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Maximum Matrix Sum

You are given an n x n integer matrix.

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

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.

Maximum Matrix Sum diagram

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
  • -10^5 <= matrix[i][j] <= 10^5

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