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.