05_recursao.ipynb

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    "Estrutura de Dados - Recursão\n",
    "==========================================\n",
    "\n",
    "Capítulo 2 do livro texto sugerido:\n",
    "Introduction to Algorithms, Fourth Edition\n",
    "By Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein\n",
    "https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/\n",
    "\n",
    "Conteúdo\n",
    "========\n",
    "\n",
    "Muitos algoritmos complexos podem ser resolvidos através da sua subdivisão em partes menores, posteriormente reunidas na solução final.\n",
    "\n",
    "Esta divisão do problema pode ser feita até se encontrar um problema mínimo com solução trivial.\n",
    "\n",
    "A este processo se dá o nome de recursão, e a estratégia é conhecida como dividir para conquistar.\n",
    "\n",
    "Um algoritmo que pode ser implementado com recursão é o de ordenação Merge-sort.\n",
    "\n",
    "Assim como todo o algoritmo recursivo, precisamos estabelecer o caso comum e a condição de parada das recursões.\n",
    "\n",
    "Para o merge sort existem duas condições de parada, sendo ambas triviais:\n",
    "- Caso a lista tenha até um elemento, ela já está ordenada\n",
    "- Caso a lista tenha dois elementos, ordenam-se os dois elementos"
   ],
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   "cell_type": "code",
   "execution_count": 62,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[]\n",
      "[1]\n",
      "[1, 2]\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "def mergeSortCondicaoParada(lista):\n",
    "    # Se só tem um elemento, já está ordenada\n",
    "    if len(lista) <= 1:\n",
    "        return lista\n",
    "    # Se tem dois elementos, comparação é trivial\n",
    "    if len(lista) == 2:\n",
    "        if lista[0] > lista[1]:\n",
    "            return [lista[1], lista[0]]\n",
    "        else:\n",
    "            return lista\n",
    "    # Retorna None caso não seja ainda não tenha\n",
    "    # atingido uma condição de parada\n",
    "    return None\n",
    "\n",
    "print(mergeSortCondicaoParada([]))\n",
    "print(mergeSortCondicaoParada([1]))\n",
    "print(mergeSortCondicaoParada([2,1]))\n",
    "print(mergeSortCondicaoParada([3,2,1])) # não atende a condição de parada len(lista) > 2"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Agora que temos a condição de parada, precisamos tratar o caso comum, onde a lista terá mais de dois elementos e precisará ser dividida em duas partes, as quais serão ordenadas separadamente e depois juntas"
   ],
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   "cell_type": "code",
   "execution_count": 63,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resultado ordenado: []\n",
      "Resultado ordenado: [1]\n",
      "Resultado ordenado: [1, 2]\n",
      "Resultado ordenado: [1, 2, 3]\n",
      "Resultado ordenado: [1, 2, 3, 4]\n",
      "Resultado ordenado: [1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "def mergeSort(lista):\n",
    "    listaAtendeCondicaoParada = mergeSortCondicaoParada(lista)\n",
    "    # Retorna lista já ordenada caso já atenda o critério de parada\n",
    "    if listaAtendeCondicaoParada is not None:\n",
    "        return listaAtendeCondicaoParada\n",
    "\n",
    "    # Quebra a lista em duas metades e chama o mergeSort novamente\n",
    "    metade = len(lista)//2\n",
    "    metadeEsquerdaOrdenada = mergeSort(lista[:metade])\n",
    "    metadeDireitaOrdenada = mergeSort(lista[metade:])\n",
    "\n",
    "    # Junta metades ordenadas\n",
    "    listaFinal = []\n",
    "    while True:\n",
    "        # Se apenas a metade esquerda tiver elementos,\n",
    "        # copia todos os elementos para a lista final\n",
    "        if metadeEsquerdaOrdenada and not metadeDireitaOrdenada:\n",
    "            listaFinal.extend(metadeEsquerdaOrdenada)\n",
    "            break\n",
    "        # Se apenas a metade direita tiver elementos,\n",
    "        # copia todos os elementos para a lista final\n",
    "        elif not metadeEsquerdaOrdenada and metadeDireitaOrdenada:\n",
    "            listaFinal.extend(metadeDireitaOrdenada)\n",
    "            break\n",
    "        else:\n",
    "            # Caso ambas metades contenham elementos,\n",
    "            # copia o menor primeiro elemento entre as duas listas ordenadas\n",
    "            if metadeEsquerdaOrdenada[0] < metadeDireitaOrdenada[0]:\n",
    "                listaFinal.append(metadeEsquerdaOrdenada[0])\n",
    "                metadeEsquerdaOrdenada.pop(0)\n",
    "            else:\n",
    "                listaFinal.append(metadeDireitaOrdenada[0])\n",
    "                metadeDireitaOrdenada.pop(0)\n",
    "    return listaFinal\n",
    "\n",
    "print(\"Resultado ordenado:\", mergeSort([]))\n",
    "print(\"Resultado ordenado:\", mergeSort([1]))\n",
    "print(\"Resultado ordenado:\", mergeSort([2,1]))\n",
    "print(\"Resultado ordenado:\", mergeSort([3,2,1]))\n",
    "print(\"Resultado ordenado:\", mergeSort([4,3,2,1]))\n",
    "print(\"Resultado ordenado:\", mergeSort([5,4,3,2,1]))"
   ],
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   "cell_type": "markdown",
   "source": [
    "Podemos observar a árvore de execução recursiva decorrente das chamadas do mergeSort.\n",
    "\n",
    "Aqui utilizaremos a ferramenta PyInstrument para fazer a impressão desta árvore.\n",
    "\n",
    "Perceba que o mergeSort chama a si mesmo duas vezes para processar cada uma das suas metades.\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "outputs": [
    {
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      "            |     `- \u001B[33m0.190\u001B[0m list.append\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "            `- \u001B[32m0.056\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "               |- \u001B[32m0.026\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "               |  |- \u001B[92m\u001B[2m0.012\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "               |  |  `- \u001B[92m\u001B[2m0.005\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "               |  `- \u001B[92m\u001B[2m0.011\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "               `- \u001B[32m0.026\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "                  |- \u001B[92m\u001B[2m0.011\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "                  |  `- \u001B[92m\u001B[2m0.005\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "                  `- \u001B[92m\u001B[2m0.011\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "                     `- \u001B[92m\u001B[2m0.005\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from pyinstrument import Profiler\n",
    "p = Profiler(interval=0.00001)\n",
    "p.start()\n",
    "resultado = mergeSort([500-i for i in range(500)])\n",
    "p.stop()\n",
    "print(p.output_text(color=True, show_all=True, timeline=True))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Provavelmente irá perceber que a condição de parada não foi impressa, apesar de ter sido executada.\n",
    "\n",
    "Isto é resultado da medição por amostragem feita pelo PyInstrument.\n",
    "\n",
    "Se mudarmos o intervalo de amostragem, podemos aumentar a probabilidade de uma amostra aparecer."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  _     ._   __/__   _ _  _  _ _/_   Recorded: 18:23:22  Samples:  6\n",
      " /_//_/// /_\\ / //_// / //_'/ //     Duration: 0.001     CPU time: 0.001\n",
      "/   _/                      v4.3.0\n",
      "\n",
      "Program: /usr/local/lib/python3.10/dist-packages/ipykernel_launcher.py -f /home/gabriel/.local/share/jupyter/runtime/kernel-52e1595c-cc7e-44ce-95b2-61140f46f792.json\n",
      "\n",
      "\u001B[31m0.001\u001B[0m run_ast_nodes\u001B[0m  \u001B[2mIPython/core/interactiveshell.py:3265\u001B[0m\n",
      "|- \u001B[31m0.001\u001B[0m run_code\u001B[0m  \u001B[2mIPython/core/interactiveshell.py:3416\u001B[0m\n",
      "|  `- \u001B[31m0.001\u001B[0m \u001B[48;5;24m\u001B[38;5;15m<module>\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3508207992.py:1\u001B[0m\n",
      "|     `- \u001B[31m0.001\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|        `- \u001B[31m0.001\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |- \u001B[33m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |  `- \u001B[33m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |     `- \u001B[33m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |        |- \u001B[32m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|           |        `- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |           `- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |              `- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSortCondicaoParada\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/1625165271.py:1\u001B[0m\n",
      "|           |- \u001B[32m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|           |- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mmergeSort\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/3417733175.py:1\u001B[0m\n",
      "|           |  `- \u001B[32m0.000\u001B[0m list.pop\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "|           `- \u001B[32m0.000\u001B[0m list.pop\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "`- \u001B[32m0.000\u001B[0m __exit__\u001B[0m  \u001B[2mcontextlib.py:139\u001B[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from pyinstrument import Profiler\n",
    "p = Profiler(interval=0.0001)\n",
    "p.start()\n",
    "resultado = mergeSort([100-i for i in range(100)])\n",
    "p.stop()\n",
    "print(p.output_text(color=True, show_all=True, timeline=True))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Tangente recursiva\n",
    "\n",
    "A mesma estratégia recursiva pode ser utilizada para resolver os mais diversos problemas.\n",
    "\n",
    "Podemos utilizar recursão, por exemplo, para calcular o valor aproximado da tangente de um ângulo."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tangente de Pi/4 é 1.00\n",
      "Tangente de Pi/2 é -9651074695810.24\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 720x720 with 1 Axes>",
      "image/png": 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ECSHE2LgcThS3m5CY4d8iqq/XNu42Goc7SyYm4RlfBmEXAU8PcexERVG2KYrymqIos304JqEDr7anAK1Zq9uE2W7HMOgMKI+bQoixcTvdWBx2DEHRw543cqPWgSQTJkbikyBMURQLUAA8N8jhz4BMVVWPAe4BXhriGpcrivKpoiifNjQ06DZWMX5e7ZYP4OzCplowOe39H0mzViGEN7jdYHHYweKNfSOP7BMmxEh8lQk7C/hMVdW6ow+oqtquqmpn3+9fBcyKosQPct7DqqouVFV1YUJCgv4jFmPm1W75AM5uHJgxORxHfCyxlxBivFRV0YKwce8bidSECY/5Kgi7mCGWIhVFSVYU7d9cRVGO7xtTk4/GJXRQWQmhoRAzfJ3r6Lm6cShmjENlwuSpUwgxRm7FQJBrdPtGjmrLosNIECZGouvbkQCKooQBZwA/POyzKwBUVX0Q+DrwI0VRnEAPcJGqyr+6gcyrjVpBy4QZzBjcziM+lm2LhBDj5TaYCHENnwnr6YGOjtEvR0p5vhgt3YMwVVW7gLijPnvwsN/fC9yr9ziE73i1R5jbBW4bDqMFg6O3/2N5O1II4Q0uoxmLo3vYIGz03fJlOVJ4RjrmC6+rqPBmt/weABwmC0ZcRxySRJgQYrycJgtB6vDLkbJlkdCLBGHCqxwOrU+YN9tTgBaEGZRD0ZaiIMGXEGLcnCYLZoZfjhzdlkVIYb7wmARhwqtqarSJx5tbFgE4zBYMhkMTnBTmCyG8wWG2EIRdMmHCLyQIE17l9fYUrm7cLgWHxYLRdOS/rv1PmfK4KYQYA4etF4fFgkWxgTliyPNGv2/kkX3CZGoSI5EgTHiV17vlO7tx9FgAMFoOvUcihflCiPFqbawGwGx0gME85Hn19RAerrXeGZ5MTMIzEoQJr9KlW35fEGYOshxxSFpUCCHGo61OC8JMJtew541lyyKQTJgYmQRhwqsqKrQnxsjhm0+Pnqsbuy0IAHNISP/HUhMmhBivjmZtndE0dBIMGO2WRUiKXnhMgjDhVXo0arXbtAyYJTTMSxcVQgjoamkGwBQ0/IQ1+kyYvB0pPCNBmPCqykovLkUCuLqx9QVhIYel147cwNuL9xNCTBk9bS0AmEOMw57n8ZZFffOTBGFiJBKECa/yard80DJhDm05MiTqyM0opSZMCDEevZ3tAJjDg4c8x+2GhgbPliNlUVKMlgRhwmvsdq12wmvtKUCrCXNombDQ6ENBmKLIU6YQYnzsXVofQkvY0K89NjeDyyXLkUIfEoQJr6mu9nKjVgBnNzaXFoRFxiX3fyyF+UKI8bL3aPvRBsd4u1GrzElidCQIE17j9fYUoNWEubTlyOjE1CFOkglPCOE5Z68NgJDYuCHPGfWWRYBkwoSnJAgTXuP1bvmgZcLcB4OwtP6P5U1wIcR4uZ0OAMLik4c8x6NMmExMwkMShAmv0SsT1usOwmy3YzyqmY8U5gshxkN1uLS5JWToTNjotywa5PoyNYkRSBAmvKayEqKiIGLoLdg85+zCpgZhttuO+FgeOIUQ4+V2Q5DDBuahu0vX14PBALGxo7miTEzCMxKECa/xensK0FpUKGaMfcsGh5OnTCHEeKiqgsVhB/PwhfkJCWAcvpXYENcfx+DElCBBmPCaigov14OB1qJCsWB02o/4+MhmrTLTCSE851aMWFz2ETNho1+KlMJ84RkJwoTXeL1bPmiZMIMFo9s54JDMb0KI8XApJoJcwy9HjnrfSJA6CeExCcKEV9hs2hOj14MwVzcOgwXDUUGY9AkTQoyXy2jG4h55OdKjLYuAg3OSZMLESCQIE15RWal99fpypLMbu8mCQXUPPCZvRwohxsFpsmBR9VuOFGIkEoQJr9ClPQVoNWGmIAzKkUGYbFskhBgvh8mCRbWBefBXuu02hY4OqQkT+pEgTHjFwUyYHjVhDrMFo+HIyU0K84UQ4+UwWzArDlAG/1HY3mYCPO8RJvkwMVoShAmv0KVbPuB2dGG3WDCYBv6rKrGXEGKs3C4XdosFk2HgSz8HtbdqfSlGXROmSCZMeEaCMOEVFRUQEwNhYV68qKri6HSComCyHNmkR15CEkKMR2tDtTa3GF1DntPe6mkmTCYm4RkJwoRX6NKewtWLo9cCgMliGeZEedwUQnimvbEGAKNpkJd+Dp4zxuXIgyQTJkYiQZjwCl265ffWYusLwswhwUcckkyYEGI82htqATBbhp5M2lq0DLxkwoReJAgTXqFLt/zOMuy9QQBYQgeuc/Y/ZcrjphDCQ50tDQCYgobej6i91UR4OISGenp16RMmRkeCMDFuPT3Q1KRDJqxrP3ablgkLCg8/4pA0axVCjEdPexsAphDzkOe0txk9W4qUwnzhIQnCxLjp1p6is4xeh5YJC42KHnBYJjghxFj1trcDYAkfOs3V3mrysB5MliOFZyQIE+OmV3sKusrocmmdrMNi4o44JH3ChBDjYevsACAocvBGrQDtLcYxbFl0iExNYiQShIlx061bfmcZ3W5tGTI8JsHLFxdCTGXOni4AgqJjhjynrU0yYUJfEoSJcdNt38iuMrpcIQBEJaYecUi2LRJCjIe7txeAsPjkIc/paJWaMKEvCcLEuFVUQFwchIR48aLOHuipocelFebHJB0Z4UlhvhBiPNx2OwARiUOn8N1uZcw9woQYDQnCxLjp0iOs+wAAvW4zJocDS/DA4tlDT5kShAkhPON2uTE5HJjDhy918Kwm7ODTobSoEKMjQZgYN1265XeWAWBzmzD3PbEeTpq1CiHGw+0Ci8MO5shhzxvLcqRMT2K0JAgT46ZLJqxLC8LsqgmTc2AQBofnv+RxUwjhGbdqIMhhA3PUsOeNZzlSMmFiJBKEiXHp6oKWFn265WMIwqkYMQ4ShElNmBBiPFyKEYvTy5kwpDBfeEaCMDEueranICwTt2LC4HIOfo5McEKIMXIrJiwuO1iGzoQZDCpxcUMeHoQsRArPSBAmxkXPRq2EZeEymDC6BwZhRzZr9fK9hRCTntNoweK2gXHojvkRUS4M4/gpKZkwMRIJwsS4fPGF9nXWLC9fuGs/hGfjMpkxqK5BT5EJTggxVg6jGbNqH/Ytn8joIbLwQznsWpITE6MhQZgYl82bITt7fMWrAzg6wNZ0KAhTBkZbUhMmhBgPp8mCGcew50RGDf4AOFryoChGIkGYGJfNm2HxYi9ftK89BWHZOMxBGAyDz2TSJ0wIMVZ2cxAmhs90RcV4mAk7qk+YECORIEyMWXW11iPM60FYX3sKd8g0HBYLRtPAf02lT5gQYqzcLhd2iwWTYfggK8LjTJi8HSk8I0GYGLPNm7WvemXCOhwRqAYDRpNxwClHFubLTCeEGL2OlnptbjG6Bz3utGs/GqOix7EcKQ+KYhQkCBNj9vHHYDbDscd6+cKdZWAKo3TXbgBCogd/hVyWI4UQY1H6xYcAhIUNHoR1dZgBiPR0OVI28BYekiBMjNnmzTB/PgQHe/nCXfshLJvKL7cDkJSXN+AUWY4UQoxV5c5tAMSkhAx6vLvTBEBU1FhrwiQRJkZHgjAxJi4XfPqpDkuRoNWEhWfTWl0NQN6i5YOeJk+ZQoixODi3pOSnDHq8o03LhEV42qLiKDJHiZFIECbG5MsvtS2LvB6EqWpft/xsejttBHd3k5IzsAmZ1IQJIcaqt9NGSHc3sRnTBj3eWKM1cE1NH3zf2qHJcqTwjARhYkx0K8q3NYGzE8KzsRNEaGeLl28ghJjqHFiI62qCkORBj9dVasuUIUPUjA3p8KdDWY8UoyBBmBiTzZshNhZyc7184a6DPcKy6AmNIsjdO+hp0qxVCDFW3aHRxDmaIHLGoMfrqobeymh0tDlJMmFiJBKEiTH5+GMtC+b1Avmu/QC09YTTFRFJUMjA9hQHyQQnhPBUS30VXRGRxBoHD8J6e6G5bqxvG0n6S3hGgjDhsfZ22LVLp6L8vh5hRV+WAhCZlDDoaYoiLSqEEJ4r+mgjANHh7RAUN+D47t3gdnsnmJIHRTESCcKExz79VJtcdAvCLLFUFe8FIGXGnEFPk8J8IcRY1OzZCUBkyuDZru3bx3N1aVEhPCNBmPDYwaL844/X4eJ97Sna6xoAsJ64QoebCCGmqoNzS8LswQtat28Hk8XDgvyDpFmr8JDJ3wMQgWfzZsjL0wrzva6zDKLnYetxEWZoJyYxbdDTpFmrEGIs7D1OIgzthGXMH/T4tm2QmNrt20GJKUsyYcIjqqoV5Z9wgh4Xd2uF+eFZ2AzBhHS3jTiWvt/pMBghxGRkN4QQ1z14Ub6q9gVhaT1jvHrf06F66HpCDEeCMOGRAwegrk6nerCeWnDbISyb7vBoLNiGPFUyYUKIsegKjybWPXgQVlcHjY2QNOZM2JF9wiQIEyORIEx4RLcmrdDfI6y+xUxvaBjB4UHDni6ZMCGEJ2r27aInNIxYUzOEZQ04frAoPzF9rJmwg1QpzBejonsQpijKfkVRdiiK8oWiKJ8OclxRFOUfiqLsVRRlu6IoC/Qekxi7zZshKAjmzdPh4n3tKfbtqQUgOnXwbtYgzVqFEJ4r2fIOABFRdjAMLInuD8LGmgmTwnzhIV8V5p+qqmrjEMfOAvL6fi0GHuj7KiagzZthwQKwWHS4eF8QVn2gEYglfc6xw54uE5wQwhP1e0uAaKKnRQ96fPt2SEuDkPCxbtwt+S/hmYmwHLkGeFzVfAxEK4oy+Nb2wq8cDti6VaeifNCWI4OTaW9sQ3G7mXHC6UOeKn3ChBCe6mxoRnG7ST5m/qDHt23zbpZfpiYxEl8EYSqwXlGUrYqiXD7I8TSg4rA/V/Z9JiaY7du1LT10qQcDLRMWno3NphLe0UZIeJRONxJCTEUOm5vojlYsSQMjLbtd65Z/zDHjuIFs4C085IvlyKWqqlYpipIIvKkoyh5VVTd5epG+AO5ygGnTpnl7jGIUdC3KB609RfwS7OZQgnvahz1VkTePhBAespnDiOsZ/M3IoiIt2z9vHox1MfLoyEvmKDES3TNhqqpW9X2tB14Eju6zXgVkHPbn9L7Pjr7Ow6qqLlRVdWFCwuD7CQp9bd4MiYmQmanDxd1O6K7AHZpJZ0QMFoNj2NOlMF8I4Qm3y0VHRCyxahNEWgccP1iU763lSEmEidHQNQhTFCVMUZSIg78HVgI7jzqtEPhW31uSJwBtqqrW6DkuMTabN2tZMF16dHVXgOqitt6MIyiIkKjQEb9FnjKFEKO1/8st2IOCiLK0gzlywPHt27UXjvLzx3MXyYQJz+i9HJkEvKhoP7VNwFOqqr6uKMoVAKqqPgi8CpwN7AW6ge/oPCYxBi0tWrr+W9/S6QZ9b0bu39cORBOXMfySsxTmCyE8UfbZhwBExA3+FLl9O8yaBWazL0clpjpdgzBVVUuBAWWOfcHXwd+rwE/0HIcYv08+0b7qVw+mBWG11R1gjiZzvie7g0sQJoQYXmPpPjAmEpM7+Htf27bBGWeM8yb9T4fanCTPh2IkE6FFhQgAmzdr88uiRTrdoLMMFAOtbXaMTie5C5YNe7psWySE8ERPcxtGp5PkYwY+4DU0QE3NON+MBGTbIuEpCcLEqGzeDDNnQuTAUgrv6NoPoRnYnAbC21swBwWP+C2ybZEQYrQcLgOxHc2Y4uYOOLZjh/ZVl51AhBiGBGFiRKp6qChfN51lEJaNzRJOkL1zxNOPrAnTb1hCiMmhxxJJnG3w9hTeezNSCvOFZyQIEyMqLYWmJh075QN0leEMmkZnZAwWk3tU3yITnBBiNBy2XtojY4hRWyA0fcDx7dshKUlrwTMuhz0dSsWEGA0JwsSIdG/S6uyBnhqqa4JwmUyEx4y85il9woQQo7X3s/e0uSW0B5SBP/a2b9dnKVIeFMVIJAgTI/r4YwgNhdmzdbpBVzkAFQe0Bq1xWdkeXkBmOiHE0Mq/0F7vjkgKGnDM6YSdO70VhEn+S3hGgjAxos2bYeFCMOnV0KSvPUVdgxaETV940ojfItsWCSFGq+WA9qCXMDNvwLGSErDZ9AnCZI4SI5EgTAyrpwe++ELnovyu/QC0daiYbTayZo/cB0OatQohRsve1onFZiNxztIBxw4W5Y+/PcXhVEmKiVGRIEwM6+WXwW6HVat0vElnGRgs9KhBhHW0YDAaR/VtEnsJIUbDrlqI7WzGEDOwpmL7di3LP2PgS5OeUyQTJjwjQZgY1lNPQUoKnHKKjjfpLIOwTHqDIwhydI/qW6QwXwgxWl0hUcTZmyBi4HLk9u1aABY0sFxsXCQRJkZDgjAxpJYWePVVuOgiGGVyamy6ynCYptEZGU1Q0OinLgm9hBAj6elsoz0imkhDK5hCBxz37puRkgkTnpEgTAzp//5PW4q85BKdb9RZRmV1JKrBQHh8zKi+RbYtEkKMxp6PN2hzS7hrwLGWFjhwQIIw4T8ShIkhPfUU5OXBccfpeBNHO9ibqarVUm1JeQOXC4Yk2xYJIUZQufNzACLTowYc0227IhVZjxSjIkGYGFRNDbz9tpYF0zXr1LkfgIYm7SZ5i5aP6tukJkwIMRqdlZUAJB9z7IBjXn8zUgrzhYf06vwkAtyzz2oTyMUX63yjvh5hbT0mgs3dpOTMGvW3ygQnhBiJvctGiLGb+BlnDTi2fTvExWkvH3mHbFskPCOZMDGop57SliGtVp1v1KkFYd1KCKGdLaP+tiObtUo0JoQYnE0JIa5r6I27583TI9uvzUnyoChGIkGYGKCkBLZs8UEWDLQgzBRGd2g0Qe7eUX+bNGsVQoxGR2gMsY4mCE464nO3W6sJ8249mOS/hGckCBMDPP20FuRceKEPbtZVRi9ZdEVEEhSiZx8MIcRU01JfRWdEJOHmzgHprtJS6O72chAmNWHCQxKEiSOoqrYUecopkJ7ugxu27aa6VntCjUxKGPW3SYsKIcRIij7aCEB49MAfddu2aV+9/mbkQTJHiVGQIEwc4fPPoajIB73BALoqoHMv5c1ab7AU68AtRYYjT5lCiOHU7f4CgKjM5AHHtm8HgwFmezbtjEAyYcIzEoSJIzz9NJjN8LWv+eBmddpTam2rtl9I/gmnjfpbpUWFEGIkPbW1AKQtWjbg2PbtkJ8PISH63V+CMDESCcJEP7dbC8LOOgtiY31ww9qNEJRAh81IWEc7sckZHn17/wQnM50QYhC2XpWIjnaisk8acMy72xX1UaRFhfCMBGGi33vvQVWVj5YiVVXLhCWdhs0QTHB3m0ffLjVhQoiR9JjCie1ugvCcIz5vbtYK83WrB+sjz4diJBKEiX5PPQVhYbB6tQ9u1r4HemogeQXd4dEEYRvHxWSmE0IM1B4WQ5S7FYyWIz5/7TXt6+mn63VnmZPE6EgQJgBto+7nnoOvfAVCQ31ww1qtHqyuN5Pe0DCCw4M8+nbpEyaEGE7Nvl30hIYRbukZcKywEJKSYNEiPe58aHKSqUmMRIIwAcAbb0BLi4+WIkFbigzLomjnXgCiUwe+vTQSmeCEEEMp+eQtAMLjj3zAs9u1TNjq1drbkV538AlRSibEKEgQJgBtKTIuDs44wwc3c7ug7h1IXkH93hIA0ucM3Fx3OEduWySEEEdqLt4JQGx+7hGfv/sudHRAQYH+Y5A5SoxEgjBBZ6eWnr/gAq09he5aPgNHKyStoKOhBcXtZsYJnhVnSIsKIcRwehu1uSXzhFVHfF5YqLWl0K8eTDnsn0IMT4IwQWGhtn2Hz5Yi++rBSDoNm00lvKONkPAojy8joZcQYig2h5HojlaCU47r/0xVtflu5Uo9+4NJTZgYPQnCBI8/DtOmwZIlPrph3UaImgMhSfQGRRDc0+7xJaQwXwgxnI6gGGJ6miAorv+z7dvhwAHfLEUKMRoShE1xW7ZoRfk/+IFORapHc/VCw/uQvIKSrZtoi00gPHyMiXt1wG+EEIKSrZtoik0kxVR3xOdr12oPcOeco+PNFYWDc5I8H4qRSBA2xd1wA8THw1VX+eiGjR9pgVjSCra+9CwAM0/1vDhDmrUKIYby+YtPAZA5P/6IzwsL4YQTtPYU+jn0dqQEYWIkEoRNYZs2wfr18NvfQkSEj25auxEUIySdQktjF2HtrRx35gVjupQqmTAhxCA6mrqIam8l55wr+j+rrIStW323FCnPiWI0JAibolRVy4KlpMCPf+zDG9duhNhFdHU7aYlJJaqnEYPR6PFlJBMmhBhMV1sz9TEZTO/aiyFxaf/nL7+sfdU/CJPCfDF6EoRNUevXa3tF3nCDnm8JHcXRDs1bIHkF7z/7MI6gIJLzs8d8OZnghBBHe//ZB7EHBZGSbAPDoQe8wkLIyYGZM30wCJmbxChJEDYFHcyCZWbC97/vwxvXvQuqC5JXULF9F0ank6WX/HBMl5I+YUKIwdRv24HR6cS65mv9n3V2wsaNWhZM9yy6IpkwMXoShE1Ba9fCp5/CTTeBxTLy+V5TtxGMwRB/Ih2maGKaqohJTPPhAIQQk12LOZ7Mpv1Ezr6w/7P167XtinxTDybbFonRkyBsinG54He/g/x8uPRSH9+8diMkLGXHBxtpj4kjKtI05ksduW2RPG4KIWDHpldoiYkn3VwNluj+zwsLISYGTjrJt+ORTJgYiQRhU8z//gc7d8Itt4Bp7DGQ53rqoG0nJK1g++uFAMxbtXrMl5NmrUKIo+1+9XkAMk+c0f+Zy6UV5Z99to+2ZeNQnzAhRiJB2BTidGpLkHPnavtE+lTdW9rX5BW0tTiIaG1i3vKxB2EgsZcQ4kjtbW5iW5uYfvbP+z/76CNoavJhl3ypCRMe8GUuRPjZ449DSQm89JKPuuMfrm4jmKNpc6fQEpdKUsuBcV1OCvOFEIdra6yhLi6DeY1fQGRe/+eFhVoG7MwzfTseBQnCxMgkEzZF2GzaEuSiRX7aN612IyQt5/1n/o3TbCZ9jtUPgxBCTFYfPHUfTrOZ5Mwj+w4WFsLy5RAV5auRSEW+GD0JwqaIf/5T27j2ttv80Oi0sxS69kPSCqr37MNkt7P04rG1pjhImrUKIQ7XvLsEs93OrK8f6rtTVKT98u2DpyxHitGTIGwK6O6GP/wBTj4ZzjjDDwOo3QiAO2E57UFxxDRXEx4dP8I3jax/gpOZTogpze1y0RCaQlZzGWE5q/o/X7dO+7p6fOWnYyMPimIUpCZsCrjzTqit1d6M9EsGqXYjhKTwxZZddEZFkxraO+5LSiZMCHHQFxteoD0yhvnsAsOhVyALC+GYY7TG1D4jhfnCA5IJm+S2btVqwb7+dVi2zA8DUN3am5FJK/hy43oAFhSc751LS58wIQSwd/1aAKaftqT/s8ZG+OADWLPGP2OS50QxGhKETWJdXXDJJZCcDA895KdBtO4EWwMkr6C9E6Ka67Eef9q4LytvRwohDmrrsZDYXEfm6T/r/+zVV8Ht9seLSIf6hEkmTIxEliMnsZ//XGtJ8dZbEBvrp0HUbgCg0ZVHc3wpaS37vXZpmd+EEA1VpdTGZ3Bsw1YIOjTRvfQSpKbCggW+HpHkwKaKnuYeSl4toaiwiOisaM74i+dF1xKETVIvvAD/+hdce632erZfqCqUPgIxx/JB4Su4jUFMO/YYr1xaObwptTxuCjFlffLkPbiN0STnR/d/VlGhFeVfeaV/60dlapp8mvc1U1RYRNHaIg68fwDVpRKeEk6cNW5M15MgbBKqqIAf/EDrCXbLLX4cSN1GaPsSTniUusINWKLTWXrhL71yaSnMF0IAtJRWExQbzJyLftH/2d//rgVAP/+5HwakyAbek4nqVqn6pKo/8GrY1QBA4txElv52KdYCK6kLU1EMY/s/XIKwScblgm99C+x2eOopX+2VNoQ9f4fgRNzp59MWvp2Y1mqCwyK8dnl5yhRianO7XNRFpJPVXEpw8nEAtLbCww/DhRf6+K3IfvJ2ZKBz9Dgo3VBKUWERxeuK6arrQjEqZJ6cyYLLF2BdbSVmeoxX7iVB2CTz17/CO+/AI49Abq4fB9JeDNWvwNyb+eTV5+gOj2RamN1rl5fCfCHElsJ/0xkeSZKhs39SePBB6OyEa67x79hk26LA0lXfRfErxRStLWLf+n04e5xYIizknZVHfkE+eWfnERIT4vX7ShA2iWzZAr/7HZx/Pnz7234eTNE/wGCB3Cso+s+1EJXJ4q9f6tVbSLNWIaa2A+9uhJhZ5J2rdWO12eDuu7Wm1PPn+2lQUisRMBr3NGrLjIVFVHxYASpEZkRy7HePxbrGStYpWRgtxpEvNA4ShE0SnZ3wjW9ASorWjsKv84C9BUr/A1mXQEgS7TYTMY21ZM053mu3kHlOCNHiiCClsZr0JdcC8MQTWmPq//7Xn6OS5ciJyu1yU/FhhbbMWFhMU3ETACkLUjjlplOYsWYGScckofjwB4wEYZPEVVfB3r3aUmSMd5aqx27fv8HVDdarqNm3i5b4FDJay3W8ocx0Qkw1Nfu+pDY+jQWNn4LRgtutlWPMnw8rVvh7dKoU5k8Q9k47+9bv0wKvl4vpaerBYDaQfVo2i69aTP7qfKIyfLa7+wAShE0C//ynVgN2/fXa/pB+5XZC0T2QuBxi5vPRg1ejGiKYfoL3smAgNWFCTHWfPXk3qiGNlHkZgNaSoqhIeyHJv5lypT8FJpkw/+io7qBonZbtKt1YisvmIjgmmPxz8skvyCf3zFyCIoP8PUxAgrCA98wz8MMfwllnwU03+Xs0QOVL0H0AFv4DgNoDzYREKCw57zdev5VMcEJMXbU1NsIiOpl30fWAlgXLzNRqYv3qiCaGwhdUVaV+R31/fVf1lmoAYqbHsOjHi7AWWJm2dBoG08TbJEiCsAD28stw6aXanpDPP+/ndhQHFf0dwqdD6rl89OJ/aEjOJLu9HHNQsFdvoyjglnlOiCnp4+cfpDJ5OosbP8IclcGHH2r7RN59N5gm0E81eVDUj8vhonxTeX99V+v+VlAgfXE6p91+GjPWzCB+ZrxP67vGYgL96yo88fbb2qbc8+drafjQUH+PCGjaAg0fwIK/g8HItjfewRKTyqqrrvP6rSb4f1dCCB3t2fAeQbHTWPSDHwJaFiw2Fr73PT8PDDhYDCZTlPf1tvay9/W9FBUWUfJqCbY2G6ZgE9PPmM6y65eRf24+4cnh/h6mR3QLwhRFyQAeB5LQcrMPq6p691HnLAfWAmV9H/2fqqq36jWmyWLzZm1T2txceP11iIz094j6FN0NpgjI+Q7b3nqJuuRsMprLSJymd8MyedwUYqrYtuF/lCfncVz9FuLm/ZGiIli7VquJDQvz9+iOJJmw8Wstb+3Pdu1/Zz9up5vQhFBmfm0m1gIr00+fjiXM4u9hjpmemTAn8CtVVT9TFCUC2Kooypuqqu466rz3VFU9V8dxTCrbt2v1X4mJ8OabEDe27aq8r7sayp+F/CvBHMnm517AFJfJih/+VJfbHZEJk5lOiCljx/MvYIrP49hLvgrA3/4GFgv8VJ+pZgykRcV4qKpKzdaa/vquum11AMTPiOeEX57AjDUzSFuchsE48eq7xkK3IExV1Rqgpu/3HYqi7AbSgKODMDFKJSWwcqW29Lhhg9YTbMIouR9UF1h/SsnWTdQlZJPcWEbm7IW63VImOCGmlpItb1GWaGVO/TbSTvo9tbXw2GPwne9oD6YTguwd6TGnzcn+t/ezZ+0eitcV01HVgWJQyDgpgzPuOAPraitx+RMl4+BdPqkJUxQlCzgW2DzI4RMVRdkGVANXq6r6pS/GFGgOHIDTT9f2hnz7bcjO9veIDuPsgb0PQvoaCJ/Ou/+5GTUum6WXfku3W0qLCiGmnk//8wBqwizmFZwEisI//gEOB/zqV/4e2dGkRcVIupu6KXm1RNsm6I192DvtmEPN5K7KJb8gn/xz8gmNnwjFzvrSPQhTFCUceAH4uaqq7Ucd/gzIVFW1U1GUs4GXgLwhrnM5cDnAtGnT9BvwBFRaCqtWaRvTvv02zJzp7xEdZf+TYGsC68+pKtlJfVQGSfVlzDzxFl1ve2iCk5lOiMmuqngbZTH5zKj7kpyznqOjAx54AL76Vcgb9KeGv0hh/lCa9zVTtFZbZjzw/gFUl0p4SjhzvzEXa4GV7NOyMQVPrfcFdf3bKopiRgvAnlRV9f+OPn54UKaq6quKotyvKEq8qqqNg5z7MPAwwMKFC6fMT91334WvfQ3cbnj1VViwwN8jOoqqam0pYuZD4sm8+cfv4IjJ5riCs3W9rbwdKcTU8uG9t+GIm8PsU3JBUXjwQe3B9Ne/9vfIjiY1YQepbpWqT6q0ZcbCYhp2NQCQNC+JpdcuxVpgJfW4VBTD1J3Q9Xw7UgH+DexWVfXOIc5JBupUVVUVRTkeMABNeo0p0Pz733DFFZCTo7WhmFhPe32qCqHtSzjhUZrrKqkNTiaxtoyFZ+nfOVYSYUJMDc015ZSG5pBbU8TsG5+gvBxuuQXOPhsWL/b36MThHN0OSjeWUrRW2yaoq64LxaiQdUoWCy5fgLXASky2v/fWmzj0zISdBFwK7FAU5Yu+z64DpgGoqvog8HXgR4qiOIEe4CJVnerPDlrd1zXXwF13aYX4zz4L0dH+HtUg7G2w5ScQNQcyL+aVa3+CLSydWcd4d4uiwUhNmBBTxzt3/JreyFnMyI5GxcAVV2if33+/f8c1KGXqZcI66zopeaWvvuvNfTh7nARFBpF7Vi7WNVZyV+USEhPi72FOSHq+Hfk+IyyLq6p6L3CvXmMIRO3tcPHF2tLjT38Kd945sTpAH+GL30BvDZz8Il2dndSqkcTVVXCKr/ZPmiITnBBTWVdrE2WGdKbV7ee43/2TJ5/S+iPefbe2TdHEM/nfjlRVlcY9jf31XZUfV4IKUdOiOPZ7xzJjzQwyT87EaDH6e6gT3kT98T4llZbC6tXaJrQPPED/096EVPcO7H0IZl4NcYt4+cYr6Q5PYO70WJ/cXlGkMF+IqWDjX66iMzyPExIbaGgycdVV2hLkT37i75GNbDJlwtxONxUfVmj9u9YW0by3GYCU41JYfstyrAVWkuYlTfhtgiYaCcImiHff1bYhcrlg/Xo47TR/j2gYzm7Y/H0Iz4W5t+Cw9VLVYSTGWcvKG3yT2JT/zoWY/By2Xvb3xJLcUc2Jf3uQy74HbW3wr3+BccImWSbP25G2Dhv71u+jaG0RJa+U0NPcg9FiJPu0bE781Ynkn5tPZPpE2bIlMEkQ5me9vfC732ldn/PzJ3AB/uG2/w4698Hp74IplHV3XENHdCzHhPZg8OHM2P+UOZkeN4UQ/Tb8+UpaojNYzk7WvxXKE09o8+WcOf4e2UgCt09Ye1U7xeuKKVpbRNlbZbjsLkJiQ8g7Jw/rGis5K3MIigjy9zAnDQnC/OiTT+Cyy2DPHvjhD7VNaCMi/D2qETRu1lpS5P0IEk/G7XJRUd1FpMHG6uv/5rNhSGG+EJOb2+WirNFMnKGR+Tf8k2MWwowZ2h6RE1qAFearqkrd9rr+ZcaarTUAxOTEsOjKRcxYM4OMJRkYTJNjm6CJRoIwP7DZ4NZb4U9/gtRUeOMN7S3ICc9lg83fhZA0mP8nANbecS2tcUnMUBsxmsx+HqAQYrJ4408/oiEujSU9X3DTbdGUl8P770PQhE/CTPzCfJfdRfmm8v79GdvK20CB9BPSWfHHFVjXWImfES/1XT4gQZiPffaZlv3auRO++13t7ceoKH+PapS+/AO07YLlr4I5kv07P6G4WSGmu5Y1f/qLT4cic4MQk9f+Lzaxoz2G5O5qwr96H/84HX78YzjpJH+PzDMTKRPW29pLyWslFBcWU/JaCbY2G6ZgE9PPmM7JvzuZ/HPzCU8K9/cwpxwJwnzEbofbb4c//AESEuDll+Gcc/w9Kg+0bIMv/whZl0LqWbhdLl697wGccWksXX0awWG+X0eVmjAhJh+3y8XbD/0TR1wmJy7L4BtXpZKaCn/8o79HNloT5wmxdX9rf7ar/N1y3E43oQmhzPzaTKwFVnLOyMEcKisY/iRBmM5UFQoLta01iovhm9+Ef/wDYgKpYbDbCZu/B0GxcNxdAPzv5p/RkJxFbncVC1ae7/MhSSZMiMnp5Rsu5UCylcWtWygsfpmdO2HtWogMlJfw/FgTpqoqNVtr+uu76rbXARA/M54Tf3Ui1gIraYvTMBilvmuikCBMR59+CldfrbWfsFoDMPt10J6/QfNWWPocBMWxY9MrlLqjia87wEX/eNBvw5I+YUJMLl++9Qw7Ddlk1pWS8r2n+f0SuOACKCjw98g856vnRGevk7K3yygqLKK4sJiO6g4Ug8K0pdM4444zsBZYicuL89FohKckCNPBgQNw3XXw5JPa0uP998P3vw/mQMz61r8H22+CjPNg2tdx2Hp559