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` "magic square" subgrids are there? (Each subgrid is contiguous).

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/09/11/magic_main.jpg)

**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: ![](https://assets.leetcode.com/uploads/2020/09/11/magic_valid.jpg) while this one is not: ![](https://assets.leetcode.com/uploads/2020/09/11/magic_invalid.jpg) 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`