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Algorithms

Alice and Bob take turns playing a game, with Alice starting first.

Initially, there is a number <code>n</code> on the chalkboard. On each player&#39;s turn, that player makes a move consisting of:

<ul>
	<li>Choosing any <code>x</code> with <code>0 &lt; x &lt; n</code> and <code>n % x == 0</code>.</li>
	<li>Replacing the number <code>n</code> on the chalkboard with <code>n - x</code>.</li>
</ul>

Also, if a player cannot make a move, they lose the game.

Return <code>true</code> if and only if Alice wins the game, assuming both players play optimally.

&nbsp;
Example 1:

<pre>
Input: n = 2
Output: true
Explanation: Alice chooses 1, and Bob has no more moves.
</pre>

Example 2:

<pre>
Input: n = 3
Output: false
Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>

divisorGame

Divisor Game

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Game Theory

爱丽丝和鲍勃一起玩游戏，他们轮流行动。爱丽丝先手开局。

最初，黑板上有一个数字&nbsp;<code>n</code>&nbsp;。在每个玩家的回合，玩家需要执行以下操作：

<ul>
	<li>选出任一&nbsp;<code>x</code>，满足&nbsp;<code>0 &lt; x &lt; n</code>&nbsp;且&nbsp;<code>n % x == 0</code>&nbsp;。</li>
	<li>用 <code>n - x</code>&nbsp;替换黑板上的数字&nbsp;<code>n</code> 。</li>
</ul>

如果玩家无法执行这些操作，就会输掉游戏。

只有在爱丽丝在游戏中取得胜利时才返回&nbsp;<code>true</code>&nbsp;。假设两个玩家都以最佳状态参与游戏。

&nbsp;

<ol>
</ol>

示例 1：

<pre>
输入：n = 2
输出：true
解释：爱丽丝选择 1，鲍勃无法进行操作。
</pre>

示例 2：

<pre>
输入：n = 3
输出：false
解释：爱丽丝选择 1，鲍勃也选择 1，然后爱丽丝无法进行操作。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>