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 = 1Output:trueExplanation:Alice can remove 1 stone winning the game because Bob doesn't have any moves.

**Example 2:**

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

**Example 3:**

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

**Example 4:**

Input:n = 7Output:falseExplanation: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 = 17Output:falseExplanation:Alice can't win the game if Bob plays optimally.

**Constraints:**

`1 <= n <= 10^5`

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