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.

Input: 2
Output: true
Explanation:
Alice chooses 1, and Bob has no more moves.

Input: 3
Output: false
Explanation:
Alice chooses 1, Bob chooses 1, and Alice has no more moves.

• 1 <= N <= 1000

1. Iteration
   • Time complexity: $O(n)$
   • Space complexity: $O(1)$
2. Even-odd
   • Time complexity: $O(1)$
   • Space complexity: $O(1)$