Apriori Algorithm for Recommender System.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 1 - Apriori Algorithm for Recommender System (33 points)\n",
    "\n",
    "**Task Definition:** In this programming assignment, you are required to implement the Apriori algorithm and apply it to mine frequent itemsets for recommendation. You are required to implement the algorithm from scratch by using only native Python libraries and NumPy. For efficiency you will need to convert the items to ids and sort them.\n",
    "\n",
    "**Input:** The provided input file (`video_games.txt`) contains the favourite video games of 4096 users. Each line in the file corresponds to a user and represents a list of video games the user likes. An example:\n",
    "\n",
    "*Torchlight 2;Transistor*\n",
    "\n",
    "In the example above, the corresponding user likes the video games \"Torchlight 2\" and \"Transistor\".\n",
    "\n",
    "**Output:** You need to implement the Apriori algorithm and use it to mine frequent itemsets. Set the relative minimum support to 0.055 and run the algorithm on the 4096 lists of video games. In other words, you need to extract all the itemsets that have an absolute support larger or equal to 226."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: uncomment the packages you used, please do not import additional non-native packages\n",
    "# You may change the imports to the following format: from [package] import [class, method, etc.]\n",
    "\n",
    "import collections\n",
    "import itertools\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Loading the data and preprocessing (3 points)\n",
    "**Task:** Solve the tasks explained in the TODOs and comments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Greedfall', 'Code Vein', 'Path Of Exile', 'The Outer Worlds', 'Bastion', 'Hades', 'The Outer Worlds', \"Assassin's Creed Origins\", 'Legend of Grimrock 2', 'Darkest Dungeon', 'Pillars of Eternity', 'Persona 5 Strikers', 'Transistor']\n"
     ]
    }
   ],
   "source": [
    "# TODO: read the data from the input file /data/video_games.txt (1 points)\n",
    "\n",
    "dtypes = [('favorite_games', object)] #defining the data type for the favorite games column\n",
    "rows = [] #an empty list to store the rows\n",
    "\n",
    "with open('video_games.txt', 'r') as file:\n",
    "    for line in file:\n",
    "        games = line.strip().split(';')\n",
    "        rows.append((games,))\n",
    "\n",
    "data = np.array(rows, dtype=dtypes)\n",
    "first_user_games = data[0]['favorite_games']\n",
    "print(first_user_games)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Item-to-ID Dictionary:\n",
      "{\"Assassin's Creed Origins\": 0, 'Bastion': 1, 'Bloodborne': 2, 'Chrono Trigger': 3, 'Code Vein': 4, 'Crosscode': 5, 'Cyberpunk 2077': 6, 'Dark Souls 3': 7, 'Darkest Dungeon': 8, 'Diablo III': 9, 'Dragon Age: Inquisition': 10, 'Dragon Age: Origins': 11, 'Dragons Dogma: Dark Arisen': 12, 'Dying Light 2 Stay Human': 13, 'Elden Ring': 14, 'Fable II': 15, 'Fallout 4': 16, 'Fallout New Vegas': 17, 'Fire Emblem: Three Houses': 18, 'Genshin Impact': 19, 'Greedfall': 20, 'Grim Dawn': 21, 'Hades': 22, 'Hogwarts Legacy': 23, 'Horizon Zero Dawn': 24, 'Kingdom Come: Deliverance': 25, 'Kingdom Hearts 3': 26, 'Legend of Grimrock 2': 27, 'Mass Effect Legendary Edition': 28, 'Middle-Earth: Shadow of War': 29, 'NieR: Automata': 30, 'Path Of Exile': 31, 'Persona 5 Strikers': 32, 'Pillars of Eternity': 33, 'Scarlet Nexus': 34, 'Soulstice': 35, 'Stardew Valley': 36, 'Tales of Arise': 37, 'Tales of Berseria': 38, 'The Last Oricru': 39, 'The Legend of Zelda: Breath of the Wild': 40, 'The Outer Worlds': 41, 'The Witcher 3: Wild Hunt': 42, 'Torchlight 2': 43, 'Transistor': 44, 'Undertale': 45, 'Weird West': 46, 'Wolcen': 47, 'Yakuza Kiwami': 48}\n",
      "\n",
      "ID-to-Item Dictionary:\n",
      "{0: \"Assassin's Creed Origins\", 1: 'Bastion', 2: 'Bloodborne', 3: 'Chrono Trigger', 4: 'Code Vein', 5: 'Crosscode', 6: 'Cyberpunk 2077', 7: 'Dark Souls 3', 8: 'Darkest Dungeon', 9: 'Diablo III', 10: 'Dragon Age: Inquisition', 11: 'Dragon Age: Origins', 12: 'Dragons Dogma: Dark Arisen', 13: 'Dying Light 2 Stay Human', 14: 'Elden Ring', 15: 'Fable II', 16: 'Fallout 4', 17: 'Fallout New Vegas', 18: 'Fire Emblem: Three Houses', 19: 'Genshin Impact', 20: 'Greedfall', 21: 'Grim Dawn', 22: 'Hades', 23: 'Hogwarts Legacy', 24: 'Horizon Zero Dawn', 25: 'Kingdom Come: Deliverance', 26: 'Kingdom Hearts 3', 27: 'Legend of Grimrock 2', 28: 'Mass Effect Legendary Edition', 29: 'Middle-Earth: Shadow of War', 30: 'NieR: Automata', 31: 'Path Of Exile', 32: 'Persona 5 Strikers', 33: 'Pillars of Eternity', 34: 'Scarlet Nexus', 35: 'Soulstice', 36: 'Stardew Valley', 37: 'Tales of Arise', 38: 'Tales of Berseria', 39: 'The Last Oricru', 40: 'The Legend of Zelda: Breath of the Wild', 41: 'The Outer Worlds', 42: 'The Witcher 3: Wild Hunt', 43: 'Torchlight 2', 44: 'Transistor', 45: 'Undertale', 46: 'Weird West', 47: 'Wolcen', 48: 'Yakuza Kiwami'}\n"
     ]
    }
   ],
   "source": [
    "# TODO: determine the unique items and create a dictionary that maps an item to its id using enumerate (1 points)\n",
    "unique_items = np.unique(np.concatenate(data['favorite_games']))\n",
    "\n",
    "#create a dictionary that maps items to their IDs using enumerate\n",
    "item_to_id = {item: i for i, item in enumerate(unique_items)}\n",
    "\n",
    "#create a dictionary that maps IDs to their items\n",
    "id_to_item = {i: item for i, item in enumerate(unique_items)}\n",
    "\n",
    "print(\"Item-to-ID Dictionary:\")\n",
    "print(item_to_id)\n",
    "print(\"\\nID-to-Item Dictionary:\")\n",
    "print(id_to_item)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "is_executing": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mapped Records:\n",
      "[0, 1, 4, 8, 20, 22, 27, 31, 32, 33, 41, 41, 44]\n",
      "[8, 11, 13, 27, 39, 40, 45]\n",
      "[26, 43]\n",
      "[3, 12, 13, 14, 18, 20, 22, 28, 30, 32, 34, 35, 38, 41, 45, 46]\n",
      "[2, 15, 19, 27, 29, 34, 41, 41, 46]\n",
      "[8, 10, 24, 46]\n",
      "[5, 8, 14, 31, 35]\n",
      "[18, 20, 22, 33, 46]\n",
      "[3, 8, 10, 14, 20, 24, 25, 26, 28, 31, 38, 41, 44]\n",
      "[1, 2, 4, 5, 8, 10, 11, 12, 17, 19, 20, 32, 38, 41]\n",
      "[15, 24, 27, 30, 32, 39, 42]\n",
      "[3, 37, 43]\n",
      "[6, 10, 21, 25, 31, 43, 45]\n",
      "[4, 5, 23, 37]\n",
      "[11, 28, 45]\n",
      "[6, 20, 27, 38, 45, 47]\n",
      "[1, 3, 8, 14, 16, 25, 27, 45, 46, 48]\n",
      "[0, 1, 3, 9, 17, 22, 27, 32, 34, 41, 44, 48]\n",
      "[12, 19, 20, 21, 30, 38, 39, 42, 43, 48]\n",
      "[2, 3, 5, 7, 8, 9, 11, 14, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 41, 42, 43, 44, 47, 48]\n",
      "[0, 8, 10, 22, 34, 38, 42, 47]\n",
      "[0, 8, 9, 10, 14, 17, 20, 32, 41, 41, 44, 45]\n",
      "[1, 6, 19, 24, 28, 29, 32, 33, 34, 37, 40]\n",
      "[3, 7, 17, 22, 30, 33, 39, 40, 46]\n",
      "[0, 3, 15, 16, 19, 28, 32, 38, 44]\n",
      "[4, 14, 16, 18, 23, 39]\n",
      "[2, 6, 8, 33, 41, 44, 45]\n",
      "[22, 40, 41, 46]\n",
      "[0, 2, 4, 5, 17, 20, 21, 29, 30, 34, 36, 38, 41, 45]\n",
      "[4, 19, 20, 21, 22, 26, 30, 33, 34, 42, 47]\n",
      "[2, 5, 23, 25, 35]\n",
      "[2, 4, 15, 21, 23, 30, 34, 35, 41, 45]\n",
      "[0, 15, 21, 22, 33]\n",
      "[11, 29, 34, 35, 47]\n",
      "[13, 17]\n",
      "[43, 44]\n",
      "[1, 10, 30, 34, 47]\n",
      "[3, 19, 24, 29, 39]\n",
      "[5, 10, 41]\n",
      "[17, 18, 19, 26, 33, 42]\n",
      "[13, 16, 25, 27, 48]\n",
      "[2, 10, 43]\n",
      "[15, 21, 32, 42, 45]\n",
      "[3, 5, 15, 22, 36]\n",
      "[14, 23, 26, 42]\n",
      "[1, 3, 22, 23, 31, 43]\n",
      "[0, 4, 10, 22, 28, 42, 46, 48]\n",
      "[2, 19, 29, 30, 35, 39, 40]\n",
      "[3, 4, 5, 13, 14, 17, 21, 26, 29, 33, 38, 39, 41, 45]\n",
      "[23, 24, 48]\n",
      "[0, 3, 5, 7, 11, 13, 16, 17, 18, 19, 21, 25, 26, 30, 33, 34, 36, 41, 44, 45, 47]\n",
      "[0, 4, 7, 10, 11, 12, 26, 30, 42, 48]\n",
      "[0, 5, 6, 14, 15, 18, 20, 21, 32, 37, 44, 48]\n",
      "[7, 10, 18, 31, 34]\n",
      "[22, 31]\n",
      "[1, 7, 9, 12, 14, 17, 20, 23, 26, 27, 28, 29, 31, 35, 37, 42, 45, 47]\n",
      "[2, 19, 22, 31, 40, 41, 44, 47]\n",
      "[0, 3, 5, 6, 11, 14, 16, 26, 27, 28, 31, 34, 36, 48]\n",
      "[14, 24, 26]\n",
      "[0, 1, 5, 21, 30, 32]\n",
      "[4, 31, 37, 39]\n",
      "[1, 2, 8, 9, 11, 18, 19, 22, 31, 34, 36, 44, 46]\n",
      "[2, 11, 28, 36, 46, 48]\n",
      "[14, 20, 36, 37, 43]\n",
      "[2, 4, 5, 6, 9, 10, 15, 16, 19, 22, 23, 24, 26, 27, 32, 36, 39, 40, 46, 48]\n",
      "[2, 4, 20]\n",
      "[1, 25, 47]\n",
      "[1, 15, 17, 28, 39]\n",
      "[0, 2, 5, 13, 14, 15, 17, 23, 26, 29, 31, 34, 44, 45]\n",
      "[2, 22, 41, 43, 44]\n",
      "[30, 38]\n",
      "[13, 14, 15, 41]\n",
      "[0, 1, 2, 3, 5, 12, 19, 21, 31, 33, 34, 36, 38, 39, 41]\n",
      "[4, 7, 8, 16, 17, 19, 20, 23, 24, 27, 29, 30, 32, 34, 37, 38, 41, 41, 43, 45]\n",
      "[9, 25, 27]\n",
      "[0, 1, 4, 6, 10, 11, 12, 13, 16, 18, 36, 37, 39, 40, 43, 44, 45, 47]\n",
      "[2, 8, 9, 18, 19, 32, 45]\n",
      "[7, 13, 17, 18, 20, 23, 28, 32, 35, 44, 48]\n",
      "[2, 14, 18, 20, 21, 24, 28, 33, 46]\n",
      "[40, 46, 48]\n",
      "[0, 2, 6, 15, 20, 27, 34, 35, 36, 38, 39, 40, 47, 48]\n",
      "[9, 25, 28, 29, 32, 40, 42]\n",
      "[13, 18, 27, 35]\n",
      "[31, 40, 42]\n",
      "[5, 7, 32, 42, 47]\n",
      "[2, 6, 7, 13, 15, 18, 23, 26, 29, 30, 31, 34, 35, 37, 39, 45]\n",
      "[3, 13]\n",
      "[1, 2, 4, 11, 20, 23, 29, 32, 41]\n",
      "[3, 39, 41, 42]\n",
      "[1, 4, 5, 7, 8, 9, 12, 13, 14, 16, 19, 23, 24, 25, 28, 32, 37, 38, 39, 40, 42, 47, 48]\n",
      "[1, 9, 12, 16, 38, 39, 42, 45]\n",
      "[16, 24, 37]\n",
      "[7, 14, 42]\n",
      "[1, 2, 6, 7, 9, 10, 12, 13, 14, 16, 23, 30, 31, 33, 38, 39, 40, 41, 41, 45, 48]\n",
      "[7, 24, 31, 41]\n",
      "[14, 17, 18, 22, 29, 36, 37, 40]\n",
      "[0, 3, 4, 7, 30]\n",
      "[8, 15, 22, 36, 40, 42]\n",
      "[6, 8, 23, 26, 36, 38, 47]\n",
      "[17, 23, 31]\n",
      "[1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 38, 39, 41, 41, 42, 43, 44, 45, 46, 47, 48]\n",
      "[8, 13, 14, 16, 20, 35, 36, 43]\n",
      "[1, 38, 44]\n",
      "[4, 18, 22]\n",
      "[3, 12, 20, 28, 43]\n",
      "[5, 8, 9, 10, 18, 21, 24, 27, 30, 33, 36, 43, 45]\n",
      "[0, 4, 17, 18, 21, 26, 31, 46]\n",
      "[2, 7, 8, 17, 18, 21, 26, 29, 38, 41, 43]\n",
      "[0, 2, 5, 18, 19, 35, 38, 44]\n",
      "[2, 13, 22, 25, 28, 29, 33, 40]\n",
      "[2, 11, 12, 36, 38, 41]\n",
      "[1, 9, 10, 15, 16, 35]\n",
      "[8, 9, 11, 17, 18, 21, 26, 27, 32, 33, 39, 41, 41, 42, 43, 46]\n",
      "[4, 29, 48]\n",
      "[7, 9, 10, 11, 12, 15, 16, 18, 19, 23, 24, 31, 36, 39, 41, 42]\n",
      "[1, 4, 17, 29, 45, 46]\n",
      "[5, 6, 13, 15, 18, 20, 21, 29, 33, 37, 39, 46]\n",
      "[3, 4, 8, 21, 26, 29, 32]\n",
      "[0, 12, 20, 25, 31, 36, 37, 47]\n",
      "[0, 20, 23, 25]\n",
      "[19, 25, 26, 46]\n",
      "[3, 7, 20, 22, 29, 33, 44]\n",
      "[1, 17, 22, 23, 26, 33, 34, 39, 40, 43]\n",
      "[1, 12, 13, 15, 36, 42, 44]\n",
      "[1, 13, 16, 19, 20, 24, 26, 31, 36, 39, 40, 41, 47]\n",
      "[3, 6, 12, 25, 28, 30, 31, 34, 35, 39]\n",
      "[8, 16, 18, 39]\n",
      "[0, 6, 11, 19, 20, 29, 30, 34, 40, 42, 43, 46]\n",
      "[8, 14, 26, 28, 30, 46, 47, 48]\n",
      "[1, 10, 11, 16, 20, 21, 32]\n",
      "[7, 11, 18, 19, 21, 24, 25, 36, 37, 38, 43, 44, 46, 48]\n",
      "[0, 27, 34, 41, 43]\n",
      "[0, 1, 4, 11, 12, 19, 26, 28, 29, 32, 45]\n",
      "[12, 34, 38]\n",
      "[1, 8, 12, 15, 18, 23, 37, 41]\n",
      "[12, 24, 32, 44]\n",
      "[2, 6, 8, 12, 16, 17, 20, 21, 25, 40, 43, 48]\n",
      "[4, 13, 19, 28]\n",
      "[3, 5, 19, 20]\n",
      "[22, 25, 39]\n",
      "[10, 17, 29, 37, 41, 42, 47]\n",
      "[2, 4, 11, 12, 16, 17, 20, 23, 25, 28, 29, 32, 36, 38]\n",
      "[22, 24, 28, 41]\n",
      "[9, 13, 15, 20, 22, 29, 47, 48]\n",
      "[5, 37, 44]\n",
      "[12, 19, 33, 35]\n",
      "[2, 18, 37]\n",
      "[3, 7, 10, 13, 15, 16, 23, 24, 25, 27, 30, 32, 33, 34, 36, 40, 43, 44, 48]\n",
      "[0, 2, 4, 25, 29, 38, 40, 41]\n",
      "[10, 12, 13, 14, 22, 23, 33, 41, 44]\n",
      "[9, 22, 24, 29, 30, 31, 44, 45]\n",
      "[31, 46, 48]\n",
      "[1, 12, 26, 46, 48]\n",
      "[4, 27]\n",
      "[8, 20]\n",
      "[16, 26, 29, 32]\n",
      "[0, 10, 19, 20, 32, 36, 39, 40, 41, 44, 48]\n",
      "[7, 22]\n",
      "[18, 24, 41]\n",
      "[1, 14, 20, 31, 34, 38, 46, 48]\n",
      "[1, 5, 10, 19, 36, 43]\n",
      "[9, 25, 35, 37, 41]\n",
      "[7, 8, 24, 46]\n",
      "[2, 5, 6, 9, 11, 15, 17, 19, 20, 21, 22, 24, 27, 29, 30, 31, 34, 36, 37, 38, 39, 40, 41, 41, 44, 45, 47]\n",
      "[0, 6, 35, 41, 48]\n",
      "[3, 5, 7, 19, 23, 25, 33, 34, 45, 46]\n",
      "[3, 9, 11, 28, 47]\n",
      "[4, 5, 6, 18, 20, 24, 28, 33, 38, 42, 46, 47]\n",
      "[21, 24, 37, 38, 41]\n",
      "[1, 4, 11, 16, 17, 23, 38, 39, 40, 41, 43, 46]\n",
      "[9, 14, 24, 45]\n",
      "[5, 6, 8, 9, 10, 12, 20, 22, 26, 28, 44, 48]\n",
      "[2, 8, 17, 19, 27, 32, 43]\n",
      "[6, 13, 14, 15, 41, 42]\n",
      "[2, 3, 18, 27, 39]\n",
      "[0, 2, 4, 16, 18, 25, 31, 38, 40, 41, 41, 42]\n",
      "[7, 9, 11, 25]\n",
      "[8, 14, 17, 23, 31, 39, 46, 47]\n",
      "[3, 5, 15, 20, 26, 29, 39, 43]\n",
      "[0, 6, 7, 9, 32, 39, 47]\n",
      "[4, 8, 18, 27, 28, 29, 38, 43, 45, 47]\n",
      "[2, 3, 8, 11, 16, 18, 29, 33, 35, 39, 40, 42, 44, 45]\n",
      "[1, 3, 9, 10, 11, 22, 26, 34, 38, 42, 47, 48]\n",
      "[1, 2, 5, 19, 22, 33, 44]\n",
      "[1, 9, 12, 13, 15, 16, 24, 29, 37, 41, 48]\n",
      "[8, 19, 23]\n",
      "[7, 41]\n",
      "[8, 10, 21, 24, 25, 27, 28, 34, 38]\n",
      "[0, 7, 10, 14, 19, 20, 28, 33, 37, 38, 41, 44]\n",
      "[16, 36, 37, 45]\n",
      "[10, 15, 16]\n",
      "[2, 8, 13, 14, 16, 22, 25, 26, 36]\n",
      "[14, 18, 46, 48]\n",
      "[16, 33, 42, 44, 48]\n",
      "[0, 12, 46]\n",
      "[35, 38, 46]\n",
      "[14, 24, 28, 35, 43]\n",
      "[9, 10, 13, 15, 18, 21, 22, 23, 24, 25, 31, 34, 38, 40, 48]\n",
      "[4, 37, 38, 42, 44, 48]\n",
      "[1, 9, 19, 20, 46]\n",
      "[22, 31, 35]\n",
      "[5, 7, 39]\n",
      "[2, 5, 6, 12, 13, 15, 22, 30, 47]\n",
      "[5, 13, 14, 18, 35, 36, 41, 44, 46]\n",
      "[10, 21, 28, 33]\n",
      "[0, 9, 17, 22, 42, 44, 45, 47]\n",
      "[6, 29, 38, 41]\n",
      "[6, 10, 23]\n",
      "[25, 26, 47]\n",
      "[7, 12, 23, 34, 44]\n",
      "[8, 18, 24, 28, 29, 30, 34, 47]\n",
      "[2, 3, 4, 8, 24, 27, 28, 30, 35, 36, 37, 38, 47]\n",
      "[0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 47, 48]\n",
      "[4, 12, 15, 18, 21, 32, 37, 41, 44, 45, 48]\n",
      "[1, 7, 11, 14, 15, 35, 37, 39, 42, 47]\n",
      "[0, 6, 7, 12, 13, 15, 27, 38, 45, 47, 48]\n",
      "[0, 3, 5, 6, 12, 13, 14, 15, 19, 20, 22, 28, 29, 34, 36, 39, 41, 47, 48]\n",
      "[1, 5, 6, 7, 9, 11, 13, 14, 15, 20, 23, 26, 27, 29, 35, 37, 41, 44, 46]\n",
      "[0, 1, 10, 11, 13, 20, 21, 22, 24, 29, 38, 42, 45, 46, 48]\n",
      "[4, 5, 13, 16, 21, 24, 30, 37, 39, 40, 41, 45]\n",
      "[12, 22]\n",
      "[3, 6, 14, 20, 24, 32, 33, 34, 36, 41, 46, 47]\n",
      "[5, 14, 20, 32, 35, 37, 40]\n",
      "[2, 3, 4, 5, 6, 10, 15, 29, 37, 39, 40, 41, 45]\n",
      "[9, 11, 24, 44, 45]\n",
      "[1, 2, 4, 5, 10, 13, 20, 28, 35, 37, 40, 42]\n",
      "[2, 32, 33, 43]\n",
      "[0, 3, 4, 7, 11, 18, 19, 23, 24, 25, 30, 41, 45]\n",
      "[29, 37, 38]\n",
      "[6, 10, 12, 15, 19, 22, 33]\n",
      "[24, 41]\n",
      "[20, 41]\n",
      "[12, 38]\n",
      "[3, 20, 23, 34]\n",
      "[4, 7, 8, 12, 19, 24, 28, 32, 39, 44]\n",
      "[0, 15, 28, 33, 34, 37, 41, 44, 48]\n",
      "[2, 7, 9, 10, 22, 24, 33, 35, 41]\n",
      "[9, 11, 12, 27]\n",
      "[4, 8, 16, 18, 24, 28, 37, 46]\n",
      "[11, 21, 28, 31, 34, 42]\n",
      "[7, 21, 25, 34, 45, 48]\n",
      "[3, 6, 11, 28, 34, 41]\n",
      "[2, 7, 19, 27, 29, 30, 33, 37, 44, 47]\n",
      "[14, 15, 17, 19, 44]\n",
      "[19, 20, 26, 39, 43, 44, 45, 46, 47]\n",
      "[6, 12, 16, 24, 25, 38]\n",
      "[2, 4, 5, 8, 22, 34, 35, 38, 43]\n",
      "[20, 21, 26, 33, 48]\n",
      "[18, 21, 25, 31, 33, 44]\n",
      "[2, 7, 9, 11, 19, 25, 31, 39]\n",
      "[23, 27, 47]\n",
      "[1, 2, 4, 6, 8, 10, 11, 13, 15, 16, 18, 25, 30, 35, 36, 40, 41, 43, 44, 46, 47]\n",
      "[0, 1, 3, 5, 7, 8, 11, 14, 17, 22, 24, 31, 32, 34, 35, 37, 43, 45]\n",
      "[4, 16, 46]\n",
      "[13, 23, 40]\n",
      "[5, 23, 44]\n",
      "[4, 14, 16, 18, 22, 47]\n",
      "[7, 20, 31, 36]\n",
      "[6, 7, 17, 21, 27]\n",
      "[1, 3, 8, 21, 22, 23, 31, 32, 35, 37, 40, 41, 41, 43, 45, 46, 48]\n",
      "[20, 27]\n",
      "[3, 5, 11, 19, 25, 34, 36, 41, 45, 48]\n",
      "[4, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 48]\n",
      "[2, 7, 10, 13, 14, 16, 19, 24, 25, 27, 30, 32, 33, 35, 37, 39, 41, 45, 46]\n",
      "[1, 10, 13, 15, 24, 32, 37, 43, 44]\n",
      "[2, 10, 11, 20, 30, 35, 38, 39, 43, 45, 47]\n",
      "[1, 15, 24, 25, 36, 38, 40, 41, 41, 43]\n",
      "[2, 3, 14, 28, 33, 34, 37, 41, 43]\n",
      "[2, 3, 6, 14, 15, 21, 23, 24, 25, 26, 28, 29, 31, 37, 39, 42, 43, 46]\n",
      "[8, 11, 14, 27, 45, 48]\n",
      "[4, 7, 15, 18, 20, 28, 31, 33, 43]\n",
      "[2, 3, 6, 15, 24, 26, 32, 35, 47]\n",
      "[2, 4, 10, 12, 14, 19, 24, 30, 33, 35, 37, 38, 41, 43, 44, 45, 47, 48]\n",
      "[35, 40, 42]\n",
      "[0, 4, 7, 12, 13, 17, 19, 21, 30, 39]\n",
      "[5, 9, 13, 16, 23, 27]\n",
      "[0, 4, 8, 12, 15, 21, 24, 27, 33, 34, 37, 40, 41, 42, 44]\n",
      "[9, 16, 22, 23, 28, 34, 37, 40, 41, 46]\n",
      "[1, 14, 32, 35, 41, 48]\n",
      "[2, 6, 8, 9, 11, 12, 15, 17, 20, 27, 28, 29, 30, 33, 37, 44, 45, 46, 47]\n",
      "[0, 2, 3, 6, 9, 10, 13, 15, 19, 21, 22, 23, 25, 27, 28, 35, 36, 39, 42]\n",
      "[9, 15]\n",
      "[7, 15, 47]\n",
      "[5, 35]\n",
      "[1, 10, 11, 14, 16, 21, 25, 26, 27, 31, 33, 35, 36, 48]\n",
      "[4, 6, 13, 20, 23, 27, 34, 38, 41, 44]\n",
      "[38, 42]\n",
      "[19, 22, 27, 32, 44]\n",
      "[2, 4, 6, 9, 10, 17, 18, 20, 21, 23, 28, 29, 30, 31, 33, 34, 35, 38, 39, 41, 42, 43, 44, 45, 47]\n",
      "[5, 21, 36]\n",
      "[0, 4, 6, 9, 28, 30, 35, 36, 37, 41, 48]\n",
      "[0, 2, 4, 6, 10, 11, 12, 14, 15, 20, 21, 22, 23, 29, 30, 31, 32, 34, 37, 38]\n",
      "[10, 22, 43]\n",
      "[10, 16, 23, 45]\n",
      "[0, 28, 33, 41, 42, 47]\n",
      "[1, 2, 9, 16, 18, 19, 29, 35, 37, 39, 41, 42, 45]\n",
      "[6, 14, 15, 22, 31, 33, 35, 39, 41, 41, 43, 45, 47]\n",
      "[0, 2, 10, 15, 16, 17, 21, 23, 27, 28, 31, 35, 36, 38, 40, 41]\n",
      "[24, 47, 48]\n",
      "[5, 10, 11, 20, 28, 29, 37, 38, 39, 40, 42, 43]\n",
      "[0, 1, 2, 6, 15, 17, 27, 35, 37, 45]\n",
      "[3, 9, 19, 43, 44]\n",
      "[0, 3, 5, 12, 13, 24, 32, 33, 46, 47]\n",
      "[7, 14, 30, 45]\n",
      "[3, 9, 11, 17, 19, 38, 41]\n",
      "[0, 21, 26]\n",
      "[15, 37, 41, 44]\n",
      "[8, 11, 19, 22, 28, 32, 40, 45, 46]\n",
      "[9, 10, 16, 20, 35]\n",
      "[2, 7, 19, 22, 44, 48]\n",
      "[6, 21, 25, 35, 38, 47]\n",
      "[3, 6, 13, 14, 27, 30, 41, 42, 43]\n",
      "[6, 9, 22, 41, 46]\n",
      "[1, 2, 4, 21, 28, 41, 43, 44]\n",
      "[12, 19, 21, 25, 34]\n",
      "[1, 13, 14, 21, 26, 28, 29, 32, 36, 47]\n",
      "[4, 6, 8, 13, 14, 23, 27, 28, 29, 30, 32, 38, 41, 46]\n",
      "[13, 18, 34, 38, 40]\n",
      "[0, 3, 6, 11, 15, 16, 19, 20, 21, 27, 33, 39, 41, 41, 43, 46, 47]\n",
      "[10, 23, 25, 37, 41]\n",
      "[1, 9, 26, 34, 42, 44]\n",
      "[33, 46]\n",
      "[12, 18, 44, 46]\n",
      "[27, 28, 45]\n",
      "[24, 27, 29, 38, 48]\n",
      "[1, 3, 4, 14, 20, 31, 37, 40, 45]\n",
      "[1, 27, 45]\n",
      "[1, 8, 23, 26, 35, 40]\n",
      "[3, 5, 8, 12, 13, 21, 26, 27, 29, 30, 32, 34, 36, 41, 42, 45]\n",
      "[21, 33]\n",
      "[0, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 20, 23, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48]\n",
      "[7, 8, 17, 20, 34, 37, 39, 43, 47]\n",
      "[0, 2, 3, 5, 6, 7, 14, 15, 16, 17, 18, 19, 22, 25, 26, 27, 28, 29, 30, 34, 38, 40, 41]\n",
      "[3, 14, 27]\n",
      "[6, 13, 17, 31, 32, 33]\n",
      "[3, 5, 6, 18, 20, 28, 32, 34, 35]\n",
      "[11, 13, 23, 31, 41, 43, 45, 48]\n",
      "[1, 23, 28, 31, 42, 47]\n",
      "[26, 30, 36, 39, 41, 42]\n",
      "[16, 18, 30, 33, 37]\n",
      "[11, 17, 25, 29, 33, 38, 41]\n",
      "[3, 15, 23, 27, 30, 39]\n",
      "[1, 6, 7, 24, 38]\n",
      "[2, 3, 13, 16, 17, 23, 25, 31, 34, 37, 38, 42, 44]\n",
      "[7, 24, 27, 36]\n",
      "[0, 4, 5, 6, 10, 13, 19, 22, 25, 39, 41, 44, 46]\n",
      "[29, 33]\n",
      "[7, 24, 28, 36, 41, 41]\n",
      "[3, 13, 34, 36, 43, 45]\n",
      "[7, 10, 46]\n",
      "[9, 13, 14, 18, 25, 30, 31, 32, 34, 37, 38, 45]\n",
      "[13, 14, 19, 23, 25, 29, 31, 32, 33, 36, 37, 40, 41, 43]\n",
      "[15, 48]\n",
      "[7, 29, 47]\n",
      "[0, 31, 34]\n",
      "[1, 9, 26, 35, 36, 46]\n",
      "[1, 9, 21, 26, 28, 33, 37, 41]\n",
      "[1, 15, 16, 34]\n",
      "[0, 17, 35, 40]\n",
      "[1, 3, 23, 31, 34, 36]\n",
      "[36, 38, 39, 44, 47]\n",
      "[9, 37, 41]\n",
      "[2, 11, 14, 21, 22, 29, 33, 45, 47]\n",
      "[11, 19, 22, 41]\n",
      "[9, 17, 25, 28, 46, 47]\n",
      "[16, 19, 34, 46]\n",
      "[0, 1, 18, 26, 29, 32, 37, 38, 40, 46, 48]\n",
      "[16, 26, 29, 33]\n",
      "[5, 8, 13, 14, 45]\n",
      "[9, 18, 21, 33, 38, 39, 41]\n",
      "[6, 12, 15, 36, 43]\n",
      "[6, 8, 14, 15, 17, 25, 26, 42, 48]\n",
      "[0, 2, 17, 21, 30, 45]\n",
      "[7, 11, 22, 26, 28, 29, 32, 36, 40, 41, 45, 47, 48]\n",
      "[0, 5, 9, 11, 16, 18, 20, 22, 24, 25, 29, 34, 39, 41, 41, 42, 43, 46, 47]\n",
      "[3, 5, 8, 14, 15, 16, 17, 20, 23, 27, 29, 30, 33, 37, 43, 44, 48]\n",
      "[0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 18, 22, 23, 25, 26, 27, 31, 33, 34, 37, 39, 41, 44, 47]\n",
      "[18, 20, 29, 33, 40]\n",
      "[0, 11, 16, 23, 26, 29, 33, 42]\n",
      "[7, 38]\n",
      "[5, 40, 48]\n",
      "[7, 14, 20, 23, 24, 27, 32, 33, 38]\n",
      "[0, 11, 13, 33]\n",
      "[0, 10, 12, 13, 17, 19, 20, 23, 32, 41, 44, 45, 48]\n",
      "[5, 22, 42, 43]\n",
      "[4, 13, 19, 34, 36, 47]\n",
      "[14, 17, 23, 44, 46]\n",
      "[12, 13, 37]\n",
      "[4, 46]\n",
      "[5, 9, 11]\n",
      "[0, 4, 7, 8, 16, 26, 28, 32, 41]\n",
      "[9, 18, 21]\n",
      "[7, 10, 11, 36]\n",
      "[4, 18, 22, 31, 41, 43, 48]\n",
      "[23, 34, 36, 40, 47]\n",
      "[23, 37, 44]\n",
      "[14, 17, 18, 28, 34, 36, 41, 41, 47, 48]\n",
      "[6, 12, 13, 14, 15, 16, 17, 20, 23, 26, 29, 32, 34, 37, 42, 43, 44, 46, 47]\n",
      "[28, 29, 38, 39]\n",
      "[0, 1, 2, 3, 5, 7, 8, 12, 13, 16, 18, 19, 20, 22, 24, 25, 26, 28, 30, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48]\n",
      "[15, 18, 31, 41]\n",
      "[13, 33, 45]\n",
      "[3, 5, 6]\n",
      "[29, 31]\n",
      "[16, 18, 21, 30]\n",
      "[3, 10, 28, 29, 34, 41, 41, 48]\n",
      "[0, 4, 5, 7, 11, 12, 13, 14, 15, 17, 18, 19, 22, 26, 27, 28, 30, 34, 38, 41, 42, 44, 45, 46, 47]\n",
      "[2, 4, 19, 21, 27]\n",
      "[19, 22, 24, 25, 31, 43]\n",
      "[27, 28]\n",
      "[8, 31]\n",
      "[12, 24, 35, 39, 48]\n",
      "[28, 29, 31, 46]\n",
      "[5, 18, 26, 37]\n",
      "[47, 48]\n",
      "[3, 13, 18, 35, 45]\n",
      "[13, 17, 35, 41, 42]\n",
      "[6, 8, 32, 40, 47]\n",
      "[4, 15, 21, 26, 38, 43, 44, 47]\n",
      "[1, 6, 25, 28, 29, 30, 48]\n",
      "[22, 44]\n",
      "[3, 7, 14, 17, 43]\n",
      "[4, 36]\n",
      "[4, 9, 17, 23, 27, 40, 41, 43]\n",
      "[4, 11, 15, 24, 34, 41, 42]\n",
      "[1, 25]\n",
      "[1, 2, 4, 5, 6, 8, 9, 12, 13, 14, 16, 18, 20, 21, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 43, 45, 48]\n",
      "[0, 20, 27]\n",
      "[1, 24, 35]\n",
      "[28, 37, 39, 40]\n",
      "[8, 41, 47]\n",
      "[10, 22, 24, 32]\n",
      "[4, 7, 9, 13, 16, 17, 18, 24, 30, 31, 32, 35, 36, 38]\n",
      "[4, 9, 19, 28, 38, 46]\n",
      "[1, 4, 5, 9, 13, 17, 19, 21, 22, 25, 30, 35, 38, 44]\n",
      "[0, 1, 2, 4, 5, 7, 8, 9, 10, 12, 15, 16, 18, 19, 20, 22, 23, 24, 28, 30, 31, 32, 34, 36, 37, 40, 41, 46, 47, 48]\n",
      "[2, 15, 19, 27, 29, 31, 33]\n",
      "[0, 2, 3, 5, 7, 8, 10, 11, 12, 13, 15, 17, 18, 21, 25, 27, 29, 32, 34, 35, 38, 40, 41, 41, 43, 44, 45, 47, 48]\n",
      "[1, 2, 4, 12, 18, 47]\n",
      "[23, 34, 39]\n",
      "[6, 11, 12, 16, 18, 21, 24, 34, 48]\n",
      "[13, 19, 34, 36]\n",
      "[3, 4, 7, 8, 10, 12, 13, 19, 23, 27, 28, 29, 33, 36, 38, 40, 41, 44]\n",
      "[0, 4, 8, 11, 15, 17, 25, 26, 32, 41, 45, 46]\n",
      "[11, 15, 23, 26, 31, 33, 35, 37, 41]\n",
      "[16, 24]\n",
      "[5, 24, 31, 34, 41, 43]\n",
