approx_svd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\jyc02\\anaconda3\\envs\\project\\lib\\site-packages\\lightfm\\_lightfm_fast.py:10: UserWarning: LightFM was compiled without OpenMP support. Only a single thread will be used.\n",
      "  \"LightFM was compiled without OpenMP support. \"\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.sparse import csr_matrix\n",
    "from lightfm import LightFM\n",
    "from lightfm.evaluation import auc_score, precision_at_k\n",
    "\n",
    "data = pd.read_csv('preprocessed.csv')\n",
    "sample_size = 150000\n",
    "if len(data) > sample_size:\n",
    "    data = data.sample(n=sample_size, random_state=42)\n",
    "\n",
    "unique_users = data['customer_id'].unique()\n",
    "unique_items = data['product_id'].unique()\n",
    "user_map = {id: idx for idx, id in enumerate(unique_users)}\n",
    "item_map = {id: idx for idx, id in enumerate(unique_items)}\n",
    "data['user_idx'] = data['customer_id'].apply(lambda x: user_map[x])\n",
    "data['item_idx'] = data['product_id'].apply(lambda x: item_map[x])\n",
    "\n",
    "num_users = len(unique_users)\n",
    "num_items = len(unique_items)\n",
    "row = data['user_idx']\n",
    "col = data['item_idx']\n",
    "rating = data['star_rating']\n",
    "input_matrix = csr_matrix((rating, (row, col)), shape=(num_users, num_items))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse.linalg import svds\n",
    "from sklearn.utils.extmath import randomized_svd\n",
    "\n",
    "interaction_matrix = input_matrix\n",
    "interaction_matrix = interaction_matrix.astype(np.float32)\n",
    "\n",
    "k = 20 # number of latent factors\n",
    "u, s, vt = svds(interaction_matrix, k=k)\n",
    "\n",
    "s_diag_matrix = np.diag(s)\n",
    "interaction_matrix_reconstructed = np.dot(np.dot(u, s_diag_matrix), vt)\n",
    "\n",
    "def recommend_items(user_id, interaction_mat, k=10):\n",
    "    user_row = interaction_mat[user_id,:]\n",
    "    item_ids = np.argsort(user_row)[::-1][:k]\n",
    "    return item_ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "Top 5 recommendations for user 41510: [ 234  441  991 1791  141]\n",
      "Top 5 recommendations for user 49685: [ 85  96 501  82 139]\n",
      "Top 5 recommendations for user 131181: [256 141 840 249 234]\n",
      "Top 5 recommendations for user 44214: [  85  266 1459 3085  793]\n",
      "Top 5 recommendations for user 69065: [ 82 501 234 510 141]\n",
      "Top 5 recommendations for user 29971: [ 501  249  141  234 1072]\n",
      "Top 5 recommendations for user 131344: [ 85 249 141  82  96]\n",
      "Top 5 recommendations for user 88826: [ 141  249  234 1037   85]\n",
      "Top 5 recommendations for user 7931: [234 501 836  96 155]\n",
      "Top 5 recommendations for user 37325: [256 141 234 249 840]\n",
      "Top 5 recommendations for user 38212: [ 256  141  592 1037 1010]\n",
      "Top 5 recommendations for user 2649: [ 96  85  82 249 139]\n",
      "Top 5 recommendations for user 88583: [256 141 234 249 836]\n",
      "Top 5 recommendations for user 54191: [ 791  501 1037   85  139]\n",
      "Top 5 recommendations for user 55806: [ 155   85  245  249 1330]\n",
      "Top 5 recommendations for user 19369: [234 592 256 840 141]\n",
      "Top 5 recommendations for user 50442: [ 256  836 1037  510  155]\n",
      "Top 5 recommendations for user 2372: [ 256  836 1037  510  155]\n",
      "Top 5 recommendations for user 76956: [791 256 501 598 836]\n",
      "Top 5 recommendations for user 47041: [ 501  791 1037   85  139]\n",
      "Top 5 recommendations for user 38697: [ 141  435  788 5229  991]\n",
