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.*;

public class Main{
    public static void sort(Vector<Integer> vector){
        int start=0,end=vector.size();
        for(int i=0;i<end-1;i++) {
            int min=vector.get(i);
            int minpos=i;
            for(int j=i+1;j<end;j++){
                if(min>vector.get(j)){
                    minpos=j;
                    min=vector.get(j);
                }
            }
            int temp=vector.get(minpos);
            vector.setElementAt(vector.get(i),minpos);
            vector.setElementAt(temp,i);
        }
    }
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        Vector<Integer> vector=new Vector<Integer>();
        for(int i=0;i<n;i++){
            vector.add(sc.nextInt());
        }
        sort(vector);
        Vector<Integer> result=new Vector<Integer>();
        for(int i=1;i<n+1;i++){
            if(i%2==0){
                result.add(vector.lastElement());
                vector.remove(vector.size()-1);
            }
            else{
                result.add(vector.firstElement());
                vector.remove(0);
            }
        }
        for(int i=0;i<n;i++){
            System.out.println(result.get(i));
        }
    }
}