<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:
        leny, lenx = len(grid), len(grid[0])
        
        
        def magic(y1, x1):
            unique = set()
            dicy = defaultdict(int)
            dicx = defaultdict(int)
            leftright = 0
            rightleft = 0
            for y in range(y1, y1+3):
                for x in range(x1, x1+3):
                    unique.add(grid[y][x])
                    dicy[y] += grid[y][x]
                    dicx[x] += grid[y][x]
                    if  grid[y][x] > 9 or grid[y][x] < 1:
                        return False
            
            x = x1
            for y in range(y1, y1+3):
                leftright += grid[y][x]
                x += 1
            y = y1
            for x in range( x1+3-1, x1-1, -1):
                rightleft += grid[y][x]
                y += 1
                
            total = set()
            total.add(rightleft)
            total.add(leftright)
            for key in dicy:
                total.add(dicy[key])
            for key in dicx:
                total.add(dicx[key])
            
            return len(unique) == 9 and len(total) == 1
        
        
        count = 0
        for y in range(leny-2):
            for x in range(lenx-2):
                if magic(y, x):
                    count += 1

        return count
16500