4_RecommendingMovies.ipynb

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    "# Recommending Movies Using Affinity Analysis\n",
    "\n",
    "Here, we will look at affinity analysis that determines when objects occur frequently together. This is colloquially called market basket analysis, after one of the use cases of determining when items are purchased together frequently.\n",
    "\n",
    "The key concepts of this chapter are as follows:\n",
    "- Affinity analysis\n",
    "- Feature association mining using the Apriori algorithm\n",
    "- Movie recommendations\n",
    "- Sparse data formats\n",
    "\n",
    "## Affinity analysis\n",
    "\n",
    "Affinity analysis is the task of determining when objects are used in similar ways. In the previous section, we focused on whether the objects themselves are similar. The data for affinity analysis is often described in the form of a **transaction**. Intuitively, this comes from a transaction at a store—determining when objects are purchased together. \n",
    "\n",
    "However, it can be applied to many processes:\n",
    "- Fraud detection\n",
    "- Customer segmentation\n",
    "- Software optimization\n",
    "- Product recommendations\n",
    "\n",
    "Affinity analysis is usually much more exploratory than classification. We often don't have the complete dataset we expect for many classification tasks. For instance, in movie recommendation, we have reviews from different people on different movies. However, it is unlikely we have each reviewer review all of the movies in our dataset. This leaves an important and difficult question in affinity analysis. If a reviewer hasn't reviewed a movie, is that an indication that they aren't interested in the movie (and therefore wouldn't recommend it) or simply that they haven't reviewed it yet?\n",
    "\n",
    "## Algorithms for affinity analysis\n",
    "\n",
    "With a naive rule creation, such as our previous algorithm, the growth in time needed to compute these rules increases exponentially. As we add more items, the time it takes to compute all rules increases significantly faster. Specifically, the total possible number of rules is 2n - 1. For our five-item dataset, there are 31 possible rules. For 10 items, it is 1023. For just 100 items, the number has 30 digits. Even the drastic increase in computing power couldn't possibly keep up with the increases in the number of items stored online. Therefore, we need algorithms that work smarter, as opposed to computers that work harder.\n",
    "\n",
    "The classic algorithm for affinity analysis is called the **Apriori algorithm**. It addresses the exponential problem of creating sets of items that occur frequently within a database, called **frequent itemsets**. Once these frequent itemsets are discovered, creating association rules is straightforward.\n",
    "\n",
    "The intuition behind Apriori is both simple and clever. First, we ensure that a rule has sufficient support within the dataset. Defining a minimum support level is the key parameter for Apriori. To build a frequent itemset, for an itemset (A, B) to have a support of at least 30, both A and B must occur at least 30 times in the database. This property extends to larger sets as well. For an itemset (A, B, C, D) to be considered\n",
    "frequent, the set (A, B, C) must also be frequent (as must D).\n",
    "\n",
    "These frequent itemsets can be built up and possible itemsets that are not frequent (of which there are many) will never be tested. This saves significant time in testing new rules.\n",
    "\n",
    "Other example algorithms for affinity analysis include the **Eclat** and **FP-growth** algorithms. There are many improvements to these algorithms in the data mining literature that further improve the efficiency of the method.\n",
    "\n",
    "## Choosing parameters\n",
    "\n",
    "To perform association rule mining for affinity analysis, we first use the Apriori to generate frequent itemsets. Next, we create association rules (for example, if a person recommended movie X, they would also recommend movie Y) by testing combinations of premises and conclusions within those frequent itemsets.\n",
    "\n",
    "For the first stage, the Apriori algorithm needs a value for the minimum support that an itemset needs to be considered frequent. Any itemsets with less support will not be considered. Setting this minimum support too low will cause Apriori to test a larger number of itemsets, slowing the algorithm down. Setting it too high will result in fewer itemsets being considered frequent.\n",
    "\n",
    "In the second stage, after the frequent itemsets have been discovered, association\n",
    "rules are tested based on their confidence. We could choose a minimum confidence\n",
    "level, a number of rules to return, or simply return all of them and let the user decide\n",
    "what to do with them.\n",
    "\n",
    "Here, we will return only rules above a given confidence level. Therefore, we need to set our minimum confidence level. Setting this too low will result in rules that have a high support, but are not very accurate. Setting this higher will result in only more accurate rules being returned, but with fewer rules being discovered.\n",
    "\n",
    "## The movie recommendation problem\n",
    "\n",
    "Product recommendation is big business. Online stores use it to up-sell to customers by recommending other products that they could buy. Making better recommendations leads to better sales. When online shopping is selling to millions of customers every year, there is a lot of potential money to be made by selling more\n",
    "items to these customers.\n",
    "\n",
    "**Aside**: Product recommendations have been researched for many years; however, the field gained a significant boost when Netflix ran their Netflix Prize between 2007 and 2009. This competition aimed to determine if anyone can predict a user's rating of a film better than Netflix was currently doing. The prize went to a team that was just over 10 percent better than the current solution. While this may not seem like a large improvement, such an improvement would net millions to Netflix in revenue from better movie recommendations.\n",
    "\n",
    "## Obtaining the dataset\n",
    "\n",
    "Since the inception of the Netflix Prize, Grouplens, a research group at the University of Minnesota, has released several datasets that are often used for testing algorithms in this area. They have released several versions of a movie rating dataset, which have different sizes. There is a version with 100,000 reviews, one with 1 million reviews and one with 10 million reviews.\n",
    "\n",
    "The datasets are available from http://grouplens.org/datasets/movielens/ and the dataset we are going to use is the MovieLens 1 million dataset. Download this dataset and unzip it in your data folder."
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   "source": [
    "DATA = 'data/ml-100k/'\n",
    "RATINGS = DATA + 'u.data'\n",
    "MOVIES = DATA + 'u.item'"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "import pandas as pd"
   ]
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       "   UserID  MovieID  Rating            Datetime\n",
       "0     196      242       3 1997-12-04 15:55:49\n",
       "1     186      302       3 1998-04-04 19:22:22\n",
       "2      22      377       1 1997-11-07 07:18:36\n",
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    "all_ratings = pd.read_csv(RATINGS, delimiter=\"\\t\", header=None, names = [\"UserID\", \"MovieID\", \"Rating\", \"Datetime\"])\n",
    "all_ratings[\"Datetime\"] = pd.to_datetime(all_ratings['Datetime'],unit='s')\n",
    "all_ratings.head()"
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    "## Sparse data formats\n",
    "\n",
    "This dataset is in a **sparse matrix** format. Each row can be thought of as a cell in a large feature matrix, where rows are users and columns are individual movies. The first column would be each user's review of the first movie, the second column would be each user's review of the second movie, and so on.\n",
    "\n",
    "There are 1,000 users and 1,700 movies in this dataset, which means that the full matrix would be quite large. We may run into issues storing the whole matrix in memory and computing on it would be troublesome. However, this matrix has the property that most cells are empty, that is, there is no review for most movies for most users. There is no review of movie #675 for user #213 though, and not for most other combinations of user and movie."
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       "Empty DataFrame\n",
       "Columns: [UserID, MovieID, Rating, Datetime]\n",
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    "all_ratings[all_ratings['MovieID']=='675'].head()"
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    "all_ratings[all_ratings['MovieID']=='213'].head()"
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    "## The Apriori implementation\n",
    "\n",
    "**Goal:**  produce rules of the following form: i*f a person recommends these movies, they will also recommend this movie.*\n",
    "\n",
    "We will also discuss extensions where a person recommends a set of movies is likely to recommend another particular movie. To do this, we first need to determine if a person recommends a movie. We can do this by creating a new feature Favorable, which is True if the person gave a favorable review to a movie:"
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       "    UserID  MovieID  Rating            Datetime  Favorable\n",
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    "# Not all reviews are favourable! Our goal is \"other recommended books\", so we only want favourable reviews\n",
    "all_ratings[\"Favorable\"] = all_ratings[\"Rating\"] > 3\n",
    "all_ratings[10:15]"
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       "     UserID  MovieID  Rating            Datetime  Favorable\n",
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    "all_ratings[all_ratings[\"UserID\"] == 1].head()"
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    "We will sample our dataset to form a training dataset. This also helps reduce the size of the dataset that will be searched, making the Apriori algorithm run faster. We obtain all reviews from the first 200 users:"
   ]
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   "cell_type": "code",
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    "# Sample the dataset. \n",
    "# You can try increasing the size of the sample, but the run time will be considerably longer\n",
    "ratings = all_ratings[all_ratings['UserID'].isin(range(200))]"
   ]
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       "    UserID  MovieID  Rating            Datetime  Favorable\n",
       "16     122      387       5 1997-11-11 17:47:39       True\n",
       "20     119      392       4 1998-01-30 16:13:34       True\n",
       "21     167      486       4 1998-04-16 14:54:12       True\n",
       "26      38       95       5 1998-04-13 01:14:54       True\n",
       "28      63      277       4 1997-10-01 23:10:01       True"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We start by creating a dataset of each user's favourable reviews\n",
    "favorable_ratings = ratings[ratings[\"Favorable\"]]\n",
    "favorable_ratings.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "199"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We are only interested in the reviewers who have more than one review\n",
    "favorable_reviews_by_users = dict((k, frozenset(v.values)) for k, v in favorable_ratings.groupby(\"UserID\")[\"MovieID\"])\n",
    "len(favorable_reviews_by_users)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Favorable</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MovieID</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>258</th>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Favorable\n",
       "MovieID           \n",
       "50             100\n",
       "100             89\n",
       "258             83\n",
       "181             79\n",
       "174             74"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# FLet's see the top five movies list\n",
    "num_favorable_by_movie = ratings[[\"MovieID\", \"Favorable\"]].groupby(\"MovieID\").sum()\n",
    "num_favorable_by_movie.sort_values(\"Favorable\", ascending=False).head()"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Apriori algorithm\n",
    "\n",
    "The Apriori algorithm is part of our affinity analysis and deals specifically with finding frequent itemsets within the data. The basic procedure of Apriori builds up new candidate itemsets from previously discovered frequent itemsets. These candidates are tested to see if they are frequent, and then the algorithm iterates as\n",
    "explained here:\n",
    "\n",
    "1. Create initial frequent itemsets by placing each item in its own itemset. Only items with at least the minimum support are used in this step.\n",
    "2. New candidate itemsets are created from the most recently discovered frequent itemsets by finding supersets of the existing frequent itemsets.\n",
    "3. All candidate itemsets are tested to see if they are frequent. If a candidate is not frequent then it is discarded. If there are no new frequent itemsets from this step, go to the last step.\n",
    "4. Store the newly discovered frequent itemsets and go to the second step.\n",
    "5. Return all of the discovered frequent itemsets.\n",
    "\n",
    "This process is outlined in the following workflow:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "## Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "\n",
    "def find_frequent_itemsets(favorable_reviews_by_users, k_1_itemsets, min_support):\n",
    "    counts = defaultdict(int)\n",
    "    for user, reviews in favorable_reviews_by_users.items():\n",
    "        for itemset in k_1_itemsets:\n",
    "            if itemset.issubset(reviews):\n",
    "                for other_reviewed_movie in reviews - itemset:\n",
    "                    current_superset = itemset | frozenset((other_reviewed_movie,))\n",
    "                    counts[current_superset] += 1\n",
    "    return dict([(itemset, frequency) for itemset, frequency in counts.items() if frequency >= min_support])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 16 movies with more than 50 favorable reviews\n",
      "I found 93 frequent itemsets of length 2\n",
      "I found 295 frequent itemsets of length 3\n",
      "I found 593 frequent itemsets of length 4\n",
      "I found 785 frequent itemsets of length 5\n",
      "I found 677 frequent itemsets of length 6\n",
      "I found 373 frequent itemsets of length 7\n",
      "I found 126 frequent itemsets of length 8\n",
      "I found 24 frequent itemsets of length 9\n",
      "I found 2 frequent itemsets of length 10\n",
      "Did not find any frequent itemsets of length 11\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "frequent_itemsets = {}  # itemsets are sorted by length\n",
    "min_support = 50\n",
    "\n",
    "# k=1 candidates are the isbns with more than min_support favourable reviews\n",
    "frequent_itemsets[1] = dict((frozenset((movie_id,)), row[\"Favorable\"])\n",
    "                                for movie_id, row in num_favorable_by_movie.iterrows()\n",
    "                                if row[\"Favorable\"] > min_support)\n",
    "\n",
    "print(f\"There are {len(frequent_itemsets[1])} movies with more than {min_support} favorable reviews\")\n",
    "# We use sys.stdout.flush() to ensure that the printouts happen while the code is still running.\n",
    "sys.stdout.flush()\n",
    "for k in range(2, 20):\n",
    "    # Generate candidates of length k, using the frequent itemsets of length k-1\n",
    "    # Only store the frequent itemsets\n",
    "    cur_frequent_itemsets = find_frequent_itemsets(favorable_reviews_by_users, frequent_itemsets[k-1],\n",
    "                                                   min_support)\n",
    "    if len(cur_frequent_itemsets) == 0:\n",
    "        print(f\"Did not find any frequent itemsets of length {k}\")\n",
    "        sys.stdout.flush()\n",
    "        break\n",
    "    else:\n",
    "        print(f\"I found {len(cur_frequent_itemsets)} frequent itemsets of length {k}\")\n",
    "        #print(cur_frequent_itemsets)\n",
    "        sys.stdout.flush()\n",
    "        frequent_itemsets[k] = cur_frequent_itemsets\n",
    "# We aren't interested in the itemsets of length 1, so remove those\n",
    "del frequent_itemsets[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll notice that the number of itemsets grows as the length increases before it shrinks. It grows because of the increasing number of possible rules. After a while, the large number of combinations no longer has the support necessary to be considered frequent. This results in the number shrinking. This shrinking is the benefit of the Apriori algorithm. If we search all possible itemsets (not just the supersets of frequent ones), we would be searching thousands of times more itemsets to see if they are frequent.\n",
    "\n",
    "## Extracting association rules\n",
    "\n",
    "Now, we have a list of frequent itemsets. These aren't exactly association rules, but they are similar to it. A frequent itemset is a set of items with a minimum support, while an association rule has a premise and a conclusion.\n",
    "\n",
    "We can make an association rule from a frequent itemset by taking one of the movies in the itemset and denoting it as the conclusion. The other movies in the itemset will be the premise. This will form rules of the following form: *if a reviewer recommends all of the movies in the premise, they will also recommend the conclusion.*\n",
    "\n",
    "For each itemset, we can generate a number of association rules by setting each movie to be the conclusion and the remaining movies as the premise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "  frozenset({100, 181, 313}): 66,\n",
       "  frozenset({181, 258, 313}): 60},\n",
       " 4: {frozenset({1, 7, 50, 56}): 72,\n",
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       "  frozenset({1, 7, 50, 98}): 76,\n",
       "  frozenset({1, 7, 50, 100}): 76,\n",
       "  frozenset({1, 7, 50, 172}): 76,\n",
       "  frozenset({1, 7, 50, 174}): 88,\n",
       "  frozenset({1, 7, 50, 181}): 84,\n",
       "  frozenset({1, 7, 56, 64}): 60,\n",
       "  frozenset({1, 7, 56, 79}): 60,\n",
       "  frozenset({1, 7, 56, 98}): 72,\n",
       "  frozenset({1, 7, 56, 100}): 60,\n",
       "  frozenset({1, 7, 56, 172}): 68,\n",
       "  frozenset({1, 7, 56, 174}): 76,\n",
       "  frozenset({1, 7, 56, 181}): 60,\n",
       "  frozenset({1, 7, 64, 79}): 56,\n",
       "  frozenset({1, 7, 64, 98}): 64,\n",
       "  frozenset({1, 7, 64, 100}): 52,\n",
       "  frozenset({1, 7, 64, 172}): 60,\n",
       "  frozenset({1, 7, 64, 174}): 68,\n",
       "  frozenset({1, 7, 64, 181}): 60,\n",
       "  frozenset({1, 7, 79, 98}): 72,\n",
       "  frozenset({1, 7, 79, 100}): 52,\n",
       "  frozenset({1, 7, 79, 172}): 64,\n",
       "  frozenset({1, 7, 79, 174}): 72,\n",
       "  frozenset({1, 7, 79, 181}): 64,\n",
       "  frozenset({1, 7, 98, 100}): 56,\n",
       "  frozenset({1, 7, 98, 172}): 68,\n",
       "  frozenset({1, 7, 98, 174}): 80,\n",
       "  frozenset({1, 7, 98, 181}): 64,\n",
       "  frozenset({1, 7, 100, 172}): 52,\n",
       "  frozenset({1, 7, 100, 174}): 60,\n",
       "  frozenset({1, 7, 100, 181}): 56,\n",
       "  frozenset({1, 7, 172, 174}): 80,\n",
       "  frozenset({1, 7, 172, 181}): 64,\n",
       "  frozenset({1, 7, 174, 181}): 72,\n",
       "  frozenset({1, 50, 56, 64}): 68,\n",
       "  frozenset({1, 50, 56, 79}): 64,\n",
       "  frozenset({1, 50, 56, 98}): 88,\n",
       "  frozenset({1, 50, 56, 100}): 76,\n",
       "  frozenset({1, 50, 56, 127}): 60,\n",
       "  frozenset({1, 50, 56, 172}): 76,\n",
       "  frozenset({1, 50, 56, 174}): 104,\n",
       "  frozenset({1, 50, 56, 181}): 72,\n",
       "  frozenset({1, 50, 64, 79}): 68,\n",
       "  frozenset({1, 50, 64, 98}): 88,\n",
       "  frozenset({1, 50, 64, 100}): 68,\n",
       "  frozenset({1, 50, 64, 127}): 56,\n",
       "  frozenset({1, 50, 64, 172}): 72,\n",
       "  frozenset({1, 50, 64, 174}): 88,\n",
       "  frozenset({1, 50, 64, 181}): 84,\n",
       "  frozenset({1, 50, 79, 98}): 80,\n",
       "  frozenset({1, 50, 79, 100}): 56,\n",
       "  frozenset({1, 50, 79, 172}): 72,\n",
       "  frozenset({1, 50, 79, 174}): 92,\n",
       "  frozenset({1, 50, 79, 181}): 84,\n",
       "  frozenset({1, 50, 98, 100}): 72,\n",
       "  frozenset({1, 50, 98, 127}): 60,\n",
       "  frozenset({1, 50, 98, 172}): 88,\n",
       "  frozenset({1, 50, 98, 174}): 108,\n",
       "  frozenset({1, 50, 98, 181}): 96,\n",
       "  frozenset({1, 50, 100, 127}): 88,\n",
       "  frozenset({1, 50, 100, 172}): 68,\n",
       "  frozenset({1, 50, 100, 174}): 88,\n",
       "  frozenset({1, 50, 100, 181}): 84,\n",
       "  frozenset({1, 50, 127, 174}): 64,\n",
       "  frozenset({1, 50, 172, 174}): 104,\n",
       "  frozenset({1, 50, 172, 181}): 100,\n",
       "  frozenset({1, 50, 174, 181}): 108,\n",
       "  frozenset({1, 56, 64, 79}): 56,\n",
       "  frozenset({1, 56, 64, 98}): 80,\n",
       "  frozenset({1, 56, 64, 100}): 64,\n",
