<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:
const int mod=1e9+7;
bool type_match(int first_type,int second_type,int first_color,int second_color){
    if(first_color==0){
        if(second_color==1){
            if(first_type==0){
                if(second_type==2)return false;
            }else if(first_type==1){
                if(second_type==1)return false;
            }else if(first_type==2){
                if(second_type==2 or second_type==3)return false;
            }else{
                if(second_type==0 or second_type==2 or second_type==3)return false;
            }
        }else{
            if(first_type==0){
                if(second_type==2 or second_type==3)return false;
            }else if(first_type==1){
                if(second_type==1 or second_type==2 or second_type==3)return false;
            }else if(first_type==2){
                if(second_type==2)return false;
            }else{
                if(second_type==0)return false;
            }

        }
    }else if(first_color==1){
        if(second_color==0){
            if(first_type==0){
                if(second_type==3)return false;
            }else if(first_type==1){
                if(second_type==1)return false;
            }else if(first_type==2){
                if(second_type==0 or second_type==2 or second_type==3)return false;
            }else{
             if(second_type==2 or second_type==3)return false;   
            }
        }else{
            if(first_type==0){
                if(second_type==0 or second_type==1)return false;
            }else if(first_type==1){
                if(second_type==0 or second_type==1 or second_type==3)return false;
            }else if(first_type==2){
                if(second_type==2)return false;
            }else{
            if(second_type==0)return  false;
            }
        }
    }else{
  if(second_color==0){
    if(first_type==0){
                if(second_type==3)return false;
            }else if(first_type==1){
                if(second_type==1)return false;
            }else if(first_type==2){
                if(second_type==0 or second_type==1 or second_type==2)return false;
            }else{
                if(second_type==0 or second_type==1)return false;
            }
  }else{
    if(first_type==0){
                if(second_type==0 or second_type==1 or second_type==3)return false;
            }else if(first_type==1){
                if(second_type==0 or second_type==1)return false;
            }else if(first_type==2){
                    if(second_type==2)return false;
            }else{
            if(second_type==1)return false;  
            }
  }
    }
    return true;
}
    int numOfWays(int n) {
        vector<vector<vector<int>>> dp(
            n, vector<vector<int>>(3, vector<int>(4, 0)));
        for (int i = 0; i < 3; i += 1) {
            for (int k = 0; k < 4; k += 1) {
                dp[dp.size() - 1][i][k] = 1;
            }
        }
        for (int i = dp.size() - 2; i >= 0; i -= 1) {
            for (int color = 0; color < 3; color += 1) {
                for (int type = 0; type < 4; type += 1) {
                    for (int next_color = 0; next_color < 3; next_color += 1) {

                        if (color == next_color)
                            continue;

                        for (int next_type = 0; next_type < 4; next_type += 1) {
                            if(!type_match(type,next_type,color,next_color))continue;
dp[i][color][type]=(dp[i][color][type]+dp[i+1][next_color][next_type])%mod;
                        }
                    }
                }
            }
        }
        int ans=0;
        for(int i=0;i<3;i+=1){
            for(int j=0;j<4;j+=1){
                ans=(ans+dp[0][i][j])%mod;
            }
        }
        return ans;
    }
};
22475