benfords-law.ipynb

{
  "cells": [
    {
      "metadata": {
        "_uuid": "e87af36cffe7fff5d4fe7887945e894bc261c754"
      },
      "cell_type": "markdown",
      "source": "# Benfords Law\nAccording to Benfords Law, the distribution of numbers in a very large dataset should approximately be distributed as $log_{10}(\\frac{j+1}{j})$.\nI would consider 50.000 news articles to be a rather large, but slightly biased dataset. The digit 2 will probably appear much more often than the above distribution says (21st century)."
    },
    {
      "metadata": {
        "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
        "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5",
        "trusted": true
      },
      "cell_type": "code",
      "source": "import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport math\nimport re\nimport os\nos.listdir('../input')",
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 57,
          "data": {
            "text/plain": "['articles1.csv', 'articles3.csv', 'articles2.csv']"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a",
        "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
        "trusted": true,
        "scrolled": true
      },
      "cell_type": "code",
      "source": "df = pd.read_csv('../input/articles1.csv')\ndf.head(5)",
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": "   Unnamed: 0     id                                              title  \\\n0           0  17283  House Republicans Fret About Winning Their Hea...   \n1           1  17284  Rift Between Officers and Residents as Killing...   \n2           2  17285  Tyrus Wong, ‘Bambi’ Artist Thwarted by Racial ...   \n3           3  17286  Among Deaths in 2016, a Heavy Toll in Pop Musi...   \n4           4  17287  Kim Jong-un Says North Korea Is Preparing to T...   \n\n      publication                         author        date    year  month  \\\n0  New York Times                     Carl Hulse  2016-12-31  2016.0   12.0   \n1  New York Times  Benjamin Mueller and Al Baker  2017-06-19  2017.0    6.0   \n2  New York Times                   Margalit Fox  2017-01-06  2017.0    1.0   \n3  New York Times               William McDonald  2017-04-10  2017.0    4.0   \n4  New York Times                  Choe Sang-Hun  2017-01-02  2017.0    1.0   \n\n   url                                            content  \n0  NaN  WASHINGTON  —   Congressional Republicans have...  \n1  NaN  After the bullet shells get counted, the blood...  \n2  NaN  When Walt Disney’s “Bambi” opened in 1942, cri...  \n3  NaN  Death may be the great equalizer, but it isn’t...  \n4  NaN  SEOUL, South Korea  —   North Korea’s leader, ...  ",
            "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>Unnamed: 0</th>\n      <th>id</th>\n      <th>title</th>\n      <th>publication</th>\n      <th>author</th>\n      <th>date</th>\n      <th>year</th>\n      <th>month</th>\n      <th>url</th>\n      <th>content</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>17283</td>\n      <td>House Republicans Fret About Winning Their Hea...</td>\n      <td>New York Times</td>\n      <td>Carl Hulse</td>\n      <td>2016-12-31</td>\n      <td>2016.0</td>\n      <td>12.0</td>\n      <td>NaN</td>\n      <td>WASHINGTON  —   Congressional Republicans have...</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>17284</td>\n      <td>Rift Between Officers and Residents as Killing...