<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:
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int n=grid.size();
        int m=grid[0].size();
        if(n<3 || m<3){
            return 0;
        }
        int cnt=0;
        for(int i=2;i<n;i++){
            for(int j=2;j<m;j++){
                int r=1;
                int l=0;
                for(int k=2;k>=0;k--){
                    l+=grid[i][j-k];
                }
                for(int k=1;k<3;k++){
                    int s=0;
                    for(int l=0;l<3;l++){
                        s+=grid[i-k][j-l];
                    }
                    if(s!=l){
                        r=0;
                        break;
                    }
                }
                if(r==0){
                    continue;
                }
                r=l;
                int c=1;
                l=0;
                for(int k=2;k>=0;k--){
                    l+=grid[i-k][j];
                }
                for(int k=1;k<3;k++){
                    int s=0;
                    for(int l=0;l<3;l++){
                        s+=grid[i-l][j-k];
                    }
                    if(s!=l){
                        c=0;
                        break;
                    }
                }
                if(c==0 || l!=r){
                    continue;
                }
                int d=0;
                for(int k=2;k>=0;k--){
                    d+=grid[i-k][j-k];
                }
                int d1=0;
                for(int k=2;k>=0;k--){
                    d1+=grid[i-2+k][j-k];
                }
                if(d1!=d || d1!=r){
                    continue;
                }
                unordered_set<int> s;
                bool f=1;
                for(int k=2;k>=0;k--){
                    for(int l=2;l>=0;l--){
                        if(s.find(grid[i-k][j-l])!=s.end()){
                            f=0;
                            break;
                        }
                        s.insert(grid[i-k][j-l]);
                        if(grid[i-k][j-l]>9 || grid[i-k][j-l]==0){
                            f=0;
                            break;
                        }
                    }
                    if(f==0){
                        break;
                    }
                }
                if(f==0){
                    continue;
                }
                cnt++;
            }
        }
        return cnt;
    }
};
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