<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:
    bool check(int a1,int b1,int c1,int a2,int b2,int c2){
        return !(a1 == b1 || b1 == c1 || a2 == b2 || b2 == c2 || a1 == a2 ||  b1 == b2 || c1 == c2);
    }
    int MOD = 1e9 + 7;
    int F(int n,int x,int y,int z,vector <vector <vector <vector <int>>>> &dp){
        if(n == 0) return 1;
        if(dp[n][x][y][z] != -1) return dp[n][x][y][z];
        int ans = 0;
        for(int a = 0;a < 3;a++){
            for(int b = 0;b < 3;b++){
                for(int c = 0;c < 3;c++){
                    if(check(x,y,z,a,b,c))
                        ans = (ans + F(n - 1,a,b,c,dp)) % MOD;
                }
            }
        }
        return dp[n][x][y][z] =  ans;
    }
    
    int numOfWays(int n) {
        int ans = 0;
        vector <vector <vector <vector <int>>>> dp(n+1,vector <vector <vector <int>>>(3,vector <vector <int>> (3,vector <int>(3,-1))));
        for(int a = 0;a < 3;a++){
            for(int b = 0;b < 3;b++){
                for(int c = 0;c < 3;c++){
                    if(a!=b && b!=c)
                        ans = (ans + F(n - 1,a,b,c,dp)) % MOD;
                }
            }
        }
        return ans;
    }
};
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