<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:
        magicSquares = 0
        
        for i in range(len(grid) - 2):
            for j in range(len(grid[0]) - 2):
                if self.isMagicSquare(grid, i, j):
                    magicSquares += 1
        
        return magicSquares

    def isMagicSquare(self, grid: List[List[int]], i: int, j: int) -> bool:
        if i + 2 < len(grid) and j + 2 < len(grid[0]):
            nums = [
                grid[i][j], grid[i][j+1], grid[i][j+2],
                grid[i+1][j], grid[i+1][j+1], grid[i+1][j+2],
                grid[i+2][j], grid[i+2][j+1], grid[i+2][j+2]
            ]
            
            if sorted(nums) != list(range(1, 10)):
                return False

            row1 = sum(nums[0:3])
            row2 = sum(nums[3:6])
            row3 = sum(nums[6:9])
            col1 = nums[0] + nums[3] + nums[6]
            col2 = nums[1] + nums[4] + nums[7]
            col3 = nums[2] + nums[5] + nums[8]
            diag1 = nums[0] + nums[4] + nums[8]
            diag2 = nums[2] + nums[4] + nums[6]
        
            return (row1 == row2 == row3 == col1 == col2 == col3 == diag1 == diag2)
        
        return False

16000