Small GCD Sort

There are $N$ players, numbered from $1$ to $N$. Player $i$'s score is defined to be $\gcd(i, N)$. Here, $\gcd(i, N)$ refers to the largest positive integer that divides both $i$ and $N$. Your task is to find an ordering of the players, from left to right, that satisfies the following conditions: - Between two players with different scores, the one with a higher score must appear somewhere to