      "[20, 29, 46]\n",
      "[0, 1, 2, 3, 5, 9, 15, 16, 18, 20, 34, 36, 37, 40, 41, 43, 45]\n",
      "[9, 15, 25, 34]\n",
      "[11, 19, 28]\n",
      "[0, 4, 6, 8, 29, 31, 32, 42, 43, 44, 45]\n",
      "[8, 20]\n",
      "[3, 25, 33, 34]\n",
      "[4, 13, 32, 40]\n",
      "[1, 4, 6, 9, 11, 14, 15, 23, 28, 30, 31, 33, 34, 36, 38, 48]\n",
      "[7, 25, 32]\n",
      "[6, 46]\n",
      "[3, 41]\n",
      "[13, 29, 31, 40, 41]\n",
      "[7, 29, 33, 44, 46]\n",
      "[5, 7, 12, 19, 22, 25, 35, 39, 40, 44]\n",
      "[1, 4, 7, 9, 17, 18, 19, 25, 27, 28, 31, 32]\n",
      "[2, 3, 11, 23, 32, 42]\n",
      "[0, 3, 22, 26, 29, 37, 46]\n",
      "[8, 28, 41, 48]\n",
      "[0, 2, 3, 6, 16, 17, 18, 20, 27, 30, 41, 44]\n",
      "[10, 34, 41, 47]\n",
      "[3, 5, 8, 10, 12, 14, 15, 21, 22, 23, 27, 34, 36, 38, 39, 40, 41, 43, 45, 46, 48]\n",
      "[9, 23, 27, 28, 29, 31, 45, 48]\n",
      "[4, 6, 7, 12, 33, 39]\n",
      "[1, 2, 6, 7, 8, 12, 16, 26, 30, 31, 32, 35, 41, 44]\n",
      "[10, 25, 31, 33, 41, 43, 45]\n",
      "[9, 18, 19, 21, 22, 28, 33, 35, 37, 46, 48]\n",
      "[4, 18, 24, 36, 37, 44]\n",
      "[12, 22, 23, 25, 27, 41]\n",
      "[11, 14, 15, 19, 21, 26, 27, 28, 32, 36, 38, 40, 42, 46, 47, 48]\n",
      "[12, 24, 35, 38, 39, 40, 45, 46]\n",
      "[0, 2, 4, 6, 13, 15, 27, 33, 35, 42, 46]\n",
      "[31, 44]\n",
      "[5, 11, 32, 45]\n",
      "[2, 24]\n",
      "[1, 5, 14, 15, 25, 31, 34, 40, 46]\n",
      "[0, 5, 9, 16, 18, 23, 29, 33, 37, 47]\n",
      "[3, 11, 30, 32, 46, 48]\n",
      "[2, 9, 19, 23, 34, 38, 46]\n",
      "[0, 9, 14, 28]\n",
      "[4, 6, 10, 11, 14, 25, 26, 29, 41]\n",
      "[0, 4, 10, 14, 22, 26, 28, 37, 39]\n",
      "[2, 5, 23, 28, 46]\n",
      "[1, 8, 9, 15, 16, 21, 26, 29, 31, 33, 37, 43, 47, 48]\n",
      "[2, 18, 22]\n",
      "[8, 13, 15, 18, 20, 23, 27, 33, 34, 38, 48]\n",
      "[4, 5, 12, 23, 26, 27, 41, 44, 47, 48]\n",
      "[7, 28]\n",
      "[0, 6, 8, 12, 18, 21, 27, 28, 31, 35, 38, 39, 41, 46]\n",
      "[2, 16, 17, 33, 39, 45, 47]\n",
      "[3, 21]\n",
      "[3, 6, 7, 39, 41, 42]\n",
      "[0, 5, 10, 12, 15, 17, 22, 24, 26, 27, 28, 29, 30, 31, 32, 34, 39, 44, 46]\n",
      "[1, 25, 31, 42]\n",
      "[0, 1, 4, 5, 7, 9, 12, 13, 14, 17, 20, 22, 23, 25, 26, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 41, 45, 48]\n",
      "[0, 1, 6, 8, 11, 13, 14, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 32, 33, 34, 36, 37, 38, 39, 41, 45, 46, 47, 48]\n",
      "[34, 41]\n",
      "[0, 3, 9, 19, 30, 31, 47]\n",
      "[2, 30, 39]\n",
      "[0, 1, 21, 31, 45]\n",
      "[1, 11, 20, 21, 23, 24, 30, 34, 38, 40, 41]\n",
      "[17, 19, 47, 48]\n",
      "[3, 5]\n",
      "[2, 3, 6, 17, 18, 22, 26, 27, 32, 37, 44]\n",
      "[1, 3, 6, 16, 22, 26, 34, 35]\n",
      "[11, 35, 47]\n",
      "[1, 4, 13, 24, 41]\n",
      "[3, 5, 21]\n",
      "[0, 1, 3, 4, 8, 9, 23, 25, 26, 35, 39, 46]\n",
      "[3, 10, 15, 16]\n",
      "[3, 11, 21, 39]\n",
      "[6, 12, 16, 25, 38]\n",
      "[4, 24, 33, 35, 46, 47]\n",
      "[5, 10, 15, 17, 19, 21, 22, 26, 27, 29, 42, 45]\n",
      "[21, 22]\n",
      "[11, 18, 31]\n",
      "[2, 10, 23, 24, 25, 33]\n",
      "[11, 17, 25, 28, 37, 43]\n",
      "[19, 46]\n",
      "[0, 20, 22, 28, 32, 35]\n",
      "[1, 4, 7, 14, 22, 23, 26, 30, 31, 34, 37, 38, 41, 43, 44]\n",
      "[1, 24, 28, 32, 41, 47]\n",
      "[14, 23, 33, 36, 37, 40, 45]\n",
      "[0, 7, 11, 12, 13, 15, 20, 21, 23, 24, 26, 27, 29, 30, 31, 32, 33, 35, 37, 45, 48]\n",
      "[1, 14, 16, 21, 22, 31, 35, 45, 47]\n",
      "[0, 1, 2, 3, 7, 11, 12, 17, 19, 22, 23, 25, 26, 27, 28, 29, 30, 32, 41, 41, 44, 46, 47, 48]\n",
      "[2, 7, 12, 36, 44, 46]\n",
      "[27, 31, 35, 39]\n",
      "[5, 17]\n",
      "[0, 2, 41]\n",
      "[8, 18, 24]\n",
      "[18, 25, 27, 37, 42]\n",
      "[1, 2, 4, 5, 9, 18, 20, 21, 25, 29]\n",
      "[0, 2, 13, 45]\n",
      "[16, 24, 26, 36]\n",
      "[31, 41, 44]\n",
      "[3, 4, 16, 17, 35, 48]\n",
      "[5, 11, 22, 27, 39]\n",
      "[0, 1, 5, 6, 7, 8, 9, 13, 14, 15, 18, 20, 21, 22, 23, 27, 28, 30, 32, 33, 35, 36, 37, 39, 40, 41, 45, 47, 48]\n",
      "[1, 6, 18, 21, 28, 31, 36, 39, 45, 46]\n",
      "[2, 5, 11, 13, 21, 29, 30, 37, 43]\n",
      "[3, 8, 12, 15, 22, 27, 30, 33, 36, 41, 43, 46]\n",
      "[7, 10, 13, 20, 26, 33, 45]\n",
      "[10, 25, 39]\n",
      "[1, 5, 8, 19, 24, 32, 45]\n",
      "[4, 44]\n",
      "[2, 11, 12, 14, 16, 18, 23, 24, 27, 29, 33, 34, 36, 40, 41, 48]\n",
      "[1, 18, 30, 47]\n",
      "[4, 28, 39]\n",
      "[9, 15, 41]\n",
      "[2, 4, 5, 13, 19, 22, 25, 29, 33, 34, 37, 44, 48]\n",
      "[0, 10, 30, 32, 40]\n",
      "[9, 13, 34, 39, 43, 48]\n",
      "[0, 4, 5, 10, 20, 26, 33, 34, 35, 41, 41, 42, 47]\n",
      "[0, 7, 15, 22, 46, 47]\n",
      "[18, 29, 44]\n",
      "[4, 6, 20, 44]\n",
      "[10, 29, 34]\n",
      "[18, 21, 24, 36]\n",
      "[10, 26, 27, 30, 38]\n",
      "[16, 25, 27, 40, 41]\n",
      "[13, 17, 36, 48]\n",
      "[6, 14, 37]\n",
      "[13, 16, 31, 43, 44]\n",
      "[0, 1, 2, 10, 12, 13, 18, 33, 47, 48]\n",
      "[4, 12, 46]\n",
      "[25, 34, 40, 48]\n",
      "[2, 28, 30]\n",
      "[1, 2, 9, 12, 18, 36, 40]\n",
      "[1, 5, 6, 17, 20, 21, 25, 31, 35, 45]\n",
      "[3, 4, 10, 13, 21, 25, 47]\n",
      "[5, 37]\n",
      "[1, 10, 47]\n",
      "[15, 19, 20, 29, 38, 41, 45]\n",
      "[1, 3, 4, 9, 10, 29, 30, 41, 42]\n",
      "[21, 27]\n",
      "[4, 9, 11, 16, 18, 31, 36, 40, 41, 42, 44]\n",
      "[0, 4, 5, 9, 10, 12, 13, 16, 17, 19, 25, 27, 28, 32, 36, 37, 38, 39, 43, 44, 47]\n",
      "[0, 26]\n",
      "[0, 1, 2, 5, 10, 11, 12, 14, 16, 18, 21, 22, 27, 28, 29, 30, 31, 33, 34, 36, 40, 41, 41, 42, 43, 44, 45, 48]\n",
      "[3, 4, 6, 9, 10, 13, 20, 21, 25, 27, 31, 32, 38, 39, 40]\n",
      "[8, 10, 32, 39, 41, 41, 48]\n",
      "[19, 28]\n",
      "[6, 8, 16, 19, 26, 47, 48]\n",
      "[7, 8, 12]\n",
      "[4, 33, 35]\n",
      "[35, 37, 43]\n",
      "[13, 15, 26, 27, 33, 35, 37, 39, 42, 44]\n",
      "[14, 22, 26, 37, 41]\n",
      "[14, 16, 19, 24, 25, 30, 34, 37, 48]\n",
      "[17, 29, 33, 42, 46]\n",
      "[2, 24, 30, 40]\n",
      "[0, 1, 11, 13, 34, 43, 47, 48]\n",
      "[6, 22, 34]\n",
      "[1, 4, 5, 7, 8, 10, 11, 18, 27, 32, 33, 36, 40, 43, 45, 48]\n",
      "[9, 14, 20, 21, 35, 38, 41]\n",
      "[17, 21, 27, 37]\n",
      "[10, 37]\n",
      "[4, 5, 7, 8, 15, 18, 23, 25, 30, 31, 33, 41, 44, 45, 47]\n",
      "[2, 19, 21, 24, 43]\n",
      "[6, 8, 12, 15, 27, 31, 32]\n",
      "[26, 40]\n",
      "[27, 39, 40]\n",
      "[1, 2, 9, 13, 15, 17, 18, 24, 25, 29, 33, 34, 38, 41, 42]\n",
      "[45, 47]\n",
      "[1, 3, 7, 8, 16, 17, 24, 29, 37, 38, 41, 43, 46, 48]\n",
      "[5, 20, 22, 36]\n",
      "[9, 15, 16, 44]\n",
      "[3, 5, 8, 13, 18, 20, 23, 25, 29, 36, 37, 39, 42, 43, 44]\n",
      "[5, 6, 7, 13, 24, 29, 43, 46]\n",
      "[2, 6, 10, 18, 27, 28, 40, 45]\n",
      "[13, 16, 18, 19, 24, 46]\n",
      "[23, 26, 29, 31, 40, 41, 46, 48]\n",
      "[0, 1, 24, 33]\n",
      "[0, 2, 4, 9, 10, 11, 12, 14, 16, 18, 20, 21, 24, 25, 26, 28, 30, 34, 35, 37, 41, 42, 45, 46]\n",
      "[8, 9, 10, 15, 17, 18, 23, 34, 43]\n",
      "[2, 36, 39]\n",
      "[16, 23, 26]\n",
      "[11, 27, 34, 41, 41, 48]\n",
      "[0, 23, 25]\n",
      "[1, 5, 10, 13, 14, 15, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 43, 44, 47]\n",
      "[4, 5, 6, 10, 13, 15, 16, 17, 19, 22, 26, 27, 30, 31, 33, 34, 35, 37, 38, 41, 44, 46]\n",
      "[41, 43]\n",
      "[5, 6, 33, 39, 42, 47]\n",
      "[3, 4, 14, 21, 22, 42]\n",
      "[11, 29, 33, 45]\n",
      "[3, 4, 13, 22, 30, 39, 41, 42]\n",
      "[1, 9, 17, 20, 22, 41, 42]\n",
      "[0, 1, 3, 5, 29, 32, 33, 40, 41, 47]\n",
      "[19, 30, 41]\n",
      "[0, 6, 8, 11, 14, 16, 19, 20, 21, 23, 24, 25, 26, 29, 33, 35, 39, 40, 41, 41, 42, 44, 45, 47]\n",
      "[16, 22]\n",
      "[5, 11, 42]\n",
      "[6, 18, 23, 33, 39, 45]\n",
      "[0, 1, 4, 11, 22, 26, 32, 33, 35, 38, 41, 42, 46]\n",
      "[7, 10, 15, 23, 25, 32]\n",
      "[1, 6, 9, 13, 21, 22, 26, 29, 31, 36, 41, 47]\n",
      "[5, 9, 10, 19, 30, 45]\n",
      "[5, 7, 8, 11, 13, 17, 19, 21, 24, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 45]\n",
      "[3, 4, 32, 34, 39, 46, 47]\n",
      "[12, 17, 33, 38]\n",
      "[17, 32]\n",
      "[4, 9, 10, 11, 18, 23, 24, 29, 35, 40, 42, 45, 47]\n",
      "[0, 10, 12, 14, 18, 21, 24, 26, 34, 36, 38, 41, 42, 47]\n",
      "[0, 3, 11, 19, 20, 29, 41, 47]\n",
      "[14, 39, 45]\n",
      "[4, 23, 32, 44, 45, 48]\n",
      "[3, 6, 7, 9, 15, 20, 21, 31, 36, 37, 45]\n",
      "[20, 28, 29]\n",
      "[0, 5, 18, 20, 25, 29, 33, 38, 40, 41, 44, 48]\n",
      "[0, 2, 4, 5, 7, 9, 14, 17, 21, 24, 29, 33, 35, 38, 39, 47, 48]\n",
      "[13, 35]\n",
      "[2, 5, 6, 8, 10, 11, 12, 13, 17, 20, 22, 23, 25, 27, 28, 30, 33, 41, 43, 45]\n",
      "[42, 44, 45, 46]\n",
      "[4, 19, 25, 27, 28, 43]\n",
      "[2, 6, 8, 16, 18, 20, 26, 32, 39, 41]\n",
      "[20, 32, 35, 38, 46]\n",
      "[1, 30]\n",
      "[2, 15, 36]\n",
      "[25, 37]\n",
      "[0, 4, 13, 27, 35, 38, 42, 48]\n",
      "[5, 9, 11, 17, 28, 32, 34, 40, 46]\n",
      "[0, 2, 7, 8, 13, 15, 20, 28, 33, 38, 43, 47]\n",
      "[8, 9, 19, 20, 27, 36, 38, 43]\n",
      "[5, 10, 13, 31, 32, 35]\n",
      "[1, 5, 6, 9, 14, 17, 19, 25, 27, 34, 36, 44, 48]\n",
      "[0, 2, 13, 40]\n",
      "[8, 9, 33]\n",
      "[3, 26, 41, 42]\n",
      "[5, 6, 7, 10, 11, 15, 19, 22, 30, 32, 34, 35, 36, 37, 38, 42, 43, 46]\n",
      "[2, 20, 22, 38, 40, 41]\n",
      "[2, 11, 33, 34]\n",
      "[10, 19, 21, 22]\n",
      "[17, 29, 31, 35, 42]\n",
      "[4, 5, 12, 14, 18, 35, 41, 45]\n",
      "[0, 2, 3, 8, 26, 35, 40]\n",
      "[4, 5, 13, 15, 17, 18, 25, 26, 28, 35, 38, 41, 43, 44, 48]\n",
      "[14, 16, 17, 45, 46]\n",
      "[5, 6, 9, 12, 16, 17, 31, 32, 40, 46]\n",
      "[22, 34]\n",
      "[2, 10, 16, 19, 25, 41]\n",
      "[1, 31, 33]\n",
      "[3, 5, 6, 8, 18, 21, 23, 32, 36, 37, 40, 41, 42]\n",
      "[2, 11, 37, 42]\n",
      "[6, 19, 20, 27, 46, 47]\n",
      "[11, 13, 17, 20, 28, 30, 32, 33, 35, 36]\n",
      "[41, 41, 44, 45]\n",
      "[8, 11, 18, 20, 34]\n",
      "[1, 6, 14, 20, 22, 25, 26, 34, 40, 43, 45, 48]\n",
      "[3, 16, 24, 33]\n",
      "[2, 9, 13, 16, 24]\n",
      "[5, 18, 24, 27, 47]\n",
      "[10, 15, 31, 32, 37, 45, 47]\n",
      "[3, 5, 6, 14, 16, 18, 21, 22, 27, 31, 32, 35, 37, 43, 44]\n",
      "[8, 14, 24, 28, 30]\n",
      "[28, 46]\n",
      "[33, 34, 40, 41, 48]\n",
      "[7, 12, 13, 16, 23, 26, 34, 39, 47]\n",
      "[1, 5, 13, 17, 21, 35, 38, 39, 41]\n",
      "[0, 4, 5, 8, 12, 13, 17, 23, 36, 38, 45, 47, 48]\n",
      "[0, 1, 4, 5, 7, 10, 14, 15, 17, 20, 22, 26, 29, 37, 38, 40, 41, 42, 43, 47]\n",
      "[0, 33, 41]\n",
      "[13, 17, 26, 28, 30, 43]\n",
      "[0, 2, 4, 6, 11, 12, 16, 17, 18, 21, 22, 24, 25, 26, 29, 30, 32, 33, 34, 37, 39, 40, 41, 42, 44, 47, 48]\n",
      "[13, 17, 18, 25]\n",
      "[10, 11, 15, 16, 17, 19, 22, 27, 35, 37, 38, 39, 40, 47]\n",
      "[22, 42]\n",
      "[20, 45]\n",
      "[7, 9, 17, 18, 19, 25, 27, 28, 29, 32]\n",
      "[1, 9, 15, 19, 24, 25, 32, 35, 38, 41, 41, 46]\n",
      "[12, 23]\n",
      "[0, 6, 20, 38, 39, 41, 47, 48]\n",
      "[10, 43]\n",
      "[1, 36]\n",
      "[4, 12, 17, 26, 28, 30, 31, 35, 37, 39, 41, 42, 45, 48]\n",
      "[2, 13, 15, 25, 26, 28, 45]\n",
      "[5, 35, 40]\n",
      "[1, 6, 7, 8, 11, 17, 18, 22, 23, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 40, 41, 41, 47]\n",
      "[1, 15, 17, 23, 32, 34, 35, 36, 39, 40, 41, 42, 48]\n",
      "[16, 31, 44]\n",
      "[2, 6, 14, 19, 24, 26, 27, 28, 33, 41, 41, 43]\n",
      "[3, 7, 8, 11, 17, 20, 23, 33]\n",
      "[1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 48]\n",
      "[0, 2, 6, 10, 13, 17, 18, 20, 21, 22, 23, 25, 26, 28, 32, 41, 41, 43, 46, 48]\n",
      "[12, 14, 15, 21, 25, 29, 30, 31, 38, 42]\n",
      "[6, 8, 9, 10, 12, 17, 18, 28, 31, 34]\n",
      "[10, 11, 16, 23, 24, 25, 26, 29, 37, 38, 39, 42, 44, 48]\n",
      "[1, 2, 3, 4, 7, 8, 9, 14, 21, 23, 26, 36]\n",
      "[4, 7, 10, 18, 21, 25, 27, 44]\n",
      "[6, 15, 21, 27, 29, 41]\n",
      "[2, 10, 16, 22, 32, 35, 41, 42]\n",
      "[2, 42, 45]\n",
      "[3, 12, 14, 21, 37, 47]\n",
      "[3, 33, 45]\n",
      "[3, 4, 6, 12, 14, 15, 21, 23, 33, 39, 41, 42, 45]\n",
      "[2, 21, 37]\n",
      "[4, 12, 16, 19, 21]\n",
      "[6, 29, 45]\n",
      "[5, 10, 11, 12, 17, 24, 38]\n",
      "[4, 23]\n",
      "[10, 11, 19, 40]\n",
      "[2, 5, 6, 10, 11, 12, 17, 18, 22, 24, 25, 26, 32, 34, 39, 41, 43, 44, 47]\n",
      "[19, 35, 47, 48]\n",
      "[21, 41, 43, 45]\n",
      "[4, 21, 28, 34, 48]\n",
      "[1, 7, 17, 18, 30, 33, 35, 38, 40, 46]\n",
      "[3, 10, 15, 23, 31]\n",
      "[2, 4, 7, 20, 22, 36, 37, 39, 45, 46]\n",
      "[19, 21, 31, 33, 39]\n",
      "[2, 7, 12, 24, 29, 34, 39, 41, 47]\n",
      "[0, 3, 4, 7, 13, 14, 17, 24, 26, 29, 35, 41, 43, 46]\n",
      "[2, 3, 13, 16, 17, 19, 27, 36, 40, 41]\n",
      "[8, 19, 34]\n",
      "[3, 4, 5, 12, 13, 20, 24, 29, 32, 34, 38, 39, 40, 44, 45]\n",
      "[4, 5, 6, 7, 11, 21, 22, 25, 29, 36, 41, 43, 44, 47]\n",
      "[17, 25, 31, 34, 35]\n",
      "[4, 33, 44]\n",
      "[5, 40]\n",
      "[16, 22]\n",
      "[3, 9, 17, 20, 23, 24, 25, 28, 32, 34, 40, 41, 44, 48]\n",
      "[6, 16]\n",
      "[9, 17, 20]\n",
      "[10, 11, 14, 23, 45]\n",
      "[2, 3, 17, 19, 20, 23, 32, 35, 36, 44, 47]\n",
      "[5, 8, 13, 21, 22, 32, 36, 40, 47]\n",
      "[11, 12, 21, 39, 42]\n",
      "[2, 7, 16, 21, 26, 34, 39, 40, 46]\n",
      "[3, 7, 10, 32, 45, 48]\n",
      "[1, 2, 3, 4, 6, 7, 12, 17, 21, 22, 29, 30, 32, 37]\n",
      "[2, 11, 25, 28, 30, 33, 39, 41, 44]\n",
      "[9, 22, 44]\n",
      "[14, 23, 31, 40]\n",
      "[1, 4, 15, 20, 25, 41, 41]\n",
      "[1, 8, 10, 11, 14, 15, 27, 28, 43, 48]\n",
      "[7, 33, 35]\n",
      "[7, 12, 20, 30]\n",
      "[20, 24, 26, 48]\n",
      "[11, 13, 14, 23, 28, 33, 42, 43]\n",
      "[34, 42]\n",
      "[6, 21, 24, 25, 27, 33, 41, 45]\n",
      "[0, 1, 4, 5, 11, 13, 16, 24, 28, 30, 34, 35, 39, 41, 43, 46, 47, 48]\n",
      "[0, 1, 2, 3, 7, 10, 11, 17, 22, 23, 25, 28, 29, 30, 31, 34, 37, 39, 40, 41, 43, 45]\n",
      "[1, 13, 17]\n",
      "[0, 12, 23, 32, 34, 39, 47]\n",
      "[1, 7, 13, 16, 26, 28, 30, 31]\n",
      "[5, 7, 18, 31, 41]\n",
      "[0, 12, 29, 36, 45]\n",
      "[1, 2, 5, 11, 14, 17, 23, 38, 43, 46, 47]\n",
      "[1, 2, 3, 7, 10, 12, 14, 15, 17, 18, 21, 23, 24, 26, 32, 33, 38, 39, 41, 42, 44, 45, 46]\n",
      "[7, 14, 19, 29, 41, 43]\n",
      "[3, 19]\n",
      "[2, 5, 11, 15, 16, 20, 21, 22, 27, 28, 29, 30, 34, 35, 40, 41, 42]\n",
      "[0, 4, 5, 7, 12, 16, 23, 27, 32, 33, 38]\n",
      "[10, 12, 22, 26, 34, 45]\n",
      "[2, 5, 9, 20, 22, 26, 32, 41, 45, 46]\n",
      "[15, 18, 23, 32, 37, 38]\n",
      "[14, 20, 23, 39, 41, 48]\n",
      "[0, 1, 2, 6, 12, 27, 33, 46]\n",
      "[8, 11, 25, 31, 48]\n",
      "[0, 1, 3, 4, 5, 8, 9, 11, 13, 26, 29, 33, 37, 43, 44, 46]\n",
      "[2, 28, 29, 32]\n",
      "[3, 5, 18, 20, 21, 31, 46]\n",
      "[3, 9, 16, 24, 29, 37, 41]\n",
      "[16, 23, 31, 39]\n",
      "[3, 19, 25]\n",
      "[7, 8, 15, 17, 26, 28, 29, 32, 33, 37, 38, 40, 45]\n",
      "[4, 16, 23, 33, 38, 47, 48]\n",
      "[3, 22, 23, 34, 38, 46]\n",
      "[0, 1, 4, 6, 7, 8, 12, 13, 22, 26, 30, 31, 36, 38, 40, 48]\n",
      "[4, 9, 11, 13, 14, 15, 16, 20, 28, 29, 30, 34, 39, 41]\n",
      "[3, 4, 9, 14, 15, 17, 19, 21, 25, 26, 27, 28, 33, 40, 41, 47]\n",
      "[2, 5, 10, 12, 17, 20, 25, 30, 39, 40, 47]\n",
      "[29, 30, 32, 46]\n",
      "[5, 8, 12, 13, 20, 26, 35, 40]\n",
      "[0, 1, 9, 13, 16, 23, 25, 27, 30, 38, 42, 43, 45]\n",
      "[9, 17, 23, 24, 41]\n",
      "[2, 3, 5, 6, 11, 16, 18, 25, 26, 27, 29, 41]\n",
      "[5, 6, 13, 15, 20, 21, 33, 35, 40, 43, 44, 45, 48]\n",
      "[13, 46]\n",
      "[2, 9, 14, 25]\n",
      "[14, 25, 27, 38, 43]\n",
      "[6, 8, 25, 45]\n",
      "[3, 4, 5, 6, 8, 13, 16, 31, 35, 37, 41, 44, 45, 46]\n",
      "[24, 31, 36]\n",
      "[7, 20, 45]\n",
      "[0, 3, 4, 11, 12, 14, 15, 16, 18, 21, 23, 31, 33, 36, 38, 41, 43, 48]\n",
      "[1, 4, 6, 10, 18, 28, 35, 39, 42, 43, 44, 46]\n",
      "[1, 16, 26, 36, 38]\n",
      "[3, 6, 9, 19, 21, 33, 34, 37, 45, 48]\n",
      "[6, 7, 8, 13, 27, 30, 38]\n",
      "[6, 11, 12, 20, 31, 34, 40, 41]\n",
      "[4, 5, 43]\n",
      "[2, 8, 18, 19, 20, 21, 23, 27, 29, 39, 41, 42, 46]\n",
      "[6, 17, 24, 41, 44]\n",
      "[2, 3, 20, 31, 37, 42, 46]\n",
      "[1, 2, 5, 10, 14, 18, 19, 21, 22, 29, 37, 38, 42, 43, 46, 48]\n",
      "[8, 18, 41, 41]\n",
      "[1, 4, 6, 8, 12, 13, 14, 15, 19, 22, 24, 25, 28, 32, 37, 38, 48]\n",
      "[1, 2, 9, 11, 12, 21, 24, 25, 27, 31, 34, 38, 39, 44, 47, 48]\n",
      "[9, 13, 17, 22, 33, 40, 46]\n",
      "[0, 19, 39]\n",
      "[1, 2, 7, 15, 20, 25, 34, 37, 41, 43]\n",
      "[21, 23, 33, 37, 38]\n",
      "[7, 25, 48]\n",
      "[7, 9, 14, 18, 24, 27, 29, 35, 42]\n",
      "[8, 10, 17, 18, 24, 25, 28, 30, 37, 41, 43, 44]\n",
      "[3, 8, 15, 29]\n",
      "[0, 2, 3, 4, 6, 7, 10, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 45, 46, 47]\n",
      "[29, 33, 34, 41]\n",
      "[2, 15, 20, 22, 25, 29, 31, 35, 36, 39, 41, 41, 46, 47]\n",
      "[13, 23, 31, 32, 35, 38, 41, 43, 47]\n",
      "[21, 26, 39, 41, 42, 48]\n",
      "[25, 41]\n",
      "[1, 5, 7, 8, 9, 11, 13, 16, 17, 18, 19, 21, 22, 28, 29, 36, 38, 43, 45, 46, 47, 48]\n",
      "[0, 2, 3, 14, 21, 24, 46]\n",
      "[14, 25, 37, 44, 46]\n",
      "[6, 7, 11]\n",
      "[3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 20, 23, 24, 27, 29, 30, 31, 34, 40, 45, 46, 48]\n",
      "[0, 20, 26, 33, 36, 38, 41]\n",
      "[2, 3, 9, 12, 29, 31, 33, 40, 42, 47]\n",
      "[0, 6, 16, 30]\n",
      "[4, 6, 24, 27, 28, 29, 34, 44, 48]\n",
      "[26, 34]\n",
      "[0, 15, 16, 20, 25, 27, 28, 35, 38, 39, 41, 41, 42, 43, 46, 47, 48]\n",
      "[0, 2, 5, 7, 8, 9, 12, 13, 14, 19, 21, 24, 25, 27, 30, 41, 43, 45, 46]\n",
      "[10, 29, 47, 48]\n",
      "[1, 5, 7, 9, 12, 15, 16, 17, 24, 30, 39]\n",
      "[1, 4, 25, 48]\n",
      "[21, 35]\n",
      "[4, 8, 25, 27, 28, 29, 33, 40, 41]\n",
      "[14, 18, 32]\n",
      "[0, 6, 29, 31]\n",
      "[4, 5, 11, 17, 23, 41]\n",
      "[2, 3, 8, 12, 16, 20, 25, 33, 38, 39, 40, 41, 43]\n",
      "[7, 20, 25, 28, 34]\n",
      "[27, 34]\n",
      "[4, 30, 39]\n",
      "[19, 32, 41]\n",
      "[3, 11, 41, 43]\n",
      "[8, 20, 21, 27, 33, 34, 38, 41, 42, 44, 47, 48]\n",
      "[3, 9, 27, 28, 31, 37, 41, 43, 46]\n",
      "[33, 40]\n",
      "[1, 6, 26, 30, 34, 43, 45]\n",
      "[24, 42, 44]\n",
      "[4, 5, 7, 8, 15, 28, 35, 37, 39]\n",
      "[0, 9, 11, 26, 28, 38, 41, 44]\n",
      "[1, 13, 14, 16, 17, 34, 46, 47, 48]\n",
      "[9, 15, 41]\n",
      "[3, 13, 22, 24, 31, 32, 39, 41, 47]\n",
      "[14, 23]\n",
      "[12, 39, 43]\n",
      "[10, 11, 41]\n",
      "[2, 3, 12, 39]\n",
      "[15, 33, 34, 39, 41, 43, 46]\n",
      "[1, 7, 9, 13, 17, 24, 28, 29, 32, 34, 41, 47]\n",
      "[7, 8, 16, 17, 18, 22, 34, 41]\n",
      "[1, 14, 41, 43]\n",
      "[0, 11, 12, 15, 18, 27, 33]\n",
      "[2, 4, 6, 7, 9, 11, 13, 14, 15, 18, 21, 23, 24, 25, 28, 30, 31, 32, 35, 37, 38, 40, 44, 45]\n",
      "[4, 7, 8, 10, 15, 16, 21, 27, 30, 31, 38, 44, 46]\n",
      "[2, 4, 6, 9, 27, 40, 41]\n",
      "[1, 9, 16, 18, 20, 24, 37, 41]\n",
      "[4, 17, 22]\n",
      "[22, 40, 47]\n",
      "[3, 9, 10, 15, 23, 24, 25, 28, 29, 34, 38, 39, 40, 42, 47, 48]\n",
      "[2, 10, 12, 13, 15, 23, 25, 29, 32, 33, 37, 41, 44, 48]\n",
      "[12, 36]\n",
      "[0, 1, 9, 18, 24, 30, 40, 41]\n",
      "[4, 7, 13, 27, 42, 43]\n",
      "[1, 2, 18, 25, 28, 31, 32, 41, 43, 44, 45]\n",
      "[17, 31]\n",
      "[16, 18, 19, 33, 43, 45]\n",
      "[3, 5, 21, 27, 28, 34, 37, 44]\n",
      "[1, 12, 16, 29, 41, 41, 44, 46, 47, 48]\n",
      "[1, 6, 7, 12, 16, 31, 32, 34, 41, 42, 46]\n",
      "[0, 2, 3, 5, 9, 14, 20, 24, 35, 37, 40, 41, 43]\n",
      "[2, 5, 9, 10, 12, 14, 18, 21, 22, 24, 26, 34, 35, 37, 39, 42, 44, 46, 47]\n",
      "[5, 12, 13, 14, 15, 16, 19, 21, 23, 25, 26, 28, 31, 33, 36, 41, 43, 45]\n",
      "[6, 24]\n",
      "[6, 20, 27, 32, 38]\n",
      "[21, 25, 37, 38, 43, 45]\n",
      "[0, 1, 3, 12, 13, 31, 32, 40, 44, 46]\n",
      "[7, 22, 47]\n",
      "[0, 15, 19, 26, 30, 31, 36, 38, 47]\n",
      "[22, 24, 36, 37]\n",
      "[0, 1, 3, 4, 5, 6, 7, 8, 11, 15, 16, 19, 20, 22, 26, 28, 30, 31, 33, 36, 40, 41, 42, 44, 45, 47]\n",
      "[8, 30]\n",
      "[2, 28, 31, 35, 36, 38, 39, 48]\n",
      "[8, 11, 12, 19, 34, 35, 41]\n",
      "[5, 20, 36, 41]\n",
      "[0, 26]\n",
      "[0, 11, 26, 41]\n",
      "[15, 27, 31, 47]\n",
      "[0, 4, 6, 7, 9, 10, 14, 20, 22, 23, 24, 28, 30, 31, 32, 33, 34, 37, 41, 41, 42, 43, 44, 47]\n",
      "[16, 17, 21, 22, 33, 35, 39, 48]\n",
      "[0, 19, 29, 48]\n",
      "[7, 18, 22, 29, 36]\n",
      "[33, 36]\n",
      "[1, 22, 27]\n",
      "[0, 5, 6, 13, 14, 39]\n",
      "[2, 16, 18, 25, 26, 27, 36, 42, 48]\n",
      "[2, 3, 7, 9, 10, 11, 13, 18, 24, 27, 29, 30, 32, 35, 39, 40, 41]\n",
      "[0, 7, 9, 17, 34, 38, 41, 47]\n",
      "[4, 7, 10, 11, 27, 36, 46]\n",
      "[0, 1, 8, 11, 15, 18, 23, 37, 46]\n",
      "[5, 8, 37, 43]\n",
      "[0, 2, 38, 39, 41]\n",
      "[9, 15, 21, 22, 33, 38, 40, 42, 44, 45]\n",
      "[3, 16, 26]\n",
      "[0, 5, 8, 9, 14, 16, 19, 24, 26, 30, 31, 43, 44]\n",
      "[1, 2, 3, 10, 14, 18, 20, 23, 24, 34, 40, 42, 48]\n",
      "[0, 1, 5, 6, 7, 11, 14, 17, 18, 21, 24, 28, 31, 33, 36, 41, 45, 48]\n",
      "[0, 17, 25, 36, 38]\n",
      "[43, 48]\n",
      "[1, 2, 3, 6, 7, 9, 14, 15, 16, 20, 22, 24, 32, 37, 38, 39, 40, 45, 47, 48]\n",
      "[11, 20, 21, 22, 33, 37, 41, 42, 44]\n",
      "[16, 28, 31, 37, 40, 47]\n",
      "[1, 2, 3, 4, 7, 9, 10, 11, 12, 13, 18, 21, 23, 24, 26, 28, 32, 33, 34, 35, 42, 47]\n",
      "[5, 18, 22, 23, 25, 40, 46]\n",
      "[5, 8, 17, 20, 28, 29, 30, 31, 44]\n",
      "[13, 20]\n",
      "[4, 5, 7, 13, 23, 28, 29, 30, 31, 32, 33, 35, 36, 37, 39, 44, 45, 47, 48]\n",
      "[19, 38, 43]\n",
      "[19, 21]\n",
      "[2, 7, 14, 26, 27, 28, 29, 31, 37, 42, 43, 47]\n",
      "[0, 14, 23, 28, 30, 32, 33, 37, 39, 48]\n",
      "[11, 24]\n",
      "[4, 10, 13, 35, 42, 47]\n",
      "[3, 25, 47]\n",
      "[5, 23, 46]\n",
      "[2, 13, 18, 22, 26, 44]\n",
      "[1, 17, 20, 22, 23, 32, 39, 42]\n",
      "[5, 10, 11, 18, 19, 20, 31]\n",
      "[17, 32, 39]\n",
      "[3, 5, 20, 25, 37, 41]\n",
      "[4, 35]\n",
      "[3, 6, 8, 9, 10, 11, 12, 15, 16, 18, 22, 23, 28, 30, 34, 38, 39, 43, 46]\n",
      "[2, 3, 7, 8, 12, 23, 26, 33, 35, 39]\n",
      "[0, 8, 27, 36, 38, 41]\n",
      "[20, 30, 33]\n",
      "[34, 35, 44]\n",
      "[0, 12, 13, 14, 15, 16, 17, 18, 23, 24, 26, 29, 31, 35, 39, 42, 46]\n",
      "[0, 1, 2, 5, 6, 9, 13, 15, 19, 21, 22, 25, 26, 29, 31, 34, 35, 36, 37, 38, 40, 41, 41]\n",
      "[0, 1, 6, 11, 25, 29, 41]\n",
      "[2, 19, 21, 26, 36, 37]\n",
      "[10, 17, 23]\n",
      "[9, 10, 15, 16, 19, 23, 24, 26, 28, 31, 32, 34, 37, 45, 46]\n",
      "[15, 17, 22, 41]\n",
      "[4, 7, 8, 12, 13, 16, 23, 24, 25, 26, 28, 30, 40, 44, 48]\n",
      "[1, 3, 18, 26, 32]\n",
      "[10, 13, 17]\n",
      "[2, 22, 27, 46]\n",
      "[7, 8, 11, 12, 19, 21, 22, 26, 29, 32, 33, 34, 36, 40, 43, 44]\n",
      "[4, 7, 10, 17, 18, 20, 22, 23, 35, 40, 41, 43, 44, 46, 47]\n",
      "[24, 28]\n",
      "[1, 10, 13, 23, 28, 30, 31]\n",
      "[6, 11, 12, 17, 38, 39]\n",
      "[22, 28]\n",
      "[28, 47]\n",
      "[3, 4, 7, 12, 13, 16, 21, 24, 26, 27, 39, 43]\n",
      "[15, 40, 41, 42]\n",
      "[0, 1, 15, 27, 28, 30, 33, 43]\n",
      "[22, 28]\n",
      "[11, 12, 26, 29, 32, 34]\n",
      "[0, 3, 4, 5, 10, 12, 13, 17, 26, 29, 30, 31, 37, 40, 41, 45]\n",
      "[11, 29, 44]\n",
      "[4, 14, 27, 34, 47, 48]\n",
      "[2, 5, 15, 19, 23, 25, 29, 30, 31, 33, 35, 39, 40, 41, 46, 48]\n",
      "[1, 2, 4, 6, 13, 18, 25, 35, 43]\n",
      "[23, 26, 33]\n",
      "[19, 28, 33, 43, 44, 45, 46]\n",
      "[0, 2, 12, 14, 16, 17, 21, 29, 33, 34, 37, 42, 48]\n",
      "[0, 36, 39, 45, 48]\n",
      "[2, 25, 43, 44]\n",
      "[2, 5, 15]\n",
      "[9, 14, 33, 41]\n",
      "[0, 2, 3, 4, 6, 7, 15, 17, 22, 26, 27, 29, 41, 45, 48]\n",
      "[2, 6, 8, 10, 11, 28, 30, 38, 44, 45, 47, 48]\n",
      "[4, 16, 36, 40, 48]\n",
      "[12, 14, 16, 48]\n",
      "[0, 2, 4, 7, 8, 9, 10, 11, 15, 17, 19, 20, 23, 24, 25, 26, 28, 29, 30, 31, 32, 34, 36, 39, 40, 41, 41, 43, 44, 45, 47, 48]\n",
      "[2, 5, 33, 34, 38, 39, 44]\n",
      "[3, 4, 19, 20, 21, 24, 27, 30, 33, 35, 38]\n",
      "[15, 35, 41, 47]\n",
      "[7, 13, 37]\n",
      "[2, 19, 28]\n",
      "[0, 9, 14, 16, 23, 24, 29, 37, 38]\n",
      "[2, 4, 6, 12, 15, 20, 23, 24, 28, 29, 31, 33, 34, 35, 36, 37, 40, 41]\n",
