Gamma_Poisson_mixture_model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter, defaultdict\n",
    "from scipy.special import gammaln\n",
    "import random\n",
    "from sklearn.feature_extraction.text import ENGLISH_STOP_WORDS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Filtered vocabulary list : ['compared', 'cash', 'appeared', 'hearing', 'able', 'november', 'declined', 'issued', 'really', 'line', 'live', 'saudi', 'management', 'woman', 'african', 'residents', 'weapons', 'legal', 'visit', 'development', 'fighting', 'hes', 'ruling', 'injured', 'stocks', 'aug', 'angeles', 'convention', 'banks', 'signed', 'lead', 'middle', 'spent', 'ended', 'anonymity', 'effect', 'operations', 'governments', 'living', 'taxes', 'august', 'remain', 'equipment', 'jury', 'navy', 'deputy', 'parents', 'education', 'david', 'showed', 'israeli', 'immediately', 'increased', 'forced', 'clear', 'measure', 'son', 'society', 'tried', 'chicago', 'oct', 'december', 'base', 'murder', 'charge', 'primary', 'questions', 'damage', 'fair', 'seeking', 'september', 'french', 'homes', 'soviets', 'believed', 'moved', 'hundreds', 'considered', 'buy', 'staff', 'independent', 'securities', 'investment', 'nuclear', 'spoke', 'airport', 'investors', 'doesnt', 'different', 'movement', 'firm', 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'lifethreatening', 'kiesner', 'dwash', 'spur', 'superiors', 'proving', 'boyfriend', 'outlet', 'sprayed', 'auditorium', 'scandals', 'regimes', 'threeweek', 'condemn', 'llosas', 'contender', 'ulster', 'unrealistic', 'narez', 'resent', 'crying', 'blackburn', 'traces', 'anita', 'efficiently', 'beita', 'lundgren', 'bofill', 'andreotti', 'incest', 'merc', 'inspiration', 'casinos', 'xhosas', 'tolerated', 'worn', 'cites', 'lax', 'lindsay', 'oxygen', 'fellows', 'hike', 'rewrite', 'newmont', 'descent', 'involuntary', 'nih', 'lois', 'uprisings', 'switched', 'debates', 'presleys', 'markey', 'angels', 'mpaa', 'aon', 'marino', 'centuries', 'dealership', 'casual', 'mediator', 'analyzing', 'flaws', 'authorization', 'hampered', 'headquartered', 'egg', 'basements', 'kidder', 'stunned', 'jeffer', 'bethlehem', 'mutiny', 'hallway', 'haul', 'stein', 'reef', 'objection', 'nam', 'proposition', 'reelected', 'ramsey', 'subsidized', 'audubon', 'destructive', 'efficiency', 'bolsheviks', 'brothels', 'progovernment', 'belonged', 'pumped', 'deposition', 'mandated', 'treaties', 'quartet', 'hamadi', 'bloomberg', 'nicolae', 'scherer', 'bolivia', 'floating', 'premiums', 'patrolman', 'villa', 'palmer', 'aristides', 'fln', 'rehnquist', 'dominate', 'finishing', 'stretched', 'celebrity', 'abm', 'tribute', 'ranger', 'creditor', 'favorably', 'abctvs', 'amritsar', 'vindicated', 'responses', 'eclipses', 'slapps', 'tenants', 'sdi', 'kennebunkport', 'joey', 'uncomfortable', 'justification', 'heflin', 'payne', 'rutah', 'capita', 'exceptional', 'koppers', 'scholars', 'raping', 'inviting', 'yegor', 'danny', 'destroyer', 'celebrating', 'hanged', 'wildly', 'rigs', 'screenplay', 'commanding', 'yearearlier', 'pfeiffer', 'temptation', 'unicef', 'cna', 'burbank', 'disturbances', 'lobbyists', 'legalizing', 'ukrainian', 'slope', 'mistrial', 'gebelwilliams', 'bizarre', 'minimize', 'inspect', 'milkens', 'disposed', 'spends', 'cove', 'pring', 'catastrophe', 'prolonged', 'puette', 'sheehan', 'protects', 'penitentiary', 'ricardo', 'treasures', 'arc', 'completing', 'gunpoint', 'sniper', 'underscored', 'hourly', 'toshiki', 'seiders', 'advancement', 'silk', 'doomed', 'chairmen', 'barrett', 'bongo', 'disturbance', 'identical', 'sequence', 'accomplish']\n",
      "Filtered number of words: 8776\n"
     ]
    }
   ],
   "source": [
    "# 단어 불러오기\n",
    "with open('./datasets/ap/vocab.txt', 'r') as f:\n",
    "    vocab = [word.strip() for word in f]\n",
    "\n",
    "# 문서 불러오기\n",
    "articles = []\n",
    "with open('./datasets/ap/ap.dat', 'r') as f:\n",
    "    for line in f:\n",
    "        parts = line.strip().split()\n",
    "        total_words = int(parts[0])\n",
    "        word_counts = Counter({int(word_count.split(':')[0]): int(word_count.split(':')[1]) for word_count in parts[1:]})\n",
    "        articles.append((total_words, word_counts))\n",
    "\n",
    "# 불용어 리스트\n",
    "stopwords = set(ENGLISH_STOP_WORDS)\n",
    "\n",
    "# 단어 빈도 계산\n",
    "word_freq = defaultdict(int)\n",
    "for total_words, word_counts in articles:\n",
    "    for word_idx, count in word_counts.items():\n",
    "        word_freq[word_idx] += count\n",
    "\n",
    "word_freq_arr = np.array([word_freq[i] for i in range(len(vocab))])\n",
    "\n",
    "# 빈도 기반 단어 제거\n",
    "low_threshold = np.percentile(word_freq_arr, 5)\n",
    "high_threshold = np.percentile(word_freq_arr, 95)\n",
    "low_freq_words = set(np.where(word_freq_arr <= low_threshold)[0])\n",
    "high_freq_words = set(np.where(word_freq_arr >= high_threshold)[0])\n",
    "\n",
    "# 길이가 2이하인 단어 제거\n",
    "short_words = {i for i, word in enumerate(vocab) if len(word) <= 2}\n",
    "\n",
    "# 단어 제거 리스트 생성\n",
    "words_to_remove = short_words | low_freq_words | high_freq_words | {i for i, word in enumerate(vocab) if word in stopwords}\n",
    "\n",
    "# 단어 필터링\n",
    "filtered_vocab = [word for i, word in enumerate(vocab) if i not in words_to_remove]\n",
    "\n",
    "print(f\"Filtered vocabulary list : {filtered_vocab}\")\n",
    "\n",
    "# 문서 데이터 필터링\n",
    "filtered_articles = []\n",
    "for total_words, word_counts in articles:\n",
    "    filtered_word_counts = Counter({word_idx: count for word_idx, count in word_counts.items() if word_idx not in words_to_remove})\n",