m1KJFxnPGdS/1WjC9vRwoxuTh6e/jwhQ0YIhOYv+pU1nwtgthYbeUgsBzqJK1XJqy7sZuSV0soKixi3xv7sHfaMYeZyV2Vi7XASt7ZeYTGh+pzc+FVEoR5UXu7Vrdwl7Zix7XXwm9+E0CF90dr3QnvFkB4Fix6CICnr/sxzYmZzDa2kr9ouV+HJ4SYPF7+7aVUJ85lSe82rrj9j9TXw6ZNkJTk75F5Sp8cWPPeZvas3UNxYTEH3j+A6laJSI1g7jfnYi2wkn1qNqZg+ZEeaOT/MS9oa9O2GbrzTmho0Oq+/vAHmDbN3yMbh64D8PYqMIXCqW9AcDwfv/QY5WHpJNWWct69j/h1eLJtkRCTx5bn7mJn5CzyanbzSMszbN4ML7wACxf6e2TjM55MmNvlpmpzVX9hfePuRgCS5iWx9LqlzFgzg5TjUqSNRICTIGwcamq0TWQfeEDLgp1xhvYGZKBPHNia4O0zwdkJZ7wHYZl0tjby8dufEGwJYfUvr/FpZ/zByLwjxOTQ2VzHJ++XEBoUSk34j3jmIQt/+hOcd56/RzZGyqE+YZ4GYY5uB6UbStmzdg8lL5fQVd+FwWQga3kWC3+0EOtqK9FZ0V4fsvAfCcLGYO9erbv9o4+C06nt+fib38CCBf4emRc4u+Gdc6GzDE5bD9FzAXj2hl/SlpDDwjhIy5sYe4ZIZwohAt9rN/yIxqRjmNNSw9fvPoXvfld7mzxwebZ3ZGddp7ZNUGERpW+W4ux1EhQVRN7ZeVgLrOSuyiU4Oli/4Qq/kiDMA1u3wl/+As8/DyYTfOc72tuPubn+HpmXuJ3w/oXQtBmWPQ+JJwOw4ZG/URk/ndS6vZxz03/9PEiNZMKECHzvPfAbdiXOY2bVDi557DmWL9dWFibLf9+DPSiqqkrj7sb++q7KzZWgQlRmFAsuX4C1wErmskyMlgm7Q7nwIgnCRtDZCc8+Cw89BFu2aL1qrrkGrroKUlL8PTovUlX45IdQ/TIsul97GxIo//JTtn1ZSYTbzdduvN3PgzySJMKECFzl295h6147MWovf3rzj2RmKrzwAlgs/h7ZOA0SQbqdbg58cICitVp9V8u+FgBSF6Zy6q2nYi2wkjg3Ueq7piAJwobw+efw8MNam4mODpg1C/7+d/j2twP4bcfhbL8BSh+BOb/TNucGasv28NJDj9AbEcPJ8zKITc7w8yAPGTBXqerkeXwWYpKrLfmMV/79LN0RsfRsiWF/Wx6bN0NsrL9H5j2qqtJV38WLl66n+JVielt6MVqMZK/IZsnVS8hfnU9kWqB0oBV6kSDsMJ2d8PTTWvD16acQHKw1Crz8cliyZBL/jN/zd/jydsj5Acy9BYCW+iqeu+NO2uOSWZQSxLILr/DvGAejHv2Hyfp/kBCTR0tNKYV3309TbCrRu3u5+Z2rWb8e8vL8PbLxa69sx9xiw9Bpo7elh4aWBkrqSrCutpJfkE/OyhyCIib8DuTCh6Z8ENbbC6+9Bs88A+vWQU8PzJmjNQj85jcDbHshT7ld8MWvYc+dkP5VbRlSUehqa+apm2+kJSGdeeE2Vv3oVn+PdIBJGxALMYl1tTTw4u9voTYhi+RdTfzw+Xt59FFYvtzfIxsbVVWp21bX30aiZmsNP/5LJxFuFVOwmaT8ZK7eejUGk2wTJAY3JYMwhwPeekvLer34otZeIiFBK7T/5jfhhBOmwA95Ryd8eAlUrYP8n8KCO8Fgwt7bzeO//SWNydnMUBv5yjX3+HukQzqi6FVVJREmxARm7+nkhWuvoiLFSsbOCi5/8V888QR84xv+HplnXHYX5ZvK+wvr2w60gQLpJ6Sz4o8riMl5CmOkE4vDTFBUMIYp+VNWjNaU+dfDbte6L7/wgvZ2Y2OjVmR/3nlw8cVw2mnaG49TQlcFvLsa2nbCwnsh/ycAuJwO/vOLK6hPziG3u4oL//ywnwc6tIFBspTpCzFRuRx2XvjFdylLmU32rlJ++PJjvPQSnHuuv0c2Or2tvZS8VkLR2iL2vrYXW7sNU4iJnDNyOOWmU8g7J4/wpHDt5FcO/SCRNjpiJJM67Ghq0pYa162D11/XMl4hIdpmsBddBKtWaXVfU0rjJ7BpDbi64ZRXIPVMANwuF/+56rvUJueS2bqfb9z1Hz8PdGQywQkx8bldLl742cUUp8wjZ08xP3n9Cd54A04+2d8jG1n12moe/9XjlL9bjtvpJiwxjFnnz8K6xsr0FdMxhw62d66k5MXoTaogTFWhqEgLutatgw8+ALdb23vs/PNh9Wo4/XQIC/P3SP3kwHPw0bcgOBlO2wDRs/sPPf6r71GVmEtawz6+dffED8AkEyZEYHjp519nd/J8ckuK+cWGx3j7bWVCNrZW3SrVW6spKiyi4oMKOAVKHywlISaBE68+kRlrZpB2fBqKYfRBljwoipEEfBBWXw8bN8KGDdqvAwe0z+fNg+uu0wKvhQvBMJXrIlVVe/tx+w0QvwROfgmCEwDtKfWJ31xOeUw2KbV7+e69j/p9S6LRGLRFhRBiwnC7XBT+6nx2xM8np7SE6zf9h/feN2G1+ntkhzh7nZS9VUZRYRHF64rpqO5AMSgEnRWEAwcL/72Qc846x8Orjn3bIjH1BGQQ1t6udarfsAG2bdM+i47W6rp++1s4+2zIzPTrECeOnjrYcgVUvgRZ34TF/wSjtgbb29XBf6/5MdVJuSTVlPKdu/8ZEAHYQTLBCTEx9Xa0sPbXP2BP8jFkl+/jL1se4r0PLGRMgFaD3Y3dFL9STHFhMXvf2Iujy4El3ELuqlzyC/LJOzuPF7a9QOl7pQSnjqFeZdK/1SW8KSCDsJISuOceWLpU2zD79NO1fRsDKH7wjfL/wac/1t6EPPYOmPHL/gmiqmQnL971d5qScsloKuXSux/CHBQ4BXKyHCnExFS9+yNeu+dhKpPnMn13CfeVPMzGd0NJSPDfmJqKm/rbSFR8UIHqVolIi+CYbx2DtcBK1qlZmIK8+eNQm4/kQVGMJCCDsLw8+OILCA3190gmqN4G2PJjqHgeYhfBiY9C1Kz+w1tff5Z3139Ed1wKswytnP+Px/w31nGQCU6IiWXb2nt5590SOuLSifm4kY1JT7Bxk+/rcN0uN5UfV2rLjIXFNO5pBCB5fjLLbliGtcBKyoIUnbYJ8mwDbzG1BWQQFhkpAdiQDjyvBWCONjjmjzDzag5vVPPKPbewvcaG0WRm2awUTrn4x34c7NhJJkyIieXtO67g4+ZYzCYLjW/Gk/bD3/Pod3x3f3uXndINpRStLaL45WK6G7oxmAxknZrFop8sIn91PtGZ0b4bEPKgKEYWkEGYGERvI3x6JRx4FmKPgxMeheg5/YfdLhdPXvtDSkPTie5o4axvXUj+ouV+G67XyWwnhF+4nU5evuYCPo+aR2JHHZu2fJVrH17JvHn637uztpPil4spWltE6YZSnL1OgqKCyD8nn/yCfHJX5RIc5esyC8mBidGTICzQuV1Q9hhsuxbsLTDvNpj1azAc6l/T1dbMk7/9OTXJOSTWlnLRLbcTk5jmx0GPn9S+CuF/Xc11FF77U4pTjyGrvJT3u2/m4TeziYjQ536qqtKwq6F/mbFycyWoEJUZxYLLFzBjzQymLZuG0ezHAuHDJid5NhQjkSAsUKkqVL+m7f3Y9iXEnQCnPgQxRz5+bl73BB+/+SGtyTlktpRx6T3/wmgarMFg4FEHbOAthPCVz577C5vfK6M+dTZZX+6j8+R/8vBPgrz+gOR2ujnw/oH+wvqWfS0ApC5KZfkty5mxZgaJcxN1qu8ahwk2HDExSRAWiJq3wue/hrq3IDwXlj4PGecd8QRm7+3m6et+woHwDIKCw1gQ5WD1TY/6b8xepgzowSNBmBC+YO9u55VfX8bO2LmEBIcTtrmbubc97tUGrLYOG/ve2KfVd71STG9LL8YgI9NXTGfJNUvIPzefyLRI793Qq5T+6UgyYWIkEoQFks79sO16KH8KguLhuHsg74dHLD0CfPraM3z46ru0xGeRVFvKub/4Fen5PijQ8KGJ9tArxFTwxQt/5+N39lCXMJ/s/fsoC/0xVz93glfefmyvbO/Pdu1/ez8uu4uQuBCsBVasBVZyVuZgCbeM/0a6O/R2pARhYiQShAWC7mrYfQeU3AeKAWZfBzN/DZaoI06z93bzzA0/5UBIKubQCOaFdPPVBwKz/YTHZLYTQjf27g5e+fW3+TJmFkGhkcR+3sqcGx/nW+PIfqmqSt22Ovas3UNxYTE1n9UAEJsXy/E/Ox5rgZWMEzMwmAJxuxOZj8ToSBA2kbXt0oKv/U+A6oLsy2DerRCaPuDUzze8wPsvrac5YRqJtaWc/dOfkTnrOD8M2jekRYUQvrFt7f1sfvMLahLmkXWglI6073PF88swjeGnh8vuYv+7+ylaq2W82ivaQYGMEzM4/c+nYy2wEmeNm3j1XZ6QwnzhAQnCJhpVhYYPYPdfoGodGEMg53KY+UsInz7g9ObaCtb+8QaqIqdhDo9mblAnX7n3kYDafmisZIITQj/NVUVsvPV6ihJnYgmPIfnLBpbd/m+m53r2Y6OnpYe9r+2laG0RJa+VYO+wYwoxkbMyh+U3Lyf/3HzCEn3czVVXyhFfhBiOBGEThdsFVYWw6y/Q9LFW8zX3Zsj7CQTHDzjdYevl/26/hgPdQXTHTiepdh+rfnIlWXOO9/3Y/UAyYULow9HbzWvXfZ8SYyqdqXOZvn8vhrmXcckfTx91LWZLWYtW37W2iPJN5agulbCkMOZcNAdrgZXsFdmYQybHW9rDkQdFMRIJwvytpwZK/wP7/g2dpVq2a+F9MP3bYBp8W4A3//UXdm3fT2tcErE91Ry/YDqn3HSTb8c9ARwxwclsJ8S4bfjrLyk50EN9vJWUumrCO+L46j3/JTx8+O9T3SrVn1b3B171O+sBSJidwEm/PgnrGitpi9JQDFMhPSTbFonRkyDMH9xOqHkd9v4Tql/R6r0Sl8P8P0H6eWAYfClx21sv8eFzL1GfnE2YOYi5lg6+cvf9U2Lp8WiBXDIixETz2f89zI7X32d/Wg6RFpVpe+tY9af7SEkb+keEo8dB2VtlWuPUdcV01nSiGBUyl2Wy8s6VWAusxObE+vBvMUFITZjwgARhvtS5X8t4lf4HeqogOEnb23H69yAyb8hvK93+MW89dD81cVkYY1LJbi/nK9f/icjYRN+NfQJSh/mTEGJkJR++ytZ/P0ZJmhVTfDo5JSXMvfJ2jjlh2qDndzd2a9sEFRax7419OLodWMIt5K7KxbrGSu5ZuYTGyca+QoyWBGF6622Eiheg/Bmof1f7LGUVLLwH0s4d0OPrcMVb3mHTf/5NbVwW7vhskutLWfmTn06Zuq/hSCZMiLH7csP/sf3pZ9mXmo87fQbTy/eSePplrLx95YBzm4qb+pcZKz6sQHWrRKRFcMxlx2AtsJJ1ahamIPlRcohkwsToyX85erC3QsWL2mbatRu05cZIq1ZoP/3bEDb4U+ZBX77/Gh88+TR1CVkQn01SQxknXnQhc0+5xQeDD1Qy2wkxks8K/8ueta+wLy0f0qxkH9hHxPwzKbj5lv4HG7fLTeXHlf2BV1NREwDJ85NZdsMyZqyZQfKxyYHdRkJ3qhSFiVGRIMxb7G1afVf5s1q9l9sOYdkw8xrIvAii542Yvvl84/+x5fmXqE3MxhCfSXJjGUu/dRkzT7jVR3+JwDHgf0p55BRiSB8+/RBlG95lX3oehtQ8ph/YS+zS8zjrVm1usXfZKX2zVKvvermY7oZuDGYDWcuzOP5KrXFq1LSoEe4iNJIJE6MnQdh4dJZC5Tqtn1f9u6A6ISQN8q+EaRdC3KIRAy+3y8Wmp+9nz/ufUpecjSluGmmNZSz/wRXkzF/io79I4JGHcCGG53Y6WX/nzdQX76csPRdTynRy9heTfs43OeX3v6ejpoOt/9xKcWExpRtKcfY6CY4OJu/sPPIL8sldlUtwVLC//xqBRwrzhQckCPOE2wVNm7Wgq2odtH2pfR41C2b+CtJWQ/yJ2tZCI+hqa+bVu2+hpsFOS3wyQTEpZDSVsuJHV03qTvf6kdlOCID2hlreuPk3NCkh1CWkEJyQTl5ZETkXfJ/si35GUWER/zrhX1RtrgIgOiua4354HNYCK9OWTcNonnpvW+tBnhPFaEgQNpKuCqh9s+/XBrA1gmKExJMh5/ta4BWRM+rLlW7/mE2PPEi9JYGesFiiDI3kO2pZ9YsbiElM0/EvMrnIcqQQR9qx8VW+fOIxKhOm0ZU4nbjmBvLL95F58g9o7+1i88++5PXS9wFIOz6NU287FWuBlcQ5iVLf5VWSCROjJ0HY0RwdUPcO1K7XAq/2Iu3z4GTtrcbUsyF1FVhiRn1Jt8vFpqfuo+jDT6lPyMIdnUVCXTnzpsew8oa/T8k+X0KI8XM5nLz211to3VdKWVoO7syZZFbvJ6Xehtm2nLI39lH8n7cwBhmZfvp0TvrNSeSfm09EaoS/hz55SUArPCBBmKMDGj7Uarrq34WmT7TaLmMIJJ6i7duYcgZEzfH4P66K3Z/zzn/uo9EeQntMPJaYdFKa9rP4gguYe8rN+vx9pgjZtkhMZbvfe4ftjz5EQ0Q8TTHxWJIyydlfQld1HhWbcnA73ITGlzFjzQzyC/LJOSMHS7jF38OeciQTJkYy9YIwewvUvwf1m7Sgq+VzrYWEYoLYhVrz1OQzIOEkMAZ5fHmHrZc3//VXDuzYS0NiJu6wDGK7qpjhbuSMn/2a2OQMHf5SQoIwMdnZurp45dbr6Gxqpjw1G/e0GaTWVZH7WQmlG6dR0jWDuPw4Tvi5FWuBlfQT0zEYR65PFd6mIC0qxGhN7iBMdWvLiY0fHfrVtgtQwRAE8Yth1rWQdArEnQDmETZIG8aX773Klhf+R6Mxlq7IKIKjkkht3s/8c8/huFVTb19HvUnGX0wVHzzzBBVvvExNXCrtEbGEEkTu3hLqP4unujiNjCUZnHajFesaK/HWeH8PV0hNmPDA5ArC7C3QtOWwoGszOFq1Y5YYLdCadmFf0HU8GMf3+nVl0Tbee+wBGtvcNCemQXQWCXUHyEkys+pX1xMSLn11fEZmOzGJ7PpwEzseeZg2Syg1SWmQOYNp1eXEft5IxZYcDCu+wim/tZJ3Th5hCWH+Hq4YhDwnitEI3CDM0QHNn0HzFmj6FJo/hc59fQcViJ4DmRdogVf8iRCZP6rWESNpb65nw8N/pW5/I42JGbiDUogy1pPdcYATLryU/EXLx30PMTLJhInJpv5AOe/++fd02R1UpGTizsgjoame/C/20FA8jfiTzsP6CyuXrMjGHDL0dmfCz6RPmPBAYAZhbV/Cc1H01wGFZWr1XLk/0L7GLQJzpNdu19vVwVuP/p3KnSU0xaRjDwonLNxNWst+Zq9cyeLVstzofzLbicDT0dzM+j/eQk9jIxUpmdgTM4joaCe3uISOyiSmn3weM35rJW1RGopBnjwCjQRhYiSBGYQZgmDudRC3UAu6ghO8foverg7eefwfHNi+h+aoNGwhIVii04hrqSD7uLksv/Q3mIOkm7S/yNuRIlB1tjTzxh9vpbehnsqkafSGxxJkDiWzshxHQwTZp17InB8dQ2xOrL+HKsZEOeKLEMMJzCAsIhfm/s7rl7X3dvP2Y3dT/sVuWiJT6A0NxRKTQWxLJanJWZz282sIi5KJcSKQ5UgRSLrb23nt1pvobayjKimDnrAYLKZQMqoPoLZayDnjWxx79WJCYkP8PVQxbrIcKUYvMIMwL+pqa+adx++hatfevsArDHNsBrHNFcxMyuC0q35JeLS8cTThyWwnJpjm2lo23PZ7HJ0tVCel0x0RjTkolGnV5SgdFmZ+7QfMu2kRpqApPw1PPtKhQozSlPyvv6W+incfu4e60mqao9OwBwdjickgpqUSa3wqp/30l0TGJvp7mGIYshwpJqLKoiLe/8tfcaq9VCZnYEtIxBIZRUbNAQw9FuZfdiUzVx0r2wRNZkpfnzDk2VCMbMoEYTX7dvH+U/+ksbqF5rh0nOYQgiNTiGutJG1WLsu/dbUsNQohPLbz3U3s/Pe/sZtVKlKm4ZyWQUh3N9OqylHckSz5+S/JPC7f38MUPiMBthi9SR2E7f54A5+99D9a2900JaShGqIJDTeQ1FxO5oK5nPLNa7AEh/p7mGIMJBMm/GnTv/9L9Vuv0RURQlVSOmrOdCI628ku34cxJJGVN95ATLr3XxgSgUUyYWIkugdhiqKsAu4GjMC/VFX901HHg4DHgeOAJuBCVVX3j+VebpeLT15+kj3vvE2bM5jW+GQISSOqp4GMlv3kLT2JE8+7DqNJeuxMOjLbCR057Q5evf2vdBdvpyUuhvr4ZMi3Et/cQN7eIoKS8jj71t8THC4PdULejhSjp2sQpiiKEbgPOAOoBLYoilKoququw077HtCiqmquoigXAX8GLhztPXq7Onj3yfuo2PYlbUHxdEZFQ1QmsQ3VTO+sYN7Zqznm1DVe/FuJiUBKaoTeWusaWH/zbbg666lLSKItKgbytf0arXt2E73gJM688Uap7xJHkmatwgN6Z8KOB/aqqloKoCjKM8Aa4PAgbA1wc9/vnwfuVRRFUdWh//V12m383x+voaG8jpaYVGzBIZhiMolpqiIt3M6JF36HzNkL9fkbiQlKZjsxfkUfbOHzh+7HaXRohfXJsZgcEaTVVZJU20jO1y7k+Jtv9vcwhRCThN5BWBpQcdifK4HFQ52jqqpTUZQ2IA5oHOqiDY1N7LCHExKpENtaTXLeNJZd+mNiElK9PHwxUUlNmPCWdx95gpoNr9IdEUxVUjrunCxCu7vIqDmAUQnlxF/+gsy5s/w9TBEwJBMmRi9gCvMVRbkcuBwgIy6ak7OjWXqhdK2fqmQFSIyV0+7g5Ztvp7d8Ny2xsdTHJ4HVSkxrE7mlxZjiMjjn9zcSGhnh76GKgKT0/1OCMDESvYOwKiDjsD+n93022DmViqKYgCi0Av0jqKr6MPAwwMKFC9VTv3WVLgMWAUpmOzGMpqoaNtz6R1w9DdQmptAREQV5ffVdRXuIXnAiq26SPWCFt8h8NFX0dLbx7hP3gQKrfnidx9+vdxC2BchTFCUbLdi6CLjkqHMKgcuAj4CvA28NVw8mBEgmTIys6MNP+fyB+3Ga7FSmZGBLjcPkiCS95gCpNQ3kXXAJx605y9/DFJONFOZPeg1Vpbz33wepL6+lpa/he1xdxcjfOAhdg7C+Gq8rgTfQWlQ8oqrql4qi3Ap8qqpqIfBv4L+KouwFmtECNSE8JLOdgA8ef4EDr/8ftjALlcnpuHIztfquqnKMxgiW/eYa0qy5/h6mmArkQXFSKd3+MZv/9zgtTb00x6fhMoURHJlMXGslKdZsTvnp7WO6ru41Yaqqvgq8etRnNx72+17gfL3HISYXKcwXAKpb5Y07HqL183dpj4mgJikNrPlEt7WQU1aCOWEa59x6IyER4f4eqpgyJBM2WXz5/mt8tvYFWrsNNCemgTmJiJAWUlrKyVp4LCdfPP669IApzBdCCIDe9h5ev+0ueiq20xrfV1g/YwaJjbXkF+8mcs5CVv35eoxmmd6EPyiH/VMEErfLxWfrn+PL9W/Q6gqhNS4JwjOI7q0lq3U/s05fyXGrLsBgNHrtnjJLiYA0IBMmj5yTWntVG2/cdgfOthIaExNojokH6wxS66uwluwh5fSzOEUK68UEI9PSxOd2udhc+Di7336HNkMU7TFxhxq+d1Vy3JqvM+ukM3W7vwRhYpKQ2W4yUVWV+p11vH3nvai9e2lITqIlORYl0Up6bQUJzc3kXngxC8+52d9DFeJI8tbQhHdwi8PdGzfSYoymIzoWJSaLuIZK8u0OFl94GdPnneCTsUgQJgKSzHOTj9vpZv+mMj76138wuPbSmJJAc1Y8ilsLvBJbm5n7vR8we+nJ/h6qEMOQmrCJyO1ysfX1/7Fz/Ru0KpG0x8T1B15pLhcnffNy0vPn+XxcEoSJyUFmu4Bk77Szb/0+Pn3yBczKTprS4mm0JqC4raTVVZJQXsLc73yf2cuW+3uoQnhAlaKwCWL3R2/yyXNP0+IKpS02ASU6k7iGKvIdTpZ+8wdkzDjWr+OTIEwEJHk7MnB1VHdQtK6I7S+8R5BlCz0ZYVTNSwdmklpbyYwDxcy4+DKOOX2lv4cqxBhIJszfasv28M4j/6Cx2UFTYjpEZRJXX0mevZYlF3+HrDnHe+9mbhe07QS3A+I837NagjARkGQ5MnCoqkr9jnqKCovYufZzwsI/Q5muUr04E5fJSlxzA9b9u5l29hqWSHG9CHSKbFvkD11tzWz451+p3ldDU3wGLlMSUaZGstrKOf78i5l54hneuZGtCRo/hsaPtF9Nn4CzE1LOhFNf9/hyEoSJSUJmu4nE5XBRvqmcosIiiguLMYQUET+/hY4VmTSETCe8s4OcihKijzmWldf9XdpJCCHGZPO6J9jx+hs0RqRhCwkhNDyelOZyZq1YzuI1N4yvnYSqQkcJ1L8LDe9rQVdHiXZMMUL0MZB9GcSfCAlLxnQLmflEQJJM2MTT29bL3tf3UrS2iJJXS3CpbWQtKyf47AhqE1Npc8aRWV1GWGICZ998G8FhYf4eshA6kOVIvTVUlbLxwTuob3HTkpCCMTaL+MYDZE3LY8Vvfo85OGRsF1bd0PYl1G869Ku3VjsWlKAFW9O/q32NWwim8c9hEoSJyUFmO79oLW+leF0xRWuL2P/OfpxOJ2kn1pHxlQ7K07LYa7GS0FTPjIoi5v/gJ1gXn+TvIQuhPxUpzPcyt8vFu0/eS/FHW2mMzcBpSSLaUE9uTxXLv/cz0vLmeH5RVYWOYqh5E+o2akGXvVk7FpoOySsg8WRIPAUi8nV5+pcgTAQkKcz3D1VVqfmshqLCIorWFlG3rQ6A6Flh5Hy1iJbkKGriUrDYYsmsKSV21mzOvP5uDCaZasQUIRt4e1VbYw2v3X0bte3QFpuIOSadxOYDzFy+lCVfH8NyY28D1G6E2je1X919G2+HZUP6Gi3gSjwZwrJ8suQiM6MQYlhOm5P9b+/XAq/CIjqqOlAMChknZWC9Iha16wMqUjMpCckjsbGOmTX7WHr1daTmzvD30IXwA0mBeUPRJ2/xwX8fpSEshd6QRKLVOma4GzjjZ78hNjlj9Bdyu6DpY6h6GWregJbPtc/N0ZB8Gsy+DpLPgIgcXf4eI5EgTAQkyYTpq7upm5JXSyguLGbv63uxd9oxh5nJPTOX6WflULrnBXpb36Y4MRuwklVVSmxWOmff9Q/JegnRNx9JJswzbpeLt//7D4o3f0FDYhbEZpNQv5+FM+Zz6g0eZL0cHVCzHqrWQfUrYGsExaTVcs29FVJWQuxxYPD/XOX/EQjhDTLbjVvz3ub+bNeB9w+gulTCU8KZ+425WAusxB2byBs3X8OWbe9QH59EsCmV/Io95H/t6yw45xZ/D1+ICUI28PaUw9bLujtvoKKmm9a4JIKiUkhvLuOkS7+N9fhRzi3dlVBZCFWFUPc2uO1giYGUsyC9QGshYYnW9e8xFhKEiYAkb0eOn+pWqdxc2V/f1bi7EYDEuYksvXYp1gIrqcel0lDTwoYbr6ZpfTjNqWnEtTQyq6aE0264lbj06X7+WwgxwUhN2Kj1dnWw7o4bqGxRaY+JI9Jgw+qs56yrbyAqPmXkC/TUwoHn4cCzWgsJgIg8yL8S0gog4aQJke0azsQenRCjJrPdaDi6HZRuKNX6d60rpqu+C4PJQOYpmSy8YiH5q/OJyY4B4MDeWp763rdpjImhdVomiY11zGuvYPVf7sNkCfLz30SIiU+CsMF1tTWz7o4bqOqy0BkVS7S7jnkh3RRcfydGk3n4b7Y1QcX/QfkzUP+O1lYiag7Muw0yvgZRgVWLKkGYCEhSEzZ6nXWdFL9cTHFhMfve3Iezx0lQZBB5Z+eRX5BP7qpcQmIO9dUp2lbOlr/9jvrEeDqyppPcUM2xNhvn3nWP1HsJMSLliC/ikPbmetbd8Ttq7GF0RSQRY69hQZSLc264Z/h6L1cvVLwEZY9rbzSqTi3jNft6mHYhRM/22d/B22RGFQFJliOHpqoqjXsaKVqr1XdVflwJKkRNi2LB9xdgLbCSeXImRsuRk15ddRfrr/0p9YmxdObkkFpXiTXCwVl/v0+CLyFGTZYjj+aw9fJ/t1/Dge4gusNTiW2rYvb0GM684b7hg6/WL2Hfv7Tgy94ModNgxi8h8yKImT8pfhDIzComhyk+27mdbio+rGDP2j0UFxbTvFdrOJhyXArLb16OdY2VpHlJKINMWj098Owvr6fH1EL99ExS6quYEwdn3PPg+Lb8EGIKC/zwwDve/Ndf2LV9P61xScT2VDPfmsiKGx4Yem5xdkH5/2DfP7VtggxmSP8q5Hxfa56qGHz7F9CZBGEiIE2CB6Bxs3fa2fvGXooLiyl+pZieph6MFiPZp2Vzwi9OwFpgJTI9csjvd7ngqd8/hqvybcozsolsD+LYzlLOvfvfkvkSYqykMB+AbW+9xIfPvUR9cjZh5iDmWjr4yt33Dx18te2Gon/A/ifB2QGRM+DYOyD7WxCc4NvB+5DMtGKSmBqzXUd1B0XrtLcZyzaW4bK7CIkNIe+cPKwFVnJW5hAUOXzRvKpC4aNb6Nj4d/ZPz8GUmMrsmp2s/P3fiEyY5qO/iRCT2dSYjwZTs28Xr975J6rjsjDGpJLdXs5Xrv8TkbGJA09WVWj4AHb/RevpZQyGaRdAzg+0NxunwNO2BGEiIE2VwnxVVanfUd+/zFj9aTUAMTkxLLpyEdYCK9NOmobBNLoUffEeGx/efAX1WYn05uSSV7WHJT/6LpnH3a7nX0OIKWRqZsJcTgfP3vQzKlyR2OKzSa4vY+VPriRrzvEDT3a7tH5eu/6idbMPioO5N0PeTyA43udj9ycJwoSYYFwOF+WbyvsL69vK20CB9MXprPjjCqwFVuJnxg9a3zUUhwMevvY5gjvfoHJmFum15cw7ZQaLbnlWx7+JEFPR1Hs7ctcHb/DWk8/RlJRBfF0Fy89azuLVgzRZdfVqRfa7/6ZtnB0+HRbeB9O/DaZQn497IpAgTASkAfFHgD9y9rb2svf1vRStLaLktRJsbTZMwSamnzGdk393Mvnn5BOeHD6ma2/+yMHOv/2INmsS7ZZEFnTs4Zx7/it1X0LoLMCnpRG5XS6evelKytRYlOhEZrgbOf+ehwbWfbmdsO/fsONm6K3Vtgw66VnIOG/CN1PV29T+24tJJPBmu9b9rf31XeXvluN2uglNCGXm12Zq9V1n5GAOHaFx4TA6OuDuXxaSalhL5dxpZNSWseySs8lbJkuPQuhGmRrbFu3+eANvPf40jUnTiK87wOnf/gbW40878iRV1Wq9vvgNtO+BhKWw5ElIOnVK1HuNhgRhIiAF4n+/qlul5rOa/m2C6rbXARA/M54Trz4Ra4GVtOPTMBjH/wr2urVOqv9zJcZZsdSRxHEdX3L2PU9J9ksI3U3umjC3y8Vzt1xFqTMSNToJq7OOC+55eGD2q/ET+OIaqN8EkVY4+SVtK6FAnLx1JDOymCQm5mzn7HVS9naZtk1QYTEd1R0oBoVpS6dxxh1naBtj58V57X5dXfD7KzZiDXmS2mMzSa/bz9ILTse6XLJfQvjaZAvC9n3xIW889C8akjOJb6zgtEsvZOaJZxx5Usc+2HYdHPgfBCfCoge0Hl9TfNlxKPK/ighIE7kmrLuxm5JXSygqLGLv63txdDkwh5nJXZWLtcBK3jl5hMZ5vwh19254/Gd3kzC/ghpLCsd17OCsu5/CaLZ4/V5CiKEogDrp1iPfe/ZBPv50L/bYFPJsNVz4jweO3OfR2Q3bb4Tif4Bihjk3wcxfgTnCf4MOABKEiYA00TLazXub+9tIHHj/AKpbJSI1gnmXzsNaYCX71GxMwfr95/bkk9D4xFWEL47A1O1kxcJ05n/1D7rdTwgxhEnYrPWF23/Fnu4Qgl1Ozly6kIVnXXTkCQ0fwMffgY4SyPkezPs9hKT4Z7ABRoIwMUn4drZT3SqVmyv767sadzcCkDQviWXXL8NaYCXluBSP2kiMRW8v/PynNpa0/4DWE3JIqyvnrJ98m7TZJ+t6XyHE5OdyOnj8V9/nQOx04loq+cpVPyU9f96hE5w9sP0G2HMXhGXCire0onsxahKEiYDkj+VIR7eD0g2lWn3XumK66rswmAxknpLJwisWYi2wEp0Vrfs4Dtq7F350SSnfnHsLZbNysNbsYM1fHiQkcmo1OxRiYlH6nwkDORPWXFvBs7f8jvrk6aTU7uXSv95LSHjUoRMaPoKPv631+8q9Ao79iyw9joEEYUIMo7Ouk+KXiykuLGbfm/tw9jgJigwi7+w88gvyyTsrj+DoYJ+P6/nn4fEbX+Orp6+jPCaLBe3bOee+/8mG20L4XeC3qNj98QbWP/UibYmZ5PZUcfG9jx6aW1y9Wu3Xnr9BSDqc9iYkn+7fAQcwCcJEQNJr2yJVVWnc3agtMxYWUflxJagQlRnFgu8vwFpgJfPkTIwW/wQ7qgq33QbNL9/JstW1tBuiODm6keW3vOCX8QghhhaImbC3H7+bLTurcIVFcnyyhVU/evjQwebP4cNLtJ5fuZfDsX8Fc6T/BjsJSBAmpjy3082BDw70t5Fo3tsMQMpxKSy/ZTnWAitJ85J0r+8acZxu+NWvIP6L64hbaSSos5fTTp/NnHN+6NdxCSEOM9HeGvLAur/fyLYmlVBHL2ecuZxjV5x36GDFi/DhN8ESA6e+ASkr/TfQCaS7GzZuBJMJzjrL8++XIEwEpPFmwmwdNszdZsw1Zu5IuoOe5h6MFiPZK7I58Vcnkn9uPpHpE+cJz+mE738fUkpuRz3NSEJrHQVXfp8U6yCb4wohJoRAyoSt/+ef2dakEtnSwPm/+BkpObO0A6oKu/8CX/wW4hbDyWshJMm/g/Wzmhp4+WVYtw42bICeHjjtNAnCxFQ2itmuvaq9P9tV9lYZYd8Ow93jJv/cfPIL8slZmUNQRJAPBuuZ3l646CJIr7yHiDO7iGpvYfWPvysBmBAT0qE+YYEShG165n4+3d9OeGcrX7vqykMBmMsOW66A0v9A5kWw+BEwhfh3sH6gqvDFF1rQtW4dfPqp9nlWlvZwvHo1nHLK2K4tQZgISKPJ+KuqSt32OorWavVdNVtrAIjNjeX4nx7Pm6Fv4oxw8pVrvqLvYMehowPWrIH0hsfIOKeK4J4ezvlmAakzT/D30IQQgwmwvSO3vPI0H35xgGB7LwXfu5S0vDnaAVsTvHeetu3QnJtg7k0BvdTqKVWFHTvgmWe0X2Vl2l9/8WL4wx+goABmzx7//yQShImANNRypMvuYv+7+/szXm0H2kCB9BPSWfGnFVgLrMTPiEdRFF77w2sTeqZsbNTS2xkd/8cxBTvApXLm6hPIWrTK30MTQozCRM+E7Xj3Zd55ZytGVFZ97Symz+t7uGsvgnfOge5KbcPtrEv8O1AfKik5FHjt2gVGI6xYAddfD+eeC0leXomVIExMCvve3MvnhdXsfW0vtnYbphATOWfkcPKNJ5N/bj7hSeH+HqJHKith5UrIsG/g5DXvYVcsnLl0GjNOvdjfQxNCDGsCP9kdpmTrJtYXbsRtsnD6qQuYddKZ2oHajfDe18Fg1pqvJizx70B9oK4OnngCnn4atm7VPlu2DO6/H772NUhM1O/eEoSJgNTd2HXEn9+95V2aW2cy6/xZWNdYmb5iOuZQ8xDfPbHV1GgTQLphM6tXv0RHUCSnzQrlmIKf+HtoQogRTfxtiyr2fM7L/30Oe2gEy47N5rhVF/YdeBHevwAirXDKyxCe5ddx6snt1t5qfOghWLtWe/lp4UL429/gggsgPd0345AgTAQE1a1SvbW6f5ugN3ckAYeCrHMePJvEU85DMQTGU+hQuru1WoNoxy6+8dVHaApP4OQ0O4u/eYO/hyaE8MQEnYrqD+zlxfsepjsqjsXTY1h6/g/6DmyCDy6G2IVw6utgiRr+QgGqthb+8x/45z+1Oq+4OLjqKq3AfsYM349HgjAxYTl7nZS9XUbRWm2boI7qDhSDwrSl05h3yVy2PrWn/9yk2YkQ4AGY2w3f+haU7Gjmb9+9g+qYdJZENrLsR/f7e2hCiNGawBt493Z18L8//5m2uBQWxBs4/bu/0g607oB3CyA8G5a/POkCMFWFN9/Usl6FhVrWa/lyuP12+OpXIciPL8VLECYmlO7GbkpeLaFobRF739iLo8uBOcxM7qpcrGus5J2dR2hcKE8+yRFB2GRwww3wwgvwv+9ezq6kuRzv2suKq//r72EJITwycd+OfPq6n9KUmM1sYyvn/Owu7cOucnh7FZjCtCasQXH+HaQXOZ3w3HPw5z/Dtm0QHw8//zn84AeQn+/v0WkkCBN+11TS1L/MWPFBBapbJSI1gnmXzsNaYCX71GxMwUf+q6rXtkX+8uij8Mc/wr2X/Z7d6bPJq/mSsx78n7+HJYQYE20+mkiZsE3P3E9FdCbJtfv4+gOPax/amrQAzNkFZ7wHYdP8O0gv6enRlhzvuENbcpwxAx55BC65xL9Zr8FIECZ8zu1yU7W5qj/watzTCEDSMUksu34Z1jVWUhak+H2bIF959124/HK4YGUJ7pgGIjqNnP7bG/09LCHEmEy8eaulvopPN+8h1GDkq9f2zS3ObnjnXOgsg9PWQ/Rc/w7SC1pbtTca//53aGjQenrdeadWZ2sw+Ht0g5MgTPiEvctO6YZSrb7r5WK6G7oxmAxkLc9i4Y8XYi2wEp0ZPerrDYjPJtIjpwdKSuC88yAnR+X87F/zZfR8lsd3kpg1x99DE0KM00SZlp6/+bd0JOWyJC2ExGm54HbC+xdC8yew9HlIPNnfQxyXtjZtyfHee7UG16tWwW9/CyefPPH7y0oQJnTTWdtJ8cvFFK0tonRDKc5eJ0FRQeSdnYd1jZXcVbkERwV76W4TZLbzQHOz1vxPUeCei37AB8xnZt12TrnpBX8PTQgxVgd/6k+QbYteu//3VCflktawjzNuelwb1Cc/hOqXYdEDkPFVfw9xzBwOrdj+llu05tYXXqgFX/Pn+3tkoydBmPAaVVVp2NXQ362+cnMlqBCVGcWCyxcwY80Mpi2bhtFsHPe9JvrTzUjsdq0J4P798Opj7/DF1mji7PWcfZu8CSlEYJs4k1PNvl3sLGsjyt7LRbfdqX24/QYofQTm3Ah5V/h3gGOkqtpbjr/+NRQXa286/u1vsGCBv0fmOQnCxLi4nW4OvH9Aq+8qLKJlXwsAqYtSOfXWU7EWWEmcm+j1+q5AL8y/6ip45x144r8u6t95gO5EKycvTCE81st7Yggh/MbfmbC1f/0zvYmZLF0ym/DoeKh+Db68HXJ+AHNv9u/gxujTT+Hqq7VaWqtVC8YOrigEIgnChMds7Tb2vrGX4sJiil8pprelF2OQkekrprPkmiVYV1uJSI3w7aD8Pdt5YMMGePBBbSJJKTqf91KOYW7zDhZd+Ly/hyaEGLeJ0aLihdt/RV3KdLLa9nPiV28FR7u2DBk5ExbeE3BRS1WVttT4xBNaq4n77tNaTZgDc2OUfhKEiVFpq2ijeF0xRYVFlL1VhtvhJiQuBGuBFWuBlZyVOVjCLT4bT4DNH/26u7U3IfPz4QdnPsaLG/NJbqnk3L8+5u+hCSG8YQI0ay3ZuomSDjOxHdVcfMd92odf/FbbkPuMD8A4wfo0DENV4bHHtP5evb1w7bXwm99A1CTpJytBmBiUqqrUbatjz9o9FBcWU/NZDQCxubEs/tlirGusZJyYgcE0Ud77DYxM2E03aX1r3n6zg4/+byOumAxO+uqpWELC/D00IYTX+G8+cjkdrP/3Y7hikll+/moswaFQ9y6UPADWn0PCiX4bm6dqarSH1pdfhqVLtd5fubn+HpV3SRAm+rnsLva/u5+itVp9V3tFOyiQfkI6K/60AmuBlfgZ8ROif1cg1oRt3ar1rLn8crC9dgn7kxYyv6eIOSv+4O+hCSG8xr+ZsGduvJLGpGnkO2qZe8q5Wj+wzd+H8OlwzG2+H9AYqCo8/TRceaXWePWuu+BnP5u4vb7GQ4KwKa63tVfbJqiwiL2v7cXWbsMUYiJnZQ7Lb15O3jl5hCeF+3uYAc/h0DaITUqC6360mWeenU1GXRmr75FtiYSYXJQjvvhSU/V+KtQY4usOcOE9D2sf7rgJOvfCaRu1rYkmuPp6uOIKePFFOOEEbTcRq9Xfo9KPBGFTUEtZS38bifJN5bidbsKSwph1wSysBVamnz4dc8jErnYMtGatd94JX3yhTSy7Hv09vTGLmDl7Bgbj+Nt1CCEmmL7pyNfT0qt33YYtPIOlxy7W5pamLbDnTu1tyOTTfDuYMXjuOfjxj6G9XWu++qtfwWSfIiUImwJUt0r11ur+Zcb6HfUAJMxK0N5mLLCSdnwaisH/y4xjN3GDsJISuPlmrS/Y6Sfs5qEPZpBeV8aJNz3q76EJIbxNOfR2pC+DsM7WRmqJJr7uAEtvuglcdtj8PQhOgWP/6ruBjIHTqRXe33cfLFyoFeLPmuXvUfmGBGGTlLPXSdlbZVph/bpiOms6UYwKmcsyWXnnSqyrrcTmxvp7mGM2AcrSRsXt1l6jDgqCe+6BD//2azrDF3JslvynJ8Tk5J/Jad0dN9IdnsS8vHjtg11/hNYdcMo6sEzcVwlbWuCCC7TWPb/6FfzpT2CaQtPjFPqrTn7djd0Uv6JtE7Rv/T4cXQ4s4RZyz8olf3U+eWfnERoX6u9h6mOCLkc+8ojWVPCf/4S4sGr2uKaT1FDF8hse8PfQhBA689W0ZO/tpqbbQoy9mjNuuB9ad8KXf4DMSyDtXN8MYgyKi2H1au2N8Ucege98x98j8j0JwgJcU3GT1q1+bREVH1agulUi0yM55rJjsBZYyVqehSlo8v3fHAiZsJoarSHr8uXwve/Buzf+hJao+ZwQXC+1YEJMWr4vzF935+/oiIrh2IgwDIoKH38XzFFw3N2+G4SHNm6Er39dy3pt3AjLlvl7RP6hy09nRVH+CqwG7MA+4DuqqrYOct5+oANwAU5VVRfqMZ7JxO1yU/lxZX99V1NREwDJ85M5+XcnYy2wknxs8oRoI6GnQGhR8dOfgs0GDz8Mqq2N3W3JxCn1nP63v/t7aEIIXWnzkS8yYW6Xi8raXqIUG+dcfxcU/R2at8CSpyE4Xv8BjMEDD2jz44wZsG4dZGf7e0T+o1eK5E3gWlVVnYqi/Bm4FvjNEOeeqqpqo07jmBTsXXZK3yylaG0RxS8X093YjcFsIGt5Fsf/9Hisq61ETZu4a/6+MbGCsLVr4YUXtPqGvDz44PbLqY+bxQL3foymif3mqRBiHA4rzPeF1+77Pa1xicxSmjGqNtj5B0g9GzIv9NEIRu/wAvxzzoGnnoLISH+Pyr90CcJUVV1/2B8/Br6ux30ms46aDopf1uq7SjeU4rK5CI4OJu/sPKxrrOScmUNwVLC/h+k3EznRp6pw443aU94vfwm4etlTFU5kcCtn3PoPfw9PCKEr3zZrLS2qJjw4jNW33gZlj4OjFWZfP+Emye5u+OpXYf16rQD/z3+e/O0nRsMXxULfBZ4d4pgKrFcURQUeUlX1YR+MZ0JSVZWGLxv667uqPqkCIDormoVXLMRaYGXasmkYzfJv7aAmUGH++vWwfbu2xYbZDJ/+40dUJmYxr6uI4DAfb2wuhJi0Nj56F82JaeTaqgkODYOiuyF2EcRPrK2J7HatRc+bb2ovKX3/+/4e0cQx5iBMUZQNQPIgh65XVXVt3znXA07gySEus1RV1SpFURKBNxVF2aOq6qYh7nc5cDnAtGnTxjrsCcXtdFP+Xnl/49SW0hYA0o5P49TbTsVaYCVxTuKkr+8ai4lcE/bXv0JqKlxyCeB2sHu3g9DILk675g5/D00IoTvfzddFm3cQEhHPub++Gapfh45iWPLkhMqCOZ3aXPj66xKADWbMQZiqqqcPd1xRlG8D5wIrVHXwNIWqqlV9X+sVRXkROB4YNAjry5I9DLBw4cKJ8xPXQ7Z2G3tf30tRYRElr5bQ29KLMcjI9BXTWfLrJVhXW4lIlWxJoPrsM+1Nn7/8BSwW2PHoLylNzmNWyy6iElL9PTwhhN4U37wd+fFLj9GQnElWWzlR8Snw1mUQkgoZE6f652CfxBdegL/9TQKwwej1duQq4NfAKaqqdg9xThhgUFW1o+/3K4Fb9RiPv7VVtFG8TqvvKnu7DLfDTUhcCNYCq1bfdUYOlnCLv4cZUCZqJuyvf9UKTS+/HHC72PVxHZbYCE7++e/9PTQhhB+oqj6JqS9efwtLbBqrrvottH4JtW/CMX8A48T4WaKq8ItfaHs/3nRTX32sGECvmrB7gSC0JUaAj1VVvUJRlFTgX6qqng0kAS/2HTcBT6mq+rpO4/EpVVWp/aK2v76r9vNaAGLzYll81WKsBVYylmRgME7CLeH9ZQLUhJWVwf/+pxWdRkVByYu3UJQ0k/zGXSRl5ft7eEIIn1A4/KFQjyBsx7svU5+URXpzGUmZ+bD5cjAGQ87l3r3RONx0E/zjH9rbkDfd5O/RTFx6vR2ZO8Tn1cDZfb8vBY7R4/7+4LK72P/Ofi3wKiyivaIdFMhYksHpfz4d6xor8daJ2bMlEE2gkod+d92lve1z1VWAqrLjje0YEuZywhXyCCjElOGDFhUfPfM/DPGZnPbDK6G3Efb/F7IunTB9we64A37/e/jud+HOOyfmfD1RTL5W6j7U09JDyaslFBcWU/JaCfYOO+ZQMzkrc1h+y3Lyz8knLDHM38OcIvybCWtqgn//G77xDUhLgwNv3cWuhLlkNxaRNVeWIoWYqrydpN/3xYfUx2eS1LSfrDnHw5e3g6sXrFd590Zj9PDDcM01cP752u8lABueBGEeailt6c92lW8qR3WphCeHM+eiOVgLrGSvyMYcIs049TbR/sO+/36tD87VV2t/3v7CRtzxCzn2G5f5d2BCCB/Td3La9J+HcEdncdI3vgkuOxTfB8lnQPRsXe87Gs8+C1dcAWedBU88IX3ARkOCsBGobpWqLVX9bSTqd9YDkDgnkZN+cxLWAitpi9JQDBMsKpjkJlJhfk+PVvtwzjkwezbgslFhyiS14QCzlt7it3EJIfzP25mwNjWcuIYqZp10Jux/Cnqq4fh/evcmY7B7t7YB90knwfPPa2+Hi5FJEDYIR4+Dso1lWuC1rpjO2k4Uo0LmskzOvOtM8lfnE5sT6+9hisP5sTD/0UehsRF+/Wvtz2VvPUB9bBJz23b5bUxCCH/Rr0VF8ZZ3aItLZHpXhTbn7bkLIvIhdZX3b+YBmw0uvhjCwrSXk0JD/TqcgCJBWJ+uhi6KXy6muLCYfev34eh2YImwkHdWHvkF+eSdnUdITIi/hyn6TJTlSJdL63+zeDEsW6Z9VvrGmxBxPNlnFPh3cEII3ztqcvLm8+Fnhf8DUxKzTz8TGj+C5k9h4X2g+PdN+2uvhW3btM24U1L8OpSAM6WDsMaiRorWavVdFR9WgAqRGZHM/858rAVWspZnYbTIonZg8E8m7MUXYd8+bR80RQFUlbquKKLUFo5ZeZFfxiSE8D89nhNbGrsJD2ll/orz4KOLwRwN0/1bd7p+vfZm+I9/DOee69ehBKQpFYS5XW4qP6pkz9o9FBcW01TcBEDyscmcctMpWAusJM9Plm2CAsBEqAlTVa0zfm4ufOUr2mfdlR+zPzabrOYSDFKVKsQUNLBPmDd0tTXTEptGQssBDL2VUPECzLgaTP57A7+hAS67DGbN0tpSCM9N+iDM3mln35v7KFpbRMkrJXQ3dmMwG8g+NZvjf3Y81gIrURlR/h6mCECbNsGWLfDAA4feAtrx9N04LDOJzc/07+CEEH6iz3Lke08/iMNiIXVGjvZGJArk/8Q7Fx8DVdX6gLW0wBtvQIhU64zJpAzCOmo6tG2CCoso3VCKy+YiODqYvLO1+q7cVbkERwX7e5hiHAZkwvxQmP/Xv0JCgvYkeFBdWRemOAcnXioNWoWYslS8vh5ZtWMPpphpLL3g2/DeIsj4GoRN8+5NPPDAA/Dyy/D3v8O8eX4bRsCbFEGYqqo0fNnQv01Q1SdVAERnR7PwRwuxFliZtnQaRrMsD01evg3Cdu+GV16BW2897AnQ1sSB4CxSmg5oG+oKIaYenQrz283RxDRVE9WxARytYP25dy48Bl9+qW3PtmoV/OxnfhvGpBCwQZjL4eLA+wf6C+tby1oBSDs+jdP+cBrWAisJsxOkvmuS8vf/rf/7HxgM8MMfHvps7yt/oyk6npTuVr+NSwjhb97ftmjHuy/THhNHrs0GlS9BpBXiT/DiHUavt1drRxERobXn8fdcHOgCMghrLWvljsQ76G3txRhkZPrp01l67VLyz80nIiXC38MTPuDvwvzCQliyBBITD31WvmkrxCxhxrnyVqQQQuONTNj219ZBSCrzV50LNRdBznf9Fv389rewY4e2FJmU5JchTCoBGYT1tvcy45szyC/IJ2dlDpYwac075fmwJqyyEj77THszsp/bQbUtkZiWRmYvO8dnYxFCTDTeD45a2x1E9jYxe0YUVHZD0gqv32M01q+Hu++Gn/5U2yFEjF9ABmHJxySz5j9r/D0M4Uf+TIEXFmpfCw7rxdq25yXK47PIbi72z6CEEBODl2vCWuqraIlLI7mlHGo3ao1Zk5aP76Jj4HLBL34B+flaX0ThHQEZhAkxkO8yYYWF2kRktR76bM8Lj+MyLSRhjv830RVCTABeelD84OmHcJlMZMydCXWvQMxxYIn2zsU98MwzsGuXVg8r7Si8x797HQgxRv7KhLW3w1tvHZkFA6itUrDYbJx0yZX+GZgQYoLwbiaspqgMs83G0q99Exo3Q7LvlyIdDrjpJjjmGPja13x++0lNMmFicvBRTdj69dqEdHgQ5m7ZRVlYDkktFYRFycbuQgjvcLtctIfEE9NSTZhtB6hOvwRhjz2mbc+2bp32VrjwHvmfUwQkf70dWVgIcXFw4omHPitZdzdtkdFExQX5ZAxCiInMe5mwz998ns7IaGLiw6BuIxiCIP6kcY7PMzab1g9x8WIpxteDBGFCjJLTqTVoPeccMB2WQ67csg+AeV/9lp9GJoSYMJQj+4SNJwjbtfFNAI77yoVaUX7CEjD5tiDr4YehogL+8AfpCaYHCcJEQPJHJuzDD6G5+ah6MHsLFa504prqyDvuZN3HIIQIFOOfk9q6ILqpnrzZM6F1m89bU3R1acHX8uVw2mk+vfWUIUGYmBx8UBNWWAgWC6xceeizls8fpyJ+GjHuZt3vL4QIBN5Zjqyv2EdLfCoRdELd29qHPq4Hu/deqKuD226TLJheJAgTAcnXE4Kqwtq12tNgxGGbMhStexm30UjywkW+HZAQYoLqW44c5xz14TP/xG00krlgvlYPZo6E2IXjH94otbVp/cDOOgtO8m0Z2pQiQZgISL5ejiwqgr17j1qKdDupbQgjuLeHZRf9SNf7CyEC05gzYaVVBPX2sOyiH2r1YImngMF3DQ3uugtaWrQsmNCPBGFiktA3CDvYJX/16kOfueveY19ULoktFViCQ3W9vxAiQPQ/IY59TnK7XLSFJxHdUoPF1QCd+3xaD9bUBHfeqfUEW7DAZ7edkiQIEwHJ18uRhYXaZJSefuiz4pceoDMsgsiUGN8ORggxgY2/Jmxz4eN0h0cQlxqtZcHAp/Vgf/kLdHbCLbf47JZTlgRhYnLQsTC/oUF7M/LoLvlVO5sAWHj+d3S7txAiMI3nObH4vU0AHP/1b2lBWHASRPlmS7TaWrjnHvjGN2C27MKmOwnCREDyZSbslVe0GO+IIKxjH/uVbBIaq8mcdZzvBiOEmNi8sIF3u81CTEMNmTMXQN1bkHSazya9228Hu13bpkjoT4IwMUnolwkrLISMDJg//9Bn9Z89T2V8OlGGTt3uK4QIYH0xk6dBWGXJDpoTUog09ULbLuit9dlSZEUFPPQQfPe7kJvrk1tOeRKEiYDkq7cje3vhjTe0LNjh9yx550NQFNIXLtblvkKIQDW+jNXWwqdBUchatFBrTQE+K8p/9FFtb9zrrvPJ7QQShAkxrLfegu7ugfVgnY02AOasKBjku4QQU9f4liPbqmsBmHvquVo9WPh0CM/y0tiGpqrw5JNw8smQpf/tRB8JwkRAGpAJ06kwv7BQa856yilHft7pCCGsq4O41Cxd7iuECGzKGLPzvd0OQjs7iEtOh/p3fJYF++ILrR/iJZf45HaijwRhYpLwfhDmdmtB2KpVEBR0+AEnbcYYIrtavH5PIUSAG2dhvt0QTEh3GzRvBUe7z+rBnnoKzGatN5jwHQnCREDyxYtCW7dCTc3ApUg6y2gOiyPE3aX/IIQQAUY54ounusOisbh7D6sH03/nbLcbnn5ae+CMi9P9duIwEoSJgOSLwvzCQjAa4eyzj/y8uXgTXWHhBIXIfz5CiOF5kgmrP7CXnrBwgsMsWj1Y9DwITtBvcH3eew+qquDii3W/lTiK/BQRk4MONWGFhbB0KcTGHvl51afvARCakur1ewohAl3fBt5jeDAs3vw2ANFJ8dDwgc/qwZ5+GkJDB8n6C91JECYCkt7LkfX1sH37wCwYQGu59vZS8pyF+g5CCBF4xlETVle8G4DpmaHgtvmkHsxuh+eeg