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

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