    "    filtered_total_words = sum(filtered_word_counts.values())\n",
    "    filtered_articles.append((filtered_total_words, filtered_word_counts))\n",
    "# 필터링된 단어 수와 문서 수 출력\n",
    "print(f\"Filtered number of words: {len(filtered_vocab)}\")\n",
    "\n",
    "articles = filtered_articles\n",
    "# 인덱스 에러가 발생하기 때문에 단어 개수 자체, vocab은 그대로 유지해야함\n",
    "num_words = len(vocab)\n",
    "num_docs =len(filtered_articles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1, Log-Likelihood: 12.842971418429155\n",
      "Iteration 2, Log-Likelihood: 12.871418223475613\n",
      "Iteration 3, Log-Likelihood: 12.897390241888548\n",
      "Iteration 4, Log-Likelihood: 12.924620737310413\n",
      "Iteration 5, Log-Likelihood: 12.946283007321451\n",
      "Iteration 6, Log-Likelihood: 12.970711151359138\n",
      "Iteration 7, Log-Likelihood: 12.991573752319066\n",
      "Iteration 8, Log-Likelihood: 13.011221272515266\n",
      "Iteration 9, Log-Likelihood: 13.026719676150847\n",
      "Iteration 10, Log-Likelihood: 13.045415579911046\n",
      "Iteration 11, Log-Likelihood: 13.058813154815015\n",
      "Iteration 12, Log-Likelihood: 13.075938623617516\n",
      "Iteration 13, Log-Likelihood: 13.08516165425553\n",
      "Iteration 14, Log-Likelihood: 13.096758236081882\n",
      "Iteration 15, Log-Likelihood: 13.106832651926561\n",
      "Iteration 16, Log-Likelihood: 13.115410508947756\n",
      "Iteration 17, Log-Likelihood: 13.12133724090405\n",
      "Iteration 18, Log-Likelihood: 13.13197116718925\n",
      "Iteration 19, Log-Likelihood: 13.136481142655418\n",
      "Iteration 20, Log-Likelihood: 13.141921301087992\n",
      "Iteration 21, Log-Likelihood: 13.14732851815511\n",
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     "data": {
      "image/png": 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9FPTbP8/bL2mg0WjEihUrRHBwsLCzsxMBAQFi6dKloqKiot7+r1+/XoSFhQk7Ozvh4+MjnnvuOXHr1q167TZu3CiCg4OFXC4Xffv2FUePHhVDhw6962n+za1HCCGmT58uAIjo6OhGt9mUz3Xo0KHNOj29oc+4pKRETJs2Tbi6ugoABsepqqpKvP3226J79+5CLpcLNzc30adPH7FixQqhUqn07QCIefPmNfieW7duFZ06dRJyuVyEhYWJbdu26eu43ZUrV8SQIUOEg4ODAKA/5b+h4y9E045rY59P3d/HDz74QAwZMkR4eHgIuVwuQkJCxCuvvGKwj0R1SYSo08dLRGa3YMECfPDBBygpKeFtGIiIzIBzkIjM7PbT94Ga+RI7d+7Egw8+yHBERGQmnINEZGaRkZEYNmwYunbtipycHGzduhVqtRrLli0zd2lERPctBiQiM3vkkUfw73//G1u2bIFEIkHv3r2xdetWDBkyxNylERHdtzgHiYiIiKgOzkEiIiIiqoMBiYiIiKgOzkEykk6nQ2ZmJpydnS3unlFERETUMCEEiouL4e/vDxubxvuJGJCMlJmZWe9mjkRERGQd0tPT0b59+0bXMyAZqfby9Onp6fr7ahEREZFlU6vVCAgIuOttZhiQjFQ7rObi4sKAREREZGXuNj2Gk7SJiIiI6mBAIiIiIqqDAYmIiIioDgYkIiIiojoYkIiIiIjqYEAiIiIiqoMBiYiIiKgOBiQiIiKiOhiQiIiIiOpgQCIiIiKqgwGJiIiIqA4GJCIiIqI6GJCIiIjuoqisCkIIc5ehp9HqzF3CPY8BiYiILEJpZTUqNNo2ea+qah3Kq35/r6s5xXjnhytISC+q1/at/15Br7/GImLF/zDtw5P49udMk4QlIQS2Hk/Bsr2/IEddAQDIUVdgy9FkXM8rafR1x67lodeK/2HyB3FILShttF2WqrzNPs/mSC8sw7/PZSBLVW7uUu5IIiwpElsRtVoNpVIJlUoFFxcXc5dDRKQnhMCvmWqEeDnBQSY1ahs6nYCNjcTElQGqcg1u3iqHrVQChdwW7VwdAABxyQX4086z0GgFRnT3wZgIf/Tu4AY3haxJ2y2prMaxq3kI83NBsKeiwTYarQ7/+N9VHLmah6TcYmh1Aj3aKaF0sMOxa/kAAJnUBm9NDMeE3u0BAF+cTsOruy/W29ajPf2weEQYAOBSlhq74zNw8noBwnxdMLSLFwZ2dEd3fyWqtDqcSMpHjroSf+jmA//f9hcA3jt4DWtjrwIAnOW2GBXui+9+zkK5RgtPJxm+fm4QAj0M9yW1oBRj1/8EVbkGAOAok2J0uB/KNFpIJRIM6OiOIA8Ftp+4gdhLOfBxkWPxiDCM7umH5LwSqMo0iAhwhUJuCyEEslQVsLeTwv0On3NpZTVktjawk9bvU1FXaOAks9X/rqjKNTh4OQcnkgtwLbcES0Z0waBQT337xOxiTPvwJApKqwAAPdsrEebrDH9XBwzr4o1eAa6N1mEqTf3+ZkAyEgMS0b2joKQSNwrK0CvAFVIThgKdTmDTkWQk55XgjTHdoXSwQ0J6EV74PB4KmS26+bugs48zAtwc4eJgi1x1JYorNBj/QHsoHe0ghMCOEzdwo6AM3fxcEN5eiS4+zrCxkeB82i18cjINro52mD6gAzp6OQGo6YFY/O8LOHI1D17Ocvw5qhMi2itxOUuNCo0OPdsr0d1fCZmtDbQ6gX0XMrH5yHVkq8qhdLCDjY0EuepKVGi0GN3TDy9Fd0bQbYGjuEKD4opqeDrJYWsjwS+ZKpy6XghfpT2iu/pAJwT2JtzE6ZRCOMqkcLa3gwSARivwc0YRzqfdgu62b53+Qe4Y0tkT7x1MQlUDw0ZBHo6Y2Ls9/jgwEKpyDf53KRv5JVVwsbeFndQGReUapBaU4scruajQ6OAkt8VHM/tiYEcP6HQCOiFg+9sX+5v7LmHr8ZQGj5VEAoR4OSEpt6bnZlQPXwS4O+Lj4ymo1gn8OaoTYrr5YP8v2dh0JBla3d2/Om1tJBCAvq2NBIju6oMHOrihqKwKHxy9DgAI9lQgJf/3niAHOynKNVoEejjipejO+PbnTGSpKjCwoztOJBUgMacYEe2VcJBJcfJ64V3rqN2/2m97mdQG4e2VSCssQ15xJQDAy1mOMF9nhPk6I9BDgQqNFnnFlTh5vQAXbqrg5ijDjIGBmD6gA7yc5cgrqcTa/13FrrPpCPV2wisjwpBbXIF3fkhEUZlG/74u9rb4dv6DCPJU4Eq2GtM+PIXC0iq4K2S4VVaFugnk8T7tsSC6E9wVMtjbSlslpDMgtTIGJKLWUVZVjWqdgIu9XYPrq6p1+PJsOs6n3UJltQ52NhL8oZsvort5Q27beG9JcYUGW45eRzc/F4zs4YvKah0+OHIdu89nILWgDAAw/oF2WDspAhJJ/T/KBSWViL2UA6WDHUK9neDqKINEUvPlV1alhVYn0N7NAfZ2NTVUaLRYuCsB31/MBgD0C3LD6gk9MWVLHPJLqu74GfQKcMXnTw/ErrPpeOPbXw3WeTrJEOShwNnUWwbLu/u7QOlgh0tZaoMvqIZIbSRwc7QDIEF+SeVd27ZzdYBEUtM7cPu2a7/IaylkUthIJCiurL7jNj1+660oKtcYBI2R3X0x56FgfJuQieNJ+QahwU4qgUZ7568rJ7ktSn7r7ZjYuz2OJOYip7gS0wd0QA9/JRZ/fQEAsGJsd0R19YbURoJT1wtxs6gcI3v4IthDgX/EJmLDoWSD7T7a0w/vT31A/3uRkF6EV7++gKs5xbC3k8LDSYZHwv3wh64+uJJdjKNX8xCfVqT/bDt6KuCukNU7ZgDwUnRnzH84FJ+eSsXBy7mY2j8AvTu4YeLmE0gvbHgIystZju/mPwhvZzm+/TkTKfmlcHW0g7q8GseT8nA1pwRRYd54ekhHHLmah/U/JqGkshou9rZQyG2RparQb8vWRoLqJoS92znKpNDqBCqrG54H1dFLgZhuvjh5vQAJ6UXo7OOE4WHe+NeJVJRrtAhvp8QncwagUqvFiaQCpBeW4VKWGv/9Jbvett4c1wMzBgY2q767YUBqZQxIRKZx+1DOgUs5WPTvn6Gp1uHvT0RgVLgfgJou/pT8UvxyU4WNh5ORVlhWbztujnaIDPFAd38lACA5twTO9rb4c1QnKB3sMGfHWRy5mgcA6BPohlulVbh+2xdw7b+wX/5DZ8yIDMSXZ9KRo65ERy8FslUV2PZTCkqr7j6fw9fFHk72tiitrEaWqgJ2UgnktlKUVFbrv+S7+rlgQXQnXM5S40Z+KdIKy1BcUQ1fpT0uZKigKtegV4ArLt5UQaurGXJSl1fj54wilP1Wg40EGPdAO6jLNTh4JdfgX+Ld/V2w5vGeOHvjFj44koxyjRbd/F0gt5XifNot3Lot5Lg62uHphzri4TBvFFdUo1qng7ezPYorNHj/xyT8eCW33j7e/qXqJLfFgGB3XM0t1n+hB3sqMK5XO9hIgOLKagghYCORINBDgSGdPdHezREAaj7XEynYe/4mHu3pj9ce6WrQg6cq0+BQYi4+On4dv9xUQ2ojwaAQD4T5OqO4ohqV1TooHezg6STDkM5e6OzjjPmfnceByzmNHp8/DemIpY90veMxPHW9AGdTbyHjVjns7WyweERYg0OVQogGw3TtutogUjusdi2nGN9dyELGrZqem+FdvDF7cFCD