<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:
        rows = len(grid)
        cols = len(grid[0])
        ans = 0

        for row in range(rows-2):
            for col in range(cols-2):
                if self.isMagicGrid(grid, row, col):
                    ans += 1
        
        return ans

    def isMagicGrid(self, grid, row, col):
        visited = [False] * 10

        for r in range(3):
            for c in range(3):
                num = grid[row+r][col+c]
                if num < 1 or num > 9:
                    return False
                if visited[num]:
                    return False
                visited[num] = True
        
        d1 = grid[row][col] + grid[row+2][col+2] + grid[row + 1][col + 1]
        d2 = grid[row+2][col] + grid[row][col+2] + grid[row + 1][col + 1]
        if d1 != d2:
            return False
        
        r1 = grid[row][col] + grid[row][col+1] + grid[row][col+2]
        r2 = grid[row+1][col] + grid[row+1][col+1] + grid[row+1][col+2]
        r3 = grid[row+2][col] + grid[row+2][col+1] + grid[row+2][col+2]
        if not (r1 == d1 and r2 == d1 and r3 == d1):
            return False

        c1 = grid[row][col] + grid[row+1][col] + grid[row+2][col]
        c2 = grid[row][col+1] + grid[row+1][col+1] + grid[row+2][col+1]
        c3 = grid[row][col+2] + grid[row+1][col+2] + grid[row+2][col+2]
        if not (c1 == d1 and c2 == d1 and c3 == d1):
            return False
        
        return True
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