       "  frozenset({1, 56, 64, 127}): 60,\n",
       "  frozenset({1, 56, 64, 172}): 56,\n",
       "  frozenset({1, 56, 64, 174}): 80,\n",
       "  frozenset({1, 56, 64, 181}): 52,\n",
       "  frozenset({1, 56, 79, 98}): 64,\n",
       "  frozenset({1, 56, 79, 100}): 64,\n",
       "  frozenset({1, 56, 79, 172}): 56,\n",
       "  frozenset({1, 56, 79, 174}): 72,\n",
       "  frozenset({1, 56, 79, 181}): 52,\n",
       "  frozenset({1, 56, 98, 100}): 84,\n",
       "  frozenset({1, 56, 98, 127}): 64,\n",
       "  frozenset({1, 56, 98, 172}): 68,\n",
       "  frozenset({1, 56, 98, 174}): 100,\n",
       "  frozenset({1, 56, 98, 181}): 68,\n",
       "  frozenset({1, 56, 100, 127}): 72,\n",
       "  frozenset({1, 56, 100, 172}): 56,\n",
       "  frozenset({1, 56, 100, 174}): 88,\n",
       "  frozenset({1, 56, 127, 174}): 72,\n",
       "  frozenset({1, 56, 172, 174}): 80,\n",
       "  frozenset({1, 56, 172, 181}): 64,\n",
       "  frozenset({1, 56, 174, 181}): 72,\n",
       "  frozenset({1, 64, 79, 98}): 72,\n",
       "  frozenset({1, 64, 79, 172}): 56,\n",
       "  frozenset({1, 64, 79, 174}): 72,\n",
       "  frozenset({1, 64, 79, 181}): 68,\n",
       "  frozenset({1, 64, 98, 100}): 68,\n",
       "  frozenset({1, 64, 98, 127}): 68,\n",
       "  frozenset({1, 64, 98, 172}): 72,\n",
       "  frozenset({1, 64, 98, 174}): 92,\n",
       "  frozenset({1, 64, 98, 181}): 72,\n",
       "  frozenset({1, 64, 100, 127}): 60,\n",
       "  frozenset({1, 64, 100, 174}): 72,\n",
       "  frozenset({1, 64, 100, 181}): 52,\n",
       "  frozenset({1, 64, 127, 174}): 68,\n",
       "  frozenset({1, 64, 172, 174}): 72,\n",
       "  frozenset({1, 64, 172, 181}): 68,\n",
       "  frozenset({1, 64, 174, 181}): 76,\n",
       "  frozenset({1, 79, 98, 100}): 52,\n",
       "  frozenset({1, 79, 98, 172}): 68,\n",
       "  frozenset({1, 79, 98, 174}): 84,\n",
       "  frozenset({1, 79, 98, 181}): 72,\n",
       "  frozenset({1, 79, 100, 174}): 64,\n",
       "  frozenset({1, 79, 172, 174}): 76,\n",
       "  frozenset({1, 79, 172, 181}): 64,\n",
       "  frozenset({1, 79, 174, 181}): 80,\n",
       "  frozenset({1, 98, 100, 127}): 68,\n",
       "  frozenset({1, 98, 100, 172}): 56,\n",
       "  frozenset({1, 98, 100, 174}): 76,\n",
       "  frozenset({1, 98, 100, 181}): 56,\n",
       "  frozenset({1, 98, 127, 174}): 64,\n",
       "  frozenset({1, 98, 172, 174}): 84,\n",
       "  frozenset({1, 98, 172, 181}): 80,\n",
       "  frozenset({1, 98, 174, 181}): 84,\n",
       "  frozenset({1, 100, 127, 174}): 72,\n",
       "  frozenset({1, 100, 172, 174}): 64,\n",
       "  frozenset({1, 100, 172, 181}): 56,\n",
       "  frozenset({1, 100, 174, 181}): 60,\n",
       "  frozenset({1, 172, 174, 181}): 88,\n",
       "  frozenset({7, 9, 50, 56}): 68,\n",
       "  frozenset({7, 9, 50, 64}): 60,\n",
       "  frozenset({7, 9, 50, 100}): 68,\n",
       "  frozenset({7, 9, 50, 174}): 72,\n",
       "  frozenset({7, 9, 56, 64}): 64,\n",
       "  frozenset({7, 9, 56, 100}): 72,\n",
       "  frozenset({7, 9, 56, 174}): 72,\n",
       "  frozenset({7, 9, 64, 100}): 60,\n",
       "  frozenset({7, 9, 64, 174}): 64,\n",
       "  frozenset({7, 9, 100, 174}): 68,\n",
       "  frozenset({7, 50, 56, 64}): 92,\n",
       "  frozenset({7, 50, 56, 79}): 100,\n",
       "  frozenset({7, 50, 56, 98}): 100,\n",
       "  frozenset({7, 50, 56, 100}): 100,\n",
       "  frozenset({7, 50, 56, 127}): 72,\n",
       "  frozenset({7, 50, 56, 172}): 112,\n",
       "  frozenset({7, 50, 56, 174}): 128,\n",
       "  frozenset({7, 50, 56, 181}): 100,\n",
       "  frozenset({7, 50, 56, 258}): 68,\n",
       "  frozenset({7, 50, 64, 79}): 80,\n",
       "  frozenset({7, 50, 64, 98}): 88,\n",
       "  frozenset({7, 50, 64, 100}): 80,\n",
       "  frozenset({7, 50, 64, 127}): 64,\n",
       "  frozenset({7, 50, 64, 172}): 88,\n",
       "  frozenset({7, 50, 64, 174}): 100,\n",
       "  frozenset({7, 50, 64, 181}): 88,\n",
       "  frozenset({7, 50, 64, 258}): 60,\n",
       "  frozenset({7, 50, 79, 98}): 96,\n",
       "  frozenset({7, 50, 79, 100}): 84,\n",
       "  frozenset({7, 50, 79, 127}): 60,\n",
       "  frozenset({7, 50, 79, 172}): 96,\n",
       "  frozenset({7, 50, 79, 174}): 112,\n",
       "  frozenset({7, 50, 79, 181}): 92,\n",
       "  frozenset({7, 50, 79, 258}): 68,\n",
       "  frozenset({7, 50, 98, 100}): 80,\n",
       "  frozenset({7, 50, 98, 127}): 60,\n",
       "  frozenset({7, 50, 98, 172}): 92,\n",
       "  frozenset({7, 50, 98, 174}): 112,\n",
       "  frozenset({7, 50, 98, 181}): 88,\n",
       "  frozenset({7, 50, 98, 258}): 72,\n",
       "  frozenset({7, 50, 100, 127}): 84,\n",
       "  frozenset({7, 50, 100, 172}): 88,\n",
       "  frozenset({7, 50, 100, 174}): 104,\n",
       "  frozenset({7, 50, 100, 181}): 100,\n",
       "  frozenset({7, 50, 100, 258}): 80,\n",
       "  frozenset({7, 50, 127, 172}): 64,\n",
       "  frozenset({7, 50, 127, 174}): 76,\n",
       "  frozenset({7, 50, 172, 174}): 124,\n",
       "  frozenset({7, 50, 172, 181}): 104,\n",
       "  frozenset({7, 50, 172, 258}): 68,\n",
       "  frozenset({7, 50, 174, 181}): 112,\n",
       "  frozenset({7, 50, 174, 258}): 76,\n",
       "  frozenset({7, 50, 181, 258}): 80,\n",
       "  frozenset({7, 56, 64, 79}): 80,\n",
       "  frozenset({7, 56, 64, 98}): 96,\n",
       "  frozenset({7, 56, 64, 100}): 88,\n",
       "  frozenset({7, 56, 64, 127}): 72,\n",
       "  frozenset({7, 56, 64, 172}): 88,\n",
       "  frozenset({7, 56, 64, 174}): 96,\n",
       "  frozenset({7, 56, 64, 181}): 76,\n",
       "  frozenset({7, 56, 64, 258}): 56,\n",
       "  frozenset({7, 56, 79, 98}): 96,\n",
       "  frozenset({7, 56, 79, 100}): 92,\n",
       "  frozenset({7, 56, 79, 127}): 64,\n",
       "  frozenset({7, 56, 79, 172}): 96,\n",
       "  frozenset({7, 56, 79, 174}): 108,\n",
       "  frozenset({7, 56, 79, 181}): 80,\n",
       "  frozenset({7, 56, 79, 258}): 68,\n",
       "  frozenset({7, 56, 98, 100}): 104,\n",
       "  frozenset({7, 56, 98, 127}): 68,\n",
       "  frozenset({7, 56, 98, 172}): 96,\n",
       "  frozenset({7, 56, 98, 174}): 108,\n",
       "  frozenset({7, 56, 98, 181}): 80,\n",
       "  frozenset({7, 56, 98, 258}): 80,\n",
       "  frozenset({7, 56, 100, 127}): 80,\n",
       "  frozenset({7, 56, 100, 172}): 96,\n",
       "  frozenset({7, 56, 100, 174}): 108,\n",
       "  frozenset({7, 56, 100, 181}): 76,\n",
       "  frozenset({7, 56, 100, 258}): 64,\n",
       "  frozenset({7, 56, 127, 172}): 64,\n",
       "  frozenset({7, 56, 127, 174}): 76,\n",
       "  frozenset({7, 56, 172, 174}): 120,\n",
       "  frozenset({7, 56, 172, 181}): 96,\n",
       "  frozenset({7, 56, 172, 258}): 68,\n",
       "  frozenset({7, 56, 174, 181}): 100,\n",
       "  frozenset({7, 56, 174, 258}): 72,\n",
       "  frozenset({7, 56, 181, 258}): 60,\n",
       "  frozenset({7, 64, 79, 98}): 84,\n",
       "  frozenset({7, 64, 79, 100}): 72,\n",
       "  frozenset({7, 64, 79, 127}): 56,\n",
       "  frozenset({7, 64, 79, 172}): 72,\n",
       "  frozenset({7, 64, 79, 174}): 80,\n",
       "  frozenset({7, 64, 79, 181}): 72,\n",
       "  frozenset({7, 64, 79, 258}): 56,\n",
       "  frozenset({7, 64, 98, 100}): 80,\n",
       "  frozenset({7, 64, 98, 127}): 68,\n",
       "  frozenset({7, 64, 98, 172}): 84,\n",
       "  frozenset({7, 64, 98, 174}): 92,\n",
       "  frozenset({7, 64, 98, 181}): 72,\n",
       "  frozenset({7, 64, 98, 258}): 60,\n",
       "  frozenset({7, 64, 100, 127}): 68,\n",
       "  frozenset({7, 64, 100, 172}): 72,\n",
       "  frozenset({7, 64, 100, 174}): 80,\n",
       "  frozenset({7, 64, 100, 181}): 64,\n",
       "  frozenset({7, 64, 127, 172}): 56,\n",
       "  frozenset({7, 64, 127, 174}): 68,\n",
       "  frozenset({7, 64, 172, 174}): 92,\n",
       "  frozenset({7, 64, 172, 181}): 80,\n",
       "  frozenset({7, 64, 172, 258}): 56,\n",
       "  frozenset({7, 64, 174, 181}): 84,\n",
       "  frozenset({7, 64, 174, 258}): 56,\n",
       "  frozenset({7, 64, 181, 258}): 56,\n",
       "  frozenset({7, 79, 98, 100}): 84,\n",
       "  frozenset({7, 79, 98, 127}): 52,\n",
       "  frozenset({7, 79, 98, 172}): 88,\n",
       "  frozenset({7, 79, 98, 174}): 104,\n",
       "  frozenset({7, 79, 98, 181}): 80,\n",
       "  frozenset({7, 79, 98, 258}): 76,\n",
       "  frozenset({7, 79, 100, 127}): 60,\n",
       "  frozenset({7, 79, 100, 172}): 76,\n",
       "  frozenset({7, 79, 100, 174}): 88,\n",
       "  frozenset({7, 79, 100, 181}): 68,\n",
       "  frozenset({7, 79, 100, 258}): 64,\n",
       "  frozenset({7, 79, 127, 172}): 56,\n",
       "  frozenset({7, 79, 127, 174}): 64,\n",
       "  frozenset({7, 79, 172, 174}): 104,\n",
       "  frozenset({7, 79, 172, 181}): 80,\n",
       "  frozenset({7, 79, 172, 258}): 60,\n",
       "  frozenset({7, 79, 174, 181}): 88,\n",
       "  frozenset({7, 79, 174, 258}): 68,\n",
       "  frozenset({7, 79, 181, 258}): 60,\n",
       "  frozenset({7, 98, 100, 127}): 64,\n",
       "  frozenset({7, 98, 100, 172}): 76,\n",
       "  frozenset({7, 98, 100, 174}): 88,\n",
       "  frozenset({7, 98, 100, 181}): 60,\n",
       "  frozenset({7, 98, 100, 258}): 68,\n",
       "  frozenset({7, 98, 127, 172}): 52,\n",
       "  frozenset({7, 98, 127, 174}): 64,\n",
       "  frozenset({7, 98, 172, 174}): 100,\n",
       "  frozenset({7, 98, 172, 181}): 80,\n",
       "  frozenset({7, 98, 172, 258}): 68,\n",
       "  frozenset({7, 98, 174, 181}): 88,\n",
       "  frozenset({7, 98, 174, 258}): 76,\n",
       "  frozenset({7, 98, 181, 258}): 64,\n",
       "  frozenset({7, 100, 127, 172}): 56,\n",
       "  frozenset({7, 100, 127, 174}): 68,\n",
       "  frozenset({7, 100, 172, 174}): 96,\n",
       "  frozenset({7, 100, 172, 181}): 76,\n",
       "  frozenset({7, 100, 174, 181}): 80,\n",
       "  frozenset({7, 100, 174, 258}): 60,\n",
       "  frozenset({7, 100, 181, 258}): 60,\n",
       "  frozenset({7, 127, 172, 174}): 68,\n",
       "  frozenset({7, 172, 174, 181}): 108,\n",
       "  frozenset({7, 172, 174, 258}): 76,\n",
       "  frozenset({7, 172, 181, 258}): 68,\n",
       "  frozenset({7, 174, 181, 258}): 72,\n",
       "  frozenset({9, 50, 56, 64}): 72,\n",
       "  frozenset({9, 50, 56, 98}): 72,\n",
       "  frozenset({9, 50, 56, 100}): 76,\n",
       "  frozenset({9, 50, 56, 127}): 60,\n",
       "  frozenset({9, 50, 56, 174}): 84,\n",
       "  frozenset({9, 50, 64, 98}): 76,\n",
       "  frozenset({9, 50, 64, 100}): 72,\n",
       "  frozenset({9, 50, 64, 127}): 64,\n",
       "  frozenset({9, 50, 64, 174}): 80,\n",
       "  frozenset({9, 50, 98, 100}): 68,\n",
       "  frozenset({9, 50, 98, 127}): 64,\n",
       "  frozenset({9, 50, 98, 174}): 68,\n",
       "  frozenset({9, 50, 100, 127}): 72,\n",
       "  frozenset({9, 50, 100, 174}): 80,\n",
       "  frozenset({9, 50, 100, 181}): 72,\n",
       "  frozenset({9, 50, 127, 174}): 60,\n",
       "  frozenset({9, 50, 174, 181}): 72,\n",
       "  frozenset({9, 56, 64, 98}): 84,\n",
       "  frozenset({9, 56, 64, 100}): 80,\n",
       "  frozenset({9, 56, 64, 127}): 76,\n",
       "  frozenset({9, 56, 64, 174}): 88,\n",
       "  frozenset({9, 56, 98, 100}): 84,\n",
       "  frozenset({9, 56, 98, 127}): 76,\n",
       "  frozenset({9, 56, 98, 174}): 84,\n",
       "  frozenset({9, 56, 100, 127}): 84,\n",
       "  frozenset({9, 56, 100, 174}): 88,\n",
       "  frozenset({9, 56, 127, 174}): 76,\n",
       "  frozenset({9, 64, 98, 100}): 76,\n",
       "  frozenset({9, 64, 98, 127}): 80,\n",
       "  frozenset({9, 64, 98, 174}): 80,\n",
       "  frozenset({9, 64, 100, 127}): 76,\n",
       "  frozenset({9, 64, 100, 174}): 84,\n",
       "  frozenset({9, 64, 127, 174}): 72,\n",
       "  frozenset({9, 98, 100, 127}): 84,\n",
       "  frozenset({9, 98, 100, 174}): 72,\n",
       "  frozenset({9, 98, 127, 174}): 68,\n",
       "  frozenset({9, 100, 127, 174}): 72,\n",
       "  frozenset({9, 100, 174, 181}): 60,\n",
       "  frozenset({50, 56, 64, 79}): 76,\n",
       "  frozenset({50, 56, 64, 98}): 104,\n",
       "  frozenset({50, 56, 64, 100}): 88,\n",
       "  frozenset({50, 56, 64, 127}): 80,\n",
       "  frozenset({50, 56, 64, 172}): 92,\n",
       "  frozenset({50, 56, 64, 174}): 112,\n",
       "  frozenset({50, 56, 64, 181}): 88,\n",
       "  frozenset({50, 56, 64, 258}): 64,\n",
       "  frozenset({50, 56, 79, 98}): 88,\n",
       "  frozenset({50, 56, 79, 100}): 88,\n",
       "  frozenset({50, 56, 79, 127}): 68,\n",
       "  frozenset({50, 56, 79, 172}): 92,\n",
       "  frozenset({50, 56, 79, 174}): 116,\n",
       "  frozenset({50, 56, 79, 181}): 88,\n",
       "  frozenset({50, 56, 79, 258}): 64,\n",
       "  frozenset({50, 56, 98, 100}): 104,\n",
       "  frozenset({50, 56, 98, 127}): 76,\n",
       "  frozenset({50, 56, 98, 172}): 100,\n",
       "  frozenset({50, 56, 98, 174}): 132,\n",
       "  frozenset({50, 56, 98, 181}): 100,\n",
       "  frozenset({50, 56, 98, 258}): 84,\n",
       "  frozenset({50, 56, 100, 127}): 88,\n",
       "  frozenset({50, 56, 100, 172}): 96,\n",
       "  frozenset({50, 56, 100, 174}): 128,\n",
       "  frozenset({50, 56, 100, 181}): 88,\n",
       "  frozenset({50, 56, 100, 258}): 60,\n",
       "  frozenset({50, 56, 127, 172}): 80,\n",
       "  frozenset({50, 56, 127, 174}): 104,\n",
       "  frozenset({50, 56, 127, 181}): 68,\n",
       "  frozenset({50, 56, 172, 174}): 136,\n",
       "  frozenset({50, 56, 172, 181}): 116,\n",
       "  frozenset({50, 56, 172, 258}): 84,\n",
       "  frozenset({50, 56, 174, 181}): 128,\n",
       "  frozenset({50, 56, 174, 258}): 88,\n",
       "  frozenset({50, 56, 181, 258}): 80,\n",
       "  frozenset({50, 64, 79, 98}): 92,\n",
       "  frozenset({50, 64, 79, 100}): 64,\n",
       "  frozenset({50, 64, 79, 127}): 56,\n",
       "  frozenset({50, 64, 79, 172}): 80,\n",
       "  frozenset({50, 64, 79, 174}): 92,\n",
       "  frozenset({50, 64, 79, 181}): 88,\n",
       "  frozenset({50, 64, 79, 258}): 52,\n",
       "  frozenset({50, 64, 98, 100}): 84,\n",
       "  frozenset({50, 64, 98, 127}): 92,\n",
       "  frozenset({50, 64, 98, 172}): 108,\n",
       "  frozenset({50, 64, 98, 174}): 120,\n",
       "  frozenset({50, 64, 98, 181}): 104,\n",
       "  frozenset({50, 64, 98, 258}): 68,\n",
       "  frozenset({50, 64, 100, 127}): 76,\n",
       "  frozenset({50, 64, 100, 172}): 76,\n",
       "  frozenset({50, 64, 100, 174}): 100,\n",
       "  frozenset({50, 64, 100, 181}): 84,\n",
       "  frozenset({50, 64, 127, 172}): 76,\n",
       "  frozenset({50, 64, 127, 174}): 88,\n",
       "  frozenset({50, 64, 127, 181}): 68,\n",
       "  frozenset({50, 64, 172, 174}): 112,\n",
       "  frozenset({50, 64, 172, 181}): 112,\n",
       "  frozenset({50, 64, 172, 258}): 72,\n",
       "  frozenset({50, 64, 174, 181}): 116,\n",
       "  frozenset({50, 64, 174, 258}): 76,\n",
       "  frozenset({50, 64, 181, 258}): 76,\n",
       "  frozenset({50, 79, 98, 100}): 72,\n",
       "  frozenset({50, 79, 98, 127}): 52,\n",
       "  frozenset({50, 79, 98, 172}): 92,\n",
       "  frozenset({50, 79, 98, 174}): 112,\n",
       "  frozenset({50, 79, 98, 181}): 96,\n",
       "  frozenset({50, 79, 98, 258}): 68,\n",
       "  frozenset({50, 79, 100, 127}): 60,\n",
       "  frozenset({50, 79, 100, 172}): 68,\n",
       "  frozenset({50, 79, 100, 174}): 88,\n",
       "  frozenset({50, 79, 100, 181}): 68,\n",
       "  frozenset({50, 79, 100, 258}): 52,\n",
       "  frozenset({50, 79, 127, 172}): 68,\n",
       "  frozenset({50, 79, 127, 174}): 84,\n",
       "  frozenset({50, 79, 172, 174}): 128,\n",
       "  frozenset({50, 79, 172, 181}): 112,\n",
       "  frozenset({50, 79, 172, 258}): 72,\n",
       "  frozenset({50, 79, 174, 181}): 128,\n",
       "  frozenset({50, 79, 174, 258}): 80,\n",
       "  frozenset({50, 79, 181, 258}): 76,\n",
       "  frozenset({50, 98, 100, 127}): 76,\n",
       "  frozenset({50, 98, 100, 172}): 80,\n",
       "  frozenset({50, 98, 100, 174}): 100,\n",
       "  frozenset({50, 98, 100, 181}): 80,\n",
       "  frozenset({50, 98, 100, 258}): 60,\n",
       "  frozenset({50, 98, 127, 172}): 80,\n",
       "  frozenset({50, 98, 127, 174}): 88,\n",
       "  frozenset({50, 98, 127, 181}): 68,\n",
       "  frozenset({50, 98, 172, 174}): 128,\n",
       "  frozenset({50, 98, 172, 181}): 120,\n",
       "  frozenset({50, 98, 172, 258}): 84,\n",
       "  frozenset({50, 98, 174, 181}): 124,\n",
       "  frozenset({50, 98, 174, 258}): 96,\n",
       "  frozenset({50, 98, 181, 258}): 84,\n",
       "  frozenset({50, 100, 127, 172}): 72,\n",
       "  frozenset({50, 100, 127, 174}): 88,\n",
       "  frozenset({50, 100, 127, 181}): 80,\n",
       "  frozenset({50, 100, 172, 174}): 104,\n",
       "  frozenset({50, 100, 172, 181}): 96,\n",
       "  frozenset({50, 100, 174, 181}): 104,\n",
       "  frozenset({50, 100, 174, 258}): 68,\n",
       "  frozenset({50, 100, 181, 258}): 72,\n",
       "  frozenset({50, 127, 172, 174}): 104,\n",
       "  frozenset({50, 127, 172, 181}): 88,\n",
       "  frozenset({50, 127, 174, 181}): 84,\n",
       "  frozenset({50, 127, 181, 258}): 68,\n",
       "  frozenset({50, 172, 174, 181}): 164,\n",
       "  frozenset({50, 172, 174, 258}): 104,\n",
       "  frozenset({50, 172, 181, 258}): 100,\n",
       "  frozenset({50, 174, 181, 258}): 108,\n",
       "  frozenset({56, 64, 79, 98}): 88,\n",
       "  frozenset({56, 64, 79, 100}): 76,\n",
       "  frozenset({56, 64, 79, 127}): 64,\n",
       "  frozenset({56, 64, 79, 172}): 68,\n",
       "  frozenset({56, 64, 79, 174}): 88,\n",
       "  frozenset({56, 64, 79, 181}): 64,\n",
       "  frozenset({56, 64, 79, 258}): 52,\n",
       "  frozenset({56, 64, 98, 100}): 108,\n",
       "  frozenset({56, 64, 98, 127}): 96,\n",
       "  frozenset({56, 64, 98, 172}): 92,\n",
       "  frozenset({56, 64, 98, 174}): 120,\n",
       "  frozenset({56, 64, 98, 181}): 80,\n",
       "  frozenset({56, 64, 98, 258}): 72,\n",
       "  frozenset({56, 64, 100, 127}): 96,\n",
       "  frozenset({56, 64, 100, 172}): 76,\n",
       "  frozenset({56, 64, 100, 174}): 104,\n",
       "  frozenset({56, 64, 100, 181}): 64,\n",
       "  frozenset({56, 64, 127, 172}): 64,\n",
       "  frozenset({56, 64, 127, 174}): 96,\n",
       "  frozenset({56, 64, 127, 181}): 56,\n",
       "  frozenset({56, 64, 172, 174}): 96,\n",
       "  frozenset({56, 64, 172, 181}): 84,\n",
       "  frozenset({56, 64, 172, 258}): 64,\n",
       "  frozenset({56, 64, 174, 181}): 88,\n",
       "  frozenset({56, 64, 174, 258}): 64,\n",
       "  frozenset({56, 64, 181, 258}): 60,\n",
       "  frozenset({56, 79, 98, 100}): 92,\n",
       "  frozenset({56, 79, 98, 127}): 60,\n",
       "  frozenset({56, 79, 98, 172}): 80,\n",
       "  frozenset({56, 79, 98, 174}): 104,\n",
       "  frozenset({56, 79, 98, 181}): 72,\n",
       "  frozenset({56, 79, 98, 258}): 68,\n",
       "  frozenset({56, 79, 100, 127}): 76,\n",
       "  frozenset({56, 79, 100, 172}): 76,\n",
       "  frozenset({56, 79, 100, 174}): 104,\n",
       "  frozenset({56, 79, 100, 181}): 64,\n",
       "  frozenset({56, 79, 100, 258}): 60,\n",
       "  frozenset({56, 79, 127, 172}): 56,\n",
       "  frozenset({56, 79, 127, 174}): 80,\n",
       "  frozenset({56, 79, 172, 174}): 100,\n",
       "  frozenset({56, 79, 172, 181}): 80,\n",
       "  frozenset({56, 79, 172, 258}): 64,\n",
       "  frozenset({56, 79, 174, 181}): 88,\n",
       "  frozenset({56, 79, 174, 258}): 68,\n",
       "  frozenset({56, 79, 181, 258}): 56,\n",
       "  frozenset({56, 98, 100, 127}): 92,\n",
       "  frozenset({56, 98, 100, 172}): 84,\n",
       "  frozenset({56, 98, 100, 174}): 120,\n",
       "  frozenset({56, 98, 100, 181}): 72,\n",
       "  frozenset({56, 98, 100, 258}): 72,\n",
       "  frozenset({56, 98, 127, 172}): 60,\n",
       "  frozenset({56, 98, 127, 174}): 92,\n",
       "  frozenset({56, 98, 127, 181}): 52,\n",
       "  frozenset({56, 98, 172, 174}): 108,\n",
       "  frozenset({56, 98, 172, 181}): 92,\n",
       "  frozenset({56, 98, 172, 258}): 84,\n",
       "  frozenset({56, 98, 174, 181}): 100,\n",
       "  frozenset({56, 98, 174, 258}): 88,\n",
       "  frozenset({56, 98, 181, 258}): 76,\n",
       "  frozenset({56, 100, 127, 172}): 68,\n",
       "  frozenset({56, 100, 127, 174}): 104,\n",
       "  frozenset({56, 100, 127, 181}): 52,\n",
       "  frozenset({56, 100, 172, 174}): 104,\n",
       "  frozenset({56, 100, 172, 181}): 80,\n",
       "  frozenset({56, 100, 174, 181}): 88,\n",
       "  frozenset({56, 100, 174, 258}): 64,\n",
       "  frozenset({56, 100, 181, 258}): 52,\n",
       "  frozenset({56, 127, 172, 174}): 84,\n",
       "  frozenset({56, 127, 172, 181}): 60,\n",
       "  frozenset({56, 127, 174, 181}): 64,\n",
       "  frozenset({56, 172, 174, 181}): 116,\n",
       "  frozenset({56, 172, 174, 258}): 88,\n",
       "  frozenset({56, 172, 181, 258}): 80,\n",
       "  frozenset({56, 174, 181, 258}): 80,\n",
       "  frozenset({64, 79, 98, 100}): 76,\n",
       "  frozenset({64, 79, 98, 127}): 68,\n",
       "  frozenset({64, 79, 98, 172}): 80,\n",
       "  frozenset({64, 79, 98, 174}): 100,\n",
       "  frozenset({64, 79, 98, 181}): 80,\n",
       "  frozenset({64, 79, 98, 258}): 56,\n",
       "  frozenset({64, 79, 100, 127}): 64,\n",
       "  frozenset({64, 79, 100, 172}): 52,\n",
       "  frozenset({64, 79, 100, 174}): 72,\n",
       "  frozenset({64, 79, 100, 181}): 52,\n",
       "  frozenset({64, 79, 127, 174}): 72,\n",
       "  frozenset({64, 79, 172, 174}): 84,\n",
       "  frozenset({64, 79, 172, 181}): 76,\n",