      "[4, 12, 14, 16, 19, 21, 32, 34, 37, 38, 39, 42, 46, 47]\n",
      "[4, 30]\n",
      "[2, 13, 14, 21, 22, 25, 37, 43]\n",
      "[8, 10, 16, 19, 33, 34, 41, 46]\n",
      "[0, 8, 42]\n",
      "[8, 10, 14, 19, 20, 23, 28, 32, 36, 40, 41, 42, 46]\n",
      "[20, 23]\n",
      "[5, 10, 16, 23, 25, 35, 42, 44, 47]\n",
      "[6, 27, 36, 41]\n",
      "[6, 10, 19, 20, 21, 22, 26, 27, 29, 32, 38, 46]\n",
      "[2, 13, 37]\n",
      "[7, 9, 16, 23, 33, 36]\n",
      "[34, 35, 38]\n",
      "[1, 6, 15, 24, 31]\n",
      "[8, 9, 10, 11, 12, 17, 24, 30]\n",
      "[12, 31, 32, 40, 41, 44]\n",
      "[3, 5, 7, 8, 10, 13, 14, 15, 19, 21, 22, 27, 31, 34, 39, 41, 42, 44, 45, 47]\n",
      "[8, 15, 18, 22, 34, 37, 38, 39, 41, 42, 43, 46]\n",
      "[5, 8, 9, 11, 12, 16, 18, 23, 26, 29, 38, 43, 44, 48]\n",
      "[14, 26, 29, 38, 46]\n",
      "[12, 24, 28, 32, 38, 40]\n",
      "[2, 8, 10, 44, 46]\n",
      "[2, 3, 4, 9, 10, 14, 15, 16, 17, 18, 22, 24, 26, 29, 36, 39, 40, 41, 46, 47]\n",
      "[2, 5, 7, 8, 9, 10, 18, 22, 24, 29, 34, 41, 47]\n",
      "[0, 10, 16, 24, 32, 33, 34, 39, 44, 45, 48]\n",
      "[1, 4, 14, 19, 20, 22, 23, 29, 30, 36, 37, 41, 42]\n",
      "[5, 35, 46, 47]\n",
      "[2, 4, 11, 18, 25, 26, 34, 42, 43, 47]\n",
      "[0, 3, 9, 10, 19, 26, 27, 30, 35, 48]\n",
      "[13, 42, 45, 47]\n",
      "[12, 26, 32, 34, 39]\n",
      "[18, 27, 38]\n",
      "[16, 17, 18, 22]\n",
      "[3, 12, 17, 19, 28, 29, 30, 31, 33, 43]\n",
      "[5, 13, 23, 36, 41]\n",
      "[2, 10, 15, 21, 23, 25, 36, 45]\n",
      "[9, 24, 40, 42]\n",
      "[11, 17, 41]\n",
      "[4, 12, 17, 32, 35]\n",
      "[4, 16, 22, 33, 41, 44]\n",
      "[4, 6, 7, 12, 31, 41, 42, 43]\n",
      "[24, 34]\n",
      "[15, 20, 30, 34, 35, 39, 40, 43, 47]\n",
      "[5, 7, 18, 21, 25, 31, 34, 42]\n",
      "[0, 5, 9, 32, 35, 37, 40]\n",
      "[2, 5, 11, 24, 27, 41]\n",
      "[13, 34, 44]\n",
      "[1, 5, 11, 15, 17, 22, 25, 29, 31, 32, 34, 45]\n",
      "[1, 5, 6, 7, 9, 10, 13, 14, 16, 17, 19, 20, 21, 24, 26, 29, 40, 46, 48]\n",
      "[1, 5, 13, 21, 24, 25, 26, 27, 35, 39, 44, 45, 46]\n",
      "[7, 15, 37, 38]\n",
      "[0, 5, 22]\n",
      "[2, 30, 33]\n",
      "[4, 5, 6, 7, 11, 12, 31, 36, 47]\n",
      "[16, 19, 20, 24, 35, 36]\n",
      "[17, 25, 47]\n",
      "[18, 22, 23, 32, 38, 43]\n",
      "[3, 20, 26]\n",
      "[2, 20]\n",
      "[0, 3, 7, 8, 9, 11, 12, 19, 24, 32, 33, 34, 41, 42, 46, 47]\n",
      "[4, 14, 18, 29]\n",
      "[1, 2, 15, 26, 27, 31, 34, 35, 43, 44, 47]\n",
      "[28, 31, 34, 46, 47, 48]\n",
      "[12, 14, 19, 22, 24, 25, 32, 33, 38, 46, 47, 48]\n",
      "[7, 8, 16, 27, 32, 34]\n",
      "[11, 13, 19, 30, 37]\n",
      "[2, 14, 26, 30, 43]\n",
      "[13, 17, 30, 36, 45]\n",
      "[13, 16, 20, 34, 41]\n",
      "[3, 6, 18, 26, 46]\n",
      "[12, 29, 47]\n",
      "[28, 45]\n",
      "[3, 4, 11, 12, 16, 18, 21, 24, 25, 28, 38, 40, 45]\n",
      "[1, 2, 5, 7, 10, 13, 16, 21, 23, 26, 27, 34, 35, 38, 44, 45, 48]\n",
      "[8, 12, 13, 16, 27, 29, 31, 35, 41]\n",
      "[0, 1, 4, 10, 12, 25, 35, 38, 40, 44]\n",
      "[17, 19]\n",
      "[0, 31, 37, 45]\n",
      "[4, 7, 9, 10, 14, 15, 16, 24, 25, 27, 30, 33, 34, 35, 38, 40, 41, 43, 44, 47, 48]\n",
      "[0, 1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 18, 19, 20, 21, 23, 24, 26, 27, 28, 29, 32, 34, 36, 37, 38, 40, 43, 46, 47]\n",
      "[17, 18, 22, 33, 41]\n",
      "[2, 4, 7, 13, 16, 21, 26, 31, 36, 43]\n",
      "[0, 1, 10, 14, 16, 22, 27, 32, 41, 44]\n",
      "[2, 3, 6, 10, 19, 25, 29, 31]\n",
      "[23, 28, 33]\n",
      "[0, 41]\n",
      "[4, 14, 29, 34, 45]\n",
      "[0, 2, 5, 41]\n",
      "[4, 16, 18, 21, 23, 37, 38, 39, 41, 42, 46]\n",
      "[1, 18, 21, 29, 36, 39]\n",
      "[10, 14, 25]\n",
      "[0, 7, 28, 36]\n",
      "[1, 3, 6, 9, 12, 18, 20, 25, 28, 32, 35, 39, 43, 45, 46]\n",
      "[36, 44]\n",
      "[4, 15, 16, 40, 47]\n",
      "[0, 5, 22, 25, 29, 33, 41, 44, 46]\n",
      "[5, 12, 37, 38]\n",
      "[1, 4, 5, 11, 25, 27, 30, 34, 44, 48]\n",
      "[1, 5, 12, 14, 16, 26, 33, 35, 37, 39, 42, 44, 46]\n",
      "[11, 19, 37, 43]\n",
      "[3, 7, 14, 41]\n",
      "[19, 35, 44]\n",
      "[7, 8, 13, 21, 34, 44]\n",
      "[23, 38, 41]\n",
      "[1, 2, 7, 11, 14, 17, 18, 23, 24, 26, 31, 43, 44, 45, 46, 47]\n",
      "[13, 14, 15, 20, 25, 27, 36, 38, 45, 46, 47]\n",
      "[30, 33, 35, 38, 41, 47]\n",
      "[8, 18, 21, 22, 31, 32, 37, 47]\n",
      "[5, 10, 11, 14, 17, 18, 25]\n",
      "[2, 5, 6, 14, 17, 18, 19, 26, 31, 37, 41, 44]\n",
      "[0, 2, 4, 6, 8, 11, 14, 15, 16, 19, 20, 22, 24, 27, 29, 31, 35, 41, 43, 46, 48]\n",
      "[0, 12, 13, 20, 24, 30, 34, 38, 43, 46, 47]\n",
      "[4, 6, 11, 30, 31, 34, 40, 41]\n",
      "[1, 2, 19, 30, 31, 32, 35, 36, 40, 44]\n",
      "[20, 22, 29]\n",
      "[0, 2, 12, 19, 25, 34, 35, 39, 40, 41, 44, 46]\n",
      "[4, 10, 17, 20, 24, 29, 35, 37]\n",
      "[8, 12, 18, 28, 32, 34, 39]\n",
      "[20, 24, 36]\n",
      "[7, 19, 26, 27, 44]\n",
      "[21, 22, 34]\n",
      "[9, 12, 16, 18, 34, 41, 46]\n",
      "[0, 1, 2, 4, 9, 17, 20, 24, 29, 31, 32, 33, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48]\n",
      "[6, 11, 12, 19, 33]\n",
      "[12, 27, 37]\n",
      "[2, 5, 6, 7, 8, 14, 30, 31, 33, 35, 37, 38, 40]\n",
      "[1, 3, 9, 11, 15, 21, 22, 29, 36, 37, 39, 44, 45, 48]\n",
      "[0, 9, 12, 13, 14, 15, 16, 19, 22, 27, 28, 36, 38, 39, 44, 45, 47]\n",
      "[1, 10, 22, 38, 40, 41, 41]\n",
      "[2, 9, 15, 25, 34, 36, 37]\n",
      "[11, 21, 23, 42, 47, 48]\n",
      "[0, 2, 6, 7, 11, 12, 13, 16, 17, 18, 23, 24, 25, 28, 33, 35, 36, 38, 39, 46, 47, 48]\n",
      "[11, 13, 21, 23, 29, 31, 35, 36, 39, 42, 44]\n",
      "[1, 2, 14, 18, 19, 30, 33, 38, 42, 46, 48]\n",
      "[5, 11, 20]\n",
      "[11, 12, 29]\n",
      "[0, 28, 30, 35, 44, 45]\n",
      "[11, 12, 13, 14, 21, 24, 32, 43]\n",
      "[15, 48]\n",
      "[0, 3, 5, 7, 8, 10, 11, 13, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 29, 32, 33, 36, 39, 43, 44, 45, 46, 48]\n",
      "[0, 1, 21, 33, 41]\n",
      "[3, 14, 35]\n",
      "[7, 8, 9, 14, 15, 19, 25, 27, 28, 31, 32, 36, 37, 40, 46, 47]\n",
      "[0, 4, 13, 15, 20, 39]\n",
      "[0, 5, 12, 32, 37]\n",
      "[2, 6, 10, 21, 36, 37, 40, 41]\n",
      "[4, 6, 31, 36, 39, 46]\n",
      "[5, 8, 22, 26, 31, 32, 34, 37]\n",
      "[3, 12, 19, 21, 29, 33, 34, 35, 40]\n",
      "[29, 32]\n",
      "[19, 27, 36, 44]\n",
      "[3, 12, 26]\n",
      "[2, 11, 16, 34, 42]\n",
      "[18, 24, 39, 47]\n",
      "[4, 5, 17, 20, 21, 23, 25, 27, 28, 29, 32, 33, 35, 37, 40, 46, 47]\n",
      "[1, 8, 13, 15, 22, 24, 30, 31, 33, 36, 37, 47, 48]\n",
      "[22, 32, 33]\n",
      "[8, 15, 28, 33, 43, 46]\n",
      "[2, 3, 4, 5, 6, 9, 13, 15, 19, 20, 27, 30, 36, 40, 43]\n",
      "[12, 20, 33]\n",
      "[8, 26, 39]\n",
      "[8, 13, 18, 42, 46]\n",
      "[6, 11, 12, 38]\n",
      "[7, 16, 18, 24, 34]\n",
      "[6, 11, 13, 19, 22, 24, 42]\n",
      "[9, 10, 12, 15, 18, 20, 21, 26, 43, 45]\n",
      "[2, 19, 26, 28, 43]\n",
      "[2, 5, 9, 13, 37, 46, 48]\n",
      "[0, 6, 18, 29, 32, 41, 41, 42, 43]\n",
      "[2, 15, 41]\n",
      "[0, 2, 3, 9, 16, 21, 22, 26, 31, 38, 41]\n",
      "[2, 8, 10, 12, 13, 14, 17, 19, 23, 24, 26, 27, 28, 32, 33, 37, 38, 41]\n",
      "[4, 19, 48]\n",
      "[0, 34, 39, 46]\n",
      "[1, 2, 7, 11, 12, 13, 15, 18, 19, 25, 29, 36, 41, 47, 48]\n",
      "[2, 3, 9, 15, 16, 18, 21, 23, 30, 36, 40, 44, 45, 47, 48]\n",
      "[8, 11, 23]\n",
      "[10, 12, 23, 26, 42, 47]\n",
      "[9, 26, 37, 48]\n",
      "[0, 1, 5, 7, 14, 19, 29, 33, 40, 41, 43]\n",
      "[31, 44]\n",
      "[15, 18, 27, 35, 36, 40, 46]\n",
      "[7, 25, 30, 35, 36]\n",
      "[9, 11, 46]\n",
      "[4, 42, 47]\n",
      "[20, 21, 26, 39, 40]\n",
      "[17, 21, 33, 42]\n",
      "[22, 48]\n",
      "[1, 26, 33, 37, 38, 39, 42, 44]\n",
      "[0, 3, 9, 22, 24, 29, 41, 42, 44]\n",
      "[3, 4, 7, 22, 32, 36, 37, 40, 44]\n",
      "[2, 5, 14, 17, 28, 30, 32, 33, 34, 36, 40]\n",
      "[3, 7, 10, 11, 14, 25, 32, 35, 36, 44, 46]\n",
      "[3, 10, 22, 27, 29, 31, 33, 36, 37, 39, 42]\n",
      "[4, 13, 23, 27, 29, 37]\n",
      "[1, 4, 5, 10, 13, 29, 41, 44]\n",
      "[4, 6, 8, 14, 15, 18, 21, 22, 23, 32, 40, 48]\n",
      "[7, 11, 18, 21, 25, 27, 28, 32, 33, 40, 42, 45]\n",
      "[10, 16, 18, 22, 29, 33, 41]\n",
      "[14, 26, 34, 48]\n",
      "[16, 18, 19, 33]\n",
      "[11, 35, 41]\n",
      "[1, 7, 36]\n",
      "[2, 6, 16, 27, 32, 47]\n",
      "[12, 14, 18, 20, 24, 28, 29, 33, 39, 43, 45, 48]\n",
      "[22, 48]\n",
      "[2, 3, 4, 11, 18, 21, 25]\n",
      "[25, 34, 39, 41]\n",
      "[1, 5, 7, 11, 13, 23, 28, 29, 30, 31, 40, 41, 46]\n",
      "[3, 10, 14, 17, 41, 41, 44]\n",
      "[0, 28, 31]\n",
      "[2, 11, 27, 28, 33, 36]\n",
      "[0, 3, 4, 10, 11, 12, 14, 15, 16, 17, 21, 25, 26, 28, 29, 31, 32, 33, 36, 37, 38, 39, 41, 41, 42, 43, 48]\n",
      "[4, 10, 11, 25]\n",
      "[3, 9, 39]\n",
      "[7, 12, 17, 32, 42, 43, 45]\n",
      "[11, 12, 18, 23, 35, 48]\n",
      "[18, 34, 36]\n",
      "[0, 12, 16, 19, 21, 22, 31, 33]\n",
      "[14, 16, 18, 34, 48]\n",
      "[1, 19, 21, 27, 30]\n",
      "[1, 8, 18, 19, 26, 31, 37, 42, 43, 45, 47]\n",
      "[5, 21, 34]\n",
      "[1, 36, 38]\n",
      "[11, 13, 24, 26, 27, 41, 47]\n",
      "[32, 39]\n",
      "[4, 22]\n",
      "[5, 7, 13, 22, 23, 24, 27, 31, 32, 37, 41, 45, 48]\n",
      "[6, 9, 14, 37, 38]\n",
      "[0, 7, 12, 23, 29, 30, 31, 32, 34, 39, 40, 41, 41, 42, 45, 46, 47]\n",
      "[0, 1, 4, 7, 11, 13, 15, 17, 18, 22, 30, 31, 41, 43, 47, 48]\n",
      "[19, 20, 42]\n",
      "[11, 13, 24, 26, 33, 38, 39, 41, 42]\n",
      "[5, 10, 15, 20, 35, 39, 43]\n",
      "[16, 18, 25, 27, 28, 32, 44, 48]\n",
      "[0, 3, 4, 5, 6, 8, 19, 20, 21, 22, 23, 25, 28, 29, 33, 36, 37, 42]\n",
      "[25, 26, 27, 28, 32, 34, 35, 37, 41, 48]\n",
      "[0, 1, 13, 14, 15, 17, 20, 25, 30, 34, 38, 41]\n",
      "[2, 15, 20, 38, 47]\n",
      "[7, 16, 23, 27, 31, 46, 47, 48]\n",
      "[1, 2, 36]\n",
      "[13, 43]\n",
      "[1, 36, 37, 40]\n",
      "[4, 15, 17, 24, 34, 43]\n",
      "[13, 14, 15, 26, 32, 34, 35]\n",
      "[2, 6, 7, 8, 12, 24, 33, 34, 38]\n",
      "[9, 38]\n",
      "[0, 1, 10, 12, 14, 16, 17, 18, 21, 23, 31, 39]\n",
      "[1, 25, 42, 47, 48]\n",
      "[8, 13, 38, 40]\n",
      "[1, 10, 17, 18, 21, 22, 29, 33, 36, 40, 44, 46]\n",
      "[21, 40, 45]\n",
      "[7, 18, 23, 25, 29]\n",
      "[22, 25, 32, 45]\n",
      "[9, 20, 31, 33, 44]\n",
      "[31, 33]\n",
      "[1, 4, 8, 9, 10, 15, 25, 26, 28, 41, 42, 43, 46]\n",
      "[10, 14, 26, 32, 38, 47]\n",
      "[1, 3, 13, 14, 33, 40, 44]\n",
      "[5, 7, 8, 12, 14, 15, 16, 18, 20, 26, 28, 30, 33, 36, 37, 39, 40, 43, 44, 48]\n",
      "[17, 27, 34]\n",
      "[5, 14, 16, 40, 41, 42, 46]\n",
      "[16, 36, 37, 40, 41, 43, 45]\n",
      "[11, 44]\n",
      "[6, 7, 8, 9, 11, 14, 17, 18, 29, 34, 36, 40]\n",
      "[8, 11, 27, 28, 33, 36, 44, 46]\n",
      "[13, 23, 29, 34]\n",
      "[5, 26, 27, 42]\n",
      "[0, 2, 5, 17, 18, 30, 35, 41, 41, 42, 44, 47]\n",
      "[0, 5, 11, 17, 19, 30]\n",
      "[8, 39]\n",
      "[0, 2, 15, 19, 21, 29, 30, 32, 40, 41, 43, 45, 46]\n",
      "[4, 6, 10, 15, 32, 34, 35, 36, 40, 41, 42, 47]\n",
      "[14, 20, 25, 32, 44, 48]\n",
      "[2, 17, 23, 38, 47]\n",
      "[9, 13]\n",
      "[5, 9, 22, 28]\n",
      "[16, 48]\n",
      "[14, 18]\n",
      "[10, 15, 20]\n",
      "[0, 1, 7, 10, 11, 13, 14, 15, 24, 33, 38, 39, 46]\n",
      "[13, 21]\n",
      "[9, 11, 15, 42]\n",
      "[6, 15, 26, 27, 33, 39, 41, 48]\n",
      "[24, 39, 46]\n",
      "[5, 10, 15, 19, 21, 22, 26, 46]\n",
      "[41, 44]\n",
      "[2, 17, 23, 28, 40]\n",
      "[6, 17, 24, 26, 39, 47]\n",
      "[17, 27, 28, 31, 32, 34, 45, 48]\n",
      "[8, 9, 20, 26, 33, 34, 37]\n",
      "[1, 4, 6, 8, 9, 16, 18]\n",
      "[21, 26, 41]\n",
      "[2, 5, 6, 7, 9, 13, 19, 20, 22, 23, 32]\n",
      "[20, 45]\n",
      "[2, 7, 13, 25, 47]\n",
      "[7, 9, 28, 38, 41]\n",
      "[15, 26, 30, 32, 46]\n",
      "[1, 6, 12, 33]\n",
      "[8, 42, 43]\n",
      "[1, 3, 23, 33, 38, 39, 47]\n",
      "[4, 7, 44]\n",
      "[2, 3, 4, 5, 9, 11, 15, 20, 21, 31, 34, 35, 44, 45, 46]\n",
      "[13, 21, 38]\n",
      "[0, 13, 23]\n",
      "[11, 16, 26, 28]\n",
      "[3, 4, 5, 6, 13, 16, 17, 20, 21, 23, 27, 30, 35, 37, 39, 40, 44, 46]\n",
      "[18, 24]\n",
      "[1, 2, 7, 11, 27, 36, 45]\n",
      "[26, 27, 29]\n",
      "[3, 7, 23, 46, 47]\n",
      "[7, 26, 31, 47, 48]\n",
      "[6, 10, 12, 24, 26, 29, 37, 43]\n",
      "[1, 16]\n",
      "[14, 18, 24, 32, 38, 42, 47]\n",
      "[21, 27, 41]\n",
      "[2, 3, 4, 12, 16, 19, 24, 32, 35, 38, 39, 41]\n",
      "[13, 21, 41, 42, 43, 44]\n",
      "[1, 2, 3, 13, 15, 16, 20, 29, 36]\n",
      "[34, 36, 44]\n",
      "[9, 10, 19, 24, 29, 32, 36, 37, 41, 45]\n",
      "[8, 21, 37, 41, 41]\n",
      "[4, 5, 10, 21, 22, 25, 34, 39, 42, 45]\n",
      "[22, 27, 31, 41]\n",
      "[4, 9, 20, 23, 24, 36]\n",
      "[0, 7, 8, 20, 23, 24, 31, 43]\n",
      "[1, 3, 6, 12, 13, 14, 18, 19, 23, 24, 25, 26, 29, 34, 36, 41, 47]\n",
      "[7, 20, 41]\n",
      "[7, 12, 15, 17, 19, 25, 30, 41]\n",
      "[18, 41]\n",
      "[4, 8, 9, 10, 12, 13, 24, 25, 26, 27, 30, 32, 34, 36, 38, 42, 43, 45, 47, 48]\n",
      "[1, 2, 4, 5, 7, 10, 12, 17, 19, 21, 23, 26, 28, 30, 34, 36, 41, 41, 44, 45, 46]\n",
      "[5, 12, 26, 27, 41, 46]\n",
      "[7, 9, 33, 41, 41]\n",
      "[39, 43]\n",
      "[2, 4, 41]\n",
      "[7, 11, 16, 36]\n",
      "[7, 8, 9, 13, 17, 18, 25, 28, 29, 30, 31, 34, 40, 44, 45, 46, 48]\n",
      "[2, 13, 19, 23, 41, 42, 45, 46]\n",
      "[6, 17, 38, 45]\n",
      "[0, 26, 34]\n",
      "[0, 1, 2, 3, 5, 8, 9, 10, 12, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 28, 29, 30, 31, 32, 38, 39, 40, 41, 41, 44, 45, 46, 48]\n",
      "[0, 5, 11, 22, 30]\n",
      "[26, 40]\n",
      "[5, 17, 18, 21, 23, 26, 28, 40, 41, 42, 47]\n",
      "[5, 11, 40]\n",
      "[1, 7, 13, 18, 19, 22, 23, 24, 25, 26, 27, 28, 35, 39, 41, 43, 44, 45, 46, 48]\n",
      "[7, 17, 29, 38, 39]\n",
      "[14, 19, 20, 27]\n",
      "[2, 6, 7, 13, 17, 25, 32, 35, 42]\n",
      "[10, 19, 26, 31, 32, 35, 41]\n",
      "[4, 13, 17, 26, 29, 30, 36, 41, 47]\n",
      "[1, 4, 11, 15, 21, 26, 27, 40, 41, 47, 48]\n",
      "[17, 18, 19, 37, 38, 39]\n",
      "[1, 8, 14, 21]\n",
      "[0, 2, 4, 6, 10, 12, 20, 22, 25, 28, 29, 33, 38, 44]\n",
      "[18, 23, 31, 39]\n",
      "[1, 3, 4, 8, 14, 17, 18, 21, 22, 24, 26, 29, 35, 36, 38, 46]\n",
      "[2, 4, 7, 12, 13, 16, 18, 26, 27, 29, 33, 35, 36, 44, 48]\n",
      "[9, 16, 25, 37, 45]\n",
      "[4, 23, 37]\n",
      "[1, 13, 15, 17, 22, 34, 35, 38, 39, 43]\n",
      "[7, 17, 27, 36, 46, 47]\n",
      "[0, 3, 4, 11, 14, 15, 18, 20, 35]\n",
      "[8, 12, 15, 46, 47, 48]\n",
      "[0, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 18, 19, 21, 22, 23, 25, 30, 31, 32, 33, 37, 38, 42, 43, 45, 46, 47]\n",
      "[38, 46]\n",
      "[7, 10, 13, 14, 28, 33]\n",
      "[4, 5, 7, 16, 20, 22, 25, 26, 30, 31, 36, 44, 47]\n",
      "[2, 3, 6, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 23, 28, 29, 31, 34, 41, 42, 46, 48]\n",
      "[0, 6, 8]\n",
      "[3, 5, 7, 14, 17, 29, 30, 35, 40, 41, 48]\n",
      "[3, 20, 21, 41, 48]\n",
      "[3, 6, 10, 11, 12, 15, 27, 38, 40, 41, 43, 48]\n",
      "[3, 5, 6, 19, 21, 29, 33, 40, 43, 45, 48]\n",
      "[1, 2, 6, 9, 11, 12, 20, 21, 25, 30, 31, 37, 42, 43, 44]\n",
      "[0, 1, 2, 4, 6, 7, 9, 12, 13, 15, 16, 17, 18, 19, 22, 23, 24, 25, 27, 29, 30, 34, 35, 37, 39, 42, 45, 46, 48]\n",
      "[13, 18, 35]\n",
      "[0, 15]\n",
      "[4, 22, 24, 25, 29, 31, 34, 35, 38, 39, 40, 41, 46]\n",
      "[2, 25, 32]\n",
      "[13, 25, 33, 34, 39, 41, 47, 48]\n",
      "[1, 4, 5, 6, 14, 16, 17, 18, 19, 22, 40, 46, 48]\n",
      "[6, 13, 14, 15, 17, 18, 29, 41]\n",
      "[1, 18, 22, 25, 28, 32, 40, 46]\n",
      "[16, 39, 46]\n",
      "[4, 5, 7, 11, 27, 28, 36, 38, 42, 43, 47]\n",
      "[1, 3, 4, 19, 32]\n",
      "[0, 1, 3, 7, 18, 22, 27, 40, 41, 45]\n",
      "[37, 41, 48]\n",
      "[15, 24, 26, 27]\n",
      "[2, 6, 7, 10, 14, 18, 27, 30, 34, 37, 38, 39, 45]\n",
      "[22, 27, 41]\n",
      "[4, 29, 30, 31, 36, 41, 44]\n",
      "[8, 27, 34, 37]\n",
      "[6, 14, 26, 35]\n",
      "[21, 32, 34]\n",
      "[0, 4, 8, 10, 17, 27, 35, 37, 38, 46, 48]\n",
      "[11, 15, 29]\n",
      "[11, 19, 21, 44]\n",
      "[4, 28, 31, 32]\n",
      "[1, 4, 12, 13, 19, 20, 28, 31, 34, 35, 38, 41, 46, 48]\n",
      "[7, 12, 16, 17, 20, 23, 24, 27, 34, 36, 42, 43, 48]\n",
      "[12, 23, 31]\n",
      "[5, 14, 18, 21, 24, 25, 36, 37, 38, 43, 47]\n",
      "[1, 2, 27, 28, 44]\n",
      "[10, 29, 48]\n",
      "[38, 48]\n",
      "[1, 12, 21, 25, 32, 40, 45]\n",
      "[3, 5, 7, 20, 22, 27, 30, 31, 32, 34, 35, 36, 38, 39, 41, 44]\n",
      "[0, 2, 3, 4, 5, 24, 25]\n",
      "[0, 7, 14, 19, 21, 22, 31, 34, 35, 37, 40, 41, 44, 48]\n",
      "[2, 5, 21, 24, 29, 38]\n",
      "[1, 15, 19, 21, 23, 25, 36, 41, 45]\n",
      "[23, 32, 43]\n",
      "[0, 2, 3, 5, 10, 11, 14, 17, 18, 20, 25, 26, 30, 31, 32, 34, 35, 36, 38, 39, 41, 41, 42, 43, 44, 45, 47]\n",
      "[10, 22, 36, 37]\n",
      "[1, 15, 40]\n",
      "[1, 26, 27, 30, 32, 38, 41, 42, 45]\n",
      "[3, 23, 24, 34, 43]\n",
      "[12, 21]\n",
      "[26, 40, 45, 46]\n",
      "[11, 31]\n",
      "[2, 14, 29, 31, 37, 44, 48]\n",
      "[26, 34, 41]\n",
      "[15, 19, 38, 41]\n",
      "[15, 30, 41, 47]\n",
      "[20, 36]\n",
      "[30, 43]\n",
      "[3, 4, 12, 14, 19, 20, 24, 25, 26, 31, 34, 35, 39, 40, 41, 43]\n",
      "[7, 11, 12, 13, 28, 32, 41, 41, 44]\n",
      "[2, 13, 17, 23, 27, 47]\n",
      "[14, 17, 45, 48]\n",
      "[0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 31, 34, 35, 36, 37, 41, 42, 43, 44, 45, 46, 47, 48]\n",
      "[1, 3, 5, 8, 9, 16, 18, 22, 24, 34]\n",
      "[5, 9, 13, 21, 24, 28, 39, 43, 45]\n",
      "[18, 19, 21, 23, 24, 35, 36, 37, 38, 43, 47]\n",
      "[1, 14, 24, 27, 37, 42, 44]\n",
      "[0, 4, 6, 9, 15, 16, 20, 25, 33, 38, 43, 45]\n",
      "[1, 6, 22]\n",
      "[16, 21, 31, 38, 41]\n",
      "[7, 23, 42, 43]\n",
      "[3, 8, 9, 19, 23, 25, 26, 28, 29, 41]\n",
      "[14, 48]\n",
      "[8, 24, 31, 32]\n",
      "[0, 1, 3, 10, 11, 12, 13, 16, 17, 19, 20, 25, 35, 36, 39, 40, 45]\n",
      "[9, 24, 28, 29, 30, 32, 35, 48]\n",
      "[13, 17, 33, 34, 41]\n",
      "[4, 5, 9, 20, 21, 24, 26, 31, 37]\n",
      "[11, 14, 18]\n",
      "[2, 25, 27, 31, 33, 43, 44]\n",
      "[26, 41]\n",
      "[4, 45, 46]\n",
      "[0, 7, 10, 11, 16, 31, 37, 47, 48]\n",
      "[5, 15, 17, 32, 35]\n",
      "[3, 11, 20, 32, 38, 42]\n",
      "[13, 24]\n",
      "[4, 24, 37]\n",
      "[6, 8, 9, 19, 30, 31, 39]\n",
      "[9, 15, 22, 23, 24, 26, 37, 43]\n",
      "[1, 3, 4, 5, 7, 16, 19, 21, 27, 29, 33, 37, 40, 41, 43, 44, 48]\n",
      "[14, 18, 22, 26, 33, 46]\n",
      "[4, 6, 13, 15, 19, 20, 21, 25, 28, 29, 33, 38, 44, 47, 48]\n",
      "[2, 3, 4, 11, 12, 13, 14, 25, 26, 31, 33, 34]\n",
      "[2, 8, 12, 16, 22, 28, 31, 33, 35, 39, 40, 41, 43, 48]\n",
      "[7, 9, 10, 15, 17, 26, 27, 31, 32, 48]\n",
      "[4, 5, 8, 20, 29, 35, 37, 39, 44, 47]\n",
      "[2, 6, 13, 16, 18, 23, 30, 36, 38, 39, 41]\n",
      "[1, 2, 5, 7, 11, 20, 24, 32, 36, 45, 46]\n",
      "[4, 5, 19, 26, 43, 44]\n",
      "[7, 43, 44, 45]\n",
      "[16, 33]\n",
      "[11, 22, 33, 47]\n",
      "[2, 3, 6, 9, 10, 15, 17, 20, 23, 26, 30, 33, 37, 40, 41, 43, 44]\n",
      "[0, 2, 6, 9, 18, 19, 21, 22, 28, 29, 31, 38, 39, 41, 41, 43, 44, 45, 47]\n",
      "[2, 6, 12, 17, 19, 23, 28, 30, 36, 40, 44, 46, 48]\n",
      "[9, 13, 14, 18, 27, 33, 47]\n",
      "[5, 16, 22, 25, 26, 33, 35, 47]\n",
      "[11, 12, 18, 27, 39, 41, 42, 44, 46]\n",
      "[10, 12, 22, 28, 33, 38, 39, 45, 46, 47]\n",
      "[1, 12, 18, 28, 39, 40, 41, 44]\n",
      "[3, 9, 42]\n",
      "[2, 4, 5, 6, 7, 9, 13, 15, 18, 20, 32, 40, 41, 41]\n",
      "[7, 47]\n",
      "[3, 9, 25, 28, 30, 37, 41, 45]\n",
      "[2, 5, 28, 30, 34, 35, 41, 44]\n",
      "[0, 1, 2, 4, 7, 9, 10, 15, 16, 19, 23, 28, 31, 32, 33, 34, 37, 38, 39, 40, 41, 43, 45, 46]\n",
      "[35, 44]\n",
      "[0, 5, 8, 13, 15, 16, 22, 23, 24, 39, 43]\n",
      "[4, 5, 22, 30, 35, 36, 39, 45]\n",
      "[0, 4, 19, 20, 28, 29, 31, 34, 40, 44]\n",
      "[12, 27, 45]\n",
      "[12, 16, 19, 24, 44, 47]\n",
      "[1, 7, 17, 38, 48]\n",
      "[7, 21, 22]\n",
      "[2, 4, 6, 8, 16, 18, 27, 29, 33, 46]\n",
      "[25, 32, 43]\n",
      "[9, 35, 39, 41]\n",
      "[0, 10, 28, 30, 38, 40]\n",
      "[3, 8, 11, 13, 18, 19, 25, 26, 29, 30, 36, 39, 41, 41, 47]\n",
      "[9, 23, 25, 29, 41, 47]\n",
      "[0, 13, 15, 24, 27, 28, 29, 31, 41, 43, 47]\n",
      "[28, 29, 41, 45]\n",
      "[5, 15, 22, 30, 33, 38, 42, 45]\n",
      "[4, 14, 19, 22, 29, 41]\n",
      "[5, 40, 45, 46]\n",
      "[3, 5, 18]\n",
      "[5, 11, 13, 14, 17, 23, 25, 26, 27, 38, 39, 41]\n",
      "[10, 14, 18, 21, 25, 26, 32, 47]\n",
      "[1, 6, 8, 9, 12, 15, 18, 23, 24, 26, 27, 28, 29, 30, 33, 35, 36, 38, 41, 44, 48]\n",
      "[15, 31, 32, 36, 42, 43, 46]\n",
      "[0, 2, 6, 12, 15, 16, 18, 23, 32, 38, 40, 46, 48]\n",
      "[8, 14, 15, 25, 30, 39, 42, 44]\n",
      "[1, 5, 13, 16, 17, 23, 24, 26, 30, 32, 37, 41]\n",
      "[1, 15, 23, 26, 30, 43, 45]\n",
      "[16, 42, 45]\n",
      "[0, 4, 26, 29, 32, 34]\n",
      "[15, 18, 20, 25, 38, 40, 41, 45]\n",
      "[4, 10, 22, 28, 31, 34, 35, 41]\n",
      "[4, 7, 15, 16, 18, 25, 30, 35, 38]\n",
      "[0, 11, 18, 19, 28, 30, 32]\n",
      "[0, 4, 14, 16, 17, 43]\n",
      "[7, 13, 17, 19, 23]\n",
      "[0, 1, 4, 5, 6, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 31, 34, 47]\n",
      "[6, 13, 14, 21]\n",
      "[2, 6, 14, 44]\n",
      "[12, 19, 37]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 17, 19, 22, 23, 29, 32, 34, 40, 41, 42, 43, 44]\n",
      "[6, 9, 13, 14, 17, 43]\n",
      "[38, 48]\n",
      "[6, 7, 9, 13, 14, 17, 23, 31, 32, 37, 38, 44, 48]\n",
      "[0, 2, 6, 7, 9, 12, 14, 16, 19, 21, 23, 26, 29, 32, 38, 44]\n",
      "[6, 12, 14, 28, 31, 41]\n",
      "[1, 4, 7, 14, 17, 21, 23, 25, 29, 43]\n",
      "[13, 14, 20, 21, 25, 26]\n",
      "[13, 14, 34]\n",
      "[4, 6, 14, 17, 25, 43, 48]\n",
      "[0, 2, 7, 9, 10, 13, 14, 28, 34, 38]\n",
      "[6, 7, 12, 13, 14, 16, 19, 22, 38, 47]\n",
      "[1, 7, 9, 14, 23, 25, 34, 41, 43, 48]\n",
      "[13, 25]\n",
      "[2, 14, 38]\n",
      "[6, 21, 25]\n",
      "[4, 23, 44, 48]\n",
      "[0, 1, 6, 10, 14, 19, 31, 37, 41, 48]\n",
      "[0, 7, 13, 16, 25, 44]\n",
      "[0, 6, 14, 16, 19, 21, 23, 24, 26]\n",
      "[0, 4, 14, 16, 21, 23, 28, 29, 34, 37, 44]\n",
      "[0, 1, 2, 4, 6, 7, 9, 10, 12, 14, 16, 17, 19, 23, 24, 25, 34, 38, 41, 42, 43, 44]\n",
      "[0, 4, 10, 12, 13, 14, 25, 28, 37, 38, 42, 44, 48]\n",
      "[5, 12, 13, 19, 21, 28, 29, 38]\n",
      "[4, 5, 19]\n",
      "[16, 19, 21, 22, 29]\n",
      "[4, 6, 14, 16, 20, 21, 25, 29, 32]\n",
      "[1, 16, 31, 43]\n",
      "[0, 1, 5, 6, 12, 14, 16, 19, 22, 23, 25, 26, 29, 37, 41]\n",
      "[16, 29]\n",
      "[7, 17, 19]\n",
      "[19, 28]\n",
      "[0, 1, 4, 6, 7, 9, 13, 14, 16, 17, 19, 21, 22, 26, 29, 31, 34, 38, 43, 44]\n",
      "[2, 14, 48]\n",
      "[6, 10, 25]\n",
      "[7, 14, 26]\n",
      "[6, 13, 29, 43]\n",
      "[0, 6, 7, 9, 14, 17, 28, 29, 34, 44]\n",
      "[0, 1, 2, 4, 5, 6, 7, 9, 13, 14, 19, 23, 25, 26, 29, 31, 34, 37, 42, 43, 44]\n",
      "[0, 1, 2, 4, 6, 9, 13, 14, 17, 19, 23, 25, 44]\n",
      "[7, 17, 21, 23, 25, 37, 43, 47]\n",
      "[4, 19, 44]\n",
      "[0, 1, 2, 4, 6, 14, 16, 17, 23, 29, 38, 44]\n",
      "[4, 7, 13, 14, 16, 19, 22, 29]\n",
      "[0, 16, 21]\n",
      "[7, 14, 23, 34]\n",
      "[6, 9, 34]\n",
      "[4, 6, 14, 16, 23]\n",
      "[1, 6, 7, 9, 13, 14, 16, 19, 21, 23, 24, 26, 29, 31, 34, 40, 43, 47, 48]\n",
      "[6, 7, 12, 13, 17, 23, 24, 26, 29, 31, 32, 34, 37, 41, 43]\n",
      "[2, 4, 5, 9, 13, 19, 23, 34]\n",
      "[4, 7, 9, 13, 14, 16, 23, 26, 29, 42, 44]\n",
      "[7, 19, 23, 43]\n",
      "[4, 6, 7, 14, 17, 34, 37, 42]\n",
      "[1, 13, 14, 23]\n",
      "[2, 4, 7, 16, 37, 41]\n",
      "[9, 16, 22, 34]\n",
      "[9, 23, 25, 26, 29, 34, 38, 43]\n",
      "[6, 7, 16, 20, 26, 37]\n",
      "[0, 4, 5, 6, 9, 14, 23, 34, 43]\n",
      "[4, 5, 6, 7, 12, 13, 19, 24, 25, 28, 31, 32, 34, 37, 38, 43, 44]\n",
      "[4, 5, 9, 19, 23, 38]\n",
      "[6, 14, 25]\n",
      "[0, 4, 6, 14, 24, 25, 26, 32, 44]\n",
      "[4, 6, 9, 16, 23, 25, 43, 44]\n",
      "[13, 22, 42]\n",
      "[1, 13, 16, 29, 32, 44]\n",
      "[0, 4, 6, 9, 12, 13, 14, 17, 19, 25, 29, 32, 38, 43]\n",
      "[6, 16, 17]\n",
      "[0, 4, 6, 9, 13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 34, 37, 38, 41, 43, 44, 48]\n",
