRuYPgkAANBKUBADAACXbNeuXRo2bJhKSkpaZTGsktVqVbt27ZSRkcFC+wAAAK0ABTEAAHBJiouLNWDAAOXn53v9mmH1YbPZFBERoezsbAUGBpodBwAAAJeBRfUBAMAlefLJJ5WXl+cTxTDp3EL7eXl5euqpp8yOAgAAgMtEhxgAAGiw9PR0jRgxwuwYptm8ebPi4uLMjgEAAIBLREEMAAA0iK9NlbwQUycBAAC8H1MmAQBAg/jaVMkLMXUSAADA+9EhBgAA6s3Xp0peiKmTAAAA3omCGAAAqBfDMNS/f3/t27fPZ7vDzmez2dS7d2/l5OTIYrGYHQcAAAANwJRJAABQL+np6crNzaUY9h9ut1u5ubnasmWL2VEAAADQQBTEAABAvSxYsEB2u93sGC2K3W7XggULzI4BAACABmLKJAAAqFNBQYG6detGd1gNbDabDh06pLCwMLOjAAAAoJ7oEAMAAHVavHixuIZWM8MwtHjxYrNjAAAAoAHoEAMAABd19uxZRUZG6ujRo2ZHabFCQ0OVl5fHlFIAAAAvQYcYAAC4qFWrVlEMq8ORI0e0atUqs2MAAACgniiIAQCAi1q+fLlsNpvZMVo0m82mZcuWmR0DAAAA9cSUSQAAcFEREREqKCgwO0aLFxERoby8PLNjAAAAoB4oiAEAgFoVFhaqS5cuZsfwGoWFhQoJCTE7BgAAAOrAlEkAAFCrrKwssyN4Fc4XAACAd6AgBgAAapWVlcX6YfVks9koiAEAAHgJCmIAAKBWO3bsEKsr1I9hGNqxY4fZMQAAAFAPFMQAAECtMjMzVVFRYcqxZ8yYIcMwZBiGXC6XIiMja3wuLi7O83hcXJzn8RkzZjRr3oqKCmVmZjbrMQEAAHBpKIgBAIAaFRUV6fDhw6Ydf+bMmZ4/22y2Zi9wXYqCggIVFRWZHQMAAAB1oCAGAABqZGZhp0ePHho+fLgkafv27ZLkFQUxSTpx4oTZEQAAAFAHCmIAAKBGpaWlph17xowZslqtOnz4sGbNmiVJ6tOnj2JjY03LVF9mnjcAAADUDwUxAABQo7KyMtOOPX36dEnS8uXLtXv3bu3evVtS1WmULZWZ5w0AAAD1Q0EMAADUqLy83JTjxsXF6eqrr5YkLV26tMr/77zzTgUEBNTrzpdm3R3zzJkzphwXAAAA9Wc3OwAAAGiZ2rRpY8pxz+8C27x5syTJbj83ZOnYsaMSExNVXFzs2aZTp06eP4eEhHj+/O233zZt0Fq0bdvWlOMCAACg/ugQAwAANfL392/2YwYGBmry5MmevwcFBSkoKEjt27f3PDZz5kzPFEpJeuihh9ShQwd16NDBs96YpCrbNCczzhsAAAAahoIYAACoUUBAQLMfc/LkyZ7i18CBA2WxWDz/PfbYY5KkkSNHqqysTO+//74kKSEhQSdPntTJkyeVkJAgSfrLX/6i/fv3N3t+yZzzBgAAgIahIAYAAGoUHBzc7MesnC6Zm5ur7OzsKs8lJydLkmw2m2bMmKF7771Xzz77rLKzs1VWVqaysjJlZ2frmWee0b333tvc0T2CgoJMOzYAAADqx2KYteIsAABo8cLDw3X48GGzY3iN8PBw5efnmx0DAAAAdaBDDAAA1ComJkZWK8OF+rDZbIqJiTE7BgAAAOqBES4AAKjV4MGDZbFYzI7hNQYPHmx2BAAAANQDBTEAAFCr6Ohoud1us2N4BbfbrejoaLNjAAAAoB5YQwwAANSqsLBQXbp0MTuG1ygsLFRISIjZMQAAAFAHOsQAAECtOnfurPDwcLNjeIWIiAiKYQAAAF6CghgAALioIUOGyGazmR2jRWNBfQAAAO9CQQwAAFzU1KlTWUesDm63W9OmTTM7BgAAAOqJNcQAAMBFuVwuRURE6OjRo2ZHabFCQ0OVl5cnu91udhQAAADUAx1iAADgoux2u5KSkmS1MmyoidVqVVJSEsUwAAAAL0KHGAAAqFNBQYG6devG1Mka2Gw2HTp0SGFhYWZHAQAAQD1xqRcAANQpPDxcDoeDLqgL2O12JSYmUgwDAADwMhTEAABAvSQlJcnlcpkdo0VxuVxKSkoyOwYAAAAaiCmTAACgXgzDUP/+/bVv3z6mTurcVMk+ffooOztbFovF7DgAAABoADrEAABAvVgsFi1cuJBi2H+43W4tXLiQYhgAAIAXoiAGAADqLS4uTnPmzPH5O05arVbNnTtXw4cPNzsKAAAALgFTJgEAQIMUFxdrwIABys/P98luMZvNpsjISO3Zs0eBgYFmxwEAAMAl8O3LuwAAoMECAwO1ZMkSnyyGSeemSi5ZsoRiGAAAgBejIAYAABrMV6dOMlUSAACgdWDKJAAAuCS+NnWSqZIAAACth29d1gUAAI0mMDBQKSkpCggIaPWdYlarVQEBAVqxYgXFMAAAgFagdY9eAQBAk4qKilJqaqr8/PxabVHMarWqTZs2Sk1NVVRUlNlxAAAA0Aha58gVAAA0m9jYWKWkpMhqtba6oljle0pJSVFsbKzZcQAAANBIWteoFQAAmCI+Pl6rV69uVZ1ilZ1hq1ev1pgxY8yOAwAAgEbEovoAAKDRbN26VQkJCSotLfXqhfZtNpsCAgKUlpamW265xew4AAAAaGSt4xIuAABoEWJjY5WRkaGIiAiv7RSzWq2KiIhQRkYGxTAAAIBWyjtHqgAAoMWKiopSdna2kpKSJJ3rtvIGlTnnzJmj7OxsFtAHAABoxZgyCQAAmkx6erqmT5+uvLw8VVRUmB2nVlarVZGRkVq6dKmGDx9udhwAAAA0MTrEAABAk4mLi2vR3WIXdoVRDAMAAPANdIgBAIBmkZ6ertmzZys3N1d2u10ul8u0LJXH79u3rxYtWkQhDAAAwMfQIQYAAJpFXFyccnJytHnzZjkcDtlstmZfeN9qtcpms8nhcGjz5s3KycmhGAYAAOCD6BADAACmOHz4sBYvXqwFCxboyJEjstlscrvdjX6cyv2GhoYqKSlJDz74oMLCwhr9OAAAAPAeFMQAAICpXC6XVq1apWXLlikzM1P5+fmSzhWyDMNo0GL8VqtVFovFU1iLiIhQTEyMpk2bpvHjx8tutzfJewAAAIB3oSAGAABalMLCQu3cuVNZWVnavn27tm3bpoKCgjpfFx4erpiYGA0ePFjR0dGKjo5WSEhIMyQGAACAt6EgBgAAWryioiKdOHFCpaWl2rhxo+bOnasPPvhA3bt3V0BAgIKCghQcHGx2TAAAAHgJ5g0AAIAWLzg42FPwOnjwoCRp0KBBioyMNDMWAAAAvBR3mQQAAAAAAIBPoSAGAAAAAAAAn0JBDAAAAAAAAD6FghgAAAAAAAB8CgUxAAAAAAAA+BQKYgAAAAAAAPApFMQAAAAAAADgUyiIAQAAr3DmzBmdOHFC3377rSTp5MmTOnHihFwul8nJAAAA4G0shmEYZocAAACoS2hoqI4ePVrt8ZEjR2rjxo0mJAIAAIC3okMMAAB4heuvv14Wi6Xa44MHDzYhDQAAALwZHWIAAMAr/POf/9TNN99c5TF/f38dPHhQXbp0MSkVAAAAvBEdYgAAwCvcdNNNio+Pl9V6bvhitVo1d+5cimEAAABoMDrEAACA1zi/S6xt27Y6dOgQBTEAAAA0GB1iAADAa9x0002Kjo6WJN13330UwwAAAHBJ6BADAABeJTU1VVOnTtXu3bt11VVXmR0HAAAAXoiCGAAAaPGKiopUVFSk0tJSlZWVqby8XG3atJG/v78CAgIUHBys4OBgs2MCAADAS9jNDgAAAHC+wsJCZWVlKSsrS9u3b9e2bdt0+PDhOl8XFhammJgYDR48WNHR0YqOjlbnzp2bITEAAAC8DR1iAADAVC6XSytXrtTy5cv18ccfq6CgQJJks9lkGIYqKirqvS+r1SqLxSK32y1JCg8P15AhQzR16lRNmDBBdjvXAgEAAEBBDAAAmKSgoECLFy/WggULdPToUdlsNk8hqzFV7jc0NFSPPPKIZs2apbCwsEY/DgAAALwHBTEAANBsDMNQenq6FixYIKfTKUlNUgSrTWUHmcPhUFJSkuLi4mSxWJrt+AAAAGgZKIgBAIBmkZ6ertmzZys3N1d2u10ul8u0LJXH79u3rxYuXKi4uDjTsgAAAKD5Wc0OAAAAWrfi4mLNnTtXI0aM0L59+yTJ1GLY+cfft2+fRowYoUcffVTFxcWmZgIAAEDzoUMMAAA0mfT0dE2fPl15eXkNWhy/uVmtVkVGRmrJkiV0iwEAAPgAOsQAAECjO78rLD8/v0UXwySpoqJC+fn5dIsBAAD4CDrEAABAo9q1a5cmTpzY4rvCalPZLZaSkqKoqCiz4wAAAKAJUBADAACNZuvWrUpISFBpaWmz3j2ysdlsNgUEBCg1NVWxsbFmxwEAAEAjY8okAABoFKmpqRo1apRKSkq8uhgmSW63WyUlJRo1apTS0tLMjgMAAIBGRocYAAC4bGlpaRo3bpwqKiq8cppkbaxWq6xWq1avXq34+Hiz4wAAAKCRUBADAACX5cMPP9To0aN19uzZVlUMq2S1WuXn56cNGzYwfRIAAKCVoCAGAAAu2a5duzRs2DCVlJS0ymJYJavVqnbt2ikjI4OF9gEAAFoBCmIAAOCSFBcXa8CAAcrPz/f6NcPqw2azKSIiQtnZ2QoMDDQ7DgAAAC4Di+oDAIBL8uSTTyovL88nimHSuYX28/Ly9NRTT5kdBQAAAJeJDjEAANBg6enpGjFihNkxTLN582bFxcWZHQMAAACXiIIYAABoEF+bKnkhpk4CAAB4P6ZMAgCABvG1qZIXYuokAACA96NDDAAA1JuvT5W8EFMnAQAAvBMFMQAAUC+GYah///7at2+fz3aHnc9ms6l3797KycmRxWIxOw4AAAAagCmTAACgXtLT05Wbm0sx7D/cbrdyc3O1ZcsWs6MAAACggSiIAQCAelmwYIHsdrvZMVoUu92uBQsWmB0DAAAADcSUSQAAUKeCggJ169aN7rAa2Gw2HTp0SGFhYWZHAQAAQD3RIQYAAOq0ePFicQ2tZoZhaPHixWbHAAAAQAPQIQYAAC7q7NmzioyM1NGjR82O0mKFhoYqLy+PKaUAAABegg4xAABwUatWraIYVocjR45o1apVZscAAABAPVEQAwAAF7V8+XLZbDazY7RoNptNy5YtMzsGAAAA6okpkwAA4KIiIiJUUFBgdowWLyIiQnl5eWbHAAAAQD1QEAMAALUqLCxUly5dzI7hNQoLCxUSEmJ2DAAAANSBKZMAAKBWWVlZZkfwKpwvAAAA70BBDAAA1CorK4v1w+rJZrNREAMAAPASFMQAAECtduzYoaZeXWHGjBkyDEOGYcjlcikyMrLG5+Li4jyPx8XFeR6fMWNGlf317t1bv/3tb5Wbm6uSkhKdPHlSn3/+ud577z0NGzasyd6HYRjasWNHk+0fAAAAjYeCGAAAqFVmZqYqKiqa9BgzZ870/Nlms1UrcDXEuHHjtHv3bj388MO65pprdOrUKX3xxRfq1KmTZsyYofvvv78REtesoqJCmZmZTbZ/AAAANB4KYgAAoEZFRUU6fPhwkx6jR48eGj58uCRp+/btknTJBbHOnTtr2bJlateunU6cOKGEhARdeeWVioqKUteuXdWvXz8tX7680bLXpKCgQEVFRU16DAAAAFw+CmIAAKBGzVHYmTFjhqxWqw4fPqxZs2ZJkvr06aPY2NgG7+uuu+5Shw4dJEkvvPCC0tLSqjyfm5urdevWXX7oOpw4caLJjwEAAIDLQ0EMAADUqLS0tMmPMX36dEnS8uXLtXv3bu3evVtS1WmU9TVgwADPn9PT0yVJHTt29Kw1VvlfU2uO8wYAAIDLQ0EMAADUqKysrEn3HxcXp6uvvlqStHTp0ir/v/POOxUQEFCvAlZN21Sue+ZyuZSZman8/PzGil2npj5vAAAAuHwUxAAAQI3Ky8ubdP/nd4Ft3rxZRUVFev755yWd6+xKTExUcXGxZ5tOnTp5/hwSEuL587fffitJ2rNnj+exyimXxcXFGjJkiKfQ1hzOnDnTbMcCAADApaEgBgAAatSmTZsm23dgYKAmT57s+XtQUJCCgoLUvn17z2MzZ870TKGUpIceekgdOnRQhw4dPOuNSfJs85e//EWnTp2SJD377LO65ZZbmiz/xbRt29aU4wIAAKD+KIgBAIAa+fv7N9m+J0+e7Cl+DRw4UBaLxfPfY489JkkaOXKkysrK9P7770uSEhISdPLkSZ08eVIJCQmSzhXB9u/fL0k6duyYpk2bptLSUnXt2lVbt27VV199pZ07d+qJJ55osvdyoaY8bwAAAGgcFMQAAECNAgICmmzfldMlc3NzlZ2dXeW55ORkSZLNZtOMGTN077336tlnn1V2drbKyspUVlam7OxsPfPMM7r33nurvHb16tW6/vrr9bvf/U5ffvmlQkND1aNHD+3du1eLFy9WfHx8k72nSk153gAAANA4LEZz3G4JAAB4naKioirrdqF+jh8/ruDgYLNjAAAA4CLoEAMAADUKDg5WWFiY2TG8Snh4OMUwAAAAL0BBDAAA1ComJkZWK8OF+rDZbIqJiTE7BgAAAOqBES4AAKjV4MGDZbFYzI7hNQYPHmx2BAAAANQDBTEAAFCr6Ohoud1us2N4BbfbrejoaLNjAAAAoB5YVB8AANSqsLBQXbp0MTuG1ygsLFRISIjZMQAAAFAHOsQAAECtgoOD1blzZ7NjeIWuXbtyV04AAAAvQUEMAABUcebMGX3wwQeaNWuWwsPDVVhYyDpi9XD06FH17t1bP/zhD7V161ZVVFSYHQkAAAC1YMokAADQ6dOntXbtWjmdTq1Zs0anT59W79695XA41KlTJz311FNmR2zxnnnmGR09elQrVqzQkSNHFBoaqokTJyoxMVEjR45UmzZtzI4IAACA/