CF220C.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?

小象有两个长度为 $n$ 的排列 $a$ 和 $b$，其中每个排列均由 $1$ 到 $n$（含）的整数组成。记排列 $a$ 的第 $i$ 个元素（$1 \le i \le n$）为 $a_i$，排列 $b$ 的第 $j$ 个元素（$1 \le j \le n$）为 $b_j$。

排列 $a$ 与 $b$ 之间的距离定义为：某个相同数字在 $a$ 中的位置与在 $b$ 中的位置之差的绝对值的最小值。更形式化地，该距离为满足 $a_i = b_j$ 的所有 $(i, j)$ 对中，$|i - j|$ 的最小值。

排列 $b$（含 $n$ 个元素）的循环移位编号 $i$（$1 \le i \le n$）是指排列 $b_i\,b_{i+1}\,\dots\,b_n\,b_1\,b_2\,\dots\,b_{i-1}$。一个排列共有 $n$ 个循环移位。

小象想知道：对排列 $b$ 的所有 $n$ 个循环移位，每个循环移位与排列 $a$ 之间的距离分别是多少？

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.

第一行包含一个整数 $n$（$1 \leq n \leq 10^5$）—— 排列的长度。
第二行包含排列 $a$，由 $n$ 个互不相同的、取值范围在 $1$ 到 $n$（含端点）之间的整数组成，数字之间以单个空格分隔。
第三行以相同格式给出排列 $b$。

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.

在 n 行中输出 n 个整数——即各循环移位对应的答案。请按照排列 b 中循环移位的编号顺序输出答案，即先输出第 1 个循环移位的答案，再输出第 2 个循环移位的答案，依此类推。