Alice and Bob play a game with piles of stones arranged in a row.

There is an even number of piles, where piles[i] represents the number of stones in the $i^{ ext{th}}$ pile. The total number of stones across all piles is odd, so there can be no ties.

Alice and Bob take turns, with Alice making the first move. On each turn, a player takes all the stones from either the beginning or the end of the current row of piles. This continues until no piles remain. The player with the higher total number of stones wins.

Assuming both players play optimally, return true if Alice wins the game, or false otherwise.

Constraints:

• $2 \leq$ piles.length $\leq 500$

• piles.length is even.

• $1 \leq$ piles[i] $\leq 500$

• sum(piles[i]) is odd.

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.