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.*;
import java.util.*;

public class B {
    private static final boolean FILE_IO = false;

    static StringTokenizer st;
    static BufferedReader in;
    static PrintWriter out;

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

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

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    static String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String str = in.readLine();
            if (str == null) return null;
            else st = new StringTokenizer(str);
        }
        return st.nextToken();
    }

    public static class Repl {
        public char a, b;

        public Repl(char a, char b) {
            this.a = a;
            this.b = b;
        }
    }

    public static class Pair {
        public char a;
        public int count;

        public Pair(char a, int count) {
            this.a = a;
            this.count = count;
        }
    }

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

        int N = nextInt();
        int a[] = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = nextInt();
        }

        Arrays.sort(a);
        for (int i = 0; i < N; i++) {
            if (i % 2 == 0)
                out.print(a[i / 2] + " ");
            else
                out.print(a[N - (i / 2) - 1] + " ");
        }

        // --
        out.flush();
        out.close();
    }

}