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.Arrays;
import java.util.Scanner;


public class prac {
	 public static void main(String[] args) {
	        Scanner get=new Scanner(System.in);
	        int n=get.nextInt();
	        Integer a[]=new Integer[n];
	        for(int i=0;i<n;i++)
	        	a[i]=get.nextInt();
	        Arrays.sort(a);
	        for(int i=0;i<a.length/2;i++)
	        {
	        	System.out.print(a[i]+" "+a[a.length-1-i]+" ");
	        }
	        if(a.length%2==1)
	        	System.out.print(a[a.length/2]);
	        
	        
	 }

}