lattice-programming/lattices.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lattice Programming\n",
    "\n",
    "## What is a lattice\n",
    "\n",
    "- Very generic math structure\n",
    "- For practical purposes: just a **finite** set with a subset relation\n",
    "- Paired with ``fixpoint operators``: functions that either\n",
    "    - Take a point and follow the lines upwards\n",
    "    - Stay in the same place\n",
    "- Conditions above can be relaxed, but at the cost of complexity\n",
    "\n",
    "## Lattice programming\n",
    "- Partial solutions\n",
    "- Guaranteed termination\n",
    "- Very modular / elegant\n",
    "- A sane way to define recursive functions\n",
    "- Not an implementation, just an underlying theory to build upon\n",
    "\n",
    "## Example Visualization\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graphviz import Digraph\n",
    "from IPython.display import Image\n",
    "\n",
    "def new_graph(name: str):\n",
    "    return Digraph(\n",
    "        name=name,\n",
    "        node_attr={\"shape\": \"circle\", \"style\": \"filled\"},\n",
    "        graph_attr={\"bgcolor\": \"transparent\", \"splines\": \"line\", \"rankdir\": \"BT\"},\n",
    "        edge_attr={\"arrowsize\": \"0.75\"},\n",
    "        strict=True,\n",
    "    )\n",
    "\n",
    "def render(dot: Digraph):\n",
    "    dot.render(filename=dot.name, format=\"png\", directory=\"./graphs\")\n",
    "    return f\"graphs/{dot.name}.png\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BUFC3bl3TOX4VRREPP/wwxx13HAcccABXXHHFFu87btw4unfvTqtWrUrt+VeuXMnLL7/MxRdfTFFREQceeCDHHXccN910E9OnT9/l48dxzJQpU7j33nvp3r07bdu25dBDD+W8885jxIgRxHFcCq/i966++mr2339/Bg4cuNnf33bbbbRt25YuXbrQq1cv1q9fX+oZdkVhYaHleV4j0zlEJHupUBCRbFQrjmOroKDAdI5fvfbaawwePJgTTjiBMWPGMGDAgD/d5+eff+bqq6/m4YcfZsmSJaX6/H369OG+++6jc+fODBs2jPHjx3PPPfcwffp0TjvtNEaPHr1Lx//pp58477zz+Omnn3jooYf4+OOP+de//kXdunW55ZZb6NOnTym9ksSbb77JmDFjtnqff/zjH4wbN45LLrmEF198keeee65UM+yqmjVrAqTPm1REso4KBRHJRgUA1apVM53jV5MmTQLgnHPOIT8/f7P36d+/P61bt+bll1+mcuXKpZ6hR48enHPOORQUFJCbm0vbtm3p3bs3URTx0EMP7fLxHcehT58+NG7cmJycHOrVq8c//vEPqlevzpAhQygpKSmFVwELFy6kd+/eHH/88du8b5UqVTj11FPJzc3l008/LZXnLy3Vq1cnDMPqpnOISPbSjh8iko1qAdSoUcN0jl8tX74c27apUqXKFu9z9913k5OTUybPf9ddd2329iZNmpCTk8PPP/9MHMdY1s71/2rQoAGff/75n273PI86deowbdo0SkpKSKVSO3X8Tf3973/nmGOO4YADDmD48OHb9ZiqVauyfPnyXX7u0rShUKgE5ALrTOcRkeyjKwoiko1qWpZF1apVTef4VRiG27xPWRUJW7N27VrWr19Po0aNdrpI2JpVq1Yxa9YsmjVrRl5e3i4f7/XXX+f777/nhhtu2OHHbs9/g/JUvfqvFxNqmswhItlLVxREJBvlua4bua6rkyXbMGrUKAAuu+yyUj1ucXEx3333HQ8//DAFBQXcd999u3zMBQsW8MADD9C3b9+tXpmpKDaZXlbxX4yIVEgaJEUkG6Ucx4lMh9iU7/ulMu2mNC1ZsoS+ffvSs2dPunTpUmrHHThwIIcccgjnnXcejuPwyCOP0KjRrm/uc+edd3LcccfRvn37HX5sKpUiCIJdzlCaNukaXv6XkkREUKEgItkpx3Xd0t+Pcxf88ssv1K5d23SMXy1fvpy//OUvHHTQQdxxxx2leuzLL7+cyZMn8+abb9KgQQNOOeWULW5hur2GDh3KrFmzuP7663fq8bvvvjsLFixIq+lHmxSOKhRExAgVCiKSjVKe56VFobBixQqefvpp5s2bxxlnnGE6DpCsS7j88stp2LAhvXv3xrZLf6jwPI8GDRpw++2307lzZ/r378/EiRN36ljz58+nT58+3HPPPVSqVGmnjnHqqaeyevVq+vfvz7Jly3bqGKVNhYKImKY1CiKSjZyy+PK7o2677TaGDRuGbdtcdNFFnH322aYjEYYh119/PbVr1+a+++4rkyLhjw4//HDef/99xo4dy8EHH7zDjx8zZgzFxcVceOGFm/19//796d+/PwBvvfUWe+2115/u0717d3755Rf69+/Pk08+SVFREY8//vgOZylNm/ztHZM5RCR7qVAQkWxUkg7z0f/xj39w880389FHH/HXv/6VlStXcueddxrNdNddd+H7Po888giO89v3027dutGrVy9atmxZ6s+58cz5ihUrdurxZ555Jmeeeeafbh8xYgS33HILV111FZdffvlWj9GvXz8GDRrE3//+d7p06VIqOzDtKt/3N/5jerWMFpGsYf6UmohI+Vvv+37p7/W5E/Ly8jjmmGNo1qzZrzsMmfLPf/6T77//nn79+pX6wuoHH3yQm2++ebO/GzduHAAtWrQo1efcEe+99x6FhYX07NkzLYoEYNMGdCoURMQIFQoiko1KgiBIq8+/KlWqUFxcXKrHvPnmm9l///2ZO3fuNu87bNgwBgwYwNSpU2nfvj3777//735+/vnnXTo+wNtvv83jjz/OvHnzKCkpYd68efTt25cRI0aw33770bNnz106/q5YvXp12hQIG+mKgoiYpqlHIpKN1qVbobA9zczGjh3LVVdd9bvb9t9/fyDpRvzHL9qLFy+mcuXK1K1bd5vH3pmrGTty/L/85S80bNiQUaNG8frrr7No0SI8z2Pvvffmf/7nfzjnnHP+1FBuR46/qbvvvptXXnnl13/fuEZhW+sOyqKh3K7QFQURMU2Fgohko+VRFFmrV69Om8ZcqVSKON76RkyHHXYYX3755XYdb9WqVXz++ed07959uxYkP/bYY9t13J09fl5eHieffDInn3xymRx/U3fccccOb+kahmHa9bHYZM1GemzDJCJZJ63OqImIlJPFkPQKSBe1a9cmjmOWLFmyy8eK45j777+fvLy8P12BKA0V/fh/FAQBK1asoE6dOmX+XDti2bJlWJYVAju3yltEZBepUBCRbLQE0qtQ6NixIwCDBw/e5VxLlixhzpw5PPnkkxQUFJRGvIw6/qaKi4t57rnnCIKAoqKiMn2uHbVixQocx1kJpEXPDxHJPuk1IVNEpHxUBVYMGDDg1y/o6eCpp55i2LBhzJkzh3bt2jFgwADTkTLabbfdxltvvcUee+zBsccey5VXXlkufSO214ABAxg8ePAP69ev38d0FhHJTioURCQrOY6z5o477qi0vXPmRcrbXXfdxbBhwz70ff8w01lEJDulz6kTEZFy5Lru3Hnz5pmOIbJFs2fPDnzf/850DhHJXioURCQrBUEwszz25xfZWbNnzw6Bn0znEJHspUJBRLJSGIYzZ8+eXbLte4qUvyiKWLRokQf8aDqLiGQvFQoikq2+/+mnn7ROS9LSvHnzCMPQBr43nUVEspcKBRHJVl+uXLnSW7x4sekcIn8yY8YMSLZF/dpwFBHJYioURCRbfQHw3XdaKyrp57vvviOVSs0BVpnOIiLZS4WCiGSrxZ7nLdlw5lYkrUyfPj0Ow3Cy6Rwikt1UKIhI1orj+PNvv/1WXW8l7Xz99dclYRh+YTqHiGQ3FQoikrWCIBj36aef+qZziGxqyZIlzJs3LweYYDqLiGQ3FQoiks0mLFiwILVw4ULTOUR+NWXKFCzLioD/ms4iItlNhYKIZLOJlmWFn3/+uekcIr+aMmUKnudNA1aYziIi2U2Fgohks2LP87797LPPTOcQ+dUnn3xSUlJS8oHpHCIiKhREJKuVlJS89eGHH6pDs6SFZcuWMX36dA/4j+ksIiIqFEQk270zZ86c1M8//2w6hwgfffQRlmWFwGjTWUREVCiISLab4DjO6vHjx5vOIcK4ceNix3E+Ro3WRCQNqFAQkWznA++NHTs2NB1EslsYhnz44YeB7/sjTGcREQEVCiIihGE4dOLEidby5ctNR5Es9sknn7Bq1SoPeM10FhERUKEgIgIwLI7jYPRoTQsXc0aOHBl7njcVmGk6i4gIqFAQEQFYZVnWOyNHjgxMB5HsFAQB//nPfwLf918wnUVEZCMVCiIiQBiGQz755BNnyZIlpqNIFpowYQLFxcUu8IrpLCIiG6lQEBFJvGHbdvGwYcNM55AsNHTo0NDzvHHAT6aziIhspEJBRCSxLgiCZ4YMGeLHcWw6i2SRxYsXM27cOMv3/cdNZxER2ZQKBRGR3wz65ZdfvEmTJpnOIVnkjTfewLKsYuB101lERDalQkFE5Ddfep736ZAhQ9RTQcpFGIYMGTLED4LgKWCd6TwiIptSoSAisgnf9x8YPXq0/fPPP5uOIlng3XffZdGiRQ7Q33QWEZE/UqEgIvJ7rzqOM+f555/XQgUpc88++6xv2/brwPems4iI/JEKBRGR3wt933/o1VdfjVasWGE6i2SwSZMm8c0333hhGD5gOouIyOaoUBAR+bPBURStfv75503nkAw2YMCAwHXdCcB/TWcREdkcFQoiIn+2KgiC3s8880y4bNky01kkA02ePJlJkya5QRDcZjqLiMiWqFAQEdm8R8IwXPHMM8+YziEZ6JFHHglc1x0LjDGdRURkS1QoiIhs3uogCO574YUXwkWLFpnOIhlkwoQJTJ482Q2C4FbTWUREtkaFgojIlv0ziqKF/fr1i0wHkcwQhiG9e/f2Xdd9C/jIdB4Rka1RoSAismVrgyC4ftiwYdZXX31lOotkgJdffplZs2ZZQRBcbzqLiMi2qFAQEdm6lxzHmXjfffcFcazWCrLzVq5cyaOPPhpEUdQXmGE6j4jItqhQEBHZhiAIrvnqq6+cN99803QUqcD69u0br127diVwr+ksIiLbQ4WCiMi2fWpZ1mP3339/sGTJEtNZpAL67LPPGDp0qBUEwf8D1MlPRCoEx3QAEZGKII7jD+M4vmDevHlVjjnmGJ1kke1WUlLCFVdc4a9evfr9KIpuNp1HRGR7abATEdk+q4MguPydd95xPvjgA9NZpAIZMGAAc+bMCYIguMR0FhGRHWGZDiAiUpHYtv1sXl7emW+++aZXq1Yt03EkzX322WdceOGFcRzHVwADTecREdkRKhRERHZMnud5Xx544IH1Bg4c6FqWPkZl81atWsVJJ53kL1my5IMwDLsC2jZLRCoUrVEQEdkxJVEUfTJ37tyLq1WrZrVs2dJ0HklTf/vb36JvvvlmeRiGRwBrTOcREdlRKhRERHbcHCCeOHHiYR06dLBq165tOo+kmSFDhvDss88SRVEPQN36RKRC0jVzEZGdY7uu+3Z+fv6Rr776qrvbbruZziNpYurUqZx33nlRGIZ3Av8wnUdEZGdp1yMRkZ0TBUFwZnFx8bzrrrsuKCkp4ccffzSdSQyaOXMmS5Ys4eqrr/aBd4H7TGcSEdkVKhRERHbeMt/3b5o6dapVVFTEggULTOcRg9577z26dOkSL1++fHUYhjcBkelMIiK7QoWCiMiOqwfcBEwHhsRx7Kxbty6eNm2a4VhiShRFfPPNN+H69evjKIqqA18AE4CLgWpm04mI7BwVCiIi2ycfOB8YA8wG7gEab/jdauDuPn368Pbbb5tJJ0b16dOHsWPHxsCNJNugWsDBwBPAImAo0B3wjIUUEdlB2vVIRGTLbKAIuA14HjgZ2GvD7Rs/PyOSL4f/Z9t2wQcffHBAmzZt7Hr16pnIKwY8++yzDBgwII7j+DySwqAJ0BRwSQoGh6SoPAe4DtgbWA78bCSwiMh20q5HIiJbdgdwFxCy+RMrAfAt0GbDfWzHcV50HOfUQYMGOW3bti2/pGLEG2+8we233w5JsfjghpvrAN8BeVt42Mb303GALkGJSNrSFQURkS2bAHQkuYqwuc9LCziR384Mx3EcvwG0Gjly5L4dOnSwd9999/JJKuVu1KhR3HLLLTFJQdlrk18VAyuBrmz+hFxMUlQMKPOQIiK7QFcURES2rgYwGSjk9/PLfeAp4C+beUyO67ojc3NzOz355JNu8+bNyyGmlKcRI0bwt7/9LYqi6EGShe1/ZAOTgJYkU5A28oGxJEVEWOZBRUR2gRYzi4hsXWVgFclZ4HjDbTGwhmTtwuasD4Lg2LVr175z/vnnh//973/LIaaUl1deeYVbb71141WBzRUJkKxduYzfj7MBsA5YAaTKNKSISClQoSAismVtgY+BXOB//vC7a4HFW3ns+jAMewZBMPzKK68MP/roo7LKKOXoqaee4u677yaO49ujKNpSkbDRZySLm32SwmEtcAVwKPARUL9Mw4qI7CKtURAR2bwzgWEk00e6AuOBEuBIkuLh2u04RhjH8atxHDd6++23W9StW9dq2rRpmQWWshNFEb169YoHDRoESdH44DYestFHJNPTcknWs7wBvAacDVwPfALMKvXAIiKlQIWCiMjvOcD9QF+Sxabnk5wJhmRxc0Pgb8D2tmGO4jh+PY5ja/To0YevXLmSoqIiLEtLxCqKtWvXcsMNN0RvvfVWGMfxucDgHXj4OuAXYBzw4obblgHPAYu7SWcAACAASURBVAeS7Ko1D5hSipFFREqFCgURkd9UBV4GziLpqNub39YlbPQG218kbGoMMO+rr746bvbs2XGnTp0s13W39RgxbMGCBVx22WXBlClTisMwPBoYuROHmQpM/MNtJSTvNR/oB+wBvEsyRUlEJC3olJaISGJfkqlG1YAeJFNCykIXx3Fe2WeffXL79evnFRYWltHTyK6aNGkS1113XbBmzZqffN/vRtIboSycBjwNfAqcQtLJWUTEOC1mFhFJ1iB8QtIt90DKrkgAeDcMwxY//vjj1z179vTHjx9fhk8lO2vo0KFceumlUXFx8bu+7x9I2RUJkFxZ6ECyuPljQPvpikha0NQjEcl21wLPkkwpOoVk/nhZWxFF0bNRFO01fPjw1itXrqR9+/Y4jj6STVu2bBk33nhj+NxzzxFF0T1xHF9Oss6grC0AXgC6kDRw+xaYVg7PKyKyRRqVRCRb5ZAsSr2RZHHy9ST73JeXII7jYcCcb7755ujRo0fTrl07p0aNGuUYQTb10UcfcckllwQzZ85cGEVRd5IFx+VpDTAE2Juk07NF0pxNRMQIFQoiko02LhztAJxE+X8h3NSUOI5fXrly5eGvvPLKbvn5+Xbz5s21K1I5WrNmDQ888EB8//33W77vDw3D8FhghqE4IfAmMJ9k960WwNski55FRMqVRiIRyTYHk+xjv4pkX/t0md7hAbdblnVr8+bNo3vuucdr1KiR6UwZb9y4cfz9738Pli5dujYIgitJpv+ki0OBocBckoJW/RZEpFypUBCRbHIW8CTJVqVnkSxeTjf7u677TBzHrS+55BL7kksuITc313SmjLNw4UL69OkTvf3227bjOC+HYXg1sNB0rs3Yh2T9TB2SNTSaiiQi5UaFgohkAwe4F7iJZM/660jv/eod4GrHce6tUaOGd+ONN3rHHnuspiOVgvXr1/Pcc88xcODAMAzDBUEQXA6MMJ1rG/JIpscdB1zJjjV8ExHZaVqjICKZrirwCltvopZuYmBiHMdPrVu3ruC9995rPX78+GCfffZx6tSpYzpbhRRFEe+88w5XXXWVP3bs2MD3/bujKDoT+MZ0tu2wsTlbCfAIas4mIuVEp6dEJJPtS7IwNJ+kidoks3F2WlvXdfsFQVBUVFQUXnXVVU6LFi1MZ6oQ4jhm9OjR9OvXz//xxx9dy7JejKLoZpJ5/xXRqcAzqDmbiJQDFQoikqm6kmw1+S1wMvCL2Til4mjP8+7zff/Aww47LLz00kudVq1amc6UlqIo4v3332fgwIHB9OnTHcdx3gjD8Hbga9PZSkErknULIcmC/Ex4TSKShlQoiEgmuhboA7wEXAqsNRun1B3ned7dvu+33X///f2LL77Y69y5M7Zts2TJEmrVqmU6X7nb+LrXrVvHG2+8wdNPP+3Pnz/ftW17eBiGdwKfm85YygpIptQdCJxLUjiIiJQqFQoikklygIHAOSRN1HqbjVPmOjmO89coio6rW7dusN9++3mtWrXiggsuMJ2r3N18880EQcCECRP8NWvWxMAzURT1wVw/hPKQAh4jWXvzf8AtpP/6GxGpQFQoiEim2AN4HWgEnAH8x2ycctUYeBA43rKs+PDDD4969uzpdOjQAc/zTGcrM6tWreL9999n6NChwRdffOGSLO59hKRRWTbN3b8M6E/y/r+QpMOziMguU6EgIpkgXZuolZeDgA+BXOBBz/MO9n2/qHLlyuHRRx/tdO3a1Tr44INxXddwzF1XXFzMmDFjGDlyZPjRRx9ZURSFlmUNC8NwPXA2MIfk75EJa1J2RCeS5mzzUHM2ESklKhREpKLbtInamcAKo2nKXyPgE5JtYB3gcJKmXPWAnqlU6uySkpIDc3Jyonbt2llHHHGEXVRURN26dc0l3kFz5sxh4sSJvP/++/7EiROdMAyxbfuTMAxfAl4EFgM3AveRTL35FigCis2lNqIhMAw1ZxORUqJCQUQqqorWRK0sFJAUCfWAjXOM2gJT/nC/vYHjXdftHsfxYWEY5uy1114l7dq1S7Vu3Zo2bdqw1157lV/qrYiiiBkzZjBlyhQmT54cf/LJJ/7SpUtTruuuiKLo7SiKRgJvAUv/8NArSKYdeYAPfEDSoCwo1xdgnpqziUipUaEgIhVRVZIzyUcBl5N8Mco2lUjOGLfmtyIBkvUK323lcbnAoUBnz/MOD8OwbRRFqfz8fL9p06ZW06ZN3X333Zd9992XwsJCatSoUSbh4zhm0aJFzJo1i5kzZzJjxgy+/fbbkpkzZzrr1693HMcptixrQhAEHwLvkfQN2FoheA7wLGBv+PeQ5H1xUZm8gPRmAX8lucLyJHAVSfEkIrJDVCiISEWTKU3UdoVDsiajG/DHhQd12bH5+SmSLTYPAvZPpVIHBUHQJIqiHICcnJxwjz32CPbcc0+voKDArlGjBjVq1KB69epUqlSJ3NxcUqkUAFWqVGH16tUArF27Ft/3WbVqFcuWLWP58uUsX76chQsXBrNnzw4XLFjgBUFgA7iuu8qyrC99358MTAU+JumYvCNXiE7kz1uERsDdwF07cJxMouZsIrJLVCiISEWSiU3UdkZ/4C8kBcMf5QGrd/H4Dsl0pQYbfvYG6ruuu4fjOLXjOK4ZhmH1MAxzt3kgx1njuu7SOI4XR1G0MAiCecCPwE8b/vcHSqdL8hHA+5u5PQYuAZ4qheeoiNScTURERDLetSTzzV8gmXaTrW4hOVMeb+YnovxPAFUCagC1SAqKGht+yntf1oPY/N8kJnnfdC3nPOmkgGTNxiqSHZFEREREMkIuydzzgGThcjZrSrKrU8jmi4VdvZJQkTVl80WCv+F/vwGqGEtnngs8SvK+6YVmFIiIiEgFtwfwX2AJcLThLOkiD7iUZC5/DKznty/F2TwHvZDfFwglJF+K3yOZcrO5aVrZ6DKSv82/gcqGs4iIiIjslENImkdNJzlbLL/XhKRIGAasI/ly/KPRRGZV5bciYSnwNknhlDIZKk11AhYAnwP1DWcRERER2SFnAWtIvuxVM5wlXT1E0n3XAaoD15Cd28RuZJPMwz+DpDioS3Lm/AyTodJYQ+BLkmLqcLNRRERERLbNIZk/HZM0z7K3fvesVYlkOtYtpoOkuddJOnbL5uWRbLO7HrjYcBYRERGRLaoBjALWAucZzpLuzif5clfbdJA014Wk6GxuOkgas0g2CQiBgZT/blUiIiIiW9WYpDfCHJJtLmXrPibpJyFbZwEzgIdNB6kATgWKSbp972Y4i4iIiAgAxwLLgI+AOoazVAQtSc6SH244R0VxE8n7Szv8bFsrkgXxM4EWhrOIiIhIlruWZMpDtjdR2xGPk1x90T7426eAZDrbhaaDVBCbNmfrYTiLiIiIZCE1Uds5eSQN1641HaSCeZGkH4dsHzVnExERESMKgU9Idu05ynCWiuYKkm1ja5oOUsEcSjJd6wDTQSqYjc3ZXkZTt0RERKSMHQLMR03UdtZk4CnTISqoL4EnTIeogDZtzra32SgiIiKSqc5GTdR2RQeSs+LtTAepoK4GVpM0p5Mdo+ZsIiIiUiY2NlHbON9ZTdR2zrMkZ3Vl51Qj2f7z/5kOUkFt2pztEsNZREREJAPU5LcmaucazlKR1SA5G36Z6SAV3JPA12hx7s5SczYREREpFWqiVnr+F1gJ5JsOUsG1Jpm+1dF0kApuY3O2D1FzNhEREdlBG5uoTUBN1HaVRbL4u7/pIBliEvC86RAZoCVqziYiIiI7aNMmarmGs2SCI0nOgrc2HSRDXAysA3Y3HSQDFACjUXM2ERER2QY1USsbrwDjTYfIIJWApcCNpoNkCBfoh5qziYiIyBaoiVrZqEPS8Ooc00EyTD+SKTPagav0qDmbiIiI/MmmTdSaGM6SaW4DFqMpXKWtGckZ8KNNB8kwas4mIiIiv1ITtbJjkywWfcB0kAw1FnjVdIgMtCfwGWrOJiIikrXURK3sHU/y921sOkiGOgvwSabNSena2JzNB64ynEVERETKkZqolY8RJH9nKRspkmkyd5gOkqHUnE1ERCTLqIla+diLZPeonqaDZLhewM8kO/dI2di0OZu2pBUREclQxwLLURO18nAvMA+dhS1rDUnOeJ9oOkiG29ic7XvUnE1ERCTjqIla+fGAucBdpoNkiXeAkaZDZAE1ZxMREckwaqJW/k4j+XvXNx0kS5xEsmi8kekgWeCPzdm0CYKIiEgFpSZqZowGhpkOkUUcYBZwv+kgWWTT5mxVDGcRERGRHaQmamY0ITnbeqzpIFnmTpJ9/3NMB8kias4mIiJSAZ1NsvXpW6iJWnnrS3J22zEdJMvUJTnDfabpIFlGzdlEREQqCDVRM6sSyTSvm00HyVKvAWNMh8hCeSQdstWcTUREJE3VBP6DmqiZdAGwHqhtOEe2OgaI0fadJqg5m4iISJpSE7X08DEwxHSILGYBM4BHTAfJYqeg5mwiIiJpQ03U0kMrkrPZh5kOkuX+SvL/B+3EY46as4mIiBi26aX+QUDKbJys9zjJVR3LdJAsV0Ay/e4i00GyXC3UnE1ERMSIXOA51EQtXeQBK0i6X4t5L5D0DxGz1JxNRESknKmJWvq5AlhDsqBczOtEMg3sANNBBFBzNhERkXLRgaSJ2jTURC2dTAYGmw4hvzOVZEqepIeOJM3ZvkDN2UREREqdmqilpw4kZ6/bmQ4iv3MVsBqoYTqI/GrT5mydDWcRERHJCGqilt6eAz43HUL+JB9YiRqApRs1ZxMRESklmzZRO8dwFvmzGiRnrS81HUQ2axDwDdqJKt2oOZuIiMgu2rSJ2oGGs8jm/S/JWet800Fks1qTTAvrZDqIbJaas4mIiOwENVFLfxYwHehvOohs1Sck26VKemoJ/ICas4mIiGyTmqhVHEeRnK3e33QQ2aqLgPXojHU6U3M2kTKkuZdS1nJI9u7fjeQDvRZQieRL7KZ7Yq8gWXC7imSP/0XAYmAeyRdf2bpc4AngTOA2oLfZOGmpBlCX396HtUgWe1fht6IqIHkPxiTvwyUk78OFJO/J0vIKydUeTWtJb5WAuSQbAfxfKR3TJnkfFmzys3Ensk13WVoLrCMpVJZs8vPzht/Jb1ygD3A1yX+nW0nGE9k6jc+yTSoUpLTUJrkM3ApokUql9ovjuIHv+7XY5H3meV7keV7oum5cuXLleOPtxcXFdhRFrFu3zo2i6Nf7W5YVep73SxzH3/u+/w3JPtpfbvhZWV4vLs0VAq8D+wCnAe+bjWOUDexL8l5s6ThOC9d1mwRBsFcYhr9r1pSbmxvYth1XqlQp9jwvBgjDkNWrV9uAtWbNGnfT+zuOs9Z13TlBEEwPw/BrfnsvTiMpMLZXHWA2ydlqTWtJf48A3UneVzvy5bMyyXSYlkBL13WbO47TyPf9ulEU/boA17KsuFKlSgFA1apVfz3+unXrrJKSEisIArukpMTZ9MCe5y21LGtWEATToiiaSvI+nEpSRGSzy0im870BXEiyWYBofJZdoEJBdtZ+QGfbtju4rtu5pKSkLkD16tVLmjZtajds2NAtLCxkjz32oE6dOtSsWZMaNWpQqVKlbR541apVLF26lGXLljFv3jzmzp3LvHnzmDFjhv/dd99Za9eudS3Lij3Pm1FSUvIB8BHJl+N5ZfqK01MHku0CVwAnksx7zyYpoAjo5LruoXEcHxKGYWXbtuPCwsKSpk2bpvbcc0+rsLCQwsJCateuTbVq1ahevTqet/XNUsIwZPny5SxfvpzFixczZ84c5s2bx+zZs+Pp06eXzJ492wvD0LZte73jOJ/6vv8BybqQD0k6LW/JbcD/APVIzhhLemsGfA10BUZt5X4FwBFAUSqV6uz7/n5xHDs5OTlhw4YNwyZNmqQ2vg8LCwupWbMm1atXp3r16tsMsH79epYtW8ayZcv45ZdfmDt3LnPnzuWnn34Kp02bFi5evDgF4Hne4iAIPozjeBzJ+3AKydWxbNKR5DPxF5LPxJ+MpjFD47OUGhUKsr1ygWOA41Kp1AklJSV1KlWqFLRp08Zq27at06pVK5o0aUKNGmXfn2jevHlMnz6dyZMn89lnn/nffvutEwSBnUqlvi0pKXkTGA58TOZfej4beJJkfu5ZJMVCNqgDnOQ4znHAkWEYVqpdu3bJgQce6LVu3dpq2bIl++yzDzk5OWUaIggCfvjhB7766iumTJnCp59+WjJnzpyUbdu+bdvjgiAYTnKlZ9YmD7NJFl++DPy1TANKaRoDLAVO/sPtbYETPM87IQiC1pZlse+++/oHHXRQqlWrVjRv3pzCwkJsu2zbl6xatYoZM2bwxRdfMHny5HDy5MnRqlWrPNd1l0ZRNCKKoreAt0l2CcoGe5JcVdiL5CrrB2bjlDmNz1JmVCjI1rhAF9u2z7As6+Qoiio1bdo0OPzww72OHTvSokWLMh8At8f69euZNGkS48ePZ8yYMSVz585Nua67IAiCfwFDgEmmM5YyB7iX5ItmtszHrQmc5nne2UEQdEilUvEhhxxCp06dnI4dO7LHHnuYzgfAokWLmDBhAuPHj4/GjRsXrVmzxvE8b7Lv+y8CL5FsVTsMaArMMBpWdsSZJM3x9iZZR3BmKpU6p6SkZK+CgoKSzp07pzp27Ej79u2pUqXKVg9UHuI4Zvr06UyYMIGxY8f6X3zxhQv4lmWNCMNwCMmXtfWGY5a1POBZ4ATgeuBRs3FKncZnKRcqFGRzCoFzUqnUtSUlJXX33nvvsEePHk737t3Zfff03/xj5syZjBo1ihEjRpT8/PPPKc/zZvq+/yTJ2fclpvPtoprAv0kur19K5s9xP8BxnL8A59q27R588MFW165d7aOPPnq7LpObFEURn3/+Oe+++248fPjwoLi42AUWxHG8EDiAHVvXIGZVBWY7jrMoDMNGBQUFfpcuXbxjjjmGNm3aYFnpPZSuXLmSMWPGMHLkyODjjz+2gTVhGP4LeIxkbUOmskhOqNxH8vl/FUlX54pM47OUq/T+dJPydoDnedcHQXBGtWrVwpNPPtk75ZRT2HPPPU3n2mnffPMNr7zySjx8+PDQ9/0Y+HcURfeRNCOraBoDb5KcKTsJ+NRsnDKTAs7wPO9W3/ebNGnSxD/jjDO8bt26UblyZdPZdkpJSQljxozhpZdeCiZNmuS6rjs3CIJHSTrLLjedT7aoDvAX13Wvj+O4ypFHHsmpp55qt2/fPu2Lgy1ZvHgxb775Ji+99FLJ/PnzU67rTgyC4D5gBJm7nqE78CLJYttTSHYxq2g0PosRFfOTTkrb8Z7n/d33/bbNmzcvueiii1JHHnkkjuNs+5EVRHFxMcOHD+epp57yFyxY4DqO82YQBH8HPjedbTt1A/5FsqiyJ8lCvUyTB1zluu4NcRzX6Natm3XeeedZTZs2NZ2rVM2aNYsXX3yR1157LQzDcF0QBI+QbO241HQ2+dW+tm3fHsfxWdWqVYvOP/98r2fPnuUyx7u8RFHExx9/zDPPPBNOnDjR8Txvhu/7d5NMB8nEqYwtSdYtuCQnWiabjbPdND6LUSoUslsXz/Pu832/befOncOLLrrIad26telMZSqKIt577z0GDRoUTJs2zXEc540wDG8n+QKejja9dP4U8P+AEqOJSl8l4ArXdW93XTfv7LPPds8++2x2220307nK1IoVK/j3v//NM888E6xdu7YkCIIHgL5kz6L0dNTAtu074jg+t169euHll1+e6tat2zZ3yKroZsyYwdNPPx29/fbbluu635eUlNxCsnNQpl1hqEXSw+Qg4HzgNbNxtkrjc/qPz1lBhUJ2auq6br8gCI5u3759eN111znNmzc3nancTZw4kQceeMD/7rvvXMuyXoyi6AZggelcm8j0JmoWcEoqleoL1Dn11FOdSy+9lFq1apnOVa7Wrl3LkCFDeOKJJ4J169atCcPwDpK541rDUH7ygBts2761oKCAK664wuvRo0dGnbXdHnPnzmXQoEHRa6+9ZrmuO9X3/auA8aZzlbJ0b86m8ZkKMT5nDRUK2aWGbdv3x3F8aZMmTcJbbrnFa9u2relMRkVRxNtvv82DDz4YrFixYn0QBHeSNFgy/SUt05uoHeC67oAwDA/s0aNHfPXVV9sFBQWmMxm1atUqBg4cyAsvvBDZtj3T9/2/kPnbOppmARe7rts7Nzc3/5prrvFOPfVUXNfd5gMz2YwZM+jVq1c4adIk23Gcl8MwvJ7M2wd/Y3O2YcAFmG/OpvH5D9J4fM4qKhSyxymu6z6el5dX9YYbbvCOP/74tNg6LV2sXbuWwYMHM3jw4NCyrGm+75+HuTmsmdxErTJwl2VZ17dq1Sq69dZb3WbNmpnOlFZmzZpF7969w3Hjxtm2bT8TRdH/AstM58pAjV3XfSqKokPOOOMM68orr7SqVatmOlNaef/99+nVq5e/aNGikg3FwiAyazpSujRn0/i8FWk2PmcdFQqZb3fHcQaFYXh8jx494htuuMGuWrWq6Uxpa9asWdx+++3B559/bluW9WAURbdTvmsCziEZjDOxiVonz/Ne8DxvjxtvvNHt2bNnhd05pjyMGjWKe+65JyguLl4RBMFFJDteya6zgf+1bfsfDRs2tO69915vv/32M50pba1bt47HHnuM5557LnYc52Pf988ms7od70ly9XZv4FTK9yqexucdkAbjc1bSKJ3ZjnUc5/mCgoL8e++9N9W+fXvTeSqEOI4ZOnQovXv3DqMo+tb3/VOBaWX8tJncRM0D/m5Z1s2dOnWK77zzTqci7PedDlauXEmvXr3i4cOHW7ZtPxFF0XXAGtO5KrA9Xdd9MY7joquuusq+8MILs24dws765ptvuPXWW4NZs2atD4LgcpLtRjNFHvAMyVWF8mrOpvF5Jxgan7OaPiEzk2fbdt84jh/p1q1b7j//+U+3YcOGpjNVGJZl0bx5c7p27Wp/9tlnNZcuXXp5HMfzgSll9JQ1SebJngZcBDxE5lzer+953nuu6/b829/+5tx44412OnSurShycnI48sgjrUaNGjF+/PhWwFlRFH1AxdwH3rSTHMd5r7CwcO8nnnjC7dKli6Z37IDddtuNHj162CtXrvS+/PLLno7jNInj+B0qfgMzSM5Kv0LSrfoBkjVi71I2J2s0Pu8CA+Nz1lOhkHnquq470nXdk+69917nyiuvtFKplOlMFVK1atXo0aOH7fu+O3ny5BMcx9krjuNRlO5CqibAe8AeQBfgnVI8tmnHOI4zeq+99trjqaee8oqKikznqbD22Wcfjj/+ePuLL76otmjRoovjOP4B+Mp0rgpi49W6R3v06OE9+uijbt26dU1nqpBc16VTp05Wy5YtGTNmTLM4jk+NouhdMqcHyASSue93Al2BtyjdRc4an0tJOY3PgqYeZZqDXdcdXqdOnWqPPvqo16hRI9N5MsYHH3zATTfdFARB8JXv+8dROjuAbGyi9hVJE7VM2vrtJsuy7uvatSt33XWXXalSJdN5MkIQBDz44IO8+OKL2Lb98IYtA0PTudJYddd1hwKH33777c7JJ59sOk/GmD9/Ptdee20wY8aM9WEYnga8bTpTKSqL5mwan8tIGY3PsoGuKGSOnrZtj+jQoUPlQYMGuXXq1DGdJ6M0aNCAY445xv7www8L1q5de24YhqPY+ekfFnATMBh4ATgdWFlKUU1zbdseCNx4ww032DfccIOV6c2qypNt23Ts2JH69eszZsyYgyzLOjCO42FkxvSP0ra353ljq1at2nrw4MHuYYcdZjpPRsnPz+eEE06w58+f782YMeNMYBHwqelcpWQByWfzkSQ9bKYD3+7C8TQ+l6FSHp/lD1QoZIbrLct68vTTT3fuv/9+Oycnx3SejFS9enW6d+9uf/bZZ5UWLlx4YRzHnwA/7OBhcoGngWuAvwE3kzlnhPNc1x3uOE6Pvn372ieddJLpPBmrcePGtGvXzh41alTDOI6Pj6LodczvA59ODnBd98P69evXee6557wGDRqYzpORXNflyCOPtGzbtj755JPjbNvOj+P4P6ZzlZK1JFd8dydp0FaJZDe6HV0/pvG5HJTS+CyboUKh4rsLuO/GG2+0rr76akvbTZat3NxcjjvuOHvWrFnODz/8cFYcx1+y/TsuFAKjgHYku2s8X1Y5Dajued57VapUOfipp55y27VrZzpPxqtbty5HH320PXr06Frr1q07JYqi18icK1O7oshxnPcPOuig/EGDBrk1atQwnSfjHXjggey555588MEHB1uWVT+O4xFkxoYMEcm6sfnA3SRTkt5m+6/gaXwuR7s4PssWqFCouCzgQcuybr777rutM844w3SerOE4DkcddZS1fPly+6uvvjoNmAV8sY2HdSDprrye5HJ2JjWLqeF53ui8vLyWTz/9tNe0aVPTebJG9erVOfbYY52xY8dWXbVq1VlRFL1J5iws3RmHOY7zbseOHXMeeeQRR2tjyk+TJk1o3ry59e6777a0LKtFHMdvkDlbPH8GjAFuBM4gKR6Wb+X+Gp8N2cnxWbZChUIFZdv2Q7Zt/0+vXr3s448/3nScrGNZFh07drRWr15tTZ069QRgBlveheYS4GVgPNCdpAtopqjped74WrVqNXvhhRe8vffe23SerFO5cmW6dOlijxs3LnfFihWnR1E0lMxq1Le9Otu2/W7Xrl1TDz74oKO1MeWvfv36tG7d2h45cmQToHkcx6+RGVcWAGYDL5FsY/1XYBJbaDyn8dmsHRyfZRtUKFRM9wB/vf/+++1u3bqZzpK1LMuiqKiINWvWWF988cXJwDcbfjZygPuBXiRzXC8B1pV/0jJT1fO896tVq9bs+eef9woLC03nyVqVKlWiW7duzocffpi7atWqU8MwfBlYZTpXOTrYcZxRRxxxRKp37962mqiZU69ePdq1a2ePGDGiSRzHDeM4fpPMKRZW/v3RLwAAIABJREFUkjSaa0Oy5e5y4JM/3EfjcxrYjvFZtpM+TSueG4B/3HPPPZbOVKSHQw45hEWLFjFt2rQecRyPJznLlMlN1AByXdcdlZ+f3+b555/36tWrZzpP1svJyeGoo45yRo0aVXnt2rUnRlH0IplVmG5JK8dxxh566KE5ffr0cVzXNZ0n69WtW5f99tvPHjly5P6WZdXc0JgtU/hsuTmbxuc0s4XxWXaACoWK5TRg4E033WSddtppprPIBpZlceihh1o//vij9eOPP54Sx/FU4HWgADiaZAFzJrEcx/lXTk7OUdpRJr1UqlSJo446yhk+fHhV3/c7bSgWMmVXrc2p57ruuDZt2uQ/+uijrqYbpY/69evToEEDa9SoUe1IpsJNNJ2plE0AvgZuJ1l3ZgH9NT6nl82Mz8NItvKV7aRCoeJo5zjOm2eddZZz5ZVXauuENGNZFp07d7YmTZpkLVq06Kgo+v/snXmczdX/x1+f7Y4xgzG2GETZi2EQMhNStpQvoZRUKkm7+rX4aqeoJCXlW5ZSCiX7li0zopStsu9rRAazmPv5fM75/fGeyWBmzHI/n/O5d87z8fDAuPdz3mPe97zO+5z3+33Yr6CLenaLts0BRqiq+uBHH32kNWrUSLQtkouIjIxEfHy8NmvWrBjOeX3O+XeibXKIUoZhrIyJian62WefGSVLlhRtj+QiatWqhbCwMOXnn3/uCOB3FO0uAi+yFXR7c4KmaU9KffYmF+lzD8bYVAApou0KFmSgEBxU03U9KSEhoeSwYcNU2WLNm2iahrZt22qLFy8ukZaWlsYY+xiht5vbF8C7b7zxhnrTTTeJtkWSC9HR0WjQoIE6f/78+pzzdNDuZyihaJr2bURERIsvvvjCKF++vGh7JLnQpEkTHD9+HNu3b++WuZsbahdh+XRdHy712dtk0+fwtLS0toyxLxB6+uwIMlDwPoau6wsrV65cY/z48bq8rMXblChRAvHx8drMmTMrMcYqcM4XiLYpgDRSVXXuPffco/Xv31+qocepXr06SpYsqaxZs+YmUNpHKJ1u/VdV1QEff/yxXrduXdG2SC5DQkKCsnbtWpw8efJWxthkhE7tjNTnICLE9dkxZKDgcVRVHWcYxi2ff/65UbFiRdHmSPJBVFQUrrzySnXx4sXNQYuzzaJtCgBRhmGsio2NLTNixAhNVVXR9kjyQWxsLPbs2cP3799/a2a9QihcyHazoigTnnvuObVjx46ibZHkA1VVER8fr86aNSvCNM1GnPNvRNsUCKQ+Bx8hqs+OIgMFb9Odc/7O22+/rTZt2lS0LZICcPXVV+Ps2bP4888/O2eK4inRNhUFVVUnlypV6rpJkyYZERERos2R5JOsfuKLFi3S0tLSWjDGPkdwd9+qoOv68g4dOoQ/88wz8lQriIiIiEBsbKw2a9asWpzzk7i0rWiwIfU5SAk1fXYaGSh4lyqapv3Qo0cP3wMPPCAFMQi57rrrsGzZMuXs2bPtGGMTELy3lPblnL80atQorX79+qJtkRQQwzAQFxenffvtt9U45+cQxPUKmqZNi4qKuuaTTz6RaR5BSOXKlcEYU9avX39zZr3CMdE2FRKpz0FOCOmz48hAwaPouv595cqVa33wwQey5V+QomkamjVrps6YMaMCY4wD+FG0TYWgmqZpi/r06WP07dtXCmKQUqFChazuM20553MRnLeDPwjgmXHjxmmyJW/w0rRpUyQlJfFTp061ZYx9iiBcoEl9Dn5CRJ9dQQYK3uRezvnT48aN06pVqybaFkkRiI6ORnh4uLp27dp4zvlMBFn/Zk3TvqlcuXLtMWPGyIusgpzY2FisXr2a/fPPP/GZC7RgSkGqomnavHvuuSesZ8+eom2RFAFVVdG8eXP1m2++KccY8wNIFG1TAZH6HCIEuz67haxI9B7ldV1//6677kJsbKxoWyQBoG/fvmjQoAEMw/gCwRWc92GMdRo+fLgh0zyCH1VVMXz4cJ1zfg2Ap0TbUxA0TRtXvnz5sEcffVS0KZIAUL16dTz66KOaqqqvAgimfEapzyFGEOuza8hAwWNomvZ+dHR0xBNPPCHTPEIEVVXx2muv6YyxxqD0iWCgtK7rY3v27Im4uDjRtkgCRI0aNfDwww9rqqoOBxAs26G32rbdbfjw4UZ4eLhoWyQB4r777kOtWrWg6/onom3JL1KfQ48g1WdXkYGCt2hh2/ZdQ4YMkbeMhhh16tTBXXfdpeq6/jaAaNH25IOXwsLCSktBDD0eeOABVK5cWdU07R3RtuQDn2EYYzp37sxatGgh2hZJANE0DS+//LJhWdYNALqLticfSH0OUYJQn11FBgreQdF1fUxcXJzVvn170bZIHGDQoEGIiIgIBzBUtC2X4WpVVZ986qmn9KioKNG2SAKMYRh47rnnDNu2ewNIEG3PZXgCQPWnnnpKalUIEhsbiy5dujDDMMYAKCHanjyQ+hziBJE+u46cfL1DT9u2r3vxxRdlC4UQJTIyEk888YShqurjADzbtkXTtLerV6+OXr16iTZF4hA33ngjmjdvbhuGMUq0LXlQVtO0V/r3769VqVJFtC0Shxg8eLCqKEoVAI+ItiUPpD6HOMGizyKQgYI30AzDeLNTp068Xr16om2ROEjPnj1RpUoVrqrqK6JtyYWGjLHuTz/9tKFpsq4rlHn22Wd10zSbA+gs2pZceCY8PDzsvvvuE22HxEEqVaqEu+++W9N1/WUApUTbkwNSn4sJQaDPQpCBgjfoY9v21Y888oj8eYQ4qqrikUceMTjn9wCoK9qei9E07a3atWtb7dq1E22KxGEaNGiAhIQE2zCMEQC8VotSTtO0wQ899JARGRkp2haJw9x///3QdT0SwCDRtuSA1Odigtf1WRTS8cWjGobx6i233AJ5iVDxoGvXrqhataqtquoQ0bZcRKxt212efPJJQ1G8tm6UOMHjjz+umabZCN47VXg6IiJC79Onj2g7JC5QtmxZ3HPPPbqu6y8A8FKlsNTnYoaH9VkYMlAQT1fTNK+W18AXH1RVxYMPPmhwzu8GUFW0PVmoqvpczZo1rYQEr9e3SgJF/fr10apVK0vX9edF25KNkrquP96vXz/ZDrUY0bdvXyiKUgrAvaJtyYbU52KGV/VZJDJQEIyu68/Fx8dbV199tWhTJC7StWtXREVFMXjnqL0KgN4PPPCAPE0oZvTv31/PbFF5nWhbMumvqmpE7969RdshcZHo6Gh069ZNNQzjRXjk4iupz8UTD+qzUGSgIJZYy7Ja33fffbpoQyTu4vP50LdvX0PX9UcBeGHbdFDp0qV5585ey0CROE3Lli1Ru3ZtU1XVx0TbAkAxDGNwt27d1LJly4q2ReIy9913n2JZVlUAXUTbAqnPxRYP6rNQZKAglgHVqlXzX3edVzbyJG5y++23g3MeCaCHYFN0XdcH3HHHHYbP5xNsikQEffr0MQDcAUD06rytaZo1e/fuLY+1iiFXXnklmjVrZmua9rBoWyD1uVjjIX0WjgwUxBGu63q/O+64wydTPYon5cqVQ9u2bblhGKL7h3e1LKtCt27dBJshEcUtt9wCn8+nArhLpB2qqj58zTXXmLINZfGld+/eOmOsE4AYgWZIfS7meEifhSMDBXH04pyXvO2220TbIRFIz549NdM0rwdQS5QNuq4PaNWqlVWtWjVRJkgEU7JkSXTq1EkzDGOgQDPKAujRu3dvealVMebGG29EZGQkA9BPoBlSnyWe0GcvIAMFQei63jchIYHLPNzizfXXX48yZcpYoLQPEZRljN3crVs3mYdbzLn11lsV0zSvBVBfkAndNU1TO3ToIGh4iRfw+Xzo3Lmz4fP5hAUKUp8lgCf02RPIQEEMZRlj7Tp37uyJzg4Scaiqik6dOhk+n+8eQSb00DRNadOmjaDhJV6hWbNmKFu2rB9ATxHj67p+V0JCAuQFa5LOnTvD7/fXA9BAwPBSnyUAPKHPnkAGCmLoLhdnkiwyRbEuBOzk6rp+Z3x8vFycSbJE0efz+foKGD7atu22HTt2lIszCeLi4lC2bFkTYoJWqc+SfxGpz15BBgoC0DStW8uWLRERESHaFIkHaNKkCUqVKmUCuMXloSMYY21uuukmuTiTAADat28Pv99fB0ANl4fupKqqcsMNN7g8rMSLqKqKm2++2fD5fN3dHlvqsyQ7AvXZM8hAwX0MAO1vuOEGuTiTACBRTEhI0A3DuNXloW9kjBmtWrVyeViJV4mLi0OJEiUsAJ3cHFdV1c6xsbG2PNmSZBEfHw/TNGMBVHRxWKnPkgsQqM+eQQYK7tPatu2I1q1bi7ZD4iESEhIU27avB1DKxWE71alTx1+hQgUXh5R4GcMw0KJFC0XTNDd3z1RVVbu0adNGdjuS/EvLli2haRoHcLOLw0p9llyCIH32DDJQcJ8bK1eu7JetKCXZuf7668EY0wG4plA+n69jQkKCvGFNcgGtW7fWALSDe/pwjWVZ0fJkS5Kd8PBwNGrUyAZwo4vDSn2WXIIIffYSMlBwGV3X21x33XVy50xyAdHR0YiJifHDvYmonN/vvyouLs6l4STBQlxcHGzbjgBwrUtDti5RooRVt25dl4aTBAvNmzc3fD6fa4GC1GdJTgjQZ08hAwV30TnnzRs3biyvepRcQvPmzX2GYbR1abjrFUVRYmNjXRpOEizUrl0b4eHhFlwSRVVV42NjY6GqUo4kF9K4cWP4/f4r4U6dgtRnSa64rM+eQs7M7nKtbdvhjRs3Fm2HxIM0btwYjLFmANwopGtRtWrVjDJlyrgwlCSYUFUVmQv3690YT9f1hCZNmsgL/ySXEBsbC0VRFAAtXBhO6rMkV1zWZ08hAwV3iTUMg9WsWVO0HRIPUq9ePdi2XQLA1U6PpWla04YNG8r6BEmONGjQQDcMo5kLQ0WYplmtfv1i26JckgelSpVCxYoV/QDcOPqU+izJFTf12WvIQMFdGtaoUcPStGIXkEryQa1ataCqKgfQyOmxNE1rXKdOHXnELsmR2rVrwzTNWgCcDiYbcs6VOnXqODyMJFhp0KCBrqqq43MipD5L8sBNffYaMlBwEV3Xm9SvX1/u4kpyJCwsDJUrV/bD+SLSKL/fX6lWrVoODyMJVmrXrp3V5cPpFXzDsLAwu0qVKg4PIwlW6tSpoxqG0dTpcaQ+S/LCRX32HDJQcBFVVevJY01JXlx99dWGqqpOt3+pBUCRvijJjRo1aoBSw1Hb4aFqV69e3ZaFzJLcqFGjBkzTrA6Hc8OlPksuh0v67Dnk7OweummalWJiYoQZwBjD+++/j1tuuQVNmzbFI488kutrExMT0bVrVwSyK86ZM2cwffp0PPDAA2jdujWaNWuGW265Bc8//zy2b99e5OdzzrFhwwYMHz4cXbt2RVxcHG644Qb069cP8+bNA+f8kvcMHToUcXFx6NixI0aMGIGMjIwi21EUqlWrpuq67vTirKaiKLxy5coOD5Mzoe6HOfH444+jYcOGGD9+fI7/7jU/DAsLQ5kyZfwAajg5jqIoV1155ZXCCplF+2Jh5qyiEmy+GBMTk3W65eSE5Xl99qJ+FpVg80WX9NlzyEDBPapxzjWRE9HMmTMxYcIE3HbbbVi5ciU+/vjjS15z8OBBPP7443j//fdx8uTJgI4/atQovPnmm2jXrh1mz56NpKQkvPHGG9i+fTt69+6N5cuXF+n5+/btQ79+/bBv3z689957WLNmDaZOnYrKlSvjxRdfxKhRoy55z7Bhw5CYmIgHH3wQX331Fb744osi2VBUYmJiwDl3elurZnR0tGkYYtqFh7ofXsycOXOwcuXKPF/jNT8EgKpVqwKAo75oGEbtmJgYYTok2hcLM2cVhWD0xWya6aQvel6fvaifRSFYfdEFffYcMlBwj2oAIGoXFwDWrVsHAOjbty9Klcr5JvKxY8eicePGmD59OkqWLBlwG7p3746+ffuifPnyKFGiBOLi4jBy5EgwxvDee+8V+fmapmHUqFGoU6cOwsLCULVqVQwbNgxRUVH4+uuv4ff7L3lPREQEevXqhRIlSuDXX38tsg1FoUqVKjBNsyyAMAeHqSpSEIuDH2Zx/PhxjBw5ErfeeutlX+slPwSAatWq+TRNq+HkGJzzqsV9TizMnFUYgtUXK1SoAE3TGIArHRwmKPTZi/pZGILVF13SZ88he1e7RwVFUVC2bFlhBiQnJ0NVVUREROT6mtdffx1hYc58Bl577bUcv163bl2EhYXh4MGD4Jxn5UYXmJo1a2Ljxo2XfN0wDFxxxRXYtm0b/H4/fL6c69VKly6N5OTkQo0dKDL9QwFQDsARh4apWLFiRWGf/VD3w+y8+uqr6NChA5o2bYq5c+fm6z1e8EMAKFeuHDRNq2zbtlNDKJZllYmOjnbq+ZdFtC8Wdc4qCMHqi4qioHTp0tapU6fKOziM5/XZ6/pZEILVF13SZ88hTxTco1x4eLip6+Jis/wIvlOCmBfp6enIyMhArVq1ArI4u5izZ89i//79qF+/PiIjI/N8rYOLonyRTajKOTWGYRhXREVFCfvsFxc//P7777F79248++yzBX6vaD8EgKioKCiK4uTiLIpzrolcnHnVFwsyZ+WHEPBFDgfnRASJPueEl/QzPwSzL7qhz15Enii4R7kyZcow0UZ4kSVLlgAABgwYENDnpqSkYOfOnXj//fdRvnx5vPnmmwF9vhNERUVl/dGxBZqqquXljcyXEkg/PHbsGN555x2MHj06z91qLxMVFQXbtp1cxZcDAOmL53FizgoFXyxbtqy6d+9eRwOFYNXnYNLPYPdFN/TZi8gTBfeIEP3BME0zIMeGgeTkyZMYPXo0br/9dnTs2DFgzx0/fjxatWqFfv36QdM0jBkzBpe7N8Dn88GyrIDZUBiy5UA76SyRIn2xOPjhK6+8gltuuQUtWrQo8Hu94IcA+SJjLNzBISIBCF0weMkXCzNn5YdQ8MVSpUppyPQXhwhKffaSfuaHYPdFl/TZc8hAwT3CRHWZyeKvv/5CpUqVhNqQneTkZAwcOBDNmzfHyy+/HNBnP/zww1i/fj3mzJmDmjVromfPnrm2YMuiYsWKOHbsmNDjzWxC4Vi+A+dcqC+Guh9+++232L9/PwYPHlyo93vBDwHyRcaYk47iAygHWhRe8sXCzFmXI4R8UYWzBaRBp89e08/LEQq+6IY+exEZKLiHzzCMwCcQ5oPTp09j0qRJOHLkCO68804RJlxCeno6Hn74YVx11VUYOXIknLhwyTAM1KxZEy+99BLatWuHsWPHYu3atbm+vlevXkhNTcXYsWNx6tSpgNuTHxRFyerw4WSgYIgQxeLgh0ePHsWoUaPwxhtvIDy8cJvxXvBD4N8FvALAKWcJyzaOq3jRF4GCz1l5EUq+6PP5oCiKk6dbQaXPXtTPvAgVX3RDn72IrFFwD0PXddcnoqFDh2L27NlQVRX9+/fH3Xff7bYJl2DbNgYPHoxKlSrhzTffdGSSu5i2bdti2bJl+PHHH9GyZcscX9O1a1f89ddfGDt2LD777DO0bt0an3zyieO2XYymady2bcfyITjnuqY5esnpJRQXP1y5ciVSUlJw//335/jvY8eOxdixYwEA8+fPR/Xq1S95jVf8MNsC3gfAdGAIHaCWjG7iRV/MifzMWXkRSr6o6zo0TQtzMPUkaPTZq/qZF6Hki07rsxeRgYJ7mJZlBf5qw8swbNgwvPDCC/jpp5/w3HPP4cyZM3jllVfcNuMCXnvtNZimiTFjxlywSOjSpQtGjBiBRo0aBXzMrCPD06dP5/qaDz74AJ9++ileffVVdOzYMSAdHgqDbdsKgMA0rM4BRVEst49vi4sf9unTB3369Lnk6/PmzcOLL76Ixx57DA8//HCez/CKH5rmv7GBU75oAe53MvGiL+ZEfuasvAglX7QsC7ZtO3ktb9Dos1f1My9CyRed1mcvIlOP3MNvmqbrExEAREZGokOHDqhfv/6/HRJEMW7cOOzevRsffPBBwIsI3333Xbzwwgs5/ltiYiIA4Nprr831/UuXLkVMTAxuv/12YZMQ5xy2basAHBNFRVHMbItA1yguflhUvOCHwL+BAoczpwlAptgWZ18s6pzlNF7xRb/fD855upNDBIM+e1k/ncYLvuiGPnsReaLgHn4RgpidiIgIpKSkBPSZL7zwAubPn49Fixbhcrf9zp49+99r6fPb9aAgzweABQsWoEaNGrjttttQvnx5nDhxAtOmTcO8efPQoEED3H777bm+NzU1VeiFOwCy33zpZKAg1BeLgx8WBS/4IUC+qKqqyZhjXSMzADGBQhaifREo+JxVTH2RwdnFmef12Yv6Wdx80Q199iIyUHCPlNTUVKEG5Ocylh9//BGPPfbYBV9r2LAhALpN8eKJ4sSJEyhZsiQqV6582WcXZueuIM8fOHAgrrrqKixZsgTff/89/v77bxiGgRo1auCpp55C3759L3t5khMX1hSEtLS0rD866Sxns43jOqHuh9l5/fXXMWPGjH//npWLe7n8WtF+CJAvqqqa7mCgkALQAkAUon2xMHNWcfTFlJQUG87OiZ7XZy/qZ3HzRZf02XPIQME9Tp4+fdrdqr2L8Pl84Dzv09U2bdrg999/z9fzzp49i40bN6Jr1675Kqj66KOP8vXcwj4/MjISPXr0QI8ePQo0Tha2bQtPQ8nWzeGEU2Mwxo4nJydf49TzL0eo+2F2Xn755QK3LvSCHwLki5qm/eNgAelJgNo8ikK0LxZ0ziquvnjy5EkG4G8nh/C6PntNP4ujL7qhz15E1ii4x4n09HRd5IUhlSpVAuccJ0+eLPKzOOd46623EBkZecluWyBw+vkXY1kWTp8+jSuuuMLxsfIi26LJsYnINM1jp06dEnYLqfTD3PGKHwLki5xzJwUxWVEUW2TbTemLueMxX1SQGVg6hNRnDz3/Yrzii27osxeRgYJ7nOCcC+1FHR8fDwCYMGFCkXfxTp48iUOHDuGzzz5D+fKBv83c6ednJyUlBV988QUsy0Lr1q0dHetyZPoHB/CPg8Oc+Pvvv4UpovTDnPGSHwLki7ZtH3NwCK7r+hmRJwrSF3PGS77IOcfZs2d1OBwoSH32zvOz4yVfdEmfPYf45MPiQ00Ae7766itH2pfll4kTJ2L27Nk4dOgQrrvuun+Lo4orQ4cOxfz581GlShV07twZgwYNcqUvdW5MmTIFo0eP/sc0zXIODvNcuXLl3li5cqWwc1zphxfiNT8EgD59+vj/+OOP8QCecGoMn8+3uU+fPg2fffZZp4a4LNIXL8Rrvnj8+HG0b98eANoAWOXQMFKfPYjXfNElffYcMlBwD11RlHMjR47UOnfuLNoWiUcZMWIEZsyYsd7v9zd1cJheiqJM++233xQRt+JKgoOEhAR/cnLyiwDec2oMRVG+bd++fffRo0fL021JjmzYsAH9+vUDgOoADjo0jNRnyWVxSZ89h5yc3cMyDOP4kSNHRNsh8TCHDh1ilmXtcHiYvZxz5ejRow4PIwlWMjIycPr0aR+AvU6Owznfs3//fnGJ4RLPc+TIEaiqagFwUjylPksui0v67DlkoOAijLFte/bsEW2GxMPs3r3bZIw5PRHtAsD37dvn8DCSYGX//v1ZHVh2OjzUzgMHDmgOtmCVBDl79+6FrusHATh6hbfUZ8nlcEmfPYcMFFzEsqz1W7duLVZXf0vyT0ZGBo4cOeIDsNnhoZJ9Pt+xHTuK3XwnySc7duzI2sV12kl+z8jI0A4fPuzwMJJgZdu2bcyyrHVOjyP1WZIXLuqz55CBgrv8vnfvXt22Hd0YkQQpu3btAmNMgQsTkW3bG3bs2JF3A3lJsWXnzp3QdX0nAKcXTr8risJ37nT64EISrGzbts1ijLmxOJP6LMkVN/XZa8hAwV02WZal7t3raNqvJEjZtm0bNE07B8Dx82/btjf88ccfcvdMkiNbt261LMv6zYWhUg3DOLht2zYXhpIEGykpKTh+/LgPQP5uvCsaUp8lueKmPnsNGSi4y++apqVv3LhRtB0SD7JhwwaoqvorHM7FzWTNoUOHwk6fPu3CUJJggjGGjRs3gjH2kxvjWZa1av369bKgWXIJGzduBKdimbUuDCf1WZIrLuuzp5CBgrvYiqL8smHDBpnyIbmEdevW+U3TXOHScKsB8E2bNrk0nCRY2LFjB9LT03WQjzgOYyxp06ZNkAXNkovZsGEDfD7fPgDHXRhO6rMkV1zWZ08hAwWXsSzrx19//dUUbYfEW5w8eTKrUMqVXVwApwzD2LN+/XqXhpMECxs2bICmaakA/nBpyJ/OnTunb9++3aXhJMHCunXrLL/fv9Kt8aQ+S3JCgD57ChkouM+KI0eO+A4edOreGEkwsmbNmqwuM67s4gKA3+9fnJiYKOsUJBewevVqG8AKAG5t8f+p6/o/a9ascWk4STCQnp6O33//XQWw3MVhpT5LLkGEPnsJGSi4z2pN01JXry6W/ibJhcTERK5p2hoAZ10cdtGOHTt8J0+edHFIiZcxTRM///wzt217vovDMsbYglWrVsmdXMm/rF27FrZtKwCWuDis1GfJJQjSZ88gAwX3MQEsW7VqVbEriJHkDGMMiYmJlmmac10eermqqqYURUkW69evx7lz53QAi9wclzG2cOPGjVpKSoqbw0o8TFJSEgzD2Ax36hOykPosuQCB+uwZZKAgANu256xduxapqamiTZF4gA0bNuDs2bMGgHkuD52qquqPy5Ytk6IoAQAsW7YMPp9vJ4B9Lg+9mDHGV61a5fKwEi/CGMMPP/xg+v3+790eW+qzJDsC9dkzyEBBDDNt2+Y//vijaDskHmDBggXw+XzbAGx1e2zLsr5etWoV5E6uhDGGhQsXmn6//wsBw5/UNG35okWLZNAqwW+//YZTp04ZAKYLGF7qs+RfROqzV5BAYLdvAAAgAElEQVSBghhOqaq6fMGCBVIUizmMMSxevNj0+/1TBJkwkzHGV65cKWh4iVdYt24dkpOTDQDfihjfsqyvExMTFRm0ShYtWgSfz7cVYhZnUp8lADyhz55ABgqCsCzrq6SkJOXUqVOiTZEI5KeffsLp06d1iNk5A4BkVVV/mDNnjrzwqpgzb9487vP5fgcg6prkWYwxe8kSN2tXJV7D7/dnnWwJW5xJfZYAntBnTyADBXHMUBQlbe7cYlsfIwHw3XffMcMw1gDYJcoGy7I+Xbt2rXbkyBFRJkgEk5aWhkWLFtl+v/9/As04pSjK99OnT5fdj4oxy5cvR0pKigZARApcFlKfJZ7QZy8gAwVxpFuWNeWbb77x0w31kuLGyZMnsWLFCpim+YlgU+ZqmnZi5syZgs2QiGLBggXw+/0cwFci7bBte/yff/5pbNsm6lBDIpoZM2ZYmqYtAnBYoBlSn4s5HtJn4chAQSyfHjx40PfLL7+ItkMigJkzZ0JRlFQIygnPhmVZ1qfTp083TVNu5hZHpk6dagKYAUB0rsUKwzD2zZgxQ67OiiH79+/HunXrNMuyxou2BVKfizUe0mfhyEBBLBt0Xf9p8uTJMj+8mOH3+zFlyhTTsqyPAKSLtgfAuNOnTysLFiwQbYfEZdauXYudO3cajLExom0BwE3THDVr1iwm88OLH5MnT+a6rh8C4OaFf7kh9bmY4kF9FooMFARjWdbIpKQkfdeuYp0CV+yYO3cukpOTVQAfibYlk8MAvpkwYYIpj9qLFxMnTrR0XV8FwCtbpxMZY6nTpk0TbYfERf755x/Mnj2bmab5FgBPdByS+lw88aA+C0UGCuKZZxjG7okTJ8rVWTGBMYYJEyaYiqJ8BeCQaHuyYIy9u3fvXj0xMVG0KRKX2Lp1K9asWaNbljVStC3ZSLMs68MpU6aY6enFfjOv2PDll1+Cc34WwOeibcmG1Odihlf1WSQyUBAPM03ztfnz52Pv3r2ibZG4wLx583Do0CGNMfamaFsuYpOmaQvHjBkjTxWKCR9++KFtGMZmAAtF23IR76emplpff/21aDskLnDq1ClMmTLFsixrBIA00fZkQ+pzMcPD+iwMGSh4g6mapu3+5JNPmGhDJM7CGMPHH39sKooyBcB20fZcjG3bL+zcuVNfsWKFaFMkDrNlyxYkJiZqpmm+AMBrkeEJ27ZHf/rpp6a8gC30mTRpEizLSgEwTrQtOTBV07Q9b7/9Ntu0aZNoWyQO4nV9FoUMFLyBbZrmfxcuXKjItoChzbfffovDhw+rjLHXRNuSC7+rqjpr9OjRpm17Ik1Y4hDvvvuuZRjGOnjvNCGLd9PT0zMmT54s2g6Jgxw7dgxfffWVbVnWGwDOCjQlAkAsgNsBPA/gUwBJAI6Ypnl1UlKSeuzYMYHmSZwmCPRZCDJQ8A4zNE375Y033rBk2kdocvbsWbz//vsW53wMAM+eY9u2/X8HDhzA9OnF+jLKkGbZsmVYt26dZprmM6JtyYNTtm2/NnHiRFteBhi6jBo1inHOj8D904SaACYAWA3gOIAUABtBbYJfBdAPQGsAFQGkq6r65+effy71OUQJFn0WgQwUvAO3LOvJzZs3a0uXLhVti8QBxo0bh7S0tDQAw0Xbchl2M8bGjBkzxkpOThZtiyTAmKaJd955x9Q0bRoAr1auRwFoA8C2bTutd+/eSEpKEm2TJMBs2rQJCxcuVE3TfALAOZeHPwDysVYAKmT7ugKgBAAfAAbAD+AWxtgDUp9DlyDSZ9eRgYK3+FnTtK9HjBhhkr9KQoUdO3bg66+/ZrZtPwfgH9H25INhGRkZZ8aMGSO3z0KMiRMn4ujRo1m+KBoFwNWgdI/XAcwBdRo5BWAlgPcYY6VOnz4NwzCEGSkJPLZt4/XXXzczW/POEmECgP9e5jUc5JsrIPU5ZAlCfXYVTbQBkgvhnK/KyMgYmJqaGhYfH6+ItkdSdBhjePzxx61//vlnE2PsEXivcDQnMhhjh7Zs2XJ7kyZNYBgGIiMjRdskKQJ///03jh49iueff962bXsIgEUCzYkFLQ4/APAMgF4AWgKoD6B0ttfZAMZpmvbX2rVrr+rVq5cmA4bQYPLkyVi4cCGzbbsrgBOCzNgC4G7QCdbFG6c8899m/vsFqc8hR5Dqs6vIEwXvccKyrKenTp2KzZs3i7ZFEgCmTp2KLVu2wDTNfvDIRUKXoSSAdgBqKYpycuDAgTh48KBomyRFJC0tDb1794Zt2xkAogF0xoWLcjf5A0AkgLDMvyuZf86++LJAwcxTtm0/cuLECf+4cV5siiMpKAcPHsRHH31kZxaNbhVkRiNQsFoLl26acgADAXxz0delPocYQajPriMDBW/yuaZpK55//nl54VCQs2fPHowePdpmjA0H8Kdoe3KhAoD/ABgF4DcAZwAsB/Aq57wcAP/y5cvlLkuQs2LFCliWxTjn4QBeALAAlOKzDcCHAO4EEOOSOTaAx5G7Bpmg3d47Ml97xLbtpz///HO+fv16l0yUOIFt23j++ectzvl2AG8LMKEegC8ArAdwFcjHfgUFplk8D+B/ubxf6nOIECT6LBx5dOZdqui6vuU///lPqVdeeUUGdEGI3+9Hnz59rL179/5pmmZz0OLHC5QC0ANAAoC2oBxxDiADVMSXhQXgawA/APhi3LhxSEhIcNdSSUDYunUr+vTpw2zb/i/oZzwUF+6imgB0kCb8BQoUV4HSLv52yCwFVEx9HYDs+UQWgGMAmmXa8i+aps0rW7Zsh9mzZxulS4s6DJEUhXHjxmH8+PEmY6wZADe35auDahL6A9gJYASAL0EFyzcDWAKaB1/L/JUXUp+DHA/rs+eQNQre5SxjbMeWLVvurFOnDq666irR9kgKyKhRo7Bq1aoMy7LaQlwObk5wAJ8D6AhKQQFo0aZne40J2mnuBuA3TdMarF69uk63bt208PBwV42VFI20tDQ89NBDZmpq6lrG2EMAfgTVA1yJ8xqg4fzGUSSAawG0ADAGznSjaQngW1CQAJw/WWCggLUdgD0Xv4lz/oPf73/o0KFDJTp06CA3uoKMl19+GV9++SXnnH8E4CvQz9tpKgJ4KXO8KwC8COAhUCvUrJPSPQDaA/g+898vh9TnIMfD+uw5ZCTsbWaqqvq/F1980dq3b59oWyQFYMmSJZgyZQps2x4AYLdoey7CBO2q5ZZOxACkg9KR0gHAtu2HU1JS/ho8eLAlL2ILLl555RV25MiRVNM0+4B+tgxAHwBHcGG6RXYUAI8ACHR/3BgA40G969NBpwbvZbODAegK4Pdc3v+3ZVl3LV68WJk6dWqATZM4yYkTJ7By5UqTc54B4AlQd5lvQAXD5RwYshzo1GBf5hjPA6gLSinKaRK7C8DgAjxf6nOQ4nF99hwyUPA4jLHHLMv6bdCgQWZKSopocyT5YN++fRg6dKilquo40NG2F1kHuuAop4WiAspXz76jm2yaZtcNGzbY7733nqxXCBI+//xzLF68WLEs605Q29EskgHcCvr5X/zzNEFpGDMROEqCFmrbAHQCcD/o1GAjqG/5mUw7+oNaUebFEs75y2+//Tb77bffAmiixCls28bgwYOtlJSUI6AglYNSIHsCmAK68OxnUO3MtUUcrhTI13YDeACURlQbdDqWkcf7DqGAHW+kPgcfQaLPnkKmHnkfxhhbnJaW9sCuXbt8HTt2VBVFnrh7leTkZNx///3m2bNnN9q2nVWI6UVaAXgSlK9u4MLUj6EAJuXwnmOc8/2bNm3qUa1aNdStW9cdSyWF4qeffsLQoUMZ53wIKNXsYo6DgsGeF33dAqUfbQflchcFBdT6dDaoy9IoUBCafYWfASqq/g1UVJ0fElVVbb5ixYqanTp10kqVKlVEMyVOMmzYML5y5UrTsqwbQbUv0QCa4nxdjAKgCqhm6jEAA0CFxumgE4H8EAE6EfgWdKPyB6CgZDlyPzkrKlKfg4gg0mdPIQOF4OAMY2z1gQMH+qWkpKitW7eWM5EHMU0Tjz32mLVr165TlmW1By1+vEZJAG8A+Ay0u/segNsy/80CdcJ5LI/3bwYQsXLlylZNmjRRqlat6qStkkKya9cuDBgwwLJt+zvO+dN5vPQPUIpGM1CwmBUopgIYmfn1VQDOFsKM5gCmAXgawDzQCcY85Lxo2wiqncg3nPO5tm33+PHHH6O6du2qhYWFXf5NEteZNGkSJk6cCMbYnTj/M/4RFDCWwflNCiXbn0uB6lfW4MKgMid8oJOD7wHcBOATAL1BrXXzOkEIFFKfg4Ag0WdPIgOF4OEA53zH5s2be5YpU0Zp1KiRaHsk2WCM4cUXX2SrV69Ot207Ad7Me+wCYCGA60GLtydAIlwfdNy/D1TgfDlxXaaq6rU//PBDnRtvvFGNjo6+zMslbnL8+HH069fPTEtL+9myrP/g8rtmSwF0AFANwC+gRdfMzD/3B+3SngK1k8wPMQDeBaW27QV12PoYQF65GYVJZ/MzxuakpKT027hxY1iXLl1UTZOS5iWWLFmC119/nXPOn8GFp5QWgCRQUXFOKdAmgPkAns3j8QaAB0G++h9QClPW6ZUTBfh5IfXZwwSJPnsWOasGF38CSF+9evVNVapUUerVqyfaHgkAzjmGDRvG582bZzPGuoIWWF6iEmihNhKUe94FtEucxSrQDtytuDCPPTc453wu5/zmRYsWXXHTTTdpZcqUCbTNkkJw6tQp3HvvveaJEyf2mqbZHnQycDkYaFHWE+QHWe1Qd4EKPyNBdQTtQTu8J3N5TklQUDEdFCw8mfn3v3J5fSA4wxhbeuzYsXt37NihdejQQVVVWXrnBZKSkvD0008zAB9xzl/J4SV/gQKGdriwVTsD1dDcjMxmChehgnx1Jii1aAaA2zN/z4+/O4XUZw8SBPrseWSgEHysBuBbsWJFfI0aNZTatWuLtqfY8/7772Pq1Kmcc34XaMHlFRQA/UA7bNUB3AtKO7pYTFMBTAZQkOuXLcbYDMuyuixcuLB8hw4dZJ64YFJSUvDggw9aBw4cOGqaZgIKdv9BCsgHLg4UTdCJw1zQYuwl0E7uTzh/UpGfOgQn+YtzvuLAgQN9d+3apd18882KzBMXy8aNG/HII4/YjLGvGWMDkfuJ0U+ggKAyLlyP6KCAIRHnW6hm+dl3oJOIhZl/n4LCpcY5gdRnj+FhfQ4aZKAQnCxXVbXcsmXLmteoUUOpVauWaHuKLaNHj8akSZM45/weUD62V7gKtLP7NKh/eDfkfblRYY7qMxhj35qm2eOHH34o0759exksCCI5ORkPPviguWvXrn8sy4pHwYK+LPJKOfsLwERQd6KXQDu660EFqPmtQ3CSQ5zzn/ft23fXwYMHlXbt2inyZEEM69atw8CBAy3LsuYyxu5G3nclcAArATwMCkBtAG+BgtZhIH9aCSAOdGLwWObfe4LqrLyYZy712SN4WJ+DChkoBCmc80Wc89JLly5tWalSJaV+/fqiTSpW2LaN7t27Y8WKFYxz/gBoV8sL6AAeB3X+MEG5u58A8Ds0XjpjbPq5c+dumTNnTnRCQoKsWXCZkydPon///uaePXv+tizrBuRwUVmAYKAWltNALU5fB+3s7gfQHZevQ3CaPZzzpN27d9+xZcsWtX379qqu65d/lyRgJCUl4dFHH7Vt255l23Yf5C9gPAUKRLuBgs97AGwApRb1BwWm94JSe3qCOmPllv7mCaQ+i4VzjpEjR/IpU6Zwj+lzUCIDheBmCQDfypUrEyIjIxEbGyvanmKBaZoYOnQoW7duHeOca6Dc7B0ADgs2rTEo/eMuAO+ABPeAC+OmMsa+sW27w/z58yu0aNFCq1ixogvDSg4cOID777/fPHLkyEHLsloj/60kC0tJ0B0Id4CCAgbaCV4JbxQI7uOcJx46dOjOTZs2qe3bt1d9Pp9om4oF8+fPx7PPPssYY1MYY/1QsFOlDQBqAHgKdEtuK1AKWzPQHFYalKY0Bc5tegQaqc8CME0T//3vf9n3339vc857gS71kxQBGSgEP8sBpKxZs+bmf/75B/Hx8TI/10HOnDmDQYMG2UlJSRmMsdtBOdnXgnZWW4F6zx9x2ayslqeTQV1muoJOFNzsEX2OMfa1bdutZs2adWXdunXVGjVquDh88WPjxo24//77rdOnT/9pmmZbAEcdHC6nOoQeoGLnuqDA9BpQwJDmoB35YT/nfMnRo0d7Ll++3GjXrp0WGRkp2KTQZvz48XjzzTehKMp7jLHHkHe6UW7MBhXBjwW1bT4COkl4GlRE/yzofoV1KFxqnQikPrvIRfp8K6jdt6SIyEAhNFgD4M8tW7b8548//kCbNm3kLpoD7N+/H/3797f27NlzwrKsNqD2fmEAEkCdOK4EMBB0adAWuBMwdAJNhvEAhgAYhIIVsQYSP2Psa855tYULFzaOjIxU5C6aMyxYsABPPvmk7ff7F1uW1QXUJcYp8roPIRXUv/5XUJ75MyhYK1WnOMI5n56SktJ1zpw5pVu0aKFVqFBBsEmhR0ZGBl599VX+5ZdfcgCPcc6HF/JRDQB8BEorSgHNYy/g/AnZHtBpQjxoU0QDdWsLhlvipT67QA76vFa0TaGCDBRChy2c82VHjhzpvnDhQqNly5aazBUPHCtWrMCAAQOsM2fOZO3e7sr8p99BCygd5z9PVUGLprZwLmCIBvA+gNGggKULgB8gXjgZ53wOgIyffvrpxn379vH4+HjFMAzBZoUGU6dOxaxZszBmzBgA+IAx1h/OXSpVkPsQdgL4FOdbqd4IShURmUuezBj7yjTNljNnzqxeqVIlVeaKB46jR49iwIAB1po1a85lnq5OLcRjaoDaNn8KOrV6DBRsbs/htamZY5wG1ce0BbAM3ul4lBdSnx0kD32WBAAZKIQWhxhjX6WlpSXMnDnzipiYGLVOnTqibQpqbNvGhx9+iOHDh4NzPtmyrB64sNNGOuiegjic/zxltVupCjoqbw5gKwLXT74XqDVgbQD3AXgZ3hPLJABr9+zZ023p0qVqy5YttbJly4q2Kag5duwYXn75Zfbzzz8DwKjMS6ycCAwLex9CVivVpaAahhdBpw5rHbIzP5xjjH3FGAtbsWJF/LFjx3irVq0UWeRcNJKSkvDQQw9Zx48f321ZVlsUfPe2GihdbRLoFub/A50i/JGP9/4Mmv/uB23SbAPViHkdqc8BJh/6LAkAMlAIPc4yxr7gnJf94Ycfrjt48CBv2bKlIo86C87BgwcxcOBAc+nSpRbnfCDn/FXkXKC3FVSEd3HyqZr5tdqgnvJFTceoCUoBeR7nW55uLOIznWQ35/yblJSU9jNmzKgQHR2tXnPNNaJtCkp++OGHrB2zw5zzKNDt2g0B/IjAXTIVqPsQDoJ2iP0AXgPdv/Ar3K/dyYKDdp437dixo+uiRYvUJk2ayFSkQpCRkYFRo0bxt956S7Fte5plWV1RsA2QCqCNja9Adye8ANpM2YCCBZNHAUwAbdK8D+BqAItBwaqXkfocIAqgz5IiIgOF0IRxzhcBWLdnz54uc+bM0evXr6/FxMSItiso4Jzju+++wxNPPGGfOHFiu2VZ7UEdLHIjGZRjWxeXfqYYqMXfpCKYlNXydAaoQDmrFaVTKSeBJJkxNtG2bWPVqlWtt2zZwpo3b65GRESItisoOHv2LIYNG8bGjBmjZP4/dgUFiBVBAeggAMdQ9IAxrzqEwsBAl099A+AmUKpIedBJk6iuNds451+mpqa2/O6772J8Pp/aqFEjyPsW8sfWrVvxyCOPWImJiRmc8/6Zty3nd2FeDsArAL4G+e3roELlX1C4wmeAfHMR6BTiWdAtzUmgz4OXkfpcBAqhz5IiIgOF0GYnY2zyuXPnrpk1a1btY8eO8WbNmim6rsM0Tcjj90vZv38/nnzySWvatGlgjI22bftO5G/HbCdo0ZZ1qsAzfz0F6gxTWGJBO7z9AHwAan26rwjPEwEDdf9Yefjw4ZunTZsWUbZsWbV+/fqQHUByZ8mSJRg4cKD5xx9/nGGM3cU5fwe0MCsNys82QMX0twHoCFokFbQmoCB1CIXhHwBfgHz2OVC6yFY4d9fD5TjDGPucMXbul19+uWHp0qWsUaNG8nQhD86dO4cxY8bgpZde4mfOnPnFsqybQIXE+SESFHzOAM1lbwHoC/LVQHVl2woKQDqDgpEUUADidXLU57CwMNF2eZYi6LOkCEiVLj700nX944iIiNIxMTHG5MmTER4eLtomz5Ceno4JEyZgwoQJtqIo20zTvBcFT7lYjvMdkGxQQVUpADeAFmEFIRyUYjQEJHoPgQQx2CkJ4HVFUZ6OjY1lQ4YM0WWB6YXs378fI0eOtBMTE1VVVT9njA3GhXm3NUF3FmSfv01QYPoWgDdx+V37kqBTqqGgxfxLoAW9k1wB6mrTE7RwHATqmS+KOrquT2KMtbzzzjuVRx99VCldurRAc7zH8uXL8dZbb5l///2337btZ0CbHvlJEYoA8CBo/goHBaJvgm72dgod5M9DQadhD8DjF7Nlo5eu6x9HRkaWfvbZZ41bb71VnnRlI0D6LCkkMlAoXjQD5eqWrl+/vjlkyBCjcePGom0SCuccCxcuxDvvvGOdOnXKb9v2K6Cc18KkXNwE6jzkB+3yrgX9f1cA0Ab5PwloA2A8aGH1CmhxVdjjea/SVNf1T2zbbtqjRw/++OOPq+XKlRNtk1BSUlIwfvx4TJkyhamquss0zYEAVuTy8vWgC/YunsMZqNPWvci5JkYBLdTfAaUCvQtgBIBzAfgW8sutoIWjD1TE6nSAkhcKgAd0XR9ZokSJ0k8++aTeq1cvaFrxPmzfuXMnRowYYf/yyy+qpmnTbdsejPzVmPhADRZeBZ18jQV1NXKzwLQlqDtSSdDnYLGLYxeFsqqqvsU5f6hevXq21OeA67OkkMhAofhwAyiFJQrANF3Xoy3LurlFixb2008/rRXHItO1a9fi3XffNXfs2KErivIVY+xZFD2/9UfQ4n5l5t/LgxZ7JUABQF5iWxa0aHsIwHzQjmuwXCxUGBQAPXVdf19V1Uq9evXSHnroIRS3gCE9PR1ff/01/ve//1nnzp1Ls237ZVBP+bzEcDBoAZZb/uBxUCCR/RK25qB2uq1AxaTPQdyxfRlQnvpjoIXcIwD2C7IFoBSZZ1VVHVKhQgUMHDjQ6N69e7ELGA4fPoxPP/2UzZw5U9F1/XfTNB8FpQldDgNUI/AqKJ1tMmgeFOlfH4OK8T8EBaTBcqNzPV3XP5D67Ig+SwqBDBSKB48CGJP5ZwXU4/8zAJ11XX/TsqzGN954o/3AAw9ojRo1EmakGzDGsGzZMnz66afW1q1bNU3T5ti2PRT5a8uXH3y4VJAqggIHFZRbnpN49gLtvjFQSsi3AbInGCgJYJCu6//VdT2yb9+++t13343y5cuLtstRzpw5g+nTp2PSpElmWlqaaVnWu6CFfH4uT6sK4AAuncMtULvI23A+3S0G1GnmQVBu+dPwTres1qAOSVeCAod34e6N4hdzlaqqr3DO+1arVs0aMGCAr0uXLgj1e0B27dqFiRMnsvnz5yu6ru/x+/1DQHPQ5U4yVVBXq+GgOxEmgX6Oh520twD0A51ebQHVdwVTf32pz4HXZ0khkIFCaKMDeA+08MxOLIDNmX9WANxqGMZrpmk2jo2Ntfr376+3bds2pHIk09LSMHfuXEyaNMk8cuSIrmnaPMuyXgG15XODGNAiLQV0GdXJbF8fC+pk8yWo+Pkfl2zyGpEAHtd1/VkAZW677TblnnvuUWvVqiXaroBy6NAhTJ06FTNmzLAty8qwLGsMqBVpQfOpfwalE2Z9UDlocXcfgDSIqUMoDAbohOQ10ILuIYjPP66jqurLnPM7y5Yta997772+22+/HWXKlBFsVuDgnOOXX37BpEmT7NWrV2s+n2+X3+9/DVQYfLlgTQHQFXRLckMA34HuzdjtqNGFox4oFakWaNNsilhzCkSx0OevvvoKuq6L1GdJHshAIXSJBk3eCbiwu1UGaEGWU1pDvK7rg23b7hYVFWV3797d6NWrF6pWreqCuc6wZcsWzJ49m8+aNcs6d+4cAExjjL0JMYXB1UGpSacA3AzaiXsXdJz6MKgYWkKnMncahjHUNM3a9erVs+644w69S5cuKFmypGjbCoVpmlixYgW+//57a/Xq1ZqmaScsyxoHyrfNzwlCTjwO2ghQQDu/n4Py/5uD8rRF1iEUhmtBxbLNQbvAQxC4OyIKyxUABuq6/gyAkjfeeCN69eqltmjRImg7dp04cQJz5szBtGnT/EeOHPHpuv6zZVnDQQXA+SlUvgnkT3GgwPQl5HyTspcIAwWi/wfSxQEo/OdOFDnq89GjR9G8eXPRthWKLH3+5ptvwDlniqJ8LVCfJbkQnDOd5HLUBvWXro5Lc5h/Bi0i8qIqgLt9Pt9Tfr//inr16lndunXTO3TogIoVKzpgbmDZvXs3Fi9ejPnz5/sPHDjgMwxjt2manwKYCOBvwebVAvATqBNIGGih9wqC404EETTVNG0ggHtUVdVbtWqlduzYUbn55ps937WLMYaNGzdi8eLFfO7cuVZKSoququpK27Y/BjALRb8cqjKAQ6BAsxtIXDeBiucjIL4OoTAooBOFd0Cf1YGgm55FEw6ga1hY2GMZGRk3lC9f3uzYsaPRoUMHNGnSxPNBw5kzZ7By5UosXLjQWrNmjQogzbbtqaA8/vymocUDGAaqtVoK8q1g2/G9CXSqlgFq07parDmF4gJ9LlWqFB80aJAS5PpcAjSf9QTwvWATJRfh7dlNUhg6g1oP+kBH+tnxg3bqns7ns3QAnVRVvVNRlB6MsRINGjSw2rZta8THx6NBgwauH3/atn1JgWFGRgZ+++03JCUlYeXKlf6DBw/6dF0/blnWVNAxuld6atVWIYYAACAASURBVJcA3UQ6JPPvv4OKzEXvmgYD5QDcYRjGXZZlXR8WFmZff/31SkJCgta6dWtUrlxZtH0AgJMnT2L16tVITEzkiYmJVmpqqmEYxgbTNL8EXT4W6NuJXwEVPofhfB0CA4lt7wCP5SZVQEWo3UEpeU/DO60uGwLo4/P5+vr9/mqVKlXyt2nTxhcfH48WLVpccuqV05zlBjt27EBSUhJWrVplbty4UeOcW4qiLMgMEOYi/ydMLUEBQntQgDAEwDpnrHaFiqBaig6g2oo3ILYuprDEg2rfDmqaVskL+pwT+dTnpSD/MjN/TxRosuQiZKAQWhig/Ms7QBNfTrcE3wPK1ywoJQB0AnCLYRi3maZZsWTJklZcXJwSFxenNW7cGHXr1oXTfcjHjh2L3r17Y+vWrdiwYQN+/fVXc8uWLZppmqrP59vu9/vngERwNbzVUjQBlFZRDSRMi0GT43pQ4anX00K8RBUA/9E0rSuAdrZtl6hcubK/WbNmRlxcnNKwYUNcddVVjheg2raNffv24Y8//sCGDRuwbt06/4EDB3yqqpqqqiZZljUPtGAv6B0aBSGnOoTTmeM+CDpFC2ZuBe1666AdbK/VWDQD0M0wjNssy2qoqiqvW7eu1bRpU19cXBwaNGiAuXPn4v7774fP53PMiNTUVOzcuRObN2/Gr7/+yn777Tf7zJkzhq7rpxhj8xlj80Gd1M4W4LHXgoLPXqBT0JcQOumRCoAnQJ3DfgLpolcKsPNDVdBJUDlQIP0QPKDPAHD8+PHC6PM3oI0NDtLC1vBOw4VijwwUQpN2oD78V+HSYKE2AtP5oSGAtqqqxmua1tY0zYoAUK5cOX+9evW0mjVrajExMYiJiUHlypURHR2NMmXKID+3TqalpSE5ORknTpzA0aNHcfjwYRw+fBjbt283N23alLX64z6fb4/f718Bat+3DJSG4TWiQLmxjwFYCGp5eiDz3xqDhPdnAP+BTD8qDGGgnbUEXdfbcs6vs207XNM0VrVqVbNevXq+6tWrKzExMahatSoqVKiAqKgoREVF5Wu37dSpUzh9+jROnDiBw4cP49ChQzh48CC2b9+esW/fPsOyLFVVVb+maetN01wJ2gn7Ec6fEl3uPoQRAJ4E/d+ILgwuKlGgBd1DABbgws+Ql6gI2g1t7fP52pmmWY9zrgJA7dq1rUaNGulZc2KVKlVQvnx5REVFITIy8rIPNk0TycnJSE5OvmBO3LdvH9u2bZt1/PhxH+ccuq6f4pwn2rb9I6h5wnoUfMOkPqgw+W5Qt5lhoFPqUORa0K52VVCd2HSx5uSLEgDWALgG1MhgCujG8+y4rs+7du0yt2/fjtTUVAMF1+dPAPQHbXZaoDq+65D/u4ckDiIDhdClDmgCiQVNJgZoN6kM8lewVlBiADQC0EhV1Ya6rtfnnNcwTTM6+4vCwsJswzBYZGTkBeLFGENKSopqmqZmmua/KzhFUZhhGMc553tM0zwOWlD/Cdqhd/MSn8KQn93QlgCWgC5quwPyIpmiogOoCxLKRpqmXavrej3Lsqratn1BUUPJkiVNn8/HS5QoccHnISMjQ8nIyFDS09N1zvm/c6Sqqn7DMA5ZlrXTtu3NoNSxP0D+6GaP9magIui87kNQQYvqepmvF3kDcqC4+FROdCvVy1EKtMDuCGCxYRjhiqJcbZrmFZzzfzdwNE1jYWFhdnh4ODcM4wJfTE1NVU3TVM6dO3dBrZmu62dUVd1nWdZ2xtgmkC/+jqKdXl0JSit6AFSc/CqoWNkJvfAS4aDA+gmQZg4EdQ3zIgooI6AnaK6zQE0MHrzM+9zQ5z9B3RR/z/y9IPo8ErSxkRWpmKA0zetAd8JIBCIDhdBlDoCrQYvV90DFjitArTndpCSoqLpctl8+0C5hdmwAZwCkg3KRT4KKNA/jfNFnX9BiO2s39TuHbS8sBc2vbg1KRZoJam3ppZSpUKICqItNOdAufDRImC5upXQO5IenQQW1J0FidRRiKeh9CNEAfgW1rOwEby+q80tWnc+LoO9tAChQ8yLNQaeFAP3chmX+WQcVbmb5YjlQ8XkkLq0rOwMKQk/g/Lx4CAVLIbocVUHdgB4GLc5GAJiA0PCXgtADdKfHMdDlcZvEmpMjL4LqKrLWbhYovfDhQj4vkPpcFIaAPiPZjzRM0EZMAmQdn0QScDqBdoFuvOhrD4kxJ2AMBy3ibNCNxSXEmnMJCmjhchqU3nVTAd57M2gSnojzffElEoDE/HmQUB8AXSKVX5qAdkdfc8AukTQEsBa0iB6BCxcYXuEn0GLHAm0YeI3yoP+7dNCt2AOQ+03fxYWsFtbpoB1uL22mdgRpH8/2K6tBSbAzCPS9cFz6/S2C9EuJJKCEg3YQC1Ow7HW+x/mJ0gKlXHiFa3F+YTAGtENYUDqBAqEPA2iXJHhRQIWke0EX9b2KwgXHA0CnVN0DZpk3UEHf2xkAO0G1WV7hTtD/edaCZ3PeL3eVaJAvnQadlD0P7226iEQD/Z9kLVKvEGsOAEohTMGFPsVBdW0fCLQrUNyFS4Og7L8mwltBm0QS1LwKEs4YwXY4wW5cOHmkQfwkboBE5RyocLBpEZ/XAxRsjC7icyTBTTNQEaANSrcrqp9/BsoZDq1rrokY0CYCA/1fRef9cscpAUoPyr7wSYf4hU4kaK46BUpleh60sSTJmRYgzfkLtIkjirKgot6cdtwzQPVKwc4tuPR7MzN/TQc1ZZBIJAHgapAgPSPaEAfQQZPGxceSnwq0qTWALaD8yedxaYepwtILdGISaukikssTA+pYZoNqihoH6LklQP3KN6Nwp13BQC9Q3vRRUA2TKP4L+vxevPCpJsiekqA0mr9Am0gjQE0tJJenNKhhAAOdFDvX4zZ3hoDmAxM5nyiMEmBToGkN+n5s0PeYBpqvvHFBjkQSQswFFfY520BeDHWR85GkDerm4CZlQKJhgzrLXOnAGPdlPn/IZV4nCQ2KUoeQX6qDirNDMS0xi7KgQIuB5sOqLo9fCbRxkNNc1cFlW3yg1KzDoLSVEaD/H0nB6QcqIF8HajHuNjEAngXVvmUFCFmbZSMF2BNorgF9P0mg+xSeAAULok8HJZKQohvog+alPN1A8h/kLL4mqAOMW9wKWsidBImwk2TdsuulWgxJYAlUHUJ+aQ/a7X7cwTG8QBtQi89k0G66Ww0CJiL3oswnXLJBBy1sd4MWlOMhPkUzFKgLupPkDJyf+3PjNVBdyShQ0M8BvCnIlkBSCtSgIItIUA3NYDHmSCShRziAPfBmZ41A8TzO76Lk9OtWh8e/AtQTnYNyJss7PF4WT4GChUEujSdxj0DXIeSXIaCFa4JL44kiHBR4+UH/z/UdHq8JLk0NcbM7jQoKOrdnjvcFgJoOj1ncMEA+ZYP0wM0TGgV0ovBO5t81UCekzi7a4CYfgr5f2QVQIgkAr4N2OaqINsRBJoNEOCtXM0uATwFYCeBRh8ZVQLtzJ0E7dDc7NE5evAT63kXtYkkCi1N1CPlFAV2kdRShPWdkEQvKd3a6leodoNvX/8KFOeRZGxxJDo0LUCvmDSCfmo7QLFr3EjeBUrr2gfLr3SAe5Edup9qKoj5I90I1EJJIXKMWqID5KdGGOEwSaKfsK5DYc1CnBCepBbp6PqvlaaTD4+XFMNAi4G6BNkiKhht1CPmlFKgQ/yeIKdB0Gx2UgnQWdHNsK4fHy6qp+giUjrQZtKgMNDeB8uazajKKyyLSC1QA/Z+boFOGQDWzyI3xyPuCxVBkKYB5oo2QSIKd+aDbC0OxgDk72S9cUUD5i07tsGdveboRdMOqFxgJyi+/Q7QhkgLhdh1CfqkH+hyFQnvF/FITdAs6Ay28Sjs0TkdQoFAx29cCeWlUa9BpFAfwA4C4AD5bkn8UUAB6DvTzcKp43gdqaRuKHQ3zojvosyqigFwiCQl6gD5EbQXbIYKfAIx14LnXgwKvNAS25WkgUEA7lH44X5MhCQyi6hDyyx2gxabI0w0R9AIVhR4GzaOB5v8ynx1oWoB2sbNSmW5wYAxJwbkGdGqUDLpsL9D0BM0hoXg/Ul5ooJO4twXbIZEEJeGgHcrPRRsiiI8BJAbweRGglCYLVPNQJ4DPDiQKaCc0AzJ308uIrkMoCO+BAuMmog1xmWjQz4iDFt+BXIR9CWqdHCiuAdUeMABrQN2rJN4iHJSiykGbAoG8r2Q26Jbo4sh/AfwDSt2USCQFYDgobaC4XkjyCOj7D8Rtp7cA2A+ajAYE6JlOooIWIqkonqdJXsZLdQj5RQcFxzsBRIk1RQidQZsupxC4VqqbQRsPRaUeaNFpZT6zVwCeKXGW7qDmF1sRmA2CaNDGUHGtT6sAqsPsL9oQiSSYqAXKiXSrL7cXybrJsUYRnlEJJMJZLU8rFN0s19AAfA3KeQ/1NpfBgFfrEPJLJQCHQDvrxbEdYUmcP1FcBVqgF5b/Z++8w6Sosj78dpqBYUiKSDAAggFFCSoqKIiI64KoILtGzJhwVQygi4LiohhAFFdd4+Kqn6iwGFgTRkQwoqKIIsEMSoYBpkN9f5xpp5jp7ulQqbvP+zzzrMt01z1Qv7p1z70nlCALu1NyuMZuyGlHGEk6H4L3NzCUanYF3kbe0yPJ7Zm6BJlT3Cym4TaPI1W9FEVJk1lI5Q4rk+PyjYbIMfzxWXw3XvL0d2Rhd4yFdjlJCHgeiYs90GVbihmv5yGkyyHIAvfvbhviIp2Bj5AdzLFkVxGqM7L5sG8W390FCV/ZisxNw/BWnpSSPn7khKoSeJXs54V5FG+IcZxDkGfK7mplilIQnIQskHu5bYgH+A7pMZAJeyBVQqLIjl2+79KUIJWv1lJ8MeZuk095COkyHPn7FHP+S7yU6iYk3Kd7ht8/E1noZ1KJrhlyolGBhKwNo7g3ggqJg5HGYSvJ/LnqgLzv+1ptVB7yIYXdVFZRLKEM2WV61G1DPMJ0pHFUOphf/p8hk3ehUB9ZqK4COrpsSzGQj3kImfAokq/Tzm1DXKYd228qNEzze3cCH6f52YaIltYjz+9I8itkTUmPRsgiN4acGKV7UjUOqZ6lp0pwNnLiubPbhiiKl7mF4k5grslY4Js0PtcFCSeoIPtwAq/TAImt/hVp9qRYT77nIaRLPWShuwCtNBIPU/wNyeE4IY3vvIY0WUtFA8QpWIMkvo4lfUdEyV+GIk3/PqLuyno+5NR8gt1G5Qn1kXDhYg6NVJSUdECOs4e7bYiHOBHZ7UsWPmROUHybwl9ANwY+QHa527psS6FRKHkI6dIGeSk/7rIdXqFm4YPmKT67Erg8ye9KkLCiX5AF460UZ6WpYqYt0geoAjnlTsbhiN46OWFUnnAbcsJS6A1mFSUr/ofEy2rcajV7IBPpIQl+dyzSqGUt+VHy1CqaILvBS4BWLttSCBRiHkK6HI042Re4bYiH+DOpSym3ROakPjX+PFT1+R+RssaTSe1sKIVNEDlFiiLhs00TfOZfaKWfmuyOzEl2NElUlLzmL0hso2b8b48PCcUaZvozO5so5Qs7AV8Ci9EwtWwp9DyEdBmLVG3p4bIdXsJ8UvkW24eQ/AmZe5pV/X8/Eq62BImvfgB9JpVq+iA75CvYvsx1PWSTa4QbRnmcF4DZbhuhKF6iDNkZf9hlO7zKe8C9Vf89BIkl/gkJSypmdkYa/nwO7OiyLflEseQhpIsfqar1PboDXpOuyOldPPcpBFyDnBrEdfQ14mhNRZPDlcTshJS5DiM6CiDaiVD4IY7ZEHfG93PbEEXxChOQY259SSfmPqRs2qvIqUsm1UkKnV2Bpcjx9Q4u25IPFFseQro0RXbE30BDH2sSQk6etiDJ3y8D84FPEB1NQ/LLFCUVPuRkfDPwPvA6Em6s1MaHnJZPcdsQRfECeyIJzBe7bYhHCSIv4hjSgC5RrkKxsztyIvU+6kAlo5jzENJlf2QRoxVYEtMecciNqp//oTpSMqcjsBDRkC6Ek3MFEhbayG1DFMVtZiNH21pDuTYHIBV+wsikWlepuWKmA/Azslue7w3mrETzEDLjVMQpH+K2IR7jMGSuNpB/nwrkJK+fm0YpecsIJFzNQE42G7hrjidpgoSGXuK2IYriJicjO5yawLw99alOJHwXCReJAse7aVQe0AnJ33iN4o65B81DyIV7kbKe+7ptiAfYHznRNBAn/Lyq/z6C7Uup7uSWgUpe8gHS9PAEpETxIqQXkLI9/wK+ongqGirKdjREEuIedNsQj9ELiU1ch9Sf9lf9+RLgBreMyiMOQJo7vQyUumyLW2geQm6EkMZ+iyneY/+OVIc8zgOOq/rzs5BQ0XgexwDkpGo121dmU5RkdGD78rotkPl6K3L66U/yvWLkABKXIlaUouB25OWiO1FCUySGPIaURtulxu+nI7WolbrpjoTaTKe4ElM1D8E6WiChbP+luHbz2iIaiiA5UUPY/u8/Eem4a6Yx0jMhCsxCGtkpSjJuRjYJzeHGPmRjrBI5EdbyutW8CzznthGK4jQdkQlBmxwJQ4BVyMLkpCSfGQN865hF+c9hSPjIMxS+s6B5CPZwGDJPXe22IQ6wG+IghJEwkKEk3tl9HXgkyTV6IL1NNiN61LwzpSY+JLflliS/Pwh5z61EGv8pEqIdQYp2KErRMBvZlSr2F0kb5Mg1XvI0VZjDiciOnSbqps9RSEnHxyjM42zNQ7CfEchLulCTdndC8qG2IJXDhpHasV6J7PwmI15KdStSIelAS6xUCoVe1N0foBHwOPJenEzxhpDGCSEnMDe7bYiiOMVpyIK3u9uGuIgfeSFvBL4BjkzjO+2QCVbLo2ZGP2TR8hCFFUKieQjO8TSScNnGZTusZEfEQagAfkAW/3UtyFohc1A681UHJPwtjCz2tKqNAjIPf5zmZ4cgnZu/QBuP3YhEHRS706QUAQ2RjsL3u22Ii+yPNCuqRF7U6T74PmA9Gq6VDScg/96T3TbEAjQPwXnKkbrv88n/F3VDZMd/HVIhbCRSZS0djkUchWZpfj7eYGs98B3QNyNLlUKjHrLwvzyD77QB3kMc2lQnWYVOS+QddprbhiiK3UxEEpjTfdEUEvWR0JBtyMTXMYtrvIeUblQy5yRkd/NOtw3JEs1DcJcOyOL6PrcNyZIGiH7WIHPwWDKv6DQSOX3IlJZIIYYYcvpVjPO/An9F5uBMTz+DiF6jSFLvDtaalTdMA+a6bYSi2Mm+iEd8vtuGuMARwNfIzpq55Gmm/BMJN1Gy40zkZXO924ZkgOYheIeByGL3HLcNyYASZFf/FyTU8VakkVM2PAm8mIMtxyGOxq+oo1uMvAi8lMP3j0Ri9Vcg79RiI57foXk/SkHiQ8IkPqQwk0qT0YTtS57umuP1LkR2lAsp1t5pzkHuxyi3DUkDzUPwHrcgib9ef1mHkMX4UiRH5wFg5xyvuRAYn+M1mlBdSvUlpNqSUvjshGwUnpzjdZoBM5ECA7ciOi8mPgMedtsIRbGDM5AXw8FuG+IgxyG7H79g3e7ZociOQjuLrles/A35d7zSbUOSoHkI3sUP/A/Z1fRiCI0fOYH6FlmYPYAkIedKadX1/mrBtQB6ImVYtZRqcXAZcqJeZtH1hiLamUdxvQ8vRPI1dnTbEEWxkkZIAvM/3TbEIVohjb7i8bhWPtANkMXjCRZes1gZgdwjLyWHJ8pD0NMj77EDslP/Gt5Z4PqQzYnPkDliGrCHhdfvijjX+1h4zXpU5219XDWGUph8hPU74R2BBYgDcqrF1/Yq5Uiu1FVuG6IoVnIXUlrQi7tvVhKv8LEBWILU8LeDJUjzNSV3bkQWVae7bIfmIeQfnZGdvXFuG4JUE/qYagdhTxvGOAv5+9rRvLAT8D7VleBU+4XFPoiT2duGa9dDQtniG3PF0GdoMtLzxCubFIqSE/shk/+5bhtiM/shL7ow9r/onkPbuVvJLUi8a66xs9mieQj5yxnIAmWQS+P3BN5GFmGvAV1sHGsSkmNmF/HeMhuQsKk+No6lOMt4JAzXzvzE45ENya8p/JOpDsj7or/bhihKrviAt4APKNwE5ngXUiePzscgpwqKddyOOLQDHRxT8xAKgweRxe3eDo55CPA61Q7CQQ6MORtnkihrhm4WaynMQsGHnJTmmgSfDjsj+UOVyKlsoa47AF4FZrlthKLkSrwUZaEmMPcEvsL5ZLwTkJdopjXQleT4kPr427B/l0bzEAqLUmQz5HPs7z7cCQktMpCeKul0SLaK35AiAE4xBFiJtcUgFOc5EtGrU52VfUji9DbEibYikd+LHI+sA+wIM1QUR2gE/AxMcdsQG2jM9uX9dnd4/HbIxHuow+MWOj5kd7gCexZgmodQuOwKrAKesun6+yAOQgzpDn2cTeMkozX2xZinwury0orzPIK9IWvJOBAJYVsFDHBhfLsJIAUV8rWBqKJwNxIvWGglvLzQMMiHVHm40KXxC5kA0lRqM9Y29NE8hMKnD5LrcpmF12yDLJQjSA+DIbhz+vRnxFFwaz6PN6xcR24NKxVnqYfcMydPosw0pNrRfACo75IddjEKWIv9J5mKYjmdkKTes902xEJaAs8gL8tpuF/BaQ7FU27WaQLIPV5P7mFzmodQXFyLzH25Opm7IroJI7uGw3C3wskoJEzOTepTXUp1DlIaU/E2pyAazrXRX64MQRbUC5H1SaHQDGn+eJ7bhihKJviQKhzvURhx1/GSp+uB74Cj3TXnD+5F/o0VeygBXkReLt2y+L7mIRQnPmRD4VfEScyUnZCqaVuQhm7DsKccaaY8hYT+eIH9kfCreCnVUnfNUVIwC5lHvcDuiINZgbWnfm7zb6SXhKLkDWcjx+R2lulzig7AG8iOyGS8dbx3AbII1cWnfdRHKr2sAvZN8zuah6A0BL4E5iIOZzrsgGhlA5LAOxJvLYC/BP7hthEm4qVUNwLf4HzuhFI3zZF3p1WdvK0giDxnEaSyViFU1Io3QuzhtiH5TqEtpvyId7wH0BRJHG5Q9dO46jMbkTjrzUiM4EZkR3wZ8pDYQSMkjvRZ3ItJtIIQ0rX3RmARcD7SVdJLHIL0bdgDabziRT0UAmXIrtg+QC9E38k4EGkueCjwBHANsrPsNF6dH4qJvZBKSI+ReveyHLgECe2JImV670ZOFKwiVz0EEKf3NCQkz0u0RaqV9UMKEVyNOFtKcpyaHy5H3qEtsFbPVnAkkitmIM0233HXnJz5ACmZnk13an1fVJHPjkJDJN71EJ/Pt3dJSUmncDjcNhaL/bFTVa9evUhpaWmsfv36RqNGUjFz06ZNbNmyxbd161b/li1b/ji69vv9kVAo9H0kEvkiGo1+jQjsbWC1BbZOQXZT90LElI8chrxw2gA3AXcgL3CvENfD4T6f78iSkpKm4XB4d4/qoVBoRHWZvV5IzLiZ1sANSJzoO8AVOHcUnE/zQ7FxItIY8WwkPMBMGbIBcR1ycvVPpPHf+hzHtEMPP1RWVq42DGM+csLqRT0MQcIxI8ClaEPKOG7ODx8Dn+Ld+PkmwP2IdqYAVyEnIPnImVSvW35O8Tl9X6QgnxyFesDhwJElJSX9wuFwZ8MwArvuuuu2vfbaK9SmTRt/mzZtaNu2LbvtthtNmjRJ66KbNm1ixYoVrFixgqVLl7Js2TJjyZIllcuXLy8xDINQKLSosrLyFeRF8CbiOWZCF6QE2rnUfinmA42AccBwZLE3DCmt5jb5qodCozEShrQTMtGuQBZ7lwJ/Rxzj0cDjyC6VXage8os7gYuQsIBPkVCks5Dwh0bIAmUCkguTDaqHapoiOQvnI2WrL0K6ARcTXtHD7ki4Wm9k4ehlhiKO+pfIjvx37pqTFaVILtwUZB0Txyt68ML8UCf54Ch08/v9Z/r9/qGRSKRxixYtwj179gx16dKFQw45hObNm9syaEVFBZ9//jnvv/8+c+bM2fbtt9+W+Hy+sGEYzxuGMRXpcljX0ZIPSayNIaK0c6FkBwOQiaIcCQH4l7vmAPmth0KlGdJpvAQ5aboWcRzuQBYoW20cW/WQnwSR06i2wG3AlcAuSEjSGLIPTVM9JKc3MofvhDhk9yDvpkLGa3p41zCMUuAoJOnc6+yDlMVuB1yMhI7mG7cCZyCnCvt7TA9emh+S4lVHoRVwXklJybmVlZW7tW3btnLQoEElxx57LDvv7E41sbVr1/LKK68wc+bMyMKFC4OhUOi3cDj8KHKstSTJ185FSvl1Az5zylYLaIG8vM9AKpVcgnQfdYtC0UMh0w/4LxIu8gySi2NXHoLqIf/xA+cgcfQB4CEkbvunLK6lekif+ogjdhWSy3U+qfOL8hHVg7XUQ073LgX+gzgMm1y1KDO6A3eXlJS0qqys3EX1kDlecxTa+v3+kcA5DRs2ZODAgaGBAwey9957u23XdqxYsYIXXniBGTNmhH/77beA3++fFo1G/4HUIo7TFFiMeOBXuGJo5vgQ52Aikvh2EfCKi/YUkh4KFXMewnykzv0aJClujcVjqR7yHx9yUnkTUs7zLaAncDPbhwakg+ohezoji5L9kEXgePJjhzsVqgd76YeET29BEvjfd9ecOlE9WIRXHIU9/H7/SMMwztlpp51iZ599dmjIkCGUlnqpCl5tYrEY77zzDlOmTAkvXrw4GAgEXo5GozciC6b7kKS9vcmPBOY9kNOPXki40d9xb9egEPVQaCTLQ9gVib1dixyvZxtjbkb1UBj0RRKTuyEV4K5HNlMuRsJgBiBH8HWherCGIHJa/A+qm9fNc8mWXFA9OEdzJDzwaEQ3N+G98DXVg8W47Sg09vv94wzDuKRFixaxYcOGBU888UQCATcbbWaOYRi8/fbb3HfffeGvvvoq5PP53jIM43AkOe8/LptXF0EkPngsUnf7fCRD3w0KVQ8vGYZxIYWRQOgDTkJC05LlIbRHnIUVyC5Utg6n6qEw6IEsKnoBryO9p1XO9wAAIABJREFUED6p8ZlHgBOQUro1q2fFUT3YQzukys1RSAjYVUiZR6+jenAHHxJaehvSqO0MUlcUcgrVg0246SicFgwGJ5eVlTW6+uqrQwMHDsTv97tojjXMnj2b8ePHh1evXh2JRqMjkd15L5URNdMVOX7eB3no3Tx+Lmg9rFmzZlskErkWOWnyqh7qIpN+CHshYSVLgD+ReXUH1UP+0x05aRqAFHW4juR12eshi44gUoq5osbvVQ/2MwR5X1UiVe5muGRHOqge3OdAJNG5CZKP6WaHctWDjbjhKHQIBoMPR6PRnoMHD+byyy/3NW7cuO5v5RFbt27l/vvv57HHHosFAoEvKysrz0ZqJ3uFMiSu/CrkBT4MCQFwA9WD98m2H8L+SBm4T4CBpFf9SPWQ/+yH6OUkJJRlNKKDutgdaeD4CtLsCVQPTrMz0twuXshiONKB3SuoHrxFQ+RU+Xxk0/EKajv5dqJ6cACnHYVTA4HAQ3vssUdw7NixoU6dOjk8vLMsW7aMG2+8MfLpp58Si8WuQjqLul0i9c/IrlFjJATgQdyzSfXgvh5SYUU/hC5In4V3kB3LVI17VA/e1kNd7I2cGpyG1F4fhyw2M+FoJE9hOLBB9eCaHrz0noij84P79yAZJyGld38BTgE+d2BM1YNDenAqeKue3++faBjGhMGDBwcnT54caNmypUNDu0fTpk05/vjj/Q0bNvTPmzevn9/vP8gwjJdxp237zsix1QSkfvmfca89u+rBfT2kwocs6v8LHIs0x/or2e1i/Iro7AbEaZhO7eQ31YO39VAXuyOhiw8iDY6GIzHMX2ZxraVI+NFfgeGqB9f08C2y8CtH8kuOQqrcuNFZVucH9/VQF18B/4e8L8YgeWl2JeGqHhzWgxMnCnuFQqH/lpSUtB8/fnywT58+DgzpPT7++GOuvPLKyMaNG1dVVlaeiLMJw16KPVU94LoeUpFJHkIm9AReRhyFs6h2FlQPeFoPqdgFuBq4ANlJvAV4mNxiaFUPeE4PXZAkZzdy2VQPeE4PqQgiJ8+jkZyF87DWuVQ94Lwe7M72OCQYDM7v0KFD++nTpxftTQXo1q0bM2bMCHbr1m3nQCDwDnCcA8O2A15FPP3pSGiAm06C6qEKl/SQitZIedz5SHhQN2Ao1jVNm4OUCx6CLDp8qB7+wIN6SEUzpNLVN8g9/RvQAdmBzsVJUD1U4TE9fIokpt+IhCF9CBzswLiqhyo8podURJAKij2BA5BeAMdYdG3VQxVO68HO0KO+gUDg5R49etS///77g02bNrVxqPygfv369O/f379q1arAokWLTkZ24WqWCbSCIBJb/iyy6DsBKX/nZkMd1UMNHNRDKsqAEcDTSA+Ey5ByuXZ0VV4KfIE012oUCATuVT1U4xE9pGIHZKH4FJKofguSdDyf3Gup6/xQA4/pIYYUvvg/oA/yDLdGKpvZ8V5RPdTAY3qoix+Rfgv7IfPEDkiuWrbzhOqhBk7qwS5H4TSfz/dc//79g7fddlugpKTEpmHyD5/PR+/evX0lJSXMmzfvOGRn9S0Lh+gMzAROpbp6xfcWXj8bVA9JcEAPSYfGujyETFgMBHw+30jVQ21c1EMqypFqJs8AByF5TqcidkUsuL7OD0nwoB7WIgUNliGaOAf4GvjOwjFUD0nwoB5SsQ14DtHK9UjluzeBNRleR/WQBKf0YIejMAx45Nxzz/Vfd911vnxrduEUXbt29TVp0sT33nvv9QJCpFc+MBVlSJWRx5AHcwByouB2DWbVQxrYoIdUHAhMQ170LyLHli9izaKvLoYBt6seUuOwHpJRitRHn4F0Vb4PcS5nk7p6VSbo/JAGHtGDmc+AqUi/lNuBfZEFSq6lMVUPaeBBPaTiMyT0+S/AKOS0Id2qSKqHNLBbD1b/qw/2+Xz/Hj58uH/48OH4fG43fvY2nTp1omXLlr4333zzCGSnJtsqAb2Bl4AjkPKEFwO/WWJkbqgeMsBCPSSjNVLz+j7EmRxU9d/Zdk7OFNVDBjigh2SEkCTEGcDxyA7ySchJ5TYLx1E9ZICLekjGJkQjHyMJ7VcidmUb/qB6yAAP6iEVvyObmOWIY7kfUn0xVW8d1UMG2KkHKx2F3n6/f+aQIUMCI0aM0DuaJnvvvTf16tVj3rx5f0IWb59l8PWmwGTgHqR0XX/k4fNCrWXVQxbkqIdkOJmHkAzVQxbYpIdk+BGHYAZwMnLqNBgJOcq0s3ZdqB6ywGE9pMs3SLWrHZGE5yOBuWQWYqJ6yAKP6iEZUeB1ZK1yGbIZ8SHwQ4LPqh6ywC49WOUo7B8IBF7v169f6U033eRXzy8zunTpQkVFhe+LL74YaBjGB8CSNL42BGlM1AE4G4kB3GCjmZmgesiBLPWQCLfyEGqiesgBC/WQjLiDMB0JNfpf1f9/HHtOm1QPOeCAHrJhG1L++HXEybwOCWWcR90bV6qHHPCoHlKxFJlbeiBJ8QGk105cJ6qHHLBDD1Y4Cs2DweC8bt26NZo0aVIgGAxacMni49BDD2XFihUsXbp0sGEYz5K89nBbpPLEKKTO/fHAAofMTAfVgwVkoIdkuJmHYEb1YAEW6CEZfZETg+FIouFgZHd4nUXXr4nqwQJs1EOu/IA03qtEThcGIRsTPyf5vOrBAjysh2RsRqqnrQduQk6hXgfqqx5yx2o95Oqq+YPB4KtNmzY9YsaMGaHGjRvneLniJhKJcPrpp4e/+eab78LhcFe277gXBC5BPPBfkCSft5y3MiWqBwupQw/JaI10QT4P2aW5AvccSdWDhWSph2T0RRpnHYjkN43G/rAF1YOFWKwHO2iP9NY4HGn4eR3bh7CpHiwkD/SQjG7Ak4AvGAz+0LRp08NVD7ljpR5ybbh2rWEYR06aNElvqgUEg0EmTpwYKikpae/3+yeafrU/UsP6duBeoBPecxJA9WApKfSQiDKkxv0iJMzobKTeuZunTaoHC8lQD8k4DKmI8Rqym3cQctrkRGyz6sFCLNKDnSwBjkLC2U5HKt0cbfq96sFC8kAPyfgYcRZmG4bRW/VgDVbqIZfQo8N9Pt+/r776an+/fv1ysUEx0bBhQ3bbbTf/K6+8ciDS/+AEpAzdD0iy8lO4X/I0EaoHG6ihhyVIwzIzXslDqInqwQbS0EMyDkaaLk5AwkCGIuWUf7HF0NqoHmwgBz04yWdITHpnpPnWvsAWn8/3L9WDteSJHhLR3efz3aN6sBar9JCto9AwGAy+06tXr7JrrrlGk00sZo899mDdunXGV199daxhGAchFWouwRslTxOherCRuB4WLVp0rGEY/wY2Vv3KK3kINVE92EgKPSRiX+QUciJSMu9sJMxohf2W/oHqwUYy1INbbEJyYRYCFwUCgb/26tWrRPVgPXmiBzM6P9iIFXrI9o7cWV5efumsWbNC2krbHrZt28bAgQPDK1eufDkajQ502546UD3YjEkPL0Sj0UuBMXgjDyERqgebqaGHwQk+0hYpeHAuEo52E9KA0Y3SyaoHm0lDD17invLy8gtUD/aRZ3rQ+cFmctVDNjkK+/n9/suuvPJKvak2UlpaypgxY0LRaPQ4JKTEq6geHMCkh0HAmXgnD6EmqgcHqKEH8/ywG/AAUtv+cOAc4ABkN9cNJ0H14AAp9OA19vP7/RepHuwlz/Sg84PN5KqHTB0FXygUun+vvfYyBg0alOlYSoYcdthh9OnTJxoKhe4D6rltTwJUDw5i0sMFSEjJVLzRXC+O6sFBaswPuwK3Ig7CMUioYidEIzGXTFQ9OIi+LxQzqgfFTC56yNRRGBqJRA678cYbg35/rgWTlHQYNWpUwO/37wJc5bYtCVA9OIxJD5e5bUsCVA8OY9LDm8CpwKVIE8Z/4X7RA9WDw+j7QjGjelDMZKuHTJKZQ8Fg8PlBgwY1POmkkzTbxCEaNmyIYRj+jz/+uLthGP8EtrptUxWqBxdQPShmTHqoZxjGfkjOilsnCGZUDy6g84NiRvWgmMlWD5m4cacahtHy/PPP15vqMKeddhqlpaWlSDiBV1A9uITqQTFTpYcSJLndK6geXELnB8WM6kExk40e0nUU/CUlJX8fMGAArVq1ys46JWvKy8s544wzgsFg8Gqg3G17UD24iupBMaN6UMyoHhQzqgfFTDZ6SNdRGBwOh9ufd955GkjmEmeccQbBYLABMMxtW1A9uI7qQTGjelDMqB4UM6oHxUymekjrRoVCodH9+vUz2rRpk4ttSg40btyYk08+ORgMBkcBITdtUT24j+pBMaN6UMyoHhQzqgfFTKZ6SMdR2C8cDu9/6qmnqvfnMqeccgrRaLQZ4GaPc9WDR1A9KGZUD4oZ1YNiRvWgmMlED+ncrLOaN28e7tKlS+6WKTnRqlUrOnfuHA0EAme6aIbqwSOoHhQzqgfFjOpBMaN6UMxkooe6HIVAMBg8c/DgwSGfT5PTvcDxxx8fNAzjBKCJC8OrHjyG6kExo3pQzKgeFDOqB8VMunqoy1HoF4lEmvXv3986y5ScOOaYYwgEAn7gJBeGVz14DNWDYkb1oJhRPShmVA+KmXT1kNJR8Pv9p+6///7h3Xff3VLjlOwpLy+nT58+vlAoNNTpsVUP3kP1oJhRPShmVA+KGdWDYiZdPaR0FAKBwJ/69Onjaoa8UptevXr5o9HooUADJ8dVPXgT1YNiRvWgmFE9KGZUD4qZdPSQylHYJxwONzv44IOtt0zJie7duxOLxYLAYQ4Oq3rwKKoHxYzqQTGjelDMqB4UM+noIZWj0KdevXqRjh07Wm+ZkhPNmzdnl112qQSOdHBY1YNHUT0oZlQPihnVg2JG9aCYSUcPSR2FQCBw1MEHH+wLBAK2GKfkRo8ePUpKSkqOcWo81YO3UT0oZlQPihnVg2JG9aCYqUsPSR0Fn8/Xp3v37npXPcrBBx9MOBw+AGjoxHiqB2+jelDMqB4UM6oHxYzqQTFTlx6SOQotI5FI43333dc+y5Sc6NixI4ZhBIC9HRhO9eBxVA+KGdWDYkb1oJhRPShm6tJDMkdhb4A2bdrYZJaSK61atSIUCsVw5kFXPXgc1YNiRvWgmFE9KGZUD4qZuvSQzFHYq379+pEdd9zRPstMxGIx7rrrLvr370+3bt246KKLkn723XffZcCAARxwwAGWjb9hwwamTZvGueeeS48ePTjwwAPp378/I0eOZPHixQm/M3r0aLp27coxxxzDrbfeyrZt2yyzJx38fj+tWrUKA3s5MFxR6cEwDD799FP+8Y9/MGDAALp27coRRxzB0KFDefHFFzEMo9Z3VA/2UZcesnl+M0H1UCee0oMZO+aHRFx66aV06tSJBx54IOHvVQ/24fb8kAjVw3Z4Sg/ZzOe5ku96SOootGnTJmafWdszffp0Hn74YQYOHMhbb73FfffdV+szP/zwA5deeil33XUXq1evtnT8O++8k/Hjx3PkkUcyc+ZM5syZw7hx41i8eDF/+ctfeOONN2p95+abb+bdd9/lvPPO44knnmDq1KmW2pQOHTp0CPl8vn0cGKqo9LB8+XKGDh3K8uXLmThxIu+//z5PPvkkLVu25Nprr+XOO++s9R3Vg33UpYdsnt9MUD3Uiaf0APbODzV5/vnneeutt1J+RvVgH27PDzVRPdTCU3rIZj7PhULQQ0JHIRgMdmzfvn2JvWZV8+GHHwJw+umn07Bh4tyaKVOm0LlzZ6ZNm0ZZWZnlNpx44omcfvrpNGvWjHr16tG1a1cmTJhALBZj4sSJCb/ToEEDhgwZQr169fjoo48st6ku2rRp4w+FQvvZPU4x6iEQCHDnnXey5557Ulpayi677MLNN99MkyZNeOqpp6isrKz1HdWDPaSjh2ye30xQPSTHi3qwe36Is2rVKiZMmMBxxx1X52dVD/bghfkhjuqhNl7UQzbzeTYUih6Cif4wEAjs1qJFC3utMrFu3Tr8fj8NGiRvFHjTTTdRWlpqy/g33nhjwj/fa6+9KC0t5YcffsAwDHw+X8LPNWrUiHXr1tliWypatWpFLBZrafc4xaaHtm3bsmDBglp/HgqFaNGiBV9//TWVlZWUlCSe+1QP1lKXHnJ9futC9ZAar+kB7J0fzIwdO5Z+/frRrVs3XnjhhbS+o3qwFrfnBzOqh9p4TQ+5zueZUCh6SBZ61LC8vNxGk7YnGo3W+RknJv2abNmyhW3bttG+ffs6J5F0/g5WU1ZWRjQatW+7rBrVA7Bx40ZWrFjBPvvsQ13/HqoH68j23zKT5zcbVA9/4Dk9ODE/zJgxg++++46rrroq4++qHqzDK/OD6iEpeaGHTObzdCgkPSQ8UYhGow3q169vr1V5wKuvvgrAsGHDXLYkMWVlZfGSVqWAbdkvxa6HTZs28e2333LXXXfRrFkzxo8f77ZJCVE9bI9dz6/qYXvyRQ9WsnLlSm6//XYmTZqU8mTDS6getsfK+UH1kByv68GO+bzQ9JDwRCEWi5U5+ZcLh8OWHPNYyerVq5k0aRKDBw/mmGNSNzAsKSkhEok4ZFk1pntka9OUYtbDAw88wKGHHsrQoUMJBAJMnjyZ9u3bp/yO6sFastFDJs9vJqgeapMPerCaMWPG0L9/f7p3757xd1UP1uKF+UH1kBwv6yGb+TwdCk0PiRyFYCwWK7EzAawmv/76KzvvvLNj49XFunXruPDCCznooIO44YYb6vx88+bNWblypePHRQ496EWthwsuuIBPPvmE559/nrZt23LSSSclLXEWR/VgLZnqIdPnNxNUD7XwvB6s5tlnn2XFihWMGDEiq++rHqzF7flB9ZAST+shm/m8LgpRD4kchTKAevXq2WiSsH79eh599FF+/vlnTj75ZNvHS4ctW7ZwwQUX0K5dOyZMmIDfnyyNo5ohQ4awefNmpkyZwtq1ax2wUjAd59kZAFjUegBJcmrbti3XX389Rx55JFOmTGHevHlJP696sIZs9JDN85spqoft8LQerOaXX37hzjvvZNy4cWQbTqF6sAYvzA+qhzrxtB4g8/k8FYWqh0Q5ClsAy8pDJWP06NHMnDkTv9/POeecw2mnnWbreOkQjUYZMWIEO++8M+PHj097EhkwYAC//vorU6ZM4aGHHqJHjx7cf//9NluLuSlHhY3DFK0eEtG7d29mz57N22+/zSGHHJLwM6qH3MlGD9k+v7mgevCuHuzgrbfeYtOmTZx99tkJfz9lyhSmTJkCwEsvvcRuu+1W6zOqh9zxyvygeqgTz+ohEenM56koVD0kchTCfr8/vHnz5pCdRt18882MGjWKuXPncs0117BhwwbGjBlj55B1cuONNxIOh5k8eTKBQOCPP//zn//Mrbfeyv7775/we3fffTcPPvggY8eO5ZhjjrEkYz4dNm/eHP/PjTYOU7R6SEQ89nH9+vVJP6N6yJ1s9JDt85sLqgfv6sEOTjnlFE455ZRaf/7iiy9y7bXXMnz4cC644IKU11A95I5X5gfVQ514Vg+JSGc+T0Wh6iGhS+33+7dUVNjpZArl5eX069ePffbZ548KBG7xz3/+k++++467774748So119/ndatWzN48GDHbio49qAXnR7uuOMORo0alfB37777LgD77Ze8T43qwRoy0UMuz29dqB5S40U9eBnVgzV4ZX7IFdWDNaSrh1znc7vxoh4Slkf1+/2bN2/e3MhOo8w0aNCATZs2WXrNUaNG8dJLL/Hyyy/TunXrlJ+dOXPmH22+s8lS37x5M02bNs3KzlzYvHkzPp8vahjGFjvHKTY9AMyaNYs2bdowcOBAmjVrxu+//87TTz/Niy++SMeOHRk8eHDS76oerKUuPWTz/KoerMNresiGTPWQC6oHa/HC/JALqgdrSWd+yHQ+L3Y9JHQUfD7fxoqKCts79pnGq/Mzb7/9NsOHD9/uzzp16gRI97uaN/b333+nrKyMli3r/mtYsTtlR0OnuqioqCAQCGyxu5RWsenhwgsvpF27drz66qvMmDGD3377jVAoRJs2bbj88ss5/fTT62zopHqwdLyUv8/m+VU9WIfX9AD2zg9mbrrpJp555pk//n88BrmuuGLVg6Xjpfy93fODGdVDbbymh2zm82LXQ7KGaz+tWrVqT9stq6KkpATDMFJ+plevXnzxxRdpXW/jxo0sWLCAAQMGpJWwdO+996Z13WREo1FXjjNXrlxJIBD4ze4Hvdj0UF5ezqBBgxg0aFBa16+J6sFa6tJDps+v6sFavKYHsHd+MHPDDTdkXGJT9WAtbs8PZlQPtfGaHjKdz1UPSXIUIpHIV0uWLLE3Td3EzjvvjGEYrF69OudrGYbBLbfcQnl5ea0dJTuIRCKsX7+eFi1a2D5WTZYtW2ZEIpGFdo+jekgf1YP1qB6yQ/VQN6oH61E9pI/qwXpUD9mRSg/J3KPFy5Ytc+zso2fPngA8/PDDrFu3LqdrrV69mh9//JGHHnqIZs2aWWFeUjZt2sTUqVOJRCL06NHD1rESsWTJkspoNPqVA0OpHtJA9WAPqofsUD3UjerBFlQPaaB6sAfVQ3ak0kOym3c08Oq7775LkyZN7LPMxCOPPMLMmTP58ccfOfjgg/9IPvIqo0eP5qWXXqJVq1Yce+yxXHzxxY7UbY9jGAYHHXRQdNu2becDj9o8nOqhDlQP9qJ6yAzVg7dQPdiL6iEzVA/ewut6SOYo7AasePzxx+ncubOtBirZ8csvv9CvXz+AHsBcm4dTPXgc1YNiRvWgmFE9KGZUD4qZuvSQzGX5IRAIVHz99dd22qbkwOLFiwEMYJEDw6kePI7qQTGjelDMqB4UM6oHxUxdekjmKBjAOx988EHMJruUHPnggw8oKSlZBKx1YDjVg8dRPShmVA+KGdWDYkb1oJipSw9Jg6Ci0ejr77//fjQW03vrRebOnVtZWVn5slPjqR68jepBMaN6UMyoHhQzqgfFTF16SJUt8camTZtC3377rQ1mKbmwbt06li5dGgLedHBY1YNHUT0oZlQPihnVg2JG9aCYSUcPqRyFz4LB4Pr58+dbb5mSE1X3xADmODis6sGjqB4UM6oHxYzqQTGjelDMpKOHVI5CzDCM2e+88469bfuUjHn33XeNYDD4KZBbkeDMUD14FNWDYkb1oJhRPShmVA+KmXT0kLJQazQafeqDDz4IrFy50nLjlOzYtm0br776ajQcDj/u9NiqB++helDMqB4UM6oHxYzqQTGTrh7q6ujwfCAQ2Dhr1iwLTVNyYfbs2WzdutUHPO3C8KoHj6F6UMyoHhQzqgfFjOpBMZOuHupyFCojkciT06dPr7TONCUXnn/++WggEHgd+NWF4VUPHkP1oJhRPShmVA+KGdWDYiZdPaTTI/rx5cuXl2izDPdZs2YN77//vj8Sidjdcj0VqgePoHpQzKgeFDOqB8WM6kExk4ke0nEU3g+FQsuefvppwwLblBx45pln8Pl8m4DnXTRD9eARVA+KGdWDYkb1oJhRPShmMtFDOo6CEQ6Hb5kxY4bxyy+/5G6dkhVbtmxh6tSp4Wg0OgnY4qIpqgcPoHpQzKgeFDOqB8WM6kExk6ke0nEUAB7z+Xy//vvf/1Yv0CWefvppNm/eHAXucdsWVA+uo3pQzKgeFDOqB8WMw3qoB+wKHAT0B84CRgETgf8Ap8ZisdhFF11EOBx2wBylJpnqIV1HIRyJRCZMmzbN+O2337K3TsmKbdu28cgjj4Sj0ejdwO9u24PqwVVUD4oZ1YNiRvWgmHFIDyXAx8BmZIf6e+AD4EXgIWAscAlwKtDbMIyvvv/++9i6dU62clAgOz2k6ygAPGgYxrr//Oc/2VmnZM306dNZv369AUxy2xYTqgeXUD0oZlQPihkP6MEHtAJ6AmcAY4CDIpFIbNiwYWzbts0ls4oTh/RQCbwL1E/wuwBQijgTBvAE0EPnB3fIRg+ZOApbIpHIzVOnTo1+//33mVunZMWrr77KbbfdZsRisc+APwOHAk1dNgtUD66wbt067r777kgsFrsHd0rcJUP14AL5oIc5c+YQiWhDVidwWA9+4ARgBDAF+B/wLbAV+AlZOD4GjAZONwzj5+XLl0e14ZZzOKyHSYgjkIwY8DAwFNik7wvnyVYPmTgKAPf4fL7F48aNi2b4PSVL3nvvPSMWi21B4v0eBuYCa6p+3gMeQCbqPwFtyfye5oLqwWEmTZpkbN26dT0wzm1bEqB6cBgP6SEAtAdOBP6ONPC5MBKJ+G+++WYjGAy6alyx4LAeYsA5wJ3A+cg7qD2ycxzHjyweFwBddX5wFof1sAoJN0qUeGAgOQoXILoBfV84TrZ6yHRRGQmHwxfMmzfP/9prr2X4VSVTFi5cyIwZM4jFYucgOzYx06+bAocBZwO3Irs5S4EKoI9DJqoeHGTu3LnMmDGDSCRyCbDebXsSoHpwkPj84LAefEAbJEnxGmAq8DkSm/wtMB3ZQT4J2BOY9dNPP6F6sB+X9DAGWQSWJPl9JbAE6Aus1vnBORzUQ3MkB2EF0BUIJfjMbcDVbH/ioO8LB8lFD75sBvT7/f9u2rTpKbNmzQqVlZVlcwmlDmKxGEOGDAkvXbp0biQS6Y04dU8gL+Bk23MxYCHQmdRHgJaierCfWCzGUUcdFf39998jSILYXGT35mPcLXdXC9WD/SSYH5zkTaA3sggMVP3UJAzMBo7z+/0Pqx7sxWU9PI+cJtRcIIaBH5ENrT/CHHR+sB+H9LAH8DfgPORe/xtxCKYB3ZF5wQCuQk4TEqJ6sJ9c9ZBVmEosFrt63bp1W26//XYtd2YTDz74IEuWLCESiVxQ9UcxJLbvDRIf7YHczytx0EkA1YMTPPjgg6xZsyYGvAYMBu5AYoA3Al8C9yL62IssNwCsQvVgPwnmBye5iupd5GROwhfIpkZE9WA/LuqhLxLyWnPzKgz8giQ0bxcLrXqwH5v10BNxBhYDA4DrgNbAZUhuygSqnYQLSeETBxRHAAAgAElEQVQkgOrBCXLVQ7bx7Kui0ehpzz77LC+++GKWl1CS8fHHH3PvvfcasVjsSuRhjBNGYoA/prazEEYWjIucsXI7VA82UkMPfwE+BeLZoQGgIxIj/CjwNbABeB24nsQLObtRPdhIivnBMROAp0i8YRFBFoh/RsKRQPVgKy7pYQDwEfAqEnJm3sCKAKuBXsDPCb6rerARm/TgB45DTrLfBdoh+Sl7ApOpftZBTry/Qipe/SuNa6sebMQKPeS08+j3++8OhUIXP/PMM4G2bdvmcimlirVr13LCCSeE169f/1o0Gh1A4tOBxsgD24Hq414D+A7x7O9B8hbWOmDyH6gerCeJHlojyYFNSe0I3AVc4YCZCVE9WE+a84Pd7IAkww1j+53kCHLC1R1ZPG6H6sF6XNBDX+AfwMHIZsQoxHHcH5mTDKQ2+2HI+ygpqgfrsUEP5UjvgyuRRPVZyNrivTq+15QM1x+qB+uxSg85VciJxWJXxmKxBZdffnlYayPnTiwWY+TIkdENGzb8Ho1GzyD5TV0PHINUGQhX/TyH7CxfDpyJTNIjSVzX2BZUD9aSQg8/Ibs7sWRfRXb0xtpvZXJUD9aSwfxgF/WQOWUpMAh4heqTrRgyD/UlgZMAqgercVgPPYG3kNDHDUgVvqMRJwEkof2/yOKwF3U4CaB6sBqL9dCC6gTlici974i8d+pyEiCLTUrVg7VYqYdcS2mGw+HwX1asWFE5ZsyYmGFoiFku3HXXXcyfP9+IRCLHI+VPU/EjcBRy5OdH4gTDyFFfeyRO8DrkpV1z588uVA8WUoce5gHnJvmqH3EY3a6MpHqwkAznByvxAUOQcIIbgPuRXJjTgE1VnzGQsMhPUlxH9WAhDumhJ5K8/i7yfjkYcRA+SvDZ0cCRSPhjOqgeLMQiPeyPlFxfhuQX3APsjpQ1tTusLa6H8BlnnGEsWuRGFHXhYOX8YEX88lrDMN7/7rvvTluzZo3/iCOOcDWRMl956qmnuOeeewzDMM5FjvfSYTVSWWQDUrc8TiXi9T+EHB3eiBwfrsT+HAbVgwWkqYfPgSbI7l7c6Q8ju0BHA8tJ/6VtF6oHC8hyfrCCQ4H/QxzP2UiDreeAbVU/FUjFm7OR0qh1oXqwAAf00BNplnYTUt70FCTkJFHOQZzfkFPuTFA9WIAFeuiJFMSYiIQ234IUx3gdZ6rqNQD+ClxvGEaH1atX+wKBAKqH7LB6frAq0XG5YRjffPnllyeVlpb6unTpYtFlC5+KigpeeeUVbrzxxngZsfszvMTPyHFwwssjD/rjwG7AeCTJcCmyY2AXqoccmDVrFmPHjk1XD7OBw4FdkOc5hizcGiOl6g4C3gfW2WZw3ageciBDPVjFXsB9yMJhMVJpawq1T6k+ReaTqRlcW/WQAzbroSdSFGEc8m4ZWvXfP1k8jhnVQw7koIcS5FTwcSTX5DdgOFLydB7VYYV2EUA2tMYimjsJSZKOAld/+eWXx6geMseO+cHKiihfAmvnzZt3bOvWrdl7770tvHThMmfOHK6++mqAd5D43602DLMeqUQwHemxMAF5ISzEvrbuqocsmDt3LiNGjIgBEw3DuCmNr8SQe3sqcrowDqlI8yISMnAaEhIQQhwGt7pgqh6yIAs95EozZDfxUeT9cA5SPWtlks/HgM+yGEf1kAU26qEH2zsIZyFhZissHCMVqocsyFIPjZCwoqeR98Yc5DkfB3xji6Hbsy9wCeKgXAzsA5QiIY5RZH0yHtVDxtg1P1hdOnE+UPLmm2/23HHHHX377ruvxZcvLN58802uvPLKaCwW+9gwjMOQOsStkKPe1TYMuQp4BjllOBa4GXloP8GeCkmqhwx48803ufzyy6OxWOypWCx2cQZf3YKUKTwEmfDjzsAK4EEkNG00Uq5uMWkkGtqE6iEDctBDNpQBI4BnkUZKI5HcJjvjklUPGWCTHg4D/omEFf2ChJBdj4QtOo3qIQOy0ENb5OTgCSS/8SngZOBh7D0xAnECrgQeQRzQQ5HKSFC9Do0hTupfkdMM1UMG2Pm+sKPG+hvA1nfeeeeobdu2+Q499FAbhsh/Zs6cyciRI2OGYfzHMIwhSKWiHZEd/78hOzy/Yk+I0A/IA/sJcrQ8Ggld+Yjq5ESrUD2kgVkPsVjsXJJXNErGb0hnzJrlImLIhDsV6ILsFh+IJCduyM3qrFA9pIEFekgXP3Lk/19k8+CfyIv6fZypqqR6SAMb9HAoElo2AZk74idHdoakpoPqIQ0y1ENX5D7/CwlBvgs4HXnmnXwHHIE4JpC4uIoPOeEw51GqHtLA7veFXc2Y3gNWLFiwYODq1auNnj17+nw+zUmJ88gjjzB+/HgMw7jNMIzhSALqaiRRMIA8MLsjzsOZVV9bSPKOzNnyDRLD9guye3gNciz5IbUXnLmgekhBAj1k+5CnCivaiJwmfYJo6krkJOIjnC+zqXpIgYV6qIu+yAnCJUio2nHI4qHSpvGSoXpIgcV6OIRqB+F35N6Pwn0HwYzqIQVp6sGPNMW7F7nXMaQK4jBkk8iOEOe6eA/JfdqH2hU3w8ALSJRDou+pHpLgxPvCzq6tC4DPFy1adNKiRYs4/PDD/aWlpTYO5322bdvGTTfdFHvssccMJDbvVtOvFyKVJZogD1H8QWqM9Ey4tOq/F2PtLkAMqYV9PzJ5XF41lg9ZRFoV0656qEEderCLb5BwpABS0eQE5N7YffRcE9VDDRzUwz5Uh5ssRMqaPoD1p4mZoHqogcV6OAApdXknUirxEiS8zImY9GxQPdQgTT2UInlpTyGJycuQd/qVSC6RXZsO6TILOVVoxPbrzwiyUZGs6IbqoQZOrh+ccMt6BIPB55o1a9Z04sSJJZ06dXJgSO+xfPlyrrjiisjy5cu3RiKR04DnE3zseGRHLxX3IhOAXeyAnCz8DTmS/gcSw2iVw6B6IG092M2eiJ76IHGrV2BPbkwqVA84podWwBik/8YC4Gok4d1LqB6wVA/7I6GlJyEhiOORndt8QfVAWnpojiwWLwEaAtOQheNXzlqakjIkYf5EZLOzCeIsRBGn9c40rqF6wPn1g50nCnF+iMVij23durXbc8891660tNTXuXNniuno6LXXXuOiiy6KrF279qtIJHIkUnosEYuB/sDO1D6aiyDhAWdjb6jIFiTZ+d9Aa+QlMwRxGqyYdFQP6evBblYD/0F2nS6q+vkN6c/gFKoH+/XQAElUnobEKI9E7rWXwk3iFLUe1q5dy5w5c6zQQyeknO3dyEnRxcgGkFdPEJJR1HqAOueH9ojz/zhyavQIEuc/FZnLvcIuwMtIvsQJiH1nIeucb5Bw2HROO1QPLqwfnHAUACpisdiThmFsmz9//pELFy6MdenSxd+wYUOHhneHtWvXMm7cOOOee+4hFotNiUajf0HiQlPxNbU77kaQMKD+WJ+nkIwNiGPyDLAfMhn1Qzo9f5/jtVUP6evBCT5DmvM1R06Q+gAf4NyLpij1sGjRIu644w5jypQpdunBj1S6eh6pVz4ROfafj/N5KZlQlHpYu3Ytw4YNM5544glisdi90Wh0CJnrYT/EQbgH2an9GxJ2YndXXTspWj2keF/0BO5AToSbIydFQ4H/IfloXqIH0u9nG/Ju+QT4serneOSEIZMyvKoHh9cPTjkKIC+mOcAbv/zyS++nnnqqUTAY9Hfq1IlAwEkz7CcWi/Hss89yySWXRL7++uvfY7HYqYZh3E164TvfIw20dkXuTxjYjOwKziLzzpe58jviLLwMHIl0ee6JhC7kYovqwb2eBonYitzjF5GJeyxSU38OziS3Fp0errnmmuiiRYtiwGWGYYzDWj30RfqmnIvUSz8BeAn7myhZRdHp4ZJLLomsWrVqvWEYZYZhRIFXqN3gLhn7IqEb/0R2Zv9W9fOlLUY7T1Hqocb7wkASlKciFarWIeGDlyBVypzaRMyE85H5Zw6y0Wnux7IA2Q3PJvxR9eDg+sGt85oQcHEgELi1ZcuWgdGjR4d69OjhkinWsmjRIsaNGxdZuHCh3+fz3RuLxUaTefJxN6TykIEcyx2NxPZ1QyaKuVbanCF9gduR2NfnkOPs5TleU/XgLfzAech9Xo0kt7/k4PjFpIdBiEN2IfCYBUPsi3Tk/jPi9I1ATgHzmWLSww3IfNoY2Rk+B6lMlYyOSNWiU5HQ0HFVn/fyiVGuFJMeRiP38hzkWd4F2TAcjzgHXiWIVDC6BpmPrsO+ROpi04Pj6we3A7tah0Kh28Ph8CkHHHBA9Lzzzgv07t3bZZOy45tvvuGRRx6Jzpo1yx8IBOZFIpELgC9yuOSzwMFAd6R8aSnwJFIB6SRk99ct/MBgJFmqBXLMPYHcm7apHrxFS+S+noEsOofjXKdWKA49PIwsAkDijC9CThAzZRdkl/Fc5Gj/KqTbeyFRDHoA+D9kfo2Xyn4CcSTNVanMDsIipIJZoTsINSl0PfyG3Pe/IYvhJ5FTI6/nmeyI5EN1R3IPnnNo3ELXg2vrB7cdhThHBYPBsZFIpGfnzp0jF154YTBfPMLPP/+c++67LzpnzpxAKBT6IhwOjwVmkPuE3QHxwM1ddANI05TTkcXbtBzHyJUSJCHppqr/noAkz23J8bqqB29xJBILuztyyjAeZ2vtF7IeTkNCCfxI6MD3wCDSTygvR5yCa5CFxfWIw5HPequLQtYDyJz6MNUFLSKILoYgc+u1iIPwNbJb+x/cL3vpJoWmh2VIBbqTkVK29yPv1TXuWZo2nYCZyInCiUjpdacpND24vn7wiqMQp2cwGBwTiUT67rnnnuHBgweHjj32WJo2bVr3Nx1k06ZNvPbaa0yfPj2yYMGCYCgU+rDqhv4P+2+oD1msXY5UsviXzeOlQzkSJ3kdclx+E1J9Idd4aNWDdwghR99jkVOFS5AENScpRD20RHpYxOfiSNVnrgYmpxgmhFRAMzvpk3GnkZJbFKIeQE5pf2b793OUasdhEXK/n8BbeU5uk+962Ig4/P2R3eN7kU2EfHmmByCa/Bw5EXM6n7Im+a4Hz6wfvOYoxDnQ7/cP9/l8QwzDqNezZ8/Y8ccfH+zVqxduNdmIRqO89957vPDCC8bs2bONaDQa9fv9L0QikSm4U4t8JHALslAY68L4iWiG7G5ejuyK3IA1x+GqB++wBxJq9idkJ/MqnH8hFJoeliD/rnHiz8uTwAXUDkXqC0xCupw+ipQw9lIpRKcpND2ANMLbN8GfG8BbyInCr9ZZXFDkkx7uRzYLrkHu93uIE/giHlkkpoEPsX88Uj1vON5KrM4nPXhy/eBVRyFOPeC4YDB4TjQa7RcKhYzOnTvTrVu3QNeuXTnwwAMJBoO2Df7jjz8yb9485s6dG33vvfdiFRUVoWAw+FkkEnkU8ZzdLm15MbJom4Iszr0yseyOnC6ch5R1HYU14lc9eIfjEN01RCph3YPz4Q+Food7gGHIyYCZCOJwn4hUrzkQKYl4BOKAX8v2oYnFTqHoAaR60QXU7qcT50Ok7KSXFmReI6Eedt9990CHDh0YMmSIm3p4AZlDrwZ2QioD3U7+5bGVI0UYjkdOnO9x1ZrUFNL84ChedxTMtAT6+/3+o/x+/9GRSGTH+vXrR7p27epr3759oE2bNrRp04Z27dqxww47ZHTh9evXs3z5cpYtWxb/iX300UfRjRs3hoLB4AbDMN6IRqOzkcovXmtSdArSHO0pJJHRS+UP90NOFYYgTdyuAT616Nq26GHlypVUVFSwYcOGfNWDkzRAYuKvRHoxXIg4hm6QsR62bNnCzz//zB577JHywg7MDyciCX/J5uPfkOIFpyH9La5Cdh6V5OTr+yK+yXIutcuXG4hGnkPKTuZaPKKYiOvhaMMwBhuGEXBJDz7gMuT+RpFF9u1IT4F8Y1ckfn534C94cCc8Bfk6P7hCPjkKNekI9PH7/YcGg8FO0Wi0fTQarQ9Qr169SJMmTaJlZWWUlZX5ysvL/Y0aNQoCbNy4MbJ58+ZYRUWFsWnTJjZs2BCoqKgIAvj9/spQKPRdOBxeGIvF5gNvIAsgryeK9UcSm18H/or3Yhr7ImFSXZGXnB07oZboYc2aNcHKysoA5LUenOYAZAf04Kr/vR73S8DWqYdIJBLw+/2+du3aGS7PD02QMrQ1d49jSMWzZkheyGiKr7KNVXj9fbEb4nBfgNzz25AFZIOq34eR+34ZktyqZMc/EEdsDLDGQT10Q+7dqUhi+gPIfUy3T4bX6Im8y39FThOWu2pN7nh9fnCVfHYUEtEaidtth5ToaogcjZUDjao+s8n0s77qZynSufJ78vcl3B2pr/w58uC6vVCriQ8p6/oPoA0SW30D2zdgsZps9HAMcqR/CNIQJl/14DQ+pBLXnciiZhSSiOclaurhKmTSfgH354fPkN4kIP9+PqSy1BZkwXgX0tlUsQ4vvC/MDsKvSJx3vBDE80iCKEhzqbZIFZkTchyzWDkY6T3gR5yFW2r83mo9+JFNvJHIO+UTpODAk3jr5D9ThiFhp/9FCipkU845H/DC/KAolrMfUkHlQ2QX0ouEkInmZ+ThupXqh84LfIE83De7bUiesgPyMowiVZH2dtecpByO3Oco8hJwm9sQW2KIcxBFnGgv2KZYz67Ic7IF2Y0dhpSUNHMhcjr8N8RxPBxZYJ6DkimlyOItgjjcd9o4Vj1gKFK+NopsRPS1cTynCCJlWmPIeztZ/oyiKB6nLVJF5SukCZNXKUN2WtYiMdgjkcncTcqoLk+5CQkJUbKjJ+J0bUGqctVz1ZraPI3s3EeRPB+3uYxqR2EacBRQAfzdTaMUy2mOLLK2IOFkl5F83muFhESYuR2ZmzrYZWCBcgfV4VtR7DntbI7Mdb8jDt5UYB8bxnGDZkjozEYkp0pRlDynJRLKsBzY011T6mQHtn9xDqN2Ep9T9EZeJAbyUrneJTsKhSCyENoAfIuEdXmBFlQvGsJIgzK36IA4BjFgLpLHE+cqZPdz/wTfU/KLuINQgYQkXEZ2znMpEhL5Hu7Nk/nGoYhzYJh+XrHw+h2Q06EKpFT0WLx7op8NByBJt0uQqAVFUQqEpsjC41egi8u2pMMuSIJXBKkhPsQFG65D4sLjL5P1SFyikhutkN01AzmG39Vdc7iBakfBQE61nD5GjzvIW5EGWon07gfeQSqFhZwzTbGQnah2EH4gewfBTEf0tCldypBFrvl5N0i/83kqeiLzWQzZCLkMqG/Bdb3EEOQE621Ey4qiFBgNkJ2TdUh8az6wD9U7rHOQydgpZrH9zlMYCYlSrGEAkui1Cfl3dWNHNIg4z0aNnwMdGr8EWVDEQ+4uo3Zsupk9kUXhDfabplhI3EHYjOSajMTa8LsRyPx0sIXXLETuobaTYCA5ctkQQhbP86uuM6fq/xfa6Y4P0WwM2cDTjQpFKWBKkIX3VvIrtvAQpAOpAbwGdLJ5PB+yeKv5QlmHVDlQrKE+cjS/FdkpP9Th8QcjLz/zPd6G/WFmPmRB8R2yeMwkif8KZLHTzR7TFAtpRm0HwY5dZj9SLOBbdH5KRk9qP+vxny0ZXqsh4tR/T3WC8iGWWeotyoHpyBx9rsu2KIriEAHgX8hi4yx3TcmYvkhMbhjZ2Whl0zh7kviFEka6XivW0gE57YohYUlOxfS+Q3XCuvnnQxvHPBSJKY8iTvvuGX7fjxz9L6B292bFG+yIOMDrkTh1uxwEM62R/hv32jxOPlKO5OglcxQM0rs/LZH7uhbJtZpM5s9vPrEHEvr7G9DLZVsURXEYHzABmTivcNmWTPFTezfW6opEZ1E74S3+8xuFF3vqFYYgoUCrkUR2O3u77EPyhYMdZVL3QhyD+KnYATlcqy1ScWRs7mYpFhJ3ENZRXb2tzMHx4ydk/R0cMx9ogPSbuBs5dYk/4+YctFS5Ul2QDYww0gBvLJL3V8gcgTi5n1LYzpCiKHUQjzu81W1DsqAEWUyuRBaWVu7a3U/iWNb4n11k0ThKbZogO3URZMd/X5vGuYfku4sG1pVJ3RH5+4SBL6lumpUrf6u6plP5FEpydmB7B2Es7vWDeQKZE3d2afx84FPEWX+M6hylmkU+fMgJ9gtVv1+A9EMohvj8YYgT9X846+gqiuJRzkQWHFPIz6Yp5YiTsAGpJJKoWVGmxButGUjy6GokNOY+pBpSvxyvr9RNF2Ae8sKajPWx1w8CryPdbVcgSdVbqL7vudZWj/cGWQf8iPWlfv1I3s6XeK8vRbHQkOr+L7/jroMQpzESZvNfl+3wKk2QTYhBpj/bk+pwx1LEIfiS6gTl47D3dNMrlAIPI5uHYymOv7OiKGlyArJI+g/5u2MSryxiLjGZ7UR3LFIjujFSy95AQkcUZ/EjL+3fkcW2XWVyT0DucahqzKZIzHc2xEPjllHdbdyusrptEQd5nE3XVxKTyEFo7KZBNYh3bT7bbUM8yIlI2FHNPKhmyD39CSloMJXi6hOwE7LxsAE43l1TFEXxKn2QSeIF8jsGvw2S6BxFdqR753i9Zsgism+O11GypwXy4o4h+mxj8fXPRPJdcqUvEtYQ7/bawoJr1sUlyIngQQ6MVezETy/XIHPlrXjLQTBzB9q1ORFT2L5YwR7IieVm5PRvMtlvEuQrnZFTqG+p3f1bURRlOw5CYmzfxrsvwHQ5EAktiSePds7hWpuAc6wwSsmJXkhIQAWyi1tq0XX/Rva11KG634dT5XvN+JCwuK/QECS7iDsIq6l2EKwuoGA12rU5MYuQ+9cNceYjSD+Xy5Ck52Ljr4iT9AqFn6CtKIpFdERi/T8GmrtsixX0BT6iuhxluyyu8TVaYcYrhJCX+iZgMdac9FyPLCAypRXVHcQ/Ao60wJZsaIMsYMe7NH6h0gDR2q9UOwj5tJjaF+3abGYXxJmP5x98hIQ25prTlo/4kHdavIlaMf4bKIqSA22Ab5ASpNksrL1GvMHVN0j86QNkVhXkVSTJS/EO7YCXkBf+NHJzau9AwtTSpQG1E+jdLgRwIeKwdHfZjkLA7CBsJP8cBDPatVlOhIYhpU0NYBbQw1WL3KUhkuy+lfzrpaQoiofYGYm3/hlnQynsJIS8MH6megGQTpWSh5CQEsV7HIfE165FFnfZhFk8iBy910U8uTqun7F4J5/HB7yMnIx4xaZ8I+4g/EL1/LCDqxblTrxr8yKKr9TlzsgzuhpZFH8HzHfTIA/QHjlR+QndVFAUxQKaIOXhVlNYLerjpSvXUt0YKVW8+xgkzEXxJmXIgmAbEjKX6e7ptKqfVPQFPkPKtT6AN8PyWiOanuC2IXlGKdUbCJuQhNZC6kMQ79o8xW1DHGJ/5BndgvSUGIv0M/kBGO2eWa5zDJKI/wmwm8u2KIpSQJQhR7UbgaNdtsVqdkB2Dbcgu9LJQkjOrvqM1pX2Nnshu6dRZKGQbk37V5BThUTsS3WI0wt4v4rM+cjfv6fbhuQB8aaNP1HtIDhRqcoNiqFrc0/kGY0hYaaXUX26thfyDB/qjmmuMwwJQXsSPXFUFMUGSoCnkOPbwS7bYge7Up2U+gW16/UfhbxkdnLYLiVzfEh40CokhGRoGt+ZB9xZ4892oVoTHwBHWGijnfgQx/5rdEGQDLODsJnCdhDMPInssHvxNCxbSpD5+gNSN0i7GMkpytc+QdlSCjyKzGMjXbZFUZQCxwdMQiacc122xS7MZS7nUL0r26Hqz7q5ZJeSOU2RBWAUeBO5t8n4Crih6r/LkVCFCqRj81Dy7ySpNRJicIfbhniMuIPwI7Lp8QDQ0lWLnKUxoukZbhtiAY2QE4PvkXDAaaSOuX8OeN4Bu7xEK2QTZD3iPCmKojjCSORo9yq3DbGRQ5AulfFwk/2Qv/OJLtqkZMeBSIOlSsRxSFQr/SfgCmQR+SuyyB5JfvclOBdxkvLlJMRO4g7CD1RXPWvlqkXucTiii3zt2twGCRddh5wQTKbuePsAkqNxma2WeYuuiBP1Dak3SRRFUWzhUuRlc6vbhthMX6RpURjZYb4h9ccVjxJEFgnrkconx9b4/RZklzmeqFwoIWYvIX/fcrcNcYkQciL0HdUOQrF13U1EPnZt7oo0SAsjSedjSb/p3YHIps9+tljmPU5B3lf/w/uNARVFKWBORybt+3C/hryd+JEY2K3IQjIfurIqiWmFLDbiJ0UDkC7kBtLBdg/3TLOFVsjpyCS3DXGYuIOwBHUQEpEvXZv9SMjMa8gz+ilyXzPNMxiJ5GbkWwhhpgSQ95OBnLR4+d4qilIkHIfsxj5F4SeJzUA6ea5EjrFHosmi+cpfkTKiBhJ2ZAB9XLXIPs5CTv96uWyHE8QdhG8Rp34qhdEw0g72Rebu69w2JAGlyH38Cgn5fI3cYuxfBZ6wwC4v0wjJwdhCegUcFEVRHKM3EtLxOoUd4jAJSQwrp3ZXXt25yQ+aUl0O9xskAXIr4ijka8x2OkwHllK4z2f81O8bqh2EQjsdsoMr8VbX5p2QufVn5CRoKuLQ5EIJEmZ1To7X8TIdkIZ6PwIHuWyLoihKQroh5SjnI41tCpERyAsszk7IonMbsvM1hMI/2s5X4h25VwG/s32DveMQRyGGLEwKJT/BTEvkFOxutw2xmLiDsBh1ELLBK12b2yOhMpuRBpi3Yl2y+ZHI893Gout5jWOR09G5FEeJX0VR8pi9kSoLCynMeOCTkBCOkhp/vieyMx1DThx6/397dx6n5bz/cfx1r9MybYoSLVOJQhRKimxxLEWIkI6DX9lPliNLSNKR7eDkkKUcBwlJWQ6dEKKSpWQpVJPQotRo2uZert8fn0ZTzTTbfd/Xdd/3+/l49JDmnuv6zHy+131fn+u7pTYsKUcvbCjKFuxmpN4OX++B3Uj0x9rvb9jE50ybd3MB1kYzYdPE4gJhAdsKhDauRpS+indt/qcL5+6OvXdGsQnnfyXxBcsIbK5KJvor9pn0LBoGK/umQWQAACAASURBVCJpojn24b2YzPvg7ozdUJY15vkwbPiVg42pPThFcUnpugAfYDfHLwJ5ZbyuN5azHGzp1LuxG5cPgQOTH2ZKTQSWAHXcDqSKiguEb7EbpBdJr5V7vOo8Urdrc/EE5ZnYdfcpNqY+WcM3Z2KT2TNJDeDfaBM1EUlTu2FP1pcDHVyOJZGaYB9sR5fzuuOBz9h2I6PJlKnVAnvCHMeGVXQq5/UXYHMWSjoYu8GIYL0Q6XpjvaPdseFXj7gdSCUV31zOZdt11dbViDJPsndtzsWegOdjOXwNOCJJ5ypWB+txOjvJ50mlvbBdqNdgnzUiImkpF3uq/hvJ/zBIFR828bUiK0r4sCefxUNexgCNkxeaYAXq3ViOvsV+/xVxJbbJ2o58WK5/xVZGypSVRIqfHp/gdiAV4MMKhC/YViDs62pEmStZuzY3wfY8+A1Yj70XpiqHvbC2ninzjo7AHsAtQNeBiGSAHGyoQyFwosuxJMoPwNBKvL54Eu0v2Ifk3dgydpI4YexJ5Vrspv6v2AZrFXULtlpOWXbDbm7i2NCyTPiAfgl7suvVnpLiAuFzthUI+7kaUXYo3rX5wgQc6yDsutmEFeLDsGsplR7EisxMcD72u3yDnedZiYikrQDwFPZUPRO6f9+lauNda2NjSddhN7MlV92RqinutVmErZZS1SJsFDCnAq87CpuovxG76Unn/DXChpk85nYgOyguEIqH7r2G5vqk2v3YQ42qzjHrjuUtDnyJPSipkZjQKm0+tgt1OiveRC2+9b+ZtsiCiAg+7MMnin1opLOngf9W4/sbsm0d/3zs96E3/srriu0qW/y0uUU1jvUY1lNQESGsx2I9NqwsHYbvlOUc7ObjT24HstXx2MTWOHaj2dHdcLJWDjAPmEHFJxiHsaF587F5XDOwgs/N5aIbY23pJBdjqK7dsCG8m7BV2UREMtoQ7I17mMtxVMdw7KlydTXDeiai2IdrRcfTZ7t9scKgeGWpgxJwzPHYELnK2AsbvuNgN7V7JyAON7yIbdJU38UYjsd6dIoLhPImn0vyFe/afFM5r6uLFc7LsEnDL+KdDb/Ow2JK100G98XmIiwDDnU5FhGRlLkcewr8EOm5Odn/YU+TE6U929/4HpLAY2eShlibiQBfA6cm8NhvAmOr+L29sOVG12E3TOm2Q3cjbPz4Ey6c+3hs9Ra1fW+6nrJ3bc7DrsdCoGDr35ulLrQKeQpbHjkdnYy9p8xAi2CISBYqftLzbyo36dQLTsRubBok+LhdgffZtua/1oY3tdg2t+MnbKhWom/GPwL+UY3vr4X1km3GJt8enoCYUuk0UjtE43hsB/fiAkFPS72ptF2bD8GWHo5gBfIQ3O2N2pUlwO1uB1FJPux3GsN6nHfc3FNEJGucgk0KfRX3JrpVRXvsBicRQ15Kczw2PrgI+6DYM0nn8brijbWWYE8t7yZ5K/R8RWKGw7XFbnxj2M1UwwQcM1XGY0vAJroALqk7MJ1tBYJXhqhI2Yp3bX4dy5mDFcMD8PZDnjZYrN3dDqQSagD/wYowbaImIoItxbcOW0nIq8s07igX+wDqlcRzFN8kL2bbaj5efWqXDMexbd38Z7B12JNpGXBNAo/XF1tRaAV2Q5UOQ+waYuuzV3UI1q50x67x4gKhtKEs4j05WPv9GcvdFyT3fS+RBmEPGNLlifze2Dyd1cCxLsciIuIpB2AfRHOw8dLpYA1wRQrOE8aG2qzces4hpFfvS2W1Y/v5Ggem6Ly/Axcl+Jj1sXHbUWxI2f4JPn4y9MZ+96cn6HjdsaErxfnskqDjSnLtgfWwrcaG0z2Drd2fzF2bE+1FbO5ROuiGPVT4Epv7ISIiO2iFbWT2DemxeswX2FP+VKmDFQm/Az+SnHH6bmrKthWgPgWOSeG5/dj4/DOTdPxO2Hj8Iqxw8PoKLM9imwNWZ2Os7thys8XLZB5d/bAkBfbB2uhGYBX2Htd069fqk5xdm5PBh8V/nduBVMBAbI+h19BGnCIiu7Qn9kQlH+9P5J0MPO/CeffCbqgjWFHVl/QY1lKW4k3ofseG/7ixp0R97Ib2+CSew4/9bAXYz5msoiQR6mOTxv9dhe89ArvhKS4QUlnwSdWV3CDtB2z1rlqlvO4obDjgn1MXWpUcTHLnkSVCEG2iJiJSaQ2Aj7FuWC/vxvpP4EMXz1+8l0AcmAn0cDGWqvBjY59/wZaaHQbUdCmWFthNRSrGze+JDeMo3nuhOpvEJdOpWIx9Kvj6rmxfIGiMtff5sfkGs9iWt76U31P5ANXbtTkVrsOGTXn15rshNiRvPd5+aCAi4km1gbeBtXh3xYobsG54tx3G9mPAvfwErdiOqzq5Pea5A/b72zeF5zwa6xHagBVJXpxw+QzlD0E6nO0LhONSEJdUTx2sx2Ap1jvwGlboVVRVdm1OtTeBCW4HUYYO2CIVP6KNBUVEqiyM7Xq7Adt4xmvOxcbTe2V5wOOBz7AP/hexOR9esz82IbL4abpXhpcdicWU7JWVdhTChl1tAhbivZvsetgwqWdL+VoXthUIH5E+K+Fksz2xovQ37En2GGw536qo6K7NbghjP99AtwMpxanY8MMPcP8BiYhI2gtgu8VGgAvdDWUn3bCbpOZuB1KCDxs68D02Oc4LT+vBJqcXT1T+BBvn7CWnYLl0a+hTa+wJaBx7iu+FnBUr/t0UD4/owLYhbx+jAiEdHIy1qyJs+dthVG+ierHiXZu9thdGceHf2u1ASthxE7WQu+GIiGQOH3APdmMy2OVYSmqGdzfzCWFP05ZjT9aSuVHZruRiNyUbsWEOXt1PoHiXcLf1wn5Pv2FDQ7wyvnocFtNkts2JUYHgbT6sl7G412ce9p6QyKWVi3dt/gb3iuzSDMMWxPCKXGAiVlRd5XIsIgnhxQ9ykSHA37Gi4UaXYwGbjLYCeARbKjWXbctebsQ2+inExngvwPZASLXawJXY8IAi4H7gQay3IZmC2J4Ew7FhAKOwJRc3J/m8u1IfG2bRHPu9lMxXJ2x420W4my+w2P6G5Ww+cBm2v4hbDsTyeDq2MeJA4GXs5rM6dpUPr1w/6SgM9MPmUO2PDQsbhe2qXN2clWZvbKW6Z4GrE3jc6rSPD7GhfJckMJ6qaga8iv0cfbFdyUVEJEkuxJ7K/JPUPm2tBfQE/h4KhWaEQqE12IeuAzjhcDhap06doiZNmmxu0qTJ5rp1627JycmJlnxNMBgsCIfDn2ArhvQitetlN8R6FTYBS0juEqTHYze4xROVd0/SeXalUvnKzc0tCoVCMbyTL7AhPh9h7f0hF85/ANuGGM3DioU4cFYVjpXu1086qIf1Qv2EPQh4htRtVng+1jaqOpcske3jn9g1k+jNE6viSGyDurlAS3dDEUks9SiIl50OjMeeal6EfSgkQz2gbygU+nMsFjs8Ho8HmzVrVtSlS5dwq1atyMvLo2XLljRt2hS/v/R7bsdxWLFiBfn5+eTn57NkyRI++eSTosWLF4eBeDAY/CISifxn68+zKkk/R0nNgVuAi7FekBuxoQOJcChwHzb/4GXsifiiBB27IjIxXz7gAuz3GsXy9UySz7k/1nt3PvA1cCfbehCeBE7DioiV5RwnE/PhRa2wAuESrI08DdyLFQypNB679jtQsd6fpLSPWbNmFeXn53uhfQwERmO9CRdivSAiGUOFgnjdsdgb8HTgHOxJeaL0CAQCVziOc1ogEAgcd9xxvh49evg7d+7MHnskZo7p2rVrmTNnDh988IEzderU+ObNm32BQGBqNBp9hG2rAiVTe2wcb19s99wbsRWTqqIZMBS7UfkEGzYzo/ohVlg25Gs34HZsGNn7wOXYcItEao+1g/OAb7EehB2HGNXFeou+wAr20mRDPrzgEKxAOA9bZnMM8Bi2oo4b6mM9T5+z6703Mr19BIF/AFdgw2RvSvL5RFyhQkHSwWHAf4GvgN7Yzr7VcVIoFLo9Eol06dChQ/TMM88MnnDCCeTm5pb/ndWwZcsW3nnnHV599dXozJkzg6FQ6JtIJHIHdpMWT+rJbe30UdiE7Jex3obvK/i9DbAnz3/FblSGkpix6xWVjfnqDvwL2+/hH1ixV915H+2wm5nzsOLjHmy8eVk/y3HYfh39sKFJxbIxH6nmx1ahuhHbAftzbFja81hvgtuOAt7Denp33NU7G9pHI2xJ70OxnsBXE3x8Ec9QoSDpoj0wFZtUfBLwaxWOcWgoFHo8Eol07NatW2zQoEGBjh07JjTIivruu+94/PHH41OnTvUFg8EfIpHIZSRuaNCuHI9NdG6HrXAzDFsxqTQh4C/YkJQANswhFROki2V7voLY08o7seEUVwJvVeE4rbBC72Js4uco4Dls+cbyjAHOwIYgNcvyfKRCLlbIXYvtPfImViBMczOoMjwA/B/QEfiB7LleD8IKgxg2PO/rBB1XxJNUKEg6aYk94YwCJ2JPtyuigd/vH+k4zqCOHTtGb7zxxlC7du2SFWOlLF26lPvuuy82ffr0QCAQeDEWi12Dre6RTH5srfx7sAnIo7FVpkoOZeiF3Qg0x4Y53EbqhjooX9trik1QvwBb0eZybHO08uRhT6QvAr6jcgVCsTrYjVDE5/PlKR9J0xhb9epKrFh4ERhJ4oedJVIONgRxk9/vn+s4zsAsaB9nYw9YPsUm+1flgZVIWlGhIOmmCfZUdXesWPiqnNf3DAaDL+Tm5tYZMmRI6JRTTsHn816z/+CDD7jzzjsjv/76ayQWi10MvJCC04axyXcjsOLhXmxjrbvYNkRpCLZ6UqooX2U7BVvpZQ+sl+F+Sh+G0hIbYnQRNrzsbipfIBTrGQgEXq5Zs2atW265Jah8JFxbrNdoIDak8lGscF/tZlCVMMjn842uW7euc+ONN2by9erDlqH9O7Yx6JUkb3ENEU8JuB2ASCUVYm/yJ2OTaT+g9FU/gsBwn8/3+Iknnljj8ccfDx544IGe/BADaNGiBeecc05g/fr1ofnz558VCAT2dhxnGskdjxzDJjY/iRVgN2DDUzZhv9+HsPX0U0H5Kt/3wONYUXcrNiRoHtvafwusl2gcNob6ZmxoyFwqP5+kZD7CTz75ZED5SKju2L4sD2O5Gon1GE0jPVbNKW4fo/70pz/5Mvx6zQUmYNfSIKxIz7Q5MSJl8uZVLVK+WtgOmN2xG6b/lfhag1AoNAXoevPNNwfOOqsqy8G7Z9q0adxyyy3RSCTyXSQSOZHkLn+4G1YgDMaGs+QDR2NDVYZhE/aSTfmqvH2wJ889gUnYMpUDsGEVdwNjqfpNsvKRHCFsBam/YQs0fIQV4xNJrxvPbGofrbFdyvfAVo57PxUxiniJCgVJZ2FsrfnTsbXgJwJ7hUKhafXq1Ws9ZsyYUNu2bV0NsKp+/vlnLrvssuiyZct+jUajx2HLWCZSGBsTPQy7oRyBPeGMYivt3ImNwZ2NDT/6IMHnL6Z8VV1zrFg4FesxeJ7q7zeifCReXWxRgOuAvbAJyiOwayvdZFP7KN4n5mds0nJF58SJZJRU7ngrkmhFWIHwNNY1fFMwGPxkr732av3CCy+k7YcYwF577cV//vOfYPv27XcPBoMzgS4JOrQPezL2LTbcYQz21Owhtj2BXohN2jscGwbxPtZjc1CCYijWVvmqkmZYvhZim15dgy2lei62sssBVTyu8pFYLbHenaVY4T0Jm2Dei/QsErKpfQzEhoG9A3RDRYJkMRUKku5i2JPxMT6f77b99ttvj2effTbUuHFjt+Oqtnr16vHUU08Fu3btmhsIBN4BDq7mIbtiG6S9gM1NKN54q6x9KT7B1tLvCTTE1nJ/EbvZqa4WwWDwQ+WrUvbGCoTvsF60G7Hen4eAq7DhLGFsk7SHsBWLKkr5SJyOWE/n98CfsVy0YNs+JOkoW9pHDvAUttLbSGyp2nSYMyKSNBp6JJmgUSgUmtWsWbPm//nPf0J169Z1O56EikQiXH755dE5c+asj8Vih2M3ipVRPJSoeHfm67FJsJXhw4Yi/R17ov00NqF2VSWPA8pXZe2Brav/V+z3/QB2I1PafhZ+oP/W12zGJjQ/U87xlY/q82O7yP8VGwo2F9sobzzpvzpOtrSPDbFYbAnWw3oBNjdBJOupUJB0VysUCs1o2LDhAePHjw81atTI7XiSorCwkAsvvDC6ePHinyORyKFUbPnEhtj+B5djN0dDsHX4q6N4E7Y7sNVAHsGWU11fwe9XviquuEC4euv3348NFavIDs1NsBWQ+gNvYD0O+aW8TvmonhzgHOzaao9NUB6FXWep2rk8mbKmfZx33nmx/Pz8qOM4RwOz3I5JxCs09EjSmt/vHx0Ohw986qmnMvZDDCA3N5cxY8YEGzRo0DQYDD7Hrq/dWtiNyyJsY7UrsLHs1S0SwJ6OPg60wSZkXrr1PEOwYS+7pHxVyO7Y2PZ8thVlbbEhLBUpEsB2MB8AHIPtzPwNNnE9p+SLlI8q2x1r84uxdfU/w+aGdAdeIzOKhKxqH+PGjQvsvvvu/mAweAe6NxL5g/ZRkHR2juM4d913333+gw9O1fBj99SqVYtOnToFXnnllTzHcTZjTy9L8mPDg14FTsImuJ4DzCTxNy6Rred/AitMbsLG866k7BVmlK9da4T1AI0H9seKhXOB6VR9qdOlWI5+B4ZiQyoWYDe4ykfltcYKrmeAI7Bcnb31/zNtl161DxFRoSBpa59AIPBW//79g/3798+aIXSNGzemZs2avpkzZx6LrURUvAb4cdhSfldiPQe9sIKhKMkhbcLmPTyDLdd5FzZGezHb7+isfG2fr5IaYXtZjMd6fhJRIJQUx1bZmYCt7nIHcHAgELi+f//+AeWjQroD92HFd2Nsomt/YAoVH3aXTnS9Vq59iGSsrHkDkMwSDAbfzcvL6z5hwoRQKBRyO5yUchyHSy+9NDZnzpwfIpFIX2xScfFE5WuB+S6Gtz9we4l4hgCfK19/5OtAtk1ubYjNHbgGm5h8P/BPkr/Kyhk+n29sq1atar300kvKR9mTjf3AKVhvWVdseNHDwHPYamsZS9drhdqHSFbQODxJR/1isdjRt99+e9Z9iAH4fD6GDh0aiMfjbbDVVVphY9F74m6RAPA1NhTjWGyjqTnAm8rX0IDjOG2wickNseEri7D5IyOxNfdHkZqlGMNA3TvuuEP5sHzsKBdbR/9brFduDdajcCjWc5bRRQJ6fy2vfYhkFQ09knRTJxgMvtWnT5+a/fr1y9oesXr16uE4jv+zzz6LOI7TDfjS7Zh2kI+tR74oEAhc2qdPn7Dy5fg///zzHo7jXI2ttX83tmHge6TuqaWuH7bLx1GO4/wbm8PRBFs6eDzQG5gK9MN6eZa5FmxqqX1QZvsQyUrqUZB0c1UoFGowePDgrG+7F110EY0aNfL5/f6b3Y6lDA7QPBwO11K+LF8NGzb0+3y+T7FeoHuBDSkOQ9fPVlvzEfD7/Q9gy84uwTZv/Ce2ud0AbPfrbKL2sVWJ9nGL27GIuCnr3wwkrdQKBoPXX3DBBcH69eu7HYvrcnJyGDRoUAi4GGjqdjylUL5KKM6Xz+frhg3LSjXlo4TifDiOcxY2bO9GbAjYMGy4UbZR+yghDd5fRVJChYKkk0F+v79u//793Y7DM04//XS2fqhf63YspVC+duByvpSPHWzNRxR4BdunYpPLIblJ7WMHHn9/FUkJFQqSLvzBYPBvZ599dqBBgwZux+IZ4XCYiy++OBQIBC4H6rgdTwnKVylczJfyUYpwOMwll1zixesn1dQ+SuHh91eRlFGhIOni2Gg0uufZZ5/tdhyec9ppp+Hz+XKAM9yOpQTlqwwu5Uv5KINHr59UU/sog9qHZDsVCpIW/H7/gHbt2kXy8vLcDsVz6tWrR48ePZxgMPgXt2MppnyVzY18KR9l8+L1k2pqH2VT+5Bsp0JB0kFtn893Vp8+fbJvUe8K6t27dyAWix0FNHM7FpSvcqU4X8pHOTx2/aSa2kc5srx9SJZToSDpoEcsFqt5wgknuB2HZx155JGEw+E4cJLbsaB8lSvF+VI+yuGx6yfV1D7KkeXtQ7KcCgVJB8e2bNmyqGHDhm7H4VmhUIhDDjkEv99/nNuxoHyVK8X5Uj7K4bHrJ9XUPsqR5e1DspwKBfG8cDh8Yrdu3cLJOn48HufBBx/klFNO4ZBDDuGyyy4r87Uffvghp556KgcddNAujzl06FA6derEiSeeyN13382WLVsSHfZOunTpEvD7/T0BV3dUdTtfv//+Oy+++CIXX3wx3bp149BDD+WUU05hyJAhLFxY+v5ZmZwvt/PhOA5ffPEFd911F6eeeiqdOnXiqKOOYsCAAbz++us4jrPTMTM5H17jdvsozVVXXcWBBx7ImDFjSv262odI6qhQEK+rF4lE9u/cuXPSTvDKK6/w1FNP0bt3b6ZPn86jjz6602uWLVvGVVddxYMPPsiaNeXvxTRixAg+/PBDLrnkEp577jmeeeaZZIS+nS5duhCNRhsA7ZJ+srK5nq/777+fkSNHcswxxzB58mRmzJjBnXfeycKFCzn77LN59913dzpmBufL9Xzk5+czYMAA8vPzeeCBB5g5cybPP/88e+65JzfddBP333//TsfM4Hx4jevtY0dTpkxh+vTpu3yN2odI6qhQEK9r5ziOb7/99kvaCebMmQNA//79qVOn9KWyR48ezcEHH8yLL75IrVq1KnTc2rVr07dvX2rUqMGnn36asHjL0rZtW/x+vwO0T/rJyuaJfPXp04f+/fvTqFEjatSoQadOnRg1ahTxeJwHHnig1O/J0Hx5Ih+BQID777+ftm3bkpOTw957782IESOoX78+48ePp6ioaKfvydB8eI0n2kexVatWMWrUKHr16lXucdU+RFIj6HYAIuXYNxQKxZo0aRJI1gnWrVuH3++ndu3aZb5m+PDh5OTkVOn4devWZd26dVUNr8JCoRB77LFH0YoVK/ZN+snK5nq+7rjjjtID23dfcnJyWLZsGY7j4POVPoIgw/Llej7y8vKYO3fuTv8eCoVo0qQJCxYsoKioiHC49NEvGZYPr3G9fZQ0bNgwTjjhBA455BBee+21Ch1f7UMkudSjIF6379577x31+5PXVGOxWLmvqWqRUJlzJELr1q2DgKuFghfyVZpNmzaxZcsW2rRpU2aRUN1zVFYK8uXZfKxfv56lS5fSrl07cnNzk3KOyvLA9ZNqnmkfkyZNYtGiRVx//fVJO0d1ZWH7EFGhIN7m9/vb5OXlJW2iXaZp2bJlIBwOu9Y17uV8TZ06FYCBAwe6HMk2yc6XF/NRWFjIF198wZVXXkmjRo0YOXKk2yH9we3rJ9W80j5WrlzJvffey/DhwyvU8+CWbGsfIqBCQTzO7/fvVr9+/aSuMhGJRMoc9pAI4XCYaDSatOOXVLduXXw+X/2UnKwUXs3XmjVr+Mc//sGZZ57JiSeeuMvXZlK+vJaPMWPG0LVrVwYMGEAgEOChhx6iTZs2u/yeTMqH13ilfdx+++2ccsopdOnSpdLHV/sQSS4VCuJpfr+/XrKfMK1YsYLGjRsn7fh77LEHK1euTEn3eO3atYnH47sex5FEXszXunXruPTSSznssMO47bbbyn19JuXLa/kYNGgQn3/+OVOmTCEvL4+zzjqrzCUwi2VSPrzGC+3j5ZdfZunSpVx77bVVOr7ah0hyqVAQT/P5fHUruspQZRUUFDBu3Dh++eUX+vXrl5RzAPTt25cNGzYwevRo1q5dm7TzgPsfZF7L16ZNmxg0aBCtWrVi1KhRVGQsdibly2v5AJsUmpeXx6233soxxxzD6NGjmTVrVpmvz6R8eI3b7WP58uXcf//93HnnndSsWbNK51H7EEkurXokXlcjGcOChg4dyuTJk/H7/Vx00UWcf/75CT9HsVNPPZUVK1YwevRonnzySbp168Zjjz2WlHPVqFEDx3GqN/O6miF4JV+xWIxrr72Wxo0bM3LkyAoVCZBx+fJMPkpz9NFH88477/D+++9z+OGHl/qaDMuH17jaPqZPn05hYSF/+ctfSv366NGjGT16NABvvPEGzZs33+k1ah8iyaVCQbxu4+bNmxN+0BEjRnDjjTfy8ccfc8MNN/D7779z++23J/w8AA8//DBPPPEEw4YN48QTTyx3hZfq2LRpE36/f1M8Hk/aOcrhmXzdcccdRCIRHnroIQKBbas/nnzyydx999106NCh1O/LsHx5Jh+lKb5JLSgoKPM1GZYPr3G1fZx77rmce+65O/3766+/zk033cSVV17JoEGDdnkutQ+R5NLQI/E0x3F+37hxY1KOnZubywknnEC