Alice and Bob play a game, with Alice taking the first turn.

Initially, an integer n is given. On each player’s turn, that player performs the following steps:

1. Chooses an integer x such that $0 <$ x $<$ n and n $\\%$ x $= 0$.

2. Replaces the current number n with n $-$ x.

If a player cannot make a move, they lose the game.

Return true if Alice wins the game assuming both players play optimally, and false otherwise.

Constraints:

• $1 \leq$ n $\leq 1000$

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.