6AgBgCAjyosLNTKlSvldDq1bt06nTlzRlFRUXI4HEpMTNTAgQNlsVjkcrkUERGho0ePmh25xQoNDVVeXp7sdrvcbrcyMzPldDrldDp14MABdezYUWPHjlViYqISEhIUGBhodmQAAACfRkEMAAAfcvDgQa1YsUJOp1NbtmyRYRiKjY1VYmKiJk2apJ49e9b4uhdeeEHz5s1jGmANrFarnn/+eT3zzDPVnjMMQ5988omnOPbJJ5/I399fY8aMkcPh0Pjx41mEHwAAwAQUxAAAaOVycnI8BZkdO3bIz89Po0ePlsPh0IQJExQaGlrnPgoKCtStWze53e5mSOxdbDabDh06pLCwsDq33b9/v+dr8fHHH8tqtSouLk4Oh0OTJk1SZGRkMyQGAAAABTEAAFoZwzC0Y8cOOZ1OJScnKzc3V4GBgbr99tvlcDh0++23q2PHjg3e75133qkVK1bI5XI1QWrvZLfb5XA49P777zf4tYcPH1ZKSoqcTqc2btwol8ulm266SQ6HQw6HQ3379m2CxAAAAJAoiAEA0Cq4XC5lZGQoOTlZK1asUF5enkJCQjRhwgQ5HA6NHj1aAQEBl3WMzZs3a+TIkY2UuPXYvHmz4uLiLmsfJ06c0Jo1a5ScnKzU1FSVlJSof//+SkxMlMPh0A033MCdPgEAABoRBTEAALxUaWmp1q1bJ6fTqVWrVunYsWOKjIz0dBgNGzZMdru90Y5nGIb69++vffv2MXVS56ZK9unTR9nZ2Y1arCopKfF8XVeuXKmioiJ169bN83UdOnSobDZbox0PAADAF1EQAwDAi5w8eVJr1qyR0+nU2rVrVVxcrH79+nnuDBkdHd2knUTp6ekaMWJEk+3f26Snp2v48OFNtv+zZ89qy5YtcjqdWrFihfLz89W5c2dNmDBBiYmJGjVqlPz9/Zvs+AAAAK0VBTEAAFq4I0eOeNaa2rBhg86ePavBgwd7ptP169evWfPMnTtXb731lk/fcdJqtSopKUlvvPFGsx2zoqJC27dv9yzK/+9//1vt27evsjZchw4dmi0PAACAN6MgBgBAC/TFF194FsX/6KOPZLFYNHz4cCUmJmrSpEm66qqrTMtWXFysAQMGKD8/3yenTtpsNkVGRmrPnj0KDAw0JYNhGMrJyVFycrKcTqd27typNm3aVLl7aNeuXU3JBgAA4A0oiAEA0AIYhqHPPvvMU+DYvXu32rZtqzFjxsjhcGj8+PHq3Lmz2TE9fH3qZFNPlWyoL7/8UitWrJDT6dSHH34oSRo6dKhn3bHu3bubnBAAAKBloSAGAIBJKioqtG3bNk8RbP/+/erQoYPGjh0rh8OhhIQEXXHFFWbHrJUvTp00Y6pkQ33zzTdauXKlkpOTtX79epWXl+v666/3TLEdMGAAd6wEAAA+j4IYAADN6OzZs9q8ebOSk5OVkpKiw4cPq2vXrpo4caIcDoduvfVWtW3b1uyY9eJrUydbwlTJhjp16pTWrl0rp9OpNWvW6Ntvv1WfPn08xbEbb7xRVqvV7JgAAADNjoIYAABNrLi4WGlpaXI6nVq9erVOnDihHj16eO4MOWTIENlsNrNjXpJdu3Zp2LBhKikpadWdYlarVe3atVNGRoaioqLMjnNJysrKtGHDBjmdTqWkpKiwsFDh4eGaNGmSHA6H4uLi5OfnZ3ZMAACAZkFBDACAJnD8+HGtXr1aTqdTaWlpKi0t1bXXXuvpzLnuuutazbS1rVu3atSoUTp79myrLIpZrVa1adNG69evV2xsrNlxGoXL5dLWrVs9d6w8ePCggoODNX78eDkcDo0ZM0bt2rUzOyYAAECToSAGAEAjKSgo8CxsvmnTJrndbsXExHiKYL179zY7YpNJS0vTuHHjVFFR0aqKYlarVVarVWvWrNGYMWPMjtMkDMPQzp07PcWx7OxstWvXTgkJCXI4HBo3bpyCgoLMjgkAANCoKIgBAHAZ9u7dK6fTqeTkZG3btk12u10jR46Uw+HQxIkTFR4ebnbEZpOWlqaJEye2mk6xys6wFStWKD4+3uw4zSY3N9dTHPvnP/8pu92uW2+91fOZDgsLMzsiAADAZaMgBgBAAxiGoV27dnnuDLlnzx4FBARU6aYJDg42O6Zptm7dqoSEBJWWlnr1Qvs2m00BAQFKS0vTLbfcYnYc0+Tl5SklJUXJyclKT09XRUWFhgwZIofDIYfDoV69epkdEQAA4JJQEAMAoA5ut7vKektfffWVgoKCPOstxcfHs97SeXbt2qWJEycqLy/PKzvFrFarIiMjlZKS4rUL6DeFY8eOVVkXr6ysTIMGDfJMCf7Od77TatbFAwAArR8FMQAAanDmzJkqd+T75ptvFBYWpkmTJikxMZE78tWhuLhYTz31lH7zm9/IZrN5RbdYZc5HH31UL730kgIDA82O1GIVFxcrNTXVc+fUkydPqmfPnlXunGq1Ws2OCQAAUCsKYgAA/Mfp06e1du1aOZ1OrVmzRqdPn1bv3r09v+TfdNNN/JLfQOnp6Zo+fXqL7xar7ApbunSphg8fbnYcr1JeXq5NmzbJ6XRqxYoVOnLkiEJDQzVx4kQ5HA7deuutatOmjdkxAQAAqqAgBgDwaYWFhVq5cqWcTqfWrVunM2fOKCoqyjMNbODAgUwDu0wtuVuMrrDG5Xa7lZmZ6ZlefODAAXXs2FFjx46Vw+FQQkKC2rdvb3ZMAAAACmIAAN9z8OBBrVixQsnJycrIyJBhGIqNjVViYqImTZqknj17mh2xVUpPT9fs2bOVm5sru90ul8tlWpbK4/ft21eLFi2iK6wJGIahTz/91HMDik8++UT+/v4aM2aMHA6Hxo8fr5CQELNjAgAAH0VBDADgE3Jycjy/mGdlZcnPz0+jR4+Ww+HQhAkTFBoaanZEn2AYhrZs2aIFCxYoOTlZhmE061RKq9Uqi8WixMREJSUlafjw4XQANpP9+/d7CtEff/yxrFar4uLi5HA4NGnSJEVGRpodEQAA+BAKYgCAVskwDG3fvt0zdSs3N1eBgYG6/fbb5XA4dPvtt6tjx45mx/Rphw8f1uLFi7VgwQIdOXKkyaZTVu43NDRUSUlJevDBBxUWFtbox0H9ff3110pJSZHT6dSGDRvkcrl04403eqYq9+3b1+yIAACglaMgBgBoNVwul7Zs2eJZ3DsvL08hISGaMGGCHA6HRo8erYCAALNj4gIul0urVq3SsmXLlJmZqfz8fEnnClkN7SCr7ACrLKxFREQoJiZG06ZN0/jx42W325vkPeDSnThxQmvWrJHT6dTatWtVUlKi/v37e25mccMNN9DFBwAAGh0FMQCAVystLdW6devkdDq1atUqHTt2TJGRkZ5fpocOHUoRxMsUFhZq586dysrK0vbt27Vt2zYVFBTU+brw8HDFxMRo8ODBio6OVnR0NGtUeZnS0lL94x//8Hw/Hz9+XN26ddOkSZM83882m83smAAAoBWgIAYA8DonT56s0lFSXFysfv36eaZbRUdH01HSyhQVFenEiRMqLS1VWVmZzpw5o7Zt28rf318BAQEKCgpScHCw2THRiM6ePVul4zM/P1+dO3eu0vHp7+9vdkwAAOClKIgBALzCkSNHlJKSouTkZG3cuFFnz57VjTfeKIfDIYfDoX79+pkdEUATqaio0I4dOzw3xvj3v/+t9u3bV1kTsEOHDmbHBAAAXoSCGACgxTpw4IBnUfyPPvpIFoulyl3prrrqKrMjAmhmhmEoJydHTqdTycnJ2rlzp9q0aVPlrrFdu3Y1OyYAAGjhKIgBAFoMwzD06aefeopgu3fvVtu2bTVmzBg5HA6NHz9enTt3NjsmgBbkq6++0ooVK+R0OpWRkSFJGjp0qKd7tHv37iYnBAAALREFMQCAqSoqKpSZmekpgu3fv18dOnTQ2LFj5XA4dNttt6l9+/ZmxwTgBb755hutXLlSTqdT69atU3l5ua6//nrP+oIDBgxgfUEAACCJghgAwATl5eXavHmznE6nUlJSdPjwYXXt2lUTJ06Uw+HQrbfeqrZt25odE4AXO3XqlNauXSun06k1a9bo22+/VZ8+fTx3oL3xxhtltVrNjgkAAExCQQwA0CyKi4uVlpYmp9OpVatW6eTJk+rRo4fnl9MhQ4bIZrOZHRNAK3TmzBlt2LBBycnJSklJUWFhocLDwzVp0iQ5HA7FxcXJz8/P7JgAAKAZURADADSZ48ePa/Xq1XI6nUpLS1NpaamuvfZaz/Sl6667julLAJqV2+3W1q1bPXesPHjwoIKDgzV+/Hg5HA6NGTNG7dq1MzsmAABoYhTEAACNKj8/37PA9ebNm+V2uxUTE+PpBOvdu7fZEQFA0rkbefzrX//yFMeys7PVrl07JSQkyOFwaNy4cQoKCjI7JgAAaAIUxAAAl+3f//63Z1H8bdu2yW63a+TIkXI4HJo4caLCw8PNjggAdar8tyw5OVn//Oc/Zbfbdeutt3r+LQsLCzM7IgAAaCQUxAAADWYYhnbt2uXpqtizZ48CAgKqdFUEBwebHRMALlleXp5SUlI83a4VFRWKiYnxTPnu1auX2REBAMBloCAGAKiXynV3KjvBvvrqKwUFBXnW3YmPj2fdHQCt0rFjx6qsh1hWVqZBgwZ5poJ/5zvfYT1EAAC8DAUxAECtKu/M5nQ6lZKSom+++UZhYWGaNGmSEhMTuTMbAJ9TXFys1NRUOZ1OrV69WidPnlTPnj2r3DHXarWaHRMAANSBghgAoIrTp09r7dq1cjqdWrNmjU6fPq3evXt7pgnddNNN/LIHAJLKy8u1adMmz0WDr7/+WqGhoZo4caIcDoduvfVWtWnTxuyYAACgBhTEAAAqLCzUypUr5XQ6tW7dOp05c0ZRUVGeItjAgQOZDgQAF1FRUaHMzEzP2ooHDhxQx44dNXbsWDkcDiUkJKh9+/ZmxwQAAP9BQQwAfNTBgwe1YsUKJScnKyMjQ4ZhaOjQoXI4HJo0aZJ69uxpdkQA8EqGYejTTz/1FMc++eQT+fv7a8yYMXI4HBo/frxCQkLMjgkAgE+jIAZAklRUVKSioiKVlpaqrKxM5eXlatOmjfz9/RUQEKDg4GDuGtgK5OTkeH5By8rKkp+fn0aPHi2Hw6EJEyYoNDTU7IgA0Ors37/fcwHi448/ltVqVVxcnOcCRGRkpNkR0QgYSwGAd6EgBvigwsJCZWVlKSsrS9u3b9e2bdt0+PDhOl8XFhammJgYDR48WNHR0YqOjlbnzp2bITEulWEY2r59u+fOkLm5uQoMDNTtt98uh8Oh22+/XR07djQ7JgD4jK+//lopKSlyOp3asGGDXC6XbrzxRs8U9b59+5odEfXAWAoAvB8FMcAHuFwurVy5UsuXL9fHH3+sgoICSZLNZpNhGKqoqKj3vqxWqywWi9xutyQpPDxcQ4YM0dSpUzVhwgTZ7fYmeQ+oP5fLpS1btsjpdGrFihXKy8tTSEiIJkyYIIfDodGjRysgIMDsmADg806cOKE1a9bI6XRq7dq1KikpUf/+/T13rLzhhhtYv7GFYCwFAK0PBTGgFSsoKNDixYu1YMECHT16VDabzTP4akyV+w0NDdUjjzyiWbNmKSwsrNGPg9qVlpZq3bp1cjqdWrVqlY4dO6bIyEjPL1VDhw5lgA0ALVhpaan+8Y9/eP4dP378uLp166ZJkyZ5/h232Wxmx/Q5jKUAoPWiIAa0MoZhKD09XQsWLJDT6ZSkJhm41abyqqfD4VBSUpLi4uK4ut1ETp48WaWzoLi4WP369fMUwaKjozn3AOCFzp49W6XTNz8/X507d9aECROUmJioUaNGyd/f3+yYrRZjKQDwDRTEgFYkPT1ds2fPVm5urux2u1wul2lZKo/ft29fLVy4UHFxcaZlaU2OHDlSZe2Zs2fPavDgwZ61Z/r162d2RABAI6qoqNCOHTs8N0T597//rfbt21dZC7JDhw5mx2w1GEsBgO+gIAa0AsXFxXryySf15ptvNlkr/6WqzDN37lzNnz9fgYGBZkfyOl988YWcTqeSk5P10UcfyWKxVLk72VVXXWV2RABAMzAMo8rdgnfu3Kk2bdpUuVtw165dzY7plRhLAYDvoSAGeLn09HRNnz5deXl5DVrQtblZrVZFRkZqyZIlXOGsg2EY+uyzzzy/8OzevVtt27bVmDFj5HA4NH78eO5IBQDQV199pRUrVig5OVkffvihJGno0KFyOBxyOBzq3r27yQm9A2MpAPBNFMQAL9WSr2TWhiuctauoqNC2bds8RbD9+/erQ4cOGjt2rBwOh2677Ta1b9/e7JgAgBbqm2++0cqVK5WcnKz169ervLxc119/vWdK/YABA1iH6gKMpQDAt1EQA7zQrl27NHHixBZ/JbM2lVc4U1JSFBUVZXYc05SXl2vz5s1yOp1KSUnR4cOH1bVrV02cOFEOh0O33nqr2rZta3ZMAICXOXXqlNauXSun06k1a9bo22+/VZ8+fTzFsRtvvFFWq9XsmKZiLAUAoCAGeJmtW7cqISFBpaWlXnElszY2m00BAQFKTU1VbGys2XGaTXFxsdLS0uR0OrV69WqdOHFCPXr08NwZcsiQIbLZbGbHBAC0EmVlZdqwYYPn4kthYaHCw8M1adIkJSYmavjw4fLz8zM7ZrNiLAUAkCiIAV4lNTVVkyZN0tmzZ73yauaFrFar/Pz8lJKSovj4eLPjNJnjx49r9erVcjqdSktLU2lpqa699lrPlfrrrruOaSwAgCbncrm0detWOZ1OOZ1OHTx4UMHBwRo/frwcDofGjBmjdu3amR2zSTGWAgBUoiAGeIm0tDSNGzdOFRUVrWIAV8lqtcpqtWr16tWtaiBXUFCgFStWyOl0atOmTXK73YqJifEUwXr37m12RACADzMMQzt37vQUx7Kzs9WuXTslJCTI4XBo3LhxCgoKMjtmo2IsBQA4HwUxwAt8+OGHGj16dKu5mnmhyqubGzZs8OqW/71798rpdCo5OVnbtm2T3W7XyJEj5XA4NHHiRIWHh5sdEQCAGuXm5nqKY//85z9lt9t16623en6GhYWFmR3xsjCWAgBciIIY0MLt2rVLw4YNU0lJSascwFWyWq1q166dMjIyvGZxWMMwtGvXLk8RbM+ePQoICKhydT04ONjsmAAANEheXp5SUlKUnJys9PR0VVRUaMiQIXI4HHI4HOrVq5fZERuEsRQAoCYUxIAWrLi4WAMGDFB+fr5XL/paXzabTREREcrOzm6xtxF3u9366KOPlJycrBUrVujLL79UUFCQZ/2V+Pj4Vr/+CgDAdxw7dqzKOphlZWUaNGiQZwmA73znOy16HUzGUgCA2lAQA1qwuXPn6q233mrVVzMvZLValZSUpDfeeMPsKB5nzpypcoeub775RmFhYZ47dMXFxfncHboAAL6nuLhYqampcjqdWrVqlU6dOqWrr77a0zk2ZMgQWa1Ws2NWwVgKAFAbCmJAC5Wenq4RI0aYHcM0mzdvVlxcnGnHP336tNauXSun06k1a9bo9OnT6t27txwOhxITE3XTTTe1uEE/AADNpby8XJs2bZLT6dSKFSt05MgRhYaGauLEiUpMTNTIkSPVpk0bUzMyljJ3LAUALR0FMaAF8rX2/guZ1e5fWFiolStXyul0at26dTpz5oyioqI8RbCBAwe26GkhAACYwe12KzMz07Mo/4EDB9SxY0eNHTtWiYmJSkhIaPbpe4ylmDoJAHWhIAa0QL7Y3n+h5mr3P3jwoFasWCGn06ktW7bIMAzFxsYqMTFRkyZNUs+ePZv0+AAAtCaGYeiTTz7xFMc++eQT+fv7a8yYMXI4HBo/frxCQkKaPAdjKaZOAkBdKIgBLYyvt/dfqCna/XNycjwD9R07dsjPz0+jR4+Ww+HQhAkTFBoa2qjHAwDAV+3fv9/zM/fjjz+W1WpVXFycHA6HJk2apMjIyEY/JmOpqpg6CQA1oyAGtCCGYah///7at2+fT7b3X8hms6l3797Kycm5rKmKhmFox44dcjqdSk5OVm5urgIDA3X77bfL4XDo9ttvV8eOHRsxOQAAuNDXX3+tlJQUJScna+PGjXK5XLrppps8i/L37dv3so/BWKqqxhpLAUBrREEMaEE2b96skSNHmh2jxanpyqZhGPr1r38tl8ulH/7wh9Ve43K5lJGRoeTkZK1YsUJ5eXkKCQnRhAkT5HA4NHr0aAUEBDTXWwAAAOc5ceKE1qxZo+TkZKWmpqqkpET9+/dXYmKiHA6HbrjhhmoFHMMw9Nhjj+nWW2/VpEmTatwvY6ma0SUGANVREANakDvvvFMrVqyQy+UyO0qLYbfb5XA49P7773seMwxDTz/9tObPny9/f38dP35cAQEBKisr07p165ScnKxVq1bp2LFjioyM9Fx5HjZsmOx2u4nvBgAAXKikpETr1q2T0+nUypUrVVRUpG7dunl+fg8dOlQ2m0179uzRtddeK4vFoiVLluiee+6pti/GUtXVNJYCAFAQA1qMgoICdevWjfb+GthsNh06dEhhYWEyDEM//OEP9eqrr3qef+KJJ3To0CGtXbtWxcXF6tevn2cQPXjwYKYIAADgJc6ePastW7bI6XRqxYoVys/PV+fOnTVhwgSVl5frT3/6k9xutywWixYvXqz777/f81rGUrU7fywFADjHanYAAOcsXrxY1KdrZhiGFi9erIqKCs2dO7dKMUySXnvtNX355Zd6+umnlZOTo5ycHL300ku68cYbKYYBAOBF/Pz8NGrUKL355ps6ePCgMjMz9cADDygjI0N//OMfPcUuwzD0wAMP6O233/a8lrFU7SrHUgCA/6JDDGgBzp49q8jISB09etTsKC1WaGio+vXrp/T09GrPXXHFFTp27Jj8/PxMSAYAAJraF198oauvvrrG55KSkvTaa68xlqpDaGio8vLyWD4CAP6DDjGgBVi1ahUDuDocOXJEH330kefvFovFUwA7ffq0tmzZYlY0AADQxFJSUiRV/flfaeXKlYyl6uHIkSNatWqV2TEAoMXg8gDQAixfvlw2m401Ly7CZrNpwoQJeuutt5STk6PPP/9cn3/+ubKzs7V//35ZrdT3AQBordq3b69evXpp4MCB6t+/v/r166f+/furb9++CgoK0uTJkxlL1cFms2nZsmVyOBxmRwGAFoEpk0ALEBERoYKCArNjtHgRERHKy8szOwYAAGhhGEvVD2MpAPgvCmKAyQoLC9WlSxezY3iNwsJChYSEmB0DAAC0EIylGoaxFACcwxwjwGRZWVlmR/AqnC8AAHA+xgYNw/kCgHMoiAEmy8rKks1mMzuGV7DZbAziAABAFYyl6o+xFAD8FwUxwGQ7duwQM5frxzAM7dixw+wYAACgBWEsVX+MpQDgvyiIASbLzMxURUVFo+xrxowZMgxDhmHI5XIpMjKyxufi4uI8j8fFxXkenzFjRpX99e7dW7/97W+Vm5urkpISnTx5Up9//rnee+89DRs2rMq2bdu21eOPP66tW7eqqKhIZWVl+uqrr7Ru3To98cQTjfL+KioqlJmZ2Sj7AgAArUNrGEtt2rRJhmHoiy++qPL6d99917PvxsBYCgD+i4IYYKKioiIdPny40fY3c+ZMz59tNlu1QVlDjBs3Trt379bDDz+sa665RqdOndIXX3yhTp06acaMGbr//vs923bq1EmZmZl67bXXdMstt8jPz0///ve/VVFRobi4OL366quX87aqKCgoUFFRUaPtDwAAeK/WMpZqToylAOAcCmKAiRpzMNKjRw8NHz5ckrR9+3ZJuuRBXOfOnbVs2TK1a9dOJ06cUEJCgq688kpFRUWpa9eu6tevn5YvX+7Z/s0331RUVJQk6fXXX1dISIi+853vqGfPnurcuXOVwWVjOHHiRKPuDwAAeKfWMpZqboylAICCGGCq0tLSRtvXjBkzZLVadfjwYc2aNUuS1KdPH8XGxjZ4X3fddZc6dOggSXrhhReUlpZW5fnc3FytW7dOktSxY0fdeeedkqRdu3bp+9//vs6cOePZ9tSpU/rDH/5wSe+pNo153gAAgPdqDWMpMzCWAgAKYoCpysrKGm1f06dPlyQtX75cu3fv1u7duyXpkrqzBgwY4Plzenq6pHOFr8o1LM5fy+Kaa66R3W6XJGVkZHgedzqdVba9nCkHF2rM8wYAALxXaxhLmYGxFABQEANMVV5e3ij7iYuL09VXXy1JWrp0aZX/33nnnQoICKjXoKumbSoXqXW5XMrMzFR+fn6trz9/Qdvc3Fzt2rWr3u+hIc7vQAMAAL6rtYylmrs4xlgKACiIAaZq06ZNo+zn/CuXmzdvVlFRkZ5//nlJ565GJiYmqri42LNNp06dPH8OCQnx/Pnbb7+VJO3Zs8fzWOU0geLiYg0ZMsQzOKyUm5srl8slSbrllls8jz/55JO6++67L/Od1axt27ZNsl8AAOBdWsNYqvK5C/d7/r5Pnz59KW+rVoylAICCGGAqf3//y95HYGCgJk+e7Pl7UFCQgoKC1L59e89jM2fO9LT9S9JDDz2kDh06qEOHDp41MiR5tvnLX/6iU6dOSZKeffbZKoWuC506dUrvv/++JOnGG2/U888/L6u1af9paYzzBgAAvF9rGEtJ8nTVd+jQQQ888IBsNptuuOEGjRw5ssp+GwtjKQCgIAaYKiAg4LL3MXnyZM+AbeDAgbJYLJ7/HnvsMUnSyJEjVVZW5ilcJSQk6OTJkzp58qQSEhIknRu47d+/X5J07NgxTZs2TaWlperatau2bt2qr776Sjt37tQTTzxRLcPcuXM9A7XnnntOx48f186dO7V58+bLfn81aYzzBgAAvF9rGUu9/fbbOnbsmCRp8eLFKi8vV1ZWltq3b6+KigrNnz//st/n+RhLAQAFMcBUwcHBl72Pyhb/3NxcZWdnV3kuOTlZkmSz2TRjxgzde++9evbZZ5Wdna2ysjKVlZUpOztbzzzzjO69994qr129erWuv/56/e53v9OXX36p0NBQ9ejRQ3v37tXixYsVHx/v2fb48eOKiYnRj3/8Y+3YsUNWq1X9+vVTaWmpUlNTNXv2bK1YseKy32uloKCgRtsXAADwXq1lLJWfn69bbrlFf/7zn/X111+roqJCJ06c0IYNG3Tbbbfpgw8+uOz3eT7GUgAgWQwzb28CQOHh4Tp8+LDZMbxGeHj4RRf2BwAAvoWxVMMwlgKAc+gQA0wWExPT5GtutRY2m00xMTFmxwAAAC0IY6n6YywFAP/FTw7AZIMHD5bFYjE7htcYPHiw2REAAEALwliqYRhLAcA5FMQAk0VHR8vtdpsdwyu43W5FR0ebHQMAALQgjKXqj7EUAPwXa4gBJissLFSXLl3MjuE1CgsLFRISYnYMAADQQjCWahjGUgBwDh1igMk6d+6s8PBws2N4hYiICAZwAACgCsZS9cdYCgD+i4IY0AIMGTJENpvN7BgtGovAAgCA2jCWqhtjKQCoioIY0AJMnTqVtS/q4Ha7NW3aNLNjAACAFoixVN0YSwFAVawhBrQALpdLEREROnr0qNlRWqzQ0FDl5eXJbrebHQUAALQwjKXqxlgKAKqiQwxoAex2u5KSkmS18i1ZE6vVqqSkJAZwAACgRoylLo6xFABUR4cY0EIUFBSoW7dutPvXwGaz6dChQwoLCzM7CgAAaKEYS9WOsRQAVMclFKCFCA8Pl8Ph4MrdBex2uxITExnAAQCAi2IsVTPGUgBQMwpiQAuSlJQkl8tldowWxeVyKSkpyewYAADACzCWqo6xFADUjCmTQAtiGIb69++vffv20e6vc+39ffr0UXZ2tiwWi9lxAABAC8dYqirGUgBQOzrEgBbEYrFo4cKFDOD+w+12a+HChQzgAABAvTCWqoqxFADUjoIY0MLExcVpzpw5Pn+XJKvVqrlz52r48OFmRwEAAF7CMAx98cUX8vf3pwgkafz48YylAKAWTJkEWqDi4mINGDBA+fn5PnmF02azKTIyUnv27FFgYKDZcQAAgBfYt2+fZs+erY0bN+quu+7S1q1bdfjwYZ8dS/n5+amsrEx33323Xn/9dYWGhpodCwBaFN9uQQFaqMDAQC1ZssQnB3DSufb+JUuWUAwDAAB1Onv2rH7+859r0KBBOnDggFJTU/XnP/9Zf/zjH316LJWamqo//vGPWr9+vfr376/f//73ohcCAP6LghjQQvnq1EmmSgIAgPr65z//qcGDB+vpp5/WnDlz9Nlnnyk+Pl4SY6m4uDhNmzZNOTk5Gj9+vB544AHdeuut2rt3r9kRAaBFYMok0IL52tRJpkoCAID6OH36tJ555hm98cYbuv766/XOO+/ohhtuqLYdY6n/Wr9+vWbPnq38/Hw9++yz+uEPf6g2bdqYlBQAzOdbl0sALxMYGKiUlBQFBAS0+qubVqtVAQEBWrFiBcUwAABQq9WrV2vgwIF655139Morr2jbtm01FsMkxlLnGz16tD799FM9/vjjevbZZxUdHa3MzEwTkgJAy9C6fyoArUBUVJRSU1Pl5+fXagdyVqtVbdq0UWpqqqKiosyOAwAAWqCvv/5ad911l8aPH68BAwbos88+0w9+8APZ7faLvo6x1H+1a9dOP//5z7Vjxw75+/vrlltu0dy5c3X69OnmCwsALUTr/IkAtDKxsbFKSUmR1WptdQO5yveUkpKi2NhYs+MAAIAWxjAMLV68WP3799emTZu0bNkyrV27Vj179qz3PhhLVRUVFaXMzEy9+uqrevfddzVgwACtXLmyiZMCQMvSun4aAK1YfHy8Vq9e3aqublZezVy9erXGjBljdhwAANDC5ObmauTIkZo1a5YmTZqknJwcTZ06VRaLpcH7YixVlc1m0+OPP649e/Zo0KBBmjhxou68804dPny4idICQMvSOn4SAD4iPj5eGzZsULt27WSz2cyOc1lsNpvatWunDRs2eO4GBQAAIEnl5eV68cUXdd111ykvL0/r16/Xu+++q5CQkMvaL2Op6rp37641a9boz3/+s7Zs2aL+/ftr0aJFqqioaMS0ANDyUBADvExsbKwyMjIUERHhtVc3rVarIiIilJGRoVtuucXsOAAAoAX5+OOPdcMNN+j555/XE088oU8//VSjRo1qtP0zlqrOYrHorrvuUk5Oju644w7Nnj1bI0aM0Oeff94IaQGgZfLOnwCAj4uKilJ2draSkpIkyWuucFbmnDNnjrKzs1lAHwAAeJw6dUpJSUmKjY1Vu3btlJWVpfnz5ysgIKDRj8VYqmadOnXS7373O23cuFFff/21rrvuOs2bN09nzpxp1OMAQEtgMQzDMDsEgEuXnp6u6dOnKy8vr0W3tlutVkVGRmrp0qUaPny42XEAAEALsmLFCs2ZM0cnTpzQz372M82ZM6fZilSMpWpWWlqqF198Ub/4xS/Up08fvfPOO9wACUCrQocY4OXi4uJa9BXOC69kUgwDAACVCgoKdMcdd8jhcHi6th577LFmHc8wlqpZQECAfvazn2nnzp3q0KGDhg4dqv/5n//RyZMnm+X4ANDU6BADWpH09HTNnj1bubm5stvtcrlcpmWpPH7fvn21aNEiCmEAAMCjoqJCixYt0k9+8hMFBATojTfe0J133nlJd49sTIylauZ2u/Xb3/5WTz31lK644gq9+eabSkxMNC0PADQGOsSAViQuLk45OTnavHmzHA6HbDZbsy8Wa7VaZbPZ5HA4tHnzZuXk5FAMAwAAHpVdTv/zP/+jKVOmKCcnR1OmTDG9GCYxlqqNzWbzdKjdeOONnq6+/Px8U3MBwOWgQwxoxQ4fPqzFixdrwYIFOnLkiGw2m9xud6Mfp3K/oaGhSkpK0oMPPqiwsLBGPw4AAPBeZ86c0fz58