      "[0, 13, 14, 19, 25, 34, 37]\n",
      "[0, 4, 16]\n",
      "[1, 4, 23, 31, 34]\n",
      "[0, 4, 6, 9, 10, 13, 14, 16, 17, 19, 20, 23, 25, 38, 47, 48]\n",
      "[4, 6, 21, 23, 38]\n",
      "[0, 4, 6, 31, 34]\n",
      "[0, 4, 6, 14, 16, 37, 43]\n",
      "[4, 7, 13, 16, 25, 43]\n",
      "[23, 25, 38]\n",
      "[0, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 23, 25, 26, 34, 38, 40, 41, 43, 44, 48]\n",
      "[0, 2, 4, 12, 14, 23, 24, 34, 41, 44]\n",
      "[4, 7, 37]\n",
      "[7, 9, 16, 29, 37]\n",
      "[4, 13, 26, 28, 34, 44]\n",
      "[0, 4, 6, 7, 9, 12, 14, 16, 17, 19, 23, 48]\n",
      "[23, 26, 48]\n",
      "[7, 13, 48]\n",
      "[0, 2, 4, 5, 6, 7, 9, 12, 13, 14, 16, 17, 19, 20, 21, 22, 24, 25, 26, 28, 29, 31, 34, 38, 43, 44]\n",
      "[13, 14, 23]\n",
      "[4, 6, 14, 17, 23, 32, 34, 40, 41, 43]\n",
      "[0, 1, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 25, 29, 31, 38, 41, 43, 44, 47, 48]\n",
      "[1, 2, 4, 6, 9, 14, 16, 19, 23, 29, 34, 37, 41, 47, 48]\n",
      "[4, 6, 14, 16, 19, 29, 32, 38, 40, 41, 48]\n",
      "[1, 5, 6, 14]\n",
      "[4, 6, 13, 14, 37, 44]\n",
      "[7, 14, 19, 25]\n",
      "[4, 5, 6, 7, 13, 20, 23, 24, 40, 41, 42, 44]\n",
      "[1, 13, 14, 16, 22, 26, 42]\n",
      "[6, 10, 19, 25, 42]\n",
      "[0, 6, 9, 13, 16, 21, 23, 26, 29, 41]\n",
      "[21, 23, 34, 43]\n",
      "[0, 4, 7, 13, 19, 26]\n",
      "[19, 23]\n",
      "[0, 2, 4, 5, 6, 9, 10, 12, 13, 16, 17, 22, 23, 24, 25, 26, 29, 42, 43, 47]\n",
      "[7, 12, 21, 23, 40]\n",
      "[5, 9, 22, 38]\n",
      "[5, 6, 9, 13, 14, 31, 32, 37, 41]\n",
      "[1, 5, 6, 10, 12, 13, 23, 24, 25, 34, 42, 44]\n",
      "[0, 12, 13, 14, 16, 19, 21, 26, 34]\n",
      "[4, 14, 48]\n",
      "[0, 5, 6, 7, 9, 10, 16, 19, 21, 23, 25, 26, 29]\n",
      "[0, 4, 7, 13, 34, 44]\n",
      "[6, 7, 9, 13, 16, 17, 23, 26, 37, 38, 41, 42, 43, 44]\n",
      "[4, 23]\n",
      "[0, 6, 10, 12, 13, 14, 16, 21, 29, 34, 38, 40, 44]\n",
      "[0, 4, 7, 9, 13, 14, 31, 32, 34, 44]\n",
      "[6, 14, 19, 25, 34, 43]\n",
      "[0, 4, 14, 25, 26]\n",
      "[5, 6, 13, 19, 43, 44]\n",
      "[0, 4, 6, 7, 13, 22, 23, 31, 34, 44]\n",
      "[13, 16, 43, 44]\n",
      "[9, 13, 14, 17, 43]\n",
      "[1, 16, 19, 23, 28]\n",
      "[6, 7, 9, 17, 21, 23, 25, 31, 48]\n",
      "[1, 6, 7, 12, 14, 16, 43]\n",
      "[2, 4, 6, 23]\n",
      "[7, 14, 16]\n",
      "[5, 6, 9, 14, 16, 23, 26, 38, 40, 44]\n",
      "[0, 23, 29, 44]\n",
      "[0, 4, 6, 7, 9, 13, 14, 17, 21, 43, 48]\n",
      "[0, 4, 5, 6, 7, 10, 12, 13, 14, 17, 21, 23, 40]\n",
      "[9, 16, 41]\n",
      "[0, 6, 14, 19, 20, 34, 41]\n",
      "[13, 43, 48]\n",
      "[0, 9, 13, 19, 25, 43]\n",
      "[7, 12, 25, 26]\n",
      "[0, 6, 7, 9, 12, 13, 14, 17, 19, 23, 24, 25, 48]\n",
      "[4, 6, 16, 23, 37, 38, 42, 44, 48]\n",
      "[0, 4, 13, 17, 23, 25, 31, 34, 48]\n",
      "[2, 4, 10, 16, 23, 24, 26, 32, 34, 38, 41]\n",
      "[9, 14, 31]\n",
      "[12, 19, 29]\n",
      "[2, 6, 14, 21]\n",
      "[1, 4, 5, 6, 7, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 47, 48]\n",
      "[2, 4, 6, 7, 9, 10, 13, 14, 16, 21, 23, 25, 26, 29, 31, 34, 37, 38, 41, 42]\n",
      "[0, 4, 7, 9, 12, 14, 16, 22, 25, 28, 43, 44]\n",
      "[9, 19, 41]\n",
      "[0, 4, 5, 6, 9, 10, 13, 14, 16, 17, 19, 22, 23, 24, 25, 26, 29, 31, 37, 38, 43, 44, 48]\n",
      "[0, 4, 9, 16, 34, 43]\n",
      "[0, 1, 4, 6, 7, 13, 14, 19, 22, 23, 29, 37, 48]\n",
      "[4, 25]\n",
      "[4, 6, 14, 38]\n",
      "[0, 14, 16, 37, 43]\n",
      "[2, 13, 38]\n",
      "[4, 7, 21, 23, 32]\n",
      "[2, 10, 14, 16, 25, 43, 48]\n",
      "[0, 4, 6, 7, 9, 10, 12, 13, 16, 17, 25, 28, 31, 34, 43, 48]\n",
      "[6, 7, 10, 12, 13, 14, 16, 23, 31, 38]\n",
      "[6, 13, 38]\n",
      "[1, 4, 6, 7, 12, 14, 23, 37, 43, 44]\n",
      "[6, 13, 23]\n",
      "[0, 12, 14, 16]\n",
      "[2, 6, 9, 12, 24, 25]\n",
      "[4, 19, 23, 25, 28, 29, 41]\n",
      "[4, 38, 43]\n",
      "[0, 2, 4, 5, 6, 7, 9, 10, 13, 14, 16, 17, 19, 21, 23, 24, 25, 28, 29, 31, 34, 37, 41, 43, 44, 47, 48]\n",
      "[4, 9, 25]\n",
      "[0, 2, 4, 5, 6, 9, 10, 12, 13, 14, 16, 19, 20, 21, 23, 25, 26, 29, 32, 34, 37, 38, 43, 44]\n",
      "[10, 13, 17, 24, 25, 48]\n",
      "[2, 9, 13, 23, 28, 29, 31]\n",
      "[6, 9, 31]\n",
      "[7, 23, 43]\n",
      "[4, 21, 26]\n",
      "[4, 5, 6, 7, 9, 13, 14, 16, 17, 19, 22, 23, 26, 38, 43, 48]\n",
      "[4, 7, 9, 13, 14, 16, 19, 21, 23, 25, 41, 43, 44]\n",
      "[7, 9, 10, 12, 16, 21, 23, 25, 41]\n",
      "[0, 6, 19, 37, 41, 43]\n",
      "[0, 4, 6, 9, 14, 17, 20, 23, 25, 29, 37, 41, 48]\n",
      "[0, 4, 22]\n",
      "[6, 9, 12, 19, 43, 47]\n",
      "[7, 14, 19, 25, 37, 40, 44]\n",
      "[6, 7, 14, 22, 23]\n",
      "[2, 4, 6, 10, 16, 26, 31, 43, 48]\n",
      "[21, 25, 29]\n",
      "[0, 4, 7, 10, 12, 13, 14, 19, 28, 31, 34, 42, 43, 44]\n",
      "[2, 4, 6, 9, 12, 14, 16, 17, 19, 23, 32, 34, 37, 43, 48]\n",
      "[0, 6, 9, 13, 14, 16, 17, 19, 23, 28, 31, 42, 43, 44]\n",
      "[1, 6, 7, 12, 13, 14, 23, 34, 41]\n",
      "[0, 2, 4, 7, 12, 13, 14, 16, 17, 23, 25, 26, 28, 29, 37, 43, 44, 48]\n",
      "[19, 34]\n",
      "[9, 13, 14, 24, 29, 34, 47]\n",
      "[0, 14, 23, 25]\n",
      "[13, 23]\n",
      "[0, 12, 14, 16, 34, 43]\n",
      "[6, 9, 13, 43]\n",
      "[0, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 19, 20, 21, 22, 23, 24, 25, 26, 29, 34, 37, 44, 48]\n",
      "[0, 4, 6, 9, 21, 23, 25, 42]\n",
      "[4, 14, 19]\n",
      "[2, 10, 13, 23]\n",
      "[0, 9, 20]\n",
      "[0, 2, 4, 9, 10, 13, 14, 16, 17, 23, 24, 32, 37, 42]\n",
      "[13, 19, 38]\n",
      "[0, 4, 5, 6, 7, 13, 14, 16, 19, 21, 23, 26, 31, 32, 34, 38, 43, 44, 47]\n",
      "[4, 5, 13, 17, 23, 24, 37, 43, 44]\n",
      "[0, 4, 7, 9, 12, 13, 14, 16, 19, 21, 23, 25, 31, 32, 34, 38, 43, 48]\n",
      "[4, 6, 7, 16, 48]\n",
      "[0, 2, 4, 14, 16, 17, 23, 29, 37, 43]\n",
      "[0, 14, 44, 47]\n",
      "[0, 1, 4, 6, 7, 9, 10, 13, 14, 16, 17, 19, 21, 22, 23, 24, 25, 26, 29, 31, 32, 34, 38, 41, 42, 43, 44, 47, 48]\n",
      "[0, 1, 13, 16]\n",
      "[7, 12, 19, 23, 25, 44]\n",
      "[0, 1, 4, 7, 9, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 25, 31, 38, 42, 43, 44, 48]\n",
      "[6, 17, 44]\n",
      "[0, 23]\n",
      "[13, 14, 16, 20, 21, 23, 25, 44]\n",
      "[7, 21, 29]\n",
      "[0, 4, 6, 9, 13, 16, 17, 19, 21, 23, 25, 29, 34, 37, 38, 41, 42, 43, 44, 48]\n",
      "[0, 4, 12, 13, 14, 16, 21, 25, 29, 38, 48]\n",
      "[4, 6, 12, 14, 19, 23, 34, 40]\n",
      "[7, 9, 16, 24, 25, 44]\n",
      "[7, 9, 12, 13, 14, 41, 43]\n",
      "[13, 16, 44]\n",
      "[0, 9, 19, 21, 38]\n",
      "[4, 7, 13, 14, 16, 22, 23, 25, 29, 41, 43, 44]\n",
      "[17, 23, 26, 29]\n",
      "[0, 6, 7, 9, 13, 14, 16, 21, 23, 24, 32, 34, 44]\n",
      "[2, 6, 9, 13, 29, 48]\n",
      "[7, 12, 14, 19, 21, 23, 41, 43]\n",
      "[6, 29]\n",
      "[4, 5, 6, 12, 21, 23, 24, 25, 31, 34, 38, 41, 43, 48]\n",
      "[4, 6, 7, 9, 14, 19, 23, 29, 32, 37, 41, 42, 43, 44, 48]\n",
      "[1, 4, 5, 6, 7, 13, 19, 21, 23, 24, 25, 34, 37, 40, 44]\n",
      "[0, 4, 6, 7, 13, 14, 19]\n",
      "[9, 19, 38, 41]\n",
      "[0, 1, 4, 6, 7, 9, 12, 13, 14, 16, 17, 19, 20, 21, 22, 24, 31, 38, 40, 43, 44]\n",
      "[0, 6, 9, 12, 13, 14, 19, 23, 25, 26, 29, 34, 43, 48]\n",
      "[0, 4, 6, 7, 9, 14, 26, 29, 38, 41, 43]\n",
      "[6, 7, 14, 16, 25, 37]\n",
      "[0, 6, 13, 14, 16, 19, 22, 23, 25, 26, 28, 38, 40, 41, 43, 47, 48]\n",
      "[5, 7, 13, 31]\n",
      "[4, 21]\n",
      "[0, 31, 38]\n",
      "[5, 7, 13, 14, 22]\n",
      "[0, 7, 43]\n",
      "[4, 16, 23, 40]\n",
      "[13, 20, 44]\n",
      "[13, 14, 19, 20, 26, 41]\n",
      "[34, 44]\n",
      "[2, 6, 7, 10, 14, 25, 43]\n",
      "[0, 4, 20, 22, 23, 29]\n",
      "[0, 12, 21]\n",
      "[0, 2, 4, 7, 12, 14, 16, 17, 19, 23, 28, 29, 32, 34, 38, 43, 44]\n",
      "[0, 4, 6, 7, 9, 12, 14, 16, 19, 20, 24, 38]\n",
      "[2, 5, 6, 37, 44]\n",
      "[7, 25, 38, 41]\n",
      "[6, 44]\n",
      "[6, 7, 9, 13, 14, 19, 20, 21]\n",
      "[4, 6, 13, 17, 19, 34, 42, 43, 48]\n",
      "[0, 4, 5, 6, 7, 9, 13, 16, 17, 19, 25, 29, 34, 37, 41, 43]\n",
      "[14, 23, 25, 28, 29, 34]\n",
      "[0, 4, 7, 14, 38]\n",
      "[6, 19, 26, 29, 40]\n",
      "[0, 5, 7, 9, 12, 13, 14, 16, 17, 19, 22, 23, 25, 28, 34, 37, 38, 48]\n",
      "[0, 16, 22, 25]\n",
      "[4, 14, 19, 20, 21, 43]\n",
      "[6, 7]\n",
      "[0, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 19, 21, 22, 23, 25, 28, 29, 31, 32, 34, 37, 38, 41, 43, 48]\n",
      "[0, 4, 5, 6, 12, 13, 14, 16, 19, 23, 25, 28, 29, 31, 34, 41, 42, 44, 47, 48]\n",
      "[0, 6, 13, 14, 16, 19, 23, 25, 29, 42]\n",
      "[13, 47]\n",
      "[0, 4, 6, 10, 14, 16, 22, 25, 26, 43, 44, 48]\n",
      "[0, 4, 5, 43]\n",
      "[6, 14, 23, 43]\n",
      "[9, 32, 43]\n",
      "[13, 14]\n",
      "[0, 4, 7, 13, 14, 16, 19, 21, 22, 23, 24, 34, 37, 38, 44]\n",
      "[1, 2, 4, 6, 12, 13, 14, 16, 19, 23, 25, 26, 31, 34, 38, 42, 43, 44]\n",
      "[17, 32]\n",
      "[4, 9, 14, 16, 20, 23, 31, 34, 44]\n",
      "[0, 12, 25]\n",
      "[0, 13, 17]\n",
      "[0, 6, 14, 19, 21, 23, 29, 40, 43]\n",
      "[7, 10, 14, 16, 23, 28, 31, 32, 34, 44]\n",
      "[0, 1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 31, 34, 37, 38, 40, 41, 42, 43, 44, 48]\n",
      "[0, 4, 7, 12, 17, 23, 29, 48]\n",
      "[1, 7, 9, 29, 43]\n",
      "[4, 7, 17, 24, 25, 26, 37, 43, 48]\n",
      "[10, 22, 44]\n",
      "[4, 7, 14, 17, 21, 22, 28, 29, 43]\n",
      "[4, 9, 13, 14, 17, 21, 48]\n",
      "[0, 2, 4, 6, 7, 9, 12, 13, 14, 16, 17, 19, 23, 25, 26, 37, 41, 44, 47, 48]\n",
      "[0, 1, 2, 4, 6, 7, 9, 13, 14, 16, 19, 21, 23, 25, 26, 29, 34, 38, 40, 41, 43, 44, 47, 48]\n",
      "[4, 37, 47]\n",
      "[6, 9, 13, 16, 23, 25, 48]\n",
      "[0, 4, 21, 26, 34, 43]\n",
      "[9, 41]\n",
      "[6, 10, 47]\n",
      "[4, 7, 12, 16, 19, 21]\n",
      "[0, 2, 4, 5, 6, 7, 12, 13, 14, 16, 17, 22, 23, 26, 29, 31, 34, 38, 43, 44, 48]\n",
      "[2, 6, 12, 17, 21, 23, 25, 38]\n",
      "[9, 23]\n",
      "[19, 25, 29]\n",
      "[14, 23, 24, 25, 26, 42, 43]\n",
      "[6, 16, 19, 23]\n",
      "[2, 4, 9, 14, 44]\n",
      "[17, 42, 43]\n",
      "[4, 6, 23, 38]\n",
      "[4, 12, 13]\n",
      "[0, 9, 10, 14, 19, 23, 24, 25, 34, 38, 43, 48]\n",
      "[0, 2, 4, 5, 6, 7, 9, 12, 13, 14, 16, 17, 19, 21, 22, 23, 26, 31, 34, 37, 38, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 29, 34]\n",
      "[0, 1, 9, 12, 23, 28, 34, 37, 42, 48]\n",
      "[0, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 34, 38, 40, 41, 42, 43, 44, 48]\n",
      "[6, 10, 14, 38]\n",
      "[0, 4, 5, 6, 7, 9, 13, 14, 16, 19, 20, 21, 23, 25, 26, 29, 31, 32, 34, 38, 40, 42, 43, 44, 48]\n",
      "[6, 12, 13, 16, 25, 29, 31, 38]\n",
      "[7, 9, 26, 38, 44]\n",
      "[0, 21, 37]\n",
      "[4, 7, 9, 10, 23, 26, 37]\n",
      "[2, 4, 6, 7, 9, 13, 14, 16, 19, 21, 34, 43, 44, 48]\n",
      "[5, 12, 13, 14]\n",
      "[1, 6, 14, 16, 17, 23, 26, 40, 42, 43, 48]\n",
      "[0, 1, 2, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 32, 34, 37, 38, 41, 42, 43, 44, 47, 48]\n",
      "[10, 19]\n",
      "[4, 7, 9, 13, 23, 41, 43, 44]\n",
      "[0, 4, 14, 16, 23]\n",
      "[1, 9, 13, 14, 26, 29, 37]\n",
      "[4, 9, 14, 16, 17, 21, 23, 29]\n",
      "[6, 13, 16, 23, 29, 31, 48]\n",
      "[5, 12, 17, 34, 43]\n",
      "[0, 14, 37]\n",
      "[9, 21, 48]\n",
      "[4, 6, 7, 9, 13, 14, 16, 21, 22, 23, 25, 31, 34, 44, 47, 48]\n",
      "[4, 23, 25]\n",
      "[1, 2, 4, 5, 13, 23, 29]\n",
      "[6, 7, 10, 13, 19, 29, 38, 44]\n",
      "[22, 23]\n",
      "[4, 6]\n",
      "[0, 1, 2, 4, 5, 6, 9, 12, 13, 14, 16, 17, 19, 21, 22, 23, 24, 25, 26, 28, 29, 31, 34, 37, 38, 40, 41, 42, 43, 44, 48]\n",
      "[14, 23, 25]\n",
      "[4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 23, 29, 31, 34, 37, 38, 43, 48]\n",
      "[0, 4, 5, 6, 7, 9, 12, 13, 16, 17, 19, 23, 25, 26, 31, 34, 43, 47]\n",
      "[9, 12, 23, 34, 43]\n",
      "[1, 7, 9, 13, 14, 16, 23]\n",
      "[2, 9, 25]\n",
      "[7, 13, 16, 24]\n",
      "[4, 6, 7, 10, 13, 14, 16, 17, 19, 22, 23, 25, 28, 29, 31, 34, 37, 43, 44, 48]\n",
      "[7, 14, 26, 38, 41, 48]\n",
      "[6, 7, 10, 14, 19, 25, 26, 31, 38, 42]\n",
      "[13, 14, 19, 26]\n",
      "[0, 4, 5, 6, 10, 14, 19, 24, 26, 43, 44]\n",
      "[0, 1, 6, 7, 10, 12, 14, 19, 23, 25, 28, 31, 38, 43, 44]\n",
      "[7, 10, 14, 23, 25, 40]\n",
      "[4, 14, 26, 41, 44, 48]\n",
      "[4, 7, 48]\n",
      "[6, 14, 22, 23, 25, 26, 29, 32, 43, 44, 47]\n",
      "[16, 37, 44]\n",
      "[5, 6, 7, 9, 14, 21, 23, 25, 31, 34, 44]\n",
      "[0, 6, 7, 12, 14, 23, 29, 31, 43]\n",
      "[5, 6, 17, 26]\n",
      "[1, 4, 7, 10, 14, 21, 24, 29, 37, 38, 43, 48]\n",
      "[1, 4, 6, 7, 9, 10, 13, 14, 16, 19, 21, 22, 23, 24, 25, 26, 34, 38, 40, 42, 43, 44]\n",
      "[0, 1, 2, 4, 6, 7, 9, 10, 13, 14, 16, 17, 21, 23, 29, 44]\n",
      "[5, 16]\n",
      "[13, 14, 16, 28, 29, 38, 44, 48]\n",
      "[4, 7, 9, 34]\n",
      "[0, 6, 13, 21, 23]\n",
      "[4, 9, 14, 16, 19, 23, 25, 28, 38, 43, 47]\n",
      "[0, 17, 29]\n",
      "[21, 23]\n",
      "[25, 29, 31, 34]\n",
      "[2, 4, 13, 14, 23, 41, 44, 48]\n",
      "[5, 13, 25, 29, 31, 42]\n",
      "[0, 7, 16]\n",
      "[23, 31]\n",
      "[13, 17, 22, 23]\n",
      "[0, 1, 4, 5, 6, 7, 9, 12, 13, 14, 16, 19, 20, 21, 23, 31, 32, 34, 38, 40, 41, 42, 44, 48]\n",
      "[1, 4, 12, 14, 19, 40, 42]\n",
      "[1, 4, 7, 9, 16, 23, 25, 29, 34, 37, 38, 43, 44]\n",
      "[5, 14, 23, 24, 25]\n",
      "[0, 4, 9, 14, 16, 19, 21, 23, 24, 25, 26, 32, 37, 43, 48]\n",
      "[7, 9, 16, 28, 29]\n",
      "[2, 19, 29]\n",
      "[6, 9, 12, 13, 22, 23, 25, 41]\n",
      "[13, 14, 16, 23, 26, 34, 41, 43, 48]\n",
      "[16, 21, 34]\n",
      "[4, 23, 29]\n",
      "[0, 1, 2, 4, 5, 6, 7, 9, 10, 13, 14, 16, 17, 21, 23, 25, 26, 29, 38, 43, 47, 48]\n",
      "[2, 5, 6, 24, 43, 48]\n",
      "[4, 6, 34, 47]\n",
      "[14, 16, 19, 21, 24, 25, 34, 37, 43, 44]\n",
      "[1, 2, 4, 7, 9, 13, 14, 16, 19, 21, 23, 24, 29, 32, 34, 37, 43, 44]\n",
      "[0, 9, 14, 16, 34, 38, 40, 43, 44, 47]\n",
      "[4, 7, 14]\n",
      "[0, 1, 2, 4, 6, 7, 9, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 25, 26, 31, 32, 34, 38, 40, 41, 42, 43, 44, 47, 48]\n",
      "[1, 26, 34]\n",
      "[4, 6, 9, 28, 29, 31, 34, 38, 47]\n",
      "[1, 6, 14, 34, 40]\n",
      "[0, 4, 14, 23, 38]\n",
      "[1, 4, 6, 9, 12, 14, 23, 25, 32, 38]\n",
      "[4, 9, 12, 14, 16, 19, 23, 25, 34]\n",
      "[16, 23, 26]\n",
      "[13, 14, 23, 24, 29, 43]\n",
      "[12, 14, 16, 48]\n",
      "[0, 1, 2, 4, 6, 7, 9, 12, 13, 14, 17, 19, 21, 26, 29, 31, 37, 38, 40, 43, 44, 47, 48]\n",
      "[0, 2, 4, 6, 9, 13, 14, 16, 24, 43, 44]\n",
      "[26, 29]\n",
      "[2, 23, 34, 37]\n",
      "[4, 19, 23, 40]\n",
      "[21, 34, 43]\n",
      "[1, 9, 14, 16, 19, 25, 26, 47]\n",
      "[9, 16, 26, 38, 43]\n",
      "[0, 1, 4, 6, 12, 14, 23, 25, 26, 34, 38]\n",
      "[9, 14, 23, 31]\n",
      "[0, 4, 7, 9, 12, 13, 14, 21, 23, 24, 25, 26, 28, 32, 34, 43, 44]\n",
      "[5, 14, 24, 42]\n",
      "[4, 6, 9, 13, 14, 16, 17, 21, 23, 37, 47]\n",
      "[9, 31, 41]\n",
      "[6, 19]\n",
      "[0, 4, 12, 13, 14, 16, 19, 23, 44]\n",
      "[7, 16, 32, 34, 38]\n",
      "[4, 14, 21, 23]\n",
      "[19, 37, 47]\n",
      "[0, 2, 4, 7, 9, 14, 19, 21, 23, 25, 26, 37, 38, 43, 44, 48]\n",
      "[9, 17, 20, 23, 38]\n",
      "[23, 34]\n",
      "[0, 7, 9, 13, 17, 19, 23, 24, 25, 34, 38, 48]\n",
      "[0, 4, 9, 16, 21, 23, 24, 32, 34, 42, 43]\n",
      "[20, 21, 23]\n",
      "[0, 23, 44]\n",
      "[4, 12, 13, 14, 31, 32, 44]\n",
      "[0, 1, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 19, 21, 22, 23, 24, 25, 26, 28, 29, 32, 34, 37, 38, 40, 41, 42, 43, 44, 47, 48]\n",
      "[2, 4, 9, 19, 21, 44]\n",
      "[0, 4, 6, 19, 23, 25, 28, 42, 43, 44, 48]\n",
      "[6, 9, 16, 29]\n",
      "[0, 5, 7, 14, 25, 29, 31, 34, 43, 44, 48]\n",
      "[14, 25]\n",
      "[5, 7, 12, 16, 19, 23, 25, 31, 48]\n",
      "[9, 10, 16]\n",
      "[4, 6, 9, 12, 13, 23, 28, 37, 40, 42]\n",
      "[0, 13, 19]\n",
      "[4, 6, 13, 16, 17, 23, 25, 26, 31, 32, 34, 43, 44]\n",
      "[4, 21, 34, 43]\n",
      "[0, 4, 6, 14, 16, 19, 23, 37, 41, 43]\n",
      "[34, 40]\n",
      "[4, 5, 6, 7, 9, 22, 23, 25]\n",
      "[9, 12, 48]\n",
      "[0, 7, 13, 16, 21, 22, 38]\n",
      "[4, 6, 7, 13, 14, 16, 17, 20, 24, 32, 43, 44, 48]\n",
      "[9, 16, 25]\n",
      "[1, 6, 13, 21]\n",
      "[6, 23, 34]\n",
      "[1, 4, 5, 6, 7, 9, 12, 14, 19, 23, 41, 43, 47, 48]\n",
      "[4, 19, 23, 37, 43]\n",
      "[1, 9, 10, 12, 13]\n",
      "[10, 13, 16, 23, 25, 41]\n",
      "[0, 2, 6, 10, 14, 16, 21, 22, 23, 25, 26, 34, 37, 43, 48]\n",
      "[0, 1, 5, 9, 16, 17, 21, 40]\n",
      "[6, 13, 14, 23, 34, 41, 43]\n",
      "[0, 9, 12, 16, 38, 43, 44]\n",
      "[13, 16, 25, 29, 31, 38]\n",
      "[4, 6, 19]\n",
      "[0, 6, 9, 14, 19, 26, 32, 43, 48]\n",
      "[4, 6, 12, 13, 17, 19, 20, 23, 28, 29, 34]\n",
      "[13, 23]\n",
      "[6, 14, 22, 23, 47]\n",
      "[17, 19, 34, 38]\n",
      "[2, 5, 6, 9, 13, 14, 19, 32, 37, 43]\n",
      "[1, 2, 4, 6, 7, 12, 13, 14, 16, 22, 23, 25, 26, 32, 34, 38, 40, 41, 42, 43]\n",
      "[9, 29, 48]\n",
      "[16, 17, 21]\n",
      "[9, 12, 14, 19, 20, 29, 31, 38]\n",
      "[0, 7, 14, 31]\n",
      "[0, 10, 14, 16, 19, 23, 25, 34, 43, 48]\n",
      "[7, 12, 26, 34, 42]\n",
      "[10, 16, 24]\n",
      "[6, 7, 9, 16, 19, 22, 24, 31]\n",
      "[43, 48]\n",
      "[0, 9, 13, 19, 21, 23, 26, 42]\n",
      "[7, 19, 23, 34, 44]\n",
      "[9, 12, 19, 43, 44]\n",
      "[4, 6, 7, 14, 16, 21, 23, 43]\n",
      "[0, 1, 4, 5, 6, 12, 14, 16, 17, 19, 20, 21, 23, 24, 25, 28, 34, 37, 38, 42, 43, 44]\n",
      "[0, 4, 7, 13, 17, 23, 41]\n",
      "[2, 6, 13, 14, 17, 21, 26, 29, 31]\n",
      "[14, 19, 26, 43]\n",
      "[0, 14, 37, 41]\n",
      "[6, 20, 42]\n",
      "[1, 2, 6, 7, 12, 14, 16, 21, 23, 37, 43]\n",
      "[5, 6, 9, 16, 19, 20, 21, 22, 25, 26, 31, 34, 38, 41, 43]\n",
      "[1, 4, 6, 7, 12, 13, 14, 16, 19, 22, 23, 24, 25, 26, 34, 38, 43, 47]\n",
      "[0, 5, 6, 9, 13, 23, 25, 34, 42, 44, 48]\n",
      "[7, 10, 13, 19, 23]\n",
      "[7, 10, 12, 13, 17, 23, 44]\n",
      "[4, 16, 17, 31]\n",
      "[4, 22, 23]\n",
      "[6, 12, 13, 14, 23]\n",
      "[5, 6, 9, 10, 12, 13, 14, 16, 19, 20, 21, 23, 24, 26, 32, 41, 43]\n",
      "[7, 9, 13, 14, 23, 24, 29, 43]\n",
      "[14, 25, 37, 43]\n",
      "[7, 9, 12, 14]\n",
      "[0, 1, 2, 4, 6, 10, 14, 16, 21, 22, 23, 28, 29, 31, 32, 38, 40, 44]\n",
      "[4, 9, 19, 38, 47]\n",
      "[2, 4, 6, 13, 14, 16, 23, 40]\n",
      "[19, 20, 34, 42]\n",
      "[13, 19, 29]\n",
      "[7, 20, 29, 32]\n",
      "[1, 4, 6, 12, 13, 14, 16, 17, 23, 26, 29, 37, 41]\n",
      "[0, 6, 9, 13, 16, 19, 37]\n",
      "[4, 5, 6, 7, 9, 13, 16, 19, 20, 23, 25, 26, 44, 48]\n",
      "[0, 7, 14]\n",
      "[0, 1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 19, 23, 25, 26, 29, 32, 37, 40, 43, 44, 47, 48]\n",
      "[6, 9, 12, 23, 25, 38]\n",
      "[5, 10, 13, 14, 17, 26, 32]\n",
      "[6, 7, 13, 21, 31, 41, 43, 44]\n",
      "[5, 7, 10, 21, 34, 40]\n",
      "[1, 4, 6, 9, 12, 13, 14, 16, 17, 19, 22, 23, 25, 31, 37, 38, 42, 47]\n",
      "[0, 9, 25, 43, 44]\n",
      "[0, 1, 4, 6, 7, 9, 13, 16, 17, 19, 22, 31, 34, 38, 41]\n",
      "[7, 19, 23, 24, 25]\n",
      "[4, 6, 12, 13, 14, 16, 38, 43]\n",
      "[9, 34, 41, 44, 48]\n",
      "[1, 4, 6, 9, 13, 16, 20, 23, 24, 26, 29]\n",
      "[0, 14, 23]\n",
      "[7, 16, 29, 37, 38, 43]\n",
      "[0, 4, 7, 10, 12, 13, 14, 16, 19, 21, 24, 25, 28, 34, 37, 38, 41, 43, 44]\n",
      "[6, 7, 12, 17, 19]\n",
      "[4, 13, 31, 41]\n",
      "[7, 14, 48]\n",
      "[29, 44]\n",
      "[4, 6, 7, 9, 10, 13, 14, 16, 17, 23, 25, 26, 29, 31, 34]\n",
      "[1, 12, 14, 21, 29]\n",
      "[5, 16, 17, 23, 29, 34, 37, 43]\n",
      "[0, 2, 4, 7, 9, 12, 13, 17, 19, 25, 26, 29, 34, 37, 43, 44]\n",
      "[2, 4, 6, 13, 14, 23, 29, 37, 43]\n",
      "[7, 19]\n",
      "[0, 9, 13, 14, 16, 17, 22, 23, 34, 44]\n",
      "[4, 5, 9, 13, 14, 16, 19, 24, 26, 41, 42, 44]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 17, 23, 26, 29, 37, 41, 42, 44]\n",
      "[0, 1, 7, 9, 12, 13, 14, 19, 23, 24, 25, 40, 41, 43, 44, 48]\n",
      "[5, 7, 17, 25, 26, 31, 34, 38, 41, 43, 44, 48]\n",
      "[0, 12, 34]\n",
      "[0, 4, 6, 7, 9, 10, 13, 14, 19, 22, 23, 29, 32, 38, 41, 44]\n",
      "[1, 4, 5, 6, 7, 9, 12, 13, 14, 16, 19, 21, 25, 34, 37, 43, 44]\n",
      "[2, 5, 6, 14, 16, 17, 21, 22]\n",
      "[1, 4, 13, 14, 43]\n",
      "[0, 6, 7, 9, 12, 14, 16, 21, 24, 28, 29, 31, 32, 34, 38, 41, 44]\n",
      "[6, 14, 16, 44]\n",
      "[2, 12, 14]\n",
      "[0, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 20, 22, 23, 25, 26, 29, 34, 38, 41, 42, 43, 48]\n",
      "[17, 29]\n",
      "[4, 6, 7, 10, 12, 13, 14, 19, 20, 23, 25, 29, 38, 41, 43, 47, 48]\n",
      "[13, 14, 19, 23, 25]\n",
      "[1, 6, 7, 13, 14, 17, 34]\n",
      "[7, 9, 25, 26, 43]\n",
      "[0, 4, 6, 9, 10, 12, 13, 14, 16, 21, 22, 23, 25, 29, 31, 34, 38, 43]\n",
      "[0, 4, 6, 7, 12, 14, 21, 23, 25, 26, 32, 37, 38, 43, 48]\n",
      "[4, 6, 7, 9, 12, 13, 16, 20, 24, 25, 26, 29, 34, 37, 41, 43, 48]\n",
      "[1, 4, 5, 6, 7, 9, 12, 14, 16, 19, 21, 22, 23, 31, 34, 37, 38, 41, 43, 44, 47, 48]\n",
      "[1, 4, 37, 40, 42]\n",
      "[1, 4, 19, 23]\n",
      "[2, 7, 14, 19, 21, 23, 31, 43]\n",
      "[0, 1, 4, 7, 13, 14, 16, 23, 26, 42]\n",
      "[4, 6, 7, 9, 12, 13, 16, 21, 25, 34, 43]\n",
      "[0, 6, 21]\n",
      "[4, 7, 9, 10, 14, 19, 23, 32, 38, 43]\n",
      "[0, 2, 7, 12, 14, 21, 48]\n",
      "[0, 7, 14, 19, 21, 31]\n",
      "[34, 43]\n",
      "[6, 17, 23, 29, 38]\n",
      "[6, 7, 9, 13, 14, 16, 19, 21, 23, 24, 26, 29, 37, 38, 40]\n",
      "[12, 13, 19, 23, 43]\n",
      "[12, 13, 32]\n",
      "[12, 13, 34]\n",
      "[7, 9, 23]\n",
      "[4, 6, 7, 9, 10, 12, 13, 16, 17, 23, 26, 29, 32, 34, 37, 38, 42, 43, 44]\n",
      "[0, 1, 6, 7, 9, 13, 16, 19, 21, 23, 25, 37, 38, 41, 42, 43, 44, 48]\n",
      "[2, 9, 13, 14, 16, 19, 23, 24, 25, 26, 31, 42]\n",
      "[7, 21, 22]\n",
      "[13, 23, 31]\n",
      "[7, 25, 34, 43]\n",
      "[2, 5, 12, 13, 16, 23, 28, 41, 44, 47]\n",
      "[1, 4, 7, 17, 38, 41, 42]\n",
      "[0, 4, 6, 9, 12, 14, 17, 21, 25, 26, 29, 32, 34, 37, 43, 44]\n",
      "[0, 4, 5, 6, 9, 12, 13, 14, 17, 19, 23, 29, 34, 38, 41, 43]\n",
      "[7, 14, 29, 37, 48]\n",
      "[0, 6, 9, 12, 13, 19, 22, 23, 25, 26, 34, 41]\n",
      "[7, 9, 10, 12, 14, 34]\n",
      "[5, 16, 38, 41]\n",
      "[4, 14, 23, 25]\n",
      "[0, 4, 6, 7, 9, 12, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 34, 43]\n",
      "[4, 13]\n",
      "[6, 19, 23]\n",
      "[2, 4, 42]\n",
      "[6, 17, 25]\n",
      "[4, 6, 9, 10, 13, 14, 16, 17, 19, 26, 29, 31, 37, 41, 43, 44, 47]\n",
      "[0, 4, 10, 13, 14, 16, 19, 34, 41, 43]\n",
      "[6, 14, 16, 19, 24]\n",
      "[0, 1, 4, 6, 9, 10, 12, 13, 14, 16, 19, 21, 23, 25, 28, 29, 31, 32, 34, 42, 43, 44]\n",
      "[13, 21, 43]\n",
      "[9, 14, 21, 25, 29, 38]\n",
      "[7, 16, 23]\n",
      "[4, 5, 7, 13, 16, 19, 31, 34, 41, 43, 48]\n",
      "[7, 9, 12, 13, 19, 22, 25]\n",
      "[9, 14, 23]\n",
      "[7, 9, 12, 13, 14, 17, 34, 37]\n",
      "[0, 7, 12, 13, 14, 19, 22, 29, 43]\n",
      "[0, 14, 29]\n",
      "[6, 13, 19, 20, 21, 23, 40, 48]\n",
      "[1, 2, 7, 12, 16, 23, 25, 28, 34, 37, 38, 43, 44]\n",
      "[6, 9, 13, 14, 17, 19, 23, 24, 25, 29, 32, 44]\n",
      "[9, 13, 16, 19, 23, 37, 43]\n",
      "[1, 6, 21, 31, 34, 43]\n",
      "[0, 1, 2, 4, 5, 6, 7, 9, 10, 12, 14, 16, 23, 24, 26, 31, 32, 34, 37, 38, 43]\n",
      "[13, 16]\n",
      "[7, 17, 19]\n",
      "[1, 4, 7, 13, 14, 21, 37, 44]\n",
      "[4, 9, 14, 22, 23]\n",
      "[6, 7, 9, 13, 16, 23, 44]\n",
      "[4, 7, 14, 17, 25, 41, 43]\n",
      "[4, 6, 7, 13, 14, 16, 23, 25, 29]\n",
      "[6, 16, 29, 34, 38, 41, 44]\n",
      "[13, 19]\n",
      "[1, 6, 10, 31, 32, 34, 43]\n",
      "[2, 6, 21, 24]\n",
      "[0, 4, 5, 6, 7, 9, 12, 13, 14, 16, 19, 20, 21, 25, 31, 34, 37, 38, 41, 42, 43, 44]\n",
      "[4, 16, 19, 43, 48]\n",
      "[2, 4, 6, 7, 13, 14, 23, 29, 31, 34, 37, 38, 41, 44, 48]\n",
      "[7, 12, 13, 16, 23, 26, 43, 47]\n",
      "[6, 7, 19, 23, 24, 29]\n",
      "[10, 13, 16, 17, 23, 29, 41]\n",
      "[0, 4, 16, 19, 24, 32, 34, 42, 44, 48]\n",
      "[4, 7, 23, 26, 29, 37]\n",
      "[4, 6, 7, 14, 16, 19, 25, 44]\n",
      "[1, 12, 23, 34, 37, 40, 48]\n",
      "[0, 1, 6, 10, 12, 14, 16, 19, 21, 22, 23, 34, 44, 48]\n",
      "[0, 7, 14, 43]\n",
      "[4, 12, 34, 43]\n",
      "[2, 4, 6, 9, 14, 17, 19, 20, 26, 41, 42, 48]\n",
      "[2, 23, 28, 37, 43]\n",
