Write a function to find the maximum sum of a contiguous subarray in a given array of integers. The function should first divide the array into two halves, then find the maximum sum subarray for each half, and finally return the maximum of these two sums.
Example:

Input: [2, -1, 3, -4, 5, -6]
Output: 8

Explanation: The maximum sum of a contiguous subarray is 8, which is obtained by taking the subarray [3, -4, 5].

Answer rating: 100% (QA)

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