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).

Constraints:

- `1 <= n <= 105`