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.

爱丽丝和鲍勃轮流玩游戏，爱丽丝首先出发。

最初，黑板上有一个数字N. 在每个玩家的回合中，该玩家进行以下操作：

• 选择0 <x <N且N％x == 0的任何x。

• 用N - x替换黑板上的数字N.

  此外，如果玩家无法移动，他们将失去游戏。

当且仅当Alice赢得比赛时才返回True，假设两个玩家都达到最佳状态。

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.

网上思路

• 总结奇偶性规律, 特别简单，一行代码

• https://xingxingpark.com/Leetcode-1025-Divisor-Game/

• 动态规划，没有看的太懂
• http://www.codeleading.com/article/2789848511/