{leetcode}/problems/stone-game-iv/[LeetCode - 1510. Stone Game IV ^]
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:
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1 ⇐ n ⇐ 105