<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>

b=[]
def gen(s,n):
    global b
    if len(s)==n:
        fl=False
        for i in range(1,n):
            fl|=s[i]==s[i-1]
        if not fl:
            b.append(s)
        return
    gen(s+"0",n)
    gen(s+"1",n)
    gen(s+"2",n)
class Solution:
    def colorTheGrid(self, m: int, n: int) -> int:
        global b
        dp=defaultdict(lambda :-1)
        mod=10**9+7
        b=[]
        gen("",m)
        # print(b)
        def rec(i,prev):
            if i==n:
                return 1
            if dp[i,prev]!=-1:
                return dp[i,prev]
            ans=0
            for cl in b:
                if prev==-1 :
                    ans+=rec(i+1,cl)
                    ans%=mod
                    continue
                fl=False
                for id in range(len(cl)):
                    fl|=prev[id]==cl[id]
                if fl==False:
                    ans+=rec(i+1,cl)
                    ans%=mod
            dp[i,prev]=ans
            return ans
        x=rec(0,-1)
        print(x)
        return x%mod
2484