</td>\n      <td>New York Times</td>\n      <td>Benjamin Mueller and Al Baker</td>\n      <td>2017-06-19</td>\n      <td>2017.0</td>\n      <td>6.0</td>\n      <td>NaN</td>\n      <td>After the bullet shells get counted, the blood...</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>17285</td>\n      <td>Tyrus Wong, ‘Bambi’ Artist Thwarted by Racial ...</td>\n      <td>New York Times</td>\n      <td>Margalit Fox</td>\n      <td>2017-01-06</td>\n      <td>2017.0</td>\n      <td>1.0</td>\n      <td>NaN</td>\n      <td>When Walt Disney’s “Bambi” opened in 1942, cri...</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>17286</td>\n      <td>Among Deaths in 2016, a Heavy Toll in Pop Musi...</td>\n      <td>New York Times</td>\n      <td>William McDonald</td>\n      <td>2017-04-10</td>\n      <td>2017.0</td>\n      <td>4.0</td>\n      <td>NaN</td>\n      <td>Death may be the great equalizer, but it isn’t...</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>17287</td>\n      <td>Kim Jong-un Says North Korea Is Preparing to T...</td>\n      <td>New York Times</td>\n      <td>Choe Sang-Hun</td>\n      <td>2017-01-02</td>\n      <td>2017.0</td>\n      <td>1.0</td>\n      <td>NaN</td>\n      <td>SEOUL, South Korea  —   North Korea’s leader, ...</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "_uuid": "4df388d860c7f5ac98f3ca6c8f422c5e30b1404c"
      },
      "cell_type": "markdown",
      "source": "## Parse and find all numbers in 50.000 news articles (with titles)"
    },
    {
      "metadata": {
        "trusted": true,
        "_uuid": "7b40124d2b704b119058746f03adb3a86c9d7a01"
      },
      "cell_type": "code",
      "source": "numbers = []\nfor i, row in df.iterrows():\n    article_txt = row['content']\n    title_txt = row['title']\n    \n    article_numbers = re.findall(r'[1-9][0-9]*', article_txt)\n    title_numbers = re.findall(r'[1-9][0-9]*', title_txt)\n    \n    numbers.extend(article_numbers)\n    numbers.extend(title_numbers)",
      "execution_count": 31,
      "outputs": []
    },
    {
      "metadata": {
        "_uuid": "e7b243c403c659db5a5a1e158bd65f0815470e3f"
      },
      "cell_type": "markdown",
      "source": "## Count first and second digits of all numbers"
    },
    {
      "metadata": {
        "trusted": true,
        "_uuid": "71df8d56c020aea5f6fa832c3314349df32fb71f"
      },
      "cell_type": "code",
      "source": "first_digit = {}\nsecond_digit = {}\n\nfor num in numbers:\n    try:\n        first_digit[num[0]] += 1\n    except KeyError:\n        first_digit[num[0]] = 1\n    \n    try:\n        try:\n            second = num[1]\n        except IndexError:\n            continue\n        \n        second_digit[num[1]] += 1\n    except KeyError:\n        second_digit[num[1]] = 1",
      "execution_count": 33,
      "outputs": []
    },
    {
      "metadata": {
        "_uuid": "359f47172aeab2418c4a5c21298b98521ca68a13"
      },
      "cell_type": "markdown",
      "source": "## Plot results\n"
    },
    {
      "metadata": {
        "trusted": true,
        "_uuid": "43ad2c9bc88e4e9d74fb48bab3fc2e17cc2e66fb"
      },
      "cell_type": "code",
      "source": "plt.figure(figsize=(20, 7))\n\nplt.subplot(131)\nplt.bar([num for num in first_digit], [first_digit[num] for num in first_digit])\nplt.title('Occurences of first digits')\nplt.xlabel('First digit')\nplt.ylabel('Occurences')\n\nplt.subplot(132)\nplt.bar([num for num in second_digit], [second_digit[num] for num in second_digit])\nplt.title('Occurences of second digits')\nplt.xlabel('Second digit')\nplt.ylabel('Occurences')\n\nplt.subplot(133)\nplt.bar([num for num in range(1, 10)], [math.log10((num + 1) / num) for num in range(1, 10)])\nplt.title('Benfords Law')\nplt.xlabel('First digit')\nplt.ylabel('Distribution')",
