A permutation ~P~ of length ~N~ is the sequence ~P_1, P_2, \ldots, P_N,~ consisting of ~N~ distinct integers, each of them in the range ~[1, N]~.

A sketchy permutation is a permutation ~P~ such that for all integer ~i~ ~(1 \le i \le N)~, it satisfies constraint that ~P_{P_i} = N - i + 1~.

You have the integer ~N~. Find some sketchy permutation ~P~ of length ~N~.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~, the required permutation length.

Output Specification

Print -1 if the sketchy permutation ~P~ of length ~N~ does not exist.

Otherwise, print ~N~ distinct integers ~P_1, P_2, \ldots, P_N (1 \le P_i \le N)~, the required permutation.

If there are multiple such permutations, print the lexicographically smallest one.

Sample Input 1

1

Sample Output 1

1

Sample Input 2

5

Sample Output 2

2 5 3 1 4

Sample Input 3

2

Sample Output 3

-1