<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>

class Solution {
public:
    const int mod=1e9+7;
    int dp[5001][3][3][3];
    int rec(int lev, int a,int b, int c){
        if(lev==-1)return 1;
        if(dp[lev][a][b][c]!=-1)return dp[lev][a][b][c];
          
        int ans=0;
        for(int i=0;i<3;i++){
            for(int j=0;j<3;j++){
                for(int k=0;k<3;k++){
                    if(i==a || j==b|| k==c || i==j || j==k)continue;
                    ans=(ans%mod +rec(lev-1,i,j,k)%mod)%mod;
                }
            }
        }

        return dp[lev][a][b][c]=ans%mod;
    }
    int numOfWays(int n) {
        memset(dp,-1,sizeof(dp));
        int ans=0;
        for(int i=0;i<3;i++){
            for(int j=0;j<3;j++){
                for(int k=0;k<3;k++){
                    if(i==j || j==k)continue;
                    ans=(ans%mod+rec(n-2,i,j,k)%mod)%mod;
                }
            }
        }
        return ans;
    }
};
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