Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Little Elephant and Shifts

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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* ≤ 10^{5}) — 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

2

1

0

1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/25/2017 21:19:43 (c2).

Desktop version, switch to mobile version.
User lists

Name |
---|