Divisor Game
James and Oliver take turns playing a game, with James 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
with0 < x < N
andN % x == 0
where 1 <= N <= 1000. - Replacing the number
N
on the chalkboard withN - x
.
Also, if a player cannot make a move, they lose the game.
Return True
if and only if James wins the game, assuming both players play optimally.
Example 1:
Input: 2
Output: true
Explanation:
James chooses 1
, and Oliver has no more moves.
Example 2:
Input: 3
Output: false
Explanation:
James chooses 1
, and Oliver chooses 1
, and James has no more moves.