<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) {
        // vector<vector<int>> rows = {
        //     {0,1,0}, {0,1,2}, {0,2,0}, {0,2,1},
        //     {1,0,1}, {1,0,2}, {1,2,0}, {1,2,1},
        //     {2,0,1}, {2,0,2}, {2,1,0}, {2,1,2}
        // };

        vector<vector<int>> edges = {
            {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<long>> grid(1);
        grid[0].resize(12, 1);
        for(int i = 1; i < n; i++){
            vector<long> nextRow(12, 0);
            for(int j = 0; j < 12; j++){
                for(int k : edges[j]){
                    nextRow[k] += grid[i-1][j];
                    if(nextRow[k] > 1000000007) nextRow[k] %= 1000000007;
                }
            }
            grid.push_back(nextRow);
        }
        long ret = 0;
        for(int j = 0; j < 12; j++) ret += grid[n-1][j];
        ret = ret % 1000000007;
        return ret;
    }
};
26165