Yelp_Reco_System.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from six.moves import cPickle\n",
    "import numpy as np\n",
    "from scipy.sparse import csr_matrix\n",
    "from sklearn.decomposition import TruncatedSVD\n",
    "from scipy.sparse.linalg import svds\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import mean_squared_error\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Data Loading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading the review data file and business file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_full = pd.read_csv('review.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>business_id</th>\n",
       "      <th>cool</th>\n",
       "      <th>date</th>\n",
       "      <th>funny</th>\n",
       "      <th>review_id</th>\n",
       "      <th>stars</th>\n",
       "      <th>text</th>\n",
       "      <th>useful</th>\n",
       "      <th>user_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>0</td>\n",
       "      <td>2016-07-12</td>\n",
       "      <td>0.0</td>\n",
       "      <td>VfBHSwC5Vz_pbFluy07i9Q</td>\n",
       "      <td>5.0</td>\n",
       "      <td>My girlfriend and I stayed here for 3 nights a...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>cjpdDjZyprfyDG3RlkVG3w</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>0</td>\n",
       "      <td>2016-10-02</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3zRpneRKDsOPq92tq7ybAA</td>\n",
       "      <td>3.0</td>\n",
       "      <td>If you need an inexpensive place to stay for a...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>bjTcT8Ty4cJZhEOEo01FGA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>0</td>\n",
       "      <td>2015-09-17</td>\n",
       "      <td>0.0</td>\n",
       "      <td>ne5WhI1jUFOcRn-b-gAzHA</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Mittlerweile gibt es in Edinburgh zwei Ableger...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>AXgRULmWcME7J6Ix3I--ww</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>0</td>\n",
       "      <td>2016-08-21</td>\n",
       "      <td>0.0</td>\n",
       "      <td>llmdwOgDReucVoWEry61Lw</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Location is everything and this hotel has it! ...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>oU2SSOmsp_A8JYI7Z2JJ5w</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>0</td>\n",
       "      <td>2013-11-20</td>\n",
       "      <td>0.0</td>\n",
       "      <td>DuffS87NaSMDmIfluvT83g</td>\n",
       "      <td>5.0</td>\n",
       "      <td>gute lage im stadtzentrum. shoppingmeile und s...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0xtbPEna2Kei11vsU-U2Mw</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              business_id  cool        date  funny               review_id  \\\n",
       "0  uYHaNptLzDLoV_JZ_MuzUA     0  2016-07-12    0.0  VfBHSwC5Vz_pbFluy07i9Q   \n",
       "1  uYHaNptLzDLoV_JZ_MuzUA     0  2016-10-02    0.0  3zRpneRKDsOPq92tq7ybAA   \n",
       "2  uYHaNptLzDLoV_JZ_MuzUA     0  2015-09-17    0.0  ne5WhI1jUFOcRn-b-gAzHA   \n",
       "3  uYHaNptLzDLoV_JZ_MuzUA     0  2016-08-21    0.0  llmdwOgDReucVoWEry61Lw   \n",
       "4  uYHaNptLzDLoV_JZ_MuzUA     0  2013-11-20    0.0  DuffS87NaSMDmIfluvT83g   \n",
       "\n",
       "   stars                                               text  useful  \\\n",
       "0    5.0  My girlfriend and I stayed here for 3 nights a...     0.0   \n",
       "1    3.0  If you need an inexpensive place to stay for a...     0.0   \n",
       "2    3.0  Mittlerweile gibt es in Edinburgh zwei Ableger...     0.0   \n",
       "3    4.0  Location is everything and this hotel has it! ...     0.0   \n",
       "4    5.0  gute lage im stadtzentrum. shoppingmeile und s...     0.0   \n",
       "\n",
       "                  user_id  \n",
       "0  cjpdDjZyprfyDG3RlkVG3w  \n",
       "1  bjTcT8Ty4cJZhEOEo01FGA  \n",
       "2  AXgRULmWcME7J6Ix3I--ww  \n",
       "3  oU2SSOmsp_A8JYI7Z2JJ5w  \n",
       "4  0xtbPEna2Kei11vsU-U2Mw  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_full.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_bus = pd.read_csv('business.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Columns in business data file are:\n",
      "address\n",
      "attributes_AcceptsInsurance\n",
      "attributes_AgesAllowed\n",
      "attributes_Alcohol\n",
      "attributes_Ambience\n",
      "attributes_BYOB\n",
      "attributes_BYOBCorkage\n",
      "attributes_BestNights\n",
      "attributes_BikeParking\n",
      "attributes_BusinessAcceptsBitcoin\n",
      "attributes_BusinessAcceptsCreditCards\n",
      "attributes_BusinessParking\n",
      "attributes_ByAppointmentOnly\n",
      "attributes_Caters\n",
      "attributes_CoatCheck\n",
      "attributes_Corkage\n",
      "attributes_DietaryRestrictions\n",
      "attributes_DogsAllowed\n",
      "attributes_DriveThru\n",
      "attributes_GoodForDancing\n",
      "attributes_GoodForKids\n",
      "attributes_GoodForMeal\n",
      "attributes_HairSpecializesIn\n",
      "attributes_HappyHour\n",
      "attributes_HasTV\n",
      "attributes_Music\n",
      "attributes_NoiseLevel\n",
      "attributes_Open24Hours\n",
      "attributes_OutdoorSeating\n",
      "attributes_RestaurantsAttire\n",
      "attributes_RestaurantsCounterService\n",
      "attributes_RestaurantsDelivery\n",
      "attributes_RestaurantsGoodForGroups\n",
      "attributes_RestaurantsPriceRange2\n",
      "attributes_RestaurantsReservations\n",
      "attributes_RestaurantsTableService\n",
      "attributes_RestaurantsTakeOut\n",
      "attributes_Smoking\n",
      "attributes_WheelchairAccessible\n",
      "attributes_WiFi\n",
      "business_id\n",
      "categories\n",
      "city\n",
      "hours_Friday\n",
      "hours_Monday\n",
      "hours_Saturday\n",
      "hours_Sunday\n",
      "hours_Thursday\n",
      "hours_Tuesday\n",
      "hours_Wednesday\n",
      "is_open\n",
      "latitude\n",
      "longitude\n",
      "name\n",
      "neighborhood\n",
      "postal_code\n",
      "review_count\n",
      "stars\n",
      "state\n"
     ]
    }
   ],
   "source": [
    "print(\"Columns in business data file are:\")\n",
    "for i in df_bus.columns:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Data Exploration, Data Cleaning and Matrix Building "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.a. Number of businesses in each city:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x25702ac4a58>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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DShsTlMxVQsw+NHIQQghRQspBCCFECSkHIYQQJaQchBBClNCEtHhVoslrIQaHlIMQtIsA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\nhBCixP8H7SFKmPp6bfAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25702ac42b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_bus_groups = df_bus.groupby('city').count()\n",
    "df_bus_city = df_bus_groups['name']\n",
    "df_bus_city_sorted = df_bus_city.sort_values(ascending = False)\n",
    "df_bus_city_sorted[:30].plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.b. Different Type of Businesses and their Count:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x25700948cf8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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X3Wm5spua1F3btTd37/9Per8oLUylNe61H+CuulvhD/gLgR81kZ+OjxgyV9l3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\njgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x257009485c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "uniq_cat_dict = {}\n",
    "for i in df_bus.categories:\n",
    "    cat = str(i).split(',')\n",
    "    for j in cat:\n",
    "        if j not in uniq_cat_dict.keys():\n",
    "            uniq_cat_dict[j] = 1\n",
    "        else:\n",
    "            uniq_cat_dict[j] += 1\n",
    "uniq_cat_series = pd.Series(uniq_cat_dict)\n",
    "uniq_cat_series.sort_values(ascending = False, inplace = True)\n",
    "uniq_cat_series[:30].plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.c. Business and City Ordered pairs and their count:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x257017c98d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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R13tP5cAHPMFnUjblCFwP3dKQdGLF8U/gg5/lOR591XEP8mfjEwhn4dekeC8Y\nUKwY9KK3d+HnWOTAijTI08VLizvpGXhFXSGaXJO6+7JF6f78EL707PFVosBre5SF5nquu2Zi+LUr\n0vgd141xbQAkvRf3EX6hpKKVXQFXXhX/NrM/S1pM0mJmdrWkL9bIvtrMXipptpl9Rj5IO+xl3uqO\nMbN3NijzTrjBWkdSsUa1ItUDO4fhL8ND8Au7PT7AW8eyZnZVGnz6PfBpSb/AjcIwzCe9tJqi0yT9\nqibfp83saUmtyTp3S3pRSabVnfDlDuUrshv+AlkXOLmQ/iQ+jtBTOczs1PTZ6eUJgKRd8LAc65Re\nIisClV1QeMtqQ4aMw5txN8UDJW1vZoeVytNPHWfJm9kb0uf6HfJpyebobW/8Zb6+pOIzsSIexqPu\nPzrqQtLH8PGwFSS1aritF97pHYrU5Jo0vS8xs4PS5/b9lE1yjfTc5JrVkPOO68i4NgB4KIGr8C6P\nwwvpT1r97N+/SFoe76v8nqRHqX/QWzNan5K0NvBnfFC1Evlo+5uBSRR0V+oyehR3w3sav0EXlLl0\nDq1jb0p5WxMDQ16L4Sm5x8atko7D5zksVyP7oKSV8an4MyQ9jruuFcs6K3028mAys2n4S+CtZnZu\nk2OalKOF3FviPQy/HsV+4YdwV8bdaa80PAn8b00ZXgC8tjVGIekUPMTA6/HB7yJ91fFI5CWtgzsy\nFHVR1ZfdRG834s/DuriPeosn8cHbKpro4ji8Jt32TJf7yivoek2a3pdlJL2a4bo4sw+yTfTcks0Z\nG8p5x3VkkRgDgAUDwRNoV+Swh0EpUh9eq9gP9wf+Xs3Ay5F4n+UO+E1u+GBmZe1U0uV4s3MWsOCG\nNbNhTUNJy1QNOqXfFkwblwe6Oh33iV5P0qbAe83s/TXHvgKYg8dEOjqd33Fmdn2F7ETcIC2Jv+xW\nwgNMza3Ku3Dctkn2cktT8ku/b4XHMmq9bORqGD4OkeSXwl1tJ9F+/T4/wnL8Cp8IU74eF1TIftTM\njiulHWpmJ1TI3oPPxCwGfrvBzDaUu/1uVpAdFR3nyqca4N74AHtLF1bulkuyjfWWQ64uJD0X778u\n3hOVrafMa5IzTnYWPrv+Vtr1dshIZJN8Iz0rf2yo8TuuK9aD69BYb3jogD/h7lFz0nZXn/9jaWCl\nLjJ3ZOS3JR7I6i7cfexe4Dfpt4MZCqR1Ax4b6JZe/qeP579qxbZkjezdwC54y2O11tYh758wFEDu\nY62tD+W4NeP8hk1Ion5S1YF49NJpuBvkPDzw3XLAl8ZCxz3o4h5SiJAG5cjR2x7pees6AzdTF8fg\nrsFXpufkMmpmtOdeE3wS5g6yT2ctAAAgAElEQVS4G+hEvLLymZp858Dw4Gojlc3RM96CWYahiakb\nAj8YqY6bbOO9C6jFh/FZgPO7CUp6kuEDQU/g3QAftkKoWVV49Uh6ArjdqruYfiVpEzMrdwNUMQ33\ndW6z/olv4oO41wGY2QNqn7RS2xyuGehqnd+pVmh1SLq9g+znrL3GcDNuiB7HaxYrAw+n5uV7LHX/\ntPIws8vqyljBRDN7SUPZnHL8WNKu5utMVyKfNPc2vC/74sJPK+BdHGV54S+lS/EQFwI+bkOtzf8r\nyY+WjnPl5+E17ybumV31VuB4fBZy13s+UxdvAV5oNa3kUr5Z14S8cbI78PkLD3crR6YsNNdz1thQ\nzjuuG4uKAXgQqHSJquAreD/p2fiNsg9+0e4BzsADqLU4EJ/MdHXa3w6Pw/1CSZ+14T7UWwPvkHQf\n/qC1uj5eynD+amaXVBXQvL+z1Wx8IPUrWuoqOQSvadQxD+8K+37a3xt4BI8J/i08vGyLy3Bjcnba\n3yeV+Qm8FlX0arocuNDMrgCQtCM+mH0uPoC7RUH2aklfwgfMF7xwrOQOV+B6SRtZYUZpB3LKcSjw\ncUn/Av7F0PVYsSDzK/yBXZ12L44n8RpiG2Zmkn5kZi/HJ1N1Y7R0nCv/FN73fhXt16Sqe6KJ3lo8\n0rDCA3m6uI+Gs1d7uCY542SrA3dJupF2vQ3rOsuUheZ6zh0bynnHdWSRGAOQ9G18gOTHtCt+mGuY\npBvMbItS2vVmtqWk28xs00L6JcC7LYWZkLQmPtPx3fjElJeU8plYVb5UyyiX4wvpa/klObsktzo+\ny/F1+MW8EjjU6lfMutbMtqlKk3SnFXyBJf3SzLYqyf7SzLZSYd5BSp9pZlNKsjPNbIqkW83sZYX0\nqxmOWX2f5e24gZpLu+GsmgfQuBy5pOvbcjW8saaVh6RvAN+xiolJFbKjouNceUmVnmNmNr3bOXQ5\nv6/hFY4f0X4fX1whm6OL83BX0J+W8q30nc+8JjnjZNtW5WEVA8o5sr3SZGwo5x3XjUWlBfBw2qpq\nKGWelfRWPLwCeFOzRdnaTbL2GEOP4s3SxyQNi+1tZr+XtDU+BXuafJR/+ZpybF36bP3/gpe3PP7H\nAWa2X9ezGmKCCjMSJa2H10zAaxlFlpe0hZndkGRfWShv2WvgMbmL3jlpf2/g8VTGNvdVa+gOV2DP\nDNnG5UhdA/sB65vZ0ZKeB6xlZsPmckjaC3cTvAY3QCdJ+j8zO78si7vivlfS74G/07mlNyo6zpU3\ns+mSlsXj3d9TkdcCcvSGj+88i3tRLfg7PHRBmRxdXJ62pjS+JgUj8Td8nkwtZvbzVLGbbB6v6zn4\nBLYRyUJ3Pat6IlirtbU89b0eOe+4ztgYDDT0a6NBbH188sQl+KDx/PT9BenYrUuyJ+OtiqlpuySl\nLQdcXZH3UUmmNZi7NvDLEZ7TNZnyu+KDZ1fjL7Pf4/72ywGHlWRfkW6o+9I2G+9DXQ54a0l2ddwj\n6pa0nYTX/JaiFMUQj8Z6Or7EHri3xYFdyt0o9ntmORqH0cVj5axR2J9AfUTSiVVbjeyo6LgHXbyR\n5iGQs8IPZ9ybjXWR5ButM9D0mtBDiHXcTfMm4LdpfzIeimFEsk30nHQ0L33+B39n/Tl9v69Dvo3f\ncV2v2Ugv+lhs+AvmJnws4A+450yj0LBd8hXu1/9VfPm1t9BhlB930RLNwsyugPs8X5+2L5IWcSjJ\nHYPPoHwNHvhrc7os7oB7LG2aHvJlGpznStQsGlMhu3wDmcvwpQFb8eqXwAfO6+SzYr9nlKNxGN1y\n+fD+58oy466Jw7ax1HEPuqgKgVx3fjl6WxuffNVqhf8AWHukuiBjnYGm14ShcOqtwHFvTNvZwOdr\n8r0VN6hN9NZYNkfPuFPIroX9XagJdtnvbdT/oC+F7BJbvyT7Qnzy2B1p/6XAJzvkPZG00g8+I3fY\nS7oge2Ppwi5HvQE4D3+5vzBtR1MRnRGvyZe3n3Uow3PwMBPfSvuTSesiV8g2rqnja6jeBdyf9jfF\nfbirZG9Kn8Ubu9bljYzY75nluAFvgreuxwTqXTu/hAcFe0faLgO+WCN7eyrz7bj77jPUR30dFR33\noouKa1Kn4xy9XYHXfJdO27uBK/qgi8brDPRwTa5tklalN7wyU6u3prI5egZmVemnQ75Z77hOW/YB\nC2Mjb0GRn+PNzq5+9eQ36T6Ch8adl479NWlRlgrZYS/EmrTnN0kr/PYD3L20dfGXrco3/da4pk7G\nfAS862m1wo29JTUrP6Xfb6fgo55eJP0oRyuM7h9oFkb3zbgHxVepWVGu5rjNcRfbMdNxD7rICYHc\nWG9N7+MedDHsxVmV1uM1mVN8hvDZ/XNqZI/D56fcjc8qvhA4ZqSyOXrGjewn8YmSE/GYYZVGNsk3\nfsd11WMvB431RsPY+km2ce2UzCZd+v31eG3yy9TEtE9y1wOvKuxviQf1KstVTVAaViMo/Daz4vzq\njGGOLqpqkHX5bo433Z9In7+hc1z7qtjvHxlpOdJvG+IT6w6mD92CHf6nbmWrUdFxD9fkOeklcxNe\nuz6GDt2DTfWGB0FsuXMKH4iubKFm6uI7NFxnoIdrsjM+TnZN2n4H7FQjuxhemTsPH1R9DzXdwDmy\nOXrGJ/idwNBYz9eAVTvkmdUC77QtKl5A78K7UFoTKq6lfnT/T5I2YGh1nbdQP3Hjn2b2L6VJWPK4\n9dalLLPxGiz4wGId/w/4rjx+EHjcoQU++vLIjhsDK6l9QtqKFKavV/Cv5O3ROr8NqJ/883f5ugQt\n2S3xl3YVjecjmNnNyV3tRfhL4R5LoS1q5I9LrqOt2O/vs3p3vtx5EUunPMGNeRsamjTTCji24Cdq\nfN/VHsa3tShL3STEUdFxrrz5qnSfkHRsOq+/dcgXuuitwLtwx4hWqJTr8fkzVeTo4n34+Xw0leNa\nvNVSSc41MbPL5eEgNkxJd1vN+gVm9qyk6XhrHvxernwH5MgW6Kpn87DPh8ICz8DlrLTuSImcd1xn\nerEaY7nhfWjHZsg/H/ctfgpvel1HvQdHbpPurbjXzXR8YfP7gLfUlPnNBes+LEwCPsV+Gj7qP62w\nnYhHKa0rw+vxJuB84Ht47Wa7GtnGNXXc4+R7+KSyR/FF3CvDO+AzTg/Ba0Hn44O8dSEKFqdDLXeE\n5TgUn535GXw1rNup6ZLLvOeOKmyfwJvylbXp0dJxD7rYBK89/j5ts4CXjERv6dodkqG3RrpI+ebW\n9nOuyV6ksTyGwrJXOlbgk6Z+n56pa/FnepuRymbq+Wy84rcc/i56mIrV0Qryjd9xXfU60odlLDY6\nDIoWZNYs7S9HhwHdJJPVpCPPlbB2acmS3KuayJWOWQ13/XwDsHrF70sWvi+BtzReQsVLGpjSw/9/\nGzeCr03bNDyIXp3894F1uuTZSzlm47Wl4jWv6ltejB76SNNDWXkPjaaOe9TFr4DtC/vbUb+0YSO9\npd9qx3Z60UVB7spOv/dyTYrnlz63xoOx7UHqTquQnQW8qLD/Qmq6YHNkM+/PVgyg/fAxqiVr5LLf\ncd22RaUL6GZ5TPLz8EkgwLDZiLelGaffx71taptQkj6CB1t6AA+f8K2G5VjM2meP/pn66exXSDoM\nH7QtlrlcrrmSPk6XkLGS7sJrg+eY2W/xAGt1/EHSRbgurjazOzvIfkseWvb7wPet2cLbr7D22YY/\nk9SpO2x1YI6kX9Oui2LXVy/lEO1xk/7DUHN7AeZN99tUsaRfZabSFNyorZD2n8DXgi3G3hlNHfei\ni+XM7OrWjpldI48aWUUjvSV+IV8C9Bzar11xRnuOLlrMS3lfVMq3auGXptekeD7glaRTzOwiSZ+u\nKceSVpg4Z2a/kVS3kH2OLDTX85Ipnz2Br5vZv1W9oH3jd1xTFhUDsCZ+k+xaSDPaZyOug7uH7gN8\nIb1svo8PFv+DdtbBA7vdl2TOM7M/NSjH5ZKuoD0OT12gp/emzw+XyrxeSe4ivJbyUzoEgcNX/NkH\nuFLSn1IZzrWKkNi4S91b8EVXzpR0Pv4iuaEsaL6i0ItS3hfI45Z8Hzc0w0JcJP4jaYNkiJD0/C5l\nP7bDbyMpxzTgBkkXpv09qV9UZC3gTnkcl+ILpyqOyxn4PIVfAKTZ39NoX8Vq1HTcoy7mycObt+JX\n7Y93UVSRo7dt02cxbIdRmNFOhi4KzAdm4IPXdavDFWlyTVr8QdKp+Pvgi2kcrq6iNlPS6QzpbT/q\nF5vKkYXmej4V78q9Dbg2zTauGjvJecc1YpGIBZRLGjDbBVfU9rhr534lGeE38T54E/E2XJkXmtmT\nHfJ+M7AVLFjI+sI62YZlzY5vkwbX9sbdGufiD1tlK0a+0M1e+Hmugb9EPtEh702T7FuBP1optkuS\n2QG/uefhepgIvLNYA604ZnV8mUBwT6aOBrdJOZLcy2m/HpWLlSgv5kttTJuavPuu41x5+YIin6F9\n8fZPm9njNXk20lsuPehiWYBuL7Cca5JCNOyMe/TdK2ktYBMzu7JCdmlSeHaG9HayVQwa58gWjumq\nZ0nrm9l9hX3hM73v7ZBv13dcI0bSfzRWG73NRpwMfAofiKqc5FKQXRzYCR9Ee6pPZV4CeD/edD4H\n93oYNt0d+ByFWYCZ/7FdKvM/u8gtj6/Peise3bFObjF8kPkM4I/AjzrILo3XvjalSxx63FDdj3dh\nnY3Xdmr98DPLsXi6PxrN2O1SztZM7K/itbLt8BrwyXRwDhgtHfcin3GujfRGwxntubqg4ez+Xq4J\ncFaTtLHYmuiZTFfwgkzjd1zdtki0AFK3y/m45w24O+VeZrZTSW49vGa8Lz5Acg5eA6ntQ5UvVr5P\nOu7PeG36azWyb8IfgDUY8os2q3YlPDWVoVXm/fG43weV5J5Mcv8CWq6UlXkm+Vek83sz/iI9h4ou\nLEnL4NPg98VrIJcn2SuttPyepNckuT1xr4VzgAssrb5UU46cpfFuA3a09qirV1opamFuOSR9EPcK\neYSh/lWzigBhqdV0Et5dsRT+YP69qGdVRzktnF57tNPR1HEP8i/EJypOov2aDIvQmqm38/AXTCuq\n6AH4i/otJbnGukjy1+GLtMxI+6/DWyxbl+Syrkk65mYrRJpNrpW3m9lGFbLl1e1aGVetHtZYNsl3\n1LOGXMGPo31NgxVxL6CNKdHLO64jC8Mq9mBFu85GxL0gfo9P0OroRYFbziPxafa3425ltbNvC8fN\npeFkIzJmLzfM7/PAb/FJPh8B1u0gezbuNng+3jfbaULQA7jL3gcpeRl0OOaspO+T8ZfqScCJHeS7\nxuHpsRxz6eBGWZKdiQfMugV/+b+TmvgwDfMbNR33qIvb8LknrwRe3tr6oLcmz15jXRTL2yQt85oc\nga/z8Ay+ellrBbM/U+NKTsbqdjmyTfRMpis4Ge+4xjrrRyajvdFgNiLeLGy6tNs8fKbkJpnlaBz5\nM71oJhX2J1Efb2X3dFG/TH1cn6PwUNVN/nsqDd3D6MF/mPyl8Y7HB8v3T9uPgS/3oRxX0yWKZEG2\nNYN6diGtzk3yULwWJtzl9Wa8BTMmOu5RF127DHrUW9cZ7Tm6KBzTeHZ/kl8aD3Xxcbzb41PAp2pk\nv5BRjkr30JHK5uiZirkEVATGy3nHNd0WlS6gSQytgGT4TflBKwycjPL/t9wVt8VX3ikvjvHDimNe\nj4/4/wZ/kbwAD4z105LcsXgY3e+lpH3xh/nwPp9G30jdAoeYWaPZh2lQay/aB8/Otx5vPg3NCt0Y\nn438E9qvx1cqjrkW96D4Nt6X/jDwDqtYPENpUQ1JO+GDfkcC06xiAZuFjYZiyh+C18IvpF0XjxVk\ne9Hb5niLr21Gu5ndOsJyr4bP7m91+VwLHGX1CyFdjnvGlBdYP75C9ioz26FTWjov8IH1xemwul2O\nbJLP0nO5y6oubTQY1wZA0gfM7OvjoBzTOvxsVvDZl7SlpZWHkofDi/GX3l1W4ekgaTbwMjN7Nu0v\njrcUqtzbFioaWo94BTwUdcel8SRdaWY7jkI5jur0u5l9puKYiXhf7FLA/+Ihi082s7kVsrPN7KVy\n//drzOxCSbeY2Wb9OYP+IXdlrsOs0D+dozdJbypWbJKhUd0LOqO8nzezj/dw3B3WZV3pNA6xHN5j\nsB0s8LlfEY9Q+uKCbOOxhR7GhhrpWdKr8Iivh+GD3C1WxJ0kGq/s1Svj3QCMiRVsiqTVrbv7YlaZ\nkwHYrlVTSw/aNePUAGzb6XcruVSO5ktTvhrbRGCumf2lz3lPw32u18e9nBbHr8nL+/k/C4Omehut\nZ6/XfCWdBpxkHdYnlnQo/jJdm/Y1df+Kh08fs8pkEz2n52k73EPwm4WfngQusQ5uoH2jn/1J/d6o\nifbX5Zhi/+3pVPTf1hy3CvUxXN6AT1x5CHdb6xSrJ6vMeJfP7/HoiNPxyTv7dJDfijS9HO9P/wr1\nsY5yYqIcl/S2JB5r/E/A/hVye+KD0JXRFUuy84A31W29lgMPRvYoHpTrj8DuDcqyFT7x6DepXPOA\neTWyrWBjK6f91TrcG33XcaYuJuNdknfQJeRGjt56fPa66gIfrF4Fj5E1bOuQ9124p9w9DK0LUBe+\noms8KLw7+TZ82chf0zkiamPZXu5P0vOLt6ybLP7T0zuuMq9eDhqrjfbR/OL2JPDXmmNasch3wmcK\nb1p3M+OhYldMN9/9eP/iVyrkZgMbFm6GTrHv/0L+snRr4QPBewDP7aKT2enCb5q+H1pXHvJiorTi\nkfwPbohWpeSVgY/D/Bz4At79c2SXsv4Z91+fVrGdMYJy3AFMSN+fD/y6wb2U4+0xbE2IqrTR0HEP\nuvgFHsPqRbgr4Q875NdYb3igsdkVW6cXb1dd4F2GrWUQy1ulQU7HTazaamRbkVNrgxXiXmGvx8c2\n9qJz/P3Gsr3cn3jcpEaB/JJ843dct228h4K43fK7EFr9frviA3e3pUHIKlYys79KeneSPSp1yZR5\nxszuBjCzGySt0OH/5+NeL50LOTSw1OLB9Lm2pLWtNLBUKotJ2gM4wcxOlzS1RjYrJkr63BWfC/FY\nhdq2ATY1s/+k2Za/wAfy6vi9lWIaNaBJOf5lZvMBzGyehkJud+IJM7usk0DqQ34OsHqaWVvsQ167\n5rB+6zhXfgUbmgX+JUl19w3k6e0+3K8/hya6uCvnmZa0onnMm9rZ+RWcjOvu5LR/AL7ewLsLMotZ\nmoMAnCfpiA755chC/v15GvAhSzPpJW2X0l5dI5/zjuvIeDcAvTBL0pV4/+0R6WX9bI3sEvJp4m/F\n5wLUsYba45G37Vv7qP6TVhFeoIKZ+Nq4rZjmxQtoeJTNKp5MN+D+wDZp0LguIFVOTJRLJN2Ne3m8\nP/VhPl2S+ZelST1m9lSDm66Xm7JJOdaVdGLdvpkdsqAAQ4b2aklforMHx3sZ6kOeVSj/X/F4+FX0\nW8e58stI2qxQ1mWL+6Xza6w3/FrXxR2qI0cXTTkb74KdxdC6Di0Mr2GXaRKscGW1r8PRtm/tnn05\nspCnZ8gL5Ad577iOjPdB4I+b2eczj1kM91CZZ2Z/Se5m61h79MKW7F64i991ZvZ+eVCzL5nZm0ty\nOd4TP7T2KJd15fxffDbvE/hsvgut+yIeSHou7g99k5n9Qj4zcDurmIWrjJgoSX4VvGutVcNf0cz+\nWPj9KXxyC/iDuEHar5xJKuklZnZHt3PqoRx1LR7wgkwvyGZ5cKRjDrFSVEpJS1t1fJi+6jhXPtOb\nJUdvXzezD3SSryhrV11IeoeZfScn31xSK2gvaw9WeL61zw7O8exrLJvkG+s5yV+I9+MXA/lNMbM9\nq47Pecd1Y1wbgF5JD81kCitrmdm1C69E9UhaHx8I3gPv//u8jdDHuuI/1qBdF5UhkSW9BI/RUpQ9\ns/D7xE7/00ONsZJu5RhtqjxVunmv9EvHI5UfDzTVRcO8OnoMVXWVqodghQsTtQfyA58T8RmrCeRX\nOGbk77jcQYPxvuH9fLcDj+Mz8f5B/Rqmy+ATfU7GByvPoGZwcpTLvDHel/474K1dZLfEg2j9DfeK\n+A/ev10luztwLx7++L4ke2eN7FFJX4/gD88f8VrTWOuir+UAPoRPwCunfxA4rJT2XDyEwhxgM4YC\nkW2HLys4pjoeL9ckQ9eNdZGR59Vp+zUeK2sm3h30b7zlXndc42CFi9qW847rmtfCPplRUM7t6cXe\n8qDYEF/8pUr2vPTi/S0+nf1KfGB1LMr5fHxa+w3kxVBpHNMGd11bjRSCAg8be1oHvS3GkIfBmrgv\n8sK4fn0rB+6RsVRF+tKUvFnSPXA1PuB4dWG7mHq31VHT8Xi5Jhm6bqyLHvI+h0LoFtxz5js1sgeT\nXHjT/ir4WgILXUc15Z1RUd5OXkmN33HdtpEO0CwUJO0haYuan582s6eT3NLm3jsvqpF9gZkdiUeF\nnI57L2zS/xKDpLVK3gBz8cHny/HazXr4QN+HSgPOwzCfvbq4mf3HzKbhNdQq/m0+c3MxSYuZN4Hr\n1h74h/ls5GckrYj7MVdGORwpkqZLOiV1b4x2OczM/lWR+E9Kg9RmNt3MtsdDRGxf2Ha3inAfidHU\n8Zhdk6ZImiJpnZqfc3RRzvf9kvaWVOeYsqEVJoGZjy3V5f0eK0y+Mu9KeU+TciwkVq8o7xod5HPe\ncR1ZVL2AtgA2kbSEme1S+u1BSSvjk2NmSHqc9lmBRVrhl/+SXkZ/xIO2NULuivlH67zyUYuzgA0k\nXWBmH8EXiW4NwCzf9D+Bp+SLQdwq6Tg8pk2dx8Bf5EsLXgt8T9Kj+NyKKmYmvX0Lb2L/Dff1Hw2+\njhu8A4CP9asckt6Pzz24wMyeKaSvaSkUdTGt4vj9zey7wKQqI2wVsXIYXR2PRBdrAY9Zh8VKCrKV\neqvhg8BLJf3GzPYu/Zaji2HFwPvA98O7ksrMkfRt4Lv4c7M/3lVXxWKSZKl6LPeUW6pRIXzpyYfN\n7A/9lE3ydXp+VoXlStNYW6fB2Zx3XOcyJR39VyKfar0SHgfk3xW/vxu4AK/1fwd/ER9pZqc2zP/z\n6dgqQ1QlL2Aja7Zmal0eExke0+YbljweSrLL4f2Di+EP1krAd60QIKzmPybhvu9/suolJ8vy0/GJ\nQ9+wHrx++liOg/Hm8ERLcYkkvR2fFPRh3NMCvJ//uFTeoufLe83s1DqvL6uOMTRWOs6V/ynupdWq\ncHSSHaa3BvmvYKWV83rVRcP/WwYPd91aivJafK7BMDdaubvvJDy8guGhFh4wsw+XZSuOnY6PHVQZ\nuJ5lk3ylniXtjPv9t9zHtwEOMrMrGuTZ8R3X9fhFwQDI3TUvN7MnJX0SH5g72houYyfpfjMrr8Vb\nJ/tmM7tgBGVdtdPv/XgYKv7zB01uwCRbu7RhhWwjvckXqVkPeKWZlWv0aCiIXJEn8PGMU6se4l7K\n0eH4XfBwwy9J5bgTjw9fOTFMDWI+dfm/vuu4F/k+VTi2wvua/y5pf/zZO8EaenzV6SK1wD6Pr+y3\ni6SN8LDTp5fkWhPBqvJeUGsupS8GHITPRxA+tvdtq1iYpkO5hxm4fsh2yGN13MEDPNx21v3X8zPS\ny8DBWG9kTLevOf6BDNn7O/xWFetks5LMfQxNdf8PHr/lz+n7faOkn9oyj1AXjWW75HMCPqHnjWn7\nLr72wTdosFRfXTnoY0yUlF/jmE8LS8dleWpi6lARWwf3iKrdav6vceiRzGt3GT4G1hrgXoLSIkEp\n/ebC96vqfqv5j6Vwb641OsjkxNZqLJtk1kz35WVpfyMKHmm4e+pKhf3t07PyISocF/p5H7W2RWUQ\neNgUcxr26SVymjmdZq8ead4K2RqPwzGd9ih+mNn65iF4rwDeaGarm9lq+MulbiBxLMnRRaWspEsk\nXVzazpJ0aGqql9nMzN5mZpekbX+8tXAwXqPstczvMq8d7ghMwD2ijm2QXx2fB15jZmvjk/S+0GM+\nI9Zxhvwshlwj5+PB7u5N32eVZFfoslXxjPkbphV65IQOsk3K22J1MzuXNIPVvE+8qoZefB7Lreu2\nZ1XSNyVtnL6vhK9JfCZwi6R9a8pxCj6utinwUXwuTt08ixxZ8G7lKxgKI/IbfKZ5i3NJ43eSXoZ7\nJd6PG9uTyaOnrpxFZRC46xTzqkG71k/kDbJ2UmRO3JdXmNn7FmRqdpmkTnFzgPqBZdVPiBGlUBBq\nn7Zell22JHsS1ecsYOWafObhL9zvp/298XGJF+IDlgeU5CeUBrnWA1ZPv/1rBOXoW0yUROOYT6Op\n4xx5M1s/HfNNPNjgpWl/F/x5KcoOG8NoQNfQIzm6KPB3+QzW1kDtlni3YBmr+V61/5rCM/dOvG9+\nT/ns+csYul+L5MTWypGFZOSS/jCzZyQVjdyyNjSesz8+B+n41IU1bDJoH99xC1hUDMBb8SnmXzaf\n+rwW7YsoQ+dayQnFHUm3U/+ADfMOKZAT6+RPabyi6LXQZDGNOg+nTgHm7i7tdwri9ePS/swOsnW/\nbWZm2xT2L5F0rZltI6mqv/nDwHWSfovreH3c5XU5hhYb76UcfYuJksiJ+TSaOu5FF40rHKmVdiA+\nAbE4k7QqcN/eeOiRA83sj8l4f6kkk6OLFh/C51dsIOmXeIXiLRVyrWsg2q+H0jFFiu6+r8dr1KRy\n15WvZeAOAF5TZeAqZJvE4YLuRq5YqNfiS2RiZs/WlLfxO64pi8og8FlmdkC3tIz8Jnb63WoGuJQR\n9yUNBh9Fu9fCZ2wUBoHHGklz8PUAijX6y81sI9UsApOM5Yb4TX+3dRn4bViOnmOiVLW01MNKY+MF\nSVfg42PFCsc2ZrZThex5eKXhbbg78n7AHDM7dAzKuZeZnScPgfIA7r8u4B6r9tRrfE3kcZGOB/6A\nT+DbML38lwDuMLMNK/LPia3VWDbJvxxf4P0lpBDRwFta96d8xbm1cFfu3fE1v/+d3iuXmNmUTufe\nF3oZOBjrjdJgDz4D9urUZNMAACAASURBVK6FUI5hA5ZVaaXfV6TDIg80GFgebxve5XI//pBdg/eF\n7ob3Zx5Wc8yr8Yfn7a2tD+UQ/qL7VNpveSI1OfbzwCWkAbpFfcP7x0/AZ4jfkr5XLrDC0EzdlnPF\nktSHS2kceqRhOW8ufvZZBy/EJ1beik/ma6XvBBzf4biJwOvS9+eQucB9lzItgbe0XsLwNQkE7IO7\nc69TSN+MBgsu9WMb1y2A1Nz6ON6P+FQrGb8RTzOzbnG5+12etoBgqQl4u5ltVCG7CT5A1Bq4+hMw\n1Up+8hpaf3ZrfNDxy8DHzaxupvO4IKdGL+ks3Cf9VobGUcyGh8XNLcMpeJfPa83sxfIAWVea2StG\nku+ijHzG8LPWIbKspBvN7JWSrgXej0+AvNEK6wcXZGfiL6nzgCm48Z5sPazrm/Kbgb8UX4a3WNqw\nhvMQ+oWk9+Auo6ua2QaSJgPftNKi8kl2S+AkfJ3vpfCK6N/MbKWavG8DfoCHaRg2T2dcMBZWpg9W\n9AsL+f+PwOPDFFcoexLv068sG/ArYPvC/nbAryrkWrWxLwBvK6aN542MGj0+Y1OjUIZWbfKWQlrl\nClssgi2tTF1sQsNVpfBgYqvg3ZPz8BAT76uRnZk+ZxfSht3HGeVcCm9V3AtsW94Wgt5uTWUq3kPD\n3FFbuqBhHK4kPxH3FpqFt6I+Aqy3sO+VtjIu7AJkXKh10ktnm9bW8Lg9gC36VIbGhqjqRVST9mPg\nVDwg3cp4kLLaZQIrjl+LhtEO8Rpc7ZqxJdn34wOAS1T8dlYycCfjNaKTgBM75HUesFaPOu9UjhvS\ng9gyBBPqjCcjnEuSUd6+6LgHXTSqcPRwPtemF+SZ+Ozp/216f3bSBWnJxIW9te4BhipiS1C/5GXP\nxhAP3Xwm8J9ROIee33GLhBeQpGPxZuhdFLoQ8JuzG53iBpX/p2NIAzM7Qh4IayIFDyqrjsM9T9KR\ntC/ycF+FXBMPp06UYwx1olMclzKdYrNMwWeYNu0/XB24S9KNtK/G1aS536kcJwIX4t4hx+BeJJ+s\nySfHhbe9AHkxn/ql41z5xqtKyUOYHGcpAFnqOvuwmVXp7gDc0+0D+Mv/efgciSYM04Wkr5nZYcAZ\nkobdPw3vidxr0omfS/o4vpLa63Eje0mNbE4crlY5J+HP+N74PfjREZa3isbvuDLjegyghaR7gJda\ng8BWI/yfbiENKg1R1U2r9kUehBurT1tpkYd+eDhJeVP+NcKp68mL5BAze7ih/LZV6dZs6cxueW8I\n7IDr+CozqwwQJunHuHfI6/BYQP/A+703rZIvHZsV8ykdM+LwADkoY1WpKk+t8vhW6bel8PEew711\nhkVX7VK2BbqQ9HIzmzXSeyLnmnQyFsmT7EB8MqHwiVvfrqrcqDoO18nm0Xmr/vcGfID9PHwcYF7D\ncxuV2FqVjHYTq09NnMvo4ElTkh21vl7gHjIXl6C7F1AjDycypvwXjsmZ5t44rALu/fM4/rBc3NpG\nqNtewhRsScFjA/eTrmwK494db8IHMMG7znoOG9GjjjuGBhiJPN6nf2K6bi0voFVqZGcX72PcyaJu\nEZvdcHfNa/BgZfcDu4xUF2O50cHjC6/BL17YXxx4Toe8lsIDwG1Cl3ANuBtqL+V9Bd7K+mLN7317\nxy3UC5OhkAvw+Pmnppv8RGr6nMno6003xcWl7Sz8ZThscRbyDFHHQTkyB5bpIcYQGXFcGIrJslPS\nw6bUuOpRMXhHxQAeacWmdF5/pf08/1qSParTVlOOWygMLuNdFXVlbuzCm/OAZeq4UfybXuWTTMcK\nR5L5KHAdXvN9V/r+0RrZu/F1M1r7G1C/OlpXXeCLmcyu2zqUeVQqdsD1RX3hM2or+/VpaAyB/dNn\n48pMZpn7Np61SIwBMPRybkJOX29uSIOn8P6/q2jvy65yZzwVv9hXA0jaDg/5+up0zBeAL0j6gjVw\nZ7WMKf8FcqauNw6rYA2b6Wa2dfrsGjvGeptktSDme8rjWdUvKLJx24HuwvvyGtkjzScrtWI+fRmP\n+VTlmpuj426hAXqWL7sdS6p0O075HCefDd/qOjva6kMPP2rtXRwtr6EqmujiDTXHdqPxNVFe9OBl\nrOAya2Z/SxM+qzgeH2ifm/5nA+AnuKEu0hoXqLrvq7qWcqPl9jyeVWaRMABWiNnegJxwDbkhDXIM\nUaNBOcsbWIa8GEM5U9e7hlWQdJ2ZbS3pSdpvWHlRbMWavFuxjLZOx11X8zDmhimYJ+kQPEgX+ABe\nWz9rcS6JpFZY4QVzSWqKm/OA5YQSaBr/phf5jhWOMuahsCvDYZe4U9KleOAyw2viNynF/7H2ldK6\n6sLSLHtJX7TSOJukLzJ8gaAWOdckx4D/XdLmlhaXl8/e/UdNvo2MoQ2tJ/JTM/tl8Td5eO0yuRXR\nnHdcZ0baHBmLDXehOh8ffJ3X2mpkG/f14v7p6xX21yP1vzNCX3zcO+VIfGGKSXiz9UcVcsfii8Ff\nindJXUKH/nS83/2TKc+JwCeoWT8UX+T8Q3iQrNb5Vfrrpxtoc9LapPjari/t0/X7FN70/0zabgM+\nWSPbeJ1mfNm8c/CH8BE85HRl6F/yXHgbu+Zm6nhz4Jf4S/yXeHTIWh3jLZRG8lXlK6eR0SVXOGZa\nh+2MEehiWFcdnbuAcq5J47k1eH/7b/GulF/gXc0vr5E9BX9O35HuzR/jrYI3UbFmdM05VqVdW5dG\nxdgMfRzPWlS8gK7D+4K/igeeeife/D+qQraxV42kXfGaQVuQMryP7z1m9rWS/GT8ptqI9tpp1QzK\nohcQDMUCKnsBZXk4aZRiDKXunv2A55vZZ+VxTp5rZpVLEDat0SfZOXhrq7WO6bL4g/DiCtlbzGwz\nDc2QXhI3cK8dyfmlvBu1tJQR8ynJT8Qfxp+mYxe3ggeQMuPflPJeool8jhfQaNJAF/8Pf8aejz93\nLVYAfmkeKrwq35w4XFkeX+kea+n47g46ntbh1M1SK1XSq/CW12H4O6vFisD/lMuhjNhayWtptplV\nraedTy9WY6w3YFb6vL2Q9osa2ay4QXhNYlN8avqwgd+S7HV4v+ls/EXyafzlW5RpNKmnIN94YLl0\nXJPBvsZxXPDazTfwoGDgXiU31cg2rtEXznHlwv7KwI9rZG9Mn9fi8VNWp9TaIw1YkiaglbeafBu3\ntMgbMH5P0vFv0/5kahYuKd+bDa7xbXj31QYNZIteQDcDX6PkBUTe4jHvYaiGKeAMvCUym/oB8Sa6\nWAlvvX4/PUOtrdKTrcdr0rWGjIcPIckN23Kfx1Le2+KVtIdpd2b4UKtMJfms2FrA9+jTjOIRZzAW\nG978XQwf+f8A8D94bagokx2uIR2XE9KgqyGifQWjkxqcW2MPpySfM+W/8dR18sIqzKFgLHE3wjkd\nyvwjvEb2Hbzr4EG862bYudIgTAG+0A54M3zYVlOGxi68ZFQiaBBKAJjBkOts2eusU3ffRLqEEiCj\nwkGGJxkevXLJ9P1tqQyr4bXquspX47AKBb2ujXcVrVc+txFck67GglRxo1nXVrYxbF2/9LkC3Str\nORXRn+Hvtqua3EedtkViEBhvSj0HX9z7aHzptKlFAcv0qoH6IGXUr/LzdGqC3SvpA/hLbY1ytoXv\nTdaFzRlYhvzBvrmSFjdfD3WapF/V5PvvNGhnKd8J1MfW/x3eBdbyTlia9uZ8mQvT1uKaOkEz+3b6\nei3eTVAl05qpOdsarguNv/iWpOC9VabHAeN/mtm/Wg5TqcvGSjK74f3/Z9F5XYc2zAdMjwOOS92P\nRwJfxF9+LW5MeSPpJDP7YIf8cjzJnrGhrpA3AGea2Z+Bn8pnwVbRRBet3z6At6AfYeg+M9zHvijX\nyzXp6vFlQ93H77buawUfildeAPbFX9TPx6N2ngi8pua4FSTdQgPPrFS+SXj35EslYTVhpvFWd3/o\nxWqM5Ybf7F/KPKZR3CAyg5ThA0bLA+viNYULgC1LMjdXfe+jPhrFGErpjeO44P3/F+O182PwGvNe\nNbKNa/SFYxpNoMEn7RS7i1YBPlcjezXup340sHEXveXMJckZMD4Of0HdjS9CciFwTI1sdvwb/KXQ\nagXciIdsKP5erG03ut9ILdlS2szyfYx3nSyDv6Q3LvxW2drL1MVcYLUMPXS9JvQWtPF+3JDsUPcu\nAG4tfD8bOLSJzmkeEDIrtlY/t0VlEPhnwA7WoLDKC9fQOKRBqkUca2Yd4/RIegq/uYW3LlpuYy1X\nyXINp/HAcpLPmfI/kbyp603DKkytSi+Uvc1tNw22tzw4WoPt7zV3RSznnRum4LkMxVpZEZ9y/7mm\nZS6XtSDfdMC4aygBpfg3Nf7eVN2b6biuoQSKuumkp9IxXRePkfQG/Jotji9O8p6Uvi0+BrNbL7oo\nyF4NvN58LeBGZFyTnF6AZXHHkn3wltSPgXPM7LqCzM14K+5xvNv1tZbCrkiaYxXODOm322z4gG9V\n2hwyYmupOiz1362DG3ZtXouIATgeH1A6D/h7K93afZBbso29atJN+DK8ZtU1SFkTQ6TM1cZyPJyS\nfKMYQwX5RnFc0k11pw3FbFkBvykrg201zTfJ3g28wUoTaKx6habZ+FyHf6b9ZfHa6cZl2dJxm+A1\n5b3NbKlOst3IrEQsBzxtqRshVRSWNrOnCjI9xb+RtKGlNYo7lDWrwpGOKXqSGX4PfdZKnmSpC2eF\n4r2VzldWsd5AQ118KH3dGPe8+Qntz15x2c1i3o2vSZLPmVvTOmYVPITGfma2eCE92xim3xtV1nIq\nokm+b2s0LCoGYFpFslnF5CBJl+FdF7ULYhRkcx/IroZIUtvs1Jp8FshImmVmL5d0u5ltktJ+YWZ1\n/YqtPJos/LEbw91ca2vewOaFci2Gv3iH1ShzavRJ/lorTLiTdxL/3Non4bV++yge6XIa/nJ6F95f\nPazfWdKL8Zr/W/Bm/jnABWY2bHJOTksrsxJxPb6a1N/S/vL4ojSVYzJNkLS/mX1XNYuAF1+SuRWO\n0v8s3+Q5aUoTXajHZTczr0musdgWv492wQfbf2BmF5Rksoxh+r1pQMjciuhMM5ui5Cqd0n71/9s7\n83BJiirt/043ItjSLUI7IpvD2irKMuzIIIgbIiougIAog9sg7o5+gwr6oeioOIgsotiNOyoiyOMo\ni4CC0LI1+w4CiigISH8jCsr5/jhRXVFZkZkRmVm36t6O93nyubcyIyOjIrLiRJzlPU3euWlhBFbV\nNycUj6ZrKJvoK/BUbKLxfdIV807q4TwRORU4XZ1fLyxbMT8fM16fR9+oFGNYXgZJCPknPnQdSKJV\nOCqhXkiIJtU0moKFmDvhi1X1npIyftneTmtn3E6rpGytwdhDLZWA+z6li4LAKj2FSuCulAWH+7w9\n8FXMnrWOiGyKCfB/r6onArV9UTbBRyBlTF4NbBwpLO7AnEC+B3xQVf83VM6pqh4snAuW9a4/iDmu\n1OHwiDI+kmmpyzAtBIDbAYR0pyF6gFqvGmlIaRApiF6KrVq/Ixb48xC24pyNRbV+QVWXeOVrPZwK\nSPECSuFxqaVVaFgv9A2JvR3XfZgAewXDAhSNoClw6oXbVPXoqnIeVlbVc91keCdwuIj8EhMKRaRw\nPsVQCSTx32galUDqggNMCPZI/1DjfRrajTVANK2CpPPfpIxJlLBw79BCVf1EVbmmEJEtMaP4MxlU\nRQ0I/AYL0TY5GgbbOE1UQP6XWwmT8PeUDP4o25EiiBCLMFwdeERd8o3C9SjDcuGeKMOSO388pgf1\nV943YXEVRdXV0zDPmF1c2XOxIJSQOiW63oTvlSyUReSnwB4awU8vIhdh7no/wPyof4f1/caBstEG\nY7EcEt8FejuQNTA7xOWBskH+m+I579qQUbd4Tow76UDMiyu04Di2sOBARBar6jbiGdzL3iHvnpcB\n56vqIyKyZ2iME/viaIb5b+7FYkrm6nA0f8qYnIq5atYKCxE5T1V3DtXdFk5t9UEsaHKZS7X2+ZAa\nc2t11sbpIACKcCqTczRAD5Ci63XlUygNOhdEkuDh5MqneAGFbCc9aJngimhDUr0ishbmtbADrp8x\nV7rfNnm+V++XMc+NMxi0yQwZEt3kdAMWhfx/MY+hz6rqJW3a4OqOpRIITejL9LjeuSQqgUI7Shcc\nXrkfYGq8L2HR4u/C3qG9K+45FvNVvwJzfS7zyortiwG7kH9ORK7TGqN/FRKFxScx77hTGHyHrqio\nv1YYunIXqmPE7QJubjsUeAAbv69gi5rbsHiGS1PrnBYqoAA2xCIHQ4jW9YrIx7DVa28AF4nI9zXg\nRgigw4ah7wDnJLd+EFcCp4t5AlR6ODkciBmWetd/gX3HUHtrVVYi8h9O734M4d1NyHaSYpMBG5Nv\nY30NJrQWYr7ivXY8taoCDXMd3eOOWYT15b26ZwOvdzut/0dJf3nlaxcRIrKLqv68Z8fwsKFYEI+/\nu1rGfyPm5dTDKrhdUwErYvr5FQrf62HM4B2Em2xjPEnejnm7rInFcJwFHOwXEJFtMAqO+1zdB7vf\ny7sDZaP7wsN8EVlHB/lvVnfXhnZ0KQu70ERfgZ7q1FcDKYN2viJ2Bw4Tcw/dloIK08NhIvJVhnci\nod1TzEJ0IWb/m4vlw34PtgjdERPmIbbTSkyLHYC3RRL3917g/xQnZFc22qtGEkjKStq1MebOuEGL\n7xbl4SSW7zPKZ1pE3oKtUG4RkV6Gr9dgPswH+C+XiLxCVX+cuGpKWtGLyBJV3azqnJgxrjfG62AG\nN8FW7Hepi2ItqX+O1hjkUnZaEuGaKyIfV9XDYsZPROZhAW1HAh/2yi0tEWy9+9ZV1TvFXHJVO/TY\nqYOIXIVlV+v9No7CdNlvA07zV7YpfeHdk0rEmEIImaQFqENRGLpzy4Shqn635L5vYq7S1+FFOwd+\n28WF6KuAoYWo/5sRkVv9eSf0G4uCTkG02VQeRPAGeWWjScrc9R6Nbu/vzcBrpuh7RXMM0YzHJTq7\nEsZt82ZshboCRo97dkX5c7BV/2x37EeBJMwrewKwm/f5ZcDnS8puh7n63eU+b4oFuoXKfh5TFe1P\nDekXaeSDs0PnK/oihf9mEyJ5nyKfPUScR0lUNI6G2I3vNzFHg1nFd7FlX6Tw36SMSS1po1e2Nu0m\nRsrnc18dhc0v83EU2yV1V2Zv88pFcWtRwTJQNiZ1x7RRAYn51G7IoEQPBXakeNX8DXNRPBtbfb4I\nuFBEvujqH1B/aERmq1RIvGE5hWOoCY/LUWIUu9/HIiGrEszPV1V/tbdIRN5TUf5AbIv6Bey7/sqd\nCyEl4c1/E+/NEuPC20OKa+4dzhh9CvBzdb/GECSS/8bDiSTwPkXg7dji4HuY6qzMDRbsd3AuxvG/\nCrZ7elzMZ74sYUptX1Soi9arUBdB2pikeHwtwlQrh7rPN7v2n+SVWUFV/yrmFr0I80h6reuPsuxh\nAJeIyLNV9fqKMhDPrbXAqRAFWN9TJwolvFl1mBYCQEQOwrZba2E+u9sCF1PQ06XqekkgKfOeESuI\nYnGm9/8yw3KgXIqu7nE3mT+IrYQ+6V1bOXSDqu4sfVqFE8UCzYK0CsD9IrIffQ+OfbDJNQg1PW8w\nqKWk7o8wSFNQVffdMpi5MkjspWl2i5RFxMaYSuJg4CQxLvoBKoFCvRs7YRyDqKxyCVgDUzXshfHl\nnIIFzg1Fkavq28Qyaj2KCawfiEhPR1/mchjTFzthXlivCNxfJpAhbUxShEVM2s0mwhCcG65Tb/4N\nSqOzYxeiUarpJDTZNkz1gblRrYQjZcL0aqeUlP05JBG8RZGUubIHubY8iPlWP4KtdLr8rrNCdWKr\njqvd83v/9z5fXSi7O/bS3wt8xTu/E2azqGvDczEvo0dLrq+Drbrvw/z/f4Sjvi0pPx/zhz4Ro9L9\nGgXKXa/sUzED5ZX0ee2DXPGYS+f2rtyKGF3yd0vKLvSfXdYGGpAPeveuihnp/lFy/TzS6Jujsso1\nbOuarr/uAfaPvCeazK6uLxLbmjQmRJA2emXPx9SjPTr0bSkksnfnnw9sjamULsUote/AoufL2rFu\n6AiUO6Dq8MrVzmsxZfxjWuwAMH6Rv4oIIvJEVb3RGWBDiPaqkQClgYiUUhpgu5CtgEvUVswL6JKa\n1VDm4RQt/VX1TDGKgIHQdSzIZq/QPRKmVXh/Sf0pK3qA0zHysXMoWaF7dT8AvFviaAp8b5bfYeRj\nB5eUjdppqeo/RORfnPogatclw1QCry9c71E63A6cLyJR/DcMenz1qARSPbBC7d0C27W9CLODDfnp\nh6CeEbSi7rq+eGP1I/QbgZPRY9JAC/A+bDGzvlisyHwCnlY6uIvZSkTm1/WHmgF/U/p00b9U1asC\n5U6WOG6tJkF/lZguXkCnYQP5Hkzt8yBm5NwtUHZh8RzlngjRJGXu+qWqupWILME8JP7W2PrerzPK\nwyny5Y+etAL3XoKpdL6vNbQKYrkC3sJwhGNZQFx0H4lHU6CqXdIUFJ9TFUuSQj54B30qgTM04I0k\nDflvuoaIfBzbHd6ACfifagIbZ0T9MX1xTOhWTCW0pqoGF6WJY5IaWxOVdjMVIvJu7HfSa+OrgRNV\n9ZhCuShuLWkQ9FfbxukgAHy4FcY8zGrfaqAkgaTMXY8WRF1DRM7HtrKV0l9VFzWoezZmKN43svyv\nsBX95Xgr+qLQ8sofgfGg/ySi7sXYCuwM7UepXqteDlSpdnN9k1YE8Xh1lLrwxi4iXL8dqmOmEkio\n73FsF9LTW/d+/KXMoQl1J/eFG7t9gQ9h3lyfVNWrS8qmLOxiSBu3Au5W1Xvd5zfSf4cO15Y5tl2d\nVwPb9QShs99cXOzn1IWoKxMV9FfbxukgACQt0XusVw3SgtKgY0FUa1gehfQv1J9CqxC1oi/sbuZg\nao/eilM1TO9QS1MgItdibquPicgbMFXVi7EMTYdpOOYjOpYkBZJAJSCJ/DdSQyXQoK3rVl0P1etU\nDl/D3vOyDHG9slF94Vbcb8LGbTGWrOWmuvtiESMsxIK4dlXVB8Q8x74LHIK5pD5LVUsD7hLacQ3m\n1daLpVgJy7P93EK5pIVol5guNoDaFG8eYr1qetejScp8oaOOwEksreSQIIqFRHo4uZfoOOC4VOkv\ncaHrdwIXiUgtrQJwpojsVrei12Zus3c7NZC63c27MJWFj2Q315S2pCwigF+JyJeIoxK4nWH+mz8A\nG2Fh/cX36D5VTUkXWomGguN4bNf7RTG72iItz1FQ2xcicjD2vp8LvDS2TSljonEeX7O9Vf5emGrm\nVOBUp+INtSFaGDosBBY7zQFYgNfXAuWi2XK7xkTvAMTLB4p5vgD9fKAakfWnStfboD1FIq7ZWLDH\ns1vUeQ19w/Jm4gzLqho01jZ8Ri2PS5me2tdPp67o3YrzIVX9s/u8M/Yj+A22YwmF/K+OGXZ3dc85\nC4sy/pNXpmmGpigXXkngfBLjci9CS2wLSfw3IvJCzFhbSyUwaohFM++D+cvfjQmsb/q735i+cGqo\nP2KLLX/yqVRDJY5JrbBwu8jN1Nw+bwTe2nsXiipH755dMWG4LaZeqhKGvXt6FA8C/EIDFA8lOxav\n2c04u6KgHbiUjfogIUdr4N6NgVtLrq2Fudr9EVuJnQqsFSiXnGs0oX2Xur9LsOxJ4OUgbVjnNhRc\n9oCPufbuXXPvnA7HbTHwDPf/ZsD92Lb/ZCxVYNN6k91caeHCS4lrboN234AX+Yt5e13v/r8yUP6b\nmHroZGw1uZAS99lRHpib5LtdW87AVszHYLvK1LqCrpGUuEg2GRNMl9879sXchYuRzodiqt7TMc/B\n3mJ4A+CimmfPwzzQ7saCGt+Mi7wvlPtGzLlxHmNvQORg79CbmLDAoKPKXhYS6BpIpzRoNdmX1Hka\nRkFxOObmdzrwk5Z1JoeuE0Gr4H6k87zPO2Or9fcSiKHAi08APgf8l/t/FsOxC9E0Ba78CsCqhXNz\nMO+h0PeLjiUJ3Fu1iKilEvDK7oYlIT8P8z+/E9vJzMGot4fa3PX7VvEdgwna3XtzPbYIWqNwrZhI\nPoZWoRNf9qoxCZQti63ZFttJzPHObUS1b3+0MGSYrmE2TuAXzkctREcy7lP1grVqpAU8iZuUrnYD\nMBSs0aDeoZV26Jx3LVoQNWzPTph//dBqIrGeJjwui7HEEld6564NlIle0TPI23IF8BJ/TAtlH3Vl\nPozlOD2AQDBMiz6J3mmRtoj4H8zX/Sqvz0snbtL4b76C5WUe1e/qNkzAbh2amFyZ3QLnnti0LzDB\ndwgFDiQskG8X9y69qc2YBO6NFhY19UQJQ4Y1Bkup0BiQuBDt9B2Yiod00PG9KL2P4VYUZROZu7aq\ne6n/tXeUlIsmKXPlOxdEjGCbiPkUn4uxEN6FJYwGEzDB7S2w2P31BcBVxe/v/V+5onfnj8YMW0dj\nUZM9gro1GF49roZtq89zP4iDKKzwW/ZJ5zstV29PsPj9tqRQZhf3d8/QUVH3DZhgvImSqO8O2v9e\nzJX3jSXXh35nZb+9yL5YCWP9vAhzzrgeM47fiQm8zTr4TiMhbSRBGLprURqDYh+VnRvFMV28gJY6\ng/D+wI7O+PqEUMFYrxqHFJIyMO8TFZFXAker6klSQqOcgBQPpyhoMx6XGO8bn3RnF2ylgxovSqjO\n92Bb5DWA52vfYPh0+uRbvTb/CWMCPUFE1sQMjteJyIc0EB2aClV9tfv3cGesnEdF2slYgzGWBnE1\nnNFRRLbFXDt97EQz/puXlrWvCUTkLIxquZeRaltM6L4N503llX06FmG9sohsTn/s52KcPCHU9oW2\n82aLGhMdAWmjwxFA0fPtYiwpUQj/IwFywkCbk7i1OsVUSJkOJO/TsZDtHd3ndShfsTTW9Ua04wJs\n0rvFtannBdSkrpEZlkueV8njgv0Qv4UJjPsw1dFqhTLRK3p3Plnfi/2YPosJ75OoUIFgk9J+wMe8\n92LrkrLROy0SGX0J0gAAGMlJREFUDMauvRdhE91F2GrzeR2O26YYrfk7gU1b1rXE+//l2Op7I/f5\n0kLZA9x3X+r+9o4zKKfRHllfpIyJKx+lBYh89tOxRdkNWKzJFu54AZb1rOy+H3vH2a5fQraIJG6t\nLo+RP6CzhpoBclf3/5MwnptQuRRdbzRJmfciRAmihO/V+WQ/wjEQYG9MbbCmd35zPP2+d/58IvW9\nGOfN5Zjg2Z0I0jTMR/1YHHe6+9FfWlI2yiDnriUtIjC97XMw/v6QN8gbK45SIjZsJ3stlq3qE65d\nh7QYv8XYxP4RN9Gs6c7PreiLJNVJXV+0aHsKIWStsKCvHioeS4GHC2WThWFJu9YGvtNVn3RxTAsV\nkFjo/1uxIK31sa3pCRjVcRG/FZGnYFL0bBF5kPJAsGiSMgBVvdcFg2zoTt3PIJ10E5wpLqOV2wZu\ngamXGkV7pkISaRU0kP1IBzOM+XxEL8VUat8RkVD08he0H738UUwXvKk7PuXUSlX+4duo6hYicqVr\nx4NOfeV/v2WxJCLycO80LpakpFtqyQfFoxJQ8yX/l16/icjhOkglsFXgGcv4b+jndy7i39x37FEJ\nfAZTOYT4dGKwL2ZkfxT4DHCyiPwCeCWmfw9hExEZys+rHuVDYl80RQohZC1poyaoidSy4p0sIq/R\ndpHjv8UE4wAkkVurS0wLAYAxPG6NrWBwk1WQ31vTdL1PUtUPxTYiURDF4nhgUzHSs//AJuCv049O\nHjXeTZ89cB9s8l0PW9UfTZ/JEBLZCDVN31ua8rECjzmbSU/nPB+PMsG14UjgSBE5UiMCBx1iFhFf\nxoLVcHreT9OnEjgRj1FSVQ/p/e+EbI//5hIGczUUIQwuTP7BoB0mCWpcMwd5bfm5+w4fUtWy3NY+\nI+tK9MnkfET3RQukLOxShAWu3U9j0LZwV6BYrTAs1Onn2Z6F9ccQGyiJC9FOMe4tSOTWacBDBRNc\nQW8I0nS9RxCw7Fe0YwmmvvC9HFr5apPo4ZRY96mYrndW1Xfy/v82FnVLqB1MgQdH4vfbF9uG/xab\nSG8CXldStpELLyWuuXgeUpga6vBQn3rnVsAm3xswAblxxLPfh00Yh7tjCfDeqezjQJueCPysTV90\n0IbgmHjXoz2+XD23YNQVd2ALiOtKyr7fOw7FdmNVKuMDvGNfYIeSclPi8RN89jhfpoQB/y9sG38j\nxmF+GsYcGCpbq+tl0E3scUxH2PPVfbiiHdGCKOG7dWZYDtS9K2bYvQ1blS0I9RdmxO3xIj3HuzaU\nl9S79gR331O6aGuL77gA2yG+EyPxKisX7cJLxCIC082v4P6/Ec/IyHD8xMGYQfR4Eo17mErwXa69\n0XmbR9jfqwK3NO2LFs9t5C5NvbC4CnNB7v2md8ZoZmLaNCQMa8qvDXwwcD5pIdrpeI77hYrsuFmY\njuz7WFj3Wxj2Hhm5Vw0Jgiihzs4Ny4FnlIau0zJ72LgPNyE9j75nRjCKk4SdVvE84UVENJUAtsi4\nF+fHT0U2t8J9Y6cSKLT5Osx4/M6mfdGiHSlG/BQtwGXu71X0gyV/nfDu3VJTZnXgHdhO5Dbgc961\nRgvRLo+JJoOrgojsoKoXBc7X6nqbkJS5crMww9yLsdXkz7AI2Fad6NqzoaqeI5ZkeraqLm1Tp1f3\napjKY39MbfMtTF//XFV9gSuzAoXsYWLc5aL1WblGDhFZTQN5dMWSxb8J+2H1xkA1TMR2AfBTzCi9\nI+Zyt0Q9al5JJB90fu5rAGdp31C7EUZH4TNgrlv1/bTE4C8jIB9MRaHtfwf+oIEkMrF90eD5yYSQ\nKf0mIudgv/0jscn6jxiF8/aBstfQf89mY16En1DVLxXKrYJRTLwBo5Y4DdhLVddK+OpTg6mQMk0P\nrJP3wXKXbuLO7Y6tYofIs9z1Wl0vHZKUUaLXS7j/LVjqvNvc5w2piEZOrDuax2XSDuJoCm6iJo+z\nVzYllqRT11wS4yFIpBJo0J4dML/0mzEbzh3A7TX3PM312ToU3Hqn6H2o/d6BfqvVAmA8TLMwde4B\nmLqtjBdpXe9YkxJXZWwlfwG20Ogtsof6l0RurZH061QPZOKgL8IoDY7EIikXYuqXV1XcU6vrJZ3S\nIFkQJXzHzg3LXj1JoeuTdlBPU3Aq8LSE+tYlLpakU84nmvPfjCRGxP2GXuYm9dV6R0nZaCPpiN+F\nFELI6H7DvM984sSVgWfW3FMpDN17uxizjfwn5jEYEgAjYctN6tepHsjEQb+Wvl5uJcwl7ek199Tq\nekkgKXPnFpEoiBK+Y+eG5WJf1J2bhAOLC1jX+7wttsI/CPheyT1b0k8Gf0bvKCkbvdOiY84nGnpP\n4UWx0kFEa/Gdiyzb2Eja8fuRYsRPERaX4a22MaFcFkyYJAwxd+pDMTvKXzHX34387+T9X7sQHUm/\nTvVAJg56ceKunbyI8KohndIgWRAlfMdRGZaTQtdJoFUY0VhH0xR45a7Dtuw7Y0brnYCdyuoncqfF\naF1zo72niKQSSHh27z34NEa3sR31xvNkIykeJTewQUf9lmLETxEWIZfdq0rKtvEYei7wKdwCpPj+\nEbEQHcUx6YFgC8QSK4MN6Pruc1V06F6Y8eVAtcjddbCX3Uc0SZnDo+pSwKkFmNysLpl0B/gwZli+\nBiPl+gnw1ZZ1vgQzjq6FrX56WIoJmxCOw1Y0u2C0A0sxFUsoinUU+Jsj1lsbm9Q3V9XfichcTE8b\nwv2q+sXY+lX10R5pnTN8a0nZWvJB6WdHK6L3bg7lO8YuPAb8PqbBqjpAHicia2MLhqb4fOHzlv7j\nCBMmPiQiT8YClb4lIn+knwWuDBeJyB1YXMmRmAqkLaIJIUkjbbxPRPZQl3rT3XN/SdnHVPVPIjJL\nRGap6nkuOnsAhWh4AFT1Guw3/p+9MsDPReR72PuwKqZdQETWwIzcI8dEewG18J5YlwqvmtAABepY\nVkZE/gLc2ruEvdC3UpPGrinKPJwa1BMdut7znJCKZOyjhIhsQJ+m4DZMR92jKfimqn4hcM9RWKrE\nMxhMmTjkdSKWK/ghjH/nEEwlc72qDgl8MSbMN2A7j1+6RcQLVPXrxbJTCTdpXK2FpOIN6llPVW+v\nO+fOz8GMmrOwYKZ5wLd0MEXnk7BF0t+9c+/AmHb3VtXvt2mvqy96TGI8vryy62OecWu6U3dj/Ey3\nBcr2PIY+je0Egh5DInI+tniqi5g/mf5C9Huq+jtXbnPMtvWzuN5pjkkXAEkTtfu8jK5BVdcXkQ2B\nE1T1hV6Z84kYIFVd5M43EkQ17Z6NJc9YE/ipql4rIrvjXN56k3AbiOX5Heo/DYSui8hiYHvsB7aF\no1U4q4t2NIH7EeyKbbeDNAWSlo83yYU31TU3kkogCSVUAr9R1f1a1jvgJunOXa6qQRryiAXVJZg9\n7F73+dUY9877sMjll7dpb2w7vHLJAtztcqRmjGuFoSu3EiZ89sWMzEUOrGNVdUmT+a1zTIWeqelB\nA+8JInS9JBrlSHTji/xuixiRYdl7RnToOgm0CjPloDw0P8VgPDIvGSKpBBLqW4CRtN3GYFKaN5W1\nOaYvGKSCeKsrP9997sTdOGVM3PV1ifP4moepSS9zx+fxXDOb1uuVL7X50NA7rMtjZBV3NOjJ3hMk\netVUDdAoB4oRGpYrnlkZuk4krcKkHDE/XprFkqQYjKfMS4YSKoGE+1+JLTT+RD/J/EIs3mL7pn2B\nLWAOw2xXD9Cf/Neo+u0ltj1lTFIE+KnYbmU9dxwG/LBtvZHfaezcWhNtBNZm2YMuEJEe/e+LsA7+\nccUzYoxyKbTGsRilYbkMT8Je8jL8ATP2rYD13xbaIopzCvA1TJC+3n3eH5vQ9vTKnIRNnL8Gvigi\nd2LeLx9W1R+V1JtiMI4yDDaFWCa312FCbE1a0I+r6unA6SKynapeHHlbTF+8DqM7uBmbJH8qIldh\nwjDkVNEEKWMSzR4MrK+qfpa8j4tI2W85pd5aNJzfOsVECwAfkRM1jMCrZkQD1cTDKQlSErpeUjZI\nq0DYM2RSEPPj3RLLSvW4083ej7kmVgnblEVEz0vmF8R7yVRCwlQC62lLKgHfpiAi+xSvq+q7ArfV\n9oWaDvwI7zkXY774n1HVm9q0OaUdHlKExSMi8nxVvdCV3QHT87etNwkJ81unmGgjcFfoyqumS4zC\nsFzzjFIeF1f2JowfaErcz8rgfoCHY7rWFegLxKGdi5toPlj48X5OVbfzyhR5YYYMoIF6ow3GsYbB\nFIjII9iO5SPAhaqqInJ7qA8S6y1zhQSWJT4p3jMS/qtUJI5JisfXplj+jXnu1IPAAap6daBsdL3T\nBTNGAEyFV02XmEoPgBgPFbFEL+9Q1T+2fV4biMiNWCj95XjJMUITqohshtlf5mGTwgOYLeYqr0wn\nLrxliwinEvy92yUiIisD/6Sqv4mpt+RZ78VSb87BfOlPAc5uKwBmGirGJFloicWboKoPS4n79KQI\nwy4xkwTAIvq63m0wQ0qdrndsSHVFbfiMPTDD6DMwn+V1MY7/oaxGIrIlRud7LYM+9Xs0fX4TiMhi\nVd0m8Z5lP97AteidVpNFhIhchhlQH3WfV8QokFsH0InIepjuf2/M4HgYcJqq3tyy3vkYLcGzGVwY\n7OKV2RDT3z+AGdq/gvnU3wYcpKqXtmlDQls7WdilaAFE5C5VXadxo6cRZpIAuJZ0Xe/YEOsr3PIZ\nV2E6/HNUdXMx2ut9VPWtgbLXYan9rsFLq6iqF7RpQ0Jbe2qZ12N98ENKgrtE5H1VdanqUV7Z6J1W\nk0WEiCxR1c0K5zoPoBOR52LCYC9VbRVZKyJnYbuKD2B5Ig4A7lMvPaqIXIipRuZiO7L3YDr3HYEj\nUoV0i7YuInJMOhQWd6vq2t7niRCGo8BMEgDJut5Jwag8AETkMlXd0gmCzZ1w/LWqbh0oe4Gq7tTV\ns1Mh4aCuHrSwOj3Mu/Y2THD5hT/ulT2fyJ1Wk0WEiJwNHKODVALvUi/wMBWjVg+KC/oSkat7KrDi\n+PuCTURuVdUNQtcK9YboMf6Muei+XwORxhFtjR6TrrQAxR3ApAjDUWDaeAFFYOReNaOCjs4DIIXH\n5XIROZIIWoVRQFV3BlN7FCcKpwrxy/oT/Kv8zwGkuPA2cc19O9a3x7rPd2PuqG1wnrPJ1FEJLGpY\nf4/76vci8nLMB73oYfS4939RtfY4YRzl6vo29rvbG+PXuglz2X1Bg7amjEm0x5cMesgNXAL+qXDu\nyap6orvv7dqntjhbRIo8Y9MKM2kHMHKvmumGFA+VkhX4wMp7KhDauUk1TUH0Tq9up9XGYCwRVAKx\nGLV60KlFfomtlo/BVrYf7+1iXJleX/j9gPu8nqoOEfSF7DcicomqbttULZYyJilagETb0LJ6prOm\nIYSZtAO4a5Tb5ukIVf1f6fOnnCyOP6Wk7M5T27pBiMgC4DnAPBHxA7nm4hkq2yBip/Ws1DpFZB5m\nnP1X9/kCLE3gnxs1ktEHCKnqme7fP2PBWiEk9wXwuIi8HsvbDfBa/7EN6kttR4oWIGW+WODVs37h\nGdPaM2smCYBRb5unHcQjxsNWTmsCJwBD+uniRIblVWg1kSViY4yi4SmAT4O8FIsuXYbC9n2Dwg+y\njbqvySIiJhq5MUahHhTL1Xs85q66iYg8D9hDVY/wijXpi32xHBvHYeNzCbCfmGvsOxs2N6UdKcIi\nZb5oIgynBWaSCmjkXjXTDWJRsVtj/Eg9iudrNEyLeyo2kfWCgfYHNlXVTiayWEgETcGo1H0pBmPv\nWsgLKGgknRS4XcoHgS9778W1qrqJV+Z8RuymHNnW6HakGM9T5otRG+XHiRkjAHyMYts8HdHTyYrj\n+BcLXb8itEIe90Qmg9THQ1CPpmBUP8gmiwiJiEaeNIjIpaq6lQzmfhgY64Z9MR/brT0TT7ugqge2\naGvKRH0+DYRWhG2oUb3TATNJBbQMo9g2T1NcIPH8KSmcKKPAZQllR6Lua6h7fzvwdadCA0clkPLc\nMeB+sUQoPV6g11L4vTTsi9Mx4/I5eFHcbZDYjkakjRHzxSjIICcCM3IHkGGQNP6UWlqFScEkqvsk\ngkpgUiDmVnsilgDoQSyPwX7agr7C1Tsxqq9RaQFmmnYhC4CMAUgFrcIUPb+WpqBQfuJ+kDJNqATE\n3IRnaQeuq66+I4BfqepPuqgvY/TIAmAGQhJC1yWBVmEqIBE0BZMOKVAJTApGPdZikcBzsEDCx+h7\nZc1tU2/G6DBr3A3IGAkWYhmv7sGSV3wNWyV/AEvU7WMV7/hA4fMqU9ReH6up6klYopULnAFx2zG0\now0mdVU10rFW1VVUdZaqrqyqc93nPPlPMPIOYAZCGvC4uGvLvELGBelHjv4MS1V4D/ADbUmA1jWk\nmkpgI1V94hQ3KQldjrWILFDVG6VP6DcAneyscss1ZqQXUEYjHheYjJXrEc6j5v30aQreO94mBbH7\nuBvQEl2O9fuwgMPPlzxnkrPKLdfIO4AZCGnA4+Lum9a8JlOJ6R4clMc6A/IOYKYiOnR9hLQKjRBJ\nUzAJmHbUI1Mx1iKyPcOBYF9vW2/GaJB3ADMQiSHxE8WiGkNTMAmYxFiEOox6rEXkG9iOcwn9QDDV\ncLL5jAlAFgAzEKPiTxllm71n1dIUTBomMRYhhFGPtYjcADx7UtVeGcPIbqAzEy/FVmDfEZF7ROR6\nEbkduAVLK/gFj7fkPBE5REQGApdEZEUR2UVETmZqqQ1qaQomDar6mKr+fpInf4dRj/W1WAKYjGmC\nvAOY4YggupooVcaoaAoyRj/WYkmFNsNSMvpZ5fZo0eyMESILgIxlmCRVRtc0BRmDGMVYi0gwp7Sq\nXtBF/RndIwuAjInApFFSZGQsD8g2gIxJwaRRUmQkQkT2FJFbROTPIvKwiCwVkbGQCmbEIe8AMiYO\nk0BJkZEOEbkVeIWq3jDutmTEIe8AMiYReVUyPfGHPPlPL+RI4IyMjK5wmYicAvyIQS+gH46vSRlV\nyAIgYyIwaZQUGY0wF/gLloGuBwWyAJhQZBtAxkRg0igpMjKWB2QBkDERmDRKiox0uECzfwOew2A6\nzwPH1qiMSmQjcMakYNIoKTLS8Q2MCuIlwAXAWkAO5Jtg5B1AxkRg0igpMtLRc98VkatV9Xku2vhn\nqpoTwkwoshE4YyKgqn8FjgOOmyRKiowkPOb+PiQimwD3YrkBMiYUWQBkTBxU9TEmnAE0I4gTRWRV\n4KPAGcCTgY+Nt0kZVcgqoIyMjIzlFHkHkJGR0QqZyG/6IguAjIyMtshkfdMUWQWUkZHRCURkdVW9\nf9ztyIhHjgPIyMhoBRHZXUTuA64Wkd+KyPbjblNGHLIAyMjIaItPATuq6jOA1wBHjrk9GZHIAiAj\nI6Mt/q6qNwKo6mKyTWDaIBuBMzIy2uJpBU+ggc/ZC2hykQVARkZGW3yFwVV/8XPGhCJ7AWVkZGQs\np8g2gIyMjIzlFFkAZGRkZCynyAIgIyOjE4jIP8ecy5gcZAGQkZHRFU4NnPvBlLciIxrZCygjI6MV\nRGQBlgZynojs6V2ai5caMmPykAVARkZGW2wM7A48BXiFd34p8JaxtCgjCtkNNCMjoxOIyHaqevG4\n25ERjywAMjIyOoGIzMdW/M/E0y6o6oHjalNGNbIKKCMjoyucDvwSOAf4x5jbkhGBvAPIyMjoBCKy\nRFU3G3c7MuKR3UAzMjK6wpkistu4G5ERj7wDyMjI6AQishSYAzzqDgFUVeeOtWEZpcgCICMjI2M5\nRVYBZWRkdAIx7CciH3Wf1xaRrcfdroxy5B1ARkZGJxCR44HHgV1U9VkisipwlqpuNeamZZQgu4Fm\nZGR0hW1UdQsRuRJAVR8UkRXH3aiMcmQVUEZGRld4TERmAwrLAsMeH2+TMqqQBUBGRkZX+CJwGpYT\n+JPAhcCnxtukjCpkG0BGRkZncMygL8RcQM9V1RvG3KSMCmQBkJGR0QlE5GjgFFX91bjbkhGHrALK\nyMjoClcAHxGRW0XksyKy5bgblFGNvAPIyMjoFCLyVOA1wN7AOqq64ZiblFGCvAPIyMjoGhsACzBa\n6BvH25SMKuQdQEZGRicQkc8AewK3AacAp6nqQ+NtVUYVciBYRkZGV7gD2E5V7x93QzLikFVAGRkZ\nrSAi+wGo6glYfmD/2jvH0qiMKGQVUEZGRiuIyBWqukXx/9DnjMlC3gFkZGS0hZT8H/qcMUHIAiAj\nI6MttOT/0OeMCUJWAWVkZLSCiPwFuBVb7a/v/sd9Xk9V54yrbRnVyF5AGRkZbfGscTcgoxnyDiAj\nI6MVRES0ZiKJKZMx9cg2gIyMjLY4T0QOEZF1/JMisqKI7CIiJwMHjKltGRXIO4CMjIxWEJGVgAOB\nfYF/Bh4CVgJmA2cBx6rqkvG1MKMMWQBkZGR0BhF5ArA68EimgZh8ZAGQkZGRsZwi2wAyMjIyllNk\nAZCRkZGxnCILgIyMjIzlFFkAZGRkZCynyAIgIyMjYznF/wdSTwY7IlBDMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x257017c91d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "business_city = {}\n",
