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 {|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.
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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