Permutation logarithm

Given two permutations (p = (p_1, p_2, ..., p_N)) and (q = (q_1, q_2, ..., q_N)) of the numbers from (1) to (N), your task is to determine the smallest non-negative integer (d) such that applying the permutation (p) (d) times to the sequence ((1, 2, ..., N)) results in the sequence (q).

Input

The input begins with a single line containing the natural number (N) ((1 $\le$ N $\le$ 2 $\times$ 10^5)). The next two lines provide the permutations (p) and (q). Each line contains (N) integers, representing the respective permutation.

Output

Output the smallest non-negative integer (d) for which (p^d = q). If no such (d) exists, print (-1).

Examples