    "n = len(df_bus)\n",
    "for i in range(n):\n",
    "    k1 = str(df_bus.categories.iloc[i]).split(',')\n",
    "    k2 = df_bus.city.iloc[i]\n",
    "    for j in k1:\n",
    "        k = (j,k2)\n",
    "        if k not in business_city.keys():\n",
    "            business_city[k] = 1\n",
    "        else:\n",
    "            business_city[k] += 1\n",
    "business_city_series = pd.Series(business_city)\n",
    "business_city_series.sort_values(ascending = False, inplace = True)\n",
    "business_city_series[:30].plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inferences from 2.a, 2.b and 2.c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that most of the businesses listed on the Yelp are Restaurants, Shopping places and Recreational Centers. For this given data set (obtained from Yelp's Website), top cities with maximum businesses are Las Vegas, Phoenix, and Toronto."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.d. Cleaning the review data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dropping the unwanted columns like 'text': review text, 'useful': Number of people rated it useful, 'date',etc.\n",
    "The columns left are 'user_id', 'business_id' and 'stars'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>business_id</th>\n",
       "      <th>review_id</th>\n",
       "      <th>stars</th>\n",
       "      <th>user_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>VfBHSwC5Vz_pbFluy07i9Q</td>\n",
       "      <td>5.0</td>\n",
       "      <td>cjpdDjZyprfyDG3RlkVG3w</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>3zRpneRKDsOPq92tq7ybAA</td>\n",
       "      <td>3.0</td>\n",
       "      <td>bjTcT8Ty4cJZhEOEo01FGA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>ne5WhI1jUFOcRn-b-gAzHA</td>\n",
       "      <td>3.0</td>\n",
       "      <td>AXgRULmWcME7J6Ix3I--ww</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>llmdwOgDReucVoWEry61Lw</td>\n",
       "      <td>4.0</td>\n",
       "      <td>oU2SSOmsp_A8JYI7Z2JJ5w</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>DuffS87NaSMDmIfluvT83g</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0xtbPEna2Kei11vsU-U2Mw</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              business_id               review_id  stars  \\\n",
       "0  uYHaNptLzDLoV_JZ_MuzUA  VfBHSwC5Vz_pbFluy07i9Q    5.0   \n",
       "1  uYHaNptLzDLoV_JZ_MuzUA  3zRpneRKDsOPq92tq7ybAA    3.0   \n",
       "2  uYHaNptLzDLoV_JZ_MuzUA  ne5WhI1jUFOcRn-b-gAzHA    3.0   \n",
       "3  uYHaNptLzDLoV_JZ_MuzUA  llmdwOgDReucVoWEry61Lw    4.0   \n",
       "4  uYHaNptLzDLoV_JZ_MuzUA  DuffS87NaSMDmIfluvT83g    5.0   \n",
       "\n",
       "                  user_id  \n",
       "0  cjpdDjZyprfyDG3RlkVG3w  \n",
       "1  bjTcT8Ty4cJZhEOEo01FGA  \n",
       "2  AXgRULmWcME7J6Ix3I--ww  \n",
       "3  oU2SSOmsp_A8JYI7Z2JJ5w  \n",
       "4  0xtbPEna2Kei11vsU-U2Mw  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_reduced = df_full.drop(['text','useful','cool', 'date', 'funny'], axis = 1)\n",
    "df_reduced.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.e. Merging the business data with the review data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Merging the business data and the review data on the 'business_id'. Information like 'city' of the business and 'categories' of the business were taken from the business data file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>business_id</th>\n",
       "      <th>review_id</th>\n",
       "      <th>stars</th>\n",
       "      <th>user_id</th>\n",
       "      <th>city</th>\n",
       "      <th>categories</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>VfBHSwC5Vz_pbFluy07i9Q</td>\n",
       "      <td>5.0</td>\n",
       "      <td>cjpdDjZyprfyDG3RlkVG3w</td>\n",
       "      <td>Edinburgh</td>\n",
       "      <td>Hotels,Hotels &amp; Travel,Event Planning &amp; Services</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>3zRpneRKDsOPq92tq7ybAA</td>\n",
       "      <td>3.0</td>\n",
       "      <td>bjTcT8Ty4cJZhEOEo01FGA</td>\n",
       "      <td>Edinburgh</td>\n",
       "      <td>Hotels,Hotels &amp; Travel,Event Planning &amp; Services</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>ne5WhI1jUFOcRn-b-gAzHA</td>\n",
       "      <td>3.0</td>\n",
       "      <td>AXgRULmWcME7J6Ix3I--ww</td>\n",
       "      <td>Edinburgh</td>\n",
       "      <td>Hotels,Hotels &amp; Travel,Event Planning &amp; Services</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>llmdwOgDReucVoWEry61Lw</td>\n",
       "      <td>4.0</td>\n",
       "      <td>oU2SSOmsp_A8JYI7Z2JJ5w</td>\n",
       "      <td>Edinburgh</td>\n",
       "      <td>Hotels,Hotels &amp; Travel,Event Planning &amp; Services</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>uYHaNptLzDLoV_JZ_MuzUA</td>\n",
       "      <td>DuffS87NaSMDmIfluvT83g</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0xtbPEna2Kei11vsU-U2Mw</td>\n",
       "      <td>Edinburgh</td>\n",
       "      <td>Hotels,Hotels &amp; Travel,Event Planning &amp; Services</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              business_id               review_id  stars  \\\n",
       "0  uYHaNptLzDLoV_JZ_MuzUA  VfBHSwC5Vz_pbFluy07i9Q    5.0   \n",
       "1  uYHaNptLzDLoV_JZ_MuzUA  3zRpneRKDsOPq92tq7ybAA    3.0   \n",
       "2  uYHaNptLzDLoV_JZ_MuzUA  ne5WhI1jUFOcRn-b-gAzHA    3.0   \n",
       "3  uYHaNptLzDLoV_JZ_MuzUA  llmdwOgDReucVoWEry61Lw    4.0   \n",
       "4  uYHaNptLzDLoV_JZ_MuzUA  DuffS87NaSMDmIfluvT83g    5.0   \n",
       "\n",
       "                  user_id       city  \\\n",
       "0  cjpdDjZyprfyDG3RlkVG3w  Edinburgh   \n",
       "1  bjTcT8Ty4cJZhEOEo01FGA  Edinburgh   \n",
       "2  AXgRULmWcME7J6Ix3I--ww  Edinburgh   \n",
       "3  oU2SSOmsp_A8JYI7Z2JJ5w  Edinburgh   \n",
       "4  0xtbPEna2Kei11vsU-U2Mw  Edinburgh   \n",
       "\n",
       "                                         categories  \n",
       "0  Hotels,Hotels & Travel,Event Planning & Services  \n",
       "1  Hotels,Hotels & Travel,Event Planning & Services  \n",
       "2  Hotels,Hotels & Travel,Event Planning & Services  \n",
       "3  Hotels,Hotels & Travel,Event Planning & Services  \n",
       "4  Hotels,Hotels & Travel,Event Planning & Services  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_merged = df_reduced.merge(df_bus[['city','categories', 'business_id']], how = 'outer', on= 'business_id')\n",
    "df_merged.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_cleaned = df_merged.dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.f. Getting the top Business and City for which highest number of reviews are obtained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def topm_num_reviews_for_city_n_biz(df,m):\n",
    "    business_city_count = {}\n",
    "    n = len(df)\n",
    "    for i in range(n):\n",
    "        k1 = str(df.categories.iloc[i]).split(',')\n",
    "        k2 = df.city.iloc[i]\n",
    "        for j in k1:\n",
    "            k = (j,k2)\n",
    "            if k not in business_city_count.keys():\n",
    "                business_city_count[k] = 1\n",
    "            else:\n",
    "                business_city_count[k] += 1\n",
    "    business_city_count_series = pd.Series(business_city_count)\n",
    "    business_city_count_series.sort_values(ascending = False, inplace = True)\n",
    "    return business_city_count_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2570222d550>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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V0cBzwP4uvz/wnKquDxzvcojIhthSrhsB44CTRWSQiAwCTgLGAxsCe7ssDecIgiAI+oGU\nNcJVVf/um0t6UGAH4HcePxnYzf9P8G18/44iIh5/vqr+S1UfAmZjq/JtBcxW1Tmq+hJwPjDBj6k7\nRxAEQdAPJC336l8DM4D1sa+CB4HnfX1vgLnAmv5/TeAxAFV9WUQWYOt7rwncVEi2eMxjpfit/Zi6\nc/Q5Iw//3x5xDx/3gUV1uiAIgtclSQPhqvqKqm4KjMC+DN5WJea/UrOvr+J7ICIHiMh0EZk+b968\nKpEgCIKgD8iynlLV54HrgLHASiLS+lIZATzu/+cCawH4/hWB+cX40jF18c80nKOcr1NVdYyqjhk2\nbFhOkYIgCIIMUqynhonISv5/WeB9wL3AtcBHXGwicLH/n+Lb+P5rVFU9fi+3rhoFjAZuAW4FRrul\n1FLYYPkUP6buHEEQBEE/kDKmMRyY7OMaSwAXqOqlInIPcL6IfBeYCZzu8qcDvxKR2dgXxl4Aqnq3\niFwA3AO8DBykqq8AiMjBwFRgEHCGqt7taX215hxBEARBP9BWaajqHcBmFfFzsPGNcvw/gT1r0joa\nOLoi/jLgstRzBEEQBP1DkvVU0J0qSysIa6sgCBZ/wo1IEARBkEwojSAIgiCZUBpBEARBMqE0giAI\ngmRiIHwRE4PmQRAsTsSXRhAEQZBMKI0gCIIgmVAaQRAEQTIxpjGAiPGPIAgGOvGlEQRBECQTSiMI\ngiBIJpRGEARBkEwojSAIgiCZUBpBEARBMm2tp0RkLeBs4M3Af4BTVfUEEVkZ+A0wEngY+KiqPici\nApwA7AK8CHxKVW/ztCYC3/Ckv6uqkz1+C+AsYFlsXY3DVFXrztHrUi8GhKVVEAT9QcqXxsvAF1X1\nbdja4AeJyIbA4cDVqjoauNq3AcZjS7mOBg4ATgFwBTAJ2BpbWGmSiAz1Y05x2dZx4zy+7hxBEARB\nP9BWaajqE60vBVVdiK0PviYwAZjsYpOB3fz/BOBsNW4CVhKR4cDOwDRVne9fC9OAcb5viKre6OuC\nn11Kq+ocQRAEQT+QNaYhIiOxpV9vBlZX1SfAFAuwmoutCTxWOGyuxzXFz62Ip+EcQRAEQT+QrDRE\n5E3AhcDnVfWFJtGKOO0gPhkROUBEpovI9Hnz5uUcGgRBEGSQpDREZElMYZyrqhd59FPetYT/Pu3x\nc4G1CoePAB5vEz+iIr7pHN1Q1VNVdYyqjhk2bFhKkYIgCIIOaKs03BrqdOBeVf1xYdcUYKL/nwhc\nXIjfV4yxwALvWpoK7CQiQ30AfCdgqu9bKCJj/Vz7ltKqOkcQBEHQD6Q4LHw3sA9wp4jM8rivAccB\nF4jI/sCjwJ6+7zLM3HY2ZnK7H4CqzheRo4BbXe5IVZ3v/w+ky+T2cg80nCMIgiDoB9oqDVX9E9Xj\nDgA7VsgrcFBNWmcAZ1TETwc2roh/tuocQT5V8zpiTkcQBLnEjPAgCIIgmVAaQRAEQTKhNIIgCIJk\nYuW+oAcx/hEEQR2hNIJeEQomCN5YhNIIXjPCM28QvP4JpREMSELBBMHAJAbCgyAIgmRCaQRBEATJ\nRPdU8LontysrBu+DoHPiSyMIgiBIJpRGEARBkEx0TwVBA9GVFQTdiS+NIAiCIJlQGkEQBEEyoTSC\nIAiCZNqOaYjIGcAHgadVdWOPWxn4DTASeBj4qKo+58u1noCt3Pci8ClVvc2PmQh8w5P9rqpO9vgt\n6Fq17zLgMFXVunP0usRBsIjIGf+IGe/B65WUL42zgHGluMOBq1V1NHC1bwOMB0Z7OAA4BV5VMpOA\nrYGtgEm+Tjguc0DhuHFtzhEEQRD0E22VhqreAMwvRU8AJvv/ycBuhfiz1bgJWElEhgM7A9NUdb5/\nLUwDxvm+Iap6oy8Te3YprapzBEEQBP1Epya3q6vqEwCq+oSIrObxawKPFeTmelxT/NyK+KZz9EBE\nDsC+Vlh77bU7LFIQDEyiKysYSPT1QLhUxGkH8Vmo6qmqOkZVxwwbNiz38CAIgiCRTr80nhKR4f4F\nMBx42uPnAmsV5EYAj3v8dqX46zx+RIV80zmCIKghvkqCRU2nSmMKMBE4zn8vLsQfLCLnY4PeC7zS\nnwocUxj83gk4QlXni8hCERkL3AzsC/y0zTmCIOgDFqWjx5hJv/iSYnJ7HvaVsKqIzMWsoI4DLhCR\n/YFHgT1d/DLM3HY2ZnK7H4Arh6OAW13uSFVtDa4fSJfJ7eUeaDhHEASLEfF19PqirdJQ1b1rdu1Y\nIavAQTXpnAGcURE/Hdi4Iv7ZqnMEQfDGJUfBhDJaNITDwiAI3vBEV106oTSCIAgGCIvqS6ovv7rC\n91QQBEGQTCiNIAiCIJlQGkEQBEEyoTSCIAiCZEJpBEEQBMmE0giCIAiSCaURBEEQJBNKIwiCIEgm\nlEYQBEGQTCiNIAiCIJlQGkEQBEEyoTSCIAiCZEJpBEEQBMkMeKUhIuNE5H4RmS0ih/d3foIgCN7I\nDGilISKDgJOA8cCGwN4ismH/5ioIguCNy4BWGsBWwGxVnaOqLwHnAxP6OU9BEARvWAa60lgTeKyw\nPdfjgiAIgn5AbFnvgYmI7AnsrKr/5dv7AFup6iEluQOAA3zzrcD9paRWBZ7JOHWO/OIsO1Dy8XqT\nHSj5GAiyAyUfA0F2oOSjTnYdVR3W9mhVHbABeCcwtbB9BHBEB+lMX1Tyi7PsQMnH6012oORjIMgO\nlHwMBNmBko/cPJfDQO+euhUYLSKjRGQpYC9gSj/nKQiC4A3L4P7OQBOq+rKIHAxMBQYBZ6jq3f2c\nrSAIgjcsA1ppAKjqZcBlvUzm1EUovzjLDpR8vN5kB0o+BoLsQMnHQJAdKPnIzXM3BvRAeBAEQTCw\nGOhjGkEQBMEAIpRGEARBkMyAH9PoBBFZAtgEWAP4P+BuVX2qzTFDC/IPq+p/+iAfqwHvLqR7F2bu\nVpu2iCwP/FNVX2mQySpfbtkWxbXoMB9Lq+q/+uLcwWvLonqGMs6/yOqARfh+JNcXOeXrpB5qzOfi\nNKYhIusBXwXeBzwAzAOWAd4CvAj8ApjculgisiJwELA3sFRBfnXgJuBkVb22kP6WwCeB9wDD6boB\n/wv8WlUXutz2wOHAysBM4OlCPtYDfgf8SFVf8Ju/F/AJYEvgX8DSnpfLgFNV9YHc8nVQtlz5EZ7v\n99D9Yfxf4PJOrrGICLCnX4uxwH/8mL95uqep6pxCHoYDH6vJw5VaerhT8+yyYyrkrlLV+ZQQkXdS\n/1yco6oLSvJJaYvIMsAHq/JbtiLMkXX5pYBdKuQvU9X7OilfB89QUh4yr8MiqQNyy+Zpp74jOfVF\nTh2QnC4ZLG5K4zzgFOCPFRXGasDHgedUdbLHTQPOBi5R1edL8lsA+wB3qurpInIp8CxwMTCd7jdg\ne+ADwPdV9VIR+QHwU1V9tCKPg7EXYJCqXigi1wNXebp3FR6klT3djwO/V9VzcsqXU7YOrsWZmDuX\nS2uuxRbA4ap6Q2a61wHX+7W4vfW15WXbHnthf6uq54rIacC62AtYlYdNgK+o6p88jaQ8e5qHAg8B\nM0py78Ze+m+27q2IXA48Tv1z8SHgx6o6RUQ+lZq2iHzbj72uQnZ7//9FVb0jR9bz/A1gD+CGGnkB\nvqSqd2WWL+deJ+UB+Ehm2RZJHYBV/jnvU847klNf5NQByemW9zfSm5mBb6QArJ4gs1oH6S7ZFzKv\n8bXYuM3+pYD1O0h36QSZpfx3kzZyywBvyc0z1ppctkFuU2DHwvaqCXle1X+T0wY+0CbN1YAxubK+\nPaGN/HDMXU9W+TLvdVIecss2UMKiekcGQuj3DCyiG7YnsIL//wZwEbB5g/z+pe1BwKQG+VWBcR5q\nXxjgMGAI1mo6HbgN2KlGdr1WpQlsh7VIV+pt+bAW7PL+/5PAjzEfM3V5zpVfFnhrwj1JThcYWVAO\n2wCfA4YknGNFYMMEuaQ8D7SAGa60vQ4dyC7bpMxcpsd1Bbbri2fI5do2GDKv1VHA4ML2EODMBvmk\nOqCTsmXkOae+yKkDktNNymdf3qiBEoA7/Hcb4I+YO/WbG+R/jY0fDAc2xtyX/LBGdg/gUeBcP+5h\n4MM1srf7786Y+5NNgNtqZGdhhgnrAw8Cx2N9u70qH3CHPyyb+P/DgOubrl2qPLAr5hzyId/eFJjS\nB+nOApbEFOkc4KfApTWyV/sLMdTvyyzgBw3lS8oz8H1Pd0k/xzPAJxvS3R3rY14AvAAsBF6okU1O\n25+xIcDywH3AE8CXeyvr8hv5s/43rAvqZmqULtZ19lW/h8v6PbmxD+711lj3z6O+vQnWpdLafwn2\n7lSGhrIdi3VnvQPYye/5wb2tA3LK5vLvBqYBf/Vn+SFgTo1sTn2RUwckp5sSOjpooAdgZuHB+Xgx\nruGYj/nL+yjw7ga52yl0VWEDYbe3ubEn4IqlLh+tmwh8GTikjWxy+QrpfgtvTTU9MDny/lKuWDx3\nq8y9TLd4LQ5NvBb7A0c15SEnz8As//0wMBkbTKy8zy43G3hb4vOZnHZB9hNYq3bJhmucLOtyfwLe\nX9h+H/CnGtnlgZ8BN2IK5AhgiT641zcB65Tux12F/9s2hTbX+X3Y4PPjJHQFkVAHdPA+3YctIrca\nsEor1Mjm1Bc5dUByuilhsTS5Bf4mIr/AHprvicjSNMxJEZHRWIvhQuBtwD4iMlNVX6wQX0K7m7bN\na0h7hohcCYwCjhCRFTCLoCr+LSJ7AxOxgT+wl76KnPItFJEjsE/p9/pqiHXp5sq/rKoLzOipLVnp\nulv8fYDdPK5OdrCIDMM+17+VkI/UPLfOtwtwnqrOb3PMU6p6b8L5c9NeUkSWxK7Dz1T13yKifSAL\n1r0xrbWhqleJyI9qZP+NVcDLYuNFD2m9yWbOvV5CVR8plf9Vc3NVvb4h/7WIyHuxSvJI4O3Az0Tk\n06r6eI18ah2Q+z4tUNXLE7OdU1/k1AE56banU20zkAOwHNZdMNq3h9PQh4e1BloDkAJ8EbN7rpL9\nMfYZ+0kPl2Jma1WySwCb42MTWCvjHTWyGwInAnv79ijMuqJX5QPeDHwBeI9vrw3s23AtkuWx/tGP\nY5/po7Eui5/3QbobAyfjXTZ+Lb5eI7sXcA9mmgxm/XRxQ/mS8gwc58/FTKxSGEbF57/fh92xCuo3\nmIVXK273mjwkpe2yh2LdR5f5s7kOZjnTK1mXvxj7Yhjh4XDquxdvxyrgJf1eXgz8rg/u9YXYgPdt\n2DjC5zELubLcaMxE9B6sm2cONd08Ln8Lha42vx/3Ncgn1QE5ZSvc6x9gyzxs3go1sjn1RU4dkJxu\nSlisTG7LuAnaMq1trTA9c7khWrJVFpHR6vMjSvGtuQTbYA/XDar624Y8DMUe+GI+bsgsSl3aSeVb\nVIjIcsDXsT5jwbwRH6Wq/3wt85FDKc/Qlecekwj93r2gqq/4cUNU9cmSzJkNp1NV/XRNPtqm3VCG\nwar6cm9lRWQVbMB4G4+6AfiWVs9FGaOq00tx+6jqr1Ly0ZC/1bDG0vuwZ2gaNvbwTEnuT8AkbKzv\nQ8B+2JSBSTXpDtLSBFkRWUVVn62RT64DchCRayuiVVV3qJHPqi8y6rg+q4cWS6UhIrsCP8Im1DyN\ntQbuU9WNSnI7qOo1IrJ7VTqqelFF2seo6tfaxXn8f2GfvCOwAdqx2OBhjwfGP4+Pxb44ijd23U7L\n57Jjsdb02zAzv0HA31V1xaoy58qnkpOu2ASmo+l5Ld5SIbs08ClsULcoe0BZ1uX3LCv5qjiP37gi\nD2c3lTOVnLRF5AP0LN+RfSC7e/kZL8e1KlOxeUM9qFEwff4MicgMVd1CRO5U1bd73B9V9T0luU+q\nzWn6Qk1+f1ySz6oDFtX74Wnn1Bc5dUByuiksrmMaR2EX5ipV3UxsZuTeFXLbAtfQNYZQRDEztjLj\ngLKC+EBFHNiN2hK4SVW3F5ENgO/U5PlMulpS2+MtqRrZ1PKBDV7uBfwWGAPsi7U46mgrLyKXYNen\nElXdtZf5OAv4LvBDbBBxP+r7YM/Guio+iCmajwNNa64c4XlojBORSZjp84ZYd894bOC4rmI/sSJ6\nAeau4eJO0xaRn2NdEdsDv8Qmu91Sk4dkWadlqlnk66W4X2PXdgZ2z4vPpGLdgWWS77WIjMSe+Xd6\n1J+xyXoPl0T/KeY94QGxNXb+hg0ul1nef1eoOl8FuXVA1vskNpN8EvBej7oeOFJLXgKcnPoipw7I\nSbc9nfZrDeSAL2eI9cMu4f9QU14sAAAgAElEQVRv6WWan8X6oP+B9b+2wgPA+TXH3Oq/s+iagzGr\nRnaG/95ZiKvru04uX0H2jkLcXxKuXa08HVi05OQj81rMLKaL9blfUyE3HmshPoV1h7TCWVXXDjMD\nXYIuc8XVsdnAddftVKx75xAP1wEnYSaOP+k07UK5Wr9vwlykdCyLmV4e79fix4Xwy9Yz28t3Jede\n34g1Cpby8CkqTHmxSu9NWGv5TGwsZGxv87ooy+b7LsQq6HU9TAIuqpHNqS9y6oDkdFPC4vql8byI\nvAl7ic8VkaeB2j5g7+LYA5tU9uo10e6f9RdgNvXHYgOGLRaq6tM1Sc8VkZWAPwDTROQ5zPyvitSW\nVG75XhTz8TNLRL6P2e4vXyObJK+dWbTk5ONfPnb0oIj8N83X4t/++7yIvA2rCNepkHscc+ewK9Zq\nbrEQ+J8K+f9T89/zsogMwboAqlrVLdYHdlAfPxCRU4ArgfdjSqLTtP/Pf18UkTUwVzajein7NGY2\n+0+6f5UtpPuz3Q0RWRO7tsV3pKpfPOdeL6GqxXGhs0TkwLKQqt7qeVBV3a8uj4W8DgM+Q893um6M\nKaUOgPz3aT1V3aOw/R0RmVUjm1Nf5NQBOem257XW1K9Ra2B5rK9xMGbCeig1ttEufwVm+fIVzGri\ni9gncp28YJXYGq2QkKdtsQprqZr95ZbURdS0pHLKh73ky2KTviZhLcpam/UceTIsWjLT3RrrXlgb\n+BXWWq+zm/8sNrFve8y+/hngoIbyfaUi7rCKuJOBlYD/xr4mZ9I8o/h+YMXC9oq4tQ4lm/ictIFv\nuuwewJNYJXVUb2VdfpmMd+p72ETWy7AJd5dQb2mVc6+PxXxMjcB8NX0B6zYbAqxckHunP2fFSYAn\nN+T3L57nj/r12APYo0E+qQ7IKZvL3whsU9h+NzWTIkvHtasvsuq41HRTwmI5EJ6LiNylqhsnyh6I\n9Sc+S1c/u6rqhhWyVYOHC1X13xXxrztyLVoGAiJym6puXoqbqaqbNRwzErNuuqNBZn+ssrsOa1S8\nFzgGOA/4tqp+udO0C7JLYxV9VX94tqwP6k6i6+tBsGe5yuDgfsxMs09d1YvIYw27lwd2VdU/icjN\n2BjNlNa9anpvRWSWqm6akY/kOiAHEdkUm8C5InZ95wOfUtXbK2QXSX3R1+kult1TIrKQngO1C7Du\niS9qwb228xcRebuqlrsRqvgiNvN3XoLsbcBawHPYA7MS8IR/Sn5GVV/tJqkZXG7l+RdaMGPNKZ+I\n3Nkg+10tmSBmyi+rqleL9Rk8AnxbRP6IVUTdyElXRH7fIHuaqr5UkD20fC6XnaGqdxXk9sYGyUeJ\nyJSC7ApYA6Cc380r4tYDHtGSCat3pV2JtcK3wu7117RrItmXS/I5afew6hGRBdh4z9OdyjpnYi3r\nGRQm1NUwBxsvaqs0cu61qq7VkM4grEHyJ5d9TGomAVZwqYjsoqqXtcuvk1QH5L5PqjoL2MS7IdFm\nN+Q59UVOHZecbgqLpdLAPhkfxyw/BLN2eDPWhXAGZrlSZBvgUyLyEPZStFpc76hIey7WWkjhCsyt\n+VQAEdkJs766AOui2LogOweb5HWeb38M659/C3AaNju6k/Jdjr1cv/btvfyYBdggcNlqJEc+Zxwm\nJ93HvDzFazEf8yN0GvY53uJdWNfepb69C2YxdJiInKuqrRnOf8G6a1bFTBVbLMQm+pU5GZsQ1fI1\ntLH/X0VE/ltVr2wJqqqKyB9UdQts0ls7ktPG3KO8E7jWt7fDXG+8RUSO1O7zJHJkweaJXJKQX7C1\nGmaJyNUUFIeqVint5Hvtz884eo4lnKg2z6KV/mMi8i5AfUzhUKBpBv5hwNdE5CXgJbre6SE18ql1\nQNb7JCKHYcp5IXCaNxgOL93jFjn1RU4dkJNuezrt1xrIgeqZuzf5bw8fP9jneY9Qk/YvMbO5L2MP\n7qG4f6QK2el1cZSsF7BJgmXZG/z37lJ8cvmAP1fI/tl/76zblyJP3jhMTrrXl7ZbkygB7intm4p7\n+/TtFbAXe7mybEFmdcyM9IPUuLMHzgc2Kmxv6GVct3zvfP9JwJaJz2dy2tjYQdnX2UWYv6q7OpX1\n/cd62BJTyO+gfgbyxKrQB/e65ZDwaKzb9ygqxmEwZX8u1pB6GjiHhD781EBiHdDB+5TjhDCnvsip\nA5LTTQmL65fGf0Tko9ggLVhfaIsegzhqvm+2wabkn+mWF2+qSfsJD3UtliLzReSrWCUB1mJ+zj+7\ny/MOhonI2tq1uM/a2IsC1lIqklO+N4nI1qp6s6e7FV1lq7K2SJZXt2gB/o6NZzSRk4/VRWSEqs71\n7TWwrzDo2T2yNl1WQ639I1X1RRGpmuW9Jzb/4zpMGf1URL6sqr8riW6ghVXhVPUeEdlMVedItZ+o\n7YHPisgjmFl209dqTtojtbuvs6exdULmi0i5TzpHFrpmgm9TiFO65hR0RdqiPssCa6vq/RVpFcm5\n1yPVJ+vV4e/LPqr6iTbnLR4jmOPGUap6lIisBQxX1cp5Kxl1QO771Lqhu2DGDrdLzQNEXn2RUwfk\npNuevtLUAylgLbZLMEuaef5/fczqYZsK+Uku81ffXoOKFkXpmJQ1CFbF5gbM9PBTrPLrsQAL9lA9\ninUtXAc8gk0aXB74fKflw1qRd2IumR/CukG28nQ/WpHntvJ04K46Jx+YdcdjmEuJq/y67OqyXyrJ\nfgdzY/11Dzd73PJUzJ/B7NpXK2wPo/rr8zfYCmnbejgZ+5xfmoq5DOR9rSan7fsupat1f4nHLQ9c\n26lsB+/Uh0h3g59zr3+ImSq3O/91mfk9Bfv6u9e3h1bdt9w6IKdsLn8mNt71APb1uwI+D6mX9UVO\nHZCcbkoI6ynM0gLYDPtsbFlm3KEVrUQR2RCzhhiOtSLmYtYQtf2rIvImVf17Qj6WBjbwdO/TPvTh\nJDYzVbS0VGUn8iKyrf/dHetHPce39wYe1gqXKrn58Fbthti1uFtV/69Bdmu6fIH9SVVvapB91Q2F\nb7cm2b29JLcstvjTq+liFfA/geXK99O/DHug1UttJqftrdLdS7IXasWLmyPr8itgZrrF2crfVV/r\nviQ7A9gBq7xb78id5etWOqbtvRaRCVi/vNJ97GHlktzRmAXSb7AvOTDB22rSvU1VN5eCZZyI3K6q\nm9TIJ9cBGWUTrOt2GGaK/ryYv681tdkSL6m+yKXP0u1N62OgBmzw+Gq8Hxfrq/1Gg/wt/tvylb88\n9WsW5KxB8C4SbcuxVsg3MOsgsDkQH+xt+bB+7dOxhezBKuL9q2Rz5WkYh+llustik8x+7tvrA+Mb\n8jwW9zSKefBcu0H2B9g4yKc8XA58ryEfSSv8Ya3PO/z3AayrotJTcgdprwO8r/CcrNBHsr/FxhLe\n4uEo6j3X3uy/KWun5NzrOZhRwJLYvINB2LrVZblrK0KPmf/F/HparXd6GA1rSJBYB3TwPlV+VdTI\n5tQXOXVAcrpJ+ez0wIEcsBbTVtQs7FIh/yXgF/4AfwabkHNIjWxVV0bdAjo3Y6ZubfNB18Si1kOw\nLPUuBJLLh1WKH6VrQG4wFQN2nchj1ivrFrZH4d0BvUz3PMyXV+taLFf3wmOK9nK6uhXWpEaJF47Z\nA7M+OZ76VReTVyWsOX5zzFS6V2n783gr8KBvjwau7q2s768a0K975nLc4Ofc66lYi73d9Vw3Ja6w\n7xNYd+nfMMV4P7Bng3xSHdDB+5RjIJFTX+TUAcnpJuWz0wMHcqDL10rxIjVaCWDuHn6A9bG+v0Eu\nZw2CqtZZnYKZniGbXL7ca5GZ9jhsvOE6Dw8DO/dBulXXok52Ftal0bYFnPkMJa9K2JBGX6x4OAvr\ney7K1lXAybK+7ybgnYXtsbgFToXscljleys2F+BoamaUZ97rM7GvhkZrxKprSZtWPNbVe5CHtqsq\nklAHdPA+3YOZ6D5I15do3b3OqS9yrnFyuilhcbWeesYnSymAiHwEs3hq4g5sIBJssLSOT2Of8a1J\nQzdQbzmUY1v+kvd1t/K8HvUTqXLK9w/vR23JjsVsyutIllfVK8Rcum/gUfdp/YzhnHy8JCLLFGRH\n0dOCrMW/VFXFV6gTW5uiB4XJUEJ365I6+/2cVQmR7q64W4ve1E0AzUn7X6r6UktWRAZTYQHYgSzA\ngcA5PpYGZoW2T5Wg2gp2XxeR42yzsW88517P9VBpjSjmkXUjYEXpPnlxCAX37zUsTZf10lJtZCGt\nDsh9n8YnnLdFTn2RUwfkznFpplNtM5ADZllwFTYh6W/YOMQ6DfIfxayVJmPuqR8CPlIhNwg4LiMf\nybblWCvneqyiORdrtW/X2/JhldefsQf7z9gC97WrduXIY4tRreD/W26261Yly0l3HPbl8rTfk4fx\nVdUqZL+KdQE8iCnvP1GyNuvwGUrujnH5SYXwdax7pK4lntPV832sq+4+f0Z+DxzdB7KDcF9M2DyO\nxjkP2JKpM/09eQT7Wtq4L545P2bpmvgJ2NfIs/7bCicC72pI7zDMKeN3sBUH76Smy9nlU+uATsq2\nDbCf/x+GmQH3tr7IqQP6dI5Lr16sgRYoTGzy7eVpGAgsyCWZYfq+2sG3gsyYDvO/CmZm+0Fg1d6U\nD1iy8H8w1lrbuBjfG3mXa7ng3gb4o7/gN/c23cI9mICtd105Aa8gOx4bn/gJzQPmS5DYl0v37phb\nsfU92jr4w1rAjc9cTtqe589gg9a/8/+VYwA5si5fuxRshexfgO0L29vR02V+J8/QVliFXhyk/WmF\n3DtT89p6NoHlS+9KbfdiuzqgF8/xJNqY8pJRX5BXB3RUD7XNw6JItL8C5tlzGtaFNCTjuPIs1SXK\ncYV9P8Ra1HtjA5q7Yk7VijIzMQuaI2nTl4r1eX4dc6HcZ+XDWhSnYWaSKQONWfKtcvrvscDHi3Gd\npOsv7ldp+CosyP4E2KqDZ+Rcmq2rPkKG99fCcWO88nvYw+3AFp2mjQ3MrtXXsqXjvoGtyT0cU3ZD\n6p4rEgxAOnyGbsIsvhoHabFK/GvYuiVntEJDuncWrzXWldU0vtNYB3RSNj+u7ZhbZn2RUwckp5sT\nlmDxYk2sUn8P5g/pDyLyMR8raOIKEZkqIp8SkU8B/0vXmEWZ1TE78V2w7pk96T4bEzU77w9iA2AX\nisgsEfmqiKxTkd7e+GI5InKziHxebC2E3pbvbdiA5TexPs2f+HyGOnLlAf4mIr/APu0v877x8jOV\nk+6nsU/p60XkzyJysNgayFU8BpwkIg+KyNFiy6emMBy4W0SuFpEprVDY/wngURE5W0TG+6zZFM4A\nPqeqI1V1JDb4emZJJiftNTEnejeIyIEismofyRb5LOaA8xZsXY27sS6dKuaIyDdFZKSHb2BdOEU6\neYaWUHN2WaTKEeHFmPHAVdj72Qp1nAncLCLfFpFvY8rp9Ab5dnVAJ2UDeEmtBlcAEemx9kZmfZFc\nB