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 65,
          "data": {
            "text/plain": "Text(0,0.5,'Distribution')"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<matplotlib.figure.Figure at 0x7f192f659978>",
            "image/png": 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kSdJImaCSJI1EkkVJbk3yrV7sU0m+2V43JPlmi++W5Ke9fR/rHfO0JFckWZbkhCRp8W2T\nLElyTfu7TYunlVuW5PIkT53uzy5JkiRpdSaoJEmjcgqwoB+oqldW1T5VtQ/wGeCzvd3Xju2rqjf0\n4icChwPz2mvsnEcC51XVPOC8tg1wYK/s4e14SZIkSSNkgkqSNBJVdSGwctC+1gvqd4HT13SOJDsA\nW1bVRVVVwGnAwW33QcCp7f2p4+KnVediYOt2HkmSJEkjYoJKkjQTPRO4paqu6cV2T3JZkguSPLPF\ndgKW98osbzGAR1fVzQDt76N6x9w4wTGSJEmSRmDTUVdAkqQBDmX13lM3A7tW1e1Jngb8W5K9gAw4\nttZy7kkfk+RwumGA7LrrrmuttCRJkqT1Yw8qSdKMkmRT4HeAT43Fqureqrq9vb8UuBZ4Al3vp517\nh+8M3NTe3zI2dK/9vbXFlwO7THDMaqrqpKqaX1Xz586d+2A/miRJkqQJmKCSJM00zwO+U1W/HLqX\nZG6SOe39HnQTnF/Xhu7dlWT/Nm/Va4DPt8MWAwvb+4Xj4q9pq/ntD9w5NhRQkiRJ0miYoJIkjUSS\n04GLgCcmWZ7ksLbrEB44OfqzgMuT/A9wFvCGqhqbYP2NwMeBZXQ9q85p8eOA5ye5Bnh+2wY4G7iu\nlf9n4I+n+rNJkkYvyYIkVydZluTIAfvfkOSKJN9M8pUke/b2vaMdd3WSF05vzSVp4+QcVBuQ3Y78\nwrRd64bjXjxt15K0YaqqQyeIv3ZA7DPAZyYovxTYe0D8duCAAfECjljH6j4ow74/e0+WpNW1Xrcf\noXtAsRy4JMniqrqqV+yTVfWxVv5lwAeABS1RdQiwF7Aj8F9JnlBV9w2rvv47XpLsQSVJkiRpw7Mv\nsKyqrquqnwFnAAf1C1TVj3qbD+f+BTMOAs5o8x9eT9fjdt9pqLMkbdSGlqBKsijJrUm+NS7+J62r\n7JVJ3tuLD+xGO1HX3CS7J/lakmuSfCrJZi3+0La9rO3fbVifUZIkSdKMtBNwY297eYutJskRSa4F\n3gu8eV2ObccfnmRpkqUrVqyYkopL0sZqmD2oTgEW9ANJfovuicSvVtVewPtavN+NdgHw0SRzel1z\nDwT2BA7tjQ1/D3B8Vc0D7gDG5i45DLijqh4PHN/KSZIkSdp4ZECsHhCo+khVPQ54O/DX63JsO97V\nXiVpigwtQVVVFwIrx4XfCBxXVfe2MmNLfk/UjXZg19y2UtNz6SbKBTgVOLh3rlPb+7OAA1p5SZIk\nSRuH5cAuve2dgZvWUP4M7v89sa7HSpKmwHTPQfUE4Jlt6N0FSZ7e4hN1o50ovh3ww6paNS6+2rna\n/jtb+QewS64kSZK0QboEmNemBdmMbrTG4n6BJPN6my8GrmnvFwOHtKlDdgfmAV+fhjpL0kZtulfx\n2xTYBtgfeDpwZpI9mLgb7aAEWq2hPGvZt3qw6iTgJID58+cPLCNJkiRpdqmqVUneBJwLzAEWVdWV\nSY4BllbVYuBNSZ4H/JxuypCF7dgrk5wJXAWsAo4Y5gp+kqTOdCeolgOfbUt8fz3JL4DtWXM32kHx\n24Ctk2zaekn1y4+da3mSTYGteOBQQ0mSJEkbsKo6Gzh7XOxdvfdvWcOxxwLHDq92kqTxpnuI37/R\nzR1FkicAm9ElmybqRjuwa25LcH0JeHk770Lg8+394rZN239+Ky9JkiRJkqQZaGg9qJKcDjwH2D7J\ncuAoYBGwKMm3gJ8BC1vyaMJutIO65rZLvB04I8m7gcuAk1v8ZOATSZbR9Zw6ZFifUZIkSZIkSQ/e\n0BJUVXXoBLteNUH5gd1oB3XNbfHr6Fb5Gx+/B3jFOlVWkiRJkiRJIzPdQ/wkSZIkSZKk1ZigkiRJ\nkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmg\nkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnS\nSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmS\nJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCS\nJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJI\nmaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiSNRJJFSW5N8q1e7Ogk\n30/yzfZ6UW/fO5IsS3J1khf24gtabFmSI3vx3ZN8Lck1ST6VZLMWf2jbXtb27zY9n1iSJEnSRExQ\nSZJG5RRgwYD48VW1T3udDZBkT+AQYK92zEeTzEkyB/gIcCCwJ3BoKwvwnnauecAdwGEtfhhwR1U9\nHji+lZMkSZI0QkNLUA16Mt7b9+dJKsn2bTtJTmhPsy9P8tRe2YXt6fc1SRb24k9LckU75oQkafFt\nkyxp5Zck2WZYn1GStP6q6kJg5SSLHwScUVX3VtX1wDJg3/ZaVlXXVdXPgDOAg1qb8FzgrHb8qcDB\nvXOd2t6fBRww1oZIkiRJGo1h9qA6hQFPxpPsAjwf+F4vfCAwr70OB05sZbcFjgL2o/sRclQv4XRi\nKzt23Ni1jgTOa0/Mz2vbkqTZ403tYcWi3j1/J+DGXpnlLTZRfDvgh1W1alx8tXO1/Xe28g+Q5PAk\nS5MsXbFixYP/ZJIkSZIGGlqCag1Pxo8H/hKoXuwg4LTqXAxsnWQH4IXAkqpaWVV3AEuABW3fllV1\nUVUVcBqDn4z3n5hLkma+E4HHAfsANwPvb/FBPZxqPeJrOtcDg1UnVdX8qpo/d+7cNdVbkiRJ0oMw\nrXNQJXkZ8P2q+p9xu9b1yfhO7f34OMCjq+pmgPb3UWuoj0/