698BcLCdL+dOIoEYWKS8G4mbPt27evCQeKsrnYVVJUZJ57u1XsKIaa2joZmUFVyU9tAMUHiybrfc/16aG6WtyL9xeTvAQgxFnrXhB0MwubOHXis0xVBZEcb4dHxXr2nEGIyGHsmzGZzE97RRnDXhxB3PJgjvDy2gZ56SivGX7lS91uJQUgmTIhBbNsGKSmQcHRNbG8jLeZYwnukPYUQYjDKYf/0MAgzhhLS0wbNn/pkKbKzE9auhfPP19pTCN+TIEwEJL2btW7fDvPmDfzc3bqLpvA4gun16v2EEJOM4tmc5Ha56IqIIYJuUN2QdKpOAzuksFDbEUSWIv1HgjAhjuJwwK5dgwdhDV++jS04GEt4sO8HJoSY+MZYmF9R9AX24GCiQ+zaB5GzvDywgZ56CjIy4KSTdL+VGIIEYSIg6VkTVlysvTF0zDEDj9Vt3wZAeEaW1+4nhBCln74PQFKsE4yhEJyo6/2amuCNN7TeYAaJBPxG/qcXk4T3grCDRfmDZcLaqtsAmDZP2lMIIQYztkxYfeleAFKTerQNu3Xuw/P88+B0ylKkv0kQJgKSnvPT9u1akarVOvBYV6cZg8uFdbH+W4kIIQLRkYX5o9XV3I7B5SIlsQHCsr0/rKM89RTMnDn4w6bwHQnCREDSszB/+3ZtcrJYjjrgstGuRhHV3oIlONRr9xNCTF6jnZpsDghvb8Vo2w/h+gZhFRWwaZOWBfPFPrxiaBKEiUnCe0HYtm1DPB127KUpKI5QW5vX7iWEmGQORjUevh1pM4cTbGsHRxuEZXl/XId55hntq+wV6X8ShImApNfTW1OTtpHtYEGYq2UnzRGxBBkc+txcCDEJeF4T5nI66IqMIcxg0z7QORP21FOweDHk5Oh6GzEKEoSJycFLy5E7dmhfBwvCar7YhNNsxhwd6ZV7CSEmL0+ate77/AOcZjMxEX0n61gTtmsXfPGFFORPFBKEiYCkV4uKg29GDtaeonG39vZSbNZ0r9xLCDEZeZ6mL/v8YwCSEvp+JOuYCXv6aa0lxQUX6HYL4QEJwoQ4zPbt2lZFSUkDj3U0aEsF2QtO9PGohBABYwzNWpvLywGYlq6CORos0d4fV99YnnoKVqyA5GRdbiE8JEGYCEh6ZsLmzRv87cvOnhBMDgfTj5EgTAgxPMWDwvyuti5MDgeJ8a1ajzCd7NsHpaVw3nm63UJ4SIIwIfq4XLBz5xBvRvbU0KLEEtXejNEkO90KIYbieSbM7jIS3t6Coadc13qwzZu1r0uW6HYL4SEJwkRA0qNP2N690NMzRBDWvoem4DhC7B3jvo8QQhyuNziCIHsndO3XtR5s82YIC4PZs3W7hfCQBGEiIOmxHDncdkX2+u20RkRjMrvHfR8hxCTmYU1Yb1cHXRHRhJhd4OrRPRO2aBEYjbrdQnhIgjAh+mzfrk1Os2YNPFb9+Ue4jUZC4uN8PzAhRADx7O3I4k/exm00EhPdV+agUybMZtNaUyxerMvlxRhJECYCkl6ZMKsVgoMHHmstqwEgMSdv3PcRQkwF2pw0UiasYufnAKSk9k08OgVhn38OdrsEYRONBGFicvBCTdjBNyMH09Gkfc1ZuHTc9xFCTGaebeDdUlkFQFZ2XxAWlqnDmA4V5UsQNrFIECYCkre3LWprg/37hwjCnF20OyIJ6u0hLW+IKE0IIcDjmrCejh6CenuIi2qH4EQwhekyrM2bIT0dUlN1ubwYIwnCxCQxvkzYcNsV0V5MsyGWiM4WDFLRKoQYjb5YbKQgzI6F0I5WDN36t6eQLNjEo1sQpijKzYqiVCmK8kXfr7OHOG+VoihFiqLsVRTlt3qNR0wu3q4JG+7NSNqLaAqJI8jRNa57CCGmAs+WI3tCIglydevanqKhQWvSesIJulxejIPembC7VFWd3/fr1aMPKopiBO4DzgJmARcrijLIu2lC6Gv7doiO1tL1R+uu+oy2yGjMwZIFE0KMZPTLke3N9XRFRhMUZIDuA7plwqQebOLy93Lk8cBeVVVLVVW1A88Aa/w8JhEAvN2sdcjtioDa7dsACE+MH9c9hBBTychzUtFHGwGIiQsDt0O3LYs2b9ba7xx3nC6XF+OgdxB2paIo2xVFeURRlJhBjqcBFYf9ufL/27v/6Kjqc9H/78/8zE/5GcWCRry2QAKTEBykhmjENiHYhRxi77eo6VXsKe2xSMEiubX1tqfnsLgtXVBTLzFdxV79qnAOVVAuIqWIIBCFIuVSiKRWDFhN0iAJQ5L5ue8fezIkZCaZZHZIZvK81sKQmT17Pm7jJ888n89+nuBjQvRR/4OwQEDfExbpzsjms80AjJskSVohRC/6sDH/76f0fRATMoO/HgcwEzZtGqSkDMjpRQxiCsKUUruVUifC/LkX2AD8FyAX+BT4ZYzv9W2l1BGl1JHGxsZYTiUSgJF3R545Ay4X5OSEeVILcLHZBsCXZt1l3JsKIRKU6vKlJ82f1gPwX74UDMIGYE9YIADvvSdLkUOVJZYXa5r2lWiOU0r9Btge5qlPgBs6fT8h+Fi496oCqgBuvfXW2ItCibhm5Mb8P+urjeEzYZfq+Nw3ipRLLjLG39zv9xBCDC8dU1RPmbD2Vi/JZhcjUwL6K1JuNHwcp0/rJXhkU/7QNJB3R17f6dt/Ak6EOeww8EWl1ESllA34BvDaQI1JiHCOH9eDurBNbVtqOG8ZQ+qlz6/6uIQQ8Sj6NL3HlETKpQv6nZEpE8BsM3w01dX6V8mEDU0DuSfs50qp/6uUOg7cBSwHUEp9QSm1A0DTNB/wPeBN4BTwH5qm/WUAxyQShJEb848fh1tugdRwNRJbPqApdQy2QHu/zy+EGI56b1vUmjpSn1tcH0HqTQMyinffhREj9JZsYuiJaTmyJ5qmlUV4/O/AvE7f7wC6la8Qom9iC8LC7gcDmj86yqXUm7nWb+/3+YUQw0iUG1Yb6v5KW2oa4wI2uPQRXDdnQIbz7rvgdIJpsGshiLDkP4uIS0ZtzNf8Jj78MPKdkY0nawEY8YXrjHlDIUSCi+7uyNPvvgXAyOsyoPWTAbkzsrVV/5ApS5FDlwRhIkH0LxPma09G03po3P2ZB4AvTJ7W34EJIYaxSEFYfW0NADfccj2gDcidkUePgt8vQdhQJkGYiEtG7QnztemFc8IuR3ou0OxKA01j0pfv7tf5hRDDTbBtkep5TrrY0ASaxhcnBztqD0AQJpvyhz4JwsSw5m1LIT0dMjPDPNnyAee1MaRfbOaa0dde9bEJIeJQlMVa3e4AaRebSbMG77wegOXId9+FiRPhWpm+hiwJwkRcMqpOmL8tmWnTImxabfmAJusYktua+3VuIYSIxG1OIamtRb8z0mSF5C8Y/h7vvitZsKFOgjCRGPq5HOltS4m4Hyxw4SRNaWOw4o1hYEKI4aX3TFjA7+dS+ihsePQgLOVGMJkNHcWnn8LZsxKEDXUShIm4ZMTdkZrfiua3RAzCPv/rn3EnJZGcnhz7mwkhhgnV6Z/hnf3gGJ6kJFLSk/XyFAOwH+zdd/WvEoQNbRKEibhkxHJkwKPX/ooYhJ3+DICRE6SnvBCif8Jlwv525B0gOLe4PhqQ/WDV1WC1wvTphp9aGEiCMDFsBbx6EDYtXPWJgI+Wf+iR3o2OGVdxVEKIuBZFmr7hb38F4MbsbHA3DlgmLDcXkpIMP7UwkARhIi4ZkwlLwmxr55prwjzp+Zzz7aMx+f1Mum1gKlkLIRJZ5LZFl8636HNLdvC2bINbFvn9cOSILEXGAwnCRGLox8Z8zWfDkhyhJ6S3mfOM4ZqLF7AlpcQ4OCHE8NF1T1i4qcnthbSWC9h89foDBmfCTp4El0uCsHggQZiIS8ZszLdgsnrCP+ltock+hpR2KU8hhOgL1eVLOG5rGnb3RX0/GBi+J0w25ccPCcJEguhbJiwQAM1vxmQJX37C39bE+fTRJJvcRgxOCDFMXZkJ8/u8XLpmFDazXw/CzCmQZGw11epqGD0abrnF0NOKASBBmIhLse4JO38eQGGy+MI+3/TxB/isVuwp1v4MTwgxXIUmp/Bz0mcf6XNLUmoSXDoDaTcZk9rvpKNIq8GnFQNAgjAxLDU06F9N1vCZsNYmfa+G2W6/WkMSQiSEnou1tjTppW+sSTa9RpjBm/IvXoS//EWWIuOFBGEiLsXawDsUhEXIhLV9/g8ALCmpfR2aEEJE5GpqBMCanDIgNcKOHNGnQwnC4oMEYSIudQ3CFH1djqwP3pQUaU+Yu1nfkG9NH9nnsQkhhrFeGnhfutAEQHKKFbzNht8Z2bEpf+ZMQ08rBogEYSIB9H3jQ2/Lkd5LrQDYJAgTQvRJsERFhGmp/WILAGlJfv0Bg4Ow6mr44hf1jfli6JMgTMSlWDfm60GYhsnsD/u8t1UvXZE6UmYyIUR/hC/W6nZdBGBEUnArhMHLkSdPQk6OoacUA0iCMJEA+pcJU2Y/qPDBm69dnyBTR4+NaWRCiOGm5/nIE8yypye16Q+k3WTYO2sanD0LN95o2CnFAJMgTMSlWDfm19eDMoXflA/g9wYAuGbMdX0dmhBChFw5NXndeu3BNGszWEeAbZRh79XUBO3tcMMNhp1SDDAJwkT8U33fmB/KhEXg8+lR3sjrxscyMiHEcKN6blvkc+tbHdItxjfuPndO/ypBWPyQIEzEpViLEDY0AOYeMmF+MyoQIH2UsZWshRCJrufJye/1owIBbFqd4fvBzp7Vv06YYOhpxQCSIEwkiH5kwkyRM2HegAWbx4PJbI51YEKIYaxb2yJ/AKvHg6ntY8MzYR1BmGTC4ocEYSIudasT1oc9YW1telVp1UMmzIcFqzdCc28hhIioo4F3+DkpEFD63OJvMzwTdu4cWCxwnWxljRsShIn418e1yY4aYRH3hGkaXmxYfRKECSH6qJdirQEUlo65xcA7I0HPhI0fD5LAjx8ShIm4FEudsFAQFunuSH8bHpMdi1+CMCFE/0T6aBjAjLVjbhmAPWGyHyy+SBAm4lIsbYt6zYR5m/EoG2Z/+Gr6QggRWc+ZML/JgrVjbjE4E3bunOwHizcShIkE0LflyI6+kREzYd4WPBYbFi3ynjEhhAiv5/koYLZiD3gg6VqwpBr2rpomQVg8kiBMxKVYirV2ZMKIlAnzNOM22zFpke+eFEKInoVvW+SzWLHjNnwpsrER3G5Zjow3EoSJ+Kegr8uRqamgVCD8Ab4WPFYbpkjPCyFEJL1szPdbbCThgdSbDH1bKU8RnyQIE3Gp+56w6NXX93ILtzcYhJljrAgrhBiGep43vDYbKbRJtXwBgGWwByCEIfq4HHltD4XwvRcb8FmtKEvif0bxer2cO3eO9vb2wR6KGEKSkpKYMGECVqt1sIcSt8K1LfK0t+KzWrGbPJA0ztD3k2r58UmCMBGXYsmENTTATTdFfv5i46eACdMw+AV07tw50tPTuemmm1Cx9oISCUHTNJqamjh37hwTJxqbrRkeIv9/9Hm9nq6ymTyGbsoHPQizWnv+gCmGnsT/qC+GCeMyYW1N+s59U1JyrIMa8trb2xkzZowEYCJEKcWYMWMkOxqz7hvzmxv+DoDN7AZLiqHvdu6cngUzyW/1uCL/uURc6hIzqOjrhAUC+l1EPe0Ja7/wOQC2FGMnyaFKAjBxJfmZiEHHtQtzCS826fVx7BYPmI2dX86elf1g8UiCMJEAov+Fcf48+P09Z8LcF13A8AnCxNDn8/n4+c9/TlNT02APRfQq8t2Rrc3BD3gWj+GZMKmWH58kCBNxqb91wjpqhPUUhPlc+jJMUvqIfoxM9EVTUxO5ubnk5uYybtw4xo8fH/re47n6baOOHTvGjh07Buz8K1euJDs7m5UrV/bpdT/96U+ZPHky5eXl+P39q19XWVnJ888/36/Xir4L99GwtfkCADab29BMWCAAn3wimbB4JBvzRVzqb+/ILkHYh+GP8bZ5wQopI0f2c3QiWmPGjOHYsWMA/OQnPyEtLY0f/OAHgzaeY8eOceTIEebNm9ev1/t8PiyWyNNqVVUV58+fxxxlh+WO8/3sZz8DYP78+f0aF8B3vvOdfr9W9EXkTJjbdRGwYbcbmwlraACvV4KweCSZMJEAol+O7GhZ1NOeMJ9HL9KaOnJMLIMS/fSb3/wGp9NJTk4OpaWltLa2AvDQQw/x2GOPcfvtt3PzzTezZcsWAAKBAP/yL//C5MmT+epXv8q8efNCz/3pT3/izjvvZMaMGRQXF/Ppp58CUFhYyKpVq5g5cyZf+tKX2L9/Px6Ph6eeeorNmzeTm5vL5s2buXTpEosXL2bmzJlMnz6dbdu2dRvv3r17KSgoYP78+WRlZeH3+1m5ciVOpxOHw8Gzzz4L6AGUy+VixowZbN68mcbGRkpLS3E6nTidTg4cOADowWhZWRn5+fmUlZX1eNzixYspLCzk5ptv5umnnw6N6fnnn8fhcJCTk0NZWVno+LVr1/Z4jYUBethP5wleZ5vd2D1hUp4ifkkmTMQlQzJhEfg8QCqkjzW2js9Q9/2d3+fYZ8cMPWfuuFzWz13fp9csXLiQf/7nfwbgRz/6Eb/97W9ZunQpAJ9++invvPMONTU1zJ8/n/vuu49XXnmFM2fOcPLkSRoaGpgyZQqLFy/G6/WydOlStm3bRkZGBps3b+bJJ59k48aNgJ5leu+999ixYwc//elP2b17N//6r//KkSNH+PWvfw3AD3/4Q+bMmcPGjRu5cOECM2fO5Ctf+QqpqV3LCxw9epQTJ04wceJEqqqqGDFiBIcPH8btdpOfn09RURGvvfYaaWlpoczf/fffz/Lly5k9ezZ1dXUUFxdz6tQpAE6ePMk777xDcnJyj8fV1NTw1ltvcfHiRSZNmsR3v/tdTp8+zb/9279x8OBBxo4dy/nz5/t0jYVRut8d6W1rBxvYkoy9O1IKtcYvCcJEAlB92hNmMsHo0ZGP8fn0paKR1443YnCij06cOMGPfvQjLly4gMvlori4OPTcggULMJlMZGVlUR9Ma77zzjt8/etfx2QyMW7cOO666y4APvjgA06cOMFXv/pVAPx+P9dff33oXAsXLgRgxowZnDlzJuxYdu3axWuvvRbKILW3t1NXV8eUKVO6HDdz5sxQTa1du3Zx/PjxUDauubmZ2trabjW3du/ezcmTJ0Pft7S04HLpN4XMnz+f5OTkXo+75557sNvt2O12rr32Wurr69mzZw9f//rXGTt2LACjw/yw93SNRawiL0d63R6wgT15YDJhEoTFHwnCRFzqXqIiOvX1kJEBPW3J8fn1J0cMs0xYXzNWA+Whhx5i69at5OTk8Lvf/Y69e/eGnrPb7aG/a70E3pqmkZ2dzaFDh8I+33Eus9mMz+eLeI7f//73TJo0qcf36pwZ0zSNioqKXgObQCBAdXU1SUlJPZ6vp+M6X4+e/j2u1NM1FjEKzkfhpiW/V7+pwmr3Glqs9exZsNshGHeLOCJ7wkSCiD4T1mNFaS2AV7Nic7sxWxK/Yv5QdPHiRa6//nq8Xi8vvvhir8fn5+fz+9//nkAgQH19fSigmDRpEo2NjaEgzOv18pe//KXHc6Wnp3Px4sXQ98XFxVRUVIQCvvfff7/X8RQXF7Nhwwa8Xi8Ap0+f5tKlS92OKyoqoqKiIvR9xzJlf4/rMGfOHP7zP/8zVM4i3HJkX6+x6L/OnxUCvgA2txtl1sDcPajur47yFFLeLf5IECbiUn/bFvUahPlceLBj9V798ghC97Of/YzbbruN/Px8Jk+e3OvxpaWlTJgwgaysLB588EHy8vIYMWIENpuNLVu2sGrVKnJycsjNzeXgwYM9nuuuu+7i5MmToY35P/7xj/F6vTgcDrKzs/nxj3/c63i+9a1vkZWVRV5eHlOnTmXJkiVhM1RPP/00R44cweFwkJWVRWVlZdjzRXtch+zsbJ588knuvPNOcnJyWLFiRbdj+nqNRV9Eno/8AU2fW8wphkZM587JUmS8Ur2l9IeiW2+9VTty5MhgD0MMouZmeHDk67zOfPifI+GuReD8X72+7pZbYOZMeOklWP7vy8EO636w7vIBrefYsmI555Kv5/vrno58ogRx6tSpbvub4pHL5SItLY2mpiZmzpzJgQMHGDdueC0nGy1Rfjb644U9L/C3/X9j9oLZ3J1zd99e/Nkf4ctfofm6LzPy3YPs2QPBbYpUfue/4U4ewbLZL0Npo2HjzcyEO+8EKQM3dCml/qRp2q1XPi57wkRc6m+x1vr6nstT4GnGo2xYfJIJiydf+9rXuHDhAh6Phx//+McSgIlBFDnDFVAmbD5jN+X7/XqhVilPEZ8kCBPxL8q0fmsruFy9LEd6W3Cb7Jj9XmPGJq4K2VguhgwV+e7IgMlCUsDYQq319XogJsuR8Un2hIm41J86YY3B7H/PQVgzHrMNs9a/1jBCCBGJ32TBGpDyFOIyCcJEXOq+Mb/3ICyaQq14W/CYbZgkCBNC9EvH5NS9WKvfYsOmeQ3NhEm1/PgmQZhIANEtR0bTsghvM26rHaXi74YVIcRQoDr9s2sQ5rPasGFsJkyq5cc3CcJEXOrPxvyoM2FWG8okBXeEEDEIM4X4rDbsymN4odbk5J67gIihS4IwEf9U35YjMzIiHxNov4DXZsNkkf81rpa0tDQAzpw5w0svvTTg7+f1ern33nspLCykrKwMt9sd8zl37tzJpEmTuOWWW1izZo0BoxRxK8LGfL/Pi9dmw6aM3ZgvhVrjm9wdKeJSfyachgZITdX/ROJq/AyYgNkm1fKvto4g7P7774/6NT6fD4ulb9OY1Wpl27ZtfR1eRH6/n0cffZQ//OEPTJgwAafTyfz588nKyjLsPUQ8CT85na/XN28lmdyGL0fKUmT8ko/7IkH0ngnrtUYY0H7hcwAsdgnCrrby8nL2799Pbm4u69atw+/3s3LlSpxOJw6Hg2effRbQy1EUFBR0CXQWLFjAjBkzyM7OpqqqKnTOnTt3kpeXR05ODvPmzQP0YG/OnDk4HA7uvvtu6urqAGhsbKS0tBSn04nT6eTAgQMAvP322+Tm5pKbm8v06dO7tDUCeO+997jlllu4+eabsdlsfOMb3zA0yBPxrSMT1tL4GQB2s/GZMAnC4pdkwkRc6nZ3ZJR7wnrcDwa0X2gGwJqU3P/Bxamd39/JZ8c+M/Sc43LHMXf93KiOXbNmDWvXrmX79u0AVFVVMWLECA4fPozb7SY/P5+ioiIAjh49yokTJ5g4cSIAGzduZPTo0bS1teF0OiktLSUQCLBkyRL27dtHZmZmqIfi0qVLefDBB1m8eDEbN27kscceY+vWrSxbtozly5cze/Zs6urqKC4u5tSpU6xdu5ZnnnmG/Px8XC5Xt0ban3zyCTd0+i04YcIE3n333ZivnYhXHRvzu85JLU36/1tJ5jbDMmE+H/z97xKExTMJwkT8i3JtsqEBbrqp52M8F9sAsKcZ90lV9M+uXbs4fvw4W7ZsAaC5uZna2lpsNhszZ84MBWCg91d89dVXATh79iy1tbU0NjZSUFBAZmYmAKODO5cPHjzIK6+8AkBZWRlPPPEEALt37+bkyZOhc7a0tOByucjPz2fFihU88MADLFy4kAlSC0D0JMKesEvn9YbqSVa3YZmwzz6DQEDKU8QzCcJEXOpPsdb6erjttp6P8bbq7Yrsqen9G1gcizZjdbVomkZFRQXFxcVdHt+7dy+pnTb27d27l927d3Po0CFSUlIoLCykvb094nlVhKA9EAhQXV3dLdNVXl7OPffcw44dO8jPz+fNN9/s0vR6/PjxnO0o1gScO3eO8ePH9+nfVSS+9ot6lt1mNa5EhRRqjX+yJ0zEpe7FWnsWCOgV83tbjvS1BwBIGTGq/4MT/ZKent5lv1VxcTEbNmzA69VbSJ0+fZpLly51e11zczOjRo0iJSWFmpoaqqurAZg1axb79+/n448/BggtR95+++1s2rQJgBdffJGCggIAioqKqKioCJ332LFjAHz44YdMmzaNVatW4XQ6qamp6fL+TqeT2tpaPvroIzweD5s2bWL+/PlGXBIRl8JnwtpaWgCw2YzLhEkQFv8GJBOmlNoMTAp+OxK4oGlabpjjzgAXAT/gC9dhXIjo9JwJO39eD8R6C8K8bsAGqaPHGDc0ERWHw4HZbCYnJ4eHHnqIZcuWcebMGfLy8tA0jYyMDLZu3drtdXPnzqWyspIpU6YwadIkZs2aBUBGRgaVlZUsWLCAhoYGpk+fzvbt26moqODhhx/mF7/4BRkZGTz33HOAvqT56KOP4nA48Pl83HHHHVRWVrJ+/XreeustTCYT2dnZlJSUdHl/i8XCr3/9a4qLi/H7/SxevJjs7OwBv14ivnguuYAR2JOMz4TJcmT8GpAgTNO0/6/j70qpXwLNPRx+l6Zp/xiIcYjE1deN+VEVagV8Xv3E6aN7uY1SGMblcgF66Yg9e/Z0eW716tWsXr26y2OFhYUUFhaGvrfb7bzxxhthz11SUkJJSQmPP/44Tz31FACZmZnd3gdg7NixbN68udvjnbNjkcybNy9096UY7sK3LfK2t4NlBDa727BirefO6SV3Ro405HRiEAzocqTSN1/8V+DlgXwfIXoTVcuigA+fXy9Ncc3YcQM/KHFVLFq0iNdffz20rCnEgFLh2xZ53fp+U1uycSUqOspTSKHW+DXQG/MLgHpN02ojPK8Bu5TeqO9ZTdOqIhwnRBd93ZgfdcuigB2AUddJfj9RvPyyfAYUg8/v8UFqMAgzcDlSliLjW7+DMKXUbiBcuuBJTdM6KhUuoucs2GxN0z5RSl0L/EEpVaNp2r4I7/dt4NsAN954Y3+HLRKSQcuR3hY8ARtWjwerPamHA4UQIpJIbYsCWD0eTGbNsEzYuXNwxc3DIs70OwjTNO0rPT2vlLIAC4EZPZzjk+DXBqXUq8BMIGwQFsySVQHceuutvdcjEAmtr3dHNjSAydRLk1tvC25sWL2eWIcnhBi2VJcvHQIB7fLcYkAmzOuFTz+VOyPj3UDuCfsKUKNp2rlwTyqlUpVS6R1/B4qAEwM4HpHQeo7L6+v1xt1mcw8HeZvxYMfikyBMCBGrrhvz/Zq6PLcYkAn7+9/1c8tyZHwbyCDsG1yxFKmU+oJSakfw2+uAd5RSfwbeA/6Ppmk7B3A8IoF0yYQpRTR7wnq7MxJvCx5lkyBMCNF/kYoBY8bqMy4Tdi6Y3pBMWHwbsCBM07SHNE2rvOKxv2uaNi/4979pmpYT/JOtadq/D9RYRKKLbjmy9yCsGY+yYfL7jBmWiEpaWhqgN9Z+6aWXBvz9vF4v9957L4WFhZSVleF2u2M+5+LFi7n22muZOnWqASMU8S38nrCAMmPxB+/QNSATJoVaE4NUzBdxqduHzV425tfXR5cJc5vtmAIShA2G/gRhPl/f/1tZrVa2bdvG3r17eeGFF7Db7X0+x5Ueeughdu6URL647MopKmC2Yg0YlwmTICwxSBAm4lJf6+I0NPRSIwz0TJjZhknz93tcov/Ky8vZv38/ubm5rFu3Dr/fz8qVK3E6nTgcDp599llA7xVZUFDA/PnzycrKAmDBggXMmDGD7OxsqqouV7rZuXMneXl55OTkhIqpnjlzhjlz5uBwOLj77rupq6sDoLGxkdLSUpxOJ06nkwMHDgDw9ttvk5ubS25uLtOnT+/SWqnDHXfcEWoQLoa5CA28/WYrVs0HJjuYetqcGp1z5yA9Ha65JuZTiUEkDbxFgoicCWttBZcryj1hVhs29/C8+fb734dgu0TD5ObC+vXRHbtmzRrWrl3L9u3bAaiqqmLEiBEcPnwYt9tNfn4+RUVFABw9epQTJ04wceJEADZu3Mjo0aNpa2vD6XRSWlpKIBBgyZIl7Nu3j8zMzFDvyKVLl/Lggw+yePFiNm7cyGOPPcbWrVtZtmwZy5cvZ/bs2dTV1VFcXMypU6dYu3YtzzzzDPn5+bhcrm4NvoXoSUcQ5rNasbZ7DS/UKuKbBGEiLvVlY35jo/41quVIazrXmKT89FCwa9cujh8/zpYtWwC9UXdtbS02m42ZM2eGAjDQ+z6++uqrAJw9e5ba2loaGxspKCggMzMTIJSpOnjwIK+88goAZWVlPPHEEwDs3r2bkydPhs7Z0tKCy+UiPz+fFStW8MADD7Bw4UImyO1ookdd2xZ18Fnt2JTX0EKtEoTFPwnCRALoOWiKqmUREGi/gMc2BrNleAZh0WasrhZN06ioqKD4imqUe/fuJTU1tcv3u3fv5tChQ6SkpFBYWEh7e3vE86pId68FAlRXV3fLdJWXl3PPPfewY8cO8vPzefPNN5k8eXIM/2YisXVfjgz4/XhsNmwmn6GFWnNyDDmVGESyJ0wkhh425kfbvLv9wnlQCrNVPpsMhvT09