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

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Choose any two adjacent elements of matrixand 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.

因为2个相邻的数字可以同时乘以-1，所以我们就可以将任意的数字组合乘以-1，这时候就要计算数组中一共有多少个负数，如果是偶数个，那么一定可以全部取正，如果是奇数个，我们就让最小的那个数字变成负数即可；

剩下就是几个变量，求和项（所有数取绝对值），负数的数量，最小的数（绝对值之后）；

然后分2种情况依次返回即可；

题目不算太难的。

Constraints:

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

2 <= n <= 250

-105 <= matrix[i][j] <= 105

Runtime: 6 ms, faster than 93.02% of Java online submissions for Maximum Matrix Sum.

Memory Usage: 53 MB, less than 36.05% of Java online submissions for Maximum Matrix Sum.