Problem K. Kendall

Author:A. Tyshchenko, A. Klenin   Time limit:1 sec
Input file:Standard input   Memory limit:512 Mb
Output file:Standard output  

Statement

Let X, Y be sequences each consisting of N unique integers and 1 ⩽ xi,yi⩽ N. The Kendall correlation coefficient between these sequences is

τ = ijsgn(xi − xj)sgn(yi − yj).

sgn(x) = x < 0⇒  − 1, x > 0⇒  + 1, x = 0⇒ 0.

Suppose that sequence X is 1, 2, …, N. Your program must find sequence Y such that τ(X, Y) = 0.

Input format

Input contains a single integer N — number of elements in a sequence.

Output format

Output must contain N integers — sequence Y. If the required sequence does not exist, output  − 1. If there are several solutions, output any of them.

Constraints

1 ≤ N ≤ 105

Sample tests

No. Standard input Standard output
1
6
-1
2
4
4 1 2 3

0.055s 0.007s 13