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.util.*;
import java.io.*;

public class LuckyPermutation {
    public static InputReader in;
    public static PrintWriter out;

    public static final int MOD = (int) (1e9 + 7);

    public static void main(String[] args) {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
        
        int n = in.nextInt();
        if(n <= 3 || n%4 >= 2) {
            out.println(n == 1 ? 1 : -1);
            out.close();
            return;
        }
        int[] p = new int[n + 1];
        
        if((n&1) == 1)
            p[n/2 + 1] = n/2 + 1;
        int no = 1;
        for(int i = n/2; i >= 1; i--, no++) {
            if((i&1) == 0) {
                p[i] = no;
                p[n - i + 1] = n - no + 1;
            } else {
                p[i] = n - no + 1;
                p[n - i + 1] = no;
            }
        }
        for(int i = 1; i <= n/2; i++) {
            if(p[i] == i || p[i] == n - i + 1) {
                p[i]--;
                p[n - i + 1]++;
                p[i + 1]++;
                p[n - i]--;
                break;
            }
        }
        boolean pos = true;
        for(int i = 1; i <= n/2; i++) {
            if(p[i] == i || p[i] == n - i + 1 || p[i] <= 0 || p[i] > n) {
                pos = false;
            }
        }
        if(pos)
            for (int i = 1; i <= n; i++)    out.print(p[i] + " ");
        else
            out.println(-1);

        out.close();
    }

    static class Node implements Comparable<Node> {
        int next;
        long dist;

        public Node(int u, int v) {
            this.next = u;
            this.dist = v;
        }

        public void print() {
            out.println(next + " " + dist + " ");
        }

        public int compareTo(Node n) {
            return Integer.compare(-this.next, -n.next);
        }
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public String readString() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}
