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 zsort
{
  public static void main(String args[])
  {
     Scanner in=new Scanner(System.in);
     int n=in.nextInt();
     int a[]=new int[n];
     int b[]=new int[n];
     int i,k=0;
     for(i=0;i<n;i++)
        a[i]=in.nextInt();
     Arrays.sort(a);
     for(i=0;i<n;i+=2)
       b[i]=a[k++];
     if(n%2==0)
     {
         for(i=n-1;i>=0;i-=2)
            b[i]=a[k++];
        }
     else
     {
         for(i=n-2;i>=0;i-=2)
            b[i]=a[k++];
        }
     for(i=0;i<n;i++)
        System.out.print(b[i]+" ");
    }
}