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Alex and Lee continue their games with piles of stones. There are a number of piles **arranged in a row**, and each pile has a positive integer number of stones `piles[i]`

. The objective of the game is to end with the most stones.

Alex and Lee take turns, with Alex starting first. Initially, `M = 1`

.

On each player's turn, that player can take **all the stones** in the **first** `X`

remaining piles, where `1 <= X <= 2M`

. Then, we set `M = max(M, X)`

.

The game continues until all the stones have been taken.

Assuming Alex and Lee play optimally, return the maximum number of stones Alex can get.

**Example 1:**

Input:piles = [2,7,9,4,4]Output:10Explanation:If Alex takes one pile at the beginning, Lee takes two piles, then Alex takes 2 piles again. Alex can get 2 + 4 + 4 = 10 piles in total. If Alex takes two piles at the beginning, then Lee can take all three piles left. In this case, Alex get 2 + 7 = 9 piles in total. So we return 10 since it's larger.

**Constraints:**

`1 <= piles.length <= 100`

`1 <= piles[i] <= 10 ^ 4`