<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 {
    int n,m;
    const int M=1e9+7;
    private:
    int solve(int i, int msk, vector<int> &v, vector<vector<int>> &dp, map<int,vector<int>> &mp){
        if(msk==(1<<n)-1) return 1;
        if(i>=m)return 0;
        if(dp[i][msk]!=-1)return dp[i][msk];
        int res = solve(i + 1, msk, v, dp, mp) % M;
        for(auto &it:mp[v[i]]){
            cout<<it<<endl;
            if(!((1<<it)&msk)){
            int x=msk|(1<<it);
            res=(res+solve(i+1,x,v,dp,mp))%M;
            }
        }
        res%=M;
        return dp[i][msk]=res;
    }
public:
    int numberWays(vector<vector<int>>& hats) {
        map<int,vector<int>>mp;
        vector<int>v;
        n=hats.size();
        for(int i=0;i<n;i++){
            for(int j=0;j<hats[i].size();j++){
                mp[hats[i][j]].push_back(i);
            }
        }
        for(auto &i:mp){
            v.push_back(i.first);
        }
        m=v.size();
        //sort(v.begin(),v.end());
        vector<vector<int>>dp(m+1,vector<int>((1<<10),-1));
        return solve(0,0,v,dp,mp);
    }
};
19000