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 sc = new Scanner(System.in);
       int n = sc.nextInt();
         int a[] = new int[n];        
     for (int i = 0; i < n; i++) 
        a[i] = sc.nextInt();
     
       Zsort(a);  
       for(int i = 0 ; i <a.length ; i++)
    	   System.out.print(a[i] + " ");
     
    	
    }
    public static void Zsort(int [] a) {
    	Arrays.sort(a);
    	int j =1;
    	int temp = 0;
    	for(int i = 2 ; i<a.length ;i+=2)
    	if(a[i] > a[i-1]) {
    		temp = a[j];
    		a[j] = a[i];
    		a[i] = temp;
    		j+=2;
    		
    	}
    }
    
 }