2Smm05faZ+BFrCBrwmY+eaTwLlt5NuaYfYiL5tgrfEHaZhpjlmvHI9ZJF2DeaDsdfmwT+LDMDPC\nB6np586Vx7pZdsdcL4BVyDv1RT6wdQd+ig2SXon3CVfIrYd9qd2JVXhfo9kUc9uqUJIZgs2ovhxz\nCncK8N4216zWJ1GnaWMt1G1d5nE/Zl8quiNyZDt8hodi4wi3YS3YE4ChffAMXYh1Ud2GjbN8Hvht\nhVy2jyRgC2zQ9zBgswT5pDog8zlONucvHJNaX+TWcUnptr1OffFADdSADTJ+Cxusqp3Yk5nmGlif\nccsH1W9oWIQJa3m/H2uJPgn8IeEc2/mL+a++Kh/2NbMv9rn8VEIe2soDv0qJ62U+3uPX4qUE2S1c\n9pU+fIZWwVrktwOPVezf3MPxXjlsR5drkHbKuTHtkuwgzOndTODFvpDF+uY/h/kkOh9bFGpwH167\nlGdoNT/3Mx7Op3o877vALpnnH+Tv69qt8FqWrSCbZM7vsln1RWod0Ek9VJtWX13EgRL84fgy1nK5\nH7OeaNdPuDvW97cAeAFzY/xCjexUrMWwtIf/AqZWyL3HK47HsZbypyms7FYhvyXWynkEs6I6sObl\nSS4f1o+7JzYG8xRmGTKeihm3HcrfVtoeRIVn2Q7S3QyzBHoIs1A5hNIAYOmc4z3NJ7GWaw+rl4L8\nWGzw+e+YGe8rDfd6qN/ra7DusJ9UyFzbEJpmLLdNuyD7dmzgfDY2UavWOixT9heYJc1OHs4GTq2R\nfQs2nnCl5/maqvKl3mvg4Mz3eiHmXO+f/r/2HXX5QzAldDdt5kek1gG5z3Fm+ZLrC/LqgKx6KCmv\nvS3sQAqYhccjmEbPsUiYXXfRK2TbzqL1SqCxsivIHoN9Lk7Hl73si/Jh/nyexqxo2g7A5shjkxsX\nYq4yXii8ZM9SMknOTPdIfwlmYZMm12mQ3d4rsSexrpiJpFnKTcfckszEFM5+wDGF/StgcxUu87RP\nJXPws+HcyWljLchvYoYSd2JdcJXdbjmypeNyvBvcjjVktsK+6Lag50B/zr2unPjYV8Hf6WSz0nZ1\nQAfv08LCu9EjlGRz6oucOiA53axruyhv3GsdsG6B7JebjP49rIXVWnhFMDfD15Rk1slIbxLmvrpP\ny5daiXYq78cc25fpYpMmN0yU/aNXYsMy89yabX5HIe4vhf/PYBZWH6KNOWUp3cOw8QrB1ly5jdL4\nTk7aWB/40cDbE86dLFs6bibmmry1PZJ6dy1tfShl3utspYFZKv7QQ6VftoLstWR0tbWrAzp5P/y4\nI7EuwBX8+TiQ0jr1mfVFTh2QnG5OeEN7uS3MMN0W89b6B7qvSnZRxTEj6VrtSjGrjENU9aFFnN0B\nh4hcrao7tosbSIjIDZiTyV9irf0nMC/Fm/j+5dRmP+eme7uqbiIiO2OWU9/E1k/YvCDTUdqLChF5\nP2ZR9FdM2a2POd+7qiDT8jZ7KNbS/j3d35HUVSzL534Zm5jWYxcVM/R9JvqWmNIFszqcoaqHl+Ra\nM/M3At6KWUEV8/vjknx2HZCDiNysqlu3i3s9sbi6EUmluDTji1i/bgvF+i4BEJGDVfVnqvowZm77\nhsVdfCwPrCoiQ+ly1TAEG3gcyOyDDQoeDPwP5shtj9bOXlTqbRfbGSgKQ0TGqupNqjpNRN6KmZMK\nNh5VdkFfXj+6uN65YjOTO+FOdRfkiewCbKqq/wEQkcnYl9LhJbkV/PdRD0vR7EIkuQ7okFdE5BPY\nAL9iyq7deuwDmjf0l0YLEVlVVZ9pI3NbsdX4RkZs3ePPYwri8cKuFzDX7j/rl4z1IyJyJmZDPwoz\nbRyErT2xRb9mrIKB8CxLYZ2LRPk7MLc68317Zez6Vq15MwybMDhb09ePaVsHdIL3TJyAmZArNsbw\neW98vj5ZFH1e/R3o3r98OhX9yy73QczX0+PYfIAmXzad9MF+3/OxJOb7/hngkzWy78bdHgCfxCyp\n1ulN+Vw22T9Urjxt7M17ke5YbDEisJbZ96mZ8Yy5kG81ftbDWqS1fdl+nadhXTJzWqFN3peg/ezb\nlpPClXx7Fdr4JEpNuyA7NCXNdrI5zzI2yP4HbA7MedgCQr2+18DXUvNQeA4eAc7CrJYeAvaqkNsf\n60a7Eet+3LVNusl1QO5znBsy64ucOiA53aR89kVhB1ogcTF3zBRvA/+/NXB9Q5pFS6FiaDLPneW/\nH/YHfWXqrVPu8AdgE/9/WF1+UsvXStd/a/1DdSqPffYfilmU/A7r8qnzbZWTbutavAOzBvpiw7WY\njk0yHO4v/SXA2Q3luw8zk1wNq9hXocLKBrOWGYJ1w92HjX18uSHdHutWVMXlpo05bhziz86jWHfR\nj3sjCzxP4nK9fq8+g40PfBm4KOH9y3rmUoPf4109vTfXyNyFG0dgXWc3tssriXVAh+9TsvsT8uqL\nnDogOd2UsLi5EWnRo3+5EFfkZVW9D0BtofgVKmRa3KmqQyrCCtrTrXaLJQv5OE+bBw1fVruzE4AT\nVPWEhvyklg+6+k8/AJyiqhfT3MebI38yZnp5cuH/KX2Qbvla/Ij6a7GE2ljBHsDPVPVDmLKpY4Gq\nXq6qT6vqs61QIbehqr6AOUy8DLON7+E2XESW8a6SVUVkqIis7GEk9eM7SWk7K7rs7ti93gIbyO+N\n7DzgRw2hyAqqepqq3q+qP8AsrNqR+8zVIiKbtwJdDYPHgDU8rsxLqjoPQFXn0OXqvI6cOgDyy5bj\n/iSnvsipA3LSbcviOhA+Q0SuxPqXjxBbC/k/FXKrSfd1ELpta8nSogMuEZH7sHUKPud9rXXrfi8U\nkSOwrqn3ul+iJWtkU8sHXf6h3gd8r8Y/VKfyW2r3NZevEZG6dQhy0v2HiHwZuxbbia3jXXctlhCR\nLTFX4wd4XA+fToUK5loR+QHWrVC0kimvNb2kiCyJVew/U9V/i6/ZUeKzdI3vzKDrxX0Bc9leRWra\nAINFZDjm3+vrNTK5sgtV9fo2abVYRkQ2o6tcyxa3K64b5D9zTUzHJui11iYpVoyKzXMpMkJETqzb\nVtVDS/K5dUBu2ZZT1a827C+SU1/k1AE56bZlsRwI90pmU9os5i4ik5rSUdXvFGS/pqrHdJCXoVj3\n1StiCwQNUdUnK+TejFV8t6rqH0VkbWzg7+xOy+eyy2HrU9ypqg94pfJ2Vb2yJr/J8iJyG7aE5oO+\nvS62xnSPFmBmumtgCuNWVb3Wr8WOqnpmhewO2KTIP6vq0Z6HL6nq50py11aV11FV7Vb5iMihmMfd\n27FW5drAOar6nqoERORQVT2xFLe0VixKlZO2iOyJme/+SVU/5+X7garu0amsiFykqruXj68pV9Z1\n82OynrnSsROAJ73Vj4j8D/YVuQCzQPq9NiwAJSITm9JX1ckl+eQ6wOVz36fvYvOA6hygluVT64vk\nOiAn3aQ8Lo5KA169SKMprO6lqjf0Qz42xhafL+ajhyLoIN2s8ol5iy3KPtom/bbyIrIj5k10DtYC\nXAdzLFhb0eTmYyAhIoNV9eWafT0sknKslJrSfr3Syb0WkWMwVyiDVXV8IX4UNhg+ARsQP0ZVZ/V5\nphNJLZvYipHLYy5rXqJmHkpBPrm+yKkD+rIeWiy7p0Tkv7CB5BGYS4qxmDVFj1bRIs7HJMyB3YZY\n3/V4bIWtqq+HsZhX17dhfaSDgL+r6ooVssnlE5FdsX7qNTCrkrWxwdeNavKcLK+qV4st9/pW7GWo\nXe41J13vbmpdi9aSnf+qetHE3IB/0dMpvhA7leS+gI1nnF6KPwTzHfSTirQ/UE4Xm+FblHkzZmrb\nrdsGG5CuXHo2NW2XWwazCCqX79O9kV2U5D5zRVT1azXxD4nIxZi13D6YL6zXXGnklk1V242RFNPO\nqS9y6oDkdJPQXlo0DMSAL8BCl9XABsBv+ikfS9Bl6bA6cEmNbKNPpE7Lh3WBrELXgknbU+OULlce\nm/m8UmF7KLamRG/TvRVTRDOxsYzPAEfWyF6BjSvcB+zoL8L3K+TuApaqiF+aCkd2wM89rccwVy93\nAqdXyE3EXFYspLuzwinA7jV5TkrbZX+LuVd50M91JWYc0CvZRfzc59zrKhPWzQr718Wsj24m0e/T\nQCmb7xesq/Wbvr0WNYuHkVdf5NQByekmXYP+uviL+Mbe6r+z8LWH6cAff+K5JgBb1+y7xX9n0GVT\nfXeNbKNPpE7LV0j3dszS6NV89Va+6pzU+y7KSXeG/xZXTqu7Fi3ZlimkYJO+ynLJq7aV0mv9vgm4\nsiGNPTKemeS0C5VTS3ZJarzn5sjWHD+cmrW6c0LmvW40YcUGd2dhnly/CHyhGHqb10VZNt93CmYQ\nca9vD229vxWyOfVFTh2QnG5KWCy7p4C5IrISNilpmog8R/eZy42UB+PasDXwdu+THl/aN93zcRp2\nw/6OrZJWxYsishQwS0S+j9nu91jly8kp3/Mi8ibgBuBcEXkam3NSR478EiIi6k+kmMVXnflhTrr/\n8Gtxu/dxP4FVrFX823+fFPP79DjWmuuBiKyuqk+V42rSbbnTeNEH5p/FLFXKaX5SVc8BRpascIBa\nC7yktJ1W+Z73fuknqTd7zZGt4lfAeiJyoap+qUnQB4Dna3V3ZM697mHCKrbSXosj8VXvqH8G2iIi\nn8Ou84WaMHbUUAfkvk9bq+rmIjITQFWf82e7ipz6IqcOyEm3Pa+1pu6HlsG22ISgHI+lx2CTxC7v\nw3yMxOYPVC7YhA0iL4O1BCZhM8JT1g1vLB+meJbAxq8mYpPxVm5IL1keW1jmt1i30A7ABcCP+iDd\ndf1arIR1t5yIrw5YIbsrZgf/DqylejsVq65hC+ZM9+u1goftsJdnYoX8N/38e9Dl2LBHFxnwWf+d\nVBVq8pyUtsv+F9Y6fS9mcPB065y9kW24/wJslCB3FTYr+4e9vNeXYut6POjXZGl6MfGsIb8HYeNk\nUxLlK+uADt6nm7Hu5tt8exgJC8LRpr4oySbXcTnp1qbR1zdnoAbg0T5Kp7EPti/zQcY4TGa6WUs9\n1sn7y/PfWF/zhdjYQvKCNDn5oM1SliXZygV+sAHA67EW5zP+f3xCektjiqmyG9JleiyYlZjXtmlX\nHJPTFdZDFpsRXBsy0k5SMG2eoawlgwdiaHqOsXXhp2CTEo/G1ovZMyPtnPd6kcj2OLa/L/hreGNr\nl9PMUQT00kVCUz56+RDkpJssmyKPdUltBqzWl+n24lr0SQMhJV0yfRe91uWryfND2JfIQ1j30DOu\nSF8BHirJ9pWCqbzXdLBkcOL5Vsd8Ml3u2xtibt/r5DtuDCa8HxtgXzoHk7jYW2rar4VsOSyubkSq\n0IZ931TVhSKyDebLZTJm4VJFb10kNOWjN+Skm5uHbvIi8nMR2cj/r4gNxp0NzBSRvRdhPlKpc6ew\nKNI9BniPqq6BdTcd24dpLxJZVR2lqutiSxd/SFVXVdVVMAVYdgU+A+vWm4Epx79iy6LOo6fb9Cbq\n7nU3U1UfF+sLz8BnYRYqAh4AACAASURBVOVruXL5KzZzv46cOqBMj7JJlzuZlbFuwvMwn2NPSdca\nJR2l3Q+y3VisBsKrBiJbu2geRGs3GFekrRsBEfkp1TdFsH7bomzd5C+h5Dojp3zStbhMleyyPSLz\n5N+jqv/t//cD/qqqu/mchcuxFyQ7XRGp8xnV41q04bVUzN18F4m5c+irtBe17JaF+4iqXi4iR3U7\nWHUUWEMBGw+4zLfHU/JrlXmvj8BMaZcVkRcKci9hzv0aSTBWWVVVL/DzoKovi0jTOhaNdUDu+4Qp\nVPX9w+kapBZK65Bk1hc5dUByujksVkqDZmdjJzTsy/En81HMjcAP1abvD6f7wjRgLbM6yvvKDuKK\n3FfazinfhyqljEsr4nLkXyr8fz82GI6qPinSo2Gbk26dryawNZxfxa1F6l6ITituROSShnRXqYhP\n9l2Uk7aI3Nkgu3qnsiWeEZFvAOf48Z/EuqmqaKtgyLjXqnoscKyIHKuqRzQcV0eT1SKYBd4q+HXx\nybMLGtJrVwdkvU8tZevnbrd2SE59kVMH5KSbzGLrRiQHyfOL9CtV3add3OKMmD+iHwF/wyaybeAK\nYzBwl6pu8BrkoYdTwiKqmrQ6WrnFKiLbtkm3m6M/yfNflpy2iKzTRvaRTmSLeDfJJMzaCsyM9Dta\n4QVVRKZiY3hFBfNeVd256dwpiMiamPXgq41Y7aXLH/+C/ymwMe4uHfiI1vtm6thfVkJe+n3Rq74k\nlAZ5iqD8AHjldaeqbvgaZHVAICJvwcxg3wz8RFXP8vidMcuXL/Zj9rKQGl9HbyREZAjwH212BJis\nYDLPfRywF3APXV1Eqqq7luT2BK7wcYdvYAteHaWqM8tyqvpbMV9Vj9Hl4uZ+Vf03FYg5/7tDVTfu\nTVnqCKWxGJKiCIp9sNhawlDog+3wEzsI+g0ReTtmwNAamH0Gm7NyV8MxbRVMZh7ux1YYrPRZVpC7\nQ1Xf4QPVxwI/xFb/27okd5vaZLqsilpEzgWO0D5yoFnqsvwCNu/qVbT3yy70G4vbmEYWOYNxfdAH\nGwwAUlusbxB+gbniuBZARLbDnvt3lQXLCkZE2iqYROZgRg6NSoN0Y5Vnvft0lIhMKe8sf8EUGA7c\nLSK3AP9IkG9HcezhNHoxzjbQeEN8abSztMhVBJ32wUqGKwNpdtNQlk12eyIiY4AnVPVv7WQ7kU8l\nJ12xRWMWqOpL7WQT0kpqsb4REJHbtfsiWpVxHv8X4OslBXOMqvZQMBXH1t5rEbkQW6r0arovinVo\nSe5SbAztfZhJ7v9hPpXK+V8Kawj8Cpsh343ymFThuMrxpjr5lLL1lsz6IqcOyHKpUuaN8qXRaGmh\nqkekKoK6Plisj7cdgk0K/AQ27b+JZD9AtLckKXII8A4R+auqfiwhz7nyqeSkewHWcjxfVQ9vEhSR\nKzAfTCep6hUVIjnm1cV0j8Gsb36p1cvDluVzXuLktEVkMtY9elK7Vn6C7BwR+Sb2rIENbj9Uk9zy\nWlgnRVWvE5E632hlmu51a23ydqRYLeINi5tE5F3qy76m0E45NLCo3g/Iqy9y6oCcdHse/Eb40mhH\n6mCcyyb1wfZRvgRbT/ruRZD2Cqq6sC/lcyrK3Hz4YOXb1dZCbpJbC5vQNVZtnfXy/qQWa8VxuwHr\nAZuo6r4J+U0eYM9JW2ytkbUx99qNy4i2kxVbxOc7WAUiWMPn26r6XIXs74Hb6K5gxqjqbk15KKWR\n9cyVjk0yVhGRn6jq56XGvLmuu0mq17P5h9YsllRxfMdle92hvZyuPxADmS4BMH8wSS6hsclrb0qU\nbevKgA7cNOSUD7g6Ja6w791YqxKsYvgxsE5ieWsdPWI275thLfwdgNXbpDUEs3xZG2/c9NGz8br1\ndeTXcMgiSHdIu2cac4R4IqY4ZmJzAob29hnCVp77HdZgm9MKFXK3lbYHAfdUyG3hv9tWhYbyJa1n\n05v3I+E+HEaX6/LT/VpXPpspdQAlN/Ll0HE+F/WD3h+BTP9Q5CmCC7GJZr/wl+hE4MSGdD9K1+In\ngymt3UCGH6Cc8mFeYlfGvL4OpUsRjcR9+9el7Q/tJv7/MOD6XtyL9bDB1TmYW4dzvJK4A7jJX87W\nugQrAF/B3JLM9v2zMNPJ87CZ6K10Z/pLVQ4zKVUwpfwk+TrC7Pq/5nk/oxUa0s1R5N/3ymFJrC//\nGeCTNbK/dtnlscmeTwBfrpG9hK7unlb4ld/DHgsXYV9CM7HlUx/BZjFv3OZ+piiY5GcIW0FuR5db\nB/g2Zsrb2n8EtsDVy8ALHhZi78ixnT6XFflIWs+mt+8HzevvtOqJnf3ebVL3LJNWB0zy8GvM9cuP\nPPwV6wrt7Fr11UUfSIGuxWiOBT5ejKuRz1EEE6tCjeyt5XNTv1DKz4FdCtvjqXcz3rZ8/jA/hA0u\ntpTSQ5gSqfQC68e1XDh/C/8qanhwU1o752G2/T2+FoDVMH9AE337KkyJrFKSE6zP9mfApz1uvabQ\nrnyF7boW61+A72FKf49WaEg3uaFC12prH8Z8HK1MjTvwguwnsFbtklSsNOgyJ2AVxIc8nIMN9J9E\ntWL8C7B9YXs76he7SlYwmc9Q1YJbf6yQS1IQ2Cp1d9SFhuNuwLqlzsaU+v9U3ZOcstWcp+lrvPUM\nnYC796d+UbPkOg5bwXGFwvYKmAVhUp57pNfpgQM5kOmjnwxFkJmP6zD3EK0HbSz1La4ZFXHTe1s+\n4JDMPF+Pte4ewCbvteasVMn2yuNvH97vEa3Kz6/F8hUyWS1WMld6zHyJ7/bf04Bx/r/u/t2NKYrf\n4t0rDbI31MVRsVJbTaVYl3aOgmk9Q39NeIb+jHW7XYR5gf0wNhGvSnZNzBz4va1QIbNOU2i4f+vQ\ncz2b9XtTtg6e4zOxCv4BrBt1BSrqBZfNqQPuo9D97rL3dZzPvijsQAsswn5rEvtgXXZzfykW+O9f\nsUH0KtmpWGt9pD/AXwem9kX5/EX7OLYQ0b7Avg2yb8b6PN/j22vXyZNXUf4RW09gHIVWT0nmHU2h\n5phPY91SD/r2W4CrGsqX2mL9LoUvvwT5nJf4OH+RW2ugD6P+q+RQbOD+MuyLax0qWuIuey+wdmF7\nbfwrquq+AL/HFoQa6eEbwB9q0s5RMDnP0JaYo70RWKV5IWbEUHXNHvbrcImH2gWVgO+lxOWGnLL5\n/pxuyyWwOmMl316l4blPrgOwuuR2rOvv21iX7xEdX4PeXsSBGMj00U+eImjsg209KP47ChvH2Ajz\ngVO7shbWRXGCVyStgcYeA+H+YN2Vcy2wVuLJmHXIT6npeiscsw7wvsLDWVfJ51SU62IK6zSsC2E6\ncHxJ5o8NoUcr2o+ZhXUrFLsAG1t+NLRYsa+P1lfIfzDrqtb2Cw1p5iryofiCVX7smzPu6eCa+F2A\nRzF/YNdh3UgfwMZDPl+Th9bg9m3AT6gf3E5WMBnlGAT8IFE22VjF5Xt0GVHRPYW9+2dhXxYjsHHI\nv2OV7JYV+a1tkNTkI6fbUrDB9W/5dsvyrS7tbYD9/P8wYFSD7OZYl/WhZCwaV5lWbw4eqKH8wFDT\nb13Y31YRFGTb9sHS1R2V3NdZODZloPFcCi3KNrL3kmF9BHwGuJWulvtoaqytOqgoh2OmzSdhCrrj\nftVCmjf5b+urp7G7gMwWa0Y+2jZU/FrVhpp0V/QKbbqHHwErNuRjaWwAdVMqBr9dplLptClfjoIZ\n68/Q3zHvCq9gkzOrZK9JeT5JNFYBDsQaJf+g+3jGQ8A5FfJ/Ag4AvoR90e2JdVO9n4rKHRugrr3+\nFfI5X+On+Ltxb+Ga31ojO8mf3b/69ho0ryC4CTan5GDMtLvjZ32xmtyX4xakxLKqerWIiJpH0G+L\nyB+xG1Pmnz5n4AERORh70FYryWS7Msh005Dj8uAu7JP6iYp9VRwEbIWtbYyax89y+Vr8Qgt28qr6\nhIh8H+uX7YaIPIhZCf0aMyc8RFX/U5cJEdkAM1FeppD+rytE/ywiXwGWEZHtPf9Vrt9bfBh4q7b3\ndfRh4BpVXeDbKwHbqeofag5JWUyoyb220nMBJDCrrbuwAXmAfbBunLr1HbbAvgT+v71zj7tsLP//\n+zPjGEYppZLTOCWFECXJlIp0IIdkKpKSb4i+qm9KpVIIIR2ULzoJySGRiCHlOAxDpDHSr6+IQuMw\nmFy/P657edZe+15732vPs5/9zH7uz+u1Xnuvta9173uvvdZ93fd1+FyL4UlnmNkPKzLX4TNPJJ1g\nZvvVdSokiy0wz93Yv06ugm/hk4OzgE3wFeZaNbI3AedJOovWe7l6LR4HZknqmDmO318X4YN0ORF0\nnsXJFZc1s5MAJO1jZmeF45dIOioiPx+YLemSSn/rrk2TsgubmfNm3RTafChkuMewAx7CfmOQvVc1\ntVwkHYBPBs/Gx8MfSzrJzE6oabsjhkppWO/8UCmKoMAn8Bn2/sCXga1xx3kZb2eEyqBTvYwyknmA\n8ISsVLwA+GNQMOWHrS4T9Ekze0qhLoac7txqZJtUXTseX07vht/sV0i60szuqgrKOaHegpfJvBgP\nQbwKHxCq+BQ+U7wDX35fjF/LOqRyHX3BzM4pdsyzkL8AtCiNJhMVM9uzy3fGMNXM3lPa/5KkWTFB\nST/Co8dm0cpWUFUa5aInW3T5/mQFU4aZzZE02Zyi/pRAQxLDCngwwrTy6bQr0KTM8aDkHwF2C/fj\ni/BxbllJy1o7IWF54vLvDp8V+FXYUpGUyR7wdOiz26qcPqduYvWUmZmkQrZTdv5euEJ6LMgeAVyN\nm6qbY2GWKeN5IyHSoiSb6oxLtsEG+RUbyCY7Ghteh61iWwf5I/FB8A58iX4O8NWKTM+x8+E674fb\n2/9TIzM7XOsibv3F1JiQ8Nl7ra8oIp8UXk3c/t3J7JWcM0CD+tX4w/360v4WwNU1skmmSEpmU7qY\nUGn1FSWZW0kMX+3nhpthHsSjz2aHLfafPo6br2aX3hf7j9W0vTS+Wk3pR7J/FQ+rPh+vNf9V3I+z\nc43sf4d7eC6+iriamkjJ8FuWKu0v1ele7rYNJY1IQ1qQycDXzaxO+1flLwPeZB0uXC9UBk1oGppS\nHsiL9KxlZpfKi81MthrKg7Di2guf6Qufuf8g9nubrOgkHY2vNJbFb/Df4b6guRHZ68zsNZJm4qGd\nj+I3eVu9gzC7fgNuG/8Z7qisLcAkqboqBMDMTqvI/S/wMG5jNlzRPc/M9ujQdip/2UX45OQQM9sg\nrOZuMrNXRmQ3wAff5fH/41/AHhahUwkmnv3NrKMpUtLjuOIUvjIpqiLKu2yvKsk+SzGuRLrxcL/d\nj9+bB4a+f9vM5kRkTyH+jHyoIrcWbnKqmizXIAJJc/DZdTcur1U7fW6VAlaS3oHnvixhZqtL2hA4\nLPZMB/lG9XeCWfZN+H/xWzO7vUPft6H0nJrZJTVyB+HWkHOC7LuAU83sm3Vtd8KwKo1G/FApiqAk\nezRun621wUra2MxmqgFzZkMeoBuI2IzN7LMR2b1x880KZjY1PHzfNbM31fy+ZYD5xcAbbvIlzezx\nGvnUgXJnPALq/lg7FdnvAZ/GZ1774yuZ262GlynYid8O7Io7YS+yUmnSXhCuw+dxW7RwP81XLCzx\nI/JNJirXm9mmKpUBlTTLzDbs0J8pocGqCaUscznuAO9oimwyUDZRMJXvWAI3LxqedxFlKJZUNr0t\nhdvq77V2lturcB/jsfjqck98/Ir5HYtrsY11Z4dVt+e+LBMmMtOAGaX/bnZV4auH+juSpgJ/M7Mn\ng3n6VcAPzezhTv1LgbyS4evD7u9sIUoBDKvSuAhf1iUViklRBCXZUyJNWHVm1CuUVkXtBjPbRIHm\nOxz7g0VoqoP9+zV4JEjtTV6SvwYPt3007C8L/Kam7SYD5SQ8V2R1M/uypFXwMNPr6q8GSFoT51u6\nsYvcZHzWtRcwzcxWqJFrNGNNRZOJiqQZeIb5JeaOz83xHIK2SUZQiO9hxLld9PewiGzSJKXJQNl0\nJh7OfTvOcHAXPlCuDnzUzC7q1FY4dxK+WpxWOT7TzDYu37uSfmdmW1bkiuJHr8C5y35FqwI9piI/\nAzdZnmclf0dQeq/HZ+iX20h1ymvNbLOKwn/2OYz8niar8Vn4JHA14Nd4dNQ6ZrZdRHZHnLHghfg1\nLpR4nbVhA3xFbrjS6Ej82QlD5QgvITXSokCqMw5LcGZKmk2985jYDaZm0VOPh5t6ljxa6e94LH4M\nTRzb4LbPZxWWmT0aTFoxJEUiBZyIO/Wm4QEE8/CHddOYsKSV8Dj1xcL+68yszZkq6c244noznkD5\nQ1w51eEURmasWxNmrJF218btxqvROlhPq8oGpDrYwZPDzsep73+Px9jvXCN7Hu7Yndmt7dgKtgaX\ny+tYdBwo8fyFvzaZiQccjWePzwmfT8UH765KA5+8rRI5nhqsUkQQ/TVsS4StDm/DE0RPl5eIfRif\nTEzGV5fHmlk58OBWSe8DJocJyP54HlQU1qDsAj5ZXBAUwnFmdoJCJFUERwLv6GS+KqAcPZWEVI5+\noFlUS6INdvvU9kpoEj31fjxs7+O4zfhl+Gw0hiskFdE92wD74jOYOjwm6dXFzF5SQR8eQ5OBMjmc\nUE4rPh13xpejgNpmXMA+uC9jPzOr62cZqeHVZ+Gz5R+U+tAJTSYqt+EBCc/Wr6Y+DHNlM3tbpy+W\ndJWZvV7SPFrvzbrZZ5OBsomCKfAPa/VfzAX+UdP3os8Kr/fhpskqUqIWMbMmkYWY2Xw88fXbkhbH\now2f6GAS2g/PsH4S51W7OPQnirrVOPH6O09L2g03Nxfh2YvXNH1/isIIGNXoqaE0TzVFoiIoZJNs\nsEH2CKvUMYgdC8eTq6g1gRo4toP8pvggfG849GJgVzObGZFNqroWZK/FFeD1QXmsiJu9NorI/glP\nQJrf5LemIMzst8QZAC7DZ6xfN7N1KnIzzawufDjWbpKDPci2OZRjx8Lxk4ATzGx2al+aoNtAKWkp\nXMHsjpuZqgrmxMpMHEnfwWfWZ+LP1c64Yvw9xM2+XfrYKFglnBMLQnkET5D8Xj/urZp+NDFbrodP\ngq42s0Kh72pmXy/JFPk5W+H5V+fS+uzFTOqz8ez2+WF/Kfw5jJqou/ZzGJVGU7t1E0UQOTdqgw2f\nxQaHqP1TCdFT4XcdgkfQHINTcmyJ244/bGbXd+tvCsJAUsyC7zCzp2vkmgyUu+OO6lfjzK47AZ+z\nkWSqsuyv8QzpqPO9IrspI5FkS4Y+P9nBtrspHpr6XHyGOAUPo76mIvdFfHZ8Dq0PZSxBLAnB5PZS\nnH32fYyYxabgwQnrRs75I17n4e7Qj24O6MLhacBVNoq1zxNn4nV+vwJWnYzJg0DWovVZvbIikxys\nEuSPw81+p4dDu+KrmKVxH9n7687t0m4jZaSG/tWE7290bcM55egpgHeTo6daoYaRFpHzaxVBRHYd\n4Fdmtmbp2MdwM9Aa+IBeYDk81X96pJ1y9BT48vVLVoqeCr/rh/ggcyC+ZP8lrji+YpE615K2xwfH\nwqYaNVlImmZml5VmMi1oOjuMQYnhhPLQ0VfhVOnlAfugiOz1uIL9Ge7w3wN4mZkdGpFNnrFKujty\n2DpMPLpOVIKS3QN3dt5QOn0e/hDHZolRR7TFHdCH4rP6op13A2eZ2VdibYwHSPownpS5Mp6UuDk+\n0646wpODVYL8lWb2htgxSbeZ2Sti5yX0t5Eyargav5u4xaOnIA1Jq5vZ3eF9MZkQHsXY+2TCxjDh\nZqw2Ejn6O5y/DjCn5rMyod2/ceba91RklscdqKfTSs0cIyBM5gGiRNdd7R/1dTrm4ANwx6QvAtcW\n7iiubtHiQzQgemz4/+0V2xr811HK7vBZEtdRD31uwl9WW5ejJDMlvDap6Hg7rUlcS9Oh4FYfrsHe\njPCQCadAeSRckzpm19m4ki3qhqwLnBGRS74vS9cimfG3wW9sSj//wdhW0/bzS9tL8UnhYTWypxHY\ncMP+86rXo/Rs1Fbq7GUbVkd4E1qQJs44zCzK71KRaUJl0ISmoSnlAXjVu1st3D0d+lyswj5sHZLj\nKugaiVRxzqr0fjE8QartHjSzk+VRXsXqbY7Vx9s/FpyyNwcH+t/xBMI6JHEdSYrmhFg7j1OBJvxl\nv5V0DB4CCV6j4bBw3xT4KR5QMZORe/PZbuCr2Cr+gg/AhYlkSVpXuv3GAYw4xHfDZ9hr4LQxx+Mr\n4irmm9l8SUha0szuCKv3FlhzCpZPAlfJOc+KsN995fk3bebTBlhR0irFMywPHX9B+KwtF8Uipto6\nWHsi4jeDdaFt1Yz7SZ41EZoHllT9g5Pk1DdrayQUufx9x1SPpWBYlUZSpEWBFEVQRooNNsh9HJ9x\n3s/IoG74zP9ZsdL7bjxA60oqyk1ODe+LNuqWsJ8CLpR0BR3i1Uu4O/gUzsAJ+zopm64DZfXayknV\n9gU+yoiNlYrMlrhv5//Cb1tJ0vvN7PcR8T0YiST7JP6/7NShz6nh1eVQ4KXwVcSNtPM4FWgyUTmZ\nLiSEZrZ9eF29w2+p4kmcyPIS/Ddtgw+cx4e2UgkHe8UCG/F/bY8npv0TuFQeGh7D3+RkkOfiJIEP\nMRKE8SzUIFglHL8wmAzXZcQ3VyjTnmz5AY2UURP/ajAhFZiEmzHrxqZJkp5nwXwtaQXax/P34ibK\nxTq00xhD59PoJdIinJeqCJJssEG2K5WBGtA01Nm3S/2N2bl/Q6DhoLQasZrQRElL436g9+IroAuA\nn5nZVRHZpEikIPtcXJl/AJ9FH1t3XeQZ7x8wsz+G/ZfjfD2bVOQm40vy2gnBaEHS8qEPdXQRSQ72\nINuW/R07Fo5vgZtuHpM0Hf9PvmntxHu1gQkFmsx6e4GkG/HM/IdwbrFpZnZb+Ox2M3t5l/O3wk27\nF1kl+ELpmeN9882FScHm+Oovpoxi5yT7V+VZ7AUW4CvHb5jZnyKyH8A54H4eDu2Mc8T9KCK7rSUk\nViZjNG1d42Wjod0a+DA+qD6Ex5w/gc+yY7JJNtjw2eV08VnQmTDtlopsChmdKvvRkrGJ1+V5+My6\njliwK9EjvnT/Gu7v+BwJtQiqv7vuWDj+G5oRFp6C29pbtoTzFqfGP0BzIssmJITFynKD8P4AakoG\nB/kl8JXsK3HzX9+es8h3b49PHO4Dvl86vhUeLBI7p1HBtJLMpNgzSg++uYa/Mfo/dZBfKP9ql7bX\nw1fY+wHrdZF9O251OLTYev3eYTVPpXL0FzgAHwCvMbOtQ5RPXZJQVxtsyX44F5ghqROVQcfZVwW9\nJFpdKuktZtZW46IOYca3K7AtXkxnl4jMZGAX8xXdo/gMKoZ7gAfwh/ZxYC9pxCJncTPZjXL+qWLW\ntDv+n8YwF/idpPNo/a+Pr5Ev19p4dsZaFVJraOUk/AE9M9agmf1H0sbBTJeydP8YcFpYvTxLQlgj\nu8DMTNK78Czhk+tWFJK2Y6SSooDVJSXRd4wGzOyCsBpezlo5027A76cYmtDrlxHNHLcwg7feaOhT\n8Juw6vlF4n+dbLYM98MX6ODrkjTFzP4dzFH3USoXIGkFi4SES/oubq7fGk9W3Qn3pfaEYVUaybQg\nAUnOuIAUG2wTKoMmNA1NKQ/AixJ9StKTwNPUhNyWvutu3Ox2JnCw1RD0NRgoj2Jk8E21q+6D+6M+\nFfp7JfXZqw8Al+APRR3dSbnfZ5f3JZ2Oh/ZW8Y3S+wXAPWb2tw5NJ09Uwn+0gRJICIF5cvK76cAb\nwqBalyV8DL3Td4wKzAMWHqoca7uH1LBgmhKDVVQTwDDSlXbzTUMchFP2LJA0ny7PE838qykFt6oB\nEgWK6xLzbb7OzF4lzxH7kjx8uXczXZqyHG7IE+v2xP/gafhNv7hFiMIq59XaYBt89wwaEKaVPk9K\ntGrYl8k4XXcbGV6NfKPY+dGEpMMtwurbQzuxPJvJONX0mxu0c0rksFnJUatIBEtFuG3VJU8IfB+e\nwfs7ebTOGy0SxaVKboJ8SXeFVfIVxhPUvGBat/Zikwvh/oSXWiRar19o6l9t4utq2I+CZPEaXAH9\nE4+orKum2BFDudJQ80iLHcLbLwZn1PLUzM4k/chCAo8Fgjh5TYe2DFOlZY/2snogKKmkEq5KJEwL\nq4etgSSlQcKKTl6F70SLULyHz6cBzwmmjdPNbDc5P1Xs/ysHCbwNn6k2QsqMNVyHxyUtb61hsLVI\nNIeUV1ofpXOFwaLd+/AVRLH/V+ojuG6TdCGt9B3XF07hsVDmPeACSctYq6P/OIsHdXQNVrFSyHpQ\nmrvj/+81eGGjhYKkqALu8Dw1MVs+Ien1FoJO5EEQUT41ST9kpCbNHV3avSBYR47CIwANN1P1hKFc\naaRGWpTkn1UEnY6F48lFVdQ8e7Qfq4cjwvd2pS8P8l/FleYZtK4eOlKTd/j+d+Fmpvn4DfsA/p+s\nhdd+uBQ43MwekLSymf0tmFXaYKXSsJJuxgs0tTHUBtme6T5C+2fikTJJtaCbTlRUotbu0o9Ywa1H\nzWz5mj7Uwer60i9I2havO/GEpB1jSkseNr4B7rz/ER6OvKNVaOLVLGpxMdxH9Em81v3XLBKB1ONv\nKpN9LoWzEMyM9SPINym70KTg1jTcErElbpKahScZHtel/0viCaBJk6FoG8OoNKpQF1qQFEWg3oqq\n9IXKoAnUvCDV5ZHDVvNwJg+U8nj1LXACxCfw8NQrLcJMGzM9VY8FH02RxxHrby31QsqMVQ14tYJ8\n04lKahW85IJb4w2STsSd2jfiUXUxQsYbzQksDwX+z9zRH+Nsm81IsMqGCsEqZrZrRe6/cOXyW9w0\n1LZiGU1IehlwpJntVvN5V7Nl5JwUX1cxTm2K+0n2wSebMf6y5+AKdBUz2zs8i+uY2QVV2STYGIbk\nDWqjhhaEHmpd1x2vke0LlUHD334RsGyf2n5Padsdjxlvq7fdQ7tttaip1Jju9frRILx6IX9DNCS0\n02+skbshvN5SjprdMwAAIABJREFUOhalScFn4efgRIv3476ylcfiPgvfvxmwYuXYoeF5em/NOVeE\n5/DPOGtrMWGryl0fXmfhlSQhQp2D5yLdF/7jW+gQwj5Kv1mx/vbY1pK4/+qzdAmNxZXiNXj+x47A\nCzu0ewa+2r817C8du3ap27D6NJIiLczsa8DXGjrjkm2w9I/KoAkaFaSS9CLgcOAlZratnK75tWZ2\nclXW0iORkiDpo/iMaW15oliB5fBokdFAx/BqdWYS3svMbmhvMoq2kFC1FudaU60Z/WZx5tomBbdO\nwaNrioJO08OxbRL7vLA4CVccAMipUlbDc5nOwUklq9gVHyg/ZGb3BUf/URG5pMxx/BnrG4KjvRyK\nvSFQWwWvodkyueAWrgg3BtYP5zws6WqL15SZama7ymt1YG4ujJp1UzCUSsMa0oLQTBF8Bw+X3ADX\n3ifjdsitqoLWPyqDJmhUkArP8TgFHzjBCRnPwH9nN9RVXUvFmfgM6mvAZ0rH55lZtYhPR9ttB3QL\nrz6FESbha/GIuh1wxXEipUGxjMSJSi/FuZoU3FrRzMrmkFMlfaKH7+wVi4Vruxh+Hz0O7GRmz6im\n+mNQFGfj9w7Ag0ToZSw9WKWXSoNNUJ40LABOtzi9TYGkvKCArgW3CpjZgQDycsx74vftSvhqpYqn\n5EwPFs6ZSlrhtNovH8oNz2Z+DZ4o8wbgDR1kk7NuCWYFfOm4V/lYSWZaeN0xtg362nS5boUZ4KbS\nsToG3a6Mvw2/e5nwOiW2jdLvOwen+vginv9xHnBh7LeSyCTc4LuTM/rxAIq2LF98ZrlizbmX4quL\nyWGbzigznHbp+/dwpX8bnp9UMN5uhZcEiJ2zN55AelfYXyvWZxIzx4EZeIb0KpXjS+BRfqfhzuUx\nuSaR/tWaLfGV2isT2/k4PpmbE675F4pxJyK7DW4GfAD4CU5P8sZef8NQrjTqIi1oDQ0tIznrlpFk\nq/cDWyqebLUVTmXyjurJdE4yHDVIOtPMdlFNvXKrKeKDs8Y+n5FZyeb48rcN1mBFJ6/UtzftNbfL\ny/Sf41notxFndl2YVUzxfd1mrL0wCQNJDvYmGf0n4KvaKl6K27xjddA/BHwLt3MbXrt6zCKmzOyj\nkl6PB4fcD/xcUsEAW7c6+i98cndtaOPPkmIZ06mZ4z2FsHdDF7NlkwJoncyWiwF7SppL94JbS4d+\nzLR6BmjwBi4J5t7NQ5sHmNmDif2NNjh0Gw34ocLnSc64ILsSnhW6ZdhfBSfXG/jvrvTzxeF11djW\n4bxX42U5Hwmvd+LRV3XySSs6fAA7As92fdaBPoDr0nHGSmcusMc6tNvVwR7uyX3Ddb2XkTok9+CD\n0IYl2bbaDKXPbh30/dXgekdXRaXPrw2vN4XXxWh1+jcOVimduzgerffcXvtfausq4CPAf+NRezuH\n/3Ob4jfUnJdSfyf6jMaeVWrqqxCpsxLOX760vzVu1j2IheAlG8qQW0nXm9mmkmbhLLNPqkNmpRpk\n3Qb5VfGl96XBVjvZzOaVPu83lUFfEWzSRbnXP1l9udcmsfNdM1sl1a1+ADCzW+o+k+dV/Aynzfip\nmUVntt3Cq9UDk3A4LykktCTfrTb3nWa2ds25f7I4k3DKam5cITj3H8ZDiffDleofzeyQityoZo43\nRfn+lTTHWhkEFjprO7Szl1UCTiR93cw+U9q/m5FV+Cr4JEW4yfWvVqLSl3QtsIOZ3SupyIn6Gp4T\n87SZfbiXfg6leYr0SAsg3RkHIGlvfMaxAjAVNxd8F6+3UGDT2KkEKgNGiPj6DsWTwx6z9nKvmwL/\nz8zuM7MFkjbGVwP3SPqixZPlmhA9XiBpOzO7sEN3TwyvS+Irnlvx6/YK3O792g7nHoUPPCcRybRW\nItdRnVJIQBP+Mqx7Rv+fY9dLnjA3t+ac8/As4UsZSeQc7/gMXplxNp4lfyHxbOUmwSr9QD/NlgV2\nkjTfzH4Szvs2Fcd2oRTkJITnF/dHuC+qtDdLm1kx7k3HWX6PluetNTbRlTsx1BvuX3gnHeizSXTG\nhc9m4YNv2VFcG6eND0zT8YfiDDqYevr0+2/AK+DdhCuMPXHe/arcjYTlLW5muhdXGl8Gfl7TdlLs\nfDg+D3+4nqC0XK+RPZ1WU80GtJey/DKlpTteIvNa4Md4DYK665GcZ9PwOnd0sPfQ3tq4KeNUfAa+\nH+7EvRNYu+7eHMt7q4/37BaRY40o4vvQp76ZLUuyS+MMBLvhEXzf7NDuzMixGyr7ZTr2G4G3lq9n\nz9di0DdIn/7gRhz9TRQBXWywJbnFwg1ze3jw1xnQtUhKDqOUPIfP+L9Yvj41bY/qQNnp+6rHKr9n\ntfBg7hT2r+/Q9haMRGlNx52Jq47yNe86UUlsZ0lcyR8dtg9RqgEekf8KsN0g7rNKP87G6zdM6iAz\nOQyO/w2sH45tj/u+2hI3SYha7PNvSvY7VM7r6l+l1S+xKj7B+xad68FfjNenWS2ccwhOslmWOQ4P\nYz8OuLu4H3E/T891dobVPNWUo/9JM3uqyHcJNv06Z88Vkgozxza4DbbMR1OlMnibjd0SOobU5LDJ\nkhYzj8R4E26CKxC9T6wB0SM0WqbfGZbfP8b/h+n4DLva31Vwu+7JwMfMK7aJzhTpyXk2kf4/3+qr\nDSYTWaYg5BI8icffd5KxSo7IZ+UUK0VEjVk9bXe/8B1c2R0vp4o/1dpJ9U7Gc06uC3L34ObHz5jZ\nuZE2U6IW+4le8z9SzJblOvDF69vDZsTpznfDw2wLM/qV4VgZn8CTJ1+MF/0qfJMrMZKH1RyDnpWM\n8mygp0gL4Ejc3n0HHg1xDhETTpCdhJuzzsJDRPeGtmp5Y0pl0OWarIoP0lPCTXYMniFalTsEj+o5\nD5/pFEESa1IfY5+8oqP5Mv1gXBn/MrxfuiLzDjxG/Y/4zPZLuFntJOAHHa5HoxkrHlJ5PB4h9sdu\n7Zb2J3eST/jfZjCO8w0Sf8PyeIb//8NXEHsyMtu9lbASCffno8BKHdoaaNRir/8HfVqNJ/a5caXP\npHYHfWP16WI1sluToAi6nL9FZb+npWyfrsUBKcfC8c3xjNVlSsfWBl5dI588UNIwDLrhbxRe5OZX\nuIlm6Q6yyeHVpXMOxB3LbYMUCxES2uU7Y+G5dxMPz12VeGjlgYxxyddSH56Pr7ZvwBkJdsUDMmbU\n3DtdTU3hd745vH8OXiFwrH5Pcrh0hza6mi3x5M1d8KCOD8TuuSC3Nj5B+g2eE3YZ7SHeM+jDxGPM\nb6Yx+