<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 n;
    int mod=1e9+7;
    int func(int i, int marks, vector<int>& v, unordered_map<int, vector<int>>& mp, vector<vector<int>>& dp){
        if(marks==((1<<(n))-1)) return 1;
        if(i==v.size() || v[i]>40) return 0;

        if(dp[marks][i]!=-1) return dp[marks][i];

        int ans=0;
        for(auto j : mp[v[i]]){
            if((marks & (1<<j))==0){
                ans=(ans+func(i+1, (marks | (1<<j)), v, mp, dp))%mod;
            }
        }
        ans=(ans+func(i+1, marks, v, mp, dp))%mod;

        return dp[marks][i] = (ans)%mod;
    }

    int numberWays(vector<vector<int>>& hats) {
        unordered_map<int, vector<int>> mp;
        n=hats.size();
        for(int i=0; i<n; i++){
            for(auto h : hats[i]){
                mp[h].push_back(i);
            }
        }

        if(n> mp.size()) return 0;

        vector<int> v;
        for(auto it=mp.begin(); it!=mp.end(); it++){
            v.push_back(it->first);
        }

        vector<vector<int>> dp((1<<n)+1, vector<int>(41, -1));

        return func(0, 0, v, mp, dp);
    }
};
14800