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`