Given an $n imes n$ integer matrix, you are allowed to perform the following operation any number of times:

• Select any two adjacent cells in matrix and multiply both values by $-1$.

Two cells are adjacent if they share a common edge horizontally or vertically.

Return the maximum possible sum of all elements in matrix after applying the operation any number of times.

Constraints:

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

• $2 \leq$ n $\leq 250$

• $-10^5 \leq$ matrix[i][j] $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.