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Language: Perfect Permutation
Description A permutation of 1.. n {A} is called a Perfect Permutation if the sequence {|_{n}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.
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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