Alice and Bob take turns playing a game, with Alice starting first.
\n\nInitially, 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.
\n\nGiven a positive integer n, return true if and only if Alice wins the game otherwise return false, assuming both players play optimally.
\n
Example 1:
\n\n\nInput: n = 1\nOutput: true\nExplanation: Alice can remove 1 stone winning the game because Bob doesn't have any moves.\n\n
Example 2:
\n\n\nInput: n = 2\nOutput: false\nExplanation: Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).\n\n\n
Example 3:
\n\n\nInput: n = 4\nOutput: true\nExplanation: n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).\n\n\n
\n
Constraints:
\n\n1 <= n <= 105Compiled with clang 11 using the latest C++ 20 standard.
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