20jJL8W0D09CqxN4vE97dPVzwYnkfCTlluC1R7rigQ5ud9yH25VVVUNdXg0fFzkAIDmvFOfTbiHIU4HwdkpodQJXc4qRmF2MK9nFyLhVDie5FC4Odghvp8SgUE+cT7uFD4+l4Ofb5mhFBLhiUUxnnEguwLafUmAntcHLf+iMPw4MhK3UBrnqCjz6/nHkFv8ewgcEu2PLjL5QOtb/B9C51Fv4675LBu+xZmJPTOoX0OR9bQoGpFbGgERkqLxKC4kE+h4UoOZL4j8Xs/D+b8Mn7goZJKjpiah9VFbr0MnbCQHujvW+jMf18kdqYRkS0osMAoCXsxzTB3SAm6MM2eoK7I7PQI664Z4Qf6U9ege6Yd+FLMhtbWAjkeh7Pbyd5Vj6SBgeDvPBdz9n4v/2/gKgfs9IrTBfZ8htbZCcV4rSqmoIURNUHGU18znqBihne1tsmdEXUhsJZmw9hcpqHXxc5Ng7bzD8lA71tg8AZ28UYvpHp/T/Op/Qux3+8URNr1ZVtQ7xabeQmF2MBzt5IuS3YbWMW2W4klWM0qpqyKQ2iOrqA5ltw+fgCCGQW1yJwtIqlFRWo6ufC5zktg22BWq+qAt/my+ikEvR3s0RCpkUhaVVuFVWhUAPBeykNhBCICG9CNU6gT4d3Ew6NCKEQHJeKTwUsrvOSarW6vDO/xJx81Y5Rof7wVFuixXf/orr+aXoH+SOT58e0OBcGkuk1QnYSNBoCDOH8iotctQVKNdo9cO9QM3/01IbSb3fpfi0W5i97Qzauzlg4R864+Ew77vuj1YnUKHRorJaBwc7qdHz6BrDgNTKGJDofnToSi7++0sWLmcVI0tVDj+lA/yU9rhRUIqk3BLoBODjIkcHd0cEuDsir7hSP/m1qZ4aHAwbCfBRnbkiHgoZgj0VGNbFC7MHB0Nx2x9irU7gdEohLt4swq+ZakglEgR5KrD3/E2DXqLNf+yNXgFu2HQ4CXI7KeY/HGowlPfX7y7h459q3rernwsiO3rgRkEpKqu1+OOAQIzs4Vvvj3ttL4IQArfKNEgrLEN5lRYarQ492in1k1+PXcvDZ6fS8OeoTujqd+e/Gft/ycafvziP3h1cseOp/nccOqS7q6zW4uT1QvQPcjf5ly3dXWtN+DcWA1IrY0Cie9XFDBWOJeUh2EOBHu2U8HGxh0arw1+/u4Qvz6Y3e3syqQ2eGxaCQSEeKCytggCgdLDTP2ylElzMUOFyVjH6Brlh8G9nvHx/MQv/+zUbAzp6YFgXr0Z7XO5EXaHB4q8u4IdL2XhtVFc8PaTjHdtrdQK74zPgp3TA4FAPs/7LXV2hgbPc1qJ6D4juBQxIrYwBiSzFudRC2Egkjc5JyCwqxwufn0dJRTWe6NseY3v5w1Mhh6pcg89Op2F3fAa8nOWY2r8DLmWq8eGx66g7Z7N27oxEAkwf0AGDQzwR4O6ILFUFMovK0c7VAT0DlJBJbZBWWIbUgjKkFZahpLIaj/dprx8KMpeSyuo7DiMR0f2DAamVMSCRJTh4OQdzdpwFAAzp7IXFI7qgRzulfv2vmSo8tf1Mvfk5EglgI5E0eqryQ508causCleyivWTcf2U9lg7qRciQzxaaW+IiFpfU7+/+U8qIisghEBecSVsbCSwt5PCSW6L1IJSLPgyQd/m6NU8HL2ahyGdvTCulz9OJBdg34VMVGh06OzjhGn9O+Df8Rn45aYaQgBaIdDNzwWzBwfhZlE5vjxTM3y2clwPRHX1AVAz5KT+bTK1v6tDoxN/iYjuNWbtQTp69CjeeecdnDt3DllZWdizZw/GjRunX798+XJ88cUXSE9Ph0wmQ58+fbBq1SoMGDCg0W2uXr0au3fvxpUrV+Dg4IBBgwbh7bffRpcuXfRtKioq8PLLL+OLL75AZWUlRowYgY0bN8LHx6fJtbMHiVqLEALpheXwd7WHrdQGecWVeGr7GVy8qdK36ezjhAqNDmmFZejdwRVrHo/A+h+v4dufM+sNjz0Y6okN03tD6VAzGbm8SouSympotDr4Ke31c1yEEDVnZVnQZEoiIlNr6ve3Wf85WFpaioiICGzYsKHB9Z07d8b69etx8eJFHD9+HEFBQYiJiUFeXl6j2zxy5AjmzZuHkydPIjY2FhqNBjExMSgt/f1MlpdeegnfffcdvvrqKxw5cgSZmZmYMGGCyfePqLlU5RrM//w8hrxzCCP/eQzf/ZyJKVviDMIRAFzNKUFaYRk8nWTYML03Qr2d8O6UB3B40XDMjAxEJ28nTO0fgF1/isS/nuqvD0cA4CCTwstZDn9XB4MJwBKJhOGIiOg3FjMHSSKR1OtBqqs29R04cABRUVFN2m5eXh68vb1x5MgRDBkyBCqVCl5eXvjss8/w+OOPAwCuXLmCrl27Ii4uDgMHDmzSdtmDRKZSWlmNy1lqXLypwkfHUnCzqP7Vc/2V9vjs6YEI9HDErTINTqcU4EKGCqN7+ukvjEhERHd3z81BqqqqwpYtW6BUKhEREdHk16lUNf/ydnd3BwCcO3cOGo0G0dHR+jZhYWHo0KFDswISkTFKKqvxbUImUgtKkVFUjitZalzPLzW4CGKAuwP+Nj4chxPzsOPEDfi52uOzuQMR4F5z9WF3hQwje/hhZA8/M+0FEdG9z+ID0r59+zBlyhSUlZXBz88PsbGx8PT0vPsLAeh0OixYsACDBw9Gjx49AADZ2dmQyWRwdXU1aOvj44Ps7Pr3galVWVmJysrfzwRSq9XN3xm6LwghcDwpHy72duju76K/UWZyXgn+tPOc/maYt/NxkaOHvxIPdHDFzEFBcLa3w0OdvDBveCgcZVKDq1MTEVHrs/iANHz4cCQkJCA/Px8ffvghJk2ahFOnTsHb2/uur503bx5++eUXHD9+vMV1rF69GitWrGjxdujeVlWtw9LdF/F1fAaAmvtUhfk6w00hw8nkAhRX1twPaXS4P/xd7RHi5YTu7Vzg7Wzf4Pbc73JbBSIiah0WH5AUCgVCQ0MRGhqKgQMHolOnTti6dSuWLl16x9fNnz8f+/btw9GjR9G+fXv9cl9fX1RVVaGoqMigFyknJwe+vr6Nbm/p0qVYuHCh/rlarUZAgGlvoEfWKVddgV+z1CiuqMYXp9NwIrkAUhsJFDIp1BXVBnfw7h/kjg3Te8PLWW7GiomI6G4sPiDVpdPpDIa66hJC4IUXXsCePXtw+PBhBAcHG6zv06cP7OzscPDgQUycOBEAkJiYiLS0NERGRja6XblcDrmcX2pUI6+4Et8k3MR/LmbhfFqRwTqFTIoN03vjoU5euJylRlphGQpLq6CQS/FoT3+ruVEmEdH9zKwBqaSkBElJSfrnKSkpSEhIgLu7Ozw8PLBq1SqMHTsWfn5+yM/Px4YNG3Dz5k088cQT+tdERUVh/PjxmD9/PoCaYbXPPvsM33zzDZydnfXzipRKJRwcHKBUKjFnzhwsXLgQ7u7ucHFxwQsvvIDIyEhO0Ka7ylZVYMV3vyL2Uo7+CtNAzXWJ3BUyeDvb47lhIfqbkfZopzS4sjUREVkHswaks2fPYvjw4frntUNYM2fOxObNm3HlyhXs2LED+fn58PDwQL9+/XDs2DF0795d/5rk5GTk5/9+t/BNmzYBAIYNG2bwXtu2bcOsWbMAAOvWrYONjQ0mTpxocKFIorqScktwPa8EA0M8kF5YhjnbzyJbXQEA6BXgiom92yGmuy98XBqeQ0RERNbJYq6DZG14HaR7x/m0W/j250xUVusgAfBwmDceDvPGfy5m4eVdP6OyWgdbGwmkNhJUVuvQydsJ7019QN9LRERE1uOeuw4SkalptDr888A1bDycZHB7jk9PpaGjpwLX82uuvu6ukKGwtArVOoHBoR7YOL2PwZWpiYjo3sOARPelLFU5nvskHgnpRQCAR8J9EebrgoKSSnx1LkMfjp5+KBivjuqKm7fKkZxXggc7eXKSNRHRfYABie4rQgjEXS/Anz8/j/ySKigd7PC38eEY3fP3q1K/GN0ZX5xJQ5CHAo+E1yzv4OGIDh6O5iqbiIjaGAMS3RfSCsrw/o/X8FNSPjJVNZOsu/m54IMZffS38KjlrpDh+WGh5iiTiIgsBAMS3fNiL+Vg4a4EFFdUAwDspBKM69UOf32sBxxkvIUHERHVx4BE9xwhBL46l4GfkvKRXliG+N8u5Ngn0A0LojuhT6AbHGX81SciosbxW4LuKSWV1Xjlq5/x318Mbzz81OBgLH0kjBOsiYioSRiQyOolZhfjX3E3kKWqwJUsNTJVFbCTSvDMkI7o5qdEZx8ndPJxNneZRERkRRiQyGoJIfDJqTSs3HcJldU6/XI/pT02TO+N3h3czFgdERFZMwYkskpXstVY9Z/LOHat5jYzQzp74ZEevvB0kmNAR3c42/NCjkREZDwGJLIKN/JL8d3PmchUlSNLVYGjV/OgE4BMaoMlo8Iwe1AQbGwk5i6TiIjuEQxIZNEuZaqx8j+XcCK5oN66R8J9sXhEGII8FWaojIiI7mUMSGSxErOLMe2jkygq00AiAYZ29sIDAW5wd5KhV3tXhLdXmrtEIiK6RzEgkUVKyS/FH7eeQlGZBhEBrtgw7QG0d+OtPoiIqG0wIJHFySuuxIytp5BXXIkwX2fsmN0Pro4yc5dFRET3EV41jyxKWVU15uw4g4xb5Qj0cMTOOQMYjoiIqM0xIJHFKKmsxgufnceFDBXcHO2wfXZ/eDnLzV0WERHdhzjERhbhxys5+MueX5ClqoDM1gYfzeyLYJ6dRkREZsKARGb3xek0vLr7IgCgg7sj1jzeE30C3c1cFRER3c8YkMisrmSr8ca3vwIAZgwMxGuPdIWDTGrmqoiI6H7HgERmU1ZVjfmfnUdltQ7DunhhxdjuvBo2ERFZBE7SJrN5c99lJOWWwNtZjr8/EcFwREREFoMBiczi0JVcfH46DQCwbnIveDrxbDUiIrIcDEjU5m6VVmHx1xcAAHMeDMbgUE8zV0RERGSIAYnalEarw+KvLyCvuBKh3k54ZUQXc5dERERUDydpU5sprtDg+U/jcexaPmxtJFg7KQL2djxjjYiILA8DErWJ4goNpmw5iV8z1XCwk2Lj9N7o2d7V3GURERE1iAGJ2sTfvr+CXzPV8HSS4eNZ/RiOiIjIonEOErW649fy9WesvT+VPUdERGT5GJCoVZVUVmPJb2esPRkZiMgQDzNXREREdHcMSNRqhBB49esLuFlUjgB3BywZGWbukoiIiJqEAYlazaYjydh3IQt2UgnWTeoFhZxT3oiIyDowIFGrOHQlF+/8kAgAWD62O/oGuZu5IiIioqZjQCKTU5Vp8Mq/f4YQwPQBHTB9QKC5SyIiImoWswako0ePYsyYMfD394dEIsHevXsN1i9fvhxhYWFQKBRwc3NDdHQ0Tp061aJtAsCsWbMgkUgMHiNHjjThnt3f3tp/GfklVQjxUuD1Md3MXQ4REVGzmTUglZaWIiIiAhs2bGhwfefOnbF+/XpcvHgRx48fR1BQEGJiYpCXl2f0NmuNHDkSWVlZ+sfnn3/eon2hGqdTCvH56XQAwOoJPSG35ZWyiYjI+ph11uyoUaMwatSoRtdPmzbN4PnatWuxdetWXLhwAVFRUUZts5ZcLoevr2/zCqY70mh1eG3PRQDAlH4B6B/MeUdERGSdrGYOUlVVFbZs2QKlUomIiIgWb+/w4cPw9vZGly5d8Nxzz6GgoMAEVd7fPjmZiqTcErgrZHh1FE/pJyIi62Xx513v27cPU6ZMQVlZGfz8/BAbGwtPT88WbXPkyJGYMGECgoODkZycjNdeew2jRo1CXFwcpNKGh4QqKytRWVmpf65Wq1tUw72mqKwK7x64BgB4OaYzXB1lZq6IiIjIeBYfkIYPH46EhATk5+fjww8/xKRJk3Dq1Cl4e3sbvc0pU6bofw4PD0fPnj0REhKCw4cPNzp0t3r1aqxYscLo97zXvXvgGlTlGoT5OmNy3wBzl0NERNQiFj/EplAoEBoaioEDB2Lr1q2wtbXF1q1bTfoeHTt2hKenJ5KSkhpts3TpUqhUKv0jPT3dpDVYs5T8Uuw8mQoAWPZoN9hKLf7XioiI6I4svgepLp1OZzDUZQoZGRkoKCiAn59fo23kcjnkcrlJ3/de8cGRZGh1AsO7eGFwaMuGP4mIiCyBWf+pX1JSgoSEBCQkJAAAUlJSkJCQgLS0NJSWluK1117DyZMnkZqainPnzuGpp57CzZs38cQTT+i3ERUVhfXr1zdpm7XrX3nlFZw8eRI3btzAwYMH8dhjjyE0NBQjRoxos32/V+SqK7A7/iYAYN7wUDNXQ0REZBpm7UE6e/Yshg8frn++cOFCAMDMmTOxefNmXLlyBTt27EB+fj48PDzQr18/HDt2DN27d9e/Jjk5Gfn5+U3a5vbt2yGVSnHhwgXs2LEDRUVF8Pf3R0xMDN588032EBlh608pqNLq0DfQjbcTISKie4ZECCHMXYQ1UqvVUCqVUKlUcHFxMXc5ZqGu0GDw6h9RXFmNj57si+huPuYuiYiI6I6a+v3N2bRktE9PpqG4shqdvJ3wcJjxZxUSERFZGgYkMkqFRouPf0oBAPxpaAhsbCRmroiIiMh0GJDIKHvO30RecSX8lPYYG+Fv7nKIiIhMigGJmk2rE/jw6HUAwJwHgyGz5a8RERHdW/jNRs0Weykb1/NL4WJviyn9O5i7HCIiIpNjQKJm0ekE1h+queL4k5FBcJJb3bVGiYiI7ooBiZrlm59v4pebajjJbTFrcJC5yyEiImoVDEjUZBUaLd7ZnwgAeG5YCDydeGFNIiK6NzEgUZNtPZ6CTFUF2rk6YM6DweYuh4iIqNUwIFGTlFVVY9PhZADAKyO6wN5OauaKiIiIWg8DEjXJ+bQilFRWw9eF1z0iIqJ7HwMSNcnplEIAQP9gd141m4iI7nkMSNQkZ1NrAlK/YHczV0JERNT6GJDorjRaHeJTiwAA/YMYkIiI6N7HgER39WumGuUaLZQOdujk7WTucoiIiFodAxLd1dkbNcNrfQPdOP+IiIjuCwxIdFe1E7Q5/4iIiO4XDEh0R0IInE29BQDoF+Rm5mqIiIjaBgMS3VFyXikKS6sgt7VBeDtXc5dDRETUJhiQ6I7+dykbAPBAB1fIbPnrQkRE9wd+41GjqrU6fBKXCgB4vE+AmashIiJqOwxI1KgDl3OQqaqAu0KGR3v6mbscIiKiNsOARI3afuIGAGBKvwDenJaIiO4rDEjUoCvZapy8XgipjQR/HBho7nKIiIjaFAMSNeiL0+kAgJhuPvB3dTBzNURERG2LAYnqEULgwOUcAMCE3u3NXA0REVHbY0Cieq7lliDjVjlktjYYHOph7nKIiIjaHAMS1fPjlVwAQGRHDzjKbM1cDRERUdtjQKJ6agPSw2HeZq6EiIjIPBiQyICqTINzv917jQGJiIjuVwxIZODotTxodQKdvJ0Q4O5o7nKIiIjMggGJDHB4jYiIiAGJbiOEwLFreQCAYV0YkIiI6P7FgER6SbklyC+pgr2dDXoHupq7HCIiIrMxa0A6evQoxowZA39/f0gkEuzdu9dg/fLlyxEWFgaFQgE3NzdER0fj1KlTLdomUNNT8vrrr8PPzw8ODg6Ijo7GtWvXTLhn1unk9QIAQJ9AN8htee81IiK6f5k1IJWWliIiIgIbNmxocH3nzp2xfv16XLx4EcePH0dQUBBiYmKQl5dn9DYBYM2aNXjvvfewefNmnDp1CgqFAiNGjEBFRUWL98manbxeCAAYGMyLQxIR0f1NIoQQ5i4CACQSCfbs2YNx48Y12katVkOpVOLAgQOIiooyaptCCPj7++Pll1/GokWLAAAqlQo+Pj7Yvn07pkyZ0qR6a2tRqVRwcXFp0mssmRACfVceQEFpFb56NhL9gtzNXRIREZHJNfX722rmIFVVVWHLli1QKpWIiIgwejspKSnIzs5GdHS0fplSqcSAAQMQFxdnilKtUlJuCQpKa+Yf9WyvNHc5REREZmXx95HYt28fpkyZgrKyMvj5+SE2Nhaenp5Gby87OxsA4OPjY7Dcx8dHv64hlZWVqKys1D9Xq9VG12CJOP+IiIjodxbfgzR8+HAkJCTgxIkTGDlyJCZNmoTc3Nw2r2P16tVQKpX6R0BAQJvX0Jo4/4iIiOh3Fh+QFAoFQkNDMXDgQGzduhW2trbYunWr0dvz9fUFAOTk5Bgsz8nJ0a9ryNKlS6FSqfSP9PR0o2uwNEIIfQ/SwBAGJCIiIosPSHXpdDqDoa7mCg4Ohq+vLw4ePKhfplarcerUKURGRjb6OrlcDhcXF4PHvSI5rxQFpVWQ23L+EREREWDmOUglJSVISkrSP09JSUFCQgLc3d3h4eGBVatWYezYsfDz80N+fj42bNiAmzdv4oknntC/JioqCuPHj8f8+fPvus0OHTpAIpFgwYIFWLlyJTp16oTg4GAsW7YM/v7+dzyD7l52Pq3m5rQR7V05/4iIiAhmDkhnz57F8OHD9c8XLlwIAJg5cyY2b96MK1euYMeOHcjPz4eHhwf69euHY8eOoXv37vrXJCcnIz8/v0nb3L59OwBg8eLFKC0txTPPPIOioiI8+OCD2L9/P+zt7Vtzdy1WQnoRAKBXB1ez1kFERGQpLOY6SNbmXroO0iP/PIZLWWpsmt4bo8L9zF0OERFRq7nnroNEraOsqhpXsmsuWcAeJCIiohoMSPe5ixkq6ATg62IPP6WDucshIiKyCAxI97nztfOPAlzNWgcREZElYUC6zyWkFQEAHuDwGhERkR4D0n1MCIH4307xZw8SERHR7xiQ7mNZqgrkFldCaiNBOC8QSUREpMeAdB87/9vwWhcfZzjKLP6+xURERG2GAek+diK55gKb/YLczFwJERGRZWFAuo8du1YTkB7q5GXmSoiIiCwLA9J9KrWgFGmFZbC1kWBgiIe5yyEiIrIoDEj3qdreo96BbnCSc/4RERHR7Zr8zVh709emWLt2rVHFUNs5di0PADCkk6eZKyEiIrI8TQ5I58+fN3geHx+P6upqdOnSBQBw9epVSKVS9OnTx7QVkslVa3U4kVQAgPOPiIiIGtLkgHTo0CH9z2vXroWzszN27NgBN7eaM6Bu3bqF2bNn46GHHjJ9lWRSP2cUobiyGq6OdujRjtc/IiIiqsuoOUj/+Mc/sHr1an04AgA3NzesXLkS//jHP0xWHLWOo1dr5h8NDvWE1EZi5mqIiIgsj1EBSa1WIy8vr97yvLw8FBcXt7goal0Jv92gNrIjz14jIiJqiFEBafz48Zg9ezZ2796NjIwMZGRk4Ouvv8acOXMwYcIEU9dIJpaSXwoA6OTtZOZKiIiILJNR53dv3rwZixYtwrRp06DRaGo2ZGuLOXPm4J133jFpgWRaVdU6ZNwqAwAEeyrMXA0REZFlMiogOTo6YuPGjXjnnXeQnJwMAAgJCYFCwS9cS5dWWAadABQyKbyc5eYuh4iIyCK16AqBCoUC7u7u+p/J8tUOrwV7KSCRcII2ERFRQ4yag6TT6fDXv/4VSqUSgYGBCAwMhKurK958803odDpT10gmdOO3gBTkwUBLRETUGKN6kP7yl79g69ateOuttzB48GAAwPHjx7F8+XJUVFRg1apVJi2STOf6bwGpI+cfERERNcqogLRjxw589NFHGDt2rH5Zz5490a5dOzz//PMMSBYsJb8EQM0QGxERETXMqCG2wsJChIWF1VseFhaGwsLCFhdFredGfs0ZbBxiIyIiapxRASkiIgLr16+vt3z9+vWIiIhocVHUOkorq5GtrgDAU/yJiIjuxKghtjVr1mD06NE4cOAAIiMjAQBxcXFIT0/H999/b9ICyXRuFNTMP3JXyODqKDNzNURERJbLqB6koUOH4urVqxg/fjyKiopQVFSECRMmIDExkTertWAp+jPYHM1cCRERkWUz+jpI/v7+nIxtZWpP8Q/25C1GiIiI7sTogFRUVIStW7fi8uXLAIDu3bvjqaeeglKpNFlxZFr6U/x5BhsREdEdGTXEdvbsWYSEhGDdunUoLCxEYWEh1q5di5CQEMTHx5u6RjKRFF4kkoiIqEmM6kF66aWXMHbsWHz44Yewta3ZRHV1NebOnYsFCxbg6NGjJi2SWk4I8XtA8uQcJCIiojsxKiCdPXvWIBwBgK2tLRYvXoy+ffuarDgynWx1BYrKNJDaSBDixTlIREREd2LUEJuLiwvS0tLqLU9PT4ezs3OLiyLTu5SpBgCEejnB3k5q5mqIiIgsm1EBafLkyZgzZw6+/PJLpKenIz09HV988QXmzp2LqVOnmrpGMoHagNTd38XMlRAREVk+owLS3//+d0yYMAFPPvkkgoKCEBQUhFmzZuHxxx/H22+/3eTtHD16FGPGjIG/vz8kEgn27t1rsH758uUICwuDQqGAm5sboqOjcerUqbtud8OGDQgKCoK9vT0GDBiA06dPG6wfNmwYJBKJwePZZ59tct3W6FJWTUDqxoBERER0V0YFJJlMhn/+85+4desWEhISkJCQgMLCQqxbtw5yubzJ2yktLUVERAQ2bNjQ4PrOnTtj/fr1uHjxIo4fP46goCDExMQgLy+v0W1++eWXWLhwId544w3Ex8cjIiICI0aMQG5urkG7p59+GllZWfrHmjVrmly3NdIHJD8GJCIioruRCCGEuYsAAIlEgj179mDcuHGNtlGr1VAqlThw4ACioqIabDNgwAD069dPf684nU6HgIAAvPDCC3j11VcB1PQg9erVC++++67R9dbWolKp4OJi2aGjuEKD8OX/AwCcX/YHuCl4mxEiIro/NfX726gepNLSUixbtgyDBg1CaGgoOnbsaPBoDVVVVdiyZQuUSmWjN8StqqrCuXPnEB0drV9mY2OD6OhoxMXFGbT99NNP4enpiR49emDp0qUoKytrlbotweWsYgCAv9Ke4YiIiKgJjDrNf+7cuThy5AhmzJgBPz8/SCQSU9elt2/fPkyZMgVlZWXw8/NDbGwsPD09G2ybn58PrVYLHx8fg+U+Pj64cuWK/vm0adMQGBgIf39/XLhwAUuWLEFiYiJ2797daB2VlZWorKzUP1er1S3cs7ZzKVMFgPOPiIiImsqogPTf//4X//nPfzB48GBT11PP8OHDkZCQgPz8fHz44YeYNGkSTp06BW9vb6O3+cwzz+h/Dg8Ph5+fH6KiopCcnIyQkJAGX7N69WqsWLHC6Pc0J84/IiIiah6jhtjc3Nzg7u5u6loapFAoEBoaioEDB2Lr1q2wtbXF1q1bG2zr6ekJqVSKnJwcg+U5OTnw9fVt9D0GDBgAAEhKSmq0zdKlS6FSqfSP9PR0I/bGPHgGGxERUfMYFZDefPNNvP7662aZt6PT6QyGum4nk8nQp08fHDx40KD9wYMHERkZ2eg2ExISAAB+fn6NtpHL5XBxcTF4WAONVoer2SUAgG5+vJEwERFRUzR5iO2BBx4wmGuUlJQEHx8fBAUFwc7OzqBtU29YW1JSYtBrk5KSgoSEBLi7u8PDwwOrVq3C2LFj4efnh/z8fGzYsAE3b97EE088oX9NVFQUxo8fj/nz5wMAFi5ciJkzZ6Jv377o378/3n33XZSWlmL27NkAgOTkZHz22Wd45JFH4OHhgQsXLuCll17CkCFD0LNnz6Z+HFbjel4pqrQ6OMlt0d7NwdzlEBERWYUmB6Q7nX5vrLNnz2L48OH65wsXLgQAzJw5E5s3b8aVK1ewY8cO5Ofnw8PDA/369cOxY8fQvXt3/WuSk5ORn5+vfz558mTk5eXh9ddfR3Z2Nnr16oX9+/frJ27LZDIcOHBAH5wCAgIwceJE/N///Z/J988S1N6gNsRLARub1ptMT0REdC+xmOsgWRtruQ7Sh0evY9X3l/FoTz+sn9bb3OUQERGZVateB4msR2phTQ9SoIejmSshIiKyHk0eYnN3d8fVq1fh6ekJNze3O177qLCw0CTFUculFZYDADq4MyARERE1VZMD0rp16+Ds7AwALbpFB7WttIKaHqQO7gozV0JERGQ9mhyQZs6c2eDPZLm0OoGMW7/1IHGIjYiIqMmaHJCac2sNS560fD/JLCpHtU5AJrWBr4u9ucshIiKyGk0OSK6urne955oQAhKJBFqttsWFUculF9ZcyLO9mwOkPMWfiIioyZockA4dOtSadVArSP0tIHF4jYiIqHmaHJCGDh3amnVQK0irDUg8g42IiKhZjL4O0rFjx/DHP/4RgwYNws2bNwEAO3fuxPHjx01WHLVMWgEDEhERkTGMCkhff/01RowYAQcHB8THx+tvHqtSqfC3v/3NpAWS8diDREREZByjAtLKlSuxefNmfPjhhwY3qh08eHCTb1RLrS+1oPYq2rwGEhERUXMYFZASExMxZMiQesuVSiWKiopaWhOZgKpMA3VFNQAgwN3BzNUQERFZF6MCkq+vL5KSkuotP378ODp27Njioqjlau/B5uUsh6OsyXPxiYiICEYGpKeffhovvvgiTp06BYlEgszMTHz66adYtGgRnnvuOVPXSEbg/CMiIiLjGdW18Oqrr0Kn0yEqKgplZWUYMmQI5HI5Fi1ahBdeeMHUNZIRUn87gy2QAYmIiKjZjApI1dXV+Mtf/oJXXnkFSUlJKCkpQbdu3eDk5IT8/Hx4enqauk5qpqTcEgBAiLeTmSshIiKyPkYNsU2ZMgVCCMhkMnTr1g39+/eHk5MTcnJyMGzYMBOXSMa4llsMAAhlQCIiImo2owJSWloa5s6da7AsKysLw4YNQ1hYmEkKI+PpdALJuTWTtBmQiIiIms+ogPT999/jxIkTWLhwIQAgMzMTw4YNQ3h4OHbt2mXSAqn5bhaVo1yjhZ1UwjlIRERERjBqDpKXlxf+97//4cEHHwQA7Nu3D71798ann34KGxuj715CJpKUVzP/KNhTAVspjwcREVFzGX2BnICAAMTGxuKhhx7CH/7wB+zcuRMSicSUtZGRknJqAlInb2czV0JERGSdmhyQ3NzcGgxAZWVl+O677+Dh4aFfVlhYaJrqyCi1E7R5BhsREZFxmhyQ3n333VYsg0yp9hT/TgxIRERERmlyQJo5c2Zr1kEmIoTAtdqA5MOAREREZIwmByS1Wg0XFxf9z3dS247aXl5xJYorqmEjqZmkTURERM3XrDlIWVlZ8Pb2hqura4PzkYQQkEgk0Gq1Ji2Smq629yjQQwG5rdTM1RAREVmnJgekH3/8Ee7u7gCAQ4cOtVpB1DL6W4x4cXiNiIjIWE0OSEOHDm3w59sVFRXh+++/b3lVZLTaM9g4/4iIiMh4Jr2KYGpqKmbMmGHKTVIz6W8xwh4kIiIio/Eyy/eY9FtlAIBAD95ihIiIyFgMSPeQaq0OWaoKAEB7NwYkIiIiYzEg3UOyVBXQ6gRktjbwdpabuxwiIiKr1ax7sb333nt3XH/z5s0WFUMtk15YM7zW3tUBNja8Lx4REZGxmhWQ1q1bd9c2HTp0MLoYapmMW+UAgPbuHF4jIiJqiWYNsaWkpDTp0VRHjx7FmDFj4O/vD4lEgr179xqsX758OcLCwqBQKODm5obo6GicOnXqrtvdsGEDgoKCYG9vjwEDBuD06dMG6ysqKjBv3jx4eHjAyckJEydORE5OTpPrtlS1E7QD3BzMXAkREZF1a/EcpIyMDOh0OqNeW1paioiICGzYsKHB9Z07d8b69etx8eJFHD9+HEFBQYiJiUFeXl6j2/zyyy+xcOFCvPHGG4iPj0dERARGjBiB3NxcfZuXXnoJ3333Hb766iscOXIEmZmZmDBhglH7YEn0Q2ycoE1ERNQiEiGEaMkGXFxckJCQgI4dO7asEIkEe/bswbhx4xpto1aroVQqceDAAURFRTXYZsCAAejXrx/Wr18PANDpdAgICMALL7yAV199FSqVCl5eXvjss8/w+OOPAwCuXLmCrl27Ii4uDgMHDmxSvbW1qFQqi7n33MRNJ3Au9RbWT3sAj/b0N3c5REREFqep398t7kFqYb5qsqqqKmzZsgVKpRIRERGNtjl37hyio6P1y2xsbBAdHY24uDgAwLlz56DRaAzahIWFoUOHDvo21ipDP8TGHiQiIqKWaNYkbXPYt28fpkyZgrKyMvj5+SE2Nhaenp4Nts3Pz4dWq4WPj4/Bch8fH1y5cgUAkJ2dDZlMBldX13ptsrOzG62jsrISlZWV+udqtdrIPWodFRotctQ19QVwkjYREVGLtLgH6bXXXtPfxLY1DB8+HAkJCThx4gRGjhyJSZMmGcwnaiurV6+GUqnUPwICAtq8hju5WVRzBpujTAo3RzszV0NERGTdWhyQli5dWq83xpQUCgVCQ0MxcOBAbN26Fba2tti6dWuDbT09PSGVSuudkZaTkwNfX18AgK+vL6qqqlBUVNRom4YsXboUKpVK/0hPT2/ZjplY7QTtADdHSCS8BhIREVFLGDXEtnDhwgaXSyQS2NvbIzQ0FI899lir9CzpdDqDoa7byWQy9OnTBwcPHtRP9tbpdDh48CDmz58PAOjTpw/s7Oxw8OBBTJw4EQCQmJiItLQ0REZGNvq+crkccrnlXp269hpIAe48xZ+IiKiljApI58+fR3x8PLRaLbp06QIAuHr1KqRSKcLCwrBx40a8/PLLOH78OLp169bodkpKSpCUlKR/npKSgoSEBLi7u8PDwwOrVq3C2LFj4efnh/z8fGzYsAE3b97EE088oX9NVFQUxo8frw9ACxcuxMyZM9G3b1/0798f7777LkpLSzF79mwAgFKpxJw5c7Bw4UK4u7vDxcUFL7zwAiIjI5t8Bpslqr0GEk/xJyIiajmjAlJt79C2bdv0p8ipVCrMnTsXDz74IJ5++mlMmzYNL730En744YdGt3P27FkMHz5c/7y2Z2rmzJnYvHkzrly5gh07diA/Px8eHh7o168fjh07hu7du+tfk5ycjPz8fP3zyZMnIy8vD6+//jqys7PRq1cv7N+/32Di9rp162BjY4OJEyeisrISI0aMwMaNG435KCxGRmFtDxIDEhERUUsZdR2kdu3aITY2tl7v0K+//oqYmBjcvHkT8fHxiImJMQgv9xJLuw7S2PXHcSFDhQ9m9MGI7o3PpSIiIrqftep1kFQqVYNnkuXl5elPf3d1dUVVVZUxmycj6OcgcYiNiIioxYwKSI899hieeuop7NmzBxkZGcjIyMCePXswZ84c/eTo06dPo3PnzqaslRpRVlWNwtKaMNqek7SJiIhazKg5SB988AFeeuklTJkyBdXV1TUbsrXFzJkzsW7dOgA1V6f+6KOPTFcpNermb71HLva2cLHnNZCIiIhayqiA5OTkhA8//BDr1q3D9evXAQAdO3aEk5OTvk2vXr1MUiDdXcZvF4n0d2XvERERkSm06FYjTk5O+msd3R6OqG3V9iC1d2NAIiIiMgWj5iDpdDr89a9/hVKpRGBgIAIDA+Hq6oo333wTOp3O1DXSXdTeZqQde5CIiIhMwqgepL/85S/YunUr3nrrLQwePBgAcPz4cSxfvhwVFRVYtWqVSYukO6vtQWrHHiQiIiKTMCog7dixAx999BHGjh2rX9azZ0+0a9cOzz//PANSG/u9B4mn+BMREZmCUUNshYWFCAsLq7c8LCwMhYWFLS6Kmoc9SERERKZlVECKiIjA+vXr6y1fv349evbs2eKiqOmqqnXIKa4AwDlIREREpmLUENuaNWswevRoHDhwAJGRkQCAuLg4pKen4/vvvzdpgXRn2aoKCAHIbW3g6SQzdzlERET3BKN6kIYOHYqrV69i/PjxKCoqQlFRESZMmIBff/0VO3fuNHWNdAcZRWUAanqPJBKJmashIiK6Nxh9HSR/f/96k7F//vlnbN26FVu2bGlxYdQ0nH9ERERkekb1IJHl4DWQiIiITI8Bycpl8jYjREREJseAZOXYg0RERGR6zZqDNGHChDuuLyoqakktZATOQSIiIjK9ZgUkpVJ51/VPPvlkiwqiptPpBDKLeA0kIiIiU2tWQNq2bVtr1UFGyC+pRJVWBxsJ4Ku0N3c5RERE9wzOQbJiGb/NP/J1sYedlIeSiIjIVPitasWyVTXDa34cXiMiIjIpBiQrlqOuCUi+LhxeIyIiMiUGJCuW/VtA8naRm7kSIiKiewsDkhXLVVcCAHzYg0RERGRSDEhWjENsRERErYMByYpxiI2IiKh1MCBZsdohNvYgERERmRYDkpUqqaxGSWU1AMCbAYmIiMikGJCsVO38Iye5LZzkzbogOhEREd0FA5KVqg1IPpx/REREZHIMSFbq94DE4TUiIiJTY0CyUjmcoE1ERNRqGJCsVI7+FH8GJCIiIlNjQLJSnINERETUeswakI4ePYoxY8bA398fEokEe/fu1a/TaDRYsmQJwsPDoVAo4O/vjyeffBKZmZl33GZxcTEWLFiAwMBAODg4YNCgQThz5oxBm1mzZkEikRg8Ro4c2Rq72Go4xEZERNR6zBqQSktLERERgQ0bNtRbV1ZWhvj4eCxbtgzx8fHYvXs3EhMTMXbs2Dtuc+7cuYiNjcXOnTtx8eJFxMTEIDo6Gjdv3jRoN3LkSGRlZekfn3/+uUn3rbVlqzjERkRE1FrMegGdUaNGYdSoUQ2uUyqViI2NNVi2fv169O/fH2lpaejQoUO915SXl+Prr7/GN998gyFDhgAAli9fju+++w6bNm3CypUr9W3lcjl8fX1NuDdtRwiB3OLf7sOmZEAiIiIyNauag6RSqSCRSODq6trg+urqami1WtjbG