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 zscore
{
  public static void main(String[] args)
  {
    int i,n;
    Scanner sc=new Scanner(System.in);
    n=sc.nextInt();
    int[] a=new int[n+1];
    int[] b=new int[n+1];
    for(i=1;i<n+1;i++)
    {  a[i]=sc.nextInt();}
    int flag=0;
    Arrays.sort(a); 
    b[1]=a[1];
int j=2,m=n;
    for(i=2;i<n+1;i++)
    {
      if(i%2==1) 
      {  b[i]=a[j];
         j++;}
      else
      {  b[i]=a[m];
        m--;}
   }
   for(i=2;i<n+1;i++)
     if((i%2==1&&b[i]>b[i-1])||(i%2==0&&b[i]<b[i-1])) 
      { flag=1;
          break;}
    if(flag==0)
      for(i=1;i<n+1;i++)
        System.out.print(b[i]+" ");
    else
      System.out.println("Impossible");
  }
}