      "Top 5 recommendations for user 21705: [ 256  598  245  249 1330]\n",
      "Top 5 recommendations for user 73827: [ 840 2525  717  984 8272]\n",
      "Top 5 recommendations for user 83837: [791 256 501 598 836]\n",
      "Top 5 recommendations for user 112327: [592 256 234 840  96]\n",
      "Top 5 recommendations for user 2878: [234 592 840  96 256]\n",
      "Top 5 recommendations for user 101377: [840 234  96 256 501]\n",
      "Top 5 recommendations for user 3667: [141 592  82 155 501]\n",
      "Top 5 recommendations for user 125: [1010  840  788  249  141]\n",
      "Top 5 recommendations for user 8235: [ 791  501 1037   85  139]\n",
      "Top 5 recommendations for user 63952: [141 234 840 435 245]\n",
      "Top 5 recommendations for user 84475: [234 501  82 155 510]\n",
      "Top 5 recommendations for user 60140: [791 510 501 249 836]\n",
      "Top 5 recommendations for user 66407: [ 234  501  441 1791  991]\n",
      "Top 5 recommendations for user 9873: [ 592  840 1010   85 1072]\n",
      "Top 5 recommendations for user 57872: [234 592 141 441 435]\n",
      "Top 5 recommendations for user 63700: [ 139 1010   96 4661  182]\n",
      "Top 5 recommendations for user 20129: [234 256 501 249 836]\n",
      "Top 5 recommendations for user 56495: [ 840 2525  245  717  141]\n",
      "Top 5 recommendations for user 26707: [ 85  96 501 139  82]\n",
      "Top 5 recommendations for user 33844: [ 791  501 1037  139   85]\n",
      "Top 5 recommendations for user 45049: [ 141  592 1010  840   85]\n",
      "Top 5 recommendations for user 10763: [ 249  256  840  598 1072]\n",
      "Top 5 recommendations for user 54595: [ 510 3068   15 4980 2719]\n",
      "Top 5 recommendations for user 84609: [ 155  234  592  141 1010]\n",
      "Top 5 recommendations for user 97361: [ 96 249  85 234  82]\n",
      "Top 5 recommendations for user 86880: [256 592 234 840  96]\n",
      "Top 5 recommendations for user 334: [1037  836  510  598  234]\n",
      "Top 5 recommendations for user 47765: [ 791  501 1037   85  139]\n",
      "Top 5 recommendations for user 115279: [592 234 256 840  96]\n",
      "Top 5 recommendations for user 54593: [ 510 3068   15 4980 2719]\n",
      "Top 5 recommendations for user 89118: [256 141 249 245 840]\n",
      "Top 5 recommendations for user 4516: [256 141 234 245 249]\n",
      "Top 5 recommendations for user 5905: [256 155  40  67 127]\n",
      "Top 5 recommendations for user 98181: [234  96 245 141  82]\n",
      "Top 5 recommendations for user 114747: [256 141 249 234 836]\n",
      "Top 5 recommendations for user 104160: [1037   85  141  234  592]\n",
      "Top 5 recommendations for user 10680: [ 840 2525  717  984 1072]\n",
      "Top 5 recommendations for user 92786: [1010  234  245  141  592]\n",
      "Top 5 recommendations for user 41494: [234 510  96 245  82]\n",
      "Top 5 recommendations for user 94103: [ 598  177  185 1946 5767]\n",
      "Top 5 recommendations for user 128917: [ 155 1330 2525   88 2199]\n",
      "Top 5 recommendations for user 2245: [510  82 501 155 141]\n",
      "Top 5 recommendations for user 92932: [ 234  592  141 1037   85]\n",
      "Top 5 recommendations for user 76111: [234  96 592 840 141]\n",
      "Top 5 recommendations for user 1631: [234 592 141 441 435]\n",
      "Top 5 recommendations for user 1113: [234 501 155  96  82]\n",
      "Top 5 recommendations for user 36839: [791 501 836 155 249]\n",
      "Top 5 recommendations for user 130636: [256 141 234 249 836]\n",
      "Top 5 recommendations for user 92935: [ 791 1037  249  510  501]\n",
      "Top 5 recommendations for user 44777: [  85  155  266 1459 3085]\n",
