<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:
    def numMagicSquaresInside(self, grid: List[List[int]]) -> int:
        
        def verify(i, j):
            rows = [0]*3
            cols = [0]*3
            diag = 0
            antidiag = 0
            visited = set()
            for di in range(-1,2,1):
                for dj in range(-1, 2, 1):
                    ni, nj = i+di, j+dj
                    if grid[ni][nj] < 1 or grid[ni][nj]>9 or grid[ni][nj] in visited:
                        return False
                    visited.add(grid[ni][nj])
                    rows[di+1] += grid[ni][nj]
                    cols[dj+1] += grid[ni][nj]
                    if di==dj:
                        diag += grid[ni][nj]
                    if di+dj == 0:
                        antidiag += grid[ni][nj]
            for i in range(3):
                if rows[i] != 15 or cols[i] != 15:
                    return False
            return diag == 15 and antidiag == 15
        
        m, n = len(grid), len(grid[0])
        cnt = 0
        for i in range(1, m-1):
            for j in range(1, n-1):
                if verify(i,j):
                    cnt += 1
        return cnt
16600