Movie recommendation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TzJOXl6cTJ04oGAwqHA6rvb1dubm50f12u10ej0ctLS26/fbbre0RAACIGzFdUbnllltU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fe2fa3da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VAABgLEIFAAAYi1ABAADGIlQAAICxCBUAAGAsQgUAABiLUAEAAMYiVAAAgLHCO7vgtm3b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\nsQgVAABgrP8PU3ANA4ZDt3QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8ff40f01d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcdefaults()\n",
    "import matplotlib.mlab as mlab\n",
    "\n",
    "fpath = 'u.data'\n",
    "data = pd.read_csv(fpath,header=None, sep='\\t')\n",
    "df = data\n",
    "\n",
    "movie_counts = df[1].value_counts().tolist()\n",
    "user_counts = df[0].value_counts().tolist()\n",
    "plt.hist(movie_counts, np.linspace(0, 500, 25))\n",
    "plt.show()\n",
    "plt.hist(user_counts, np.linspace(0, 800, 25))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1653, 1582]\n",
      "         user  movie  rating    timestamp  bi_score\n",
      "0           1    242     5.0  889751633.0  0.360956\n",
      "1           2    242     5.0  888552084.0  0.360956\n",
      "2           3    242     0.0          0.0  0.360956\n",
      "3           4    242     0.0          0.0  0.360956\n",
      "4           5    242     0.0          0.0  0.360956\n",
      "5           6    242     4.0  883268170.0  0.360956\n",
      "6           7    242     0.0          0.0  0.360956\n",
      "7           8    242     0.0          0.0  0.360956\n",
      "8           9    242     4.0  886958715.0  0.360956\n",
      "9          10    242     0.0          0.0  0.360956\n",
      "10         11    242     0.0          0.0  0.360956\n",
      "11         12    242     5.0  879960826.0  0.360956\n",
      "12         13    242     2.0  881515193.0  0.360956\n",
      "13         14    242     4.0  876964570.0  0.360956\n",
      "14         15    242     0.0          0.0  0.360956\n",
      "15         16    242     0.0          0.0  0.360956\n",
      "16         17    242     0.0          0.0  0.360956\n",
      "17         18    242     5.0  880129305.0  0.360956\n",
      "18         19    242     0.0          0.0  0.360956\n",
      "19         20    242     0.0          0.0  0.360956\n",
      "20         21    242     3.0  874951617.0  0.360956\n",
      "21         22    242     0.0          0.0  0.360956\n",
      "22         23    242     0.0          0.0  0.360956\n",
      "23         24    242     0.0          0.0  0.360956\n",
      "24         25    242     0.0          0.0  0.360956\n",
      "25         26    242     0.0          0.0  0.360956\n",
      "26         27    242     0.0          0.0  0.360956\n",
      "27         28    242     0.0          0.0  0.360956\n",
      "28         29    242     0.0          0.0  0.360956\n",
      "29         30    242     5.0  885941156.0  0.360956\n",
      "...       ...    ...     ...          ...       ...\n",
      "1586096   914   1641     0.0          0.0 -0.020147\n",
      "1586097   915   1641     0.0          0.0 -0.020147\n",
      "1586098   916   1641     0.0          0.0 -0.020147\n",
      "1586099   917   1641     0.0          0.0 -0.020147\n",
      "1586100   918   1641     0.0          0.0 -0.020147\n",
      "1586101   919   1641     0.0          0.0 -0.020147\n",
      "1586102   920   1641     0.0          0.0 -0.020147\n",
      "1586103   921   1641     0.0          0.0 -0.020147\n",
      "1586104   922   1641     0.0          0.0 -0.020147\n",
      "1586105   923   1641     0.0          0.0 -0.020147\n",
      "1586106   924   1641     0.0          0.0 -0.020147\n",
      "1586107   925   1641     0.0          0.0 -0.020147\n",
      "1586108   926   1641     0.0          0.0 -0.020147\n",
      "1586109   927   1641     0.0          0.0 -0.020147\n",
      "1586110   928   1641     0.0          0.0 -0.020147\n",
      "1586111   929   1641     0.0          0.0 -0.020147\n",
      "1586112   930   1641     0.0          0.0 -0.020147\n",
      "1586113   931   1641     0.0          0.0 -0.020147\n",
      "1586114   932   1641     0.0          0.0 -0.020147\n",
      "1586115   933   1641     0.0          0.0 -0.020147\n",
      "1586116   934   1641     0.0          0.0 -0.020147\n",
      "1586117   935   1641     0.0          0.0 -0.020147\n",
      "1586118   936   1641     0.0          0.0 -0.020147\n",
      "1586119   937   1641     0.0          0.0 -0.020147\n",
      "1586120   938   1641     0.0          0.0 -0.020147\n",
      "1586121   939   1641     0.0          0.0 -0.020147\n",
      "1586122   940   1641     0.0          0.0 -0.020147\n",
      "1586123   941   1641     0.0          0.0 -0.020147\n",
      "1586124   942   1641     0.0          0.0 -0.020147\n",
      "1586125   943   1641     0.0          0.0 -0.020147\n",
      "\n",
      "[1586126 rows x 5 columns]\n"
     ]
    }
   ],
   "source": [
    "import itertools\n",
    "\n",
    "user_id = data.iloc[:,0]\n",
    "item_id = data.iloc[:,1]\n",
    "rating = data.iloc[:,2]\n",
    "\n",
    "\n",
    "base_path = 'ua.base'\n",
    "train_data = pd.read_csv(base_path,header=None, sep='\\t')\n",
    "test_path = 'ua.test'\n",
    "test_data = pd.read_csv(base_path,header=None, sep='\\t')\n",
    "train_data.columns = ['user','movie','rating','timestamp']\n",
    "\n",
    "users = train_data.iloc[:,0].unique()\n",
    "movies = item_id.unique()\n",
    "indices = list(itertools.product(users, movies))\n",
    "list_of_indices = np.array([list(elem) for elem in indices])\n",
    "matrix_index = pd.DataFrame(list_of_indices, columns=['user', 'movie'])\n",
    "# print(matrix_index)\n",
    "result = pd.merge(matrix_index, train_data, how='outer')\n",
    "result.fillna(0, inplace=True)\n",
    "\n",
    "overall_avg = sum(train_data['rating'])/len(train_data['rating'])\n",
    "\n",
    "lambda2 = 25\n",
    "lambda3 = 10\n",
    "only_item_test = list(set(movies) - set(train_data['movie']))\n",
    "print(only_item_test)\n",
    "bi_movie = []\n",
    "train_data_unique_movies = list(set(train_data['movie']))\n",
    "for movie in train_data_unique_movies:\n",
    "    all_users_for_movie = train_data[train_data['movie']==movie]\n",
    "    length_user = 0\n",
    "    bi_user = []\n",
    "    for index, row in all_users_for_movie.iterrows():\n",
    "        if row['rating']==0:\n",
    "            continue\n",
    "        else:\n",
    "            length_user+=1\n",
    "            bi_user.append(row['rating']-overall_avg)\n",
    "    bi_movie.append(sum(bi_user)/(lambda2+length_user))\n",
    "remaining = [0 for i in range(len(only_item_test))]\n",
    "bi_movie = bi_movie+remaining\n",
    "total_movies = train_data_unique_movies + only_item_test\n",
    "\n",
    "bi_score = list(zip(total_movies, bi_movie))\n",
    "bi_score_list = np.array([list(elem) for elem in bi_score])\n",
    "bi_score_dict = dict(zip(total_movies, bi_movie))\n",
    "bi_score_df = pd.DataFrame(bi_score_list, columns=['movie', 'bi_score'])\n",
    "result_bi = pd.merge(result,bi_score_df,how='outer')\n",
    "result_bi.fillna(0, inplace=True)\n",
    "print(result_bi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         user  movie  rating    timestamp  bi_score  bu_score  \\\n",
      "0           1    242     5.0  889751633.0  0.360956  0.032686   \n",
      "1           1    302     0.0          0.0  0.591625  0.032686   \n",
      "2           1    377     0.0          0.0 -0.382280  0.032686   \n",
      "3           1     51     4.0  878543275.0 -0.037731  0.032686   \n",
      "4           1    346     0.0          0.0  0.131028  0.032686   \n",
      "5           1    474     0.0          0.0  0.644964  0.032686   \n",
      "6           1    265     0.0          0.0  0.307024  0.032686   \n",
      "7           1    465     0.0          0.0 -0.017929  0.032686   \n",
      "8           1    451     0.0          0.0 -0.147659  0.032686   \n",
      "9           1     86     5.0  878543541.0  0.347134  0.032686   \n",
      "10          1    257     4.0  874965954.0  0.239762  0.032686   \n",
      "11          1   1014     0.0          0.0 -0.380116  0.032686   \n",
      "12          1    222     4.0  878873388.0  0.104691  0.032686   \n",
      "13          1     40     3.0  876893230.0 -0.444662  0.032686   \n",
      "14          1     29     1.0  878542869.0 -0.706947  0.032686   \n",
      "15          1    785     0.0          0.0 -0.210783  0.032686   \n",
      "16          1    387     0.0          0.0 -0.088939  0.032686   \n",
      "17          1    274     0.0          0.0 -0.031179  0.032686   \n",
      "18          1   1042     0.0          0.0 -0.227833  0.032686   \n",
      "19          1   1184     0.0          0.0 -0.256307  0.032686   \n",
      "20          1    392     0.0          0.0  0.047053  0.032686   \n",
      "21          1    486     0.0          0.0  0.189869  0.032686   \n",
      "22          1    144     4.0  875073180.0  0.308556  0.032686   \n",
      "23          1    118     3.0  875071927.0 -0.278669  0.032686   \n",
      "24          1      1     5.0  874965758.0  0.315731  0.032686   \n",
      "25          1    546     0.0          0.0 -0.458662  0.032686   \n",
      "26          1     95     4.0  875072303.0  0.253408  0.032686   \n",
      "27          1    768     0.0          0.0 -0.292804  0.032686   \n",
      "28          1    277     0.0          0.0 -0.022787  0.032686   \n",
      "29          1    234     4.0  876892355.0  0.232695  0.032686   \n",
      "...       ...    ...     ...          ...       ...       ...   \n",
      "1586096   943   1366     0.0          0.0 -0.097070 -0.088447   \n",
      "1586097   943   1611     0.0          0.0 -0.038802 -0.088447   \n",
      "1586098   943   1668     0.0          0.0 -0.020147 -0.088447   \n",
      "1586099   943   1564     0.0          0.0 -0.097070 -0.088447   \n",
      "1586100   943   1604     0.0          0.0  0.018314 -0.088447   \n",
      "1586101   943   1574     0.0          0.0 -0.097070 -0.088447   \n",
      "1586102   943   1448     0.0          0.0  0.015304 -0.088447   \n",
      "1586103   943   1671     0.0          0.0 -0.097070 -0.088447   \n",
      "1586104   943   1625     0.0          0.0  0.018314 -0.088447   \n",
      "1586105   943   1665     0.0          0.0 -0.058609 -0.088447   \n",
      "1586106   943   1325     0.0          0.0 -0.097070 -0.088447   \n",
      "1586107   943   1670     0.0          0.0 -0.020147 -0.088447   \n",
      "1586108   943   1341     0.0          0.0 -0.097070 -0.088447   \n",
      "1586109   943   1352     0.0          0.0 -0.097070 -0.088447   \n",
      "1586110   943   1636     0.0          0.0  0.018314 -0.088447   \n",
      "1586111   943   1681     0.0          0.0 -0.020147 -0.088447   \n",
      "1586112   943   1638     0.0          0.0 -0.020147 -0.088447   \n",
      "1586113   943   1667     0.0          0.0 -0.020147 -0.088447   \n",
      "1586114   943   1675     0.0          0.0 -0.020147 -0.088447   \n",
      "1586115   943   1460     0.0          0.0 -0.020147 -0.088447   \n",
      "1586116   943   1594     0.0          0.0  0.072309 -0.088447   \n",
      "1586117   943   1626     0.0          0.0 -0.097070 -0.088447   \n",
      "1586118   943   1645     0.0          0.0  0.018314 -0.088447   \n",
      "1586119   943   1659     0.0          0.0 -0.097070 -0.088447   \n",
      "1586120   943   1682     0.0          0.0 -0.020147 -0.088447   \n",
      "1586121   943   1674     0.0          0.0  0.018314 -0.088447   \n",
      "1586122   943   1640     0.0          0.0 -0.020147 -0.088447   \n",
      "1586123   943   1637     0.0          0.0 -0.020147 -0.088447   \n",
      "1586124   943   1630     0.0          0.0 -0.020147 -0.088447   \n",
      "1586125   943   1641     0.0          0.0 -0.020147 -0.088447   \n",
      "\n",
      "         predicted_rating  \n",
      "0                3.917469  \n",
      "1                4.148138  \n",
      "2                3.174233  \n",
      "3                3.518782  \n",
      "4                3.687541  \n",
      "5                4.201477  \n",
      "6                3.863537  \n",
      "7                3.538584  \n",
      "8                3.408854  \n",
      "9                3.903647  \n",
      "10               3.796275  \n",
      "11               3.176398  \n",
      "12               3.661204  \n",
      "13               3.111851  \n",
      "14               2.849566  \n",
      "15               3.345730  \n",
      "16               3.467574  \n",
      "17               3.525334  \n",
      "18               3.328680  \n",
      "19               3.300206  \n",
      "20               3.603566  \n",
      "21               3.746382  \n",
      "22               3.865069  \n",
      "23               3.277844  \n",
      "24               3.872244  \n",
      "25               3.097851  \n",
      "26               3.809921  \n",
      "27               3.263709  \n",
      "28               3.533726  \n",
      "29               3.789208  \n",
      "...                   ...  \n",
      "1586096          3.338310  \n",
      "1586097          3.396578  \n",
      "1586098          3.415233  \n",
      "1586099          3.338310  \n",
      "1586100          3.453695  \n",
      "1586101          3.338310  \n",
      "1586102          3.450685  \n",
      "1586103          3.338310  \n",
      "1586104          3.453695  \n",
      "1586105          3.376772  \n",
      "1586106          3.338310  \n",
      "1586107          3.415233  \n",
      "1586108          3.338310  \n",
      "1586109          3.338310  \n",