      "[6, 7, 9, 19, 21, 29]\n",
      "[4, 6, 7, 12, 13, 14, 19, 23, 26, 31, 34, 40, 42, 43]\n",
      "[4, 23]\n",
      "[4, 6, 12, 13, 16, 17, 19, 21, 23, 25, 31, 48]\n",
      "[0, 13, 14, 16, 29, 38]\n",
      "[6, 10, 13, 21, 24, 37, 48]\n",
      "[42, 48]\n",
      "[0, 4, 6, 7, 9, 13, 16, 19, 21]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 17, 19, 21, 23, 25, 28, 32, 34, 37, 38, 43, 47, 48]\n",
      "[4, 6, 13, 14, 16, 23, 38, 44]\n",
      "[4, 6, 13, 14, 16, 23, 26, 34, 37, 48]\n",
      "[0, 4, 6, 9, 20, 25, 34, 43]\n",
      "[0, 4, 7, 13, 14, 16, 23, 34, 43]\n",
      "[16, 23]\n",
      "[9, 13, 16, 20, 29, 34, 43]\n",
      "[0, 4, 9]\n",
      "[13, 38]\n",
      "[14, 22, 44]\n",
      "[14, 16, 17, 23, 24, 25, 26, 31, 37, 38, 43, 48]\n",
      "[4, 7, 19, 23, 25, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 16, 19, 29, 31, 34, 38, 40, 41, 44]\n",
      "[4, 6, 7, 12, 13, 14, 16, 32, 47, 48]\n",
      "[1, 10, 14, 19, 22, 26, 38, 42]\n",
      "[4, 7, 10, 14, 17, 25, 43]\n",
      "[6, 14, 16, 17, 19, 23, 26, 34, 43, 44]\n",
      "[4, 14, 25, 34]\n",
      "[0, 6, 13, 19, 21, 23, 26]\n",
      "[1, 16, 23, 34]\n",
      "[1, 12, 16, 25, 26, 28, 31, 42, 44]\n",
      "[13, 22, 26, 41]\n",
      "[0, 13, 16, 41, 44]\n",
      "[7, 12, 16, 19, 23, 47]\n",
      "[0, 4, 6, 10, 12, 19, 44]\n",
      "[0, 1, 4, 5, 6, 7, 9, 12, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 28, 29, 32, 34, 38, 43, 44, 48]\n",
      "[4, 44]\n",
      "[0, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 19, 20, 21, 23, 24, 25, 28, 29, 32, 34, 37, 41, 42, 44, 47, 48]\n",
      "[0, 4, 6, 7, 13, 29, 34]\n",
      "[6, 23]\n",
      "[4, 34]\n",
      "[0, 2, 4, 6, 7, 12, 13, 14, 16, 23, 24, 25, 26, 38, 43]\n",
      "[1, 6, 7, 16, 19, 34, 38]\n",
      "[34, 44]\n",
      "[6, 13, 14, 16, 17, 25, 31, 44]\n",
      "[14, 19, 21, 42]\n",
      "[5, 6, 7, 9, 12, 34, 38, 43, 44]\n",
      "[0, 9, 13, 19, 28, 34]\n",
      "[0, 6, 21, 48]\n",
      "[0, 9, 10, 13, 14, 38]\n",
      "[0, 4, 6, 9, 12, 16, 29, 34, 44]\n",
      "[14, 26]\n",
      "[6, 19, 42]\n",
      "[4, 6, 9, 10, 12, 17, 19, 23, 25, 26, 38, 40, 44]\n",
      "[0, 4, 6, 7, 12, 13, 14, 16, 17, 19, 21, 23, 29, 32, 34, 40, 41, 43, 44]\n",
      "[25, 44]\n",
      "[0, 1, 2, 4, 7, 9, 14, 16, 19, 23, 37, 43, 48]\n",
      "[0, 1, 4, 13, 14, 16, 17, 21, 23, 25, 26, 37, 38]\n",
      "[0, 6, 7, 14, 38]\n",
      "[9, 13, 42]\n",
      "[0, 14, 21, 34]\n",
      "[7, 16]\n",
      "[4, 9, 14, 19, 21, 25, 34, 41, 43, 44, 48]\n",
      "[0, 7, 14, 23, 43]\n",
      "[4, 14, 22, 23, 44]\n",
      "[9, 13, 19]\n",
      "[16, 22, 26, 44, 48]\n",
      "[0, 1, 4, 7, 9, 14, 17, 19, 23, 24, 28, 29, 37, 44]\n",
      "[0, 4, 7, 13, 14]\n",
      "[1, 13, 14, 16]\n",
      "[4, 6, 7, 9, 12, 14, 24, 34, 47]\n",
      "[9, 12, 14, 16]\n",
      "[7, 14, 23, 24, 26]\n",
      "[0, 1, 4, 6, 7, 9, 12, 16, 19, 23, 29, 31, 34, 38, 48]\n",
      "[0, 1, 6, 12, 14, 16, 17, 25, 42, 43, 44]\n",
      "[0, 2, 5, 6, 7, 9, 13, 14, 21, 25, 34, 42, 48]\n",
      "[0, 4, 5, 6, 7, 13, 14, 19, 21, 23, 37, 41, 43, 44, 48]\n",
      "[4, 7, 13, 14, 23, 26, 47]\n",
      "[0, 14, 17, 48]\n",
      "[4, 12, 34, 40, 48]\n",
      "[0, 1, 2, 9, 12, 13, 16, 32, 38]\n",
      "[0, 4, 9, 19, 31, 37, 40, 43, 48]\n",
      "[4, 9, 13, 14, 42]\n",
      "[13, 14, 16, 43]\n",
      "[4, 9, 14, 21, 29, 34, 40]\n",
      "[6, 14, 16, 22, 24]\n",
      "[5, 12, 28, 34]\n",
      "[0, 1, 4, 6, 7, 9, 13, 14, 16, 17, 21, 23, 25, 29, 34, 37, 38, 44, 47, 48]\n",
      "[5, 13, 14, 19, 25, 34, 38, 43, 44]\n",
      "[0, 1, 4, 6, 12, 13, 14, 25, 28, 29, 31, 43, 44, 48]\n",
      "[0, 6, 9, 12, 13, 14, 17, 32, 34, 37, 38, 41, 42, 44]\n",
      "[9, 13, 25, 44]\n",
      "[0, 2, 4, 10, 14, 16]\n",
      "[7, 9, 19, 22, 25, 26, 31]\n",
      "[14, 19, 21, 23, 43]\n",
      "[0, 6, 9, 12, 13, 14, 16, 21, 23, 26, 31, 32, 34, 44, 48]\n",
      "[4, 17, 23, 29]\n",
      "[4, 6, 9, 19, 23]\n",
      "[0, 4, 7, 9, 10, 14, 19, 21, 23, 34, 38, 43, 48]\n",
      "[1, 9, 13, 16, 17, 19, 23, 28, 34]\n",
      "[0, 6, 7, 14, 16, 19, 25, 26, 28, 38]\n",
      "[10, 12, 16, 19, 24, 26, 32, 34, 37, 41, 42, 43, 44]\n",
      "[4, 16, 19]\n",
      "[4, 7, 13, 19]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 17, 19, 20, 21, 22, 25, 34, 37, 41, 42, 43, 48]\n",
      "[0, 4, 5, 6, 13, 14, 19, 21, 23, 25, 34, 38, 44]\n",
      "[6, 7, 17, 42, 44, 48]\n",
      "[13, 23]\n",
      "[5, 7, 10, 14, 16, 22, 28, 29, 31, 37, 38]\n",
      "[7, 14, 23]\n",
      "[0, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 25, 26, 28, 29, 32, 34, 37, 38, 41, 43, 44, 48]\n",
      "[0, 9, 14, 16, 22, 23, 38, 41, 43, 44]\n",
      "[0, 2, 4, 5, 6, 7, 9, 12, 13, 14, 16, 21, 23, 24, 32, 34, 40]\n",
      "[4, 6, 7, 12, 13, 14, 21, 23, 26, 32, 38, 44, 48]\n",
      "[4, 9, 19, 41]\n",
      "[19, 25, 26, 29, 31, 32, 37, 44]\n",
      "[0, 1, 6, 9, 10, 12, 13, 16, 19, 23, 25, 29, 40, 41, 43, 44]\n",
      "[6, 7, 14, 22, 31, 38, 43, 44, 48]\n",
      "[1, 4, 13, 14, 16, 34, 41, 43, 48]\n",
      "[6, 7, 13, 22, 23, 26, 43]\n",
      "[0, 5, 23, 26, 38]\n",
      "[4, 6, 9, 10, 12, 13, 14, 16, 21, 23, 24, 25, 26, 31, 41]\n",
      "[6, 7, 9, 43]\n",
      "[14, 31, 43]\n",
      "[4, 40, 44]\n",
      "[0, 48]\n",
      "[6, 14, 19, 25, 34, 38, 43, 48]\n",
      "[23, 25, 31, 41, 47, 48]\n",
      "[0, 4]\n",
      "[0, 4, 25, 32]\n",
      "[2, 23, 44]\n",
      "[0, 1, 4, 6, 9, 12, 13, 14, 16, 17, 26, 29, 34, 38, 43]\n",
      "[7, 14, 22, 40]\n",
      "[0, 1, 4, 6, 13, 16, 17, 19, 21, 22, 23, 24, 25, 32, 34, 41, 43]\n",
      "[0, 1, 6, 13, 25, 31]\n",
      "[2, 4, 6, 9, 10, 14, 16, 19, 21, 23, 29, 32, 43, 44]\n",
      "[6, 7, 13, 25, 38]\n",
      "[0, 22, 44]\n",
      "[6, 38]\n",
      "[6, 7, 16, 26, 48]\n",
      "[6, 9, 14, 23, 34, 44]\n",
      "[0, 6, 14, 19, 23, 24, 43, 44]\n",
      "[13, 23, 38]\n",
      "[14, 23, 25, 44]\n",
      "[0, 6, 7, 23]\n",
      "[4, 9, 21, 25, 44]\n",
      "[2, 23]\n",
      "[0, 5, 6, 19, 48]\n",
      "[2, 7, 13, 14, 16, 19, 23, 34]\n",
      "[6, 7, 9, 13, 25, 32, 48]\n",
      "[0, 4, 6, 9, 12, 16, 23, 37, 38, 41, 44, 48]\n",
      "[6, 7, 9, 14, 16, 23, 25, 34, 41, 42, 44, 48]\n",
      "[14, 17, 21, 25, 38, 44]\n",
      "[14, 23, 24, 29, 34, 38, 41]\n",
      "[0, 4, 5, 6, 7, 10, 12, 13, 14, 16, 19, 20, 21, 23, 25, 37, 38, 41, 42, 48]\n",
      "[5, 6, 9, 13, 14, 16, 23, 26, 34, 37, 43, 48]\n",
      "[6, 25, 38]\n",
      "[10, 43]\n",
      "[13, 26, 32, 37, 42]\n",
      "[6, 19, 23, 34]\n",
      "[4, 12, 16, 21, 34, 41, 48]\n",
      "[1, 9, 14, 19, 23, 37, 38, 41, 44]\n",
      "[2, 4, 5, 16, 19, 34]\n",
      "[19, 21, 23, 31, 41, 44]\n",
      "[4, 7, 13, 14, 23, 24, 31, 32, 40, 42, 43, 44]\n",
      "[0, 6, 7, 9, 12, 14, 23, 25, 32, 34]\n",
      "[2, 23, 44]\n",
      "[4, 6, 23, 47]\n",
      "[0, 1, 7, 14, 21, 23, 25]\n",
      "[0, 2, 9, 12, 14, 23, 38, 41, 44]\n",
      "[0, 16, 17, 26]\n",
      "[4, 7, 13, 14, 16, 23, 29, 43, 48]\n",
      "[4, 14, 16, 21, 38, 41]\n",
      "[0, 1, 32, 42, 44]\n",
      "[0, 4, 6, 9, 12, 14, 16, 21, 23, 31, 40, 42, 44]\n",
      "[4, 9, 14]\n",
      "[0, 1, 4, 6, 12, 14]\n",
      "[2, 4, 6, 16, 17, 23]\n",
      "[0, 2, 4, 9, 10, 13, 14, 23, 26]\n",
      "[0, 6, 22]\n",
      "[0, 1, 4, 6, 14, 23, 25, 38, 41, 43]\n",
      "[9, 10, 38, 42]\n",
      "[4, 6, 13, 25, 43]\n",
      "[7, 13]\n",
      "[38, 48]\n",
      "[4, 20, 23]\n",
      "[0, 1, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 29, 31, 34, 37, 38, 43, 44, 48]\n",
      "[7, 25, 44]\n",
      "[1, 6, 9, 23, 38]\n",
      "[1, 7, 9, 12, 13, 14, 16, 19, 25, 28, 32, 34, 47]\n",
      "[6, 22, 37]\n",
      "[9, 12, 14]\n",
      "[7, 14, 21, 23, 25, 28]\n",
      "[5, 13, 43, 44]\n",
      "[6, 7]\n",
      "[6, 7, 13, 24, 25, 28]\n",
      "[1, 14, 29, 34, 43]\n",
      "[12, 24, 25, 44, 48]\n",
      "[0, 4, 9, 14, 19, 23, 32, 34, 38]\n",
      "[4, 6, 7, 12, 17, 24, 29, 44, 47]\n",
      "[4, 7, 9, 14, 19, 21, 23, 41, 43]\n",
      "[4, 5, 13, 14, 16, 28, 32, 38, 41, 44, 47]\n",
      "[4, 6, 13, 14, 16, 23, 41, 48]\n",
      "[0, 2, 4, 5, 6, 9, 10, 12, 13, 14, 16, 21, 22, 23, 25, 26, 28, 34, 37, 38, 41, 48]\n",
      "[0, 12, 13, 14, 22, 31]\n",
      "[14, 17, 23]\n",
      "[0, 1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 25, 29, 31, 34, 37, 38, 43, 44, 48]\n",
      "[0, 1, 4, 6, 7, 12, 14, 16, 21, 23, 25, 26, 29, 43, 44, 47]\n",
      "[0, 4, 6, 21, 25, 32, 38, 44, 48]\n",
      "[2, 4, 6, 7, 12, 13, 14, 16, 19, 21, 23, 25, 26, 28, 32, 34, 44]\n",
      "[6, 14, 23, 26, 34, 43]\n",
      "[6, 9, 10, 14, 16, 19, 23, 29, 37, 43]\n",
      "[23, 34]\n",
      "[9, 34]\n",
      "[7, 12, 19, 29, 43, 44]\n",
      "[24, 26, 34]\n",
      "[6, 38]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 29, 34, 43, 48]\n",
      "[4, 6, 12, 16, 19, 23, 43]\n",
      "[4, 9, 12, 13, 14, 16, 19, 23, 25, 34]\n",
      "[0, 4, 6, 9, 14, 34, 43]\n",
      "[0, 6, 12, 16, 19, 23, 29, 38]\n",
      "[6, 16, 19, 23, 43]\n",
      "[4, 6, 7, 13, 14, 23, 29, 43]\n",
      "[13, 16, 19]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43, 44, 48]\n",
      "[7, 14, 16, 19, 23, 25, 29, 38, 43]\n",
      "[4, 13, 16]\n",
      "[0, 7, 9, 14, 16, 19, 29, 38, 43]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[0, 6, 7, 13, 14, 19, 23, 38, 44]\n",
      "[9, 29]\n",
      "[6, 14, 16]\n",
      "[0, 4, 9, 12, 13, 14, 48]\n",
      "[6, 9, 12, 13, 19, 25, 29, 44]\n",
      "[14, 23, 38]\n",
      "[9, 14, 29, 44, 48]\n",
      "[0, 9, 13]\n",
      "[4, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 29, 34, 38, 44, 48]\n",
      "[23, 44]\n",
      "[9, 14]\n",
      "[0, 6, 7, 9, 14, 16, 25, 34]\n",
      "[0, 6, 7, 16, 19, 23, 29, 34, 38, 43]\n",
      "[12, 14, 23]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 34, 43, 44, 48]\n",
      "[0, 6, 9, 14, 25, 29, 34, 43]\n",
      "[0, 4, 14, 19, 25]\n",
      "[0, 6, 44]\n",
      "[7, 9, 13, 14, 23, 34, 38]\n",
      "[14, 16, 23, 29]\n",
      "[0, 4, 6, 7, 9, 12, 14, 19]\n",
      "[4, 19]\n",
      "[16, 25]\n",
      "[7, 12, 13, 14]\n",
      "[4, 12, 13, 23, 25, 29, 38, 48]\n",
      "[4, 6, 7, 9, 14, 23, 44]\n",
      "[0, 6, 9, 13, 14, 16, 29, 34, 44]\n",
      "[4, 6, 7, 16, 25, 29]\n",
      "[6, 14, 19]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 29, 34, 43, 48]\n",
      "[0, 7, 9, 12, 13, 14, 23, 25, 29, 38, 43, 44]\n",
      "[0, 4, 6, 7, 14, 16, 23, 25, 38, 43, 44]\n",
      "[6, 13, 43]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 16, 23, 43, 48]\n",
      "[13, 14, 34, 38]\n",
      "[0, 4, 7, 9, 13, 14, 16, 25, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 34, 38, 43, 44, 48]\n",
      "[19, 25]\n",
      "[0, 9, 14]\n",
      "[0, 13, 14, 16, 34, 48]\n",
      "[4, 13]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 29, 43, 44]\n",
      "[0, 6, 9, 14, 16, 23, 43]\n",
      "[4, 6, 9, 14, 16, 19, 23, 34, 43, 48]\n",
      "[14, 16, 23]\n",
      "[0, 4, 9, 25, 43, 44]\n",
      "[0, 14]\n",
      "[6, 13, 19, 25, 34]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[4, 6, 7, 9, 12, 13, 14, 16, 23, 29, 34, 38]\n",
      "[4, 9, 29]\n",
      "[13, 23, 29]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 34, 43, 44, 48]\n",
      "[23, 29, 44]\n",
      "[13, 14, 25, 29, 43]\n",
      "[0, 4, 6, 7, 13, 19, 34, 38, 43]\n",
      "[0, 13, 23, 44]\n",
      "[6, 19]\n",
      "[0, 4, 6, 9, 13, 14, 25, 29, 38, 44, 48]\n",
      "[4, 6, 9, 14, 16, 19, 23, 25, 29, 44, 48]\n",
      "[0, 6, 13, 14, 23, 48]\n",
      "[0, 4, 6, 13, 14, 16, 19, 25, 29, 43, 44, 48]\n",
      "[6, 7, 23, 34]\n",
      "[0, 4, 6, 9, 12, 13, 19, 23, 38, 43, 48]\n",
      "[6, 7, 12, 13, 14, 19, 23]\n",
      "[4, 7, 9, 13, 14, 16, 23, 34, 38, 43]\n",
      "[4, 23, 34]\n",
      "[16, 23, 25]\n",
      "[14, 44]\n",
      "[4, 23, 44]\n",
      "[4, 13, 14, 23, 34, 38, 44]\n",
      "[4, 6, 13, 19, 43, 44]\n",
      "[4, 6, 7, 9, 13, 14, 16, 19, 23, 34, 38, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 23, 25]\n",
      "[16, 19, 25, 43]\n",
      "[9, 16, 19, 23, 34, 38, 48]\n",
      "[4, 6, 14, 23, 29, 38]\n",
      "[7, 12, 13, 23, 34, 38, 43]\n",
      "[6, 9, 23, 25, 34, 48]\n",
      "[0, 4, 14, 23, 25, 44]\n",
      "[0, 14, 19, 25, 34]\n",
      "[7, 14, 23, 25]\n",
      "[4, 6, 9, 14, 25, 43]\n",
      "[4, 6, 9, 14, 34, 48]\n",
      "[4, 7, 13, 14]\n",
      "[7, 14, 23, 34, 43, 48]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 25, 34, 38, 43]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 34, 38, 43, 44]\n",
      "[0, 7, 9, 14, 23, 25]\n",
      "[0, 4, 7, 9, 13, 14, 16, 19, 23, 29, 44]\n",
      "[4, 7, 9, 12, 29, 34, 38]\n",
      "[13, 16, 19, 48]\n",
      "[0, 7, 19]\n",
      "[12, 13, 14, 19, 23, 29, 38, 44, 48]\n",
      "[4, 12, 14, 16, 23, 48]\n",
      "[0, 7, 19, 34]\n",
      "[4, 9, 13, 14, 23, 25, 34, 43, 44, 48]\n",
      "[0, 4, 43]\n",
      "[6, 7, 12, 19, 43]\n",
      "[6, 7, 9, 12, 14, 29, 43]\n",
      "[0, 7, 9, 13, 14, 16, 19, 23, 25, 34, 38]\n",
      "[0, 4, 6, 9, 14, 23, 34, 43, 44]\n",
      "[4, 14, 19, 25, 29, 38, 48]\n",
      "[7, 12, 19, 23, 43, 44]\n",
      "[0, 4, 12, 13, 16, 23]\n",
      "[0, 4, 13, 19, 29, 34, 48]\n",
      "[7, 13, 16]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 6, 9, 12, 13, 14, 23, 29, 34, 43, 44, 48]\n",
      "[4, 6, 7, 13, 14, 16, 23, 25, 29, 34, 38, 43, 48]\n",
      "[14, 16, 29, 43]\n",
      "[4, 6]\n",
      "[0, 4, 6, 7, 12, 16, 19, 29, 34, 38, 48]\n",
      "[4, 13, 14, 16, 23, 43]\n",
      "[0, 9, 14, 16, 19]\n",
      "[4, 6, 7, 13, 14, 23, 25, 29, 34, 38, 43]\n",
      "[4, 6, 14, 38, 43]\n",
      "[6, 9, 13, 14]\n",
      "[0, 4, 9, 13, 14, 16, 19, 25, 44]\n",
      "[0, 7, 14, 16, 43]\n",
      "[4, 38, 44, 48]\n",
      "[4, 7, 14, 25, 44]\n",
      "[23, 34, 38]\n",
      "[4, 6, 16, 19, 29]\n",
      "[0, 4, 7, 13, 14, 19, 23, 34]\n",
      "[0, 9]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 48]\n",
      "[9, 19, 23, 48]\n",
      "[0, 4, 12, 14, 38]\n",
      "[6, 7, 12, 23, 43, 44]\n",
      "[0, 7, 43]\n",
      "[0, 4, 6, 7, 9, 12, 13, 19, 23]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 23, 25, 29, 34, 38, 43, 44]\n",
      "[0, 4, 6, 7, 12, 13, 14, 16, 19, 23, 25, 29, 34, 43, 44, 48]\n",
      "[6, 29, 44]\n",
      "[0, 4, 7, 9, 13, 23, 25, 34, 38]\n",
      "[4, 7, 34]\n",
      "[12, 16, 19, 29, 43, 44]\n",
      "[0, 6, 7, 13, 14, 16, 29, 34, 48]\n",
      "[4, 6, 13, 14, 16, 23, 25, 44]\n",
      "[6, 12, 14, 43]\n",
      "[4, 9, 12, 14, 16, 23, 25, 43, 44]\n",
      "[0, 9, 12, 19, 23, 29, 34, 43]\n",
      "[4, 6, 12, 23, 34, 38]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 34, 38, 43, 44, 48]\n",
      "[4, 6, 16, 29]\n",
      "[9, 12, 38]\n",
      "[6, 7, 9, 12, 16, 34, 44]\n",
      "[4, 7, 14, 16, 19, 29, 34, 43]\n",
      "[4, 6, 9, 13, 14, 23, 25, 29, 44]\n",
      "[12, 16, 23, 48]\n",
      "[0, 4, 7, 16, 19, 34, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 23, 29, 34, 38, 43, 44, 48]\n",
      "[0, 7, 9, 12, 14, 19, 23, 38, 43, 44, 48]\n",
      "[6, 7, 9, 13, 16, 19, 25, 29, 43]\n",
      "[6, 7, 23, 38]\n",
      "[9, 12, 13, 19, 38, 44, 48]\n",
      "[6, 7, 19, 23, 43]\n",
      "[6, 14, 19, 48]\n",
      "[4, 12]\n",
      "[0, 4]\n",
      "[0, 6, 14, 16, 23]\n",
      "[6, 7, 9, 12, 16, 19, 23, 25, 29, 34, 38]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 29, 34, 38, 43, 44, 48]\n",
      "[0, 6, 13, 23]\n",
      "[0, 4, 7, 9, 13, 14, 16, 23, 25, 29, 38, 44, 48]\n",
      "[0, 4, 7, 13, 16, 19, 38]\n",
      "[0, 4, 9, 13, 16, 19, 23, 29, 43]\n",
      "[4, 13, 38]\n",
      "[4, 19, 23, 38]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[7, 9, 13, 14, 16, 34, 48]\n",
      "[7, 13, 34]\n",
      "[6, 9, 16, 23, 43]\n",
      "[4, 6, 12, 14, 23, 44, 48]\n",
      "[0, 9, 12, 13, 14, 19, 25, 34, 38]\n",
      "[0, 4, 6, 9, 13, 14, 23, 25, 29, 43]\n",
      "[4, 7, 14, 19, 23, 25, 29, 43, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[14, 16, 19, 29]\n",
      "[14, 43]\n",
      "[0, 7, 19, 25, 29, 43, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 48]\n",
      "[0, 6, 7, 9, 13, 16, 23, 25, 43, 48]\n",
      "[7, 9, 12, 13, 19, 25, 29, 44]\n",
      "[9, 23]\n",
      "[9, 14, 38]\n",
      "[4, 6, 7, 12, 13, 14, 19, 34, 38, 43, 44, 48]\n",
      "[9, 12, 23]\n",
      "[4, 7, 12, 13, 14, 19, 23, 48]\n",
      "[7, 9, 29]\n",
      "[9, 13, 29, 44, 48]\n",
      "[7, 12, 16, 34, 48]\n",
      "[0, 7, 14, 16, 19, 23, 29, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 19, 23, 25, 34, 38, 43, 44, 48]\n",
      "[4, 7, 9, 16]\n",
      "[0, 4, 6, 9, 13, 14, 16, 19, 23, 25, 29, 34, 44, 48]\n",
      "[34, 38, 44]\n",
      "[4, 44, 48]\n",
      "[6, 13, 25]\n",
      "[4, 9, 13, 14, 16, 19, 23, 25, 44]\n",
      "[0, 13, 19, 23, 29, 43]\n",
      "[0, 13, 16, 23, 43]\n",
      "[9, 12, 14, 43]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[4, 6, 7, 13, 16, 25]\n",
      "[0, 4, 6, 7, 9, 12, 14, 23, 25, 29, 34, 44, 48]\n",
      "[0, 6, 7, 12, 13, 14, 16, 25, 43, 48]\n",
      "[4, 9, 13, 44]\n",
      "[0, 7, 23]\n",
      "[0, 4, 6, 7, 12, 14, 16, 19, 23, 34, 38, 48]\n",
      "[6, 7, 9, 13, 14, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 6, 7, 12, 19, 23, 25, 38, 43, 44]\n",
      "[0, 6, 12, 13, 16, 19, 23, 29, 43, 44, 48]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 23, 25, 34, 38, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 6, 7, 9, 13, 14, 16, 23, 29, 38, 43, 44]\n",
      "[9, 13, 16, 44]\n",
      "[4, 6, 44]\n",
      "[0, 12, 19, 23, 29]\n",
      "[0, 6, 7, 13, 14, 16, 23, 34]\n",
      "[6, 23, 25, 29, 34]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 6, 7, 13, 14, 23, 34, 43]\n",
      "[0, 16, 34, 44]\n",
      "[0, 4, 14, 23]\n",
      "[0, 13, 14, 16, 25]\n",
      "[4, 6, 13, 14, 16, 19, 23]\n",
      "[0, 4, 9, 12, 13, 14, 16, 23, 25, 29, 34, 43, 44, 48]\n",
      "[4, 9, 12, 14, 19, 23, 29, 34, 38, 44]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[13, 19, 23]\n",
      "[4, 12, 14, 16, 19, 23, 34, 43, 44]\n",
      "[4, 7, 13, 14, 29]\n",
      "[6, 7, 13]\n",
      "[0, 13, 23, 38, 43, 44]\n",
      "[7, 14, 25]\n",
      "[6, 13, 43]\n",
      "[34, 43, 44]\n",
      "[0, 4, 7, 12, 13, 16, 19, 23, 38, 43]\n",
      "[14, 38, 43]\n",
      "[0, 4, 7, 14, 16, 19, 38, 43]\n",
      "[6, 7, 23, 44]\n",
      "[4, 12, 14, 16, 19, 23, 25, 34, 43, 48]\n",
      "[0, 4, 6, 7, 14, 23, 25, 34, 38, 43]\n",
      "[0, 7, 19]\n",
      "[0, 13, 14, 34]\n",
      "[4, 7, 9, 12, 13, 14, 16, 19, 23, 48]\n",
      "[0, 4, 6, 9, 13, 14, 16, 23, 34, 43, 44, 48]\n",
      "[7, 19, 23]\n",
      "[4, 9, 13, 19, 29, 38, 44]\n",
      "[6, 13, 16, 38, 44]\n",
      "[4, 6, 7, 9, 12, 13, 14, 16, 25, 34, 38, 43, 44]\n",
      "[0, 4, 12, 14, 16]\n",
      "[6, 19, 25, 34]\n",
      "[7, 14, 16, 23, 25, 29, 38, 44, 48]\n",
      "[13, 16, 23, 25, 38]\n",
      "[0, 4, 6, 12, 13, 14, 16, 19, 23, 25, 29, 43]\n",
      "[4, 12, 14, 16]\n",
      "[6, 9, 14, 19, 43, 48]\n",
      "[4, 6, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 43, 44]\n",
      "[4, 6, 7, 9, 12, 13, 14, 19, 29, 43, 44]\n",
      "[4, 6, 12, 13, 14, 16, 25, 29, 34, 43, 44]\n",
      "[4, 6, 7, 14, 16, 19, 34, 43]\n",
      "[0, 6, 9, 12, 16, 43]\n",
      "[0, 4, 6, 9, 14, 16, 23]\n",
      "[4, 13, 14, 23, 38]\n",
      "[4, 6, 9, 14, 25, 43, 48]\n",
      "[4, 6, 7, 12, 13, 23, 25, 34, 38, 43]\n",
      "[6, 38, 44]\n",
      "[0, 6, 7, 13, 16, 29]\n",
      "[0, 7, 9, 13, 16, 23, 43, 48]\n",
      "[6, 12, 13, 34, 38, 43, 44]\n",
      "[4, 6, 7, 9, 12, 13, 14, 23, 29, 43]\n",
      "[0, 4, 7, 9, 16, 19, 44]\n",
      "[0, 6, 7, 12, 14, 23, 29, 34, 38, 43, 44]\n",
      "[0, 4, 6, 7, 12, 16]\n",
      "[25, 34]\n",
      "[6, 7, 16, 19, 43, 44]\n",
      "[4, 6, 7, 14, 19, 25, 34, 43, 44, 48]\n",
      "[7, 13, 16, 34]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 43, 44]\n",
      "[0, 9, 13, 19, 23, 25]\n",
      "[0, 12, 16]\n",
      "[6, 7, 9, 13, 14, 19, 29, 44]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 29, 38, 43, 44]\n",
      "[0, 43]\n",
      "[4, 25, 34, 43]\n",
      "[6, 7, 9, 12, 13, 14, 29, 34, 48]\n",
      "[6, 44]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 23, 43, 44, 48]\n",
      "[4, 6, 14, 19, 43, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 38, 48]\n",
      "[0, 4, 6, 7, 9, 12, 14, 16, 23, 25, 34, 43]\n",
      "[6, 23, 43]\n",
      "[13, 14, 23]\n",
      "[4, 6, 7, 9, 13, 23, 29, 44]\n",
      "[0, 4, 6, 9, 13, 14, 19, 23, 43, 44, 48]\n",
      "[4, 7, 9, 14, 19, 23, 38, 48]\n",
      "[13, 23, 34, 44]\n",
      "[0, 4, 9, 12, 14, 16, 19, 23, 29]\n",
      "[13, 14, 19, 23, 25, 29]\n",
      "[16, 19, 34, 43]\n",
      "[4, 6, 16, 29, 34]\n",
      "[7, 12, 13, 14, 38, 43, 48]\n",
      "[0, 6, 9, 12, 14, 16, 23, 29, 34, 43, 44, 48]\n",
      "[4, 25, 44]\n",
      "[4, 6, 9, 34, 48]\n",
      "[6, 7, 9, 12, 14, 16, 23, 43]\n",
      "[7, 9, 12, 16, 23, 34, 44]\n",
      "[14, 16, 19, 23, 34, 38]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 34, 43, 44, 48]\n",
      "[0, 7, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 19, 23, 29, 43, 44, 48]\n",
      "[4, 25, 44]\n",
      "[6, 7, 13, 14, 16, 23, 34, 44]\n",
      "[6, 7, 9, 13, 14, 16, 23, 25, 38]\n",
      "[0, 7, 13, 14, 38, 44]\n",
      "[0, 4, 6, 7, 9, 14, 19, 23, 29, 34, 43]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 43, 44, 48]\n",
      "[0, 16]\n",
      "[4, 6, 9, 13, 14, 34, 38, 43, 44]\n",
      "[0, 4, 7, 13, 23, 25, 34, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 25, 38, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 44]\n",
      "[6, 14, 23]\n",
      "[0, 4, 6, 9, 13, 16, 23, 29, 43, 44, 48]\n",
      "[4, 12, 16, 19, 29, 48]\n",
      "[0, 4, 7, 12, 23, 25]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 43, 44]\n",
      "[0, 14, 23, 44]\n",
      "[6, 9]\n",
      "[4, 9, 43]\n",
      "[9, 23, 48]\n",
      "[0, 12, 16, 25]\n",
      "[0, 4, 6, 12, 13, 14, 16, 23, 34, 38, 43]\n",
      "[0, 4, 6, 7, 12, 13, 14, 16, 19, 34, 38, 44, 48]\n",
      "[6, 14, 16, 23, 25, 34, 38, 43]\n",
      "[4, 6, 7, 13, 19]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 23, 25, 38, 43, 44]\n",
      "[6, 44]\n",
      "[0, 9, 16, 23, 38, 48]\n",
      "[0, 16, 44, 48]\n",
      "[0, 4, 13, 16, 34]\n",
      "[0, 6, 7, 9, 13, 23, 38]\n",
      "[9, 12, 13, 14, 16, 23, 25, 34, 38, 43, 48]\n",
      "[0, 4, 16]\n",
      "[0, 14, 23]\n",
      "[7, 9, 23]\n",
      "[6, 7, 9, 14, 23, 29, 34, 43, 44]\n",
      "[6, 9, 16, 23, 25]\n",
      "[0, 4, 6, 13, 14, 19, 23, 25, 34, 38, 43, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 38, 43, 44]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 19, 23, 25, 29, 38, 43, 44]\n",
      "[0, 6, 7, 9, 14, 23, 25, 34, 38]\n",
      "[6, 7, 9, 13, 14, 16, 23, 34, 38]\n",
      "[6, 7, 12, 13]\n",
      "[0, 4, 6, 7, 13, 14, 16, 23, 29, 43, 44]\n",
      "[0, 6, 9, 16, 23]\n",
      "[4, 6, 7, 9, 12, 13, 14, 25, 29, 43, 44]\n",
      "[4, 6, 7, 12, 14, 16, 23, 25, 38]\n",
      "[0, 6, 9, 12, 13, 14, 19, 23, 48]\n",
      "[6, 7, 9, 12, 14, 16, 19, 23, 25, 38, 43, 48]\n",
      "[4, 6, 25, 38, 48]\n",
      "[4, 12, 48]\n",
      "[4, 6, 7, 14, 16, 23, 38]\n",
      "[4, 14, 16]\n",
      "[4, 6, 9, 12, 13, 19, 34, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 29, 34, 38, 43, 44]\n",
      "[4, 12, 23, 25]\n",
      "[0, 7, 9, 12, 16]\n",
      "[6, 9, 14, 38]\n",
      "[7, 13, 14, 16, 19, 23, 38, 44, 48]\n",
      "[4, 9, 12, 14, 43]\n",
      "[14, 16, 19, 23]\n",
      "[0, 6, 19, 23, 44]\n",
      "[0, 34, 38]\n",
      "[0, 6, 12, 23, 29, 44]\n",
      "[0, 6, 13, 43, 48]\n",
      "[14, 38]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 23, 34]\n",
      "[0, 4, 6, 7, 14, 23, 29, 38, 43, 44]\n",
      "[6, 12, 16, 23, 38]\n",
      "[6, 19, 43]\n",
      "[7, 12, 23]\n",
      "[14, 23]\n",
      "[0, 4, 19, 34]\n",
      "[12, 14, 23, 25]\n",
      "[4, 6, 7, 9, 14, 29, 44, 48]\n",
      "[0, 4, 6, 14, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 19, 23, 44]\n",
      "[0, 4, 7, 9, 13, 14, 16, 23, 38, 43, 44]\n",
      "[13, 16, 19, 29, 48]\n",
      "[6, 12, 13, 14, 43, 44]\n",
      "[0, 6, 7, 9, 12, 14, 16, 25, 43]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[0, 14, 16, 23, 25]\n",
      "[0, 4, 6, 9, 14]\n",
      "[4, 6, 7, 14, 16, 19, 23, 25, 34, 43]\n",
      "[6, 9, 19, 29, 43, 44]\n",
      "[7, 9, 48]\n",
      "[0, 12, 14, 23, 43]\n",
