<p>A <code>3 x 3</code> <strong>magic square</strong> is a <code>3 x 3</code> grid filled with distinct numbers <strong>from </strong>1<strong> to </strong>9 such that each row, column, and both diagonals all have the same sum.</p>

<p>Given a <code>row x col</code> <code>grid</code> of integers, how many <code>3 x 3</code> magic square subgrids are there?</p>

<p>Note: while a magic square can only contain numbers from 1 to 9, <code>grid</code> may contain numbers up to 15.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_main.jpg" style="width: 322px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
<strong>Output:</strong> 1
<strong>Explanation: </strong>
The following subgrid is a 3 x 3 magic square:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_valid.jpg" style="width: 242px; height: 242px;" />
while this one is not:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_invalid.jpg" style="width: 242px; height: 242px;" />
In total, there is only one magic square inside the given grid.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[8]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>row == grid.length</code></li>
	<li><code>col == grid[i].length</code></li>
	<li><code>1 &lt;= row, col &lt;= 10</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 15</code></li>
</ul>

class Solution {
public:
    bool yes(int x,int y,vector<vector<int>>&grid){
        if(x+2>=grid.size()||y+2>=grid[0].size())return 0;
        vector<int>marked(10,0);
        for(int i=x;i<x+3;i++){
            for(int j=y;j<y+3;j++){
                if(grid[i][j]>=10)return 0;
                marked[grid[i][j]]++;
            }
        }
        for(int i=1;i<10;i++){
            if(marked[i]!=1)return 0;
        }
        map<int,bool>mp;
        mp[grid[x][y]+grid[x][y+1]+grid[x][y+2]]=1;
        mp[grid[x+1][y]+grid[x+1][y+1]+grid[x+1][y+2]]=1;
        mp[grid[x+2][y]+grid[x+2][y+1]+grid[x+2][y+2]]=1;
        mp[grid[x][y]+grid[x+1][y]+grid[x+2][y]]=1;
        mp[grid[x][y+1]+grid[x+1][y+1]+grid[x+2][y+1]]=1;
        mp[grid[x][y+2]+grid[x+1][y+2]+grid[x+2][y+2]]=1;
        mp[grid[x][y]+grid[x+1][y+1]+grid[x+2][y+2]]=1;
        mp[grid[x+2][y]+grid[x+1][y+1]+grid[x][y+2]]=1;
        if(mp.size()!=1)return 0;
        return 1;
    }
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int answer=0;
        for(int i=0;i<grid.size();i++){
            for(int j=0;j<grid[0].size();j++){
                if(yes(i,j,grid))answer++;
            }

        }
        return answer;
    }
};
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