Description

A permutation of 1..n {A_n} is called a Perfect Permutation if the sequence {|A_i − i|} is a permutation of 0..(n − 1).

For example, {3, 2, 4, 1} is a perfect permutation for {2, 0, 1, 3} is a permutation of 0..3.

Given an integer n, your mission is to find a perfect permutation of 1..n.

Input

The input consists of several lines. Each line contains a positive integer n ≤ 1000.

Output

The output contains one line for each line in the input. If no such perfect permutation exists, output a single number 0 otherwise the perfect permutation. If more than one solution exist, you can output anyone.

1
2
4

1
0
3 2 4 1

Source

POJ Monthly--2006.04.28, Dagger@PKU_RPWT