4YGBwcHHD9+3GDZ4cOH4e3tjS5duuC5555DQUFBa5VtcrfKNNBoBQDAy4lzkIiIiEzNai7BXFFRgSVLlmDq1KlwcXFpsI2zszMiIyPx5ptvomvXrvDx8cHnn3+OuLg4hIaG6tuNHDkSEyZMQHBwMJKTk/Haa69h1KhRiIuLg1QqbXDblZWVqKys1D9Xq9Wm3cFmqB1e81DIILO1qoxLRERkFawiIGk0GkyaNAlCCGzatOmObXfu3ImnnnoK7dq1g1QqRe/evTF16lScO3dO32bKlCn6n8PDw9GzZ0+EhITg8OHDiIqKanC7q1evxooVK0yzQy2UU8yLRBIREbUmi+9+qA1HqampiI2NbbT3qFZISAiOHDmCkpISpKen4/Tp09BoNOjYsWOjr+nYsSM8PT2RlJTUaJulS5dCpVLpH+np6UbvU0vl8hR/IiKiVmXRPUi14ejatWs4dOgQPDw8mvxahUIBhUKBW7du4YcffsCaNWsabZuRkYGCggL4+fk12kYul0Mut4xAkq2qGepjDxIREVHrMGtAKikpMei1SUlJQUJCAtzd3eHn54fHH38c8fHx2LdvH7RaLbKzswEA7u7ukMlkAICoqCiMHz8e8+fPBwD88MMPEEKgS5cuSEpKwiuvvIKwsDDMnj1b/54rVqzAxIkT4evri+TkZCxevBihoaEYMWJEG38CxslWlwPgGWxEREStxawB6ezZsxg+fLj++cKFCwEAM2fOxPLly/Htt98CAHr16mXwukOHDmHYsGEAgOTkZOTn5+vXqVQqLF26FBkZGXB3d8fEiROxatUq2NnZAQCkUikuXLiAHTt2oKioCP7+/oiJicGbb75pMT1Ed3OzqGaIzd/VwcyVEBER3ZskQghh7iKskVqthlKphEqluuu8KFOLXnsESbkl+HTuAAwO9WzT9yYiIrJmTf3+tvhJ2mRICIHMopohNvYgERERtQ4GJCujLq9GWZUWAODHOUhEREStggHJytz8rffIQyGDvV3DF7UkIiKilmFAsjIcXiMiImp9DEhWJlNVG5A4vEZERNRaGJCsTOZvp/j7KdmDRERE1FoYkKxM7RBbOw6xERERtRoGJCvDOUhEREStjwHJyvwekDgHiYiIqLUwIFmRaq0OOcU1N6plDxIREVHrYUCyIrnFldDqBOykEng5Wcd944iIiKwRA5IVqR1e81Xaw8ZGYuZqiIiI7l0MSFak9ira/jzFn4iIqFUxIFmRLFXNNZA4/4iIiKh1MSBZEZ7BRkRE1DYYkKwIr4FERETUNhiQrEjtbUY4B4mIiKh1MSBZkbySmmsgeTnzFH8iIqLWxIBkJbQ6gYLfApK3CwMSERFRa2JAshKFpVXQCcBGAngoGJCIiIhaEwOSlcgtrpl/5K6QQ8qLRBIREbUqBiQrkVfM+UdERERthQHJSjAgERERtR0GJCtRewabNwMSERFRq2NAshK5avYgERERtRUGJCuhvwaSEwMSERFRa2NAshKcg0RERNR2GJCsRH4x5yARERG1FQYkK5HLHiQiIqI2w4BkBcqqqlFSWQ2AAYmIiKgtMCBZgfziKgCAvZ0NnOS2Zq6GiIjo3seAZAXySmpuM+LtbA+JhLcZISIiam0MSFaAZ7ARERG1LQYkK6CfoM1rIBEREbUJswako0ePYsyYMfD394dEIsHevXv16zQaDZYsWYLw8HAoFAr4+/vjySefRGZm5h23WVxcjAULFiAwMBAODg4YNGgQzpw5Y9BGCIHXX38dfn5+cHBwQHR0NK5du9Yau2gS7EEiIiJqW2YNSKWlpYiIiMCGDRvqrSsrK0N8fDyWLVuG+Ph47N69G4mJiRg7duwdtzl37lzExsZi586duHjxImJiYhAdHY2bN2/q26xZswbvvfceNm/ejFOnTkGhUGDEiBGoqKgw+T6aQh6vgURERNSmJEIIYe4iAEAikWDPnj0YN25co23OnDmD/v37IzU1FR06dKi3vry8HM7Ozvjmm28wevRo/fI+ffpg1KhRWLlyJYQQ8Pf3x8svv4xFixYBAFQqFXx8fLB9+3ZMmTKlSfWq1WoolUqoVCq4uLg0b2ebac72Mzh4JRdvTQjHlP7195uIiIiapqnf31Y1B0mlUkEikcDV1bXB9dXV1dBqtbC3tzdY7uDggOPHjwMAUlJSkJ2djejoaP16pVKJAQMGIC4urtVqbwleJJKIiKhtWU1AqqiowJIlSzB16tRGE5+zszMiIyPx5ptvIjMzE1qtFp988gni4uKQlZUFAMjOzgYA+Pj4GLzWx8dHv64hlZWVUKvVBo+2wjlIREREbcsqApJGo8GkSZMghMCmTZvu2Hbnzp0QQqBdu3aQy+V47733MHXqVNjYtGxXV69eDaVSqX8EBAS0aHtNpdMJ5JcwIBEREbUliw9IteEoNTUVsbGxd53vExISgiNHjqCkpATp6ek4ffo0NBoNOnbsCADw9fUFAOTk5Bi8LicnR7+uIUuXLoVKpdI/0tPTW7hnTVNUrkG1rmaamCdP8yciImoTFh2QasPRtWvXcODAAXh4eDT5tQqFAn5+frh16xZ++OEHPPbYYwCA4OBg+Pr64uDBg/q2arUap06dQmRkZKPbk8vlcHFxMXi0hdzimjPr3BUy2Ekt+nARERHdM8x6Y6+SkhIkJSXpn6ekpCAhIQHu7u7w8/PD448/jvj4eOzbtw9arVY/R8jd3R0ymQwAEBUVhfHjx2P+/PkAgB9++AFCCHTp0gVJSUl45ZVXEBYWhtmzZwOoOVtuwYIFWLlyJTp16oTg4GAsW7YM/v7+dzyDzlzyeJFIIiKiNmfWgHT27FkMHz5c/3zhwoUAgJkzZ2L58uX49ttvAQC9evUyeN2hQ4cwbNgwAEBycjLy8/P161QqFZYuXYqMjAy4u7tj4sSJWLVqFezs7PRtFi9ejNLSUjzzzDMoKirCgw8+iP3799c7+80ScII2ERFR27OY6yBZm7a6DtIHR5Kx+r9XMOGBdlg7uVervQ8REdH94J68DtL9iNdAIiIiansMSBaOQ2xERERtjwHJwjEgERERtT0GJAuXx4tEEhERtTkGJAuXq665DpI3AxIREVGbYUCyYBUaLdQV1QAALyfLuwQBERHRvYoByYLV3oNNZmsDFwezXrKKiIjovsKAZMFuv4q2RCIxczVERET3DwYkC8ZrIBEREZkHA5IF4yn+RERE5sGAZMEYkIiIiMyDAcmC6a+B5MSARERE1JYYkCxYrromIHm7MCARERG1JQYkC8YeJCIiIvNgQLJg+ZyDREREZBYMSBZKCMFJ2kRERGbCgGShVOUaVGl1ABiQiIiI2hoDkoWq7T1SOthBbis1czVERET3FwYkC8XhNSIiIvNhQLJQtWeweTrJzFwJERHR/YcByUL93oNkb+ZKiIiI7j8MSBaqoLQKAOChYA8SERFRW2NAslC8BhIREZH5MCBZqHzOQSIiIjIbBiQL9fsQG3uQiIiI2hoDkoWqHWLz5BAbERFRm2NAskBCCOT/1oPEITYiIqK2x4BkgYorq1FVXXObEU8n9iARERG1NQYkC1Q7vOYkt4W9HW8zQkRE1NYYkCyQfoI2h9eIiIjMggHJAuknaHN4jYiIyCwYkCwQr4FERERkXgxIFii/pHaIjT1IRERE5sCAZIF+70FiQCIiIjIHswako0ePYsyYMfD394dEIsHevXv16zQaDZYsWYLw8HAoFAr4+/vjySefRGZm5h23qdVqsWzZMgQHB8PBwQEhISF48803IYTQt5k1axYkEonBY+TIka21m81WG5C8OMRGRERkFrbmfPPS0lJERETgqaeewoQJEwzWlZWVIT4+HsuWLUNERARu3bqFF198EWPHjsXZs2cb3ebbb7+NTZs2YceOHejevTvOnj2L2bNnQ6lU4s9//rO+3ciRI7Ft2zb9c7nccnprCjjERkREZFZmDUijRo3CqFGjGlynVCoRGxtrsGz9+vXo378/0tLS0KFDhwZfd+LECTz22GMYPXo0ACAoKAiff/45Tp8+bdBOLpfD19fXBHthehxiIyIiMi+rmoOkUqkgkUjg6uraaJtBgwbh4MGDuHr1KgDg559/xvHjx+sFscOHD8Pb2xtdunTBc889h4KCgtYsvVlqe5B4FhsREZF5mLUHqTkqKiqwZMkSTJ06FS4uLo22e/XVV6FWqxEWFgapVAqtVotVq1Zh+vTp+jYjR47EhAkTEBwcjOTkZLz22msYNWoU4uLiIJU2fOXqyspKVFZW6p+r1WrT7dxtKjRaFFdWA+AQGxERkblYRUDSaDSYNGkShBDYtGnTHdvu2rULn376KT777DN0794dCQkJWLBgAfz9/TFz5kwAwJQpU/Ttw8PD0bNnT4SEhODw4cOIiopqcLurV6/GihUrTLdTjagdXpNJbeBibxWHh4iI6J5j8UNsteEoNTUVsbGxd+w9AoBXXnkFr776KqZMmYLw8HDMmDEDL730ElavXt3oazp27AhPT08kJSU12mbp0qVQqVT6R3p6utH7dCe3D69JJJJWeQ8iIiK6M4vuoqgNR9euXcOhQ4fg4eFx19eUlZXBxsYw90mlUuh0ukZfk5GRgYKCAvj5+TXaRi6Xt8mZbrU9SBxeIyIiMh+zBqSSkhKDXpuUlBQkJCTA3d0dfn5+ePzxxxEfH499+/ZBq9UiOzsbAODu7g6ZrGYCc1RUFMaPH4/58+cDAMaMGYNVq1ahQ4cO6N69O86fP4+1a9fiqaee0r/nihUrMHHiRPj6+iI5ORmLFy9GaGgoRowY0cafQH28zQgREZH5mTUgnT17FsOHD9c/X7hwIQBg5syZWL58Ob799lsAQK9evQxed+jQIQwbNgwAkJycjPz8fP26999/H8uWLcPzzz+P3Nxc+Pv7409/+hNef/11ADW9SRcuXMCOHTtQVFQEf39/xMTE4M0337SIayHxNiNERETmJxG3X2KamkytVkOpVEKlUt11XlRzrPjuV2z76QaeHRqCV0eFmWy7RERE1PTvb4ufpH2/0eoEZFIbDrERERGZEXuQjNRaPUgAIISAVidgK2V+JSIiMqWmfn9b9Fls9yuJRAJbKU/xJyIiMhd2URARERHVwYBEREREVAcDEhEREVEdDEhEREREdTAgEREREdXBgERERERUBwMSERERUR0MSERERER1MCARERER1cGARERERFQHAxIRERFRHQxIRERERHUwIBERERHVYWvuAqyVEAIAoFarzVwJERERNVXt93bt93hjGJCMVFxcDAAICAgwcyVERETUXMXFxVAqlY2ul4i7RShqkE6nQ2ZmJpydnSGRSEy2XbVajYCAAKSnp8PFxcVk27Uk3Efrd6/vH8B9vBfc6/sHcB+NIYRAcXEx/P39YWPT+Ewj9iAZycbGBu3bt2+17bu4uNyzv+y1uI/W717fP4D7eC+41/cP4D421516jmpxkjYRERFRHQxIRERERHUwIFkYuVyON954A3K53NyltBruo/W71/cP4D7eC+71/QO4j62Jk7SJiIiI6mAPEhEREVEdDEhEREREdTAgEREREdXBgERERERUBwOShdmwYQOCgoJgb2+PAQMG4PTp0+YuySirV69Gv3794OzsDG9vb4wbNw6JiYkGbYYNGwaJRGLwePbZZ81UcfMtX768Xv1hYWH69RUVFZg3bx48PDzg5OSEiRMnIicnx4wVN19QUFC9fZRIJJg3bx4A6zuGR48exZgxY+Dv7w+JRIK9e/carBdC4PXXX4efnx8cHBwQHR2Na9euGbQpLCzE9OnT4eLiAldXV8yZMwclJSVtuBd3dqd91Gg0WLJkCcLDw6FQKODv748nn3wSmZmZBtto6Li/9dZbbbwnjbvbcZw1a1a9+keOHGnQxpKP4932r6H/JyUSCd555x19G0s+hk35fmjK38+0tDSMHj0ajo6O8Pb2xiuvvILq6mqT1cmAZEG+/PJLLFy4EG+88Qbi4+MRERGBESNGIDc319ylNduRI0cwb948nDx5ErGxsdBoNIiJiUFpaalBu6effhpZWVn6x5o1a8xUsXG6d+9uUP/x48f161566SV89913+Oqrr3DkyBFkZmZiwoQJZqy2+c6cOWOwf7GxsQCAJ554Qt/Gmo5haWkpIiIisGHDhgbXr1mzBu+99x42b96MU6dOQaFQYMSIEaioqNC3mT59On799VfExsZi3759OHr0KJ555pm22oW7utM+lpWVIT4+HsuWLUN8fDx2796NxMREjB07tl7bv/71rwbH9YUXXmiL8pvkbscRAEaOHGlQ/+eff26w3pKP49327/b9ysrKwscffwyJRIKJEycatLPUY9iU74e7/f3UarUYPXo0qqqqcOLECezYsQPbt2/H66+/brpCBVmM/v37i3nz5umfa7Va4e/vL1avXm3GqkwjNzdXABBHjhzRLxs6dKh48cUXzVdUC73xxhsiIiKiwXVFRUXCzs5OfPXVV/plly9fFgBEXFxcG1Voei+++KIICQkROp1OCGHdxxCA2LNnj/65TqcTvr6+4p133tEvKyoqEnK5XHz++edCCCEuXbokAIgzZ87o2/z3v/8VEolE3Lx5s81qb6q6+9iQ06dPCwAiNTVVvywwMFCsW7eudYszkYb2cebMmeKxxx5r9DXWdBybcgwfe+wx8fDDDxsss6ZjWPf7oSl/P7///nthY2MjsrOz9W02bdokXFxcRGVlpUnqYg+ShaiqqsK5c+cQHR2tX2ZjY4Po6GjExcWZsTLTUKlUAAB3d3eD5Z9++ik8PT3Ro0cPLF26FGVlZeYoz2jXrl2Dv78/OnbsiOnTpyMtLQ0AcO7cOWg0GoPjGRYWhg4dOljt8ayqqsInn3yCp556yuAGzdZ+DGulpKQgOzvb4JgplUoMGDBAf8zi4uLg6uqKvn376ttER0fDxsYGp06davOaTUGlUkEikcDV1dVg+VtvvQUPDw888MADeOedd0w6dNEWDh8+DG9vb3Tp0gXPPfccCgoK9OvupeOYk5OD//znP5gzZ069ddZyDOt+PzTl72dcXBzCw8Ph4+OjbzNixAio1Wr8+uuvJqmLN6u1EPn5+dBqtQYHGwB8fHxw5coVM1VlGjqdDgsWLMDgwYPRo0cP/fJp06YhMDAQ/v7+uHDhApYsWYLExETs3r3bjNU23YABA7B9+3Z06dIFWVlZWLFiBR566CH88ssvyM7Ohkwmq/el4+Pjg+zsbPMU3EJ79+5FUVERZs2apV9m7cfwdrXHpaH/B2vXZWdnw9vb22C9ra0t3N3drfK4VlRUYMmSJZg6darBTUD//Oc/o3fv3nB3d8eJEyewdOlSZGVlYe3atWastulGjhyJCRMmIDg4GMnJyXjttdcwatQoxMXFQSqV3lPHcceOHXB2dq43fG8tx7Ch74em/P3Mzs5u8P/V2nWmwIBErW7evHn45ZdfDObnADAY7w8PD4efnx+ioqKQnJyMkJCQti6z2UaNGqX/uWfPnhgwYAACAwOxa9cuODg4mLGy1rF161aMGjUK/v7++mXWfgzvZxqNBpMmTYIQAps2bTJYt3DhQv3PPXv2hEwmw5/+9CesXr3aKm5pMWXKFP3P4eHh6NmzJ0JCQnD48GFERUWZsTLT+/jjjzF9+nTY29sbLLeWY9jY94Ml4BCbhfD09IRUKq03Sz8nJwe+vr5mqqrl5s+fj3379uHQoUNo3779HdsOGDAAAJCUlNQWpZmcq6srOnfujKSkJPj6+qKqqgpFRUUGbaz1eKampuLAgQOYO3fuHdtZ8zGsPS53+n/Q19e33kkT1dXVKCwstKrjWhuOUlNTERsba9B71JABAwaguroaN27caJsCTaxjx47w9PTU/17eK8fx2LFjSExMvOv/l4BlHsPGvh+a8vfT19e3wf9Xa9eZAgOShZDJZOjTpw8OHjyoX6bT6XDw4EFERkaasTLjCCEwf/587NmzBz/++COCg4Pv+pqEhAQAgJ+fXytX1zpKSkqQnJwMPz8/9OnTB3Z2dgbHMzExEWlpaVZ5PLdt2wZvb2+MHj36ju2s+RgGBwfD19fX4Jip1WqcOnVKf8wiIyNRVFSEc+fO6dv8+OOP0Ol0+nBo6WrD0bVr13DgwAF4eHjc9TUJCQmwsbGpNyxlLTIyMlBQUKD/vbwXjiNQ06vbp08fRERE3LWtJR3Du30/NOXvZ2RkJC5evGgQdGvDfrdu3UxWKFmIL774QsjlcrF9+3Zx6dIl8cwzzwhXV1eDWfrW4rnnnhNKpVIcPnxYZGVl6R9lZWVCCCGSkpLEX//6V3H27FmRkpIivvnmG9GxY0cxZMgQM1fedC+//LI4fPiwSElJET/99JOIjo4Wnp6eIjc3VwghxLPPPis6dOggfvzxR3H27FkRGRkpIiMjzVx182m1WtGhQwexZMkSg+XWeAyLi4vF+fPnxfnz5wUAsXbtWnH+/Hn9GVxvvfWWcHV1Fd988424cOGCeOyxx0RwcLAoLy/Xb2PkyJHigQceEKdOnRLHjx8XnTp1ElOnTjXXLtVzp32sqqoSY8eOFe3btxcJCQkG/2/Wnvlz4sQJsW7dOpGQkCCSk5PFJ598Iry8vMSTTz5p5j373Z32sbi4WCxatEjExcWJlJQUceDAAdG7d2/RqVMnUVFRod+GJR/Hu/2eCiGESqUSjo6OYtOmTfVeb+nH8G7fD0Lc/e9ndXW16NGjh4iJiREJCQli//79wsvLSyxdutRkdTIgWZj3339fdOjQQchkMtG/f39x8uRJc5dkFAANPrZt2yaEECItLU0MGTJEuLu7C7lcLkJDQ8Urr7wiVCqVeQtvhsmTJws/Pz8hk8lEu3btxOTJk0VSUpJ+fXl5uXj++eeFm5ubcHR0FOPHjxdZWVlmrNg4P/zwgwAgEhMTDZZb4zE8dOhQg7+XM2fOFELUnOq/bNky4ePjI+RyuYiKiqq33wUFBWLq1KnCyclJuLi4iNmzZ4vi4mIz7E3D7rSPKSkpjf6/eejQISGEEOfOnRMDBgwQSqVS2Nvbi65du4q//e1vBuHC3O60j2VlZSImJkZ4eXkJOzs7ERgYKJ5++ul6/9C05ON4t99TIYT44IMPhIODgygqKqr3eks/hnf7fhCiaX8/b9y4IUaNGiUcHByEp6enePnll4VGozFZnZLfiiUiIiKi33AOEhEREVEdDEhEREREdTAgEREREdXBgERERERUBwMSERERUR0MSERERER1MCARERER1cGARERkpKCgILz77rvmLoOIWgEDEhFZhVmzZmHcuHEAgGHDhmHBggVt9t7bt2+Hq6trveVnzpzBM88802Z1EFHbsTV3AURE5lJVVQWZTGb06728vExYDRFZEvYgEZFVmTVrFo4cOYJ//vOfkEgkkEgkuHHjBgDgl19+wahRo+Dk5AQfHx/MmDED+fn5+tcOGzYM8+fPx4IFC+Dp6YkRI0YAANauXYvw8HAoFAoEBATg+eefR0lJCQDg8OHDmD17NlQqlf79li9fDqD+EFtaWhoee+wxODk5wcXFBZMmTUJOTo5+/fLly9GrVy/s3LkTQUFBUCqVmDJlCoqLi1v3QyOiZmNAIiKr8s9//hORkZF4+umnkZWVhaysLAQEBKCoqAgPP/wwHnjgAZw9exb79+9HTk4OJk2aZPD6HTt2QCaT4aeffsLmzZsBADY2Nnjvvffw66+/YseOHfjxxx+xePFiAMCgQYPw7rvvwsXFRf9+ixYtqleXTqfDY489hsLCQhw5cgSxsbG4fv06Jk+ebNAuOTkZe/fuxb59+7Bv3z4cOXIEb731Vit9WkRkLA6xEZFVUSqVkMlkcHR0hK+vr375+vXr8cADD+Bvf/ubftnHH3+MgIAAXL16FZ07dwYAdOrUCWvWrDHY5u3zmYKCgrBy5Uo8++yz2LhxI2QyGZRKJSQSicH71XXw4EFcvHgRKSkpCAgIAAD861//Qvfu3XHmzBn069cPQE2Q2r59O5ydnQEAM2bMwMGDB7Fq1aqWfTBEZFLsQSKie8LPP/+MQ4cOwcnJSf8ICwsDUNNrU6tPnz71XnvgwAFERUWhXbt2cHZ2xowZM1BQUICysrImv//ly5cREBCgD0cA0K1bN7i6uuLy5cv6ZUFBQfpwBAB+fn7Izc1t1r4SUetjDxIR3RNKSkowZswYvP322/XW+fn56X9WKBQG627cuIFHH30Uzz33HFatWgV3d3ccP34cc+bMQVVVFRwdHU1ap52dncFziUQCnU5n0vcgopZjQCIiqyOTyaDVag2W9e7dG19//TWCgoJga9v0P23nzp2DTqfDP/7xD9jY1HSq79q1667vV1fXrl2Rnp6O9PR0fS/SpUuXUFRUhG7dujW5HiKyDBxiIyKrExQUhFOnTuHGjRvIz8+HTqfDvHnzUFhYiKlTp+LMmTNITk7GDz/8gNmzZ98x3ISGhkKj0eD999/H9evXsXPnTv3k7dvfr6SkBAcPHkR+fn6DQ2/R0dEIDw/H9OnTER8fj9OnT+PJJ5/E0KFD0bdvX5N/BkTUuhiQiMjqLFq0CFKpFN26dYOXlxfS0tLg7++Pn376CVqtFjExMQgPD8eCBQvg6uqq7xlqSEREBNauXYu3334bPXr0wKefforVq1cbtBk0aBCeffZZTJ48GV5eXvUmeQM1Q2XffPMN3NzcMGTIEERHR6Njx4748ssvTb7/RNT6JEIIYe4iiIiIiCwJe5CIiIiI6mBAIiIiIqqDAYmIiIioDgYkIiIiojoYkIiIiIjqYEAiIiIiqoMBiYiIiKgOBiQiIiKiOhiQiIiIiOpgQCIiIiKqgwGJiIiIqA4GJCIiIqI6/h8v9GqiHVn5zwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
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   ],
   "source": [
    "# 하이퍼파라미터 설정\n",
    "K = 10  \n",
    "# 디리클레 사전분포 하이퍼파라미터 (gamma)\n",
    "gamma = 0.1  \n",
    "\n",
    "# 감마분포 사전분포 하이퍼파라미터 (alpha)\n",
    "alpha = 0.1  \n",
    "beta = 0.1  \n",
