<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:
        def isMagic(i, j):
            once=[False]*10
            rowSum=[0]*3
            colSum= [0]*3

            for a in range(i-1, i+2):
                for b in range(j-1, j+2):
                    x= grid[a][b]
                    if x < 1 or x > 9: return False
                    rowSum[a-i+1] += x
                    colSum[b-j+1] += x
                    if once[x]: 
                        return False  # it's not unique
                    once[x]=True

            for b in once[1:]: 
                if not b: return False

            for sum in rowSum:
                if sum!=15: return False
            for sum in colSum:
                if sum!=15: return False
            
            return grid[i-1][j-1]+grid[i+1][j+1]==10 and grid[i+1][j-1]+grid[i-1][j+1]==10
        
        r, c = len(grid), len(grid[0])
        if r < 3 or c < 3: 
            return 0

        cnt=0
        for i in range(1, r-1):
            for j in range(1, c-1):
                if grid[i][j] == 5 and isMagic(i, j): 
                    cnt+=1
        return cnt
16500