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`