      "Top 5 recommendations for user 128330: [234 256  96 501 155]\n",
      "Top 5 recommendations for user 91719: [ 96 256 234 155 501]\n",
      "Top 5 recommendations for user 23002: [1037   85  141  592  234]\n",
      "Top 5 recommendations for user 124951: [234 592 840 256  96]\n",
      "Top 5 recommendations for user 117775: [ 791   96  141 1010  245]\n",
      "Top 5 recommendations for user 59754: [ 256  592  245  598 1037]\n",
      "Top 5 recommendations for user 5220: [256 141 234 249 840]\n",
      "Top 5 recommendations for user 38284: [ 791  501  836  155 1037]\n",
      "Top 5 recommendations for user 137812: [ 592  141 1010   85  791]\n",
      "Top 5 recommendations for user 101533: [256 141 234 249 245]\n",
      "Top 5 recommendations for user 124341: [234  96 245 141 592]\n",
      "Top 5 recommendations for user 13187: [ 85 592  96  82 141]\n",
      "Top 5 recommendations for user 135966: [ 791  501 1037   85  139]\n",
      "Top 5 recommendations for user 44135: [592 234 256 840  96]\n",
      "Top 5 recommendations for user 5298: [256 141 249 234 840]\n",
      "Top 5 recommendations for user 17770: [510  82 155 791 501]\n",
      "Top 5 recommendations for user 82044: [ 840  256 1010   85  592]\n",
      "Top 5 recommendations for user 108465: [ 85 592  96  82 141]\n",
      "Top 5 recommendations for user 41858: [ 139  141   96 4661 1010]\n",
      "Top 5 recommendations for user 137261: [256 141 234 249 836]\n"
     ]
    }
   ],
   "source": [
    "selected_num_user = 5000\n",
    "rand_selection = np.random.choice(num_users, selected_num_user, replace=False)\n",
    "points = []\n",
    "\n",
    "for user_id in rand_selection:\n",
    "    item_ids = recommend_items(user_id, interaction_matrix_reconstructed, 5)\n",
    "    print(\"Top 5 recommendations for user {}: {}\".format(user_id, item_ids))\n",
    "    points.append(item_ids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dOiAnJ6fJ35NarYa/vz9Gjx6N999/v9nwNW7cOOzZs8cSPMw2btyIgIAAu8KpM9j7vh2RmJgIoK4PTn3vvPOOzViVSmVzeXlmZqZNsz9H/u2MHTsWQF3Iqe/IkSM4ceJEqy7xtldTdbb277CtAgMDMWnSJDz99NOorq7G999/L/kxSHo8I0KS0Ov1eO+99/CHP/wBAwcOtDQ0A+oae61duxZCCNx6662WsyFPPPGEzVw1AJSVleHTTz/F5s2b8ec//9nhWlavXo1JkyZh4sSJmD17Nrp06YKSkhKcOHECR48exfvvvw8AGDZsGKZMmYL+/fujY8eOOHHiBDZt2oQRI0YgICAAQN1p39WrV2P69OlITU1FcXExli1bZtXUqSlxcXEAgDfffBPBwcHQaDTQ6/WNnhoHgIyMDIwfPx6JiYmYP38+1Go13njjDRw/fhzvvvuupN00g4KCsGLFCsyaNQslJSW4/fbbER4ejosXL+Kbb77BxYsXsXLlSgB1l2bfdNNNGDZsGBYsWIDrrrsOv/zyCz766COsXr0awcHBSE9Px44dO5CYmIjnnnsOOp0Ob7/9NjIzM7Fs2bJGL+lWgiPv214TJkzAqFGj8MQTT6C8vBxDhgzB//73P2zatMlm7JQpU7B+/Xr07dsX/fv3x1dffYXly5fbnMno2bMn/P398fbbb6Nfv34ICgpC586dLVNd9fXp0wf33XcfVqxYAS8vL0yaNAl5eXl49tln0a1bN8ybN8+xX5IDmqvT3r/DtkpNTYW/vz9uvPFGREVFobCwEBkZGdBqtZbLi8nFKbxYllxcU5fvNuX06dNi7ty54rrrrhN+fn7C399fxMbGiscee0zk5uaK6upqER4eLgYOHNjkPmpra0XXrl3F7373uybHtHTlyDfffCOmTZsmwsPDha+vr4iMjBRjx44Vq1atsoxZsGCBGDJkiOjYsaPw8/MTPXr0EPPmzROXLl2y2teGDRtEv379hEajEbGxsWLLli12XTUjRN1VG3q9Xnh7ezd5dUF9Bw4cEGPHjhWBgYHC399fDB8+XGzfvt2h916f+SqV999/v9Hn9+3bJ5KTk4VOpxO+vr6iS5cuIjk52WZ8Tk6OuOOOO0RoaKhQq9Wie/fuYvbs2aKystIy5rvvvhMpKSlCq9UKtVotBgwYYPN+m6qnqX9n5itE6l+CCkA89NBDdv1OmjqePe+7sWPXrzU3N9ey7fLly+Luu+8WHTp0EAEBAWL8+PHi5MmTNv8mfv31V3HPPfeI8PBwERAQIG666SZx4MCBRq/Oevfdd0Xfvn2Fr6+v1X4au3zXaDSKl19+WfTu3Vv4+vqKsLAwMX36dMultGajR48W119/vWiosX/PjWl41UxzdQph39+hI5+9udbAwEDL4w0bNojExEQREREh1Gq16Ny5s5g2bZrlSilyfSohhHBu9CEiIiKqwzUiREREpBgGESIiIlIMgwgREREphkGEiIiIFMMgQkRERIphECEiIiLFuHRDM5PJhPz8fAQHB0vazImIiIjkI4RAWVkZOnfuDC+v5s95uHQQyc/Pt7mbJxEREbmH8+fPt3jTTJcOIuZ7EZw/f96ultpERESkvNLSUnTr1s2uewq5dBAxT8eEhIQwiBAREbkZe5ZVcLEqERERKYZBhIiIiBTDIEJERESKYRAhIiIixTCIEBERkWIYRIiIiEgxDCJERESkGAYRIiIiUoxLNzQjovYnt6gcSf/YhyqjgJ+3Crv+PBr68EClyyIihTCIEJHT9FiYCZP47XGVUSDx1c/gpQLOZCQrVxgRKYZTM0TkFA1DSH0mUfc8EXkeBhEikl1uUXmTIcTMJOrGEZFnYRAhItkl/WOfpOOIqP1gECEi2VUZWzgd4uA4Imo/GESISHZ+3i3fCtyRcUTUfjCIEJHsdv15tKTjiKj9YBAhItnpwwPh1cLJDi8V2E+EyAMxiBCRU5zJSG4yjLCPCJHnYkMzInKaMxnJ7KxKRFYYRIjIqfThgfhhyWSlyyAiF8GpGSIiIlIMgwgREREphkGEiIiIFMM1IkREEvrqzK+47c2Dlsf/776RGNyjo4IVEbk2BhEiIonELLC9g7A5lOQt5eXJRI3h1AwRkQQaCyGOPE/kqRhEiIja6Kszv0o6jsiTMIgQEbVR/TUhUowj8iQMIkRERKQYBhEiIiJSDIMIEVEb/b/7Rko6jsiTMIgQEbWRvX1C2E+EyBaDCBGRBFrqE8I+Is6z8/DPiFmQafnZefhnpUuiZqiEEELpIppSWloKrVYLg8GAkJAQpcshImoRO6sqq7l+LQyDzuPI9zeDCBERtQv2NI1jGHEOR76/OTVDRERuz97pF07TuB4GESIicntzt34j6ThyHgYRIiIiUgyDCBERESmGQYSIiNzeG78fIOk4ch4GESIicnuT47tKOo6ch0GEiIjaBTaVc08MIkRE1G7kLU22mX554/cDGEJcmI/SBRAREUlpcnxX5HEKxm3wjAgREREphkGEiIiIFMMgQkRERIphECEiIiLFMIgQERGRYhhEiIiISDEMIkRERKQYBhEiIiJSDIMIERERKYZBhIiIiBTDIEJERESKYRAhIiIixTCIEBERkWIYRIiIiEgxsgaRjIwMDB06FMHBwQgPD8fUqVPxww8/yHlIIiIiciOyBpF9+/bhoYcewqFDh5CVlYXa2lpMmDAB5eXlch6WiIiI3IRKCCGcdbCLFy8iPDwc+/btw6hRo1ocX1paCq1WC4PBgJCQECdUSERERG3lyPe3j5NqAgAYDAYAgE6na/T5qqoqVFVVWR6XlpY6pS4iIiJShtMWqwoh8Nhjj+Gmm25CXFxco2MyMjKg1WotP926dXNWeURERKQAp03NPPTQQ8jMzMTnn3+Orl27NjqmsTMi3bp149QMERG5jKvVRry0Mwd5xRWI1vljfL9IXK6sQXiwBvF6Hby9VEqXqDiXm5p5+OGH8dFHH2H//v1NhhAA8PPzg5+fnzNKIiIicljqxiPIyimyPD4AYPMX5y2Po7QapKfEIikuSoHq3JOsUzNCCKSlpWHr1q3Ys2cP9Hq9nIcjIiKSTcMQ0phCQyUe3HwUu44XOKkq9ydrEHnooYewefNmvPPOOwgODkZhYSEKCwtx9epVOQ9LREQkqavVxhZDCACY1zos3p4Do8lpF6W6NVmDyMqVK2EwGDBmzBhERUVZfrZs2SLnYYmIiCT10s4cu8cKAAWGShzOLZGvoHZE1jUiTmxRQkREJJu84gqHX1NUVilDJe0P7zVDRETUgpjQAIdfEx6skaGS9odBhIiIqAVPTY61e6wKdVfPxOsbb95J1hhEiIiIWuCv9sb42PAWx5k7iKSnxLKfiJ0YRIiIiOywZubQFsNIpFaDldMHsY+IA5x6rxkiIiJ3tmbmUHZWlRiDCBERkQP81d54YervlC6j3eDUDBERESmGZ0SIiIiaUX8qJiY0AE9NjoW/2lvpstoNBhEiIqImzFqbjX0//tYh9cBPwKZD5zA+NhxrZg5VsLL2g1MzREREjej37MdWIaS+rJwipG484uSK2icGESIiogYSXt6DqzWmZsdk5RTharXRSRW1XwwiRERE9RgqanD+V/vuEu/IzfCocQwiRERE9dy9/rDdY1tzMzyyxiBCRERUT77B/rvmtuZmeGSNQYSIiKiezlr775rryM3wqHEMIkRERPWsnR1v17jRvXXsJyIBBhEiIqJ6tAG+iA71b3aMv68XNtw9wkkVtW8MIkRERA3s+8vYJsNIt47+OPHCJCdX1H6xsyoREVEj9v1lLAwVNbh7/WHkGyrRWavB2tnx0Ab4Kl1au8IgQkRE1ARtgC/+39wblS6jXePUDBERESmGQYSIiIgUwyBCREREimEQISIiIsUwiBAREZFiGESIiIhIMQwiREREpBgGESIiIlIMgwgREREphkGEiIiIFMMgQkRERIphECEiIiLF8KZ3RETktl7deQyv7b9gefzIqC54bPJA5QpqgdEkcDi3BEVllQgP1iBer4O3l0rpshSlEkIIpYtoSmlpKbRaLQwGA0JCQpQuh4iIXEjMgswmn8tbmuzESuyz63gBFm/PQYGh0rItSqtBekoskuKiFKxMeo58f3NqhoiI3E5zIcSe551t1/ECPLj5qFUIAYBCQyUe3HwUu44XKFSZ8hhEiIjIrby685ik4+RmNAks3p6DxqYfzNsWb8+B0eSyExSyYhAhIiK3Un9NiBTj5HY4t8TmTEh9AkCBoRKHc0ucV5QLYRAhIiKSUVFZ0yGkvn8fOYfqWpPM1bgeBhEiIiIZdfDztWvctmP56Pvsx8jYmSNzRa6FQYSIiNzKI6O6SDpOblknf7F7rEkAq/fnelQYYRAhIiK3Ym+fEFfpJ5JXXO7wa9YcyPWYaRoGESIicjst9QlxlT4iu44X4PDpYodfZxLApuw86QtyQQwiRETklvKWJttMvzwyqotLhZAHNh9FdSuvyj1bUiFtQS6KLd6JiMhtPTZ5oMtMwdRnNAk8sPlom/YRrQuQqBrXxjMiREREEvvk27Z1SvVSATNGxEhTjItjECEiIpLY/e993abXpyboofbxjK9oTs0QERFJaOiLWa1+rZeqLoQsnBwrYUWujUGEiIhIIiVXqnHxSrXd40MDfTF3zHU4W1KBaF0AZoyI8ZgzIWYMIkRERBL5w+qDDo1/dHwvzBiul6ka98AgQkREJJG8Yscuue2uDcSzH3yHvOIKxIQG4KnJsfBXe8tUnWtiECEiIpJAxs4c1Jjsbxri46XCrA1HLI8P/ARsOnQO42PDsWbmUDlKdEmeNRFFREQkg+paE9YcyHXoNbVNhJasnCKkbjzS6HPtEYMIERFRG23KzoMDJ0NalJVThKvVRul26MIYRIiIiNpIjnbsL3nIHXgZRIiIiNpIjnbsji58dVcMIkRERHbK+bkUPRZkImZBJnosyETOz6UA6tqxe6mkPVZMqGfca4ZXzRAREdkhZkGm1WMTgMmvHwBQdyfg1AQ9Vu93bMFqc57ykO6qPCNCRETUgoYhpLHnF06Oxf2j9DZnRrxUQGKfTg4db3xsuMf0E+EZESIiomaYp1/sGbdwciwen9AXm7LzrNq2f3X2V+z94aJd+2EfESIiIrKYcm36xZ5x1bUmmxCi9vFCvF6HKK2m2dcHqL1xfNFEjwohAKASQkh45bO0SktLodVqYTAYEBISonQ5RETkgVqalqnPSwWrfiL176a763gBHtx8FABQ/4vXPJPzzz8OQsdANYrKKhEerEG8XgdvqVfAOokj39+cmiEiImqGF+oWptqjYVMzk4BlAevCybFYOX0QFm/PQYGh0