       "  frozenset({64, 79, 174, 181}): 84,\n",
       "  frozenset({64, 98, 100, 127}): 92,\n",
       "  frozenset({64, 98, 100, 172}): 72,\n",
       "  frozenset({64, 98, 100, 174}): 96,\n",
       "  frozenset({64, 98, 100, 181}): 60,\n",
       "  frozenset({64, 98, 127, 172}): 76,\n",
       "  frozenset({64, 98, 127, 174}): 100,\n",
       "  frozenset({64, 98, 127, 181}): 64,\n",
       "  frozenset({64, 98, 172, 174}): 104,\n",
       "  frozenset({64, 98, 172, 181}): 96,\n",
       "  frozenset({64, 98, 172, 258}): 68,\n",
       "  frozenset({64, 98, 174, 181}): 96,\n",
       "  frozenset({64, 98, 174, 258}): 68,\n",
       "  frozenset({64, 98, 181, 258}): 64,\n",
       "  frozenset({64, 100, 127, 172}): 60,\n",
       "  frozenset({64, 100, 127, 174}): 88,\n",
       "  frozenset({64, 100, 127, 181}): 52,\n",
       "  frozenset({64, 100, 172, 174}): 76,\n",
       "  frozenset({64, 100, 172, 181}): 68,\n",
       "  frozenset({64, 100, 174, 181}): 76,\n",
       "  frozenset({64, 127, 172, 174}): 72,\n",
       "  frozenset({64, 127, 172, 181}): 64,\n",
       "  frozenset({64, 127, 174, 181}): 68,\n",
       "  frozenset({64, 172, 174, 181}): 104,\n",
       "  frozenset({64, 172, 174, 258}): 72,\n",
       "  frozenset({64, 172, 181, 258}): 68,\n",
       "  frozenset({64, 174, 181, 258}): 72,\n",
       "  frozenset({79, 98, 100, 127}): 60,\n",
       "  frozenset({79, 98, 100, 172}): 64,\n",
       "  frozenset({79, 98, 100, 174}): 88,\n",
       "  frozenset({79, 98, 100, 181}): 56,\n",
       "  frozenset({79, 98, 100, 258}): 60,\n",
       "  frozenset({79, 98, 127, 174}): 64,\n",
       "  frozenset({79, 98, 172, 174}): 100,\n",
       "  frozenset({79, 98, 172, 181}): 84,\n",
       "  frozenset({79, 98, 172, 258}): 64,\n",
       "  frozenset({79, 98, 174, 181}): 92,\n",
       "  frozenset({79, 98, 174, 258}): 72,\n",
       "  frozenset({79, 98, 181, 258}): 60,\n",
       "  frozenset({79, 100, 127, 174}): 76,\n",
       "  frozenset({79, 100, 172, 174}): 76,\n",
       "  frozenset({79, 100, 172, 181}): 60,\n",
       "  frozenset({79, 100, 174, 181}): 64,\n",
       "  frozenset({79, 100, 174, 258}): 52,\n",
       "  frozenset({79, 127, 172, 174}): 72,\n",
       "  frozenset({79, 172, 174, 181}): 112,\n",
       "  frozenset({79, 172, 174, 258}): 76,\n",
       "  frozenset({79, 172, 181, 258}): 68,\n",
       "  frozenset({79, 174, 181, 258}): 72,\n",
       "  frozenset({98, 100, 127, 172}): 60,\n",
       "  frozenset({98, 100, 127, 174}): 84,\n",
       "  frozenset({98, 100, 127, 181}): 52,\n",
       "  frozenset({98, 100, 172, 174}): 80,\n",
       "  frozenset({98, 100, 172, 181}): 72,\n",
       "  frozenset({98, 100, 174, 181}): 72,\n",
       "  frozenset({98, 100, 174, 258}): 64,\n",
       "  frozenset({98, 100, 181, 258}): 52,\n",
       "  frozenset({98, 127, 172, 174}): 72,\n",
       "  frozenset({98, 127, 172, 181}): 64,\n",
       "  frozenset({98, 127, 174, 181}): 60,\n",
       "  frozenset({98, 172, 174, 181}): 112,\n",
       "  frozenset({98, 172, 174, 258}): 88,\n",
       "  frozenset({98, 172, 181, 258}): 80,\n",
       "  frozenset({98, 174, 181, 258}): 84,\n",
       "  frozenset({100, 127, 172, 174}): 68,\n",
       "  frozenset({100, 127, 172, 181}): 56,\n",
       "  frozenset({100, 127, 174, 181}): 52,\n",
       "  frozenset({100, 172, 174, 181}): 88,\n",
       "  frozenset({100, 174, 181, 258}): 60,\n",
       "  frozenset({127, 172, 174, 181}): 80,\n",
       "  frozenset({172, 174, 181, 258}): 104,\n",
       "  frozenset({50, 100, 181, 313}): 76},\n",
       " 5: {frozenset({1, 7, 50, 56, 64}): 70,\n",
       "  frozenset({1, 7, 50, 56, 79}): 70,\n",
       "  frozenset({1, 7, 50, 56, 98}): 80,\n",
       "  frozenset({1, 7, 50, 56, 100}): 65,\n",
       "  frozenset({1, 7, 50, 56, 172}): 80,\n",
       "  frozenset({1, 7, 50, 56, 174}): 90,\n",
       "  frozenset({1, 7, 50, 56, 181}): 75,\n",
       "  frozenset({1, 7, 50, 64, 79}): 65,\n",
       "  frozenset({1, 7, 50, 64, 98}): 75,\n",
       "  frozenset({1, 7, 50, 64, 100}): 60,\n",
       "  frozenset({1, 7, 50, 64, 172}): 70,\n",
       "  frozenset({1, 7, 50, 64, 174}): 80,\n",
       "  frozenset({1, 7, 50, 64, 181}): 75,\n",
       "  frozenset({1, 7, 50, 79, 98}): 80,\n",
       "  frozenset({1, 7, 50, 79, 100}): 60,\n",
       "  frozenset({1, 7, 50, 79, 172}): 75,\n",
       "  frozenset({1, 7, 50, 79, 174}): 85,\n",
       "  frozenset({1, 7, 50, 79, 181}): 80,\n",
       "  frozenset({1, 7, 50, 98, 100}): 60,\n",
       "  frozenset({1, 7, 50, 98, 172}): 80,\n",
       "  frozenset({1, 7, 50, 98, 174}): 95,\n",
       "  frozenset({1, 7, 50, 98, 181}): 80,\n",
       "  frozenset({1, 7, 50, 100, 172}): 60,\n",
       "  frozenset({1, 7, 50, 100, 174}): 70,\n",
       "  frozenset({1, 7, 50, 100, 181}): 70,\n",
       "  frozenset({1, 7, 50, 172, 174}): 95,\n",
       "  frozenset({1, 7, 50, 172, 181}): 80,\n",
       "  frozenset({1, 7, 50, 174, 181}): 90,\n",
       "  frozenset({1, 7, 56, 64, 79}): 60,\n",
       "  frozenset({1, 7, 56, 64, 98}): 75,\n",
       "  frozenset({1, 7, 56, 64, 100}): 55,\n",
       "  frozenset({1, 7, 56, 64, 172}): 65,\n",
       "  frozenset({1, 7, 56, 64, 174}): 75,\n",
       "  frozenset({1, 7, 56, 64, 181}): 60,\n",
       "  frozenset({1, 7, 56, 79, 98}): 70,\n",
       "  frozenset({1, 7, 56, 79, 100}): 60,\n",
       "  frozenset({1, 7, 56, 79, 172}): 70,\n",
       "  frozenset({1, 7, 56, 79, 174}): 75,\n",
       "  frozenset({1, 7, 56, 79, 181}): 65,\n",
       "  frozenset({1, 7, 56, 98, 100}): 70,\n",
       "  frozenset({1, 7, 56, 98, 172}): 75,\n",
       "  frozenset({1, 7, 56, 98, 174}): 85,\n",
       "  frozenset({1, 7, 56, 98, 181}): 70,\n",
       "  frozenset({1, 7, 56, 100, 172}): 60,\n",
       "  frozenset({1, 7, 56, 100, 174}): 70,\n",
       "  frozenset({1, 7, 56, 172, 174}): 85,\n",
       "  frozenset({1, 7, 56, 172, 181}): 70,\n",
       "  frozenset({1, 7, 56, 174, 181}): 75,\n",
       "  frozenset({1, 7, 64, 79, 98}): 65,\n",
       "  frozenset({1, 7, 64, 79, 172}): 60,\n",
       "  frozenset({1, 7, 64, 79, 174}): 65,\n",
       "  frozenset({1, 7, 64, 79, 181}): 65,\n",
       "  frozenset({1, 7, 64, 98, 100}): 55,\n",
       "  frozenset({1, 7, 64, 98, 172}): 70,\n",
       "  frozenset({1, 7, 64, 98, 174}): 80,\n",
       "  frozenset({1, 7, 64, 98, 181}): 65,\n",
       "  frozenset({1, 7, 64, 100, 174}): 60,\n",
       "  frozenset({1, 7, 64, 100, 181}): 50,\n",
       "  frozenset({1, 7, 64, 172, 174}): 75,\n",
       "  frozenset({1, 7, 64, 172, 181}): 65,\n",
       "  frozenset({1, 7, 64, 174, 181}): 70,\n",
       "  frozenset({1, 7, 79, 98, 100}): 55,\n",
       "  frozenset({1, 7, 79, 98, 172}): 75,\n",
       "  frozenset({1, 7, 79, 98, 174}): 85,\n",
       "  frozenset({1, 7, 79, 98, 181}): 75,\n",
       "  frozenset({1, 7, 79, 100, 174}): 60,\n",
       "  frozenset({1, 7, 79, 172, 174}): 80,\n",
       "  frozenset({1, 7, 79, 172, 181}): 65,\n",
       "  frozenset({1, 7, 79, 174, 181}): 75,\n",
       "  frozenset({1, 7, 98, 100, 172}): 55,\n",
       "  frozenset({1, 7, 98, 100, 174}): 65,\n",
       "  frozenset({1, 7, 98, 100, 181}): 50,\n",
       "  frozenset({1, 7, 98, 172, 174}): 85,\n",
       "  frozenset({1, 7, 98, 172, 181}): 70,\n",
       "  frozenset({1, 7, 98, 174, 181}): 80,\n",
       "  frozenset({1, 7, 100, 172, 174}): 65,\n",
       "  frozenset({1, 7, 100, 172, 181}): 50,\n",
       "  frozenset({1, 7, 100, 174, 181}): 55,\n",
       "  frozenset({1, 7, 172, 174, 181}): 80,\n",
       "  frozenset({1, 50, 56, 64, 79}): 60,\n",
       "  frozenset({1, 50, 56, 64, 98}): 85,\n",
       "  frozenset({1, 50, 56, 64, 100}): 65,\n",
       "  frozenset({1, 50, 56, 64, 127}): 60,\n",
       "  frozenset({1, 50, 56, 64, 172}): 65,\n",
       "  frozenset({1, 50, 56, 64, 174}): 85,\n",
       "  frozenset({1, 50, 56, 64, 181}): 65,\n",
       "  frozenset({1, 50, 56, 79, 98}): 70,\n",
       "  frozenset({1, 50, 56, 79, 100}): 65,\n",
       "  frozenset({1, 50, 56, 79, 172}): 65,\n",
       "  frozenset({1, 50, 56, 79, 174}): 80,\n",
       "  frozenset({1, 50, 56, 79, 181}): 65,\n",
       "  frozenset({1, 50, 56, 98, 100}): 80,\n",
       "  frozenset({1, 50, 56, 98, 127}): 60,\n",
       "  frozenset({1, 50, 56, 98, 172}): 80,\n",
       "  frozenset({1, 50, 56, 98, 174}): 110,\n",
       "  frozenset({1, 50, 56, 98, 181}): 85,\n",
       "  frozenset({1, 50, 56, 100, 127}): 70,\n",
       "  frozenset({1, 50, 56, 100, 172}): 65,\n",
       "  frozenset({1, 50, 56, 100, 174}): 95,\n",
       "  frozenset({1, 50, 56, 127, 174}): 75,\n",
       "  frozenset({1, 50, 56, 172, 174}): 95,\n",
       "  frozenset({1, 50, 56, 172, 181}): 80,\n",
       "  frozenset({1, 50, 56, 174, 181}): 90,\n",
       "  frozenset({1, 50, 64, 79, 98}): 80,\n",
       "  frozenset({1, 50, 64, 79, 172}): 65,\n",
       "  frozenset({1, 50, 64, 79, 174}): 75,\n",
       "  frozenset({1, 50, 64, 79, 181}): 80,\n",
       "  frozenset({1, 50, 64, 98, 100}): 70,\n",
       "  frozenset({1, 50, 64, 98, 127}): 70,\n",
       "  frozenset({1, 50, 64, 98, 172}): 85,\n",
       "  frozenset({1, 50, 64, 98, 174}): 100,\n",
       "  frozenset({1, 50, 64, 98, 181}): 90,\n",
       "  frozenset({1, 50, 64, 100, 127}): 60,\n",
       "  frozenset({1, 50, 64, 100, 174}): 75,\n",
       "  frozenset({1, 50, 64, 100, 181}): 65,\n",
       "  frozenset({1, 50, 64, 127, 174}): 65,\n",
       "  frozenset({1, 50, 64, 172, 174}): 85,\n",
       "  frozenset({1, 50, 64, 172, 181}): 85,\n",
       "  frozenset({1, 50, 64, 174, 181}): 90,\n",
       "  frozenset({1, 50, 79, 98, 100}): 55,\n",
       "  frozenset({1, 50, 79, 98, 172}): 80,\n",
       "  frozenset({1, 50, 79, 98, 174}): 95,\n",
       "  frozenset({1, 50, 79, 98, 181}): 90,\n",
       "  frozenset({1, 50, 79, 100, 174}): 65,\n",
       "  frozenset({1, 50, 79, 172, 174}): 90,\n",
       "  frozenset({1, 50, 79, 172, 181}): 80,\n",
       "  frozenset({1, 50, 79, 174, 181}): 95,\n",
       "  frozenset({1, 50, 98, 100, 127}): 65,\n",
       "  frozenset({1, 50, 98, 100, 172}): 65,\n",
       "  frozenset({1, 50, 98, 100, 174}): 80,\n",
       "  frozenset({1, 50, 98, 100, 181}): 70,\n",
       "  frozenset({1, 50, 98, 127, 174}): 65,\n",
       "  frozenset({1, 50, 98, 172, 174}): 100,\n",
       "  frozenset({1, 50, 98, 172, 181}): 100,\n",
       "  frozenset({1, 50, 98, 174, 181}): 105,\n",
       "  frozenset({1, 50, 100, 127, 174}): 70,\n",
       "  frozenset({1, 50, 100, 172, 174}): 75,\n",
       "  frozenset({1, 50, 100, 172, 181}): 70,\n",
       "  frozenset({1, 50, 100, 174, 181}): 75,\n",
       "  frozenset({1, 50, 172, 174, 181}): 110,\n",
       "  frozenset({1, 56, 64, 79, 98}): 70,\n",
       "  frozenset({1, 56, 64, 79, 172}): 55,\n",
       "  frozenset({1, 56, 64, 79, 174}): 70,\n",
       "  frozenset({1, 56, 64, 79, 181}): 55,\n",
       "  frozenset({1, 56, 64, 98, 100}): 80,\n",
       "  frozenset({1, 56, 64, 98, 127}): 75,\n",
       "  frozenset({1, 56, 64, 98, 172}): 70,\n",
       "  frozenset({1, 56, 64, 98, 174}): 100,\n",
       "  frozenset({1, 56, 64, 98, 181}): 65,\n",
       "  frozenset({1, 56, 64, 100, 127}): 70,\n",
       "  frozenset({1, 56, 64, 100, 174}): 80,\n",
       "  frozenset({1, 56, 64, 127, 174}): 75,\n",
       "  frozenset({1, 56, 64, 172, 174}): 70,\n",
       "  frozenset({1, 56, 64, 172, 181}): 60,\n",
       "  frozenset({1, 56, 64, 174, 181}): 65,\n",
       "  frozenset({1, 56, 79, 98, 100}): 65,\n",
       "  frozenset({1, 56, 79, 98, 172}): 65,\n",
       "  frozenset({1, 56, 79, 98, 174}): 80,\n",
       "  frozenset({1, 56, 79, 98, 181}): 65,\n",
       "  frozenset({1, 56, 79, 100, 174}): 75,\n",
       "  frozenset({1, 56, 79, 172, 174}): 70,\n",
       "  frozenset({1, 56, 79, 172, 181}): 60,\n",
       "  frozenset({1, 56, 79, 174, 181}): 65,\n",
       "  frozenset({1, 56, 98, 100, 127}): 75,\n",
       "  frozenset({1, 56, 98, 100, 172}): 60,\n",
       "  frozenset({1, 56, 98, 100, 174}): 95,\n",
       "  frozenset({1, 56, 98, 127, 174}): 75,\n",
       "  frozenset({1, 56, 98, 172, 174}): 85,\n",
       "  frozenset({1, 56, 98, 172, 181}): 75,\n",
       "  frozenset({1, 56, 98, 174, 181}): 85,\n",
       "  frozenset({1, 56, 100, 127, 174}): 85,\n",
       "  frozenset({1, 56, 100, 172, 174}): 70,\n",
       "  frozenset({1, 56, 172, 174, 181}): 80,\n",
       "  frozenset({1, 64, 79, 98, 172}): 70,\n",
       "  frozenset({1, 64, 79, 98, 174}): 85,\n",
       "  frozenset({1, 64, 79, 98, 181}): 75,\n",
       "  frozenset({1, 64, 79, 172, 174}): 70,\n",
       "  frozenset({1, 64, 79, 172, 181}): 65,\n",
       "  frozenset({1, 64, 79, 174, 181}): 75,\n",
       "  frozenset({1, 64, 98, 100, 127}): 75,\n",
       "  frozenset({1, 64, 98, 100, 174}): 80,\n",
       "  frozenset({1, 64, 98, 100, 181}): 50,\n",
       "  frozenset({1, 64, 98, 127, 174}): 80,\n",
       "  frozenset({1, 64, 98, 172, 174}): 85,\n",
       "  frozenset({1, 64, 98, 172, 181}): 80,\n",
       "  frozenset({1, 64, 98, 174, 181}): 80,\n",
       "  frozenset({1, 64, 100, 127, 174}): 70,\n",
       "  frozenset({1, 64, 100, 174, 181}): 55,\n",
       "  frozenset({1, 64, 172, 174, 181}): 80,\n",
       "  frozenset({1, 79, 98, 100, 174}): 65,\n",
       "  frozenset({1, 79, 98, 172, 174}): 85,\n",
       "  frozenset({1, 79, 98, 172, 181}): 75,\n",
       "  frozenset({1, 79, 98, 174, 181}): 85,\n",
       "  frozenset({1, 79, 172, 174, 181}): 80,\n",
       "  frozenset({1, 98, 100, 127, 174}): 70,\n",
       "  frozenset({1, 98, 100, 172, 174}): 60,\n",
       "  frozenset({1, 98, 100, 172, 181}): 60,\n",
       "  frozenset({1, 98, 100, 174, 181}): 60,\n",
       "  frozenset({1, 98, 172, 174, 181}): 90,\n",
       "  frozenset({1, 100, 172, 174, 181}): 60,\n",
       "  frozenset({7, 9, 50, 56, 64}): 70,\n",
       "  frozenset({7, 9, 50, 56, 100}): 75,\n",
       "  frozenset({7, 9, 50, 56, 174}): 85,\n",
       "  frozenset({7, 9, 50, 64, 100}): 65,\n",
       "  frozenset({7, 9, 50, 64, 174}): 75,\n",
       "  frozenset({7, 9, 50, 100, 174}): 80,\n",
       "  frozenset({7, 9, 56, 64, 100}): 70,\n",
       "  frozenset({7, 9, 56, 64, 174}): 75,\n",
       "  frozenset({7, 9, 56, 100, 174}): 80,\n",
       "  frozenset({7, 9, 64, 100, 174}): 70,\n",
       "  frozenset({7, 50, 56, 64, 79}): 90,\n",
       "  frozenset({7, 50, 56, 64, 98}): 105,\n",
       "  frozenset({7, 50, 56, 64, 100}): 90,\n",
       "  frozenset({7, 50, 56, 64, 127}): 75,\n",
       "  frozenset({7, 50, 56, 64, 172}): 100,\n",
       "  frozenset({7, 50, 56, 64, 174}): 115,\n",
       "  frozenset({7, 50, 56, 64, 181}): 95,\n",
       "  frozenset({7, 50, 56, 64, 258}): 65,\n",
       "  frozenset({7, 50, 56, 79, 98}): 105,\n",
       "  frozenset({7, 50, 56, 79, 100}): 100,\n",
       "  frozenset({7, 50, 56, 79, 127}): 70,\n",
       "  frozenset({7, 50, 56, 79, 172}): 110,\n",
       "  frozenset({7, 50, 56, 79, 174}): 125,\n",
       "  frozenset({7, 50, 56, 79, 181}): 100,\n",
       "  frozenset({7, 50, 56, 79, 258}): 75,\n",
       "  frozenset({7, 50, 56, 98, 100}): 100,\n",
       "  frozenset({7, 50, 56, 98, 127}): 70,\n",
       "  frozenset({7, 50, 56, 98, 172}): 105,\n",
       "  frozenset({7, 50, 56, 98, 174}): 125,\n",
       "  frozenset({7, 50, 56, 98, 181}): 100,\n",
       "  frozenset({7, 50, 56, 98, 258}): 85,\n",
       "  frozenset({7, 50, 56, 100, 127}): 80,\n",
       "  frozenset({7, 50, 56, 100, 172}): 105,\n",
       "  frozenset({7, 50, 56, 100, 174}): 125,\n",
       "  frozenset({7, 50, 56, 100, 181}): 95,\n",
       "  frozenset({7, 50, 56, 100, 258}): 65,\n",
       "  frozenset({7, 50, 56, 127, 172}): 75,\n",
       "  frozenset({7, 50, 56, 127, 174}): 90,\n",
       "  frozenset({7, 50, 56, 172, 174}): 140,\n",
       "  frozenset({7, 50, 56, 172, 181}): 120,\n",
       "  frozenset({7, 50, 56, 172, 258}): 80,\n",
       "  frozenset({7, 50, 56, 174, 181}): 125,\n",
       "  frozenset({7, 50, 56, 174, 258}): 85,\n",
       "  frozenset({7, 50, 56, 181, 258}): 75,\n",
       "  frozenset({7, 50, 64, 79, 98}): 90,\n",
       "  frozenset({7, 50, 64, 79, 100}): 75,\n",
       "  frozenset({7, 50, 64, 79, 127}): 60,\n",
       "  frozenset({7, 50, 64, 79, 172}): 85,\n",
       "  frozenset({7, 50, 64, 79, 174}): 95,\n",
       "  frozenset({7, 50, 64, 79, 181}): 90,\n",
       "  frozenset({7, 50, 64, 79, 258}): 60,\n",
       "  frozenset({7, 50, 64, 98, 100}): 80,\n",
       "  frozenset({7, 50, 64, 98, 127}): 75,\n",
       "  frozenset({7, 50, 64, 98, 172}): 95,\n",
       "  frozenset({7, 50, 64, 98, 174}): 110,\n",
       "  frozenset({7, 50, 64, 98, 181}): 90,\n",
       "  frozenset({7, 50, 64, 98, 258}): 65,\n",
       "  frozenset({7, 50, 64, 100, 127}): 70,\n",
       "  frozenset({7, 50, 64, 100, 172}): 80,\n",
       "  frozenset({7, 50, 64, 100, 174}): 95,\n",
       "  frozenset({7, 50, 64, 100, 181}): 80,\n",
       "  frozenset({7, 50, 64, 127, 172}): 65,\n",
       "  frozenset({7, 50, 64, 127, 174}): 80,\n",
       "  frozenset({7, 50, 64, 172, 174}): 110,\n",
       "  frozenset({7, 50, 64, 172, 181}): 100,\n",
       "  frozenset({7, 50, 64, 172, 258}): 70,\n",
       "  frozenset({7, 50, 64, 174, 181}): 105,\n",
       "  frozenset({7, 50, 64, 174, 258}): 70,\n",
       "  frozenset({7, 50, 64, 181, 258}): 70,\n",
       "  frozenset({7, 50, 79, 98, 100}): 85,\n",
       "  frozenset({7, 50, 79, 98, 127}): 55,\n",
       "  frozenset({7, 50, 79, 98, 172}): 100,\n",
       "  frozenset({7, 50, 79, 98, 174}): 120,\n",
       "  frozenset({7, 50, 79, 98, 181}): 100,\n",
       "  frozenset({7, 50, 79, 98, 258}): 80,\n",
       "  frozenset({7, 50, 79, 100, 127}): 65,\n",
       "  frozenset({7, 50, 79, 100, 172}): 85,\n",
       "  frozenset({7, 50, 79, 100, 174}): 100,\n",
       "  frozenset({7, 50, 79, 100, 181}): 85,\n",
       "  frozenset({7, 50, 79, 100, 258}): 65,\n",
       "  frozenset({7, 50, 79, 127, 172}): 65,\n",
       "  frozenset({7, 50, 79, 127, 174}): 75,\n",
       "  frozenset({7, 50, 79, 172, 174}): 120,\n",
       "  frozenset({7, 50, 79, 172, 181}): 100,\n",
       "  frozenset({7, 50, 79, 172, 258}): 70,\n",
       "  frozenset({7, 50, 79, 174, 181}): 110,\n",
       "  frozenset({7, 50, 79, 174, 258}): 80,\n",
       "  frozenset({7, 50, 79, 181, 258}): 75,\n",
       "  frozenset({7, 50, 98, 100, 127}): 65,\n",
       "  frozenset({7, 50, 98, 100, 172}): 80,\n",
       "  frozenset({7, 50, 98, 100, 174}): 100,\n",
       "  frozenset({7, 50, 98, 100, 181}): 75,\n",
       "  frozenset({7, 50, 98, 100, 258}): 65,\n",
       "  frozenset({7, 50, 98, 127, 172}): 60,\n",
       "  frozenset({7, 50, 98, 127, 174}): 75,\n",
       "  frozenset({7, 50, 98, 172, 174}): 115,\n",
       "  frozenset({7, 50, 98, 172, 181}): 100,\n",
       "  frozenset({7, 50, 98, 172, 258}): 80,\n",
       "  frozenset({7, 50, 98, 174, 181}): 110,\n",
       "  frozenset({7, 50, 98, 174, 258}): 90,\n",
       "  frozenset({7, 50, 98, 181, 258}): 80,\n",
       "  frozenset({7, 50, 100, 127, 172}): 65,\n",
       "  frozenset({7, 50, 100, 127, 174}): 80,\n",
       "  frozenset({7, 50, 100, 172, 174}): 110,\n",
       "  frozenset({7, 50, 100, 172, 181}): 95,\n",
       "  frozenset({7, 50, 100, 174, 181}): 100,\n",
       "  frozenset({7, 50, 100, 174, 258}): 70,\n",
       "  frozenset({7, 50, 100, 181, 258}): 75,\n",
       "  frozenset({7, 50, 127, 172, 174}): 80,\n",
       "  frozenset({7, 50, 172, 174, 181}): 130,\n",
       "  frozenset({7, 50, 172, 174, 258}): 85,\n",
       "  frozenset({7, 50, 172, 181, 258}): 80,\n",
       "  frozenset({7, 50, 174, 181, 258}): 85,\n",
       "  frozenset({7, 56, 64, 79, 98}): 95,\n",
       "  frozenset({7, 56, 64, 79, 100}): 80,\n",
       "  frozenset({7, 56, 64, 79, 127}): 65,\n",
       "  frozenset({7, 56, 64, 79, 172}): 85,\n",
       "  frozenset({7, 56, 64, 79, 174}): 95,\n",
       "  frozenset({7, 56, 64, 79, 181}): 80,\n",
       "  frozenset({7, 56, 64, 79, 258}): 60,\n",
       "  frozenset({7, 56, 64, 98, 100}): 95,\n",
       "  frozenset({7, 56, 64, 98, 127}): 80,\n",
       "  frozenset({7, 56, 64, 98, 172}): 100,\n",
       "  frozenset({7, 56, 64, 98, 174}): 110,\n",
       "  frozenset({7, 56, 64, 98, 181}): 85,\n",
       "  frozenset({7, 56, 64, 98, 258}): 70,\n",
       "  frozenset({7, 56, 64, 100, 127}): 85,\n",
       "  frozenset({7, 56, 64, 100, 172}): 85,\n",
       "  frozenset({7, 56, 64, 100, 174}): 95,\n",
       "  frozenset({7, 56, 64, 100, 181}): 70,\n",
       "  frozenset({7, 56, 64, 127, 172}): 65,\n",
       "  frozenset({7, 56, 64, 127, 174}): 80,\n",
       "  frozenset({7, 56, 64, 172, 174}): 105,\n",
       "  frozenset({7, 56, 64, 172, 181}): 90,\n",
       "  frozenset({7, 56, 64, 172, 258}): 65,\n",
       "  frozenset({7, 56, 64, 174, 181}): 95,\n",
       "  frozenset({7, 56, 64, 174, 258}): 65,\n",
       "  frozenset({7, 56, 64, 181, 258}): 60,\n",
       "  frozenset({7, 56, 79, 98, 100}): 100,\n",
       "  frozenset({7, 56, 79, 98, 127}): 60,\n",
       "  frozenset({7, 56, 79, 98, 172}): 100,\n",
       "  frozenset({7, 56, 79, 98, 174}): 115,\n",
       "  frozenset({7, 56, 79, 98, 181}): 90,\n",
       "  frozenset({7, 56, 79, 98, 258}): 85,\n",
       "  frozenset({7, 56, 79, 100, 127}): 75,\n",
       "  frozenset({7, 56, 79, 100, 172}): 95,\n",
       "  frozenset({7, 56, 79, 100, 174}): 110,\n",
       "  frozenset({7, 56, 79, 100, 181}): 80,\n",
       "  frozenset({7, 56, 79, 100, 258}): 70,\n",
       "  frozenset({7, 56, 79, 127, 172}): 65,\n",
