A8757 | Little Elephant and Shifts

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 $a$ ?

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.

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.