jImUqvBzQOi8EKm9fYorQbpKbFIiotq4ztwbTwjQkRE1Iycn0stV8e0lpcKOPnCJKh9vGA0CRzOLbGc+fi1vAoPvfM1Gn4Zm8+FrJw+yO3CiCPf37KuEdm/fz9SUlLQuXNnqFQqfPDBB3IejoiISHKxXdv+f4RNoq4NPAB4e6kwomcobhnYBfF6HV7IPGETQoDfpm8Wb8+BUcr+8S5G1iBSXl6OAQMG4PXXX5fzMERERLLKW5rc5n001gb+cG6J1XRMQwJAgaESh3NL2nx8VyXrGpFJkyZh0qRJch6CiIjIKfKWJiPn51JMef0ATKj7f/I70hKQnXsJL2SeaPH1jbWBLyprOoS0Zpw7cqnFqlVVVaiqqrI8Li2179ptIiIiZ4jtGoIzDc6OXBcZhCU7TzR7910vVV0b+IbCg5u/pNfRce7IpfqIZGRkQKvVWn66deumdElERETNUvt4ITVB3+yY1AQ91D62X7nm/iJNXaSrQt3VM/F6XdsLdVEuFUQWLlwIg8Fg+Tl//rzSJRERUTtScqUaE179DAMX78aEVz9DyZVqSfbbXHv3+0fV9RFpyHz1zKS4SAjAJoyYH6enxLptPxF7uNTUjJ+fH/z8/JQug4iI2qGhL2bhYr3gcflqDQa9mIVOQWoceWZ8m/ffVHv3xs6E7DpeYNNPpKFID+kj4lJBhIiISA4NQ0h9F69UY+iLWZKEEbWPF+5J6NHsGHOH1YZLSsyPA9TeuH9UD6SN7dWuz4SYyRpErly5glOnTlke5+bm4tixY9DpdOjevbuchyYiIgJQNx3TVAgxu3ilGiVXqqELUstai9EksHh7TqN9Q8wqqo342yc/oXMHf6zZfxpFZdUID1bjvftGyl6fEmTtrPrZZ58hMTHRZvusWbOwfv36Fl/PzqpERNRWE179DD8Wlbc4rnd4IHY/NkbWWrJPF+OuNYda/XqpppHk5jL3mhkzZgxcuIM8ERF5gKIy+xak2juuLdraD0TKaSRX4VJXzRAREUktPNi+6Qx7x7WFFP1AzNNI7QWDCBERtWvv3TdS0nFtYe4b0lZ3vnlQgmpcA4MIERG1a7ogNTq1sMizU5DaKQtBvb1USE+x7SniqHO/VuC5D4/jrQNnUF1rkqAy5TCIEBFRu3fkmfFNhhFnLQA1mgSyTxejqtaE7h3927SvyhqBjdln8ULmCfR99mNk7MyRqErnYx8RIiLyCEeeGY+SK9W4882DTr8k1p4GZq1lEsDq/bkAYNXBdfeX+bjvP19bHr95+w2YMKSz5MdvK1kv320rXr5LRETurqkGZlJTqYAfXpgEtY8XYhZkNjkur8FN++TgyPc3p2aIiIhkYk8DM6kIAWw4mNdsCAHQ4vPOxiBCREQkk8O5Ja2ajhkfG46jz4xH7/BABPja3+Z9+7Fzdo3b/WW+wzXJhWtEiIiIZGJvA7ObrguFSqVCTGgAnpocC3+1NwBg92Nj8Oh7X+ODY/YFh2/zW+4gCwD3/edr5LnIehEGESIiIpnY28DsocReGNEztNHnKqqNUpbkcjg1Q0REJBNzA7OmJldUAKK0GsTrdU3uY2hM08/V5+umd+plECEiIpJJ/QZmDWOC+XF6Siy8mwkRs0bGQGVHxvjbtAF48/Yb7KrL3nHOwCBCREQko6S4KKycPgiRDVq7R2o1WDl9EJLiopp9/Z6Tv8Df17vZMeNjwzFlYBe7+4S4Uj8R9hEhIiJyAqNJ4HBuCYrKKhEeXDcdc6WyFnevP4x8QyU6azVYOzse2gBfy2ta6kGiAnBvgh5PJ1u3jXenPiIMIkRERAoYvXwPzhZftdkeHeqPfX8ZC6NJ4Male1BY2vSVNxHBahxc+H/w9lKhutaETdl5OFtSgWhdAKL81Ji79RvLWGd2VnXk+5tXzRARETlZUyEEAM4WX8Xo5XswdWCXZkMIAPxSVo3DuSX47IdfsOZALkz1Ti14qYD7R+mt2r67IgYRIiIiJzJU1DQZQszOFl/FPz49Zdf+/nXgND49edFmu/keNPmXr+L/YiMt00HNLYxVAoMIERGRE929/rCk+2sshNS3/dtCbP+2EEDdpcLpKbEtLpB1Jl41Q0RE5ET5MtyB114Fhko8sPkoPjp6QbEaGmIQISIicqLOWvu6rcrpkX8fw70bjihdBgAGESIiIqdaOzte6RIAAJ+cKELqRuXDCIMIERGRE2kDfNG9o/JnRQAgK6cIVxW+lw2DCBERkZPNGqlXugSL+zd9qejxGUSIiIgkZDQJZJ8uxofHLiD7dDGMJtu+oWdLKhSorHH7f7qEXccLFDs+L98lIiKSyK7jBVi8PQcF9a6MaeyS2R9/KVOivCY9uPkoTr00WZEeIzwjQkREJAHzfWEKGlyeW2ioxIObj1rOOmTszMGhMyVKlNgkASDreKEix2YQISIij2PP9Imj+1u8PafRm9OZty3enoOr1UasOZDbpmOFBflCjhMXCz/4Tvqd2oFTM0RE5FHsnT5xxOHcEpszIfUJ1DUTe2lnDtqSefp3DcFHaQlWN7jLyTfgy7OXW7/Tayqqatu8j9bgGREiIvIY9k6fOKqozL5uqWcuXrFrnL+P9dez2luFZbfGYUDXDpjx1hd4Ycf3+OOwaDx/SxwmSdSuPSxILcl+HMUzIkRE5BFamj5RoW76ZHxspMOLNsOD7esL8r/T9q0NuVprsnpcbRR4Yttxy+MDPwGbDp3D+NhwvHbnILyYeaLR9+WIR8b1aeMeWodnRIiIyCPYO31yONfxhaTxeh2itBo4+5qTrJwi9F+0q80hBACez/y+zWtlWoNBhIiIPIK90yf2jqvP20uF9JRYAHB6GKkxtTzGHuVVRjz63lFpduYABhEiIvII9k6f2DuuoaS4KKycPgiRDW5qp/F1n6/aHd8WorpWomRjJ64RISIij2CePik0VDY6laECEKnVIF6va/UxkuKiMD42EodzS1BUVom8SxX42yc/tnp/ziYAbMrOwz0JPZx2TPeJaURERG3Q3PSJ+XF6Smybu4t6e6kwomcopvTvjPeOnGvTvpTg7PbzDCJEROQxmpo+idRqsHL6oFb3EWlMS4tjXVW0LsCpx+PUDBEReZSG0yfhwXXTMVLfZ6U1i15dwcHTl5w6NcMgQkREHsc8fSKn1i56VdqnJy/iarUR/mpvpxyPUzNEREQyUKq3iBRe2pnjtGMxiBAREclAyd4ibZVX7LwFqwwiREREjaiuNeGtA2fw3IfH8daBM63qr9HU4lhX113n77RjcY0IERFRAxk7c7DmQK7VnXKX7DyB1AQ9Fk6OdWhf5sWx01YfxFcS3CXXGSbERjrtWAwiRERE9WTszMHq/bk2200Clu2OhpEHNn/pNiEEAC5frXHasTg1Q0REdE11rQlrDtiGkPrWHMh1aJrmarURWTlFbS3NqZx5xQ+DCBER0TWbsvPQ0g1oTaJunL2ceQWKVNrS5t5RDCJERETX2Nve3JE26M68AkUqUjd3aw7XiBAREV1jb3vzaF0ANn72I57b9ZNl2/NJvTBzTG+bsTGhATjwk81mukYlhGjhJJRySktLodVqYTAYEBISonQ5RETUzlXXmtD32Y+bnZ7xUqHZ5/OWJls9vlptRL/ndklUofxev7U/pgzr1qZ9OPL9zakZIiKia9