1975. Maximum Matrix Sum

https://leetcode.com/problems/maximum-matrix-sum

Description

You are given an n x n integer matrix. You can do the following operation any number of times:

• Choose any two adjacent elements of matrix and multiply each of them by -1.

Two elements are considered adjacent if and only if they share a border.

Your goal is to maximize the summation of the matrix's elements. Return the maximum sum of the matrix's elements using the operation mentioned above.

Example 1:

**Input:** matrix = [[1,-1],[-1,1]]
**Output:** 4
**Explanation:** We can follow the following steps to reach sum equals 4:
- Multiply the 2 elements in the first row by -1.
- Multiply the 2 elements in the first column by -1.

Example 2:

**Input:** matrix = [[1,2,3],[-1,-2,-3],[1,2,3]]
**Output:** 16
**Explanation:** We can follow the following step to reach sum equals 16:
- Multiply the 2 last elements in the second row by -1.

Constraints:

• n == matrix.length == matrix[i].length

• 2 <= n <= 250

• -105 <= matrix[i][j] <= 105

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