C77rYqLi9mwYUOo5+Pp06e5dOlSt9c1NzczatQoUlJSqKmpobq6GoBZs2axf/9+Pv74Y4DQcuTtt9/Opk2bAHjxxRcpKCgAoKioqEuz7mPBtdkPP/yQadOmsWrVKpxOJzU1NQb/m4tE1DkUa276DJTSgzADMmEej/7hUjJh8U+CMBH/elmOjDYIa/u8GQCL3WbQwERfOBwOzGYzOTk5rFu3jm9961tkZWWRl5fH1KlTWbJkSdi7IefOnYvP52PKlCmUl5cza9YsADIyMqisrGTBggWMHz+eb37zmwBUVFTw3HPP4XA4eOGFF/jVr34F6EuaR44cweFwkJWVRWWlXmFn/fr1TJ06FYfDgdVqpaSkpNsYFi1axJe//GU++OADJkyYwG9/+9uBukxiqAuzMb+54RMAkizG7An75BP9vBKExT/5yC/ilgrzt3CiDcK8F/Usi1U2Xl9VLpcL0EtH7Nmzp8tzq1evZvXq1V0eKywspLCwMPS93W7njTfeCHvukpISSkpKePzxx3nqqacAyMzM7PY+AGPHjmXz5s3dHu+cHYtEmoSLy7q3LbrYpE9Cdqsxe8I6ylPI9sT4J5kwkSAiZ8Lq6yEtDVJ6mfs8Lr2Gjy0l2ciBiUG2aNEiXn/99dCyphBXx+W2Ra7z+t1BSRaPIZkwqZafOCQTJuJWl1XIXvaE9XpnJOBtCwCQlJYe++DEkCFZKnF1dc/MtzZ/DoDd6pZCraILyYSJ+NdL5daog7B2PZBLHjHCiFEJIYajMHvC2ltaAEiytYMlNdyr+uTsWRg5Us/wi/gmQZiIW13nuhgzYX43Po+eGE4ZIZXPhRDGcbfq+02TbG2GLUfKfrDEIEGYSAA93x1ZXx9Ny6IWPD69h2D6mCjSZkIIEVbXYq2aBt7WNgCSbJcMW46UpcjEIEGYSACRlyMDAb1ifu/V8ptx+/XSFCMyvmDg2IQQw4vq9M9gENbuBiApyWVIJkyCsMQhQZiIW12WIyNszD9/Xg/EouobGdCDsJHXjjdmgCIqacGNLWfOnOGll14a8Pfzer3ce++9FBYWUlZWhtvtjul8Z8+e5a677iIrK4vs7OxQ3TEhOvi9en07W5In5kxYe7v+wVKWIxOD3B0pEkDkTFhHy6JoMmGegB2zz0dSqtwdORg6grD7778/6tf4fD4slr5NY1arlW3btvV1eBFZLBZ++ctfkpeXx8WLF5kxYwZf/epXycrKMuw9RBwJszHf5/Nj9vkwWwMxZ8I+0eu+SiYsQUgmTMStaDbmdxRqjWZPmBsbNk9sWRHRf+Xl5ezfv5/c3FzWrVuH3+9n5cqVOJ1OHA4Hzz77LKD3iiwoKGD+/PmhQGfBggXMmDGD7OxsqqqqQufcuXMneXl55OTkMG/ePEAP9ubMmYPD4eDuu++mrq4OgMbGRkpLS3E6nTidTg4cOADA22+/TW5uLrm5uUyfPr1LayWA66+/nry8PEBvvTRlyhQ+6fhNKQQQ8GtYO+aWGDNhUp4isUgmTCSInoOwaJYjvZoNi9dj7LDiyZ++D58fM/aco3JhxvqoDl2zZg1r165l+/btAFRVVTFixAgOHz6M2+0mPz+foqIiAI4ePcqJEyeYOHEiABs3bmT06NG0tbXhdDopLS0lEAiwZMkS9u3bR2ZmZqh35NKlS3nwwQdZvHgxGzdu5LHHHmPr1q0sW7aM5cuXM3v2bOrq6iguLubUqVOsXbuWZ555hvz8fFwuV7cG352dOXOG999/n9tuu63/10zEuTANvDWFtWNuiTET1lGoVZYjE4MEYSIBRF6OjDoI8zTjNtkx+6Sq+lCxa9cujh8/zpYtWwC9UXdtbS02m42ZM2eGAjDQ+z6++uqrgL5Hq7a2lsbGRgoKCsjMzARg9Gi99MjBgwd55ZVXACgrK+OJJ54AYPfu3Zw8eTJ0zpaWFlwuF/n5+axYsYIHHniAhQsXMiHCbz+Xy0VpaSnr16/nmmuuMfhqiPjRvW1RABOWjrlFMmGiEwnCRGKIsDG/vh5MJhgzppfX+1rwKBsm/zAOwqLMWF0tmqZRUVFBcXFxl8f37t1Lampql+93797NoUOHSElJobCwkPb29ojnVRGK+wYCAaqrq7tlusrLy7nnnnvYsWMH+fn5vPnmm0yePLnLMV6vl9LS0lCgJkTHnKRpEFAWLP6OTFhsxVrr6yE9vfc2bCI+yJ4wEbdCv0tV5DphDQ2QkaEHYj3yNOM22zBpPiOHKPogPT29y36r4uJiNmzYEOr5ePr0aS5dutTtdc3NzYwaNYqUlBRqamqorq4GYNasWezfv5+PP/4YILQcefvtt7Np0yYAXnzxRQoKCgAoKirq0qz72LFjAHz44YdMmzaNVatW4XQ6qamp6fL+mqbxyCOPMGXKFFasWGHEpRDxLDgxdY71/SYz5o65JcblyEuXpFJ+IpEgTCSAnpcjo2lZhLcFj9mOSfMbNyzRJw6HA7PZTE5ODuvWreNb3/oWWVlZ5OXlMXXqVJYsWYLP1z1Injt3Lj6fjylTplBeXs6sWbMAyMjIoLKykgULFjB+/Hi++c1vAlBRUcFzzz2Hw+HghRdeCJWUePrppzly5AgOh4OsrCwqKysBWL9+PVOnTsXhcGC1WikpKeny/gcOHOCFF15gz549oQ38O3bsGMhLJYa0MHvCzDYsgeDPbozLka2tkgVLJLIcKeJWNHXCog/CmnFbxpHqjlx5XwwMl8sF6KUj9uzZ0+W51atXs3r16i6PFRYWUlhYGPrebrfzxhtvhD13SUkJJSUlPP744zz11FMAZGZmdnsfgLFjx7J58+Zuj3fOjoUze/ZstB4ayIvhTdPAZ7Vi9RiXCUuNvf2kGCIkEyYSQOTlyKhaFoF+d6TVhlnJL9NEs2jRIl5//fXQsqYQA6tr2yIAn9WGhWCWXTJhohPJhIn4F3k1MupMWMDdjNtmx2SRzyWJ5uWXXx7sIYjh5IobP/w+Px6bHatZMmGiO/mNI+JWb8VaW1vB5YouCPNebEYzmbBYzYaNTwgh/O0X0EwmbOaA/oBkwkQnEoSJBBA+FRZ1jTDA3dIKgNlqNWpQQohhqet85HXpvdPs5gAoM5him2MkE5ZYJAgTcau3jflRtywCPBf1liLWZLsBIxNCDHcd01Pgkj4R2W1+PQsWoU5dtFpbJQhLJBKEiQQQfmN+1JkwTcN7Sd80a5M8vxAiFqrrxnx/axMASbZAzIVaQc+EyTSVOCQIE/GrS7HW7qIOwvxteN36PSpJaenGjE1ELS1YefLMmTO89NJLA/5+Xq+Xe++9l8LCQsrKynC7Y2/afuHCBe677z4mT57MlClTOHTokAEjFfGp63wUcDcDkGTzx7wpHyQTlmjk7kiRILpnwur1rRhRNO9uxuOxQxIkpUvPv8HSEYTdf//9Ub/G5/NhsfRtGrNarWzbtq2vw+vRsmXLmDt3Llu2bMHj8dDa2mro+UX80jwtACTZ/TFvyvf5wOORTFgikUyYiFuq89/C7An7xz/0yarXCcvbgttrAyBl5Ggjhyj6oLy8nP3795Obm8u6devw+/2sXLkSp9OJw+Hg2WefBfRekQUFBcyfP5+srCwAFixYwIwZM8jOzqaqqip0zp07d5KXl0dOTg7z5s0D9GBvzpw5OBwO7r77burq6gBobGyktLQUp9OJ0+nkwIEDALz99tuhSvjTp0/v0loJ9LZJ+/bt45FHHgHAZrMxcuTIAb1WYii7IjPv0VttJSf5Ys6EdcT2kglLHJIJE3Grt/2t7e2QnBzFiTzNeHx6EJY+Jpry+gnq+9+HYL9Ew+Tmwvr1UR26Zs0a1q5dy/bt2wGoqqpixIgRHD58GLfbTX5+PkVFRQAcPXqUEydOMHHiRAA2btzI6NGjaWtrw+l0UlpaSiAQYMmSJezbt4/MzMxQ78ilS5fy4IMPsnjxYjZu3Mhjjz3G1q1bWbZsGcuXL2f27NnU1dVRXFzMqVOnWLt2Lc888wz5+fm4XK5uDb4/+ugjMjIyePjhh/nzn//MjBkz+NWvftWlybgYRq6cmPxtgJXkZG/MmbCO1qmSCUsckgkTCaJ7JszjAZstipf6WvD49bsi08dEU15fXA27du3i+eefJzc3l9tuu42mpiZqa2sBmDlzZigAA73vY05ODrNmzeLs2bPU1tZSXV1NQUEBmZmZAIwerWc5Dx48SFlZGQBlZWW88847AOzevZvvfe975ObmMn/+fFpaWnC5XOTn57NixQqefvppLly40G350+fzcfToUb773e/y/vvvk5qaypo1awb8+og44WsDICnJLZkw0Y1kwkTcUl025ncPwtxusEdTccLTjNuvR2ujrptg2PjiTpQZq6tF0zQqKiooLi7u8vjevXu7ZJn27t3L7t27OXToECkpKRQWFtLe3h7xvCpCCjUQCFBdXd0t01VeXs4999zDjh07yM/P580332Ty5Mmh5ydMmMCECRO47bbbALjvvvskCBvWVPCf+pykNL1dVnJym2TCRDeSCRMJIPwv1aiDMG8LnoANk99P6gjZEzZY0tPTu+y3Ki4uZsOGDaGej6dPn+ZSx2+hTpqbmxk1ahQpKSnU1NRQXV0NwKxZs9i/fz8ff/wxQGg58vbbb2fTpk0AvPjiixQUFABQVFTUpVn3seDS7Icffsi0adNYtWoVTqeTmpqaLu8/btw4brjhBj744AMA/vjHP4b2qonh6Mr5yIfJ78dmaZVMmOhGMmEiMYTZmB/1cqS3BQ92rB6P8eMSUXM4HJjNZnJycnjooYdYtmwZZ86cIS8vD03TyMjIYOvWrd1eN3fuXCorK5kyZQqTJk1i1qxZAGRkZFBZWcmCBQtoaGhg+vTpbN++nYqKCh5++GF+8YtfkJGRwXPPPQfoS5qPPvooDocDn8/HHXfcQWVlJevXr+ett97CZDKRnZ1NSUlJtzFUVFTwwAMP4PF4uPnmm0PnFAL8+tzia5VMmOhGgjCRAGJcjvQ248GG1Rt7vSjRdy6XC9BLR+zZs6fLc6tXr2b16tVdHissLKSwsDD0vd1u54033gh77pKSEkpKSnj88cd56qmnAMjMzOz2PgBjx45l8+bN3R7vnB2LJDc3lyNHjvR6nBgGrlzuNmlYvG7wt8ZcrFUyYYlHliNF3Lo810Vejow2E+bGhtnnNWpoYghZtGgRr7/+emhZU4iBpbp8wQQWn1fPhMW4HCmZsMQjmTCRIMIvR0abCWs32TH75Zd0Inr55ZcHewhiWNLnJM1sCs4tWszLkZIJSzySCRNxq7c6YX3amG+yYQr4DBmXEGI46zoxaRYz5kDwA55kwsQVJAgTiSGmjfnNeMw2TJrf+HEJIYa1gMWMuWNuMWhjvmTCEocEYSL+xVonzNuCx2LHRMDwoQkhhpkrUvR+q+VyEGZAiQql4IpSdiKOSRAm4lY0G/OjDsKsNkyqeyAnhBB903U+8lptWEzBD3gGZMJSUnrfiiHihwRhIkHEthzptdowm2VmGwxpaWmA3lj7pZdeGvD383q93HvvvRQWFlJWVobbHXtpkl/96ldMnTqV7Oxs1g+xzgNicHRUzPfZrFg7gjADMmGyHyyxyN2RIm51yYSF2RMWbSbM13oRv8WC2Wo2dHyibzqCsPvvvz/q1/h8vm69HHtjtVrZtm1bX4cX0YkTJ/jNb37De++9h81mY+7cuXzta1/jlltuMew9RDy5/GHObm7Db7FgtQTnJwMyYbIfLLFIJkzEvwi5+WiDMHezXinfYrUaOSrRR+Xl5ezfv5/c3FzWrVuH3+9n5cqVOJ1OHA4Hzz77LKD3iiwoKGD+/Pmh9kALFixgxowZZGdnU1VVFTrnzp07ycvLIycnh3nz5gF6sDdnzhwcDgd33303dXV1ADQ2NlJaWorT6cTpdHLgwAEA3n77bXJzc8nNzWX69OldWisBnDp1ittuu42UlBQsFgt33nknr7zyyoBfLzFEdZqPxtiaALB2fE4woFirBGGJRTJhIn51ib36txxpJoC3XT/IkhTNBrLEtXPnTj777DNDzzlu3Djmzp0b1bFr1qxh7dq1bN++HYCqqipGjBjB4cOHcbvd5OfnU1RUBMDRo0c5ceIEEydOBGDjxo2MHj2atrY2nE4npaWlBAIBlixZwr59+8jMzAz1jly6dCkPPvggixcvZuPGjTz22GNs3bqVZcuWsXz5cmbPnk1dXR3FxcWcOnWKtWvX8swzz5Cfn4/L5erW4Hvq1Kk8+eSTNDU1kZyczI4dO7j11luNuoQijo2wNQNgtwUnKwNKVMhyZGKRIEwkiK5BmKZFlwkzo+Fp1w+yJicP1OBEP+zatYvjx4+zZcsWQG/UXVtbi81mY+bMmaEADPS+j6+++ioAZ8+epba2lsbGRgoKCsjMzARg9Gi9OfvBgwdDmaqysjKeeOIJAHbv3s3JkydD52xpacHlcpGfn8+KFSt44IEHWLhwIRMmTOgyzilTprBq1SqKiopITU0lNzcXs1mWtoevy58OR9ovAJ2CMAOKtUomLLFIECbilgrztw6+YN3VaIIwt0fPhNnThvfsFm3G6mrRNI2KigqKi4u7PL53715SO/0m2rt3L7t37+bQoUOkpKRQWFhIe3t7xPOqCMvXgUCA6urqbpmu8vJy7rnnHnbs2EF+fj5vvvkmkydP7nLMI488wiOPPALAD3/4w26BmhhOLv98jbC1AJCcZFwm7LrrYjqFGGJkT5hIDFdszO+44a335UgNTzAIS75m5AAMTEQrPT29y36r4uJiNmzYEOr5ePr0aS51VKvspLm5mVGjRpGSkkJNTQ3V1dUAzJo1i/379/Pxxx8DhJYjb7/9djZt2gTAiy++SEFBAQBFRUVdmnUfO3YMgA8//JBp06axatUqnE4nNTU13cbQ0NAAQF1dHa+88kqfbi4QiUojzaY3p09KlkyYCE8yYSJuhRIaYTIbHUFY75mwAB6vHWyQIkHYoHI4HJjNZnJycnjooYdYtmwZZ86cIS8vD03TyMjIYOvWrd1eN3fuXCorK5kyZQqTJk1i1qxZAGRkZFBZWcmCBQtoaGhg+vTpbN++nYqKCh5++GF+8YtfkJGRwXPPPQfoS5qPPvooDocDn8/HHXfcQWVlJevXr+ett97CZDKRnZ1NSUlJtzGUlpbS1NSE1WrlmWeeYeTIkQN5qcRQ1mk+SrPrQVhop4M5tiqrsics8UgQJhJE10yYR7/hMapMmNurH5Q6euxADEz0wuXSf1FZrVb27NnT5bnVq1ezevXqLo8VFhZSWFgY+t5ut/PGG2+EPXdJSQklJSU8/vjjPPXUUwBkZmZ2ex+AsWPHsnnz5m6Pd86ORbJ///5ejxHDT4pN77idmqL0LFiMVVYlE5Z4ZDlSxK2e6oRFnwnT8Pj0IOyaseOMHaAYEhYtWsTrr78eWtYUYmCp0D+TbW0AJKdpMe8HA8mEJSLJhIkEEONyZEA/aOS1XzB6YGIIePnllwd7CGI46fh0qCDJrt8gkpYSgNbYoqdAANraJBOWaCQTJhJEDMuRARsqECB91LUDNDYhxLCjadhsHlQggN3ui7lQa5ueVJNMWIKRTJiIW5c35sOVQVhfliPdmh2rx4NpmNZ20jQtYtkGMTxpYdqAiWhdzoRZbV7wgElrM6RvJEgmLNFIJkwkgO4BREcmLJogrB07Vq9nAMY19CUlJdHU1CS/dEWIpmk0NTV1q5cmonV5PrLafVg8XvC3GtI3EiQTlmgkEybiVpfkTb/rhAVwY8PsG55B2IQJEzh37hyNjY2DPRQxhCQlJUnBWQOYbH6U1w++VrCNjOlckglLTDEFYUqprwM/AaYAMzVNO9Lpuf8OPAL4gcc0TXszzOsnApuAMcCfgDJN04bnb0MRA0Usy5EeZcPsG553zlmt1i7tf4QQMQp9OtQw2TQ9CPO3gjm2G38kE5aYYl2OPAEsBPZ1flAplQV8A8gG5gL/SykVbsPN/wTWaZp2C/A5etAmRB/FthzpMdkwB3wDMC4hxPBzuUQFdg3lD2bCZE+YCCOmIEzTtFOapn0Q5ql7gU2aprk1TfsI+Csws/MBSt8JPAfYEnzofwMLYhmPGM76vxzpMdswaRKECSGMpdkUJp8me8JERAO1MX88cLbT9+eCj3U2BrigaaHffuGOESKinoq19iUT5rXYMBEwfHxCiOHocmY+YDOj+TXJhImIVG93RSmldgPhSok/qWnatuAxe4EfdOwJU0r9GqjWNO3/D37/W+ANTdM6sl4opcYGj7kl+P0NwWOmRhjHt4FvB7+dBITLwA11Y4F/DPYg4pBct76Ta9Y/ct36Tq5Z/8h167t4vmaZmqZlXPlgrxvzNU37Sj/e7BPghk7fTwg+1lkTMFIpZQlmw8Id03kcVUBVP8YyZCiljmiadutgjyPeyHXrO7lm/SPXre/kmvWPXLe+S8RrNlDLka8B31BK2YN3QH4ReK/zAZqegnsLuC/40H8Dtg3QeIQQQgghhpSYgjCl1D8ppc4BXwb+j1LqTQBN0/4C/AdwEtgJPKppmj/4mh1KqY57dVcBK5RSf0XfI/bbWMYjhBBCCBEvYqoTpmnaq8CrEZ77d+Dfwzw+r9Pf/8YVd00muLheTh1Ect36Tq5Z/8h16zu5Zv0j163vEu6a9boxXwghhBBCGE96RwohhBBCDAIJwgaIUurrSqm/KKUCSqlbOz1+k1KqTSl1LPinstNzM5RS/1cp9Vel1NPBgrbDRqRrFnzuvwevywdKqeJOj88NPvZXpVT51R/10KKU+olS6pNOP1/zOj0X9hoK+TnqC6XUmeA8dUwp1VGWaLRS6g9Kqdrg11GDPc7BpJTaqJRqUEqd6PRY2GukdE8Hf/aOK6XyBm/kgyvCdUvoOU2CsIETtqVT0IeapuUG/3yn0+MbgH9Gv5v0i+gtn4aTPrXBCrbCegYoAbKARcFjh7t1nX6+dkCfWokNO/Jz1C93BX++Oj4slQN/1DTti8Afg98PZ7+j+/wd6RqVcHnO/zb674Hh6neE/72XsHOaBGEDpIeWTmEppa4HrtE0rTpYvuN5hlkbp360wZoJ/FXTtL8FG79vCh4ruuu1ldgwJj9HsbsXvfUcSAs6NE3bB5y/4uFI1+he4HlNV41eP/P6qzLQISbCdYskIeY0CcIGx0Sl1PtKqbeVUgXBx8ajt27qIG2cLovUBiua9ljD0feCyxobOy0LybWKTK5N32jALqXUn4KdTACu0zTt0+DfPwOuG5yhDWmRrpH8/PUuYee0mEpUDHfRtHQK41PgRk3TmpRSM4CtSqnsARvkENPPayY66ekaoi9l/Az9F+XPgF8Ci6/e6MQwMFvTtE+UUtcCf1BK1XR+UtM0TSklt933QK5RnyT0nCZBWAz609JJ0zQ34A7+/U9KqQ+BL6G3bJrQ6dAe2zjFqwFog9Vbe6yEE+01VEr9Btge/DaaVmLDlVybPtA07ZPg1wal1KvoS0D1SqnrNU37NLiU1jCogxyaIl0j+fnrgaZp9R1/T8Q5TZYjrzKlVEbH5kGl1M3omzH/FkxTtyilZgXvivwm0sapQ6Q2WIeBLyqlJiqlbOibNF8bxHEOuiv2kvwT+s0OEEUrsWFMfo6ipJRKVUqld/wdKEL/GXsNvfUcSAu6SCJdo9eAbwbvkpwFNHdathz2En1Ok0zYAFFK/RNQAWSgt3Q6pmlaMXAH8K9KKS8QAL6jaVrHRsR/Qb87JBl4I/hn2Ih0zTRN+4tSqqMNlo+ubbC+B7wJmIGNwZZZw9nPlVK56Kn7M8AS0FuJRbqGw52maT75OYradcCr+udELMBLmqbtVEodBv5DKfUI8DHwXwdxjINOKfUyUAiMVXprv/8BrCH8NdoBzEPfWN4KPHzVBzxERLhuhYk8p0nFfCGEEEKIQSDLkUIIIYQQg0CCMCGEEEKIQSBBmBBCCCHEIJAgTAghhBBiEEgQJoQQQggxCCQIE0IIIYQYBBKECSGEEEIMAgnChBBCCCEGwf8DGsy0ZxpM8DoAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Para entender de onde saiu a função tangente\n",
    "# fica o vídeo do Mathologer https://www.youtube.com/watch?v=Lk_QF_hcM8A\n",
    "#\n",
    "# tan(x) =                   x\n",
    "#          -----------------------------------------\n",
    "#           1 - x^2\n",
    "#              -------------------------------------\n",
    "#               3 - x^2\n",
    "#                  ---------------------------------\n",
    "#                   5 - x^2\n",
    "#                      -----------------------------\n",
    "#                       7 - x^2\n",
    "#                          -------------------------\n",
    "#                           9 - x^2\n",
    "#                              ---------------------\n",
    "#                               11 - x^2\n",
    "#                                   ----------------\n",
    "#                                     13 - x^2\n",
    "#                                         ----------\n",
    "#                                           15 - x^2\n",
    "#                                               ----\n",
    "#                                                ...\n",
    "\n",
    "PI = 3.14159265359\n",
    "\n",
    "#Define função recursiva da tangente\n",
    "def tan_recursion(den, level, maxLevel, radQuadrado):\n",
    "    if level < maxLevel:\n",
    "        valor_calculado = den - radQuadrado / tan_recursion(den+2,level+1,maxLevel,radQuadrado) # caso comum\n",
    "    else:\n",
    "        valor_calculado = den # condição de parada\n",
    "    return valor_calculado\n",
    "\n",
    "\n",
    "#Define função tangente\n",
    "def tan(rad, maxLevel):\n",
    "    radQuadrado = rad*rad #calcula o quadrado\n",
    "    if rad == 0.0:\n",
    "        return 0.0\n",
    "    valor_calculado = rad / tan_recursion(1, 0, maxLevel,radQuadrado)\n",
    "    return valor_calculado\n",
    "\n",
    "#Define função que converte graus em radianos\n",
    "def grau_para_rad(angulo):\n",
    "    return angulo*PI/180\n",
    "\n",
    "\n",
    "#Calcula dois exemplos de tangente recursivo com 100 iterações\n",
    "print(\"Tangente de Pi/4 é %.2f\" % tan(grau_para_rad(45),10))\n",
    "print(\"Tangente de Pi/2 é %.2f\" % tan(grau_para_rad(90),10))\n",
    "\n",
    "#Cria lista com valores de -180 a 175, a cada 5 (-180,-175,-170,...)\n",