7du3+WBEnGaZNm8Zee+3FmWeemdQPMbAVZfx+/4aknmQXvJKvf/3rXyxatIiHH3640hOfMylfXsjHfffdx4033ljq1z788EMADjjggDK/P5Py4TVeaB/VpfYhklzqURBPi8fj6zZsSO77cu3atSksLEza8Tds2ECDBg2Sdvwdz+Xz+dan5GSl8EK+Jk+ezKOPPgpQpVVUMilfXsgHwJtvvknLli3p3bs3jRo1YvXq1UyYMIHXX3+d9u3bc+aZZ5b5vZmUD6/xSvuoDrUPkeRSoSCeFo1Gf/3tt9/iJLH3q7zNtwDef/99rrzyyu3+7cADDwRsN9Fd3ehU9ByJUFBQQDweX52Sk5XCC/lKxNPLTMmXF/Jx6aWX0qpVK6ZOncqkSZP49ddfCYVCtGzZksGDB9O/f/9yNzTMlHx4jRfaR0nDhw/npZde+uP/i+colDfvQO1DJHlUKIjX/bB48eIIkLQJZOFwGMdxdvmaHj16MH/+/CodPxaLJXWfhpIWLVoUjUQi36TkZKVzPV+PPPJItY6fYflyPR+5ubmcccYZnHHGGVU6foblw2tcbx8l3XbbbRVawrgktQ+R5NIcBfG6hcuXLw8lc0Odxo0bljR59QAAIABJREFU4zgOa9asSfixo9EoBQUFNGnSJOHHLs2iRYviwMKUnKx0ylclpCBfykcleOD6STW1j0rIwvYhokJBPG9hLBbz//zzz0k7Qffu3QF46qmnWLduXcKOW1hYyDPPPEM0GqVbt24JO25ZNm3axNq1a8O4XCgoXxWTonwpHxXkkesn1dQ+KihL24eICgXxvAV+vz/61VdfJe0Exx57LNdccw0fffQRxx13HJdddlm1jzl06FCOPPJIJk6cyKBBgzj99NMTEOmuffPNN8Vd/FUbI5UYylcFpShfykcFeeT6STW1jwrK0vYhQmpmAIlUQygUmtmrV68ud9xxh9rrLvzrX//iqaeeWl5UVNTUzTiUr4pJVb6Uj4rxyvWTamofFZOt7UNEPQrieZFIZOrHH38ccTsOr5s5c2YkGo3+1+04lK+KSVW+lI+K8cr1k2pqHxWTre1DRIWCpIN3V6xYEV62bJnbcXjWhg0bmD9/fiAej7/rdiwoX+VKcb6Uj3J47PpJNbWPcmR5+5Asp0JB0sFHwWDwt//+Vw9zyjJt2jQcx4kDb7kdC8pXuVKcL+WjHB67flJN7aMcWd4+JMupUJB0EI1Go8+98sorRRVdjzvbTJ48Oerz+d4AEr8GYeUpX+VIcb6Uj3J47PpJNbWPcmR5+5Asp0JB0sV/fv7553AyV+dIV6tWreLTTz8NxGKxp92OpQTlqwwu5Uv5KINHr59UU/sog9qHZDsVCpIu5oRCoYXjx4+Pux2I17zwwgsEAoEC4E23YylB+SqDS/lSPsrg0esn1dQ+yqD2IdlOhYKkjUgkctcbb7zh+/HHH90OxTMKCwt57rnnotFo9B6gyO14SlK+duZmvpSPnXn5+kk1tY+dqX2IqFCQ9PJ8IBD4cdy4cRpIu9Vzzz3Hli1btgCPuh1LKZSvHbicL+VjBx6/flJN7WMHah8iKhQkvcQikcjIV1991fnpp5/cjsV1BQUFPP3009FYLPYAsM7teEqhfJXggXwpHyV4IB9eo/ZRgtqHiFGhIOlmrM/nWzh8+PCY24G47cEHH3Q2b978O/CA27HsgvK1lUfypXxs5ZF8eI3ax1ZqHyJGhYKkm2gkEhk0c+ZM/7vvZu/eN19//TUTJ04kGo1ehbefdilfeCpfygeeyofXqH2g9iFSks/tAESqwu/3P9ewYcO+kydPDtWpU8ftcFIqEonQr1+/yOLFi2dFo9EegOfHFCtf3sqX8uGtfHhNcfuYOHFiqGbNmtSoUcPtkFJG7UNke+pRkLQUj8cHr127dt2tt96adV3k9913n7No0aJoNBq9mDT5EFO+vJUv5cNb+fAQH3BwPB7/bvXq1U7v3r0dvz+7bhPUPkS2l13vAJJJfo1Go33fffdd3/jx492OJWXef/99nn/+eV8sFhsIfO92PJWgfHkrX8qHt/LhptbAQOBFbOfhL4BhjuPECwoKnIkTJ7oaXCqpfYjsLOB2ACLVsBRwZs6c2aNz586+Pffc0+14kiYejzNkyBAee+yxuOM4zzqOc4fbMVVB1uQLYNGiRVx66aXRWCz2lOM4d7kdTymUj+zUGOgNDAYeAYYCJwHtgNolXtcfmK/2IZLdNEdB0p0/EAhMqlGjxsnPPvtssE2bNm7HkxQrV67krLPOiq5bty4IxIH/Ac8CrwKFrgZXOVmTr379+kUKCgo+i0QixwCb3Y6pDMpHdjkPe99wgBgQKuU1UWAsMAi1D5Gsp0JBMkE4GAy+XadOnW4vvPBCqGnTpm7Hk1CFhYX0798/8uOPPy6JRCIfAhdjxYIP2y10Mvbh/zbpsXtoNuWrK/Cb2zGVQ/nIHn7gY6ATZRcJ3wGHsO1mWe1DJIupUJBMUS8UCn3coEGDfcaOHRtq0aKF2/EkxOrVqxk4cGBkyZIlv0aj0c7AemzsbCO2zTGKYsMINwKTsLHGb2JPDL0qW/L1s9sxVZDykT1aAV8DpS1ltBkrIr7d4d/VPkSylCYzS6YoiEQiR/72229f9OvXLzpv3jy346m2n376iQsuuCCSn5+/PBqNHoV9iP0OXMH2124QK/prA+cAU4BlQNcUh1wZ2ZKvdKF8ZI9C4DNKX9FnIDsXCaD2IZK1NJlZMsmmeDw+Ph6Pd3nttdda7rPPPv68vDy3Y6qSzz//nIsuuiiybt26+ZFI5Ei2/xD7BjgcaMHO13AA62GYCdyDt5f3y5Z8pQvlI/OdBbyB9SYswXomi98z/g3cuYvvVfsQyUIqFCTTROLx+AuO4zR78803Dy4sLKRz586+QCA9mno8HufJJ5/klltucaLR6JvRaLQXpe8M+iFwOTuPM45ivQknAJuSG21CZEu+0oXykZnqAw8Bo4BXgF7A68BlWI/kIuA0IFLOcdQ+RLJMelzdIpUTdxxnCrDo66+/Pun999/nsMMOC9SvX9/tuHZp5cqVXHfddbFJkybF4/H49fF4fDBlT04uALYAx7NtrpGz9c9I4L2kB5w42ZCvdKJ8ZJaTgLeA/bBVj0Zhv5d12L4JxwLHAb9U8HhqHyJZRIWCZLIvHcd5uaCg4NgXXnhh90gk4jvooIMIBoNux7WdaDTKM888w+DBg2M///zzT7FY7CSgIrscfQKcCezGtjkLU7GehhrAdLw99GhHmZ6vdKN8pLd6wMPAA9iKaCcDO04u+Ax4f+t/K0vtQyQLaNUjyQYB4IpAIDCyUaNG4WuvvTb0pz/9Cb/f3bn8juPwwQcf8MADD0Tz8/OdeDx+F/a0rzJreHcGZm39+wjgNuB84AngA+wJYrot95fJ+UpHykf6ORF4EhuaOAhbQjlZ1D5EMpgKBckmewYCgXvi8fh5TZs2jQ0aNCjUq1evlD8Bi8fjTJs2jcceeyzy/fffB4PB4BvRaHQwNk64KkZjSx6eiu2vANARWyo1CvQB5lc3bhe4mq/ly5cTCARo1KhRovOVrkrNxzfffEOHDh1SFkQSrp9MUhe4F/g/4GVsDsKaFJ07U99fRbKaCgXJRm38fv9NwIB69eo5p512Wqh3797ss88+ST3pjz/+yOuvv86kSZMiK1euDPr9/ldisdgIYG41D10Xu5YLdvj3RsAErNfhIuClap7HLa7ka8aMGdx6660EAoHIqlWrEpmvdPdHPnJzcwGCTz/9dDpfP5miO/A0UAcrEF5xKY5Me38VyWoqFCSbNQcuDofDFxUVFe3dunXryPHHHx/q3LkzBx10EDk5OdU6eCwWY/78+cyePZvp06dHvvrqq1AwGFwdjUb/jQ0NWpiIH6IcQWxI0g3Ycqm34O2N2HYl5fna+qUlWG/NN9WMP9Mcgk2arwUEMvT6SQc1gduBv2Fj768AfnU1IpMN768iGU+FgohdB92B88Lh8ClFRUXNQqFQfP/994+1bds21LJlS/Ly8thzzz2pVasWtWvXpk6dOvh8PtavX8/GjRvZuHEjK1asID8/nyVLlrBo0aLovHnzfFu2bAmEQqFVsVjsv/F4/AXgf7hzo15y3sK5wFoXYkiUVOXrLWD81nOOBq5y7Sf2nlxgBnAQ8APWY5XJ149XHYH1IuwODAEedzWa0mXD+6uIiGSR5sCFwOOhUOijUCi0hm1Lj+7yTzAYLAiHw58CT2GTCJPb3145HYF87MbuQHdDSahk5atOidfGgatT8tN4XwB4DVtz3wE+3+HrmXr9eEkN4G5sDtKbwF7uhlMpah8iaUQ9CiIVUx/YG3uSmgs02PrvBUDh1j+/AKtdia7iMmXeQnkSka8g229A5QBnAK8mOtg08wh2k1a8vPYHQI9yvidTrh8vOBwYB+yJDSn0Yi9CZal9iIiIeEQQexoZ3/pf7adStijb9ypswYqsbHUT9nso+aR3iqsRZY+SvQhvYTfWIiIiIklxPrAR+C/bnuDJ9grZ/qY4gk0Ube5mUC45h52LhBjwrJtBZYkOwBfYE/aBaDSAiIiIpECmzltIlNLGTxdhK6rUczGuVDsK+7l3LBSKgMdcjCvTBbFJyluAD4HW7oYjIiIi2aYR8A6wHujrcixe8xOlT6yMAFOxG7lM1x74Hes92PH3sAV4wL3QMtoBwGdYr98QwN2tjkVERCRrad5C6b6j9B4FB+uJ6epaZKlzJdazEmf7ORsOsBkY7l5oGalkL8JHaGUfERER8QjNW9jePLZNZI5u/fMicBzZNU48DJwNzGFbT0Jx0XSDi3FlmvbAJ2zrRVDBLiIiIp7SCc1bKPYRdkO8EHtyHgN6uxqRu17A9k24F9u0z8F2Apbq8QN/xXpoZgL7uRuOiIiISNkaAe9i8xbOcjkWNw3C1q0vNg2Y7FIsbmuE3cj+eev/52C7fHd3LaLM0Ap4H9iEehFEREQkTWjews76YROZ02kn3ES5AetFqOV2IBnChy11WogNcTvY3XBEREREKq8/mrdQLAysAm5xO5AU82ETux9yO5AMkYf12BVhRXjY3XBEREREqq543sL32LKN2ewfwGKya7nK47H5CNme++oq7kVYD8zHrisRERGRtKd5C2Y/7Kb5OLcDSaGXsA2/pOpaYHNcIqgXQURERDKQ5i2Yj4HxbgeRIo2xITL93Q4kjfUFfgO+Bg51ORYRERGRpMr2eQsXY3sJ7O52IClwE5rEXFVNsFWyYtj8jhx3wxERERFJjWyet1AbKAAGux1Ikvmw/D7gdiBpqC+2o/Ui4CiXYxERERFJud3J3nkLY4Bv3A4iyU7E5mO0dzuQNNIYeAUbnjcGKypFREREslK2zlvojN1Ed3U7kCR6BZjudhBppC/wK7Yq1tHuhiIiIiLiHdk4b+EL4Em3g0iSJtgk5nPdDiQN7I6tDFXci5DrbjgiIiIi3tMJWEr2zFu4CttZt67bgSTBUGA1UMPtQDzuFOAXbL5ONi2ZKyIiIlJp2TRvoT6wAfg/twNJMD+wBLjX7UA8rD7We+AAL5I9vWgiIiIi1bLjvIVM3sX4WWC220Ek2MlY7tq6HYhH/Qn4CVgO9HY5FhEREZG0VDxv4U0y94nr0dhT5YNdjiORJgPvuB2EB9Vl+16E3dwNR0RERCS9Zfq8BR/wHfCw24EkyN5ABDjb7UA85gTgR2AF0MflWEREREQyRqbPW7iRzNm9+HZsiU/tImxqYbsqx7FehEbuhiMiIiKSeTJ53kJjbCnR890OpJoC2Oo9d7sch1d0x3rCVpGZBa6IiIiIp1xAZs5beAXrNUlnvbBCbh+3A3FZTaxYigGvA03dDUdEREQke2TivIVTSP+b7NeBqW4H4bKuwEJsKNlAl2MRERERyUq7A+9h8xbOdDmWRPBjxc/f3Q6kipoBUTIjF1VRA+tFiGK7i+/lbjgiIiIi2S3T5i0Mx1bFCbkdSBUMx/YFSMfYq6sL8C2wDvUiiIiIiHhKpsxbKH4qf7rbgVRSENtA7C63A0mxEDAEm4j+NpY/EREREfGYTJm38DY21j+dnI716rR2O5AU6gB8DmwA/orthyEiIiIiHpUJ8xbOxlbLae52IJXw361/skEQ60XYAswA2rgbjoiIiIhUVLrPWwgDK4Fb3Q6kgpqTnsOlquIA4FNsmNsQ0q9tiYiIiAjbz1uo73IslXUfNowq4HYgFXAX8AuZPYm5uBdhM/Ax0NbdcERERESkug5h27yF/V2OpTL2xXpETnA7kHIEgZ+xFY8yVXvgE2ATViykQ/EmIiIiIhWQrvMWZgAT3A6iHGdh8ylauB1IEvixpU43ALOA/dwNR0RERESSIR3nLVyITZjd3eU4duV/pN8KTRXRCpiOLXs6DPUiiIiIiGS8C7AhJOkwb6EmsBa41u1AytAK603o5XYgCeTDehEKgXnAwe6GIyIiIiKplE7zFh4FFuDNNfpHAcvInKftLYF3gQjW6xR2NRoRERERcUW6zFs4BHCAbm4HsoPiJVxvdzuQBCjuRfgdmI/9zkVEREQki6XLvIXPgXFuB7GDc7C9E9JpU7jS7Am8xrZehBx3wxERERERLxmAzVt4A2/OW7gC2w/CS7G9C0x2O4hq6gv8BnwNHOZyLCIiIiLiUcXzFr7De/MW6mFLdF7qdiBbtcZ6YU52O5AqagK8ik3EHgPUcjccEREREfE6L89b+Dcwx+0gtroP+JH0nMTcF1gNLAJ6uByLiIiIiKSRIPAQ3pu3cBQ2qbmjy3GEgVXAUJfjqKw9gIlYXscAtd0NR0RERETS1UBsszMvzVv4BhjtcgznYRN/93I5jsroC/wKLAGOcTkWEZGs4sW1vUVEEuEI4GVs860+2KRXN/0NuAVoik1u3lEI2wRtP2BfoG0wGGzp9/vr+Hy+OkDdeDwe9vv9W4B18Xj893g8/nssFluM7dWwcOufH7Hei9K8D6wBzkjkD5Yk9YGHgf7AE8D12LAyERFJERUKIpLJmmLFwgHAhcArLsbSCPgJ+D/gP9gcgU7AscFgsKfjON1isVgNn89Hw4YNi1q1auXfe++9gzVr1qRmzZrUqVOHYDBIUVER69evZ+PGjWzatInFixdHlixZQmFhYQggGAyui8Vi0xzHeQebs7Fw6/n3w3o1TgLeTvUPX0knY8VB8R4Jr7sbjohIdlKhICKZLgz8E7tBvwe4GRvr7oaXsV6DGcFg8IJoNFq/Xr16kSOOOCLYuXNn3/7770/Lli2pWbNmpQ9cUFDAkiVLmDdvHrNmzYp9+umnzubNm4OhUGhpJBJ5Ctu5+BigDe79/OWph+VoIPASMAhY62pEIiJZTIWCiGSLgVjBMA04H1iXwnPnAgMDgcBfY7FY82bNmhX16dMnfOyxx9K6deuknDAWizF//nymTp3KlClTIgUFBcFgMPhNNBodgd2Ex5Jy4qo7EXgSm5B+Kem/z4OISNpToSAi2STV8xYaAFcFg8FrA4FAbp8+fQK9e/fmwAMPTPJptxeLxfjoo4+YPHlyfNq0ab5AILA0EoncCTwLFKU0mJ3VBe7FenxeBi7D5lGIiIjLVCiISLZJxbyFMHB9IBC4pUaNGuEBAwYEzz//fOrVq5eEU1XOjz/+yBNPPOG89tprjs/nWxmNRq8BJrgUTk+sF6EGViC4OYdERER2oEJBRLJRDjYM6RISP2/huFAoNMbn87UcNGhQ4Pzzz6d2be8t+798+XIeffTR+KRJk/zBYHB6NBq9lG0Tn5OtFnAbthLUROBybCM1ERHxEBUKIpLNEjlvoZ7f7380Ho+f26NHj+jNN98cbNq0aUKCTKa5c+cyfPjwyKJFi3zAiHg8PoLkzl/oBozDVoH6K7YClIiIeJAKBRHJdomYt3BoIBCYWKdOnT1HjBgR6tGjR0IDTLZYLMZzzz3Hgw8+GAM+jkQi5wDLE3yamsDtWC/CW9ichF8SfA4REUkgFQoiItWbt3C13++/79BDD/Xdc889wYYNGyYjvpRYsGAB11xzTWTFihWF0Wj0HOB/CTr04cDTQBPgBuDxBB1XRESSKOB2ACIiHrAeWwGoOXA39vT7Xcre4RjA7/f7/wUMveKKKwLDhg3ze3EuQmU0atSIPn36BJYtW5azaNGi/sDPwBfVOGQNYAQ2Yflz4E/YJnAiIpIGVCiIiJgY8Bo25GY49hT8TWBzKa8NBwKB5/1+/wX33nuv/5xzzsHny4wO2nA4TM+ePX05OTm+WbNm9cZ6nqdX4VAHAW9gKxsNBq4Ffk9YoCIiknQqFEREtvcZ1pvwV+DPW//+a4mv1woGg2+Gw+ETx4wZEzjyyCPdiDHpOnbsyG677caMGTN6+P3+Bo7jvFXBbw1h8xDGY/M9TsJ+hyIikmZUKIiI7GwZdqPbC7gJWLD1TygYDE6uWbPm0U8//XSwQ4cObsaYdAcccAB5eXm+adOmdXYcJ0T5w4YOxHoRzgSGYcuepnIHbBERSSAVCiIipSs5b2EUUDMQCJwfCAROf+KJJ4IHHHCAu9GlSJs2bWjWrJnvnXfeOQooAGaV8rIg23oRlmK9CFPY9RwPERHxOBUKIiJlK563sBIY7Pf7u/7rX/8KHHrooS6HlVpt27YlJyeH2bNnn4gNJ/qmxJf3B14H+mK9CP8HrEl5kCIiknAqFEREypcHXHj33Xf7jz32WLdjcUWnTp1Yu3Yt3377bS/HcSYCa7GlTsdj+yGcBExGvQgiIhkjM5bpEBFJntaBQGDe2WefXevmm2/O6vfMaDTKn//85+i3336bH4lE1mJzEm4F/kFyd3MWEREXZPWHnohIOXJCodDs5s2bt58wYUIoJyfH7Xhct2LFCvr06RMpLCxcBJwBfOt2TCIikhx+twMQEfGwWwKBwP4PP/ywioStmjRpwl133RUC9gNauhyOiIgkkQoFEZHStfH7/TdeddVVwebNm7sdi6cce+yx9OzZMx4KhR7Ddl8WEZEMpEJBRKQUwWDwkZYtW3Leeee5HYonDRkyxO/3+/cChrgdi4iIJIdWPRIR2dkZ8Xj85oceeiiw1157uR2LJ+Xm5hIOh/2zZ8/u5jjOf9DGaiIiGUc9CiIi2/OFQqE7TzjhhFjHjh3djsXT+vfvz+67747f77/J7VhERCTxVCiIiGzvlEgk0v6SSy5Rj2s5gsEgAwcODAF/AdT1IiKSYVQoiIiUEAqFhh511FHRdu3auR1KWjj99NOpX78+wHVuxyIiIomlQkFEZJsjIpFIl4EDBwbdDiRdhMNhLrnkklAgELgMqOt2PCIikjgqFEREtvL7/Rfm5eVFDjroILdDSSt9+vTB7/eHgDPdjkVERBJHhYKIiKnh9/v7nXnmmSG3A0k3ubm5HH300b5QKHSR27GIiEjiqFAQETG9YrFY7kknneR2HGmpV69e/kgk0g3t1iwikjFUKIiIAIFA4JwuXbrE9thjD7dDSUtHHnkkubm5UeAMt2MREZHEUKEgIgI+n893/JFHHqlJzFUUDAY54ogjAsFgsKfbsYiISGKoUBARgQ7RaLRe586d3Y4jrXXu3NnvOE4PQPM8REQygAoFERE4tnbt2tG2bdu6HUda69KlC7FYrCZwqNuxiIhI9alQEJGsFwgEjuzcubPf78+ct8RffvmFq666isLCQgD+8Y9/8NZbbyX1nC1btqRBgwZFQPeknkhERFIicz4VRUSqKBgMdmjbtm3GvB8uWLCAfv36ccQRR5CbmwvAWWedxYMPPsjo0aOTeu6tv8f9knoSERFJiYz5YBQRqaJAJBJpnpeX53YcFdK5c2cGDBhQ5tcLCwu58sorOf744zn33HP/+PdmzZrx0EMP8fjjj/P2228nLb5WrVoFw+HwgUk7gYiIpIwKBRHJdnnxeDzUsmVLt+NIiHHjxrF69WouvfTSnb6277770rNnT+69915isVhSzp+Xl0c8Ht83KQcXEZGUUqEgItluH4AWLVq4HUe1OY7DxIkT6dChA2XtB3HcccexcuVKPvjgg6TE0KJFC6LRaF1gt6ScQEREUkZrhotIttstEAjEc3NzE/rgpKio6I9hPsuXLycnJ4eOHTty5pln0qNHD0pOnF67di2PPfYY06dPZ9WqVdSpU4dOnTpx6aWXst9+Ntz/6aef5v777wfgiy++4MADbXSP3+9n3rx5ACxcuJA1a9bQs2fZWxkUH++jjz7imGOOSeSPDECDBg2K/7ob8FvCTyAiIimjHgURyXZ1atSokfBxOCNHjuS5557j5ptv5qOPPmLKlCnk5eVx9dVX89lnn/3xul9//ZV+/frx9ttvM3ToUD766CPGjh1LQUEB/fv3/6MIuPDCC5k/fz41a9akY8eOzJ8/n/nz5//xdYAffvgBgMaNG5cZV3FPw/fff5/oHxmA2rVrF/+1TlJOICIiKaNCQUSyXZ2aNWs6iT7orFmzaNOmDV27diUnJ4eGDRty3XXX7TTE6aGHHuKXX37hhhtu4Mgjj6RWrVq0adOGe++9F8dxGDlyZIXP+euvvwL8sdJRaXJzc/H5fKxevbpqP1g5VCiIiGQOFQoiku1yc3NzE14odO/enblz53LHHXfw5ZdfEo/HAXj99dc57LDD/njdO++8g9/v56ijjtru+xs1akTr1q355ptvWLlyZYXOWVRUBEAwuOtRpYFAgM2bN1fmx6kwFQoiIplDcxREJNv5knHQW265hYMOOojJkydz8cUXA3DIIYfQt29fjjvuOMBu7Is3ROvatWuZx1q6dOkuhxMVC4fDAESj0V2+LhaLUaNGjQr9HJXl8/3x60zK71VERFJHhYKIZLv1hYWFCb+p9fl89OrVi169ehGNRpkzZw5PP/00gwcP5m9/+xsDBgwgHA5Tp04dNm7cyGeffUYgEKjQccuy++67A/xRfJSmsLAQx3Fo1KhR5X+oCihx7vVJOYGIiKSMhh6JSLZbv3nz5oQXCl27dmXJkiWADQXq2rUrDz/8MD6fb7ulSY8//nhisRhffPHFTscYO3YsPXv23G7Pgxo1ahCJRP74/1NPPZWXX34ZgDZt2gDscqjSqlWrANhnn32q8dOVbcOGDcV//T0pJxARkZRRoSAi2a5w06ZN5T/Kr4Lhw4fz3XffUVRUxG+//cbYsWNxHIfOnTv/8ZrBgwfTrFkzbr31VmbMmEFhYSEFBQW89NJLPProo1x//fXb9TS0b9+e/Px8VqxYwbx58/jpp5/o1KkTYBuq7bbbbixcuLDMmBYsWADAEUcckYwfuWShoB4FEZE0pzGkIpLtTgbemDlz5i5XC6qshQsXMmHCBD777DN++eUXcnJyaNGiBWeccQZnnHHGdkOICgoKePzxx3n33XdZsWIFderUoV27dvzlL3/h8MMP3+64+fn53H777Xz77bfUq1ePiy++mH79+v3x9YcffpixY8cyderUUjddu+6665g7dy5vv/12uZOeq2LmzJkMHDgQoBGwJuEnEBGRlFGhICLZbh/guwkTJtC+fXu3Y6m2wsJCTjvtNHr06MFtt9223dcWLlxI3759GTVqFCeddFJSzj9+/Hjuueee9Vt3ZxajsYDWAAAHYUlEQVQRkTSmoUciku2W+P3+aH5+vttxJERubi6jR4/mf//7H+PHj//j33/66ScGDx7MJZdckrQiAazHw+/3f5e0E4iISMqoUBCRbBcNhUI/Fk88zgTt2rVjwoQJf8x5AHjppZe4+uqrufrqq5N67sWLF0eLioq+TOpJREQkJbQ8qohkvWg0+uX333/fkgx6eNK0aVMeeeSRP/7/mmuuScl5Fy5cGAcWpORkIiKSVBnzoSgiUlWxWOzD2bNnx4p3T5aqWbp0KWvXrg0DM9yORUREqk+FgogIvFdYWBj6/vvv3Y4jrX3yyScEAoFNwBy3YxERkepToSAiAvOCwWDB7Nmz3Y4jrc2ePdvx+XwzgEi5LxYREc9ToSAiAnHHcd6dMWNGrPyXSmlisRgff/xxNBqNTnU7FhERSQwVCiIiQCwWe3H27Nn+1atXux1KWpoxYwbr168PAhPdjkVERBJDhYKIiHnV7/dvePPNN92OIy1NmTIlHgqFZgGZs86siEiWU6EgImI2x+PxCa+++mqR24Gkm8LCQt577z0nEomMdTsWERFJHBUKIiJbxePxp7///vvwV1995XYoaWXKlCnEYrEY8JLbsYiISOKoUBAR2WZGKBSa8/jjj2tScwVFo1GefPLJCDAGKHA7HhERSRwVCiIiJUQikbvee++9gPZUqJhXX32V1atX++Px+P1uxyIiIomlQkFEZHtTQqHQgieeeELbNJcjFovx5JNPRnw+39PAUrfjERGRxFKhICKyPScSidz61ltv+b788ku3Y/G0559/nuXLlxOPx+9yOxYREUk8n9sBiIh4UTAY/F/z5s17vPLKK6FAIOB2OJ6zevVqTj755OimTZv+DtzmdjwiIpJ46lEQESlFNBq9PD8/nwkTJrgdiieNGjUqHolEfgVGuR2LiIgkhwoFEZHSfR+Px+998MEHoz///LPbsXjK+++/z1tvveWPRqODgA1uxyMiIsmhoUciImWrEQqFPmnTps1+zz33XCgUCrkdj+tWrlxJnz59ohs3bnw+Fov92e14REQkeTTwVkSkbNF4PP6/tWvXDiwsLAx27949qx+uxGIxLrvssujy5cuXRaPR3oB2sRYRyWAqFEREdu03x3GWfvnll2e2adOG1q1bux2Pa+677z7eeeedSDQaPRr4ye14REQkuVQoiIiUb77f72/0zjvvHNqpUyffXnvt5XY8KffMM8/w6KOPOo7j/Bl41+14REQk+bK6G11EpBL8gUDghVAo1OeZZ54JtmvXzu14UubNN9/kxhtvdBzH+RugHZhFRLKECgURkYrLCQaDb+fm5h4xbty4UJs2bdyOJ+nee+89rrnmmngsFrsfuMHteEREJHW0PKqISMVtiUajvQoLCz/t379/dO7cuW7Hk1STJk1i8ODBccdxngSGuB2PiIikluYoiIhUTlE8Hn82Ho8fMHny5H3btGnja9WqldsxJdyzzz7LiBEjcBznHsdxBrsdj4iIpJ4KBRGRyos5jvMK0Hzq1KkH5eTk+A4++GB8vvQfzblp0yaGDRsWHzdunANcAdztdkwiIuIOFQoiIlUTdxxniuM4Gz755JPj5s2b53Tr1s1fs2ZNt+Oqsh9++IFLLrkk8tlnn22Ix+NnAePdjklERNyT/o+/RETc1zUYDE6sV69eo5EjR4aOOOIIt+OplHg8zosvvsi9994bi8fjn0aj0bPQPgkiIllPPQoiItX3UzweH1dUVLTflClT2i1atCjesWNHX+3atd2Oq1xff/01V111VeTVV18lGo2OisfjA4B1bsclIiLuU4+CiEhinRwKhR4NBAJNL7/88uC5555LjRo13I5pJ6tWreKxxx5zXn75ZYLB4KxIJDIQ+MrtuERExDtUKIiIJF4N4MZAIDCkdu3agb/85S+hfv36kZub63Zc/PLLL4wdO9aZOHFiHPgtGo1eBzwLOC6HJiIiHqNCQUQkeRoBgwOBwOCcnJycvn37Bnv37k3btm1TGkQ8HmfOnDlMmjTJeeuttxyfz7c8Go3eBYwFtqQ0GBERSRsqFEREkq8ecEUoFLo0Eok0a926ddEZZ5wRPuaYY2jWrFlSThiPx1mwYAFvv/02kydPjqxZsyYUCoW+iEQiDwPPAZGknFhERDKGCgURkdTxAd38fv8An893biwWy91jjz2KunbtGurSpYvvgAMOYO+99yYUClX6wJs2bSI/P5+5c+cye/bs+KxZs2IbNmwIBYPBX6LR6DhseNGCRP9AIiKSuVQoiIi4IwR0AY4NhUInxmKxw+LxeMjv9ztNmjQpat26dWjPPff05+bmkpubS61atcjJyWHjxo1//CkoKGDZsmXRxYsXx9esWRMGCAQCG4DpsVjsf8B7wHw0/0BERKpAhYKIiDfUAPYD2gL7+v3+doFAYG+/398AqBuPx2s7jpPj8/k2+v3+DY7jFMbj8dXRaHQxsHDrnwXAIiDm2k8hIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiKyK/8P5uHqiub2TYEAAAAASUVORK5CYII=",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from more_itertools import powerset, distinct_combinations\n",
