1025. Divisor Game

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

Initially, there is a number N on the chalkboard. On each player's turn, that player makes a move consisting of:

• Choosing any x with 0 < x < N and N % x == 0.
• Replacing the number N on the chalkboard with N - x.

Also, if a player cannot make a move, they lose the game.

Return True if and only if Alice wins the game, assuming both players play optimally.

Example 1:

Input: 2

Output: true

Explanation: Alice chooses 1, and Bob has no more moves.

Example 2:

Input: 3

Output: false

Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.

Note:

1. 1 <= N <= 1000