> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/1975-maximum-matrix-sum.md).

# 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:**

![](https://assets.leetcode.com/uploads/2021/07/16/pc79-q2ex1.png)

```
**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:**

![](https://assets.leetcode.com/uploads/2021/07/16/pc79-q2ex2.png)

```
**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`

## ac

```java
```