      "[0, 4, 7, 12, 13, 19, 23, 25, 34, 38, 44]\n",
      "[4, 6, 7, 13, 14, 25, 43]\n",
      "[13, 19, 25]\n",
      "[4, 6, 13, 14, 19, 23, 29, 34, 43, 48]\n",
      "[4, 6, 12, 19, 23, 25, 29, 44]\n",
      "[16, 34]\n",
      "[12, 23]\n",
      "[4, 7, 9, 13, 16]\n",
      "[6, 7, 9, 13, 14, 16, 23, 34, 44]\n",
      "[29, 38]\n",
      "[4, 12, 23]\n",
      "[6, 9, 12, 13, 14, 19, 48]\n",
      "[9, 14]\n",
      "[0, 13, 43]\n",
      "[0, 19, 23]\n",
      "[4, 6, 16]\n",
      "[6, 7, 13, 16]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 34, 44, 48]\n",
      "[0, 4, 14, 25, 34]\n",
      "[0, 14, 29, 34]\n",
      "[6, 23]\n",
      "[6, 14, 25]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 34, 38, 43, 44, 48]\n",
      "[4, 6, 7]\n",
      "[7, 9, 12, 13, 14, 19, 23, 25, 34, 44]\n",
      "[0, 4, 6, 7, 9, 16, 25, 29, 38, 43]\n",
      "[0, 4, 23]\n",
      "[4, 7, 9, 14, 19, 23, 29, 38, 48]\n",
      "[0, 4, 7, 13, 14, 16, 25, 29, 43, 44]\n",
      "[0, 4, 7, 12, 14, 25, 43]\n",
      "[4, 6, 12, 13, 14, 16, 19, 23, 25, 34, 38, 44]\n",
      "[4, 6, 7, 14, 23, 34, 43, 44, 48]\n",
      "[9, 14, 34, 44, 48]\n",
      "[4, 6, 9, 14, 23]\n",
      "[0, 6, 7, 9, 13, 16, 19, 23, 34, 43, 44]\n",
      "[0, 4, 12, 13, 14, 16, 23, 29, 34, 43, 44]\n",
      "[7, 12, 13, 23]\n",
      "[7, 19, 34]\n",
      "[6, 7, 14, 16, 29]\n",
      "[9, 13, 14, 19]\n",
      "[0, 4, 6, 7, 12, 13, 16, 23, 29, 34, 38, 48]\n",
      "[6, 12, 14, 29, 43]\n",
      "[4, 7, 9, 13, 14, 16, 19, 23, 25, 29, 43, 44, 48]\n",
      "[7, 14]\n",
      "[4, 6, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 43, 44, 48]\n",
      "[14, 25]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 29, 34, 43, 44, 48]\n",
      "[0, 13, 14, 34]\n",
      "[13, 38]\n",
      "[0, 7, 12, 19, 23, 25, 29, 38, 44]\n",
      "[6, 9, 29, 43]\n",
      "[7, 12, 23, 34, 43]\n",
      "[13, 14, 16, 25, 38, 43]\n",
      "[12, 13, 23, 25, 29]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 34, 38, 43, 44, 48]\n",
      "[0, 4, 9, 12, 13, 16, 23, 29, 38, 43]\n",
      "[6, 13, 25, 34]\n",
      "[0, 4, 16, 23, 25, 48]\n",
      "[4, 6, 7, 13, 14, 16, 23, 29, 38, 43, 44]\n",
      "[12, 38]\n",
      "[0, 13, 16, 23, 29]\n",
      "[4, 6, 7, 9, 13, 19, 23, 25, 29, 34, 43, 44, 48]\n",
      "[6, 7, 13, 14, 16, 19, 23, 38, 44]\n",
      "[0, 6, 9, 16]\n",
      "[0, 4, 9, 13, 16, 23, 29, 38, 44]\n",
      "[6, 12, 13, 16, 19, 23, 25]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[0, 4, 9, 14, 19, 23, 48]\n",
      "[4, 14, 23, 38]\n",
      "[4, 14, 19, 44]\n",
      "[4, 6, 9, 12, 13, 14, 23, 25, 34, 38, 44, 48]\n",
      "[0, 23, 48]\n",
      "[4, 7, 12, 13, 14, 16, 19, 23, 25, 34, 38, 43]\n",
      "[7, 14]\n",
      "[4, 6]\n",
      "[6, 9, 12, 14, 19, 23]\n",
      "[4, 7, 14, 23]\n",
      "[0, 6, 12, 16, 25]\n",
      "[4, 9, 25, 29]\n",
      "[6, 19, 25]\n",
      "[0, 6, 9, 16, 19, 23, 25, 29, 34, 38]\n",
      "[4, 6, 7, 9, 14, 16, 23, 29, 48]\n",
      "[4, 6, 13, 14, 23, 25, 38, 43, 48]\n",
      "[7, 14, 19, 23, 29, 34, 48]\n",
      "[0, 4, 6, 7, 9, 12, 16, 19, 29]\n",
      "[6, 14, 43]\n",
      "[0, 6, 9, 16, 38]\n",
      "[0, 6, 16, 34, 43, 48]\n",
      "[13, 14, 19]\n",
      "[0, 13, 14, 16, 19, 23, 44]\n",
      "[0, 4, 6, 12, 13, 14, 23, 25, 34, 38, 43, 44]\n",
      "[6, 7, 9, 12, 13, 16, 19, 34]\n",
      "[0, 4, 14, 25, 29, 48]\n",
      "[4, 7, 19, 25]\n",
      "[19, 43, 48]\n",
      "[6, 9, 23, 43]\n",
      "[9, 23, 44]\n",
      "[13, 19]\n",
      "[0, 6, 7, 9, 12, 14, 16, 19, 23, 29, 34, 38, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43]\n",
      "[13, 14, 16, 23]\n",
      "[4, 6, 13, 19, 43]\n",
      "[9, 12, 13, 14, 23, 29, 43]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34]\n",
      "[4, 6, 7, 9, 14, 19]\n",
      "[0, 9, 13, 14, 19, 25, 34]\n",
      "[0, 6, 7, 9, 13, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 16, 19, 23, 25, 34, 38, 43, 48]\n",
      "[6, 13, 16]\n",
      "[0, 4, 6, 7, 9, 12, 14, 16, 19, 23, 25, 29, 38, 43, 44, 48]\n",
      "[0, 4, 7, 9, 13, 14, 16, 23]\n",
      "[0, 4, 6, 9, 13, 14, 16, 23, 25, 34, 43, 44]\n",
      "[0, 4, 7, 9, 13, 14, 19, 23, 29, 43, 44]\n",
      "[4, 6, 7, 9, 12, 19, 25, 29, 34, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[9, 14, 16, 19, 23]\n",
      "[0, 4, 7, 16, 23, 38]\n",
      "[14, 25, 44]\n",
      "[4, 6, 9, 16, 19, 29, 34, 38]\n",
      "[14, 16]\n",
      "[7, 9, 12, 13, 16, 34]\n",
      "[0, 14, 23, 25]\n",
      "[0, 13, 14, 43]\n",
      "[4, 6, 14, 25, 34, 43]\n",
      "[7, 14, 34]\n",
      "[4, 6]\n",
      "[0, 4, 6, 7, 14, 16, 19, 25, 29, 34, 43, 44, 48]\n",
      "[0, 4, 9, 14, 16, 23]\n",
      "[9, 12, 16, 34]\n",
      "[4, 13, 16, 19, 25, 44]\n",
      "[6, 9, 12, 13, 14, 16, 19, 23, 29, 44, 48]\n",
      "[0, 4, 6, 9, 13, 14, 19, 23, 29, 34, 38, 44, 48]\n",
      "[6, 7, 13, 14, 25, 34, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 14, 16, 19, 23, 29, 38, 43, 44]\n",
      "[7, 43, 48]\n",
      "[6, 7, 9, 13, 14, 29, 44, 48]\n",
      "[12, 19, 29]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 25, 34, 38, 43, 44, 48]\n",
      "[0, 4, 7, 9, 23, 29, 38, 43]\n",
      "[4, 6, 9, 13, 16, 23, 29, 38]\n",
      "[6, 7, 9, 16]\n",
      "[0, 4, 6, 14, 16, 23, 48]\n",
      "[0, 4, 7, 12, 13, 16, 19, 23, 29, 34, 38, 43, 44, 48]\n",
      "[4, 14]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[9, 13, 19, 29]\n",
      "[0, 4, 12, 14, 23]\n",
      "[4, 38, 43]\n",
      "[0, 12, 13, 14, 16, 23]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 38, 43]\n",
      "[6, 7, 16, 23, 34]\n",
      "[4, 6, 13, 14, 19, 23, 29, 43, 48]\n",
      "[0, 4, 6, 7, 9, 16, 34]\n",
      "[0, 4, 23]\n",
      "[0, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 43, 44]\n",
      "[4, 9, 25, 29, 38]\n",
      "[4, 6, 7, 9, 12, 13, 14, 16, 19, 25, 38, 44, 48]\n",
      "[0, 4, 6, 7, 12, 14, 19, 34, 38, 44]\n",
      "[0, 6, 13, 19, 38]\n",
      "[4, 7, 13, 19, 25, 38, 48]\n",
      "[4, 7, 12, 13, 16, 19, 23, 29, 34, 38, 48]\n",
      "[4, 7, 13, 19, 23, 34, 38, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 7, 9, 13, 16, 23, 29, 38, 44]\n",
      "[13, 14, 19]\n",
      "[0, 6, 9, 12, 14, 16, 19, 23, 38, 44]\n",
      "[14, 48]\n",
      "[0, 13, 19, 23, 34, 38, 48]\n",
      "[4, 12, 19]\n",
      "[4, 9, 13, 14, 16, 19, 25, 34, 43]\n",
      "[9, 29, 48]\n",
      "[6, 12, 19]\n",
      "[7, 9, 14, 16, 19, 23, 34, 43]\n",
      "[0, 43, 48]\n",
      "[14, 16, 19, 23, 25, 38, 43, 44]\n",
      "[0, 7, 19, 25, 29, 43]\n",
      "[4, 7, 13, 16, 19, 23, 25, 34, 38, 44]\n",
      "[4, 6, 9, 12, 13, 14, 16, 23, 25, 38, 43, 44]\n",
      "[6, 12, 16, 23, 43]\n",
      "[6, 9, 14, 19, 25, 29, 34, 43, 44]\n",
      "[16, 44]\n",
      "[4, 7, 23, 43]\n",
      "[0, 44]\n",
      "[4, 9, 44]\n",
      "[14, 23, 34, 44]\n",
      "[0, 6, 7, 9, 12, 13, 14, 16, 23, 34, 43, 44, 48]\n",
      "[0, 6, 7, 12, 13, 14, 16, 19, 23, 25, 34, 43]\n",
      "[0, 12, 13, 14, 16, 19, 23, 25, 34, 38]\n",
      "[6, 14, 16, 19, 43, 44]\n",
      "[0, 4, 6, 7, 9, 13, 14, 19, 23, 29, 34, 43, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 43, 44, 48]\n",
      "[19, 29, 43, 44, 48]\n",
      "[0, 7, 23]\n",
      "[0, 43]\n",
      "[9, 23]\n",
      "[6, 7, 14, 16, 19, 23, 25, 34, 38, 43]\n",
      "[0, 13, 16, 23, 34, 43]\n",
      "[0, 4, 6, 7, 12, 14, 23, 34, 38, 43, 48]\n",
      "[0, 23]\n",
      "[0, 7, 9, 13, 16, 19, 23, 34, 44]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 25, 38, 44]\n",
      "[7, 43, 48]\n",
      "[4, 6, 7, 13, 19, 23, 29, 34]\n",
      "[6, 14, 23]\n",
      "[7, 12, 34, 38]\n",
      "[6, 19, 29, 44]\n",
      "[4, 6, 7, 14, 19, 23, 25, 38]\n",
      "[4, 6, 13, 19, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[7, 9, 16, 23, 44]\n",
      "[4, 6, 7, 13, 14, 16, 25, 29, 34, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44]\n",
      "[7, 14, 19, 34, 38]\n",
      "[9, 34]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 23, 25, 29, 34, 38, 43, 48]\n",
      "[0, 7, 14, 23, 25, 38]\n",
      "[4, 6, 7, 9, 13, 14, 19, 23, 38]\n",
      "[0, 6, 9, 12, 14, 16, 19, 23, 25, 34, 44, 48]\n",
      "[7, 23]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[0, 4, 6, 9, 12, 13, 14, 25, 38, 44, 48]\n",
      "[0, 4, 6, 7, 12, 13, 16, 25, 29, 43]\n",
      "[0, 6, 9, 13]\n",
      "[13, 14, 34]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 25, 34, 38, 43, 44]\n",
      "[0, 6, 29]\n",
      "[7, 23, 44]\n",
      "[4, 6, 13, 16, 19, 25]\n",
      "[7, 13, 43]\n",
      "[9, 34, 38, 48]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 43, 44, 48]\n",
      "[4, 6, 7, 13, 14, 16, 19]\n",
      "[4, 25, 34, 43]\n",
      "[0, 6, 9, 16, 29, 44]\n",
      "[6, 13, 14, 23, 34]\n",
      "[0, 4, 6, 7, 14, 25, 29]\n",
      "[7, 12]\n",
      "[0, 4, 29, 48]\n",
      "[4, 6]\n",
      "[13, 25, 44]\n",
      "[6, 16, 23, 25, 34]\n",
      "[4, 7, 23, 25, 29]\n",
      "[0, 4, 9, 25, 34]\n",
      "[0, 4, 6, 7, 13, 14, 23, 29, 34, 44, 48]\n",
      "[12, 13, 14, 48]\n",
      "[19, 43]\n",
      "[4, 6, 7, 12, 14, 16, 19, 23, 34, 38, 48]\n",
      "[0, 9, 23]\n",
      "[6, 13, 16, 23]\n",
      "[7, 14, 44]\n",
      "[6, 12, 13, 25, 34]\n",
      "[6, 48]\n",
      "[14, 16, 19]\n",
      "[0, 4, 6, 9, 12, 14, 16, 19, 23, 25, 34, 38, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 25, 34, 43, 44]\n",
      "[0, 4, 6, 7, 23, 25, 29, 34, 38]\n",
      "[0, 7, 9, 13, 16, 23, 25]\n",
      "[0, 4, 6, 7, 14, 16, 19, 25, 29, 34]\n",
      "[4, 13, 16, 23, 48]\n",
      "[16, 43]\n",
      "[25, 29, 38]\n",
      "[6, 16, 19, 23, 48]\n",
      "[4, 6, 7, 12, 13, 14, 16, 19, 23, 25, 38, 43]\n",
      "[0, 4, 9, 14, 16, 19, 23, 38]\n",
      "[0, 6, 7, 9, 13, 19, 23, 25, 34, 43, 44, 48]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 25, 34, 43, 48]\n",
      "[4, 6, 12, 14, 25, 34, 43, 44]\n",
      "[4, 6, 12, 13, 16, 25, 29, 48]\n",
      "[4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 38, 44, 48]\n",
      "[4, 12, 13, 14, 23, 43]\n",
      "[13, 23]\n",
      "[4, 7, 9, 13, 43]\n",
      "[0, 7, 9, 12, 13, 14, 19, 23, 34, 38, 43, 44]\n",
      "[6, 7, 12, 14, 23]\n",
      "[0, 4, 6, 9, 12, 14, 23]\n",
      "[0, 4, 12, 13, 14, 16, 43]\n",
      "[4, 13, 23]\n",
      "[0, 4, 6, 9, 13, 14, 19, 38]\n",
      "[9, 23, 34, 44]\n",
      "[9, 13, 14, 16]\n",
      "[0, 9, 16, 44]\n",
      "[4, 6, 9, 13, 19, 23, 44]\n",
      "[0, 4, 6, 7, 12, 13, 14, 19, 23, 25, 38, 43, 48]\n",
      "[0, 6, 7, 13, 14, 19, 23, 25, 29, 38, 43, 44]\n",
      "[6, 9, 12, 14, 16, 23, 29, 43, 44]\n",
      "[0, 4, 7, 9, 13, 29, 44]\n",
      "[6, 7, 9, 25, 44]\n",
      "[6, 13, 14, 16]\n",
      "[4, 9, 14, 38]\n",
      "[9, 13, 23, 44]\n",
      "[7, 9, 16, 19, 34, 38, 44]\n",
      "[0, 6, 44]\n",
      "[4, 13, 16, 23, 43]\n",
      "[6, 7, 9, 12, 16, 23]\n",
      "[4, 19, 29, 34]\n",
      "[4, 13, 16, 23]\n",
      "[0, 6, 7, 13, 23, 25, 38, 43]\n",
      "[0, 16, 43, 48]\n",
      "[6, 16, 23]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[7, 13, 16, 23, 43]\n",
      "[0, 4, 12, 13, 14, 16, 23, 25]\n",
      "[7, 29, 44]\n",
      "[0, 4, 6, 7, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43, 44, 48]\n",
      "[4, 6]\n",
      "[6, 13]\n",
      "[25, 29]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 25, 29, 44, 48]\n",
      "[6, 7, 16]\n",
      "[6, 12, 13, 14, 16, 19, 25, 34]\n",
      "[7, 12, 13, 14]\n",
      "[6, 14, 16, 23, 25]\n",
      "[12, 14, 19, 23, 25]\n",
      "[4, 13, 14, 16, 34, 38, 43]\n",
      "[6, 7, 9, 13, 14, 19, 23, 25, 29, 34, 43, 44]\n",
      "[6, 12, 13, 14, 16, 23, 25, 34, 38, 43, 44, 48]\n",
      "[4, 6, 7, 14, 23, 29, 34, 44, 48]\n",
      "[13, 14, 25, 38]\n",
      "[7, 12, 16, 19, 23, 25, 34, 38, 48]\n",
      "[0, 4, 6, 7, 14, 16, 19, 38, 43]\n",
      "[6, 16, 25, 38, 48]\n",
      "[7, 9, 23]\n",
      "[6, 7, 13, 23, 34, 38]\n",
      "[7, 13, 34, 38]\n",
      "[4, 14, 43]\n",
      "[13, 23]\n",
      "[6, 7, 9, 12, 14, 16, 23, 34, 43, 44]\n",
      "[44, 48]\n",
      "[0, 12, 23, 34, 48]\n",
      "[4, 6, 13, 14, 16, 19, 23, 29, 43, 44, 48]\n",
      "[4, 14, 19, 23, 38, 48]\n",
      "[6, 13, 14, 16, 23, 25, 29, 38]\n",
      "[6, 7, 14, 19, 23, 25, 34, 43, 44, 48]\n",
      "[0, 4, 12, 48]\n",
      "[13, 14, 25, 29, 44]\n",
      "[12, 43]\n",
      "[7, 9, 14, 16]\n",
      "[4, 14, 25, 34, 38]\n",
      "[4, 6, 7, 38]\n",
      "[0, 4, 6, 7, 9, 13, 14, 23]\n",
      "[0, 4, 6, 7, 9, 12, 14, 23, 25, 29, 38, 44, 48]\n",
      "[0, 7, 9, 12, 13, 14, 16, 19, 23, 34, 43]\n",
      "[0, 25, 29]\n",
      "[6, 7, 14, 16, 19, 29, 38, 48]\n",
      "[0, 4, 6, 13, 14, 23, 29, 38, 43, 48]\n",
      "[12, 23, 44]\n",
      "[14, 25, 34, 43]\n",
      "[14, 16, 34]\n",
      "[0, 4, 6, 9, 12, 13, 14, 16, 19, 23, 25, 29, 34, 38, 43]\n",
      "[0, 4, 6, 9, 13, 19, 23, 44]\n",
      "[4, 19]\n",
      "[4, 6, 9, 19, 23, 25, 43, 44, 48]\n",
      "[4, 7, 13, 19, 23, 29, 34, 38]\n",
      "[4, 29, 38, 43]\n",
      "[4, 6, 9, 14, 19, 25, 29]\n",
      "[0, 9, 13, 14, 16, 19, 25, 34, 43]\n",
      "[7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 9, 23]\n",
      "[6, 9, 13, 23]\n",
      "[6, 9, 23]\n",
      "[4, 6, 13, 14, 23, 43]\n",
      "[4, 7, 13, 14, 23]\n",
      "[0, 7, 14]\n",
      "[0, 6, 13, 14, 23, 43]\n",
      "[4, 6, 7, 9, 13, 16, 19, 23]\n",
      "[6, 7, 13, 14, 19, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 6, 9, 13, 14, 19, 23, 43]\n",
      "[0, 6, 7, 9, 13, 14, 19]\n",
      "[7, 9, 13, 23]\n",
      "[0, 13, 19]\n",
      "[0, 4, 7, 13, 19]\n",
      "[4, 6, 14, 16, 23, 43]\n",
      "[6, 9]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 6, 14, 16, 23]\n",
      "[6, 16, 23]\n",
      "[0, 4, 13, 23]\n",
      "[0, 4, 7, 9, 13, 14, 19, 23, 43]\n",
      "[0, 6, 7, 9, 13, 14, 19, 23]\n",
      "[0, 6, 7, 9, 13, 14, 16, 43]\n",
      "[0, 4, 7, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 7, 13]\n",
      "[0, 7, 9, 13, 23]\n",
      "[0, 4, 6, 9, 16, 19]\n",
      "[4, 6, 7, 13, 14, 16, 19]\n",
      "[6, 23]\n",
      "[14, 23, 43]\n",
      "[0, 6, 13, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[6, 43]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 23]\n",
      "[6, 9, 16]\n",
      "[6, 7, 9, 13, 16, 19, 23, 43]\n",
      "[6, 7, 9, 14]\n",
      "[13, 14, 19, 23]\n",
      "[4, 14, 16, 19]\n",
      "[0, 6, 7, 9, 14, 16, 19, 23, 43]\n",
      "[13, 19, 23]\n",
      "[6, 7, 16]\n",
      "[4, 9, 14, 16, 19]\n",
      "[6, 13, 16]\n",
      "[0, 4, 6, 13, 14, 16, 19]\n",
      "[0, 6, 13, 14, 16, 19, 23]\n",
      "[4, 6, 9, 13, 14, 16, 43]\n",
      "[4, 14, 16, 19]\n",
      "[4, 9, 23]\n",
      "[0, 4, 6, 7, 13, 16, 23]\n",
      "[4, 7, 43]\n",
      "[6, 14, 23, 43]\n",
      "[4, 6, 7, 13, 14, 43]\n",
      "[4, 6, 7, 13, 14, 19, 23]\n",
      "[6, 13, 16, 43]\n",
      "[0, 6, 13, 16]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 14, 16, 19, 23, 43]\n",
      "[0, 4, 14, 16, 23]\n",
      "[4, 9, 14, 16, 19]\n",
      "[4, 7, 14, 16, 23, 43]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 43]\n",
      "[6, 7, 13, 14, 19, 23]\n",
      "[6, 9, 43]\n",
      "[6, 13, 16, 23]\n",
      "[0, 6, 7, 14]\n",
      "[4, 6, 9, 14, 16, 19, 23, 43]\n",
      "[4, 14]\n",
      "[4, 13, 23]\n",
      "[4, 7, 9]\n",
      "[0, 4, 7, 9, 13, 14, 16, 23, 43]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[6, 9, 13, 14, 16, 23]\n",
      "[0, 6, 7, 9, 16, 23]\n",
      "[0, 4, 7, 16, 19]\n",
      "[6, 9, 13, 14, 19]\n",
      "[0, 7, 13, 16, 19, 23]\n",
      "[0, 4, 7, 9, 13]\n",
      "[4, 14, 19, 43]\n",
      "[6, 19, 23]\n",
      "[0, 4, 9, 13, 16, 19, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 13, 14, 23]\n",
      "[0, 43]\n",
      "[0, 4, 14, 16, 19, 23]\n",
      "[4, 13, 19, 23]\n",
      "[0, 6, 9, 13, 14]\n",
      "[4, 7, 13, 16, 19, 23]\n",
      "[4, 6, 7, 16]\n",
      "[4, 6, 9, 14, 16, 19, 23]\n",
      "[6, 14, 19, 23]\n",
      "[6, 7, 13, 14]\n",
      "[6, 13, 14, 23]\n",
      "[4, 6, 9, 14, 16, 19, 23, 43]\n",
      "[19, 23]\n",
      "[0, 7, 13, 16]\n",
      "[0, 6, 7, 9, 14, 16, 19, 23, 43]\n",
      "[14, 23]\n",
      "[7, 14, 19, 23]\n",
      "[0, 4, 7, 13, 19]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[9, 14, 19, 23]\n",
      "[0, 4, 13, 14, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[13, 23, 43]\n",
      "[14, 16, 19]\n",
      "[0, 4, 6, 7, 14, 16, 19, 23]\n",
      "[0, 4, 14, 16]\n",
      "[0, 4, 6, 14, 19, 23]\n",
      "[0, 4, 7, 9, 16, 19, 23]\n",
      "[6, 7]\n",
      "[13, 14, 19, 23]\n",
      "[7, 13]\n",
      "[0, 4, 6, 13, 16, 19]\n",
      "[4, 6]\n",
      "[0, 4, 6, 7, 9, 13, 14, 43]\n",
      "[6, 7, 14, 16, 23]\n",
      "[0, 4, 7, 13, 14, 19]\n",
      "[0, 6, 9, 14, 16, 23]\n",
      "[9, 13, 19, 23]\n",
      "[4, 6, 7, 13, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23]\n",
      "[13, 14, 19, 43]\n",
      "[4, 9, 16, 23]\n",
      "[6, 9, 14, 19, 23]\n",
      "[9, 13, 14]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 43]\n",
      "[0, 6, 9, 19, 23]\n",
      "[0, 9, 13, 14, 16, 19, 23]\n",
      "[4, 7, 43]\n",
      "[0, 9, 43]\n",
      "[6, 14, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 13, 14, 16, 23, 43]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[4, 7, 9, 13, 14, 16, 19, 23]\n",
      "[0, 4, 6, 14, 16]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 9, 13, 16, 19, 23]\n",
      "[0, 14, 16, 23, 43]\n",
      "[4, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 23]\n",
      "[0, 4, 6, 9, 13, 14, 19, 23, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 43]\n",
      "[0, 4, 7, 9, 13, 14, 16, 19, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[0, 4, 6, 7, 9, 23]\n",
      "[6, 23]\n",
      "[6, 7, 14, 19]\n",
      "[14, 23, 43]\n",
      "[0, 4, 6, 9, 13, 16, 19, 23]\n",
      "[6, 9, 14, 43]\n",
      "[4, 14, 19]\n",
      "[0, 4, 6, 9, 13]\n",
      "[0, 4, 7, 9, 14]\n",
      "[0, 6, 19, 23, 43]\n",
      "[0, 4, 6, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 6, 13, 14, 19, 23]\n",
      "[0, 4, 7, 16, 23]\n",
      "[9, 13, 16, 19]\n",
      "[0, 6, 9, 13, 14, 16, 19, 43]\n",
      "[4, 16, 23, 43]\n",
      "[9, 16, 19, 23]\n",
      "[0, 9, 13, 14]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 7, 9, 13, 16, 19]\n",
      "[4, 14, 19, 23]\n",
      "[4, 6, 7, 9, 13, 19]\n",
      "[0, 4, 7, 9, 13, 14, 19, 23, 43]\n",
      "[6, 13, 16]\n",
      "[6, 9, 13, 14, 23]\n",
      "[6, 7, 13, 19, 43]\n",
      "[4, 6, 9, 13]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[0, 13]\n",
      "[9, 13, 16, 23]\n",
      "[14, 23]\n",
      "[6, 7, 9, 13, 14, 16, 23]\n",
      "[4, 6, 7, 16]\n",
      "[4, 13, 14]\n",
      "[6, 13, 14, 16, 23]\n",
      "[6, 7, 9, 13, 14, 16, 23, 43]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19]\n",
      "[0, 4, 9, 13, 14, 16, 19, 43]\n",
      "[4, 6, 9, 13, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[6, 13, 19]\n",
      "[4, 13, 14, 23]\n",
      "[0, 6, 13, 14, 16, 23, 43]\n",
      "[4, 7, 13]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 9, 13, 14, 23]\n",
      "[6, 7, 9, 13, 14, 16, 43]\n",
      "[7, 9, 13, 14, 16, 23, 43]\n",
      "[6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 14, 43]\n",
      "[0, 7, 13, 14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[6, 7, 13, 14, 23, 43]\n",
      "[4, 14, 23, 43]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 23]\n",
      "[0, 6, 7, 13, 14, 16]\n",
      "[4, 6, 7, 9, 14, 16, 23]\n",
      "[4, 7, 14, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 7, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[7, 16, 23]\n",
      "[6, 9, 13, 14, 19, 23, 43]\n",
      "[0, 14, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[6, 9, 13, 16, 19, 23]\n",
      "[4, 6, 9, 14, 16, 23]\n",
      "[0, 4, 13, 14, 23]\n",
      "[6, 14]\n",
      "[6, 16, 43]\n",
      "[4, 9, 13, 16, 19]\n",
      "[4, 6, 7, 19, 23, 43]\n",
      "[7, 13, 14, 16, 23]\n",
      "[0, 19]\n",
      "[9, 13, 19, 23]\n",
      "[6, 16, 23]\n",
      "[4, 13, 16, 19, 43]\n",
      "[4, 7, 13, 14, 23]\n",
      "[0, 4, 6, 14, 16, 19]\n",
      "[0, 6, 7]\n",
      "[6, 7, 13]\n",
      "[13, 23]\n",
      "[4, 13, 16, 23, 43]\n",
      "[4, 7, 13, 14, 19, 23]\n",
      "[4, 6, 9, 16]\n",
      "[0, 7, 13, 19, 43]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 7, 9, 13, 16, 19, 23]\n",
      "[4, 7, 14, 16, 19, 23]\n",
      "[0, 6, 16, 19, 23]\n",
      "[4, 6, 13]\n",
      "[6, 7, 14, 19]\n",
      "[14, 16, 43]\n",
      "[0, 4, 6, 7, 13, 23]\n",
      "[4, 13, 14, 43]\n",
      "[13, 19]\n",
      "[7, 9, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 19, 23, 43]\n",
      "[0, 4, 6, 9, 14, 23, 43]\n",
      "[4, 6, 16]\n",
      "[0, 7, 9]\n",
      "[0, 4, 16]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 7, 14, 16, 23, 43]\n",
      "[0, 6, 14]\n",
      "[0, 4, 6, 13, 14, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23]\n",
      "[0, 4, 6, 7, 16, 23, 43]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19]\n",
      "[0, 4, 6, 14, 16, 19, 23]\n",
      "[6, 7, 9, 14, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 13, 14, 43]\n",
      "[14, 16]\n",
      "[6, 9, 14, 19]\n",
      "[4, 7, 13, 16, 19, 23]\n",
      "[6, 9, 13, 16, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 23, 43]\n",
      "[0, 6]\n",
      "[4, 6, 14]\n",
      "[0, 4, 6, 7, 23, 43]\n",
      "[0, 7, 19, 23, 43]\n",
      "[0, 4, 6]\n",
      "[4, 6, 9, 14, 16, 23]\n",
      "[4, 7, 23]\n",
      "[4, 6, 9, 13, 14, 16, 19, 23]\n",
      "[0, 4, 13, 43]\n",
      "[4, 16]\n",
      "[9, 16, 23]\n",
      "[6, 9, 13, 14, 43]\n",
      "[9, 14, 19, 23, 43]\n",
      "[0, 9, 13, 14, 43]\n",
      "[9, 13]\n",
      "[0, 6, 7, 13, 14, 16, 19, 23]\n",
      "[0, 4, 6, 9, 13, 16, 23]\n",
      "[0, 4, 6, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 9, 16]\n",
      "[4, 7, 9, 23, 43]\n",
      "[0, 4, 6, 13, 14, 16, 19, 23]\n",
      "[0, 4, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 9, 14, 16, 23, 43]\n",
      "[4, 6, 13, 19, 23, 43]\n",
      "[4, 6]\n",
      "[4, 7, 19, 23, 43]\n",
      "[13, 14, 16]\n",
      "[4, 6, 7, 13, 14, 23]\n",
      "[4, 43]\n",
      "[0, 6, 13, 14, 16]\n",
      "[6, 7, 13, 14]\n",
      "[0, 13, 16, 19]\n",
      "[0, 6, 13, 14, 16]\n",
      "[0, 4, 6, 7, 9, 13, 14, 23, 43]\n",
      "[4, 7, 13, 23, 43]\n",
      "[13, 19]\n",
      "[0, 7]\n",
      "[13, 14, 16, 19, 43]\n",
      "[19, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 19, 23, 43]\n",
      "[4, 6, 9, 16, 23]\n",
      "[4, 13, 14, 19]\n",
      "[4, 6, 13, 19, 23]\n",
      "[0, 4, 6, 7, 9, 14, 16, 23, 43]\n",
      "[13, 19]\n",
      "[0, 4, 6, 7, 9, 14, 16, 23, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23]\n",
      "[4, 7, 9, 14, 19, 23]\n",
      "[7, 9, 14, 43]\n",
      "[4, 6, 7, 9, 13, 16, 23, 43]\n",
      "[6, 7, 9, 43]\n",
      "[4, 6, 9, 19, 43]\n",
      "[4, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 9, 23]\n",
      "[6, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 6, 7, 13, 16, 19, 23]\n",
      "[4, 14, 19]\n",
      "[6, 7, 9, 16, 19, 23, 43]\n",
      "[4, 6, 9, 13, 14, 43]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[6, 7, 13, 16, 43]\n",
      "[6, 9, 13, 19, 43]\n",
      "[9, 16]\n",
      "[4, 6, 14, 23]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 43]\n",
      "[0, 9, 19, 23]\n",
      "[13, 23]\n",
      "[6, 9, 14, 23]\n",
      "[0, 4, 13, 16, 19, 23, 43]\n",
      "[4, 6, 9, 13, 14]\n",
      "[4, 14, 43]\n",
      "[9, 19, 23]\n",
      "[0, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 13, 43]\n",
      "[0, 6, 9, 16, 23]\n",
      "[0, 6, 7, 9, 14, 19, 23]\n",
      "[6, 9, 13, 14, 19, 23, 43]\n",
      "[4, 6, 7, 13, 19, 23]\n",
      "[0, 7, 14]\n",
      "[0, 9, 14, 23, 43]\n",
      "[0, 6, 7, 13, 14, 19, 23]\n",
      "[0, 4, 14, 43]\n",
      "[4, 6, 7, 9, 13, 16, 19, 23, 43]\n",
      "[0, 4, 19, 23]\n",
      "[4, 6, 14, 23]\n",
      "[6, 23, 43]\n",
      "[0, 7, 9, 13, 14, 16]\n",
      "[4, 6, 7, 13, 14, 16, 19, 23, 43]\n",
      "[7, 14, 16, 19, 43]\n",
      "[6, 23, 43]\n",
      "[0, 23, 43]\n",
      "[4, 9, 13, 19, 23]\n",
      "[9, 19, 43]\n",
      "[14, 16]\n",
      "[7, 13, 23, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 7, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 9, 14, 16, 19, 23, 43]\n",
      "[13, 16, 23]\n",
      "[0, 6, 13, 14, 16]\n",
      "[4, 7, 9, 13, 14, 19, 23, 43]\n",
