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.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

/**
 * Created by danielmckee on 3/25/16.
 */
public class ZSort {
    Scanner in = new Scanner(System.in);
    ArrayList<Integer> a = new ArrayList<>();
    int n;


    private void read(){
        n = in.nextInt();
        for (int i = 0; i < n; i++) {
            a.add(in.nextInt());
        }
    }

    private void solve(){
        List<Integer> evens;
        List<Integer> odds;

        Collections.sort(a);

        if (n%2 == 0) {
            evens = a.subList(0, n/2);
            odds = a.subList(n/2, n);
        }
        else {
            evens = a.subList(0, n/2+1);
            odds = a.subList(n/2+1, n);
        }

        for (int i = 0; i < n/2;i++){
            System.out.print(evens.get(i) + " ");
            System.out.print(odds.get(i) + " ");
        }
        if (n%2 != 0) {
            System.out.print(evens.get(n/2));
        }

        System.out.println();

    }




    public static void main(String[] args) {
        ZSort z = new ZSort();
        z.read();
        z.solve();

    }



}
