Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Lucky Permutation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA permutation *p* of size *n* is the sequence *p*_{1}, *p*_{2}, ..., *p*_{n}, consisting of *n* distinct integers, each of them is from 1 to *n* (1 ≤ *p*_{i} ≤ *n*).

A lucky permutation is such permutation *p*, that any integer *i* (1 ≤ *i* ≤ *n*) meets this condition *p*_{pi} = *n* - *i* + 1.

You have integer *n*. Find some lucky permutation *p* of size *n*.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}) — the required permutation size.

Output

Print "-1" (without the quotes) if the lucky permutation *p* of size *n* doesn't exist.

Otherwise, print *n* distinct integers *p*_{1}, *p*_{2}, ..., *p*_{n} (1 ≤ *p*_{i} ≤ *n*) after a space — the required permutation.

If there are multiple answers, you can print any of them.

Examples

Input

1

Output

1

Input

2

Output

-1

Input

4

Output

2 4 1 3

Input

5

Output

2 5 3 1 4

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 08:13:23 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|