<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 = 10**9 +7
        d = dict()

        def dp(row, prev1, prev2, prev3, n, mod):
            nonlocal d
            if row == n:
                return 1
            color = ("R", "Y", "G")
            res = 0
            if (row, prev1, prev2, prev3) in d:
                return d[(row, prev1, prev2, prev3)]
            for i in color:
                if i != prev1:
                    for j in color:
                        if j != i and j != prev2:
                            for k in color:
                                if k != prev3 and k != j:
                                    res += dp(row+1, i, j, k, n, mod)
            d[(row, prev1, prev2, prev3)] = res%mod
            return d[(row, prev1, prev2, prev3)]
        
        return dp(0, "",  "",  "",  n, mod)
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