<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>> dp(n, vector<int>(2, -1));
        return (int)(((long)6 * ways(n - 1, true, dp)) % 1000000007 + ((long)6 * ways(n - 1, false, dp))  % 1000000007) % 1000000007;
    }

    int ways(int n, bool isSymetric, vector<vector<int>>& dp) {
        // cout << n << endl;
        if (n == 0) {
            return 1;
        } else if (dp[n][isSymetric] != -1) {
            return dp[n][isSymetric];
        } else if (!isSymetric) {
            return dp[n][isSymetric] = (int)(((long)2 * ways(n - 1, true, dp)) % 1000000007 + ((long)2 * ways(n - 1, false, dp))  % 1000000007) % 1000000007;
        }

        return dp[n][isSymetric] = (int)(((long)3 * ways(n - 1, true, dp)) % 1000000007 + ((long)2 * ways(n - 1, false, dp))  % 1000000007) % 1000000007;
    }
};
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