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.*;
import java.util.*;
public class  Zsort
{
  public static void main(String args[])
  {
  Scanner in = new Scanner(System.in);
  int n = in.nextInt();
  int a[] = new int[n];
  int ans[] = new int[n];
  int p=0;
  for(int i=0;i<n;i++)
  {
    a[i]=in.nextInt();
  }
  Arrays.sort(a);
   for(int i=0;i<n;i=i+2)
    {
      ans[i]=a[p++];
	  //System.out.println(ans[i]+" "+p+" "+i);
    }
   for(int i=1;i<n;i=i+2)
   {
     ans[i]=a[p++];
	 //System.out.println(ans[i]+" "+p+" "+i);
   }
   for(int i=0;i<n;i++)
   {
         System.out.print(ans[i]+" ");
   }		 
  }
}  
    
   
  
   