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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;

/**
 *
 *
 * @author pttrung
 */
public class C {

    //   public static long x, y, gcd;
    //   public static int Mod = 1000000007;
    public static PrintWriter out;

    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner();
        out = new PrintWriter(System.out);
        //   System.out.println(Integer.MAX_VALUE);
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        int n = in.nextInt();
        int[] result = new int[n];
        result[0] = 1;
        int last = 0;
        boolean[] check = new boolean[n];
        check[0] = true;
        TreeSet<Integer> set = new TreeSet();
        for (int i = 1; i < n; i++) {
            set.add(i);
        }
        if (n % 2 != 0) {
            result[n / 2] = n / 2;
            check[n / 2] = true;
            set.remove(n / 2);
        }
        boolean found = true;
        a:
        while (true) {
            result[result[last]] = n - last - 1;
            check[result[last]] = true;
            set.remove(result[last]);
            last = result[last];

            //System.out.println(last);
            if (check[result[last]]) {
                if (result[result[last]] != n - last - 1) {
                    found = false;
                    break;
                }
                if (set.size() > 2) {
                    int i = set.pollFirst();
                    int j = set.first();
                    result[i] = j;
                    last = i;
                    check[i] = true;
                    continue a;
                }

                break;
            }
        }
        for (int i = 0; i < n; i++) {
            if (result[result[i]] != n - i - 1) {
                found = false;
            }
        }
        if (found) {


            for (int i = 0; i < n; i++) {
                out.print((result[i] + 1) + " ");
            }
        } else {
            out.println(-1);
        }
        out.close();
    }

    public static int cross(Point a, Point b) {
        int val = a.x * b.y - a.y * b.x;
        return val;
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * val * a;
        }
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            if (x != o.x) {
                return x - o.x;
            } else {
                return y - o.y;
            }
        }
    }
//    public static void extendEuclid(long a, long b) {
//        if (b == 0) {
//            x = 1;
//            y = 0;
//            gcd = a;
//            return;
//        }
//        extendEuclid(b, a % b);
//        long x1 = y;
//        long y1 = x - (a / b) * y;
//        x = x1;
//        y = y1;
//
//    }

    public static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        public void update(int index, int value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public int get(int index) {
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