oMX2m5NuyJItsHSJw3f47WIkf8tFFliLwMlzZzmU/Hw2Vtws9SdwJ2jdD06zljDQ7hqaX9z\n4E/4SunMDu32xcEe2u6Yb4AHALwkvN8Qj/77ZBgUalddfezvL8Kg+j+EfKHSZ4WPrepMLjuaYz7C\n5GCVMfh9yfkfNFuNfwFfhd+PmyXvoz4I5Wa8bPBrcNP7xsDGFZmFVnTR7x7ERR+DPzUp0oJmiuBU\nRniRLgt/6h3AuyPtzmDApoXwu36Jx8CfX9oux2niR+M7mjD+Ji/T8bDRt4YBZCq+ejhsFK9N7YyV\nVhqRt4cHbe2wP1AHe6f7vfT+GzhVN/gKekzNoeF725zxhIlC5T9IXo3TMGpxvGw0X41PIgSlAC8C\nflkj2xY91aUfo5foOOiL2s8/ii5264aKINkGS580fMNrsCpepOhqfFlcbK/GieVG4zt6GigZWaZH\nTSfFA0FryODvRqnPHWes+Kz9g3hkyj/wEqHgPqFOPo2BhYTSp9DKhehP7FmrDp6NVuMkRi2Ol43e\nVuPXhdeZ4X4TNcwA+ORr36AIohnh/dqGNXoqNdJiEzxv4hlJS+HL+jXNS2xW8ZSZPQNgHg1xZ40c\n5ky23wa+3S3zt18ws3sk/Q2PIb+i6fmSljWzR8P7Nc1sTkQsORIpJBneZmbzzOwKScsBGxE4hyp4\nMkRB3SVpH5y2IcZH1Au6cR3tjiecPYXTnpwm6UrgXbjCr0MT/rLRxmUhI/7vOK3LZQCSXoz/jjFB\nYFZ4KR5ZuBEj3GFTaI9oa8LDBQlRi+MJ1lvZhRtCUvL3ccXxKB5dFkNxb5XrjxvxSKvRxaA1cp+0\nfFKkBQ2ccTS0wY6XDTdJLd/DeTfjGfW7EGblddePhEgkShFZYX9SB9nN8Boaq+DZ8+cRSfgKskfi\ng9Li+KrxQWB6h9/VaMaKK7aDCeasDnKNHeyj+B8Lr+53IGFlVOr7W8eiD+H7ioF+XngttvOpsDvT\ncDXOQgarDGqj99X4aoxxInDqNpTcU9CdHyrIPI6HbYI/eFPDfhu7ZK+cRIOGEmtdh2v0lJUYMyV9\nDE8yeq+ZnRVp+wrg13jS2ZY49fIsM3tlRLaNn0fSLVZh8Ayrwq9aiW+ny++bZc71tAPwbnzgvNzM\nNqiRT+I6ago15C8bTdTkBzSWGcX+vMcqBbq6yPe0Gpe0hXWuZTFwKLEGepAVvtJdw8wOC/fQSmYW\nXW1IWh9Yj9a8p77fb0NpnkrkhwLnY0pFv4u79Au/Cls3XIYPuvcBhEH4Y7hD+kB8hldFatU1gLmS\n9meE7ntfIhxKZvYfSa9J6G+Bwuy4HV4Q51/qXJQsleuoEawBf1kf0NTU02+sL+kV1YNmdlhM2Drw\ncIVJxC74M/xrM7tV0vYEHjF8NTWe0cRs+W08x2sacBi+YjubCJedpC/gPsv18Ht4W5yJt+9KY+BL\nnX5sJEZa0KwozgwW0WQr/OHqSGNCK43IR3Bn8Yphv5ZygMTYedwn8TNG6lf/lJq6xngE0C/wCLB3\nFluN7Nfx4IWbcAWyIh2oqmvaiJq+GrYxsJBQxkHgRaU/nyxth+DBGP/bY1unkhisMh43mpVdKMy9\n5XHr5hrZ5EirUf9Ng76offqjUvmhkhXBeHswG1yLd+B5BneH/Q1xdsyq3GV4nPgP8EIzhcJ4ceza\nhc/6MlDiy/jq9sMO8s/DzY/giqstqo3mXEfJSZHhs3EREsoohlaOYp+WpMKL1ODcRpnj422jQSY7\nHpwxuaQ8Vozdm+Gz5Eir0d6G0jxFeqRFcpUvGwcRUT3ii3i00AwAM5sVfmsVO+PmqDtxZfBrSTfj\n2cV19v6uVdckfcrMjpR0AvEKgvuXZD9uZt+ywOHUCZJ2jBwr71arIzblOvog7XXI94gcK9CEv6xv\nsO6U64PAc+g9qic5anE8wpqZLY8Pn71Q0leBnYDP18g2ibQaVQyr0kiyW/eqCMbpg1mHBWb2SGVA\njQ3e/8ST6ACQdDUe+XGEmf2ppu2UgfL28HpDQl+LcqUpiJXSLWC0K42k8GpJu+F+mtUlnV/6aAoe\nY1+HRSoktJ9Qa4nhyfiMOerPSMC6wZkMIVgl7HcqhTpu0MC/ipn9RNLM8JlwE9ztVbkgu294+11J\nvwamWIciZaOJoVQaYWbyfUpx9ZK2wE1LdecsSoqgCW6V9D6cFXYtnKPpD91OMi/eEnN+l9F1oDSz\nXwZn5vpmdnCskV5gZns2PCV1xvoH/D54AU5HXmAeHmJdh7442BdRbF96vwC437rUse6AJsEq4xGp\nNdDLTMl3RI4V+6sCD5vZI2F/azyA5R5Jd5hZ3/NyhirktlukhZmN90iLUUcIpT0EeEs4dDHwZXPa\n7YVtexI+UL4FnxldjHMdtd1Uki6zSBnYiswCPP+l7SNqKL4lvQg4HOde2lbSesBrrb1sZnJ4dZBf\nBl91PiNpbZxg8SKrKX1b83vGfUhoPxEGx3I46F87iNe1Ma7CiZtC0rVmtpmkm8xso7AavzG2QlKX\nUsRFe/ShhGuj3zROr3VPkHQqI3brzXAndSe79dBD0s5WybGIHRvF74sOlJKOxu26Z9GaL/KLksxN\nTRW7pIvwiJpDzGyD8FDeZJVckaZ5NsFMsCXuZL8GN689bma7V+TyRKUCSe/EV2kvwaPlVgVuN7O2\nMNyEtmbgYacdw4nN7NSF7/noIyUvSKVSxPikqbAlPwWcZKWMcpVymyR9A3jGzD4VJnCzxsJcN2xK\n41bSaUEmBKqzl7pjDdtsPFBKOiXSlJnZh0oyvSiN681s0/K5iicSNpqxFtdI0n7hNx0Z61+eqLQj\nBFBMw4kxNwomlN3M7CNdTo21tRTu69odiAWrnFgEq4xHNFyNd6UckTS7mBBJuhH4HzO7OOy3Jcv2\nA8Pm01ikIy1GE/JC89sBL5V0fOmjKYxUdYudV1SBK+MRfKb9STObS/NIpFQfRC+rn8ckPb/os5zj\n6pGIXNMEOEl6LT5Y7RWOxZ6XJvxlEwVPm9k/JU2SNMnMLpd0RC8N9RqsMl6Q4l8t+Sn+J+wXfoq/\n4Eqx7KcYOM/YsCmNRTrSYpRxLz7QvxMPySswD8/wrsMx4dyfMsJptBKe6/G/eBZq44Ey+AW+A7zI\nzNaX9Co8Ye8rJbHJklYws3/VtDENeI6ZXVA6fBDObTRV0u/xSJ2dI6cnh1cHHIAnZZ1jZrdJWgNX\nKlXkiUo7Hpa0LE5x/xNJ/6DDRCUVi1KwSrfVOK2Z7Gfixc8eCX6Ks3A/xYa4wiz7KfpTwrUBhs08\ntUjyQ/UTkhZv6Ly91sw2qxy7xsw2l3Rz8BtUHXZdzV1ynqqDge+VzEi3mtn6JZl34Wy583GK7wfw\ngX0t/AG6FDjczB4onbMkXlVvHVzJ/QlPBqt19I/mjLWpg30ioAgiwDOWd8fLvv7EauqrDyOamC2b\n+CnGQ2DAsK00FlV+qH7iNZK+iDsjF2NkMKtLtnpG0i44kyh4glGB4rr1sqJ7jpldp9Z8kZbZp5md\nB5wnDw3eAp9N/Rv4MfARM3si0u7VQWHdVhwItt5aJZYyY5W0Iq7AXkFrBFA1AmxRDwkddZjZYxoh\nDD1NgTB00P0aYzRZjZcfimn4CpdwblV24Dxjw6Y0Bn5BxyFOxs1RM/EZeTfsjmc9fxtXEtcA0yUt\nDXw8yPQyUD4oaSojvoedqBm4zezPOFdPLdSsdkMv+AlwBp5zsA9+7zwQkcsTlQrUIKFtiNHEbNnE\nT9HUzDrqGDbz1CIdadEPxMxNo9Bm4yVy8AmcBLwOeAi4G6978Zce+/BBnNZjE1qzzecBp1oplLfH\n9mea2cYV08EVVqG01iIeEtoPSJpFSGgrmSKfjfqZCGhitpQvJwo/xZlm9n/h+EY4qefFNd8xkMCA\noVIaZSyKkRb9gKSv40rzF8Czdn4zu7FGfkWce2o1SitRaw2NnUGPA2Wwd0+ySm2TXqGGtRsatFv4\ncS7GOYHuBX5uZlMrcnmiUoEaJLQNK5r4V8eDn6IJhlZpZDgkxSJ+LGKbL+T/gEe9tJizygNzLwOl\nnFztA7Qro5ZiUE0R2j0UeEM4dAVwmAWahYVod3v8OrwMOAE3e33JzM7vcE6eqJCW0DbsaKIIFrXV\nalYaGS1QJDGui3zSQBmU0TU4N9MzxXEzOy0i23W1U5I9G6fPLtp5P7CBmbWx4KZA0hFm9mn1MWt+\n2KEGCW3DiiaKYFFbrWalMaSQ9E0z+0R4f4CZHVf67FQz26PmvK8AfzCzC0e5P8lZ6CmrnZJsLPu7\nkeKrnDsbj7y6NrW/GRlV9KoIFoXValYaQ4ryIN0kr0KeEb4M7v94GurJAhv250Cc8/8CWn0rbYl8\nTQZ9OYX7wWZ2VdjfAviGmb22x34ehUf+LEMreeKoXIdhRgiVPgQv4nUMngW9JXAX8GEzu36A3RsY\nFgVF0ATDFnKbMQLVvO8IM1uuD30BDx08Ch9UipmKES/Oc4Gk7RJXOx8DTpO0PP47/4VHVfUEc/r2\ngyWdZ2bv6rWdCYpT8BrVU3Aq8E/gmc5b4nVSRjWKb1FBSl7QooS80hhSyEnj3ohn5V4W3hfK43Iz\n26Aiv66Z3SEpugKpi7Zq0J+7gM3M7MEE2carHUlTQj//vTD9LLW3rZldVDm2j5l9dzTaH0aUV4iS\n5pjZmrHPMhZt5JXG8GJ53CdQKIryoB+bKRyEm2WOjnxmeKbqwuA24rUy2r8sYbUj6aCa40UbxzTp\nXASfl/SkmRWJVp/GFW9WGvV4pvS+qryfIWMokJXGkMLMVmso/5HwunVfOuQO7VkhBLjs04iG3Ep6\nHs45VabwuLIkUlYsHwW+N6q9daLHCyQdjGfhrhuOZdSjoJcpU8sQ9nutEZ4xzpDNUxltkPQ62sNd\nf7iQbX4wcthi7Ur6MM4yuzIwC9gc55iqyy1pXIcjBfLKc5fiK7YPTaSQ0V7QJKEtY9FFXmlktEDS\nj3DKg1mMhLsa7uDsGdV8DEkvw2nXYzgA2BS4xsy2lrQu8KVOzS9M3yr9qtYTWQKfJe8UcrFy9FQ9\nMg/XBEBWGhlVbAKs148HW9IL8FoXu+EkdufUiM43J3lD0pLBQb/OaPcnhj5Gj00EZMLQCYCsNCYI\nJL3czG4P7zc3s2tqRG/FC7qMSoigpOXwsMv3AWvjimINM1u5w2l/C/Qg5wKXSHoI534qtzubkRXB\nmhX7uY0Gz1GCXyWjFQNnYM3oP7JPY4JA0q/wiKrz8USrtWvkLscLHl1Hq8O6JyewpCdCW58Drgpc\nO3Otvp5H9fytQr9/baWyl/22nzf1q2S0YtgS2jJGkJXGkELSasC/ynkLkvbHE+zeF6PkCDJbxY6b\n2RU99uNA3HexDF5C9gzgkk5KQ17n+zYLTLhhtbKemV1bkukrM2hYyRR+lQ0Lv4qZ7dpLexkZw4JJ\ng+5ARt9wNqVM8KAwdsVXEf9Vd5KZXRHbeu2EmR1rXs/jnaE/5wIvkfRped3wGL6DU44UeCwcK+Ny\nSftJWqV8UNISkqZJOg23ofeK+WY2P7S5pJndgZeUzciY0MhKY3ixuAV6cEmHA9sC2wS/xvJ1J0na\nUdKfJT0i6d+S5kla6CxrM5trZl81L8SzaejDRTXiLSsE8wpoVf/b2/DortMl3Svpj5Lm4hX/dsPt\n56cuRJerfpXzqPhVMjImIrJ5akgh6RzcEbkyztr6CjO7T9LLgR+b2cY1580B3lE4zUehH71U+fsF\nMIOR1cW+wNZm9u6a8/tqP6/zq2RkTERkpTGkCGGOu+BEgXPxMMd/4JnNHzSzS2rO+72ZbTGK/ZhB\nwwIzIanueJy6xIDfAp8ws3+MVr9SIOn1wFpmdoq8xseyZnb3WPYhI2O8ISuNCYLA7/9K4M+dZuOS\njsNDbs+lNXqqp5rbvdYVGDQkfQHPWVnHzNaW9BLgrNFUqBkZiyKy0shogaRTIofNIlXzemi7oxlJ\n0qfM7EhJJxDJ8q7jqeoHJM0CNsJrW28Ujt0yGvkfGRmLMnJyX0YLzGzPPrbdra5A4Ue5oV99aICn\nQk6JAUhaZtAdysgYD8hKI6MFwZy0F/AKWjOhF3ql0Q1m9ktJk4H1zYshDRJnSvoe8FxJe+Mmtu8P\nuE8ZGQNHDrkdckiaKmnJ8P6NkvYPoaR1+BHu03grcAUefTWv/z11mNl/gGhk11jCzL4B/Bx34q8D\nHGpmJwy2VxkZg0f2aQw5gm1+E5zq/GKcRmQdM9uuRv4mM9uosN8HP8TFY0mfIelonPPpLDyxD+jd\nGd/D90/Gf/Obx+L7MjIWJWTz1PDjGTNbIGkH4JtmdoKkmzrIPx1eH5a0PnAfrnDGEisA/6S1WqAB\nY6I0zOw/kh6XtHyRIJmRkeHISmP48bSk3fB8iHeEY4t3kD8psLt+Hl+VLAsc2t8utqKfzvgGmA/M\nlnQJraudMYvgysgYj8jmqSGHpPWAfXCG1oKyelcz+/qAu1aLwEn1HeBFZra+pFcB7zSzr4xhH6K8\nVdViUhkZEw1ZaQw5JB1gZsclHDuoUztmdkw/+heDpCuAg4HvlXIkbjWz9ceqDxkZGXHk6KnhR2zG\nvEfk2HJdtrHEc8zsusqxBWPxxZLWknSqpGMkrSzpIkmPSrpZ0iZj0YeMjPGM7NMYUgQ/xvuANSSd\nX/poOdzJ3AIz+1I47wVm9uDY9LIWD0qaSsgKl7QTo1RJMAGn4PXQpwDXAp/AKw9uCZwIbDZG/cjI\nGJfI5qkhRahstzrwNeAzpY/mAbeY2YKK/Pb4gPk08Aywi5n9YYy62wJJawAnAa8DHgLuBqab2V/G\n4LtnmdmG4f0cM1sz9llGxkRFXmkMKczsHkl/Ax5LLKJ0OLClmd0haTPgSCBaxa/fMLO5wJsDdcek\nooLfGOGZ0vtqHZFnyMiY4MhKY4jRMN9gQahOh5ldG0qsDgQhY/0DeH7IYpIXIByjcNd1Jd2CVxmc\nGt4T9pPqmmdkDDOy0hh+pOYbvLASQdWyP5bRU8CFwDXAbMZ+dv/yMf6+jIxFCllpDD9+FbYyYo6s\n79MaJVXdH0ssZWYdQ4D7iL82rTSYkTGRkB3hEwySXga818yOGnRf6iDpQOBR4AJaC0H9awy+ewYN\nKw1mZEwk5JXGBICkFwA7A7sBLwXOGWyPuuIp4CjgEEZWRcbY+BTehtOgF9nz1UqDx47HSoMZGWOF\nvNIYUgRH9g54rsbauKLY1cxWHmjHEiDpLmCzQeeLdKs0mJExEZFXGsOLfwDXAZ8DrgpV6HbodpKk\n1c3s7m7H+ozbgMfH8PuiSKg0mJEx4ZCVxvDis8B7ceK/n0o6I/G8s4FXV479nLEtjPQfYJaky2n1\naWSG2YyMASMrjSGFmR0LHBuyq3cDzgVeIunTwDlmdmdZXtK6eInX5SXtWPpoCqWyr2OEc8NWRraj\nZmSMA2SfxgSCpFfiCmRXM5ta+exdwLuBd+J1NArMA342KEoRWDQivjIyJgqy0hhSpOQSxGQkvdbM\nru5v77ojFvFlZv892F5lZGRk89Tw4nJJXfMNgFMr582R9FkChUdx0Mw+1O8O10R8rbEoRHxlZEwU\n5JXGkELSUni+we4422013+DEWL6BpD8AvwNm4g5pAMzs7DHo8xO0R3zNNbPM+ZSRMU6QlcYEQJN8\ng0HSf4dM8PcCywA/Bc4ALslKIyNj/CBX7psAMLOnzezviQlqF0jaru+disDMjjWzzXBnvChFfIW6\n4RkZGQPc+kldAAACK0lEQVRGXmlktEDSPHym/1TYBJiZTRlQf2ojvjIyMsYeWWlkjBv0GvGVkZEx\ndsjmqYwWyDFd0ufD/sskvWaMvv5ySftJWqXSpyUkTZN0Gh71lZGRMSDklUZGCyR9By98NM3MXi7p\necBvzGzTMfjuniK+MjIyxg5ZaWS0QNKNZvZqSTeZ2Ubh2M1mtsEY9yMzzGZkjEPk5L6MKp6WNJnA\n9SRpRca+5GpmmM3IGKfIPo2MKo7HM7FfKOmrwFXA4YPtUkZGxnhBNk9ltCEw3r4JD7f9rZndPuAu\nZWRkjBNkpZHRAknHAWcMktU2IyNj/CKbpzKquBH4nKQ5ko6StMmgO5SRkTF+kFcaGVFIWgF4D84F\ntYqZrTXgLmVkZIwD5JVGRh3WBNbFKdLvGGxXMjIyxgvySiOjBZKOAHYE7sJZZs/JeRIZGRkFcp5G\nRhV3A681swcH3ZGMjIzxh2yeygBA0nQAM/susE7ls48PpFMZGRnjDtk8lQGM0IdU38f2MzIyJi7y\nSiOjgGrex/YzMjImKLLSyChgNe9j+xkZGRMU2TyVAYCkx4E5+KpianhP2F/DzJYZVN8yMjLGD3L0\nVEaBlw+6AxkZGeMfeaWRAeRSqxkZGWnIPo2MArnUakZGRlfklUYGkEutZmRkpCErjYw25FKrGRkZ\ndchKIyMjIyMjGdmnkZGRkZGRjKw0MjIyMjKSkZVGRkZGRkYystLIyMjIyEhGVhoZGRkZGcn4/3Ug\nbNVo4vLbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2570222dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "review_business_city = topm_num_reviews_for_city_n_biz(df_cleaned,10)\n",
    "review_business_city[:30].plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(217267, 6)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rest_phoenix_reviews = df_cleaned[(df_cleaned.city == 'Phoenix') & (df_cleaned.categories.str.contains('.Restaurant.', case= False))]\n",
    "rest_phoenix_reviews.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(194398, 6)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rest_toronto_reviews = df_cleaned[(df_cleaned.city == 'Toronto') & (df_cleaned.categories.str.contains('.Restaurant.', case= False))]\n",
    "rest_toronto_reviews.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_clean_df(df, min_user_review = 30, min_res_review = 0, cols = ['user_id', 'business_id', 'stars']):\n",
    "    '''Cleans the df and gets rid of the unwanted cols and also allows to filter the user and business based on the min number of reviews received'''\n",
    "    df_new = df[cols]\n",
    "    df_new.dropna(axis = 0, how = 'any', inplace = True)\n",
    "    df_new[cols[1]+'_freq'] = df_new.groupby(cols[1])[cols[1]].transform('count')\n",
    "    df_clean = df_new[df_new[cols[1]+'_freq']>=min_res_review]\n",
    "    df_clean[cols[0]+'_freq'] = df_clean.groupby(cols[0])[cols[0]].transform('count')\n",
    "    df_clean_2 = df_clean[df_clean[cols[0]+'_freq']>=min_user_review]\n",
    "    return df_clean_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_sparsity(sparse_matrix):\n",
    "    return 1 - sparse_matrix.nnz/(sparse_matrix.shape[0]*sparse_matrix.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \"\"\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9823694709290578\n",
      "0.9749094095868289\n",
      "(1010, 2107)\n",
      "(504, 2015)\n"
     ]
    }
   ],
   "source": [
    "u_20_phx = get_sparse_matrix(get_clean_df(rest_phoenix_reviews, min_user_review=20))\n",
    "u_30_phx = get_sparse_matrix(get_clean_df(rest_phoenix_reviews, min_user_review=30))\n",
    "print(get_sparsity(u_20_phx))\n",
    "print(get_sparsity(u_30_phx))\n",
    "print(u_20_phx.shape)\n",
    "print(u_30_phx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \"\"\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Reviews for Restaurants in Phoenix:  62847\n",
      "Number of Reviews for Restaurants in Toronto:  89788\n"
     ]
    }
   ],
   "source": [
    "user_min_10_phoenix_res = get_clean_df(rest_phoenix_reviews, min_user_review=10)\n",
    "print(\"Number of Reviews for Restaurants in Phoenix: \", user_min_10_phoenix_res.shape[0])\n",
    "user_min_10_toronto_res = get_clean_df(rest_toronto_reviews, min_user_review=10)\n",
    "print(\"Number of Reviews for Restaurants in Toronto: \", user_min_10_toronto_res.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique Restaurants in Phoenix = 2219\n",
      "Unique Users in Phoenix = 2953\n",
      "Unique Restaurants in Toronto = 4375\n",
      "Unique Users in Toronto = 3545\n"
     ]
    }
   ],
   "source": [
    "print(\"Unique Restaurants in Phoenix =\",len(user_min_10_phoenix_res.business_id.unique()))\n",
    "print(\"Unique Users in Phoenix =\",len(user_min_10_phoenix_res.user_id.unique()))\n",
    "print(\"Unique Restaurants in Toronto =\",len(user_min_10_toronto_res.business_id.unique()))\n",
    "print(\"Unique Users in Toronto =\",len(user_min_10_toronto_res.user_id.unique()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_sparse_matrix(df):\n",
    "    '''Converts the df into a sparse ratings matrix'''\n",
    "    unique_users = list(df['user_id'].unique())\n",
    "    unique_bus = list(df['business_id'].unique())\n",
    "    data = df['stars'].tolist()\n",
    "    row = df['user_id'].astype('category', categories=unique_users).cat.codes\n",
    "    col = df['business_id'].astype('category', categories=unique_bus).cat.codes\n",
    "    sparse_matrix = csr_matrix((data, (row, col)), shape=(len(unique_users), len(unique_bus)))\n",
    "    return sparse_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of ratings matrix for Restaurants in Phoenix = (2953, 2219)\n",
      "Shape of ratings matrix for Restaurants in Toronto = (3545, 4375)\n"
     ]
    }
   ],
   "source": [
    "sm_user_10_phoenix_rest = get_sparse_matrix(user_min_10_phoenix_res)\n",
    "print(\"Shape of ratings matrix for Restaurants in Phoenix =\",sm_user_10_phoenix_rest.shape)\n",
    "sm_user_10_toronto_rest = get_sparse_matrix(user_min_10_toronto_res)\n",
    "print(\"Shape of ratings matrix for Restaurants in Toronto =\",sm_user_10_toronto_rest.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sparsity of ratings matrix for Restaurants in Phoenix =  0.9904090019590377\n",
      "Sparsity of ratings matrix for Restaurants in Toronto =  0.9942107273826315\n"
     ]
    }
   ],
   "source": [
    "sparsity_phoenix = 1 - sm_user_10_phoenix_rest.nnz/(sm_user_10_phoenix_rest.shape[0]*sm_user_10_phoenix_rest.shape[1])\n",
    "sparsity_toronto = 1 - sm_user_10_toronto_rest.nnz/(sm_user_10_toronto_rest.shape[0]*sm_user_10_toronto_rest.shape[1])\n",
    "print(\"Sparsity of ratings matrix for Restaurants in Phoenix = \", sparsity_phoenix)\n",
    "print(\"Sparsity of ratings matrix for Restaurants in Toronto = \", sparsity_toronto)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_val_test_split(sparse_matrix, num_review_val = 2, num_review_test = 2):\n",
    "    '''Split the rating matrix into train ,val, and test marix that are disjoint matrices'''\n",
    "    nzrows, nzcols =  sparse_matrix.nonzero()\n",
    "    sparse_matrix_test = csr_matrix(sparse_matrix.shape)\n",
    "    sparse_matrix_val = csr_matrix(sparse_matrix.shape)\n",
    "    sparse_matrix_train = sparse_matrix.copy()\n",
    "    n_users = sparse_matrix.shape[0]\n",
    "    for u in range(n_users):\n",
    "        idx = nzcols[np.where(nzrows == u)]\n",
    "        np.random.shuffle(idx)\n",
    "        test_idx = idx[-num_review_test:]\n",
    "        val_idx = idx[-(num_review_val+num_review_test):-num_review_test]\n",
    "        train_idx = idx[:-(num_review_val+num_review_test)]\n",
    "        sparse_matrix_test[u,test_idx] = sparse_matrix[u,test_idx]\n",
    "        sparse_matrix_val[u,val_idx] = sparse_matrix[u,val_idx]\n",
    "        sparse_matrix_train[u,test_idx] = 0\n",
    "        sparse_matrix_train[u,val_idx] = 0\n",
    "    data = np.array(sparse_matrix_train[sparse_matrix_train.nonzero()])[0]\n",
    "    row = sparse_matrix_train.nonzero()[0]\n",
    "    col = sparse_matrix_train.nonzero()[1]\n",
    "    size = sparse_matrix_train.shape\n",
    "    sparse_matrix_train = csr_matrix((data,(row,col)),shape = size)\n",
    "    mult = sparse_matrix_train.multiply(sparse_matrix_val)\n",
    "    mmult = mult.multiply(sparse_matrix_test)\n",
    "    assert(mmult.nnz == 0)\n",
    "    return sparse_matrix_train, sparse_matrix_val, sparse_matrix_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\scipy\\sparse\\compressed.py:774: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  SparseEfficiencyWarning)\n"
     ]
    }
   ],
   "source": [
    "sm_u_10_phx_res_train, sm_u_10_phx_res_val, sm_u_10_phx_res_test = train_val_test_split(sm_user_10_phoenix_rest)\n",
    "sm_u_10_trt_res_train, sm_u_10_trt_res_val, sm_u_10_trt_res_test =  train_val_test_split(sm_user_10_toronto_rest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "51035 5906 5906\n",
      "75608 7090 7090\n"
     ]
    }
   ],
   "source": [
    "print(sm_u_10_phx_res_train.nnz, sm_u_10_phx_res_val.nnz, sm_u_10_phx_res_test.nnz)\n",
    "print(sm_u_10_trt_res_train.nnz, sm_u_10_trt_res_val.nnz, sm_u_10_trt_res_test.nnz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\scipy\\sparse\\compressed.py:774: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
      "  SparseEfficiencyWarning)\n"
     ]
    }
   ],
   "source": [
    "u_20_train, u_20_val, u_20_test = train_val_test_split(u_20_phx, num_review_val= 7, num_review_test= 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Model Building:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 SVD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "U_phx_res, S_phx_res, Vt_phx_res = np.linalg.svd(sm_u_10_phx_res_train.todense())#k = min(sm_u_10_phx_res_train.shape)-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smallest singular value =  1.21096994001e-14\n",
      "largest singular value =  225.762198309\n"
     ]
    }
   ],
   "source": [
    "print(\"smallest singular value = \",min(S_phx_res))\n",
    "print(\"largest singular value = \",max(S_phx_res))\n",
    "S_phx_res_dia = np.diag(S_phx_res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Printing top 20 singular values**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/jIBPvPnFvPyYjnKHa2ZmB8kJfo6SxBGLWjliUSvnnJwk/Fse2cn7r7yTdS9f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\nGvT/AfB0ziArVBHdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2581ee86d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(S_phx_res[:20], '-', linewidth=1)\n",
    "plt.title('Elbow Plot')\n",
    "# plt.xticks(np.arange(0, S_phx_res.shape[0]+1, 50), rotation='vertical')\n",
    "plt.xlabel('Principal Component')\n",
    "plt.ylabel('Singular Values')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "U_trt_res, S_trt_res, Vt_trt_res = np.linalg.svd(sm_u_10_trt_res_train.todense())#k = min(sm_u_10_phx_res_train.shape)-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smallest singular value =  0.176513688549\n",
      "largest singular value =  207.55450562\n"
     ]
    }
   ],
   "source": [
    "print(\"smallest singular value = \",min(S_trt_res))\n",
    "print(\"largest singular value = \",max(S_trt_res))\n",
    "S_trt_res_dia = np.diag(S_trt_res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Printing top 20 singular values**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ArHH3ITO7BbgTuBT4obt/z8z+Ddjs7l+f7bOU4HPjwMFR/uP3QbK/f8c+xicn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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2585f9c2be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(S_trt_res[:20], '-', linewidth=1)\n",
    "plt.title('Elbow Plot')\n",
    "# plt.xticks(np.arange(0, S_phx_res.shape[0]+1, 50), rotation='vertical')\n",
    "plt.xlabel('Principal Component')\n",
    "plt.ylabel('Singular Values')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def approx_err(k, A, U, S, Vt):\n",
    "    rec_A = np.dot(U[:, :k], np.dot(S[:k,:k], Vt[:k, :]))\n",
    "    idx = np.where(A>0);\n",
    "    diff = A[idx] - rec_A[idx]\n",
