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: n = 2 Output: true Explanation: Alice chooses 1, and Bob has no more moves.
Example 2:
Input: n = 3 Output: false Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.
