Alice and Bob take turns playing a game, with Alice taking the first turn. Initially, there are n stones in a pile.

On each turn, the current player must remove a positive square number of stones from the pile. A player loses the game if they cannot make a valid move on their turn.

Assuming both players play optimally, return true if Alice wins the game, or false otherwise.

Constraints:

• $1 \leq$ n $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.