> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/1510-stone-game-iv.md).

# 1510. Stone Game IV

<https://leetcode.com/problems/stone-game-iv>

## Description

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

Initially, there are `n` stones in a pile.  On each player's turn, that player makes a *move* consisting of removing **any** non-zero **square number** of stones in the pile.

Also, if a player cannot make a move, he/she loses the game.

Given a positive integer `n`. Return `True` if and only if Alice wins the game otherwise return `False`, assuming both players play optimally.

**Example 1:**

```
**Input:** n = 1
**Output:** true
**Explanation:** Alice can remove 1 stone winning the game because Bob doesn't have any moves.
```

**Example 2:**

```
**Input:** n = 2
**Output:** false
**Explanation:** Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).
```

**Example 3:**

```
**Input:** n = 4
**Output:** true
**Explanation:** n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).
```

**Example 4:**

```
**Input:** n = 7
**Output:** false
**Explanation:** Alice can't win the game if Bob plays optimally.
If Alice starts removing 4 stones, Bob will remove 1 stone then Alice should remove only 1 stone and finally Bob removes the last one (7 -> 3 -> 2 -> 1 -> 0). 
If Alice starts removing 1 stone, Bob will remove 4 stones then Alice only can remove 1 stone and finally Bob removes the last one (7 -> 6 -> 2 -> 1 -> 0).
```

**Example 5:**

```
**Input:** n = 17
**Output:** false
**Explanation:** Alice can't win the game if Bob plays optimally.
```

**Constraints:**

* `1 <= n <= 10^5`

## ac

```java
```