{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b6cc3c6b-85c7-4a04-9aef-8ffc055aa93c",
   "metadata": {},
   "source": [
    "# Names Transition Modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "initial_id",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import unicodedata \n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns \n",
    "import numpy as np \n",
    "import re \n",
    "import sys \n",
    "import os \n",
    "\n",
    "sys.path.append(os.path.abspath(\"..\")) \n",
    "from collections import Counter \n",
    "from core.utils.data_loader import DataLoader \n",
    "from core.config.pipeline_config import PipelineConfig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f1a69290-a9c0-40d0-9fe8-a06d8a466671",
   "metadata": {},
   "outputs": [],
   "source": [
    "config = PipelineConfig(\n",
    "    paths={\n",
    "        \"root_dir\": \"../data\",\n",
    "        \"data_dir\": \"../data/dataset\",\n",
    "        \"models_dir\": \"../models\",\n",
    "        \"outputs_dir\": \"../data/processed\",\n",
    "        \"logs_dir\": \"../logs\",\n",
    "        \"configs_dir\": \"../configs\",\n",
    "        \"checkpoints_dir\": \"../checkpoints\"\n",
    "    }\n",
    ")\n",
    "\n",
    "loader = DataLoader(config)\n",
    "\n",
    "def normalize_letters(s):\n",
    "    \"\"\"Normalize accents -> ascii, lowercase, keep only a-z.\"\"\"\n",
    "    s = str(s)\n",
    "    s = unicodedata.normalize(\"NFKD\", s)\n",
    "    s = s.encode(\"ascii\", errors=\"ignore\").decode(\"utf-8\")\n",
    "    s = s.lower()\n",
    "    s = re.sub(r\"[^a-z]\", \"\", s)\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "24a4ad40319f441b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = loader.load_csv_complete(config.paths.data_dir / \"names_featured.csv\")\n",
    "\n",
    "def clean_province(s):\n",
    "    return (\n",
    "        s.str.upper()\n",
    "        .str.strip()\n",
    "        .apply(lambda x: unicodedata.normalize(\"NFKD\", x)\n",
    "               .encode(\"ascii\", errors=\"ignore\")\n",
    "               .decode(\"utf-8\") if isinstance(x, str) else x)\n",
    "    )\n",
    "df['province'] = clean_province(df['province'])\n",
    "\n",
    "df_simple = df[df['identified_category'] == 'simple'].copy()\n",
    "df_simple['surname'] = df_simple['identified_name'].str.split().str[0]\n",
    "df_simple['middle_name'] = df_simple['identified_name'].str.split().str[1]\n",
    "df_simple['first_name'] = df_simple['identified_surname']\n",
    "df_simple = df_simple[df_simple['first_name'].notna() & (df_simple['first_name'].str.strip() != '')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "77abf83a2f6360f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>province</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>KINSHASA</td>\n",
       "      <td>1140620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AUTRES</td>\n",
       "      <td>1035751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>KATANGA</td>\n",
       "      <td>836220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BANDUNDU</td>\n",
       "      <td>809949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>KASAI-ORIENTAL</td>\n",
       "      <td>434497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NORD-KIVU</td>\n",
       "      <td>394999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>KASAI-OCCIDENTAL</td>\n",
       "      <td>367626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>EQUATEUR</td>\n",
       "      <td>356404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>SUD-KIVU</td>\n",
       "      <td>346152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>ORIENTALE</td>\n",
       "      <td>322756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>BAS-CONGO</td>\n",
       "      <td>295155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>MANIEMA</td>\n",
       "      <td>127813</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            province    count\n",
       "0           KINSHASA  1140620\n",
       "1             AUTRES  1035751\n",
       "2            KATANGA   836220\n",
       "3           BANDUNDU   809949\n",
       "4     KASAI-ORIENTAL   434497\n",
       "5          NORD-KIVU   394999\n",
       "6   KASAI-OCCIDENTAL   367626\n",
       "7           EQUATEUR   356404\n",
       "8           SUD-KIVU   346152\n",
       "9          ORIENTALE   322756\n",
       "10         BAS-CONGO   295155\n",
       "11           MANIEMA   127813"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(df['province'].value_counts().reset_index().head(12))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ba6e48-a7c4-4aae-8b46-872489c95faf",
   "metadata": {},
   "source": [
    "# Surname (for whole country)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e324e1c9e8da4bd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "surnames = df_simple['surname'].astype(str).str.lower().tolist()\n",
    "surnames = [re.sub(r\"[^a-z]\", \"\", name) for name in surnames] \n",
    "sequences = ['^' + s + '$' for s in surnames if s]\n",
    "\n",
    "tokens = ['^'] + list('abcdefghijklmnopqrstuvwxyz') + ['$']\n",
    "index = {t: i for i, t in enumerate(tokens)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5f80329b-423e-4966-b3c8-80e68bc58d77",
   "metadata": {},
   "outputs": [],
   "source": [
    "transitions = Counter()\n",
    "for seq in sequences:\n",
    "    for a, b in zip(seq, seq[1:]):\n",
    "        if a in index and b in index:\n",
    "            transitions[(a, b)] += 1\n",
    "\n",
    "matrix = np.zeros((len(tokens), len(tokens)), dtype=int)\n",
    "for (a, b), count in transitions.items():\n",
    "    matrix[index[a], index[b]] += count\n",
    "\n",
    "df_counts = pd.DataFrame(matrix, index=tokens, columns=tokens)\n",
    "df_probs = df_counts.div(df_counts.sum(axis=1).replace(0, 1), axis=0)    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e45b650a-4b9a-48f5-b532-4a3c25fe45b6",
   "metadata": {},
   "source": [
    "## Transition matrix for the entire country"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "67b3e0f724af646b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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33qk+ffpo9OjRqlixoiIiIpScnKzt27dbHj8/st5Ho0aNUo8ePXLcp06dOpLO335l+/bt+uijj7R06VK98sormjZtmmbNmhUw0/dn5cuXl3S+sPvjgk0lS5bUl19+qdTUVC1evFhLlizRwoULdc0112jp0qWKiIgIWjwFW1jqQl/n3HyP3Hrrrfr22281evRotWjRQjExMfL5fLruuutyLPJyes7cxPH5fGratKmmTp2a477VqlXzv56LnaMsWQXtn4vd3KhcuXKej8ny5z8k/NEzzzyjsWPHasiQIXrqqadUrlw5uVwuPfzwwxf9w0Lfvn21YsUK/78HDRoU9H7ABw8e1L///W/NmzdPmzZtUkJCgkaPHp2ra8EBoLij4ASKqeXLl+vIkSNatGiRf6ERSdq5c2dIz1u6dGn169dP/fr1U3p6uvr27at//OMfSkpKCnq7jNzOmFSvXl2StGXLFn9rYJYtW7b4Hw+XrNm5P+a3detWSfKvypqbXGvVquUfT09P186dO7OtqPr7779nu53Kn2O99957qlWrlhYtWhSQU9ZM4Z/l1Jq6devWi+aeG7n9mmW99sjIyBxXkf2zcuXKafDgwRo8eLBOnTqlTp066cknn7xgwdmgQQNJ59+7f76VhcvlUteuXdW1a1dNnTpVzzzzjB5//HGlpqb6b/UhKdvKwX+egQ6HY8eOKSUlRRMmTNC4ceP843ltIc6N2rVr64cfflDXrl0v+rW62DnKsnPnTrlcLv/MXF5cbKXh/Hrvvfd09dVX69VXXw0YP378+EUL4ylTpgTMCv95gaHMzEx9+umnmjdvnhYvXiyfz6cePXpo4sSJ6tWrV57uNRvKZwkAFHYUnEAxlTVz8cfZg/T0dM2cOTPfz3nkyBH/bJN0vn20UaNG+u9//6uMjIygBWfp0qWD3irkj1q3bq2KFStq1qxZGjJkiNxutyTpv//9r3766aeAX+LD4ffff9cHH3ygvn37Sjq/Suz8+fPVokULVapU6YLHduvWTVFRUXrhhRd03XXX+X/RfPXVV3XixAn17NkzYP/MzEy9/PLLSkxMlHT+a/Hyyy8rPj5erVq1khT4Nct6vlWrVmnlypXZWi8l6cMPP9TevXv913GuXr1aq1at0sMPP5zPM/J/SpcufdGWRUmqWLGiunTpopdfflkjRozINtN16NAhf9vzn98/MTExqlOnjn777bcLxmjVqpWioqK0Zs0a3Xjjjf7xo0ePqly5cgH7Zq3km3VrkNq1a0uSvvzyS/9jXq9Xs2fPvuhry6ucvuek8ys1h9utt96qTz/9VHPmzNHdd98d8NjZs2fl8/lUunTpXJ2jLGvXrlXjxo0VFxeX53xy88eG/IiIiMh2Pt99913t3bvXP3MeTNb3VU6efPJJzZo1SwcOHFDNmjU1btw4DR48ON/3eQ3lswQACjsKTqCY6tChg8qWLatBgwbpwQcflGEYeuONNy7YvnYx3bt3V6VKlXTllVcqISFBP/30k1588UX17NlTl1xySdDjWrVqpX/96196+umnVadOHVWsWDHbDKZ0fpbs2Wef1eDBg9W5c2f179/ff1uUGjVqaOTIkfnOPSf16tXT0KFD9d133ykhIUFz587VgQMHNG/evIseGx8fr6SkJE2YMEHXXXedbrzxRm3ZskUzZ85UmzZtAhZgks7Prjz77LPatWuX6tWrp4ULF+r777/X7Nmz/TMpvXr10qJFi3TzzTerZ8+e2rlzp2bNmqVGjRrp1KlT2XKoU6eOrrrqKg0fPlwej0fTp09X+fLl9cgjj4R8blq1aqWFCxcqMTFRbdq0UUxMjHr37p3jvi+99JKuuuoqNW3aVMOGDVOtWrV04MABrVy5Unv27PHfM7FRo0bq0qWLWrVqpXLlymnNmjV677339MADD1wwl+joaHXv3l2ff/65Jk6c6B+fOHGivvzyS/Xs2VPVq1fXwYMHNXPmTF166aW66qqrJEmNGzfWFVdcoaSkJH/x9fbbbyszMzPkc/RnsbGx6tSpkyZPnqyMjAxVrVpVS5cuDbmrICcDBgzQO++8o3vvvVepqam68sor5fV69fPPP+udd97RZ599ptatW+fqHEnn75Gada/ZgqRXr16aOHGiBg8erA4dOmjjxo168803A7oK8uPtt9/W1VdfraFDh+ZqlvhiQvksAYBCz4GVcQFYJNhtUYLdquSbb74xr7jiCrNkyZJmlSpVzEceecT87LPPcrwdRE7PMWjQoIBbY7z88stmp06dzPLly5tut9usXbu2OXr0aPPEiRP+fXK6DcX+/fvNnj17mpdccokpyX+LlJxuTWGaprlw4ULz8ssvN91ut1muXDnz9ttvD7j9R1ZupUuXzpZzTrcByUn16tXNnj17mp999pnZrFkz0+12mw0aNDDffffdgP2yXs93332X4/O8+OKLZoMGDczIyEgzISHBHD58uHns2LGAfbLO75o1a8z27dub0dHRZvXq1c0XX3wxYD+fz2c+88wzZvXq1U23221efvnl5ieffJLt65B1m47nnnvOnDJlilmtWjXT7XabHTt2NH/44YeLno/c3Bbl1KlT5m233WaWKVPGlOSPn9NtUUzTNLdv324OHDjQrFSpkhkZGWlWrVrV7NWrl/nee+/593n66afNtm3bmmXKlDFLlixpNmjQwPzHP/7hvy3MhSxatMg0DMPcvXu3fywlJcW86aabzCpVqphRUVFmlSpVzP79+5tbt27Nllu3bt1Mt9ttJiQkmI899pi5bNmyXH8f/PF8/5kkc/z48f5/79mzx7z55pvNMmXKmHFxceYtt9xi/v7779n2y/q6/Pl2JcHe1znllp6ebj777LNm48aNTbfbbZYtW9Zs1aqVOWHCBP/3ZG7P0X//+19TkvnLL79ki+2kc+fOmX//+9/NypUrmyVLljSvvPJKc+XKlWbnzp1zvNVSbp06dSpsOeb2swQAiirDNEOYzgCAIqpGjRpq0qSJPvnkE6dTQS54vV41atRIt956q5566imn0yly+vTpI8Mw9MEHHzidCgCgkOG2KACAQi8iIkITJ07USy+9lGN7MfLvp59+0ieffEIhDwDIF2Y4ASAHzHACAACEjhlOAAAAAIAlmOEEAAAAAFiCGU4AAAAAgCUoOAEAAAAAlqDgBAAAAABYooTTCVjizAn7Y547bX/M6NL2xvNm2BtPkiIi7Y1XXC5pNn32xjMc+NuWYdgbz3PG3niSzPRztse0/b1z9qS98SQZCTVtjymf1954rgh740n2v3c8Z+2NJ0kRDpzXEm5749n9dZTs/zx34mdWhgOf5yWi7I1Xuqy98cLoXiPW6RRyNMtMczqFXGGGEwAAAABgCQpOAAAAAIAlimZLLQAAAACEATN0oeH8AQAAAAAsQcEJAAAAALAELbUAAAAAEITL7pWSixhmOAEAAAAAlqDgBAAAAABYgpZaAAAAAAiCGbrQcP4AAAAAAJag4AQAAAAAWKLAtNT++OOP2r17t9LT0wPGb7zxRocyAgAAAFDcuVikNiSOF5w7duzQzTffrI0bN8owDJmmKUky/v/yw16v18n0AAAAAAD55HhL7UMPPaSaNWvq4MGDKlWqlDZv3qwvv/xSrVu31vLlyy96vMfjUVpaWsDm8XisTxwAAAAAcEGOF5wrV67UxIkTVaFCBblcLrlcLl111VVKTk7Wgw8+eNHjk5OTFRcXF7AlPz/VhswBAAAAFHWuAroVFo631Hq9Xl1yySWSpAoVKuj3339X/fr1Vb16dW3ZsuWixyclJSkxMTFgzO09Z0muAAAAAIDcc7zgbNKkiX744QfVrFlT7dq10+TJkxUVFaXZs2erVq1aFz3e7XbL7XYHDp4xLcoWAAAAAJBbjhecTzzxhE6fPi1Jmjhxonr16qWOHTuqfPnyWrhwocPZAQAAACjOXAbL1IbC8YKzR48e/v+vU6eOfv75Zx09elRly5b1r1QLAAAAACh8HC84c1KuXDmnUwAAAAAAhKhAFpwAAAAAUBAUphVhCyLOHwAAAADAEhScAAAAAABL0FILAAAAAEG4WMc0JMxwAgAAAAAsQcEJAAAAALAELbUAAAAAEAQzdKHh/AEAAAAALFEkZzi9LybZHjPigWTbY9ouItL2kOaRvbbGM8pXtTWeY4wIW8PZ/XWUHPhaukvZG0+S4UBM28VWsD2kb/M3tsd0Nb7S9pi2M2z+G3d0aXvjOcTcs8XWeMal9W2NJ0nKTLc3Xokoe+NJUgm3/TENVsKBPYpkwQkAAAAA4WBQnIeElloAAAAAgCUoOAEAAAAAlqClFgAAAACCYIYuNJw/AAAAAIAlKDgBAAAAAJagpRYAAAAAgnCxSG1ImOEEAAAAAFiCghMAAAAAYAlaagEAAAAgCGboQsP5AwAAAABYgoITAAAAAGCJAtdSa5qmJMkwWA4KAAAAgLNc1CUhKTAznK+++qqaNGmi6OhoRUdHq0mTJnrllVcuepzH41FaWlrA5sn02pAxAAAAAOBCCkTBOW7cOD300EPq3bu33n33Xb377rvq3bu3Ro4cqXHjxl3w2OTkZMXFxQVsk1LX2ZQ5AAAAACAYw8zqYXVQfHy8XnjhBfXv3z9g/K233tKIESN0+PDhoMd6PB55PJ6AsRIvjpa7RIQluQYT8UCyrfGKC/PIXlvjGeWr2hqvuLD76yjxtUT++TZ/Y3tMV+MrbY+JosHcs8XWeMal9W2NJ0nKTLc3Xokoe+NJkhO/jtvdJloqzt54YfSP6HJOp5Cjx88ddTqFXCkQ13BmZGSodevW2cZbtWqlzMzMCx7rdrvldrsDxrw2F5sAAAAAgOwKREvtgAED9K9//Svb+OzZs3X77bc7kBEAAAAAIFSOzXAmJib6/98wDL3yyitaunSprrjiCknSqlWrtHv3bg0cONCpFAEAAAAUcy4WqQ2JYwXn+vXrA/7dqlUrSdL27dslSRUqVFCFChW0efNm23MDAAAAAITOsYIzNTXVqdAAAAAAABsUiEWDAAAAAKAgKhCL3hRinD8AAAAAgCUoOAEAAAAAlqClFgAAAACCcIllakPBDCcAAAAAwBIUnAAAAAAAS9BSCwAAAABBuOioDQkznAAAAAAASxTJGU7X4EedTsEepmlvPMOBP+9EFMm3qOO8b02xN2Bmpr3xJEUMsPlzIOOcvfEkqUSU/TGNov93Sle91k6nYD27f35IzvwMsZvpsz2kUamm7TFtFxHpdAY2cOB7koVwYBN+mwcAAACAIIr+n1qtxfkDAAAAAFiCghMAAAAAYAlaagEAAAAgCFapDQ0znAAAAAAAS1BwAgAAAAAsQUstAAAAAATh4hYyIWGGEwAAAABgCQpOAAAAAIAlaKkFAAAAgCBYpTY0zHACAAAAACxBwQkAAAAAsITjBWdycrLmzp2bbXzu3Ll69tlnHcgIAAAAAM5zFdCtsHA815dfflkNGjTINt64cWPNmjXrosd7PB6lpaUFbB6Px4pUAQAAAAB54HjBuX//flWuXDnbeHx8vPbt23fR45OTkxUXFxewJc+YaUWqAAAAAIA8cHyV2mrVqumbb75RzZo1A8a/+eYbValS5aLHJyUlKTExMWAsKm1/WHMEAAAAUDyxSm1oHC84hw0bpocfflgZGRm65pprJEkpKSl65JFH9Pe///2ix7vdbrnd7oAx03PMklwBAAAAALnneME5evRoHTlyRPfdd5/S09MlSdHR0Xr00UeVlJTkcHYAAAAAgPxyvOA0DEPPPvusxo4dq59++kklS5ZU3bp1s81aAgAAAIDdXKKnNhSOF5xZYmJi1KZNG6fTAAAAAACEieOr1AIAAAAAiqYCM8MJAAAAAAUNq9SGhhlOAAAAAIAlKDgBAAAAAJagpRYAAAAAgqCjNjTMcAIAAAAALEHBCQAAAACwBC21AAAAABAEq9SGhhlOAAAAAIAliuQMp2/j17bHjLiil+0xZfDnFuRPxN8SbY3n/ehlW+NJknn6uK3xjNJlbI0H6/j2bbc9puuyRvYGdOLnh+mzN57hwN/UHYhpnjpqazyjTCVb451n2hzPge8PJ96vgE2KZMEJAAAAAOHgYp3akPDnFAAAAACAJSg4AQAAAACWoKUWAAAAAIJgldrQMMMJAAAAALAEBScAAAAAwBK01AIAAABAEMzQhYbzBwAAAACwBAUnAAAAAMAStNQCAAAAQBAsUhsaZjgBAAAAAJZwZIYzMTEx1/tOnTrVwkwAAAAAAFZxpOBcv359wL/XrVunzMxM1a9fX5K0detWRUREqFWrVhd9Lo/HI4/HEzBWIj1D7qjI8CUMAAAAoFhyGTTVhsKRltrU1FT/1rt3b3Xu3Fl79uzRunXrtG7dOv3222+6+uqr1bNnz4s+V3JysuLi4gK2SW99bMOrAAAAAABciGGapulkAlWrVtXSpUvVuHHjgPFNmzape/fu+v333y94fI4znN8usn2GM+KKXrbGKy7M4wdsjWeUSbA1nmNs/rb3fvSyrfEkyXXt32yNZ5QuY2s8WMe3+0fbY7oua2R7TNuZPnvjGcVjmQrz+H5b4xllKtkaTxLvnaKiVJzTGeTbwrIF8/fDfsfs/T05vxxfpTYtLU2HDh3KNn7o0CGdPHnyose73W653e6AMS/ttAAAAADCgIba0Dj+J5ybb75ZgwcP1qJFi7Rnzx7t2bNH77//voYOHaq+ffs6nR4AAAAAIJ8cn+GcNWuWRo0apdtuu00ZGRmSpBIlSmjo0KF67rnnHM4OAAAAAJBfjhecpUqV0syZM/Xcc89p+/btkqTatWurdOnSDmcGAAAAoLijpTY0jhecWUqXLq1mzZo5nQYAAAAAIEwcv4YTAAAAAFA0FZgZTgAAAAAoaGipDQ0znAAAAAAAS1BwAgAAAAAsQUstAAAAAARhGDTVhoIZTgAAAACAJSg4AQAAAACWoKUWAAAAAIKgoTY0hmmaptNJhN3p4/bHzEy3P2ak2954Pq+98STJYBLeElyLEH5n0mwPaXrO2B7T7p+65pF99gaU5Kp9ue0xZfrsjefEZ2v6OXvjOfEx58RvVFHRDgS1md2/qjrxMzLDY3/MCJvnnWLK2RsvjBaVq+R0Cjnqe3S/0ynkCr/NAwAAAAAsQUstAAAAAATBDF1oOH8AAAAAAEtQcAIAAAAALEFLLQAAAAAEwVqLoWGGEwAAAABgCQpOAAAAAIAlaKkFAAAAgCAMR27sW3QwwwkAAAAAsAQFJwAAAADAErTUAgAAAEAQNNSGhhlOAAAAAIAlCkTB+dVXX+mOO+5Q+/bttXfvXknSG2+8oa+//trhzAAAAAAA+eV4wfn++++rR48eKlmypNavXy+PxyNJOnHihJ555pmLHu/xeJSWlhawZT0HAAAAAITCKKBbYeF4wfn0009r1qxZmjNnjiIjI/3jV155pdatW3fR45OTkxUXFxewJT8/zcqUAQAAAAC54PiiQVu2bFGnTp2yjcfFxen48eMXPT4pKUmJiYkBY+7Ms+FKDwAAAACQT47PcFaqVEnbtm3LNv7111+rVq1aFz3e7XYrNjY2YHO73VakCgAAAKCYcRkFc8uPl156STVq1FB0dLTatWun1atXX3D/6dOnq379+ipZsqSqVaumkSNH6ty5c3k7f/lLNXyGDRumhx56SKtWrZJhGPr999/15ptvatSoURo+fLjT6QEAAABAobdw4UIlJiZq/PjxWrdunZo3b64ePXro4MGDOe6/YMECjRkzRuPHj9dPP/2kV199VQsXLtRjjz2Wp7iOt9SOGTNGPp9PXbt21ZkzZ9SpUye53W6NGjVKI0aMcDo9AAAAACj0pk6dqmHDhmnw4MGSpFmzZmnx4sWaO3euxowZk23/b7/9VldeeaVuu+02SVKNGjXUv39/rVq1Kk9xHZ/hNAxDjz/+uI4ePapNmzbpf//7nw4dOqSnnnrK6dQAAAAAFHNGAf0vL3frSE9P19q1a9WtWzf/mMvlUrdu3bRy5cocj+nQoYPWrl3rb7vdsWOHPv30U91www15On+OF5xZoqKi1KhRI7Vt21YxMTFOpwMAAAAABVaOd+tITs5x38OHD8vr9SohISFgPCEhQfv378/xmNtuu00TJ07UVVddpcjISNWuXVtdunTJc0ttgSk4AQAAAAC5k5SUpBMnTgRsSUlJYXv+5cuX65lnntHMmTO1bt06LVq0SIsXL85zJ6rj13ACAAAAQEGVzwVhLed2u3N9d44KFSooIiJCBw4cCBg/cOCAKlWqlOMxY8eO1YABA3TXXXdJkpo2barTp0/r7rvv1uOPPy6XK3dzl8xwAgAAAEARFhUVpVatWiklJcU/5vP5lJKSovbt2+d4zJkzZ7IVlREREZIk0zRzHZsZTgAAAAAo4hITEzVo0CC1bt1abdu21fTp03X69Gn/qrUDBw5U1apV/deB9u7dW1OnTtXll1+udu3aadu2bRo7dqx69+7tLzxzg4ITAAAAAIIwCmpPbR7169dPhw4d0rhx47R//361aNFCS5Ys8S8ktHv37oAZzSeeeEKGYeiJJ57Q3r17FR8fr969e+sf//hHnuIaZl7mQwuL08ftj5mZbn/MyNz1bIeNz2tvPEky6Pq2RFH55CxIzqTZHtL0nLE9pt0XsphH9tkbUJKr9uW2x5TpszeeE5+t6efsjefEx5wTv1FFRTsQ1GZ2/6rqxM/IjJxvZWGpCJvnnWLK2RsvjD6Lr+J0Cjnqceh3p1PIFX6bBwAAAABYgpZaAAAAAAiCvrDQFMmC07tqse0xI67oZXtM27lyf3FwuJhph2yNZ8TG2xqvuDB/+8n2mEa1hvYGLBVrbzxJhgMx7WaUyXmpdivZ/bkjFZPPnsgoe+MVk0syvC+G7557uRHxQM43lbeUN8PeeCVsfq86FZPLa2CT4vFpDAAAAACwXZGc4QQAAACAcHDRVBsSZjgBAAAAAJag4AQAAAAAWIKWWgAAAAAIgoba0DDDCQAAAACwBAUnAAAAAMAStNQCAAAAQBDcsjQ0zHACAAAAACxBwQkAAAAAsAQttQAAAAAQBB21oWGGEwAAAABgCUcKzg0bNsjn8zkRGgAAAABgE0cKzssvv1yHDx+WJNWqVUtHjhzJ93N5PB6lpaUFbJ70jHClCgAAAKAYMwrof4WFIwVnmTJltHPnTknSrl27QprtTE5OVlxcXMA26a2Pw5UqAAAAACCfHFk06C9/+Ys6d+6sypUryzAMtW7dWhERETnuu2PHjgs+V1JSkhITEwPGSny7KGy5AgAAAADyx5GCc/bs2erbt6+2bdumBx98UMOGDdMll1ySr+dyu91yu90BY96oyHCkCQAAAKCYcxWe7tUCybHbolx33XWSpLVr1+qhhx7Kd8EJAAAAACiYHL8P57x585xOAQAAAABgAccLTgAAAAAoqOioDY0jq9QCAAAAAIo+Ck4AAAAAgCVoqQUAAACAIGipDQ0znAAAAAAAS1BwAgAAAAAsQUstAAAAAARh0FQbEmY4AQAAAACWoOAEAAAAAFiiaLbUrv3W/phtetgfMyLS/pgoGryZ9sYrU9HeeEAIfD98ZXvMiI59bY9pO4O/cVvB9bf7nE7BekYxaGcsDq+xEOPLExo+/QEAAAAAlqDgBAAAAABYomi21AIAAABAGDBDFxrOHwAAAADAEhScAAAAAABL0FILAAAAAEGwSG1omOEEAAAAAFiCghMAAAAAYAlaagEAAAAgCMOgqTYUzHACAAAAACxBwQkAAAAAsAQttQAAAAAQBA21oXG84ExMTMxx3DAMRUdHq06dOrrppptUrlw5mzMDAAAAAITC8YJz/fr1Wrdunbxer+rXry9J2rp1qyIiItSgQQPNnDlTf//73/X111+rUaNG2Y73eDzyeDwBYyUyvXKXiLAlfwAAAABAzhy/hvOmm25St27d9Pvvv2vt2rVau3at9uzZo2uvvVb9+/fX3r171alTJ40cOTLH45OTkxUXFxewTfpirc2vAgAAAEBRZBTQrbAwTNM0nUygatWqWrZsWbbZy82bN6t79+7au3ev1q1bp+7du+vw4cPZjs9xhvOlR2yf4Yy4d4Kt8c4HjbQ/ps3MtEO2xjNi422N5xhvpq3hzDMnbI0nScYl5W2PiaLB+9Ui22NGdOxre0wUDebh32yNZ1SoZms8SZI3w954xeD3K0eUinM6g3xbU/kyp1PIUet9u51OIVccb6k9ceKEDh48mK3gPHTokNLS0iRJZcqUUXp6eo7Hu91uud3ugDEv7bQAAAAA4DjHC86bbrpJQ4YM0ZQpU9SmTRtJ0nfffadRo0apT58+kqTVq1erXr16DmYJAAAAoDgyjMLUwFrwOF5wvvzyyxo5cqT+9re/KTPzfJtfiRIlNGjQIE2bNk2S1KBBA73yyitOpgkAAAAAyCPHC86YmBjNmTNH06ZN044dOyRJtWrVUkxMjH+fFi1aOJQdAAAAACC/HC84s8TExKhZs2ZOpwEAAAAAfi46akPi+G1RAAAAAABFEwUnAAAAAMASBaalFgAAAAAKGoOe2pAwwwkAAAAAsAQFJwAAAADAErTUAgAAAEAQBh21IWGGEwAAAABgCQpOAAAAAIAlimZLbbPW9seMiLQ/ZnFg8DcRS0TY+63vfWGsrfEkqcTjM22PiaLBVb+l0ykAuRdV0ukMrOcqmr+uovCgpTY0/DYPAAAAALAEBScAAAAAwBL0KAAAAABAEAY9tSFhhhMAAAAAYAkKTgAAAACAJWipBQAAAIAg6KgNDTOcAAAAAABLUHACAAAAACxBSy0AAAAABMEqtaFhhhMAAAAAYAkKTgAAAACAJWipBQAAAIAg6KgNDTOcAAAAAABLFJgZzpSUFKWkpOjgwYPy+XwBj82dOzfocR6PRx6PJ2CsRHqG3FGRluQJAAAAAMidAjHDOWHCBHXv3l0pKSk6fPiwjh07FrBdSHJysuLi4gK2SQsX25Q5AAAAgKLMZRgFcissCsQM56xZs/Taa69pwIABeT42KSlJiYmJAWMlVrwdrtQAAAAAAPlUIArO9PR0dejQIV/Hut1uud3ugDEv7bQAAAAA4LgC0VJ71113acGCBU6nAQAAAAABDKNgboWFYzOcf2yD9fl8mj17tj7//HM1a9ZMkZGBM5RTp061Oz0AAAAAQIgcKzjXr18f8O8WLVpIkjZt2hQwbhSm8h0AAAAA4OdYwZmamupUaAAAAADIFSbAQlMgruEEAAAAABQ9FJwAAAAAAEsUiNuiAAAAAEBBZDBFFxJOHwAAAADAEhScAAAAAABL0FILAAAAAEGwSm1omOEEAAAAAFiCghMAAAAAYAnDNE3T6STC7vBv9seMiLQ/prukvfG8mfbGkySf1954JRz4OsqBNg1aQ8LvTJrtIc2Mc7bHlMvmKzE8Z+yNJ8koV9n2mLZ/Tzqx5KLd71evzT8/nBJd2ukMrGf3r6pO/Ix04ncsu19nTDl744XR9kZ1nU4hR7V//MXpFHKFGU4AAAAAgCUoOAEAAAAAlmCVWgAAAAAIglVqQ8MMJwAAAADAEhScAAAAAABL0FILAAAAAEHQURsaZjgBAAAAAJag4AQAAAAAWIKWWgAAAAAIwkVPbUiY4QQAAAAAWIKCEwAAAABgCVpqAQAAACAIOmpDU+gLTo/HI4/HEzDm9njkdrsdyggAAAAAIBWBltrk5GTFxcUFbMkzXnI6LQAAAAAo9gzTNE2nkwhFjjOcJw/aP8MZEWlvPElyl7Q3njfT3niS5PPaG6+EA19HOdCnQW9I+J1Jsz2kmXHO9phy2dwY4zljbzxJRrnKtse0/XvScODvzXa/X702//xwSnRppzOwnt2/qjrxM9KJ37Hsfp0x5eyNF0a/NW/gdAo5qvbDz06nkCuOtdQmJibqqaeeUunSpZWYmHjBfadOnRr0Mbfbnb24TD8RjhQBAAAAACFwrOBcv369MjIy/P8fjMFMDAAAAAAUSo4VnKmpqTn+PwAAAAAUFMx/habQLxoEAAAAACiYKDgBAAAAAJYo9PfhBAAAAACr0FIbGmY4AQAAAACWoOAEAAAAAFiClloAAAAACMJw0VMbCmY4AQAAAACWoOAEAAAAAFiClloAAAAACIJVakPDDCcAAAAAwBJFcobT++O3tseMaH2d7TFtF2H/28U8fdzWeEZsBVvjFReZ44baHrPExFftDVgq1t54kgzZH9N2l5SzPaR5ZK/tMY3yVW2PabvIaJvj2RvOMWfS7I3nwGddsZhecuB3LMAuvLsBAAAAIAhXcfijh4VoqQUAAAAAWIKCEwAAAABgCVpqAQAAACAIOmpDwwwnAAAAAMASFJwAAAAAAEvQUgsAAAAAQRj01IaEGU4AAAAAgCUoOAEAAAAAlqClFgAAAACCoKM2NMxwAgAAAAAsQcEJAAAAALAELbUAAAAAEASr1Iam0BecHo9HHo8nYKxEeobcUZEOZQQAAAAAkBwoOPv27avXXntNsbGx6tu37wX3jYmJUePGjXXvvfcqLi4ux32Sk5M1YcKEgLGxd/5F4wffEracAQAAAAB5Z3vBGRcX55+WDlZEZvF4PJo1a5a++eYbffzxxznuk5SUpMTExICxEqtz3hcAAAAA8oKO2tDYXnDOmzcvx/8P5scff1SbNm2CPu52u+V2uwPGvLTTAgAAAIDjCvwqtfXr19e3337rdBoAAAAAgDwq8IsGRUREqHnz5k6nAQAAAKAYYpXa0BT4GU4AAAAAQOFEwQkAAAAAsESBb6kFAAAAAKcYTNGFhNMHAAAAALAEBScAAAAAwBK01AIAAABAEKxSGxpmOAEAAACgGHjppZdUo0YNRUdHq127dlq9evUF9z9+/Ljuv/9+Va5cWW63W/Xq1dOnn36ap5jMcAIAAABAEbdw4UIlJiZq1qxZateunaZPn64ePXpoy5YtqlixYrb909PTde2116pixYp67733VLVqVf36668qU6ZMnuJScAIAAABAMK6i0VI7depUDRs2TIMHD5YkzZo1S4sXL9bcuXM1ZsyYbPvPnTtXR48e1bfffqvIyEhJUo0aNfIcl5ZaAAAAAChkPB6P0tLSAjaPx5Pjvunp6Vq7dq26devmH3O5XOrWrZtWrlyZ4zEff/yx2rdvr/vvv18JCQlq0qSJnnnmGXm93jzlWSRnODPnzrE9ZkTr62yPWSxEFMm3qPNM09ZwEfcm2RoPCIkvbz9IASeZZ0/aGs8oFWtrPEmSN8PeeBGR9saTJNNnf0xuLlnoJScna8KECQFj48eP15NPPplt38OHD8vr9SohISFgPCEhQT///HOOz79jxw598cUXuv322/Xpp59q27Ztuu+++5SRkaHx48fnOk9+mwcAAACAYAroKrVJSUlKTEwMGHO73WF7fp/Pp4oVK2r27NmKiIhQq1attHfvXj333HMUnAAAAABQlLnd7lwXmBUqVFBERIQOHDgQMH7gwAFVqlQpx2MqV66syMhIRURE+McaNmyo/fv3Kz09XVFRUbmKzVw6AAAAABRhUVFRatWqlVJSUvxjPp9PKSkpat++fY7HXHnlldq2bZt8vv9r+d66dasqV66c62JTouAEAAAAgCIvMTFRc+bM0euvv66ffvpJw4cP1+nTp/2r1g4cOFBJSf+37sbw4cN19OhRPfTQQ9q6dasWL16sZ555Rvfff3+e4tJSCwAAAABBGAX0Gs686tevnw4dOqRx48Zp//79atGihZYsWeJfSGj37t1yuf5vPrJatWr67LPPNHLkSDVr1kxVq1bVQw89pEcffTRPcQ3TtHm5Sht47ux28Z3CzD3zfdtjFgfm6eO2xjNKl7E1nmNs/rY39223NZ4kGVXq2B4TRYN5aLftMY34y2yPiaLBPLLX1nhG+aq2xpPEKrVWsXuV2lJx9sYLo7RrLnc6hRzFfrHe6RRyhZZaAAAAAIAlaKkFAAAAgGBcRaOl1inMcAIAAAAALEHBCQAAAACwBC21AAAAABBMEVml1inMcAIAAAAALFEgCs633nor6GOjR4+2MRMAAAAAQLgUiIJz+PDh+u9//5ttfOTIkfr3v/99wWM9Ho/S0tICNo/XgXsZAQAAAChyDJdRILfCokAUnG+++ab69++vr7/+2j82YsQIvfPOO0pNTb3gscnJyYqLiwvYJm/cZXHGAAAAAICLKRAFZ8+ePTVz5kzdeOONWrt2re677z4tWrRIqampatCgwQWPTUpK0okTJwK2R5rWsCdxAAAAAEBQBWaV2ttuu03Hjx/XlVdeqfj4eK1YsUJ16tS56HFut1tutztgzBNRIOpoAAAAAIUdq9SGxLGCMzExMcfx+Ph4tWzZUjNnzvSPTZ061a60AAAAAABh4ljBuX79+hzH69Spo7S0NP/jBn9RAAAAAIBCybGC82KLAQEAAACA0wrTirAFERc7AgAAAAAsQcEJAAAAALBEgVmlFgAAAAAKHNaUCQkznAAAAAAAS1BwAgAAAAAsQUstAAAAAATDKrUhYYYTAAAAAGAJCk4AAAAAgCWKZEttiZ43OJ0CwsT8fZut8Yy6rW2N5xi7V1srGWNvPCAEZtoR22Ma8ZfZHhNFg2/7BlvjRZSvams8SZIrwv6YdjOYAyrIDFapDQnvbgAAAACAJSg4AQAAAACWKJIttQAAAAAQFqxSGxJmOAEAAAAAlqDgBAAAAABYgpZaAAAAAAiGVWpDwgwnAAAAAMASFJwAAAAAAEvQUgsAAAAAQRhM0YWE0wcAAAAAsAQFJwAAAADAErTUAgAAAEAwrFIbkjzNcHq9Xn355Zc6fvy4RekAAAAAAIqKPM1wRkREqHv37vrpp59UpkwZi1LKG4/HI4/