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 $1$:

Example $2$:

Example $3$: