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
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
import java.util.*;
/**
 *
 * @author Ismael
 */
public class zSort {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int cant= in.nextInt();
        ArrayList<Integer> lista=new ArrayList<Integer>();
        for (int i = 0; i < cant; i++) {
            lista.add(in.nextInt());
        }
        Collections.sort(lista);
        int med=0;
        if(cant%2==1){
        med= (cant+1)/2;
                }else{
            med=cant/2;
        }
        for (int i = 0; i < cant/2; i++) {
            System.out.print(lista.get(i)+" "+lista.get(med+i)+" ");
        }
        if(cant%2==1){
            System.out.print(lista.get(med-1));
        }
        System.out.println("");
    }
}
