<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 funct(int ind,int x1,int x2,int x3,vector<vector<int>>& newrow,int n,vector<vector<vector<vector<int>>>>& dp){
    if(ind==n){
        return 1;
    }
    int mod=pow(10,9)+7;
    if(dp[ind][x1+1][x2+1][x3+1]!=-1){
        return dp[ind][x1+1][x2+1][x3+1];
    }
    int ans=0;
    for(int i=0;i<12;i++){
        if(x1!=newrow[i][0]&&x2!=newrow[i][1]&&x3!=newrow[i][2]){
            ans=(ans+funct(ind+1,newrow[i][0],newrow[i][1],newrow[i][2],newrow,n,dp))%mod;
        }
    }
    return dp[ind][x1+1][x2+1][x3+1]=ans;

}


    int numOfWays(int n) {
        vector<vector<int>> newrow={{0,1,2},{2,1,0},{0,1,0},{2,1,2},{1,0,2},{2,0,1},{1,0,1},{2,0,2},{0,2,1},{1,2,0},{0,2,0},{1,2,1}};
        vector<vector<vector<vector<int>>>> dp(n,vector<vector<vector<int>>>(4,vector<vector<int>>(4,vector<int>(4,-1))));
        return funct(0,-1,-1,-1,newrow,n,dp);                                                 
        
    }
};
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