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.ArrayList;
import java.util.Scanner;

/**
 * Created by Иван on 25.03.2016.
 */
public class t2 {
   public static Scanner in;
    public static void main(String args[]){
        in=new Scanner(System.in);
        int n=in.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=in.nextInt();
        }
        qsort(a,0,n-1);
        ArrayList<Integer> ar=new ArrayList<>();
      if(n%2==0) {
          for (int i = 0; i < n / 2; i++) {
              ar.add(a[i]);
              ar.add(a[n-1-i]);
          }
      } else{
          ar.add(a[0]);
          for (int i = 1; i <= n / 2 ; i++) {
              ar.add(a[n-i]);
              ar.add(a[i]);

          }

      }
        for(int i=0;i<ar.size();i++){
            System.out.print(ar.get(i)+" ");
        }




    }
    public static void qsort(int a[],int low,int high){
        int i=low;
        int j=high;
        int x=a[low+(high-low)/2];
      do {
           while (a[i] < x) i++;
           while (a[j] > x) j--;
           if(i<=j){
               int t=a[i];
               a[i]=a[j]; a[j]=t;
               i++;j--;
           }
       } while(i<=j);
        if(low<j) qsort(a,low,j);
        if(i<high) qsort(a,i,high);


    }
}