      "1586110          3.453695  \n",
      "1586111          3.415233  \n",
      "1586112          3.415233  \n",
      "1586113          3.415233  \n",
      "1586114          3.415233  \n",
      "1586115          3.415233  \n",
      "1586116          3.507689  \n",
      "1586117          3.338310  \n",
      "1586118          3.453695  \n",
      "1586119          3.338310  \n",
      "1586120          3.415233  \n",
      "1586121          3.453695  \n",
      "1586122          3.415233  \n",
      "1586123          3.415233  \n",
      "1586124          3.415233  \n",
      "1586125          3.415233  \n",
      "\n",
      "[1586126 rows x 7 columns]\n"
     ]
    }
   ],
   "source": [
    "bu_user = []\n",
    "for user in users:\n",
    "    all_movies_for_user = result_bi[result_bi['user']==user]\n",
    "    length_movie = 0\n",
    "    bu_movie = []\n",
    "    for index,row in all_movies_for_user.iterrows():\n",
    "        if row['rating'] == 0:\n",
    "            continue\n",
    "        else:\n",
    "            length_movie+=1\n",
    "            bu_movie.append(row['rating']-overall_avg-row['bi_score'])\n",
    "    bu_user.append(sum(bu_movie)/(lambda3 + length_movie))\n",
    "\n",
    "test_data.columns = ['user','movie','rating','timestamp']    \n",
    "bu_score = list(zip(users,bu_user))\n",
    "bu_score_dict = dict(zip(users,bu_user))\n",
    "test_len = len(test_data['rating'])- 6536\n",
    "bu_score_list = np.array([list(elem) for elem in bu_score])\n",
    "bu_score_df = pd.DataFrame(bu_score_list, columns=['user', 'bu_score'])\n",
    "result_bi_bu = pd.merge(result_bi,bu_score_df,how='outer')\n",
    "result_bi_bu.fillna(0, inplace=True)\n",
    "result_bi_bu['predicted_rating'] = overall_avg + result_bi_bu['bi_score']+result_bi_bu['bu_score']\n",
    "print(result_bi_bu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE Score 0.9664823070017958\n"
     ]
    }
   ],
   "source": [
    "import math \n",
    "test_data['predicted_rating'] = [overall_avg+bi_score_dict[test_data['movie'][index]]+bu_score_dict[test_data['user'][index]] for index,x in enumerate(test_data['rating'])]\n",
    "test_data['RMSE_sq'] = (test_data['rating']-test_data['predicted_rating'])*(test_data['rating']-test_data['predicted_rating'])\n",
    "RMSE_sum = sum(test_data['RMSE_sq'])\n",
    "RMSE_score = math.sqrt(RMSE_sum/test_len)\n",
    "print('RMSE Score',RMSE_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QKpXo1KnTG7V/+vRpfP/99wgLC0Pnzp1LPTYrKwsPHjzA999/DzMzMwCAp6cn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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f900cec7048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "avg_rating_per_user = []\n",
    "for user in users:\n",
    "    rating_by_user = train_data[train_data['user']==user]['rating']\n",
    "    avg_rating = sum(rating_by_user)/len(rating_by_user)\n",
    "    avg_rating_per_user.append(avg_rating)\n",
    "avg_user_rating_dict = dict(zip(users,avg_rating_per_user))\n",
    "avg_rating_range = [min(avg_rating_per_user), max(avg_rating_per_user)]\n",
    "total_width = avg_rating_range[1] - avg_rating_range[0]\n",
    "bins = 5\n",
    "bar_width_range = total_width/bins\n",
    "# print(avg_rating_range, total_width, bar_width_range)\n",
    "avg_user_df = pd.DataFrame(\n",
    "    {'user': users,\n",
    "     'avg_rating': avg_rating_per_user\n",
    "    })\n",
    "test_data = pd.merge(test_data, avg_user_df , how='inner')\n",
    "test_data['bin'] = pd.cut(test_data['avg_rating'], bins=5)\n",
    "unique_bins = test_data['bin'].unique()\n",
    "RMSE_per_bin = []\n",
    "for u_bin in unique_bins:\n",
    "    users_per_bin = test_data[test_data['bin']==u_bin]\n",
    "    RMSE_score = math.sqrt(sum(users_per_bin['RMSE_sq'])/len(users_per_bin))\n",
    "    RMSE_per_bin.append(RMSE_score)\n",
    "    \n",
    "\n",
    "y_pos = np.arange(len(unique_bins)) \n",
    "width = 1\n",
    "plt.barh( y_pos, RMSE_per_bin, .5, align='center',alpha=0.5)\n",
    "plt.yticks(y_pos,unique_bins)\n",
    "plt.xlabel('RMSE scores for users in these bins')\n",
    "plt.ylabel('5 Bins based on average rating')\n",
    "plt.title('RMSE per user')\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1680\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.4/dist-packages/ipykernel/__main__.py:46: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "100\n",
      "200\n",
      "300\n",
      "400\n",
      "500\n",
      "600\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n",
      "1200\n",
      "1300\n",
      "1400\n",
      "1500\n",
      "1600\n",
      "-0.368732676627\n",
      "-0.368732676627\n"
     ]
    }
   ],
   "source": [
    "from itertools import combinations\n",
    "import numpy as np\n",
    "\n",
    "userAvg = {}\n",
    "uniqueUsers = train_data['user'].unique()\n",
    "for user in uniqueUsers:\n",
    "    cols = train_data[train_data['user']==user]\n",
    "    userAvg[user] = cols['rating'].mean()\n",
    "\n",
    "\n",
    "uniqueMovies = train_data['movie'].unique()\n",
    "sM = np.zeros(shape=(len(uniqueMovies),len(uniqueMovies)))\n",
    "movieMatch = {}\n",
    "movieUsers = {}\n",
    "movieUserRatings = {}\n",
    "count = 0\n",
    "train_data[train_data['movie']==movie]\n",
    "for movie in uniqueMovies:\n",
    "    movieMatch[movie] = count\n",
    "    movDf = train_data[train_data['movie']==movie]\n",
    "    movieUsers[movie] = set(movDf['user'])\n",
    "    mur = {}\n",
    "    for index, row in movDf.iterrows():  \n",
    "        mur[row['user']] = row['rating']\n",
    "    movieUserRatings[movie] = mur\n",
    "    count +=1\n",
    "print (len(movieUsers))\n",
    "for i in range(len(uniqueMovies)):\n",
    "    mov1 = uniqueMovies[i]\n",
    "    for j in range(i+1, len(uniqueMovies)):\n",
    "        mov2 = uniqueMovies[j]\n",
    "        x = movieMatch[mov1]\n",
    "        y = movieMatch[mov2]\n",
    "        intersect = movieUsers[mov1]&movieUsers[mov2]\n",
    "        mur1 = movieUserRatings[mov1]\n",
    "        mur2 = movieUserRatings[mov2]\n",
    "        numer = 0\n",
    "        denom1 = 0\n",
    "        denom2 = 0\n",
    "        for inter in intersect:\n",
    "            ru1 = mur1[inter] - userAvg[inter]\n",
    "            ru2 = mur2[inter] - userAvg[inter]\n",
    "            numer += (ru1*ru2)\n",
    "            denom1 += (ru1**2)\n",
    "            denom2 += (ru2**2)\n",
    "        sim = numer/(np.sqrt(denom1*denom2))\n",
    "        sM[x][y] = sim\n",
    "        sM[y][x] = sim\n",
    "    if not i%100:\n",
    "        print (i)\n",
    "print(sM[2][3])\n",
    "print(sM[3][2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1682\n",
      "1680\n",
      "1680\n"
     ]
    }
   ],
   "source": [
    "print(len(movies))\n",
    "print(len(sM[0]))\n",
    "print(len(sM))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2288102470032716\n",
      "1.169757112707372\n",
      "1.1491524988586608\n",
      "1.074066460524835\n",
      "1.0741641600810463\n"
     ]
    }
   ],
   "source": [
    "# def find_s_m_score(x):\n",
    "#     user = x[0]\n",
    "#     movie = x[1][0]\n",
    "#     simi_score = x[1][1]\n",
    "#     r_u =  test_data[test_data['user']==user]\n",
    "#     r_n = test_data[test_data['movie']==movie]\n",
    "#     r_u_n = pd.merge(r_u, r_n , how='inner', on=['user','movie','rating','timestamp'])\n",
    "#     if len(r_u_n):\n",
    "#         return r_u_n['rating'] * simi_score\n",
    "#     else:\n",
    "#         return 0\n",
    "    \n",
    "# import heapq\n",
    "# print('begin')\n",
    "# pred_k_1 = []\n",
    "# pred_k_2 = []\n",
    "# pred_k_3 = []\n",
    "# pred_k_5 = []\n",
    "# pred_k_10 = []\n",
    "# for index,entry in enumerate(test_data.iterrows()):\n",
    "#     if index%1000==0:\n",
    "#         print(index)\n",
    "#     try:\n",
    "#         seq=sM[(entry[1]['movie']-1)]\n",
    "#         k_1=heapq.nlargest(1, enumerate(seq), key=lambda x: x[1])\n",
    "#         k_2=heapq.nlargest(2, enumerate(seq), key=lambda x: x[1])\n",
    "#         k_3=heapq.nlargest(3, enumerate(seq), key=lambda x: x[1])\n",
    "#         k_5=heapq.nlargest(5, enumerate(seq), key=lambda x: x[1])\n",
    "#         k_10=heapq.nlargest(10, enumerate(seq), key=lambda x: x[1])\n",
    "#         user_list = [entry[1]['user']]*10\n",
    "#         user_top_10 = list(zip(user_list,k_10))\n",
    "#         r_u_n_list = list(map(find_s_m_score, user_top_10))\n",
    "#     except:\n",
    "#         print(entry[1]['movie'])\n",
    "    \n",
    "# print(r_u_n_list)\n",
    "movieMap = {}\n",
    "avgRatingsX = []\n",
    "avgRatingsY = []\n",
    "mu = train_data['rating'].mean()\n",
    "for movie in uniqueMovies:\n",
    "    cols = train_data[train_data['movie']==movie]\n",
    "    numerator = cols['rating'].sum() - mu*len(cols)\n",
    "    avgRatingsX.append([movie])\n",
    "    avgRatingsY.append(cols['rating'].mean())\n",
    "    denom = lambda2 + len(cols)\n",
    "    movieMap[movie] = numerator/denom\n",
    "    \n",
    "userMap = {}\n",
    "uniqueUsers = train_data['user'].unique()\n",
    "for user in uniqueUsers:\n",
    "    cols = train_data[train_data['user']==user]\n",
    "    bi = 0\n",
    "    for movie in cols['movie']:\n",
    "        bi += movieMap[movie]\n",
    "    numerator = cols['rating'].sum() - mu*len(cols) - bi\n",
    "    denom = lambda3 + len(cols)\n",
    "    userMap[user] = numerator/denom\n",
    "\n",
    "movTest = test_data['movie'].unique()\n",
    "Xtest = []\n",
    "ytest = []\n",
    "for movie in movTest:\n",
    "    cols = test_data[test_data['movie']==movie]\n",
    "    Xtest.append([movie])\n",
    "    ytest.append(cols['rating'].mean())\n",
    "    \n",
    "movieSet = set(uniqueMovies)\n",
    "import sklearn\n",
    "from sklearn.neighbors import NearestNeighbors\n",
    "import numpy as np\n",
    "from sklearn.neighbors import DistanceMetric\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "\n",
    "def mydist(mov1, mov2):\n",
    "    if mov1[0] in movieSet and mov2[0] in movieSet:\n",
    "        x = movieMatch[mov1[0]]\n",
    "        y = movieMatch[mov2[0]]\n",
    "        return sM[x][y]\n",
    "    return mu\n",
    "\n",
    "k = [1,2,3,5,10]\n",
    "\n",
    "rms_k = []\n",
    "\n",
    "knn = KNeighborsRegressor(n_neighbors=1,algorithm='brute', metric=mydist, n_jobs=-1)\n",
    "knn.fit(avgRatingsX, avgRatingsY)\n",
    "predY = knn.predict(Xtest)\n",
    "score = (predY == ytest).sum()/len(predY)\n",
    "\n",
    "new_predY_1 = [0 for i in movies]\n",
    "new_predY_1[:1581] = predY[:1581]\n",
    "new_predY_1[1582:1652] = predY[1581:1651]\n",
    "new_predY_1[1652] = overall_avg\n",
    "new_predY_1[1581] = overall_avg\n",
    "new_predY_1[1653:] = predY[1651:]\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "rms = sqrt(mean_squared_error(ytest, predY))\n",
    "rms_k.append(rms)\n",
    "print (rms)\n",
    "knn = KNeighborsRegressor(n_neighbors=2,algorithm='brute', metric=mydist, n_jobs=-1)\n",
    "knn.fit(avgRatingsX, avgRatingsY)\n",
    "predY = knn.predict(Xtest)\n",
    "score = (predY == ytest).sum()/len(predY)\n",
    "\n",
    "new_predY_2 = [0 for i in movies]\n",
    "new_predY_2[:1581] = predY[:1581]\n",
    "new_predY_2[1582:1652] = predY[1581:1651]\n",
    "new_predY_2[1652] = overall_avg\n",
    "new_predY_2[1581] = overall_avg\n",
    "new_predY_2[1653:] = predY[1651:]\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "rms = sqrt(mean_squared_error(ytest, predY))\n",
    "rms_k.append(rms)\n",
    "print (rms)\n",
    "\n",
    "knn = KNeighborsRegressor(n_neighbors=3,algorithm='brute', metric=mydist, n_jobs=-1)\n",
    "knn.fit(avgRatingsX, avgRatingsY)\n",
    "predY = knn.predict(Xtest)\n",
    "score = (predY == ytest).sum()/len(predY)\n",
    "\n",
    "new_predY_3 = [0 for i in movies]\n",
    "new_predY_3[:1581] = predY[:1581]\n",
    "new_predY_3[1582:1652] = predY[1581:1651]\n",
    "new_predY_3[1652] = overall_avg\n",
    "new_predY_3[1581] = overall_avg\n",
    "new_predY_3[1653:] = predY[1651:]\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "rms = sqrt(mean_squared_error(ytest, predY))\n",
    "rms_k.append(rms)\n",
    "print (rms)\n",
    "\n",
    "knn = KNeighborsRegressor(n_neighbors=5,algorithm='brute', metric=mydist, n_jobs=-1)\n",
    "knn.fit(avgRatingsX, avgRatingsY)\n",
    "predY = knn.predict(Xtest)\n",
    "score = (predY == ytest).sum()/len(predY)\n",
    "\n",
    "new_predY_5 = [0 for i in movies]\n",
    "new_predY_5[:1581] = predY[:1581]\n",
    "new_predY_5[1582:1652] = predY[1581:1651]\n",
    "new_predY_5[1652] = overall_avg\n",
    "new_predY_5[1581] = overall_avg\n",
    "new_predY_5[1653:] = predY[1651:]\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "rms = sqrt(mean_squared_error(ytest, predY))\n",
    "rms_k.append(rms)\n",
    "print (rms)\n",
    "\n",
    "knn = KNeighborsRegressor(n_neighbors=10,algorithm='brute', metric=mydist, n_jobs=-1)\n",
    "knn.fit(avgRatingsX, avgRatingsY)\n",
    "predY = knn.predict(Xtest)\n",
    "score = (predY == ytest).sum()/len(predY)\n",
    "\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "rms = sqrt(mean_squared_error(ytest, predY))\n",
    "rms_k.append(rms)\n",
    "print (rms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90570\n",
      "1680\n",
      "1680\n"
     ]
    }
   ],
   "source": [
    "print(len(train_data))\n",
    "print(len(predY))\n",
    "print(len(ytest))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1653, 1582}\n"
     ]
    }
   ],
   "source": [
    "print(set(movies)-set(uniqueMovies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      movie    pred_1    pred_2    pred_3    pred_5   pred_10\n",
