840. Magic Squares In Grid

Medium

A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum.

Given a row x col grid of integers, how many 3 x 3 contiguous magic square subgrids are there?

Note: while a magic square can only contain numbers from 1 to 9, grid may contain numbers up to 15.

Example 1:

Input: grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
Output: 1
Explanation: 
The following subgrid is a 3 x 3 magic square:

while this one is not:

In total, there is only one magic square inside the given grid.

Example 2:

Input: grid = [[8]]
Output: 0

Constraints:

row == grid.length
col == grid[i].length
1 <= row, col <= 10
0 <= grid[i][j] <= 15