/XSSy+pZ8+eWrhwoUaMGGF2rItiLFWdYRj6+9//rrlz56q4uFg///nP9fDDD3vtHTsB+C4KYoAPcLlcWrVqlZYtW6bMzEzP1TybzSbDMBq0gKzVapXFYvEMBiMiIhQTE6Np06Zp/PjxstvtTfIeAACA98rIyNBDDz2kffv26cknn9TTTz8tf39/s2PVG2Op6k6cOKGf/OQnWrRokYYMGaJ33nlHAwcONDsWANQbBTHABxUWFmrnzp3KysrS9u3btW3bNhUUFNT5uvDwcMXExGjw4MGKjo5WdHS0QkJCmiExAADwRhcWTRYtWqRrr73W7FiXjbHUf23ZskUPPfSQDhw4oCeffFI//elPvarYCcB3URADIEkqKirSiRMnVFpaqjvuuEP9+/fX//7v/8rf318BAQEKCgpScHCw2TEBAIAXuHBa3fz58/U///M/rXpa3fljqbKyMp05c0Zt27b1ibHUmTNn9NJLL2n+/Pm6+uqrtXDhQsXFxZkdCwAuioIYgGqio6N1880366233jI7CgAA8DKHDh3SnDlztHLlSk2cOFFvvvmmIiMjzY6FZpCdna2HHnpIW7du1YMPPqhf/OIXrbYICMD7td5LNAAAAACajdvt1ptvvqkBAwZo+/bt+vvf/y6n00kxzIcMGDBAW7Zs0W9/+1u9//776t+/v95//33RgwGgJaIgBgAAAOCyfPrppxo6dKjmzp2re+65Rzk5OUpMTJTFYjE7GpqZ1WrVww8/rOzsbMXGxuquu+7ShAkTdPDgQbOj/X97dx4dRZW3cfzp7gAJAUIMECARFVkMoIMGRxYhILLIuAwK6oiIG24B3BVHlMXXdQSXERXFDQRkxlERlCAghIiiQFhkVUARCAiRIJKVJPf9g0lPQghZu6u6+vs5J4fQqa76pZ/ce7tv36oGgBKYEAMAAABQJTk5ORozZozOO+88/f7770pJSdFrr72miIgIq0uDxWJiYryrBFNTU9W+fXu9/PLL3k/XBACrMSEGAAAAoNKWLl2qc845R//4xz80ZswYrVmzRhdeeKHVZcFm/vrXv2rTpk264YYbdM8996hr165av3691WUBABNiAAAAACru4MGDuuWWW9SrVy9FR0dr7dq1Gjt2rOrUqWN1abCpiIgITZ48WV999ZWOHDmi+Ph4PfLII8rOzra6NABBjAkxAAAAAOUyxuiDDz5QXFyc/vOf/2jKlClKTk5WXFyc1aUhQHTt2lVr1qzR2LFjNWnSJJ199tn68ssvrS4LQJBiQgwAAADASe3cuVOXXnqp/va3v6l79+7avHmzbrvtNrndvJxA5dSuXVtjxozR+vXrFRMTo969e+umm27Sb7/9ZnVpAIIMIxgAScc+Kn3z5s3avHmzsrOzlZGRoc2bN2vHjh1WlwYAACxSUFCgF198Ue3bt9e6des0Z84cffjhh2rWrJnVpSHAtW3bVkuWLNGbb76pTz75RHFxcZo5c6aMMVaXBiBIuAw9DgBJzz33nB5++OET/mzp0qVKSEjwc0UAAMBKa9eu1fDhw7V69WolJibqySefVIMGDawuCw60b98+3X333frXv/6l/v3767XXXtPpp59udVkAHI4VYgAkSX369Dnh7Q0bNlR8fLyfqwEAAFbJysrSww8/rE6dOik7O1vLly/XP//5TybD4DNNmzbV7Nmz9emnn2rDhg1q3769Jk6cqPz8fKtLA+BgTIgBkCSde+65uvzyyxUSEuK9zeVyafTo0apXr56FlQEAAH9ZtGiRzj77bL300ksaP368UlNT1aVLF6vLQpC47LLLtGnTJt1666168MEH1blzZ61Zs8bqsgA4FBNiALzGjRtX4p24iIgIJSYmWlgRAADwh/T0dA0bNkx9+vRRixYttH79ej366KOqXbu21aUhyNSvX18vvfSSvvnmG+Xl5en888/Xgw8+qKysLKtLA+AwTIgB8CpaJVaE1WEAADibMUbvv/++4uLiNHfuXL311lv68ssv1aZNG6tLQ5C74IILtHr1aj3xxBP65z//qQ4dOuiLL76wuiwADsJF9QGUsGbNGp133nmqXbu2fvvtNybEAABwqB07dujOO+/UF198oWuuuUYvvfSSoqOjrS4LKOXHH3/UHXfcoS+//FLXX3+9Jk2apMaNG1tdFoAAxwoxACWce+656tOnj+69914mwwAAcKD8/Hw9//zz6tChg7Zs2aJ58+bpgw8+YDIMttW6dWstWrRI77zzjj777DPFxcVp2rRpYm0HgOpghRgASVJGRoYyMjKUnZ2tnJwc5eXlqXbt2goNDVVYWJgiIyMVGRlpdZkAANSIYB33Vq9ereHDh2vdunUaNWqUnnjiCd4AQ0DZv3+/7rnnHs2aNUsXX3yxXn/9dZ155plWl+UTwdpPAf7ChBgQhNLT07V69WqtXr1aK1eu1Lfffqu9e/eWe79mzZqpc+fO6tSpk+Lj4xUfH69GjRr5oWIAAKqOcU/KzMzU448/rhdffFEdOnTQ1KlTdf7551tdFlBl8+fP15133qn9+/dr3Lhxuvfee1WrVi2ry6oy+inA/5gQA4JAfn6+Pv30U82cOVPffPON0tLSJEkej0fGGBUWFlZ4X263Wy6XSwUFBZKk5s2bq0uXLrruuut0+eWXKyQkxCe/AwAAFcW4V9KCBQt0xx13aN++fRo3bpzuu+++gJ44AIocOXJEY8eO1Ysvvqizzz5bU6dOVadOnawuq0LopwDrMSEGOFhaWpqmTp2qyZMna//+/fJ4PN6BsiYV7Tc6Olp33XWXhg8frmbNmtX4cQAAOBnGvZL279+ve++9VzNnzlTv3r01ZcoUx55ahuAWSKcC008B9sGEGOAwxhglJydr8uTJ+vjjjyXJJ4NsWYreoRo4cKASExOVkJAgl8vlt+MDAIIL415pxhi99957uv/++yVJL7zwgoYOHWp5XYAv5efn64UXXtDYsWPVuHFjvfbaaxowYIDVZUminwLsigkxwEGSk5N1++23a+vWrQoJCVF+fr5ltRQdv23btpoyZYoSEhIsqwUA4EyMe6Vt27ZNt99+u7788ksNGTJEL7zwgho3bmxJLYAVduzYoTvuuEMLFy7UtddeqxdffNHST1ClnwLsy211AQCqLzMzUyNHjlTPnj21bds2SbJ0sC1+/G3btqlnz54aNWqUMjMzLa0JAOAMjHulHT16VM8884zOPvts7dixQ0lJSXr//feZDEPQadmypRYsWKBp06Zp4cKFiouL09tvvy1/rwOhnwLsjxViQIBLTk7WDTfcoN27d1fq4pv+5na7FRsbq2nTpvFuFACgyhj3Svvuu+80fPhwbdiwQffee6/Gjx+v8PBwnx4TCATp6em67777NH36dPXs2VNvvPGGWrdu7fPj0k8BgYEVYkCAKv6u0549e2w92EpSYWGh9uzZw7tRAIAqYdwr7Y8//tA999yjzp07KyQkRCtXrtTzzz/PZBjwX40aNdK0adP0xRdf6JdfftHZZ5+tp556Snl5eT45Hv0UEFhYIQYEoLVr1+qKK66w/btOZSl6N2rOnDnq2LGj1eUAAGyOca+0efPm6a677tJvv/2mCRMm6O6771ZISEiN7BtwoqysLI0fP14TJ05UXFyc3nzzTXXu3LnG9k8/BQQeVogBAWb58uXq3r17QLzrVJaid6O6d++u5cuXW10OAMDGGPdK2rdvn6655hpddtllateunTZs2KD777+fyTCgHHXr1tWzzz6rlStXqk6dOuratatGjhypP/74o9r7pp8CAhMTYkAASUpKUu/evZWVleXXj2r2hYKCAmVlZal3795asGCB1eUAAGwomMe9GTNmaOvWrd7/G2M0depUxcXF6csvv9T777+v+fPn64wzzvBl2YDjnHvuuVqxYoUmTpyot99+W+3atdOnn35aYptvv/1Wn3/+eYX2F8z9FBDoOGUSCBALFizQpZdeqsLCwoB95+lE3G633G635s2bp379+lldDgDAJoJ53Fu2bJkSEhLUpk0brV+/Xj///LNuv/12JScna9iwYZo4caKioqL8XDngPD///LPuvPNOJSUladCgQXr55ZdVu3ZttW7dWkeOHNGWLVvUsmXLMu8fzP0U4ARMiAEB4KuvvtLFF1+so0ePOmqwLeJ2u1WrVi0tXrxY3bp1s7ocAIDFgnncO3r0qM455xz98MMPMsaoV69eWr58uWJjYzVlyhT17t3boqoBZzLGaPbs2br77ruVm5uruLg4rVy5UpLUr18/ffbZZye8XzD3U4BTMCEG2NzatWvVvXt3ZWVlOXKwLeJ2u1W3bl2lpKRwIU8ACGLBPu69+OKLuvfee0tsO3z4cL300ksKCwvzc5VA8Dh48KCuu+66UqcKfvrpp7rssstK3Bbs/RTgFEyIATaWmZmpdu3aac+ePQF/TYKK8Hg8iomJ0aZNm/jIeAAIQsE+7u3du1dnnnmmsrOzS2xzwQUXKCUlRW43l/8FfCUrK0txcXHatWuXil4iu1wuNW/eXD/++KN3QjrY+ynASRhVARsbPXq0du/eHRSDrXTsQp67d+/WI488YnUpAAALBPu4d+2115aYDJOOffLb119/rblz51pRIhA0Xn/9df3yyy8lbjPGaM+ePRoxYoT3tmDvpwAnYYUYYFPJycnq2bOn1WVYZunSpUpISLC6DACAnwT7uLdo0SJdfPHFkqQ6deqoadOmOvXUU3XqqacqJiZGd999t2JjYy2uEnCujRs36s0339TevXu1c+dO7dmzR/v27VN+fr7q1KmjnJycoO+neH4Op2FCDLChYFuKfTyWZgNAcGHcOzbuLVy4UE2aNFFERIRcLpfVZQFBzxij3377TQUFBapXrx79FM/P4TCcMgnYULAtxT4eS7MBILgw7h0b91555RU1bNiQyTDAJlwulxo1aqTo6Gj6KZ6fw4FYIQbYTLAvxT4eS7MBwNkY90pi3APsh36qJPopOAUTYoCNGGMUFxenbdu2Be27T8V5PB61atVKmzdv5t1yAHAgxr2SGPcA+6GfKol+Ck7CKZOAjSQnJ2vr1q0Mtv9VUFCgrVu3atmyZVaXAgDwAca9khj3APuhnyqJfgpOwoQYYCOTJ09WSEiI1WXYSkhIiCZPnmx1GQAAH2DcK41xD7AX+qnS6KfgFJwyCdhEWlqaWrRowbtPJ+DxeLRr1y41a9bM6lIAADWEca9sjHuAPdBPlY1+Ck7ACjHAJqZOnSrmp0/MGKOpU6daXQYAoAYx7pWNcQ+wB/qpstFPwQlYIQbYwNGjRxUbG6v9+/dbXYptRUdHa/fu3SxZBwAHYNwrH+MeYC36qfLRTyHQsUIMsIG5c+cy2Jbj119/1dy5c60uAwBQAxj3yse4B1iLfqp89FMIdEyIATYwc+ZMeTweq8uwNY/HoxkzZlhdBgCgBjDulY9xD7AW/VT56KcQ6DhlErCBmJgYpaWlWV2G7cXExGj37t1WlwEAqCbGvYph3AOsQz9VMfRTCGRMiAEWS09PV+PGja0uI2Ckp6crKirK6jIAAFXEuFc5jHuA/9FPVQ79FAIVp0wCFlu9erXVJQQUHi8ACGz045XD4wX4H+2ucni8EKiYEAMstnr1aq5PUEEej4cBFwACHONexTHuAdagn6o4+ikEMibEAIutWrVKlT1zediwYTLGyBij/Px8xcbGnvBnCQkJ3tsTEhK8tw8bNqzE/lq1aqXXXntNW7duVVZWln7//Xdt2bJF7777rrp3715i2zp16uiee+7R8uXLlZGRoZycHO3cuVMLFy7UvffeW6rWXr166cMPP9Tu3buVm5urAwcOaM2aNZo4caJOP/30Sv3exhitWrWqUvcBANhLII17S5YskTFGP/30U4n7v/POO959Fxk7dqz3ttNOO63c+iqCcQ+whlP7qSLF+6tDhw4pLCysUr9rcfRTCGQhVhcABLsVK1aosLCwUve58cYbvd97PB4NGzZMTz75ZJWOf+mll2r27NmqW7eupGMfn7xv3z41b97cO3inpKRIkk455RQtXrxYHTt2lCRlZmbqhx9+UP369ZWQkKCLL75YL7zwgnffTzzxhMaMGSNJKigo0C+//KKsrCy1bNlSHTt21Pr16/Xzzz9XuNbCwkKtWLGiSr8nAMAeAmncsxrjHmANp/dTN9xwg/f7iIgIXXnllVX+tEj6KQQyVogBFsrIyNDevXsrdZ/TTz9dPXr0kCStXLlSkkq9o1RRjRo10owZM1S3bl0dOnRI/fv3V9OmTdWxY0c1adJEZ511lmbOnOnd/pVXXvFOhr344ouKiorSOeecozPOOEONGjUq8USgb9++3smwdevWKS4uTi1btlSHDh0UERGhhIQEpaamVrrmtLQ0ZWRkVOn3BQBYK9DGPTtg3AP8y+n9VEJCglq2bFmi1uLP4auCfgqBigkxwEJVGTiGDRsmt9utvXv3avjw4ZKk1q1bq1u3bpXe1zXXXKMGDRpIkiZMmKAFCxaU+PnWrVu1cOFCScfePRo8eLAkae3atbrvvvuUm5vr3fbw4cN67733vP8vqk2SbrrpJv34448l9r1s2TJ9//33la5Zkg4dOlSl+wEArBVI456dMO4B/uP0fqpo8uu7777ThAkTJB27xEnxUzyrgn4KgYgJMcBC2dnZlb5P0RLnmTNnat26dVq3bp2kqr2z065dO+/3ycnJko5NfBVdU6D4dQfatGmjkJBjZ1mnpKR4b//4449LbFv0bljRvg8fPqw1a9ZIkq644ooS2y5ZsqTSNUtVe9wAANYLpHHPThj3AP9xcj8VHh6uQYMGSZKmT5+upKQkHThwwHuKZ3XQTyEQMSEGWCgnJ6dS2xdf4jx9+vQS/w4ePFhhYWEVGiBPtE3RdRLy8/O1YsUK7dmzp8z7F7+mwtatW7V27doKHevgwYNasWKF/vjjj3JrPJnKPm4AAHsItHGvMi86q1pHRTDuAf7j5H5q0KBBqlevnvLy8vTBBx8oPz9fs2fPllT1UzyL0E8hEDEhBlgoLy+vUtsXf5dp6dKlysjI0Lhx4yT974KYmZmZ3m1OOeUU7/dRUVHe748cOSJJ2rhxo/e2oiXdmZmZ6tKli3cgL7J161bl5+dLkrp27eq9ffTo0br22mtL1Vq074iICLVv317SsZVlXbp0KXHcqih+qiYAIHAE0rhX9LPj91t838Xf4KlMHZXFuAf4j5P7qaJaPR6PfvzxR2VkZOjmm2+WVPVTPIvQTyEQMSEGWKh27doV3rb4EmdJatiwoRo2bKh69ep5b7vxxhu9S7Ql6bbbblODBg3UoEGDEtf0Ktpm9uzZOnz4sCTp8ccfLzHRdbzDhw/rX//6lyTp/PPP17hx4+R2l92FvPnmm97vp06dWu3rEhRXp06dGtsXAMB/Amnck+RdAd2gQQPdcsst8ng8Ou+889SrV68S+y2+rSSNGDFCoaGhio6O1vXXXy/p2OqJLVu2VPj3L45xD/Afp/ZTxS/87/F4vLUWfZJlUa1VRT+FgGQAWGbDhg1GUoW+hg0b5r1fu3btSvxs1KhRxhhj8vPzTWxsrJk9e3aZx/zggw9K3PfSSy81WVlZ3p/v3LnTpKammpycHO9tRduecsopZu3atd7bDx06ZFJTU83evXu9tw0bNsy7/RNPPOG9PS8vz2zevNls3LjRFBQUGGOMWbJkSYV//+JfGzdurPqDDgCwTKCNezExMSY9Pd17e9H4VfT9gAEDvNu6XC7zzTffnHBbY4x55plnqjTmMe4B/uXUfmrs2LHGGGNyc3NNREREieNNmjTJGHPsuX1YWBj9FIIGE2KAhbZv317hQWbJkiXGGGO2bNlS6mexsbHefT766KOmdu3a5rHHHjMbN2402dnZJjs722zcuNGMGTPG1KpVq9T927Zta6ZOnWp++uknk5OTYw4ePGi+//578+abb5q+ffuW2DY0NNQ8+OCDZuXKlebw4cMmKyvL7Nixw8yfP9/cdtttpQbYPn36mDlz5ph9+/aZvLw8s2/fPrNy5Urz1FNPmQ4dOlRpwN2xY4dFiQEAqiMQx702bdqYWbNmmb1795qjR4+ajIwMs2jRolLbSTINGjQwEydONNu2bTO5ubkmMzPTpKammsTERONyuao8Ica4B/iPU/up7du3G2OMSUpKKnWsCy+80FvrkCFD6KcQNFzG2PCjdIAgkZGRUep8f5Tv4MGDioyMtLoMAEAlMe5VDeMe4D/0U1VDP4VAxDXEAAtFRkaqWbNmVpcRUJo3b85gCwABinGv8hj3AP+in6o8+ikEKibEAIt17tz5pBenx/94PB517tzZ6jIAANXAuFdxjHuANeinKo5+CoGMVg5YrFOnTnK5XFaXETA6depkdQkAgGpg3Kscxj3A/+inKod+CoGKCTHAYvHx8SooKLC6jIBQUFCg+Ph4q8sAAFQD417FMe4B1qCfqjj6KQQyLqoPWCw9PV2NGze2uoyAkZ6erqioKKvLAABUEeNe5TDuAf5HP1U59FMIVKwQAyzWqFEjNW/e3OoyAkJMTAyDLQAEOMa9imPcA6xBP1Vx9FMIZEyIATbQpUsXeTweq8uwNS7YCQDOwbhXPsY9wFr0U+Wjn0KgY0IMsIHrrruO6xSUo6CgQEOGDLG6DABADWDcKx/jHmAt+qny0U8h0HENMcAG8vPzFRMTo/3791tdim1FR0dr9+7dCgkJsboUAEA1Me6Vj3EPsBb9VPnopxDoWCEG2EBISIgSExPldtMkT8TtdisxMZHBFgAcgnHv5Bj3AOvRT50c/RScgBVigE2kpaWpRYsWLM0+AY/Ho127dqlZs2ZWlwIAqCGMe2Vj3APsgX6qbPRTcAKmuwGbaN68uQYOHMi7LMcJCQnRlVdeyWALAA7DuHdijHuAfdBPnRj9FJyCCTHARhITE5Wfn291GbaSn5+vxMREq8sAAPgA415pjHuAvdBPlUY/BafglEnARowxiouL07Zt21iarWNLsVu3bq1NmzbJ5XJZXQ4AoIYx7pXEuAfYD/1USfRTcBJWiAE24nK5NHHiRAbb/yooKNCUKVMYbAHAoVwul6ZMmcK491+Me4D90E+VRD8FJ2FCDLCRTz75RLfddptCQkL4RBtJjRs3Vv369a0uAwDgQwkJCRoxYkTQj3tut1sjR45Ujx49rC4FwHHop46hn4LTBHeLBmwiLS1NV155pQYOHKjzzjtP33//vWJjY+XxeKwuzRIej0dNmzZVkyZNdP755+uhhx5SVlaW1WUBAHzkmWeeCfpx79RTT9XTTz9tdSkAykA/RT8F52FCDLBQYWGhXnvtNcXFxenrr7/W7Nmz9emnn+qss87StGnTgnZpdkFBgWbPnq01a9boiSee0Msvv6wOHTroiy++sLo0AIAPhIeHB/24N23aNIWHh1tdCoAy0E/RT8F5mBADLLJp0yZ1795dd911l66++mpt3rxZV199tfd8/GBdml18KXatWrX0yCOP6Pvvv9fpp5+ufv36aejQoTpw4IDVZQIAahjjHqcgAXZHP0U/BWfhUyYBP8vNzdVTTz2lp59+WmeccYbeeOMNJSQknHDbzMxMtWvXTnv27AmKd6M8Ho9iY2O1cePGUu8+GWP07rvv6v7775fb7dakSZM0dOhQLugJAA7CuAfA7uinAOcIrqltwGIpKSn605/+pKefflqjR4/WunXrypwMk44tzZ4zZ47CwsIc/06U2+1WWFiYPvnkkxMOti6XSzfddJO2bNmivn37atiwYerXr5927NhhQbUAAF8oGvdCQ0OtLsXnXC7XScc9APZU1E+FhIQ4/o3Z8p6fA4HO2a+wAZs4dOiQbr/9dvXo0UOnnHKK1qxZowkTJlToCX/Hjh2VlJSkWrVqOXZSzO12q3bt2kpKSlLHjh1Pum2TJk00c+ZMff755/rhhx/UoUMHPffcczp69Kh/igUA+FT9+vW9nzDs1HFPOrby+d577y133ANgL8YYffbZZ8rNzZXb7XZ8PzV79mz6KTiWc1svYAPGGP373/9WXFycZs2apcmTJ+urr75S+/btK7Wfbt26ac6cOY4cdIt+pzlz5qhbt24Vvt8ll1yiDRs26M4779Qjjzyi888/X6tWrfJhpQAAX9u8ebN69Oih+vXra9q0aY4d90JCQtSvXz/93//9n6ZMmWJ1SQAqyBijRx55RGPGjNETTzyhefPmObaf8ng8atCggR5++GHt27fP6pIAn3BWywVsZNeuXbriiit09dVX64ILLtCmTZt01113VXnA7Nevn+bNm+eolWJFK8PmzZunvn37Vvr+9erV08SJE/Xtt9/K5XLpggsu0H333acjR474oFoAgC+tXbvWu5J62bJlGjp0qKPHvc8//1wjR47UHXfcoUmTJlldGoByFBYWatSoUXr22Wc1adIkjRkzRv3793dsP/XZZ59pxYoVOnjwoLp3765ffvnF6tKAGsdF9YEaVlBQoFdffVV///vfVb9+fU2ePFkDBw6ssf0vX75c/fv3V3Z2dkBfyNPj8SgsLEwLFixQ165dq72/o0eP6sUXX9TYsWPVpEkTvfbaa7rkkktqoFIAgK+tWLFCl1xyiVq1aqWkpCRFRUV5f+bkcc8YozFjxuipp57S+PHj9dhjjzn+mkRAICooKNCtt96q9957T1OmTNHw4cNL/NzJ/dSOHTvUu3dvFRYWavHixWrVqpXFVQI1xxnT2IBNfP/99+rWrZtGjRqloUOHavPmzTU6GSYdO30yJSVFMTExAftOlNvtVkxMjFJSUmpkMkySatWqpQcffFAbNmxQmzZtNGDAAP3tb3/Tr7/+WiP7BwD4xpIlS3TxxRerQ4cOWrRoUYnJMMnZ457L5dKTTz6pJ598UmPHjtVDDz0k3qsG7CUvL0/XXXedpk+frunTp5eaDJOc3U+1bNlSKSkpCgsLU/fu3bVx40YLqwRqVmC2VsBmsrOz9fe//13nnXeeDh8+rK+++kqvvvqqIiIifHK8jh07atOmTUpMTJR07N2cQFBU54gRI7Rp0yafXKCzZcuWWrBggaZNm6aFCxcqLi5Ob7/9Ni8wAMCGPv/8cw0YMEBdu3ZVUlJSmeOm08e9v//973rppZf0/PPP66677lJhYaEfqwRQlpycHF111VX65JNP9O9//1tDhgwpc1sn91OxsbFatmyZmjRpooSEBKWmpvq5SsBHDIBq+fLLL02rVq1M7dq1zfjx401OTo5fj7906VLTokUL43a7jSTbfrndbtOiRQuTnJzst8fmwIEDZujQoUaS6dmzp/nhhx/8dmwAwMl9+OGHplatWubyyy832dnZFb6fk8e9t956y7hcLjN06FBz9OjRqjysAGrIH3/8YS666CITFhZmkpKSKnVfp/ZTv/32m/nzn/9sGjRoYJYvX16VhxWwFVaIAVV08OBB3XzzzbrooovUtGlTrV27Vo8//rjq1Knj1zoSEhJs/W7U8e869ejRw2/HbtSokaZNm6YvvvhCO3fu1Nlnn62nnnpKeXl5fqsBAFDatGnTdPXVV2vQoEH68MMPFRoaWuH7Onncu/nmmzVz5kzNmjVL1157LeMVYJFDhw6pX79+WrlypZKSktSvX79K3d+p/dQpp5yiRYsW6dxzz1WfPn20ePFiX5YJ+J7VM3JAoCksLDSzZs0yTZo0MREREWbKlCmmoKDA6rKMMcfejWrbtq2RZEJCQix9x6no+G3btvXrqrCyZGZmmoceesh4PB7ToUMHs2LFCqtLAoCg9OqrrxpJ5tZbbzX5+fnV2pdTx705c+aY2rVrm0suucRkZWVVa18AKufAgQPm3HPPNZGRkea7776r9v6c2E9lZmaa/v37mzp16phPP/202o8RYBUmxIBK+Omnn8wll1xiJJlBgwaZtLQ0q0sqpbCw0CxdutQMHjzYeDwevy/VdrvdxuPxmMGDB5ulS5eawsJCqx+SElJTU018fLxxuVxm5MiR5vDhw1aXBABB4x//+IeRZO6+++4aGx+cOu4tXLjQ1K1b1/Ts2ZOxCvCTPXv2mHbt2pkmTZqYdevW1dh+ndhP5eTkmIEDB5qQkBAze/bsGniUAP9jQgyogKNHj5pJkyaZunXrmtjYWDNnzhyrS6qQtLQ0M2HCBBMdHW0kGY/H45NBtmi/0dHRZsKECbacKCwuUPMEgEBVWFhoxo4daySZRx991Gdvljht3EtJSTENGjQwF1xwgTl48KBPjgHgmJ9//tmceeaZJjY21mzdutVnx3FSP3X06FFz/fXXG7fbbd5+++0a3z/gay5j+Og14GTWrl2rW2+9VampqUpMTNSTTz6pBg0aWF1WpeTn52vu3LmaMWOGVqxYoT179kg6dv0AY0ylPs3K7XbL5XKpoKBAkhQTE6POnTtryJAhuuyyyxQSEuKT38EXfv75Z915551KSkrSoEGD9PLLL6tZs2ZWlwUAjmKM0QMPPKBJkybp6aef1ujRo31+TCeNe6tXr1bfvn116qmn6osvvlCTJk18ejwgGP3www/q3bu3ateurcWLF+v000/3+TGd0k8VFhbqrrvu0pQpU/TPf/5TI0aM8NmxgJrGhBhQhqysLI0fP14TJ05UXFyc3nzzTXXu3NnqsmpEenq6UlNTtXr1aq1cuVLffvut0tLSyr1f8+bN1blzZ3Xq1Enx8fGKj49XVFSUHyr2HWOMPvjgA919993Ky8vTc889p1tvvVVuN585AgDVZZcXSoE+7m3YsEF9+vRRw4YNtWjRIsXExPi9BsCpvv/+e/Xp08d7wfjmzZtbUkcg91NWvPEB1AQmxIATWLhwoe644w7t2bNHjz/+uB544AHVrl3b6rJ8KiMjQ4cOHVJ2drZycnKUm5urOnXqKDQ0VGFhYWrYsKEiIyOtLtNnDh48qAcffFBvv/22unfvrjfeeENnnXWW1WUBQMDKz8/XTTfdpJkzZ2rq1Km66aabrC6phOLj3sSJEzV//nzNmzfPtuPejz/+qN69eyskJESLFy/WGWecYXVJQMBbtWqV+vXrp9NOO00LFixQ48aNrS6phOL9VPv27fXII49o0KBBtuynjDEaP368xo8fr0cffVRPPPGEXC6X1WUBJxU45zYBfpCenq777rtP06dPV69evZSUlKTWrVtbXZZfREZG2mZAtcIpp5yit956S9dff71uu+02/elPf9Lf//53jR49WnXq1LG6PAAIKLm5ubruuuv06aefatasWbr66qutLqmU4uNe06ZNFRoaqvPOO8/iqsrWunVrffXVV+rdu7e6d++uRYsW8cYNUA0pKSn6y1/+og4dOujzzz9Xw4YNrS6plOOfn5955pm27adcLpfGjRunevXq6cEHH1RmZqYmTZrEpBhsjXOCAB17R2P69Ok666yzNG/ePL311ltavHhx0EyG4X969eql9evX64EHHtD//d//6dxzz9Xy5cutLgsAAkZWVpb++te/6rPPPtPHH39sy8mwQNWiRQstW7ZMDRs2VI8ePbRu3TqrSwIC0hdffKF+/frp/PPP1xdffGHLybBA9cADD+jVV1/Viy++qNtuu817XTPAjpgQQ9DbsWOH+vXrpxtuuEF9+vTR5s2bdfPNN/NuRhALCwvTk08+qdWrV6t+/fq68MILdeedd+r333+3ujQAsLU//vhDAwYM0LJly/TZZ5/p0ksvtbokx2nWrJmSk5PVokUL9ezZU99++63VJQEBZc6cObrssst00UUXad68eapXr57VJTnOnXfeqffee09vv/22hg4dqqNHj1pdEnBCTIghaOXn5+sf//iHOnTooK1bt+qzzz7TrFmzFB0dbXVpsIlzzjlHX3/9tV5++WW9//77iouL00cffWR1WQBgSxkZGbr