<p>You are given two integers <code>m</code> and <code>n</code>. Consider an <code>m x n</code> grid where each cell is initially white. You can paint each cell <strong>red</strong>, <strong>green</strong>, or <strong>blue</strong>. All cells <strong>must</strong> be painted.</p>

<p>Return<em> the number of ways to color the grid with <strong>no two adjacent cells having the same color</strong></em>. Since the answer can be very large, return it <strong>modulo</strong> <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/2021/06/22/colorthegrid.png" style="width: 200px; height: 50px;" />
<pre>
<strong>Input:</strong> m = 1, n = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three possible colorings are shown in the image above.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/22/copy-of-colorthegrid.png" style="width: 321px; height: 121px;" />
<pre>
<strong>Input:</strong> m = 1, n = 2
<strong>Output:</strong> 6
<strong>Explanation:</strong> The six possible colorings are shown in the image above.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> m = 5, n = 5
<strong>Output:</strong> 580986
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m &lt;= 5</code></li>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>

class Solution:
    def colorTheGrid(self, m: int, n: int) -> int:
        M = 10**9 + 7
        
        def valid_masks(m):
            def is_valid(mask):
                for i in range(m - 1):
                    if (mask[i] == mask[i + 1]):
                        return False
                return True
            
            colors = [0, 1, 2]  # 0: red, 1: green, 2: blue
            masks = []
            
            def generate(mask):
                if len(mask) == m:
                    if is_valid(mask):
                        masks.append(tuple(mask))
                    return
                for color in colors:
                    generate(mask + [color])
            
            generate([])
            return masks
        
        def compatible(mask1, mask2):
            return all(c1 != c2 for c1, c2 in zip(mask1, mask2))
        
        masks = valid_masks(m)
        dp = [[0] * len(masks) for _ in range(n)]
        
        for j in range(len(masks)):
            dp[0][j] = 1
        
        for i in range(1, n):
            for j in range(len(masks)):
                for k in range(len(masks)):
                    if compatible(masks[j], masks[k]):
                        dp[i][j] = (dp[i][j] + dp[i - 1][k]) % M
        
        return sum(dp[n - 1]) % M
2733