    "    return np.linalg.norm(diff)**2/diff.shape[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582cc8ecf8>"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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raZW3X7Zq1YoBAwbw2muvcfrpp/P0009z3nnnkZGRwYsvvkjTpk3ZsGEDxxxz\nDKNHj660/X3ChAk0btyYvLw88vLyyM7OLn/s9ttvp2XLlpSWljJs2DDy8vL4xS9+wV133cXbb79N\n69a7n9k5d+5cJk2axMcff4xzjqOPPprBgwfTokULli9fzpQpU3jooYc499xzef7557nooovqZmeJ\n1EaLjjDoN3D8jfDtAlgwFRY8D8teg9RMPxy1x2nQdbjOUYgRHRHUQsXmobJmIecct9xyC3369OHE\nE0/km2++Yd26dZW+x3vvvVf+hdynTx/69OlT/tjUqVPJzs6mf//+LFq0iMWLF++zng8++IAzzzyT\nzMxMsrKyOOuss3j//fcB6NSpE/369QPgyCOPZOXKlbX5o4vUPTM4qA8M/zP8ahFcOs13KH81C56/\nEv7eBSafC588Dts3BF1tg9Igjgj29cs9ls444wxuuOEGPvnkE3bs2EF2djaPPvoo+fn5zJ07l9TU\nVDp27FjlSW97O1pYsWIFd955J3PmzKFFixZcdtllVb7Pvs4JadSoUfn9cDispiFJbKEQdDreL6f8\nA76e7a/LvOQVWD4T7Ho/71GP06D7KdCsXdAV12sxOyIws4lmtt7MFlbY1tLM3jCz5dHbej1BSVZW\nFkOGDOGKK64o7yTesmULBxxwAKmpqbz99tt89dVX+3yPQYMGMXnyZAAWLlxIXl4eAFu3biUzM5Nm\nzZqxbt06ZsyYUf6aJk2a8P333+/1vV566SUKCgrYvn07L774Iscff3xd/XFFghEKw6HHwsm3w/V5\ncPV7cPyvYXs+zLgJ7u4FDw71o482fB50tfVSLJuGHgVG7LFtHPCmc64r8GZ0vV674IILmD9/Puef\nfz4AF154Ibm5ueTk5DB58mS6d+++z9dfe+21bNu2jT59+vC3v/2NAQMGANC3b1/69+9Pr169uOKK\nKxg4cGD5a8aOHcvIkSPLO4vLZGdnc9lllzFgwACOPvpofvKTn9C/f/86/hOLBMgMDurrO5d/9jFc\nlwvD/EAK3vwT/OtI+Pcx8NafYe18Pw2GVCmmU0yYWUdgmnOud3T9M2CIc26tmR0EvOOc61bV++xt\nioklS5bQo0ePui86yWm/Sr21ZTUsfRWW/Ae++i+4CDTvAD1G+6XdUUl3RnOiTjHR1jm3FiAaBgfE\n+fNFpKFq1g6Ovtov2zfAZ9N9KHz8AHz4L8g60E+Z3eM0OPQ4CDeILtI6kbB7wszGAmMBOnToEHA1\nIlKvZLaG7Ev8snMLLHvddzTPewrmPOznPup2CvQcDZ2HQEqjqt6xQYt3EKwzs4MqNA2tr+yJzrkH\ngQfBNw3Fq0ARaWDSm/kzmvvdbA/hAAAI40lEQVSc409Q++JNWPxKNBiehLQmfhqMHqP9LKmNsoKu\nOO7iHQSvAJcCd0Rvf3jarYhIrKQ19k1DPU6DkiJY8a4PhKWv+tlSU9J9GPQ4zU+hnZEcU7fELAjM\nbAowBGhtZquBW/EBMNXMrgRWAefE6vNFRPYpJc2ftdz1JDjlbj919pJXfL/C0mkQSoFOg6H7KDh8\nJDQ7JOiKYyZmQeCcq2z2tWGx+kwRkRoJp+w6gW3EX+GbubtC4dVf++WgvtBtlL8c54F9/FDWBiJh\nO4sT3caNGxk2zGfat99+Szgcpk2bNgDMnj2btLSqr8Z0+eWXM27cOLp1q3IErYjESygE7Y/yy0m3\nQf5nsGwGfDYD3rkD3vkLND3EB0K3kdDx+Hrf2VxvL1WZSOPd//jHP5KVlcWNN96423bnHM45QvVo\n7HIi7VeRhLMt309x8dkM+OItKC6AtCzocoI/Wug6HDJbBV1lueqeR1B/vqHqic8//5zevXtzzTXX\nkJ2dzdq1axk7dmz5dNK33XZb+XOPO+445s2bR0lJCc2bN2fcuHH07duXY489lvXrKx1QJSJByWoD\n/S+C8yfDTV/Cj5/1l9/8eja8dA3ceRhMHAn//SdsWB50tdXWMJqGZozz09fWpQOPgJF31Oilixcv\nZtKkSdx///0A3HHHHbRs2ZKSkhKGDh3KmDFj6Nmz526v2bJlC4MHD+aOO+7ghhtuYOLEiYwbV+9n\n4BBpuFIz/LDTw4fDKXfB2nn+SGHZDHjjf/zS6jB/pND9VGiX4+dNSkANIwgSTJcuXTjqqKPK16dM\nmcIjjzxCSUkJa9asYfHixT8IgoyMDEaOHAn4aaLLpo8WkXogFIJDsv1ywu9g89f+egpLX4WP7oNZ\n/4TMNtF+hVOg82AfJAmiYQRBDX+5x0pmZmb5/eXLl3PPPfcwe/ZsmjdvzkUXXbTX6aQrdi6Hw2FK\nSkriUquIxEDz9v4KbAOu8mc2L38jeq7Ci/56CqmZcNgJ/kih63Bo3DLQchtGECSwrVu30qRJE5o2\nbcratWuZOXMmI0bsOSmriDRY6c3giDF+KSmEle/D0um75kKyMBz6I39dhW6joMWhcS9RQRBj2dnZ\n9OzZk969e9O5c+fdppMWkSST0sifuXzYiTDqTlj7qT9SWDodXhvnl7ZH+JPYup8St/MVNHxUdqP9\nKhKQjV/4o4Slr8KqjwAHzdrDGfdBp0E1estEnYZaRET2plUX+NHP/bIt33c2fzY9LpfhVBCIiCSa\nrDaQfbFf4kAnlImIJLl6HQT1oX+jPtH+FElO9TYI0tPT2bhxo7686ohzjo0bN5Kenh50KSISZ/W2\nj6Bdu3asXr2a/Pz8oEtpMNLT02nXLvYdUyKSWOptEKSmptKpU6egyxARqffqbdOQiIjUDQWBiEiS\nUxCIiCS5ejHFhJnlA18FXUclWgMbgi5iH1Rf7ai+2lF9tVebGg91zrWp6kn1IggSmZnlVmcuj6Co\nvtpRfbWj+movHjWqaUhEJMkpCEREkpyCoPYeDLqAKqi+2lF9taP6ai/mNaqPQEQkyemIQEQkySkI\nasHMVprZAjObZ2a5Vb8i5vVMNLP1ZrawwraWZvaGmS2P3rZIsPr+aGbfRPfhPDMbFWB97c3sbTNb\nYmaLzOz66PaE2If7qC8h9qGZpZvZbDObH63vT9Htnczs4+j+e8bM0hKsvkfNbEWF/dcviPoq1Bk2\ns0/NbFp0Peb7T0FQe0Odc/0SZAjao8CIPbaNA950znUF3oyuB+VRflgfwN3RfdjPOTc9zjVVVAL8\n2jnXAzgG+JmZ9SRx9mFl9UFi7MNC4ATnXF+gHzDCzI4B/hqtryvwHXBlgtUH8JsK+29eQPWVuR5Y\nUmE95vtPQdCAOOfeAzbtsfl04LHo/ceAM+JaVAWV1JcwnHNrnXOfRO9/j//PeAgJsg/3UV9CcN62\n6GpqdHHACcBz0e1B7r/K6ksYZtYOOAV4OLpuxGH/KQhqxwGvm9lcMxsbdDGVaOucWwv+iwQ4IOB6\n9uY6M8uLNh0F1nRVkZl1BPoDH5OA+3CP+iBB9mG0WWMesB54A/gC2OycK4k+ZTUBhtee9Tnnyvbf\n7dH9d7eZNQqqPmA8cBMQia63Ig77T0FQOwOdc9nASPxh+qCgC6qHJgBd8Ifqa4F/BFsOmFkW8Dzw\nS+fc1qDr2dNe6kuYfeicK3XO9QPaAQOAHnt7WnyrqvDBe9RnZr2Bm4HuwFFAS+C3QdRmZqcC651z\ncytu3stT63z/KQhqwTm3Jnq7HngR/w8/0awzs4MAorfrA65nN865ddH/nBHgIQLeh2aWiv+Sneyc\neyG6OWH24d7qS7R9GK1pM/AOvi+juZmVXfukHbAmqLrKVKhvRLTJzTnnCoFJBLf/BgKjzWwl8DS+\nSWg8cdh/CoIaMrNMM2tSdh8YDizc96sC8QpwafT+pcDLAdbyA2VfsFFnEuA+jLbHPgIscc7dVeGh\nhNiHldWXKPvQzNqYWfPo/QzgRHw/xtvAmOjTgtx/e6tvaYWQN3z7eyD7zzl3s3OunXOuI3A+8JZz\n7kLisP90QlkNmVln/FEA+Cu9PeWcuz3AkjCzKcAQ/GyF64BbgZeAqUAHYBVwjnMukA7bSuobgm/S\ncMBK4Oqy9vgA6jsOeB9YwK422lvw7fCB78N91HcBCbAPzawPvjMzjP+ROdU5d1v0/8rT+GaXT4GL\nor++E6W+t4A2+GaYecA1FTqVA2FmQ4AbnXOnxmP/KQhERJKcmoZERJKcgkBEJMkpCEREkpyCQEQk\nySkIRESSnIJApAbMrGPFWVRF6jMFgYhIklMQiNSSmXWOzh9/VNC1iNSEgkCkFsysG37un8udc3OC\nrkekJlKqfoqIVKINft6Xs51zi4IuRqSmdEQgUnNbgK/xs0aK1Fs6IhCpuSL8bJUzzWybc+6poAsS\nqQkFgUgtOOe2Ry8o8oaZbXfOJdQ03yLVodlHRUSSnPoIRESSnIJARCTJKQhERJKcgkBEJMkpCERE\nkpyCQEQkySkIRESSnIJARCTJ/X8ahTOcb02ZJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582cc1c898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.linspace(2,40,20, dtype = int)\n",
    "errors_svd_val = {}\n",
    "errors_svd_train = {}\n",
    "for i in k:\n",
    "    errors_svd_val[i] = approx_err(i, sm_u_10_phx_res_val.todense(), U_phx_res, S_phx_res_dia, Vt_phx_res)\n",
    "    errors_svd_train[i] = approx_err(i, sm_u_10_phx_res_train.todense(), U_phx_res, S_phx_res_dia, Vt_phx_res)\n",
    "\n",
    "plt.plot(errors_svd_val.keys(),errors_svd_val.values(), label = 'Validation')\n",
    "plt.plot(errors_svd_train.keys(),errors_svd_train.values(), label = 'Train')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582ccf80b8>"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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a1dIybNtTyp9e/ZTH319HQlwMP/if47jylD7qUG+jFCRR0q6d8e3T+5PTO4Xr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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582cbf44e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##Separately plotting the Validation error\n",
    "plt.plot(errors_svd_val.keys(),errors_svd_val.values(), label = 'Validation')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Principal Component 2')"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w3YjouemiHjZsZta8MlKvVPwR8EpgTUScKumlwMcmWkAz635TNXeVjU+RgPJU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\nzMysFA4oZmZWiv8PvoMUE7LorAgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2585f66b9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(np.ravel(U_phx_res[:,0]),np.ravel(U_phx_res[:,1]), label = 'Scatter plot for first two PCs')\n",
    "plt.xlabel('Principal Component 1')\n",
    "plt.ylabel('Principal Component 2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Best Validation MSE for SVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for SVD for Restaurants in Phoenix=  14.4831794918\n"
     ]
    }
   ],
   "source": [
    "Best_Val_MSE_SVD_Phx = approx_err(10, sm_u_10_phx_res_val.todense(), U_phx_res, S_phx_res_dia, Vt_phx_res)\n",
    "print('Best Validation MSE for SVD for Restaurants in Phoenix= ', Best_Val_MSE_SVD_Phx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Non Zero Indices in Train, Val and Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_phx_nnz = sm_u_10_phx_res_train.nonzero()\n",
    "val_phx_nnz = sm_u_10_phx_res_val.nonzero()\n",
    "test_phx_nnz = sm_u_10_phx_res_test.nonzero()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "recon_matrix_svd_phx = np.dot(U_phx_res[:, :10], np.dot(S_phx_res_dia[:10,:10], Vt_phx_res[:10, :]))\n",
    "train_preds_svd_phx = np.ravel(recon_matrix_svd_phx[train_phx_nnz])\n",
    "val_preds_svd_phx = np.ravel(recon_matrix_svd_phx[val_phx_nnz])\n",
    "test_preds_svd_phx = np.ravel(recon_matrix_svd_phx[test_phx_nnz])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2581ee722e8>"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Xsb7rZ0lR2JGJSIqqVeI3s18BxcCjFb1dQZnbz2dNNLN8M8tft66RzX0bTYcTfgo/fhu6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2585f651940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.linspace(2,40,20, dtype = int)\n",
    "errors_svd_val_trt = {}\n",
    "errors_svd_train_trt = {}\n",
    "for i in k:\n",
    "    errors_svd_val_trt[i] = approx_err(i, sm_u_10_trt_res_val.todense(), U_trt_res, S_trt_res_dia, Vt_trt_res)\n",
    "    errors_svd_train_trt[i] = approx_err(i, sm_u_10_trt_res_train.todense(), U_trt_res, S_trt_res_dia, Vt_trt_res)\n",
    "\n",
    "plt.plot(errors_svd_val_trt.keys(),errors_svd_val_trt.values(), label = 'Validation')\n",
    "plt.plot(errors_svd_train_trt.keys(),errors_svd_train_trt.values(), label = 'Train')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2585aa28f60>]"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2585f6ecdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##Separately plotting the Validation error\n",
    "plt.plot(errors_svd_val_trt.keys(),errors_svd_val_trt.values(), label = 'Validation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Best Validation MSE for SVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for SVD for Restaurants in Toronto=  13.3822481108\n"
     ]
    }
   ],
   "source": [
    "Best_Val_MSE_SVD_trt = approx_err(16, sm_u_10_trt_res_val.todense(), U_trt_res, S_trt_res_dia, Vt_trt_res)\n",
    "print('Best Validation MSE for SVD for Restaurants in Toronto= ', Best_Val_MSE_SVD_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_trt_nnz = sm_u_10_trt_res_train.nonzero()\n",
    "val_trt_nnz = sm_u_10_trt_res_val.nonzero()\n",
    "test_trt_nnz = sm_u_10_trt_res_test.nonzero()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "recon_matrix_svd_trt = np.dot(U_trt_res[:, :15], np.dot(S_trt_res_dia[:15,:15], Vt_trt_res[:15, :]))\n",
    "train_preds_svd_trt = np.ravel(recon_matrix_svd_trt[train_trt_nnz])\n",
    "val_preds_svd_trt = np.ravel(recon_matrix_svd_trt[val_trt_nnz])\n",
    "test_preds_svd_trt = np.ravel(recon_matrix_svd_trt[test_trt_nnz])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SVD with Bias Correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smallest singular value =  4.73329914437e-13\n",
      "largest singular value =  9593.52310466\n"
     ]
    }
   ],
   "source": [
    "global_bias = np.sum(sm_u_10_phx_res_train)/sm_u_10_phx_res_train.nnz\n",
    "sm_u_10_phx_res_train_wo_bias = sm_u_10_phx_res_train.todense() - global_bias\n",
    "U_phx_res_wo_bias, S_phx_res_wo_bias, Vt_phx_res_wo_bias = np.linalg.svd(sm_u_10_phx_res_train_wo_bias)\n",
    "print(\"smallest singular value = \",min(S_phx_res_wo_bias))\n",
    "print(\"largest singular value = \",max(S_phx_res_wo_bias))\n",
    "S_phx_res_dia_wo_bias = np.diag(S_phx_res_wo_bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OSzIJfjC8XW7EzMqAA8R0gp1m0YuISFwkMwa/wcwqgK8BG4E+4Mm0RhURM02yExGReEhm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\nREQkhpTgRUREYkgJXkREJIb+P2QVILYygH/UAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25702348940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.semilogy(S_phx_res_wo_bias[:1000], '-', linewidth=1)\n",
    "plt.title('Elbow Plot')\n",
    "plt.xlabel('Principal Component')\n",
    "plt.ylabel('Singular Values')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25701efb0b8>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XtrBhSSGblhVx7eKCSW9tdPf28dLh02zbU8eOvXWcaesiOz1ErztdPZFvnBZM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25702272c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_wo_bias = np.arange(1,20)\n",
    "errors_svd_wo_bias = {}\n",
    "sm_u_10_phx_res_val_wo_bias = sm_u_10_phx_res_val.todense() - global_bias \n",
    "\n",
    "for i in k_wo_bias:\n",
    "    sm_u_10_phx_res_val_wo_bias_rec = np.dot(U_phx_res_wo_bias[:, :i], np.dot(S_phx_res_dia_wo_bias[:i,:i], Vt_phx_res_wo_bias[:i, :]))\n",
    "    idx_wo_bias = np.where(sm_u_10_phx_res_val.todense()>0);\n",
    "    diff_wo_bias = sm_u_10_phx_res_val_wo_bias[idx_wo_bias] - sm_u_10_phx_res_val_wo_bias_rec[idx_wo_bias]\n",
    "    errors_svd_wo_bias[i] = np.linalg.norm(diff_wo_bias)**2/diff_wo_bias.shape[1]\n",
    "plt.plot(errors_svd_wo_bias.keys(),errors_svd_wo_bias.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_global_user_res_bias(ratings_matrix):\n",
    "    dense_matrix = ratings_matrix.todense()\n",
    "    mask_matrix = (dense_matrix>0).astype(int)\n",
    "    user_bias = np.sum(dense_matrix, axis = 1)/np.sum(mask_matrix, axis = 1)\n",
    "    res_bias =  np.sum(dense_matrix, axis = 0)/np.sum(mask_matrix, axis = 0)\n",
    "    user_bias = np.nan_to_num(user_bias)\n",
    "    res_bias = np.nan_to_num(res_bias)\n",
    "    user_bias = user_bias.reshape(-1,1)\n",
    "    res_bias = res_bias.reshape(1,-1)\n",
    "    ratings_matrix_wo_bias = dense_matrix - np.tile(user_bias, (1,dense_matrix.shape[1]))- np.tile(res_bias, (dense_matrix.shape[0], 1))\n",
    "    return user_bias, res_bias, ratings_matrix_wo_bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in true_divide\n",
      "  \"\"\"\n"
     ]
    }
   ],
   "source": [
    "user_bias_ur, res_bias_ur, train_ur = find_global_user_res_bias(sm_u_10_phx_res_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smallest singular value =  8.86290383628e-14\n",
      "largest singular value =  18648.0061968\n"
     ]
    }
   ],
   "source": [
    "U_phx_res_wo_bias_ur, S_phx_res_wo_bias_ur, Vt_phx_res_wo_bias_ur = np.linalg.svd(train_ur)\n",
    "print(\"smallest singular value = \",min(S_phx_res_wo_bias_ur))\n",
    "print(\"largest singular value = \",max(S_phx_res_wo_bias_ur))\n",
    "S_phx_res_dia_wo_bias_ur = np.diag(S_phx_res_wo_bias_ur)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zs47QTA3BGcAW4NyI+DXZwECfaWtUE0Sl1Ouuh2Zm1hFGTAhSEnA90JuK1gA3tDOoiaLc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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25701ee94a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(S_phx_res_wo_bias_ur[:20], '-', linewidth=1)\n",
    "plt.title('Elbow Plot')\n",
    "plt.xlabel('Principal Component')\n",
    "plt.ylabel('Singular Values')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582d055ba8>"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MZA3BUJKXBsDa3fVMnJ3gcTUiIiNv2CsL59yugT9AMzAPyPA/P2xmlgj8EPjxYe4/EZgN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\nIgEpLEREJCCFhYiIBKSwEBGRgP4/mbVuIIIhpoUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582ced17f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_wo_bias_ur = np.linspace(2,40,20, dtype = int)\n",
    "errors_svd_wo_bias_ur = {}\n",
    "sm_u_10_phx_res_val_wo_bias_ur = sm_u_10_phx_res_val.todense() - user_bias_ur - res_bias_ur\n",
    "\n",
    "for i in k_wo_bias_ur:\n",
    "    sm_u_10_phx_res_val_wo_bias_ur_rec = np.dot(U_phx_res_wo_bias_ur[:, :i], np.dot(S_phx_res_dia_wo_bias_ur[:i,:i], Vt_phx_res_wo_bias_ur[:i, :]))\n",
    "    idx_wo_bias_ur = np.where(sm_u_10_phx_res_val.todense()>0);\n",
    "    diff_wo_bias_ur = sm_u_10_phx_res_val_wo_bias_ur[idx_wo_bias_ur] - sm_u_10_phx_res_val_wo_bias_ur_rec[idx_wo_bias_ur]\n",
    "    errors_svd_wo_bias_ur[i] = np.linalg.norm(diff_wo_bias_ur)**2/diff_wo_bias_ur.shape[1]\n",
    "plt.plot(errors_svd_wo_bias_ur.keys(),errors_svd_wo_bias_ur.values(), label= 'Validation')\n",
    "plt.xlabel('PC')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\aakas\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in true_divide\n",
      "  \"\"\"\n"
     ]
    }
   ],
   "source": [
    "user_bias_ur_trt, res_bias_ur_trt, train_ur_trt = find_global_user_res_bias(sm_u_10_trt_res_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smallest singular value =  0.179830190971\n",
      "largest singular value =  27778.7763742\n"
     ]
    }
   ],
   "source": [
    "U_trt_res_wo_bias_ur, S_trt_res_wo_bias_ur, Vt_trt_res_wo_bias_ur = np.linalg.svd(train_ur_trt)\n",
    "print(\"smallest singular value = \",min(S_trt_res_wo_bias_ur))\n",
    "print(\"largest singular value = \",max(S_trt_res_wo_bias_ur))\n",
    "S_trt_res_dia_wo_bias_ur = np.diag(S_trt_res_wo_bias_ur)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582cdde198>"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oGMkg151yKiKFPPXlC7j1n9dw57K1bKlp5K5LKzQILzKAw60dPLRqOw++tJ2G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\nRGNPyvcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582cd9e5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_wo_bias_ur = np.linspace(2,40,20, dtype = int)\n",
    "errors_svd_wo_bias_ur_trt = {}\n",
    "sm_u_10_trt_res_val_wo_bias_ur = sm_u_10_trt_res_val.todense() - user_bias_ur_trt - res_bias_ur_trt\n",
    "\n",
    "for i in k_wo_bias_ur:\n",
    "    sm_u_10_trt_res_val_wo_bias_ur_rec = np.dot(U_trt_res_wo_bias_ur[:, :i], np.dot(S_trt_res_dia_wo_bias_ur[:i,:i], Vt_trt_res_wo_bias_ur[:i, :]))\n",
    "    idx_wo_bias_ur_trt = np.where(sm_u_10_trt_res_val.todense()>0);\n",
    "    diff_wo_bias_ur_trt = sm_u_10_trt_res_val_wo_bias_ur[idx_wo_bias_ur_trt] - sm_u_10_trt_res_val_wo_bias_ur_rec[idx_wo_bias_ur_trt]\n",
    "    errors_svd_wo_bias_ur_trt[i] = np.linalg.norm(diff_wo_bias_ur_trt)**2/diff_wo_bias_ur_trt.shape[1]\n",
    "plt.plot(errors_svd_wo_bias_ur_trt.keys(),errors_svd_wo_bias_ur_trt.values(), label = 'Validation')\n",
    "plt.xlabel('PC')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.2 Cosine Similarity with correction for bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def similarity_matrix(train_matrix, between = 'users'):\n",
    "    '''Returns the cosine similarity between users or restaurants'''\n",
    "    if between == 'users':\n",
    "        similarity = train_matrix*train_matrix.transpose()\n",
    "    else:\n",
    "        similarity = train_matrix.transpose()*train_matrix\n",
    "    similarity_dense = similarity.todense() + 1e-8\n",
    "    norm_array = np.sqrt(np.diag(similarity_dense))\n",
    "    return similarity_dense/norm_array/norm_array.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict_topk_nobias(ratings, similarity, kind='user', k=40):\n",
    "    pred = np.zeros(ratings.shape)\n",
    "    if kind == 'user':\n",
    "        user_bias = np.mean(ratings, axis =1)\n",
    "        ratings = (ratings - np.tile(user_bias, (ratings.shape[1],1)).T).copy()\n",
    "        for i in range(ratings.shape[0]):\n",
    "            top_k_users = np.argsort(similarity[:,i])[:-k-1:-1]\n",
    "            pred[i] = np.dot(similarity[i,top_k_users],ratings[top_k_users,:])/np.sum(np.abs(similarity[i,top_k_users]))\n",
    "        pred += np.tile(user_bias,(ratings.shape[1],1)).T\n",
    "    else:\n",
    "        item_bias = np.mean(ratings, axis=0)\n",
    "        ratings = (ratings - np.tile(item_bias,(ratings.shape[0],1))).copy()\n",
    "        for j in range(ratings.shape[1]):\n",
    "            top_k_items = np.argsort(similarity[:,j])[:-k-1:-1]\n",
    "            pred[:,j] = np.dot(similarity[top_k_items,j].T,ratings[:,top_k_items].T)/np.sum(np.abs(similarity[top_k_items,j]))\n",
    "        pred += np.tile(item_bias,(ratings.shape[0],1))\n",
    "        \n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_mse(pred, actual):\n",
    "    # Ignore zero terms.\n",
    "    pred = pred[actual.nonzero()].flatten()\n",
    "    actual = actual[actual.nonzero()].flatten()\n",
    "    return mean_squared_error(pred, actual)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for cosine Similarity between Restaurants = 15.8907890281\n"
     ]
    }
   ],
   "source": [
    "simi_phx_res = similarity_matrix(sm_u_10_phx_res_train, between='res')\n",
    "simi_phx_res = np.array(simi_phx_res)\n",
    "preds_cosine_phx = predict_topk_nobias(np.array(sm_u_10_phx_res_train.todense()),simi_phx_res,kind='res', k=1)\n",
    "MSE_cosine_res = get_mse(preds_cosine_phx, np.array(sm_u_10_phx_res_val.todense()))\n",
    "print(\"MSE for cosine Similarity between Restaurants =\",MSE_cosine_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for cosine Similarity between Users = 15.8907890281\n"
     ]
    }
   ],
   "source": [
    "simi_phx_users = similarity_matrix(sm_u_10_phx_res_train, between='users')\n",
    "simi_phx_users = np.array(simi_phx_users)\n",
    "preds_cosine_phx_users = predict_topk_nobias(np.array(sm_u_10_phx_res_train.todense()),simi_phx_users,kind='user', k=1)\n",
    "MSE_cosine_users = get_mse(preds_cosine_phx_users, np.array(sm_u_10_phx_res_val.todense()))\n",
    "print(\"MSE for cosine Similarity between Users =\",MSE_cosine_users)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582d2d3c50>"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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x2LkxFPwfTQ+3enpFaHf/uB/AQWeFxtpU5SPS5Jr95fVmlg+8Axzv7rPN7DfA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\nkTSnRCAikuaUCERE0pwSgYhImvv/7XDCgj5ZtN8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582d244c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errors_cs_res_phx_val = {}\n",
    "errors_cs_res_phx_train = {}\n",
    "k_cs = np.arange(1, 40)\n",
    "for i in k_cs:\n",
    "    preds_cs_res_phx = predict_topk_nobias(np.array(sm_u_10_phx_res_train.todense()),simi_phx_res,kind='res', k=i)\n",
