Alice and Bob play a game using an array of integers stones arranged in a line from left to right.

Alice plays first. On each turn, the active player chooses an integer $x > 1$, removes the leftmost $x$ stones from the row, calculates the sum of their values, adds this sum to their score, and places a single new stone with a value equal to this sum at the leftmost position of the row.

The game concludes when only $1$ stone remains in the row.

Alice seeks to maximize the difference between her score and Bob’s score, whereas Bob seeks to minimize this difference.

Assuming both players play optimally, return the resulting score difference between Alice and Bob.

Constraints:

• n $==$ stones.length

• $2 \leq$ n $\leq 10^5$

• $-10^4 \leq$ stones[i] $\leq 10^4$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.