       "  frozenset({7, 56, 79, 127, 174}): 75,\n",
       "  frozenset({7, 56, 79, 172, 174}): 120,\n",
       "  frozenset({7, 56, 79, 172, 181}): 95,\n",
       "  frozenset({7, 56, 79, 172, 258}): 75,\n",
       "  frozenset({7, 56, 79, 174, 181}): 100,\n",
       "  frozenset({7, 56, 79, 174, 258}): 80,\n",
       "  frozenset({7, 56, 79, 181, 258}): 65,\n",
       "  frozenset({7, 56, 98, 100, 127}): 80,\n",
       "  frozenset({7, 56, 98, 100, 172}): 95,\n",
       "  frozenset({7, 56, 98, 100, 174}): 110,\n",
       "  frozenset({7, 56, 98, 100, 181}): 75,\n",
       "  frozenset({7, 56, 98, 100, 258}): 80,\n",
       "  frozenset({7, 56, 98, 127, 172}): 60,\n",
       "  frozenset({7, 56, 98, 127, 174}): 75,\n",
       "  frozenset({7, 56, 98, 172, 174}): 115,\n",
       "  frozenset({7, 56, 98, 172, 181}): 95,\n",
       "  frozenset({7, 56, 98, 172, 258}): 85,\n",
       "  frozenset({7, 56, 98, 174, 181}): 100,\n",
       "  frozenset({7, 56, 98, 174, 258}): 90,\n",
       "  frozenset({7, 56, 98, 181, 258}): 75,\n",
       "  frozenset({7, 56, 100, 127, 172}): 70,\n",
       "  frozenset({7, 56, 100, 127, 174}): 85,\n",
       "  frozenset({7, 56, 100, 172, 174}): 115,\n",
       "  frozenset({7, 56, 100, 172, 181}): 90,\n",
       "  frozenset({7, 56, 100, 174, 181}): 95,\n",
       "  frozenset({7, 56, 100, 174, 258}): 70,\n",
       "  frozenset({7, 56, 100, 181, 258}): 55,\n",
       "  frozenset({7, 56, 127, 172, 174}): 80,\n",
       "  frozenset({7, 56, 172, 174, 181}): 120,\n",
       "  frozenset({7, 56, 172, 174, 258}): 85,\n",
       "  frozenset({7, 56, 172, 181, 258}): 75,\n",
       "  frozenset({7, 56, 174, 181, 258}): 75,\n",
       "  frozenset({7, 64, 79, 98, 100}): 80,\n",
       "  frozenset({7, 64, 79, 98, 127}): 65,\n",
       "  frozenset({7, 64, 79, 98, 172}): 85,\n",
       "  frozenset({7, 64, 79, 98, 174}): 95,\n",
       "  frozenset({7, 64, 79, 98, 181}): 80,\n",
       "  frozenset({7, 64, 79, 98, 258}): 65,\n",
       "  frozenset({7, 64, 79, 100, 127}): 65,\n",
       "  frozenset({7, 64, 79, 100, 172}): 65,\n",
       "  frozenset({7, 64, 79, 100, 174}): 75,\n",
       "  frozenset({7, 64, 79, 100, 181}): 65,\n",
       "  frozenset({7, 64, 79, 127, 174}): 65,\n",
       "  frozenset({7, 64, 79, 172, 174}): 90,\n",
       "  frozenset({7, 64, 79, 172, 181}): 80,\n",
       "  frozenset({7, 64, 79, 174, 181}): 85,\n",
       "  frozenset({7, 64, 98, 100, 127}): 75,\n",
       "  frozenset({7, 64, 98, 100, 172}): 75,\n",
       "  frozenset({7, 64, 98, 100, 174}): 85,\n",
       "  frozenset({7, 64, 98, 100, 181}): 60,\n",
       "  frozenset({7, 64, 98, 127, 172}): 65,\n",
       "  frozenset({7, 64, 98, 127, 174}): 80,\n",
       "  frozenset({7, 64, 98, 172, 174}): 100,\n",
       "  frozenset({7, 64, 98, 172, 181}): 85,\n",
       "  frozenset({7, 64, 98, 172, 258}): 65,\n",
       "  frozenset({7, 64, 98, 174, 181}): 90,\n",
       "  frozenset({7, 64, 98, 174, 258}): 65,\n",
       "  frozenset({7, 64, 98, 181, 258}): 60,\n",
       "  frozenset({7, 64, 100, 127, 172}): 60,\n",
       "  frozenset({7, 64, 100, 127, 174}): 75,\n",
       "  frozenset({7, 64, 100, 172, 174}): 85,\n",
       "  frozenset({7, 64, 100, 172, 181}): 70,\n",
       "  frozenset({7, 64, 100, 174, 181}): 75,\n",
       "  frozenset({7, 64, 127, 172, 174}): 70,\n",
       "  frozenset({7, 64, 172, 174, 181}): 100,\n",
       "  frozenset({7, 64, 172, 174, 258}): 70,\n",
       "  frozenset({7, 64, 172, 181, 258}): 65,\n",
       "  frozenset({7, 64, 174, 181, 258}): 65,\n",
       "  frozenset({7, 79, 98, 100, 127}): 60,\n",
       "  frozenset({7, 79, 98, 100, 172}): 80,\n",
       "  frozenset({7, 79, 98, 100, 174}): 95,\n",
       "  frozenset({7, 79, 98, 100, 181}): 70,\n",
       "  frozenset({7, 79, 98, 100, 258}): 75,\n",
       "  frozenset({7, 79, 98, 127, 174}): 60,\n",
       "  frozenset({7, 79, 98, 172, 174}): 110,\n",
       "  frozenset({7, 79, 98, 172, 181}): 90,\n",
       "  frozenset({7, 79, 98, 172, 258}): 75,\n",
       "  frozenset({7, 79, 98, 174, 181}): 100,\n",
       "  frozenset({7, 79, 98, 174, 258}): 85,\n",
       "  frozenset({7, 79, 98, 181, 258}): 70,\n",
       "  frozenset({7, 79, 100, 127, 174}): 70,\n",
       "  frozenset({7, 79, 100, 172, 174}): 95,\n",
       "  frozenset({7, 79, 100, 172, 181}): 75,\n",
       "  frozenset({7, 79, 100, 174, 181}): 80,\n",
       "  frozenset({7, 79, 100, 174, 258}): 65,\n",
       "  frozenset({7, 79, 127, 172, 174}): 70,\n",
       "  frozenset({7, 79, 172, 174, 181}): 100,\n",
       "  frozenset({7, 79, 172, 174, 258}): 75,\n",
       "  frozenset({7, 79, 172, 181, 258}): 65,\n",
       "  frozenset({7, 79, 174, 181, 258}): 70,\n",
       "  frozenset({7, 98, 100, 127, 172}): 55,\n",
       "  frozenset({7, 98, 100, 127, 174}): 70,\n",
       "  frozenset({7, 98, 100, 172, 174}): 90,\n",
       "  frozenset({7, 98, 100, 172, 181}): 70,\n",
       "  frozenset({7, 98, 100, 174, 181}): 75,\n",
       "  frozenset({7, 98, 100, 174, 258}): 70,\n",
       "  frozenset({7, 98, 100, 181, 258}): 55,\n",
       "  frozenset({7, 98, 127, 172, 174}): 65,\n",
       "  frozenset({7, 98, 172, 174, 181}): 100,\n",
       "  frozenset({7, 98, 172, 174, 258}): 85,\n",
       "  frozenset({7, 98, 172, 181, 258}): 75,\n",
       "  frozenset({7, 98, 174, 181, 258}): 80,\n",
       "  frozenset({7, 100, 127, 172, 174}): 70,\n",
       "  frozenset({7, 100, 172, 174, 181}): 95,\n",
       "  frozenset({7, 100, 174, 181, 258}): 60,\n",
       "  frozenset({7, 172, 174, 181, 258}): 85,\n",
       "  frozenset({9, 50, 56, 64, 98}): 80,\n",
       "  frozenset({9, 50, 56, 64, 100}): 75,\n",
       "  frozenset({9, 50, 56, 64, 127}): 70,\n",
       "  frozenset({9, 50, 56, 64, 174}): 90,\n",
       "  frozenset({9, 50, 56, 98, 100}): 75,\n",
       "  frozenset({9, 50, 56, 98, 127}): 65,\n",
       "  frozenset({9, 50, 56, 98, 174}): 85,\n",
       "  frozenset({9, 50, 56, 100, 127}): 70,\n",
       "  frozenset({9, 50, 56, 100, 174}): 90,\n",
       "  frozenset({9, 50, 56, 127, 174}): 75,\n",
       "  frozenset({9, 50, 64, 98, 100}): 70,\n",
       "  frozenset({9, 50, 64, 98, 127}): 75,\n",
       "  frozenset({9, 50, 64, 98, 174}): 80,\n",
       "  frozenset({9, 50, 64, 100, 127}): 70,\n",
       "  frozenset({9, 50, 64, 100, 174}): 85,\n",
       "  frozenset({9, 50, 64, 127, 174}): 70,\n",
       "  frozenset({9, 50, 98, 100, 127}): 70,\n",
       "  frozenset({9, 50, 98, 100, 174}): 70,\n",
       "  frozenset({9, 50, 98, 127, 174}): 65,\n",
       "  frozenset({9, 50, 100, 127, 174}): 70,\n",
       "  frozenset({9, 50, 100, 174, 181}): 75,\n",
       "  frozenset({9, 56, 64, 98, 100}): 90,\n",
       "  frozenset({9, 56, 64, 98, 127}): 90,\n",
       "  frozenset({9, 56, 64, 98, 174}): 100,\n",
       "  frozenset({9, 56, 64, 100, 127}): 90,\n",
       "  frozenset({9, 56, 64, 100, 174}): 95,\n",
       "  frozenset({9, 56, 64, 127, 174}): 90,\n",
       "  frozenset({9, 56, 98, 100, 127}): 90,\n",
       "  frozenset({9, 56, 98, 100, 174}): 90,\n",
       "  frozenset({9, 56, 98, 127, 174}): 85,\n",
       "  frozenset({9, 56, 100, 127, 174}): 90,\n",
       "  frozenset({9, 64, 98, 100, 127}): 90,\n",
       "  frozenset({9, 64, 98, 100, 174}): 85,\n",
       "  frozenset({9, 64, 98, 127, 174}): 85,\n",
       "  frozenset({9, 64, 100, 127, 174}): 85,\n",
       "  frozenset({9, 98, 100, 127, 174}): 80,\n",
       "  frozenset({50, 56, 64, 79, 98}): 90,\n",
       "  frozenset({50, 56, 64, 79, 100}): 75,\n",
       "  frozenset({50, 56, 64, 79, 127}): 60,\n",
       "  frozenset({50, 56, 64, 79, 172}): 80,\n",
       "  frozenset({50, 56, 64, 79, 174}): 95,\n",
       "  frozenset({50, 56, 64, 79, 181}): 80,\n",
       "  frozenset({50, 56, 64, 79, 258}): 55,\n",
       "  frozenset({50, 56, 64, 98, 100}): 100,\n",
       "  frozenset({50, 56, 64, 98, 127}): 95,\n",
       "  frozenset({50, 56, 64, 98, 172}): 105,\n",
       "  frozenset({50, 56, 64, 98, 174}): 130,\n",
       "  frozenset({50, 56, 64, 98, 181}): 100,\n",
       "  frozenset({50, 56, 64, 98, 258}): 80,\n",
       "  frozenset({50, 56, 64, 100, 127}): 90,\n",
       "  frozenset({50, 56, 64, 100, 172}): 85,\n",
       "  frozenset({50, 56, 64, 100, 174}): 110,\n",
       "  frozenset({50, 56, 64, 100, 181}): 80,\n",
       "  frozenset({50, 56, 64, 127, 172}): 75,\n",
       "  frozenset({50, 56, 64, 127, 174}): 100,\n",
       "  frozenset({50, 56, 64, 127, 181}): 70,\n",
       "  frozenset({50, 56, 64, 172, 174}): 115,\n",
       "  frozenset({50, 56, 64, 172, 181}): 105,\n",
       "  frozenset({50, 56, 64, 172, 258}): 80,\n",
       "  frozenset({50, 56, 64, 174, 181}): 110,\n",
       "  frozenset({50, 56, 64, 174, 258}): 80,\n",
       "  frozenset({50, 56, 64, 181, 258}): 75,\n",
       "  frozenset({50, 56, 79, 98, 100}): 90,\n",
       "  frozenset({50, 56, 79, 98, 127}): 55,\n",
       "  frozenset({50, 56, 79, 98, 172}): 90,\n",
       "  frozenset({50, 56, 79, 98, 174}): 110,\n",
       "  frozenset({50, 56, 79, 98, 181}): 90,\n",
       "  frozenset({50, 56, 79, 98, 258}): 75,\n",
       "  frozenset({50, 56, 79, 100, 127}): 75,\n",
       "  frozenset({50, 56, 79, 100, 172}): 85,\n",
       "  frozenset({50, 56, 79, 100, 174}): 110,\n",
       "  frozenset({50, 56, 79, 100, 181}): 80,\n",
       "  frozenset({50, 56, 79, 100, 258}): 60,\n",
       "  frozenset({50, 56, 79, 127, 172}): 65,\n",
       "  frozenset({50, 56, 79, 127, 174}): 85,\n",
       "  frozenset({50, 56, 79, 172, 174}): 115,\n",
       "  frozenset({50, 56, 79, 172, 181}): 100,\n",
       "  frozenset({50, 56, 79, 172, 258}): 75,\n",
       "  frozenset({50, 56, 79, 174, 181}): 110,\n",
       "  frozenset({50, 56, 79, 174, 258}): 80,\n",
       "  frozenset({50, 56, 79, 181, 258}): 70,\n",
       "  frozenset({50, 56, 98, 100, 127}): 85,\n",
       "  frozenset({50, 56, 98, 100, 172}): 90,\n",
       "  frozenset({50, 56, 98, 100, 174}): 125,\n",
       "  frozenset({50, 56, 98, 100, 181}): 90,\n",
       "  frozenset({50, 56, 98, 100, 258}): 75,\n",
       "  frozenset({50, 56, 98, 127, 172}): 70,\n",
       "  frozenset({50, 56, 98, 127, 174}): 95,\n",
       "  frozenset({50, 56, 98, 127, 181}): 65,\n",
       "  frozenset({50, 56, 98, 172, 174}): 125,\n",
       "  frozenset({50, 56, 98, 172, 181}): 115,\n",
       "  frozenset({50, 56, 98, 172, 258}): 100,\n",
       "  frozenset({50, 56, 98, 174, 181}): 125,\n",
       "  frozenset({50, 56, 98, 174, 258}): 105,\n",
       "  frozenset({50, 56, 98, 181, 258}): 95,\n",
       "  frozenset({50, 56, 100, 127, 172}): 80,\n",
       "  frozenset({50, 56, 100, 127, 174}): 110,\n",
       "  frozenset({50, 56, 100, 127, 181}): 65,\n",
       "  frozenset({50, 56, 100, 172, 174}): 120,\n",
       "  frozenset({50, 56, 100, 172, 181}): 100,\n",
       "  frozenset({50, 56, 100, 174, 181}): 110,\n",
       "  frozenset({50, 56, 100, 174, 258}): 75,\n",
       "  frozenset({50, 56, 100, 181, 258}): 65,\n",
       "  frozenset({50, 56, 127, 172, 174}): 100,\n",
       "  frozenset({50, 56, 127, 172, 181}): 75,\n",
       "  frozenset({50, 56, 127, 174, 181}): 80,\n",
       "  frozenset({50, 56, 172, 174, 181}): 145,\n",
       "  frozenset({50, 56, 172, 174, 258}): 105,\n",
       "  frozenset({50, 56, 172, 181, 258}): 100,\n",
       "  frozenset({50, 56, 174, 181, 258}): 100,\n",
       "  frozenset({50, 64, 79, 98, 100}): 70,\n",
       "  frozenset({50, 64, 79, 98, 127}): 65,\n",
       "  frozenset({50, 64, 79, 98, 172}): 95,\n",
       "  frozenset({50, 64, 79, 98, 174}): 110,\n",
       "  frozenset({50, 64, 79, 98, 181}): 100,\n",
       "  frozenset({50, 64, 79, 98, 258}): 60,\n",
       "  frozenset({50, 64, 79, 100, 127}): 60,\n",
       "  frozenset({50, 64, 79, 100, 172}): 60,\n",
       "  frozenset({50, 64, 79, 100, 174}): 75,\n",
       "  frozenset({50, 64, 79, 100, 181}): 65,\n",
       "  frozenset({50, 64, 79, 127, 174}): 70,\n",
       "  frozenset({50, 64, 79, 172, 174}): 100,\n",
       "  frozenset({50, 64, 79, 172, 181}): 95,\n",
       "  frozenset({50, 64, 79, 174, 181}): 100,\n",
       "  frozenset({50, 64, 98, 100, 127}): 90,\n",
       "  frozenset({50, 64, 98, 100, 172}): 80,\n",
       "  frozenset({50, 64, 98, 100, 174}): 100,\n",
       "  frozenset({50, 64, 98, 100, 181}): 75,\n",
       "  frozenset({50, 64, 98, 127, 172}): 90,\n",
       "  frozenset({50, 64, 98, 127, 174}): 105,\n",
       "  frozenset({50, 64, 98, 127, 181}): 80,\n",
       "  frozenset({50, 64, 98, 172, 174}): 125,\n",
       "  frozenset({50, 64, 98, 172, 181}): 120,\n",
       "  frozenset({50, 64, 98, 172, 258}): 85,\n",
       "  frozenset({50, 64, 98, 174, 181}): 120,\n",
       "  frozenset({50, 64, 98, 174, 258}): 85,\n",
       "  frozenset({50, 64, 98, 181, 258}): 80,\n",
       "  frozenset({50, 64, 100, 127, 172}): 70,\n",
       "  frozenset({50, 64, 100, 127, 174}): 90,\n",
       "  frozenset({50, 64, 100, 127, 181}): 65,\n",
       "  frozenset({50, 64, 100, 172, 174}): 90,\n",
       "  frozenset({50, 64, 100, 172, 181}): 85,\n",
       "  frozenset({50, 64, 100, 174, 181}): 95,\n",
       "  frozenset({50, 64, 127, 172, 174}): 85,\n",
       "  frozenset({50, 64, 127, 172, 181}): 80,\n",
       "  frozenset({50, 64, 127, 174, 181}): 80,\n",
       "  frozenset({50, 64, 172, 174, 181}): 130,\n",
       "  frozenset({50, 64, 172, 174, 258}): 90,\n",
       "  frozenset({50, 64, 172, 181, 258}): 85,\n",
       "  frozenset({50, 64, 174, 181, 258}): 90,\n",
       "  frozenset({50, 79, 98, 100, 127}): 55,\n",
       "  frozenset({50, 79, 98, 100, 172}): 70,\n",
       "  frozenset({50, 79, 98, 100, 174}): 90,\n",
       "  frozenset({50, 79, 98, 100, 181}): 70,\n",
       "  frozenset({50, 79, 98, 100, 258}): 60,\n",
       "  frozenset({50, 79, 98, 127, 174}): 65,\n",
       "  frozenset({50, 79, 98, 172, 174}): 115,\n",
       "  frozenset({50, 79, 98, 172, 181}): 105,\n",
       "  frozenset({50, 79, 98, 172, 258}): 75,\n",
       "  frozenset({50, 79, 98, 174, 181}): 115,\n",
       "  frozenset({50, 79, 98, 174, 258}): 85,\n",
       "  frozenset({50, 79, 98, 181, 258}): 75,\n",
       "  frozenset({50, 79, 100, 127, 174}): 75,\n",
       "  frozenset({50, 79, 100, 172, 174}): 85,\n",
       "  frozenset({50, 79, 100, 172, 181}): 75,\n",
       "  frozenset({50, 79, 100, 174, 181}): 80,\n",
       "  frozenset({50, 79, 100, 174, 258}): 60,\n",
       "  frozenset({50, 79, 127, 172, 174}): 85,\n",
       "  frozenset({50, 79, 172, 174, 181}): 140,\n",
       "  frozenset({50, 79, 172, 174, 258}): 90,\n",
       "  frozenset({50, 79, 172, 181, 258}): 85,\n",
       "  frozenset({50, 79, 174, 181, 258}): 90,\n",
       "  frozenset({50, 98, 100, 127, 172}): 70,\n",
       "  frozenset({50, 98, 100, 127, 174}): 85,\n",
       "  frozenset({50, 98, 100, 127, 181}): 65,\n",
       "  frozenset({50, 98, 100, 172, 174}): 90,\n",
       "  frozenset({50, 98, 100, 172, 181}): 90,\n",
       "  frozenset({50, 98, 100, 174, 181}): 90,\n",
       "  frozenset({50, 98, 100, 174, 258}): 75,\n",
       "  frozenset({50, 98, 100, 181, 258}): 65,\n",
       "  frozenset({50, 98, 127, 172, 174}): 85,\n",
       "  frozenset({50, 98, 127, 172, 181}): 80,\n",
       "  frozenset({50, 98, 127, 174, 181}): 75,\n",
       "  frozenset({50, 98, 172, 174, 181}): 140,\n",
       "  frozenset({50, 98, 172, 174, 258}): 105,\n",
       "  frozenset({50, 98, 172, 181, 258}): 100,\n",
       "  frozenset({50, 98, 174, 181, 258}): 105,\n",
       "  frozenset({50, 100, 127, 172, 174}): 80,\n",
       "  frozenset({50, 100, 127, 172, 181}): 70,\n",
       "  frozenset({50, 100, 127, 174, 181}): 65,\n",
       "  frozenset({50, 100, 172, 174, 181}): 110,\n",
       "  frozenset({50, 100, 174, 181, 258}): 75,\n",
       "  frozenset({50, 127, 172, 174, 181}): 100,\n",
       "  frozenset({50, 172, 174, 181, 258}): 125,\n",
       "  frozenset({56, 64, 79, 98, 100}): 90,\n",
       "  frozenset({56, 64, 79, 98, 127}): 75,\n",
       "  frozenset({56, 64, 79, 98, 172}): 80,\n",
       "  frozenset({56, 64, 79, 98, 174}): 105,\n",
       "  frozenset({56, 64, 79, 98, 181}): 75,\n",
       "  frozenset({56, 64, 79, 98, 258}): 60,\n",
       "  frozenset({56, 64, 79, 100, 127}): 80,\n",
       "  frozenset({56, 64, 79, 100, 172}): 65,\n",
       "  frozenset({56, 64, 79, 100, 174}): 90,\n",
       "  frozenset({56, 64, 79, 100, 181}): 60,\n",
       "  frozenset({56, 64, 79, 127, 174}): 75,\n",
       "  frozenset({56, 64, 79, 172, 174}): 85,\n",
       "  frozenset({56, 64, 79, 172, 181}): 75,\n",
       "  frozenset({56, 64, 79, 174, 181}): 80,\n",
       "  frozenset({56, 64, 98, 100, 127}): 110,\n",
       "  frozenset({56, 64, 98, 100, 172}): 85,\n",
       "  frozenset({56, 64, 98, 100, 174}): 120,\n",
       "  frozenset({56, 64, 98, 100, 181}): 70,\n",
       "  frozenset({56, 64, 98, 127, 172}): 75,\n",
       "  frozenset({56, 64, 98, 127, 174}): 115,\n",
       "  frozenset({56, 64, 98, 127, 181}): 65,\n",
       "  frozenset({56, 64, 98, 172, 174}): 110,\n",
       "  frozenset({56, 64, 98, 172, 181}): 95,\n",
       "  frozenset({56, 64, 98, 172, 258}): 80,\n",
       "  frozenset({56, 64, 98, 174, 181}): 100,\n",
       "  frozenset({56, 64, 98, 174, 258}): 80,\n",
       "  frozenset({56, 64, 98, 181, 258}): 75,\n",
       "  frozenset({56, 64, 100, 127, 172}): 70,\n",
       "  frozenset({56, 64, 100, 127, 174}): 110,\n",
       "  frozenset({56, 64, 100, 127, 181}): 60,\n",
       "  frozenset({56, 64, 100, 172, 174}): 90,\n",
       "  frozenset({56, 64, 100, 172, 181}): 75,\n",
       "  frozenset({56, 64, 100, 174, 181}): 80,\n",
       "  frozenset({56, 64, 127, 172, 174}): 80,\n",
       "  frozenset({56, 64, 127, 172, 181}): 65,\n",
       "  frozenset({56, 64, 127, 174, 181}): 70,\n",
       "  frozenset({56, 64, 172, 174, 181}): 105,\n",
       "  frozenset({56, 64, 172, 174, 258}): 80,\n",
       "  frozenset({56, 64, 172, 181, 258}): 75,\n",
       "  frozenset({56, 64, 174, 181, 258}): 75,\n",
       "  frozenset({56, 79, 98, 100, 127}): 75,\n",
       "  frozenset({56, 79, 98, 100, 172}): 80,\n",
       "  frozenset({56, 79, 98, 100, 174}): 110,\n",
       "  frozenset({56, 79, 98, 100, 181}): 70,\n",
       "  frozenset({56, 79, 98, 100, 258}): 70,\n",
       "  frozenset({56, 79, 98, 127, 174}): 70,\n",
       "  frozenset({56, 79, 98, 172, 174}): 100,\n",
       "  frozenset({56, 79, 98, 172, 181}): 85,\n",
       "  frozenset({56, 79, 98, 172, 258}): 75,\n",
       "  frozenset({56, 79, 98, 174, 181}): 90,\n",
       "  frozenset({56, 79, 98, 174, 258}): 80,\n",
       "  frozenset({56, 79, 98, 181, 258}): 65,\n",
       "  frozenset({56, 79, 100, 127, 174}): 90,\n",
       "  frozenset({56, 79, 100, 172, 174}): 95,\n",
       "  frozenset({56, 79, 100, 172, 181}): 75,\n",
       "  frozenset({56, 79, 100, 174, 181}): 80,\n",
       "  frozenset({56, 79, 100, 174, 258}): 65,\n",
       "  frozenset({56, 79, 127, 172, 174}): 70,\n",
       "  frozenset({56, 79, 172, 174, 181}): 100,\n",
       "  frozenset({56, 79, 172, 174, 258}): 80,\n",
       "  frozenset({56, 79, 172, 181, 258}): 70,\n",
       "  frozenset({56, 79, 174, 181, 258}): 70,\n",
       "  frozenset({56, 98, 100, 127, 172}): 65,\n",
       "  frozenset({56, 98, 100, 127, 174}): 105,\n",
       "  frozenset({56, 98, 100, 127, 181}): 55,\n",
       "  frozenset({56, 98, 100, 172, 174}): 100,\n",
       "  frozenset({56, 98, 100, 172, 181}): 80,\n",
       "  frozenset({56, 98, 100, 174, 181}): 90,\n",
       "  frozenset({56, 98, 100, 174, 258}): 80,\n",
       "  frozenset({56, 98, 100, 181, 258}): 65,\n",
       "  frozenset({56, 98, 127, 172, 174}): 75,\n",
       "  frozenset({56, 98, 127, 172, 181}): 60,\n",
       "  frozenset({56, 98, 127, 174, 181}): 65,\n",
       "  frozenset({56, 98, 172, 174, 181}): 115,\n",
       "  frozenset({56, 98, 172, 174, 258}): 105,\n",
       "  frozenset({56, 98, 172, 181, 258}): 95,\n",
       "  frozenset({56, 98, 174, 181, 258}): 95,\n",
       "  frozenset({56, 100, 127, 172, 174}): 85,\n",
       "  frozenset({56, 100, 127, 172, 181}): 60,\n",
       "  frozenset({56, 100, 127, 174, 181}): 65,\n",
       "  frozenset({56, 100, 172, 174, 181}): 100,\n",
       "  frozenset({56, 100, 174, 181, 258}): 65,\n",
       "  frozenset({56, 127, 172, 174, 181}): 75,\n",
       "  frozenset({56, 172, 174, 181, 258}): 100,\n",
       "  frozenset({64, 79, 98, 100, 127}): 75,\n",
       "  frozenset({64, 79, 98, 100, 172}): 60,\n",
       "  frozenset({64, 79, 98, 100, 174}): 85,\n",
       "  frozenset({64, 79, 98, 100, 181}): 55,\n",
       "  frozenset({64, 79, 98, 127, 174}): 80,\n",
       "  frozenset({64, 79, 98, 172, 174}): 100,\n",
       "  frozenset({64, 79, 98, 172, 181}): 90,\n",
       "  frozenset({64, 79, 98, 174, 181}): 95,\n",
       "  frozenset({64, 79, 100, 127, 174}): 75,\n",
       "  frozenset({64, 79, 100, 172, 174}): 65,\n",
       "  frozenset({64, 79, 100, 172, 181}): 55,\n",
       "  frozenset({64, 79, 100, 174, 181}): 60,\n",
       "  frozenset({64, 79, 172, 174, 181}): 95,\n",
       "  frozenset({64, 98, 100, 127, 172}): 70,\n",
       "  frozenset({64, 98, 100, 127, 174}): 105,\n",
       "  frozenset({64, 98, 100, 127, 181}): 60,\n",
       "  frozenset({64, 98, 100, 172, 174}): 80,\n",
       "  frozenset({64, 98, 100, 172, 181}): 70,\n",
       "  frozenset({64, 98, 100, 174, 181}): 70,\n",
       "  frozenset({64, 98, 127, 172, 174}): 85,\n",
       "  frozenset({64, 98, 127, 172, 181}): 75,\n",
       "  frozenset({64, 98, 127, 174, 181}): 75,\n",
       "  frozenset({64, 98, 172, 174, 181}): 115,\n",
