Fast forward travelling

Gritukan likes to take cyclic trips around the world. There are $N$ countries numbered $1$ through $N$ in the world. Before starting his travels, Gritukan chooses a permutation $P$ of all $N$ countries. Then, he visits all countries (some countries may be visited multiple times) using the following algorithm: - for each $v$ from $1$ to $N$ inclusive: - travel to country $v$ - travel from c