      "0       242  2.666667  3.333333  3.555556  3.200000  3.233333\n",
      "1       302  2.000000  3.125000  3.166667  3.173333  2.836667\n",
      "2       377  3.700000  3.665789  3.443860  3.626316  3.004825\n",
      "3        51  2.666667  2.666667  2.444444  2.766667  2.083333\n",
      "4       346  3.105263  2.885965  2.257310  2.621053  3.103860\n",
      "5       474  3.222222  3.055556  3.272331  3.189486  3.089160\n",
      "6       265  4.714286  4.357143  4.238095  3.476190  2.554762\n",
      "7       465  3.250000  3.375000  2.850000  2.810000  2.180000\n",
      "8       451  2.666667  2.690476  2.960317  2.600000  2.598095\n",
      "9        86  3.391304  3.295652  3.197101  2.646466  2.664900\n",
      "10      257  4.250000  3.125000  3.416667  3.050000  2.291667\n",
      "11     1014  2.500000  3.250000  3.500000  2.900000  2.816667\n",
      "12      222  3.000000  2.833333  2.777778  3.219048  3.276190\n",
      "13       40  2.666667  2.333333  2.305556  3.183333  2.751667\n",
      "14       29  2.666667  2.233333  2.488889  2.493333  2.846667\n",
      "15      785  2.826087  2.801932  2.979066  3.539866  3.281883\n",
      "16      387  2.400000  3.113043  2.608696  3.913333  3.529275\n",
      "17      274  3.818182  3.742424  3.399711  3.364357  3.077202\n",
      "18     1042  2.888889  3.015873  3.177249  3.267388  3.342266\n",
      "19     1184  3.600000  3.133333  2.853595  3.300000  3.125523\n",
      "20      392  2.500000  3.312500  3.275000  2.665000  2.482500\n",
      "21      486  1.888889  1.944444  1.962963  2.877778  2.718889\n",
      "22      144  1.000000  2.666667  2.577778  2.381818  2.649242\n",
      "23      118  3.250000  3.025000  3.183333  3.276667  2.738333\n",
      "24        1  4.000000  3.333333  3.888889  3.183333  2.726667\n",
      "25      546  3.130435  3.231884  3.096618  3.113587  3.165290\n",
      "26       95  2.500000  2.250000  2.566667  3.300000  3.120000\n",
      "27      768  2.500000  3.250000  3.500000  3.100000  2.634091\n",
      "28      277  3.297297  2.942766  2.850733  2.585000  2.657038\n",
      "29      234  4.000000  3.700000  3.133333  3.080000  3.123333\n",
      "...     ...       ...       ...       ...       ...       ...\n",
      "1652   1366  3.523827  3.523827  3.523827  3.523827  3.523827\n",
      "1653   1611  4.250000  3.942797  4.046996  3.556769  3.387219\n",
      "1654   1668  3.198347  3.792401  3.916362  3.914764  3.769813\n",
      "1655   1564  3.000000  3.319113  3.443511  3.324536  3.112521\n",
      "1656   1604  3.859694  3.942734  3.920778  3.814883  3.926051\n",
      "1657   1574  3.859694  3.942734  3.920778  3.814883  3.926051\n",
      "1658   1448  3.859694  3.942734  3.920778  3.867345  3.775180\n",
      "1659   1671  3.198347  2.985250  3.133593  3.753876  3.761752\n",
      "1660   1625  3.761905  3.091479  3.203843  2.973893  2.843130\n",
      "1661   1665  4.365657  4.188523  3.606163  3.353442  3.395582\n",
      "1662   1325  3.058824  3.174981  3.257115  2.996154  3.095356\n",
      "1663   1670  4.365657  4.188523  3.606163  3.353442  3.395582\n",
      "1664   1341  4.365657  4.188523  3.606163  3.353442  3.395582\n",
      "1665   1352  3.761905  3.091479  3.203843  2.973893  2.843130\n",
      "1666   1636  3.761905  3.091479  3.203843  2.973893  2.843130\n",
      "1667   1681  4.365657  4.188523  3.606163  3.353442  3.395582\n",
      "1668   1638  3.761905  3.091479  3.203843  2.973893  2.843130\n",
      "1669   1667  3.791262  3.230218  3.421084  3.511117  3.466509\n",
      "1670   1675  3.859694  3.529020  3.534499  3.832556  3.892890\n",
      "1671   1460  3.780392  3.605336  3.686662  3.893215  3.948165\n",
      "1672   1594  4.025773  3.991147  4.032251  3.952429  4.003042\n",
      "1673   1626  4.025773  3.951319  4.096364  3.064484  3.129880\n",
      "1674   1645  3.545455  3.785614  3.816031  3.861463  3.388043\n",
      "1675   1659  3.803468  3.914621  3.902036  4.069484  3.973837\n",
      "1676   1682  3.791262  3.797040  3.948026  3.657127  3.714853\n",
      "1677   1674  3.791262  3.797040  3.948026  4.106625  3.795973\n",
      "1678   1640  3.988506  3.889884  3.860862  3.276932  3.475241\n",
      "1679   1637  3.859694  3.908108  3.993500  4.015001  3.769317\n",
      "1680   1630  3.801843  3.850922  3.938767  3.092563  3.251096\n",
      "1681   1641  3.859694  3.702574  3.736206  3.862309  3.831371\n",
      "\n",
      "[1682 rows x 6 columns]\n"
     ]
    }
   ],
   "source": [
    "new_predY_10 = [0 for i in movies]\n",
    "new_predY_10[:1581] = predY[:1581]\n",
    "new_predY_10[1582:1652] = predY[1581:1651]\n",
    "new_predY_10[1652] = overall_avg\n",
    "new_predY_10[1581] = overall_avg\n",
    "new_predY_10[1653:] = predY[1651:]\n",
    "pred_df = pd.DataFrame({'movie' : movies,\n",
    "    'pred_1' : new_predY_1,\n",
    "    'pred_2' : new_predY_2,\n",
    "    'pred_3' : new_predY_3,\n",
    "    'pred_5' : new_predY_5,\n",
    "    'pred_10' : new_predY_10\n",
    "  }, columns=['movie','pred_1', 'pred_2','pred_3','pred_5','pred_10'])\n",
    "print(pred_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       user  movie  rating  timestamp  predicted_rating   RMSE_sq  avg_rating  \\\n",
      "0         1      1       5  874965758          3.872244  1.271833    3.603053   \n",
      "1         1      2       3  876893171          3.286766  0.082235    3.603053   \n",
      "2         1      3       4  878542960          3.197193  0.644500    3.603053   \n",
      "3         1      4       3  876893119          3.575716  0.331449    3.603053   \n",
      "4         1      5       3  889751712          3.379760  0.144218    3.603053   \n",
      "5         1      6       5  887431973          3.513846  2.208653    3.603053   \n",
      "6         1      7       4  875071561          3.817311  0.033375    3.603053   \n",
      "7         1      8       1  875072484          4.001160  9.006960    3.603053   \n",
      "8         1      9       5  878543541          3.879429  1.255679    3.603053   \n",
      "9         1     10       3  875693118          3.790590  0.625032    3.603053   \n",
      "10        1     11       2  875072262          3.805809  3.260946    3.603053   \n",
      "11        1     12       5  878542960          4.341004  0.434276    3.603053   \n",
      "12        1     13       5  875071805          3.493510  2.269512    3.603053   \n",
      "13        1     14       5  874965706          3.931050  1.142654    3.603053   \n",
      "14        1     15       5  875071608          3.790171  1.463686    3.603053   \n",
      "15        1     16       5  878543541          3.362124  2.682639    3.603053   \n",
      "16        1     17       3  875073198          3.224465  0.050385    3.603053   \n",
      "17        1     18       4  887432020          3.349706  0.422883    3.603053   \n",
      "18        1     19       5  875071515          3.822047  1.387573    3.603053   \n",
      "19        1     21       1  878542772          2.985529  3.942327    3.603053   \n",
      "20        1     22       4  875072404          4.144476  0.020873    3.603053   \n",
      "21        1     23       4  875072895          4.069837  0.004877    3.603053   \n",
      "22        1     24       3  875071713          3.467989  0.219014    3.603053   \n",
      "23        1     25       4  875071805          3.471439  0.279377    3.603053   \n",
      "24        1     26       3  875072442          3.479379  0.229804    3.603053   \n",
      "25        1     27       2  876892946          3.306656  1.707350    3.603053   \n",
      "26        1     28       4  875072173          3.945444  0.002976    3.603053   \n",
      "27        1     29       1  878542869          2.849566  3.420896    3.603053   \n",
      "28        1     30       3  878542515          3.821140  0.674271    3.603053   \n",
      "29        1     31       3  875072144          3.656779  0.431358    3.603053   \n",
      "...     ...    ...     ...        ...               ...       ...         ...   \n",
      "90540   943    685       4  875502042          3.277396  0.522157    3.392405   \n",
      "90541   943    717       4  875502116          2.922402  1.161218    3.392405   \n",
      "90542   943    720       1  888640048          3.037473  4.151298    3.392405   \n",
      "90543   943    721       5  888639660          3.333865  2.776006    3.392405   \n",
      "90544   943    722       3  888640208          3.022476  0.000505    3.392405   \n",
      "90545   943    724       1  888639478          3.380656  5.667525    3.392405   \n",
      "90546   943    732       4  888639789          3.538299  0.213168    3.392405   \n",
      "90547   943    739       4  888639929          3.258457  0.549887    3.392405   \n",
      "90548   943    756       2  875502146          3.001820  1.003643    3.392405   \n",
      "90549   943    763       4  875501813          3.335453  0.441622    3.392405   \n",
      "90550   943    765       3  888640227          3.020405  0.000416    3.392405   \n",
      "90551   943    785       2  888640088          3.224597  1.499638    3.392405   \n",
      "90552   943    794       3  888640143          3.536128  0.287434    3.392405   \n",
      "90553   943    796       3  888640311          3.213148  0.045432    3.392405   \n",
      "90554   943    816       4  888640186          2.913680  1.180092    3.392405   \n",
      "90555   943    824       4  875502483          2.927907  1.149384    3.392405   \n",
      "90556   943    825       3  875502283          3.079158  0.006266    3.392405   \n",
      "90557   943    831       2  875502283          2.626693  0.392745    3.392405   \n",
      "90558   943    840       4  888693104          2.833865  1.359871    3.392405   \n",
      "90559   943    928       5  875502074          3.061104  3.759316    3.392405   \n",
      "90560   943    941       1  888639725          3.101346  4.415654    3.392405   \n",
      "90561   943    943       5  888639614          3.389263  2.594475    3.392405   \n",
      "90562   943   1011       2  875502560          3.199342  1.438421    3.392405   \n",
      "90563   943   1028       2  875502096          3.026083  1.052846    3.392405   \n",
      "90564   943   1044       3  888639903          3.294024  0.086450    3.392405   \n",
      "90565   943   1047       2  875502146          2.855094  0.731186    3.392405   \n",
      "90566   943   1074       4  888640250          3.047967  0.906367    3.392405   \n",
      "90567   943   1188       3  888640250          2.973609  0.000696    3.392405   \n",
      "90568   943   1228       3  888640275          2.743887  0.065594    3.392405   \n",
      "90569   943   1330       3  888692465          3.294163  0.086532    3.392405   \n",
      "\n",
      "                  bin  \n",
      "0      (3.553, 4.241]  \n",
      "1      (3.553, 4.241]  \n",
      "2      (3.553, 4.241]  \n",
      "3      (3.553, 4.241]  \n",
      "4      (3.553, 4.241]  \n",
      "5      (3.553, 4.241]  \n",
      "6      (3.553, 4.241]  \n",
      "7      (3.553, 4.241]  \n",
      "8      (3.553, 4.241]  \n",
      "9      (3.553, 4.241]  \n",
      "10     (3.553, 4.241]  \n",
      "11     (3.553, 4.241]  \n",
      "12     (3.553, 4.241]  \n",
      "13     (3.553, 4.241]  \n",
      "14     (3.553, 4.241]  \n",
      "15     (3.553, 4.241]  \n",
      "16     (3.553, 4.241]  \n",
      "17     (3.553, 4.241]  \n",
      "18     (3.553, 4.241]  \n",
      "19     (3.553, 4.241]  \n",
      "20     (3.553, 4.241]  \n",
      "21     (3.553, 4.241]  \n",
      "22     (3.553, 4.241]  \n",
      "23     (3.553, 4.241]  \n",
      "24     (3.553, 4.241]  \n",
      "25     (3.553, 4.241]  \n",
      "26     (3.553, 4.241]  \n",
      "27     (3.553, 4.241]  \n",
      "28     (3.553, 4.241]  \n",
      "29     (3.553, 4.241]  \n",
      "...               ...  \n",
      "90540  (2.865, 3.553]  \n",
      "90541  (2.865, 3.553]  \n",
      "90542  (2.865, 3.553]  \n",
      "90543  (2.865, 3.553]  \n",
      "90544  (2.865, 3.553]  \n",
      "90545  (2.865, 3.553]  \n",
      "90546  (2.865, 3.553]  \n",
      "90547  (2.865, 3.553]  \n",
      "90548  (2.865, 3.553]  \n",
      "90549  (2.865, 3.553]  \n",
      "90550  (2.865, 3.553]  \n",
      "90551  (2.865, 3.553]  \n",
      "90552  (2.865, 3.553]  \n",
      "90553  (2.865, 3.553]  \n",
      "90554  (2.865, 3.553]  \n",
      "90555  (2.865, 3.553]  \n",
      "90556  (2.865, 3.553]  \n",
      "90557  (2.865, 3.553]  \n",
      "90558  (2.865, 3.553]  \n",
      "90559  (2.865, 3.553]  \n",
      "90560  (2.865, 3.553]  \n",
      "90561  (2.865, 3.553]  \n",
      "90562  (2.865, 3.553]  \n",
      "90563  (2.865, 3.553]  \n",
      "90564  (2.865, 3.553]  \n",
      "90565  (2.865, 3.553]  \n",
      "90566  (2.865, 3.553]  \n",
      "90567  (2.865, 3.553]  \n",
      "90568  (2.865, 3.553]  \n",
      "90569  (2.865, 3.553]  \n",
      "\n",
      "[90570 rows x 8 columns]\n"
     ]
    }
   ],
   "source": [
    "print(test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       user  movie  rating  timestamp  predicted_rating   RMSE_sq  avg_rating  \\\n",
      "0         1      1       5  874965758          3.872244  1.271833    3.603053   \n",
      "1         2      1       4  888550871          3.925964  0.005481    3.750000   \n",
      "2         6      1       4  883599478          3.691889  0.094933    3.631841   \n",
      "3        10      1       4  877888877          4.246013  0.060522    4.201149   \n",
      "4        13      1       3  882140487          3.471022  0.221862    3.089457   \n",