44ou1Zs0affHFF+rdu7fVJTlWVFSUFi9erPbt2+viiy9WcnKy1SUBAWHWrFm66qqrdMUVV+ijjz5SWFiY1SU51g033KB//etf+vDDDzV48GDl5uZaXRJQChNiCEqrVq3S+eefr9GjR+uOO+7Qxo0bNWDAAKvLgg15PB6NHDlSmzZtUqdOnXTVVVdp4MCB3o/GBgBI+/fvV69evbR9+3YtWbJE3bp1s7okx4uIiNCCBQvUuXNn9e/fX0lJSVaXBNja1KlTNWTIEF1//fWaOXOm4z8wyw6uuuoqffLJJ1qwYIEuv/xyZWVlWV0SUAITYggqR44c0X333acLLrhAxhitWLFCkyZNYqk0ynXqqadqzpw5+ve//60VK1YoLi5Or776qgoLC60uDQAstXv3bvXo0UP79+9XcnKybS/47ETh4eGaO3eu+vbtq8svv5xVzEAZXnzxRQ0fPlx33XWX3n77bYWE8Nly/jJgwAB9/vnnWr58ufr376/Dhw9bXRLgxYQYgsb8+fPVoUMHvfbaa3r66ae1cuVKnX/++VaXhQDicrk0aNAgbdq0Sddee60SExN14YUXauPGjVaXBgCW2LFjh7p3767s7GwtW7ZM7du3t7qkoBMaGqoPP/xQV111la6++mq9//77VpcE2IYxRk8++aTuvfdePfzww/rnP/8pt5uXwP7Wq1cvLVq0SN9//7169+6t3377zeqSAElMiCEI7N+/X9ddd50GDBig1q1ba8OGDXrooYdUq1Ytq0tDgIqMjNQbb7yh5ORkHTx4UOeee64ef/xx5eTkWF0aAPjNli1b1L17d9WqVUspKSlq1aqV1SUFrVq1aun999/XjTfeqBtuuEFTpkyxuiTAcsYY/f3vf9eYMWP0xBNP6Omnn+ZDsyzUuXNnLVmyRDt37lTPnj21b98+q0sC5DLGGKuLAHzBGKN3331X999/v9xutyZNmqShQ4cyEKJG5eTk6Omnn9bTTz+tli1b6o033lCPHj2sLgsAfGrt2rXq27evoqOjtXDhQjVt2tTqkirt119/1YgRI5SZmakffvhBaWlp6tmzpyQpMTFRf/nLX6wtsAoKCwt177336uWXX9bEiRN13333WV0SYInCwkLdfffdeuWVV/TCCy/onnvusbqkKpk6dar3VOiis11OPfVURUVF6c0331RoaKjFFVbe5s2bdfHFFys8PFyLFy/WqaeeanVJCGJMiMGRfvzxR91+++1asmSJhg4dqokTJ6px48ZWlwUH27hxo2677TZ9/fXXuvXWW/Xcc88pMjLS6rIAoMatWLFCl1xyiVq1aqWkpCRFRUVZXVKV/PLLLzrjjDNOeC3I559/Xvfff78FVVWfMUZjxozRU089pfHjx+uxxx7jzUAElYKCAt1666167733NGXKFA0fPtzqkqosMTFRr776aqnb69evr19//TVgPyVzx44d6t27t4wxWrRoESuMYRlOmYSjHD16VE899ZTOPvts/fzzz1qwYIGmTZvGZBh8rn379kpJSdGrr76qf/3rX4qLi9O//vUv8Z4DACdZunSpLr74YnXo0EGLFy8O2MkwSWrRooWuv/56eTyeErdHRETotttus6iq6nO5XHryySf11FNPaezYsXrooYcYixA08vLydN1112n69Ol6//33A3oyTJIefPDBUn2U2+3WAw88ELCTYZLUsmVLpaSkKDQ0VD169NCmTZusLglBigkxOMa3336r+Ph4Pf744xo1apS+//579e3b1+qyEETcbrfuvPNObdq0SV27dtU111yjyy+/XL/88ovVpQFAtX3++ee65JJL1LVrVyUlJalBgwZWl1Rtjz32WInJIpfLpdGjR6t+/foWVlUzHnnkEb388st6/vnnddddd/GpyHC8nJwcXXXVVfrkk0/04Ycf6rrrrrO6pGo7/fTTddNNN5WYFAsPD9eoUaMsrKpmxMbGatmyZWrcuLF69Oih1NRUq0tCEGJCDAHvjz/+0KhRo9SlSxfVqlVLK1eu1HPPPafw8HCrS0OQiomJ0UcffaSPPvpIqampat++vV5++WUVFBRYXRoAVMl//vMf/fWvf1W/fv00d+5cx4yxrVq10vXXX+89pbBBgwZKTEy0uKqaM3LkSL311lt64403dOONNyo/P9/qkgCfOHLkiP7yl79o8eLFmjt3rv76179aXVKNefTRR73fu1wuPfDAA2rYsKF1BdWgJk2aaMmSJTrzzDPVq1cvff3111aXhCDDhBgC2rx589S+fXu99dZbev755/Xtt9/q3HPPtbosQJI0cOBAbdq0SUOHDtXdd9+trl27av369VaXBQCVMm3aNF199dUaPHiw/v3vf6tOnTpWl1SjHnvsMe/3TlkdVtzNN9+smTNnatasWbr22muVl5dndUlAjTp06JD69eunlStXasGCBY47Q6RolZgk1alTxxGrw4o75ZRTtGjRIp177rnq06ePFi9ebHVJCCJMiCEg7du3T1dffbUuu+wytW/fXhs2bNB9992nkJAQq0sDSoiIiNCrr76qr776SkeOHFF8fLz+/ve/Kzs72+rSAKBcr7/+uoYNG6abb75Z06ZNU61atawuqca1atVK8fHx8ng8jlodVtw111yjjz76yLtyhjEITpGenq6LLrpImzdv1uLFi9W9e3erS/KJolVif/3rXx2zOqy4+vXr6/PPP1ePHj30l7/8RfPmzbO6JAQJPmUyQGVkZCgjI0PZ2dnKyclRXl6eateurdDQUIWFhSkyMtKRn3BXWFiot956Sw899JBq1aqll156Sddeey2fnoSAkJeXp2effVb/93//pxYtWmjKlCm66KKLrC7LZ4K1nwJOJpDaxfPPP68HH3xQd999t1544QXHjbXFszh48KB2796tNm3a2DKLmrJo0SJdccUV+vOf/6xPP/3UNqvhAqldBINAySMtLU19+vRRenq6Fi5cqHPOOcfqkmpc8SzWr1+v2NhY1a1b13ZZ1JTc3Fz97W9/09y5czVjxgxdffXVVpfkFSjtApXDhFgASE9P1+rVq7V69WqtXLlS3377rfbu3Vvu/Zo1a6bOnTurU6dOio+PV3x8vBo1auSHin1jy5Ytuv3227Vs2TLdeOONev755wP6060QvLZs2aLbbrtNKSkpjvlbpp8CSgvUdmGM0fjx4zV+/HiNGTNGEyZMCPjJsEDNwheWL1+uAQMGKC4uTvPnz/f7CziysJdAzWPnzp3q3bu3cnNztXjxYrVp08Zvx/aVQM2ipuXn5+umm27SzJkzNXXqVO/pov5EFkHEwHaOHj1q/vOf/5irrrrKNG/e3EgykozH4zFut9v7/4p8ud1u4/F4vP9v3ry5ueqqq8x//vMfc/ToUat/1QrJzc01EyZMMLVr1zZnnnmmWbx4sdUlAdVWUFBg3njjDRMREWEaN25sZsyYYQoLC60uq8Lop4DSnNAuCgsLzX333WckmWeeecZnx/E1J2ThS6tWrTJRUVHmT3/6k/n11199eiyysBcn5LF161YTGxtrzjzzTPPTTz/57Di+5oQsfKWgoMDcfvvtRpL55z//6fPjkUXwYkLMRvbs2WPGjx9vmjRp4m2AlWl8Ff0q2m90dLQZP368SUtLs/pXL9Py5ctNu3btTEhIiHnkkUdMVlaW1SUBNSotLc0MHjzYSDL9+/e3/RM7+imgNKe0i+IvQF555ZUa3be/OCULf9iwYYNp2rSpOeuss8zu3btrfP9kYS9OyWP9+vUmOjratGvXzuzZs6dG9+0vTsnC1woLC839999vJJmnn37aJ8cgCzAhZrHCwkKzZMkSM2jQIOPxeHzWCMv6KprBHjRokFmyZIltVqgcOnTI3HXXXcblcpk///nPZt26dVaXBPjUp59+amJjY03dunXNxIkTbfUOEv0UUJrT2sXRo0fN9ddfb9xut3nnnXdq5kHyE6dl4U8//vijadGihTnjjDPMjh07qr0/srAXp+Xx3XffmcjISHPuueeaAwcO1NCj5B9Oy8JfCgsLzbhx44wk8+ijj9ZI3WSB4pgQs9DSpUtN27ZtjSQTEhLi14Z4/FfR8du2bWuWLl1q6ePy8ccfm+bNm5vw8HDz0ksvmfz8fEvrAfzl8OHDZtSoUcblcpn4+HiTmppqdUn0U8AJOKFdjBs3zixYsMAYY0xOTo658sorTUhIiJk9e7avHjafcEIWVtu5c6dp1aqViYmJMZs3bzbGGLNv3z5zxx13mH379lV4P2RhL4Gex6ZNm8zIkSPNkSNHjDHGLFu2zNSvX9906dLFZGRk+PCRq3mBnoUd/OMf/zCSzD333OOdQJoxY0alVzOTBY7HhJgFjhw5YkaMGGEk3y3LrOpXUT3FByB/2b17txk4cKCRZC699FKzc+dOvx4fsIsVK1aYs88+23g8HvPAAw+YzMxMv9dAPwWU5pR2sWXLFiPJ1KpVy8ydO9f079/f1KlTx8ydO9dPj2T1OSULu0hLSzPt27c3jRs3NsnJySYuLs5IMuPHjy/3vmRhL07JY+jQoUaSueiii8zcuXNNWFiYueiii8wff/zhp0ey+pyShV28+uqrRpK59dZbzdtvv20kmdq1a5vff/+93PuSBcrChJifLV261LRo0aLSF+fz95fb7TYtWrTwy2x1QUGBefXVV02DBg1MdHS0mT17NktHEfTy8vLMU089ZerUqWPOOOMM70oOf6CfAkpzUrsYM2aM8Xg8xuVyGZfLZUJDQ82iRYv8+GhWj5OysJP09HTTsWNH43a7vY/t6aefftLnZGRhL07J48iRIyY0NNRI8vZTl1xyicnOzvbzI1p1TsnCbt577z3jcrlK/A5vv/32Se9DFjgZJsT8xM6z0mV9+WO2euPGjaZr165GOjbbf/DgQZ8cBwhUP/zwg+nVq5eRZK6//nqzf/9+nx2LfgoozWntorCw0MTGxpbYPjQ01KxevdqiR7jinJaF3WRmZpo///nPpX6HFStWlNqWLOzFaXnMmDGj1PaDBw8OiMuoOC0Lu5k3b16JiS23220SEhJOuC1ZoCKYEPODNWvWBMSsdFlfRbPVa9asqbHHJCcnxzz++OOmVq1apk2bNsyEAydRWFho3n77bRMZGWmioqLMe++9V+OrKOmngNKc2C5SUlJKbedyuUxERESlrhflb07Mwm6KLltR/Mvj8Zi77rqrxHZkYS9OzKNPnz6lVgFJMg8++KB1D3QFODELO1m3bp2pVatWqbpdLpfZtWtXiW3JAhXFhJiPffXVV6ZevXoBMytd1pfH4zH16tUzX331VbUfk2XLlpm2bduaWrVqmcceeyyglj8DVvr111/N3/72NyPJ9OnTx2zfvr1G9ks/BZTm1HYxZMgQ78+KXii4XC7TrVs3206IOTULu7n//vtNeHi4kUpebLpu3bomLy/PGEMWduPEPPbt21diMqzobzEyMtK88MILVj/kZXJiFnazadMmc/bZZxvpf6fSFtU9YcIE73ZkgcpgQsyH5s+fb+rUqROwM9PHf7ndblOnTh2TlJRU7u+em5tb6raMjAxz2223GUmmS5cuZsOGDb542AHH+/zzz81pp51mwsLCzLPPPut9oVIkPz/fHD16tEL7CuZ+CiiLU9vF/PnzvS8Qateuba644grzzjvv+PRU7OpyahZ27aNyc3PNF198Ye666y7TtGlTb91vvPEGWdiMU/O47LLLvLedeeaZ5qGHHjLLly+39emSTs3Crm3jl19+Ma+88orp3bu3d0xr2LChMYYsUHlMiPlIUlKSCQkJcUxjLN4oQ0JCTtooDxw4YJo0aWIee+wxY8yx073+9a9/maZNm5r69eubyZMnm4KCAn9FATjSH3/8Ye677z7jdrvNn/70J7Ny5UpjzLH21qdPH9O1a9dy21kw91NAWZzeLi6//HLz7rvvmqysLKsf6nI5PQu791GFhYVm1apV5vrrrzfvvvsuWdiIk9uGx+Mx/fv3N1u2bLH6Ya4QJ2cRCG3j999/N5MmTTLjx48nC1QJE2I+kJKS4qiZ6RM1yjp16pS5fPOWW27xbrdgwQLvOz1XXHFFqfO7AVTPypUrvZ8Kdu+993o/klqSmTp1apn3C/Z+CjgR2oV9kIV9kIW9kId9kIV9kAWqigmxGrZmzRpTr149xzbG4o2yXr16pS70980335TYxu12m6ZNm5r//Oc/1gQCBIG8vDzz3HPPmdDQ0BLXU4iIiDC//fZbqe2DvZ8CToR2YR9kYR9kYS/kYR9kYR9kgepwGWOMUCMyMzPVrl077dmzRwUFBVaX43Mej0cxMTHatGmTwsPDVVBQoPPOO08bNmxQYWGhd7tnnnlGDz/8sIWVAsHh0ksv1Weffeb9v9vt1vDhw/X66697bwv2fgo4EdqFfZCFfZCFvZCHfZCFfZAFqsttdQFOMnr0aO3evTsoGqMkFRQUaPfu3XrkkUckSZMnT9b69etLTIZJ0rhx47Rr1y4rSgSCRlJSUonJMEkqLCzUlClTtHLlSu9twd5PASdCu7APsrAPsrAX8rAPsrAPskC1Wb1EzSmWLl1q+TJKK7/mz59f5jLVkJAQk5ycbHVEgKO98MILZbbP6OhoYwz91NKlSy1OCXZEu7BPuyALsrDLl52yMIY87JQHWZCFXb7slEUg45TJGhBsSzWP5/F41Lx5c7Vq1UpnnXWWzjnnHMXExKh58+Zq3ry5mjRpIo/HY3WZgOPl5eVp7969SktL8359/fXXCg8P10svvRT0/RRLzHE8xm/7tAuyIAu7sFMWEnnYKQ+yIAu7sFMWAc/qGTknGDFihOMv4lfel9vtNiNHjrQ6CgBloJ+in0JptAv7tAuyIAs7fdklC2PIw055kAVZ2OnLLlkEOlaIVVNycrJ69uxpdRm2sXTpUiUkJFhdBoBi6KdKop+CRLs4npXtgixKIgv7sHq