1510 - Stone Game IV\.

Hard

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:

• <code>1 <= n <= 10⁵</code>