I encountered the following problem in the Amazon Online Assessment and didn't have any idea how to solve it. If you share your ideas, you are more than welcome.

"
You are given an array of integers. Your task is to maximize the sum by performing the following operations repeatedly until the array is empty:

Choose any element from the current array that hasn't been removed before.
Add this element to your total sum.
Remove the first and last elements of the array.
Return the maximum sum you can achieve following these steps.

Example
Input: arr = [4, 4, 8, 5, 3, 2]

Steps:

Choose 5 from [4, 4, 8, 5, 3, 2]
Remove 4 and 2
Total sum = 5
Choose 4 from [4, 8, 5, 3]
Remove 4 and 3
Total sum = 5 + 4 = 9
Choose 8 from [8, 5]
Remove 8 and 5
Total sum = 9 + 8 = 17
Output: 17
"