Magic Squares In Grid
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0840.Magic%20Squares%20In%20Grid/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0840.Magic%20Squares%20In%20Grid/images/magic_valid.jpg" style="width: 242px; height: 242px;" />
while this one is not:
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0840.Magic%20Squares%20In%20Grid/images/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>
Array; Hash Table; Math; Matrix
class Solution:
    def numMagicSquaresInside(self, grid: List[List[int]]) -> int:
        def check(i: int, j: int) -> int:
            if i + 3 > m or j + 3 > n:
                return 0
            s = set()
            row = [0] * 3
            col = [0] * 3
            a = b = 0
            for x in range(i, i + 3):
                for y in range(j, j + 3):
                    v = grid[x][y]
                    if v < 1 or v > 9:
                        return 0
                    s.add(v)
                    row[x - i] += v
                    col[y - j] += v
                    if x - i == y - j:
                        a += v
                    if x - i == 2 - (y - j):
                        b += v
            if len(s) != 9 or a != b:
                return 0
            if any(x != a for x in row) or any(x != a for x in col):
                return 0
            return 1

        m, n = len(grid), len(grid[0])
        return sum(check(i, j) for i in range(m) for j in range(n))
