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 Training {
 
      static  int a[] ;
      	       	   
        
      public static void main(String[] args) throws IOException {
 	 Scanner input = new Scanner(System.in);
       int n = input.nextInt();
       a = new int[n];
       for(int i =0;i<n;i++){
            a[i]= input.nextInt();
          
       }
        
         Arrays.sort(a);
         
  int  k  = n-1;
  
  for(int i=0;i<n/2;i++){
      
      System.out.print(a[i]+" ");
      System.out.print(a[k]+" ");
      k--;
  }
          
  if(n%2==1){
      System.out.print(a[n/2]+" ");
  }
    
 
 }  // end main 
       
  
    
      
    } // end Class