GJWkGqapbquq+qvoF8M90vWehu8/v\n0iu6M3DTGuK30T3s2HRcfLVztf1bMfmhhpIkSZKGYNoSVEkeBvwV8K5BuwfE1vfJ+KT5ZFySZpbW\nQ3bMbwNj8xguBg5pK/DtTje0++vAJcC8tmLfZnQTqS9uvWu/BLy8Hb8Q+HzvXGNzGr4cOL+VlyRJ\nkjQim669yJR5HLA78D9tLtqdgW8k2Zc1Pxl/zrj4l1t85wHlAW5JskNV3dx+6Nw65Z9EkvSgJTmd\n7h6/fZLldHMOPifJPnQPHW4A/gigqq5MciZwFbAKOKKq7mvneRNwLjAHWFRVV7ZLvB04I8m7gcuA\nk1v8ZOATSZbR9Zw6ZMgfVZIkSdJaTFuCqqquoDfcLskNwPyqui3JYrpJcc+gmxD9zpZgOhf4+94k\nuS8A3lFVK5PclWR/4GvAa4APtTJjT8aPY/Un5pKkGaSqDh0QPnlAbKz8scCxA+JnA2cPiF/H/UME\n+/F7gFesU2UlSZIkDdXQhvi1J+MXAU9MsjzJYWsofjZwHd2y4f8M/DFAVa0E/o5uCMclwDEtBvBG\n4OPtmGuBc1r8OOD5Sa6hWy3wuKn8XJIkSZIkSZpaQ+tBNcGT8f7+3XrvCzhignKLgEUD4kuBvQfE\nbwcOWMfqSpIkSZIkaUSmdRU/SZIkSZIkaTwTVJIkSZIkSRopE1SSJEmSJEkaKRNUkiRJkjY4SRYk\nuTrJsiRHDtj/tiRXJbk8yXlJHtvbd1+Sb7bX4umtuSRtnIY2SbokSZIkjUKSOcBH6Fb1Xg5ckmRx\nVV3VK3YZML+q7k7yRuC9wCvbvp9W1T7TWmlJ2sjZg0qSJEnShmZfYFlVXVdVPwPOAA7qF6iqL1XV\n3W3zYmDnaa6jJKnHBJUkSZKkDc1OwI297eUtNpHDgHN625snWZrk4iQHT3RQksNbuaUrVqx4cDWW\npI2cQ/wkSZIkbWgyIFYDCyavAuYDz+6Fd62qm5LsAZyf5IqquvYBJ6w6CTgJYP78+QPPL0maHHtQ\nSZIkSdrQLAd26W3vDNw0vlCS5wF/Bbysqu4di1fVTe3vdcCXgacMs7KSJBNUkiRJkjY8lwDzkuye\nZDPgEGC11fiSPAX4J7rk1K29+DZJHtrebw/8BtCfXF2SNAQO8ZMkSZK0QamqVUneBJwLzAEWVdWV\nSY4BllbVYuAfgUcAn04C8L2qehnwZOCfkvyC7oH+ceNW/5MkDYEJKkmSJEkbnKo6Gzh7XOxdvffP\nm+C4rwK/MtzaSZLGc4ifJEmSJEmSRsoeVFNgtyO/MG3XuuG4F0/btSRJkiRJkqaDPagkSZIkSZI0\nUiaoJEmSJEmSNFImqCRJkiRJkjRSJqgkSZIkSZI0UiaoJEmSJEmSNFImqCRJkiRJkjRSJqgkSZIk\nSZI0UiaoJEmSJEmSNFImqCRJkiRJkjRSJqgkSZIkSZI0UiaoJEmSJEmSNFImqCRJkiRJkjRSJqgk\nSZIkSZI0UiaoJEmSJEmSNFImqCRJkiRJkjRSJqgkSZIkSZI0UiaoJEmSJEmSNFImqCRJkiRJkjRS\nJqgkSZIkSZI0UiaoJEmSJEmSNFImqCRJkiRJkjRSQ0tQJVmU5NYk3+rF/jHJd5JcnuRzSbbu7XtH\nkmVJrk7ywl58QYstS3JkL757kq8luSbJp5Js1uIPbdvL2v7dhvUZJUmSJEmS9OANswfVKcCCcbEl\nwN5V9avA/wLvAEiyJ3AIsFc75qNJ5iSZA3wEOBDYEzi0lQV4D3B8Vc0D7gAOa/HDgDuq6vHA8a2c\nJEmSJEmSZqihJaiq6kJg5bjYF6tqVdu8GNi5vT8IOKOq7q2q64FlwL7ttayqrquqnwFnAAclCfBc\n4Kx2/KnAwb1zndrenwUc0MpLkiRJkiRpBhrlHFR/AJzT3u8E3Njbt7zFJopvB/ywl+wai692rrb/\nzlZekiRJkiRJM9BIElRJ/gpYBfzrWGhAsVqP+JrONagehydZmmTpihUr1lxpSZIkSZIkDcW0J6iS\nLAReAvx+VY0ljpYDu/SK7QzctIb4bcDWSTYdF1/tXG3/Vowbajimqk6qqvlVNX/u3LkP9qNJkiRJ\nkiRpPUxrgirJAuDtwMuq6u7ersXAIW0Fvt2BecDXgUuAeW3Fvs3oJlJf3BJbXwJe3o5fCHy+d66F\n7f3LgfN7iTBJ0gyxLqu9JtktyU+TfLO9PtY75mlJrmirt54wNu9gkm2TLGmrvS5Jsk2Lp5Vb1q7z\n1On+7JIkSZJWN7QEVZLTgYuAJyZZnuQw4MPAI4El/R8YVXUlcCZwFfCfwBFVdV+bQ+pNwLnAt4Ez\nW1noEl1vS7KMbo6pk1v8ZGC7Fn8bcOSwPqMk6UE5hUmu9tpcW1X7tNcbevETgcPpHm7M653zSOC8\nttrredzfHhzYK3t4O16SJEnSCG269iLrp6oOHRA+eUBsrPyxwLED4mcDZw+IX0e3yt/4+D3AK9ap\nspKkaVdVFybZbVzsi73Ni7m/p+xASXYAtqyqi9r2aXSrup5Dt6rrc1rRU4Ev0z3cOAg4rfWuvTjJ\n1kl2qKqbH+RHkiRJkrSeRrmKnyRJa9Jf7RVg9ySXJbkgyTNbbCe6uQfH9Fd1ffRY0qn9fVTvmEEr\nxD6Ai2lIkiRJ08MElSRpxhmw2uvNwK5V9RS64dufTLIl67Bya//0kz3GxTQkSZKk6TG0IX6SJK2P\n3mqvB4wtclFV9wL3tveXJrkWeAJd76ede4f3V3W9ZWzoXhsKeGuLT7RCrCRJkqQRsQeVJGnGmGi1\n1yRzk8xp7/egm+D8ujZ0764k+7fV+17D4FVdx6/2+pq2mt/+wJ3OPyVJkiSNlj2oJEkj0VZ7fQ6w\nfZLlwFF0q/Y9lG61V4CL24p9zwKOSbIKuA94Q1WtbKd6I92KgFvQzVk1Nm/VccCZbRXZ73H/Ahpn\nAy8ClgF3A68b3qeUJEmSNBkmqCRJI7Euq71W1WeAz0ywbymw94D47cABA+IFHLFOlZUkSZI0VA7x\nkyRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnS\nSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmSJEnSSJmgkiRJkiRJ0kiZoJIkSZIkSdJImaCSJEmS\nJEnSSJmgkiRJkiRJ0kiZoJIkSZK0wUmyIMnVSZYlOXLA/rcluSrJ5UnOS/LY3r6FSa5pr4XTW3NJ\n2jiZoJIkSZK0QUkyB/gIcCC/7MU6AAAgAElEQVSwJ3Bokj3HFbsMmF9VvwqcBby3HbstcBSwH7Av\ncFSSbaar7pK0sTJBJUmSJGlDsy+wrKquq6qfAWcAB/ULVNWXqurutnkxsHN7/0JgSVWtrKo7gCXA\ngmmqtyRttExQSZIkSdrQ7ATc2Nte3mITOQw4Z12