<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:
    int numOfWays(int n) {
        int MOD = 1'000'000'007;
        vector<vector<int>> nextstate = {{4, 5, 7, 8, 9}, {4, 6, 7, 8}, {4, 5, 8, 9, 11}, {5, 9, 10, 11}, {0, 1, 2, 10, 11}, {0, 2, 3, 10}, {1, 8, 9, 11}, {0, 1, 9, 10, 11}, {0, 1, 2, 6}, {0, 2, 3, 6, 7}, {3, 4, 5, 7}, {2, 3, 4, 6, 7}};
        vector<vector<int>> dp(n , vector<int> (12, 0));
        dp[0] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
        for (int i = 1; i < n; i++){
            for (int j = 0; j < 12; j++){
                for (auto index : nextstate[j]){
                    dp[i][index] += dp[i - 1][j];
                    dp[i][index] %= MOD;
                }
            }
        }
        int res = 0;
        for (int j = 0; j < 12; j++){
            res += dp[n - 1][j];
            res %= MOD;
        }
        return res;
    }
};
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