      "[0, 4, 6, 14, 19, 23, 43]\n",
      "[0, 4, 7, 13, 14, 19, 43]\n",
      "[4, 6, 7, 14, 19, 23, 43]\n",
      "[4, 6, 7, 14, 19, 23]\n",
      "[4, 6, 7, 9, 23, 43]\n",
      "[4, 6, 9, 13, 14, 16, 19, 23]\n",
      "[7, 23, 43]\n",
      "[7, 13, 19, 23, 43]\n",
      "[6, 9]\n",
      "[4, 6, 9, 19, 23, 43]\n",
      "[4, 7, 9, 13, 14, 19, 23, 43]\n",
      "[0, 14, 16, 19]\n",
      "[6, 9, 16, 19]\n",
      "[7, 9, 13, 19, 43]\n",
      "[6, 7, 9, 13, 16, 23, 43]\n",
      "[0, 43]\n",
      "[0, 13, 16, 43]\n",
      "[0, 16, 23]\n",
      "[23, 43]\n",
      "[4, 13, 43]\n",
      "[4, 7, 9, 13, 14, 16, 43]\n",
      "[0, 4, 9, 14, 16, 19, 23]\n",
      "[4, 6, 9, 14]\n",
      "[0, 4, 6, 7, 13, 14, 16, 19, 43]\n",
      "[0, 4, 6, 13, 16, 19, 23, 43]\n",
      "[0, 4, 14, 16, 23]\n",
      "[4, 13, 14, 43]\n",
      "[0, 4, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 7, 23]\n",
      "[0, 7, 13, 19]\n",
      "[7, 9, 14, 16]\n",
      "[7, 9, 13, 14, 19, 23, 43]\n",
      "[6, 9]\n",
      "[4, 6, 9, 13, 14, 16, 19, 23]\n",
      "[4, 6, 9, 13, 14, 43]\n",
      "[4, 6, 16, 19, 43]\n",
      "[13, 14, 19, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 43]\n",
      "[4, 6, 14, 16, 23, 43]\n",
      "[4, 16]\n",
      "[0, 4, 6, 7, 13, 14, 19, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 7, 9, 23, 43]\n",
      "[0, 6, 7, 9, 14, 16, 19, 23]\n",
      "[4, 6, 9, 13, 14, 16, 19, 23, 43]\n",
      "[4, 6, 14, 43]\n",
      "[0, 4, 6, 9, 13, 16, 23]\n",
      "[4, 6, 7, 9, 16, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 4, 6, 7, 14, 16, 19]\n",
      "[0, 13, 14]\n",
      "[9, 13, 14, 16, 19, 23]\n",
      "[6, 13, 14]\n",
      "[7, 9, 19, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23, 43]\n",
      "[4, 7, 13, 14, 16]\n",
      "[4, 6, 7, 9, 13, 14, 16, 23, 43]\n",
      "[0, 4, 6, 9, 13, 14, 16, 19, 23, 43]\n",
      "[6, 9, 19]\n",
      "[7, 9, 13, 14, 23]\n",
      "[4, 7, 16, 19]\n",
      "[0, 4, 6, 7, 13, 16, 19, 23, 43]\n",
      "[4, 13, 19]\n",
      "[0, 4, 7, 9, 13, 23]\n",
      "[0, 4, 13, 14, 23]\n",
      "[4, 6, 9, 14]\n",
      "[9, 23]\n",
      "[7, 13]\n",
      "[4, 6, 13, 14, 43]\n",
      "[4, 7, 9, 14, 16, 23]\n",
      "[4, 6, 14]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 43]\n",
      "[6, 7, 13, 14]\n",
      "[4, 14, 23]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 23]\n",
      "[0, 4, 6, 9, 19, 23, 43]\n",
      "[7, 13, 14, 16, 19, 23]\n",
      "[4, 14, 16]\n",
      "[0, 4, 9, 14, 43]\n",
      "[4, 13, 14, 16]\n",
      "[4, 6, 7, 9, 13, 14, 16, 23, 43]\n",
      "[0, 4, 7, 23]\n",
      "[4, 13, 16, 19, 23]\n",
      "[4, 7, 14, 43]\n",
      "[4, 6, 23]\n",
      "[4, 6, 9, 19]\n",
      "[6, 9]\n",
      "[4, 16, 19, 23]\n",
      "[14, 19]\n",
      "[0, 4, 6, 7, 9, 14, 16, 19, 23, 43]\n",
      "[0, 6, 14, 16]\n",
      "[4, 9, 23, 43]\n",
      "[0, 4, 6, 7, 16, 19, 43]\n",
      "[0, 4, 6, 13, 14, 16, 19]\n",
      "[0, 4, 6, 7, 13, 14, 23, 43]\n",
      "[0, 4, 6, 7, 14, 16, 19, 23]\n",
      "[0, 4, 6, 13, 14, 16]\n",
      "[7, 13, 14, 16, 43]\n",
      "[0, 4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[6, 14]\n",
      "[0, 6, 16]\n",
      "[4, 7, 9, 13, 14, 16, 19]\n",
      "[4, 7, 9, 13, 14, 16, 23]\n",
      "[4, 9, 16, 19, 23, 43]\n",
      "[6, 7, 9, 13, 16, 19, 23, 43]\n",
      "[0, 14]\n",
      "[13, 19, 43]\n",
      "[6, 7, 9, 13, 14, 16, 23]\n",
      "[7, 13, 16, 19]\n",
      "[4, 6, 13, 14, 23]\n",
      "[6, 9, 13, 19, 23]\n",
      "[4, 6, 9, 14, 23]\n",
      "[0, 6, 7, 13, 16, 19, 23, 43]\n",
      "[4, 7, 13, 14, 19]\n",
      "[0, 4, 6, 7, 16, 19, 23]\n",
      "[0, 4, 14, 16, 19]\n",
      "[13, 23]\n",
      "[6, 7, 9, 16, 23, 43]\n",
      "[4, 6, 7, 9, 13, 14, 16, 19, 23, 43]\n",
      "[0, 7, 9, 23]\n",
      "[4, 6, 9, 13, 14, 19, 23, 43]\n",
      "[4, 7]\n",
      "[4, 6, 9, 14, 19]\n",
      "[4, 6, 14]\n",
      "[4, 6, 13]\n",
      "[6, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 14, 16, 23]\n",
      "[6, 13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 23]\n",
      "[6, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 13, 23]\n",
      "[14, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14]\n",
      "[4, 13, 14, 16, 23]\n",
      "[6, 14]\n",
      "[14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[6, 13]\n",
      "[6, 13, 23]\n",
      "[4, 6, 14, 16]\n",
      "[6, 13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 14, 23]\n",
      "[4, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[6, 14, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[13, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[13, 14, 16, 23]\n",
      "[4, 13, 23]\n",
      "[4, 6, 16]\n",
      "[4, 14, 16, 23]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[4, 14, 23]\n",
      "[4, 14, 23]\n",
      "[14, 23]\n",
      "[6, 16]\n",
      "[13, 23]\n",
      "[4, 13, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[14, 16, 23]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 23]\n",
      "[6, 16]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 14, 16]\n",
      "[4, 6, 14, 23]\n",
      "[4, 6, 14, 23]\n",
      "[4, 14]\n",
      "[4, 6, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[6, 13, 14, 16]\n",
      "[4, 13, 14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 16, 23]\n",
      "[4, 14, 16, 23]\n",
      "[6, 13, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 14]\n",
      "[6, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 14, 16, 23]\n",
      "[4, 6, 16, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[6, 13, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[14, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[13, 23]\n",
      "[6, 14, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[6, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14]\n",
      "[13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13]\n",
      "[6, 14]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 6, 14, 16, 23]\n",
      "[13, 14]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 16, 23]\n",
      "[4, 14, 23]\n",
      "[4, 13, 23]\n",
      "[4, 6]\n",
      "[4, 6, 14, 16]\n",
      "[6, 13, 14, 23]\n",
      "[6, 13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 14]\n",
      "[4, 6, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 23]\n",
      "[4, 14]\n",
      "[6, 14, 23]\n",
      "[14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 14, 16, 23]\n",
      "[6, 14, 16]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[14, 23]\n",
      "[4, 6, 14, 23]\n",
      "[14, 16, 23]\n",
      "[13, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 13, 23]\n",
      "[4, 14]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 23]\n",
      "[13, 16, 23]\n",
      "[4, 6, 13]\n",
      "[6, 14, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[6, 14, 23]\n",
      "[14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 23]\n",
      "[6, 13, 16]\n",
      "[6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 14]\n",
      "[4, 13]\n",
      "[16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 14]\n",
      "[13, 14, 16]\n",
      "[13, 14]\n",
      "[4, 6, 16, 23]\n",
      "[14, 16]\n",
      "[6, 14, 16]\n",
      "[14, 16, 23]\n",
      "[6, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14]\n",
      "[4, 6, 13, 23]\n",
      "[14, 23]\n",
      "[14, 23]\n",
      "[4, 6, 16]\n",
      "[6, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 23]\n",
      "[4, 13, 14]\n",
      "[14, 16]\n",
      "[6, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 14, 16]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[4, 6, 14]\n",
      "[6, 16, 23]\n",
      "[4, 14, 23]\n",
      "[6, 16, 23]\n",
      "[4, 13, 14, 23]\n",
      "[4, 13, 16, 23]\n",
      "[16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 23]\n",
      "[4, 13, 14, 23]\n",
      "[4, 13, 16]\n",
      "[16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13]\n",
      "[14, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 14, 16]\n",
      "[4, 6, 14, 16, 23]\n",
      "[13, 23]\n",
      "[13, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 6, 14, 16]\n",
      "[6, 14, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 13, 14]\n",
      "[13, 14, 23]\n",
      "[4, 13, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 14, 16]\n",
      "[13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[6, 13, 14, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[6, 23]\n",
      "[4, 13]\n",
      "[4, 14, 16, 23]\n",
      "[4, 6, 16]\n",
      "[4, 6]\n",
      "[6, 13, 14, 16]\n",
      "[6, 13, 23]\n",
      "[4, 23]\n",
      "[4, 13, 14]\n",
      "[4, 6, 14, 23]\n",
      "[6, 13, 16, 23]\n",
      "[6, 14, 23]\n",
      "[13, 14, 16]\n",
      "[4, 6, 13, 14, 16]\n",
      "[6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 14, 23]\n",
      "[4, 13, 23]\n",
      "[6, 23]\n",
      "[13, 23]\n",
      "[4, 14, 23]\n",
      "[13, 23]\n",
      "[4, 13, 14, 16]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 13, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[6, 14]\n",
      "[4, 13, 14, 16, 23]\n",
      "[6, 13, 14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[6, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14]\n",
      "[4, 13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 14, 23]\n",
      "[6, 13, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 23]\n",
      "[4, 6, 13, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[6, 23]\n",
      "[6, 14, 23]\n",
      "[13, 14]\n",
      "[4, 6, 13, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 14, 16, 23]\n",
      "[16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 23]\n",
      "[13, 16, 23]\n",
      "[4, 13, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 14, 23]\n",
      "[4, 13, 23]\n",
      "[14, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[14, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[6, 13, 14, 23]\n",
      "[14, 23]\n",
      "[4, 6, 16, 23]\n",
      "[4, 6, 14, 16]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 6, 13, 14]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[6, 13, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[4, 13, 16, 23]\n",
      "[4, 6, 13, 14, 16]\n",
      "[4, 6, 13]\n",
      "[4, 6, 14, 16, 23]\n",
      "[6, 13, 16]\n",
      "[4, 6, 14, 23]\n",
      "[4, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[13, 14, 16, 23]\n",
      "[6, 14, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 16]\n",
      "[4, 14, 23]\n",
      "[4, 6, 13, 16, 23]\n",
      "[6, 14]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 14, 16, 23]\n",
      "[4, 14]\n",
      "[4, 14, 16, 23]\n",
      "[4, 6, 23]\n",
      "[6, 14, 16, 23]\n",
      "[4, 6, 13, 14, 16, 23]\n",
      "[4, 13, 14, 16, 23]\n",
      "[4, 6, 13, 14, 23]\n",
      "[6, 13, 14, 23]\n",
      "[6, 23]\n",
      "[6, 13, 14, 23]\n",
      "[6, 13, 14, 16, 23]\n",
      "[4, 16]\n",
      "[4, 14, 16, 23]\n",
      "[4, 6, 16]\n",
      "[4, 6, 13, 14, 16]\n",
      "[6, 14, 16]\n",
      "[4, 16, 23]\n",
      "[4, 13, 14]\n",
      "[4, 6, 13, 16, 23]\n",
      "[4, 6, 14, 16, 23]\n",
      "[6, 14, 16]\n",
      "[4, 6, 13, 16, 23]\n",
      "[13, 14, 16, 23]\n",
      "[4, 6, 13, 23]\n"
     ]
    }
   ],
   "source": [
    "# TODO: map the items of the records to ids and sort each record (1 points)\n",
    "mapped_records = []\n",
    "for record in data['favorite_games']:\n",
    "    mapped_record = [item_to_id[item] for item in record] #map the items to IDs using item_to_id dictionary\n",
    "    mapped_record.sort()\n",
    "    mapped_records.append(mapped_record)\n",
    "\n",
    "print(\"Mapped Records:\")\n",
    "for record in mapped_records:\n",
    "    print(record)\n",
    "\n",
    "# In the following tasks use the mapped records to compute the frequent itemsets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Apriori algorithm (21 points)\n",
    "### A) Determine the frequent 1 itemsets (3 points)\n",
    "**Task:** Solve the tasks explained in the TODOs and comments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Support of Length-1 Itemsets:\n",
      "Item: 0, Support: 1035\n",
      "Item: 1, Support: 373\n",
      "Item: 4, Support: 1556\n",
      "Item: 8, Support: 213\n",
      "Item: 20, Support: 303\n",
      "Item: 22, Support: 348\n",
      "Item: 27, Support: 246\n",
      "Item: 31, Support: 378\n",
      "Item: 32, Support: 339\n",
      "Item: 33, Support: 269\n",
      "Item: 41, Support: 620\n",
      "Item: 44, Support: 758\n",
      "Item: 11, Support: 238\n",
      "Item: 13, Support: 1489\n",
      "Item: 39, Support: 251\n",
      "Item: 40, Support: 298\n",
      "Item: 45, Support: 248\n",
      "Item: 26, Support: 415\n",
      "Item: 43, Support: 980\n",
      "Item: 3, Support: 228\n",
      "Item: 12, Support: 680\n",
      "Item: 14, Support: 1648\n",
      "Item: 18, Support: 264\n",
      "Item: 28, Support: 318\n",
      "Item: 30, Support: 218\n",
      "Item: 34, Support: 774\n",
      "Item: 35, Support: 232\n",
      "Item: 38, Support: 684\n",
      "Item: 46, Support: 250\n",
      "Item: 2, Support: 379\n",
      "Item: 15, Support: 248\n",
      "Item: 19, Support: 1046\n",
      "Item: 29, Support: 667\n",
      "Item: 10, Support: 329\n",
      "Item: 24, Support: 340\n",
      "Item: 5, Support: 363\n",
      "Item: 25, Support: 753\n",
      "Item: 17, Support: 389\n",
      "Item: 42, Support: 303\n",
      "Item: 37, Support: 390\n",
      "Item: 6, Support: 1539\n",
      "Item: 21, Support: 431\n",
      "Item: 23, Support: 1654\n",
      "Item: 47, Support: 319\n",
      "Item: 16, Support: 1383\n",
      "Item: 48, Support: 633\n",
      "Item: 9, Support: 1052\n",
      "Item: 7, Support: 1104\n",
      "Item: 36, Support: 230\n"
     ]
    }
   ],
   "source": [
    "# TODO: calculate the support of length-1 itemsets using Counter or defaultdict (1 points)\n",
    "from collections import Counter\n",
    "\n",
    "l1_items = Counter(item for record in mapped_records for item in record) #calculate the support of length-1 itemsets\n",
    "\n",
    "print(\"Support of Length-1 Itemsets:\")\n",
    "for item, support in l1_items.items():\n",
    "    print(f\"Item: {item}, Support: {support}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [],
   "source": [
    "# TODO: filter out the frequent length-1 itemsets with their support (1 point)\n",
    "min_support = 226\n",
    "\n",
    "frequent_items = {tuple([item]): support for item, support in l1_items.items() if support >= min_support}\n",
    "\n",
    "# TODO: save the length-1 frequent items to frequent_items with their support (1 points)\n",
    "# Hint: Convert the itemsets to tuples or sets so that you can use them as keys in a dictionary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### B) Determine the frequent n itemsets (15 points)\n",
    "**Task:** Solve the tasks explained in the TODOs and comments.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: implement the apriori_gen algorithm based on the lecture slides\n",
    "def apriori_gen(itemsets):\n",
    "    # TODO: generate candidates (4 points)\n",
    "    candidates = []\n",
    "    for i in range(len(itemsets)):\n",
    "        for j in range(i + 1, len(itemsets)):\n",
    "            #combine itemsets if their first (k-1) elements are identical\n",
    "            if itemsets[i][:-1] == itemsets[j][:-1]:\n",
    "                candidate = itemsets[i] + (itemsets[j][-1],)\n",
    "                candidates.append(candidate)\n",
    "                \n",
    "    # TODO: prune the candidates and return them (4 points)\n",
    "    pruned_candidates = []\n",
    "    for candidate in candidates:\n",
    "        subsets = [candidate[:i] + candidate[i + 1:] for i in range(len(candidate))] #generate all subsets of size k-1 from the candidate\n",
    "\n",
    "        if all(subset in itemsets for subset in subsets): #check if all subsets are frequent\n",
    "            pruned_candidates.append(candidate)\n",
    "\n",
    "    return pruned_candidates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: implement an algorithm to calculate the support of the given itemset (2 points)\n",
    "# You do not need to implement a Hash Tree for calculating the supports.\n",
    "def calculate_support(itemset):\n",
    "    support = 0\n",
    "\n",
    "    for record in mapped_records:\n",
    "        if set(itemset).issubset(record):\n",
    "            support += 1\n",
    "\n",
    "    return support\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frequent Itemsets:\n",
      "Itemset: (0,), Support: 1035\n",
      "Itemset: (1,), Support: 373\n",
      "Itemset: (4,), Support: 1556\n",
      "Itemset: (20,), Support: 303\n",
      "Itemset: (22,), Support: 348\n",
      "Itemset: (27,), Support: 246\n",
      "Itemset: (31,), Support: 378\n",
      "Itemset: (32,), Support: 339\n",
      "Itemset: (33,), Support: 269\n",
      "Itemset: (41,), Support: 620\n",
      "Itemset: (44,), Support: 758\n",
      "Itemset: (11,), Support: 238\n",
      "Itemset: (13,), Support: 1489\n",
      "Itemset: (39,), Support: 251\n",
      "Itemset: (40,), Support: 298\n",
      "Itemset: (45,), Support: 248\n",
      "Itemset: (26,), Support: 415\n",
      "Itemset: (43,), Support: 980\n",
      "Itemset: (3,), Support: 228\n",
      "Itemset: (12,), Support: 680\n",
      "Itemset: (14,), Support: 1648\n",
      "Itemset: (18,), Support: 264\n",
      "Itemset: (28,), Support: 318\n",
      "Itemset: (34,), Support: 774\n",
      "Itemset: (35,), Support: 232\n",
      "Itemset: (38,), Support: 684\n",
      "Itemset: (46,), Support: 250\n",
      "Itemset: (2,), Support: 379\n",
      "Itemset: (15,), Support: 248\n",
      "Itemset: (19,), Support: 1046\n",
      "Itemset: (29,), Support: 667\n",
      "Itemset: (10,), Support: 329\n",
      "Itemset: (24,), Support: 340\n",
      "Itemset: (5,), Support: 363\n",
      "Itemset: (25,), Support: 753\n",
      "Itemset: (17,), Support: 389\n",
      "Itemset: (42,), Support: 303\n",
      "Itemset: (37,), Support: 390\n",
      "Itemset: (6,), Support: 1539\n",
      "Itemset: (21,), Support: 431\n",
      "Itemset: (23,), Support: 1654\n",
      "Itemset: (47,), Support: 319\n",
      "Itemset: (16,), Support: 1383\n",
      "Itemset: (48,), Support: 633\n",
      "Itemset: (9,), Support: 1052\n",
      "Itemset: (7,), Support: 1104\n",
      "Itemset: (36,), Support: 230\n",
      "Itemset: (0, 4), Support: 544\n",
      "Itemset: (0, 44), Support: 306\n",
      "Itemset: (0, 13), Support: 505\n",
      "Itemset: (0, 43), Support: 412\n",
      "Itemset: (0, 12), Support: 291\n",
      "Itemset: (0, 14), Support: 572\n",
      "Itemset: (0, 34), Support: 305\n",
      "Itemset: (0, 38), Support: 281\n",
      "Itemset: (0, 19), Support: 441\n",
      "Itemset: (0, 29), Support: 260\n",
      "Itemset: (0, 25), Support: 296\n",
      "Itemset: (0, 6), Support: 519\n",
      "Itemset: (0, 23), Support: 540\n",
      "Itemset: (0, 16), Support: 511\n",
      "Itemset: (0, 48), Support: 254\n",
      "Itemset: (0, 9), Support: 453\n",
      "Itemset: (0, 7), Support: 455\n",
      "Itemset: (4, 44), Support: 372\n",
      "Itemset: (4, 13), Support: 800\n",
      "Itemset: (4, 43), Support: 506\n",
      "Itemset: (4, 12), Support: 318\n",
      "Itemset: (4, 14), Support: 893\n",
      "Itemset: (4, 34), Support: 352\n",
      "Itemset: (4, 38), Support: 327\n",
      "Itemset: (4, 19), Support: 522\n",
      "Itemset: (4, 29), Support: 316\n",
      "Itemset: (4, 25), Support: 355\n",
      "Itemset: (4, 6), Support: 846\n",
      "Itemset: (4, 23), Support: 889\n",
      "Itemset: (4, 16), Support: 761\n",
      "Itemset: (4, 48), Support: 303\n",
      "Itemset: (4, 9), Support: 520\n",
      "Itemset: (4, 7), Support: 556\n",
      "Itemset: (44, 13), Support: 351\n",
      "Itemset: (44, 43), Support: 302\n",
      "Itemset: (44, 12), Support: 247\n",
      "Itemset: (44, 14), Support: 373\n",
      "Itemset: (44, 34), Support: 277\n",
      "Itemset: (44, 38), Support: 235\n",
      "Itemset: (44, 19), Support: 302\n",
      "Itemset: (44, 29), Support: 251\n",
      "Itemset: (44, 25), Support: 283\n",
      "Itemset: (44, 6), Support: 355\n",
      "Itemset: (44, 23), Support: 363\n",
      "Itemset: (44, 16), Support: 314\n",
      "Itemset: (44, 48), Support: 241\n",
      "Itemset: (44, 9), Support: 317\n",
      "Itemset: (44, 7), Support: 323\n",
      "Itemset: (13, 43), Support: 475\n",
      "Itemset: (13, 12), Support: 313\n",
      "Itemset: (13, 14), Support: 851\n",
      "Itemset: (13, 34), Support: 339\n",
      "Itemset: (13, 38), Support: 296\n",
      "Itemset: (13, 19), Support: 515\n",
      "Itemset: (13, 29), Support: 292\n",
      "Itemset: (13, 25), Support: 337\n",
      "Itemset: (13, 6), Support: 803\n",
      "Itemset: (13, 23), Support: 862\n",
      "Itemset: (13, 16), Support: 742\n",
      "Itemset: (13, 48), Support: 274\n",
      "Itemset: (13, 9), Support: 515\n",
      "Itemset: (13, 7), Support: 558\n",
      "Itemset: (43, 12), Support: 263\n",
      "Itemset: (43, 14), Support: 559\n",
      "Itemset: (43, 34), Support: 309\n",
      "Itemset: (43, 38), Support: 254\n",
      "Itemset: (43, 19), Support: 420\n",
      "Itemset: (43, 29), Support: 247\n",
      "Itemset: (43, 25), Support: 304\n",
      "Itemset: (43, 6), Support: 512\n",
      "Itemset: (43, 23), Support: 513\n",
      "Itemset: (43, 16), Support: 448\n",
      "Itemset: (43, 48), Support: 240\n",
      "Itemset: (43, 9), Support: 420\n",
      "Itemset: (43, 7), Support: 453\n",
      "Itemset: (12, 14), Support: 340\n",
      "Itemset: (12, 34), Support: 276\n",
      "Itemset: (12, 38), Support: 244\n",
      "Itemset: (12, 19), Support: 271\n",
      "Itemset: (12, 25), Support: 250\n",
      "Itemset: (12, 6), Support: 335\n",
      "Itemset: (12, 23), Support: 344\n",
      "Itemset: (12, 16), Support: 310\n",
      "Itemset: (12, 9), Support: 270\n",
      "Itemset: (12, 7), Support: 294\n",
      "Itemset: (14, 34), Support: 378\n",
      "Itemset: (14, 38), Support: 341\n",
      "Itemset: (14, 19), Support: 549\n",
      "Itemset: (14, 29), Support: 309\n",
      "Itemset: (14, 25), Support: 384\n",
      "Itemset: (14, 6), Support: 902\n",
      "Itemset: (14, 23), Support: 956\n",
      "Itemset: (14, 16), Support: 813\n",
      "Itemset: (14, 48), Support: 321\n",
      "Itemset: (14, 9), Support: 567\n",
      "Itemset: (14, 7), Support: 593\n",
      "Itemset: (34, 38), Support: 264\n",
      "Itemset: (34, 19), Support: 295\n",
      "Itemset: (34, 29), Support: 227\n",
      "Itemset: (34, 25), Support: 283\n",
      "Itemset: (34, 6), Support: 354\n",
      "Itemset: (34, 23), Support: 369\n",
      "Itemset: (34, 16), Support: 328\n",
      "Itemset: (34, 48), Support: 246\n",
      "Itemset: (34, 9), Support: 312\n",
      "Itemset: (34, 7), Support: 328\n",
      "Itemset: (38, 19), Support: 262\n",
      "Itemset: (38, 25), Support: 262\n",
      "Itemset: (38, 6), Support: 312\n",
      "Itemset: (38, 23), Support: 335\n",
      "Itemset: (38, 16), Support: 288\n",
      "Itemset: (38, 9), Support: 268\n",
      "Itemset: (38, 7), Support: 288\n",
      "Itemset: (19, 29), Support: 256\n",
      "Itemset: (19, 25), Support: 301\n",
      "Itemset: (19, 6), Support: 516\n",
      "Itemset: (19, 23), Support: 546\n",
      "Itemset: (19, 16), Support: 487\n",
      "Itemset: (19, 48), Support: 243\n",
      "Itemset: (19, 9), Support: 460\n",
      "Itemset: (19, 7), Support: 472\n",
      "Itemset: (29, 25), Support: 229\n",
      "Itemset: (29, 6), Support: 309\n",
      "Itemset: (29, 23), Support: 307\n",
      "Itemset: (29, 16), Support: 264\n",
      "Itemset: (29, 9), Support: 270\n",
      "Itemset: (29, 7), Support: 271\n",
      "Itemset: (25, 6), Support: 354\n",
      "Itemset: (25, 23), Support: 368\n",
      "Itemset: (25, 16), Support: 316\n",
      "Itemset: (25, 48), Support: 231\n",
      "Itemset: (25, 9), Support: 300\n",
      "Itemset: (25, 7), Support: 308\n",
      "Itemset: (6, 23), Support: 890\n",
      "Itemset: (6, 16), Support: 772\n",
      "Itemset: (6, 48), Support: 292\n",
      "Itemset: (6, 9), Support: 561\n",
      "Itemset: (6, 7), Support: 547\n",
      "Itemset: (23, 16), Support: 817\n",
      "Itemset: (23, 48), Support: 305\n",
