<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:
        count = 0
        r = len(grid)
        c = len(grid[0])

        # Iterate over the grid to find magic squares
        for i in range(r - 2):
            for j in range(c - 2):
                # Check if the current sub-grid is a magic square
                if self.isMagic(grid, i, j):
                    # If it is, increment the count
                    count += 1

        return count
    
    def isMagic(self, grid: List[List[int]], i: int, j: int) -> bool:
        # Create a list to keep track of the numbers seen
        seen = [False] * 10

        # Check if each number in the sub-grid is valid
        for r in range(3):
            for c in range(3):
                num = grid[i + r][j + c]
                if num < 1 or num > 9 or seen[num]:
                    return False
                seen[num] = True
        
        # Check if the rows, columns, and diagonals have the same sum
        s = sum(grid[i][j:j+3])
        
        for r in range(3):
            if s != sum(grid[i + r][j:j+3]):
                return False
        
        for c in range(3):
            if s != sum(grid[i + r][j + c] for r in range(3)):
                return False
        
        if s != grid[i][j] + grid[i + 1][j + 1] + grid[i + 2][j + 2]:
            return False
        
        if s != grid[i + 2][j] + grid[i + 1][j + 1] + grid[i][j + 2]:
            return False
        
        return True
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