Q+XkhN0Dc7pqU1JDELMq0e+6u9MT42vK2lOU1bQ4ijGESIiIjqWTg5FveP0qPhMgkvFTBUb9/UzcbPfrR6vGbmULcKI87EqRkiIvJoF0quYtJr+1BeZUSgnzc+fmQ0uuj8UV1rwqbsPJwtqUC0LgAzRsSg9zMf273fhlM0AGCoqMGA53dLWb7kGqvbUY58f3OxKhEReazeT+9EtfG3/z9eWmnEjcv2QO2two9LJuOehB6SHu8/X52XdH9S6+68zu4WnJohIiKP1DCE1FdtFOj99E7JjmU0CWSfLsZnP16UbJ9ymDW2n9OPyTMiRETkcS6UXG0yhJhVGwUulFxFl3o3gHs+qZfVJbtNeT6pl+V/7zpegMXbc1BgqGx9wU4yY0SM04/JMyJERORxJr22r1XjGusT0hjzuF3HC/Dg5qNuEULuH6WH2sf5sYBBhIiIPE55lbHV41pazGl+3mgSWLw9By57RUgDjt7ITyoMIkRE5HEC/bzbNC5vabLV9AtQNx1TP6Qczi1xizMhAOC8hu62uEaEiIg8zsePjMaNy/bYNa4pM8f0bnaqpqjMvhASGuCL4ooau8bKRcmzNjwjQkREHqeLzh9q7+bPA6i9VVYLVR0VHqyxa5zSIQQA/Fr4XciJQYSIiDzSj0smNxlGzH1E2iJer0OUVqPotIe9dv256TM/cmMQISIij/Xjksn43xNjEaLxhrcKCNF4439PjG1zCAEAby8V0lPqFoA2DCOuFk704YGKHZst3omIiGTUWB+RKK0GHfx9caKwTMHK6nzz3ARoA3wl3SdbvBMRUbtgNAkczi1BUVklwoM1iNfr4N3wbnQuLikuCuNjI23ex6KPjiseREL8vCUPIY5yShB54403sHz5chQUFOD666/H3//+dyQkJDjj0ERE5KaaOpOQnhKLpLgoBStznLeXCiN6hlpte2pyLDYdOqdQRXW+fHaCoscHnLBGZMuWLXj00Ufx9NNP4+uvv0ZCQgImTZqEc+eU/eUTEZHraqojaaGhEg9uPopdxwsUqkw6/mpvjI8NV+z4M0Z0VaSTakOyrxEZNmwYBg0ahJUrV1q29evXD1OnTkVGRkazr+UaESIiz2M0Cdz08p4mm4GpAERqNfj8ybEuN03Tmqmk1I1HkJVT5KQKf3Pi+ST4q+1r7OYol1kjUl1dja+++goLFiyw2j5hwgQcPHjQZnxVVRWqqqosj0tLS+Usj4iIXFBLHUkFgAJDJQ7nlthMdyipsamkDv6+mHNjDNLG9mo0kOQWlWP/D7/dkbeDnxcuV5mcUu9LO3PwwtTfOeVYzZE1iFy6dAlGoxERERFW2yMiIlBYWGgzPiMjA4sXL5azJCIicnH2diS1d5zcDp68hD+u/6LR5y5frcHfPvkJ6w7mYenvf2e1tqXHwkyYGsxJOCuEAEBecYXTjtUcp0wOqVTWKVAIYbMNABYuXAiDwWD5OX/+vDPKIyIiF2JvR1J7x8kpZkFmkyGkvssVNVZrWxoLIc4WExqgbAHXyHpGJCwsDN7e3jZnP4qKimzOkgCAn58f/Pz85CyJiIhcnLkjaaGhstF7oJjXiMTrdc4uzUrMgkyHxgsAi7fn4LqwYMVDCFB31Y4rkPWMiFqtxuDBg5GVlWW1PSsrCyNHjpTz0ERE5Kbs6UianhKr6ELVgycvtep1BYZKTHptn8TVOG58bLhsC1UdJfvUzGOPPYZ//etfWLt2LU6cOIF58+bh3LlzeOCBB+Q+NBERuamkuCisnD4IkVrr6ZdIrQYrpw9SvI+IPdMxTalx3jKQRnXtoMGamUOVLaIe2Rua/eEPf0BxcTGef/55FBQUIC4uDjt37kR0dLTchyYiIjfWVEdSV7tk193oOwUpXYIVp3RWnTt3LubOneuMQxERUTvSWEdSahtXWaRqpnxLNSIiIjfzzuxhSpfQaq6ySNWMQYSIiMhBI/uGKV1Cq/h5q1xmkaoZgwgREVEr5C1NVroEh8V10Spdgg0GESIiolbKW5rsVtM0a2fHK12CDQYRIiKiNhjZNwyrbhto19hAp1wi0rjoUH9oA3yVK6AJDCJERERtlDS0i13jvn8xGZ2C1DJXY0urBvb9ZazTj2sPBhEiIiIJtLRmJKFXGJ794Dvsf2Isjj4zHr3DA9HB3xe9wwNlr23GjT1lP0ZrKXiSiIiIqH3JW5qMXUcu4IH/d8zmuQM/XcKBn4BNh85hfGw4dj82BgBgNAn0fGqnzJW5bhM4nhEhIiKSUNLQLshbmozxseFNjsnKKULqxiMAgNf3nJK9JlduCsczIkRERBK7Wm1EVk5Rs2Oycorwyn9P4vW9p2WtJUDtjeE9XDeI8IwIERGRxF7amWPXOLlDCADcP6qnS9+fh0GEiIhIYl+e/VXpEgAA3iogbex1SpfRLAYRIiIiCRlNAmeLK5QuAwDwx2HdXfpsCMAgQkREJKnDuSWoqDYqXQYAYPLvOitdQou4WJWIiKiN3tl/Ck/t/EHpMmzE63VKl9AiBhEiIqI2iFmQqXQJTXL1aRmAUzNERESt5soh5G+3D1C6BLswiBAREbXCO/vlb0TWFjcPsu/+N0pjECEiImoFV1wTYrZq+iC3mJYBGESIiIjalV5hfkiKi1K6DLsxiBAREbUj+nCt0iU4hEGEiIioFV6a3EfpEho1qFtHpUtwCIMIERFRK/xxlGu2Tle5ydoQMwYRIiKiVvjP/3KVLqFRFy5fVboEhzCIEBERtcL87fbdYdfZonUBSpfgEAYRIiKidsJLBcwYEaN0GQ5hECEiImonUhP0UPu411e7e1VLRETkIl5JiVW6BCupCTFYONm1arIHgwgREVEr3H6jXukSLGaNiMbTydcrXUarMIgQERG1Ut7SZKVLAAC36qTaEIMIERFRG+QtTVZ0mqZToA/i9TrFjt9WPkoXQERE5O5uv1GP22/Uw2gSuOnlPSg0VEI46dgv3NrfbW5w1xieESEiIpKIt5cK6dfOjjgjGqyaPsitp2UABhEiIiJJJcVFYeX0QYjUamQ9jr+vl9uHEIBTM0RERJJLiovC+NhIHM4tQVFZJQ6fKcbbh89LeozQQLWk+1MKgwgREZEMvL1UGNEzFACwKTtP8v1vm3uT5PtUAoMIERF5pFd3HsNr+y9YHj8yqgsemzywVfuqrjVhU3YezpZUIFoXgBkjYqw6nB6/YGhruVZCND7oFOIn6T6VohJCOGthr8NKS0uh1WphMBgQEhKidDlERNROxCzIbPI5R3uDZOzMwZoDuTDV+zb1UtW1W184ORZXKmsRt+i/rS3VRojGB98umijZ/uTgyPc3z4gQEZFHaS6EmJ+3N4xk7MzB6v25NttNApbtZy6WO15kEw4tGIfIDvIugnU2XjVDREQe49WdxyQbV11rwpoDtiGkvjUHcvHZySK7jtmSDgG+7WY6pj6PDCI5P5eix4JMxCzIRI8Fmcj5uVTpkoiIyAnqrwlp67hN2XlW0zGNMQmgRqIFEJcranA4t0SanbkQj5uaaXhKzgRg8usHALjOPQOIiMj1nS2pcPoxi8oqnX5MuXnUGRF75gWJiIjsEa0LcPoxw4Pb1/oQwIOCiL3TL5ymISJqvx4Z1UWycTNGxMBZt3hRAYjSatz65nZN8ZggMuXa9ItU44iIyP