Crazy Jumping Frogs

There are $N$ frogs, numbered from $1$ to $N$. There are also $2N$ buckets arranged in a straight line, numbered from $1$ to $2N$. Let $A_i$ denote the index of the bucket containing frog $i$. You are given the initial values of $A_i$. Every second, the following happens: - If all frogs are in the same bucket already, nothing happens. - Otherwise, each frog will jump one step towards whichever