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Magic Squares In Grid

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.

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 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.

Magic Squares In Grid diagram

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

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