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 ≤ i ≤ n ) element of the permutation a as a i , the j -th (1 ≤ j ≤ n ) element of the permutation b — as b j .
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 a i = b j .
A cyclic shift number i (1 ≤ i ≤ n ) of permutation b consisting from n elements is a permutation b i b i + 1 ... b n b 1 b 2 ... b i - 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 ?
Input
The first line contains a single integer n (1 ≤ n ≤ 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.
Output
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.