<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 check(vector<vector<int>>& grid, int x, int y) {
        vector<int> cnt(10, 0);

        // Check for valid numbers and uniqueness
        for (int i = x; i < x + 3; i++) {
            for (int j = y; j < y + 3; j++) {
                if (grid[i][j] < 1 || grid[i][j] > 9 || cnt[grid[i][j]] > 0)
                    return false;
                cnt[grid[i][j]]++;
            }
        }

        // Check rows
        for (int i = x; i < x + 3; i++) {
            int sum = 0;
            for (int j = y; j < y + 3; j++) {
                sum += grid[i][j];
            }
            if (sum != 15)
                return false;
        }

        // Check columns
        for (int j = y; j < y + 3; j++) {
            int sum = 0;
            for (int i = x; i < x + 3; i++) {
                sum += grid[i][j];
            }
            if (sum != 15)
                return false;
        }

        // Check main diagonal
        int sum = 0;
        for (int i = 0; i < 3; i++) {
            sum += grid[x + i][y + i];
        }
        if (sum != 15)
            return false;

        // Check anti-diagonal
        sum = 0;
        for (int i = 0; i < 3; i++) {
            sum += grid[x + i][y + 2 - i];
        }
        if (sum != 15)
            return false;

        return true;
    }
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        int cnt = 0;
        for (int i = 0; i < m - 2; i++) {
            for (int j = 0; j < n - 2; j++) {
                if (check(grid, i, j))
                    cnt++;
            }
        }
        return cnt;
    }
};
11000