<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 isMagicSquare(vector<vector<int>>& grid, int r, int c) {
        vector<int> values;
        for (int i = 0; i < 3; ++i) {
            for (int j = 0; j < 3; ++j) {
                int val = grid[r + i][c + j];
                if (val < 1 || val > 9) return false;
                values.push_back(val);
            }
        }

        sort(values.begin(), values.end());
        for (int i = 0; i < 9; ++i) {
            if (values[i] != i + 1) return false;
        }

        int row1 = grid[r][c] + grid[r][c+1] + grid[r][c+2];
        int row2 = grid[r+1][c] + grid[r+1][c+1] + grid[r+1][c+2];
        int row3 = grid[r+2][c] + grid[r+2][c+1] + grid[r+2][c+2];

        int col1 = grid[r][c] + grid[r+1][c] + grid[r+2][c];
        int col2 = grid[r][c+1] + grid[r+1][c+1] + grid[r+2][c+1];
        int col3 = grid[r][c+2] + grid[r+1][c+2] + grid[r+2][c+2];

        int diag1 = grid[r][c] + grid[r+1][c+1] + grid[r+2][c+2];
        int diag2 = grid[r][c+2] + grid[r+1][c+1] + grid[r+2][c];

        return row1 == 15 && row2 == 15 && row3 == 15 && 
               col1 == 15 && col2 == 15 && col3 == 15 &&
               diag1 == 15 && diag2 == 15;
    }
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int row = grid.size(), col = grid[0].size(), count = 0;
        for (int i = 0; i <= row - 3; ++i) {
            for (int j = 0; j <= col - 3; ++j) {
                if (isMagicSquare(grid, i, j)) {
                    count++;
                }
            }
        }
        return count;
    }
};
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