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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

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