# GeetCode Hub

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`

class Solution { public boolean winnerSquareGame(int n) { } }