HEzBWIiNT7kgmbwEAAADASXm+hrNJkybasWOHFbnkS3JysuLi4gK2SR+kOJ0WAAAAgCLAcBkFciss8lxwPv300xo1apQ++eQT7du3T2lpaQGb3ZKSknTixImAbczNXW3PAwAAAAAQKM99pzfccIMk6cYbb5TxhwtoTdOUYRjyer25ep7ExMRcx5w6dWrQx9xut9xud8CYl3ZaAAAAAHBcniuz1NTUsARev359rvYzWBUKAAAAgFOoR0KS54Kzc+fOYQkcrsIVAAAAAFAw5fkaTkn66quvdMcdd6hDhw7au3evJOmNN97Q119/HdbkAAAAAACFV54Lzvfff189evRQyZIltW7dOv8tSU6cOKFnnnkm7AkCAAAAgGNcRsHcCol8rVI7a9YszZkzR5GRkf7xK6+8UuvWrQtrcgAAAACAwivPBeeWLVvUqVOnbONxcXE6fvx4OHICAAAAABQBeV40qFKlStq2bZtq1KgRMP7111+rVq1a4coLAAAAABzHXTNCk+cZzmHDhumhhx7SqlWrZBiGfv/9d7355psaNWqUhg8fbkWOAAAAAIBCKM8znGPGjJHP51PXrl115swZderUSW63W6NGjdKIESOsyBEAAAAAUAjlueA0DEOPP/64Ro8erW3btunUqVNq1KiRYmJirMgPAAAAAJxTiFaELYjy3FI7ZMgQnTx5UlFRUWrUqJHatm2rmJgYnT59WkOGDLEiRwAAAABAIZTngvP111/X2bNns42fPXtW8+fPD0tSAAAAAIDCL9cttWlpaTJNU6Zp6uTJk4qOjvY/5vV69emnn6pixYqWJJln5RNsD+md+5TtMSOGjLU9pt1cNZvZG9A07Y0nScVg5TOjVJzTKQC55qpS1/6gnux/yLWUu6S98WAZI7acvQGd+DmZkW5vvKjoi++D4qUY/K5mpVwXnGXKlJFhGDIMQ/Xq1cv2uGEYmjBhQliTAwAAAAAUXrkuOFNTU2Wapq655hq9//77Klfu//6iFhUVperVq6tKlSqWJAkAAAAAKHxyXXB27txZkrRz505ddtllOd4Adffu3brsssvClx0AAAAAOCinuge5l+dFg2rVqqVDhw5lGz9y5Ihq1qwZlqQAAAAAAIVfngtOM8jF4qdOnQpYSAgAAAAAULzluqU2MTFR0vkp5XHjxqlUqVL+x7xer1atWqUWLVqEPUEAAAAAcIyLltpQ5LrgXL9+vaTzM5wbN25UVFSU/7GoqCg1b95co0aNCn+GAAAAAIBCKU+r1ErS4MGDNWPGDMXGxlqWFAAAAACg8Mt1wZll3rx5kqRt27Zp+/bt6tSpk0qWLCnTNFnBCQAAAECRQo0TmjwvGnT06FF17dpV9erV0w033KB9+/ZJkoYOHaq///3vYU8QAAAAAFA45XmG8+GHH1ZkZKR2796thg0b+sf79eunxMRETZkyJV+JnDt3Ths2bNDBgwfl8/kCHrvxxhvz9ZwAAAAAAOfkueBcunSpPvvsM1166aUB43Xr1tWvv/6arySWLFmigQMH6vDhw9keMwxDXq83X88LAAAAACFhldqQ5Lml9vTp0wG3RMly9OhRud3ufCUxYsQI3XLLLdq3b598Pl/ARrEJAAAAAIVTngvOjh07av78+f5/G4Yhn8+nyZMn6+qrr85XEgcOHFBiYqISEhLyfKzH41FaWlrA5knPyFceAAAAAIDwyXPBOXnyZM2ePVvXX3+90tPT9cgjj6hJkyb68ssv9eyzz+Yrib/+9a9avnx5vo5NTk5WXFxcwDbprY/z9VwAAAAAEMAwCuZWSBimaZp5PejEiRN68cUX9cMPP+jUqVNq2bKl7r//flWuXDlfSZw5c0a33HKL4uPj1bRpU0VGRgY8/uCDDwY91uPxyOPxBIyV+HaR3FGRQY6wyI/r7Y0nKWLIWNtj2i4z3d54ETa/b6RC9YGRb56z9sd0l7Q/JoqGs6fsj+mKsDce3x9Fhu/nVbbGc9Vva2s8SVKG5+L7hFNUtL3xiotScU5nkG/pd/VwOoUcRb3ymdMp5EqeFw2SpLi4OD3++ONhS+Ktt97S0qVLFR0dreXLlwfc68YwjAsWnG63O9u1o167i00AAAAAQDa5Kjg3bNiQ6yds1qxZnpN4/PHHNWHCBI0ZM0YuV567fAEAAADAEgar1IYkVwVnixYtZBiGLtZ9m99bmKSnp6tfv34UmwAAAABQhOSq4Ny5c6elSQwaNEgLFy7UY489ZmkcAAAAAIB9clVwVq9e3dIkvF6vJk+erM8++0zNmjXLtmjQ1KlTLY0PAAAAADkqDgs8WihfiwaF28aNG3X55ZdLkjZt2hTwmMEXGAAAAAAKpQJRcKampjqdAgAAAAAgzApEwQkAAAAABRKr1IaEZWEBAAAAAJbIc8FZq1YtHTlyJNv48ePHVatWrbAkBQAAAAAo/PLcUrtr164c77Xp8Xi0d+/esCQFAAAAAAUBi5iGJtcF58cff+z//88++0xxcXH+f3u9XqWkpKhGjRphTQ4AAAAAUHjluuDs06ePpPMV/qBBgwIei4yMVI0aNTRlypSwJgcAAAAAKLxyXXD6fD5JUs2aNfXdd9+pQoUKliUVKlfTq2yPaVzRy/aYdvP99D/bY7rqtrQ3oAMtE94Zj9geM+KhyfYGNH32xpMk07Q3XvpZe+NJkruU/TGLA3dJ+2O6IuyPWdSln3M6A1u46rexN6ATrYVR0fbHtJvH/p8hZoa93yNGqbiL71RQsUptSPJ8DefOnTutyAMAAAAAUMTk6z6cKSkpSklJ0cGDB/0zn1nmzp0blsQAAAAAAIVbngvOCRMmaOLEiWrdurUqV67Mqk0AAAAAii7qnZDkueCcNWuWXnvtNQ0YMMCKfAAAAAAARYQrrwekp6erQ4cOVuQCAAAAAChC8lxw3nXXXVqwYIEVuQAAAABAwWIYBXMrJPLcUnvu3DnNnj1bn3/+uZo1a6bIyMiAx6dOnRq25AAAAAAAhVeeC84NGzaoRYsWkqRNmzYFPMYCQgAAAACALHkuOFNTU63IAwAAAAAKHibVQpLnazizbNu2TZ999pnOnj0rSTJNM2xJAQAAAAAKvzwXnEeOHFHXrl1Vr1493XDDDdq3b58kaejQofr73/8e9gQBAAAAAIVTngvOkSNHKjIyUrt371apUqX84/369dOSJUvCmhwAAAAAOMrlKphbIZHnaziXLl2qzz77TJdeemnAeN26dfXrr7+GLTEAAAAAQOGW54Lz9OnTATObWY4ePSq3253vRFJSUpSSkqKDBw/K5/MFPDZ37tygx3k8Hnk8noCxKI8npFwAAAAAAKHL81xsx44dNX/+fP+/DcOQz+fT5MmTdfXVV+criQkTJqh79+5KSUnR4cOHdezYsYDtQpKTkxUXFxewJc+Yma88AAAAACCAYRTMrZDI8wzn5MmT1bVrV61Zs0bp6el65JFHtHnzZh09elTffPNNvpKYNWuWXnvtNQ0YMCDPxyYlJSkxMTFgLCptf77yAAAAAACET54LziZNmmjr1q168cUXdckll+jUqVPq27ev7r//flWuXDlfSaSnp6tDhw75OtbtdmdrnzU9F54VBQAAAABYL08FZ0ZGhq677jrNmjVLjz/+eNiSuOuuu7RgwQKNHTs2bM8JAAAAACErRO2rBVGeCs7IyEht2LAh7EmcO3dOs2fP1ueff65mzZopMjIy4PGpU6eGPSYAAAAAwFp5bqm944479Oqrr2rSpElhS2LDhg1q0aKFJGnTpk0Bjxn8RQEAAAAACqU8F5yZmZmaO3euPv/8c7Vq1UqlS5cOeDw/s5Gpqal5PgYAAAAALMcEWEjyXHBu2rRJLVu2lCRt3bo14DFmIwEAAAAAWfJUcHq9Xk2YMEFNmzZV2bJlrcoJAAAAAFAE5KngjIiIUPfu3fXTTz9RcAIAAAAo+lwupzMo1PJ89po0aaIdO3ZYkQsAAAAAoAjJc8H59NNPa9SoUfrkk0+0b98+paWlBWwAAAAAAEj5WDTohhtukCTdeOONAYsEmaYpwzDk9XrDlx0AAAAAOImFUUOS54KTW5gAAAAAAHLDME3TdDqJsDtzwv6Y3gz7Y0ZE2hvP9NkbT5IMmy/SLoLfDjmy+y91TpxXm1+jeeqYrfEkSb5M+2Pa3MVi7rN/zQBXw/a2x5Rs/h6x+7NVsv9zIDPd3niSbP86SlJktP0x7Wb3e8eJ2axzp+2P6S5lb7zSZeyNF0aZj/ZzOoUclXh2odMp5EqeZzi//PLLCz7eqVOnfCcDAAAAAAUKLbUhyXPB2aVLl2xjf7yWk2s4AQAAAABSPlapPXbsWMB28OBBLVmyRG3atNHSpUutyBEAAAAAUAjleYYzLi4u29i1116rqKgoJSYmau3atWFJDAAAAAAcR0ttSMK2akBCQoK2bNkSrqcDAAAAABRyeZ7h3LBhQ8C/TdPUvn37NGnSJLVo0SJceQEAAAAACrk8F5wtWrSQYRj6891UrrjiCs2dOzdsiQEAAACA41wO3EqqCMlzwblz586Af7tcLsXHxys6uhjcBwoAAAAAkGt5LjirV69uRR4AAAAAgCIm1/PDX3zxhRo1aqS0tLRsj504cUKNGzfWV199FdbkAAAAAMBRhlEwt0Ii1wXn9OnTNWzYMMXGxmZ7LC4uTvfcc4+mTp0a1uQAAAAAAIVXrgvOH374Qdddd13Qx7t37849OAEAAAAAfrm+hvPAgQOKjIwM/kQlSujQoUP5SuL48eN69dVX9dNPP0mSGjdurCFDhiguLi5fzwcAAAAAYVGI2lcLolzPcFatWlWbNm0K+viGDRtUuXLlPCewZs0a1a5dW9OmTdPRo0d19OhRTZ06VbVr19a6desuerzH41FaWlrA5vF48pwHAAAAACC8cl1w3nDDDRo7dqzOnTuX7bGzZ89q/Pjx6tWrV54TGDlypG688Ubt2rVLixYt0qJFi7Rz50716tVLDz/88EWPT05OVlxcXMCW/DzXkgIAAACA0wzTNM3c7HjgwAG1bNlSEREReuCBB1S/fn1J0s8//6yXXnpJXq9X69atU0JCQp4SKFmypNavX68GDRoEjP/4449q3bq1zpw5c8HjPR5PthlNt/ec3G53nvIImTfD3niSFBG8xdkSps/eeJJk2Hyj3dx9OxR+dreGOHFebX6N5qljtsaTJPky7Y/p9doazty3w9Z4kuRq2N72mJLN3yN2f7ZK9n8OZKbbG0+S7V9HSYosBvdBt/u940T75LnT9sd0l7I3Xuky9sYLo8xxA51OIUclJs53OoVcyfU1nAkJCfr22281fPhwJSUlKatONQxDPXr00EsvvZTnYlOSYmNjtXv37mwF52+//aZLLrnkose73e7sxeWZYlI0AAAAAEABluuCU5KqV6+uTz/9VMeOHdO2bdtkmqbq1q2rsmXL5juBfv36aejQoXr++efVoUMHSdI333yj0aNHq3///vl+XgAAAACAs/JUcGYpW7as2rRpE5YEnn/+eRmGoYEDByoz83x7WGRkpIYPH65JkyaFJQYAAAAA5IfhcuAyhCIkXwVnOEVFRWnGjBlKTk7W9u3bJUm1a9dWqVI295UDAAAAAMLK8YIzS6lSpdS0aVOn0wAAAAAAhEmBKTgBAAAAoMBxYuXiIoSGZAAAAACAJSg4AQAAAACWoKUWAAAAAIKhpTYkzHACAAAAACxBwQkAAAAAsAQttQAAAAAQDC21IWGGEwAAAABgiSI5w+lNWWB7zIiut9ke03aG/X+f8P2w3NZ4rmadbY0nyZm/mp07bWs43/6dtsaTJFeNJrbGM2LK2hqvuDDKVrI9pvn7NttjGlXq2B7TdnZ/1kW67Y3nEHPvVlvjGVXr2RpPkmT67I1nRNgbT5LcJe2PyawdbFIkC04AAAAACAsXTaGh4OwBAAAAACxBwQkAAAAAsAQttQAAAAAQDNe7hoQZTgAAAACAJSg4AQAAAKAYeOmll1SjRg1FR0erXbt2Wr16da6Oe/vtt2UYhvr06ZPnmBScAAAAABCMYRTMLY8WLlyoxMREjR8/XuvWrVPz5s3Vo0cPHTx48ILH7dq1S6NGjVLHjh3zdfooOAEAAACgiJs6daqGDRumwYMHq1GjRpo1a5ZKlSqluXPnBj3G6/Xq9ttv14QJE1SrVq18xaXgBAAAAIBCxuPxKC0tLWDzeDw57puenq61a9eqW7du/jGXy6Vu3bpp5cqVQWNMnDhRFStW1NChQ/OdJwUnAAAAAATjdOtskC05OVlxcXEBW3Jyco4v4fDhw/J6vUpISAgYT0hI0P79+3M85uuvv9arr76qOXPmhHT6uC0KAAAAABQySUlJSkxMDBhzu91hee6TJ09qwIABmjNnjipUqBDSc1FwAgAAAEAh43a7c11gVqhQQRERETpw4EDA+IEDB1SpUqVs+2/fvl27du1S7969/WM+n0+SVKJECW3ZskW1a9fOVewCV3CapilJMrjBKgAAAACnuQr/VYhRUVFq1aqVUlJS/Lc28fl8SklJ0QMPPJBt/wYNGmjjxo0BY0888YROnjypGTNmqFq1armOXWAKzldffVXTpk3TL7/8IkmqW7euHn74Yd11110XPM7j8WS7OLZERobckZGW5QoAAAAAhUliYqIGDRqk1q1bq23btpo+fbpOnz6twYMHS5IGDhyoqlWrKjk5WdHR0WrSpEnA8WXKlJGkbOMXUyAKznHjxmnq1KkaMWKE2rdvL0lauXKlRo4cqd27d2vixIlBj01OTtaECRMCxsb+7QaNv62XpTkDAAAAQGHRr18/HTp0SOPGjdP+/fvVokULLVmyxL+Q0O7du+WyYDbXMLN6WB0UHx+vF154Qf379w8Yf+uttzRixAgdPnw46LE5znB+/prtM5wRXW+zNV5x4fthua3xXM062xpPUr5u3Buyc6dtDefbv9PWeJLkqpG3v74BWczft9ke06hSx/aYKBrMvVttjWdUrWdrPEmSz2tvPFeEvfEkyfTZH9OwuU20VJy98cLI+9z9TqeQo4jRLzmdQq4UiBnOjIwMtW7dOtt4q1atlJmZecFjc7pY1ks7LQAAAAA4rkBcATtgwAD961//yjY+e/Zs3X777Q5kBAAAAAAIVYGY4ZTOLxq0dOlSXXHFFZKkVatWaffu3Ro4cGDA/WWmTp3qVIoAAAAAihvunhGSAlFwbtq0SS1btpR0/p4v0vl7xVSoUEGbNm3y78etUgAAAACg8CgQBWdqaqrTKQAAAAAAwqxAFJwAAAAAUCBZcKuQ4oSzBwAAAACwBAUnAAAAAMAStNQCAAAAQDAsXBoSZjgBAAAAAJag4AQAAAAAWIKWWgAAAAAIhpbakDDDCQAAAACwRJGc4Yy4pr/TKSBMXM27OJ1C0RRd2tZwrhpNbI2HIsQ0bQ9pVKlje0wgv4bX62prvFmnf7M1niTJFWF/TLsZzAGh6CqSBScAAAAAhAUttSHhzykAAAAAAEtQcAIAAAAALEFLLQAAAAAE42KOLhScPQAAAACAJSg4AQAAAACWoKUWAAAAAIJhldqQMMMJAAAAALAEBScAAAAAwBK01AIAAABAMLTUhoQZTgAAAACAJRyf4UxMTMz1vlOnTrUwEwAAAABAODlecK5fv17r169XRkaG6tevL0naunWrIiIi1LJlS/9+RpCpbI/HI4/HEzDmzvTI7XZblzQAAACA4sGgKTQUjp+93r17q1OnTtqzZ4/WrVundevW6bffftPVV1+tXr16KTU1Vampqfriiy9yPD45OVlxcXEBW/Lz02x+FQAAAACAPzNM0zSdTKBq1apaunSpGjduHDC+adMmde/eXb///vsFj895hvOs/TOcXEwMAOHnxI8oPs9RiNxbupqt8Wad/s3WeChCSsU5nUG+eWc+6nQKOYq471mnU8gVx1tq09LSdOjQoWzjhw4d0smTJy96vNvtzl5cnvaFKz0AAAAAxZmLP0SGwvGW2ptvvlmDBw/WokWLtGfPHu3Zs0fvv/++hg4dqr59+zqdHgAAAAAgnxyf4Zw1a5ZGjRql2267TRkZGZKkEiVKaOjQoXruuecczg4AAAAAkF+OF5ylSpXSzJkz9dxzz2n79u2SpNq1a6t06dIOZwYAAACg2GOV2pA4XnBmKV26tJo1a+Z0GgAAAACAMKFcBwAAAABYosDMcAIAAABAgcPtskLCDCcAAAAAwBIUnAAAAAAAS9BSCwAAAADBuJijCwVnDwAAAABgCQpOAAAAAIAlaKkFAAAAgGBYpTYkRbLg9C6aaXvMiL/cb3tMmab9MW3mXfmxrfEiOtxkazzHpJ+zNZzvt59sjSdJrtqX2x4TFnDih/zZU/bHLBljf0yEnwM/l/+1d43tMW3nzbA3XkSkvfEkZ36no4iCTWipBQAAAABYokjOcAIAAABAWBjM0YWCswcAAAAAsAQFJwAAAADAErTUAgAAAEAwLLAUEmY4AQAAAACWoOAEAAAAAFiClloAAAAACMbFHF0oOHsAAAAAAEtQcAIAAAAALEFLLQAAAAAEwyq1IWGGEwAAAABgCQpOAAAAAIAlHC84MzIy1LVrV/3yyy/5Ot7j8SgtLS1g82RkhjlLAAAAAMWS4SqYWyHheKaRkZHasGFDvo9PTk5WXFxcwDbpPyvCmCEAAAAAID8cLzgl6Y477tCrr76ar2OTkpJ04sSJgG1M785hzhAAAAAAkFcFYpXazMxMzZ07V59//rlatWql0qVLBzw+derUoMe63W653e6AMW9kgXhZAAAAAAo7F6vUhqJAVGabNm1Sy5YtJUlbt24NeMxgGWIAAAAAKJQKRMGZmprqdAoAAAAAgDArEAUnAAAAABRIhWhF2IKIswcAAAAAsAQFJwAAAADAErTUAgAAAEAwLGIaEmY4AQAAAACWoOAEAAAAAFiClloAAAAACIZVakPC2QMAAAAAWIKCEwAAAABgCVpqAQAAACAYF6vUhqJoFpyX1nA6A3sUgyWaXTWbOJ1CkeRd85mt8YwqtW2NB4TCPH3c9phGyRjbYxZ53kz7Y7oi7I9ZIsr+mHZz4rzarRj8Tofii5ZaAAAAAIAliuYMJwAAAACEAzPQIWGGEwAAAABgCQpOAAAAAIAlaKkFAAAAgGAM5uhCwdkDAAAAAFiCghMAAAAAYAlaagEAAAAgGBer1IaCGU4AAAAAgCUoOAEAAAAAlqClFgAAAACCYZXakHD2AAAAAACWcLzgPHv2rM6cOeP/96+//qrp06dr6dKlDmYFAAAAAAiV4y21N910k/r27at7771Xx48fV7t27RQZGanDhw9r6tSpGj58+AWP93g88ng8AWMl0jPkjoq0Mm0AAAAAxYHBKrWhcHyGc926derYsaMk6b333lNCQoJ+/fVXzZ8/Xy+88MJFj09OTlZcXFzANmnBx1anDQAAAAC4CMcLzjNnzuiSSy6RJC1dulR9+/aVy+XSFVdcoV9//fWixyclJenEiRMB25jbbrQ6bQAAAADARThecNapU0cffvihfvvtN3322Wfq3r27JOngwYOKjY296PFut1uxsbEBG+20AAAAAMLCcBXMrZBwPNNx48Zp1KhRqlGjhtq1a6f27dtLOj/befnllzucHQAAAAAgvxxfNOivf/2rrrrqKu3bt0/Nmzf3j3ft2lU333yzg5kBAAAAAELheMEpSZUqVVKlSpUCxtq2betQNgAAAADw/7lYpTYUjrfUAgAAAACKJgpOAAAAAIAlCkRLLQAAAAAUSIVoRdiCiLMHAAAAALAEBScAAAAAwBK01AIAAABAMAar1IaCGU4AAAAAgCUoOAEAAAAAliiaLbWRUU5nYA/TtDeeE+0ELv4mYoWIdj1tjWeeOWFrPCAknjNOZ4Aw8G1ZbXtMV6MOtsc092y1NZ7RoJ2t8YACgd9HQ8LZAwAAAABYgoITAAAAAGCJotlSCwAAAADhwCq1IWGGEwAAAABgCQpOAAAAAIAlaKkFAAAAgGAM5uhCwdkDAAAAAFiCghMAAAAAYAlaagEAAAAgGFapDQkznAAAAAAAS1BwAgAAAAAsQUstAAAAAATjYo4uFJw9AAAAAIAlHC84d+/eLdM0s42bpqndu3df9HiPx6O0tLSAzZOeYUWqAAAAAIA8cLzgrFmzpg4dOpRt/OjRo6pZs+ZFj09OTlZcXFzANunfH1iRKgAAAIDixjAK5lZIOF5wmqYpI4cTdurUKUVHR1/0+KSkJJ04cSJgG3PHzVakCgAAAADIA8cWDUpMTJQkGYahsWPHqlSpUv7HvF6vVq1apRYtWlz0edxut9xud8CYNyoyrLkCAAAAAPLOsYJz/fr1ks7PcG7cuFFRUVH+x6KiotS8eXONGjXKqfQAAAAAQDIcbwot1BwrOFNTUyVJgwcP1owZMxQbG+tUKgAAAAAACzh+H8558+Y5nQIAAAAAwAKOF5wAAAAAUGAVohVhCyIakgEAAAAAlqDgBAAAAABYgpZaAAAAAAiGVWpDwtkDAAAAAFiCghMAAAAAYAlaagEAAAAgGBer1IaCGU4AAAAAgCUoOAEAAAAAliiSLbURDdvbHzTDY3/MSLe98byZ9saTZFS41N6ApmlvPEkyffbHtPkGxkZMWVvjSbL9vJonj9gaT5Lkc+C9Y/fngM9rbzxJRtV6tse0/bPHiZuY2/y1dNVqbms8SdLZk7aHdDVoZ29AJ35OFgcZ5+yP6YqwP2ZhxSq1IeHsAQAAAAAsQcEJAAAAALBEkWypBQAAAICwcOIyhCKEGU4AAAAAgCUoOAEAAAAAlqClFgAAAACCYZXakHD2AAAAAACWoOAEAAAAAFiClloAAAAACMJgldqQMMMJAAAAALAEBScAAAAAwBK01AIAAABAMKxSGxLOHgAAAADAEgVihnPixIkXfHzcuHFBH/N4PPJ4PAFjbo9Hbrc7LLkBAAAAAPKnQBScH3zwQcC/MzIytHPnTpUoUUK1a9e+YMGZnJysCRMmBIyNHz1STz76d0tyBQAAAFCM0FIbkgJx9tavXx+wbdq0Sfv27VPXrl01cuTICx6blJSkEydOBGxJDz9gU+YAAAAAUDi89NJLqlGjhqKjo9WuXTutXr066L5z5sxRx44dVbZsWZUtW1bdunW74P7BFIiCMyexsbGaMGGCxo4de8H93G63YmNjAzbaaQEAAADg/yxcuFCJiYkaP3681q1bp+bNm6tHjx46ePBgjvsvX75c/fv3V2pqqlauXKlq1aqpe/fu2rt3b57iGqZpmuF4AVb4+uuv1bt3bx07dixvBx7J20kIixKR9seMtLmw9mbaG0+SZPPb0+VAl7npsz+m3YrBDZPNk0fsD+pz4L1j9+eAz2tvPElG/GW2x5TdP4qd+J60+2uZfs7eeJIzn+clL7E3niO/Ntr9/eHAfEyGA+9XV4S98S6pYG+8MPKt/sTpFHLkatsrT/u3a9dObdq00YsvvihJ8vl8qlatmkaMGKExY8Zc9Hiv16uyZcvqxRdf1MCBA3Mdt0Bcw/nCCy8E/Ns0Te3bt09vvPGGrr/+eoeyAgAAAICCKcfFU93uHLs909PTtXbtWiUlJfnHXC6XunXrppUrV+Yq3pkzZ5SRkaFy5crlKc8CUXBOmzYt4N8ul0vx8fEaNGhQwEkBAAAAAARZPHX8eD355JPZ9j18+LC8Xq8SEhICxhMSEvTzzz/nKt6jjz6qKlWqqFu3bnnKs0AUnDt37nQ6BQAAAADIroCuUpuUlKTExMSAMavWspk0aZLefvttLV++XNHR0Xk6tkAUnAAAAACA3AvWPpuTChUqKCIiQgcOHAgYP3DggCpVqnTBY59//nlNmjRJn3/+uZo1a5bnPAtmuQ4AAAAACIuoqCi1atVKKSkp/jGfz6eUlBS1b98+6HGTJ0/WU089pSVLlqh169b5is0MJwAAAAAEU0RW209MTNSgQYPUunVrtW3bVtOnT9fp06c1ePBgSdLAgQNVtWpVJScnS5KeffZZjRs3TgsWLFCNGjW0f/9+SVJMTIxiYmJyHZeCEwAAAACKuH79+unQoUMaN26c9u/frxYtWmjJkiX+hYR2794tl+v/GmD/9a9/KT09XX/9618DnifYwkTBFOj7cOYb9+G0BvfhtAb34SwSuA+nRbgPpzW4D6c1uA+nVUHtDcd9OK1RmO/Duea/TqeQI1frwnH7SGY4AQAAACCYArpKbWHB2QMAAAAAWIKCEwAAAABgiSLZUms6cA2ncWl922PaLsL+t4t56pit8YyYsrbGOx/U5msoHOB9/yXbY0b85X5b4xmx8bbGg4XOnbY/ZnRp+2Paze7rxYrDOZXkfekxW+NF3P+MrfHOK/rrAKiEzetySMVifYWw4VyFhBlOAAAAAIAlKDgBAAAAAJYoki21AAAAABAWrFIbEs4eAAAAAMASFJwAAAAAAEvQUgsAAAAAwbhYpTYUzHACAAAAACxBwQkAAAAAsAQttQAAAAAQDKvUhoSzBwAAAACwBAUnAAAAAMASjhecd911l5YvX+50GgAAAACQnWEUzK2QcLzgPHTokK677jpVq1ZNo0eP1g8//JCn4z0ej9LS0gI2T3q6RdkCAAAAAHLL8YLzo48+0r59+zR27Fh99913atmypRo3bqxnnnlGu3btuujxycnJiouLC9iSX37d+sQBAAAAABdkmKZpOp3EH+3Zs0dvvfWW5s6dq19++UWZmZkX3N/j8cjj8QSMRe3eIHdUlJVpZmNcWt/WeMWFeeqYrfGMmLK2xisuvO+/ZHvMiL/cb3tMFBHnTtsfM7q0/TFRJHhfeszWeBH3P2NrvGLDiV/H7W7JLBVnb7ww8m360ukUcuRq0snpFHKlQN0WJSMjQ2vWrNGqVau0a9cuJSQkXPQYt9stt9sdMGbaXGwCAAAAALJzvKVWklJTUzVs2DAlJCTozjvvVGxsrD755BPt2bPH6dQAAAAAAPnk+Axn1apVdfToUV133XWaPXu2evfunW3GEgAAAAAcUYhWhC2IHC84n3zySd1yyy0qU6aM06kAAAAAAMLI8YJz2LBhTqcAAAAAALCA4wUnAAAAABRYRoFY9qbQ4uwBAAAAACxBwQkAAAAAsAQttQAAAAAQjIs5ulBw9gAAAAAAlqDgBAAAAABYgpZaAAAAAAjCMAynUyjUmOEEAAAAAFjCME3TdDqJcDt9Y3vbY5Z+e4ntMYsD74p3bY0X0fkWW+MVF+bx/bbHNMpUsj0migjPWftjukvaHxNFQ/o5e+NFRdsbD0VHqTinM8g3c8v/nE4hR0b9K5xOIVdoqQUAAACAYAyaQkPB2QMAAAAAWIKCEwAAAABgCVpqAQAAACAYVqkNCTOcAAAAAABLUHACAAAAACxBSy0AAAAABMMqtSHh7AEAAAAALEHBCQAAAACwBC21AAAAABAMq9SGxPEZzoEDB2revHnavn2706kAAAAAAMLI8YIzKipKycnJqlu3rqpVq6Y77rhDr7zyin755RenUwMAAAAAhMDxltpXXnlFkrR37159+eWXWrFihaZMmaJ77rlHlStX1p49exzOEAAAAECx5XJ8jq5Qc7zgzFK2bFmVL19eZcuWVZkyZVSiRAnFx8df9DiPxyOPxxMwlun1yR3BGwMAAAAAnOR4VfbYY4+pQ4cOKl++vMaMGaNz585pzJgx2r9/v9avX3/R45OTkxUXFxewPb9trw2ZAwAAAAAuxDBN03QyAZfLpfj4eI0cOVJ9+/ZVvXr18nR8jjOc/a+1fYaz9NtLbI1XXHhXvGtrvIjOt9gar7gwj++3PaZRppLtMVFEeM7aH9Nd0v6YKBrSz9kbLyra3ngoOkrFOZ1Bvpm7fnA6hRwZNZo7nUKuON5Su379eq1YsULLly/XlClTFBUVpc6dO6tLly7q0qXLRQtQt9stt9sdMHaadloAAAAAcJzjBWfz5s3VvHlzPfjgg5KkH374QdOmTdP9998vn88nr9frcIYAAAAAgPxwvOA0TVPr16/X8uXLtXz5cn399ddKS0tTs2bN1LlzZ6fTAwAAAFCcGXRPhsLxgrNcuXI6deqUmjdvrs6dO2vYsGHq2LGjypQp43RqAAAAAIAQOF5w/vvf/1bHjh0VGxvrdCoAAAAAgDByvODs2bOn0ykAAAAAQM4Mw+kMCjUakgEAAAAAlqDgBAAAAABYwvGWWgAAAAAouGipDQUznAAAAAAAS1BwAgAAAAAsQUstAAAAAATDKrUhYYYTAAAAAGCJIjnDWXLcOPuDmqb9Me3mwF93Itr3tj1msWD6bA3nW/uFrfEkKaLrbbbHRBHh4m+xyCcnfheIjLI/ZlHn89of03Dgc4dZO9ikSBacAAAAABAWFOch4c+4AAAAAABLUHACAAAAACxBwQkAAAAAsATXcAIAAABAUFzDGQpmOAEAAAAAlqDgBAAAAABYgpZaAAAAAAiG26KEhBlOAAAAAIAlKDgBAAAAAJagpRYAAAAAgqGjNiSOz3CmpqYGfezll1+2MRMAAAAAQDg5XnBed911Gj16tDIyMvxjhw8fVu/evTVmzBgHMwMAAAAAhMLxgjM1NVUffPCB2rRpox9//FGLFy9WkyZNlJaWpu+///6ix3s8HqWlpQVsnvSMix4HAAAAABdnFNCtcHC84OzQoYO+//57NWnSRC1bttTNN9+skSNHavny5apevfpFj09OTlZcXFzANum1hTZkDgAAAAC4EMcLTknaunWr1qxZo0svvVQlSpTQli1bdObMmVwdm5SUpBMnTgRsY+7sZ3HGAAAAAICLcbzgnDRpktq3b69rr71WmzZt0urVq7V+/Xo1a9ZMK1euvOjxbrdbsbGxAZs7KtKGzAEAAAAUeYZRMLdCwvGCc8aMGfrwww/1z3/+U9HR0WrSpIlWr16tvn37qkuXLk6nBwAAAADIJ8fvw7lx40ZVqFAhYCwyMlLPPfecevXq5VBWAAAAAIBQOV5w/rnY/KPOnTvbmAkAAAAA/Ekhal8tiBxvqQUAAAAAFE0UnAAAAAAASzjeUgsAAAAABRcttaFghhMAAAAAYAkKTgAAAACAJWipBQAAAIBgWKU2JMxwAgAAAAAsQcEJAAAAALBEkWypNf+XYn/QRh3sj1kMmEf22hrPqFzb1niOMez9W5NRoYqt8YBQmCeP2B7TKMf3SJHgRNvdmZP2xisVa288J7ginM4ABQ4ttaFghhMAAAAAYAkKTgAAAACAJYpkSy0AAAAAhAWr1IaEGU4AAAAAgCUoOAEAAAAAlqClFgAAAACCoaU2JMxwAgAAAAAsQcEJAAAAALAELbUAAAAAEBQttaFghhMAAAAAYAkKTgAAAACAJWipBQAAAIAgDFapDYnjM5yDBg3Sl19+6XQaAAAAAIAwc7zgPHHihLp166a6devqmWee0d69e/N0vMfjUVpaWsDmyci0KFsAAAAAQG45XnB++OGH2rt3r4YPH66FCxeqRo0auv766/Xee+8pIyPjoscnJycrLi4uYJu0bLUNmQMAAAAo8gyjYG6FhOMFpyTFx8crMTFRP/zwg1atWqU6depowIABqlKlikaOHKlffvkl6LFJSUk6ceJEwDbm2rY2Zg8AAAAAyEmBKDiz7Nu3T8uWLdOyZcsUERGhG264QRs3blSjRo00bdq0HI9xu92KjY0N2NyRrIUEAAAAAE5zvDLLyMjQxx9/rHnz5mnp0qVq1qyZHn74Yd12222KjY2VJH3wwQcaMmSIRo4c6XC2AAAAAIqXwtO+WhA5XnBWrlxZPp9P/fv31+rVq9WiRYts+1x99dUqU6aM7bkBAAAAAPLP8YJz2rRpuuWWWxQdHR10nzJlymjnzp02ZgUAAAAACJXjBeeAAQOcTgEAAAAAclaIVoQtiArUokEAAAAAgKKDghMAAAAAYAnHW2oBAAAAoMCipTYkzHACAAAAACxBwQkAAAAAsAQttQAAAAAQFC21oWCGEwAAAABgCQpOAAAAAIAlimZL7dGjTmeAcImMcjoDhIF57rTTKQBAkWR6ztgazygVa2s8SZJp2huPFUnxZ7wnQsIMJwAAAADAEhScAAAAAABLFM2WWgAAAAAIBzpqQ8IMJwAAAADAEhScAAAAAABL0FILAAAAAEHRUxsKZjgBAAAAAJag4AQAAAAAWIKWWgAAAAAIxqClNhTMcAIAAAAALEHBCQAAAACwBC21AAAAABAMLbUhcXyG85prrtGECROyjR87dkzXXHONAxkBAAAAAMLB8RnO5cuXa+PGjVq/fr3efPNNlS5dWpKUnp6uFStWXPR4j8cjj8cTMFYi0yt3iQhL8gUAAAAA5I7jM5yS9Pnnn2v//v264oortGvXrjwdm5ycrLi4uIBt0lcbrEkUAAAAQDFjFNCtcCgQBWflypW1YsUKNW3aVG3atNHy5ctzfWxSUpJOnDgRsI3p2My6ZAEAAAAAueJ4S63x/y/CdbvdWrBggZ5++mldd911evTRR3N1vNvtltvtDhjz0k4LAAAAAI5zvOA0TTPg30888YQaNmyoQYMGOZQRAAAAAPx/rFIbEscLzp07dyo+Pj5g7C9/+YsaNGigNWvWOJQVAAAAACBUjhec1atXz3G8cePGaty4sc3ZAAAAAADCxfGCEwAAAAAKLFpqQ1IgVqkFAAAAABQ9FJwAAAAAAEvQUgsAAAAAQdFSGwpmOAEAAAAAlqDgBAAAAIBi4KWXXlKNGjUUHR2tdu3aafXq1Rfc/91331WDBg0UHR2tpk2b6tNPP81zTApOAAAAAAjGMArmlkcLFy5UYmKixo8fr3Xr1ql58+bq0aOHDh48mOP+3377rfr376+hQ4dq/fr16tOnj/r06aNNmzblKS4FJwAAAAAUcVOnTtWwYcM0ePBgNWrUSLNmzVKpUqU0d+7cHPefMWOGrrvuOo0ePVoNGzbUU089pZYtW+rFF1/MU1wKTgAAAAAoZDwej9LS0gI2j8eT477p6elau3atunXr5h9zuVzq1q2bVq5cmeMxK1euDNhfknr06BF0/6BM+J07d84cP368ee7cuSIZz4mYxeE1OhGzOLxGJ2LyGolZWOI5EbM4vEYnYhaH1+hETF5j0YmJ4MaPH29KCtjGjx+f47579+41JZnffvttwPjo0aPNtm3b5nhMZGSkuWDBgoCxl156yaxYsWKe8jRM0zTzVqIWXWlpaYqLi9OJEycUGxtb5OI5EbM4vEYnYhaH1+hETF4jMQtLPCdiFofX6ETM4vAanYjJayw6MRGcx+PJNqPpdrvldruz7fv777+ratWq+vbbb9W+fXv/+COPPKIVK1Zo1apV2Y6JiorS66+/rv79+/vHZs6cqQkTJujAgQO5zpP7cAIAAABAIROsuMxJhQoVFBERka1QPHDggCpVqpTjMZUqVcrT/sFwDScAAAAAFGFRUVFq1aqVUlJS/GM+n08pKSkBM55/1L59+4D9JWnZsmVB9w+GGU4AAAAAKOISExM1aNAgtW7dWm3bttX06dN1+vRpDR48WJI0cOBAVa1aVcnJyZKkhx56SJ07d9aUKVPUs2dPvf3221qzZo1mz56dp7gUnH/gdrs1fvz4XE9NF7Z4TsQsDq/RiZjF4TU6EZPXSMzCEs+JmMXhNToRszi8Ridi8hqLTkyET79+/XTo0CGNGzdO+/fvV4sWLbRkyRIlJCRIknbv3i2X6/8aYDt06KAFCxboiSee0GOPPaa6devqww8/VJMmTfIUl0WDAAAAAACW4BpOAAAAAIAlKDgBAAAAAJag4AQAAAAAWIKC0wFdunTRww8/7HQajiiqr900Td19990qV66cDMPQ999/73RKYePk18yJ2Hfeeaf69OljeZzidl4BAEDxxCq1QBgsWbJEr732mpYvX65atWqpQoUKTqdUJCxatEiRkZG2xpwxY4ZYSw2AXbp06aIWLVpo+vTpTqcCAJag4ATCYPv27apcubI6dOjgdCpFSrly5WyPGRcXZ3tMABeXnp6uqKgop9MAAOQRLbU6Pzt11VVXqUyZMipfvrx69eql7du3WxozMzNTDzzwgOLi4lShQgWNHTvW8lkVn8+nyZMnq06dOnK73brsssv0j3/8w7J4p0+f1sCBAxUTE6PKlStrypQplsXK4vP5lJycrJo1a6pkyZJq3ry53nvvPUtj3nnnnRoxYoR2794twzBUo0YNS+OdPHlSt99+u0qXLq3KlStr2rRplrdI+nw+PfLIIypXrpwqVaqkJ5980rJYf1SUW2r/bPHixYqLi9Obb75pe+xw6tKli0aMGKGHH35YZcuWVUJCgubMmeO/sfQll1yiOnXq6L///a8lsR988EHb36sej0cPPvigKlasqOjoaF111VX67rvvLIvXpUsXPfDAA7b+DMnp89zq78+s1/nwww+rQoUK6tGjh2Wxsrz33ntq2rSpSpYsqfLly6tbt246ffq0ZfHuvPNOrVixQjNmzJBhGDIMQ7t27bIsXo0aNbLNpLZo0cKy75PZs2erSpUq8vl8AeM33XSThgwZEtZYn3zyicqUKSOv1ytJ+v7772UYhsaMGePf56677tIdd9wR1riHDh1SpUqV9Mwzz/jHvv32W0VFRSklJSWssbLMnz9f5cuXl8fjCRjv06ePBgwYYEnMXbt2+d+jf9y6dOliSTwULRScOv+DNDExUWvWrFFKSopcLpduvvnmbB+Q4fT666+rRIkSWr16tWbMmKGpU6fqlVdesSyeJCUlJWnSpEkaO3asfvzxRy1YsMB/o1crjB49WitWrNBHH32kpUuXavny5Vq3bp1l8SQpOTlZ8+fP16xZs7R582aNHDlSd9xxh1asWGFZzBkzZmjixIm69NJLtW/fPkt/0ZSkxMREffPNN/r444+1bNkyffXVV5af19dff12lS5fWqlWrNHnyZE2cOFHLli2zNGZxsmDBAvXv319vvvmmbr/9dqfTCdnrr7+uChUqaPXq1RoxYoSGDx+uW265RR06dNC6devUvXt3DRgwQGfOnLEktt3v1UceeUTvv/++Xn/9da1bt0516tRRjx49dPToUcti2v0zxInPc+n864yKitI333yjWbNmWRpr37596t+/v4YMGaKffvpJy5cvV9++fS0t5GfMmKH27dtr2LBh2rdvn/bt26dq1apZFs9ut9xyi44cOaLU1FT/2NGjR7VkyZKwf9Z17NhRJ0+e1Pr16yVJK1asUIUKFbR8+XL/PitWrAh7gRQfH6+5c+fqySef1Jo1a3Ty5EkNGDBADzzwgLp27RrWWFluueUWeb1effzxx/6xgwcPavHixWEv5LNUq1bN/x7dt2+f1q9fr/Lly6tTp06WxEMRYyKbQ4cOmZLMjRs3WvL8nTt3Nhs2bGj6fD7/2KOPPmo2bNjQknimaZppaWmm2+0258yZY1mMPzp58qQZFRVlvvPOO/6xI0eOmCVLljQfeughS2KeO3fOLFWqlPntt98GjA8dOtTs37+/JTGzTJs2zaxevbqlMUzz/NcxMjLSfPfdd/1jx48fN0uVKmXZee3cubN51VVXBYy1adPGfPTRRy2J9+fYVr2uYAYNGmTedNNNlsfJem0vvviiGRcXZy5fvtzymH+ObdVz//H9kpmZaZYuXdocMGCAf2zfvn2mJHPlypWWxjZN69+rp06dMiMjI80333zTP5aenm5WqVLFnDx5siUx7f4Z4sTnuWmef52XX365Zc//Z2vXrjUlmbt27bItpmna+zlXvXp1c9q0aQFjzZs3N8ePH29ZzJtuuskcMmSI/98vv/yyWaVKFdPr9YY9VsuWLc3nnnvONE3T7NOnj/mPf/zDjIqKMk+ePGnu2bPHlGRu3bo17HFN0zTvu+8+s169euZtt91mNm3a1Dx37pwlcbIMHz7cvP766/3/njJlilmrVq2AzwWrnD171mzXrp3Zq1cvS76OKHqY4ZT0yy+/qH///qpVq5ZiY2P9LZG7d++2LOYVV1whwzD8/27fvr1++eUXfytIuP3000/yeDyW/bXtz7Zv36709HS1a9fOP1auXDnVr1/fspjbtm3TmTNndO211yomJsa/zZ8/3/IWabvs2LFDGRkZatu2rX8sLi7O0vMqSc2aNQv4d+XKlXXw4EFLYxYH7733nkaOHKlly5apc+fOTqcTNn98v0RERKh8+fJq2rSpfyyrs8KK95Dd79Xt27crIyNDV155pX8sMjJSbdu21U8//WRZXDt/hjjxeZ6lVatWlsfI0rx5c3Xt2lVNmzbVLbfcojlz5ujYsWO2xS+qbr/9dr3//vv+9s8333xTf/vb3+Ryhf9X0M6dO2v58uUyTVNfffWV+vbtq4YNG+rrr7/WihUrVKVKFdWtWzfscSXp+eefV2Zmpt599129+eabcrvdlsTJMmzYMC1dulR79+6VJL322mu68847Az4XrDJkyBCdPHlSCxYssOTriKKHd4mk3r176+jRo5ozZ45WrVqlVatWSTq/QEFRUbJkSadTsNypU6cknb8W7vvvv/dvP/74o+XXcRZ1f14p1jAMS1vOi4vLL7/c345lFqGVcXN6v/xxLOsXIiveQ7xXi5bSpUvbFisiIkLLli3Tf//7XzVq1Ej//Oc/Vb9+fe3cudO2HKzmcrmyfdZkZGRYGrN3794yTVOLFy/Wb7/9pq+++sqySwe6dOmir7/+Wj/88IMiIyPVoEEDdenSRcuXL9eKFSss/cPe9u3b9fvvv8vn81l6HW6Wyy+/XM2bN9f8+fO1du1abd68WXfeeaflcZ9++ml99tln+vjjj3XJJZdYHg9FQ7EvOI8cOaItW7boiSeeUNeuXdWwYUNb/qKZVdRm+d///qe6desqIiLCknh169ZVyZIlLbuA/c9q166tyMjIgNd57Ngxbd261bKYjRo1ktvt1u7du1WnTp2ArahcE1OrVi1FRkYGXCd64sQJS88rrFO7dm2lpqbqo48+0ogRI5xOB/lQu3Zt/zWGWTIyMvTdd9+pUaNGlsW182eIE5/nTjEMQ1deeaUmTJig9evXKyoqSh988IGlMaOioizrbvqz+Ph47du3z//vtLQ0ywvq6Oho9e3bV2+++abeeust1a9fXy1btrQkVtZ1nNOmTfMXl1kF5/Llyy1b4CY9PV133HGH+vXrp6eeekp33XWXLV1Ad911l1577TXNmzdP3bp1s/x3nffff18TJ07UO++8o9q1a1saC0VLsb8tStmyZVW+fHnNnj1blStX1u7duwNWNLPK7t27lZiYqHvuuUfr1q3TP//5T0tXcY2Ojtajjz6qRx55RFFRUbryyit16NAhbd68WUOHDg17vJiYGA0dOlSjR49W+fLlVbFiRT3++OOWtl5ccsklGjVqlEaOHCmfz6errrpKJ06c0DfffKPY2FgNGjTIsth2ueSSSzRo0CCNHj1a5cqVU8WKFTV+/Hi5XC5b2mgQfvXq1VNqaqq6dOmiEiVKcC++QqZ06dIaPny4/3vysssu0+TJk3XmzBlLPluz2PkzxInPcyesWrVKKSkp6t69uypWrKhVq1bp0KFDatiwoaVxa9SooVWrVmnXrl2KiYlRuXLlLDu311xzjV577TX17t1bZcqU0bhx4yz7Q/cf3X777erVq5c2b94c9lVi/6hs2bJq1qyZ3nzzTb344ouSpE6dOunWW29VRkaGZTOcjz/+uE6cOKEXXnhBMTEx+vTTTzVkyBB98sknlsTLctttt2nUqFGaM2eO5s+fb2msTZs2aeDAgXr00UfVuHFj7d+/X9L5P5g4cQszFC7FvuB0uVx6++239eCDD6pJkyaqX7++XnjhBcuXeR44cKDOnj2rtm3bKiIiQg899JDuvvtuS2OOHTtWJUqU0Lhx4/T777+rcuXKuvfeey2L99xzz+nUqVPq3bu3LrnkEv3973/XiRMnLIsnSU899ZTi4+OVnJysHTt2qEyZMmrZsqUee+wxS+PaaerUqbr33nvVq1cvxcbG6pFHHtFvv/2m6Ohop1NDPtWvX19ffPGFunTpooiICFtuIYTwmTRpknw+nwYMGKCTJ0+qdevW+uyzz1S2bFnLYtr9M8SJz3O7xcbG6ssvv9T06dOVlpam6tWra8qUKbr++ustjTtq1CgNGjRIjRo10tmzZ7Vz507Lbq+VlJSknTt3qlevXoqLi9NTTz1lS8vwNddco3LlymnLli267bbbLI3VuXNnff/99/7f48qVK6dGjRrpwIEDllx3vHz5ck2fPl2pqamKjY2VJL3xxhtq3ry5/vWvf2n48OFhj5klLi5Of/nLX7R48WLLb+e1Zs0anTlzRk8//bSefvpp/3jWdbPAhRhmUbpwCCiGTp8+rapVq2rKlCmWzqgUF/3791dERIT+/e9/O50KkKMuXbqoRYsWjs+GF5Q8gOKsa9euaty4sV544QWnUwGCKlr9MEAxsH79er311lvavn271q1b51984aabbnI4s8ItMzNTP/74o1auXKnGjRs7nQ4AAEEdO3ZMH3zwgZYvX67777/f6XSACyr2LbVAYfT8889ry5YtioqKUqtWrfTVV1+pQoUKTqdVqG3atEkdOnTQ1VdfbWmrOQAAobr88st17NgxPfvss7bcoggIBS21AAAAAABL0FILAAAAALAEBScAAAAAwBIUnAAAAAAAS1BwAgAAAAAsQcEJAAAAALAEBScAoEAzDEMffvih02kAAIB8oOAEAPjdeeedMgxDkyZNChj/8MMPZRhGWGPVqFFD06dPD+tzSudfQ58+fQLGdu3aJcMw9P3334c9HgAACI6CEwAQIDo6Ws8++6yOHTvmdCoFUkZGhtMpAABQaFBwAgACdOvWTZUqVVJycvIF9/v666/VsWNHlSxZUtWqVdODDz6o06dPS5Lmz5+vmJgY/fLLL/7977vvPjVo8P/au5+Qpv84juNPmcjUVmZpMUKUCt1B8R8EQk06tNVlZOBl9AdMvIxpIGiH1IRmHuqwoBhNlocdvhADiaBDhzXTQ6dcoGQtjZIReIk0LG3+Dj8aDC20fuP349frcdo+n8/3vTff24vP9/tZFZ8/f6a5uZm3b99y6dIlcnJytrV7+u7dO1pbWykqKqK4uBiXy8X8/DwAAwMDjI6OMjY2lq4bjUapqKgAoK6ujpycHJqbm9P1gsEgNpsNs9lMVVUVt2/fTs993xk1DAO73Y7ZbCYcDm+5VxERkT+dAqeIiGQwmUz4fD5u3brF+/fvN12TSCRwOp2cOXOGeDyOYRg8ffoUj8cDwLlz5zh16hRut5u1tTUePnxIMBgkHA5TUFBAJBLhwIEDDA4OkkwmSSaTW+ptdXUVh8OBxWJhfHyciYkJduzYgdPp5OvXr3R3d9Pa2orT6UzXbWpq4tmzZwA8fvyYZDJJJBIBIBwO09fXx7Vr15iZmcHn83HlyhVGR0czfre3t5fOzk5mZmZwOBy/emtFRET+OLn/dgMiIvLfc/r0aWpra+nv72dkZGTD/NDQEG63m66uLgAOHz6M3+/Hbrdz584dzGYzgUCAmpoavF4vkUiEgYEBGhoaACguLsZkMmGxWNi/f/+W+zIMg1QqRTAYTO+KhkIhioqKiEajnDhxgvz8fL58+ZJRt6SkBIA9e/ZkjPf393Pjxg1aWloAqKioYHp6mkAgwPnz59Prurq60mtERERk6xQ4RURkU8PDwxw/fpzu7u4Nc1NTU8Tj8YzHS9fX10mlUszNzWGz2di9ezcjIyM4HA6ampro7e397Z6mpqZ4/fo1FoslY3xlZYVEIrGtWsvLyyQSCdra2mhvb0+Pr62tsWvXroy1jY2Nv960iIjIH0yBU0RENnXs2DEcDgeXL1/mwoULGXNLS0t0dHTg9Xo3XFdWVpb+HIvFMJlMJJNJlpeXNwTF7VpaWqKhoWHT9yi/72JupxbA3bt3OXLkSMacyWTK+F5YWLjNTkVERAQUOEVE5CeuX79ObW0tlZWVGeP19fVMT09z6NChH147OTnJ8PAwDx48oKenB4/Hk/FuZF5eHt++fdtWP/X19RiGQWlpKTt37tx0zWZ18/LyADLG9+3bh9Vq5c2bN7jd7m31ISIiIlujQ4NEROSHqqurcbvd+P3+jPGenh4mJyfxeDw8f/6cV69eMTY2lj406NOnT5w9exav18vJkycJh8MYhsH9+/fTNcrLy4nFYiwsLLC4uLilftxuN3v37sXlcjE+Ps7c3BzRaBSv15s+4Ki8vJx4PM7Lly9ZXFxkdXWV0tJS8vPzefToER8+fODjx48AXL16laGhIfx+P7Ozs7x48YJQKMTNmzf/idsnIiLyx1PgFBGRnxocHCSVSmWM1dTU8OTJE2ZnZzl69Ch1dXX09fVhtVoB6OzspLCwEJ/PB/wdXH0+Hx0dHSwsLKTrzs/Pc/DgwS0/DltQUEAsFqOsrIyWlhZsNhttbW2srKykdzzb29uprKyksbGRkpISJiYmyM3Nxe/3EwgEsFqtuFwuAC5evEgwGCQUClFdXY3dbufevXvpv1ERERGR35Ozvr6+/m83ISIiIiIiIv8/2uEUERERERGRrFDgFBERERERkaxQ4BQREREREZGsUOAUERERERGRrFDgFBERERERkaxQ4BQREREREZGsUOAUERERERGRrFDgFBERERERkaxQ4BQREREREZGsUOAUERERERGRrFDgFBERERERkaz4C2zVEyO25I7OAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "letters = list('abcdefghijklmnopqrstuvwxyz')\n",
    "plt.figure(figsize=(12, 10))\n",
    "sns.heatmap(df_probs.loc[letters, letters].values,\n",
    "            xticklabels=letters, yticklabels=letters,\n",
    "            cmap=\"Reds\")\n",
    "plt.title(\"Transition probabilities (surnames)  — a -> b\")\n",
    "plt.xlabel(\"Next letter\")\n",
    "plt.ylabel(\"Current letter\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ffb0b937-fb9e-47d5-94c7-20afdf99560c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>letter</th>\n",
       "      <th>count</th>\n",
       "      <th>freq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>5638609</td>\n",
       "      <td>0.175533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1982642</td>\n",
       "      <td>0.061721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>67967</td>\n",
       "      <td>0.002116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>d</td>\n",
       "      <td>833422</td>\n",
       "      <td>0.025945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>e</td>\n",
       "      <td>1888919</td>\n",
       "      <td>0.058803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>f</td>\n",
       "      <td>161048</td>\n",
       "      <td>0.005014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>g</td>\n",
       "      <td>1189924</td>\n",
       "      <td>0.037043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>h</td>\n",
       "      <td>502652</td>\n",
       "      <td>0.015648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>i</td>\n",
       "      <td>2434995</td>\n",
       "      <td>0.075803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>j</td>\n",
       "      <td>137482</td>\n",
       "      <td>0.004280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>k</td>\n",
       "      <td>1951774</td>\n",
       "      <td>0.060760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>l</td>\n",
       "      <td>1520935</td>\n",
       "      <td>0.047348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>m</td>\n",
       "      <td>2625688</td>\n",
       "      <td>0.081739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>n</td>\n",
       "      <td>2675387</td>\n",
       "      <td>0.083286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>o</td>\n",
       "      <td>2159415</td>\n",
       "      <td>0.067224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>p</td>\n",
       "      <td>311915</td>\n",
       "      <td>0.009710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>q</td>\n",
       "      <td>1252</td>\n",
       "      <td>0.000039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>r</td>\n",
       "      <td>285818</td>\n",
       "      <td>0.008898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>s</td>\n",
       "      <td>1048120</td>\n",
       "      <td>0.032629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>t</td>\n",
       "      <td>870620</td>\n",
       "      <td>0.027103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>u</td>\n",
       "      <td>2235199</td>\n",
       "      <td>0.069583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>v</td>\n",
       "      <td>139435</td>\n",
       "      <td>0.004341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>w</td>\n",
       "      <td>417888</td>\n",
       "      <td>0.013009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>x</td>\n",
       "      <td>708</td>\n",
       "      <td>0.000022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>y</td>\n",
       "      <td>654446</td>\n",
       "      <td>0.020373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>z</td>\n",
       "      <td>386517</td>\n",
       "      <td>0.012032</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   letter    count      freq\n",
       "0       a  5638609  0.175533\n",
       "1       b  1982642  0.061721\n",
       "2       c    67967  0.002116\n",
       "3       d   833422  0.025945\n",
       "4       e  1888919  0.058803\n",
       "5       f   161048  0.005014\n",
       "6       g  1189924  0.037043\n",
       "7       h   502652  0.015648\n",
       "8       i  2434995  0.075803\n",
       "9       j   137482  0.004280\n",
       "10      k  1951774  0.060760\n",
       "11      l  1520935  0.047348\n",
       "12      m  2625688  0.081739\n",
       "13      n  2675387  0.083286\n",
       "14      o  2159415  0.067224\n",
       "15      p   311915  0.009710\n",
       "16      q     1252  0.000039\n",
       "17      r   285818  0.008898\n",
       "18      s  1048120  0.032629\n",
       "19      t   870620  0.027103\n",
       "20      u  2235199  0.069583\n",
       "21      v   139435  0.004341\n",
       "22      w   417888  0.013009\n",
       "23      x      708  0.000022\n",
       "24      y   654446  0.020373\n",
       "25      z   386517  0.012032"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_letters = \"\".join(df_simple['surname'].astype(str).str.lower().tolist())\n",
    "letters_only = [c for c in all_letters if c.isalpha()]\n",
    "\n",
    "counts = Counter(letters_only)\n",
    "letters = list(\"abcdefghijklmnopqrstuvwxyz\")\n",
    "\n",
    "# Build DataFrame with all 26 letters\n",
    "df_letters = pd.DataFrame({\n",
    "    \"letter\": letters,\n",
    "    \"count\": [counts.get(l, 0) for l in letters]\n",
    "})\n",
    "\n",
    "# Compute relative frequencies\n",
    "df_letters[\"freq\"] = df_letters[\"count\"] / df_letters[\"count\"].sum()\n",
    "df_letters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4c62f894-9d65-4470-898c-e33c20155dff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "sns.barplot(x=\"letter\", y=\"freq\", data=df_letters, color=\"steelblue\")\n",
    "plt.title(\"Letter frequency (alphabetical order)\")\n",
    "plt.xlabel(\"Letter\")\n",
    "plt.ylabel(\"Relative frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b90a37c2-a368-4df2-a2d4-4e5d0fdba63e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_sorted = df_letters.sort_values(\"freq\", ascending=False)\n",
    "\n",
    "plt.figure(figsize=(12,6))\n",
    "sns.barplot(x=\"letter\", y=\"freq\", data=df_sorted, color=\"darkorange\")\n",
    "plt.title(\"Letter frequency (descending order)\")\n",
    "plt.xlabel(\"Letter\")\n",
    "plt.ylabel(\"Relative frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "41a84964-69b1-4b3f-af5e-02118c26234d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>letter</th>\n",
       "      <th>count</th>\n",
       "      <th>freq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>5638609</td>\n",
       "      <td>0.175533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>n</td>\n",
       "      <td>2675387</td>\n",
       "      <td>0.083286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>m</td>\n",
       "      <td>2625688</td>\n",
       "      <td>0.081739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>i</td>\n",
