<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:
        
        result = 0
        rows = len(grid)
        cols = len(grid[0])
        
        
        for i in range(rows - 2):
            
            for j in range(cols - 2):
                
                primary_diagonal_sum = grid[i][j] + grid[i + 1][j + 1] + grid[i + 2][j + 2]
                
                secondary_diagonal_sum = grid[i][j + 2] + grid[i + 1][j + 1] + grid[i + 2][j]
                
                row1_sum = sum(grid[i][j : j + 3])
                row2_sum = sum(grid[i + 1][j : j + 3])
                row3_sum = sum(grid[i + 2][j : j + 3])
                
                col1_sum = grid[i][j] + grid[i + 1][j] + grid[i + 2][j]
                col2_sum = grid[i][j + 1] + grid[i + 1][j + 1] + grid[i + 2][j + 1]
                col3_sum = grid[i][j + 2] + grid[i + 1][j + 2] + grid[i + 2][j + 2]
                
                if set(grid[i][j : j + 3] + grid[i + 1][j : j + 3] + grid[i + 2][j : j + 3]) == set(range(1, 10)):

                    if row1_sum == row2_sum == row3_sum:

                        if col1_sum == col2_sum == col3_sum:

                            if primary_diagonal_sum == secondary_diagonal_sum:

                                result = result + 1
        return result
16100