       "  frozenset({64, 98, 172, 174, 258}): 85,\n",
       "  frozenset({64, 98, 172, 181, 258}): 80,\n",
       "  frozenset({64, 98, 174, 181, 258}): 80,\n",
       "  frozenset({64, 100, 127, 172, 174}): 70,\n",
       "  frozenset({64, 100, 127, 172, 181}): 60,\n",
       "  frozenset({64, 100, 127, 174, 181}): 60,\n",
       "  frozenset({64, 100, 172, 174, 181}): 80,\n",
       "  frozenset({64, 127, 172, 174, 181}): 75,\n",
       "  frozenset({64, 172, 174, 181, 258}): 85,\n",
       "  frozenset({79, 98, 100, 127, 174}): 70,\n",
       "  frozenset({79, 98, 100, 172, 174}): 80,\n",
       "  frozenset({79, 98, 100, 172, 181}): 65,\n",
       "  frozenset({79, 98, 100, 174, 181}): 70,\n",
       "  frozenset({79, 98, 100, 174, 258}): 65,\n",
       "  frozenset({79, 98, 172, 174, 181}): 105,\n",
       "  frozenset({79, 98, 172, 174, 258}): 80,\n",
       "  frozenset({79, 98, 172, 181, 258}): 70,\n",
       "  frozenset({79, 98, 174, 181, 258}): 75,\n",
       "  frozenset({79, 100, 172, 174, 181}): 75,\n",
       "  frozenset({79, 172, 174, 181, 258}): 85,\n",
       "  frozenset({98, 100, 127, 172, 174}): 65,\n",
       "  frozenset({98, 100, 127, 172, 181}): 60,\n",
       "  frozenset({98, 100, 127, 174, 181}): 55,\n",
       "  frozenset({98, 100, 172, 174, 181}): 80,\n",
       "  frozenset({98, 100, 174, 181, 258}): 65,\n",
       "  frozenset({98, 127, 172, 174, 181}): 70,\n",
       "  frozenset({98, 172, 174, 181, 258}): 100,\n",
       "  frozenset({100, 127, 172, 174, 181}): 60},\n",
       " 6: {frozenset({1, 7, 50, 56, 64, 79}): 66,\n",
       "  frozenset({1, 7, 50, 56, 64, 98}): 84,\n",
       "  frozenset({1, 7, 50, 56, 64, 100}): 60,\n",
       "  frozenset({1, 7, 50, 56, 64, 172}): 72,\n",
       "  frozenset({1, 7, 50, 56, 64, 174}): 84,\n",
       "  frozenset({1, 7, 50, 56, 64, 181}): 72,\n",
       "  frozenset({1, 7, 50, 56, 79, 98}): 78,\n",
       "  frozenset({1, 7, 50, 56, 79, 100}): 66,\n",
       "  frozenset({1, 7, 50, 56, 79, 172}): 78,\n",
       "  frozenset({1, 7, 50, 56, 79, 174}): 84,\n",
       "  frozenset({1, 7, 50, 56, 79, 181}): 78,\n",
       "  frozenset({1, 7, 50, 56, 98, 100}): 72,\n",
       "  frozenset({1, 7, 50, 56, 98, 172}): 84,\n",
       "  frozenset({1, 7, 50, 56, 98, 174}): 96,\n",
       "  frozenset({1, 7, 50, 56, 98, 181}): 84,\n",
       "  frozenset({1, 7, 50, 56, 100, 172}): 66,\n",
       "  frozenset({1, 7, 50, 56, 100, 174}): 78,\n",
       "  frozenset({1, 7, 50, 56, 172, 174}): 96,\n",
       "  frozenset({1, 7, 50, 56, 172, 181}): 84,\n",
       "  frozenset({1, 7, 50, 56, 174, 181}): 90,\n",
       "  frozenset({1, 7, 50, 64, 79, 98}): 72,\n",
       "  frozenset({1, 7, 50, 64, 79, 172}): 66,\n",
       "  frozenset({1, 7, 50, 64, 79, 174}): 72,\n",
       "  frozenset({1, 7, 50, 64, 79, 181}): 78,\n",
       "  frozenset({1, 7, 50, 64, 98, 100}): 60,\n",
       "  frozenset({1, 7, 50, 64, 98, 172}): 78,\n",
       "  frozenset({1, 7, 50, 64, 98, 174}): 90,\n",
       "  frozenset({1, 7, 50, 64, 98, 181}): 78,\n",
       "  frozenset({1, 7, 50, 64, 100, 174}): 66,\n",
       "  frozenset({1, 7, 50, 64, 100, 181}): 60,\n",
       "  frozenset({1, 7, 50, 64, 172, 174}): 84,\n",
       "  frozenset({1, 7, 50, 64, 172, 181}): 78,\n",
       "  frozenset({1, 7, 50, 64, 174, 181}): 84,\n",
       "  frozenset({1, 7, 50, 79, 98, 100}): 60,\n",
       "  frozenset({1, 7, 50, 79, 98, 172}): 84,\n",
       "  frozenset({1, 7, 50, 79, 98, 174}): 96,\n",
       "  frozenset({1, 7, 50, 79, 98, 181}): 90,\n",
       "  frozenset({1, 7, 50, 79, 100, 174}): 66,\n",
       "  frozenset({1, 7, 50, 79, 172, 174}): 90,\n",
       "  frozenset({1, 7, 50, 79, 172, 181}): 78,\n",
       "  frozenset({1, 7, 50, 79, 174, 181}): 90,\n",
       "  frozenset({1, 7, 50, 98, 100, 172}): 60,\n",
       "  frozenset({1, 7, 50, 98, 100, 174}): 72,\n",
       "  frozenset({1, 7, 50, 98, 100, 181}): 60,\n",
       "  frozenset({1, 7, 50, 98, 172, 174}): 96,\n",
       "  frozenset({1, 7, 50, 98, 172, 181}): 84,\n",
       "  frozenset({1, 7, 50, 98, 174, 181}): 96,\n",
       "  frozenset({1, 7, 50, 100, 172, 174}): 72,\n",
       "  frozenset({1, 7, 50, 100, 172, 181}): 60,\n",
       "  frozenset({1, 7, 50, 100, 174, 181}): 66,\n",
       "  frozenset({1, 7, 50, 172, 174, 181}): 96,\n",
       "  frozenset({1, 7, 56, 64, 79, 98}): 72,\n",
       "  frozenset({1, 7, 56, 64, 79, 172}): 66,\n",
       "  frozenset({1, 7, 56, 64, 79, 174}): 72,\n",
       "  frozenset({1, 7, 56, 64, 79, 181}): 66,\n",
       "  frozenset({1, 7, 56, 64, 98, 100}): 66,\n",
       "  frozenset({1, 7, 56, 64, 98, 172}): 78,\n",
       "  frozenset({1, 7, 56, 64, 98, 174}): 90,\n",
       "  frozenset({1, 7, 56, 64, 98, 181}): 72,\n",
       "  frozenset({1, 7, 56, 64, 100, 174}): 66,\n",
       "  frozenset({1, 7, 56, 64, 172, 174}): 78,\n",
       "  frozenset({1, 7, 56, 64, 172, 181}): 66,\n",
       "  frozenset({1, 7, 56, 64, 174, 181}): 72,\n",
       "  frozenset({1, 7, 56, 79, 98, 100}): 66,\n",
       "  frozenset({1, 7, 56, 79, 98, 172}): 78,\n",
       "  frozenset({1, 7, 56, 79, 98, 174}): 84,\n",
       "  frozenset({1, 7, 56, 79, 98, 181}): 78,\n",
       "  frozenset({1, 7, 56, 79, 100, 174}): 72,\n",
       "  frozenset({1, 7, 56, 79, 172, 174}): 84,\n",
       "  frozenset({1, 7, 56, 79, 172, 181}): 72,\n",
       "  frozenset({1, 7, 56, 79, 174, 181}): 78,\n",
       "  frozenset({1, 7, 56, 98, 100, 172}): 66,\n",
       "  frozenset({1, 7, 56, 98, 100, 174}): 78,\n",
       "  frozenset({1, 7, 56, 98, 172, 174}): 90,\n",
       "  frozenset({1, 7, 56, 98, 172, 181}): 78,\n",
       "  frozenset({1, 7, 56, 98, 174, 181}): 84,\n",
       "  frozenset({1, 7, 56, 100, 172, 174}): 72,\n",
       "  frozenset({1, 7, 56, 172, 174, 181}): 84,\n",
       "  frozenset({1, 7, 64, 79, 98, 172}): 72,\n",
       "  frozenset({1, 7, 64, 79, 98, 174}): 78,\n",
       "  frozenset({1, 7, 64, 79, 98, 181}): 72,\n",
       "  frozenset({1, 7, 64, 79, 172, 174}): 72,\n",
       "  frozenset({1, 7, 64, 79, 172, 181}): 66,\n",
       "  frozenset({1, 7, 64, 79, 174, 181}): 72,\n",
       "  frozenset({1, 7, 64, 98, 100, 174}): 66,\n",
       "  frozenset({1, 7, 64, 98, 172, 174}): 84,\n",
       "  frozenset({1, 7, 64, 98, 172, 181}): 72,\n",
       "  frozenset({1, 7, 64, 98, 174, 181}): 78,\n",
       "  frozenset({1, 7, 64, 100, 174, 181}): 54,\n",
       "  frozenset({1, 7, 64, 172, 174, 181}): 78,\n",
       "  frozenset({1, 7, 79, 98, 100, 174}): 66,\n",
       "  frozenset({1, 7, 79, 98, 172, 174}): 90,\n",
       "  frozenset({1, 7, 79, 98, 172, 181}): 78,\n",
       "  frozenset({1, 7, 79, 98, 174, 181}): 90,\n",
       "  frozenset({1, 7, 79, 172, 174, 181}): 78,\n",
       "  frozenset({1, 7, 98, 100, 172, 174}): 66,\n",
       "  frozenset({1, 7, 98, 100, 172, 181}): 54,\n",
       "  frozenset({1, 7, 98, 100, 174, 181}): 60,\n",
       "  frozenset({1, 7, 98, 172, 174, 181}): 84,\n",
       "  frozenset({1, 7, 100, 172, 174, 181}): 60,\n",
       "  frozenset({1, 50, 56, 64, 79, 98}): 72,\n",
       "  frozenset({1, 50, 56, 64, 79, 172}): 60,\n",
       "  frozenset({1, 50, 56, 64, 79, 174}): 72,\n",
       "  frozenset({1, 50, 56, 64, 79, 181}): 66,\n",
       "  frozenset({1, 50, 56, 64, 98, 100}): 78,\n",
       "  frozenset({1, 50, 56, 64, 98, 127}): 72,\n",
       "  frozenset({1, 50, 56, 64, 98, 172}): 78,\n",
       "  frozenset({1, 50, 56, 64, 98, 174}): 102,\n",
       "  frozenset({1, 50, 56, 64, 98, 181}): 78,\n",
       "  frozenset({1, 50, 56, 64, 100, 127}): 66,\n",
       "  frozenset({1, 50, 56, 64, 100, 174}): 78,\n",
       "  frozenset({1, 50, 56, 64, 127, 174}): 72,\n",
       "  frozenset({1, 50, 56, 64, 172, 174}): 78,\n",
       "  frozenset({1, 50, 56, 64, 172, 181}): 72,\n",
       "  frozenset({1, 50, 56, 64, 174, 181}): 78,\n",
       "  frozenset({1, 50, 56, 79, 98, 100}): 66,\n",
       "  frozenset({1, 50, 56, 79, 98, 172}): 72,\n",
       "  frozenset({1, 50, 56, 79, 98, 174}): 84,\n",
       "  frozenset({1, 50, 56, 79, 98, 181}): 78,\n",
       "  frozenset({1, 50, 56, 79, 100, 174}): 78,\n",
       "  frozenset({1, 50, 56, 79, 172, 174}): 78,\n",
       "  frozenset({1, 50, 56, 79, 172, 181}): 72,\n",
       "  frozenset({1, 50, 56, 79, 174, 181}): 78,\n",
       "  frozenset({1, 50, 56, 98, 100, 127}): 66,\n",
       "  frozenset({1, 50, 56, 98, 100, 172}): 66,\n",
       "  frozenset({1, 50, 56, 98, 100, 174}): 96,\n",
       "  frozenset({1, 50, 56, 98, 127, 174}): 72,\n",
       "  frozenset({1, 50, 56, 98, 172, 174}): 96,\n",
       "  frozenset({1, 50, 56, 98, 172, 181}): 90,\n",
       "  frozenset({1, 50, 56, 98, 174, 181}): 102,\n",
       "  frozenset({1, 50, 56, 100, 127, 174}): 84,\n",
       "  frozenset({1, 50, 56, 100, 172, 174}): 78,\n",
       "  frozenset({1, 50, 56, 172, 174, 181}): 96,\n",
       "  frozenset({1, 50, 64, 79, 98, 172}): 78,\n",
       "  frozenset({1, 50, 64, 79, 98, 174}): 90,\n",
       "  frozenset({1, 50, 64, 79, 98, 181}): 90,\n",
       "  frozenset({1, 50, 64, 79, 172, 174}): 78,\n",
       "  frozenset({1, 50, 64, 79, 172, 181}): 78,\n",
       "  frozenset({1, 50, 64, 79, 174, 181}): 84,\n",
       "  frozenset({1, 50, 64, 98, 100, 127}): 72,\n",
       "  frozenset({1, 50, 64, 98, 100, 174}): 78,\n",
       "  frozenset({1, 50, 64, 98, 100, 181}): 60,\n",
       "  frozenset({1, 50, 64, 98, 127, 174}): 78,\n",
       "  frozenset({1, 50, 64, 98, 172, 174}): 96,\n",
       "  frozenset({1, 50, 64, 98, 172, 181}): 96,\n",
       "  frozenset({1, 50, 64, 98, 174, 181}): 96,\n",
       "  frozenset({1, 50, 64, 100, 127, 174}): 66,\n",
       "  frozenset({1, 50, 64, 100, 174, 181}): 66,\n",
       "  frozenset({1, 50, 64, 172, 174, 181}): 96,\n",
       "  frozenset({1, 50, 79, 98, 100, 174}): 66,\n",
       "  frozenset({1, 50, 79, 98, 172, 174}): 96,\n",
       "  frozenset({1, 50, 79, 98, 172, 181}): 90,\n",
       "  frozenset({1, 50, 79, 98, 174, 181}): 102,\n",
       "  frozenset({1, 50, 79, 172, 174, 181}): 96,\n",
       "  frozenset({1, 50, 98, 100, 127, 174}): 66,\n",
       "  frozenset({1, 50, 98, 100, 172, 174}): 66,\n",
       "  frozenset({1, 50, 98, 100, 172, 181}): 72,\n",
       "  frozenset({1, 50, 98, 100, 174, 181}): 72,\n",
       "  frozenset({1, 50, 98, 172, 174, 181}): 108,\n",
       "  frozenset({1, 50, 100, 172, 174, 181}): 72,\n",
       "  frozenset({1, 56, 64, 79, 98, 172}): 66,\n",
       "  frozenset({1, 56, 64, 79, 98, 174}): 84,\n",
       "  frozenset({1, 56, 64, 79, 98, 181}): 66,\n",
       "  frozenset({1, 56, 64, 79, 172, 174}): 66,\n",
       "  frozenset({1, 56, 64, 79, 172, 181}): 60,\n",
       "  frozenset({1, 56, 64, 79, 174, 181}): 66,\n",
       "  frozenset({1, 56, 64, 98, 100, 127}): 84,\n",
       "  frozenset({1, 56, 64, 98, 100, 174}): 96,\n",
       "  frozenset({1, 56, 64, 98, 127, 174}): 90,\n",
       "  frozenset({1, 56, 64, 98, 172, 174}): 84,\n",
       "  frozenset({1, 56, 64, 98, 172, 181}): 72,\n",
       "  frozenset({1, 56, 64, 98, 174, 181}): 78,\n",
       "  frozenset({1, 56, 64, 100, 127, 174}): 84,\n",
       "  frozenset({1, 56, 64, 172, 174, 181}): 72,\n",
       "  frozenset({1, 56, 79, 98, 100, 174}): 78,\n",
       "  frozenset({1, 56, 79, 98, 172, 174}): 78,\n",
       "  frozenset({1, 56, 79, 98, 172, 181}): 72,\n",
       "  frozenset({1, 56, 79, 98, 174, 181}): 78,\n",
       "  frozenset({1, 56, 79, 172, 174, 181}): 72,\n",
       "  frozenset({1, 56, 98, 100, 127, 174}): 84,\n",
       "  frozenset({1, 56, 98, 100, 172, 174}): 72,\n",
       "  frozenset({1, 56, 98, 172, 174, 181}): 90,\n",
       "  frozenset({1, 64, 79, 98, 172, 174}): 84,\n",
       "  frozenset({1, 64, 79, 98, 172, 181}): 78,\n",
       "  frozenset({1, 64, 79, 98, 174, 181}): 84,\n",
       "  frozenset({1, 64, 79, 172, 174, 181}): 78,\n",
       "  frozenset({1, 64, 98, 100, 127, 174}): 84,\n",
       "  frozenset({1, 64, 98, 100, 174, 181}): 54,\n",
       "  frozenset({1, 64, 98, 172, 174, 181}): 90,\n",
       "  frozenset({1, 79, 98, 172, 174, 181}): 90,\n",
       "  frozenset({1, 98, 100, 172, 174, 181}): 60,\n",
       "  frozenset({7, 9, 50, 56, 64, 100}): 72,\n",
       "  frozenset({7, 9, 50, 56, 64, 174}): 84,\n",
       "  frozenset({7, 9, 50, 56, 100, 174}): 90,\n",
       "  frozenset({7, 9, 50, 64, 100, 174}): 78,\n",
       "  frozenset({7, 9, 56, 64, 100, 174}): 78,\n",
       "  frozenset({7, 50, 56, 64, 79, 98}): 102,\n",
       "  frozenset({7, 50, 56, 64, 79, 100}): 84,\n",
       "  frozenset({7, 50, 56, 64, 79, 127}): 66,\n",
       "  frozenset({7, 50, 56, 64, 79, 172}): 96,\n",
       "  frozenset({7, 50, 56, 64, 79, 174}): 108,\n",
       "  frozenset({7, 50, 56, 64, 79, 181}): 96,\n",
       "  frozenset({7, 50, 56, 64, 79, 258}): 66,\n",
       "  frozenset({7, 50, 56, 64, 98, 100}): 96,\n",
       "  frozenset({7, 50, 56, 64, 98, 127}): 84,\n",
       "  frozenset({7, 50, 56, 64, 98, 172}): 108,\n",
       "  frozenset({7, 50, 56, 64, 98, 174}): 126,\n",
       "  frozenset({7, 50, 56, 64, 98, 181}): 102,\n",
       "  frozenset({7, 50, 56, 64, 98, 258}): 78,\n",
       "  frozenset({7, 50, 56, 64, 100, 127}): 84,\n",
       "  frozenset({7, 50, 56, 64, 100, 172}): 90,\n",
       "  frozenset({7, 50, 56, 64, 100, 174}): 108,\n",
       "  frozenset({7, 50, 56, 64, 100, 181}): 84,\n",
       "  frozenset({7, 50, 56, 64, 127, 172}): 72,\n",
       "  frozenset({7, 50, 56, 64, 127, 174}): 90,\n",
       "  frozenset({7, 50, 56, 64, 172, 174}): 120,\n",
       "  frozenset({7, 50, 56, 64, 172, 181}): 108,\n",
       "  frozenset({7, 50, 56, 64, 172, 258}): 78,\n",
       "  frozenset({7, 50, 56, 64, 174, 181}): 114,\n",
       "  frozenset({7, 50, 56, 64, 174, 258}): 78,\n",
       "  frozenset({7, 50, 56, 64, 181, 258}): 72,\n",
       "  frozenset({7, 50, 56, 79, 98, 100}): 102,\n",
       "  frozenset({7, 50, 56, 79, 98, 127}): 60,\n",
       "  frozenset({7, 50, 56, 79, 98, 172}): 108,\n",
       "  frozenset({7, 50, 56, 79, 98, 174}): 126,\n",
       "  frozenset({7, 50, 56, 79, 98, 181}): 108,\n",
       "  frozenset({7, 50, 56, 79, 98, 258}): 90,\n",
       "  frozenset({7, 50, 56, 79, 100, 127}): 78,\n",
       "  frozenset({7, 50, 56, 79, 100, 172}): 102,\n",
       "  frozenset({7, 50, 56, 79, 100, 174}): 120,\n",
       "  frozenset({7, 50, 56, 79, 100, 181}): 96,\n",
       "  frozenset({7, 50, 56, 79, 100, 258}): 72,\n",
       "  frozenset({7, 50, 56, 79, 127, 172}): 72,\n",
       "  frozenset({7, 50, 56, 79, 127, 174}): 84,\n",
       "  frozenset({7, 50, 56, 79, 172, 174}): 132,\n",
       "  frozenset({7, 50, 56, 79, 172, 181}): 114,\n",
       "  frozenset({7, 50, 56, 79, 172, 258}): 84,\n",
       "  frozenset({7, 50, 56, 79, 174, 181}): 120,\n",
       "  frozenset({7, 50, 56, 79, 174, 258}): 90,\n",
       "  frozenset({7, 50, 56, 79, 181, 258}): 78,\n",
       "  frozenset({7, 50, 56, 98, 100, 127}): 78,\n",
       "  frozenset({7, 50, 56, 98, 100, 172}): 96,\n",
       "  frozenset({7, 50, 56, 98, 100, 174}): 120,\n",
       "  frozenset({7, 50, 56, 98, 100, 181}): 90,\n",
       "  frozenset({7, 50, 56, 98, 100, 258}): 78,\n",
       "  frozenset({7, 50, 56, 98, 127, 172}): 66,\n",
       "  frozenset({7, 50, 56, 98, 127, 174}): 84,\n",
       "  frozenset({7, 50, 56, 98, 172, 174}): 126,\n",
       "  frozenset({7, 50, 56, 98, 172, 181}): 114,\n",
       "  frozenset({7, 50, 56, 98, 172, 258}): 96,\n",
       "  frozenset({7, 50, 56, 98, 174, 181}): 120,\n",
       "  frozenset({7, 50, 56, 98, 174, 258}): 102,\n",
       "  frozenset({7, 50, 56, 98, 181, 258}): 90,\n",
       "  frozenset({7, 50, 56, 100, 127, 172}): 78,\n",
       "  frozenset({7, 50, 56, 100, 127, 174}): 96,\n",
       "  frozenset({7, 50, 56, 100, 172, 174}): 126,\n",
       "  frozenset({7, 50, 56, 100, 172, 181}): 108,\n",
       "  frozenset({7, 50, 56, 100, 174, 181}): 114,\n",
       "  frozenset({7, 50, 56, 100, 174, 258}): 78,\n",
       "  frozenset({7, 50, 56, 100, 181, 258}): 66,\n",
       "  frozenset({7, 50, 56, 127, 172, 174}): 90,\n",
       "  frozenset({7, 50, 56, 172, 174, 181}): 144,\n",
       "  frozenset({7, 50, 56, 172, 174, 258}): 96,\n",
       "  frozenset({7, 50, 56, 172, 181, 258}): 90,\n",
       "  frozenset({7, 50, 56, 174, 181, 258}): 90,\n",
       "  frozenset({7, 50, 64, 79, 98, 100}): 78,\n",
       "  frozenset({7, 50, 64, 79, 98, 127}): 66,\n",
       "  frozenset({7, 50, 64, 79, 98, 172}): 96,\n",
       "  frozenset({7, 50, 64, 79, 98, 174}): 108,\n",
       "  frozenset({7, 50, 64, 79, 98, 181}): 96,\n",
       "  frozenset({7, 50, 64, 79, 98, 258}): 66,\n",
       "  frozenset({7, 50, 64, 79, 100, 127}): 66,\n",
       "  frozenset({7, 50, 64, 79, 100, 172}): 72,\n",
       "  frozenset({7, 50, 64, 79, 100, 174}): 84,\n",
       "  frozenset({7, 50, 64, 79, 100, 181}): 78,\n",
       "  frozenset({7, 50, 64, 79, 127, 174}): 72,\n",
       "  frozenset({7, 50, 64, 79, 172, 174}): 102,\n",
       "  frozenset({7, 50, 64, 79, 172, 181}): 96,\n",
       "  frozenset({7, 50, 64, 79, 174, 181}): 102,\n",
       "  frozenset({7, 50, 64, 98, 100, 127}): 78,\n",
       "  frozenset({7, 50, 64, 98, 100, 172}): 78,\n",
       "  frozenset({7, 50, 64, 98, 100, 174}): 96,\n",
       "  frozenset({7, 50, 64, 98, 100, 181}): 72,\n",
       "  frozenset({7, 50, 64, 98, 127, 172}): 72,\n",
       "  frozenset({7, 50, 64, 98, 127, 174}): 90,\n",
       "  frozenset({7, 50, 64, 98, 172, 174}): 114,\n",
       "  frozenset({7, 50, 64, 98, 172, 181}): 102,\n",
       "  frozenset({7, 50, 64, 98, 172, 258}): 78,\n",
       "  frozenset({7, 50, 64, 98, 174, 181}): 108,\n",
       "  frozenset({7, 50, 64, 98, 174, 258}): 78,\n",
       "  frozenset({7, 50, 64, 98, 181, 258}): 72,\n",
       "  frozenset({7, 50, 64, 100, 127, 172}): 66,\n",
       "  frozenset({7, 50, 64, 100, 127, 174}): 84,\n",
       "  frozenset({7, 50, 64, 100, 172, 174}): 96,\n",
       "  frozenset({7, 50, 64, 100, 172, 181}): 84,\n",
       "  frozenset({7, 50, 64, 100, 174, 181}): 90,\n",
       "  frozenset({7, 50, 64, 127, 172, 174}): 78,\n",
       "  frozenset({7, 50, 64, 172, 174, 181}): 120,\n",
       "  frozenset({7, 50, 64, 172, 174, 258}): 84,\n",
       "  frozenset({7, 50, 64, 172, 181, 258}): 78,\n",
       "  frozenset({7, 50, 64, 174, 181, 258}): 78,\n",
       "  frozenset({7, 50, 79, 98, 100, 127}): 60,\n",
       "  frozenset({7, 50, 79, 98, 100, 172}): 84,\n",
       "  frozenset({7, 50, 79, 98, 100, 174}): 102,\n",
       "  frozenset({7, 50, 79, 98, 100, 181}): 84,\n",
       "  frozenset({7, 50, 79, 98, 100, 258}): 72,\n",
       "  frozenset({7, 50, 79, 98, 127, 174}): 66,\n",
       "  frozenset({7, 50, 79, 98, 172, 174}): 120,\n",
       "  frozenset({7, 50, 79, 98, 172, 181}): 108,\n",
       "  frozenset({7, 50, 79, 98, 172, 258}): 84,\n",
       "  frozenset({7, 50, 79, 98, 174, 181}): 120,\n",
       "  frozenset({7, 50, 79, 98, 174, 258}): 96,\n",
       "  frozenset({7, 50, 79, 98, 181, 258}): 84,\n",
       "  frozenset({7, 50, 79, 100, 127, 174}): 78,\n",
       "  frozenset({7, 50, 79, 100, 172, 174}): 102,\n",
       "  frozenset({7, 50, 79, 100, 172, 181}): 90,\n",
       "  frozenset({7, 50, 79, 100, 174, 181}): 96,\n",
       "  frozenset({7, 50, 79, 100, 174, 258}): 72,\n",
       "  frozenset({7, 50, 79, 127, 172, 174}): 78,\n",
       "  frozenset({7, 50, 79, 172, 174, 181}): 120,\n",
       "  frozenset({7, 50, 79, 172, 174, 258}): 84,\n",
       "  frozenset({7, 50, 79, 172, 181, 258}): 78,\n",
       "  frozenset({7, 50, 79, 174, 181, 258}): 84,\n",
       "  frozenset({7, 50, 98, 100, 127, 172}): 60,\n",
       "  frozenset({7, 50, 98, 100, 127, 174}): 78,\n",
       "  frozenset({7, 50, 98, 100, 172, 174}): 96,\n",
       "  frozenset({7, 50, 98, 100, 172, 181}): 84,\n",
       "  frozenset({7, 50, 98, 100, 174, 181}): 90,\n",
       "  frozenset({7, 50, 98, 100, 174, 258}): 78,\n",
       "  frozenset({7, 50, 98, 100, 181, 258}): 66,\n",
       "  frozenset({7, 50, 98, 127, 172, 174}): 72,\n",
       "  frozenset({7, 50, 98, 172, 174, 181}): 120,\n",
       "  frozenset({7, 50, 98, 172, 174, 258}): 96,\n",
       "  frozenset({7, 50, 98, 172, 181, 258}): 90,\n",
       "  frozenset({7, 50, 98, 174, 181, 258}): 96,\n",
       "  frozenset({7, 50, 100, 127, 172, 174}): 78,\n",
       "  frozenset({7, 50, 100, 172, 174, 181}): 114,\n",
       "  frozenset({7, 50, 100, 174, 181, 258}): 72,\n",
       "  frozenset({7, 50, 172, 174, 181, 258}): 96,\n",
       "  frozenset({7, 56, 64, 79, 98, 100}): 90,\n",
       "  frozenset({7, 56, 64, 79, 98, 127}): 72,\n",
       "  frozenset({7, 56, 64, 79, 98, 172}): 96,\n",
       "  frozenset({7, 56, 64, 79, 98, 174}): 108,\n",
       "  frozenset({7, 56, 64, 79, 98, 181}): 90,\n",
       "  frozenset({7, 56, 64, 79, 98, 258}): 72,\n",
       "  frozenset({7, 56, 64, 79, 100, 127}): 78,\n",
       "  frozenset({7, 56, 64, 79, 100, 172}): 78,\n",
       "  frozenset({7, 56, 64, 79, 100, 174}): 90,\n",
       "  frozenset({7, 56, 64, 79, 100, 181}): 72,\n",
       "  frozenset({7, 56, 64, 79, 127, 174}): 72,\n",
       "  frozenset({7, 56, 64, 79, 172, 174}): 102,\n",
       "  frozenset({7, 56, 64, 79, 172, 181}): 90,\n",
       "  frozenset({7, 56, 64, 79, 174, 181}): 96,\n",
       "  frozenset({7, 56, 64, 98, 100, 127}): 90,\n",
       "  frozenset({7, 56, 64, 98, 100, 172}): 90,\n",
       "  frozenset({7, 56, 64, 98, 100, 174}): 102,\n",
       "  frozenset({7, 56, 64, 98, 100, 181}): 72,\n",
       "  frozenset({7, 56, 64, 98, 127, 172}): 72,\n",
       "  frozenset({7, 56, 64, 98, 127, 174}): 90,\n",
       "  frozenset({7, 56, 64, 98, 172, 174}): 114,\n",
