<p>You have a <code>grid</code> of size <code>n x 3</code> and you want to paint each cell of the grid with exactly one of the three colors: <strong>Red</strong>, <strong>Yellow,</strong> or <strong>Green</strong> while making sure that no two adjacent cells have the same color (i.e., no two cells that share vertical or horizontal sides have the same color).</p>

<p>Given <code>n</code> the number of rows of the grid, return <em>the number of ways</em> you can paint this <code>grid</code>. As the answer may grow large, the answer <strong>must be</strong> computed modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/26/e1.png" style="width: 400px; height: 257px;" />
<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 12
<strong>Explanation:</strong> There are 12 possible way to paint the grid as shown.
</pre>

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

<pre>
<strong>Input:</strong> n = 5000
<strong>Output:</strong> 30228214
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
</ul>

const int M=1000000007;
int no_ways(int ind,int one,int two,int three,int n,vector<vector<vector<vector<int>>>> &dp){
    if(ind==n) return 1;
    if(one!=-1 && dp[ind][one][two][three]!=-1) return dp[ind][one][two][three];
    int ans=0;
    for(int i=0;i<3;i++){
        if(one==i) continue;
        for(int j=0;j<3;j++){
            if(two==j || j==i) continue;
            for(int k=0;k<3;k++){
                if(three==k || k==j) continue;
                ans=ans+no_ways(ind+1,i,j,k,n,dp);
                ans=ans%M;
            }
        }
    }
    if(one!=-1) return dp[ind][one][two][three]=ans;
    return ans;
}

class Solution {
public:
    int numOfWays(int n) {
        int ans=0;
        vector<vector<vector<vector<int>>>> dp(n,vector<vector<vector<int>>>(3,vector<vector<int>>(3,vector<int>(3,-1))));
        return no_ways(0,-1,-1,-1,n,dp);
    }
};
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