    "\n",
    "graph = new_graph(\"graph1\")\n",
    "\n",
    "domain = {1, 2, 3, 4}\n",
    "domain_subsets = tuple((str(i), set(subset)) for i, subset in enumerate(powerset(domain)))\n",
    "\n",
    "\n",
    "for label, subset in domain_subsets:\n",
    "    graph.node(name=label, label=str(subset))\n",
    "\n",
    "for (labelA, subsetA), (labelB, subsetB) in distinct_combinations(domain_subsets, 2):\n",
    "    if len(subsetB) - len(subsetA) == 1 and subsetA.issubset(subsetB):\n",
    "        graph.edge(labelA, labelB)\n",
    "\n",
    "\n",
    "Image(render(graph))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example Fixpoint Operator\n",
    "\n",
    "- Computation can start at the TOP or BOTTOM and move downwards or upwards in the lattice\n",
    "- An operator is just a function that takes and element and moves in a direction consistently\n",
    "\n",
    "## Problem\n",
    "\n",
    "- A diagnostic approach to parts of speech tagging (POS tagging)\n",
    "    - Diagnostics propose a tag, then possibly refute it\n",
    "- POS: noun, verb, adverb, subject\n",
    "### Lattice\n",
    "- Domain: pairs (word, tag) where word is a word and tag is the word's pos\n",
    "- Computation: start with the TOP, apply every operator in composition until a fixpoint is reached"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(('the', 'DET'), ('the', 'NOUN(OBJ)'), ('the', 'NOUN(SUBJECT)'), ('the', 'VERB'), ('quick', 'DET'), ('quick', 'NOUN(OBJ)'), ('quick', 'NOUN(SUBJECT)'), ('quick', 'VERB'), ('brown', 'DET'), ('brown', 'NOUN(OBJ)'), ('brown', 'NOUN(SUBJECT)'), ('brown', 'VERB'), ('fox', 'DET'), ('fox', 'NOUN(OBJ)'), ('fox', 'NOUN(SUBJECT)'), ('fox', 'VERB'), ('jumps', 'DET'), ('jumps', 'NOUN(OBJ)'), ('jumps', 'NOUN(SUBJECT)'), ('jumps', 'VERB'), ('over', 'DET'), ('over', 'NOUN(OBJ)'), ('over', 'NOUN(SUBJECT)'), ('over', 'VERB'), ('the', 'DET'), ('the', 'NOUN(OBJ)'), ('the', 'NOUN(SUBJECT)'), ('the', 'VERB'), ('lazy', 'DET'), ('lazy', 'NOUN(OBJ)'), ('lazy', 'NOUN(SUBJECT)'), ('lazy', 'VERB'), ('dog', 'DET'), ('dog', 'NOUN(OBJ)'), ('dog', 'NOUN(SUBJECT)'), ('dog', 'VERB'))\n",
      "There are 36 elements in the domain\n",
      "Which means there are (2^36 = 68719476736) possible subsets\n",
      "Can't be visualized, but can easily be encoded with bitsets/bitflags\n"
     ]
    }
   ],
   "source": [
    "from itertools import product\n",
    "\n",
    "words = (\"the\", \"quick\", \"brown\", \"fox\", \"jumps\", \"over\", \"the\", \"lazy\", \"dog\")\n",
    "tags = (\"DET\", \"NOUN(OBJ)\", \"NOUN(SUBJECT)\", \"VERB\")\n",
    "\n",
    "\n",
    "domain = tuple(product(words, tags))\n",
    "\n",
    "print(domain)\n",
    "print(f\"There are {len(domain)} elements in the domain\")\n",
    "print(f\"Which means there are (2^{len(domain)} = {2**len(domain)}) possible subsets\")\n",
    "print(\"Can't be visualized, but can easily be encoded with bitsets/bitflags\")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linguistic Diagnosis\n",
    "\n",
    "- Method stolen from classical linguistics ([uoa reference](https://ezpa.library.ualberta.ca/ezpAuthen.cgi?url=https://academic.oup.com/book/12008/chapter-abstract/161275349?redirectedFrom=fulltext)) ([non uoa, gated](https://academic.oup.com/book/12008/chapter/161275349?login=true))\n",
    "- Rooted in generative grammar\n",
    "- Don't want to misrepresent it, its a lot more sophisticated than what I'm presenting here.\n",
    "- General principle is apply rules to rule out possible interpretations\n",
    "- I'm not an expert of linguistic diagnosis, I just think it's cool\n",
    "- Given a template sentence, decide whether it's true when instantiated\n",
    "- E.g. \"The dog kicked the ball\" -> (\"Who kicked the ball?\", \"Dog\") is true, then dog is NOUN(SUBJECT) \n",
    "- Oracle-driven\n",
    "    - In classical linguistics, the linguist is the oracle\n",
    "    - Oracle can be a trained NN\n",
    "    - Or a corpus/database\n",
    "    - ... doesn't really matter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(('the', 'DET'), ('the', 'NOUN(OBJ)'), ('quick', 'DET'), ('quick', 'NOUN(OBJ)'), ('brown', 'DET'), ('brown', 'NOUN(OBJ)'))\n",
      "{('quick', 'NOUN(OBJ)'), ('fox', 'NOUN(SUBJECT)'), ('quick', 'DET'), ('the', 'NOUN(OBJ)'), ('brown', 'DET'), ('the', 'DET')}\n"
     ]
    }
   ],
   "source": [
    "# Diagnostic functions, lattice operators\n",
    "\n",
    "LatticeElement = set[tuple[str, str]]\n",
    "\n",
    "def adjacent_right_tags(word: str, element: LatticeElement) -> tuple[str]:\n",
    "    i = words.index(word)\n",
    "    if i >= len(words)-1:\n",
    "        return tuple()\n",
    "    word = words[i+1]\n",
    "    return tuple(tag for oword, tag in element if word == oword)\n",
    "\n",
    "def jumps_is_verb(element: LatticeElement) -> LatticeElement:\n",
    "    return {\n",
    "        (word, tag)\n",
    "        for word, tag in element\n",
    "        if word != \"jumps\" or tag == \"VERB\"\n",
    "    }\n",
    "\n",
    "#print(jumps_is_verb({(\"the\", \"DET\"), (\"the\", \"VERB\"), (\"jumps\", \"NOUN(SUBJECT)\"), (\"jumps\", \"VERB\")}))\n",
    "\n",
    "# Don't consider anything a DET if it doesn't come before a NOUN(SUBJECT), NOUN(OBJECT)\n",
    "def remove_det_nonoun(element: LatticeElement) -> LatticeElement:\n",
    "    return {\n",
    "        (word, tag) for word, tag in element\n",
    "        if tag != \"DET\" or {\"NOUN(OBJ)\", \"NOUN(SUBJECT)\"}.intersection(adjacent_right_tags(word, element))\n",
    "    }\n",
    "\n",
    "# Can't have two nouns next to eachother (e.g. dog cat)\n",
    "def remove_noun_nodoubles(element: LatticeElement) -> LatticeElement:\n",
    "    return {\n",
    "        (word, tag) for word, tag in element\n",
    "        if tag not in (\"NOUN(OBJ)\", \"NOUN(SUBJECT)\") or not ({\"NOUN(OBJ)\", \"NOUN(SUBJECT)\"}.issuperset(x := adjacent_right_tags(word, element)) and len(x) != 0)\n",
    "    }\n",
    "\n",
    "\n",
    "from itertools import chain\n",
    "first_three = words[:3]\n",
    "first_three_nouns_dets = tuple(chain.from_iterable(((word, \"DET\"), (word, \"NOUN(OBJ)\")) for word in first_three))\n",
    "print(first_three_nouns_dets)\n",
    "print(remove_noun_nodoubles({*first_three_nouns_dets, (\"fox\", \"NOUN(SUBJECT)\")}))\n",
    "\n",
    "# A noun always comes right before a verb\n",
    "def noun_immediately_precedes_verb(element: LatticeElement) -> LatticeElement:\n",
    "    return {\n",
    "        (word, tag) for word, tag in element\n",
    "        if tag in (\"NOUN(OBJ)\", \"NOUN(SUBJECT)\") or (\"VERB\",) != adjacent_right_tags(word, element)\n",
    "    }\n",
    "\n",
    "#print(noun_immediately_precedes_verb({(\"fox\", \"DET\"), (\"fox\", \"NOUN(OBJ)\"), (\"jumps\", \"VERB\")}))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The lattice top element, every word has every tag:\n",
      "Start size = 32\n",
      "Calling with remove_noun_nodoubles\n",
      "remove_noun_nodoubles removed 0 elements\n",
      "set()\n",
      "Calling with remove_det_nonoun\n",
      "remove_det_nonoun removed 1 elements\n",
      "{('dog', 'DET')}\n",
      "Calling with jumps_is_verb\n",
      "jumps_is_verb removed 3 elements\n",
      "{('jumps', 'DET'), ('jumps', 'NOUN(OBJ)'), ('jumps', 'NOUN(SUBJECT)')}\n",
      "Iteration 0 size = 28\n",
      "{('brown', 'DET'),\n",
      " ('brown', 'NOUN(OBJ)'),\n",
      " ('brown', 'NOUN(SUBJECT)'),\n",
      " ('brown', 'VERB'),\n",
      " ('dog', 'NOUN(OBJ)'),\n",
      " ('dog', 'NOUN(SUBJECT)'),\n",
      " ('dog', 'VERB'),\n",
      " ('fox', 'DET'),\n",
      " ('fox', 'NOUN(OBJ)'),\n",
      " ('fox', 'NOUN(SUBJECT)'),\n",
      " ('fox', 'VERB'),\n",
      " ('jumps', 'VERB'),\n",
      " ('lazy', 'DET'),\n",
      " ('lazy', 'NOUN(OBJ)'),\n",
      " ('lazy', 'NOUN(SUBJECT)'),\n",
      " ('lazy', 'VERB'),\n",
      " ('over', 'DET'),\n",
      " ('over', 'NOUN(OBJ)'),\n",
      " ('over', 'NOUN(SUBJECT)'),\n",
      " ('over', 'VERB'),\n",
      " ('quick', 'DET'),\n",
      " ('quick', 'NOUN(OBJ)'),\n",
      " ('quick', 'NOUN(SUBJECT)'),\n",
      " ('quick', 'VERB'),\n",
      " ('the', 'DET'),\n",
      " ('the', 'NOUN(OBJ)'),\n",
      " ('the', 'NOUN(SUBJECT)'),\n",
      " ('the', 'VERB')}\n",
      "Calling with remove_noun_nodoubles\n",
      "remove_noun_nodoubles removed 0 elements\n",
      "set()\n",
      "Calling with remove_det_nonoun\n",
      "remove_det_nonoun removed 1 elements\n",
      "{('fox', 'DET')}\n",
      "Calling with jumps_is_verb\n",
      "jumps_is_verb removed 0 elements\n",
      "set()\n",
      "Iteration 1 size = 27\n",
      "{('brown', 'DET'),\n",
      " ('brown', 'NOUN(OBJ)'),\n",
      " ('brown', 'NOUN(SUBJECT)'),\n",
      " ('brown', 'VERB'),\n",
      " ('dog', 'NOUN(OBJ)'),\n",
      " ('dog', 'NOUN(SUBJECT)'),\n",
      " ('dog', 'VERB'),\n",
      " ('fox', 'NOUN(OBJ)'),\n",
      " ('fox', 'NOUN(SUBJECT)'),\n",
      " ('fox', 'VERB'),\n",
      " ('jumps', 'VERB'),\n",
      " ('lazy', 'DET'),\n",
      " ('lazy', 'NOUN(OBJ)'),\n",
      " ('lazy', 'NOUN(SUBJECT)'),\n",
      " ('lazy', 'VERB'),\n",
      " ('over', 'DET'),\n",
      " ('over', 'NOUN(OBJ)'),\n",
      " ('over', 'NOUN(SUBJECT)'),\n",
      " ('over', 'VERB'),\n",
      " ('quick', 'DET'),\n",
      " ('quick', 'NOUN(OBJ)'),\n",
      " ('quick', 'NOUN(SUBJECT)'),\n",
      " ('quick', 'VERB'),\n",
      " ('the', 'DET'),\n",
      " ('the', 'NOUN(OBJ)'),\n",
      " ('the', 'NOUN(SUBJECT)'),\n",
      " ('the', 'VERB')}\n",
      "Calling with remove_noun_nodoubles\n",
      "remove_noun_nodoubles removed 0 elements\n",
      "set()\n",
      "Calling with remove_det_nonoun\n",
      "remove_det_nonoun removed 0 elements\n",
      "set()\n",
      "Calling with jumps_is_verb\n",
      "jumps_is_verb removed 0 elements\n",
      "set()\n",
      "Reached Fixedpoint\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{('brown', 'DET'),\n",
       " ('brown', 'NOUN(OBJ)'),\n",
       " ('brown', 'NOUN(SUBJECT)'),\n",
       " ('brown', 'VERB'),\n",
       " ('dog', 'NOUN(OBJ)'),\n",
       " ('dog', 'NOUN(SUBJECT)'),\n",
       " ('dog', 'VERB'),\n",
       " ('fox', 'NOUN(OBJ)'),\n",
       " ('fox', 'NOUN(SUBJECT)'),\n",
       " ('fox', 'VERB'),\n",
       " ('jumps', 'VERB'),\n",
       " ('lazy', 'DET'),\n",
       " ('lazy', 'NOUN(OBJ)'),\n",
       " ('lazy', 'NOUN(SUBJECT)'),\n",
       " ('lazy', 'VERB'),\n",
       " ('over', 'DET'),\n",
       " ('over', 'NOUN(OBJ)'),\n",
       " ('over', 'NOUN(SUBJECT)'),\n",
       " ('over', 'VERB'),\n",
       " ('quick', 'DET'),\n",
       " ('quick', 'NOUN(OBJ)'),\n",
       " ('quick', 'NOUN(SUBJECT)'),\n",
       " ('quick', 'VERB'),\n",
       " ('the', 'DET'),\n",
       " ('the', 'NOUN(OBJ)'),\n",
       " ('the', 'NOUN(SUBJECT)'),\n",
       " ('the', 'VERB')}"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Every word needs at least one part of speech\n",
    "def consistent(element: LatticeElement) -> bool:\n",
    "    return len(set(word for word, _ in element)) == len(set(words))\n",
    "\n",
    "print(\"The lattice top element, every word has every tag:\")\n",
    "assert consistent(domain)\n",
    "assert not consistent({(\"jumps\", \"VERB\")})\n",
    "\n",
    "# Every word has exactly one tag\n",
    "def model(element: LatticeElement) -> bool:\n",
    "    return consistent(element) and len(element) == len(set(words))\n",
    "\n",
    "assert not model(domain)\n",
    "assert model({(word, \"DET\") for word in words})\n",
    "\n",
    "operators = [jumps_is_verb, remove_det_nonoun, remove_noun_nodoubles, noun_immediately_precedes_verb]\n",
    "\n",
    "def with_info(operator, x: LatticeElement) -> LatticeElement:\n",
    "    print(f\"Calling with {operator.__name__}\")\n",
    "    result = operator(x)\n",
    "    print(f\"{operator.__name__} removed {len(x) - len(result)} elements\")\n",
    "    print(x.difference(result))\n",
    "    return result\n",
    "\n",
    "def compose(f1, f2):\n",
    "    return lambda x: f1(f2(x))\n",
    "\n",
    "from functools import reduce, partial\n",
    "from pprint import pprint\n",
    "all_operator = reduce(compose, map(partial(partial, with_info), operators))\n",
    "\n",
    "def fixpoint(op, start):\n",
    "    print(f\"Start size = {len(start)}\")\n",
    "    i = 0\n",
    "    while (succ := op(start)) != start:\n",
    "        print(f\"Iteration {i} size = {len(succ)}\")\n",
    "        pprint(succ)\n",
    "        start = succ\n",
    "        i += 1\n",
    "    print(\"Reached Fixedpoint\")\n",
    "    return start\n",
    "\n",
    "\n",
    "fixpoint(all_operator, set(domain))\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercises\n",
    "1. Build a sentence for which the above operators produce inconsistent results\n",
    "1. Construct more operators that complete the sentence\n",
    "1. Rebuild the code so that it starts with the empty set and adds the POS it refutes"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further Ideas\n",
    "## A fuzzier approach\n",
    "\n",
    "- We're expecting a lot from a our diagnostics to have to \"entirely refute\" a POS, a graded approach would be better\n",
    "- That's possible!\n",
    "- Now we have triples (word, tag, confidence) and give the diagnostics the ability to lower a confidence level\n",
    "- But this is no longer a simple subset relation, so it needs more general-purpose lattice theory."
   ]
  }
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