    "    error_cs_val = get_mse(preds_cs_res_phx, np.array(sm_u_10_phx_res_val.todense()))\n",
    "    error_cs_train = get_mse(preds_cs_res_phx, np.array(sm_u_10_phx_res_train.todense()))\n",
    "    errors_cs_res_phx_val[i] = error_cs_val\n",
    "    errors_cs_res_phx_train[i] = error_cs_train\n",
    "plt.plot(errors_cs_res_phx_val.keys(),errors_cs_res_phx_val.values(), label = 'Validation')\n",
    "plt.plot(errors_cs_res_phx_train.keys(),errors_cs_res_phx_train.values(), label = 'Train')\n",
    "plt.xlabel('K Neighbors')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Cosine Similarity: MSE (train/Val) vs K')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for Cosine Similarity for Restaurants in Phoenix=  14.6490906702\n"
     ]
    }
   ],
   "source": [
    "preds_cosine_phx = predict_topk_nobias(np.array(sm_u_10_phx_res_train.todense()),simi_phx_res,kind='res', k=40)\n",
    "Best_Val_MSE_Cosine_phx = get_mse(preds_cosine_phx, np.array(sm_u_10_phx_res_val.todense()))\n",
    "print('Best Validation MSE for Cosine Similarity for Restaurants in Phoenix= ', Best_Val_MSE_Cosine_phx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_cosine_phx = preds_cosine_phx[train_phx_nnz]\n",
    "val_preds_cosine_phx = preds_cosine_phx[val_phx_nnz]\n",
    "test_preds_cosine_phx = preds_cosine_phx[test_phx_nnz]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582d364e80>"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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C+MBxkKM3zkrntJUIPjSzrwBlhIfJngMwsz6AGgKLdNTO9bB2Eax7s7Hgb2itY+FG7diT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\nqwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x258607c7cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errors_cs_res_trt_val = {}\n",
    "errors_cs_res_trt_train = {}\n",
    "k_cs = np.arange(1, 40)\n",
    "simi_trt_res = similarity_matrix(sm_u_10_trt_res_train, between='res')\n",
    "simi_trt_res = np.array(simi_trt_res)\n",
    "for i in k_cs:\n",
    "    preds_cs_res_trt = predict_topk_nobias(np.array(sm_u_10_trt_res_train.todense()),simi_trt_res,kind='res', k=i)\n",
    "    error_cs_val = get_mse(preds_cs_res_trt, np.array(sm_u_10_trt_res_val.todense()))\n",
    "    error_cs_train = get_mse(preds_cs_res_trt, np.array(sm_u_10_trt_res_train.todense()))\n",
    "    errors_cs_res_trt_val[i] = error_cs_val\n",
    "    errors_cs_res_trt_train[i] = error_cs_train\n",
    "plt.plot(errors_cs_res_trt_val.keys(),errors_cs_res_trt_val.values(), label = 'Validation')\n",
    "plt.plot(errors_cs_res_trt_train.keys(),errors_cs_res_trt_train.values(), label = 'Train')\n",
    "plt.xlabel('K Neighbors')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Cosine Similarity: MSE (train/Val) vs K (Toronto Restaurants)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for Cosine Similarity for Restaurants in Toronto=  13.5467995374\n"
     ]
    }
   ],
   "source": [
    "preds_cosine_trt = predict_topk_nobias(np.array(sm_u_10_trt_res_train.todense()),simi_trt_res,kind='res', k=40)\n",
    "Best_Val_MSE_Cosine_trt = get_mse(preds_cosine_trt, np.array(sm_u_10_trt_res_val.todense()))\n",
    "print('Best Validation MSE for Cosine Similarity for Restaurants in Toronto= ', Best_Val_MSE_Cosine_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_cosine_trt = preds_cosine_trt[train_trt_nnz]\n",
    "val_preds_cosine_trt = preds_cosine_trt[val_trt_nnz]\n",
    "test_preds_cosine_trt = preds_cosine_trt[test_trt_nnz]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.3 ALS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def als(ratings_matrix, k=40, user_reg=0, res_reg=0, iters=10):\n",
    "    '''Performs ALS for a given ratings_matrix and returns predictions using the latent vector representation User (U x K) and Restaurant (R x K)'''\n",
    "    ratings_matrix = ratings_matrix.T\n",
    "    user_vec = np.random.rand(ratings_matrix.shape[1],k).T\n",
    "    res_vec = np.random.rand(ratings_matrix.shape[0],k).T\n",
    "    for i in range(iters):\n",
    "        for u in range(ratings_matrix.shape[1]):\n",
    "            user_vec[:,u] = np.linalg.solve(np.dot(res_vec,res_vec.T) + user_reg * np.eye(res_vec.shape[0]), np.dot(res_vec,ratings_matrix[:,u]))\n",
    "        for r in range(ratings_matrix.shape[0]):\n",
    "            res_vec[:,r] = np.linalg.solve(np.dot(user_vec,user_vec.T) + res_reg * np.eye(user_vec.shape[0]), np.dot(user_vec,ratings_matrix[r,:].T))\n",
    "        prediction = np.dot(res_vec.T, user_vec)\n",
    "#         error = np.mean((ratings_matrix - prediction)**2)\n",
    "    return np.dot(res_vec.T, user_vec).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582d3deda0>"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ri4jsIiV7KXtatw698H31VRhgZ8aMcNte+/ahH/7Nm+OOUESkXFGyl7IrKwv+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\noEqV0D3vnXeGXvs+/xzuuQe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8flaRb3Mvo0R/VyRZp9x9ZlFjpwHAWR5dIM2vCN/VMsXd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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582d1ac438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_features = np.linspace(1,20,5,dtype=int)\n",
    "test_error_als = []\n",
    "train_error_als = []\n",
    "for i in num_features:\n",
    "    preds_als = als(np.array(sm_u_10_phx_res_train.todense()), k=i, iters = 5)\n",
    "    test_err = get_mse(preds_als, np.array(sm_u_10_phx_res_val.todense()))\n",
    "    train_err = get_mse(preds_als, np.array(sm_u_10_phx_res_train.todense()))\n",
    "    test_error_als.append(test_err)\n",
    "    train_error_als.append(train_err)\n",
    "\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(num_features,test_error_als,'b-',label = 'validation')\n",
    "plt.plot(num_features,train_error_als,'r-', label = 'training')\n",
    "plt.title('MSE vs num_features (for ALS)')\n",
    "plt.xlabel('Number of features in a feature vector')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'MSE')"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TZS8i0sy8OXMVj/x7ARcd041zh3SJOhxpAEr2IiLNyMK127j1hekc0SWPX56l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\nWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582d4726a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_reg= np.logspace(-4,3,7)\n",
    "val_error_als = {}\n",
    "# train_error_als = {}\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "for i in user_reg:\n",
    "    val_error_als[i] = []\n",
    "    preds_als = als(np.array(sm_u_10_phx_res_train.todense()),k=10, iters = 5, user_reg=i, res_reg=i)\n",
    "    val_err = get_mse(preds_als, np.array(sm_u_10_phx_res_val.todense()))\n",
    "#         train_err = get_mse(preds_als, np.array(train.todense()))\n",
    "    val_error_als[i].append(val_err)\n",
    "#         train_error_als[i].append(train_err)\n",
    "plt.plot(np.log10(user_reg),val_error_als.values())\n",
    "#     plt.plot(np.log(res_reg),train_error_als[i], label = 'User_reg = '+ str(i))\n",
    "\n",
    "\n",
    "plt.title('MSE vs Regularization')\n",
    "plt.xlabel('Regularization (log Scale) (User Reg =  Res Reg)')\n",
    "plt.ylabel('MSE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for ALS for Restaurants in Phoenix=  14.5682667639\n"
     ]
    }
   ],
   "source": [
    "preds_als_phx = als(np.array(sm_u_10_phx_res_train.todense()),k=10, iters = 5, user_reg=0.001 , res_reg=0.001)\n",
    "Best_Val_MSE_als_phx = get_mse(preds_als_phx, np.array(sm_u_10_phx_res_val.todense()))\n",
    "print('Best Validation MSE for ALS for Restaurants in Phoenix= ', Best_Val_MSE_als_phx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_als_phx = preds_als_phx[train_phx_nnz]\n",
    "val_preds_als_phx = preds_als_phx[val_phx_nnz]\n",
    "test_preds_als_phx = preds_als_phx[test_phx_nnz]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2582d505320>"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KuzhYswY2bQqPjRuLf17Usp9+Kv0xSjpecc8T1M54K2ZlvyDI9HnEsSxb4ijtsvI+fia3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\naMDgwYNLPE5x4yrUShkiMy8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Z1VMiFcbdV5nZw8DFQGmreD/waEx+M/sCGBct/whIrU4f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\npfsR3SnnBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582d472fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_features = np.linspace(1,20,5,dtype=int)\n",
    "test_error_als_trt = []\n",
    "train_error_als_trt = []\n",
    "for i in num_features:\n",
    "    preds_als = als(np.array(sm_u_10_trt_res_train.todense()), k=i, iters = 5)\n",
    "    test_err = get_mse(preds_als, np.array(sm_u_10_trt_res_val.todense()))\n",
    "    train_err = get_mse(preds_als, np.array(sm_u_10_trt_res_train.todense()))\n",
    "    test_error_als_trt.append(test_err)\n",
    "    train_error_als_trt.append(train_err)\n",
    "\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(num_features,test_error_als_trt,'b-',label = 'validation')\n",
    "plt.plot(num_features,train_error_als_trt,'r-', label = 'training')\n",
    "plt.title('MSE vs num_features (for ALS)')\n",
    "plt.xlabel('Number of features in a feature vector')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'MSE')"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EzRFRGxG11dXVRQzVzKw8zH1zNf/9+Ct87ODdOHqM/+5ZYUqa7CXtkzN6KjA3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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582d41eda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_reg= np.logspace(-4,3,7)\n",
    "val_error_als = {}\n",
    "# train_error_als = {}\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "for i in user_reg:\n",
    "    val_error_als[i] = []\n",
    "    preds_als = als(np.array(sm_u_10_trt_res_train.todense()),k=10, iters = 5, user_reg=i, res_reg=i)\n",
    "    val_err = get_mse(preds_als, np.array(sm_u_10_trt_res_val.todense()))\n",
    "#         train_err = get_mse(preds_als, np.array(train.todense()))\n",
    "    val_error_als[i].append(val_err)\n",
    "#         train_error_als[i].append(train_err)\n",
    "plt.plot(np.log10(user_reg),val_error_als.values())\n",
    "#     plt.plot(np.log(res_reg),train_error_als[i], label = 'User_reg = '+ str(i))\n",
    "\n",
    "\n",
    "plt.title('MSE vs Regularization')\n",
    "plt.xlabel('Regularization (log Scale) (User Reg =  Res Reg)')\n",
    "plt.ylabel('MSE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for ALS for Restaurants in Toronto=  13.4499570269\n"
     ]
    }
   ],
   "source": [
    "preds_als_trt = als(np.array(sm_u_10_trt_res_train.todense()),k=10, iters = 5, user_reg=0.01, res_reg=0.01)\n",
    "Best_Val_MSE_als_trt = get_mse(preds_als_trt, np.array(sm_u_10_trt_res_val.todense()))\n",
    "print('Best Validation MSE for ALS for Restaurants in Toronto= ', Best_Val_MSE_als_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_als_trt = preds_als_trt[train_trt_nnz]\n",
    "val_preds_als_trt = preds_als_trt[val_trt_nnz]\n",
    "test_preds_als_trt = preds_als_trt[test_trt_nnz]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.4 SGD with bias correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sgd(ratings, k=40, user_bias_reg = 0.01, res_bias_reg = 0.01, user_vec_reg = 0.01, res_vec_reg = 0.01, lr = 1e-3, \n",
    "       iterations = 200):\n",
    "    '''Learn user and res biases along with latent vectors'''\n",
    "    error_array = np.zeros(iterations);\n",
    "    global_bias = np.mean(ratings[np.where(ratings)!=0])\n",
    "    user_bias = 0.1*(2*(np.random.rand(ratings.shape[0]))-1)\n",
    "    res_bias = 0.1*(2*(np.random.rand(ratings.shape[1]))-1)\n",
    "    user_vec = 0.1*(2*(np.random.rand(ratings.shape[0],k))-1)\n",
    "    res_vec = 0.1*(2*(np.random.rand(ratings.shape[1],k))-1)\n",
    "    training_idx = np.arange(ratings.nonzero()[0].shape[0])\n",
    "    np.random.shuffle(training_idx)\n",
    "    nz_rows_idx = ratings.nonzero()[0]\n",
    "    nz_cols_idx = ratings.nonzero()[1]\n",
    "    for i in range(iterations):\n",
    "    \n",
    "#         if(i%20 == 0):\n",
    "#             print('Iteration number: ', i)\n",
    "        lr = 1.0/(100 + 0.01*i)\n",
    "        np.random.shuffle(training_idx)\n",
    "        \n",
    "        temp_error_array = np.zeros(len(training_idx));\n",
    "        for datapoint_i, idx in enumerate(training_idx):\n",
    "            u = nz_rows_idx[idx]\n",
    "            r = nz_cols_idx[idx]\n",
    "            prediction = global_bias + user_bias[u] + res_bias[r] + np.dot(user_vec[u,:], res_vec[r,:].T)\n",
    "            e = (ratings[u,r] - prediction);\n",
    "            temp_error_array[datapoint_i] += e**2;\n",
    "            if i > 0:\n",
    "                user_bias[u] += lr * (e - user_bias_reg * user_bias[u])\n",
    "                res_bias[r] += lr * (e - res_bias_reg * res_bias[r])\n",
    "                user_vec[u,:] += lr * (e * res_vec[r,:] - user_vec_reg * user_vec[u,:])\n",
    "                res_vec[r,:] += lr * (e * user_vec[u,:] - res_vec_reg * res_vec[r,:])\n",
    "            \n",
    "        error_array[i] = np.mean(temp_error_array);\n",
    "#         print(error_array[i])\n",
    "            \n",
    "    predictions = global_bias + user_bias[:, np.newaxis] + res_bias[np.newaxis, :] + np.dot(user_vec, res_vec.T)\n",
    "    predictions[predictions > 5] = 5\n",
    "    predictions[predictions < 0] = 0\n",
    "    \n",
    "    return (predictions, error_array, user_vec, res_vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tuning the Iters hyper-parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iters =  10\n",
      "iters =  20\n",
      "iters =  30\n",
      "iters =  40\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2588c598c50>"
      ]
     },
     "execution_count": 438,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hLiIikiYyO9Q3b4ZXX4UtW+KuREREZKdldqi/8gqccAJ06ADPPBNCXkREpIrK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\nhEJdREQkTfx/LIWaKPBvfzkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2585a57ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iters = np.arange(10, 50, 10)\n",
    "err_sgd_test = []\n",
    "err_sgd_train = []\n",
    "for i in iters:\n",
    "    print('iters = ',i)\n",
    "    preds_sgd = sgd(np.array(sm_u_10_phx_res_train.todense()), k=10, iterations= i)\n",
    "    err_test = get_mse(preds_sgd[0], np.array(sm_u_10_phx_res_val.todense()))\n",
    "    err_train = get_mse(preds_sgd[0], np.array(sm_u_10_phx_res_train.todense()))\n",
    "    err_sgd_test.append(err_test)\n",
    "    err_sgd_train.append(err_train)\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(iters,err_sgd_test,'b-',label = 'validation')\n",
    "plt.plot(iters,err_sgd_train,'r-', label = 'training')\n",
    "plt.title('MSE_sgd vs Iterations (Restaurants in Phoenix)')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal Number of Iterations = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k =  2\n",
      "k =  3\n",
      "k =  4\n",
      "k =  6\n",
      "k =  7\n",
      "k =  9\n",
      "k =  10\n",
      "k =  12\n",
      "k =  13\n",
      "k =  15\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x258604bbe48>"
      ]
     },
     "execution_count": 439,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CXUTyY/v2cApd+uQ427eHdWVl1d31EyeGyXHat4+3XpFWSKe0iUh+dO4MZ54Z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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25859c89940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.linspace(2, 15, 10, dtype = int)\n",
    "err_sgd_test = []\n",
    "err_sgd_train = []\n",
    "for i in k:\n",
    "    print('k = ', i)\n",
    "    preds_sgd = sgd(np.array(sm_u_10_phx_res_train.todense()), k=i, iterations= 20)\n",
    "    err_test = get_mse(preds_sgd[0], np.array(sm_u_10_phx_res_val.todense()))\n",
    "    err_train = get_mse(preds_sgd[0], np.array(sm_u_10_phx_res_train.todense()))\n",
    "    err_sgd_test.append(err_test)\n",
    "    err_sgd_train.append(err_train)\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(k,err_sgd_test,'b-',label = 'validation')\n",
    "plt.plot(k,err_sgd_train,'r-', label = 'training')\n",
    "plt.title('MSE_sgd vs k (Restaurants in Phoenix)')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal K value = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predictions_sgd_phx, error_array_sgd_phx, user_vec_sgd_phx, res_vec_sgd_phx = sgd(np.array(sm_u_10_phx_res_train.todense()), k=2, iterations= 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for SGD for Restaurants in Phoenix=  1.31998829452\n"
     ]
    }
   ],
   "source": [
    "preds_sgd_phx = sgd(np.array(sm_u_10_phx_res_train.todense()),k=2, iterations= 20)\n",
    "Best_Val_MSE_sgd_phx = get_mse(preds_sgd_phx[0], np.array(sm_u_10_phx_res_val.todense()))\n",
    "print('Best Validation MSE for SGD for Restaurants in Phoenix= ', Best_Val_MSE_sgd_phx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_sgd_phx = preds_sgd_phx[0][train_phx_nnz]\n",
    "val_preds_sgd_phx = preds_sgd_phx[0][val_phx_nnz]\n",
    "test_preds_sgd_phx = preds_sgd_phx[0][test_phx_nnz]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iters =  10\n",
      "iters =  20\n",
      "iters =  30\n",
      "iters =  40\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x25859b91eb8>"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pJN566y2OO+442rRpw0EHHQRAz549+eKLL3bgalRMVle/A/TqBS+9BG+9BfvvD5ddBh06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\n/h85AJi2ocnORAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2582ef594e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iters = np.arange(10, 50, 10)\n",
    "err_sgd_test_trt = []\n",
    "err_sgd_train_trt = []\n",
    "for i in iters:\n",
    "    print('iters = ',i)\n",
    "    preds_sgd = sgd(np.array(sm_u_10_trt_res_train.todense()), k=10, iterations= i)\n",
    "    err_test = get_mse(preds_sgd[0], np.array(sm_u_10_trt_res_val.todense()))\n",
    "    err_train = get_mse(preds_sgd[0], np.array(sm_u_10_trt_res_train.todense()))\n",
    "    err_sgd_test_trt.append(err_test)\n",
    "    err_sgd_train_trt.append(err_train)\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(iters,err_sgd_test_trt,'b-',label = 'validation')\n",
    "plt.plot(iters,err_sgd_train_trt,'r-', label = 'training')\n",
    "plt.title('MSE_sgd vs Iterations (Restaurants in Toronto)')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal Number of Iterations = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k= 2\n",
      "k= 3\n",
      "k= 4\n",
      "k= 6\n",
      "k= 7\n",
      "k= 9\n",
      "k= 10\n",
      "k= 12\n",
      "k= 13\n",
      "k= 15\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2585a3cecf8>"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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efRaeeSY8ZQ5gwIB0wJ94IpSXx1VqERFpIQ0+I6Em/957IeBT07p1Yd3QoemA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\nEUkIhbqIiEhCKNRFREQSQqEuIiKSEP8fiUQs0lGuReAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2585944e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = np.linspace(2, 15, 10, dtype = int)\n",
    "err_sgd_val_trt = []\n",
    "err_sgd_train_trt = []\n",
    "for i in k:\n",
    "    print('k=', i)\n",
    "    preds_sgd = sgd(np.array(sm_u_10_trt_res_train.todense()), k=i, iterations= 30)\n",
    "    err_val = get_mse(preds_sgd[0], np.array(sm_u_10_trt_res_val.todense()))\n",
    "    err_train = get_mse(preds_sgd[0], np.array(sm_u_10_trt_res_train.todense()))\n",
    "    err_sgd_val_trt.append(err_val)\n",
    "    err_sgd_train_trt.append(err_train)\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "plt.plot(k,err_sgd_val_trt,'b-',label = 'validation')\n",
    "plt.plot(k,err_sgd_train_trt,'r-', label = 'training')\n",
    "plt.title('MSE_sgd vs k (for Restaurants in Toronto)')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal k value = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predictions_sgd_trt, error_array_sgd_trt, user_vec_sgd_trt, res_vec_sgd_trt = sgd(np.array(sm_u_10_trt_res_train.todense()), k=2, iterations= 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Validation MSE for SGD for Restaurants in Toronto=  1.22530245165\n"
     ]
    }
   ],
   "source": [
    "preds_sgd_trt = sgd(np.array(sm_u_10_trt_res_train.todense()),k=2, iterations=30)\n",
    "Best_Val_MSE_sgd_trt = get_mse(preds_sgd_trt[0], np.array(sm_u_10_trt_res_val.todense()))\n",
    "print('Best Validation MSE for SGD for Restaurants in Toronto= ', Best_Val_MSE_sgd_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_sgd_trt = preds_sgd_trt[0][train_trt_nnz]\n",
    "val_preds_sgd_trt = preds_sgd_trt[0][val_trt_nnz]\n",
    "test_preds_sgd_trt = preds_sgd_trt[0][test_trt_nnz]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Converting the Matrix Completion Problem into a Regression Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "def concatenated_SGD(U, V, matrix):\n",
    "    '''Concatenates the User Vector U (n_u x k) and Res Vector V (n_r x K) and returns a matrix of \\ \n",
    "    2k+1 x number of non-zero ratings in rating matrix (matrix)'''\n",
    "    indexes=matrix.nonzero()\n",
    "    users=U[indexes[0]]\n",
    "    rest=V[indexes[1]]\n",
    "    ratings=matrix[indexes].T\n",
    "    concat_sgd=np.concatenate((users,rest,ratings),axis=1)\n",
    "    return concat_sgd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_phx = concatenated_SGD(user_vec_sgd_phx, res_vec_sgd_phx, sm_u_10_phx_res_train)\n",
    "val_phx = concatenated_SGD(user_vec_sgd_phx, res_vec_sgd_phx, sm_u_10_phx_res_val)\n",
    "test_phx = concatenated_SGD(user_vec_sgd_phx, res_vec_sgd_phx, sm_u_10_phx_res_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_mat_phx = np.array(train_phx);\n",
    "val_mat_phx = np.array(val_phx);\n",
    "test_mat_phx = np.array(test_phx);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_train, y_train = train_mat_phx[:, :-1], np.ravel(train_mat_phx[:,-1]);\n",
    "x_val, y_val = val_mat_phx[:, :-1], np.ravel(val_mat_phx[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_iteration = 1000;\n",
    "plot_freq = 100;\n",
    "a,b = 100, 0.01;\n",
    "batch_size = 10207; #set to -1 for entire train set\n",
    "# batch_size = 5;\n",
    "weight_decay = 0.1;\n",
    "\n",
    "k = x_train.shape[1];\n",
    "#load objects here\n",
    "max_batch_size = x_train.shape[0];\n",
    "if(batch_size == -1):\n",
    "    batch_size = max_batch_size;\n",
    "assert(max_batch_size % batch_size == 0);\n",
    "no_of_batches = int(max_batch_size/batch_size);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_torch_var(x):\n",
    "        return(Variable(torch.Tensor( x )))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def plot_loss_curve(loss_array, val_array, i):\n",
    "        fig, x = plt.subplots(1,1);\n",
    "        x.loglog(np.arange(i), loss_array[:i], label=\"train\");\n",
    "        x.loglog(np.arange(i), val_array[:i], label=\"val\");\n",
    "        lgd = x.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "        x.set_xlabel('Training Iteration (log)');\n",
    "        x.set_ylabel('MSE (log)');\n",
    "        x.set_title('Iteration'+str(i));\n",
    "        fig.savefig('loss_curve.png', format='png', dpi=150,  bbox_extra_artists=(lgd,), bbox_inches='tight');\n",
    "        fig.clear()\n",
    "\n",
    "        fig, x = plt.subplots(1,1);\n",
    "        x.semilogy(np.arange(i), loss_array[:i], label=\"train\");\n",
    "        x.semilogy(np.arange(i), val_array[:i], label=\"val\");\n",
    "        lgd = x.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "        x.set_xlabel('Training Iteration (linear)');\n",
    "        x.set_ylabel('MSE (log)');\n",
    "        x.set_title('Iteration'+str(i));\n",
    "        fig.savefig('loss_curve_linear.png', format='png', dpi=150,  bbox_extra_artists=(lgd,), bbox_inches='tight');\n",
    "        fig.clear()\n",
    "\n",
    "class Net(nn.Module):\n",
    "\n",
    "    def __init__(self, k):\n",
    "        super(Net, self).__init__()\n",
    "        self.k = k;\n",
    "        self.linear1 = nn.Linear(k, 2, bias = True);\n",
    "        self.linear2 = nn.Linear(2, 1, bias = True);\n",
    "\n",
    "    def forward(self, x):\n",
    "        l_1 = self.linear1(x);\n",
    "        n_1 = F.sigmoid(l_1);\n",
    "        l_2 = self.linear2(n_1);\n",
    "        out = F.relu(l_2);\n",
    "        return out\n",
    "\n",
    "net = Net(k)\n",
    "\n",
    "optimizer = optim.Adam(net.parameters(), weight_decay=weight_decay);\n",
    "criterion = nn.MSELoss()\n",
    "\n",
    "loss_array = np.zeros(n_iteration);\n",
    "val_array = np.zeros(n_iteration);\n",
    "\n",
    "for i in range(n_iteration):\n",
    "#     print(i)\n",
    "    lr = np.true_divide(1, a + b*i);\n",
    "    optimizer.param_groups[0]['lr'] = lr;\n",
    "    \n",
    "    loss_array_minibatches = np.zeros(no_of_batches);\n",
    "    random_indices = np.random.permutation(range(max_batch_size));\n",
    "    for batch_i in range(no_of_batches):\n",
    "        selected_idx = random_indices[batch_i * batch_size : (batch_i+1) * batch_size];\n",
    "        input = get_torch_var( x_train[selected_idx, :] );\n",
    "        target = get_torch_var( y_train[selected_idx] );\n",
    "        out = net(input);\n",
    "        loss = criterion(out, target);\n",
    "\n",
    "        optimizer.zero_grad()   # zero the gradient buffers\n",
    "        loss.backward()\n",
    "        optimizer.step()    # Does the update\n",
    "\n",
    "        loss_array_minibatches[batch_i] = loss.data.numpy()[0];\n",
    "    \n",
    "    loss_array[i] = np.mean(loss_array_minibatches);\n",
    "    val_input = get_torch_var( x_val );\n",
    "    val_target = get_torch_var( y_val );\n",
    "    val_out = net(val_input);\n",
    "    val_loss = criterion(val_out, val_target);\n",
    "    val_array[i] = val_loss.data.numpy()[0];\n",
    "    \n",
    "    if(i % plot_freq == 0):\n",
    "        plot_loss_curve(loss_array, val_array, i);\n",
    "        plt.close('all');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation Error for NN for Restaurants in Phoenix =  1.45392096043\n"
     ]
    }
   ],
   "source": [
    "val_err_nn = val_array[-1]\n",
    "print('Validation Error for NN for Restaurants in Phoenix = ', val_err_nn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_nn_phx = np.ravel(net(get_torch_var(x_train)).data.numpy())\n",
    "val_preds_nn_phx = np.ravel(net(get_torch_var(x_val)).data.numpy())\n",
    "test_preds_nn_phx = np.ravel(net(get_torch_var(test_mat_phx[:, :-1])).data.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_trt = concatenated_SGD(user_vec_sgd_trt, res_vec_sgd_trt, sm_u_10_trt_res_train)\n",
    "val_trt = concatenated_SGD(user_vec_sgd_trt, res_vec_sgd_trt, sm_u_10_trt_res_val)\n",
    "test_trt = concatenated_SGD(user_vec_sgd_trt, res_vec_sgd_trt, sm_u_10_trt_res_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_mat_trt = np.array(train_trt);\n",
    "val_mat_trt = np.array(val_trt);\n",
    "test_mat_trt = np.array(test_trt);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 505,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_train, y_train = train_mat_trt[:, :-1], np.ravel(train_mat_trt[:,-1]);\n",
    "x_val, y_val = val_mat_trt[:, :-1], np.ravel(val_mat_trt[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 506,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(75608, 4)"
      ]
     },
     "execution_count": 506,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 507,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_iteration = 1000;\n",
    "plot_freq = 100;\n",
    "a,b = 100, 0.01;\n",
    "batch_size = 18902; #set to -1 for entire train set\n",
    "# batch_size = 5;\n",
    "weight_decay = 0.1;\n",
    "\n",
    "k = x_train.shape[1];\n",
    "#load objects here\n",
    "max_batch_size = x_train.shape[0];\n",
    "if(batch_size == -1):\n",
    "    batch_size = max_batch_size;\n",
    "assert(max_batch_size % batch_size == 0);\n",
    "no_of_batches = int(max_batch_size/batch_size);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 508,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_torch_var(x):\n",
    "        return(Variable(torch.Tensor( x )))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 509,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_loss_curve(loss_array, val_array, i):\n",
    "        fig, x = plt.subplots(1,1);\n",
    "        x.loglog(np.arange(i), loss_array[:i], label=\"train\");\n",
    "        x.loglog(np.arange(i), val_array[:i], label=\"val\");\n",
    "        lgd = x.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "        x.set_xlabel('Training Iteration (log)');\n",
    "        x.set_ylabel('MSE (log)');\n",
    "        x.set_title('Iteration'+str(i));\n",
    "        fig.savefig('loss_curve.png', format='png', dpi=150,  bbox_extra_artists=(lgd,), bbox_inches='tight');\n",
    "        fig.clear()\n",
    "\n",
    "        fig, x = plt.subplots(1,1);\n",
    "        x.semilogy(np.arange(i), loss_array[:i], label=\"train\");\n",
    "        x.semilogy(np.arange(i), val_array[:i], label=\"val\");\n",
    "        lgd = x.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "        x.set_xlabel('Training Iteration (linear)');\n",
    "        x.set_ylabel('MSE (log)');\n",
    "        x.set_title('Iteration'+str(i));\n",
    "        fig.savefig('loss_curve_linear.png', format='png', dpi=150,  bbox_extra_artists=(lgd,), bbox_inches='tight');\n",
    "        fig.clear()\n",
    "\n",
    "class Net(nn.Module):\n",
    "\n",
    "    def __init__(self, k):\n",
    "        super(Net, self).__init__()\n",
    "        self.k = k;\n",
    "        self.linear1 = nn.Linear(k, 2, bias = True);\n",
    "        self.linear2 = nn.Linear(2, 1, bias = True);\n",
    "\n",
    "    def forward(self, x):\n",
    "        l_1 = self.linear1(x);\n",
    "        n_1 = F.sigmoid(l_1);\n",
    "        l_2 = self.linear2(n_1);\n",
    "        out = F.relu(l_2);\n",
    "        return out\n",
    "\n",
    "net = Net(k)\n",
    "\n",
    "optimizer = optim.Adam(net.parameters(), weight_decay=weight_decay);\n",
    "criterion = nn.MSELoss()\n",
    "\n",
    "loss_array = np.zeros(n_iteration);\n",
    "val_array = np.zeros(n_iteration);\n",
    "\n",
    "for i in range(n_iteration):\n",
    "#     print(i)\n",
    "    lr = np.true_divide(1, a + b*i);\n",
    "    optimizer.param_groups[0]['lr'] = lr;\n",
    "    \n",
    "    loss_array_minibatches = np.zeros(no_of_batches);\n",
    "    random_indices = np.random.permutation(range(max_batch_size));\n",
    "    for batch_i in range(no_of_batches):\n",
    "        selected_idx = random_indices[batch_i * batch_size : (batch_i+1) * batch_size];\n",
    "        input = get_torch_var( x_train[selected_idx, :] );\n",
    "        target = get_torch_var( y_train[selected_idx] );\n",
    "        out = net(input);\n",
    "        loss = criterion(out, target);\n",
    "\n",
    "        optimizer.zero_grad()   # zero the gradient buffers\n",
    "        loss.backward()\n",
    "        optimizer.step()    # Does the update\n",
    "\n",
    "        loss_array_minibatches[batch_i] = loss.data.numpy()[0];\n",
    "    \n",
    "    loss_array[i] = np.mean(loss_array_minibatches);\n",
    "    val_input = get_torch_var( x_val );\n",
    "    val_target = get_torch_var( y_val );\n",
    "    val_out = net(val_input);\n",
    "    val_loss = criterion(val_out, val_target);\n",
    "    val_array[i] = val_loss.data.numpy()[0];\n",
    "    \n",
    "    if(i % plot_freq == 0):\n",
    "        plot_loss_curve(loss_array, val_array, i);\n",
    "        plt.close('all');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 510,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation Error for NN for Restaurants in Toronto =  1.32647287846\n"
     ]
    }
   ],
   "source": [
    "val_err_nn_trt = val_array[-1]\n",
    "print('Validation Error for NN for Restaurants in Toronto = ', val_err_nn_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 511,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_nn_trt = np.ravel(net(get_torch_var(x_train)).data.numpy())\n",
    "val_preds_nn_trt = np.ravel(net(get_torch_var(x_val)).data.numpy())\n",
    "test_preds_nn_trt = np.ravel(net(get_torch_var(test_mat_trt[:, :-1])).data.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest Regressor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 512,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for Random Forest Classifier for Restaurants in Phoenix =  1.43492244951\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "rf=RandomForestRegressor(max_depth=5)\n",
    "rf.fit(train_mat_phx[:,:4],train_mat_phx[:,4])\n",
    "preds_rf_phx=rf.predict(val_mat_phx[:,:4]).reshape(-1,1)\n",
    "MSE_rf_phx = get_mse(preds_rf_phx, val_mat_phx[:,4])\n",
    "print('MSE for Random Forest Classifier for Restaurants in Phoenix = ', MSE_rf_phx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 513,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_rf_phx = rf.predict(train_mat_phx[:,:4])\n",
    "val_preds_rf_phx = rf.predict(val_mat_phx[:,:4])\n",
    "test_preds_rf_phx = rf.predict(test_mat_phx[:,:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for Random Forest Classifier for Restaurants in Phoenix =  1.32907001402\n"
     ]
    }
   ],
   "source": [
    "rf_trt = RandomForestRegressor(max_depth=5)\n",
    "rf.fit(train_mat_trt[:,:4],train_mat_trt[:,4])\n",
    "preds_rf_trt = rf.predict(val_mat_trt[:,:4]).reshape(-1,1)\n",
    "MSE_rf_trt = get_mse(preds_rf_trt, val_mat_trt[:,4])\n",
    "print('MSE for Random Forest Classifier for Restaurants in Phoenix = ', MSE_rf_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_preds_rf_trt = rf.predict(train_mat_trt[:,:4])\n",
    "val_preds_rf_trt = rf.predict(val_mat_trt[:,:4])\n",
    "test_preds_rf_trt = rf.predict(test_mat_trt[:,:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ensemble of all the Predictors (SVD, Cosine Model, ALS, SGD, NN, RF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(51035,)"
      ]
     },
     "execution_count": 516,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_preds_svd_phx.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 517,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def build_ensemble_df(svd, cosine,als, sgd, nn, rf):\n",
    "    df =pd.DataFrame(svd)\n",
    "    df.columns = ['SVD']\n",
    "    df['Cosine'] = cosine\n",
    "    df['ALS'] = als\n",
    "    df['SGD'] = sgd\n",
    "    df['Neural_Network'] = nn\n",
    "    df['Random Forest'] = rf\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 518,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ensemble_training_phx_df = build_ensemble_df(train_preds_svd_phx,train_preds_cosine_phx, train_preds_als_phx, train_preds_sgd_phx, train_preds_nn_phx, train_preds_rf_phx)\n",
    "ensemble_validation_phx_df = build_ensemble_df(val_preds_svd_phx,val_preds_cosine_phx, val_preds_als_phx, val_preds_sgd_phx, val_preds_nn_phx, val_preds_rf_phx)\n",
    "ensemble_testing_phx_df = build_ensemble_df(test_preds_svd_phx,test_preds_cosine_phx, test_preds_als_phx, test_preds_sgd_phx, test_preds_nn_phx, test_preds_rf_phx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 519,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train_phx = np.ravel(np.array(sm_u_10_phx_res_train[train_phx_nnz]))\n",
    "y_val_phx = np.ravel(np.array(sm_u_10_phx_res_val[val_phx_nnz]))\n",
    "y_test_phx = np.ravel(np.array(sm_u_10_phx_res_test[test_phx_nnz]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ensemble_training_trt_df = build_ensemble_df(train_preds_svd_trt,train_preds_cosine_trt, train_preds_als_trt, train_preds_sgd_trt, train_preds_nn_trt, train_preds_rf_trt)\n",
    "ensemble_validation_trt_df = build_ensemble_df(val_preds_svd_trt,val_preds_cosine_trt, val_preds_als_trt, val_preds_sgd_trt, val_preds_nn_trt, val_preds_rf_trt)\n",
    "ensemble_testing_trt_df = build_ensemble_df(test_preds_svd_trt,test_preds_cosine_trt, test_preds_als_trt, test_preds_sgd_trt, test_preds_nn_trt, test_preds_rf_trt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train_trt = np.ravel(np.array(sm_u_10_trt_res_train[train_trt_nnz]))\n",
    "y_val_trt = np.ravel(np.array(sm_u_10_trt_res_val[val_trt_nnz]))\n",
    "y_test_trt = np.ravel(np.array(sm_u_10_trt_res_test[test_trt_nnz]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 522,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Phoenix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE of the ensemble of Models for restaurants in Phoenix =  1.27595753352\n"
     ]
    }
   ],
   "source": [
    "lr_phx = LinearRegression(fit_intercept=True)\n",
    "lr_phx.fit(ensemble_training_phx_df.iloc[:,-3:], y_train_phx)\n",
    "ensemble_val_pred_phx = lr_phx.predict(ensemble_validation_phx_df.iloc[:,-3:])\n",
    "MSE_ensemble_phx = get_mse(ensemble_val_pred_phx,y_val_phx)\n",
    "print('MSE of the ensemble of Models for restaurants in Phoenix = ', MSE_ensemble_phx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ridge Regression with high penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 534,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE of the ensemble of Models for restaurants in Phoenix =  1.22110620714\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "lrr_phx = Ridge(alpha = 10000)\n",
    "lrr_phx.fit(ensemble_training_phx_df.iloc[:,-3:], y_train_phx)\n",
    "ensemble_val_pred_phx = lrr_phx.predict(ensemble_validation_phx_df.iloc[:,-3:])\n",
    "MSE_ensemble_phx = get_mse(ensemble_val_pred_phx,y_val_phx)\n",
    "print('MSE of the ensemble of Models for restaurants in Phoenix = ', MSE_ensemble_phx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Restaurants in Toronto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE of the ensemble of Models for restaurants in Toronto =  1.25378321461\n"
     ]
    }
   ],
   "source": [
    "lr_trt = LinearRegression(fit_intercept=True)\n",
    "lr_trt.fit(ensemble_training_trt_df.iloc[:,-3:], y_train_trt)\n",
    "ensemble_val_pred_trt = lr_trt.predict(ensemble_validation_trt_df.iloc[:,-3:])\n",
    "MSE_ensemble_trt = get_mse(ensemble_val_pred_trt,y_val_trt)\n",
    "print('MSE of the ensemble of Models for restaurants in Toronto = ', MSE_ensemble_trt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ridge Regression with high penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE of the ensemble of Models for restaurants in Toronto =  1.15469045234\n"
     ]
    }
   ],
   "source": [
    "lrr_trt = Ridge(alpha = 10000)\n",
    "lrr_trt.fit(ensemble_training_trt_df.iloc[:,-3:], y_train_trt)\n",
    "ensemble_val_pred_trt = lrr_trt.predict(ensemble_validation_trt_df.iloc[:,-3:])\n",
    "MSE_ensemble_trt = get_mse(ensemble_val_pred_trt,y_val_trt)\n",
    "print('MSE of the ensemble of Models for restaurants in Toronto = ', MSE_ensemble_trt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Testing the best model on the test data and checking the test accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For the restaurants in Phoenix and Toronto, the best model was the ensemble model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 539,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE of the ensemble of Models for restaurants in Phoenix (test) =  1.17370661954\n"
     ]
    }
   ],
   "source": [
    "ensemble_test_pred_phx = lrr_phx.predict(ensemble_testing_phx_df.iloc[:,-3:])\n",
    "MSE_test_phx = get_mse(ensemble_test_pred_phx,y_test_phx)\n",
    "print('MSE of the ensemble of Models for restaurants in Phoenix (test) = ', MSE_test_phx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE of the ensemble of Models for restaurants in Toronto (test) =  1.09813204107\n"
     ]
    }
   ],
   "source": [
    "ensemble_test_pred_trt = lrr_trt.predict(ensemble_testing_trt_df.iloc[:,-3:])\n",
    "MSE_test_trt = get_mse(ensemble_test_pred_trt,y_test_trt)\n",
    "print('MSE of the ensemble of Models for restaurants in Toronto (test) = ', MSE_test_trt)"
   ]
  }
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