8II+SaBv2QRb2YXU/FeiYEKsGY4zi4uK0bdu2oFyqeTyPx6NWrVpp8+bNcrlcVpcDQPRTx6OfgkS7OJ6V7YIsSiIL+7B6vCCPkmgb9kEW9mF1P+UEfMpkNSQnJ2vr1q00xv8qKCjQ1q1btWzZMqtLAfBf9FMl0U9Bol0cz8p2QRYlkYV9WD1ekEdJtA37IAv7sLqfcgImxKph8uTJCgkJsboMWwkJCdHkyZOtLgPAf9FPlUY/BdpFaVa1C7IojSzsw8rxgjxKo23YB1nYB89rq4dTJqsoLS1NLVq0YHb6BDwej3bt2qVmzZpZXQoQ1OinykY/FbxoF2Xzd7sgi7KRhX1YMV6QR9loG/ZBFvbB89qqY4VYFU2dOlXMJZ6YMUZTp061ugwg6NFPlY1+KnjRLsrm73ZBFmUjC/uwYrwgj7LRNuyDLOyD57VVxwqxKjh69KhiY2O1f/9+q0uxrejoaO3evZslrYBF6KfKRz8VfGgX5fNXuyCL8pGFffhzvCCP8tE27IMs7IPntVXDCrEqmDt3Lo2xHL/++qvmzp1rdRlA0KKfKh/9VPChXZTPX+2CLMpHFvbhz/GCPMpH27APsrAPntdWDRNiVTBz5kx5PB6ry7A1j8ejGTNmWF0GELTop8pHPxV8aBfl81e7IIvykYV9+HO8II/y0Tbsgyzsg+e1VcMpk1UQExOjtLQ0q8uwvZiYGO3evdvqMoCgRD9VMfRTwYV2UTH+aBdkUTFkYR/+Gi/Io2JoG/ZBFvbB89rKY0KsktLT09W4cWOrywgY6enpioqKsroMIKjQT1UO/VRwoF1Uji/bBVlUDlnYh6/HC/KoHNqGfZCFffC8tnI4ZbKSVq9ebXUJAYXHC/A/2l3l8HgFB3KuHF8+XmRROWRhH75+vMijcmgb9kEW9sHjVTlMiFXS6tWrOX+5gjweDw0SsAD9VMXRTwUP2kXF+bpdkEXFkYV9+GO8II+Ko23YB1nYB89rK48JsUpatWqVyjvLdNiwYTLGyBij/Px8xcbGnvBnCQkJ3tsTEhK8tw8bNqzE/lq1aqXXXntNW7duVVZWln7//Xdt2bJF7777rrp3715i2zp16uiee+7R8uXLlZGRoZycHO3cuVMLFy7UvffeW6rWXr166cMPP9Tu3buVm5urAwcOaM2aNZo4caJOP/30EvWe7OtEjDFatWpVuY8pgJp1sn7KSf3T8d555x1vnT/88EOFHiv6qeBR3vhtVdtYsmSJjDH66aefSty/+N9zkbFjx3pvO+2008qt7/gajTHq1q1buY+Vr9tFsGVRVm2nnXaa9/axY8ee8LGwOgvJeXkUOffcczV9+nTt3LlTOTk52rdvn5YsWaJbbrnlhI+DP8YLJ7SNIsUzOXTokMLCwsr8vYr2b4zRwoULy36AirG6bTgpi6q0n+LIoubbRatWrfT6669r27Ztys7OVnp6ur755hs9/PDDJ32seF5beSFWFxBoVqxYocLCwpNuc+ONN3q/93g8GjZsmJ588skqHe/SSy/V7NmzVbduXUnHPk513759at68ubeBp6SkSJJOOeUULV68WB07dpQkZWZm6ocfflD9+vWVkJCgiy++WC+88IJ330888YTGjBkjSSooKNAvv/yirKwstWzZUh07dtT69et14MABrVixwnufzp07S5IOHDig7du3n7T2wsLCEvcF4B8n66ec1D/9/PPP3u3Dw8M1aNAg7/9bt26tbt26afny5Sf9Heingkd547dVbcPXiv9eRf+3ul0EaxZVYXUWkjPzuOWWW/T6668rJCREhYWF3he03bt31+mnn6633nqr1H38MV44qW3ccMMN3u8jIiJ05ZVXnvAT8E4//XT16NHD+/9evXopNja23AuDW902nJhFVZFFxVUki0suuUT//ve/FR4eLknatWuXMjMzFR8fr86dO+vZZ58tc/88r608VohVQkZGhvbu3XvSbYp36itXrpSkUrPOFdWoUSPNmDFDdevW1aFDh9S/f381bdpUHTt2VJMmTXTWWWdp5syZ3u1feeUV74vNF198UVFRUTrnnHN0xhlnqFGjRiU6i759+3pfbK5bt05xcXFq2bKlOnTooIiICCUkJCg1NVWff/65unTp4v0q8tlnn53w9uOlpaUpIyOjSr8/gMo7WT/ltP6puEGDBqlevXrKycnR999/L6n0REBZ6Kecr7zx28q24UvFJ4qLfq/BgwefdKVGEV+1i2DNojqsykJyZh5t27b1Tob9/PPPOvfcc9WqVSu1atVKjRo10lNPPVXmfX05XjipbSQkJKhly5Ylai1rTB42bJjcbrf27NmjtLQ074RGRdBPla8yWVQHWZSvIllERUVp1qxZCg8P18GDB9WzZ0+1aNFCcXFxioiI0MiRI8s9Ds9rK4cJsUqoyB9WUae+d+9eDR8+XNL/VipU1jXXXKMGDRpIkiZMmKAFCxaU+PnWrVu9y4ojIiI0ePBgSdLatWt13333KTc317vt4cOH9d5773n/X1SbJN1000368ccfS+x72bJl3heV1XXo0KEa2Q+A8p2sn3Jy/1T0hOLTTz/VG2+8IaniL/wl+imnK2/8tqpt+FrRRHFubq7+9re/KS8vz/uOdEX4ol0EaxbVZUUWkjPzuOWWWxQScuwkmXvvvVfr16/3/uzQoUN68803T3p/X40XTmobRWPyd999pwkTJkj638qv4xWtmJkxY4ZmzZolqXITGvRTJ1eZLKqLLE6uIllcc801ioiIkHTsbInk5GTvz7Kzs/XKK69U6Fg8r604JsQqITs7u9xtijr1mTNnat26dVq3bp2kqs3Et2vXzvt9UWOIiIg44fW72rRp4x3cU1JSvLd//PHHJbYtGmCK9n348GGtWbNGknTFFVeU2HbJkiWVrvlEKvK4AagZJ2tvTu2fir87OH36dH3wwQc6evRopV740085W3n5WtU2fK2o/nnz5mn79u2aP39+idvL44t2EaxZVJcVWUjOzKN4HcuWLav0/X01XjilbRRfmTp9+nQlJSXpwIEDJ1z5VXzFzPTp0/X+++9LqtyEBv1U2SqTRU0gi7JVNIvq9k9FeF5bcUyIVUJOTs5Jf358p17836KVChVpRCfapui86fz8fK1YsUJ79uwp8/7Fz7HeunWr1q5dW6FjHTx4UCtWrNAff/xRbo2VUd7jBqDmlNXenNw/Fb07uH//fiUlJSk9Pd37rl5FnxDRTznbyfK1um1U5sl1Zeo4fqK4+L8VXR3gi3YRjFlUtebi/J2F5Nw8XC5XlY5RxFfjhVPaRtHK1Ly8PH3wwQfKz8/X7NmzJZVe+VU0Rq9du1YbNmzw/lv8Z+WhnypbRbOoiT5KIouTqWgW1e2fivC8tuKYEKuEvLy8k/68eMe9dOlSZWRkaNy4cZL+d9G8zMxM7zannHKK9/uoqCjv90eOHJEkbdy40Xtb0bskmZmZ6tKli7exF9m6davy8/MlSV27dvXePnr0aF177bWlai3ad0REhNq3by/p2MqNLl26lDhuTSh+ahQA3yqrn3Jy/1T07mBkZKQOHDigjIwMXXzxxZIq/sKffsrZTjZ+W9k2in52/H6L77v4JHBl6iiaKJak9957TxkZGXr77bclqcKrA3zRLoIxi8psWxZ/ZyE5N4/idRz/acgV4avxwilto6hWj8ejH3/8URkZGbr55psllVz5VXzFTFxcnDIyMpSRkaE2bdpIqvhlD+inSu67KlnURB8lkcXx+65KFtXtn4rwvLYSDCps1apVRtIJv8LDw80ff/xx0vsvXLjQtGrVyvv/+fPnmwYNGpgGDRqY+fPne28/88wzjSQTFRVlfv/9d2OMMb/++qvp2rWr93hPP/20d/ui22bMmOG9bdy4ccbtdhtJpm3btt7bhw0bZiSZPn36eG/75ptvTGxsrHc/33zzjTHGmCVLlpT6PYu88847ZT4Wx3+tXr26sg81gCo6UT/l5P4pISGh3Mfk0UcfpZ8KcmWN33ZoG0888YT3tltuucV4PB5z3nnneetKSUnxbtu7d2/vtm+99ZYJDQ010dHRJjU11RhjTHZ2tqlbt66RZLZv337S3+uHH36wpF0EYxbh4eEmOzvbGGNMamqqiY6ONqGhoeatt97y7qN37962ycLpeZx11lnm6NGjxhhjtm/fbjp06ODdT2RkpElMTLRkvHBC2zj99NNNQUHBSWt98803jSQzbNiwch+TIUOG0E/9ly+zqEz7IQvfZhEVFWUOHTpkjDEmPT3ddO/e3Xu8unXrmvvvv7/cHHheWzlMiFXChg0byvyjK96pt2vXrsTPRo0aZYwxJj8/38TGxprZs2eXeYwPPvigxH0vvfRSk5WV5f35zp07TWpqqsnJyfHeVrTtKaecYtauXeu9/dChQyY1NdXs3bvXe1vRC87jG3FeXp7ZvHmz2bhxo7fB1tSE2MaNG6vwaAOoihP1U07un9555x1jjDF79+41LperRH0fffSRMaZiL/zpp5ytrPHbDm0jJibGpKene28v/qS5oKDADBgwwLuty+XyTgofv60xxjzzzDNGKjlRXPz+kszll1/u/Vm3bt383i6CLYuir2effbbEz4tv//XXX5fqv6zMIhjyuOWWW7yTYvn5+ebHH380P/zwg8nLyzM//fSTJeOFE9rG2LFjjTHG5ObmmoiIiBLHmzRpkjHm2PgfFhZmlixZYowx5rvvviv1OxdNxCxcuNCS8TvYsqhs+yEL32UhyQwYMMAcOXKkRA0bN2701mBVFk7FhFglbN++vcw/uqJOfcuWLaV+Fhsb693Ho48+amrXrm0ee+wxs3HjRpOdnW2ys7PNxo0bzZgxY0ytWrVK3b9t27Zm6tSp5qeffjI5OTnm4MGD5vvvvzdvvvmm6du3b4ltQ0NDzYMPPmhWrlxpDh8+bLKyssyOHTvM/PnzzW233VaqEfbp08fMmTPH7Nu3z+Tl5Zl9+/aZlStXmqeeeqrEO2ZFX0UqMyG2Y8cOf0cFBK0T9VNO7Z+Kvzv4+uuvl6rt+uuv9/5u5b3wp59ytrLGb7u0jTZt2phZs2aZvXv3mqNHj5qMjAyzaNGiUttJMg0aNDATJ04027ZtM7m5uSYzM9OkpqaaxMRE76RK0UTx77//bmrXrl3i/nXq1PG2m6J3pP3ZLoIti6Ivl8tlRowYYVJTU01mZqbJzc0127ZtM88//7ypX7++Jc+lAuF5ra/ykGTOO+888/7775tffvnF5ObmmgMHDpiUlBRz6623WjJeOKFtFK1MTUpKKnWsCy+80FvrmDFjvJMHo0ePLrXtmDFjjDH/m9CwS9twYhZFq/Aq237IwndZSDKtW7c2U6ZMMdu3b/fWsHLlyhO2F3/2U07kMiZAPl7HBjIyMkqdI4zyHTx4UJGRkVaXAQQF+qmqoZ9yNtpF1fiiXZBF1ZCFffhqvCCPqqFt2AdZ2AfPayuOi+pXQmRkpJo1a2Z1GQGlefPmNEbAj+inKo9+yvloF5Xnq3ZBFpVHFvbhy/GCPCqPtmEfZGEfPK+tHCbEKqlz587eT23CyXk8HnXu3NnqMoCgQz9VcfRTwYN2UXG+bhdkUXFkYR/+GC/Io+JoG/ZBFvbB89rK4y+rkjp16iSXy2V1GQGjU6dOVpcABB36qcqhnwoOtIvK8WW7IIvKIQv78PV4QR6VQ9uwD7KwD57XVg4TYpUUHx+vgoICq8sICAUFBYqPj7e6DCDo0E9VHP1U8KBdVJyv2wVZVBxZ2Ic/xgvyqDjahn2QhX3wvLbyuKh+JaWnp6tx48ZWlxEw0tPTFRUVZXUZQFChn6oc+qngQLuoHF+2C7KoHLKwD1+PF+RRObQN+yAL++B5beWwQqySGjVqpObNm1tdRkCIiYmhMQIWoJ+qOPqp4EG7qDhftwuyqDiysA9/jBfkUXG0DfsgC/vgeW3lMSFWBV26dJHH47G6DFvjgn6Ateinykc/FXxoF+XzV7sgi/KRhX34c7wgj/LRNuyDLOyD57VVw4RYFVx33XWcx1yOgoICDRkyxOoygKBFP1U++qngQ7son7/aBVmUjyzsw5/jBXmUj7ZhH2RhHzyvrRquIVYF+fn5iomJ0f79+60uxbaio6O1e/duhYSEWF0KEJTop8pHPxV8aBfl81e7IIvykYV9+HO8II/y0Tbsgyzsg+e1VcMKsSoICQlRYmKi3G4evhNxu91KTEykMQIWop86Ofqp4ES7ODl/tguyODmysA9/jxfkcXK0DfsgC/vgeW3VsUKsitLS0tSiRQuWbp6Ax+PRrl271KxZM6tLAYIa/VTZ6KeCF+2ibP5uF2RRNrKwDyvGC/IoG23DPsjCPnheW3VMsVZR8+bNNXDgQGZhjxMSEqIrr7ySxgjYAP3UidFPBTfaxYlZ0S7I4sTIwj6sGi/I48RoG/ZBFvbB89rqYUKsGhITE5Wfn291GbaSn5+vxMREq8sA8F/0U6XRT4F2UZpV7YIsSiML+7ByvCCP0mgb9kEW9sHz2urhlMlqMMYoLi5O27ZtY+mmji3VbN26tTZt2iSXy2V1OQBEP3U8+ilItIvjWdkuyKIksrAPq8cL8iiJtmEfZGEfVvdTTsAKsWpwuVyaMmUKjfG/CgoKNGXKFBojYCP0UyXRT0GiXRzPynZBFiWRhX1YPV6QR0m0DfsgC/uwup9yAibEqikhIUEjRowI+k+8cLvdGjlypHr06GF1KQCOQz91DP0UiqNdHGOHdkEWx5CFfdghC4k8itghD7I4hizsww5ZOAGnTNaAzMxMtWvXTnv27AnK2WqPx6PY2Fht3LhR4eHhVpcD4ATop+inUBrtwj7tgizIwi7slIVEHnbKgyzIwi7slEWgC+5p1RoSHh6uadOmBWVjlI4t1Zw2bRqNEbAx+in6KZRGu7BPuyALsrALO2UhkYed8iALsrALO2UR6JgQqyHBunSTpZpA4KCfop9CabQL+7QLsiALq9kxC4k87JQHWZCF1eyYRSDjlMkaFGxLN1mqCQQe+imgNNqFfZCFfZCFvZCHfZCFfZAFqiu4plN9LDw8XHPmzFFYWJjjZ6rdbrfCwsL0ySef0BiBAEI/BZRGu7APsrAPsrAX8rAPsrAPskB1OfuvxgIdO3ZUUlKSatWq5dhG6Xa7Vbt2bSUlJaljx45WlwOgkuingNJoF/ZBFvZBFvZCHvZBFvZBFqgOZ/7FWKxbt26aM2eO3G634xpl0e80Z84cdevWzepyAFQR/RRQGu3CPsjCPsjCXsjDPsjCPsgCVeWsvxYb6devn+bNm+eomeqimel58+apb9++VpcDoJrop4DSaBf2QRb2QRb2Qh72QRb2QRaoCi6q72PLly9X//79lZ2dHdAX+vN4PAoLC9OCBQvUtWtXq8sBUIPop4DSaBf2QRb2QRb2Qh72QRb2QRaoDGdMndpYt27dlJKSopiYmICdqXa73YqJiVFKSgqNEXAg+imgNNqFfZCFfZCFvZCHfZCFfZAFKiMw/0ICTMeOHbVp0yYlJiZKOjbbGwiK6hwxYoQ2bdrEBfwAB6OfAkqjXdgHWdgHWdgLedgHWdgHWaDCDPxq6dKlpkWLFsbtdhtJtv1yu92mRYsWJjk52eqHDICf0U8BpdEu7IMs7IMs7IU87IMs7IMscDJMiFngyJEjZuTIkUaS8Xg8lje+4l9F9YwaNcocOXLE6ocKgEXop4DSaBf2QRb2QRb2Qh72QRb2QRYoCxNiFlq6dKlp27atkWRCQkIsbYhFx2/bti2z0gC86KeA0mgX9kEW9kEW9kIe9kEW9kEWOB4TYhYrLCw0S5cuNYMHDzYej8fvSzndbrfxeDxm8ODBZunSpaawsNDqhwSAzdBPAaXRLuyDLOyDLOyFPOy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      