A permutation of 1..
n {
An} is called a Perfect Permutation if the sequence {|
Ai −
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.
The input consists of several lines. Each line contains a positive integer
n ≤ 1000.
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.