Alice and Bob take turns playing a game with Alice starting first.
In this game, there are n piles of stones. On each player's turn, the player should remove any positive number of stones from a non-empty pile of his or her choice. The first player who cannot make a move loses, and the other player wins.
Given an integer array piles, where piles[i] is the number of stones in the ith pile, return true if Alice wins, or false if Bob wins.
Both Alice and Bob play optimally.
Example 1:
Input: piles = [1] Output: true Explanation: There is only one possible scenario: - On the first turn, Alice removes one stone from the first pile. piles = [0]. - On the second turn, there are no stones left for Bob to remove. Alice wins.
Example 2:
Input: piles = [1,1] Output: false Explanation: It can be proven that Bob will always win. One possible scenario is: - On the first turn, Alice removes one stone from the first pile. piles = [0,1]. - On the second turn, Bob removes one stone from the second pile. piles = [0,0]. - On the third turn, there are no stones left for Alice to remove. Bob wins.
Example 3:
Input: piles = [1,2,3] Output: false Explanation: It can be proven that Bob will always win. One possible scenario is: - On the first turn, Alice removes three stones from the third pile. piles = [1,2,0]. - On the second turn, Bob removes one stone from the second pile. piles = [1,1,0]. - On the third turn, Alice removes one stone from the first pile. piles = [0,1,0]. - On the fourth turn, Bob removes one stone from the second pile. piles = [0,0,0]. - On the fifth turn, there are no stones left for Alice to remove. Bob wins.
Constraints:
n == piles.length1 <= n <= 71 <= piles[i] <= 7