divisor-game.md

<p>Alice and Bob take turns playing a game, with Alice starting first.</p>

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

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

<p>Also, if a player cannot make a move, they lose the game.</p>

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

<p>&nbsp;</p>

<ol>
</ol>

<div>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input: </strong><span id="example-input-1-1">2</span>
<strong>Output: </strong><span id="example-output-1">true</span>
<strong>Explanation:</strong> Alice chooses 1, and Bob has no more moves.
</pre>

<div>
<p><strong>Example 2:</strong></p>

<pre>
<strong>Input: </strong><span id="example-input-2-1">3</span>
<strong>Output: </strong><span id="example-output-2">false</span>
<strong>Explanation:</strong> Alice chooses 1, Bob chooses 1, and Alice has no more moves.
</pre>

<p>&nbsp;</p>

<p><strong>Note:</strong></p>

<ol>
	<li><code>1 &lt;= N &lt;= 1000</code></li>
</ol>
</div>
</div>