<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>

MOD = 10**9 + 7


COMB = [
    ["R", "Y", "R"],
    ["R", "Y", "G"],
    ["R", "G", "R"],
    ["R", "G", "Y"],
    ["Y", "R", "Y"],
    ["Y", "R", "G"],
    ["Y", "G", "R"],
    ["Y", "G", "Y"],
    ["G", "R", "Y"],
    ["G", "R", "G"],
    ["G", "Y", "R"],
    ["G", "Y", "G"]
]


class Solution:
    # def calc_factors(self) -> List[List[int]]:
    #     factors = []
    #     for i in range(len(COMB)):
    #         factors.append([])
    #         comb_i = COMB[i]
    #         for j in range(len(COMB)):
    #             if i == j: continue
    #             comb_j = COMB[j]
    #             if all(comb_i[k] != comb_j[k] for k in range(3)): factors[-1].append(j)
    #     return factors

    def numOfWays(self, n: int) -> int:
        # factors = self.calc_factors()
        factors = [[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]]
        
        memo = [1] * 12
        for _ in range(1, n):
            next_memo = [0] * 12
            for i in range(12):
                for j in factors[i]:
                    next_memo[j] += memo[i]
            memo = next_memo
        return sum(memo) % MOD

16900