<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>>& mat) {
        int ans=0;
        int n=mat.size(),m=mat[0].size();

        for(int i=0;i<=n-3;i++)
        {
            for(int j=0;j<=m-3;j++)
            {
                vector<int> row(3,0),col(3,0),dia(2,0);
                set<int> st;
                int flag=1;

                for(int r=i;r<=i+2;r++)
                {
                    int rSum=0;
                    for(int c=j;c<=j+2;c++)
                    {
                        if(mat[r][c]<1 || mat[r][c]>9) flag=0;
                        
                        st.insert(mat[r][c]);
                        col[c-j]+=mat[r][c];
                        rSum+=mat[r][c];
                    }
                    row[r-i]=rSum;
                }
                for(int i=0;i<3;i++)
                cout<<row[i]<<" "<<col[i]<<endl;

                if(st.size()==9){
                    dia[0]=mat[i][j]+mat[i+1][j+1]+mat[i+2][j+2];
                    dia[1]=mat[i][j+2]+mat[i+1][j+1]+mat[i+2][j];

                    
                    for(auto it:row) if(it!=15) flag=0;
                    for(auto it:col) if(it!=15) flag=0;
                    
                    if(flag && dia[0]==dia[1]  && dia[0]==row[0]) ans++;
                }
            }
        }
        return ans;
    }
};
12200