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:
<li>Choosing any <code>x</code> with <code>0 < x < 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>
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:
<li><code>1 <= N <= 1000</code></li>