<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 ROW = grid.size(), COL = grid[0].size();
        if (ROW < 3 or COL < 3)
            return 0;

        int ans = 0;
        for (int r = 0; r < ROW - 2; r++) {
            for (int c = 0; c < COL - 2; c++) {
                unordered_set<int> s;
                for (int i = r; i < r + 3; i++) {
                    for (int j = c; j < c + 3; j++) {
                        if (grid[i][j] <= 9)
                            s.insert(grid[i][j]);
                        else
                            break;
                    }
                }
                if (s.size() != 9)
                    continue;

                // horizontal
                if (grid[r][c] + grid[r][c + 1] + grid[r][c + 2] != 15)
                    continue;
                if (grid[r + 1][c] + grid[r + 1][c + 1] + grid[r + 1][c + 2] != 15)
                    continue; 
                if (grid[r + 2][c] + grid[r + 2][c + 1] + grid[r + 2][c + 2] != 15)
                    continue;    

                // vertical
                if (grid[r][c] + grid[r + 1][c] + grid[r + 2][c] != 15)
                    continue;
                if (grid[r][c + 1] + grid[r + 1][c + 1] + grid[r + 2][c + 1] != 15)
                    continue;
                if (grid[r][c + 2] + grid[r + 1][c + 2] + grid[r + 2][c + 2] != 15)
                    continue;

                // diagonal
                if (grid[r][c] + grid[r + 1][c + 1] + grid[r + 2][c + 2] != 15)
                    continue;
                if (grid[r + 2][c] + grid[r + 1][c + 1] + grid[r][c + 2] != 15)
                    continue;
                ans += 1;
            }
        }
        return ans;
    }
};
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