<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)
        vaild = [ "123", "121","131","132","212", "213", "231","232", "312","313","321","323" ]
        

        m = len(vaild)
        dp = [ [0] * m for i in range(n)  ]

        for i in range(m):
            dp[0][i] = 1

        def check(i:int, j:int) ->bool:

            for idx in range(3):
                if vaild[i][idx] == vaild[j][idx]:
                    return False
            return True

        for i in range(1,n):
            for j in range(m):
                for k in range(m):
                    if check(j,k):
                        dp[i][j] += dp[i-1][k]
                    if dp[i][j] > mod:
                        dp[i][j] -= mod

        
        return sum(dp[-1]) % mod
19200