<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:
    def numOfWays(self, n: int) -> int:
            mod = int(1e9+7)
            D = [None] * n
            t = {
                "RYR": 0, "YRY": 0, "GRY": 0,
                "RYG": 0, "YRG": 0, "GRG": 0,
                "RGR": 0, "YGR": 0, "GYR": 0,
                "RGY": 0, "YGY": 0, "GYG": 0
            }
            D[0] = t.copy()
            for k in t.keys():
                D[0][k] = 1
            for i in range(1, n):
                D[i] = t.copy()
                for k in t.keys():
                    for m in t.keys():
                        if k[0] == m[0] or k[1] == m[1] or k[2] == m[2]:
                            continue
                        D[i][k] = int( (D[i][k] + D[i-1][m])%mod )
            ans = 0
            for k in t.keys():
                ans = int( (ans + D[n-1][k])%mod )
            return ans
20600