       "  frozenset({7, 56, 64, 98, 172, 181}): 96,\n",
       "  frozenset({7, 56, 64, 98, 172, 258}): 78,\n",
       "  frozenset({7, 56, 64, 98, 174, 181}): 102,\n",
       "  frozenset({7, 56, 64, 98, 174, 258}): 78,\n",
       "  frozenset({7, 56, 64, 98, 181, 258}): 72,\n",
       "  frozenset({7, 56, 64, 100, 127, 172}): 72,\n",
       "  frozenset({7, 56, 64, 100, 127, 174}): 90,\n",
       "  frozenset({7, 56, 64, 100, 172, 174}): 96,\n",
       "  frozenset({7, 56, 64, 100, 172, 181}): 78,\n",
       "  frozenset({7, 56, 64, 100, 174, 181}): 84,\n",
       "  frozenset({7, 56, 64, 127, 172, 174}): 78,\n",
       "  frozenset({7, 56, 64, 172, 174, 181}): 108,\n",
       "  frozenset({7, 56, 64, 172, 174, 258}): 78,\n",
       "  frozenset({7, 56, 64, 172, 181, 258}): 72,\n",
       "  frozenset({7, 56, 64, 174, 181, 258}): 72,\n",
       "  frozenset({7, 56, 79, 98, 100, 127}): 72,\n",
       "  frozenset({7, 56, 79, 98, 100, 172}): 96,\n",
       "  frozenset({7, 56, 79, 98, 100, 174}): 114,\n",
       "  frozenset({7, 56, 79, 98, 100, 181}): 84,\n",
       "  frozenset({7, 56, 79, 98, 100, 258}): 84,\n",
       "  frozenset({7, 56, 79, 98, 127, 174}): 66,\n",
       "  frozenset({7, 56, 79, 98, 172, 174}): 120,\n",
       "  frozenset({7, 56, 79, 98, 172, 181}): 102,\n",
       "  frozenset({7, 56, 79, 98, 172, 258}): 90,\n",
       "  frozenset({7, 56, 79, 98, 174, 181}): 108,\n",
       "  frozenset({7, 56, 79, 98, 174, 258}): 96,\n",
       "  frozenset({7, 56, 79, 98, 181, 258}): 78,\n",
       "  frozenset({7, 56, 79, 100, 127, 174}): 84,\n",
       "  frozenset({7, 56, 79, 100, 172, 174}): 114,\n",
       "  frozenset({7, 56, 79, 100, 172, 181}): 90,\n",
       "  frozenset({7, 56, 79, 100, 174, 181}): 96,\n",
       "  frozenset({7, 56, 79, 100, 174, 258}): 78,\n",
       "  frozenset({7, 56, 79, 127, 172, 174}): 78,\n",
       "  frozenset({7, 56, 79, 172, 174, 181}): 114,\n",
       "  frozenset({7, 56, 79, 172, 174, 258}): 90,\n",
       "  frozenset({7, 56, 79, 172, 181, 258}): 78,\n",
       "  frozenset({7, 56, 79, 174, 181, 258}): 78,\n",
       "  frozenset({7, 56, 98, 100, 127, 172}): 66,\n",
       "  frozenset({7, 56, 98, 100, 127, 174}): 84,\n",
       "  frozenset({7, 56, 98, 100, 172, 174}): 108,\n",
       "  frozenset({7, 56, 98, 100, 172, 181}): 84,\n",
       "  frozenset({7, 56, 98, 100, 174, 181}): 90,\n",
       "  frozenset({7, 56, 98, 100, 174, 258}): 84,\n",
       "  frozenset({7, 56, 98, 100, 181, 258}): 66,\n",
       "  frozenset({7, 56, 98, 127, 172, 174}): 72,\n",
       "  frozenset({7, 56, 98, 172, 174, 181}): 114,\n",
       "  frozenset({7, 56, 98, 172, 174, 258}): 102,\n",
       "  frozenset({7, 56, 98, 172, 181, 258}): 90,\n",
       "  frozenset({7, 56, 98, 174, 181, 258}): 90,\n",
       "  frozenset({7, 56, 100, 127, 172, 174}): 84,\n",
       "  frozenset({7, 56, 100, 172, 174, 181}): 108,\n",
       "  frozenset({7, 56, 100, 174, 181, 258}): 66,\n",
       "  frozenset({7, 56, 172, 174, 181, 258}): 90,\n",
       "  frozenset({7, 64, 79, 98, 100, 127}): 72,\n",
       "  frozenset({7, 64, 79, 98, 100, 172}): 72,\n",
       "  frozenset({7, 64, 79, 98, 100, 174}): 84,\n",
       "  frozenset({7, 64, 79, 98, 100, 181}): 66,\n",
       "  frozenset({7, 64, 79, 98, 127, 174}): 72,\n",
       "  frozenset({7, 64, 79, 98, 172, 174}): 102,\n",
       "  frozenset({7, 64, 79, 98, 172, 181}): 90,\n",
       "  frozenset({7, 64, 79, 98, 174, 181}): 96,\n",
       "  frozenset({7, 64, 79, 100, 127, 174}): 72,\n",
       "  frozenset({7, 64, 79, 100, 172, 174}): 78,\n",
       "  frozenset({7, 64, 79, 100, 172, 181}): 66,\n",
       "  frozenset({7, 64, 79, 100, 174, 181}): 72,\n",
       "  frozenset({7, 64, 79, 172, 174, 181}): 96,\n",
       "  frozenset({7, 64, 98, 100, 127, 172}): 66,\n",
       "  frozenset({7, 64, 98, 100, 127, 174}): 84,\n",
       "  frozenset({7, 64, 98, 100, 172, 174}): 84,\n",
       "  frozenset({7, 64, 98, 100, 172, 181}): 66,\n",
       "  frozenset({7, 64, 98, 100, 174, 181}): 72,\n",
       "  frozenset({7, 64, 98, 127, 172, 174}): 78,\n",
       "  frozenset({7, 64, 98, 172, 174, 181}): 102,\n",
       "  frozenset({7, 64, 98, 172, 174, 258}): 78,\n",
       "  frozenset({7, 64, 98, 172, 181, 258}): 72,\n",
       "  frozenset({7, 64, 98, 174, 181, 258}): 72,\n",
       "  frozenset({7, 64, 100, 127, 172, 174}): 72,\n",
       "  frozenset({7, 64, 100, 172, 174, 181}): 84,\n",
       "  frozenset({7, 64, 172, 174, 181, 258}): 78,\n",
       "  frozenset({7, 79, 98, 100, 127, 174}): 66,\n",
       "  frozenset({7, 79, 98, 100, 172, 174}): 96,\n",
       "  frozenset({7, 79, 98, 100, 172, 181}): 78,\n",
       "  frozenset({7, 79, 98, 100, 174, 181}): 84,\n",
       "  frozenset({7, 79, 98, 100, 174, 258}): 78,\n",
       "  frozenset({7, 79, 98, 172, 174, 181}): 108,\n",
       "  frozenset({7, 79, 98, 172, 174, 258}): 90,\n",
       "  frozenset({7, 79, 98, 172, 181, 258}): 78,\n",
       "  frozenset({7, 79, 98, 174, 181, 258}): 84,\n",
       "  frozenset({7, 79, 100, 172, 174, 181}): 90,\n",
       "  frozenset({7, 79, 172, 174, 181, 258}): 78,\n",
       "  frozenset({7, 98, 100, 127, 172, 174}): 66,\n",
       "  frozenset({7, 98, 100, 172, 174, 181}): 84,\n",
       "  frozenset({7, 98, 100, 174, 181, 258}): 66,\n",
       "  frozenset({7, 98, 172, 174, 181, 258}): 90,\n",
       "  frozenset({9, 50, 56, 64, 98, 100}): 78,\n",
       "  frozenset({9, 50, 56, 64, 98, 127}): 78,\n",
       "  frozenset({9, 50, 56, 64, 98, 174}): 96,\n",
       "  frozenset({9, 50, 56, 64, 100, 127}): 78,\n",
       "  frozenset({9, 50, 56, 64, 100, 174}): 90,\n",
       "  frozenset({9, 50, 56, 64, 127, 174}): 84,\n",
       "  frozenset({9, 50, 56, 98, 100, 127}): 72,\n",
       "  frozenset({9, 50, 56, 98, 100, 174}): 84,\n",
       "  frozenset({9, 50, 56, 98, 127, 174}): 78,\n",
       "  frozenset({9, 50, 56, 100, 127, 174}): 84,\n",
       "  frozenset({9, 50, 64, 98, 100, 127}): 78,\n",
       "  frozenset({9, 50, 64, 98, 100, 174}): 78,\n",
       "  frozenset({9, 50, 64, 98, 127, 174}): 78,\n",
       "  frozenset({9, 50, 64, 100, 127, 174}): 78,\n",
       "  frozenset({9, 50, 98, 100, 127, 174}): 72,\n",
       "  frozenset({9, 56, 64, 98, 100, 127}): 102,\n",
       "  frozenset({9, 56, 64, 98, 100, 174}): 102,\n",
       "  frozenset({9, 56, 64, 98, 127, 174}): 102,\n",
       "  frozenset({9, 56, 64, 100, 127, 174}): 102,\n",
       "  frozenset({9, 56, 98, 100, 127, 174}): 96,\n",
       "  frozenset({9, 64, 98, 100, 127, 174}): 96,\n",
       "  frozenset({50, 56, 64, 79, 98, 100}): 84,\n",
       "  frozenset({50, 56, 64, 79, 98, 127}): 66,\n",
       "  frozenset({50, 56, 64, 79, 98, 172}): 90,\n",
       "  frozenset({50, 56, 64, 79, 98, 174}): 108,\n",
       "  frozenset({50, 56, 64, 79, 98, 181}): 90,\n",
       "  frozenset({50, 56, 64, 79, 98, 258}): 66,\n",
       "  frozenset({50, 56, 64, 79, 100, 127}): 72,\n",
       "  frozenset({50, 56, 64, 79, 100, 172}): 72,\n",
       "  frozenset({50, 56, 64, 79, 100, 174}): 90,\n",
       "  frozenset({50, 56, 64, 79, 100, 181}): 72,\n",
       "  frozenset({50, 56, 64, 79, 127, 174}): 72,\n",
       "  frozenset({50, 56, 64, 79, 172, 174}): 96,\n",
       "  frozenset({50, 56, 64, 79, 172, 181}): 90,\n",
       "  frozenset({50, 56, 64, 79, 174, 181}): 96,\n",
       "  frozenset({50, 56, 64, 98, 100, 127}): 102,\n",
       "  frozenset({50, 56, 64, 98, 100, 172}): 90,\n",
       "  frozenset({50, 56, 64, 98, 100, 174}): 120,\n",
       "  frozenset({50, 56, 64, 98, 100, 181}): 84,\n",
       "  frozenset({50, 56, 64, 98, 127, 172}): 84,\n",
       "  frozenset({50, 56, 64, 98, 127, 174}): 114,\n",
       "  frozenset({50, 56, 64, 98, 127, 181}): 78,\n",
       "  frozenset({50, 56, 64, 98, 172, 174}): 126,\n",
       "  frozenset({50, 56, 64, 98, 172, 181}): 114,\n",
       "  frozenset({50, 56, 64, 98, 172, 258}): 96,\n",
       "  frozenset({50, 56, 64, 98, 174, 181}): 120,\n",
       "  frozenset({50, 56, 64, 98, 174, 258}): 96,\n",
       "  frozenset({50, 56, 64, 98, 181, 258}): 90,\n",
       "  frozenset({50, 56, 64, 100, 127, 172}): 78,\n",
       "  frozenset({50, 56, 64, 100, 127, 174}): 108,\n",
       "  frozenset({50, 56, 64, 100, 127, 181}): 72,\n",
       "  frozenset({50, 56, 64, 100, 172, 174}): 102,\n",
       "  frozenset({50, 56, 64, 100, 172, 181}): 90,\n",
       "  frozenset({50, 56, 64, 100, 174, 181}): 96,\n",
       "  frozenset({50, 56, 64, 127, 172, 174}): 90,\n",
       "  frozenset({50, 56, 64, 127, 172, 181}): 78,\n",
       "  frozenset({50, 56, 64, 127, 174, 181}): 84,\n",
       "  frozenset({50, 56, 64, 172, 174, 181}): 126,\n",
       "  frozenset({50, 56, 64, 172, 174, 258}): 96,\n",
       "  frozenset({50, 56, 64, 172, 181, 258}): 90,\n",
       "  frozenset({50, 56, 64, 174, 181, 258}): 90,\n",
       "  frozenset({50, 56, 79, 98, 100, 127}): 66,\n",
       "  frozenset({50, 56, 79, 98, 100, 172}): 84,\n",
       "  frozenset({50, 56, 79, 98, 100, 174}): 108,\n",
       "  frozenset({50, 56, 79, 98, 100, 181}): 84,\n",
       "  frozenset({50, 56, 79, 98, 100, 258}): 72,\n",
       "  frozenset({50, 56, 79, 98, 127, 174}): 66,\n",
       "  frozenset({50, 56, 79, 98, 172, 174}): 108,\n",
       "  frozenset({50, 56, 79, 98, 172, 181}): 102,\n",
       "  frozenset({50, 56, 79, 98, 172, 258}): 84,\n",
       "  frozenset({50, 56, 79, 98, 174, 181}): 108,\n",
       "  frozenset({50, 56, 79, 98, 174, 258}): 90,\n",
       "  frozenset({50, 56, 79, 98, 181, 258}): 78,\n",
       "  frozenset({50, 56, 79, 100, 127, 174}): 90,\n",
       "  frozenset({50, 56, 79, 100, 172, 174}): 102,\n",
       "  frozenset({50, 56, 79, 100, 172, 181}): 90,\n",
       "  frozenset({50, 56, 79, 100, 174, 181}): 96,\n",
       "  frozenset({50, 56, 79, 100, 174, 258}): 72,\n",
       "  frozenset({50, 56, 79, 127, 172, 174}): 78,\n",
       "  frozenset({50, 56, 79, 172, 174, 181}): 120,\n",
       "  frozenset({50, 56, 79, 172, 174, 258}): 90,\n",
       "  frozenset({50, 56, 79, 172, 181, 258}): 84,\n",
       "  frozenset({50, 56, 79, 174, 181, 258}): 84,\n",
       "  frozenset({50, 56, 98, 100, 127, 172}): 72,\n",
       "  frozenset({50, 56, 98, 100, 127, 174}): 102,\n",
       "  frozenset({50, 56, 98, 100, 127, 181}): 66,\n",
       "  frozenset({50, 56, 98, 100, 172, 174}): 108,\n",
       "  frozenset({50, 56, 98, 100, 172, 181}): 96,\n",
       "  frozenset({50, 56, 98, 100, 174, 181}): 108,\n",
       "  frozenset({50, 56, 98, 100, 174, 258}): 90,\n",
       "  frozenset({50, 56, 98, 100, 181, 258}): 78,\n",
       "  frozenset({50, 56, 98, 127, 172, 174}): 84,\n",
       "  frozenset({50, 56, 98, 127, 172, 181}): 72,\n",
       "  frozenset({50, 56, 98, 127, 174, 181}): 78,\n",
       "  frozenset({50, 56, 98, 172, 174, 181}): 138,\n",
       "  frozenset({50, 56, 98, 172, 174, 258}): 120,\n",
       "  frozenset({50, 56, 98, 172, 181, 258}): 114,\n",
       "  frozenset({50, 56, 98, 174, 181, 258}): 114,\n",
       "  frozenset({50, 56, 100, 127, 172, 174}): 96,\n",
       "  frozenset({50, 56, 100, 127, 172, 181}): 72,\n",
       "  frozenset({50, 56, 100, 127, 174, 181}): 78,\n",
       "  frozenset({50, 56, 100, 172, 174, 181}): 120,\n",
       "  frozenset({50, 56, 100, 174, 181, 258}): 78,\n",
       "  frozenset({50, 56, 127, 172, 174, 181}): 90,\n",
       "  frozenset({50, 56, 172, 174, 181, 258}): 120,\n",
       "  frozenset({50, 64, 79, 98, 100, 127}): 66,\n",
       "  frozenset({50, 64, 79, 98, 100, 172}): 66,\n",
       "  frozenset({50, 64, 79, 98, 100, 174}): 84,\n",
       "  frozenset({50, 64, 79, 98, 100, 181}): 66,\n",
       "  frozenset({50, 64, 79, 98, 127, 174}): 78,\n",
       "  frozenset({50, 64, 79, 98, 172, 174}): 114,\n",
       "  frozenset({50, 64, 79, 98, 172, 181}): 108,\n",
       "  frozenset({50, 64, 79, 98, 174, 181}): 114,\n",
       "  frozenset({50, 64, 79, 100, 127, 174}): 72,\n",
       "  frozenset({50, 64, 79, 100, 172, 174}): 72,\n",
       "  frozenset({50, 64, 79, 100, 172, 181}): 66,\n",
       "  frozenset({50, 64, 79, 100, 174, 181}): 72,\n",
       "  frozenset({50, 64, 79, 172, 174, 181}): 114,\n",
       "  frozenset({50, 64, 98, 100, 127, 172}): 78,\n",
       "  frozenset({50, 64, 98, 100, 127, 174}): 102,\n",
       "  frozenset({50, 64, 98, 100, 127, 181}): 72,\n",
       "  frozenset({50, 64, 98, 100, 172, 174}): 90,\n",
       "  frozenset({50, 64, 98, 100, 172, 181}): 84,\n",
       "  frozenset({50, 64, 98, 100, 174, 181}): 84,\n",
       "  frozenset({50, 64, 98, 127, 172, 174}): 96,\n",
       "  frozenset({50, 64, 98, 127, 172, 181}): 90,\n",
       "  frozenset({50, 64, 98, 127, 174, 181}): 90,\n",
       "  frozenset({50, 64, 98, 172, 174, 181}): 138,\n",
       "  frozenset({50, 64, 98, 172, 174, 258}): 102,\n",
       "  frozenset({50, 64, 98, 172, 181, 258}): 96,\n",
       "  frozenset({50, 64, 98, 174, 181, 258}): 96,\n",
       "  frozenset({50, 64, 100, 127, 172, 174}): 78,\n",
       "  frozenset({50, 64, 100, 127, 172, 181}): 72,\n",
       "  frozenset({50, 64, 100, 127, 174, 181}): 72,\n",
       "  frozenset({50, 64, 100, 172, 174, 181}): 96,\n",
       "  frozenset({50, 64, 127, 172, 174, 181}): 90,\n",
       "  frozenset({50, 64, 172, 174, 181, 258}): 102,\n",
       "  frozenset({50, 79, 98, 100, 127, 174}): 66,\n",
       "  frozenset({50, 79, 98, 100, 172, 174}): 84,\n",
       "  frozenset({50, 79, 98, 100, 172, 181}): 78,\n",
       "  frozenset({50, 79, 98, 100, 174, 181}): 84,\n",
       "  frozenset({50, 79, 98, 100, 174, 258}): 72,\n",
       "  frozenset({50, 79, 98, 172, 174, 181}): 126,\n",
       "  frozenset({50, 79, 98, 172, 174, 258}): 90,\n",
       "  frozenset({50, 79, 98, 172, 181, 258}): 84,\n",
       "  frozenset({50, 79, 98, 174, 181, 258}): 90,\n",
       "  frozenset({50, 79, 100, 172, 174, 181}): 90,\n",
       "  frozenset({50, 79, 172, 174, 181, 258}): 102,\n",
       "  frozenset({50, 98, 100, 127, 172, 174}): 72,\n",
       "  frozenset({50, 98, 100, 127, 172, 181}): 72,\n",
       "  frozenset({50, 98, 100, 127, 174, 181}): 66,\n",
       "  frozenset({50, 98, 100, 172, 174, 181}): 96,\n",
       "  frozenset({50, 98, 100, 174, 181, 258}): 78,\n",
       "  frozenset({50, 98, 127, 172, 174, 181}): 84,\n",
       "  frozenset({50, 98, 172, 174, 181, 258}): 120,\n",
       "  frozenset({50, 100, 127, 172, 174, 181}): 72,\n",
       "  frozenset({56, 64, 79, 98, 100, 127}): 90,\n",
       "  frozenset({56, 64, 79, 98, 100, 172}): 72,\n",
       "  frozenset({56, 64, 79, 98, 100, 174}): 102,\n",
       "  frozenset({56, 64, 79, 98, 100, 181}): 66,\n",
       "  frozenset({56, 64, 79, 98, 127, 174}): 84,\n",
       "  frozenset({56, 64, 79, 98, 172, 174}): 96,\n",
       "  frozenset({56, 64, 79, 98, 172, 181}): 84,\n",
       "  frozenset({56, 64, 79, 98, 174, 181}): 90,\n",
       "  frozenset({56, 64, 79, 100, 127, 174}): 90,\n",
       "  frozenset({56, 64, 79, 100, 172, 174}): 78,\n",
       "  frozenset({56, 64, 79, 100, 172, 181}): 66,\n",
       "  frozenset({56, 64, 79, 100, 174, 181}): 72,\n",
       "  frozenset({56, 64, 79, 172, 174, 181}): 90,\n",
       "  frozenset({56, 64, 98, 100, 127, 172}): 78,\n",
       "  frozenset({56, 64, 98, 100, 127, 174}): 126,\n",
       "  frozenset({56, 64, 98, 100, 127, 181}): 66,\n",
       "  frozenset({56, 64, 98, 100, 172, 174}): 96,\n",
       "  frozenset({56, 64, 98, 100, 172, 181}): 78,\n",
       "  frozenset({56, 64, 98, 100, 174, 181}): 84,\n",
       "  frozenset({56, 64, 98, 127, 172, 174}): 90,\n",
       "  frozenset({56, 64, 98, 127, 172, 181}): 72,\n",
       "  frozenset({56, 64, 98, 127, 174, 181}): 78,\n",
       "  frozenset({56, 64, 98, 172, 174, 181}): 114,\n",
       "  frozenset({56, 64, 98, 172, 174, 258}): 96,\n",
       "  frozenset({56, 64, 98, 172, 181, 258}): 90,\n",
       "  frozenset({56, 64, 98, 174, 181, 258}): 90,\n",
       "  frozenset({56, 64, 100, 127, 172, 174}): 84,\n",
       "  frozenset({56, 64, 100, 127, 172, 181}): 66,\n",
       "  frozenset({56, 64, 100, 127, 174, 181}): 72,\n",
       "  frozenset({56, 64, 100, 172, 174, 181}): 90,\n",
       "  frozenset({56, 64, 127, 172, 174, 181}): 78,\n",
       "  frozenset({56, 64, 172, 174, 181, 258}): 90,\n",
       "  frozenset({56, 79, 98, 100, 127, 174}): 84,\n",
       "  frozenset({56, 79, 98, 100, 172, 174}): 96,\n",
       "  frozenset({56, 79, 98, 100, 172, 181}): 78,\n",
       "  frozenset({56, 79, 98, 100, 174, 181}): 84,\n",
       "  frozenset({56, 79, 98, 100, 174, 258}): 78,\n",
       "  frozenset({56, 79, 98, 172, 174, 181}): 102,\n",
       "  frozenset({56, 79, 98, 172, 174, 258}): 90,\n",
       "  frozenset({56, 79, 98, 172, 181, 258}): 78,\n",
       "  frozenset({56, 79, 98, 174, 181, 258}): 78,\n",
       "  frozenset({56, 79, 100, 172, 174, 181}): 90,\n",
       "  frozenset({56, 79, 172, 174, 181, 258}): 84,\n",
       "  frozenset({56, 98, 100, 127, 172, 174}): 78,\n",
       "  frozenset({56, 98, 100, 127, 172, 181}): 60,\n",
       "  frozenset({56, 98, 100, 127, 174, 181}): 66,\n",
       "  frozenset({56, 98, 100, 172, 174, 181}): 96,\n",
       "  frozenset({56, 98, 100, 174, 181, 258}): 78,\n",
       "  frozenset({56, 98, 127, 172, 174, 181}): 72,\n",
       "  frozenset({56, 98, 172, 174, 181, 258}): 114,\n",
       "  frozenset({56, 100, 127, 172, 174, 181}): 72,\n",
       "  frozenset({64, 79, 98, 100, 127, 174}): 84,\n",
       "  frozenset({64, 79, 98, 100, 172, 174}): 72,\n",
       "  frozenset({64, 79, 98, 100, 172, 181}): 60,\n",
       "  frozenset({64, 79, 98, 100, 174, 181}): 66,\n",
       "  frozenset({64, 79, 98, 172, 174, 181}): 108,\n",
       "  frozenset({64, 79, 100, 172, 174, 181}): 66,\n",
       "  frozenset({64, 98, 100, 127, 172, 174}): 78,\n",
       "  frozenset({64, 98, 100, 127, 172, 181}): 66,\n",
       "  frozenset({64, 98, 100, 127, 174, 181}): 66,\n",
       "  frozenset({64, 98, 100, 172, 174, 181}): 78,\n",
       "  frozenset({64, 98, 127, 172, 174, 181}): 84,\n",
       "  frozenset({64, 98, 172, 174, 181, 258}): 96,\n",
       "  frozenset({64, 100, 127, 172, 174, 181}): 66,\n",
       "  frozenset({79, 98, 100, 172, 174, 181}): 78,\n",
       "  frozenset({79, 98, 172, 174, 181, 258}): 84,\n",
       "  frozenset({98, 100, 127, 172, 174, 181}): 60},\n",
       " 7: {frozenset({1, 7, 50, 56, 64, 79, 98}): 77,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 172}): 70,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 174}): 77,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 181}): 77,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 100}): 70,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 172}): 84,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 174}): 98,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 181}): 84,\n",
       "  frozenset({1, 7, 50, 56, 64, 100, 174}): 70,\n",
       "  frozenset({1, 7, 50, 56, 64, 172, 174}): 84,\n",
       "  frozenset({1, 7, 50, 56, 64, 172, 181}): 77,\n",
       "  frozenset({1, 7, 50, 56, 64, 174, 181}): 84,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 100}): 70,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 172}): 84,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 174}): 91,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 181}): 91,\n",
       "  frozenset({1, 7, 50, 56, 79, 100, 174}): 77,\n",
       "  frozenset({1, 7, 50, 56, 79, 172, 174}): 91,\n",
       "  frozenset({1, 7, 50, 56, 79, 172, 181}): 84,\n",
       "  frozenset({1, 7, 50, 56, 79, 174, 181}): 91,\n",
       "  frozenset({1, 7, 50, 56, 98, 100, 172}): 70,\n",
       "  frozenset({1, 7, 50, 56, 98, 100, 174}): 84,\n",
       "  frozenset({1, 7, 50, 56, 98, 172, 174}): 98,\n",
       "  frozenset({1, 7, 50, 56, 98, 172, 181}): 91,\n",
       "  frozenset({1, 7, 50, 56, 98, 174, 181}): 98,\n",
       "  frozenset({1, 7, 50, 56, 100, 172, 174}): 77,\n",
       "  frozenset({1, 7, 50, 56, 172, 174, 181}): 98,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 172}): 77,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 174}): 84,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 181}): 84,\n",
       "  frozenset({1, 7, 50, 64, 79, 172, 174}): 77,\n",
       "  frozenset({1, 7, 50, 64, 79, 172, 181}): 77,\n",
       "  frozenset({1, 7, 50, 64, 79, 174, 181}): 84,\n",
       "  frozenset({1, 7, 50, 64, 98, 100, 174}): 70,\n",
       "  frozenset({1, 7, 50, 64, 98, 172, 174}): 91,\n",
       "  frozenset({1, 7, 50, 64, 98, 172, 181}): 84,\n",
       "  frozenset({1, 7, 50, 64, 98, 174, 181}): 91,\n",
       "  frozenset({1, 7, 50, 64, 100, 174, 181}): 63,\n",
       "  frozenset({1, 7, 50, 64, 172, 174, 181}): 91,\n",
       "  frozenset({1, 7, 50, 79, 98, 100, 174}): 70,\n",
       "  frozenset({1, 7, 50, 79, 98, 172, 174}): 98,\n",
       "  frozenset({1, 7, 50, 79, 98, 172, 181}): 91,\n",
       "  frozenset({1, 7, 50, 79, 98, 174, 181}): 105,\n",
       "  frozenset({1, 7, 50, 79, 172, 174, 181}): 91,\n",
       "  frozenset({1, 7, 50, 98, 100, 172, 174}): 70,\n",
       "  frozenset({1, 7, 50, 98, 100, 172, 181}): 63,\n",
       "  frozenset({1, 7, 50, 98, 100, 174, 181}): 70,\n",
       "  frozenset({1, 7, 50, 98, 172, 174, 181}): 98,\n",
       "  frozenset({1, 7, 50, 100, 172, 174, 181}): 70,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 172}): 77,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 174}): 84,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 181}): 77,\n",
       "  frozenset({1, 7, 56, 64, 79, 172, 174}): 77,\n",
       "  frozenset({1, 7, 56, 64, 79, 172, 181}): 70,\n",
