<p>There are <code>n</code> people and <code>40</code> types of hats labeled from <code>1</code> to <code>40</code>.</p>

<p>Given a 2D integer array <code>hats</code>, where <code>hats[i]</code> is a list of all hats preferred by the <code>i<sup>th</sup></code> person.</p>

<p>Return <em>the number of ways that the <code>n</code> people wear different hats to each other</em>.</p>

<p>Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> hats = [[3,4],[4,5],[5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> There is only one way to choose hats given the conditions. 
First person choose hat 3, Second person choose hat 4 and last one hat 5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> hats = [[3,5,1],[3,5]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 4 ways to choose hats:
(3,5), (5,3), (1,3) and (1,5)
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]
<strong>Output:</strong> 24
<strong>Explanation:</strong> Each person can choose hats labeled from 1 to 4.
Number of Permutations of (1,2,3,4) = 24.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == hats.length</code></li>
	<li><code>1 &lt;= n &lt;= 10</code></li>
	<li><code>1 &lt;= hats[i].length &lt;= 40</code></li>
	<li><code>1 &lt;= hats[i][j] &lt;= 40</code></li>
	<li><code>hats[i]</code> contains a list of <strong>unique</strong> integers.</li>
</ul>

#include <vector>
#include <iostream>
#define ll long long
using namespace std;
ll f[1 << 10][42];
ll MOD = 1e9 + 7;
class Solution
{
public:
    int numberHats = 40;
    int n;
    int prefer[12][42];
    int numberWays(vector<vector<int>> &hats)
    {
        // F[bit][i] people in bit wear hats max = i;
        memset(prefer, 0, sizeof(prefer));
        for (int i = 0; i < hats.size(); i++)
        {
            for (int j = 0; j < hats[i].size(); j++)
            {
                prefer[i][hats[i][j]] = 1;
            }
        }
        //Print prefer
        // for (int i = 0; i < hats.size(); i++){
        //     for (int j = 0; j < numberHats; j++){
        //         cout << prefer[i][j] << " ";
        //     }
        //     cout << endl;
        // }
        memset(f, -1, sizeof(f));
        f[0][0] = 1;
        n = hats.size();
        return dp((1 << n) - 1, numberHats);
    }

    ll dp(int bit, int numberHats)
    {
        if (f[bit][numberHats] != -1)
            return f[bit][numberHats];
        if (numberHats <= 0)
            return 0;
        ll res = dp(bit, numberHats - 1);
        for (int i = 0; i < n; i++)
        {
            bool check = bit & (1 << i);
            if (check && prefer[i][numberHats])
                res = (res + dp(bit ^ (1 << i), numberHats - 1)) % MOD;
        }
        // cout << "bit = " << bitset<5>(bit) << " numberHats = " << numberHats << " res = " << res << endl;
        f[bit][numberHats] = res % MOD;
        return res;
    }
};
// int main()
// {
//     vector<vector<int>> hats = {{3, 4}, {4, 5}, {5}};
//     Solution s;
//     cout << s.numberWays(hats) << endl;
// }
9800