<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 M = 1e9+7;
    int dp[5005][5][5][5];
    int solve(int n,int x,int y,int z){
        if(n==0) return 1;
        if(dp[n][x][y][z]!= -1) return dp[n][x][y][z];
        int ans = 0;
        vector<int> color={1,2,3};
        for(auto xx:color){
            if(xx==x) continue;
            for(auto yy:color){
                if(yy==y || yy==xx) continue;
                for(auto zz:color){
                    if(zz==z || zz==yy) continue;
                    ans = (ans+solve(n-1,xx,yy,zz))%M;
                }
            }
        }
        return dp[n][x][y][z]=ans;
    }
    int numOfWays(int n) {
        memset(dp,-1,sizeof(dp));
        return solve(n,0,0,0);
    }
};
39695