Alice and Bob are playing a game with several piles of stones. You are given an integer array piles, where piles[i] denotes the number of stones in the $i$th pile.

Alice and Bob take turns, with Alice making the first move. On each turn, a player chooses any non empty pile and removes any positive number of stones from that pile. The game ends when all piles are empty. The player who cannot make a move loses the game.

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

Constraints:

• n == piles.length

• $1 \leq$ n $\leq 7$

• $1 \leq$ piles[i] $\leq 7$

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.