<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>

constexpr int mod = 1000000007;
class Solution {
public:
    int numOfWays(int n) {
        vector<int> valid(27, 0);
        for (int i = 0; i < 27; i++){
            auto [l, m, r] = getColor(i);
            if (m != l && m != r) valid[i] = 1;
        }
        
        int compa[27][27];
        memset(compa, 0, sizeof(compa));
        for (int i = 0; i < 27; i++){
            if (!valid[i]) continue;
            auto [l, m, r] = getColor(i);
            for (int j = 0; j < 27; j++){
                if (!valid[j]) continue;
                auto [x, y, z] = getColor(j);
                if (l != x && m != y && r != z) compa[i][j] = 1;
            }
        }
        
        vector<vector<int>> dp(n, vector<int>(27, 0));
        for (int i = 0; i < 27; i++) dp[0][i] = valid[i];
        
        for (int i = 1; i < n; i++){
            for (int j = 0; j < 27; j++){
                if (!valid[j]) continue;
                for (int k = 0; k < 27; k++){
                    if (compa[j][k]) dp[i][j] = (dp[i][j] + dp[i - 1][k]) % mod;
                }
            }
        }
        int res = 0;
        for (int i = 0; i < 27; i++){
            res = (res + dp[n - 1][i]) % mod;
        }
        return res;     
    }
    
private:
    array<int,3> getColor(int tmp){
        int l = tmp % 3; tmp /= 3;
        int m = tmp % 3; tmp /= 3;
        int r = tmp % 3;
        return {l,m,r};
    }
};
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