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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class A implements Runnable {


    private void solve() throws Exception {
        int n = nextInt();
        int[] res = solve(n);
//        if (n < 20) {
//            solvePerebor(n);
//        }
        if (res == null) {
            System.out.println(-1);
        } else {
            for (int x : res) {
                System.out.print(x + 1);
                System.out.print(' ');
            }
        }

//        [0]
//        [1, 3, 0, 2]
//        [1, 4, 2, 0, 3]
//        [1, 7, 3, 5, 2, 4, 0, 6]
//        [1, 8, 3, 6, 4, 2, 5, 0, 7]
//        [1, 11, 3, 9, 5, 7, 4, 6, 2, 8, 0, 10]
//        [1, 12, 3, 10, 5, 8, 6, 4, 7, 2, 9, 0, 11]

//        for (int i = 1; i < 15; i++) {
//            solvePerebor(i);
//        }
    }

    private int[] solve(int n) {
        int[] res = new int[n];
        if (n <= 1) {
            return res;
        }
        Arrays.fill(res, -1);
        res[0] = 1;
        res[1] = n - 1;
        for (int i = 2; i < n / 2; i += 2) {
            res[i] = res[i - 2] + 2;
            res[i + 1] = res[i - 1] - 2;
        }
        res[n - 1] = n - 2;
        res[n - 2] = 0;
        for (int i = n - 3; i > n / 2; i -= 2) {
            res[i] = res[i + 2] - 2;
            res[i - 1] = res[i + 1] + 2;
        }
        SortedSet<Integer> avail = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            avail.add(i);
        }
        for (int x : res) {
            if (x >= 0 && !avail.contains(x)) {
                return null;
            }
            avail.remove(x);
        }
        for (int i = 0; i < n; i++) {
            if (res[i] < 0) {
                res[i] = avail.first();
                avail.remove(res[i]);
            }
        }
        if (!good(res)) {
            return null;
        }
        return res;
    }

    private void solvePerebor(int n) {
        int[] p = new int[n];
        int countP = 1;
        for (int i = 0; i < n; i++) {
            p[i] = i;
            countP *= (i + 1);
        }
        for (int perm = 1; perm <= countP; perm++) {
            if (good(p)) {
                System.err.println(Arrays.toString(p));
            }
            if (perm < countP) {
                nextPerm(p);
            }
        }
    }

    private void nextPerm(int[] p) {
        int n = p.length;
        int m = -1;
        for (int i = n - 2; i >= 0; i--) {
            if (p[i] < p[i + 1]) {
                m = i;
                break;
            }
        }
        if (m < 0) {
            System.err.println("Last one, n=" + n);
            return;
        }
        int k = m + 1;
        for (int i = m + 1; i < n; i++) {
            if (p[i] < p[k] && p[i] > p[m]) {
                k = i;
            }
        }
        int tmp = p[k];
        p[k] = p[m];
        p[m] = tmp;
        // swap m+1..n-1
        for (int i = m + 1; i < n; i++) {
            int j = n - i + m;
            if (j <= i) {
                break;
            }
            tmp = p[i];
            p[i] = p[j];
            p[j] = tmp;
        }
    }

    private boolean good(int[] p) {
        int n = p.length;
        for (int i = 0; i < n; i++) {
            if (p[p[i]] != n - i - 1) {
                return false;
            }
        }
        return true;
    }

    private BufferedReader in;
    private StringTokenizer tokenizer = new StringTokenizer("");
    private PrintWriter out;

    private String nextToken() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(in.readLine());
        }
        return tokenizer.nextToken();
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    @Override
    public void run() {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
             PrintWriter out = new PrintWriter(System.out))
        {
            this.in = in;
            this.out = out;
            solve();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    public static void main(String[] args) {
        new Thread(new A()).start();
    }
}
