Divisor Game
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 integer
xwith0 < x < nandn % x == 0. - Replacing the number
non the chalkboard withn - 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 = 2Output
trueAlice chooses 1, and Bob has no more moves.
Example 2
Input
n = 3Output
falseAlice chooses 1, Bob chooses 1, and Alice has no more moves.
Constraints
- 1 <= n <= 1000