<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>

class Solution {
public:

    int dp[41][1024];

    int numberWays(vector<vector<int>> &people,int etapa,int bitmask,int pessoas)
{
    if (dp[etapa][bitmask] != -1) return dp[etapa][bitmask];

    if (bitmask == (1<<pessoas)-1) return 1;

    if (etapa >= 40) return 0;

    int size = people[etapa].size();
    
    int pessoa;
    int res = 0;

    for (int i=0;i<size;i++)
    {
        pessoa = people[etapa][i];

        if ((bitmask & (1<<pessoa)) == 0)
        {
            res += numberWays(people,etapa+1,bitmask bitor (1<<pessoa),pessoas);
            res %= 1000000007;
        }

    }
    res += numberWays(people,etapa+1,bitmask,pessoas);

    res = res%(1000000007);

    dp[etapa][bitmask] = res;
    return res;
}

int numberWays(vector<vector<int>> hats)
{
    vector<vector<int>> peoplearg(40,vector<int>());
    memset(dp,-1,sizeof(dp));
    for (int pessoa=0;pessoa<hats.size();pessoa++)
    for (int i=0;i<hats[pessoa].size();i++)
    {
        peoplearg[hats[pessoa][i]-1].push_back(pessoa);
    }

    
 
    

    return numberWays(peoplearg,0,0,hats.size());
}

};
10400