<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 m = grid.size();
        int n = grid[0].size();
        int ans = 0;

        if (m<3||n<3) {
            return ans;
        }

        for(int r = 0; r<m-2; r++) {
            for (int c=0; c<n-2; c++) {
                if (isMagic(r, c, grid)) {
                    ans++;
                }
            }
        }
        return ans;
    }

    bool isMagic(int r, int c, vector<vector<int>>& grid) {
        unordered_set<int> s;
        for (int i=0; i<3;i++) {
            for (int j=0; j<3;j++) {
                int num = grid[r+i][c+j];
                if (num < 1 || num > 9 || s.find(num)!=s.end()) {
                    return false;
                } 
                s.insert(num);
            }
        }
        int sum = grid[r][c]+grid[r][c+1]+grid[r][c+2];
        for (int i=0; i<3; i++) {
           if (grid[r+i][c]+grid[r+i][c+1]+grid[r+i][c+2] != sum) {
            return false;
           }
        }
        for (int j=0; j<3; j++) {
           if (grid[r][c+j]+grid[r+1][c+j]+grid[r+2][c+j]!=sum) {
            return false;
           }     
        }
        if (grid[r][c]+grid[r+1][c+1]+grid[r+2][c+2] != sum) {
            return false;
        }
        if (grid[r+2][c]+grid[r+1][c+1] +grid[r][c+2]!= sum) {
            return false;
        }
        return true;
    }
};
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