       "      <td>2434995</td>\n",
       "      <td>0.075803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>u</td>\n",
       "      <td>2235199</td>\n",
       "      <td>0.069583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>o</td>\n",
       "      <td>2159415</td>\n",
       "      <td>0.067224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>b</td>\n",
       "      <td>1982642</td>\n",
       "      <td>0.061721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>k</td>\n",
       "      <td>1951774</td>\n",
       "      <td>0.060760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>e</td>\n",
       "      <td>1888919</td>\n",
       "      <td>0.058803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>l</td>\n",
       "      <td>1520935</td>\n",
       "      <td>0.047348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>g</td>\n",
       "      <td>1189924</td>\n",
       "      <td>0.037043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>s</td>\n",
       "      <td>1048120</td>\n",
       "      <td>0.032629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>t</td>\n",
       "      <td>870620</td>\n",
       "      <td>0.027103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>d</td>\n",
       "      <td>833422</td>\n",
       "      <td>0.025945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>y</td>\n",
       "      <td>654446</td>\n",
       "      <td>0.020373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>h</td>\n",
       "      <td>502652</td>\n",
       "      <td>0.015648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>w</td>\n",
       "      <td>417888</td>\n",
       "      <td>0.013009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>z</td>\n",
       "      <td>386517</td>\n",
       "      <td>0.012032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>p</td>\n",
       "      <td>311915</td>\n",
       "      <td>0.009710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>r</td>\n",
       "      <td>285818</td>\n",
       "      <td>0.008898</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   letter    count      freq\n",
       "0       a  5638609  0.175533\n",
       "1       n  2675387  0.083286\n",
       "2       m  2625688  0.081739\n",
       "3       i  2434995  0.075803\n",
       "4       u  2235199  0.069583\n",
       "5       o  2159415  0.067224\n",
       "6       b  1982642  0.061721\n",
       "7       k  1951774  0.060760\n",
       "8       e  1888919  0.058803\n",
       "9       l  1520935  0.047348\n",
       "10      g  1189924  0.037043\n",
       "11      s  1048120  0.032629\n",
       "12      t   870620  0.027103\n",
       "13      d   833422  0.025945\n",
       "14      y   654446  0.020373\n",
       "15      h   502652  0.015648\n",
       "16      w   417888  0.013009\n",
       "17      z   386517  0.012032\n",
       "18      p   311915  0.009710\n",
       "19      r   285818  0.008898"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_letters.sort_values(\"freq\", ascending=False).reset_index(drop=True).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34111d28-3f23-432e-be95-688c1471b87c",
   "metadata": {},
   "source": [
    "## Fréquence des bigrammes et trigrammes les plus utilisés"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "98c7ed61-5c2d-4d9a-9d85-e4efe4bfc402",
   "metadata": {},
   "outputs": [],
   "source": [
    "letters = list(\"abcdefghijklmnopqrstuvwxyz\")\n",
    "index = {l: i for i, l in enumerate(letters)}\n",
    "matrix = np.zeros((26, 26), dtype=int)\n",
    "\n",
    "for name in df_simple['surname'].astype(str).str.lower():\n",
    "    name = re.sub(r\"[^a-z]\", \"\", name)\n",
    "    for a, b in zip(name, name[1:]):\n",
    "        if a in index and b in index:\n",
    "            matrix[index[a], index[b]] += 1\n",
    "\n",
    "df_bigrams_matrix = pd.DataFrame(matrix, index=letters, columns=letters)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39d54a8d-044f-42d7-89fc-0a2f5522e343",
   "metadata": {},
   "source": [
    "### Fréquence des bigrammes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2a3c00fc-d319-4396-905b-cded302af650",
   "metadata": {},
   "outputs": [],
   "source": [
    "letters = list(\"abcdefghijklmnopqrstuvwxyz\")\n",
    "index = {l: i for i, l in enumerate(letters)}\n",
    "matrix = np.zeros((26, 26), dtype=int)\n",
    "\n",
    "for name in df_simple['surname'].astype(str).str.lower():\n",
    "    name = re.sub(r\"[^a-z]\", \"\", name)\n",
    "    for a, b in zip(name, name[1:]):\n",
    "        if a in index and b in index:\n",
    "            matrix[index[a], index[b]] += 1\n",
    "\n",
    "df_bigrams_matrix = pd.DataFrame(matrix, index=letters, columns=letters)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d44d59a1-7578-42c4-b076-fe65ef11cb3d",
   "metadata": {},
   "source": [
    "### Heatmap des bigrammes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "86bf7ee4-ecd7-4ac3-b005-e2e210b88ca5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 12))\n",
    "sns.heatmap(df_bigrams_matrix, cmap=\"Reds\", cbar=True, xticklabels=letters, yticklabels=letters)\n",
    "plt.title(\"Bigram frequencies in surnames\")\n",
    "plt.xlabel(\"Next letter\")\n",
    "plt.ylabel(\"Current letter\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e948cdd-c77b-48f6-b643-0a24f513afa9",
   "metadata": {},
   "source": [
    "### Tableau des bigrammes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "07a8bd99-761e-4492-a8ff-0c66185524d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "      <th>d</th>\n",
       "      <th>e</th>\n",
       "      <th>f</th>\n",
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       "      <th>j</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>5228</td>\n",
       "      <td>263129</td>\n",
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       "      <td>268202</td>\n",
       "      <td>186897</td>\n",
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       "      <td>40</td>\n",
       "      <td>173351</td>\n",
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       "      <th>b</th>\n",
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       "      <td>1</td>\n",
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       "      <td>23</td>\n",
       "      <td>16</td>\n",
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       "      <th>c</th>\n",
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       "      <td>458</td>\n",
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       "      <td>6</td>\n",
       "      <td>579</td>\n",
       "      <td>1700</td>\n",
       "      <td>0</td>\n",
       "      <td>323</td>\n",
       "      <td>0</td>\n",
       "      <td>545</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>199445</td>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "      <td>429</td>\n",
       "      <td>76782</td>\n",
       "      <td>8</td>\n",
       "      <td>17</td>\n",
       "      <td>3760</td>\n",
       "      <td>259819</td>\n",
       "      <td>54307</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>6879</td>\n",
       "      <td>66</td>\n",
       "      <td>14</td>\n",
       "      <td>79705</td>\n",
       "      <td>19</td>\n",
       "      <td>6706</td>\n",
       "      <td>1</td>\n",
       "      <td>2546</td>\n",
       "      <td>1787</td>\n",
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       "    <tr>\n",
       "      <th>e</th>\n",
       "      <td>10218</td>\n",
       "      <td>55430</td>\n",
       "      <td>1806</td>\n",
       "      <td>28464</td>\n",
       "      <td>9164</td>\n",
       "      <td>9016</td>\n",
       "      <td>8840</td>\n",
       "      <td>6778</td>\n",
       "      <td>2636</td>\n",
       "      <td>6489</td>\n",
       "      <td>...</td>\n",
       "      <td>9</td>\n",
       "      <td>70449</td>\n",
       "      <td>57711</td>\n",
       "      <td>65537</td>\n",
       "      <td>4229</td>\n",
       "      <td>4548</td>\n",
       "      <td>10063</td>\n",
       "      <td>318</td>\n",
       "      <td>54429</td>\n",
       "      <td>23871</td>\n",
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       "    <tr>\n",
       "      <th>f</th>\n",
       "      <td>38611</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>13782</td>\n",
       "      <td>198</td>\n",
       "      <td>3</td>\n",
       "      <td>22</td>\n",
       "      <td>24087</td>\n",
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       "      <td>798</td>\n",
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       "    <tr>\n",
       "      <th>g</th>\n",
       "      <td>466541</td>\n",
       "      <td>24772</td>\n",
       "      <td>9</td>\n",
       "      <td>44</td>\n",
       "      <td>102163</td>\n",
       "      <td>7</td>\n",
       "      <td>38</td>\n",
       "      <td>18597</td>\n",
       "      <td>94315</td>\n",
       "      <td>13</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>1169</td>\n",
       "      <td>25</td>\n",
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       "      <td>4</td>\n",
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       "      <td>1630</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h</th>\n",
       "      <td>126923</td>\n",
       "      <td>20</td>\n",
       "      <td>2</td>\n",
       "      <td>11</td>\n",
       "      <td>38849</td>\n",
       "      <td>16</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>221195</td>\n",
       "      <td>9</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>900</td>\n",
       "      <td>96</td>\n",
       "      <td>82</td>\n",
       "      <td>40774</td>\n",
       "      <td>4</td>\n",
       "      <td>1921</td>\n",
       "      <td>0</td>\n",
       "      <td>1048</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>i</th>\n",
       "      <td>142956</td>\n",
       "      <td>99789</td>\n",
       "      <td>5475</td>\n",
       "      <td>40211</td>\n",
       "      <td>65119</td>\n",
       "      <td>22757</td>\n",
       "      <td>11706</td>\n",
       "      <td>8267</td>\n",
       "      <td>955</td>\n",
       "      <td>6000</td>\n",
       "      <td>...</td>\n",
       "      <td>614</td>\n",
       "      <td>79659</td>\n",
       "      <td>120640</td>\n",
       "      <td>112233</td>\n",
       "      <td>5614</td>\n",
       "      <td>7655</td>\n",
