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# 1025. Divisor Game

<https://leetcode.com/problems/divisor-game>

## 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:** n = 2
**Output:** true
**Explanation:** Alice chooses 1, and Bob has no more moves.
```

**Example 2:**

```
**Input:** n = 3
**Output:** false
**Explanation:** Alice chooses 1, Bob chooses 1, and Alice has no more moves.
```

**Constraints:**

* `1 <= n <= 1000`

## ac

```java
```