       "  frozenset({1, 7, 56, 64, 79, 174, 181}): 77,\n",
       "  frozenset({1, 7, 56, 64, 98, 100, 174}): 77,\n",
       "  frozenset({1, 7, 56, 64, 98, 172, 174}): 91,\n",
       "  frozenset({1, 7, 56, 64, 98, 172, 181}): 77,\n",
       "  frozenset({1, 7, 56, 64, 98, 174, 181}): 84,\n",
       "  frozenset({1, 7, 56, 64, 172, 174, 181}): 77,\n",
       "  frozenset({1, 7, 56, 79, 98, 100, 174}): 77,\n",
       "  frozenset({1, 7, 56, 79, 98, 172, 174}): 91,\n",
       "  frozenset({1, 7, 56, 79, 98, 172, 181}): 84,\n",
       "  frozenset({1, 7, 56, 79, 98, 174, 181}): 91,\n",
       "  frozenset({1, 7, 56, 79, 172, 174, 181}): 84,\n",
       "  frozenset({1, 7, 56, 98, 100, 172, 174}): 77,\n",
       "  frozenset({1, 7, 56, 98, 172, 174, 181}): 91,\n",
       "  frozenset({1, 7, 64, 79, 98, 172, 174}): 84,\n",
       "  frozenset({1, 7, 64, 79, 98, 172, 181}): 77,\n",
       "  frozenset({1, 7, 64, 79, 98, 174, 181}): 84,\n",
       "  frozenset({1, 7, 64, 79, 172, 174, 181}): 77,\n",
       "  frozenset({1, 7, 64, 98, 172, 174, 181}): 84,\n",
       "  frozenset({1, 7, 79, 98, 172, 174, 181}): 91,\n",
       "  frozenset({1, 7, 98, 100, 172, 174, 181}): 63,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 172}): 70,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 174}): 84,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 181}): 77,\n",
       "  frozenset({1, 50, 56, 64, 79, 172, 174}): 70,\n",
       "  frozenset({1, 50, 56, 64, 79, 172, 181}): 70,\n",
       "  frozenset({1, 50, 56, 64, 79, 174, 181}): 77,\n",
       "  frozenset({1, 50, 56, 64, 98, 100, 127}): 77,\n",
       "  frozenset({1, 50, 56, 64, 98, 100, 174}): 91,\n",
       "  frozenset({1, 50, 56, 64, 98, 127, 174}): 84,\n",
       "  frozenset({1, 50, 56, 64, 98, 172, 174}): 91,\n",
       "  frozenset({1, 50, 56, 64, 98, 172, 181}): 84,\n",
       "  frozenset({1, 50, 56, 64, 98, 174, 181}): 91,\n",
       "  frozenset({1, 50, 56, 64, 100, 127, 174}): 77,\n",
       "  frozenset({1, 50, 56, 64, 172, 174, 181}): 84,\n",
       "  frozenset({1, 50, 56, 79, 98, 100, 174}): 77,\n",
       "  frozenset({1, 50, 56, 79, 98, 172, 174}): 84,\n",
       "  frozenset({1, 50, 56, 79, 98, 172, 181}): 84,\n",
       "  frozenset({1, 50, 56, 79, 98, 174, 181}): 91,\n",
       "  frozenset({1, 50, 56, 79, 172, 174, 181}): 84,\n",
       "  frozenset({1, 50, 56, 98, 100, 127, 174}): 77,\n",
       "  frozenset({1, 50, 56, 98, 100, 172, 174}): 77,\n",
       "  frozenset({1, 50, 56, 98, 172, 174, 181}): 105,\n",
       "  frozenset({1, 50, 64, 79, 98, 172, 174}): 91,\n",
       "  frozenset({1, 50, 64, 79, 98, 172, 181}): 91,\n",
       "  frozenset({1, 50, 64, 79, 98, 174, 181}): 98,\n",
       "  frozenset({1, 50, 64, 79, 172, 174, 181}): 91,\n",
       "  frozenset({1, 50, 64, 98, 100, 127, 174}): 77,\n",
       "  frozenset({1, 50, 64, 98, 100, 174, 181}): 63,\n",
       "  frozenset({1, 50, 64, 98, 172, 174, 181}): 105,\n",
       "  frozenset({1, 50, 79, 98, 172, 174, 181}): 105,\n",
       "  frozenset({1, 50, 98, 100, 172, 174, 181}): 70,\n",
       "  frozenset({1, 56, 64, 79, 98, 172, 174}): 77,\n",
       "  frozenset({1, 56, 64, 79, 98, 172, 181}): 70,\n",
       "  frozenset({1, 56, 64, 79, 98, 174, 181}): 77,\n",
       "  frozenset({1, 56, 64, 79, 172, 174, 181}): 70,\n",
       "  frozenset({1, 56, 64, 98, 100, 127, 174}): 98,\n",
       "  frozenset({1, 56, 64, 98, 172, 174, 181}): 84,\n",
       "  frozenset({1, 56, 79, 98, 172, 174, 181}): 84,\n",
       "  frozenset({1, 64, 79, 98, 172, 174, 181}): 91,\n",
       "  frozenset({7, 9, 50, 56, 64, 100, 174}): 84,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100}): 91,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 127}): 70,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 172}): 105,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 174}): 119,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 181}): 105,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 258}): 77,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 127}): 77,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 172}): 84,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 174}): 98,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 181}): 84,\n",
       "  frozenset({7, 50, 56, 64, 79, 127, 174}): 77,\n",
       "  frozenset({7, 50, 56, 64, 79, 172, 174}): 112,\n",
       "  frozenset({7, 50, 56, 64, 79, 172, 181}): 105,\n",
       "  frozenset({7, 50, 56, 64, 79, 174, 181}): 112,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 127}): 91,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 172}): 91,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 174}): 112,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 181}): 84,\n",
       "  frozenset({7, 50, 56, 64, 98, 127, 172}): 77,\n",
       "  frozenset({7, 50, 56, 64, 98, 127, 174}): 98,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 174}): 126,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 181}): 112,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 258}): 91,\n",
       "  frozenset({7, 50, 56, 64, 98, 174, 181}): 119,\n",
       "  frozenset({7, 50, 56, 64, 98, 174, 258}): 91,\n",
       "  frozenset({7, 50, 56, 64, 98, 181, 258}): 84,\n",
       "  frozenset({7, 50, 56, 64, 100, 127, 172}): 77,\n",
       "  frozenset({7, 50, 56, 64, 100, 127, 174}): 98,\n",
       "  frozenset({7, 50, 56, 64, 100, 172, 174}): 105,\n",
       "  frozenset({7, 50, 56, 64, 100, 172, 181}): 91,\n",
       "  frozenset({7, 50, 56, 64, 100, 174, 181}): 98,\n",
       "  frozenset({7, 50, 56, 64, 127, 172, 174}): 84,\n",
       "  frozenset({7, 50, 56, 64, 172, 174, 181}): 126,\n",
       "  frozenset({7, 50, 56, 64, 172, 174, 258}): 91,\n",
       "  frozenset({7, 50, 56, 64, 172, 181, 258}): 84,\n",
       "  frozenset({7, 50, 56, 64, 174, 181, 258}): 84,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 127}): 70,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 172}): 98,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 174}): 119,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 181}): 98,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 258}): 84,\n",
       "  frozenset({7, 50, 56, 79, 98, 127, 174}): 70,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 174}): 126,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 181}): 119,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 258}): 98,\n",
       "  frozenset({7, 50, 56, 79, 98, 174, 181}): 126,\n",
       "  frozenset({7, 50, 56, 79, 98, 174, 258}): 105,\n",
       "  frozenset({7, 50, 56, 79, 98, 181, 258}): 91,\n",
       "  frozenset({7, 50, 56, 79, 100, 127, 174}): 91,\n",
       "  frozenset({7, 50, 56, 79, 100, 172, 174}): 119,\n",
       "  frozenset({7, 50, 56, 79, 100, 172, 181}): 105,\n",
       "  frozenset({7, 50, 56, 79, 100, 174, 181}): 112,\n",
       "  frozenset({7, 50, 56, 79, 100, 174, 258}): 84,\n",
       "  frozenset({7, 50, 56, 79, 127, 172, 174}): 84,\n",
       "  frozenset({7, 50, 56, 79, 172, 174, 181}): 133,\n",
       "  frozenset({7, 50, 56, 79, 172, 174, 258}): 98,\n",
       "  frozenset({7, 50, 56, 79, 172, 181, 258}): 91,\n",
       "  frozenset({7, 50, 56, 79, 174, 181, 258}): 91,\n",
       "  frozenset({7, 50, 56, 98, 100, 127, 172}): 70,\n",
       "  frozenset({7, 50, 56, 98, 100, 127, 174}): 91,\n",
       "  frozenset({7, 50, 56, 98, 100, 172, 174}): 112,\n",
       "  frozenset({7, 50, 56, 98, 100, 172, 181}): 98,\n",
       "  frozenset({7, 50, 56, 98, 100, 174, 181}): 105,\n",
       "  frozenset({7, 50, 56, 98, 100, 174, 258}): 91,\n",
       "  frozenset({7, 50, 56, 98, 100, 181, 258}): 77,\n",
       "  frozenset({7, 50, 56, 98, 127, 172, 174}): 77,\n",
       "  frozenset({7, 50, 56, 98, 172, 174, 181}): 133,\n",
       "  frozenset({7, 50, 56, 98, 172, 174, 258}): 112,\n",
       "  frozenset({7, 50, 56, 98, 172, 181, 258}): 105,\n",
       "  frozenset({7, 50, 56, 98, 174, 181, 258}): 105,\n",
       "  frozenset({7, 50, 56, 100, 127, 172, 174}): 91,\n",
       "  frozenset({7, 50, 56, 100, 172, 174, 181}): 126,\n",
       "  frozenset({7, 50, 56, 100, 174, 181, 258}): 77,\n",
       "  frozenset({7, 50, 56, 172, 174, 181, 258}): 105,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 127}): 70,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 172}): 77,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 174}): 91,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 181}): 77,\n",
       "  frozenset({7, 50, 64, 79, 98, 127, 174}): 77,\n",
       "  frozenset({7, 50, 64, 79, 98, 172, 174}): 112,\n",
       "  frozenset({7, 50, 64, 79, 98, 172, 181}): 105,\n",
       "  frozenset({7, 50, 64, 79, 98, 174, 181}): 112,\n",
       "  frozenset({7, 50, 64, 79, 100, 127, 174}): 77,\n",
       "  frozenset({7, 50, 64, 79, 100, 172, 174}): 84,\n",
       "  frozenset({7, 50, 64, 79, 100, 172, 181}): 77,\n",
       "  frozenset({7, 50, 64, 79, 100, 174, 181}): 84,\n",
       "  frozenset({7, 50, 64, 79, 172, 174, 181}): 112,\n",
       "  frozenset({7, 50, 64, 98, 100, 127, 172}): 70,\n",
       "  frozenset({7, 50, 64, 98, 100, 127, 174}): 91,\n",
       "  frozenset({7, 50, 64, 98, 100, 172, 174}): 91,\n",
       "  frozenset({7, 50, 64, 98, 100, 172, 181}): 77,\n",
       "  frozenset({7, 50, 64, 98, 100, 174, 181}): 84,\n",
       "  frozenset({7, 50, 64, 98, 127, 172, 174}): 84,\n",
       "  frozenset({7, 50, 64, 98, 172, 174, 181}): 119,\n",
       "  frozenset({7, 50, 64, 98, 172, 174, 258}): 91,\n",
       "  frozenset({7, 50, 64, 98, 172, 181, 258}): 84,\n",
       "  frozenset({7, 50, 64, 98, 174, 181, 258}): 84,\n",
       "  frozenset({7, 50, 64, 100, 127, 172, 174}): 77,\n",
       "  frozenset({7, 50, 64, 100, 172, 174, 181}): 98,\n",
       "  frozenset({7, 50, 64, 172, 174, 181, 258}): 91,\n",
       "  frozenset({7, 50, 79, 98, 100, 127, 174}): 70,\n",
       "  frozenset({7, 50, 79, 98, 100, 172, 174}): 98,\n",
       "  frozenset({7, 50, 79, 98, 100, 172, 181}): 91,\n",
       "  frozenset({7, 50, 79, 98, 100, 174, 181}): 98,\n",
       "  frozenset({7, 50, 79, 98, 100, 174, 258}): 84,\n",
       "  frozenset({7, 50, 79, 98, 172, 174, 181}): 126,\n",
       "  frozenset({7, 50, 79, 98, 172, 174, 258}): 98,\n",
       "  frozenset({7, 50, 79, 98, 172, 181, 258}): 91,\n",
       "  frozenset({7, 50, 79, 98, 174, 181, 258}): 98,\n",
       "  frozenset({7, 50, 79, 100, 172, 174, 181}): 105,\n",
       "  frozenset({7, 50, 79, 172, 174, 181, 258}): 91,\n",
       "  frozenset({7, 50, 98, 100, 127, 172, 174}): 70,\n",
       "  frozenset({7, 50, 98, 100, 172, 174, 181}): 98,\n",
       "  frozenset({7, 50, 98, 100, 174, 181, 258}): 77,\n",
       "  frozenset({7, 50, 98, 172, 174, 181, 258}): 105,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 127}): 84,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 172}): 84,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 174}): 98,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 181}): 77,\n",
       "  frozenset({7, 56, 64, 79, 98, 127, 174}): 77,\n",
       "  frozenset({7, 56, 64, 79, 98, 172, 174}): 112,\n",
       "  frozenset({7, 56, 64, 79, 98, 172, 181}): 98,\n",
       "  frozenset({7, 56, 64, 79, 98, 174, 181}): 105,\n",
       "  frozenset({7, 56, 64, 79, 100, 127, 174}): 84,\n",
       "  frozenset({7, 56, 64, 79, 100, 172, 174}): 91,\n",
       "  frozenset({7, 56, 64, 79, 100, 172, 181}): 77,\n",
       "  frozenset({7, 56, 64, 79, 100, 174, 181}): 84,\n",
       "  frozenset({7, 56, 64, 79, 172, 174, 181}): 105,\n",
       "  frozenset({7, 56, 64, 98, 100, 127, 172}): 77,\n",
       "  frozenset({7, 56, 64, 98, 100, 127, 174}): 98,\n",
       "  frozenset({7, 56, 64, 98, 100, 172, 174}): 98,\n",
       "  frozenset({7, 56, 64, 98, 100, 172, 181}): 77,\n",
       "  frozenset({7, 56, 64, 98, 100, 174, 181}): 84,\n",
       "  frozenset({7, 56, 64, 98, 127, 172, 174}): 84,\n",
       "  frozenset({7, 56, 64, 98, 172, 174, 181}): 112,\n",
       "  frozenset({7, 56, 64, 98, 172, 174, 258}): 91,\n",
       "  frozenset({7, 56, 64, 98, 172, 181, 258}): 84,\n",
       "  frozenset({7, 56, 64, 98, 174, 181, 258}): 84,\n",
       "  frozenset({7, 56, 64, 100, 127, 172, 174}): 84,\n",
       "  frozenset({7, 56, 64, 100, 172, 174, 181}): 91,\n",
       "  frozenset({7, 56, 64, 172, 174, 181, 258}): 84,\n",
       "  frozenset({7, 56, 79, 98, 100, 127, 174}): 77,\n",
       "  frozenset({7, 56, 79, 98, 100, 172, 174}): 112,\n",
       "  frozenset({7, 56, 79, 98, 100, 172, 181}): 91,\n",
       "  frozenset({7, 56, 79, 98, 100, 174, 181}): 98,\n",
       "  frozenset({7, 56, 79, 98, 100, 174, 258}): 91,\n",
       "  frozenset({7, 56, 79, 98, 172, 174, 181}): 119,\n",
       "  frozenset({7, 56, 79, 98, 172, 174, 258}): 105,\n",
       "  frozenset({7, 56, 79, 98, 172, 181, 258}): 91,\n",
       "  frozenset({7, 56, 79, 98, 174, 181, 258}): 91,\n",
       "  frozenset({7, 56, 79, 100, 172, 174, 181}): 105,\n",
       "  frozenset({7, 56, 79, 172, 174, 181, 258}): 91,\n",
       "  frozenset({7, 56, 98, 100, 127, 172, 174}): 77,\n",
       "  frozenset({7, 56, 98, 100, 172, 174, 181}): 98,\n",
       "  frozenset({7, 56, 98, 100, 174, 181, 258}): 77,\n",
       "  frozenset({7, 56, 98, 172, 174, 181, 258}): 105,\n",
       "  frozenset({7, 64, 79, 98, 100, 127, 174}): 77,\n",
       "  frozenset({7, 64, 79, 98, 100, 172, 174}): 84,\n",
       "  frozenset({7, 64, 79, 98, 100, 172, 181}): 70,\n",
       "  frozenset({7, 64, 79, 98, 100, 174, 181}): 77,\n",
       "  frozenset({7, 64, 79, 98, 172, 174, 181}): 105,\n",
       "  frozenset({7, 64, 79, 100, 172, 174, 181}): 77,\n",
       "  frozenset({7, 64, 98, 100, 127, 172, 174}): 77,\n",
       "  frozenset({7, 64, 98, 100, 172, 174, 181}): 77,\n",
       "  frozenset({7, 64, 98, 172, 174, 181, 258}): 84,\n",
       "  frozenset({7, 79, 98, 100, 172, 174, 181}): 91,\n",
       "  frozenset({7, 79, 98, 172, 174, 181, 258}): 91,\n",
       "  frozenset({9, 50, 56, 64, 98, 100, 127}): 84,\n",
       "  frozenset({9, 50, 56, 64, 98, 100, 174}): 91,\n",
       "  frozenset({9, 50, 56, 64, 98, 127, 174}): 91,\n",
       "  frozenset({9, 50, 56, 64, 100, 127, 174}): 91,\n",
       "  frozenset({9, 50, 56, 98, 100, 127, 174}): 84,\n",
       "  frozenset({9, 50, 64, 98, 100, 127, 174}): 84,\n",
       "  frozenset({9, 56, 64, 98, 100, 127, 174}): 112,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 127}): 77,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 172}): 77,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 174}): 98,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 181}): 77,\n",
       "  frozenset({50, 56, 64, 79, 98, 127, 174}): 77,\n",
       "  frozenset({50, 56, 64, 79, 98, 172, 174}): 105,\n",
       "  frozenset({50, 56, 64, 79, 98, 172, 181}): 98,\n",
       "  frozenset({50, 56, 64, 79, 98, 174, 181}): 105,\n",
       "  frozenset({50, 56, 64, 79, 100, 127, 174}): 84,\n",
       "  frozenset({50, 56, 64, 79, 100, 172, 174}): 84,\n",
       "  frozenset({50, 56, 64, 79, 100, 172, 181}): 77,\n",
       "  frozenset({50, 56, 64, 79, 100, 174, 181}): 84,\n",
       "  frozenset({50, 56, 64, 79, 172, 174, 181}): 105,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 172}): 84,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 174}): 119,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 181}): 77,\n",
       "  frozenset({50, 56, 64, 98, 100, 172, 174}): 105,\n",
       "  frozenset({50, 56, 64, 98, 100, 172, 181}): 91,\n",
       "  frozenset({50, 56, 64, 98, 100, 174, 181}): 98,\n",
       "  frozenset({50, 56, 64, 98, 127, 172, 174}): 98,\n",
       "  frozenset({50, 56, 64, 98, 127, 172, 181}): 84,\n",
       "  frozenset({50, 56, 64, 98, 127, 174, 181}): 91,\n",
       "  frozenset({50, 56, 64, 98, 172, 174, 181}): 133,\n",
       "  frozenset({50, 56, 64, 98, 172, 174, 258}): 112,\n",
       "  frozenset({50, 56, 64, 98, 172, 181, 258}): 105,\n",
       "  frozenset({50, 56, 64, 98, 174, 181, 258}): 105,\n",
       "  frozenset({50, 56, 64, 100, 127, 172, 174}): 91,\n",
       "  frozenset({50, 56, 64, 100, 127, 172, 181}): 77,\n",
       "  frozenset({50, 56, 64, 100, 127, 174, 181}): 84,\n",
       "  frozenset({50, 56, 64, 100, 172, 174, 181}): 105,\n",
       "  frozenset({50, 56, 64, 127, 172, 174, 181}): 91,\n",
       "  frozenset({50, 56, 64, 172, 174, 181, 258}): 105,\n",
       "  frozenset({50, 56, 79, 98, 100, 127, 174}): 77,\n",
       "  frozenset({50, 56, 79, 98, 100, 172, 174}): 98,\n",
       "  frozenset({50, 56, 79, 98, 100, 172, 181}): 91,\n",
       "  frozenset({50, 56, 79, 98, 100, 174, 181}): 98,\n",
       "  frozenset({50, 56, 79, 98, 100, 174, 258}): 84,\n",
       "  frozenset({50, 56, 79, 98, 172, 174, 181}): 119,\n",
       "  frozenset({50, 56, 79, 98, 172, 174, 258}): 98,\n",
       "  frozenset({50, 56, 79, 98, 172, 181, 258}): 91,\n",
       "  frozenset({50, 56, 79, 98, 174, 181, 258}): 91,\n",
       "  frozenset({50, 56, 79, 100, 172, 174, 181}): 105,\n",
       "  frozenset({50, 56, 79, 172, 174, 181, 258}): 98,\n",
       "  frozenset({50, 56, 98, 100, 127, 172, 174}): 84,\n",
       "  frozenset({50, 56, 98, 100, 127, 172, 181}): 70,\n",
       "  frozenset({50, 56, 98, 100, 127, 174, 181}): 77,\n",
       "  frozenset({50, 56, 98, 100, 172, 174, 181}): 112,\n",
       "  frozenset({50, 56, 98, 100, 174, 181, 258}): 91,\n",
       "  frozenset({50, 56, 98, 127, 172, 174, 181}): 84,\n",
       "  frozenset({50, 56, 98, 172, 174, 181, 258}): 133,\n",
       "  frozenset({50, 56, 100, 127, 172, 174, 181}): 84,\n",
       "  frozenset({50, 64, 79, 98, 100, 127, 174}): 77,\n",
       "  frozenset({50, 64, 79, 98, 100, 172, 174}): 77,\n",
       "  frozenset({50, 64, 79, 98, 100, 172, 181}): 70,\n",
       "  frozenset({50, 64, 79, 98, 100, 174, 181}): 77,\n",
       "  frozenset({50, 64, 79, 98, 172, 174, 181}): 126,\n",
       "  frozenset({50, 64, 79, 100, 172, 174, 181}): 77,\n",
       "  frozenset({50, 64, 98, 100, 127, 172, 174}): 84,\n",
       "  frozenset({50, 64, 98, 100, 127, 172, 181}): 77,\n",
       "  frozenset({50, 64, 98, 100, 127, 174, 181}): 77,\n",
       "  frozenset({50, 64, 98, 100, 172, 174, 181}): 91,\n",
       "  frozenset({50, 64, 98, 127, 172, 174, 181}): 98,\n",
       "  frozenset({50, 64, 98, 172, 174, 181, 258}): 112,\n",
       "  frozenset({50, 64, 100, 127, 172, 174, 181}): 77,\n",
       "  frozenset({50, 79, 98, 100, 172, 174, 181}): 91,\n",
       "  frozenset({50, 79, 98, 172, 174, 181, 258}): 98,\n",
       "  frozenset({50, 98, 100, 127, 172, 174, 181}): 70,\n",
       "  frozenset({56, 64, 79, 98, 100, 127, 174}): 98,\n",
       "  frozenset({56, 64, 79, 98, 100, 172, 174}): 84,\n",
       "  frozenset({56, 64, 79, 98, 100, 172, 181}): 70,\n",
       "  frozenset({56, 64, 79, 98, 100, 174, 181}): 77,\n",
       "  frozenset({56, 64, 79, 98, 172, 174, 181}): 98,\n",
       "  frozenset({56, 64, 79, 100, 172, 174, 181}): 77,\n",
       "  frozenset({56, 64, 98, 100, 127, 172, 174}): 91,\n",
       "  frozenset({56, 64, 98, 100, 127, 172, 181}): 70,\n",
       "  frozenset({56, 64, 98, 100, 127, 174, 181}): 77,\n",
       "  frozenset({56, 64, 98, 100, 172, 174, 181}): 91,\n",
       "  frozenset({56, 64, 98, 127, 172, 174, 181}): 84,\n",
       "  frozenset({56, 64, 98, 172, 174, 181, 258}): 105,\n",
       "  frozenset({56, 64, 100, 127, 172, 174, 181}): 77,\n",
       "  frozenset({56, 79, 98, 100, 172, 174, 181}): 91,\n",
       "  frozenset({56, 79, 98, 172, 174, 181, 258}): 91,\n",
       "  frozenset({56, 98, 100, 127, 172, 174, 181}): 70,\n",
       "  frozenset({64, 79, 98, 100, 172, 174, 181}): 70,\n",
       "  frozenset({64, 98, 100, 127, 172, 174, 181}): 70},\n",
       " 8: {frozenset({1, 7, 50, 56, 64, 79, 98, 172}): 80,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 98, 174}): 88,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 98, 181}): 88,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 172, 174}): 80,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 172, 181}): 80,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 174, 181}): 88,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 100, 174}): 80,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 172, 174}): 96,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 172, 181}): 88,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 174, 181}): 96,\n",
       "  frozenset({1, 7, 50, 56, 64, 172, 174, 181}): 88,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 100, 174}): 80,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 172, 174}): 96,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 172, 181}): 96,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 174, 181}): 104,\n",
       "  frozenset({1, 7, 50, 56, 79, 172, 174, 181}): 96,\n",
       "  frozenset({1, 7, 50, 56, 98, 100, 172, 174}): 80,\n",
       "  frozenset({1, 7, 50, 56, 98, 172, 174, 181}): 104,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 172, 174}): 88,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 172, 181}): 88,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 174, 181}): 96,\n",
       "  frozenset({1, 7, 50, 64, 79, 172, 174, 181}): 88,\n",
       "  frozenset({1, 7, 50, 64, 98, 172, 174, 181}): 96,\n",
       "  frozenset({1, 7, 50, 79, 98, 172, 174, 181}): 104,\n",
       "  frozenset({1, 7, 50, 98, 100, 172, 174, 181}): 72,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 172, 174}): 88,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 172, 181}): 80,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 174, 181}): 88,\n",
