Stone Game V

Given an array of stone values, Alice repeatedly splits the current subarray into two non-empty parts; Bob discards the part with the larger sum (if equal Alice chooses) and Alice scores the sum of the remaining part, and the process continues on the remaining part until one stone remains. The task is to compute the maximum total score Alice can guarantee — a classic interval DP problem using prefix sums to evaluate optimal splits (n ≤ 500).