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 $*n*$ $(1 ≤ *n* ≤ 10^{5})$ — 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.