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 b {
  static Scanner sc=new Scanner(System.in);
  public static void main(String[] args) {
    int n=sc.nextInt();
    ArrayList ar=new ArrayList();
    int[] r=new int[n];
    for(int i=0;i<n;i++)
      r[i]=sc.nextInt();
    Arrays.sort(r);
    int[] a=new int[n];
    for(int i=0;i<=((n%2==0)?n/2-1:n/2);i++) {
      ar.add(r[i]);
      if(i!=n-i-1)
        ar.add(r[n-i-1]);
    }
    if(is(ar))
      for(int m=0;m<ar.size();m++)
      System.out.print(ar.get(m)+" ");
    else
      System.out.println("Impossible");
  }
  static boolean is(ArrayList ar) {
    for(int i=1;i<ar.size();i++) {
      if((i%2!=0&&(Integer)ar.get(i)<(Integer)ar.get(i-1))||(i%2==0&&(Integer)ar.get(i)>(Integer)ar.get(i-1)))
        return false;
    }
    return true;
  }
}