<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][1<<11];
    int M=1e9+7;
    int getWays(int i,int peopleMask,int count,int n,vector<vector<int>> &people)
    {
        if(count==n)
            return 1;
        if(i>40)
            return 0;
        if(dp[i][peopleMask]!=-1)
            return dp[i][peopleMask];
        int c=0;
        for(auto x: people[i])
        {
            if((peopleMask&(1<<x))==0)
            {
                c=(c%M+getWays(i+1,peopleMask|(1<<x),count+1,n,people)%M)%M;
            }
        }
        c=(c%M+getWays(i+1,peopleMask,count,n,people)%M)%M;
        return dp[i][peopleMask]=c;
    }
    int numberWays(vector<vector<int>>& hats) {
        int n=hats.size();
        vector<vector<int>> people(41);
        for(int i=0;i<n;i++)
        {
            for(auto hat: hats[i])
            {
                people[hat].push_back(i);
            }
        }
        memset(dp,-1,sizeof(dp));
        return getWays(0,0,0,n,people);
    }
};
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