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