       "  frozenset({1, 7, 56, 64, 79, 172, 174, 181}): 80,\n",
       "  frozenset({1, 7, 56, 64, 98, 172, 174, 181}): 88,\n",
       "  frozenset({1, 7, 56, 79, 98, 172, 174, 181}): 96,\n",
       "  frozenset({1, 7, 64, 79, 98, 172, 174, 181}): 88,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 172, 174}): 80,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 172, 181}): 80,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 174, 181}): 88,\n",
       "  frozenset({1, 50, 56, 64, 79, 172, 174, 181}): 80,\n",
       "  frozenset({1, 50, 56, 64, 98, 100, 127, 174}): 88,\n",
       "  frozenset({1, 50, 56, 64, 98, 172, 174, 181}): 96,\n",
       "  frozenset({1, 50, 56, 79, 98, 172, 174, 181}): 96,\n",
       "  frozenset({1, 50, 64, 79, 98, 172, 174, 181}): 104,\n",
       "  frozenset({1, 56, 64, 79, 98, 172, 174, 181}): 80,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 127}): 80,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 172}): 88,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 174}): 104,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 181}): 88,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 127, 174}): 80,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 172, 174}): 120,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 172, 181}): 112,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 174, 181}): 120,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 127, 174}): 88,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 172, 174}): 96,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 172, 181}): 88,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 174, 181}): 96,\n",
       "  frozenset({7, 50, 56, 64, 79, 172, 174, 181}): 120,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 127, 172}): 80,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 127, 174}): 104,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 172, 174}): 104,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 172, 181}): 88,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 174, 181}): 96,\n",
       "  frozenset({7, 50, 56, 64, 98, 127, 172, 174}): 88,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 174, 181}): 128,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 174, 258}): 104,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 181, 258}): 96,\n",
       "  frozenset({7, 50, 56, 64, 98, 174, 181, 258}): 96,\n",
       "  frozenset({7, 50, 56, 64, 100, 127, 172, 174}): 88,\n",
       "  frozenset({7, 50, 56, 64, 100, 172, 174, 181}): 104,\n",
       "  frozenset({7, 50, 56, 64, 172, 174, 181, 258}): 96,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 127, 174}): 80,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 172, 174}): 112,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 172, 181}): 104,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 174, 181}): 112,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 174, 258}): 96,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 174, 181}): 136,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 174, 258}): 112,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 181, 258}): 104,\n",
       "  frozenset({7, 50, 56, 79, 98, 174, 181, 258}): 104,\n",
       "  frozenset({7, 50, 56, 79, 100, 172, 174, 181}): 120,\n",
       "  frozenset({7, 50, 56, 79, 172, 174, 181, 258}): 104,\n",
       "  frozenset({7, 50, 56, 98, 100, 127, 172, 174}): 80,\n",
       "  frozenset({7, 50, 56, 98, 100, 172, 174, 181}): 112,\n",
       "  frozenset({7, 50, 56, 98, 100, 174, 181, 258}): 88,\n",
       "  frozenset({7, 50, 56, 98, 172, 174, 181, 258}): 120,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 127, 174}): 80,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 172, 174}): 88,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 172, 181}): 80,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 174, 181}): 88,\n",
       "  frozenset({7, 50, 64, 79, 98, 172, 174, 181}): 120,\n",
       "  frozenset({7, 50, 64, 79, 100, 172, 174, 181}): 88,\n",
       "  frozenset({7, 50, 64, 98, 100, 127, 172, 174}): 80,\n",
       "  frozenset({7, 50, 64, 98, 100, 172, 174, 181}): 88,\n",
       "  frozenset({7, 50, 64, 98, 172, 174, 181, 258}): 96,\n",
       "  frozenset({7, 50, 79, 98, 100, 172, 174, 181}): 104,\n",
       "  frozenset({7, 50, 79, 98, 172, 174, 181, 258}): 104,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 127, 174}): 88,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 172, 174}): 96,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 172, 181}): 80,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 174, 181}): 88,\n",
       "  frozenset({7, 56, 64, 79, 98, 172, 174, 181}): 112,\n",
       "  frozenset({7, 56, 64, 79, 100, 172, 174, 181}): 88,\n",
       "  frozenset({7, 56, 64, 98, 100, 127, 172, 174}): 88,\n",
       "  frozenset({7, 56, 64, 98, 100, 172, 174, 181}): 88,\n",
       "  frozenset({7, 56, 64, 98, 172, 174, 181, 258}): 96,\n",
       "  frozenset({7, 56, 79, 98, 100, 172, 174, 181}): 104,\n",
       "  frozenset({7, 56, 79, 98, 172, 174, 181, 258}): 104,\n",
       "  frozenset({7, 64, 79, 98, 100, 172, 174, 181}): 80,\n",
       "  frozenset({9, 50, 56, 64, 98, 100, 127, 174}): 96,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 127, 174}): 88,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 172, 174}): 88,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 172, 181}): 80,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 174, 181}): 88,\n",
       "  frozenset({50, 56, 64, 79, 98, 172, 174, 181}): 112,\n",
       "  frozenset({50, 56, 64, 79, 100, 172, 174, 181}): 88,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 172, 174}): 96,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 172, 181}): 80,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 174, 181}): 88,\n",
       "  frozenset({50, 56, 64, 98, 100, 172, 174, 181}): 104,\n",
       "  frozenset({50, 56, 64, 98, 127, 172, 174, 181}): 96,\n",
       "  frozenset({50, 56, 64, 98, 172, 174, 181, 258}): 120,\n",
       "  frozenset({50, 56, 64, 100, 127, 172, 174, 181}): 88,\n",
       "  frozenset({50, 56, 79, 98, 100, 172, 174, 181}): 104,\n",
       "  frozenset({50, 56, 79, 98, 172, 174, 181, 258}): 104,\n",
       "  frozenset({50, 56, 98, 100, 127, 172, 174, 181}): 80,\n",
       "  frozenset({50, 64, 79, 98, 100, 172, 174, 181}): 80,\n",
       "  frozenset({50, 64, 98, 100, 127, 172, 174, 181}): 80,\n",
       "  frozenset({56, 64, 79, 98, 100, 172, 174, 181}): 80,\n",
       "  frozenset({56, 64, 98, 100, 127, 172, 174, 181}): 80},\n",
       " 9: {frozenset({1, 7, 50, 56, 64, 79, 98, 172, 174}): 90,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 98, 172, 181}): 90,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 98, 174, 181}): 99,\n",
       "  frozenset({1, 7, 50, 56, 64, 79, 172, 174, 181}): 90,\n",
       "  frozenset({1, 7, 50, 56, 64, 98, 172, 174, 181}): 99,\n",
       "  frozenset({1, 7, 50, 56, 79, 98, 172, 174, 181}): 108,\n",
       "  frozenset({1, 7, 50, 64, 79, 98, 172, 174, 181}): 99,\n",
       "  frozenset({1, 7, 56, 64, 79, 98, 172, 174, 181}): 90,\n",
       "  frozenset({1, 50, 56, 64, 79, 98, 172, 174, 181}): 90,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 127, 174}): 90,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 172, 174}): 99,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 172, 181}): 90,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 174, 181}): 99,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 172, 174, 181}): 126,\n",
       "  frozenset({7, 50, 56, 64, 79, 100, 172, 174, 181}): 99,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 127, 172, 174}): 90,\n",
       "  frozenset({7, 50, 56, 64, 98, 100, 172, 174, 181}): 99,\n",
       "  frozenset({7, 50, 56, 64, 98, 172, 174, 181, 258}): 108,\n",
       "  frozenset({7, 50, 56, 79, 98, 100, 172, 174, 181}): 117,\n",
       "  frozenset({7, 50, 56, 79, 98, 172, 174, 181, 258}): 117,\n",
       "  frozenset({7, 50, 64, 79, 98, 100, 172, 174, 181}): 90,\n",
       "  frozenset({7, 56, 64, 79, 98, 100, 172, 174, 181}): 90,\n",
       "  frozenset({50, 56, 64, 79, 98, 100, 172, 174, 181}): 90,\n",
       "  frozenset({50, 56, 64, 98, 100, 127, 172, 174, 181}): 90},\n",
       " 10: {frozenset({1, 7, 50, 56, 64, 79, 98, 172, 174, 181}): 100,\n",
       "  frozenset({7, 50, 56, 64, 79, 98, 100, 172, 174, 181}): 100}}"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequent_itemsets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 15285 candidate rules\n"
     ]
    }
   ],
   "source": [
    "# Now we create the association rules. First, they are candidates until the confidence has been tested\n",
    "candidate_rules = []\n",
    "for itemset_length, itemset_counts in frequent_itemsets.items():\n",
    "    for itemset in itemset_counts.keys():\n",
    "        for conclusion in itemset:\n",
    "            premise = itemset - set((conclusion,))\n",
    "            candidate_rules.append((premise, conclusion))\n",
    "print(f\"There are {len(candidate_rules)} candidate rules\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(frozenset({7}), 1), (frozenset({1}), 7), (frozenset({50}), 1), (frozenset({1}), 50), (frozenset({1}), 56)]\n"
     ]
    }
   ],
   "source": [
    "print(candidate_rules[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now, we compute the confidence of each of these rules. This is very similar to what we did in chapter 1\n",
    "correct_counts = defaultdict(int)\n",
    "incorrect_counts = defaultdict(int)\n",
    "for user, reviews in favorable_reviews_by_users.items():\n",
    "    for candidate_rule in candidate_rules:\n",
    "        premise, conclusion = candidate_rule\n",
    "        if premise.issubset(reviews):\n",
    "            if conclusion in reviews:\n",
    "                correct_counts[candidate_rule] += 1\n",
    "            else:\n",
    "                incorrect_counts[candidate_rule] += 1\n",
    "rule_confidence = {candidate_rule: correct_counts[candidate_rule] / float(correct_counts[candidate_rule] + incorrect_counts[candidate_rule])\n",
    "              for candidate_rule in candidate_rules}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Choose only rules above a minimum confidence level\n",
    "min_confidence = 0.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5152\n"
     ]
    }
   ],
   "source": [
    "# Filter out the rules with poor confidence\n",
    "rule_confidence = {rule: confidence for rule, confidence in rule_confidence.items() if confidence > min_confidence}\n",
    "print(len(rule_confidence))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "from operator import itemgetter\n",
    "sorted_confidence = sorted(rule_confidence.items(), key=itemgetter(1), reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rule #1\n",
      "Rule: If a person recommends frozenset({98, 181}) they will also recommend 50\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #2\n",
      "Rule: If a person recommends frozenset({172, 79}) they will also recommend 174\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #3\n",
      "Rule: If a person recommends frozenset({258, 172}) they will also recommend 174\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #4\n",
      "Rule: If a person recommends frozenset({1, 181, 7}) they will also recommend 50\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #5\n",
      "Rule: If a person recommends frozenset({1, 172, 7}) they will also recommend 174\n",
      " - Confidence: 1.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for index in range(5):\n",
    "    print(\"Rule #{0}\".format(index + 1))\n",
    "    (premise, conclusion) = sorted_confidence[index][0]\n",
    "    print(f\"Rule: If a person recommends {premise} they will also recommend {conclusion}\")\n",
    "    print(f\" - Confidence: {rule_confidence[(premise, conclusion)]:.3f}\")\n",
    "    print(\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Even better, we can get the movie titles themselves from the dataset\n",
    "movie_name_data = pd.read_csv(MOVIES, delimiter=\"|\", header=None, encoding = \"mac-roman\")\n",
    "movie_name_data.columns = [\"MovieID\", \"Title\", \"Release Date\", \"Video Release\", \"IMDB\", \"\", \"Action\", \"Adventure\",\n",
    "                           \"Animation\", \"Children's\", \"Comedy\", \"Crime\", \"Documentary\", \"Drama\", \"Fantasy\", \"Film-Noir\",\n",
    "                           \"Horror\", \"Musical\", \"Mystery\", \"Romance\", \"Sci-Fi\", \"Thriller\", \"War\", \"Western\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_movie_name(movie_id):\n",
    "    title_object = movie_name_data[movie_name_data[\"MovieID\"] == movie_id][\"Title\"]\n",
    "    title = title_object.values[0]\n",
    "    return title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Get Shorty (1995)'"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_movie_name(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rule #1\n",
      "Rule: If a person recommends Silence of the Lambs, The (1991), Return of the Jedi (1983) they will also recommend Star Wars (1977)\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #2\n",
      "Rule: If a person recommends Empire Strikes Back, The (1980), Fugitive, The (1993) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #3\n",
      "Rule: If a person recommends Contact (1997), Empire Strikes Back, The (1980) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #4\n",
      "Rule: If a person recommends Toy Story (1995), Return of the Jedi (1983), Twelve Monkeys (1995) they will also recommend Star Wars (1977)\n",
      " - Confidence: 1.000\n",
      "\n",
      "Rule #5\n",
      "Rule: If a person recommends Toy Story (1995), Empire Strikes Back, The (1980), Twelve Monkeys (1995) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Confidence: 1.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for index in range(5):\n",
    "    print(\"Rule #{0}\".format(index + 1))\n",
    "    (premise, conclusion) = sorted_confidence[index][0]\n",
    "    premise_names = \", \".join(get_movie_name(idx) for idx in premise)\n",
    "    conclusion_name = get_movie_name(conclusion)\n",
    "    print(\"Rule: If a person recommends {0} they will also recommend {1}\".format(premise_names, conclusion_name))\n",
    "    print(\" - Confidence: {0:.3f}\".format(rule_confidence[(premise, conclusion)]))\n",
    "    print(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation\n",
    "\n",
    "In a broad sense, we can evaluate the association rules using the same concept as for classification. We use a test set of data that was not used for training, and evaluate our discovered rules based on their performance in this test set.\n",
    "\n",
    "To do this, we will compute the test set confidence, that is, the confidence of each rule on the testing set.\n",
    "\n",
    "We won't apply a formal evaluation metric in this case; we simply examine the rules and look for good examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Evaluation using test data\n",
    "test_dataset = all_ratings[~all_ratings['UserID'].isin(range(200))]\n",
    "test_favorable = test_dataset[test_dataset[\"Favorable\"]]\n",
    "#test_not_favourable = test_dataset[~test_dataset[\"Favourable\"]]\n",
    "test_favorable_by_users = dict((k, frozenset(v.values)) for k, v in test_favorable.groupby(\"UserID\")[\"MovieID\"])\n",
    "#test_not_favourable_by_users = dict((k, frozenset(v.values)) for k, v in test_not_favourable.groupby(\"UserID\")[\"MovieID\"])\n",
    "#test_users = test_dataset[\"UserID\"].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserID</th>\n",
       "      <th>MovieID</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Datetime</th>\n",
       "      <th>Favorable</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>244</td>\n",
       "      <td>51</td>\n",
       "      <td>2</td>\n",
       "      <td>1997-11-27 05:02:03</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>298</td>\n",
       "      <td>474</td>\n",
       "      <td>4</td>\n",
       "      <td>1998-01-07 14:20:06</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>253</td>\n",
       "      <td>465</td>\n",
       "      <td>5</td>\n",
       "      <td>1998-04-03 18:34:27</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>305</td>\n",
       "      <td>451</td>\n",
       "      <td>3</td>\n",
       "      <td>1998-02-01 09:20:17</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>286</td>\n",
       "      <td>1014</td>\n",
       "      <td>5</td>\n",
       "      <td>1997-11-17 15:38:45</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    UserID  MovieID  Rating            Datetime  Favorable\n",
       "3      244       51       2 1997-11-27 05:02:03      False\n",
       "5      298      474       4 1998-01-07 14:20:06       True\n",
       "7      253      465       5 1998-04-03 18:34:27       True\n",
       "8      305      451       3 1998-02-01 09:20:17      False\n",
       "11     286     1014       5 1997-11-17 15:38:45       True"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_dataset[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "correct_counts = defaultdict(int)\n",
    "incorrect_counts = defaultdict(int)\n",
    "for user, reviews in test_favorable_by_users.items():\n",
    "    for candidate_rule in candidate_rules:\n",
    "        premise, conclusion = candidate_rule\n",
    "        if premise.issubset(reviews):\n",
    "            if conclusion in reviews:\n",
    "                correct_counts[candidate_rule] += 1\n",
    "            else:\n",
    "                incorrect_counts[candidate_rule] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5152\n"
     ]
    }
   ],
   "source": [
    "test_confidence = {candidate_rule: correct_counts[candidate_rule] / float(correct_counts[candidate_rule] + incorrect_counts[candidate_rule])\n",
    "                   for candidate_rule in rule_confidence}\n",
    "print(len(test_confidence))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[((frozenset({64, 1, 7, 79, 50}), 174), 1.0), ((frozenset({64, 1, 98, 7, 79}), 174), 1.0), ((frozenset({64, 1, 7, 172, 79}), 174), 1.0), ((frozenset({64, 1, 7, 79, 181}), 174), 1.0), ((frozenset({64, 1, 172, 79, 56}), 174), 1.0)]\n"
     ]
    }
   ],
   "source": [
    "sorted_test_confidence = sorted(test_confidence.items(), key=itemgetter(1), reverse=True)\n",
    "print(sorted_test_confidence[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rule #1\n",
      "Rule: If a person recommends Silence of the Lambs, The (1991), Return of the Jedi (1983) they will also recommend Star Wars (1977)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.936\n",
      "\n",
      "Rule #2\n",
      "Rule: If a person recommends Empire Strikes Back, The (1980), Fugitive, The (1993) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.876\n",
      "\n",
      "Rule #3\n",
      "Rule: If a person recommends Contact (1997), Empire Strikes Back, The (1980) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.841\n",
      "\n",
      "Rule #4\n",
      "Rule: If a person recommends Toy Story (1995), Return of the Jedi (1983), Twelve Monkeys (1995) they will also recommend Star Wars (1977)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.932\n",
      "\n",
      "Rule #5\n",
      "Rule: If a person recommends Toy Story (1995), Empire Strikes Back, The (1980), Twelve Monkeys (1995) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.903\n",
      "\n",
      "Rule #6\n",
      "Rule: If a person recommends Pulp Fiction (1994), Toy Story (1995), Star Wars (1977) they will also recommend Raiders of the Lost Ark (1981)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.816\n",
      "\n",
      "Rule #7\n",
      "Rule: If a person recommends Pulp Fiction (1994), Toy Story (1995), Return of the Jedi (1983) they will also recommend Star Wars (1977)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.970\n",
      "\n",
      "Rule #8\n",
      "Rule: If a person recommends Toy Story (1995), Silence of the Lambs, The (1991), Return of the Jedi (1983) they will also recommend Star Wars (1977)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.933\n",
      "\n",
      "Rule #9\n",
      "Rule: If a person recommends Toy Story (1995), Empire Strikes Back, The (1980), Return of the Jedi (1983) they will also recommend Star Wars (1977)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.971\n",
      "\n",
      "Rule #10\n",
      "Rule: If a person recommends Pulp Fiction (1994), Toy Story (1995), Shawshank Redemption, The (1994) they will also recommend Silence of the Lambs, The (1991)\n",
      " - Train Confidence: 1.000\n",
      " - Test Confidence: 0.794\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for index in range(10):\n",
    "    print(f\"Rule #{index + 1}\")\n",
    "    (premise, conclusion) = sorted_confidence[index][0]\n",
    "    premise_names = \", \".join(get_movie_name(idx) for idx in premise)\n",
    "    conclusion_name = get_movie_name(conclusion)\n",
    "    print(f\"Rule: If a person recommends {premise_names} they will also recommend {conclusion_name}\")\n",
    "    print(f\" - Train Confidence: {rule_confidence.get((premise, conclusion), -1):.3f}\")\n",
    "    print(f\" - Test Confidence: {test_confidence.get((premise, conclusion), -1):.3f}\")\n",
    "    print(\"\")"
   ]
  }
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