<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:
        tot=[]
        def help(i,pre,tmp):
            nonlocal tot
            if i==m:
                tot.append(tmp.copy())
                return 
            for j in range(3):
                if j!=pre:
                    tmp.append(j)
                    help(i+1,j,tmp)
                    tmp.pop()
        help(0,-1,[])
        d=[set() for i in range(len(tot))]
        for i in range(len(tot)):
            for j in range(i+1,len(tot)):
                fl=True
                for k in range(m):
                    if tot[i][k]==tot[j][k]:
                        fl=False
                        break
                if fl:
                    d[i].add(j)
                    d[j].add(i)
        dp={}
        mm=10**9+7
        def help(i,pre):
            if i>=n-1:
                return 1
            if (i,pre) not in dp:
                ans=0
                for j in range(len(tot)):
                    if j in d[pre]:
                        ans+=help(i+1,j)%mm
                dp[(i,pre)]=ans%mm
            return dp[(i,pre)]
        ans=0
        for i in range(len(tot)):
            ans+=help(0,i)%mm
        return ans%mm
908