    "intervalo_impressao = list(range(-180, 180, 5))\n",
    "\n",
    "#Cria lista para guardar valores de tangente calculados\n",
    "valores_tangente = []\n",
    "valores_tangente_recursivo = [[],[],[],[],[]]\n",
    "\n",
    "#Importa biblioteca matemática para calcular a tangente\n",
    "import math\n",
    "\n",
    "iteracoes = [0,1,2,6,9]\n",
    "#Para cada um dos ângulos na lista intervalo_impressão\n",
    "for angulo in intervalo_impressao:\n",
    "    # Transformamos o ângulo em radianos\n",
    "    rads = grau_para_rad(angulo)\n",
    "\n",
    "    #Calculamos a tangente do ângulo com a biblioteca matemática\n",
    "    valores_tangente.append(math.tan(rads))\n",
    "\n",
    "    #Calculamos a tangente recursiva dos mesmos ângulos\n",
    "    # com 0,1,2,6,9 chamadas recursivas e guardamos nas listas apropriadas\n",
    "    for i in range(5):\n",
    "        valores_tangente_recursivo[i].append(tan(rads, iteracoes[i]))\n",
    "\n",
    "#Importamos a biblioteca gráfica\n",
    "import matplotlib.pyplot as pyplot\n",
    "\n",
    "fig, ax = pyplot.subplots(figsize=(10,10))\n",
    "#Plotamos os valores calculados pela biblioteca matemática\n",
    "ax.plot(intervalo_impressao, valores_tangente, 'green', label=\"Tangente referência\")\n",
    "\n",
    "\n",
    "cores = [\"purple\",\"blue\",\"orange\",\"red\", \"gray\"]\n",
    "#Plotamos os valores calculados pela função de tangente recursiva, cada uma com uma cor\n",
    "for i in range(5):\n",
    "    ax.plot(intervalo_impressao, valores_tangente_recursivo[i], cores[i], label=f\"Iterações {iteracoes[i]}\")\n",
    "\n",
    "#Limitamos a área de plotagem de -Pi a Pi (eixo X), e -10 a 10 (eixo Y)\n",
    "ax.axis([-180, 180, -10, 10])\n",
    "ax.legend()\n",
    "\n",
    "#Imprimimos os valores plotados em tela, abrindo a janela com os valores plotados\n",
    "pyplot.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Rota mais curta\n",
    "Outro exemplo já mostrado na introdução foi a procura pela rota mais curta entre dois vértices de um grafo.\n",
    "\n",
    "Criemos primeiro um grafo com rotas aéreas entre algumas cidades"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "outputs": [],
   "source": [
    "class Vertice():\n",
    "    def __init__(self, nome):\n",
    "        self.nome = nome\n",
    "        self.verticesConectados = []\n",
    "\n",
    "    def adicionarVerticeConectado(self, novoVertice, distancia):\n",
    "        self.verticesConectados.append((novoVertice, distancia))\n",
    "        novoVertice.verticesConectados.append((self, distancia))\n",
    "\n",
    "    def apagarConexao(self, vertice):\n",
    "        for (verticeConectado, distancia) in self.verticesConectados:\n",
    "            if verticeConectado == vertice:\n",
    "                self.verticesConectados.remove((verticeConectado, distancia))\n",
    "                verticeConectado.verticesConectados.remove((self, distancia))\n",
    "                break\n",
    "\n",
    "    def apagarConexoes(self):\n",
    "        for (verticeConectado, distancia) in self.verticesConectados:\n",
    "            for verticeTuple in verticeConectado.verticesConectados:\n",
    "                if verticeTuple[0] == self:\n",
    "                    verticeConectado.verticesConectados.remove(verticeTuple)\n",
    "        del self\n",
    "\n",
    "# Belém (Val-de-cans) e Brasília (Juscelino Kubitscheck)\n",
    "bel = Vertice(\"BEL\")\n",
    "bsb = Vertice(\"BSB\")\n",
    "bel.adicionarVerticeConectado(bsb, 1600)\n",
    "\n",
    "# Belo Horizonte (Confins)\n",
    "cnf = Vertice(\"CNF\")\n",
    "bel.adicionarVerticeConectado(cnf, 2100)\n",
    "bsb.adicionarVerticeConectado(cnf, 618)\n",
    "\n",
    "# São Paulo (Guarulhos)\n",
    "gru = Vertice(\"GRU\")\n",
    "bel.adicionarVerticeConectado(gru, 2472)\n",
    "bsb.adicionarVerticeConectado(gru, 876)\n",
    "\n",
    "# Rio de Janeiro (Galeão)\n",
    "gig = Vertice(\"GIG\")\n",
    "gig.adicionarVerticeConectado(gru, 360)\n",
    "gig.adicionarVerticeConectado(bsb, 936)\n",
    "gig.adicionarVerticeConectado(cnf, 340)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Em seguida, montamos a estratégia recursiva para encontrar a menor rota"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rota mais curta entre Belém e Guarulhos:2472 km passando por ['BEL', 'GRU']\n"
     ]
    }
   ],
   "source": [
    "def buscaRotaMaisCurta (verticePartida, verticeDestino, distanciaVisitada=0, verticesVisitados=None):\n",
    "    # Esta é uma função recursiva\n",
    "    if verticesVisitados is None:\n",
    "        verticesVisitados = [verticePartida]\n",
    "\n",
    "    # A condição de parada é quando o vértice de destino já está na rota,\n",
    "    # o que significa que chegamos ao destino usando a rota descrita pelos\n",
    "    # vértices visitados\n",
    "    if verticeDestino in verticesVisitados:\n",
    "        return distanciaVisitada, verticesVisitados\n",
    "\n",
    "    distanciaRotaMaisCurta = 99999999999999 # distância absurda\n",
    "    rotaMaisCurta = None\n",
    "\n",
    "    # Para cada vértice conectado ao ponto de partida, explore os vértices conectados\n",
    "    for (verticeEscala, distancia) in verticePartida.verticesConectados:\n",
    "        # Não faça duas escalas numa mesma cidade\n",
    "        if verticeEscala in verticesVisitados:\n",
    "            continue\n",
    "        # Busca a menor rota entre o vértice de escala e o destino\n",
    "        distanciaNovaRota, NovaRota = buscaRotaMaisCurta(verticeEscala,\n",
    "                                                         verticeDestino,\n",
    "                                                         distanciaVisitada+distancia,\n",
    "                                                         [*verticesVisitados, verticeEscala])\n",
    "        # Pegue sempre a rota mais curta\n",
    "        if distanciaNovaRota < distanciaRotaMaisCurta:\n",
    "            distanciaRotaMaisCurta = distanciaNovaRota\n",
    "            rotaMaisCurta = NovaRota\n",
    "\n",
    "    # Retorne as rotas parciais mais curtas\n",
    "    return distanciaRotaMaisCurta, rotaMaisCurta\n",
    "\n",
    "distancia, rota = buscaRotaMaisCurta(bel, gru)\n",
    "print(\"Rota mais curta entre Belém e Guarulhos:%d km passando por %s\" % (distancia, list(map(lambda x: x.nome, rota))))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Agora removamos a conexão direta entre Guarulhos e Belém e procuremos a rota alternativa mais curta"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rota mais curta entre Belém e Guarulhos:2476 km passando por ['BEL', 'BSB', 'GRU']\n"
     ]
    }
   ],
   "source": [
    "gru.apagarConexao(bel)\n",
    "distancia, rota = buscaRotaMaisCurta(bel, gru)\n",
    "print(\"Rota mais curta entre Belém e Guarulhos:%d km passando por %s\" % (distancia, list(map(lambda x: x.nome, rota))))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Agora removamos a conexão direta entre Brasília e Belém e procuremos a rota alternativa mais curta"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rota mais curta entre Belém e Guarulhos:2800 km passando por ['BEL', 'CNF', 'GIG', 'GRU']\n",
      "\n",
      "  _     ._   __/__   _ _  _  _ _/_   Recorded: 18:23:22  Samples:  120\n",
      " /_//_/// /_\\ / //_// / //_'/ //     Duration: 0.003     CPU time: 0.004\n",
      "/   _/                      v4.3.0\n",
      "\n",
      "Program: /usr/local/lib/python3.10/dist-packages/ipykernel_launcher.py -f /home/gabriel/.local/share/jupyter/runtime/kernel-52e1595c-cc7e-44ce-95b2-61140f46f792.json\n",
      "\n",
      "\u001B[31m0.003\u001B[0m run_ast_nodes\u001B[0m  \u001B[2mIPython/core/interactiveshell.py:3265\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __get__\u001B[0m  \u001B[2mtraitlets/traitlets.py:675\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m getattr\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m helper\u001B[0m  \u001B[2mcontextlib.py:279\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m __init__\u001B[0m  \u001B[2mcontextlib.py:102\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __enter__\u001B[0m  \u001B[2mcontextlib.py:130\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __call__\u001B[0m  \u001B[2mcodeop.py:117\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m compile\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __exit__\u001B[0m  \u001B[2mcontextlib.py:139\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|- \u001B[33m0.001\u001B[0m run_code\u001B[0m  \u001B[2mIPython/core/interactiveshell.py:3416\u001B[0m\n",
      "|  |- \u001B[92m\u001B[2m0.000\u001B[0m __call__\u001B[0m  \u001B[2mIPython/core/hooks.py:103\u001B[0m\n",
      "|  |- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|  `- \u001B[32m0.001\u001B[0m \u001B[48;5;24m\u001B[38;5;15m<module>\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2348155953.py:1\u001B[0m\n",
      "|     `- \u001B[32m0.001\u001B[0m \u001B[48;5;24m\u001B[38;5;15mbuscaRotaMaisCurta\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2064920437.py:1\u001B[0m\n",
      "|        |- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mbuscaRotaMaisCurta\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2064920437.py:1\u001B[0m\n",
      "|        |  |- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mbuscaRotaMaisCurta\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2064920437.py:1\u001B[0m\n",
      "|        |  |  `- \u001B[92m\u001B[2m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mbuscaRotaMaisCurta\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2064920437.py:1\u001B[0m\n",
      "|        |  `- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mbuscaRotaMaisCurta\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2064920437.py:1\u001B[0m\n",
      "|        |     `- \u001B[92m\u001B[2m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15mbuscaRotaMaisCurta\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2064920437.py:1\u001B[0m\n",
      "|        `- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __get__\u001B[0m  \u001B[2mtraitlets/traitlets.py:675\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m helper\u001B[0m  \u001B[2mcontextlib.py:279\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m __init__\u001B[0m  \u001B[2mcontextlib.py:102\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __enter__\u001B[0m  \u001B[2mcontextlib.py:130\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __call__\u001B[0m  \u001B[2mcodeop.py:117\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m compile\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "|- \u001B[32m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "|- \u001B[92m\u001B[2m0.000\u001B[0m __exit__\u001B[0m  \u001B[2mcontextlib.py:139\u001B[0m\n",
      "|  `- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "`- \u001B[32m0.001\u001B[0m run_code\u001B[0m  \u001B[2mIPython/core/interactiveshell.py:3416\u001B[0m\n",
      "   |- \u001B[92m\u001B[2m0.000\u001B[0m __call__\u001B[0m  \u001B[2mIPython/core/hooks.py:103\u001B[0m\n",
      "   |- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "   `- \u001B[32m0.000\u001B[0m \u001B[48;5;24m\u001B[38;5;15m<module>\u001B[0m  \u001B[2m../../../tmp/ipykernel_14477/2348155953.py:1\u001B[0m\n",
      "      `- \u001B[32m0.000\u001B[0m stop\u001B[0m  \u001B[2mpyinstrument/profiler.py:136\u001B[0m\n",
      "         |- \u001B[92m\u001B[2m0.000\u001B[0m get_stack_sampler\u001B[0m  \u001B[2mpyinstrument/stack_sampler.py:154\u001B[0m\n",
      "         `- \u001B[32m0.000\u001B[0m unsubscribe\u001B[0m  \u001B[2mpyinstrument/stack_sampler.py:77\u001B[0m\n",
      "            |- \u001B[92m\u001B[2m0.000\u001B[0m [self]\u001B[0m  \u001B[2m\u001B[0m\n",
      "            `- \u001B[92m\u001B[2m0.000\u001B[0m ContextVar.set\u001B[0m  \u001B[2m<built-in>:0\u001B[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "bsb.apagarConexao(bel)\n",
    "from pyinstrument import Profiler\n",
    "p = Profiler(interval=0.00001)\n",
    "p.start()\n",
    "distancia, rota = buscaRotaMaisCurta(bel, gru)\n",
    "p.stop()\n",
    "print(\"Rota mais curta entre Belém e Guarulhos:%d km passando por %s\" % (distancia, list(map(lambda x: x.nome, rota))))\n",
