Alice and Bob take turns playing a game, with **Alice starting first**.

There are `n`

stones arranged in a row. On each player's turn, while the number of stones is **more than one**, they will do the following:

- Choose an integer
`x > 1`

, and**remove**the leftmost`x`

stones from the row. - Add the
**sum**of the**removed**stones' values to the player's score. - Place a
**new stone**, whose value is equal to that sum, on the left side of the row.

The game stops when **only** **one** stone is left in the row.

The **score difference** between Alice and Bob is `(Alice's score - Bob's score)`

. Alice's goal is to **maximize** the score difference, and Bob's goal is the **minimize** the score difference.

Given an integer array `stones`

of length `n`

where `stones[i]`

represents the value of the `i`

stone ^{th}**from the left**, return *the score difference between Alice and Bob if they both play optimally.*

**Example 1:**

Input:stones = [-1,2,-3,4,-5]Output:5Explanation:- Alice removes the first 4 stones, adds (-1) + 2 + (-3) + 4 = 2 to her score, and places a stone of value 2 on the left. stones = [2,-5]. - Bob removes the first 2 stones, adds 2 + (-5) = -3 to his score, and places a stone of value -3 on the left. stones = [-3]. The difference between their scores is 2 - (-3) = 5.

**Example 2:**

Input:stones = [7,-6,5,10,5,-2,-6]Output:13Explanation:- Alice removes all stones, adds 7 + (-6) + 5 + 10 + 5 + (-2) + (-6) = 13 to her score, and places a stone of value 13 on the left. stones = [13]. The difference between their scores is 13 - 0 = 13.

**Example 3:**

Input:stones = [-10,-12]Output:-22Explanation:- Alice can only make one move, which is to remove both stones. She adds (-10) + (-12) = -22 to her score and places a stone of value -22 on the left. stones = [-22]. The difference between their scores is (-22) - 0 = -22.

**Constraints:**

`n == stones.length`

`2 <= n <= 10`

^{5}`-10`

^{4}<= stones[i] <= 10^{4}

class Solution {
public int stoneGameVIII(int[] stones) {
}
}