       "      <td>14137</td>\n",
       "      <td>135</td>\n",
       "      <td>46205</td>\n",
       "      <td>32395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>j</th>\n",
       "      <td>31283</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>30</td>\n",
       "      <td>11267</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>17</td>\n",
       "      <td>63052</td>\n",
       "      <td>13</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>8367</td>\n",
       "      <td>2</td>\n",
       "      <td>257</td>\n",
       "      <td>0</td>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k</th>\n",
       "      <td>1007696</td>\n",
       "      <td>127</td>\n",
       "      <td>9</td>\n",
       "      <td>15</td>\n",
       "      <td>127691</td>\n",
       "      <td>426</td>\n",
       "      <td>6</td>\n",
       "      <td>7691</td>\n",
       "      <td>274640</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>5</td>\n",
       "      <td>360</td>\n",
       "      <td>2043</td>\n",
       "      <td>31</td>\n",
       "      <td>217831</td>\n",
       "      <td>6</td>\n",
       "      <td>40067</td>\n",
       "      <td>0</td>\n",
       "      <td>20183</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>l</th>\n",
       "      <td>447225</td>\n",
       "      <td>704</td>\n",
       "      <td>47</td>\n",
       "      <td>331</td>\n",
       "      <td>272326</td>\n",
       "      <td>431</td>\n",
       "      <td>109</td>\n",
       "      <td>177</td>\n",
       "      <td>155618</td>\n",
       "      <td>7</td>\n",
       "      <td>...</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>169</td>\n",
       "      <td>117</td>\n",
       "      <td>349100</td>\n",
       "      <td>458</td>\n",
       "      <td>13036</td>\n",
       "      <td>1</td>\n",
       "      <td>3818</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m</th>\n",
       "      <td>630378</td>\n",
       "      <td>957543</td>\n",
       "      <td>57</td>\n",
       "      <td>140</td>\n",
       "      <td>69192</td>\n",
       "      <td>12061</td>\n",
       "      <td>139</td>\n",
       "      <td>27</td>\n",
       "      <td>104343</td>\n",
       "      <td>19</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>43</td>\n",
       "      <td>1257</td>\n",
       "      <td>209</td>\n",
       "      <td>485738</td>\n",
       "      <td>16584</td>\n",
       "      <td>96340</td>\n",
       "      <td>0</td>\n",
       "      <td>1746</td>\n",
       "      <td>400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n</th>\n",
       "      <td>178027</td>\n",
       "      <td>308</td>\n",
       "      <td>4846</td>\n",
       "      <td>501221</td>\n",
       "      <td>63320</td>\n",
       "      <td>1730</td>\n",
       "      <td>1072187</td>\n",
       "      <td>408</td>\n",
       "      <td>132065</td>\n",
       "      <td>19182</td>\n",
       "      <td>...</td>\n",
       "      <td>29</td>\n",
       "      <td>438</td>\n",
       "      <td>101026</td>\n",
       "      <td>94788</td>\n",
       "      <td>30568</td>\n",
       "      <td>3386</td>\n",
       "      <td>1594</td>\n",
       "      <td>0</td>\n",
       "      <td>104903</td>\n",
       "      <td>185094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>o</th>\n",
       "      <td>6033</td>\n",
       "      <td>46846</td>\n",
       "      <td>1704</td>\n",
       "      <td>22198</td>\n",
       "      <td>3292</td>\n",
       "      <td>15467</td>\n",
       "      <td>8924</td>\n",
       "      <td>7986</td>\n",
       "      <td>15828</td>\n",
       "      <td>2737</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>14504</td>\n",
       "      <td>58695</td>\n",
       "      <td>68895</td>\n",
       "      <td>7253</td>\n",
       "      <td>4673</td>\n",
       "      <td>16425</td>\n",
       "      <td>36</td>\n",
       "      <td>101989</td>\n",
       "      <td>10943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p</th>\n",
       "      <td>85530</td>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>65177</td>\n",
       "      <td>1244</td>\n",
       "      <td>0</td>\n",
       "      <td>14841</td>\n",
       "      <td>48942</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>810</td>\n",
       "      <td>28</td>\n",
       "      <td>79</td>\n",
       "      <td>44937</td>\n",
       "      <td>2</td>\n",
       "      <td>3765</td>\n",
       "      <td>0</td>\n",
       "      <td>2655</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>q</th>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1222</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r</th>\n",
       "      <td>91428</td>\n",
       "      <td>196</td>\n",
       "      <td>1888</td>\n",
       "      <td>1146</td>\n",
       "      <td>70223</td>\n",
       "      <td>37</td>\n",
       "      <td>877</td>\n",
       "      <td>10283</td>\n",
       "      <td>48804</td>\n",
       "      <td>16</td>\n",
       "      <td>...</td>\n",
       "      <td>39</td>\n",
       "      <td>617</td>\n",
       "      <td>321</td>\n",
       "      <td>1858</td>\n",
       "      <td>26502</td>\n",
       "      <td>268</td>\n",
       "      <td>5676</td>\n",
       "      <td>0</td>\n",
       "      <td>1388</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s</th>\n",
       "      <td>244729</td>\n",
       "      <td>20</td>\n",
       "      <td>1132</td>\n",
       "      <td>27</td>\n",
       "      <td>140580</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>258865</td>\n",
       "      <td>166135</td>\n",
       "      <td>19</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>158</td>\n",
       "      <td>17350</td>\n",
       "      <td>5835</td>\n",
       "      <td>72439</td>\n",
       "      <td>8</td>\n",
       "      <td>10000</td>\n",
       "      <td>2</td>\n",
       "      <td>1212</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t</th>\n",
       "      <td>189566</td>\n",
       "      <td>10</td>\n",
       "      <td>3548</td>\n",
       "      <td>671</td>\n",
       "      <td>115751</td>\n",
       "      <td>61</td>\n",
       "      <td>4</td>\n",
       "      <td>15513</td>\n",
       "      <td>68932</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>2055</td>\n",
       "      <td>166255</td>\n",
       "      <td>1722</td>\n",
       "      <td>162308</td>\n",
       "      <td>2</td>\n",
       "      <td>9482</td>\n",
       "      <td>3</td>\n",
       "      <td>2114</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>u</th>\n",
       "      <td>111689</td>\n",
       "      <td>64538</td>\n",
       "      <td>2476</td>\n",
       "      <td>34405</td>\n",
       "      <td>45750</td>\n",
       "      <td>14052</td>\n",
       "      <td>32712</td>\n",
       "      <td>30536</td>\n",
       "      <td>20865</td>\n",
       "      <td>18966</td>\n",
       "      <td>...</td>\n",
       "      <td>3</td>\n",
       "      <td>33954</td>\n",
       "      <td>109891</td>\n",
       "      <td>123781</td>\n",
       "      <td>1053</td>\n",
       "      <td>10120</td>\n",
       "      <td>17456</td>\n",
       "      <td>134</td>\n",
       "      <td>72914</td>\n",
       "      <td>44982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v</th>\n",
       "      <td>20283</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9997</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>22</td>\n",
       "      <td>44317</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>64</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>54318</td>\n",
       "      <td>4</td>\n",
       "      <td>514</td>\n",
       "      <td>0</td>\n",
       "      <td>559</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>w</th>\n",
       "      <td>234581</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>108690</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>62</td>\n",
       "      <td>40902</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>12</td>\n",
       "      <td>11</td>\n",
       "      <td>14374</td>\n",
       "      <td>3</td>\n",
       "      <td>19</td>\n",
       "      <td>1</td>\n",
       "      <td>48</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>136</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>192</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>237389</td>\n",
       "      <td>182</td>\n",
       "      <td>111</td>\n",
       "      <td>241</td>\n",
       "      <td>88532</td>\n",
       "      <td>11</td>\n",
       "      <td>42</td>\n",
       "      <td>47</td>\n",
       "      <td>135242</td>\n",
       "      <td>3</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>267</td>\n",
       "      <td>274</td>\n",
       "      <td>134</td>\n",
       "      <td>38581</td>\n",
       "      <td>383</td>\n",
       "      <td>401</td>\n",
       "      <td>2</td>\n",
       "      <td>13</td>\n",
       "      <td>57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>z</th>\n",
       "      <td>161374</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "      <td>101</td>\n",
       "      <td>46336</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>58</td>\n",
       "      <td>90575</td>\n",
       "      <td>16</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>95</td>\n",
       "      <td>18</td>\n",
       "      <td>2</td>\n",
       "      <td>38622</td>\n",
       "      <td>110</td>\n",
       "      <td>2331</td>\n",
       "      <td>0</td>\n",
       "      <td>1039</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>26 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         a       b     c       d       e      f        g       h       i  \\\n",
       "a     5228  263129  8991  116767    6306  38087    30182   75189   28541   \n",
       "b   781156     166     0    1186  226715      1       93    2932  221388   \n",
       "c     4411       1   280       0    6411      0        6   23056   23602   \n",
       "d   199445      13     0     429   76782      8       17    3760  259819   \n",
       "e    10218   55430  1806   28464    9164   9016     8840    6778    2636   \n",
       "f    38611       0     0       4   13782    198        3      22   24087   \n",
       "g   466541   24772     9      44  102163      7       38   18597   94315   \n",
       "h   126923      20     2      11   38849     16        9       8  221195   \n",
