Costly Permutations

Every Christmas, Chef has a peculiar tradition of gifting a permutation $P$ of length $N$. For each index $i$ in the permutation $(1 \leq i \leq N)$, there is an associated value $V_i$. The value $V_i$ is the number of steps needed to return to index $i$ when following this path: - Start at index $i$. - Let the current index be $k$, then, move to the index $P_k$. - Continue until you return to in