    "convergence_threshold = 1e-6\n",
    "\n",
    "# 인수 초기 설정\n",
    "N_dk = np.zeros((num_docs, K)) + gamma # topic별 할당된 문서의 개수\n",
    "N_wk = np.zeros((K, num_words)) + beta # 토픽별 할당된 단어들의 개수\n",
    "N_k = np.zeros(K) + num_words * beta # 토픽별 전체 단어들의 개수\n",
    "# 최초 람다값을 감마분포의 기댓값으로 설정함. 문서 데이터의 통계량을 이용하여 초기값을 설정할 수 있음.\n",
    "lambda_k = np.ones(K) * alpha / beta  \n",
    "\n",
    "Z = []\n",
    "for d, (total_words, word_counts) in enumerate(articles):\n",
    "    Z_current = []\n",
    "    for word_idx, count in word_counts.items():\n",
    "        for _ in range(count):\n",
    "            topic = random.randint(0, K - 1)\n",
    "            Z_current.append(topic)\n",
    "            N_dk[d, topic] += 1\n",
    "            N_wk[topic, word_idx] += 1\n",
    "            N_k[topic] += 1\n",
    "    Z.append(Z_current)\n",
    "\n",
    "# 반복횟수 설정\n",
    "num_iterations = 200\n",
    "log_likelihoods = []\n",
    "\n",
    "# Log_likelihood 계산, Possion distribution 함수값을 모두 계산하여 더함\n",
    "def compute_log_likelihood():\n",
    "    ll = 0\n",
    "    for k in range(K):\n",
    "        ll += (alpha * np.log(beta) + (alpha - 1) * np.sum(np.log(lambda_k[k])) - beta * lambda_k[k] - gammaln(alpha))\n",
    "    for d, (total_words, word_counts) in enumerate(articles):\n",
    "        for word_idx, count in word_counts.items():\n",
    "            theta_d = N_dk[d] / N_dk[d].sum()\n",
    "            ll += count * np.log(np.dot(theta_d, lambda_k * N_wk[:, word_idx]))\n",
    "    return np.log(ll) # log likelihood값이 너무 크게 계산되기 때문에 log를 할번 더 취하여 계산\n",
    "\n",
    "previous_ll = None\n",
    "\n",
    "for it in range(num_iterations):\n",
    "    # Topic 샘플링\n",
    "    for d, (total_words, word_counts) in enumerate(articles):\n",
    "        Z_current = Z[d]\n",
    "        for word_idx, count in word_counts.items():\n",
    "            for _ in range(count):\n",
    "                # d번째 데이터, w번째 단어에 해당하는 값 제외\n",
    "                current_topic = Z_current.pop(0)\n",
    "                N_dk[d, current_topic] -= 1\n",
    "                N_wk[current_topic, word_idx] -= 1\n",
    "                N_k[current_topic] -= 1\n",
    "\n",
    "                # 조건부 확률 계산(Gamma Posterior의 기댓값을 활용한 단순화)\n",
    "                topic_probs = (N_dk[d] *\n",
    "                               (lambda_k * N_wk[:, word_idx]) /\n",
    "                               N_k)\n",
    "                topic_probs /= topic_probs.sum()\n",
    "\n",
    "                # Topic 샘플링 : np.random.choice : Categorical distribution에서 샘플링\n",
    "                new_topic = np.random.choice(K, p=topic_probs)\n",
    "                Z_current.append(new_topic)\n",
    "                N_dk[d, new_topic] += 1\n",
    "                N_wk[new_topic, word_idx] += 1\n",
    "                N_k[new_topic] += 1\n",
    "\n",
    "        Z[d] = Z_current\n",
    "    \n",
    "    # lambda의 샘플링\n",
    "    for k in range(K):\n",
    "        lambda_k[k] = np.random.gamma(alpha + N_wk[k].sum(), 1 / (beta + N_k[k]))\n",
    "\n",
    "    # log-likelihood 기준 convergence시 iteration중지 \n",
    "    current_ll = compute_log_likelihood()\n",
    "    log_likelihoods.append(current_ll)\n",
    "    print(f\"Iteration {it + 1}, Log-Likelihood: {current_ll}\")\n",
    "\n",
    "    if (previous_ll != None) and (abs(current_ll - previous_ll) < convergence_threshold):\n",
    "        print(f\"Converged after {it + 1} iterations.\")\n",
    "        break\n",
    "\n",
    "    previous_ll = current_ll\n",
    "\n",
    "# 결과저장 / Normalization\n",
    "doc_topic_distr = N_dk / N_dk.sum(axis=1, keepdims=True)\n",
    "topic_word_distr = N_wk / N_wk.sum(axis=1, keepdims=True)\n",
    "\n",
    "# Log-Likelihood 시각화\n",
    "plt.plot(log_likelihoods)\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Log-Likelihood')\n",
    "plt.title('Log-Likelihood over Iterations')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic 1: orders quarter dow volume jones decline inflation compared cent stocks\n",
      "Topic 2: alleged documents fbi testimony cocaine murder hearing criminal guilty jury\n",
      "Topic 3: airlines heart researchers shuttle tests patients disease test environmental aids\n",
      "Topic 4: arab middle arabia fitzwater pentagon soviets treaty panama baker saudi\n",
      "Topic 5: art movie cbs friends college book parents hes mother film\n",
      "Topic 6: shooting fired accident ship killing navy wounded bus airport injured\n",
      "Topic 7: estate insurance loan companys savings assets cash investment firm debt\n",
      "Topic 8: education poll votes gov candidates primary candidate governor voters convention\n",
      "Topic 9: degrees weather coast fair residents river park damage homes rain\n",
      "Topic 10: democracy republics republic korea china parliament parties movement independence african\n"
     ]
    }
   ],
   "source": [
    "# 각 토픽에서 가장 확률이 높은 단어들 출력\n",
    "top_words_per_topic = 10\n",
    "for k in range(K):\n",
    "    top_words = np.argsort(topic_word_distr[k])[-top_words_per_topic:]\n",
    "    print(f\"Topic {k+1}: {' '.join(vocab[word] for word in top_words)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 결과 저장\n",
    "np.save('./results/gamma_poisson_topic_word_distr.npy', topic_word_distr)\n",
    "np.save('./results/gamma_poisson_doc_topic_distr.npy', doc_topic_distr)\n",
    "np.save('./results/gamma_poisson_topic.npy', doc_topic_distr.argmax(axis=1))"
   ]
  }
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