A student of z-school found a kind of sorting called z-sort. The array a with n elements are z-sorted if two conditions hold:

  1. ai ≥ ai - 1 for all even i, 
  2. ai ≤ ai - 1 for all odd i > 1. 



For example the arrays [1,2,1,2] and [1,1,1,1] are z-sorted while the array [1,2,3,4] isn’t z-sorted.

Can you make the array z-sorted?

Input

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of elements in the array a.

The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of the array a.

Output

If it's possible to make the array a z-sorted print n space separated integers ai — the elements after z-sort. Otherwise print the only word "Impossible".

Examples

Input

4
1 2 2 1


Output

1 2 1 2


Input

5
1 3 2 2 5


Output

1 5 2 3 2
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer buffer;

    public static void solve() {
        int n = ni();
        int[]a = ni(n);
        Arrays.sort(a);
        int s = 0, e = n-1;
        while (s<=e) {
            out.print(a[s++] + " ");
            if (s<=e) out.print(a[e--]+" ");
        }
    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    static String next() {
        while (buffer == null || !buffer.hasMoreElements()) {
            try {
                buffer = new StringTokenizer(in.readLine());
            } catch (IOException e) {
            }
        }
        return buffer.nextToken();
    }

    static int ni() {
        return Integer.parseInt(next());
    }

    static long nl() {
        return Long.parseLong(next());
    }

    static double nd() {
        return Double.parseDouble(next());
    }

    static String ns() {
        return next();
    }

    static int[] ni(int n) {
        int[] res = new int[n];
        for (int i = 0; i < n; i++)
            res[i] = Integer.parseInt(next());
        return res;
    }

    static long[] nl(int n) {
        long[] res = new long[n];
        for (int i = 0; i < n; i++)
            res[i] = Long.parseLong(next());
        return res;
    }

    static double[] nd(int n) {
        double[] res = new double[n];
        for (int i = 0; i < n; i++)
            res[i] = Double.parseDouble(next());
        return res;
    }

    static String[] ns(int n) {
        String[] res = new String[n];
        for (int i = 0; i < n; i++)
            res[i] = next();
        return res;
    }

}