<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][4][4][4];

    int solve(int row, int a0, int b0, int c0){
        if(row == 0) return 1;

        if(dp[row][a0][b0][c0] != 0){
            return dp[row][a0][b0][c0];
        }

        vector<int> color = {1,2,3};  // red, gree, yellow

        int ans = 0;
        for(auto a : color){
            if(a == a0) continue;

            for(auto b: color){
                if(b==b0 || b==a) continue;

                for(auto c : color){
                    if(c==c0 || c==b) continue;

                    ans += solve(row-1, a,b,c);
                    ans %= mod;
                }
            }
        }

        return dp[row][a0][b0][c0] = ans;
        
    }

        int numOfWays(int n) {
        return solve(n, 0, 0, 0);
    }
};
36005