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 ≤ pi ≤ n).

A lucky permutation is such permutation p, that any integer i (1 ≤ i ≤ n) 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 ≤ pi ≤ 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 
import java.io.*;
import java.util.*;

public class CFB {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000L * 1000L * 1000L + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    void solve() throws IOException {
        int n = nextInt();
        if (n % 4 == 2 || n % 4 == 3) {
            outln(-1);
            return;
        }

        if (n == 1) {
            outln(1);
            return;
        }

        int cnt = n / 4;
        List<List<Integer>> ls = new ArrayList<>();
        List<Integer> init = new ArrayList<>();
        init.add(1);
        init.add(n - 1);
        init.add(0);
        init.add(n - 2);
        ls.add(init);
        for (int i = 0; i < cnt - 1; i++) {
            List<Integer> prev = ls.get(ls.size() - 1);
            List<Integer> cur = new ArrayList<>();
            for (int j = 0; j < prev.size(); j++) {
                if (j % 2 == 0) {
                    cur.add(prev.get(j) + 2);
                }
                else {
                    cur.add(prev.get(j) - 2);
                }
            }
            ls.add(cur);
        }

        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < ls.size(); i++) {
            res.add(ls.get(i).get(0));
            res.add(ls.get(i).get(1));
        }

        if (n % 4 != 0) {
            res.add(n / 2);
        }
        for (int i = ls.size() - 1; i >= 0; i--) {
            res.add(ls.get(i).get(2));
            res.add(ls.get(i).get(3));
        }

        for (int i = 0; i < res.size(); i++) {
            out((1 + res.get(i)) + " ");
        }
    }

    void shuffle(long[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            long tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        System.out.format("%.9f%n", val);
    }
    public CFB() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFB();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}
