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
0 < x < Nand
N % x == 0.
- Replacing the number
Non the chalkboard with
N - x.
Also, if a player cannot make a move, they lose the game.
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