       "i   142956   99789  5475   40211   65119  22757    11706    8267     955   \n",
       "j    31283       2     5      30   11267      1        2      17   63052   \n",
       "k  1007696     127     9      15  127691    426        6    7691  274640   \n",
       "l   447225     704    47     331  272326    431      109     177  155618   \n",
       "m   630378  957543    57     140   69192  12061      139      27  104343   \n",
       "n   178027     308  4846  501221   63320   1730  1072187     408  132065   \n",
       "o     6033   46846  1704   22198    3292  15467     8924    7986   15828   \n",
       "p    85530      22     1       0   65177   1244        0   14841   48942   \n",
       "q        9       2     0       1       0      0        0       0       0   \n",
       "r    91428     196  1888    1146   70223     37      877   10283   48804   \n",
       "s   244729      20  1132      27  140580      7        3  258865  166135   \n",
       "t   189566      10  3548     671  115751     61        4   15513   68932   \n",
       "u   111689   64538  2476   34405   45750  14052    32712   30536   20865   \n",
       "v    20283       3     0       1    9997      0        3      22   44317   \n",
       "w   234581      11     0       9  108690      1        6      62   40902   \n",
       "x      136       3     5       0      26      0        0       6     192   \n",
       "y   237389     182   111     241   88532     11       42      47  135242   \n",
       "z   161374      33     1     101   46336      0        4      58   90575   \n",
       "\n",
       "       j  ...    q      r       s       t       u      v      w    x       y  \\\n",
       "a  19495  ...   28  48719  268202  186897   24085  75440  47762   40  173351   \n",
       "b      9  ...    1   2049      23      16  293343     16  51227    1    8320   \n",
       "c      2  ...  458    185       6     579    1700      0    323    0     545   \n",
       "d  54307  ...    0   6879      66      14   79705     19   6706    1    2546   \n",
       "e   6489  ...    9  70449   57711   65537    4229   4548  10063  318   54429   \n",
       "f      0  ...    1   1345      45      79   63527      0   4005    0     798   \n",
       "g     13  ...    2   1169      25      15  141016      4  23274    0    1630   \n",
       "h      9  ...    1    900      96      82   40774      4   1921    0    1048   \n",
       "i   6000  ...  614  79659  120640  112233    5614   7655  14137  135   46205   \n",
       "j     13  ...    0      6       1      11    8367      2    257    0      37   \n",
       "k      6  ...    5    360    2043      31  217831      6  40067    0   20183   \n",
       "l      7  ...    6      8     169     117  349100    458  13036    1    3818   \n",
       "m     19  ...    0     43    1257     209  485738  16584  96340    0    1746   \n",
       "n  19182  ...   29    438  101026   94788   30568   3386   1594    0  104903   \n",
       "o   2737  ...    7  14504   58695   68895    7253   4673  16425   36  101989   \n",
       "p      2  ...    0    810      28      79   44937      2   3765    0    2655   \n",
       "q      0  ...    0      1       2       0    1222      0      1    0       0   \n",
       "r     16  ...   39    617     321    1858   26502    268   5676    0    1388   \n",
       "s     19  ...    8    158   17350    5835   72439      8  10000    2    1212   \n",
       "t      6  ...    1   2055  166255    1722  162308      2   9482    3    2114   \n",
       "u  18966  ...    3  33954  109891  123781    1053  10120  17456  134   72914   \n",
       "v      0  ...    1     64       2       3   54318      4    514    0     559   \n",
       "w      0  ...    2      8      12      11   14374      3     19    1      48   \n",
       "x      0  ...    0      0       0       3       7      0      1   10       4   \n",
       "y      3  ...    1    267     274     134   38581    383    401    2      13   \n",
       "z     16  ...    0     95      18       2   38622    110   2331    0    1039   \n",
       "\n",
       "        z  \n",
       "a   60875  \n",
       "b      18  \n",
       "c       2  \n",
       "d    1787  \n",
       "e   23871  \n",
       "f       1  \n",
       "g       8  \n",
       "h       4  \n",
       "i   32395  \n",
       "j       1  \n",
       "k      11  \n",
       "l      14  \n",
       "m     400  \n",
       "n  185094  \n",
       "o   10943  \n",
       "p       3  \n",
       "q       0  \n",
       "r      20  \n",
       "s       7  \n",
       "t       5  \n",
       "u   44982  \n",
       "v       8  \n",
       "w       8  \n",
       "x       0  \n",
       "y      57  \n",
       "z      92  \n",
       "\n",
       "[26 rows x 26 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_bigrams_matrix.head(26)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "364580af-0604-4aab-9fad-1e777a9eab75",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Counting bigrams\n",
    "bigram_counter = Counter()\n",
    "for name in surnames:\n",
    "    for a, b in zip(name, name[1:]):\n",
    "        bigram_counter[a+b] += 1\n",
    "\n",
    "top_bigrams = bigram_counter.most_common(10)\n",
    "\n",
    "# Counting trigrams\n",
    "trigram_counter = Counter()\n",
    "for name in surnames:\n",
    "    for a, b, c in zip(name, name[1:], name[2:]):\n",
    "        trigram_counter[a+b+c] += 1\n",
    "\n",
    "top_trigrams = trigram_counter.most_common(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e67085b2-8b5b-4c1c-8339-8a9378a85697",
   "metadata": {},
   "source": [
    "### The most frequently used bigrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "412883b2-c1fd-483f-b61a-ba2bfc8b04e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bigram</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ng</td>\n",
       "      <td>1072187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ka</td>\n",
       "      <td>1007696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>mb</td>\n",
       "      <td>957543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ba</td>\n",
       "      <td>781156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>an</td>\n",
       "      <td>746783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>ma</td>\n",
       "      <td>630378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>nd</td>\n",
       "      <td>501221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>mu</td>\n",
       "      <td>485738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>ga</td>\n",
       "      <td>466541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>am</td>\n",
       "      <td>466334</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  bigram    count\n",
       "0     ng  1072187\n",
       "1     ka  1007696\n",
       "2     mb   957543\n",
       "3     ba   781156\n",
       "4     an   746783\n",
       "5     ma   630378\n",
       "6     nd   501221\n",
       "7     mu   485738\n",
       "8     ga   466541\n",
       "9     am   466334"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_bigrams = pd.DataFrame(bigram_counter.most_common(10), columns=[\"bigram\", \"count\"])\n",
    "display(df_bigrams)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fb8d1dc-38fb-4269-b22b-05dde9fb8842",
   "metadata": {},
   "source": [
    "### The most commonly used trigrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1a3c8b8c-cb78-47bf-87b3-0d105ed78af4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>trigram</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>nga</td>\n",
       "      <td>438962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>mba</td>\n",
       "      <td>400099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ngo</td>\n",
       "      <td>289073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>amb</td>\n",
       "      <td>269415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ang</td>\n",
       "      <td>266051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>ong</td>\n",
       "      <td>215334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>nda</td>\n",
       "      <td>176952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>mbo</td>\n",
       "      <td>176921</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>ala</td>\n",
       "      <td>175773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>shi</td>\n",
       "      <td>161218</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  trigram   count\n",
       "0     nga  438962\n",
       "1     mba  400099\n",
       "2     ngo  289073\n",
       "3     amb  269415\n",
       "4     ang  266051\n",
       "5     ong  215334\n",
       "6     nda  176952\n",
       "7     mbo  176921\n",
       "8     ala  175773\n",
       "9     shi  161218"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_trigrams = pd.DataFrame(trigram_counter.most_common(10), columns=[\"trigram\", \"count\"])\n",
    "display(df_trigrams)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28e65639-9082-464d-9330-71e2a028c878",
   "metadata": {},
   "source": [
    "## Name generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "28fe77f9-f9b0-4267-9dbb-3969e04b83fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Kananyikyumb',\n",
       " 'A',\n",
       " 'Nka',\n",
       " 'Kayomayi',\n",
       " 'Ngo',\n",
       " 'Ka',\n",
       " 'Bondimema',\n",
       " 'Nzongonzimba',\n",
       " 'Ndibon',\n",
       " 'Muama']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tokens = [\"^\"] + list(\"abcdefghijklmnopqrstuvwxyz\") + [\"$\"]\n",
    "index = {t: i for i, t in enumerate(tokens)}\n",
    "\n",
    "def generate_name(prob_matrix, index, tokens, max_len=12):\n",
    "    current = '^'\n",
    "    result = []\n",
    "    \n",
    "    for _ in range(max_len):\n",
    "        row = prob_matrix[index[current]]\n",
    "        next_letter = np.random.choice(tokens, p=row)\n",
    "        \n",
    "        if next_letter == '$':\n",
    "            break\n",
    "        \n",
    "        result.append(next_letter)\n",
    "        current = next_letter\n",
    "    \n",
    "    return \"\".join(result).capitalize()\n",
    "\n",
    "generated_names = [generate_name(df_probs.values, index, tokens) for _ in range(10)]\n",
    "generated_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "149339e0-e486-40a8-81da-14a92b3d6de9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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