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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.Collections;
import java.util.Scanner;
import java.util.Vector;

public class Solution{
       
	public static void main(String[] args) {
		Scanner sdf = new Scanner(System.in);
		
                int t=1;
                while(t-->0){
                    int n=sdf.nextInt();
                    Vector<Integer>ts=new Vector<Integer>();
                    while(n-->0){
                        ts.add(sdf.nextInt());
                        
                    }
                    Collections.sort(ts);
                    while(!ts.isEmpty()){
                        System.out.print(ts.remove(0));
                        if(!ts.isEmpty())
                        System.out.print(" "+ts.remove(ts.size()-1)+" ");
                        
                    }
                }
        }
}
   


