<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 {
public:
    int p = 1e9+7;
    
    void f(vector<string>&v ,char prev, int m,string temp)
    {
        if (temp.length()==m)
        {
            v.push_back(temp);
            return;
        }
        for (int i=0;i<3;i++)
        {
            char curr='0'+i;
            if (curr!=prev)
            {
                f(v,curr,m,temp+curr);
            }
        }
    }
    int fill(vector<string>&v,int m,string prev,int n,map<string,map<int,int>>&mp)
    {
        if (n==0)return 1;
        if (mp.count(prev) && mp[prev].count(n))return mp[prev][n];
        int ans = 0;
        for (int i=0;i<v.size();i++)
        {
            bool flag = true;
            for (int j=0;j<m;j++)
            {
                if (prev!="" && v[i][j]==prev[j])
                {
                    flag = false;
                    break;
                }
            }
            if (flag)ans=(ans%p+fill(v,m,v[i],n-1,mp)%p)%p;
        }
        return mp[prev][n]=ans%p;
    }
    int numOfWays(int n) {
        vector<string>v;
        string temp="";
        map<string,map<int,int>>mp;
        f(v,'#',3,temp);
        return fill(v,3,temp,n,mp)%p;
    }
};
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