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# initializes the nodes, stores children of node as a dictionary. And contains a variable denoting whether it is or is not a leaf node.\n",
    "# the .children dictionary will become a nested dictionary with the full trie.\n",
    "class TrieNode:\n",
    "    def __init__(self):\n",
    "        self.children = {}\n",
    "        self.is_leaf = False\n",
    "\n",
    "# defines the Trie class to wrap nodes\n",
    "class Trie:\n",
    "    # initializes the tree's root as a node\n",
    "    def __init__(self):\n",
    "        self.root = TrieNode()\n",
    "    # defines a method to insert new nodes based on the list of query sequences\n",
    "    def insert(self, sequence):\n",
    "        # the working node will start as the root\n",
    "        node = self.root\n",
    "        # for each character in the sequence\n",
    "        for letter in sequence:\n",
    "            # only when the character is not one the node's children (in which case, we would go down that path), we add a new child to the working node with that character\n",
    "            if letter not in node.children:\n",
    "                # we make the node's child for that character a node object\n",
    "                node.children[letter] = TrieNode()\n",
    "                # we then reset the working node to its child for that character. This means that when adding a new string, we will keep checking if the string contains prefixes that are already in the graph.\n",
    "            node = node.children[letter]\n",
    "        # when we finish executing the above code, our working node will become the leaf node, so we update its attribute accoridgly.\n",
    "        node.is_leaf = True\n",
    "\n",
    "    # this is a function to plot_trie the sequences\n",
    "    def plot_trie(self):\n",
    "        # we use the networkx package to initialize a (directed) graph object\n",
    "        G = nx.DiGraph()\n",
    "        \n",
    "        # we add nodes and edges based on the trie we constructed, starting with the root node.\n",
    "        def add_nodes_and_edges(node, parent_label=''):\n",
    "            # we iterate through each character-child pair in the trie and label the nodes and edges accordingly\n",
    "            for letter, child in node.children.items():\n",
    "                # labelling the node, and adding it to the graph\n",
    "                node_label = parent_label + letter\n",
    "                G.add_node(node_label)\n",
    "                # drawing an edge between the parent and each child\n",
    "                G.add_edge(parent_label, node_label)\n",
    "                add_nodes_and_edges(child, node_label)\n",
    "        # calls the function to draw the graph\n",
    "        add_nodes_and_edges(self.root)\n",
    "        return G\n",
    "\n",
    "# example sequences, each beginning with a start codon (AUG)\n",
    "input_sequences = [\n",
    "    'AUGGGT',\n",
    "    'AUGGGA',\n",
    "    'AUGUUA',\n",
    "    'AUGUUU',\n",
    "    'AUGUUC',\n",
    "    'AUGUAAU',\n",
    "    'AUGUAUU',\n",
    "    'AUGUACA'\n",
    "]\n",
    "\n",
    "trie = Trie()\n",
    "# inserts each seqeunce into the trie\n",
    "for sequence in input_sequences:\n",
    "    trie.insert(sequence)\n",
    "\n",
    "# plot_tries the trie\n",
    "G = trie.plot_trie()\n",
    "\n",
    "# A function to calculate positions for nodes in a hierarchical layout\n",
    "def set_hierarchical_position(G, root=None, width=1., vert_gap=0.2, vert_loc=0, xcenter=0.5):\n",
    "    # for a given node, return a dictionary of node positions based on the helper function below.\n",
    "    position = _set_hierarchical_position(G, root, width, vert_gap, vert_loc, xcenter)\n",
    "    return position\n",
    "\n",
    "# a helper function that will loop through all the nodes in the graph\n",
    "def _set_hierarchical_position(G, root, width=1., vert_gap=0.2, vert_loc=0, xcenter=0.5, position=None, parent=None):\n",
    "    # intialize a positions dictionary\n",
    "    if position is None:\n",
    "        position = {root: (xcenter, vert_loc)}\n",
    "    else:\n",
    "        # Update the position of the root node\n",
    "        position[root] = (xcenter, vert_loc)\n",
    "\n",
    "    # Get neighbors of the root node\n",
    "    neighbors = list(G.neighbors(root))\n",
    "    \n",
    "    # Uses recursion to calculate the positions of each neighbor to each other to optimize the layout\n",
    "    if len(neighbors) != 0:\n",
    "        # goes through the nieghbors of a given node, and calcualtes its neighbors\n",
    "        dx = width / len(neighbors)\n",
    "        nextx = xcenter - width/2 - dx/2\n",
    "        \n",
    "        for neighbor in neighbors:\n",
    "            nextx += dx\n",
    "            # Uses recursion to calculate the positions of each neighbor to each other to optimize the layout\n",
    "            position = _set_hierarchical_position(G, neighbor, width=dx, vert_gap=vert_gap, vert_loc=vert_loc-vert_gap, xcenter=nextx, position=position, parent=root)\n",
    "    \n",
    "    return position\n",
    "\n",
    "\n",
    "# plots the graph\n",
    "plt.figure(figsize=(12, 8))\n",
    "position = set_hierarchical_position(G, '')\n",
    "nx.draw(G, position, with_labels=True, arrows=True, node_size=3000, node_color='black', font_size=10, font_color = 'white', font_weight='bold', edge_color='black')\n",
    "plt.title('Trie of RNA sequences (with full sequence displayed)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have successfully created a trie of the set of RNA sequences from the list. We have displayed the full RNA sequence at each node, even though the true trie only stores each letter."
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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