3Y2yfEnnFqHy+kJujbVpAdzFknPSXWrW9u1xSPCSImiccREZF7amk9oCPrBRdOjsX9o/SynhmJ1Gqwsh3c3K4pHhNE7H2jHvMLISLyYHlLk22mXx4Z1aVVFy0snByLky9Mkqo0K6v+OAifPzm23YYQwIM6q+b8XGq5OqY5O9MSENuVXVyJiMgxclzw0LWDBp8vGCf5fuXmyPe3x5wAsDdcMIQQEZGjMnbmyLLfkvIaWfbrSjwmiADSzgsSEREBdR1W32yhw2pr6QJ9ZdmvK/G4hmZ5S5OR83Mpprx+ACbUJbEdnI4hIqJWemrrt5BrkcO2uTfJs2MX4nFBBKibfjnDsx9ERNRGRpNA5ncFsuzb1wvt8t4yDXlkECEiIrKH0SRwOLcERWWVCA+uayjm7aWybN+YnYerNfI0fmiPzcsawyBCRETUiF3HC7B4ew4KDL/d3yVKq8HNA6Lw0TcFVtvlUClTwHE1DCJEREQN7DpegAc3H0XDpR8Fhkqs3i/PwtSGekcGO+U4SvOoq2aIiIhaYjQJLN6eYxNCnO26TkEKV+AcDCJERET1HM4tkX3apSVeqrqb6nkCBhEiIqJ6isqUDSEAkJqgh9rHM76iPeNdEhER2Sk8WKPo8e8fpcfCybGK1uBMDCJERET1xOt1iNJqIOMNdZv0f306eVQIARhEiIiIrHh7qZCeUhcGnB1Gziu8NkUJDCJEREQNJMVFYeX0QYjUWk/TRGk1uH+UHlFaeaZvunf0l2W/rkwlhFwd8tvOkdsIExERSa2lzqpFZZX483vHJDve8UUTEaRx/xZfjnx/u/+7JSIikom3lwojeoY2u12qINK/a0i7CCGOknVqZsmSJRg5ciQCAgLQoUMHOQ9FRETkdBk7cyTZT/+uIfgoLUGSfbkbWaNXdXU17rjjDowYMQJvvfWWnIciIiJyqupaE9YccLzd+99v74/M7wtx7ter6N7RH3/7ww0eeSbETNZ3vnjxYgDA+vXr7RpfVVWFqqoqy+PS0lI5yiIiImqzTdl5MDm4ylIF4OWsH/H5k2Ph7aXEBcKux6WumsnIyIBWq7X8dOvWTemSiIiIGnW2pMLh1wjU3TjvcG6J9AW5KZcKIgsXLoTBYLD8nD9/XumSiIiIGhWtC2j1a12hjbyrcDiILFq0CCqVqtmfL7/8slXF+Pn5ISQkxOqHiIjIFc0YEdPqhmdKt5F3JQ6vEUlLS8Odd97Z7JiYmJjW1kNEROTSrlYb8dLOHOQVV6B7R3+c/fWqQ6/XBfoiXq+TqTr343AQCQsLQ1hYmBy1EBERubTUjUeQlVPUpn2M6tmRC1XrkXWNyLlz53Ds2DGcO3cORqMRx44dw7Fjx3DlyhU5D0tERCS5ezccbnMIAYAPv237PtoTWS/ffe6557BhwwbL4xtuuAEAsHfvXowZM0bOQxMREUnmw2MX8MmJi5LsSwDIPl1s0zbeU/FeM0RERM3YdbwAD2w+Ktv+o7QapKfEIikuSrZjOJsj398udfkuERGRKzGaBBZvl6aNe1MKDZV4cPNR7DpeIOtxXBWDCBERURMO55agwCBvzw/ztMTi7TkwOtqqtR1gECEiImqCsxqPeXLHVQYRIiKiJji78ZgndlxlECEiImpCvF6HKK2m1R1UHeWJHVcZRIiIiJrg7aVCekosAMgaRlSou3rGEzuuMogQERE1IykuCiunD0LHQLUs+zcHnPSUWI/sJ8IgQkRE1IKkuCg8m9xPln1HajVYOX1Qu+oj4ghZO6sSERG1F3m/lEm6v7/eMQCdO/h7fGdVBhEiIiI7/GPfGbvHhmh8UFpZ2+Tz94/S47bBXaUoy+1xaoaIiEhifj7Nf73u+r7QSZW4PgYRIiIiiV28Ut3s82eLr8JQUeOkalwbgwgREZEdVt02UNL93b3+sKT7c1cMIkRERHZIGtpF0v3ly3wPG3fBIEJERGSHnd9Ke3fczlrP66LaGAYRIiKiFhhNAs98eFzSfa6dHS/p/twVL98lIiKX80N+GSav2A+jALxVwM6HR6FP52DF6jmcW4KS8uYXoDoiWucPbYCvZPtzZwwiRETkUmIWZFo9Ngpg4mv7AQB5S5OVKEnSu+J2ClJj3xNjJdufu+PUDBERuYyGIcTR5+Ui1V1xl9/WH0eeGS/JvtoLBhEiInIJP+Tb10Ld3nFS+rW8us13331t2gDcMbSbJPW0JwwiRETkEiav2C/pOKnsOl6Ah945CtGGfYyPDcfNg9jSvTFcI0JERC7BaOc3vb3jpGA0CSzentOmEHL3yBg8d/P1ktXU3vCMCBERuQRvO+c+7B0nhcO5JShoY+OxLh39JaqmfWIQISIil7Dz4VGSjpOCFFfLnC2pkKCS9otBhIiIXIK9fUKc2U9EiqtlonUBElTSfjGIEBGRy2ipT4iz+4jE63WI0mpafcWMlwqYMSJGypLaHQYRIiJyKXlLk/HfR0ZZ1oJ4q4D/PjJKkWZm3l4qpKfEAoBNGLEnnKQm6KH24Vdtc3jVDBERuZw+nYNxOkOZLqpm1bUm/Gv/abxz+ByCNd6oqhWoqjVZno/UapCeEouvz/2KNQdyYap3aY2Xqi6ELJwcq0Dl7kUlhHDihVCOKS0thVarhcFgQEhIiNLlEBGRh8jYmYPV+3Mbfa6bzh/LbhuAeL0O3l5150Wqa03YlJ2HsyUViNYFYMaIGI8+E+LI9zeDCBERUT3NhRCz/l1D8FFagpMqcj+OfH97blwjIiJqoLrWhDdbCCEA8O3PpbhSWeuEito/BhEiIqJrNmXn2d1F9dEtX8tai6dgECEiIrrGkeZjPxQ6/+Z77RGDCBER0TWONB/T+vvKWInnYBAhIiK6xpHmY4//X2/5CvEgDCJERETXqH28kJqgb3Gcj5cKo/qGO6Gi9o9BhIiIqJ6nk2MxPrb5kPH6H2+w9BChtmEQISIiamDNzKF4/c6BCPCxDhvhQb5YNX0QkuKiFKqs/WGLdyIiokZMGdgFQ2JCMWXFfpRW1iJE44OP0kYhskPb78hLv2EQISIiakT/Rf9Fab2mZZfKazB86acI0fjg20UTFaysfeHUDBERUQMNQ0h9pZW16L/ov06uqP3iGREiIvIYr2R+jdcP5FsepyV0xvzkG6zGXCytajKEmJVW1uJiaRU6hfjJUqcn4RkRIiLyCDELMq1CCAC8fiAfMQsyrbbd+sbndu3P3nHUPAYRIiJq9xqGjeaeLymvsWuf9o6j5jGIEBFRu/ZKpn03pzOP0wXa17rd3nHUPAYRIiJq1xpOx7Q0btvcm+wab+84ah6DCBERUT2dQvwQomn+Wo4QjQ8XqkqEQYSIiKgeo0lg9Ywh0Pg2/hXJPiLS4uW7RETUrqUldLZreiYtoTN2HS/A4u05KDBUWrZ7qepuchce7Idtc2/imRCJ8YwIERG1aw37hDQlLjoSD24+ahVCAMAkgGqjQLDGF6/t+RFXq41ylOmxGESIiKjdy1ua3Ozzp1+ajMXbcyCaGXOisAybDp1Dv+d2IXXjEWkL9GAMIkRE5BHyliYjLaGz1ba0hM7IW5qMw7klNmdCmpOVU8QwIhGuESEiIo8xP/mGRqdqisrsDyFmWTlFuFpthL/aW4rSPBbPiBARkccLD9a06nUv7cyRuBLPwyBCREQeL16