The Little Elephant has two permutations a and b of length n, consisting of numbers from 1 to n, inclusive. Let's denote the i-th (1 \le i \le n) element of the permutation a as ai, the j-th (1 \le j \le n) element of the permutation b - as bj.

The distance between permutations a and b is the minimum absolute value of the difference between the positions of the occurrences of some number in a and in b. More formally, it's such minimum |i-j|, that ai=bj.

A cyclic shift number i (1 \le i \le n) of permutation b consisting from n elements is a permutation bibi+1... bnb1b2... bi-1. Overall a permutation has n cyclic shifts.

The Little Elephant wonders, for all cyclic shifts of permutation b, what is the distance between the cyclic shift and permutation a?

The first line contains a single integer n (1 \le n \le 105) - the size of the permutations. The second line contains permutation a as n distinct numbers from 1 to n, inclusive. The numbers are separated with single spaces. The third line contains permutation b in the same format.

In n lines print n integers - the answers for cyclic shifts. Print the answers to the shifts in the order of the shifts' numeration in permutation b, that is, first for the 1-st cyclic shift, then for the 2-nd, and so on.