    "print(p.output_text(color=True, show_all=True, timeline=True))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Agora removamos a conexão direta entre Confins e Belém (removendo todos as rotas possíveis)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rota mais curta entre Belém e Guarulhos:99999999999999 km passando por None\n"
     ]
    }
   ],
   "source": [
    "cnf.apagarConexao(bel)\n",
    "distancia, rota = buscaRotaMaisCurta(bel, gru)\n",
    "print(\"Rota mais curta entre Belém e Guarulhos:%d km passando por %s\" % (distancia, rota))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Como a rota inexiste (None), a distância máxima da rota é o valor de distância máxima utilizada para comparação no algoritmo."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Remontar grafo de requisitos\n",
    "\n",
    "Outro caso de uso típico é remontar um grafo de requisitos/dependências.\n",
    "\n",
    "Um grafo de requisitos representa a relação de dependência entre diversos componentes.\n",
    "\n",
    "Isto significa que um componente requer que uma série de outros componentes estejam disponíveis antes de este componente ser compilado, montado, etc.\n",
    "\n",
    "Este tipo de grafo é utilizado tanto para o desenvolvimento de software, quanto para a instalação de pacotes (Debian/Ubuntu usam Apt, Archlinux usa Pacman, Windows pode usar Apt(com Cygwin)/Pacman(com msys2)/Scoop, Mac OS pode usar Homebrew/MacPorts/Fink, distribuições de bibliotecas multiplataforma Vcpkg/Spack/etc).\n",
    "\n",
    "Um exemplo do pacote Python3 para Ubuntu:\n",
    "\n",
    "![](05_recursao/python3.png)\n",
    "\n",
    "Repare que o pacote depende de uma série de outros pacotes. Podemos olhar um deles.\n",
    "\n",
    "![](05_recursao/libpython3.png)\n",
    "\n",
    "Vamos agora implementar este grafo para um conjunto de bibliotecas do simulador de redes ns-3,\n",
    "e descobrir, usando recursão, a ordem de construção destas bibliotecas."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "outputs": [],
   "source": [
    "modulos_ns3 = {\n",
    "    # Módulo      : lista de dependencias\n",
    "    \"applications\":[\"internet\",\"stats\"],\n",
    "    \"flow-monitor\":[\"internet\",\"stats\"],\n",
    "    \"lte\":[\"fd-net-device\",\"core\",\"network\",\"spectrum\",\"stats\",\"buildings\",\"virtual-net-device\",\"point-to-point\",\"applications\",\"internet\",\"csma\",\"config-store\",\"oran\"],\n",
    "    \"netanim\":[\"internet\",\"mobility\",\"wimax\",\"wifi\",\"csma\",\"lte\",\"uan\",\"energy\",\"lr-wpan\",\"wave\",\"point-to-point-layout\"],\n",
    "    \"internet\":[\"network\",\"core\",\"bridge\",\"traffic-control\"],\n",
    "    \"network\":[\"core\",\"stats\"],\n",
    "    \"core\":[],\n",
    "    \"stats\":[\"core\"],\n",
    "    \"bridge\":[\"network\"],\n",
    "    \"traffic-control\":[\"network\",\"core\"],\n",
    "    \"fd-net-device\":[\"network\"],\n",
    "    \"spectrum\":[\"propagation\",\"antenna\"],\n",
    "    \"propagation\":[\"network\",\"mobility\"],\n",
    "    \"mobility\":[\"network\"],\n",
    "    \"antenna\":[\"core\"],\n",
    "    \"buildings\":[\"mobility\",\"propagation\"],\n",
    "    \"virtual-net-device\":[\"network\"],\n",
    "    \"point-to-point\":[\"network\"],\n",
    "    \"csma\":[\"network\"],\n",
    "    \"config-store\":[\"core\",\"network\"],\n",
    "    \"oran\":[\"core\",\"network\",\"internet\"],\n",
    "    \"wimax\":[\"network\",\"internet\",\"propagation\",\"mobility\"],\n",
    "    \"wifi\":[\"network\",\"propagation\",\"energy\",\"spectrum\",\"antenna\",\"mobility\"],\n",
    "    \"energy\":[\"network\"],\n",
    "    \"uan\":[\"network\",\"mobility\",\"energy\"],\n",
    "    \"lr-wpan\":[\"network\",\"core\",\"mobility\",\"spectrum\",\"propagation\"],\n",
    "    \"wave\":[\"core\",\"propagation\",\"wifi\",\"internet\"],\n",
    "    \"point-to-point-layout\":[\"internet\",\"point-to-point\",\"mobility\"],\n",
    "}"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Neste caso, temos vértices direcionados, já que a dependência é unidirecional."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Módulo 'antenna' é dependência dos módulos: spectrum, wifi\n",
      "Módulo 'core' é dependência dos módulos: lte, internet, network, stats, traffic-control, antenna, config-store, oran, lr-wpan, wave\n"
     ]
    }
   ],
   "source": [
    "MAPA_NOME_VERTICE_PARA_INSTANCIA = {}\n",
    "\n",
    "class VerticeDirecionado:\n",
    "    # Cria vértice\n",
    "    def __init__(self, nome, dependencias):\n",
    "        self.nome = nome\n",
    "        self.dependentes = {}\n",
    "        self.dependencias = {}\n",
    "        # Se forem passadas dependencias, as utiliza\n",
    "        if dependencias:\n",
    "            self.adicionar_dependencias(dependencias)\n",
    "\n",
    "    def adicionar_dependencias(self, dependencias):\n",
    "        global MAPA_NOME_VERTICE_PARA_INSTANCIA\n",
    "        # Para cada dependência\n",
    "        for dependencia in dependencias:\n",
    "            # Se não existir no mapa, cria um vértice sem dependências (serão resolvidas posteriormente)\n",
    "            if dependencia not in MAPA_NOME_VERTICE_PARA_INSTANCIA:\n",
    "                MAPA_NOME_VERTICE_PARA_INSTANCIA[dependencia] = VerticeDirecionado(dependencia, [])\n",
    "            # Adicionar o módulo atual a lista de dependencias de cada módulo dependido\n",
    "            MAPA_NOME_VERTICE_PARA_INSTANCIA[dependencia].dependentes.update({self.nome: self})\n",
    "            self.dependencias[dependencia] = MAPA_NOME_VERTICE_PARA_INSTANCIA[dependencia]\n",
    "\n",
    "    def __str__(self):\n",
    "        return f\"Módulo '{self.nome}' é dependência dos módulos: {', '.join(self.dependentes.keys())}\"\n",
    "\n",
    "for (modulo, dependencias) in modulos_ns3.items():\n",
    "    if modulo not in MAPA_NOME_VERTICE_PARA_INSTANCIA:\n",
    "        MAPA_NOME_VERTICE_PARA_INSTANCIA[modulo] = VerticeDirecionado(modulo, dependencias)\n",
    "    else:\n",
    "        MAPA_NOME_VERTICE_PARA_INSTANCIA[modulo].adicionar_dependencias(dependencias)\n",
    "\n",
    "print(MAPA_NOME_VERTICE_PARA_INSTANCIA[\"antenna\"])\n",
    "print(MAPA_NOME_VERTICE_PARA_INSTANCIA[\"core\"])"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Agora como podemos determinar a ordem de construção destes módulos?\n",
    "\n",
    "Primeiro temos que decidir o que pode ser construído. Para isto, façamos o seguinte"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['core']\n",
      "['antenna', 'stats']\n",
      "['antenna', 'network']\n"
     ]
    }
   ],
   "source": [
    "def modulos_podem_ser_construidos(lista_modulos_pendentes, lista_modulos_montados):\n",
    "    modulos = []\n",
    "    for modulo_pendente in lista_modulos_pendentes:\n",
    "        # Só podemos montar este módulo pendente se todas as suas\n",
    "        # dependências já estiverem na lista de módulos montados\n",
    "        pode_ser_construido = True\n",
    "        for dependencia in MAPA_NOME_VERTICE_PARA_INSTANCIA[modulo_pendente].dependencias:\n",
    "            # Checa se a dependência foi montada\n",
    "            if dependencia not in lista_modulos_montados:\n",
    "                pode_ser_construido = False\n",
    "                break\n",
    "\n",
    "        # Se o módulo atual não pode ser construído, o pulamos\n",
    "        if not pode_ser_construido:\n",
    "            continue\n",
    "        modulos.append(modulo_pendente)\n",
    "    return modulos\n",
    "\n",
    "print(modulos_podem_ser_construidos([\"core\",\"antenna\", \"stats\",\"network\", \"internet\"],[]))\n",
    "print(modulos_podem_ser_construidos([\"antenna\", \"stats\",\"network\", \"internet\"],[\"core\"]))\n",
    "print(modulos_podem_ser_construidos([\"antenna\", \"network\", \"internet\"],[\"core\", \"stats\"]))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Como temos como determinar o que pode ser construído, podemos ordenar a montagem dos componentes."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A ordem de montagem com o menor número de etapas igual a 9 é:\n",
      "Etapa 0: ['core']\n",
      "Etapa 1: ['stats', 'antenna']\n",
      "Etapa 2: ['network']\n",
      "Etapa 3: ['fd-net-device', 'virtual-net-device', 'point-to-point', 'csma', 'config-store', 'mobility', 'energy', 'bridge', 'traffic-control']\n",
      "Etapa 4: ['internet', 'uan', 'propagation']\n",
      "Etapa 5: ['applications', 'flow-monitor', 'spectrum', 'buildings', 'oran', 'wimax', 'point-to-point-layout']\n",
      "Etapa 6: ['lte', 'wifi', 'lr-wpan']\n",
      "Etapa 7: ['wave']\n",
      "Etapa 8: ['netanim']\n"
     ]
    }
   ],
   "source": [
    "def ordem_montagem_recursiva(lista_modulos_pendentes, lista_modulos_montados, numero_etapas = 0, etapas={}):\n",
    "    # Se todos os módulos já tiverem sido construídos, não temos mais o que fazer\n",
    "    if len(lista_modulos_pendentes) == 0:\n",
    "        return etapas\n",
    "\n",
    "    if numero_etapas not in etapas:\n",
    "        etapas[numero_etapas] = []\n",
    "\n",
    "    # Para cada etapa, nós construímos tudo que for possível concorrentemente\n",
    "    for modulo in modulos_podem_ser_construidos(lista_modulos_pendentes, lista_modulos_montados):\n",
    "        etapas[numero_etapas].append(modulo)\n",
    "        lista_modulos_pendentes.remove(modulo)\n",
    "        lista_modulos_montados.append(modulo)\n",
    "\n",
    "    if len(lista_modulos_pendentes) == 0:\n",
    "        return etapas\n",
    "\n",
    "    return ordem_montagem_recursiva(lista_modulos_pendentes,\n",
    "                                   lista_modulos_montados,\n",
    "                                   numero_etapas+1,\n",
    "                                   etapas)\n",
    "\n",
    "etapas_montagem = ordem_montagem_recursiva(list(MAPA_NOME_VERTICE_PARA_INSTANCIA.keys()), [], 0)\n",
    "print(f\"A ordem de montagem com o menor número de etapas igual a {len(etapas_montagem)} é:\")\n",
    "for (key, value) in etapas_montagem.items():\n",
    "    print(f\"Etapa {key}: {value}\")"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Com esta ordem de montagem, podemos executar diferentes componentes em uma mesma etapa em paralelo, já que sabemos que estes são independentes entre si.\n",
    "\n",
    "Também podemos fazer outra checagem importante recursivamente: listar todas as dependências de um componente, por exemplo, para determinar que pacotes devem ser instalados para satisfazer a aplicação que o usuário realmente quer instalar."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Módulo wifi explicitamente requer os seguintes módulos: ['antenna', 'energy', 'mobility', 'network', 'propagation', 'spectrum']\n",
      "Módulo wifi implicitamente requer os seguintes módulos: ['antenna', 'core', 'energy', 'mobility', 'network', 'propagation', 'spectrum', 'stats']\n"
     ]
    }
   ],
   "source": [
    "def lista_dependencias_recursivamente(componente):\n",
    "    lista_completa_dependencias = set()\n",
    "    for dependencia in MAPA_NOME_VERTICE_PARA_INSTANCIA[componente].dependencias:\n",
    "        lista_completa_dependencias.add(dependencia)\n",
    "        lista_completa_dependencias.update(lista_dependencias_recursivamente(dependencia))\n",
    "    return list(lista_completa_dependencias)\n",
    "print(f\"Módulo wifi explicitamente requer os seguintes módulos: {list(sorted(MAPA_NOME_VERTICE_PARA_INSTANCIA['wifi'].dependencias.keys()))}\")\n",
    "print(f\"Módulo wifi implicitamente requer os seguintes módulos: {list(sorted(lista_dependencias_recursivamente('wifi')))}\")"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Como visto, o módulo wifi explicitamente depende dos módulos `antenna`, `energy`, `mobility`, `network`, `propagation` e `spectrum`, porém também dependende de `core` e `stats` indiretamente.\n",
    "\n",
    "O gerenciador de pacotes Spack, voltado para aplicações de supercomputadores (HPC), é capaz de mostrar via linha de comando a árvore de dependências entre os pacotes.\n",
    "\n",
    "![](./05_recursao/spack.png)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
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