vQ5RWA5WDr8srrpClHk/CIEJERB7P20uF9JTYZherNiYmNECWejwJgwgRERGApLgo3D6oi0OveWpyrEzVeA4GESIiomsC/Oy/hmN8bDgXqkqAQYSIiOiaaJ19Uy29I4KwZuZQmavxDAwiRERE18wYEQOvFlasqgDseDjBKfV4AgYRIiKia9Q+XkhN0Dc75r5Reqh9+PUpFTY0IyIiqmfhtQWoaw7kwlTvMhovFZCaoLc8T9JQCSEcvVrJaUpLS6HVamEwGBASEqJ0OURE5EGqa03YlJ2HsyUViNYFYMaIGJ4JsZMj39+y/Ubz8vJwzz33QK/Xw9/fHz179kR6ejqqq6vlOiQREZFk1D5euCehB56/JQ73JPRgCJGJbFMzJ0+ehMlkwurVq3Hdddfh+PHjSE1NRXl5OV555RW5DktERERuxKlTM8uXL8fKlStx5swZu8ZzaoaIiMj9OPL97dTFqgaDATqdrsnnq6qqUFVVZXlcWlrqjLKIiIhIIU6b8Dp9+jRWrFiBBx54oMkxGRkZ0Gq1lp9u3bo5qzwiIiJSgMNBZNGiRVCpVM3+fPnll1avyc/PR1JSEu644w7ce++9Te574cKFMBgMlp/z5887/o6IiIjIbTi8RuTSpUu4dOlSs2NiYmKg0WgA1IWQxMREDBs2DOvXr4eXl/3Zh2tEiIiI3I+sa0TCwsIQFhZm19gLFy4gMTERgwcPxrp16xwKIURERNT+ybZYNT8/H2PGjEH37t3xyiuv4OLFi5bnIiMj5TosERERuRHZgsju3btx6tQpnDp1Cl27drV6zoWbuRIREZETuXSLd4PBgA4dOuD8+fNcI0JEROQmSktL0a1bN1y+fBlarbbZsS5907uysjIA4GW8REREbqisrKzFIOLSZ0RMJhPy8/MRHBwMlUqldDmNMqc+nrVxPfxsXBc/G9fFz8Z1udNnI4RAWVkZOnfu3OKFKi59RsTLy8tmfYmrCgkJcfl/GJ6Kn43r4mfjuvjZuC53+WxaOhNixutpiYiISDEMIkRERKQYBpE28vPzQ3p6Ovz8/JQuhRrgZ+O6+Nm4Ln42rqu9fjYuvViViIiI2jeeESEiIiLFMIgQERGRYhhEiIiISDEMIkRERKQYBhEiIiJSDINIK+Xl5eGee+6BXq+Hv78/evbsifT0dFRXV1uNO3fuHFJSUhAYGIiwsDA88sgjNmNIekuWLMHIkSMREBCADh06NDpGpVLZ/Kxatcq5hXogez4b/t24hpiYGJu/kQULFihdlkd64403oNfrodFoMHjwYBw4cEDpkiTj0i3eXdnJkydhMpmwevVqXHfddTh+/DhSU1NRXl6OV155BQBgNBqRnJyMTp064fPPP0dxcTFmzZoFIQRWrFih8Dto36qrq3HHHXdgxIgReOutt5oct27dOiQlJVke29uSmFqvpc+Gfzeu5fnnn0dqaqrlcVBQkILVeKYtW7bg0UcfxRtvvIEbb7wRq1evxqRJk5CTk4Pu3bsrXV7bCZLMsmXLhF6vtzzeuXOn8PLyEhcuXLBse/fdd4Wfn58wGAxKlOhx1q1bJ7RabaPPARDbtm1zaj30m6Y+G/7duI7o6Gjxt7/9TekyPF58fLx44IEHrLb17dtXLFiwQKGKpMWpGQkZDAbodDrL4+zsbMTFxaFz586WbRMnTkRVVRW++uorJUqkBtLS0hAWFoahQ4di1apVMJlMSpfk8fh341pefvllhIaGYuDAgViyZAmnyJysuroaX331FSZMmGC1fcKECTh48KBCVUmLUzMSOX36NFasWIG//vWvlm2FhYWIiIiwGtexY0eo1WoUFhY6u0Rq4IUXXsC4cePg7++PTz/9FI8//jguXbqEZ555RunSPBr/blzHn//8ZwwaNAgdO3bE4cOHsXDhQuTm5uJf//qX0qV5jEuXLsFoNNr8TURERLSbvweeEWlg0aJFjS5irP/z5ZdfWr0mPz8fSUlJuOOOO3DvvfdaPadSqWyOIYRodDs1rzWfTXOeeeYZjBgxAgMHDsTjjz+O559/HsuXL5fxHbRfUn82/LuRjyOf1bx58zB69Gj0798f9957L1atWoW33noLxcXFCr8Lz9Pw3357+nvgGZEG0tLScOeddzY7JiYmxvK/8/PzkZiYiBEjRuDNN9+0GhcZGYkvvvjCatuvv/6Kmpoam3RLLXP0s3HU8OHDUVpail9++YWfj4Ok/Gz4dyOvtnxWw4cPBwCcOnUKoaGhUpdGjQgLC4O3t7fN2Y+ioqJ28/fAINJAWFgYwsLC7Bp74cIFJCYmYvDgwVi3bh28vKxPMI0YMQJLlixBQUEBoqKiAAC7d++Gn58fBg8eLHnt7Z0jn01rfP3119BoNE1eUkpNk/Kz4d+NvNryWX399dcAYPlcSH5qtRqDBw9GVlYWbr31Vsv2rKws3HLLLQpWJh0GkVbKz8/HmDFj0L17d7zyyiu4ePGi5bnIyEgAdYuJYmNjMWPGDCxfvhwlJSWYP38+UlNTERISolTpHuHcuXMoKSnBuXPnYDQacezYMQDAddddh6CgIGzfvh2FhYUYMWIE/P39sXfvXjz99NO477772t0ttl1NS58N/25cQ3Z2Ng4dOoTExERotVocOXIE8+bNw80339w+Lhl1I4899hhmzJiBIUOGWM6+nzt3Dg888IDSpUlD4at23Na6desEgEZ/6jt79qxITk4W/v7+QqfTibS0NFFZWalQ1Z5j1qxZjX42e/fuFUII8fHHH4uBAweKoKAgERAQIOLi4sTf//53UVNTo2zhHqClz0YI/t24gq+++koMGzZMaLVaodFoRJ8+fUR6erooLy9XujSP9M9//lNER0cLtVotBg0aJPbt26d0SZJRCSGE8+MPEREREa+aISIiIgUxiBAREZFiGESIiIhIMQwiREREpBgGESIiIlIMgwgREREphkGEiIiIFMMgQkRERIphECEiIiLFMIgQERGRYhhEiIiISDH/H1WmAAR2n9E0AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PCA\n",
    "X = np.array(points)\n",
    "X = (X - np.mean(X, axis=0)) / np.std(X, axis=0)\n",
    "cov = np.cov(X.T)\n",
    "eigenvalues, eigenvectors = np.linalg.eig(cov)\n",
    "k = 2\n",
    "top_k_eigenvectors = eigenvectors[:, :k]\n",
    "X_new = np.dot(X, top_k_eigenvectors)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(X_new[:, 0], X_new[:, 1])\n",
    "plt.title(\"PCA result of recommendation items\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "project",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.16"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}