Little Elephant and Shifts - Problem

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_ib_i+1... b_nb₁b₂... 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.

Examples

Input

2
1 2
2 1

Output

1
0

Input

4
2 1 3 4
3 4 2 1

Output

3726: Little Elephant and Shifts

Description

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