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. Constraints: 1 <= n <= 1000