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Perfect Permutation
Time Limit:1000MS  Memory Limit:65536K
Total Submit:209 Accepted:74 Special Judged

Description
A permutation of 1..n {An} is called a Perfect Permutation if the sequence {|Aii|} 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 ¡Ü 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.

Sample Input

1
2
4

Sample Output

1
0
3 2 4 1

Source
POJ Monthly--2006.04.28, Dagger@PKU_RPWT

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