<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
        
        # dp[i][j] represents the number of ways to color the first i rows
        # with the i-th row ending with color pattern j
        dp = [[0, 0] for _ in range(n + 1)]
        
        # Initialize base cases
        dp[0][0] = 6  # Number of valid colorings for the first row (3 colors for each of the 3 cells)
        dp[0][1] = 6  # Number of valid colorings for the first row (3 colors for each of the 3 cells)
        
        for i in range(1, n):
            # Calculate the number of valid colorings for the current row
            dp[i][0] = (3 * dp[i - 1][0] + 2 * dp[i - 1][1]) % mod
            dp[i][1] = (2 * dp[i - 1][0] + 2 * dp[i - 1][1]) % mod
        
        # The total number of ways to color the grid is the sum of the valid colorings for the last row
        return (dp[n - 1][0] + dp[n - 1][1]) % mod

# Example usage:
solution = Solution()
print(solution.numOfWays(1))  # Output: 12
print(solution.numOfWays(5000))  # Output: 30228214
17400