<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:

        if n == 1: return 12
        mod = 10**9 + 7

        hash = {1:[2,3,5,6,11], 2:[1,4,7,9,12],3:[1,4,7,8],4:[2,3,8,11],5:[1,7,9,10],6:[1,7,8,10,11],7:[2,3,5,6,12],8:[3,4,6,12],9:[2,5,10,11],10:[5,6,9,12],11:[1,4,6,9,12],12:[2,7,8,10,11]}

        @cache
        def f(pattern,size):
            s = 0
            if size == 1:
                return len(hash[pattern])

            for p in hash[pattern]:
                s += f(p,size-1) % mod
            
            return s

          

        return (sum([f(i+1,n-1) for i in range(0,12)]) % mod)



        



        
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