PTXJ4kqVJlq5YseJBVFeSZIJKkiRJ0oYmA2I1\nsGDyKmA+8I/remxVnVRV86tq/ty5c9eropKkjgkqSZIkSRua5cAuve2dgZvGF0ryPOCvgJdV1b3r\ncqwkaWqZoJIkSZK0obkEmJdk9ySbAYcAi/sFkjwF+Ce65NStvV3nAi9Isk2bHP0FLSZJGqJNR10B\nSZIkSZpKVbUqyZvoEktzgEVVdWWSY4ClVbWYbkjfI4BPJwH4XlW9rKpWJvk7uiQXwDFVtXIEH0OS\nNiomqCRJkiRtcKrqbODscbF39d4/bw3HLgIWDa92kqTxHOInSZIkSZKkkTJBJUmSJEmSpJEyQSVJ\nkiRJkqSRMkElSZIkSZKkkTJBJUmSJEmSpJEyQSVJkiRJkqSRMkElSZIkSZKkkTJBJUmSJEmSpJEa\nWoIqyaIktyb5Vi+2bZIlSa5pf7dp8SQ5IcmyJJcneWrvmIWt/DVJFvbiT0tyRTvmhCRZ0zUkSZIk\nSZI0Mw2zB9UpwIJxsSOB86pqHnBe2wY4EJjXXocDJ0KXbAKOAvYD9gWO6iWcTmxlx45bsJZrSJIk\nSZIkaQYaWoKqqi4EVo4LHwSc2t6fChzci59WnYuBrZPsALwQWFJVK6vqDmAJsKDt27KqLqqqAk4b\nd65B15AkSZIkSdIMNN1zUD26qm4GaH8f1eI7ATf2yi1vsTXFlw+Ir+kaD5Dk8CRLkyxdsWLFen8o\nSZIkSZIkrb+ZMkl6BsRqPeLrpKpOqqr5VTV/7ty563q4JEmSJEmSpsB0J6huacPzaH9vbfHlwC69\ncjsDN60lvvOA+JquIUmSJEmSpBlouhNUi4GxlfgWAp/vxV/TVvPbH7izDc87F3hBkm3a5OgvAM5t\n++5Ksn9bve8148416BqSJEmSJEmagTYd1omTnA48B9g+yXK61fiOA85MchjwPeAVrfjZwIuAZcDd\nwOsAqmplkr8DLmnljqmqsYnX30i3UuAWwDntxRquIUmSJEmSpBloaAmqqjp0gl0HDChbwBETnGcR\nsGhAfCmw94D47YOuIUmSJEmSpJlppkySLkmSJEmSpI3UOieokmySZMthVEaSNLvZRkiSJElaH5NK\nUCX5ZJItkzwcuAq4OslfDLdqkqTZwDZCkjRMSeYmeWeSk5IsGnuNul6SpKk12R5Ue1bVj4CD6SY0\n3xV49dBqJUmaTWwjJEnD9HlgK+C/gC/0XpKkDchkJ0l/SJKH0P34+HBV/TxJDbFekqTZwzZCkjRM\nD6uqt4+6EpKk4ZpsD6p/Am4AHg5cmOSxwI+GVSlJ0qyyXm1EG6Jxa5Jv9WLbJlmS5Jr2d5sWT5IT\nkixLcnmSp/aOWdjKX5NkYS/+tCRXtGNOSJI1XUOSNGP9R5IXjboSkqThmlQPqqo6ATihF/pukt8a\nTpUkSbPJg2gjTgE+DJzWix0JnFdVxyU5sm2/HTgQmNde+wEnAvsl2RY4CpgPFHBpksVVdUcrczhw\nMd3QwwXAOWu4hiRpZnoL8M4kPwN+3mJVVS7KMcV2O3L6Rk7ecNyLp+1akmaHyU6S/ugkJyc5p23v\nCSxcy2GSpI3A+rYRVXUhsHJc+CDg1Pb+VLphg2Px06pzMbB1kh2AFwJLqmplS0otARa0fVtW1UVV\nVXRJsIPXcg1J0gxUVY+sqk2qavP2/pEmpyRpwzPZIX6nAOcCO7bt/wXeOowKSZJmnVOYujbi0VV1\nM0D7+6gW3wm4sVdueYutKb58QHxN13iAJIcnWZpk6YoVK9bzI0mSHqwkL0vyvvZ6yajrI0maepNN\nUG1fVWcCvwCoqlXAfUOrlSRpNpmONiIDYrUe8XVSVSdV1fyqmj937tx1PVySNAWSHEc3zO+q9npL\ni0mSNiCTTVD9JMl2tH/cJ9kfuHNotZIkzSZT2Ubc0obn0f7e2uLLgV165XYGblpLfOcB8TVdQ5I0\nM70IeH5VLaqqRXRzCjppuiRtYCaboHobsBh4XJL/ppvL40+GVitJ0mwylW3EYu6fv2oh8Ple/DVt\nNb/9gTvb8LxzgRck2aatxvcC4Ny2764k+7fV+14z7lyDriFJmrm27r3famS1kCQNzWRX8ftGkmcD\nT6QbNnF1Vf18LYdJkjYC69tGJDkdeA6wfZLldKvxHQecmeQw4HvAK1rxs+meli8D7gZe1669Msnf\nAZe0csdU1djE62+kmx9rC7rV+85p8YmuIUmamf4BuCzJl+jamWcB7xhtlSRJU21SCaokRwD/WlVX\ntu1tkhxaVR8dau0kSTPe+rYRVXXoBLsOGFC2gCMmOM8iYNGA+FJg7wHx2wddQ5I0M1XV6Um+DDyd\nLkH19qr6wWhrJUmaapMd4vf6qvrh2EZbyvv1w6mSJGmWsY2QJE25JE9qf58K7EA3v+CNwI4tJkna\ngEyqBxWwSZK0J9gkmQNsNrxqSZJmEdsISdIwvA04HHj/gH0FPHd6qyNJGqbJJqjOpZuv42N0jcEb\ngP8cWq0kSbOJbYQkacpV1eHt7YFVdU9/X5LNR1AlSdIQTTZB9Xbgj+gmnA3wReDjw6qUJGlWsY2Q\nJA3TV4HxQ/oGxSRJs9hkV/H7BXBie0mS9Eu2EZKkYUjyGGAnYIskT6F7CAKwJfCwkVVMkjQUk13F\n7zeAo4HHtmNCt6jSHsOrmiRpNrCNkCQNyQuB1wI7Ax/oxe8C3jmKCkmShmeyQ/xOBv4UuBS4b3jV\nkSTNQrYRkqQpV1WnAqcm+T9V9ZlR10eSNFyTTVDdWVXnDLUmkqTZyjZCkjRMeyfZa3ywqo4ZRWUk\nScMx2QTVl5L8I/BZ4N6xYFV9Yyi1kiTNJrYRkqRh+nHv/ebAS4Bvj6gukqQhmWyCar/2d34vVsBz\np7Y6kqRZyDZCkjQ0VfX+/naS9wGLR1QdSdKQTHYVv98adkUkSbOTbYQkaZo9DHAhDknawGwymUJJ\nHp3k5CTntO09kxw23KpJkmYD2whJ0jAluSLJ5e11JXA18MFR10uSNLUmlaACTgHOBXZs2/8LvHUY\nFZIkzTqnYBshSRqelwAvba8XADtW1YdHWyVJ0lSbbIJq+6o6E/gFQFWtwqXEJUkd2whJ0tBU1XeB\n7YCDgN8BfmW0NZIkDcNkE1Q/SbId3aS3JNkfuHNotZIkzSa2EZKkoUnyLuBUuiTV9sApSf56tLWS\nJE21ya7i9za6lTIel+S/gbnAy4dWK0nSbGIbIUkapkOBp1TVPQBJjgO+Abx7pLWSJE2ptSaokmwC\nbA48G3giEODqqvr5kOsmSZrhbCMkSdPgBrq25p62/VDg2pHVRpI0FGtNUFXVL5K8v6qeAVw5DXWS\nJM0SthGSpGFJ8iG64eP3AlcmWdK2nw98ZZR1kyRNvckO8ftikv8DfLaqapgVkiTNOrYRkqRhWNr+\nXgp8rhf/8vRXRZI0bOsyB9XDgVVJ7qEbwlFVteXQaiZJmi1sIyRJU66qTh11HSRJ02dSq/hV1SOr\napOq2qyqtmzb/vCQJNlGSJKGIsmZ7e8VSS4f/5rE8QuSXJ1kWZIjB+x/VpJvJFmV5OXj9t2X5Jvt\ntXjqPpUkaSKT6kGV5FmD4lV14dRWR5I029hGSJKG5C3t70vW9cAkc4CP0M1XtRy4JMniqrqqV+x7\nwGuBPx9wip9W1T7rel1J0vqb7BC/v+i93xzYl24s+HPX56JJ/hT4Q7pJDq8AXgfsAJwBbEu3bOyr\nq+pnSR4KnAY8DbgdeGVV3dDO8w7gMOA+4M1VdW6LLwA+CMwBPl5Vx61PPSVJkzKlbYQkSQBVdXNL\nNJ1cVc9bx8P3BZZV1XUASc4ADgJ+maDq/ab4xdTUWJL0YEx2iN9Le6/nA3sDt6zPBZPsBLwZmF9V\ne9MlkQ4B3gMcX1XzgDvoEk+0v3dU1eOB41s5kuzZjtsLWAB8NMmc3tOSA4E9gUNbWUnSEExlGyFJ\nUl9V3QfcnWSrdTx0J+DG3vbyFpuszZMsTXJxkoMnKpTk8FZu6YoVK9axipKkvsn2oBpvOd0PkAdz\n3S2S/Bx4GHAz3ZP232v7TwWOBk6ke9JxdIufBXw4SVr8jKq6F7g+yTK6JyWwlqclkqSherBthCRJ\nffcAVyRZAvxkLFhVb17DMRkQW5eVZnetqpuS7AGcn+SKqrr2ASesOgk4CWD+/PmuZCtJD8Jk56D6\nEPff0DcB9gH+Z30uWFXfT/I+ujHfPwW+SDcU5IdVtaoV6z/h+OXTj6paleROYLsWv7h36v4x45+W\n7DfB5zocOBxg1113XZ+PI0kbvalsIyRJGuAL7dW3tmTQcmCX3vbOwE2TvWBV3dT+Xpfky8BTgAck\nqCRJU2eyPaiW9t6vAk6vqv9enwsm2YauR9PuwA+BT9MNxxtvrNGZ6OnHRPFBwxYHNmA+8ZCkKTFl\nbYQkSQNsXVUf7AeSvGWiws0lwLwkuwPfp5sa5PfWfMgvz70NcHdV3Ztke+A3gPeue7UlSetisgmq\ns4B72hhw2lxPD6uqu9fjms8Drq+qFe1cnwV+Hdg6yaatF1X/CcfY04/lSTYFtgJWsuanIuv9tESS\ntM6mso2QJGm8hXQLIPW9dkDsl9rIizcB59LNebuoqq5McgywtKoWJ3k68DlgG+ClSf62qvYCngz8\nU5s8fRPguHGr/0mShmCyCarz6BJLP27bW9ANzfv19bjm94D9kzyMbojfAXRP378EvJxuJb+FwOdb\n+cVt+6K2//yqqiSLgU8m+QCwIzAP+Dpdz6r1eloiSVovU9lGSJIEQJJD6f4dv3v7t/+YLelW916j\nqjobOHtc7F2995fQPcwef9xXgV9Zz2pLktbTZBNUm1fV2A8PqurHLcG0zqrqa0nOAr5BNxTkMrph\ndl8Azkjy7hY7uR1yMvCJNgn6SrqEE+0JyJl0k5+vAo7oPb1/wNOS9amrJGlSpqyNkCSp56t0iylt\nD7y/F78LuHwkNZIkDc1kE1Q/SfLUqvoGQJKn0fV+Wi9VdRRw1Ljwddy/Cl+/7D3AKyY4z7HAsQPi\nD3haIkkamiltIyRJAqiq7wLfTfI84KdV9YskTwCeBFwx2tpJkqbaZBNUbwU+nWRsLqcdgFcOp0qS\npFnGNkKSNEwXAs9sk5efRzc9yCuB3x9prSRJU2pSCaqquiTJk4An0s3x9J2q+vlQayZJmhVsIyRJ\nQ5aqujvJYcCHquq9SS4bdaUkSVNrk8kUSnIE8PCq+lZVXQE8IskfD7dqkqTZwDZCkjRkSfIMuh5T\nX2ixyY4EkSTNEpNKUAGvr6ofjm1U1R3A64dTJUnSLGMbIUkaprcC7wA+1xZK2oNuBXBJ0gZksk8e\nNkmSqiqAJHOAzYZXLUnSLGIbIUkamqq6ALigt30d8ObR1UiSNAyTTVB9ETgzyceAAt4I/OfQaiVJ\nmk1sIyRJUy7J/62qtyb5d7r2ZTVV9bIRVEuSNCSTTVD9Dd1wjTfQTYD7ReDkYVVKkjSr2EZIkobh\nE+3v+0ZaC0nStFhjgirJpsDfA68DbqT74bELcD3d/FX3DbuCkqSZyTZCkjRMVXVp+3tBkrnt/YrR\n1kqSNCxrmyT9H4FtgT2q6qlV9RRgd2ArfJIhSRs72whJ0tCkc3SS24DvAP+bZEWSd426bpKkqbe2\nBNVL6FZnumss0N6/EXjRMCsmSZrxbCMkScP0VuA3gKdX1XZVtQ2wH/AbSf50tFWTJE21tSWoamxV\npnHB+xgwUaEkaaNiGyFJGqbXAIdW1fVjgbaC36vaPknSBmRtCaqrkjzg5p/kVXTdbCVJGy/bCEnS\nMD2kqm4bH2zzUD1kBPWRJA3R2lbxOwL4bJI/AC6leyL+dGAL4LeHXDdJ0sw2lDYiyROBT/VCewDv\nAramWy1wbILcd1bV2e2YdwCH0U3M/uaqOrfFFwAfBOYAH6+q41p8d+AMujm0vgG8uqp+tr51liQN\nxZruy96zJWkDs8YEVVV9H9gvyXOBvehWaDqnqs6bjspJkmauYbURVXU1sA9AkjnA94HP0a0WeHxV\nrTYBe5I9gUNaHXYE/ivJE9rujwDPB5YDlyRZXFVXAe9p5zojycfoklsnPph6S5Km3K8l+dGAeIDN\np7sykqThWlsPKgCq6nzg/CHXRZI0Cw25jTgAuLaqvptkojIHAWdU1b3A9UmWAfu2fcvafCUkOQM4\nKMm3gecCv9fKnAocjQkqSZpRqmrOqOsgSZo+a5uDSpKkUToEOL23/aYklydZlGSbFtsJuLFXZnmL\nTRTfDvhhVa0aF3+AJIcnWZpk6YoVKwYVkSRJkjQFTFBJkmakJJsBLwM+3UInAo+jG/53M/D+saID\nDq/1iD8wWHVSVc2vqvlz585dh9pLkiRJWheTGuInSdIIHAh8o6puARj7C5Dkn4H/aJvLgV16x+0M\n3NTeD4rfBmydZNPWi6pfXpIkSdII2INKkjRTHUpveF+SHXr7fhv4Vnu/GDgkyUPb6nzzgK8DlwDz\nkuzeemMdAiyuqgK+BLy8Hb8Q+PxQP4kkSZKkNbIHlSRpxknyMLrV9/6oF35vkn3ohuPdMLavqq5M\nciZwFbAKOKKq7mvneRNwLjAHWFRVV7ZzvR04I8m7gcuAk4f+oSRJkiRNyASVJGnGqaq76SYz78de\nvYbyxwLHDoifDZw9IH4d96/0J0mSJGnEHOInSZIkSZKkkbIHlSRJkiRpRtjtyC9M6/VuOO7F03o9\nSROzB5UkSZIkSZJGygSVJEmSJEmSRsoElSRJkiRJkkbKBJUkSZIkSZJGygSVJEmSJEmSRsoElSRJ\nkiRJkkbKBJUkSZIkSZJGygSVJEmSJEmSRsoElSRJkiRJkkbKBJUkSZIkSZJGygSVJEmSJEmSRsoE\nlSRJkiRJkkbKBJUkSZIkSZJGaiQJqiRbJzkryXeSfDvJM5Jsm2RJkmva321a2SQ5IcmyJJcneWrv\nPAtb+WuSLOzFn5bkinbMCUkyis8pSZIkSZKktRtVD6oPAv9ZVU8Cfg34NnAkcF5VzQPOa9sABwLz\n2utw4ESAJNsCRwH7AfsCR40ltVqZw3vHLZiGzyRJkiRJkqT1MO0JqiRbAs8CTgaoqp9V1Q+Bg4BT\nW7FTgYPb+4OA06pzMbB1kh2AFwJLqmplVd0BLAEWtH1bVtVFVVXAab1zSZIkSZIkaYYZRQ+qPYAV\nwL8kuSzJx5M8HHh0Vd38/9u7/6i7qvrO4+9PE1EUFKpoKYEGlbEDTAuaAi0ty0qLAaxgB0dYHUWH\nmXQstDptx8a2Uy3WtXC1o60dayeVDNAigQFZZhTFWH/VtgLhpwSkRKCSQiE2lB/FSoPf+ePu2Jtw\nE0LIc/fJ87xfaz3rOXeffe7+nsuTsznfu8/eAO33C1v9/YC7x45f18q2Vb5uQvkTJFmSZHWS1evX\nr3/6ZyZJkiRJkqSnrEeCaj7wcuDDVXU48E/86+N8k0yaP6p2oPyJhVXLqmpRVS3aZ599th21JEmS\nJEmSZkSPBNU6YF1VXdVeX8ooYXVfezyP9vv+sfr7jx2/ALjnScoXTCiXJEmSJEnSAE09QVVVfw/c\nneRlrehY4BZgJbBpJb7TgY+37ZXAm9pqfkcBD7ZHAK8Ejkuyd5sc/Tjgyrbv4SRHtdX73jT2XpIk\nSZIkSRqY+Z3a/UXgwiS7AXcAb2GULLskyRnAN4DXt7pXACcAa4FHW12qakOS9wDXtHpnV9WGtv1W\n4Dxgd+BT7UeSJEmSJEkD1CVBVVU3AIsm7Dp2Qt0CztzK+ywHlk8oXw0c+jTDlCRJkiRJ0hT0mINK\nkiRJkiRJ+i4TVJIkSZIkSerKBJUkSZIkSZK6MkElSZIkSZKkrkxQSZIkSZp1kixOcluStUmWTth/\nTJLrkmxMcsoW+05Pcnv7OX16UUvS3GWCSpIkSdKskmQe8CHgeOBg4LQkB29R7RvAm4GPbnHs9wLv\nAo4EjgDelWTvmY5ZkuY6E1SSJEmSZpsjgLVVdUdVPQasAE4ar1BVd1XVTcB3tjj21cCqqtpQVQ8A\nq4DF0whakuYyE1SSJEmSZpv9gLvHXq9rZTv12CRLkqxOsnr9+vU7FKgkacQElSRJkqTZJhPKamcf\nW1XLqmpRVS3aZ599tjs4SdITmaCSJEmSNNusA/Yfe70AuGcKx0qSdpAJKkmSJEmzzTXAQUkOTLIb\ncCqwcjuPvRI4LsnebXL041qZJGkGze8dgCRJkiTtTFW1MclZjBJL84DlVbUmydnA6qpameRHgMuB\nvYGfSfLbVXVIVW1I8h5GSS6As6tqQ5cTUTcLl35yam3ddc6JU2tLGjITVJIkSZJmnaq6Arhii7Lf\nGtu+htHje5OOXQ4sn9EAJUmb8RE/SZIkSZIkdWWCSpIkSZIkSV2ZoJIkSZIkSVJXJqgkSZIkSZLU\nlQkqSZIkSZIkdWWCSpIkSZIkSV2ZoJIkSZIkSVJXJqgkSYOT5K4kX01yQ5LVrex7k6xKcnv7vXcr\nT5IPJlmb5KYkLx97n9Nb/duTnD5W/or2/mvbsZn+WUqSJEnaxASVJGmofrKqDquqRe31UuDPq+og\n4M/ba4DjgYPazxLgwzBKaAHvAo4EjgDetSmp1eosGTtu8cyfjiRJkqStMUElSdpVnASc37bPB04e\nK7+gRr4C7JVkX+DVwKqq2lBVDwCrgMVt33Or6q+rqoALxt5LkiRJUgcmqCRJQ1TAZ5Jcm2RJK3tR\nVd0L0H6/sJXvB9w9duy6Vrat8nUTyp8gyZIkq5OsXr9+/dM8JUmSJElbM793AJIkTXB0Vd2T5IXA\nqiRf20bdSfNH1Q6UP7GwahmwDGDRokUT60iSJEl6+hxBJUkanKq6p/2+H7ic0RxS97XH82i/72/V\n1wH7jx2+ALjnScoXTCiXJEmS1IkJKknSoCR5TpI9N20DxwE3AyuBTSvxnQ58vG2vBN7UVvM7Cniw\nPQJ4JXBckr3b5OjHAVe2fQ8nOaqt3vemsfeSJEmS1IGP+EmShuZFwOWj3BHzgY9W1aeTXANckuQM\n4BvA61v9K4ATgLXAo8BbAKpqQ5L3ANe0emdX1Ya2/VbgPGB34FPtR5IkSVInJqgkSYNSVXcAPzyh\n/B+AYyeUF3DmVt5rObB8Qvlq4NCnHawkSZKkncJH/CRJkiRJktSVCSpJkiRJkiR1ZYJKkiRJkiRJ\nXTkHlSRJkiRJA7Rw6Sen1tZd55w4tbakSRxBJUmSJEmSpK5MUEmSJEmSJKmrbgmqJPOSXJ/kE+31\ngUmuSnJ7kouT7NbKn9ler237F469xztb+W1JXj1WvriVrU2ydNrnJkmSJEmSpO3XcwTV24Bbx16/\nD/hAVR0EPACc0crPAB6oqpcCH2j1SHIwcCpwCLAY+KOW9JoHfAg4HjgYOK3VlSRJkiRJ0gB1SVAl\nWQCcCHykvQ7wKuDSVuV84OS2fVJ7Tdt/bKt/ErCiqr5dVXcCa4Ej2s/aqrqjqh4DVrS6kiRJkiRJ\nGqBeI6h+H3gH8J32+vnAP1bVxvZ6HbBf294PuBug7X+w1f9u+RbHbK38CZIsSbI6yer169c/3XOS\nJEmSJEnSDpg/7QaTvAa4v6quTfLKTcUTqtaT7Nta+aSkW00oo6qWAcsAFi1aNLGOnjqXQpUkSZIk\nSU/F1BNUwNHAa5OcADwLeC6jEVV7JZnfRkktAO5p9dcB+wPrkswHngdsGCvfZPyYrZVLkiRJkiRp\nYKb+iF9VvbOqFlTVQkaTnH+uqn4O+DxwSqt2OvDxtr2yvabt/1xVVSs/ta3ydyBwEHA1cA1wUFsV\ncLfWxsopnJokSZIkSZJ2QI8RVFvza8CKJL8DXA+c28rPBf40yVpGI6dOBaiqNUkuAW4BNgJnVtXj\nAEnOAq4E5gHLq2rNVM9EkiRJ2olmegoFp02QJPXWNUFVVV8AvtC272C0At+Wdf4ZeP1Wjn8v8N4J\n5VcAV+zEUCVJkiRJkjRDeq3iJ0mSJEmSJAEmqCRJkiRJktSZCSpJkiRJkiR1NaRJ0iVJkiRJ0sDM\n9EIN41y0Ye5yBJUkSZIkSZK6MkElSZIkSZKkrkxQSZIkSZIkqSsTVJIkSZIkSerKBJUkSZIkSZK6\nMkElSZIkSZKkrkxQSZIkSZIkqav5vQOQZruFSz85tbbuOufEqbUlSZIkSdLO4ggqSZIkSZIkdWWC\nSpIkSZIkSV35iJ9mLR+tkyRJkqTZw3u82c0RVJIkSZIkSerKBJUkSZIkSZK6MkElSZIkSZKkrkxQ\nSZIkSZIkqSsTVJIkSZIkSerKBJUkSZIkSZK6MkElSZIkadZJsjjJbUnWJlk6Yf8zk1zc9l+VZGEr\nX5jkW0luaD9/PO3YJWkumt87AEmSJEnamZLMAz4E/DSwDrgmycqqumWs2hnAA1X10iSnAu8D3tD2\nfb2qDptq0JJ2GQuXfnJqbd11zolTa6s3R1BJkiRJmm2OANZW1R1V9RiwAjhpizonAee37UuBY5Nk\nijFKksY4gkqSJGkXNtPf4s6lb241q+wH3D32eh1w5NbqVNXGJA8Cz2/7DkxyPfAQ8JtV9ReTGkmy\nBFgCcMABB+y86CVpDnIElSRJkqTZZtJIqNrOOvcCB1TV4cAvAx9N8txJjVTVsqpaVFWL9tlnn6cV\nsCTNdSaoJEmSJM0264D9x14vAO7ZWp0k84HnARuq6ttV9Q8AVXUt8HXg38x4xJI0x5mgkiRJkjTb\nXAMclOTAJLsBpwIrt6izEji9bZ8CfK6qKsk+bZJ1krwYOAi4Y0pxS9KcZYJKkjQoSfZP8vkktyZZ\nk+RtrfzdSf5ubNnvE8aOeWdbJvy2JK8eK5+4xHi7Ybkqye1tifHdpnuWkqSZVFUbgbOAK4FbgUuq\nak2Ss5O8tlU7F3h+kv0PhVUAABLzSURBVLWMHuXb1E8cA9yU5EZGk6f/16raMN0zkKS5x0nSJUlD\nsxH4laq6LsmewLVJVrV9H6iq3xuvnORgRt+MHwJ8P/DZJJsexdjaEuPva++1IskfM1pq/MMzfmaS\npKmpqiuAK7Yo+62x7X8GXj/huMuAy2Y8QEl6mmZ6oZRx01g0xRFUkqRBqap7q+q6tv0wo2++99vG\nIScBK9qcIXcCaxktLz5xifG2hPirGH0rDqMlxk+embORJEmStD1MUEmSBivJQuBw4KpWdFaSm5Is\nT7J3K5u0lPh+2yh/PvCP7fGP8fJJ7S9JsjrJ6vXr1++EM5IkSZI0iQkqSdIgJdmD0SMWb6+qhxg9\ngvcS4DBGS4D/z01VJxxeO1D+xEKXD5ckSZKmwjmoJEmDk+QZjJJTF1bVxwCq6r6x/X8CfKK93NZS\n4pPKvwnslWR+G0U1aelxSZIkSVPkCCpJ0qC0OaLOBW6tqvePle87Vu11wM1teyVwapJnJjmQ0XLg\nV7OVJcarqoDPM1pSHEZLjH98Js9JkiRJ0rY5gkqSNDRHA28Evprkhlb268BpSQ5j9DjeXcDPA7Rl\nwy8BbmG0AuCZVfU4QJJNS4zPA5ZX1Zr2fr8GrEjyO8D1jBJikiRJkjqZeoIqyf7ABcD3Ad8BllXV\nHyT5XuBiYCGjG4//UFUPtG/S/wA4AXgUePOm1Z2SnA78Znvr36mq81v5K4DzgN0ZLS37tvaNuSRp\n4Krqy0yeJ+qKCWWbjnkv8N4J5U9YYryV38FolT9JkiRJA9BjBNVG4Feq6rokewLXJlkFvBn486o6\nJ8lSYCmjb7iPZ/S4xkHAkYwmyT2yJbTeBSxi9G36tUlWVtUDrc4S4CuMbkwWA5+a4jlKg7Jw6Sen\n2t5d55w41fYkSZIkSbu2qc9BVVX3bhoBVVUPA7cyWt77JOD8Vu184OS2fRJwQY18hdHEtvsCrwZW\nVdWGlpRaBSxu+55bVX/dRk1dMPZekiRJkiRJGpiuc1AlWQgcDlwFvKiq7oVREivJC1u1/YC7xw5b\n18q2Vb5uQvmk9pcwGmnFAQcc8PRORpIkfddMj9x0pKYkSdLs0i1BlWQPRkuIv72qHhpNNTW56oSy\n2oHyJxZWLQOWASxatMg5qiRJs8o0Hu81USRJkqSdYeqP+AEkeQaj5NSFVfWxVnzfpiXE2+/7W/k6\nYP+xwxcA9zxJ+YIJ5ZIkSZIkSRqgqSeo2qp85wK3VtX7x3atBE5v26cDHx8rf1NGjgIebI8CXgkc\nl2TvJHsDxwFXtn0PJzmqtfWmsfeSJEmSJEnSwPR4xO9o4I3AV5Pc0Mp+HTgHuCTJGcA3gNe3fVcA\nJwBrgUeBtwBU1YYk7wGuafXOrqoNbfutwHnA7oxW73MFP2kAprmaoI8dSZIkSdKuY+oJqqr6MpPn\niQI4dkL9As7cynstB5ZPKF8NHPo0wpQkSZIkSdKUdJmDSpIkSZIkSdrEBJUkSZIkSZK66jEHlSR1\nNZS5sIYShyRJkiT15ggqSZIkSZIkdeUIKkmSNGvM9MjEnqMiHQkpSZJmMxNUkiRJ0naYxqPZJiIl\nSXOVj/hJkiRJkiSpK0dQSZIk6SnrOZrIxyklSZp9HEElSZIkSZKkrkxQSZIkSZIkqSsTVJIkSZIk\nSerKBJUkSZIkSZK6MkElSZIkSZKkrkxQSZIkSZIkqSsTVJIkSZIkSerKBJUkSZIkSZK6MkElSZIk\nSZKkrkxQSZIkSZIkqSsTVJIkSZIkSerKBJUkSZIkSZK6MkElSZIkSZKkrkxQSZIkSZIkqSsTVJIk\nSZIkSerKBJUkSZIkSZK6MkElSZIkSZKkrkxQSZIkSZIkqSsTVJIkSZIkSerKBJUkSZIkSZK6MkEl\nSZIkSZKkrkxQSZIkSZIkqSsTVJIkSZIkSerKBJUkSZIkSZK6MkElSZIkSZKkrkxQSZIkSZIkqSsT\nVJIkSZIkSerKBJUkSZIkSZK6mrUJqiSLk9yWZG2Spb3jkSQNi/2EJM1uT3adT/LMJBe3/VclWTi2\n752t/LYkr55m3JI0V83KBFWSecCHgOOBg4HTkhzcNypJ0lDYT0jS7Lad1/kzgAeq6qXAB4D3tWMP\nBk4FDgEWA3/U3k+SNINmZYIKOAJYW1V3VNVjwArgpM4xSZKGw35Ckma37bnOnwSc37YvBY5Nkla+\noqq+XVV3Amvb+0mSZlCqqncMO12SU4DFVfWf2+s3AkdW1Vlb1FsCLGkvXwbcNsUwXwB8c4rtbY1x\nbM44Nmccm5urcfxAVe0zxfZm3C7QT/T6W+v5N+4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          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "_uuid": "8f6e088a23263c4de806c410a15edeeebde9c77a"
      },
      "cell_type": "markdown",
      "source": "As expected the digit 2 appears much more often than the distribution says, but apart from that, the distribution seems reasonable considering that our dataset is of course biased since we only included news articles."
    }
  ],
  "metadata": {
    "language_info": {
      "name": "python",
      "version": "3.6.4",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 1
}