      "5        15      1       1  879455635          3.410501  5.810516    2.957447   \n",
      "6        16      1       5  877717833          4.439609  0.314038    4.330769   \n",
      "7        18      1       5  880130802          3.972469  1.055820    3.880150   \n",
      "8        20      1       3  879667963          3.505529  0.255560    3.210526   \n",
      "9        21      1       5  874951244          3.282273  2.950585    2.656805   \n",
      "10       23      1       5  874784615          3.783533  1.479792    3.638298   \n",
      "11       25      1       5  885853415          3.981308  1.037734    4.014706   \n",
      "12       26      1       3  891350625          3.375731  0.141174    2.938144   \n",
      "13       38      1       5  892430636          4.195301  0.647540    3.747748   \n",
      "14       41      1       4  890692860          3.802651  0.038946    3.833333   \n",
      "15       42      1       5  881105633          3.978769  1.042912    3.716763   \n",
      "16       43      1       5  875975579          3.983854  1.032552    3.715640   \n",
      "17       44      1       4  878341315          3.813771  0.034681    3.609929   \n",
      "18       45      1       5  881013176          4.027748  0.945274    3.631579   \n",
      "19       49      1       2  888068651          3.099047  1.207904    2.668293   \n",
      "20       54      1       4  880931595          4.036793  0.001354    3.654545   \n",
      "21       56      1       4  892683248          3.972237  0.000771    3.621469   \n",
      "22       57      1       5  883698581          3.906833  1.195015    3.489583   \n",
      "23       58      1       5  884304483          3.926630  1.152123    3.826389   \n",
      "24       59      1       2  888203053          4.158410  4.658733    3.943548   \n",
      "25       62      1       2  879372813          3.572718  2.473442    3.310811   \n",
      "26       63      1       3  875747368          3.457883  0.209656    3.072289   \n",
      "27       64      1       4  879366214          3.750271  0.062364    3.573684   \n",
      "28       65      1       3  879217290          4.014733  1.029684    3.942857   \n",
      "29       70      1       4  884065277          3.734493  0.070494    3.446281   \n",
      "...     ...    ...     ...        ...               ...       ...         ...   \n",
      "90540   894   1658       4  882404137          3.556416  0.196766    3.638298   \n",
      "90541   747   1497       4  888732538          3.879865  0.014432    4.042403   \n",
      "90542   747   1659       1  888733313          3.764480  7.642350    4.042403   \n",
      "90543   747   1660       2  888640731          3.802942  3.250599    4.042403   \n",
      "90544   751   1661       1  889299429          3.328057  5.419847    3.518987   \n",
      "90545   782   1662       4  891500110          2.994721  1.010587    2.792793   \n",
      "90546   782   1663       2  891499700          2.917798  0.842352    2.792793   \n",
      "90547   782   1664       4  891499699          3.027425  0.945902    2.792793   \n",
      "90548   870   1664       4  890057322          3.397483  0.363027    3.467181   \n",
      "90549   880   1664       4  892958799          3.594779  0.164204    3.421788   \n",
      "90550   782   1665       2  891500194          2.917798  0.842352    2.792793   \n",
      "90551   782   1666       2  891500194          2.917798  0.842352    2.792793   \n",
      "90552   782   1667       3  891500110          2.956259  0.001913    2.792793   \n",
      "90553   782   1668       3  891500067          2.956259  0.001913    2.792793   \n",
      "90554   782   1669       2  891500150          2.917798  0.842352    2.792793   \n",
      "90555   782   1670       3  891497793          2.956259  0.001913    2.792793   \n",
      "90556   787   1671       1  888980193          3.137234  4.567770    3.042553   \n",
      "90557   828   1672       2  891037722          2.913811  0.835050    3.053191   \n",
      "90558   896   1672       2  887159554          2.884084  0.781605    2.988636   \n",
      "90559   835   1673       3  891034023          3.838414  0.702938    4.130435   \n",
      "90560   840   1674       4  891211682          3.858783  0.019942    4.133690   \n",
      "90561   851   1675       3  884222085          3.559127  0.312623    3.452261   \n",
      "90562   851   1676       2  875731674          3.520665  2.312423    3.452261   \n",
      "90563   854   1677       3  882814368          3.100528  0.010106    3.202899   \n",
      "90564   863   1678       1  889289570          3.115478  4.475247    3.072165   \n",
      "90565   863   1679       3  889289491          3.192401  0.037018    3.072165   \n",
      "90566   863   1680       2  889289570          3.153940  1.331576    3.072165   \n",
      "90567   883   1656       5  891692168          3.845642  1.332542    3.926357   \n",
      "90568   896   1681       3  887160722          2.976813  0.000538    2.988636   \n",
      "90569   916   1682       3  880845755          3.327143  0.107023    3.374593   \n",
      "\n",
      "                  bin    pred_1    pred_2    pred_3    pred_5   pred_10  \n",
      "0      (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "1      (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "2      (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "3      (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "4      (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "5      (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "6      (4.241, 4.929]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "7      (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "8      (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "9      (2.177, 2.865]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "10     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "11     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "12     (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "13     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "14     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "15     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "16     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "17     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "18     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "19     (2.177, 2.865]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "20     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "21     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "22     (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "23     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "24     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "25     (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "26     (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "27     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "28     (3.553, 4.241]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "29     (2.865, 3.553]  4.000000  3.333333  3.888889  3.183333  2.726667  \n",
      "...               ...       ...       ...       ...       ...       ...  \n",
      "90540  (3.553, 4.241]  3.859694  3.529020  3.372288  3.983953  4.020823  \n",
      "90541  (3.553, 4.241]  2.666667  2.333333  2.222222  2.233333  2.376667  \n",
      "90542  (3.553, 4.241]  3.803468  3.914621  3.902036  4.069484  3.973837  \n",
      "90543  (3.553, 4.241]  3.545455  3.674461  3.716922  3.585096  3.534044  \n",
      "90544  (2.865, 3.553]  3.291139  3.031646  2.687764  3.435893  3.218310  \n",
      "90545  (2.177, 2.865]  3.566176  3.110011  3.120960  3.251785  3.084256  \n",
      "90546  (2.177, 2.865]  4.036810  4.006777  3.587851  3.483102  3.372279  \n",
      "90547  (2.177, 2.865]  3.829268  3.804830  3.679980  3.230551  3.312056  \n",
      "90548  (2.865, 3.553]  3.829268  3.804830  3.679980  3.230551  3.312056  \n",
      "90549  (2.865, 3.553]  3.829268  3.804830  3.679980  3.230551  3.312056  \n",
      "90550  (2.177, 2.865]  4.365657  4.188523  3.606163  3.353442  3.395582  \n",
      "90551  (2.177, 2.865]  3.859694  3.702574  3.565429  3.300181  3.402842  \n",
      "90552  (2.177, 2.865]  3.791262  3.230218  3.421084  3.511117  3.466509  \n",
      "90553  (2.177, 2.865]  3.198347  3.792401  3.916362  3.914764  3.769813  \n",
      "90554  (2.177, 2.865]  3.823009  3.926656  3.893633  3.416478  3.559203  \n",
      "90555  (2.177, 2.865]  4.365657  4.188523  3.606163  3.353442  3.395582  \n",
      "90556  (2.865, 3.553]  3.198347  2.985250  3.133593  3.753876  3.761752  \n",
      "90557  (2.865, 3.553]  3.859694  3.702574  3.565429  3.300181  3.402842  \n",
      "90558  (2.865, 3.553]  3.859694  3.702574  3.565429  3.300181  3.402842  \n",
      "90559  (3.553, 4.241]  3.291139  3.535276  3.545576  3.908880  3.911610  \n",
      "90560  (3.553, 4.241]  3.791262  3.797040  3.948026  4.106625  3.795973  \n",
      "90561  (2.865, 3.553]  3.859694  3.529020  3.534499  3.832556  3.892890  \n",
      "90562  (2.865, 3.553]  3.859694  4.011990  4.129879  3.742498  4.038750  \n",
      "90563  (2.865, 3.553]  3.198347  3.500908  3.675863  3.319804  3.403024  \n",
      "90564  (2.865, 3.553]  3.859694  3.702574  3.565429  3.300181  3.402842  \n",
      "90565  (2.865, 3.553]  3.859694  3.702574  3.565429  3.300181  3.402842  \n",
      "90566  (2.865, 3.553]  4.386454  4.275370  4.118312  3.805520  3.902545  \n",
      "90567  (3.553, 4.241]  3.545455  3.418297  3.620789  2.757264  3.055111  \n",
      "90568  (2.865, 3.553]  4.365657  4.188523  3.606163  3.353442  3.395582  \n",
      "90569  (2.865, 3.553]  3.791262  3.797040  3.948026  3.657127  3.714853  \n",
      "\n",
      "[90570 rows x 13 columns]\n"
     ]
    }
   ],
   "source": [
    "final_test_data = pd.merge(test_data, pred_df, how = 'inner')\n",
    "print(final_test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot for k=1\n"
     ]
    },
    {
     "data": {
      "image/png": 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rVi1R/V64cAFXr15F9+7dS71m69ataNu2LapXry76fgICAuDu7g65XA65XI7A\nwEA8efIEt27dKvU76enp+Pjjj2Fubg6ZTIZPP/0U+fn5uHPnDgAgMTERjx8/RmhoKCwtLQEANjY2\nqFGjhui6iIiIiMoi+pnA7OxsLFq0CAkJCbC3t9cIceUZjbp8+TLatm1b5jUXLlzAs2fP4OzsLLrd\nV9m6dSsaNWoEJyenEs+npaXh5MmTWLJkyRv1c/z4cRgZGaFmzZqlXuPv74+dO3eiffv2MDc3x9at\nW/Hee++hTp06AJ5PdTs5OWHhwoU4duwYjI2N4enpiaCgIBgaGgrtHDt2DD169ICpqSmaNm2KoKAg\nWFhYvFH9REREpB1EjwQaGhrC29sbNWvWhJ6eHnR1dYX/lEdOTg5MTExKPf/gwQPMnDkTAQEBsLOz\nK1fbpcnOzsZff/2FHj16lHrN9u3bUatWLbi7u792P9euXcOSJUswcuRIGBgYlHqdm5sb5HI5evXq\nBV9fX8THx2PixInC9HFWVhZSUlJQq1YtxMfHY+HChTh9+jRWrlwptPH5558jLi4OW7duxbx585Ce\nno7Jkye/du1ERESkXUSPBIaFhVVIh2ZmZsjLyyvxXFpaGiZMmAAvLy8MGjSoQvoDgJ07d8LMzAxt\n2rQp8bxSqcTu3bsxePDg1+7j4sWLCA8PR1BQEHx9fUu9Tq1WY9y4cWjUqBG2b98OY2NjHD16FGFh\nYYiMjETdunVhbGyM6tWr48svvwQA2NnZwd/fH1FRURg7diwAoF69ekKbDg4OGD9+PAICApCWlob3\n3ntPdN3JyVOgr28MAKhb1wfOzj6vc/tEREQkkcTERCQmJgJ4nlkqiugQWFFcXFxw48aNYsevXbuG\nsLAw9OjRA4GBgRXaZ0JCAvz8/KCjU/LA559//gmVSoWOHTu+VvsnT57E9OnTMXLkSHTq1KnMa3Ny\ncnD37l1Mnz4dpqamAABPT084ODjg+PHjqFu3LlxcXHDx4kWN7728KORlMpkMMpnslde9rEOHmTAx\nsSnXd4iIiKjy+Pj4wMfn+SBNdnY2oqKiKqRd0dPBFaVt27Y4deqURlg5d+4cxo0bB39/f9EBUK1W\nQ6lUQqlUQq1Wo6CgAEqlstgbTI4dO4aHDx/Cz8+v1La2bduGjh07wsjIqNi5sWPHYu7cuaV+9+DB\ng/juu+8wfvz4VwZAADA3N4eTkxO2bt2Kp0+fQq1W4+jRo7h586awwtjHxwf5+fnYtGkTVCoV7t+/\nj40bN6J5EPq5AAAgAElEQVRDhw4Anv+/gAMHDggjqvfu3cOiRYvg4uICR0fHV9ZAREREVOkjgR4e\nHqhWrRoOHz4sTM+uWbMGubm5WLNmDWJiYgA8H9nq27cvAgICADzf08/W1lbY9+7MmTMYN26cMAL2\nYt/B0NBQIS0DwI4dO9C6dWtYWVmVWM/ff/+NK1eulDrd/eDBA3Tp0qXU+1mxYgUUCgXmzZsnhEWZ\nTIZx48YJW80MGjQIHTt2FO5l1qxZWLlyJQIDA6FUKlGjRg2MHj0aTZo0AfB8JfC8efMQFRWF2NhY\nmJubw8vLCwMHDgTwPAD//vvvWLRoEQoKCmBhYYHmzZtj4sSJr/j1iYiIiJ6TJScnl2/+sAKkpqZi\n6dKliI6OruyuyyUtLQ3fffedEEzfJceOHcOsWbNQWFgIf39/9O/fX+N8Xl4e/Pz8EBLygNPBRESk\nNQoLFbhzZw5WrZpU5iLOt1V2djYsLCyQkJBQ5kJbMco9EqhWq/HkyZNSR9bEcHd3f+sDIAC89957\n72QABICWLVsKb0YhIiIiepnoZwKfPXuGhQsXwsfHR3hu79ChQ1i3bp1kxRERERGRNESHwJUrV+Le\nvXtYuHChsDegi4sL9u3bJ1lxRERERCQN0dPBR44cwerVq2Fubi5stVKjRg08evRIsuKIiIiISBqi\nRwILCwuLPYCoUCjeyYcqiYiIiLSd6BDYoEEDbN26VePYH3/8AVdX1wovioiIiIikJXo6eNiwYRgz\nZgz279+PZ8+eYfz48bh69SqWLVsmZX1EREREJAHRIdDJyQmxsbFISkpCnTp1YGlpibCwMNSoUUPK\n+oiIiIhIAuXaJ9DCwgK9e/eWqhYiIiIiqiSiQ2BiYmKJx+VyOWxtbdGgQQNh1TARERERvd1Eh8CY\nmBhkZmZCpVLBzMwMOTk50NXVhampKbKysuDo6IhZs2bB0dFRynqJiIiIqAKIHrr74osv0KlTJ+zY\nsQNbt27F9u3b0blzZwQGBmLbtm1wdnbmIhEiIiKid4ToELhp0yaMHj0axsbGAAATExMMHz4cv/76\nK0xNTTF69GhcvHhRskKJiIiIqOKU693Bubm5GseePn0KhUIBADAzM4NKparY6oiIiIhIEqKfCWzV\nqhW+/fZbDBw4ELa2trh//z7Wrl2LVq1aAQBSU1Nha2srWaFEREREVHFEh8AxY8Zg6dKl+Pbbb1FY\nWAg9PT14e3tj9OjRAAB7e3vMmDFDskKJiIiIqOKIDoFGRkYICwtDaGgoMjMzUa1aNchkMuE8N40m\nIiIieneUa7NoAJDJZKhevboUtRARERFRJREdApVKJdauXYsTJ04gMzMTarVaOLdx40ZJiiMiIiIi\naYheHbxy5Urs378fn3zyCbKystC7d2/o6enBz89PyvqIiIiISAKiRwKPHDmCuXPnolatWoiLi0Ov\nXr3w4YcfYs2aNVLWRxJTqRQoLFRUdRlERESVQqXiv/NeEB0Cc3JyUKtWLQCAjo4OVCoVXFxccP78\necmKI+nduxcFudygqssgIiKqNA4OptDV1a3qMqqc6BBoZWWFhw8fwsbGBra2tjh37hwsLCz4I77j\nIiPHwdzcvKrLICIiqjS6urrQ0yv32tj/OaJ/gQ4dOiAlJQUdO3aEn58fQkJCoKuri08//VTK+khi\nBgYGMDDgSCAREZG2ER0CBw0aJPzdrVs3ODs7Izc3Fx999JEkhRERERGRdEStDi4sLMSgQYOgVCqF\nY66urmjevLnGhtFERERE9G4QFQL19PSQm5vLwEdERET0P0L0PoG+vr7cFJqIiIjof4ToZwJTUlJw\n8eJFbN++Hba2ttDR+f/5MTIyUpLiiIiIiEgaokNg06ZN0bRpUylrISIiIqJKIjoEDhgwQMo6iIiI\niKgSiX4mEAByc3Oxd+9ebNiwAQDw5MkTPHnyRJLCiIiIiEg6okcCr169itDQUJiYmODRo0fw9/fH\n1atXsXPnTkyfPl3KGklCCoUCCgXfo0hERG83vuWj4on+NZctW4b+/fujR48ewltC3NzcMH/+fMmK\nI+mNGbOI7w4mIqK3noODKWbMGMsgWIFE/5LXr1/HokWLAEDYL9DY2Bj5+fnSVEaVws5uBIyNbaq6\nDCIiolKpVAqkpy+CSqViCKxAon9JU1NTZGRkwMrKSjh2//59WFpaSlIYVQ5dXQPo6XEkkIiISNuI\nXhjSvn17REREIC0tDQDw8OFDLF26FN7e3pIVR0RERETSEB0CBwwYACsrK/Tr1w+5ubn48ssvoaur\nC39/fynrIyIiIiIJiJ4OlsvlmDhxIr7++mukp6fD0tIStra2UtZGRERERBIRPRL422+/IScnBxYW\nFmjYsCEDIBEREdE7THQI/OOPP9CrVy/MnDkTp06dkrImIiIiIpKY6OngmJgYXLhwAbt27cJ3330H\nCwsL+Pr6onPnzrC2tpayRiIiIiKqYOV6bZyrqytCQkLw22+/oW/fvjh8+DAXhhARERG9g8oVAl94\n9OgRbt26hfv378Pc3LyiayIiIiIiiYmeDlYoFNi/fz927tyJCxcuoFmzZhg7diw8PT2lrI+IiIiI\nJCA6BPbs2RPm5ubw8fHBlClTYGPDV40RERERvatEh8CpU6eiWbNmwnuDiYiIiOjdJToEfvTRR1LW\nQURERESVSHQIVCqVWLt2LU6cOIHMzEyo1Wrh3MaNGyUpjoiIiIikIXp18MqVK7F//3588sknyMrK\nQu/evaGnpwc/Pz8p6yMiIiIiCYgOgUeOHMGsWbPQq1cv6OnpoVevXpg6dSrOnz8vZX1EREREJAHR\nITAnJwe1atV6/iUdHahUKri4uDAEEhEREb2DRIdAKysrPHz4EABga2uLc+fO4caNG9DV1ZWsOCIi\nIiKShugQ2KFDB6SkpAAA/Pz8EBISgmHDhqFjx47l7jQ1NRVDhgwp9/dIvKNHj6JLly7w9vbGmjVr\nqrocIiIiesuIXh08aNAg4e9u3brB2dkZubm5r7V1zA8//ICgoKASz/32229Yvnw5AgMDS72moKAA\ny5Ytw+nTp/H48WOYmpqiZcuWCA4OhqmpabHrL1++jJEjR8LV1RWRkZHC8d9//x179+7F9evXYW5u\n/karnFUqFUaMGIErV65g3bp1cHBwKPXao0ePIjY2FmlpaTA1NUW3bt0QEBAgnI+Pj8fevXuRlpYG\nuVyOhg0bIjg4GLVr1xauuXXrFpYvX45Lly5BrVbD09MTo0aNgpGREQCgVatW2LVrF7755pvXvici\nIiL63/Va7w4GAFdXVzRv3rzcm0efPn0aGRkZaNWqVbFzt27dwpYtW1CnTp0y21CpVDAzM8P333+P\nhIQErFixAnfu3MG8efOKXatUKjFv3jw0bty42Dlra2v4+/ujb9++5bqHkvzyyy+wsLB45e9x6dIl\nTJs2DQMHDkRCQgK+//57bN68GVu2bBGuKSgowMiRI/H777/j119/Rc2aNRESEgKlUgkAePr0KSZM\nmAAXFxds3rwZcXFxSE9Px5w5c974PoiIiEg7vHYIfF0HDx6Eh4dHsbBUVFSEiIgIDB8+HGZmZmW2\nYWhoiCFDhsDJyQkymQyWlpb47LPPcPr06WLXxsTEwMPDA25ubsXOtWvXDm3btoW1tfUb3dOVK1eQ\nlJSEYcOGaeyfWJK//voLTZo0EUKws7MzunbtqhECAwIC4O7uDrlcDrlcjsDAQDx58gS3bt0CAJw7\ndw45OTkICgqCrq4uqlWrhn79+uHw4cN49OjRG90LERERaYdKD4GXL1/G+++/X+z4L7/8AkdHR3h6\ner5Wu8ePH0e9evU0jp09exbHjh1DcHDwa7UpRkFBAebOnYtvvvlGmIotS1FRUbGgqFKpkJaWhvz8\n/BK/c/z4cRgZGaFmzZoabfy7naKiIgDA33///bq3QkRERFqk0kNgTk4OTExMNI5dvXoVO3fuxOjR\no1+rzcTEROzbtw+jRo0SjuXn52PevHkICQmBXC5/o5rLsmbNGri6uqJp06YA8Mrp4DZt2uD06dM4\nePAgVCoVLl++jN27dwN4Ps37smvXrmHJkiUYOXIkDAwMAABubm4wNjbG6tWroVQq8fDhQ6xbt67U\nNoiIiIheJnphSEUxMzNDXl6e8FmlUmHOnDkYOXJkiYs6XmXHjh2IiYnBvHnzNEYYV6xYgZYtW8Ld\n3b1C6i7JuXPnsH///nKtvnVzc8PkyZPx888/Y8GCBXB0dET37t2xdu3aYtPgFy9eRHh4OIKCguDr\n6yscNzU1xdy5c7Fq1Sp8+eWXMDExQZ8+fZCamgoLC4ty3UNy8hTo6xsDAOrW9YGzs0+5vk9ERETS\nSkxMRGJiIgAI6wMqQrlCYEpKCi5dulRstKm0VbwlcXFxwY0bN4TPDx8+xI0bN7Bw4UIsWLAAAJCX\nl4dLly7h0KFDZQasDRs2ID4+HgsXLkTdunU1zh0/fhx5eXnYu3cvAEChUKCwsBCfffYZoqKiyly9\nK9bJkyeRmZkJf39/ABCmaL/++mv07t0bgYGBJX7v448/xscffyx8joqKwgcffKAxYnny5ElMnz4d\nI0eORKdOnYq14ezsjPnz5wufDx06BENDQ7i6upbrHjp0mAkTE5tyfYeIiIgqj4+PD3x8ng/SZGdn\nIyoqqkLaFR0C16xZgw0bNsDZ2RmGhobC8fKuDm7bti0iIiKgVqshk8lga2tbbGuWadOmoWHDhkK4\nKsmqVauwd+9eLFmyBE5OTsXOL1++HCqVSvi8adMmnDt3DjNnzkT16tUBPB+FVKlUKCwsBPD/0/W/\nw5iXlxfCwsKEH//f+vTpg65duwqfHzx4gJEjR2L27NmlrnBWq9W4fPky6tWrh4KCAhw4cAC7d+/G\n3LlzhWsOHjyIiIgIhIaGaoTFf7ty5QqcnJygr6+P8+fPY/ny5Rg4cCCMjY1L/c2IiIiIXhAdAnfu\n3InIyMhyjzS9zMPDA9WqVcPhw4fRpk0byGSyYqtz5XI5jIyMYGlpKRzr0qULxo8fD29vb9y/fx8b\nN26Enp4evv76awAQQmVsbCxsbGyEoPeCiYkJ9PX1YWVlJRxbt24d4uLihCDbuXNnyGQyrF+/Hra2\ntrh37x709PRKXFkMAEZGRhqLQQoLCyGTyVC9enXh+N69e7F48WLs3LkTwPMFHJGRkbh9+zbUajXq\n16+PiIgIjd91xYoVUCgUmDdvnhAOZTIZxo0bB29vbwDArl27kJycDKVSCXt7e/Tr109jypiIiIio\nLLLk5OSy9zT5P927d8fWrVvLPfJXktTUVCxduhTR0dFv3JaUdu7ciWvXrr32gpWqdOzYMcyaNQuF\nhYXw9/dH//79Nc7n5eX935tfHnA6mIiI3mqFhQrcuTMHq1ZNEhZJaqvs7GxYWFggISGh2ELb8hI9\nEujt7Y0DBw6gffv2b9QhALi7u7/1ARCAxlTvu6Zly5bYsWNHVZdBREREbynRITArKwtz5szBjh07\nNKZUASA8PLzCCyMiIiIi6YgOgXK5HF5eXlLWQkRERESVRHQIDAsLk7IOIiIiIqpE5donUK1W49Kl\nS3jw4AFsbW1Rv379ClkoQkRERESVS3QIfPz4McLDw3H16lWYmpoiNzcXzs7OmDVrVrEtXoiIiIjo\n7Sb63cEv3rKxZcsWbNu2DVu2bIGjo2OF7VpNRERERJVHdAg8c+YMQkJCYG5uDgAwNzfHN998gzNn\nzkhWHBERERFJQ3QIBAAdHZ0yPxMRERHRu0F0ivvwww+xaNEi5OXlAQByc3OxZMkSfPjhh5IVR0RE\nRETSEL0wZMSIEZg0aRK6desGc3NzZGdno06dOpg9e7aU9RERERGRBESHQGtra6xatUrYIqZGjRpo\n0KABp4SJiIiI3kHl2idQR0cHrq6ucHV1laoeIiIiIqoEHMYjIiIi0kIMgURERERaiCGQiIiISAsx\nBBIRERFpoTIXhiQmJopqxMfHp0KKISIiIqLKUWYIjImJ0fickZGBoqIimJmZIScnBzo6OrC0tGQI\nJCIiInrHlBkCN23aJPy9efNmXL16FSNHjoSJiQlyc3OxcuVK1KlTR/IiiYiIiKhiid4ncOPGjfj5\n559hYGAAADA1NcWIESMwYMAAfP7555IVSNJSqRQoLFRUdRlERESlUqn47ykpiA6BCoUCubm5QggE\ngLy8PCgU/AfzLrt3LwpyucGrLyQiIqpCDg6m0NXVreoy/qeIDoGenp4IDw/HoEGDYG9vj7t37yIu\nLg6enp5S1kcSi4wcB3Nz86oug4iIqEy6urrQ0yvXi87oFUT/mqNGjUJUVBSmTp2KgoIC6Ovro2PH\njhgxYoSU9ZHEDAwMNEZ3iYiISDuIDoFGRkYICQnB+PHjkZmZiWrVqkEmk0lZGxERERFJpFybRatU\nKpw/fx6nT5+GTCaDUqmEUqmUqjYiIiIikojokcC7d+9i0qRJuHfvHmQyGby8vHDs2DEcOnQI4eHh\nUtZIRERERBVM9Ejg0qVL4enpiZ07dwoPZjZp0gRnz56VrDgiIiIikoboEHjx4kUMGjQIurq6wrOA\nZmZmyM3Nlaw4IiIiIpKG6BBoaGiIZ8+eaRzLzMzk9iJERERE7yDRIbBFixZYunSpEARVKhVWr16N\nVq1aSVYcEREREUlDdAgMDg7Go0eP0K1bN+Tl5aFr1664du0aBg0aJGV9RERERCQB0auDTU1NsWjR\nIvz999+4c+cOLC0t4e7uDh2dcu0yQ28ZhULBV/8REZHW08Y3kpT7buvVq4d69eohLS0NDx48gJ2d\nnRR1USUZM2YR3x1MRERaz8HBFDNmjNWqICj6TufOnYsuXbrA3d0df/75J2bNmgUACA8Ph7e3t2QF\nkrTs7EbA2NimqssgIiKqMiqVAunpi6BSqRgCS/Lf//4XY8aMAQD89ttvmDJlCoyNjbFq1SqGwHeY\nrq4B9PQ4EkhERKRtRD/Qp1AoYGhoiKdPn+L27dto164dmjdvjvv370tZHxERERFJQPRIoIWFBW7e\nvInr16/D1dUVOjo6yM/PFzaOJiIiIqJ3h+gQ2KtXLwwbNgwAMGXKFABAamoqateuLUlhRERERCQd\n0SHws88+Q/PmzaGrqyusCLa3t8e4ceMkK46IiIiIpFGuJTDvvfeexueaNWtWaDFEREREVDnKFQIT\nEhJw4sQJZGRkaByPjIys0KKIiIiISFqiVwfHxsYiOjoa1tbWuHz5MurVq4cbN27AxcVFyvqIiIiI\nSAKiRwL37NmDiIgINGzYEElJSRg5ciQ8PT2RkJAgZX1EREREJAHRI4EZGRlo2LCh8FmtVqNx48Y4\nceKEJIURERERkXREh0ALCwtkZWUBAKysrHDt2jU8evQIRUVFkhVHRERERNIQPR3crFkzHD58GF26\ndIG3tzcmTJgAPT09tGrVSsr6iIiIiEgCokPg+PHjhb8DAwNhb2+PvLw8dO7cWZLCiIiIiEg65doi\n5t+8vb0rsg4iIiIiqkSiQ6BKpcKvv/6KP/74Aw8ePICNjQ18fX3h7+8PXV1dKWskIiIiogomOgRG\nR0fj4MGD+OKLL2BnZ4e7d+9i06ZNyM3NFd4pTERERETvBtEhcO/evVi8eLHGq+KaNGmCb775hiGQ\niIiI6B0jeouYoqIi2Nvbaxyzt7fnFjFERERE7yDRIdDX1xfr1q2DWq0G8Hyz6PXr16Nr167l7jQ1\nNRVDhgwp9/dIvG3btgnb+ezatauqyyEiIqK3TJnTwaNHj4ZMJgPwPPRdvHgRO3bsQI0aNfDgwQNk\nZ2fD1dW13J3+8MMPCAoKEj4nJSVhx44duHXrFmQyGerUqYOgoCC4ubmV2sazZ8+wYsUKHDlyBPn5\n+bC3t0f//v3Rtm1b4ZqCggLExsZi3759yMrKQrVq1RAUFISOHTsCAOLi4rB27VoYGhpCrVZDJpOh\nVatW+Pbbb0XfS1xcHJKSkpCVlQV9fX24uLggODgYzs7OpX5n7NixuHDhAvT19YV+hw4dim7dugEA\nUlJSMG7cOBgZGQF4/tubmZlh48aNQhuTJ0/GlStXkJ+fDyMjI3z00UcYNmwYzM3NAQDdu3dH9+7d\n4e/vL/peiIiISHuUGQKbNm1a5ufXcfr0aWRkZGhsMp2fn48BAwbggw8+gFwux5YtWxAWFoa4uDhY\nW1uX2M6aNWtw5swZLF++HDY2Nti/fz9mzJiBmJgYODk5AQCmTZsGpVKJxYsXw97eHllZWcjJydFo\nx83NDZGRka99P97e3ujZsydMTU2hUqmwefNmhIaGYvPmzUKAfplMJoO/vz8GDRpUarsymQwJCQml\ntjF48GA4OjpCLpcjNzcXixcvxsKFCzF9+vTXvhciIiLSHmWGwAEDBlR4hwcPHoSHh4dGuOnevbvG\nNb169UJcXBwuXbqENm3alNhOeno6mjdvDhsbGwBA+/btsWTJEvzzzz9wcnLCyZMncerUKfz666+w\nsLAA8PzVdy/+riiOjo7C3yqVCjo6OsjKykJ2dnaZfb2YVi9LUVFRqdvv1KlTR6MtmUyGO3fulKNy\nIiIi0mavvVn067p8+bLGlG1JLly4gGfPnpU5pdqrVy+sXLkS6enpsLOzw59//gmZTIZGjRoBAE6d\nOgU7OzusX78e+/btg56eHpo0aYJhw4ZphLO///4bn3/+OQwMDPDBBx9gyJAhsLOzK9c9HTt2DLNm\nzUJeXh5kMhl69+79yrC5fft2bNu2DdWrV4enpycCAwOF6d8X+vbtC6VSiTp16qBfv37Cvb0QHR2N\nrVu3Ij8/HwYGBpg0aVK56iYiIiLtVekhMCcnByYmJqWef/DgAWbOnImAgIAyw1idOnXg5OSEwMBA\n6OrqwsDAABMnTkT16tUBAFlZWbh58yY8PDywfv16PH36FLNmzcKcOXMQEREBAPj444/h6+uLGjVq\n4PHjx1i5ciXGjx+PmJgYGBoair6nli1bYseOHcjNzcXu3buF0cnSBAcHw8nJCaampvjnn38QERGB\ne/fuYcqUKQCAWrVqITo6GrVr14ZCocCOHTsQGhqK5cuXo27duhrtBAcH4+7du/jjjz/w3nvvia6Z\niIiItFulh0AzMzPk5eWVeC4tLQ0TJkyAl5dXmc/LAcDUqVNhYGCA3377DZaWlkhNTcV3330HfX19\ntGjRAsbGxsKCC7lcDrlcjkGDBmHUqFFQKBQwMDBA7dq1hfasrKwQGhoKPz8/nD9//rWefzQ1NUXP\nnj3x6aefombNmhpTtv/278U0derUwfDhwzFhwgQolUrI5XJUr15dCLNGRkbo06cPjh49iv3792uE\nwBfs7e3RunVrhIaGYtOmTeV6g0ty8hTo6xsDAOrW9YGzs095bpmIiIgklpiYiMTERACAUqmssHYr\nPQS6uLjgxo0bxY5fu3YNYWFh6NGjBwIDA1/ZzpUrVzBp0iRYWloCANzd3eHu7o6jR4+iRYsWqFev\nXrFFFS+enSuLTCYT9bxeaYqKiqBSqXDnzp1SQ2BJfYq5pqy6CgoKkJmZiby8PGGFsBgdOsyEiUnZ\nI5dERERUdXx8fODj83yQJjs7G1FRURXSruh9Al928uRJpKSklPt7bdu2xalTpzQCzblz5zBu3Dj4\n+/uLCoDA89D3xx9/IDMzE8Dz5wjPnDmD+vXrC/1YW1sjOjoaSqUSWVlZiIuLQ8uWLWFgYAAA2L9/\nP7KysgAAT548wfz582FpaYkPPvhA6Mff3x9xcXGl1rF582ZkZGQAADIzM7F48WLo6+uXur1NRkYG\n/vvf/+LZs2cAgOvXr2PFihXw9PSEXC4HABw/fhz37t2DWq2GQqHAb7/9hvPnz+Pjjz8GANy5cwcH\nDx7E06dPAQC3bt3CqlWr0KBBg3IFQCIiItJeokcCJ0yYgL59+6Jx48bYvHkzfvzxR+jo6GDw4MHo\n1auX6A49PDxQrVo1HD58WFj5u2bNGuTm5mLNmjWIiYkB8Hzkq2/fvggICAAATJw4Eba2tvjmm28A\nAGFhYVi1ahWGDBmCZ8+ewdLSEl988QV8fX0BAIaGhpg/fz6WLl2KHj16wMTEBC1btsTQoUOFWvbs\n2YOlS5ciPz8fZmZm+PDDD7FgwQJhgYZSqURGRgYaN25c6v2cPHkS69evR35+PkxMTFC/fn0sWLBA\nGKF88OABBg4ciLlz58Ld3R1KpRI//fQTbt++DbVaDUtLS7Rr104j/F66dAkLFy5EVlYWDA0N8f77\n72Pu3LmoV68egOcjmvHx8Zg/fz5UKhUsLCzw0UcfYeDAgaL/ORAREZF2kyUnJ4ua++zRowfi4+Oh\nr6+PwYMHY9SoUTA1NcX06dPx888/l6vT1NRULF26FNHR0a9VdGU5efIkNm/ejNmzZ1d1KeW2fft2\nREdHo7CwEGPHjhWGkV/Iy8uDn58fQkIecDqYiIi0WmGhAnfuzMGqVZOE2cK31Yst6BISEspcaCuG\n6JHAwsJC6OvrIysrC48ePRJGx548eVLuTt3d3d/6AAg83xy7IjbIrgrdunUT3kBCRERE9DLRIdDG\nxgYpKSm4efOmsF9dbm4u9PQqfW0JEREREb0h0Qmuf//+CA0NhZ6eHubOnQvg+XRpWRs6ExEREdHb\nSXQI7NChA1q3bg0Awnz5i21ZiIiIiOjdUq653Bfhr6ioCABQrVq1iq+IiIiIiCQnOgTeunULixcv\nxqVLl4rtVr1v374KL4yIiIiIpCM6BM6bNw/W1taYOnVqud6rS0RERERvH9Eh8Pr168LbMIiIiIjo\n3Sb6tXH29vbIzc2VshYiIiIiqiSiRwJ79+6N2bNno3///rCystI45+DgUOGFEREREZF0RIfAf+8N\nKJPJADx/h61MJuPCECIiIqJ3jOgQuH79einrICIiIqJKJDoE2tnZSVkHEREREVWiMkNgUlISOnXq\nBADYtWtXqdd16dKlYqsiIiIiIkmVGQI3bNgghMCff/65xGtkMhlDIBEREdE7pswQ+NNPPwl/b9iw\nQeHvZOIAACAASURBVPJiiIiIiKhyiN4nkIiIiIj+d4haGHLixAn8888/cHNzg+v/a+/e46Kq8z+O\nvwZmuChigoIiW5oo3h9l/cpum9KuRgqlbrpaWeEl08rSvGS09fh5V7xb4Q2UNctb+rMwL21aarn9\nKtQidZN1U0ISRAe5DTLM7w8fzE8SxeEanPfzLzxz5szncwa/8+Z7zpnTsSOrVq3iyy+/pG3btrz0\n0ks0aNCguusUERERkSpU7kzgli1biI6O5tNPP+XVV1/l7bff5osvvuC//uu/OHbsGMuWLauJOkVE\nRESkCpU7E7h161bmzJlD165d+e6775gwYQJr1qwhODiYiIgIxo0bVxN1ioiIiEgVKjcEnjt3jq5d\nuwJw++23YzabCQ4OBqBly5ZcvHixeiuUamW32ygqstV2GSIiIrXGbjfm52C5IdDhcDh/NplMeHp6\nlnq85BZyUjelp7+Nh4dn+SuKiIjUY0FBPri7u9d2GTWq3BBYXFxMUlKSMwza7fZS/y4uLq7eCqVa\nLVo0Dl9f39ouQ0REpFa5u7tjNt/wjdTqhXK7tdlsjB8/vtSyK/+tmcC6zdPT86rZXREREan/yg2B\nn332WU3UISIiIiI1SF8WLSIiImJACoEiIiIiBqQQKCIiImJACoEiIiIiBqQQKCIiImJALn8hTkFB\nAcnJyTgcDjp16oS3t3d11CUiIiIi1ajcEDht2jSio6MBSE9PZ/z48WRmZmIymfDz8yMmJoagoKBq\nL1REREREqk65IfCrr75y/rxy5Uo6duzIxIkTAZg7dy5xcXHOkCh1j81mw2Yz5j0TRUTEOIx4R5Dy\nuHTv4OTkZJYuXYrFYgFg1KhRjBo1qvqqk2o3dux83TtYRETqvaAgH/77v19WELxCuXviytvC2Ww2\n/P39nf/28/Pj4sWL1VOZ1IjmzcfQoEGz2i5DRESk2tjtNtLS5mO32xUCr1DunigoKGDs2LHOn8+e\nPUtAQAAAVqtVF4bUce7unpjNmgkUERExmnJD4NChQ50/d+vWjby8POe/k5KS6NChQ/VUJiIiIiLV\nptwQ+PTTT1/zsR49etCjR4+qrEdEREREaoC+LFpERETEgBQCRURERAxIIVBERETEgBQCRURERAxI\nIVBERETEgBQCRURERAxIIVBERETEgBQCRURERAxIIVBERETEgBQCRURERAxIIVBERETEgBQCRURE\nRAxIIVBERETEgBQCRURERAxIIVBERETEgGolBH7//fcMHz68Nl7aMJYvX84jjzxCWFgY3333XW2X\nIyIiIr8z5tp40SVLlhAVFeX894EDB4iLiyMjIwOAFi1aMGTIEB588MFrbmPNmjUkJCTg5eWFw+HA\nZDJxzz33EB0d7VwnLCwMDw8P3N3dnessXbqU1q1bO7exa9curFYrFouFdu3aMWLECEJCQirU1xtv\nvMGBAweIiYmhW7duZa6TmprKqlWrSE5OJi8vDz8/P/r06cOgQYPKXH/Tpk288847PPnkk6X2WUxM\nDMnJyZw+fZqwsDCmTJlS6nkjR45k5MiRhIWFVagXERERqd9qPAQmJSVx/vx57rnnHuey9u3bM2fO\nHPz9/QE4cuQIEydO5A9/+AO33nrrNbfVuXNnFi1adN3XmzlzJrfffnuZjz300EMMGDAAHx8f7HY7\nmzdvZuLEiWzevBmTyeRSXzt37qSgoKDc5128eJGuXbsyZswYmjZtyokTJ3jttdcwm80MGDCg1Lqn\nTp1iy5YtZe6DNm3a0KNHD7Zt2+ZSnSIiIiJQC4eD9+3bR7du3UqFJX9/f2cALJmxg8uzZpXlcDiu\n+VhwcDA+Pj4A2O123NzcsFqtZGdnu/QaGRkZxMfHM3HixOu+HkCHDh3o168fTZs2BSAkJIQePXpw\n6NChUusVFxcza9YsRo8eTaNGja7aTr9+/bjzzjtp2LChS7WKiIiIQC3MBB4/fpwHHnjgquW5ubn8\n9a9/xWazUVRURJcuXejevft1t/XTTz/Rv39/PD096dSpE8OHD6d58+al1pkxYwZFRUUEBgYSGRlJ\nnz59Sj1+8OBBpk+fTm5uLiaTiccff5zGjRu71NOcOXN46qmnaNasmUvPg8vhMykpiT/+8Y+llr/3\n3nsEBwdz3333sWnTJpe3KyIiInI9NR4CL168WObsVcOGDfnoo4+4dOkSBw8eJDU1FYvFcs3tPPjg\ng4SHhxMQEMC5c+eIjY1l/PjxrFq1Ci8vLwDmzZtHp06dcHd355tvvmH69OnY7XYiIyOd2+nevTsf\nffQROTk57Nixw+Ugt3XrVoCrwuWNmj9/Pna7nccff9y57MSJEyQmJrJy5coKbVNERESkPDUeAhs1\nakRubu41H7dYLDzwwANMnjwZLy8v+vXrV+Z6rVq1cv7s7+/PxIkT6du3L8nJydxxxx0Apc4FvPvu\nuxkwYAC7d+8uFQJL+Pj4MGDAACIiIso9F7FEWloaa9eu5Z133il33d8qLi5m7ty5/Otf/2LBggV4\ne3sDl2cGZ86cyQsvvOA8VF2d9ux5A4ulAQBt2vQmJKR3tb+miIiI3LidO3eyc+dOAAoLC6tsuzUe\nAtu1a8d//vOfctez2+2cPn3apW2bTKZyz8m73uPFxcXY7XZSU1NvKAQeOXKE7OxsnnvuuVLbffPN\nN+nZsyfjxo0r83mXLl1i6tSpnDt3jkWLFpUKexkZGfznP/9h3rx5xMTEAJcPlR87doz9+/cTFxdX\nbl2u6NlzKg0bun4YW0RERGpG79696d378iRNdnY2b7/9dpVst8ZD4AMPPMCsWbNKXQCya9cuOnbs\nSFBQEEVFRezYsYOkpKRSh0h/a+/evdx+++00btyYrKwsYmNj8fPzo1OnTsDl8wUdDge33norJpOJ\n7777jg8//JBnnnnGuY3NmzcTFhZGkyZNuHDhAitXrsRisdC5c2fnOoMHD+bhhx/m6aefvqqGsLAw\n7rzzzlLLBg4cyPjx469aXiI/P5/XX38dh8NBTEyMcwawRGBgIOvXry+17K233qJDhw4MHjzYuayo\nqMgZWh0OB4WFhZhMpuseQhcREREpUeMhsFu3btx0000cOHCA+++/H7h8WHX16tVcuHABDw8PgoOD\neeONN7jrrrucz3v22Wf585//zJAhQwDYvXs3ixcvJj8/n0aNGtG1a9dSoSozM5Nly5Zx9uxZzGYz\ngYGBjBgxgr59+zq3+e2337Ju3Try8/Np2LAhoaGhxMTE4OfnB1yecj1//jy33XZbmb14eHg4r/It\nYTKZ8PX1dc7uff/990yePJnVq1fTrFkzvvjiCw4fPoyHhwcDBgxwzl42b96cuLg4TCbTVdv08PDA\n29vbWRfAhAkTOHz4sDNI/+Mf/6B58+asW7fO9TdFREREDMe0Z8+e6x8/rQbff/89ixcvZsWKFTX9\n0i759ttv2bx5MzNmzKjtUly2YsUKtm3bRlFRETNnzrwqyObm5tK3b19effWsDgeLiEi9VlRkIzV1\nJsuWvYanp2dtl1Mp2dnZNG7cmI8//rjSXxNXK3cM6dKly+8+AALccccdzotM6poRI0YwYsSI2i5D\nREREfqdq5d7BIiIiIlK7FAJFREREDEghUERERMSAFAJFREREDEghUERERMSAFAJFREREDEghUERE\nRMSAFAJFREREDEghUERERMSAFAJFREREDEghUERERMSAFAJFREREDEghUERERMSAFAJFREREDEgh\nUERERMSAFAJFREREDEghUERERMSAFAJFREREDEghUERERMSAzLVdgNQuu91GUZGttssQERGpNna7\nPufKohBocOnpb+Ph4VnbZYiIiFSroCAf3N3da7uM3xWFQINbtGgcvr6+tV2GiIhItXJ3d8dsVuy5\nkvaGwXl6euLpqZlAERERo9GFISIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAo\nIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIG\npBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIi\nIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAoIiIiYkAK\ngSIiIiIGpBAoIiIiYkAKgSIiIiIGpBAohrNz587aLqFWqG9jUd/Gor6lIhQCxXCMOmiob2NR38ai\nvqUiFAJFREREDMhc2wVI7XA4HABkZ2fXciU1r7CwUH0biPo2FvVtLEbsu6Tfks/xyjDt2bOn8luR\nOicjI4OBAwfWdhkiIiJSARs2bKBZs2aV2oZCoEEVFxdz7tw5vL29MZlMtV2OiIiI3ACHw0F+fj7+\n/v64uVXurD4dDjYoNze3Sv8FISIiIjXPx8enSrajC0NEREREDEghUERERMSAFAJFREREDEjnBNZj\n8fHxbN++ndzcXNq1a8fYsWNp3bp1mevm5OSwcOFC/vnPf2IymejevTsvvfRSlZ13UJNutO8LFy4Q\nGxvLkSNHsFqtNG7cmJ49e/LMM89gsVhqofLKceX9LpGXl0dUVBQZGRns3r270icZ1wZX+96xYwcb\nN24kLS0Nb29vwsLCeOGFF2qw4qrhSt/Hjx9n2bJlnDhxAnd3d7p06cKYMWMIDAys4aor7rPPPuN/\n/ud/SElJIT8/v9zf1/oyprnSd30b01x9z0vU5XGtIj1XZkyrO3tGXPLBBx+wc+dO5s6dy9atW+nU\nqRMTJ06koKCgzPWnTZuG1Wpl3bp1rF27lqysLGbNmlXDVVeeK33n5+dz8803M2/ePBITE4mJieHg\nwYMsX768FiqvHFff7xJLly7llltuqaEqq56rfW/YsIG///3vvPLKKyQmJvL+++/z8MMP13DVledK\n3w6Hg9dee402bdqwZcsW1q1bh7u7O1OnTq2FyivO19eXRx99lDFjxtzQ+vVlTHOl7/o0poHr73mJ\nujyuudpzZcc0hcB6atu2bQwaNIhWrVrh4eFBVFQURUVF7Nu376p1f/31V77++mtGjx5No0aN8PX1\n5fnnn+fLL78kIyOjFqqvOFf6btGiBUOGDKFFixYABAUFER4ezqFDh2q67Epzpe8SX375JSdPnmTQ\noEE1WGnVcqXvvLw8Vq9ezYsvvkjnzp1xc3PD09OTkJCQWqi8clzpOzc3F6vVSnh4OO7u7nh7e9Or\nVy9SUlJqofKKu/POOwkLC3P+f72e+jSmudJ3fRrTwLXeS9T1cc2VnqtiTFMIrIdyc3NJT08nNDTU\nuczd3Z2QkBBOnDhx1fonTpzAYrGUOpTUpk0bzGZzmev/Xrnad1m++eYb2rZtW10lVouK9G21Wlm8\neDGTJ0+uU4dKruRq3z/88AM2m41Tp07x1FNP0b9/fyZNmlTnwpCrffv4+PDoo4/y8ccfY7PZyMnJ\nYefOnTzwwAM1WXaNqi9jWlWoi2NaRdWHcc0VVTGm1f+9ZEB5eXnA1d8j1KhRI3Jzc8tcv6zzZHx8\nfMpc//fK1b5/KyEhgZSUFKKioqqlvupSkb4XLlxIREREnT1kAq73bbVacTgcHDhwgEWLFvHBBx/Q\npk0bJk2a5NxWXVCR9/vBBx/ku+++o0+fPjz66KOcOXOG0aNHV3uttaW+jGmVVVfHtIqqD+OaK6pi\nTFMIrIcaNGgAXD4x+koXL16kYcOGZa5f1sCYk5NT5vq/V672faW4uDi2b9/OwoULadq0abXVWB1c\n7fuzzz7jzJkzDB48uNTyqrgPZU1yte+SZU8++SR+fn54eHgwfPhwcnNz+eGHH6q/4Criat+//PIL\nEyZMoH///uzYsYPt27fTvXt3xowZQ2FhYY3UXNPqy5hWGXV5TKuI+jKuuaIqxjSFwHqoYcOGNG/e\nnOPHjzuX2e12UlJSyjxXICQkhEuXLnHy5EnnspSUFOx2e506X8rVvkssXLiQPXv2sHjxYlq2bFkT\npVYpV/v+3//9X06dOkX//v157LHHiI6OxuFw8Je//IVdu3bVZOmV4mrfZR0Sq4sfEK72nZKSgqen\nJ5GRkZjNZjw9PRk0aBBnzpzh3//+d02WXmPqy5hWUXV9TKuI+jKuuaIqxjSFwHrq0UcfZf369Zw8\neRKbzUZ8fDxms7nM84ACAwO5++67effdd7FarVitVmJjY7n33nvr3K3lXOnbbrczbdo0jhw5wqJF\niwgICKiFiquGK32PGTOGhIQEVq5cycqVK5kwYQImk4nly5fz4IMP1kL1FedK382aNeP+++/nvffe\n4/z58xQWFhIXF0ejRo3o0qVLLVRfca70HRoaSlFREYmJidjtdgoLC9m4cSMNGjQgODi4FqqvmOLi\nYgoLC7l06RIAhYWFFBYWlvmhV5/GNFf6rk9jGrjWe30Z11zpuSrGNNOePXvq3p/CckNWr17NRx99\nRF5eHqGhoc7vETt79izPPPMMs2fPdv6i5OTksGjRIr766itMJhP33HMPY8eOrZOHTm6078OHDzNu\n3DgsFgvu7u7A5b+iTCYTiYmJtdyF61x5v6906NAhxo8fX+e+T6uEK33n5+ezdOlS9u3bh5ubG+3b\nt2fUqFG0atWqdpuoAFf6/vbbb4mPj+fUqVOYTCZat27NsGHD6lT43bFjB3PmzMFkMgH//391/vz5\ntGjRot6Oaa70Xd/GNFff8yvV1XHN1Z4rO6YpBIqIiIgYUN2JxyIiIiJSZRQCRURERAxIIVBERETE\ngBQCRURERAxIIVBERETEgBQCRURERAxIIVBERETEgBQCRURERAxIIVBEpAasX7+ev/zlL/Tp04eD\nBw/Wdjk15uzZs/Tp04f09PQq3e6hQ4cICwujuLi4SrdbUenp6YSFhZGWlnbNdRYsWEBMTEwNViVy\nfebaLkBEatfLL7/Mjz/+iMViwWQyERAQQL9+/YiIiHCuM2vWLHbt2sWQIUMYPny4c7nD4eCJJ54g\nPT2dmJgYunXrBsAXX3zBBx98wOnTpwHw9/fnj3/8I1FRUQDMnj2bTz/9FA8PD+d2TCYTQ4cOZdCg\nQTXVeo3JzMxk+fLlvPvuu7Rr1662y6lRAQEBlb5l2ezZs7Hb7UyZMqXU8pJba/1elFfPK6+8UkOV\niNwYhUARgzOZTPz1r391BrS9e/cydepUbrnlFrp27epcp1WrVnzyySc8++yzzvuSfv3113h6epb6\n8EtOTmbmzJm88cYbdO/eHYfDwenTp/npp59KvW7Pnj2v+lD/PSgqKsJsrtqh8cyZMwC0adOmwtuo\njroqwm63O99/Eanban9EEZHflR49erBw4UKOHTvmDIEAISEhpKamsm/fPnr06AHAtm3biIyMZOnS\npc71kpOTadmyJffee69zWatWrW74huZlKSoqYsmSJezfvx+bzYavry+PP/44/fr1A+Dnn39m+fLl\nHDt2jEuXLnHzzTfz5ptv0qxZM3JycoiNjeXrr7/m0qVLhIaGMmbMGP7whz8AsGbNGr799ltuu+02\nPvnkE3x8fIiPjycnJ4cVK1bwz3/+k4KCAjp06MBLL71EixYtANizZw8JCQlkZGRgNptp27Ytc+fO\nvar27du3s3jxYgAiIiIwmUwkJiZSWFhIfHw8n3/+Obm5ubRu3ZrnnnuODh06AJdvJB8XF8eQIUNY\nv3492dnZZc6olTVL9sorr9ClSxeioqLK3XenTp0iNjaWY8eOYTabuffeexk1ahReXl4ADB48mN69\ne3P06FGSk5N54okneOihh5g/fz5Hjx7FbrcTGBjIyy+/7Lyp/ZXS09MZMmQIa9euJSgoyNnXU089\nxbp168jJyeGOO+5g0qRJeHt7X/X89957j08//RSTycT+/fsxmUysXr3a+fi+fftYtWoVWVlZdOjQ\ngcmTJ+Pv7w9AYWEha9asYe/eveTk5NC6dWteeOEFQkJCAEhKSmLZsmX88ssvuLm5ccsttzBjxgx8\nfHwoLi5m06ZNbN++nczMTIKDgxk5cqRztrssDoeDpKQkpkyZQmZmJu3bt2fcuHEEBQWV+V4NHjyY\n8PBwfvzxR77//nuaNGnCqFGjuP/++wFISUlhyZIlpKSkYDKZCAoKIjo6muDg4GvWIOIKhUARcbLb\n7ezZs4eLFy9yyy23XPV4ZGQk27Zto0ePHqSnp3P48GFef/11lixZ4lyna9eurFixggULFtC9e3fa\ntWvn/FCuqJ07d3L06FFWr15No0aNOH/+POfOnQPg/PnzjB07lsjISKKjo/Hy8uJf//oXnp6eAMyY\nMYOCggKWL19OgwYNWLFiBa+++ipr1qxxBp2jR49y1113sW7dOhwOBwB/+9vfaNq0KStXrsTLy4v4\n+Hhee+01Vq1aRVFRETNnzmTOnDncdtttXLp0ieTk5DJrf+SRRwgKCmL8+PEkJiY6Z01jY2M5fPgw\n8+bNIyAggM2bNzvratq0KQBZWVn8+9//Jj4+Hje3ip3Cfb19Z7VaGTt2LE8++SRTp04lNzeXqVOn\nsnTpUl599VXnNj7++GOmTp1Khw4dsNlsxMTE0KxZM6ZNm4bZbCY1NfW6s5S/PUyalZXF6dOnSUhI\n4OLFi4wdO5YNGzbw9NNPX/XcJ554gtTU1KuC7i+//ILD4eDAgQMsW7YMh8PBpEmTWLlyJZMmTQJg\n/vz5nDt3jsWLF9OkSRO2bdvGxIkTSUhIwMfHhxkzZjBs2DAefvhh7HY7x48fx2KxAJCQkMCXX37J\n9OnTadmyJfv37+f1118nLi7O+YdAWRITE4mJicHX15fFixczZcoU4uLirvn+bd++nWnTphESEsLG\njRuZNWsWGzduxNvbm4ULF3LXXXexYMECHA4HJ0+exMfH55qvLeIqXRgiImzYsIHIyEh69+7N7Nmz\nGTlyJHffffdV64WFhZGSkkJqaiqJiYn07NmTBg0alFqnffv2LF68mMLCQpYuXcrAgQN59tln+eqr\nr0qtt3fvXiIjI4mMjCQiIoLIyEiSkpLKrM9sNlNQUMDJkyex2+00adLEOZuze/du/P39iYqKwtvb\nG5PJRGhoKL6+vmRlZXHw4EFefPFFbrrpJjw8PBg1ahQ2m61UPU2aNOHJJ5/EYrHg4eHBTz/9xA8/\n/MC4cePw8fHBbDYTFRVFeno6R48eddb0888/Y7VasVgs3HbbbeXu55KA6XA4+OSTTxg+fDgtWrTA\n3d2dgQMH0qJFC3bv3u1c32Qy8cILL+Dl5eU8f9JV19t3u3btIjg4mAEDBuDu7o6vry9Dhw5l165d\nzloBwsPDnTOUnp6emM1msrKySE1NBSA4OJjmzZuX2/eVNY0aNQqLxYKfnx/33Xefc7+6wmQyMWLE\nCLy9vWnQoAEPPfSQcztWq5Vdu3bx8ssv4+/vj5ubG4899hgNGzZ0Xpjj4eFBWloamZmZuLu707Fj\nR+cfD5s2beK5556jZcuWANx///107tyZf/zjH9etaejQoTRt2hQPDw/GjBlDamrqNf9AAOjbt6/z\n/YiIiCAvL4+ff/4ZAIvFwq+//sqZM2dwc3OjTZs23HTTTS7vJ5Fr0UygiDBw4ECioqLIz8/n7bff\n5ptvvuHxxx+/avbCw8ODXr168eGHH/L5558za9asMrfXoUMHZ2i4cOECa9eu5c033yQ+Pt75odqj\nR48bPiewV69eWK1WYmNjOXXqFJ07dyYqKop27dpx5swZ56Hd3zp79iwmk6nUzI27uzuBgYGcPXvW\nuSwwMLDU80pmngYOHOhcVnLxytmzZ+ncuTOzZ89m48aNxMXF0bRpUx555BEGDBhwQ/1YrVZsNttV\nM0otW7YsVVdJcK2MP//5z9fcd6mpqRw/fpzIyEjn+sXFxbi7u5OVleWcwf1twBs9ejR///vf+dvf\n/kZOTg7du3dnxIgRNGnS5IZqaty4canfLW9vb/Lz8yvU35WzzF5eXs7tlFyl+/zzzzsfdzgcFBUV\nkZGRAcC0adN47733eO6555whcujQoVitVvLy8njzzTeddTocDux2u/P391qufE+9vb1p3Lix8/XK\n4ufnV6p+gLy8PAAmT55MQkIC48aNw+FwOC+uKuuwuUhFKASKiJO3tzdjx47lmWeeYevWrfTv3/+q\ndSIiInj22WcJDQ2lbdu25W7zpptuYtiwYXz44YecPHmy3A/RsphMJgYOHMjAgQMpKCggLi6O6Oho\nNmzYQPPmzTly5EiZzwsICAAuB4Jbb70VuHzI++zZs6WC32/Drp+fHxaLhS1btlzzIoguXbo4z4E7\ndOgQkyZNolWrVtxxxx3l9tO4cWPnLNSV50qmpaXRvn37a9ZVFm9vbzIzM0stKzncW7KN3+67N954\ng/Xr1+Pn50eXLl2YN2/edV/jt4dzGzVqxOjRoxk9ejTnzp1j+vTpvPvuu9cM9ZW9irciz/fz88Nk\nMrFq1SqaNWtW5jqtW7cmOjoauHz+3YQJE2jWrBm9evXCw8ODmTNnlnme4/WcOXPGeSpFfn4+Vqv1\nmq9fnoCAAOdh+bS0NF5//XW8vb2dF3GJVJYOB4tIKRaLhaeeeoqEhATnjMSVbr75ZhYuXOj88Pyt\n/fv3s337dmcQycvLY+3atXh6ehIaGlqhmpKSkjh+/DhFRUVYLBa8vb2d4axXr15kZmYSHx9Pfn4+\nxcXFHD9+nOzsbPz8/Lj77rt59913OX/+PDabjWXLlmGxWMo83F2iS5cutG7dmgULFnDhwgUALl68\nyBdffEFhYSFZWVl8/vnn5OTkAODj44Obm9sNXzVrMpkIDw8nPj6eM2fOUFRUxMaNG0lLS+NPf/qT\nS/smNDSUQ4cOcerUKex2O5s2bXJejXytfVcSLsPDwzlx4gRbt27FZrMBl2dP9+/ff93X/Oyzz0hL\nS8PhcODl5YXFYrlu7789HOwqPz8/0tLSXPpOwMDAQO677z4WLlzIr7/+Clz+Xfz666/Jysqiuuag\n2QAAAmlJREFUqKiIHTt2YLVaAWjQoAHu7u6YzWYsFgsREREsW7aMU6dOAWCz2Thy5IjzEPi1rF27\nloyMDAoKCnjnnXcIDg6mU6dOFep7x44dzlnEkt95XZktVUkzgSIGV9YsS69evXj//fd5//33GTZs\n2FWP/3Z25MptNG7cmMTEROLj48nNzcXLy4uQkBDmzJlTakZk7969HDhwAPj/Q629e/fmpZdeuur1\nzp8/z5IlS/j1118xm83ceuutvPXWW8Dl8/kWLVpEbGwsgwcPpri4mJtvvtn5+JQpU4iNjWXkyJFc\nunSJ9u3bExMTc91Dam5ubsydO5f4+HhGjx5NdnY2Pj4+dO3ale7duwOXr4yeP38+RUVF+Pn5MWzY\nsBs6L7DE888/T3x8PK+88gp5eXm0bt3aecGFK/70pz/x448/8uKLLzrDy5Xvz/X2XUBAAEuXLmXF\nihWsXbsWm81G06ZNeeihh5xXqJb1+5GSksLy5cvJzs7Gy8uL22+/nVGjRl2zxsrOBPbt25dDhw7x\n2GOPAbBq1aobel50dDTvv/8+EyZMICsrC29vbzp27MjYsWMB+Pzzz1m+fDkFBQX4+voSHh5Or169\ngMuHvLds2cJbb71FRkYGHh4etG3bttTh5bL6DA8PZ8KECWRmZtKuXTumT59+zRndsvaLyWRyLj90\n6BCrVq0iNzeXhg0bct999zF48OAb6l3kRpj27NlTuT/RRERERKTO0eFgEREREQNSCBQRERExIIVA\nEREREQNSCBQRERExIIVAEREREQNSCBQRERExIIVAEREREQNSCBQRERExIIVAEREREQP6PyCeSNFx\nprB4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fd44c5be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot for k=2\n"
     ]
    },
    {
     "data": {
      "image/png": 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BGAKJiIiINBBDIBEREZEGYggkIiIi0kAMgUREREQaiCGQiIiISAMxBBIRERFpIIZAIiIi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\nXhPZScYSupMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fc71abb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot for k=3\n"
     ]
    },
    {
     "data": {
      "image/png": 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hkIiIiEgNMQQSERERqSGGQCIiIiI1xBBIREREpIYYAomIiIjUEEMgERERkRpiCCQiIiJS\nQwyBRERERGqIIZCIiIhIDTEEEhEREakhhkAiIiIiNcQQSERERKSGGAKJiIiI1BBDIBEREZEaYggk\nIiIiUkMMgURERERqSKumC6CaJZFIIJFIaroMIiKiWktTUxNaWrUvUtW+iqlKTZy4DGKxTk2XQURE\nVGvZ2Bhi7txJtS4I1q5qqcpZWY2Fvr5FTZdBRERUK8lkEmRkLINMJmMIpNpFU1MHWlrsCSQiIlI3\nnBhCREREpIYYAomIiIjUEEMgERERkRpiCCQiIiJSQwyBRERERGqIIZCIiIhIDTEEEhEREakhhkAi\nIiIiNcQQSERERKSGGAKJiIiI1BBDIBEREZEaYggkIiIiUkMMgURERERqiCGQiIiISA0xBBIRERGp\nIYZAIiIiIjXEEEhERESkhmokBKalpWHEiBE1cWm18dNPP6FXr17w8PDAmTNnarocIiIies9o1cRF\nf/zxRwQFBSk+37x5E1FRUbhx4waePXuGJUuWwM3NTXB7M2fOxNGjR0ucFxcXh507dyIrKwvGxsbw\n9vbG4MGDlc7du3cv4uLikJGRAT09PXh4eGDcuHGCrpudnY21a9fi/PnzyMnJgYmJCbp164Zhw4ZB\nW1u7zPOWLFmCixcv4t69e/Dw8EBYWJjS/mnTpuH8+fMQiUQAgOLiYkgkEowZMwb9+/dHWloaQkND\nFfsBQCqVQldXF7t27QIAfPXVV/jqq6/g4eEh6F6IiIhIvVR7CDx79iyysrLQoUMHxTZtbW107twZ\ngYGBGDNmTIXaS0pKwosXL5QCEQAcO3YM69evx5IlS+Dq6opbt25hypQpMDU1Re/evQEAW7duRUJC\nAqZPnw5nZ2e8fPkS9+7dE3ztwsJC2NnZYejQobC2tkZGRgZmzpwJqVSKsWPHlnlekyZN0LVrV+zc\nubPU/eHh4SXuZfbs2fD09AQAuLq6Ys+ePUrHjBo1Ci4uLoJrJyIiIvVW7cPBhw8fhpubm1Jos7Oz\nQ+/evdGsWTPI5XLBbT1+/Bg///wzQkJCSpyXkZGBhg0bwtXVFQDQuHFjfPjhh7h+/ToA4Pnz54iJ\nicH48ePh4uICDQ0N6OjowMHBQfD1ra2t4e/vD2trawCAjY0NvL29kZqaWu55n332Gdq0aQMDAwNB\n14mPj0fnzp1Rt27dUvdfunQJN27cQN++fQXXTkREROqt2kPg1atX0bhx4yppa9GiRRg8eDAsLCxK\n7PPw8IBMJsOZM2cgl8tx48YNXLhwAZ06dQIAXLhwARKJBHfv3sXgwYPx+eefIzQ0FDdv3nynmk6d\nOoWmTZu+Uxv/lp6ejtOnT8PX17fMY+Lj49GiRQvY2dlV2XWJiIjof1u1Dwfn5eUJ7gErT3x8PAAo\nhnbfVKdOHXTr1g1hYWGQyWQoLi6Gv78/2rRpAwDIycmBXC7H0aNHERERAUNDQ8TExCA0NBQbN26E\nvr5+hWvauHEjbt68ieDg4Mrf2Bt27typ1KP5ptzcXPz9998lniskIiIiKk+1h0AjIyMUFBS8UxsZ\nGRnYtGkTVq9eXeYxv/zyC5KSkrBmzRo0btwYDx48wNy5c1FcXIyRI0cqgmhAQABMTU0BACNGjMCO\nHTtw4cIFtG3btkI1bdiwAcnJyVixYgXMzc0rf3P/IpVKsXfvXgwfPrzMY3bv3g0jIyNFD2dFpaTM\nhLb2q8DbpIkXHBy8KtUOERERqUZSUhKSkpIAvMoGVaXaQ6CjoyNu3779Tm2cP38eubm5GDVqlNKz\ngLNmzUK3bt0wefJkXLt2De7u7oqhZ2tra3Tv3h07d+7EyJEjSx2yrcjziP+2YsUKnD59GitXrkS9\nevUqd1Ol+OuvvyCTydC9e/cyj0lMTISPjw80NCo3st+t2zwYGJQcTiciIqL3g5eXF7y8XnXS5Obm\nIjIyskrarfYQ2LlzZ4SHh0Mul5dY4uS1oqIiSKVSaGpqQlNTs0QbHh4eimHd1wYOHIgpU6Yotru4\nuCAxMRG9e/dGo0aN8PDhQ+zfvx/NmjUDAFhYWKBTp0749ddf4eDgAAMDA8TGxsLIyEgx9JqZmQl/\nf38sX74cLVq0KFGHTCbDggUL8M8//yAiIkLRo/g2RUVFKC4uhkwmg1wuh1QqhUgkKrGsTEJCArp3\n7w49Pb1S2zlx4gQeP34MHx8fQdclIiIieq3aQ6Cbmxvq1KmDo0ePKoYwX4ctkUgEkUiE6dOnAwCG\nDBmCoUOHAgACAwPRvXt3+Pv7QywWlxhyFYlEMDY2hqGhIQDgiy++wIsXLzBjxgxkZ2dDX18f7dq1\nw+jRoxXnTJ8+HatWrcLQoUOhoaGB5s2bY9GiRYrQlZmZCSMjIzRp0qTUe7lw4QJSUlKgra2tWH/w\ndbjdvXs3gFcLY0+bNg0xMTGKCSxTp07FuXPnFCH4wIEDsLKywubNmxVtX79+HdeuXUNoaGiZ38td\nu3ahY8eOMDMzE/KtJyIiIlIQpaSkVG4M9B2kpaVh5cqViIqKqu5LV0h0dDSMjIwwcODAmi6lwqKi\norBz504UFRVhwYIFaNmypdL+goIC+Pj4IDj4EYeDiYiIKqmoSIL79xdg3brp0NHRUfn1cnNzYWJi\ngsTExHeeaFsjbwxxdXV97wMggHInZLzvRo4ciZEjR9Z0GURERPSeqpF3BxMRERFRzWIIJCIiIlJD\nDIFEREREaoghkIiIiEgNMQQSERERqSGGQCIiIiI1xBBIREREpIYYAomIiIjUEEMgERERkRpiCCQi\nIiJSQwyBRERERGqIIZCIiIhIDTEEEhEREakhhkAiIiIiNcQQSERERKSGGAKJiIiI1BBDIBEREZEa\nYggkIiIiUkMMgURERERqSKumC6CaJZNJUFQkqekyiIiIaiWZrPb+HSo4BPr5+UEkEpXYLhaLYWlp\niU8++QTdu3ev0uJI9TIzIyEW69R0GURERLWWjY0hNDU1a7qMChMcAr28vLBz50706NEDlpaWePjw\nIZKTk+Hh4QGJRIKIiAhkZ2djwIABqqyXqlhExGQYGxvXdBlERES1lqamJrS0at/gquCK09LS8P33\n38PZ2Vmx7eOPP8b69euxdOlStG/fHhEREQyBtYyOjg50dNgTSEREpG4ETwy5cuUKmjdvrrTN0dER\nV65cAQC0atUKT548qdrqiIiIiEglBIdAS0tL7Nu3T2nbX3/9BQsLCwBAXl4ee5SIiIiIagnBw8Ff\nffUVvvvuOyQkJCieCbxx4wbmzp0LALh06RJ8fHxUVigRERERVR1RSkqKXOjB6enpSElJwePHj2Fh\nYQEPDw/Y2Niosj5SkYKCAvj4+CAnJ4cTQ4iIiGqJ3NxcmJiYIDExEQYGBu/UVoWmstSvXx8BAQHv\ndEEiIiIiqnkVCoGpqam4cuUKnj9/rrQ9KCioSosiIiIiItUSHAI3bNiA3377DQ4ODtDV1VVsL20B\naSIiIiJ6vwkOgbt370ZERITSOoFEREREVDsJDoFFRUVwcnJSZS1UAyQSCSSS2vveQyIiVaqtb4Ig\nEkLwb7anpycOHTqErl27qrAcqm4TJy7ju4OJiMpgY2OIuXMnMQjS/yTBv9U5OTlYsGABdu3aBTMz\nM6V9YWFhVV4YVQ8rq7HQ17eo6TKIiN47MpkEGRnLIJPJGALpf5Lg32qxWAwPDw9V1kI1QFNTB1pa\n7AkkIiJSN4JDYGhoqCrrICIiIqJqJPjdwURERET0v6PcnsChQ4ciNjYWADBw4MAy1wTcsmVL1VdG\nRERERCpTbggcPHiw4mu+FYSIiIjof0e5IfCTTz5RfN2zZ0+VF0NERERE1UPwM4G9e/cudXufPn2q\nrBgiIiIiqh6CQ6BcLldlHURERERUjd66RMyGDRsAvHpt3OuvX7t//z4sLS1VUxkRERERqcxbQ2Ba\nWhoAQCaTKb4GAJFIBFNTU0ydOlV11RERERGRSrw1BC5fvlzx/998843KCyIiIiIi1RP8TCADIBER\nEdH/jgq9ETsxMRGnTp1CVlaW0vaIiIgqLYqIiIiIVEtwT2BMTAyioqJgbm6Oq1evomnTprh9+zYc\nHR1VWR8RERERqYDgnsB9+/YhPDwcTk5OSE5Oxrhx4+Du7o7ExERV1kdEREREKiC4JzArKwtOTk6K\nz3K5HC1btsSpU6dUUhgRERERqY7gEGhiYoKcnBwAgJmZGW7evIknT56guLhYZcURERERkWoIHg5u\n06YNjh49il69esHT0xNTp06FlpYWOnTooMr6iIiIiEgFBIfAKVOmKL4OCAiAtbU1CgoK0LNnzwpf\nNC0tDREREVi/fn2FzyVhjh8/jnnz5kEikWDQoEEICgqq6ZKIiIjoPSIoBBYVFeHbb7/F3LlzIRaL\nAQCenp6VvuiPP/6oFEqSk5Oxa9cu3L17FyKRCPb29ggKCoKLi0uZbZw5cwa//vorbty4gby8PGza\ntAk2NjaK/WlpaQgNDYVIJFJsk0ql0NXVxa5duwAA06ZNw/nz5xXHFBcXQyKRYMyYMejfv7+ge4mL\ni8P+/fuRnp4OsVgMJycnjBw5Eo0aNSrznKysLKxatQpnz55FUVER7OzsMHLkSLRo0UJxTH5+PqKi\nonD06FE8f/4c5ubmmDhxIlq3bg0AWLhwIfbv3w+xWAy5XA6RSARfX1+MHDkSANChQwfs2bOH6zsS\nERFRqQSFQC0tLVy9ehWamprvfMGzZ88iKytLaRi5sLAQQ4cOxQcffACxWIwdO3YgNDQUsbGxMDc3\nL7UdXV1deHl5YeDAgQgLCyux39XVFXv27FHaNmrUKKVgGR4errT/2LFjmD17doUC7suXLzFu3Dg0\na9YMwKt3LQcHB2Pz5s2KwPym5cuXIycnBzExMTAyMkJcXBzCwsKwZcsWGBoaoqioCMHBwbCzs8NP\nP/0EU1NTPH78GHK5XKmdbt26lXrvRERERG8jeGJIly5dsG/fvne+4OHDh+Hm5qbUQ9e3b1+0adMG\nenp60NTURP/+/aGhoYErV66U2Y6zszN69OiBhg0bCrrupUuXcOPGDfTt27fMY+Lj49G5c2fUrVtX\n8P34+/vD1dUVYrEYYrEYAQEBePbsGe7evVvmORkZGfj4449hbGwMkUiETz/9FIWFhbh//z4AICkp\nCU+fPkVISAhMTU0BABYWFqhXr57guoiIiIjKI/iZwNzcXCxbtgyJiYmwtrZWCnEV6Y26evUqOnfu\nXO4xly5dwosXL+Dg4CC43beJj49HixYtYGdnV+r+9PR0nD59GitWrHin65w8eRJ6enpo0KBBmcf4\n+flh9+7d6Nq1K4yNjREfH4/69evD3t4ewKuhbjs7OyxduhQnTpyAvr4+3N3dERQUBF1dXUU7J06c\ngK+vLwwNDdG6dWsEBQXBxMTkneonIiIi9SC4J1BXVxeenp5o0KABtLS0oKmpqfhfReTl5cHAwKDM\n/Y8ePcK8efPg7+8PKyurCrVdltzcXPz999/w9fUt85idO3eiYcOGcHV1rfR1bt68iRUrVmDcuHHQ\n0dEp8zgXFxeIxWL0798f3t7eiIuLw7Rp0xTDxzk5OUhNTUXDhg0RFxeHpUuX4uzZs1i7dq2ijc8/\n/xyxsbGIj4/HokWLkJGRgRkzZlS6diIiIlIvgnsCQ0NDq+SCRkZGKCgoKHVfeno6pk6dCg8PDwQG\nBlbJ9QBg9+7dMDIyQqdOnUrdL5VKsXfvXgwfPrzS17h8+TLCwsIQFBQEb2/vMo+Ty+WYPHkyWrRo\ngZ07d0JfXx/Hjx9HaGgoIiIi0KRJE+jr66Nu3br48ssvAQBWVlbw8/NDZGQkJk2aBABo2rSpok0b\nGxtMmTIF/v7+SE9PR/369QXXnZIyE9ra+gCAJk284ODgVZnbJyIiIhVJSkpCUlISgFeZpaoIDoFV\nxdHREbdv3y6x/ebNmwgNDYWvry8CAgKq9JqJiYnw8fGBhkbpHZ9//fUXZDIZunfvXqn2T58+jTlz\n5mDcuHHo0aNHucfm5eXhwYMHmDNnDgwNDQEA7u7usLGxwcmTJ9GkSRM4Ojri8uXLSue9OSnkTSKR\nCCKR6K3Hvalbt3kwMLCo0DlERERUfby8vODl9aqTJjc3F5GRkVXSruDh4KrSuXNnnDlzRimsXLhw\nAZMnT4b2hQQLAAAgAElEQVSfn5/gACiXyyGVSiGVSiGXy/Hy5UtIpdISbzA5ceIEHj9+DB8fnzLb\nSkhIQPfu3aGnp1di36RJk7Bw4cIyzz18+DC+++47TJky5a0BEACMjY1hZ2eH+Ph4PH/+HHK5HMeP\nH8edO3cUM4y9vLxQWFiIrVu3QiaT4eHDh9iyZQu6desG4NW/Ag4dOqToUc3MzMSyZcvg6OgIW1vb\nt9ZAREREVO09gW5ubqhTpw6OHj2qGJ7dsGED8vPzsWHDBkRHRwN41bM1aNAg+Pv7A3i1pp+lpaVi\n3btz585h8uTJih6w1+sOhoSEKNIyAOzatQsdO3aEmZlZqfVcv34d165dK3O4+9GjR+jVq1eZ97Nm\nzRpIJBIsWrRIERZFIhEmT56sWGomMDAQ3bt3V9zL/PnzsXbtWgQEBEAqlaJevXqYMGECWrVqBeDV\nTOBFixYhMjISMTExMDY2hoeHB4YNGwbgVQD+448/sGzZMrx8+RImJiZo27Ytpk2b9pbvPhEREdEr\nopSUlIqNH1aBtLQ0rFy5ElFRUdV96QpJT0/Hd999pwimtcmJEycwf/58FBUVwc/PD0OGDFHaX1BQ\nAB8fHwQHP+JwMBFRKYqKJLh/fwHWrZte7mQ/ouqUm5sLExMTJCYmljvRVogK9wTK5XI8e/aszJ41\nIVxdXd/7AAgA9evXr5UBEADat2+veDMKERER0ZsEPxP44sULLF26FF5eXorn9o4cOYJNmzaprDgi\nIiIiUg3BIXDt2rXIzMzE0qVLFWsDOjo64sCBAyorjoiIiIhUQ/Bw8LFjx7B+/XoYGxsrllqpV68e\nnjx5orLiiIiIiEg1BPcEFhUVlXgAUSKR8GFZIiIiolpIcAhs3rw54uPjlbb9+eefcHZ2rvKiiIiI\niEi1BA8Hjx49GhMnTsTBgwfx4sULTJkyBTdu3MCqVatUWR8RERERqYDgEGhnZ4eYmBgkJyfD3t4e\npqamCA0NRb169VRZHxERERGpQIXWCTQxMcGAAQNUVQsRERERVRPBITApKanU7WKxGJaWlmjevLli\n1jARERERvd8Eh8Do6GhkZ2dDJpPByMgIeXl50NTUhKGhIXJycmBra4v58+fD1tZWlfUSERERURUQ\n3HX3xRdfoEePHti1axfi4+Oxc+dO9OzZEwEBAUhISICDgwMniRARERHVEoJD4NatWzFhwgTo6+sD\nAAwMDDBmzBj8/vvvMDQ0xIQJE3D58mWVFUpEREREVadC7w7Oz89X2vb8+XNIJBIAgJGREWQyWdVW\nR0REREQqIfiZwA4dOuDbb7/FsGHDYGlpiYcPH2Ljxo3o0KEDACAtLQ2WlpYqK5SIiIiIqo7gEDhx\n4kSsXLkS3377LYqKiqClpQVPT09MmDABAGBtbY25c+eqrFAiIiIiqjqCQ6Cenh5CQ0MREhKC7Oxs\n1KlTByKRSLGfi0YTERER1R4VWiwaAEQiEerWrauKWoiIiIiomggOgVKpFBs3bsSpU6eQnZ0NuVyu\n2LdlyxaVFEdEREREqiF4dvDatWtx8OBBfPLJJ8jJycGAAQOgpaUFHx8fVdZHRERERCoguCfw2LFj\nWLhwIRo2bIjY2Fj0798fH374ITZs2KDK+kjFZDIJiookNV0GEdF7Rybjfxvpf5vgEJiXl4eGDRsC\nADQ0NCCTyeDo6IiLFy+qrDhSvczMSIjFOjVdBhHRe8nGxhCampo1XQaRSggOgWZmZnj8+DEsLCxg\naWmJCxcuwMTEhH84armIiMkwNjau6TKIiN5Lmpqa0NKq8BxKolpB8G92t27dkJqaiu7du8PHxwfB\nwcHQ1NTEp59+qsr6SMV0dHSgo8OeQCIiInUjOAQGBgYqvu7Tpw8cHByQn5+Pjz76SCWFEREREZHq\nCJodXFRUhMDAQEilUsU2Z2dntG3bVmnBaCIiIiKqHQSFQC0tLeTn5zPwEREREf2PELxOoLe3NxeF\nJiIiIvofIfiZwNTUVFy+fBk7d+6EpaUlNDT+f36MiIhQSXFEREREpBqCQ2Dr1q3RunVrVdZCRERE\nRNVEcAgcOnSoKusgIiIiomok+JlAAMjPz8f+/fvx22+/AQCePXuGZ8+eqaQwIiIiIlIdwT2BN27c\nQEhICAwMDPDkyRP4+fnhxo0b2L17N+bMmaPKGkmFJBIJJBK+H5OIiN4PfEtL9RH8XV61ahWGDBkC\nX19fxVtCXFxcsHjxYpUVR6o3ceIyvjuYiIjeGzY2hpg7dxKDYDUQ/B2+desWli1bBgCK9QL19fVR\nWFiomsqoWlhZjYW+vkVNl0FERASZTIKMjGWQyWQMgdVA8HfY0NAQWVlZMDMzU2x7+PAhTE1NVVIY\nVQ9NTR1oabEnkIiISN0InhjStWtXhIeHIz09HQDw+PFjrFy5Ep6eniorjoiIiIhUQ3AIHDp0KMzM\nzDB48GDk5+fjyy+/hKamJvz8/FRZHxERERGpgODhYLFYjGnTpuHrr79GRkYGTE1NYWlpqcraiIiI\niEhFBPcEbtu2DXl5eTAxMYGTkxMDIBEREVEtJjgE/vnnn+jfvz/mzZuHM2fOqLImIiIiIlIxwcPB\n0dHRuHTpEvbs2YPvvvsOJiYm8Pb2Rs+ePWFubq7KGomIiIioilXotXHOzs4IDg7Gtm3bMGjQIBw9\nepQTQ4iIiIhqoQqFwNeePHmCu3fv4uHDhzA2Nq7qmoiIiIhIxQQPB0skEhw8eBC7d+/GpUuX0KZN\nG0yaNAnu7u6qrI+IiIiIVEBwCOzXrx+MjY3h5eWFmTNnwsKCrxojIiIiqq0Eh8BZs2ahTZs2ivcG\nExEREVHtJTgEfvTRR6qsg4iIiIiqkeAQKJVKsXHjRpw6dQrZ2dmQy+WKfVu2bFFJcURERESkGoJn\nB69duxYHDx7EJ598gpycHAwYMABaWlrw8fFRZX1EREREpAKCQ+CxY8cwf/589O/fH1paWujfvz9m\nzZqFixcvqrI+IiIiIlIBwSEwLy8PDRs2fHWShgZkMhkcHR0ZAomIiIhqIcEh0MzMDI8fPwYAWFpa\n4sKFC7h9+zY0NTVVVhwRERERqYbgENitWzekpqYCAHx8fBAcHIzRo0eje/fuFb5oWloaRowYUeHz\nSLjjx4+jV69e8PT0xIYNG2q6HCIiInrPCJ4dHBgYqPi6T58+cHBwQH5+fqWWjvnxxx8RFBRU6r5t\n27Zh9erVCAgIKPOYly9fYtWqVTh79iyePn0KQ0NDtG/fHiNHjoShoWGJ469evYpx48bB2dkZERER\niu1//PEH9u/fj1u3bsHY2PidZjnLZDKMHTsW165dw6ZNm2BjY1PmscePH0dMTAzS09NhaGiIPn36\nwN/fX7E/Li4O+/fvR3p6OsRiMZycnDBy5Eg0atRIcczdu3exevVqXLlyBXK5HO7u7hg/fjz09PQA\nAB06dMCePXvwzTffVPqeiIiI6H9Xpd4dDADOzs5o27ZthRePPnv2LLKystChQ4cS++7evYsdO3bA\n3t6+3DZkMhmMjIzw/fffIzExEWvWrMH9+/exaNGiEsdKpVIsWrQILVu2LLHP3Nwcfn5+GDRoUIXu\noTS//vorTExM3vr9uHLlCmbPno1hw4YhMTER33//PbZv344dO3Yojnn58iXGjRuHP/74A7///jsa\nNGiA4OBgSKVSAMDz588xdepUODo6Yvv27YiNjUVGRgYWLFjwzvdBRERE6qHSIbCyDh8+DDc3txJh\nqbi4GOHh4RgzZgyMjIzKbUNXVxcjRoyAnZ0dRCIRTE1N8dlnn+Hs2bMljo2OjoabmxtcXFxK7OvS\npQs6d+4Mc3Pzd7qna9euITk5GaNHj1ZaP7E0f//9N1q1aqUIwQ4ODujdu7dSCPT394erqyvEYjHE\nYjECAgLw7Nkz3L17FwBw4cIF5OXlISgoCJqamqhTpw4GDx6Mo0eP4smTJ+90L0RERKQeqj0EXr16\nFY0bNy6x/ddff4WtrS3c3d0r1e7JkyfRtGlTpW3nz5/HiRMnMHLkyEq1KcTLly+xcOFCfPPNN4qh\n2PIUFxeXCIoymQzp6ekoLCws9ZyTJ09CT08PDRo0UGrj3+0UFxcDAK5fv17ZWyEiIiI1Uu0hMC8v\nDwYGBkrbbty4gd27d2PChAmVajMpKQkHDhzA+PHjFdsKCwuxaNEiBAcHQywWv1PN5dmwYQOcnZ3R\nunVrAHjrcHCnTp1w9uxZHD58GDKZDFevXsXevXsBvBrmfdPNmzexYsUKjBs3Djo6OgAAFxcX6Ovr\nY/369ZBKpXj8+DE2bdpUZhtEREREbxI8MaSqGBkZoaCgQPFZJpNhwYIFGDduXKmTOt5m165diI6O\nxqJFi5R6GNesWYP27dvD1dW1SuouzYULF3Dw4MEKzb51cXHBjBkz8Msvv2DJkiWwtbVF3759sXHj\nxhLD4JcvX0ZYWBiCgoLg7e2t2G5oaIiFCxdi3bp1+PLLL2FgYICBAwciLS0NJiYmFbqHlJSZ0NbW\nBwA0aeIFBwevCp1PREREqpWUlISkpCQAUMwPqAoVCoGpqam4cuVKid6msmbxlsbR0RG3b99WfH78\n+DFu376NpUuXYsmSJQCAgoICXLlyBUeOHCk3YP3222+Ii4vD0qVL0aRJE6V9J0+eREFBAfbv3w8A\nkEgkKCoqwmeffYbIyMhyZ+8Kdfr0aWRnZ8PPzw8AFEO0X3/9NQYMGICAgIBSz/v444/x8ccfKz5H\nRkbigw8+UOqxPH36NObMmYNx48ahR48eJdpwcHDA4sWLFZ+PHDkCXV1dODs7V+geunWbBwMDiwqd\nQ0RERNXHy8sLXl6vOmlyc3MRGRlZJe0KDoEbNmzAb7/9BgcHB+jq6iq2V3R2cOfOnREeHg65XA6R\nSARLS8sSS7PMnj0bTk5OinBVmnXr1mH//v1YsWIF7OzsSuxfvXo1ZDKZ4vPWrVtx4cIFzJs3D3Xr\n1gXwqhdSJpOhqKgIwP9P1/8OYx4eHggNDVV88/9t4MCB6N27t+Lzo0ePMG7cOPzwww9lznCWy+W4\nevUqmjZtipcvX+LQoUPYu3cvFi5cqDjm8OHDCA8PR0hIiFJY/Ldr167Bzs4O2trauHjxIlavXo1h\nw4ZBX1+/zO8ZERER0WuCQ+Du3bsRERFR4Z6mN7m5uaFOnTo4evQoOnXqBJFIVGJ2rlgshp6eHkxN\nTRXbevXqhSlTpsDT0xMPHz7Eli1boKWlha+//hoAFKEyJiYGFhYWiqD3moGBAbS1tWFmZqbYtmnT\nJsTGxiqCbM+ePSESibB582ZYWloiMzMTWlpapc4sBgA9PT2lySBFRUUQiUSoW7euYvv+/fuxfPly\n7N69G8CrCRwRERG4d+8e5HI5mjVrhvDwcKXv65o1ayCRSLBo0SJFOBSJRJg8eTI8PT0BAHv27EFK\nSgqkUimsra0xePBgpSFjIiIiovKIUlJSyl/T5P/07dsX8fHxFe75K01aWhpWrlyJqKiod25LlXbv\n3o2bN29WesJKTTpx4gTmz5+PoqIi+Pn5YciQIUr7CwoK/u/NL484HExERO+FoiIJ7t9fgHXrpism\nQ5Ky3NxcmJiYIDExscRE24oS3BPo6emJQ4cOoWvXru90QQBwdXV97wMgAKWh3tqmffv22LVrV02X\nQURERO8pwSEwJycHCxYswK5du5SGVAEgLCysygsjIiIiItURHALFYjE8PDxUWQsRERERVRPBITA0\nNFSVdRARERFRNarQOoFyuRxXrlzBo0ePYGlpiWbNmlXJRBEiIiIiql6CQ+DTp08RFhaGGzduwNDQ\nEPn5+XBwcMD8+fNLLPFCRERERO83we8Ofv2WjR07diAhIQE7duyAra1tla1aTURERETVR3AIPHfu\nHIKDg2FsbAwAMDY2xjfffINz586prDgiIiIiUg3BIRAANDQ0yv1MRERERLWD4BT34YcfYtmyZSgo\nKAAA5OfnY8WKFfjwww9VVhwRERERqYbgiSFjx47F9OnT0adPHxgbGyM3Nxf29vb44YcfVFkfERER\nEamA4BBobm6OdevWKZaIqVevHpo3b84hYSIiIqJaqELrBGpoaMDZ2RnOzs6qqoeIiIiIqgG78YiI\niIjUEEMgERERkRpiCCQiIiJSQwyBRERERGqo3IkhSUlJghrx8vKqkmKIiIiIqHqUGwKjo6OVPmdl\nZaG4uBhGRkbIy8uDhoYGTE1NGQKJiIiIaplyQ+DWrVsVX2/fvh03btzAuHHjYGBggPz8fKxduxb2\n9vYqL5KIiIiIqpbgdQK3bNmCX375BTo6OgAAQ0NDjB07FkOHDsXnn3+usgJJtWQyCYqKJDVdBhER\nEWQy/n1UnQSHQIlEgvz8fEUIBICCggJIJPyB1WaZmZEQi3XefiAREVE1sLExhKamZk2XoRYEh0B3\nd3eEhYUhMDAQ1tbWePDgAWJjY+Hu7q7K+kjFIiImw9jYuKbLICIiAgBoampCS6tCLzSjShL8XR4/\nfjwiIyMxa9YsvHz5Etra2ujevTvGjh2ryvpIxXR0dJR6d4mIiEg9CA6Benp6CA4OxpQpU5CdnY06\ndepAJBKpsjYiIiIiUpEKLRYtk8lw8eJFnD17FiKRCFKpFFKpVFW1EREREZGKCO4JfPDgAaZPn47M\nzEyIRCJ4eHjgxIkTOHLkCMLCwlRZIxERERFVMcE9gStXroS7uzt2796teGCzVatWOH/+vMqKIyIi\nIiLVEBwCL1++jMDAQGhqaiqeBTQyMkJ+fr7KiiMiIiIi1RAcAnV1dfHixQulbdnZ2VxehIiIiKgW\nEhwC27Vrh5UrVyqCoEwmw/r169GhQweVFUdEREREqiE4BI4cORJPnjxBnz59UFBQgN69e+PmzZsI\nDAxUZX1EREREpAKCZwcbGhpi2bJluH79Ou7fvw9TU1O4urpCQ6NCq8zQe0YikfDVf0RUq/ENE0SV\nU+E/NU2bNkXTpk2Rnp6OR48ewcrKShV1UTWZOHEZ3x1MRLWajY0h5s6dxCBIVEGC/8QsXLgQvXr1\ngqurK/766y/Mnz8fABAWFgZPT0+VFUiqZWU1Fvr6FjVdBhFRpchkEmRkLINMJmMIJKogwX9i/vvf\n/2LixIkAgG3btmHmzJnQ19fHunXrGAJrMU1NHWhpsSeQiIhI3Qh+oE8ikUBXVxfPnz/HvXv30KVL\nF7Rt2xYPHz5UZX1EREREpAKCewJNTExw584d3Lp1C87OztDQ0EBhYaFi4WgiIiIiqj0Eh8D+/ftj\n9OjRAICZM2cCANLS0tCoUSOVFEZEREREqiM4BH722Wdo27YtNDU1FTOCra2tMXnyZJUVR0RERESq\nUaGpVPXr11f63KBBgyothoiIiIiqR4VCYGJiIk6dOoWsrCyl7REREVVaFBERERGpluDZwTExMYiK\nioK5uTmuXr2Kpk2b4vbt23B0dFRlfURERESkAoJ7Avft24fw8HA4OTkhOTkZ48aNg7u7OxITE1VZ\nHxERERGpgOCewKysLDg5OSk+y+VytGzZEqdOnVJJYURERESkOoJDoImJCXJycgAAZmZmuHnzJp48\neYLi4mKVFUdEREREqiF4OLhNmzY4evQoevXqBU9PT0ydOhVaWlro0KGDKusjIiIiIhUQHAKnTJmi\n+DogIADW1tYoKChAz549VVIYEREREalOhZaI+TdPT8+qrIOIiIiIqpHgECiTyfD777/jzz//xKNH\nj2BhYQFvb2/4+flBU1NTlTUSERERURUTHAKjoqJw+PBhfPHFF7CyssKDBw+wdetW5OfnK94pTERE\nRES1g+AQuH//fixfvlzpVXGtWrXCN998wxBIREREVMsIXiKmuLgY1tbWStusra25RAwRERFRLSQ4\nBHp7e2PTpk2Qy+UAXi0WvXnzZvTu3bvCF01LS8OIESMqfB4Jl5CQoFjOZ8+ePTVdDhEREb1nyh0O\nnjBhAkQiEYBXoe/y5cvYtWsX6tWrh0ePHiE3NxfOzs4VvuiPP/6IoKAgxefk5GTs2rULd+/ehUgk\ngr29PYKCguDi4lJmGy9evMCaNWtw7NgxFBYWwtraGkOGDEHnzp0Vx7x8+RIxMTE4cOAAcnJyUKdO\nHQQFBaF79+4AgNjYWGzcuBG6urqQy+UQiUTo0KEDvv32W8H3Ehsbi+TkZOTk5EBbWxuOjo4YOXIk\nHBwcyjxn0qRJuHTpErS1tRXXHTVqFPr06QMASE1NxeTJk6Gnpwfg1ffeyMgIW7ZsUbQxY8YMXLt2\nDYWFhdDT08NHH32E0aNHw9jYGADQt29f9O3bF35+foLvhYiIiNRHuSGwdevW5X6ujLNnzyIrK0tp\nkenCwkIMHToUH3zwAcRiMXbs2IHQ0FDExsbC3Ny81HY2bNiAc+fOYfXq1bCwsMDBgwcxd+5cREdH\nw87ODgAwe/ZsSKVSLF++HNbW1sjJyUFeXp5SOy4uLoiIiKj0/Xh6eqJfv34wNDSETCbD9u3bERIS\ngu3btysC9JtEIhH8/PwQGBhYZrsikQiJiYlltjF8+HDY2tpCLBYjPz8fy5cvx9KlSzFnzpxK3wsR\nERGpj3JD4NChQ6v8gocPH4abm5tSuOnbt6/SMf3790dsbCyuXLmCTp06ldpORkYG2rZtCwsLCwBA\n165dsWLFCvzzzz+ws7PD6dOncebMGfz+++8wMTEB8OrVd6+/riq2traKr2UyGTQ0NJCTk4Pc3Nxy\nr/V6WL08xcXFZS6/Y29vr9SWSCTC/fv3K1A5ERERqbNKLxZdWVevXlUasi3NpUuX8OLFi3KHVPv3\n74+1a9ciIyMDVlZW+OuvvyASidCiRQsAwJkzZ2BlZYXNmzfjwIED0NLSQqtWrTB69GilcHb9+nV8\n/vnn0NHRwQcffIARI0bAysqqQvd04sQJzJ8/HwUFBRCJRBgwYMBbw+bOnTuRkJCAunXrwt3dHQEB\nAYrh39cGDRoEqVQKe3t7DB48WHFvr0VFRSE+Ph6FhYXQ0dHB9OnTK1Q3ERERqa9qD4F5eXkwMDAo\nc/+jR48wb948+Pv7lxvG7O3tYWdnh4CAAGhqakJHRwfTpk1D3bp1AQA5OTm4c+cO3NzcsHnzZjx/\n/hzz58/HggULEB4eDgD4+OOP4e3tjXr16uHp06dYu3YtpkyZgujoaOjq6gq+p/bt22PXrl3Iz8/H\n3r17Fb2TZRk5ciTs7OxgaGiIf/75B+Hh4cjMzMTMmTMBAA0bNkRUVBQaNWoEiUSCXbt2ISQkBKtX\nr0aTJk2U2hk5ciQePHiAP//8E/Xr1xdcMxEREam3ag+BRkZGKCgoKHVfeno6pk6dCg8Pj3KflwOA\nWbNmQUdHB9u2bYOpqSnS0tLw3XffQVtbG+3atYO+vr5iwoVYLIZYLEZgYCDGjx8PiUQCHR0dNGrU\nSNGemZkZQkJC4OPjg4sXL1bq+UdDQ0P069cPn376KRo0aKA0ZPtv/55MY29vjzFjxmDq1KmQSqUQ\ni8WoW7euIszq6elh4MCBOH78OA4ePKgUAl+ztrZGx44dERISgq1bt1boDS4pKTOhra0PAGjSxAsO\nDl4VuWUiIiJSsaSkJCQlJQEApFJplbVb7SHQ0dERt2/fLrH95s2bCA0Nha+vLwICAt7azrVr1zB9\n+nSYmpoCAFxdXeHq6orjx4+jXbt2aNq0aYlJFa+fnSuPSCQS9LxeWYqLiyGTyXD//v0yQ2Bp1xRy\nTHl1vXz5EtnZ2SgoKFDMEBaiW7d5MDAov+eSiIiIao6Xlxe8vF510uTm5iIyMrJK2hW8TuCbTp8+\njdTU1Aqf17lzZ5w5c0Yp0Fy4cAGTJ0+Gn5+foAAIvAp9f/75J7KzswG8eo7w3LlzaNasmeI65ubm\niIqKglQqRU5ODmJjY9G+fXvo6OgAAA4ePIicnBwAwLNnz7B48WKYmprigw8+UFzHz88PsbGxZdax\nfft2ZGVlAQCys7OxfPlyaGtrl7m8TVZWFv773//ixYsXAIBbt25hzZo1cHd3h1gsBgCcPHkSmZmZ\nkMvlkEgk2LZtGy5evIiPP/4YAHD//n0cPnwYz58/BwDcvXsX69atQ/PmzSsUAImIiEh9Ce4JnDp1\nKgYNGoSWLVti+/bt+Omnn6ChoYHhw4ejf//+gi/o5uaGOnXq4OjRo4qZvxs2bEB+fj42bNiA6Oho\nAK96vgYNGgR/f38AwLRp02BpaYlvvvkGABAaGop169ZhxIgRePHiBUxNTfHFF1/A29sbAKCrq4vF\nixdj5cqV8PX1hYGBAdq3b49Ro0Ypatm3bx9WrlyJwsJCGBkZ4cMPP8SSJUsUEzSkUimysrLQsmXL\nMu/n9OnT2Lx5MwoLC2FgYIBmzZphyZIlih7KR48eYdiwYVi4cCFcXV0hlUrx888/4969e5DL5TA1\nNUWXLl2Uwu+VK1ewdOlS5OTkQFdXF40bN8bChQvRtGlTAK96NOPi4rB48WLIZDKYmJjgo48+wrBh\nwwT/HIiIiEi9iVJSUgSNffr6+iIuLg7a2toYPnw4xo8fD0NDQ8yZMwe//PJLhS6alpaGlStXIioq\nqlJFV5fTp09j+/bt+OGHH2q6lArbuXMnoqKiUFRUhEmTJim6kV8rKCiAj48PgoMfcTiYiGqtoiIJ\n7t9fgHXrpitGeYj+l71egi4xMbHcibZCCO4JLCoqgra2NnJycvDkyRNF79izZ88qfFFXV9f3PgAC\nrxbHrooFsmtCnz59FG8gISIiInqT4BBoYWGB1NRU3LlzR7FeXX5+PrS0qn1uCRERERG9I8EJbsiQ\nIQgJCYGWlhYWLlwI4NVwaXkLOhMRERHR+0lwCOzWrRs6duwIAIrnLl4vy0JEREREtUuFxnJfh7/i\n4mIAQJ06daq+IiIiIiJSOcEh8O7du1i+fDmuXLlSYrXqAwcOVHlhRERERKQ6gkPgokWLYG5ujlmz\nZlXovbpERERE9P4RHAJv3bqleBsGEREREdVugl8bZ21tjfz8fFXWQkRERETVRHBP4IABA/DDDz9g\nyNb+8eYAACAASURBVJAhMDMzU9pnY2NT5YURERERkeoIDoH/XhtQJBIBePUOW5FIxIkhRERERLWM\n4BC4efNmVdZBRET0/9q797goy/z/46+RmYERxAQVD1Qe8Hz4lrZlWa3hrqYpres3Sysrz2kbpmnm\nYfOxnpU8mygKaqZrarq2mIdKMy3XrbBcUjfNTVlEQAzkzAzz+8Mf9zcCBFRAvd/Pv+Cea677c881\n98x7rvu+Z0SkEpU5BNarV68i6xARERGRSnTVELhnzx66desGwM6dO0ts17NnzxtblYiIiIhUqKuG\nwI0bNxoh8N133y22jcViUQgUERERucVcNQRGRUUZf2/cuLHCixERERGRylHm7wkUERERkdtHmS4M\n+eqrr/jxxx9p27YtrVu3ZvXq1XzxxRc0a9aMV199lerVq1d0nSIiIiJyA5U6E7ht2zYmT57Mxx9/\nzOuvv86yZcs4cOAAv/nNbzhx4gQrVqyojDpFRERE5AYqdSZw+/btzJ07l/bt2/PNN98wbtw41q5d\nS2BgIL1792bMmDGVUaeIiIiI3EClhsCLFy/Svn17AO69916sViuBgYEANGzYkMuXL1dshVKhXK4c\nnM6cqi5DROSauFx6/RK5VqWGQLfbbfxtsVjw9PQsdHvBT8jJrSkhYRl2u2fpDUVEblINGvjg4eFR\n1WWI3HJKDYH5+fnExMQYYdDlchX6Pz8/v2IrlAq1aNEYfH19q7oMEZFr5uHhgdVa5h/AEpH/r9S9\nJicnh7FjxxZa9sv/NRN4a/P09CwyuysiIiK3v1JD4KeffloZdYiIiIhIJdKXRYuIiIiYkEKgiIiI\niAkpBIqIiIiYkEKgiIiIiAkpBIqIiIiYULm/WCk7O5vY2Fjcbjdt2rTB4XBURF0iIiIiUoFKDYHT\np09n8uTJACQkJDB27FiSk5OxWCz4+fkRFhZGgwYNKrxQEREREblxSg2BX375pfH3qlWraN26NePH\njwdg3rx5REZGGiFRbj05OTnk5Oi3N0VEKoJ+zURuZuX67eDY2FiWLl2KzWYDYMSIEYwYMaLiqpMK\nFxo6X78dLCJSQRo08OEvfxmtICg3pVKflb/8WbicnBz8/f2N//38/Lh8+XLFVCaVol69UVSvXqeq\nyxARue24XDnEx8/H5XIpBMpNqdRnZXZ2NqGhocbfiYmJ1K1bF4DU1FRdGHKL8/DwxGrVTKCIiIjZ\nlBoCBw4caPzdoUMHMjMzjf9jYmJo1apVxVQmIiIiIhWm1BD4wgsvlHhbly5d6NKly42sR0REREQq\ngb4sWkRERMSEFAJFRERETEghUERERMSEFAJFRERETEghUERERMSEFAJFRERETEghUERERMSEFAJF\nRERETEghUERERMSEFAJFRERETEghUERERMSEFAJFRERETEghUERERMSEFAJFRERETEghUERERMSE\nqiQEHjt2jCFDhlTFqk1j5cqV9OzZk+DgYL755puqLkdERERuMtaqWOmSJUsYNGiQ8f+hQ4eIjIwk\nKSkJgPr16zNgwAB++9vfltjH2rVrWbduHV5eXrjdbiwWCw8++CCTJ0822gQHB2O32/Hw8DDaLF26\nlMaNGxt97Nmzh9TUVGw2G82bN2fo0KEEBQVd03ZNmTKFQ4cOERYWRocOHYptExcXx+rVq4mNjSUz\nMxM/Pz+eeOIJnn766WLbb9myhXfeeYfnnnuu0GMWFhZGbGws586dIzg4mIkTJxa637Bhwxg2bBjB\nwcHXtC0iIiJye6v0EBgTE8OlS5d48MEHjWUtW7Zk7ty5+Pv7A/Ddd98xfvx47rzzTpo0aVJiX23b\ntmXRokVXXd+sWbO49957i72ta9eu9O3bFx8fH1wuF1u3bmX8+PFs3boVi8VSru3avXs32dnZpd7v\n8uXLtG/fnlGjRlG7dm1OnTrFm2++idVqpW/fvoXanj17lm3bthX7GDRt2pQuXbqwY8eOctUpIiIi\nAlVwOPjzzz+nQ4cOhcKSv7+/EQALZuzgyqzZ9XK73SXeFhgYiI+PDwAul4tq1aqRmppKWlpaudaR\nlJREVFQU48ePv+r6AFq1akWfPn2oXbs2AEFBQXTp0oWjR48Wapefn8/s2bMZOXIkNWrUKNJPnz59\nuO+++/D29i5XrSIiIiJQBTOBJ0+e5JFHHimyPCMjg2eeeYacnBycTift2rWjU6dOV+3rhx9+4I9/\n/COenp60adOGIUOGUK9evUJtZs6cidPpJCAggJCQEJ544olCtx8+fJgZM2aQkZGBxWLhqaeeombN\nmuXaprlz5/L8889Tp06dct0ProTPmJgYHn300ULL33vvPQIDA+ncuTNbtmwpd78iIiIiV1PpIfDy\n5cvFzl55e3vz4YcfkpeXx+HDh4mLi8Nms5XYz29/+1t69OhB3bp1uXjxIuHh4YwdO5bVq1fj5eUF\nwNtvv02bNm3w8PDgq6++YsaMGbhcLkJCQox+OnXqxIcffkh6ejq7du0qd5Dbvn07QJFwWVbz58/H\n5XLx1FNPGctOnTpFdHQ0q1atuqY+RUREREpT6SGwRo0aZGRklHi7zWbjkUceYcKECXh5edGnT59i\n2zVq1Mj429/fn/Hjx9OrVy9iY2Pp2LEjQKFzAR944AH69u3L3r17C4XAAj4+PvTt25fevXuXei5i\ngfj4eNavX88777xTattfy8/PZ968efz73/9mwYIFOBwO4MrM4KxZs3jllVeMQ9UVad++Kdhs1QFo\n2rQ7QUHdK3ydIiIiUna7d+9m9+7dAOTm5t6wfis9BDZv3pz//Oc/pbZzuVycO3euXH1bLJZSz8m7\n2u35+fm4XC7i4uLKFAK/++470tLSGD58eKF+33rrLR577DHGjBlT7P3y8vKYNm0aFy9eZNGiRYXC\nXlJSEv/5z394++23CQsLA64cKj9x4gQHDx4kMjKy1LrK47HHpuHtXf7D2CIiIlI5unfvTvfuVyZp\n0tLSWLZs2Q3pt9JD4COPPMLs2bMLXQCyZ88eWrduTYMGDXA6nezatYuYmJhCh0h/bf/+/dx7773U\nrFmTlJQUwsPD8fPzo02bNsCV8wXdbjdNmjTBYrHwzTff8MEHH/Diiy8afWzdupXg4GBq1arFzz//\nzKpVq7DZbLRt29Zo079/fx5//HFeeOGFIjUEBwdz3333FVrWr18/xo4dW2R5gaysLCZNmoTb7SYs\nLMyYASwQEBDApk2bCi2bOnUqrVq1on///sYyp9NphFa3201ubi4Wi+Wqh9BFREREClR6COzQoQN3\n3HEHhw4d4uGHHwauHFZds2YNP//8M3a7ncDAQKZMmcL9999v3O+ll17i97//PQMGDABg7969LF68\nmKysLGrUqEH79u0Lhark5GRWrFhBYmIiVquVgIAAhg4dSq9evYw+v/76azZs2EBWVhbe3t60aNGC\nsLAw/Pz8gCtTrpcuXeKee+4pdlvsdrtxlW8Bi8WCr6+vMbt37NgxJkyYwJo1a6hTpw4HDhzg22+/\nxW6307dvX2P2sl69ekRGRmKxWIr0abfbcTgcRl0A48aN49tvvzWC9CeffEK9evXYsGFD+QdFRERE\nTMeyb9++qx8/rQDHjh1j8eLFREREVPaqy+Xrr79m69atzJw5s6pLKbeIiAh27NiB0+lk1qxZRYJs\nRkYGvXr14vXXE3U4WESkAjidOcTFzWLFijfx9PSs6nLkNpGWlkbNmjX5+9//ft1fE1clvxjSrl27\nmz4AAnTs2NG4yORWM3ToUIYOHVrVZYiIiMhNqkp+O1hEREREqpZCoIiIiIgJKQSKiIiImJBCoIiI\niIgJKQSKiIiImJBCoIiIiIgJKQSKiIiImJBCoIiIiIgJKQSKiIiImJBCoIiIiIgJKQSKiIiImJBC\noIiIiIgJKQSKiIiImJBCoIiIiIgJKQSKiIiImJBCoIiIiIgJKQSKiIiImJBCoIiIiIgJKQSKiIiI\nmJC1qguQquVy5eB05lR1GSIitx2XS6+tcnNTCDS5hIRl2O2eVV2GiMhtqUEDHzw8PKq6DJFiKQSa\n3KJFY/D19a3qMkREbkseHh5YrXqrlZuTnpkm5+npiaenZgJFRETMRheGiIiIiJiQQqCIiIiICSkE\nioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiI\nCSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCI\niIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQ\nQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCIiIiICSkEioiIiJiQQqCISezevbuqS5BK\npPE2F423XAuFQBGT0JuEuWi8zUXjLddCIVBERETEhKxVXYBUDbfbDUBaWloVVyKVJTc3V+NtIhpv\nc9F4m0fBOBe8j18Py759+66/F7nlJCUl0a9fv6ouQ0RERK7B+++/T506da6rD4VAk8rPz+fixYs4\nHA4sFktVlyMiIiJl4Ha7ycrKwt/fn2rVru+sPh0ONqlq1apd9ycIERERqXw+Pj43pB9dGCIiIiJi\nQgqBIiIiIiakECgiIiJiQjon8DYWFRXFzp07ycjIoHnz5oSGhtK4ceNi26anp7Nw4UL+8Y9/YLFY\n6NSpE6+++uoNO+9AKl55xnv06NF8//332Gw23G43FouF4cOHExISUslVS3l9+umn/O1vf+P06dNk\nZWWxd+/eq54crn371lbe8da+fWuLiIjg8OHDXLhwAYfDQfv27RkxYsRVz+HPy8tj2bJl7N+/H6fT\nyf/8z/8wevToMp33r5nA29Rf//pXdu/ezbx589i+fTtt2rRh/PjxZGdnF9t++vTppKamsmHDBtav\nX09KSgqzZ8+u5KrlWpV3vC0WC/379yc6OpqdO3cSHR2tN4lbhK+vL08++SSjRo0qU3vt27e28o63\n9u1bm8ViYcKECfztb39jzZo1WCwWJk6ceNX7LFu2jH/9619ERESwefNmfHx8mDRpUpnWpxB4m9qx\nYwdPP/00jRo1wm63M2jQIJxOJ59//nmRthcuXODIkSOMHDmSGjVq4Ovry8svv8wXX3xBUlJSFVQv\n5VWe8S5wI75oVCrffffdR3BwMPXr1y+1rfbtW195xruA9u1b15AhQ2jWrBkeHh54e3vzzDPP8OOP\nP5Kenl5s+9zcXHbv3s3gwYOpU6cODoeDkSNHcubMGY4dO1bq+hQCb0MZGRkkJCTQokULY5mHhwdB\nQUGcOnWqSPtTp05hs9kKHTps2rQpVqu12PZycynveBfYsWMHTz75JC+++CIRERFkZWVVRrlSibRv\nm5P27dvHP//5TwICAko8fePcuXPk5uYWev2vWbMm9evXL9M+rnMCb0OZmZlA0e8RqlGjBhkZGcW2\nL+4J5uPjU2x7ubmUd7wBhg4dyl133YWPjw8//vgjs2fPJiEhgSlTplR4vVJ5tG+bj/bt28fXX3/N\nu+++y1/+8pcS25T0+l/WfVwzgbeh6tWrAxSZPr58+TLe3t7Fti/uyZKenl5se7m5lHe8AVq3bm28\naDRp0oSRI0dy4MABcnNzK7ZYqVTat81H+/bt4csvv2Tq1KlMmjSJ++67r8R2Jb3+l3UfVwi8DXl7\ne1OvXj1OnjxpLHO5XJw+fZqgoKAi7YOCgsjLy+PMmTPGstOnT+NyuYptLzeX8o53cfTTgbcn7dui\nffvWs3fvXmbOnMnUqVPp3LnzVdveeeed2O32Qq//qampJCQklGkfVwi8TT355JNs2rSJM2fOkJOT\nQ1RUFFarlUceeaRI24CAAB544AGWL19OamoqqamphIeH89BDD+mn5W4R5RnvS5cuceTIEePK4TNn\nzrB8+XI6d+6M3W6v7NKlnPLz88nNzSUvLw+4cmJ4bm5usRcDaN++9ZVnvLVv3/q2bdvG4sWLmTlz\nJh07diy1vd1u5/HHHycqKorExEQyMzN55513aNSoEe3atSv1/pZ9+/bpMqLb1Jo1a/jwww/JzMyk\nRYsWxvfGJSYm8uKLLzJnzhzjSZKens6iRYv48ssvsVgsPPjgg4SGhuqQ0S2krON94cIFpk6dyrlz\n53C73fj5+fHoo4/y3HPP4XA4qnozpBS7du1i7ty5xgxPwXfBzZ8/n/r162vfvs2UZ7y1b9/6goOD\nsVqt2Gw24P/Ge/bs2cY+3bNnT8aOHUvXrl2BK98TuHz5cj755BPjewJfe+21Mn3QUwgUERERMSEd\nDhYRERExIYVAERERERNSCBQRERExIYVAERERERNSCBQRERExIYVAERERERNSCBQRERExIYVAERER\nERNSCBQRqQSbNm3if//3f3niiSc4fPhwVZdTaRITE3niiSdISEi4of0ePXqU4OBg8vPzb2i/1yoh\nIYHg4GDi4+NLbLNgwQLCwsIqsSqRq7NWdQEiUrVGjx7N999/j81mw2KxULduXfr06UPv3r2NNrNn\nz2bPnj0MGDCAIUOGGMvdbjfPPvssCQkJhIWF0aFDBwAOHDjAX//6V86dOweAv78/jz76KIMGDQJg\nzpw5fPzxx8bvmRb8NNLAgQN5+umnK2vTK01ycjIrV65k+fLlNG/evKrLqVR169YlOjr6uvqYM2cO\nLpeLiRMnFlpe8FNqN4vS6nnttdcqqRKRslEIFDE5i8XCM888YwS0/fv3M23aNO6++27at29vtGnU\nqBEfffQRL730Eh4eHgAcOXIET0/PQm9+sbGxzJo1iylTptCpUyfcbjfnzp3jhx9+KLTexx57rMib\n+s3A6XRitd7Yl8bz588D0LRp02vuoyLquhYul8sYfxG5tVX9K4qI3FS6dOnCwoULOXHihBECAYKC\ngoiLi+Pzzz+nS5cuAOzYsYOQkBCWLl1qtIuNjaVhw4Y89NBDxrJGjRrRqFGja67J6XSyZMkSDh48\nSE5ODr6+vjz11FP06dMHgJ9++omVK1dy4sQJ8vLyuOuuu3jrrbeoU6cO6enphIeHc+TIEfLy8mjR\nogWjRo3izjvvBGDt2rV8/fXX3HPPPXz00Uf4+PgQFRVFeno6ERER/OMf/yA7O5tWrVrx6quvUr9+\nfQD27dvHunXrSEpKwmq10qxZM+bNm1ek9p07d7J48WIAevfujcViITo6mtzcXKKiovjss8/IyMig\ncePGDB8+nFatWgGwa9cuIiMjGTBgAJs2bSItLa3YGbXiZslee+012rVrx6BBg0p97M6ePUt4eDgn\nTpzAarXy0EMPMWLECLy8vADo378/3bt35/jx48TGxvLss8/StWtX5s+fz/Hjx3G5XAQEBDB69Gjj\nB+5/KSEhgQEDBrB+/XoaNGhgbNfzzz/Phg0bSE9Pp2PHjrzxxhs4HI4i93/vvff4+OOPsVgsHDx4\nEIvFwpo1a4zbP//8c1avXk1KSgqtWrViwoQJ+Pv7A5Cbm8vatWvZv38/6enpNG7cmFdeeYWgoCAA\nYmJiWLFiBf/973+pVq0ad999NzNnzsTHx4f8/Hy2bNnCzp07SU5OJjAwkGHDhhmz3cVxu93ExMQw\nceJEkpOTadmyJWPGjKFBgwbFjlX//v3p0aMH33//PceOHaNWrVqMGDGChx9+GIDTp0+zZMkSTp8+\njcVioUGDBkyePJnAwMASaxApD4VAETG4XC727dvH5cuXufvuu4vcHhISwo4dO+jSpQsJCQl8++23\nTJo0iSVLlhht2rdvT0REBAsWLKBTp040b97ceFO+Vrt37+b48eOsWbOGGjVqcOnSJS5evAjApUuX\nCA0NJSQkhMmTJ+Pl5cW///1vPD09AZg5cybZ2dmsXLmS6tWrExERweuvv87atWuNoHP8+HHuv/9+\nNmzYgNvtBuDPf/4ztWvXZtWqVXh5eREVFcWbb77J6tWrcTqdzJo1i7lz53LPPfeQl5dHbGxssbX3\n7NmTBg0aMHbsWKKjo41Z0/DwcL799lvefvtt6taty9atW426ateuDUBKSgo//vgjUVFRVKt2badw\nX+2xS01NJTQ0lOeee45p06aRkZHBtGnTWLp0Ka+//rrRx9///nemTZtGq1atyMnJISwsjDp16jB9\n+nSsVitxcXFXnaX89WHSlJQUzp07x7p167h8+TKhoaG8//77vPDCC0Xu++yzzxIXF1ck6P73v//F\n7XZz6NAhVqxYgdvt5o033mDVqlW88cYbAMyfP5+LFy+yePFiatWqxY4dOxg/fjzr1q3Dx8eHmTNn\nMnjwYB5//HFcLhcnT57EZrMBsG7dOr744gtmzJhBw4YNOXjwIJMmTSIyMtL4IFCc6OhowsLC8PX1\nZfHixUycOJHIyMgSx2/nzp1Mnz6doKAgNm/ezOzZs9m8eTMOh4OFCxdy//33s2DBAtxuN2fOnMHH\nx6fEdYuUly4MERHef/99QkJC6N69O3PmzGHYsGE88MADRdoFBwdz+vRp4uLiiI6O5rHHHqN69eqF\n2rRs2ZLFixeTm5vL0qVL6devHy+99BJffvlloXb79+8nJCSEkJAQevfuTUhICDExMcXWZ7Vayc7O\n5syZM7hcLmrVqmXM5uzduxd/f38GDRqEw+HAYrHQokULfH19SUlJ4fDhw/zpT3/ijjvuwG63M2LE\nCHJycgrVU6tWLZ577jlsNht2u50ffviBf/3rX4wZMwYfHx+sViuDBg0iISGB48ePGzX99NNPpKam\nYrPZuOeee0p9nAsCptvt5qOPPmLIkCHUr18fDw8P+vXrR/369dm7d6/R3mKx8Morr+Dl5WWcP1le\nV3vs9uzZQ2BgIH379sXDwwNfX18GDhzInj17jFoBevToYcxQenp6YrVaSUlJIS4uDoDAwEDq1atX\n6nb/sqYRI0Zgs9nw8/Ojc+fOxuNaHhaLhaFDh+JwOKhevTpdu3Y1+klNTWXPnj2MHj0af39/qlWr\nxh/+8Ae8vb2NC3Psdjvx8fEkJyfj4eFB69atjQ8PW7ZsYfjw4TRs2BCAhx9+mLZt2/LJJ59ctaaB\nAwdSu3Zt7HY7o0aNIi4ursQPCAC9evUyxqN3795kZmby008/AWCz2bhw4QLnz5+nWrVqNG3alDvu\nuKPcj5NISTQTKCL069ePQYMGkZWVxbJly/jqq6946qmnisxe2O12unXrxgcffMBnn33G7Nmzi+2v\nVatWRmj4+eefWb9+PW+99RZRUVHGm2qXLl3KfE5gt27dSE1NJTw8nLNnz9K2bVsGDRpE8+bNOX/+\nvHFo99cSExOxWCyFZm48PDwICAggMTHRWBYQEFDofgUzT/369TOWFVy8kpiYSNu2bZkzZw6bN28m\nMjKS2rVr07NnT/r27Vum7UlNTSUnJ6fIjFLDhg0L1VUQXK/H73//+xIfu7i4OE6ePElISIjRPj8/\nHw8PD1JSUowZ3F8HvJEjR/Luu+/y5z//mfT0dDp16sTQoUOpVatWmWqqWbNmoeeWw+EgKyvrmrbv\nl7PMXl5eRj8FV+m+/PLLxu1utxun00lSUhIA06dP57333mP48OFGiBw4cCCpqalkZmby1ltvGXW6\n3W5cLpfx/C3JL8fU4XBQs2ZNY33F8fPzK1Q/QGZmJgATJkxg3bp1jBkzBrfbbVxcVdxhc5FroRAo\nIgaHw0FoaCgvvvgi27dv549//GORNr179+all16iRYsWNGvWrNQ+77jjDgYPHswHH3zAmTNnSn0T\nLY7FYqFfv37069eP7OxsIiMjmTx5Mu+//z716tXju+++K/Z+devWBa4EgiZNmgBXDnknJiYWCn6/\nDrt+fn7YbDa2bdtW4kUQ7dq1M86BO3r0KG+88QaNGjWiY8eOpW5PzZo1jVmoX54rGR8fT8uWLUus\nqzgOh4Pk5ORCywoO9xb08evHbsqUKWzatAk/Pz/atWvH22+/fdV1/Ppwbo0aNRg5ciQjR47k4sWL\nzJgxg+XLl5cY6q/3Kt5rub+fnx8Wi4XVq1dTp06dYts0btyYyZMnA1fOvxs3bhx16tShW7du2O12\nZs2aVex5jldz/vx541SKrKwsUlNTS1x/aerWrWsclo+Pj2fSpEk4HA7jIi6R66XDwSJSiM1m4/nn\nn2fdunXGjMQv3XXXXSxcuNB48/y1gwcPsnPnTiOIZGZmsn79ejw9PWnRosU11RQTE8PJkydxOp3Y\nbDYcDocRzrp160ZycjJRUVFkZWWRn5/PyZMnSUtLw8/PjwceeIDly5dz6dIlcnJyWLFiBTabrdjD\n3QXatWtH48aNWbBgAT///DMAly9f5sCBA+Tm5pKSksJnn31Geno6AD4+PlSrVq3MV81aLBZ69OhB\nVFQU58+fx+l0snnzZuLj4/nd735XrsemRYsWHD16lLNnz+JyudiyZYtxNXJJj11BuOzRowenTp1i\n+/bt5OTkAFdmTw8ePHjVdX766afEx8fjdrvx8vLCZrNdddt/fTi4vPz8/IiPjy/XdwIGBATQuXNn\nFi5cyIULF4Arz8UjR46QkpKC0+lk165dpKamAlC9enU8PDywWq3YbDZ69+7NihUrOHv2LAA5OTl8\n9913xiHwkqxfv56kpCSys7N55513CAwMpE2bNte03bt27TJmEQue87oyW24kzQSKmFxxsyzdunVj\n48aNbNy4kcGDBxe5/dezI7/so2bNmkRHRxMVFUVGRgZeXl4EBQUxd+7cQjMi+/fv59ChQ8D/HWrt\n3r07r776apH1Xbp0iSVLlnDhwgWsVitNmjRh6tSpwJXz+RYtWkR4eDj9+/cnPz+fu+66y7h94sSJ\nhIeHM2zYMPLy8mjZsiVhYWFXPaRWrVo15s2bR1RUFCNHjiQtLQ0fHx/at29Pp06dgCtXRs+fPx+n\n04mfnx+DBw8u03mBBV5++WWioqJ47bXXyMzMpHHjxsYFF+Xxu9/9ju+//54//elPRnj55fhcGpKT\ncAAAASZJREFU7bGrW7cuS5cuJSIigvXr15OTk0Pt2rXp2rWrcYVqcc+P06dPs3LlStLS0vDy8uLe\ne+9lxIgRJdZ4vTOBvXr14ujRo/zhD38AYPXq1WW63+TJk9m4cSPjxo0jJSUFh8NB69atCQ0NBeCz\nzz5j5cqVZGdn4+vrS48ePejWrRtw5ZD3tm3bmDp1KklJSdjtdpo1a1bo8HJx29mjRw/GjRtHcnIy\nzZs3Z8aMGSXO6Bb3uFgsFmP50aNHWb16NRkZGXh7e9O5c2f69+9fpm0XKQvLvn37ru8jmoiIiIjc\ncnQ4WERERMSEFAJFRERETEghUERERMSEFAJFRERETEghUERERMSEFAJFRERETEghUERERMSEFAJF\nRERETEghUERERMSE/h8Rgs/pA1647gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fc71ab7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot for k=5\n"
     ]
    },
    {
     "data": {
      "image/png": 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REWkghkAiIiIiDcQQSERERKSBGAKJiIiINBBDIBEREZEGYggkIiIi0kA61V0AVS+ZTAaZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fc6fb10b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot for k=10\n"
     ]
    },
    {
     "data": {
      "image/png": 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6L8nNzYWZmRkSEhJgZGT0Rm2xJ5CIiIhIAzEEEhEREWkghkAiIiIiDcQQSERERKSBGAKJ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\nQAqBIiIiIg5IIVBERETEAf0foutCQ2lXsXYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8fe2c00cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "RMSE_per_bin_1 = []\n",
    "print('plot for k=1')\n",
    "for u_bin in unique_bins:\n",
    "    users_per_bin = final_test_data[test_data['bin']==u_bin]\n",
    "    c = (users_per_bin['rating']-users_per_bin['pred_1']) * (users_per_bin['rating']-users_per_bin['pred_1'])\n",
    "    RMSE_score = math.sqrt(sum(c)/len(users_per_bin))\n",
    "    RMSE_per_bin_1.append(RMSE_score)\n",
    "    \n",
    "y_pos = np.arange(len(unique_bins)) \n",
    "\n",
    "plt.barh( y_pos, RMSE_per_bin_1, align='center',alpha=0.5)\n",
    "plt.yticks(y_pos,unique_bins)\n",
    "plt.xlabel('RMSE scores for users in these bins')\n",
    "plt.ylabel('5 Bins based on average rating')\n",
    "plt.title('RMSE per user for k=1')\n",
    "plt.show()\n",
    "\n",
    "RMSE_per_bin_2 = []\n",
    "print('plot for k=2')\n",
    "for u_bin in unique_bins:\n",
    "    users_per_bin = final_test_data[final_test_data['bin']==u_bin]\n",
    "    c = (users_per_bin['rating']-users_per_bin['pred_2']) * (users_per_bin['rating']-users_per_bin['pred_2'])\n",
    "    RMSE_score = math.sqrt(sum(c)/len(users_per_bin))\n",
    "    RMSE_per_bin_2.append(RMSE_score)\n",
    "    \n",
    "plt.barh( y_pos, RMSE_per_bin_2, align='center',alpha=0.5)\n",
    "plt.yticks(y_pos,unique_bins)\n",
    "plt.xlabel('RMSE scores for users in these bins')\n",
    "plt.ylabel('5 Bins based on average rating')\n",
    "plt.title('RMSE per user for k=2')\n",
    "plt.show()\n",
    "\n",
    "RMSE_per_bin_3 = []\n",
    "print('plot for k=3')\n",
    "for u_bin in unique_bins:\n",
    "    users_per_bin = final_test_data[final_test_data['bin']==u_bin]\n",
    "    c = (users_per_bin['rating']-users_per_bin['pred_3']) * (users_per_bin['rating']-users_per_bin['pred_3'])\n",
    "    RMSE_score = math.sqrt(sum(c)/len(users_per_bin))\n",
    "    RMSE_per_bin_3.append(RMSE_score)\n",
    "    \n",
    "plt.barh( y_pos, RMSE_per_bin_3, align='center',alpha=0.5)\n",
    "plt.yticks(y_pos,unique_bins)\n",
    "plt.xlabel('RMSE scores for users in these bins')\n",
    "plt.ylabel('5 Bins based on average rating')\n",
    "plt.title('RMSE per user for k=3')\n",
    "plt.show()\n",
    "\n",
    "RMSE_per_bin_5 = []\n",
    "print('plot for k=5')\n",
    "for u_bin in unique_bins:\n",
    "    users_per_bin = final_test_data[final_test_data['bin']==u_bin]\n",
    "    c = (users_per_bin['rating']-users_per_bin['pred_5']) * (users_per_bin['rating']-users_per_bin['pred_5'])\n",
    "    RMSE_score = math.sqrt(sum(c)/len(users_per_bin))\n",
    "    RMSE_per_bin_5.append(RMSE_score)\n",
    "    \n",
    "plt.barh( y_pos, RMSE_per_bin_5, align='center',alpha=0.5)\n",
    "plt.yticks(y_pos,unique_bins)\n",
    "plt.xlabel('RMSE scores for users in these bins')\n",
    "plt.ylabel('5 Bins based on average rating')\n",
    "plt.title('RMSE per user for k=5')\n",
    "plt.show()\n",
    "\n",
    "RMSE_per_bin_10 = []\n",
    "print('plot for k=10')\n",
    "for u_bin in unique_bins:\n",
    "    users_per_bin = final_test_data[final_test_data['bin']==u_bin]\n",
    "    c = (users_per_bin['rating']-users_per_bin['pred_10']) * (users_per_bin['rating']-users_per_bin['pred_10'])\n",
    "    RMSE_score = math.sqrt(sum(c)/len(users_per_bin))\n",
    "    RMSE_per_bin_10.append(RMSE_score)\n",
    "    \n",
    "plt.barh( y_pos, RMSE_per_bin_10, align='center',alpha=0.5)\n",
    "plt.yticks(y_pos,unique_bins)\n",
    "plt.xlabel('RMSE scores for users in these bins')\n",
    "plt.ylabel('5 Bins based on average rating')\n",
    "plt.title('RMSE per user for k=10')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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