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Description

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: 2

Output: true

Explanation: Alice chooses 1, and Bob has no more moves.

Example 2:

Input: 3

Output: false

Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.

 

Note:

  1. 1 <= N <= 1000

Solutions

Python3

Java

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