Problem3519--Lucky Permutation

3519: Lucky Permutation

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A permutation p of size n is the sequence p1,p2,...,pn, consisting of n distinct integers, each of them is from 1 to n (1≤pin).

A lucky permutation is such permutation p, that any integer i (1≤in) meets this condition ppi=n-i+1.

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

Input

The first line contains integer n (1≤n≤105) − 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 p1,p2,...,pn (1≤pin) 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 

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