      "Itemset: (23, 9), Support: 579\n",
      "Itemset: (23, 7), Support: 594\n",
      "Itemset: (16, 48), Support: 273\n",
      "Itemset: (16, 9), Support: 511\n",
      "Itemset: (16, 7), Support: 505\n",
      "Itemset: (48, 9), Support: 247\n",
      "Itemset: (48, 7), Support: 258\n",
      "Itemset: (9, 7), Support: 472\n",
      "Itemset: (0, 4, 13), Support: 333\n",
      "Itemset: (0, 4, 43), Support: 285\n",
      "Itemset: (0, 4, 14), Support: 377\n",
      "Itemset: (0, 4, 19), Support: 288\n",
      "Itemset: (0, 4, 6), Support: 350\n",
      "Itemset: (0, 4, 23), Support: 355\n",
      "Itemset: (0, 4, 16), Support: 338\n",
      "Itemset: (0, 4, 9), Support: 305\n",
      "Itemset: (0, 4, 7), Support: 313\n",
      "Itemset: (0, 13, 43), Support: 268\n",
      "Itemset: (0, 13, 14), Support: 348\n",
      "Itemset: (0, 13, 19), Support: 291\n",
      "Itemset: (0, 13, 6), Support: 326\n",
      "Itemset: (0, 13, 23), Support: 337\n",
      "Itemset: (0, 13, 16), Support: 319\n",
      "Itemset: (0, 13, 9), Support: 295\n",
      "Itemset: (0, 13, 7), Support: 298\n",
      "Itemset: (0, 43, 14), Support: 301\n",
      "Itemset: (0, 43, 19), Support: 240\n",
      "Itemset: (0, 43, 6), Support: 277\n",
      "Itemset: (0, 43, 23), Support: 279\n",
      "Itemset: (0, 43, 16), Support: 269\n",
      "Itemset: (0, 43, 9), Support: 258\n",
      "Itemset: (0, 43, 7), Support: 252\n",
      "Itemset: (0, 14, 19), Support: 305\n",
      "Itemset: (0, 14, 6), Support: 372\n",
      "Itemset: (0, 14, 23), Support: 381\n",
      "Itemset: (0, 14, 16), Support: 361\n",
      "Itemset: (0, 14, 9), Support: 322\n",
      "Itemset: (0, 14, 7), Support: 320\n",
      "Itemset: (0, 19, 6), Support: 295\n",
      "Itemset: (0, 19, 23), Support: 300\n",
      "Itemset: (0, 19, 16), Support: 287\n",
      "Itemset: (0, 19, 9), Support: 264\n",
      "Itemset: (0, 19, 7), Support: 276\n",
      "Itemset: (0, 6, 23), Support: 354\n",
      "Itemset: (0, 6, 16), Support: 341\n",
      "Itemset: (0, 6, 9), Support: 309\n",
      "Itemset: (0, 6, 7), Support: 297\n",
      "Itemset: (0, 23, 16), Support: 343\n",
      "Itemset: (0, 23, 9), Support: 321\n",
      "Itemset: (0, 23, 7), Support: 308\n",
      "Itemset: (0, 16, 9), Support: 297\n",
      "Itemset: (0, 16, 7), Support: 283\n",
      "Itemset: (0, 9, 7), Support: 272\n",
      "Itemset: (4, 44, 13), Support: 241\n",
      "Itemset: (4, 44, 14), Support: 246\n",
      "Itemset: (4, 44, 6), Support: 240\n",
      "Itemset: (4, 44, 23), Support: 234\n",
      "Itemset: (4, 13, 43), Support: 320\n",
      "Itemset: (4, 13, 14), Support: 554\n",
      "Itemset: (4, 13, 19), Support: 328\n",
      "Itemset: (4, 13, 6), Support: 538\n",
      "Itemset: (4, 13, 23), Support: 559\n",
      "Itemset: (4, 13, 16), Support: 498\n",
      "Itemset: (4, 13, 9), Support: 328\n",
      "Itemset: (4, 13, 7), Support: 361\n",
      "Itemset: (4, 43, 14), Support: 369\n",
      "Itemset: (4, 43, 19), Support: 270\n",
      "Itemset: (4, 43, 6), Support: 342\n",
      "Itemset: (4, 43, 23), Support: 329\n",
      "Itemset: (4, 43, 16), Support: 302\n",
      "Itemset: (4, 43, 9), Support: 280\n",
      "Itemset: (4, 43, 7), Support: 302\n",
      "Itemset: (4, 14, 34), Support: 232\n",
      "Itemset: (4, 14, 19), Support: 354\n",
      "Itemset: (4, 14, 25), Support: 238\n",
      "Itemset: (4, 14, 6), Support: 596\n",
      "Itemset: (4, 14, 23), Support: 626\n",
      "Itemset: (4, 14, 16), Support: 548\n",
      "Itemset: (4, 14, 9), Support: 369\n",
      "Itemset: (4, 14, 7), Support: 372\n",
      "Itemset: (4, 34, 6), Support: 234\n",
      "Itemset: (4, 34, 23), Support: 226\n",
      "Itemset: (4, 19, 6), Support: 332\n",
      "Itemset: (4, 19, 23), Support: 340\n",
      "Itemset: (4, 19, 16), Support: 327\n",
      "Itemset: (4, 19, 9), Support: 291\n",
      "Itemset: (4, 19, 7), Support: 308\n",
      "Itemset: (4, 25, 6), Support: 233\n",
      "Itemset: (4, 6, 23), Support: 589\n",
      "Itemset: (4, 6, 16), Support: 519\n",
      "Itemset: (4, 6, 9), Support: 358\n",
      "Itemset: (4, 6, 7), Support: 352\n",
      "Itemset: (4, 23, 16), Support: 538\n",
      "Itemset: (4, 23, 9), Support: 367\n",
      "Itemset: (4, 23, 7), Support: 371\n",
      "Itemset: (4, 16, 9), Support: 326\n",
      "Itemset: (4, 16, 7), Support: 330\n",
      "Itemset: (4, 9, 7), Support: 296\n",
      "Itemset: (44, 13, 14), Support: 236\n",
      "Itemset: (44, 13, 23), Support: 232\n",
      "Itemset: (44, 14, 6), Support: 251\n",
      "Itemset: (44, 14, 23), Support: 255\n",
      "Itemset: (44, 6, 23), Support: 234\n",
      "Itemset: (13, 43, 14), Support: 332\n",
      "Itemset: (13, 43, 19), Support: 256\n",
      "Itemset: (13, 43, 6), Support: 319\n",
      "Itemset: (13, 43, 23), Support: 314\n",
      "Itemset: (13, 43, 16), Support: 295\n",
      "Itemset: (13, 43, 9), Support: 270\n",
      "Itemset: (13, 43, 7), Support: 284\n",
      "Itemset: (13, 14, 34), Support: 233\n",
      "Itemset: (13, 14, 19), Support: 340\n",
      "Itemset: (13, 14, 6), Support: 565\n",
      "Itemset: (13, 14, 23), Support: 582\n",
      "Itemset: (13, 14, 16), Support: 528\n",
      "Itemset: (13, 14, 9), Support: 364\n",
      "Itemset: (13, 14, 7), Support: 371\n",
      "Itemset: (13, 19, 6), Support: 325\n",
      "Itemset: (13, 19, 23), Support: 342\n",
      "Itemset: (13, 19, 16), Support: 308\n",
      "Itemset: (13, 19, 9), Support: 295\n",
      "Itemset: (13, 19, 7), Support: 307\n",
      "Itemset: (13, 6, 23), Support: 567\n",
      "Itemset: (13, 6, 16), Support: 497\n",
      "Itemset: (13, 6, 9), Support: 349\n",
      "Itemset: (13, 6, 7), Support: 353\n",
      "Itemset: (13, 23, 16), Support: 531\n",
      "Itemset: (13, 23, 9), Support: 353\n",
      "Itemset: (13, 23, 7), Support: 369\n",
      "Itemset: (13, 16, 9), Support: 326\n",
      "Itemset: (13, 16, 7), Support: 335\n",
      "Itemset: (13, 9, 7), Support: 311\n",
      "Itemset: (43, 14, 19), Support: 296\n",
      "Itemset: (43, 14, 6), Support: 371\n",
      "Itemset: (43, 14, 23), Support: 373\n",
      "Itemset: (43, 14, 16), Support: 329\n",
      "Itemset: (43, 14, 9), Support: 303\n",
      "Itemset: (43, 14, 7), Support: 320\n",
      "Itemset: (43, 19, 6), Support: 280\n",
      "Itemset: (43, 19, 23), Support: 284\n",
      "Itemset: (43, 19, 16), Support: 257\n",
      "Itemset: (43, 19, 9), Support: 250\n",
      "Itemset: (43, 19, 7), Support: 259\n",
      "Itemset: (43, 6, 23), Support: 343\n",
      "Itemset: (43, 6, 16), Support: 305\n",
      "Itemset: (43, 6, 9), Support: 296\n",
      "Itemset: (43, 6, 7), Support: 289\n",
      "Itemset: (43, 23, 16), Support: 316\n",
      "Itemset: (43, 23, 9), Support: 294\n",
      "Itemset: (43, 23, 7), Support: 314\n",
      "Itemset: (43, 16, 9), Support: 269\n",
      "Itemset: (43, 16, 7), Support: 269\n",
      "Itemset: (43, 9, 7), Support: 253\n",
      "Itemset: (12, 14, 23), Support: 231\n",
      "Itemset: (14, 34, 6), Support: 249\n",
      "Itemset: (14, 34, 23), Support: 249\n",
      "Itemset: (14, 34, 16), Support: 226\n",
      "Itemset: (14, 38, 23), Support: 231\n",
      "Itemset: (14, 19, 6), Support: 356\n",
      "Itemset: (14, 19, 23), Support: 377\n",
      "Itemset: (14, 19, 16), Support: 344\n",
      "Itemset: (14, 19, 9), Support: 315\n",
      "Itemset: (14, 19, 7), Support: 321\n",
      "Itemset: (14, 25, 6), Support: 238\n",
      "Itemset: (14, 25, 23), Support: 250\n",
      "Itemset: (14, 6, 23), Support: 632\n",
      "Itemset: (14, 6, 16), Support: 546\n",
      "Itemset: (14, 6, 9), Support: 385\n",
      "Itemset: (14, 6, 7), Support: 383\n",
      "Itemset: (14, 23, 16), Support: 581\n",
      "Itemset: (14, 23, 9), Support: 397\n",
      "Itemset: (14, 23, 7), Support: 399\n",
      "Itemset: (14, 16, 9), Support: 346\n",
      "Itemset: (14, 16, 7), Support: 341\n",
      "Itemset: (14, 9, 7), Support: 333\n",
      "Itemset: (34, 6, 23), Support: 238\n",
      "Itemset: (19, 6, 23), Support: 347\n",
      "Itemset: (19, 6, 16), Support: 318\n",
      "Itemset: (19, 6, 9), Support: 300\n",
      "Itemset: (19, 6, 7), Support: 292\n",
      "Itemset: (19, 23, 16), Support: 332\n",
      "Itemset: (19, 23, 9), Support: 323\n",
      "Itemset: (19, 23, 7), Support: 321\n",
      "Itemset: (19, 16, 9), Support: 287\n",
      "Itemset: (19, 16, 7), Support: 291\n",
      "Itemset: (19, 9, 7), Support: 265\n",
      "Itemset: (25, 6, 23), Support: 232\n",
      "Itemset: (6, 23, 16), Support: 547\n",
      "Itemset: (6, 23, 9), Support: 385\n",
      "Itemset: (6, 23, 7), Support: 362\n",
      "Itemset: (6, 16, 9), Support: 345\n",
      "Itemset: (6, 16, 7), Support: 339\n",
      "Itemset: (6, 9, 7), Support: 313\n",
      "Itemset: (23, 16, 9), Support: 372\n",
      "Itemset: (23, 16, 7), Support: 343\n",
      "Itemset: (23, 9, 7), Support: 333\n",
      "Itemset: (16, 9, 7), Support: 305\n",
      "Itemset: (0, 4, 13, 14), Support: 260\n",
      "Itemset: (0, 4, 13, 6), Support: 247\n",
      "Itemset: (0, 4, 13, 23), Support: 249\n",
      "Itemset: (0, 4, 13, 16), Support: 239\n",
      "Itemset: (0, 4, 13, 7), Support: 230\n",
      "Itemset: (0, 4, 43, 14), Support: 237\n",
      "Itemset: (0, 4, 14, 19), Support: 228\n",
      "Itemset: (0, 4, 14, 6), Support: 280\n",
      "Itemset: (0, 4, 14, 23), Support: 286\n",
      "Itemset: (0, 4, 14, 16), Support: 268\n",
      "Itemset: (0, 4, 14, 9), Support: 244\n",
      "Itemset: (0, 4, 14, 7), Support: 241\n",
      "Itemset: (0, 4, 6, 23), Support: 263\n",
      "Itemset: (0, 4, 6, 16), Support: 254\n",
      "Itemset: (0, 4, 6, 9), Support: 238\n",
      "Itemset: (0, 4, 6, 7), Support: 233\n",
      "Itemset: (0, 4, 23, 16), Support: 254\n",
      "Itemset: (0, 4, 23, 9), Support: 242\n",
      "Itemset: (0, 4, 23, 7), Support: 233\n",
      "Itemset: (0, 13, 14, 6), Support: 259\n",
      "Itemset: (0, 13, 14, 23), Support: 259\n",
      "Itemset: (0, 13, 14, 16), Support: 251\n",
      "Itemset: (0, 13, 14, 9), Support: 237\n",
      "Itemset: (0, 13, 14, 7), Support: 230\n",
      "Itemset: (0, 13, 6, 23), Support: 252\n",
      "Itemset: (0, 13, 6, 16), Support: 239\n",
      "Itemset: (0, 13, 6, 9), Support: 228\n",
      "Itemset: (0, 13, 23, 16), Support: 243\n",
      "Itemset: (0, 13, 23, 9), Support: 232\n",
      "Itemset: (0, 43, 14, 6), Support: 232\n",
      "Itemset: (0, 43, 14, 23), Support: 231\n",
      "Itemset: (0, 14, 19, 6), Support: 238\n",
      "Itemset: (0, 14, 19, 23), Support: 236\n",
      "Itemset: (0, 14, 19, 16), Support: 229\n",
      "Itemset: (0, 14, 6, 23), Support: 286\n",
      "Itemset: (0, 14, 6, 16), Support: 271\n",
      "Itemset: (0, 14, 6, 9), Support: 248\n",
      "Itemset: (0, 14, 6, 7), Support: 243\n",
      "Itemset: (0, 14, 23, 16), Support: 274\n",
      "Itemset: (0, 14, 23, 9), Support: 254\n",
      "Itemset: (0, 14, 23, 7), Support: 238\n",
      "Itemset: (0, 14, 16, 9), Support: 232\n",
      "Itemset: (0, 19, 6, 23), Support: 232\n",
      "Itemset: (0, 6, 23, 16), Support: 257\n",
      "Itemset: (0, 6, 23, 9), Support: 245\n",
      "Itemset: (0, 6, 23, 7), Support: 229\n",
      "Itemset: (0, 6, 16, 9), Support: 232\n",
      "Itemset: (0, 6, 16, 7), Support: 226\n",
      "Itemset: (0, 23, 16, 9), Support: 236\n",
      "Itemset: (4, 13, 43, 14), Support: 260\n",
      "Itemset: (4, 13, 43, 6), Support: 248\n",
      "Itemset: (4, 13, 43, 23), Support: 233\n",
      "Itemset: (4, 13, 43, 16), Support: 230\n",
      "Itemset: (4, 13, 14, 19), Support: 244\n",
      "Itemset: (4, 13, 14, 6), Support: 417\n",
      "Itemset: (4, 13, 14, 23), Support: 430\n",
      "Itemset: (4, 13, 14, 16), Support: 395\n",
      "Itemset: (4, 13, 14, 9), Support: 261\n",
      "Itemset: (4, 13, 14, 7), Support: 274\n",
      "Itemset: (4, 13, 19, 6), Support: 243\n",
      "Itemset: (4, 13, 19, 23), Support: 239\n",
      "Itemset: (4, 13, 19, 16), Support: 232\n",
      "Itemset: (4, 13, 19, 7), Support: 231\n",
      "Itemset: (4, 13, 6, 23), Support: 418\n",
      "Itemset: (4, 13, 6, 16), Support: 378\n",
      "Itemset: (4, 13, 6, 9), Support: 254\n",
      "Itemset: (4, 13, 6, 7), Support: 255\n",
      "Itemset: (4, 13, 23, 16), Support: 390\n",
      "Itemset: (4, 13, 23, 9), Support: 255\n",
      "Itemset: (4, 13, 23, 7), Support: 266\n",
      "Itemset: (4, 13, 16, 9), Support: 245\n",
      "Itemset: (4, 13, 16, 7), Support: 248\n",
      "Itemset: (4, 43, 14, 6), Support: 283\n",
      "Itemset: (4, 43, 14, 23), Support: 273\n",
      "Itemset: (4, 43, 14, 16), Support: 249\n",
      "Itemset: (4, 43, 14, 9), Support: 229\n",
      "Itemset: (4, 43, 14, 7), Support: 247\n",
      "Itemset: (4, 43, 6, 23), Support: 255\n",
      "Itemset: (4, 43, 6, 16), Support: 232\n",
      "Itemset: (4, 43, 23, 16), Support: 235\n",
      "Itemset: (4, 43, 23, 7), Support: 228\n",
      "Itemset: (4, 14, 19, 6), Support: 259\n",
      "Itemset: (4, 14, 19, 23), Support: 266\n",
      "Itemset: (4, 14, 19, 16), Support: 257\n",
      "Itemset: (4, 14, 19, 9), Support: 232\n",
      "Itemset: (4, 14, 19, 7), Support: 238\n",
      "Itemset: (4, 14, 6, 23), Support: 465\n",
      "Itemset: (4, 14, 6, 16), Support: 411\n",
      "Itemset: (4, 14, 6, 9), Support: 279\n",
      "Itemset: (4, 14, 6, 7), Support: 274\n",
      "Itemset: (4, 14, 23, 16), Support: 432\n",
      "Itemset: (4, 14, 23, 9), Support: 292\n",
      "Itemset: (4, 14, 23, 7), Support: 287\n",
      "Itemset: (4, 14, 16, 9), Support: 262\n",
      "Itemset: (4, 14, 16, 7), Support: 254\n",
      "Itemset: (4, 14, 9, 7), Support: 237\n",
      "Itemset: (4, 19, 6, 23), Support: 247\n",
      "Itemset: (4, 19, 6, 16), Support: 241\n",
      "Itemset: (4, 19, 23, 16), Support: 239\n",
      "Itemset: (4, 19, 23, 9), Support: 231\n",
      "Itemset: (4, 19, 23, 7), Support: 229\n",
      "Itemset: (4, 6, 23, 16), Support: 401\n",
      "Itemset: (4, 6, 23, 9), Support: 276\n",
      "Itemset: (4, 6, 23, 7), Support: 261\n",
      "Itemset: (4, 6, 16, 9), Support: 252\n",
      "Itemset: (4, 6, 16, 7), Support: 248\n",
      "Itemset: (4, 23, 16, 9), Support: 265\n",
      "Itemset: (4, 23, 16, 7), Support: 245\n",
      "Itemset: (4, 23, 9, 7), Support: 236\n",
      "Itemset: (13, 43, 14, 6), Support: 253\n",
      "Itemset: (13, 43, 14, 23), Support: 251\n",
      "Itemset: (13, 43, 14, 16), Support: 232\n",
      "Itemset: (13, 43, 6, 23), Support: 237\n",
      "Itemset: (13, 43, 23, 16), Support: 227\n",
      "Itemset: (13, 14, 19, 6), Support: 250\n",
      "Itemset: (13, 14, 19, 23), Support: 263\n",
      "Itemset: (13, 14, 19, 16), Support: 240\n",
      "Itemset: (13, 14, 19, 9), Support: 228\n",
      "Itemset: (13, 14, 19, 7), Support: 234\n",
      "Itemset: (13, 14, 6, 23), Support: 437\n",
      "Itemset: (13, 14, 6, 16), Support: 395\n",
      "Itemset: (13, 14, 6, 9), Support: 273\n",
      "Itemset: (13, 14, 6, 7), Support: 271\n",
      "Itemset: (13, 14, 23, 16), Support: 412\n",
      "Itemset: (13, 14, 23, 9), Support: 276\n",
      "Itemset: (13, 14, 23, 7), Support: 280\n",
      "Itemset: (13, 14, 16, 9), Support: 258\n",
      "Itemset: (13, 14, 16, 7), Support: 258\n",
      "Itemset: (13, 14, 9, 7), Support: 247\n",
      "Itemset: (13, 19, 6, 23), Support: 248\n",
      "Itemset: (13, 19, 23, 16), Support: 233\n",
      "Itemset: (13, 19, 23, 9), Support: 226\n",
      "Itemset: (13, 19, 23, 7), Support: 229\n",
      "Itemset: (13, 6, 23, 16), Support: 393\n",
      "Itemset: (13, 6, 23, 9), Support: 267\n",
      "Itemset: (13, 6, 23, 7), Support: 260\n",
      "Itemset: (13, 6, 16, 9), Support: 248\n",
      "Itemset: (13, 6, 16, 7), Support: 245\n",
      "Itemset: (13, 6, 9, 7), Support: 230\n",
      "Itemset: (13, 23, 16, 9), Support: 262\n",
      "Itemset: (13, 23, 16, 7), Support: 254\n",
      "Itemset: (13, 23, 9, 7), Support: 241\n",
      "Itemset: (13, 16, 9, 7), Support: 230\n",
      "Itemset: (43, 14, 19, 23), Support: 233\n",
      "Itemset: (43, 14, 6, 23), Support: 282\n",
      "Itemset: (43, 14, 6, 16), Support: 249\n",
      "Itemset: (43, 14, 6, 9), Support: 237\n",
      "Itemset: (43, 14, 6, 7), Support: 233\n",
      "Itemset: (43, 14, 23, 16), Support: 256\n",
      "Itemset: (43, 14, 23, 9), Support: 240\n",
      "Itemset: (43, 14, 23, 7), Support: 248\n",
      "Itemset: (43, 6, 23, 16), Support: 243\n",
      "Itemset: (43, 6, 23, 7), Support: 226\n",
      "Itemset: (14, 19, 6, 23), Support: 272\n",
      "Itemset: (14, 19, 6, 16), Support: 254\n",
      "Itemset: (14, 19, 6, 9), Support: 231\n",
      "Itemset: (14, 19, 6, 7), Support: 235\n",
      "Itemset: (14, 19, 23, 16), Support: 266\n",
      "Itemset: (14, 19, 23, 9), Support: 255\n",
      "Itemset: (14, 19, 23, 7), Support: 247\n",
      "Itemset: (14, 19, 16, 9), Support: 230\n",
      "Itemset: (14, 19, 16, 7), Support: 227\n",
      "Itemset: (14, 6, 23, 16), Support: 431\n",
      "Itemset: (14, 6, 23, 9), Support: 297\n",
      "Itemset: (14, 6, 23, 7), Support: 289\n",
      "Itemset: (14, 6, 16, 9), Support: 262\n",
      "Itemset: (14, 6, 16, 7), Support: 265\n",
      "Itemset: (14, 6, 9, 7), Support: 248\n",
      "Itemset: (14, 23, 16, 9), Support: 288\n",
      "Itemset: (14, 23, 16, 7), Support: 267\n",
      "Itemset: (14, 23, 9, 7), Support: 265\n",
      "Itemset: (14, 16, 9, 7), Support: 238\n",
      "Itemset: (19, 6, 23, 16), Support: 246\n",
      "Itemset: (19, 6, 23, 9), Support: 231\n",
      "Itemset: (19, 23, 16, 9), Support: 233\n",
      "Itemset: (6, 23, 16, 9), Support: 281\n",
      "Itemset: (6, 23, 16, 7), Support: 251\n",
      "Itemset: (6, 23, 9, 7), Support: 240\n",
      "Itemset: (6, 16, 9, 7), Support: 235\n",
      "Itemset: (23, 16, 9, 7), Support: 242\n",
      "Itemset: (0, 4, 14, 6, 23), Support: 229\n",
      "Itemset: (4, 13, 14, 6, 23), Support: 345\n",
      "Itemset: (4, 13, 14, 6, 16), Support: 318\n",
      "Itemset: (4, 13, 14, 23, 16), Support: 325\n",
      "Itemset: (4, 13, 6, 23, 16), Support: 312\n",
      "Itemset: (4, 14, 6, 23, 16), Support: 343\n",
      "Itemset: (4, 14, 6, 23, 9), Support: 230\n",
      "Itemset: (4, 14, 23, 16, 9), Support: 228\n",
      "Itemset: (13, 14, 6, 23, 16), Support: 325\n",
      "Itemset: (14, 6, 23, 16, 9), Support: 232\n",
      "Itemset: (4, 13, 14, 6, 23, 16), Support: 270\n"
     ]
    }
   ],
   "source": [
    "# TODO: set the initial candidates which will be used to generate the frequent length-2 itemsets (1 point)\n",
    "candidates = list(frequent_items.keys())\n",
    "\n",
    "# TODO: set the correct loop condition (1 point)\n",
    "while candidates:\n",
    "    new_candidates = apriori_gen(candidates)\n",
    "    supports = map(calculate_support, new_candidates)\n",
    "    \n",
    "    # TODO: filter out the frequent candidates (2 point)\n",
    "    frequent_new_candidates = {itemset: support for itemset, support in zip(new_candidates, supports) if support >= min_support}\n",
    "    \n",
    "    # TODO: add the frequent candidates to frequent_items (1 point)\n",
    "    frequent_items.update(frequent_new_candidates)\n",
    "\n",
    "    # replace candidates with the new ones\n",
    "    candidates = list(frequent_new_candidates.keys())\n",
    "\n",
    "print(\"Frequent Itemsets:\")\n",
    "for itemset, support in frequent_items.items():\n",
    "    print(f\"Itemset: {itemset}, Support: {support}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### C) Save your results (3 points)\n",
    "\n",
    "**Task:** Save all the frequent itemsets along with their absolute supports into a text file named “patterns.txt” and place it in the root of your zip file. Every line corresponds to exactly one frequent itemset and should be in the following format:\n",
    "\n",
    "*support:video_game_1;video_game_2;video_game_3;...*\n",
    "\n",
    "For example, suppose an itemset (Fallout 4;Genshin Impact) has an absolute support 520, then the line corresponding to this frequent itemset in `patterns.txt` should be:\n",
    "\n",
    "*520:Fallout 4;Genshin Impact*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"patterns.txt\", \"w\") as file:\n",
    "    for itemset, support in frequent_items.items():\n",
    "        itemset_names = [id_to_item[item_id] for item_id in itemset] #convert item IDs to item names in the itemset\n",
    "        itemset_str = \";\".join(itemset_names) #convert the itemset names to a semicolon-separated string\n",
    "        file.write(f\"{support}:{itemset_str}\\n\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 Recommendation (9 points)\n",
    "\n",
    "**Task:** Imagine you should recommend a movie to a user. You know that the user likes the video games \"Elden Ring\" and \"Scarlet Nexus\". Based on the result of the Apriori algorithm, implement an algorithm that gives a recommendation for this user by maximizing the confidence that the user will like the game. (6 points)\n",
    "\n",
    "**Report:** Explain your choice and report the confidence score for your recommendation. (3 points)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#convert item IDs to item names in the frequent_items dictionary\n",
    "frequent_items_with_names = {}\n",
    "for itemset, support in frequent_items.items():\n",
    "    itemset_with_names = [id_to_item.get(item_id) for item_id in itemset if id_to_item.get(item_id) is not None]\n",
    "    if itemset_with_names:\n",
    "        frequent_items_with_names[tuple(itemset_with_names)] = support\n",
    "frequent_items = frequent_items_with_names\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recommended Games:\n",
      "Code Vein\n",
      "Dying Light 2 Stay Human\n",
      "Cyberpunk 2077\n",
      "Hogwarts Legacy\n",
      "Fallout 4\n",
      "Transistor\n",
      "Kingdom Come: Deliverance\n",
      "Torchlight 2\n",
      "Yakuza Kiwami\n",
      "Dark Souls 3\n",
      "Diablo III\n",
      "Dragons Dogma: Dark Arisen\n",
      "Tales of Berseria\n",
      "Assassin's Creed Origins\n",
      "Genshin Impact\n",
      "Middle-Earth: Shadow of War\n"
     ]
    }
   ],
   "source": [
    "user_games = [\"Elden Ring\", \"Scarlet Nexus\"]\n",
    "user_game_ids = [item_to_id.get(game) for game in user_games if item_to_id.get(game) is not None]\n",
    "user_game_names = [id_to_item.get(item_id) for item_id in user_game_ids]\n",
    "\n",
    "recommendations = []\n",
    "for itemset, support in frequent_items.items():\n",
    "    if any(item in user_game_names for item in itemset):\n",
    "        recommendations.append((itemset, support))\n",
    "\n",
    "confidence_scores = {}\n",
    "for itemset, support in recommendations:\n",
    "    for item in itemset:\n",
    "        if item not in user_game_names:\n",
    "            antecedent = user_game_names\n",
    "            consequent = item\n",
    "            support_antecedent = frequent_items.get(tuple(antecedent), 0)\n",
    "            support_rule = support\n",
    "            if support_antecedent != 0:\n",
    "                confidence = support_rule / support_antecedent\n",
    "                confidence_scores[item] = confidence\n",
    "\n",
    "sorted_recommendations = sorted(confidence_scores.items(), key=lambda x: x[1], reverse=True)\n",
    "recommended_games = [game_name for game_name, confidence in sorted_recommendations]\n",
    "\n",
    "print(\"Recommended Games:\")\n",
    "for game in recommended_games:\n",
    "    print(game)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Score: 0.7142857142857143\n"
     ]
    }
   ],
   "source": [
    "confidence_score = sorted_recommendations[0][1]\n",
    "print(\"Confidence Score:\", confidence_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implemented recommendation algorithm calculates the confidence score for each potential recommendation, based on the information about the liked games of the user and the previously implemented Apriori algorithm. The recommendation is based on maximizing the confidence that the user will like the game. It is calculated by dividing the support of the recommendation (the count of occurrences of the recommendation itemset) by the support of the antecedent (the count of occurrences of the liked games). The recommendation algorithm checks for frequent itemsets that include the liked games and have additional games beyond the liked games. It calculates the confidence score for each of these itemsets and selects the recommendation with the highest confidence score."
   ]
  }
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