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.IOException;
import java.util.Arrays;
import java.util.*;

public class sorting {
	public static void main(String[]args) throws IOException {
	    Scanner sc=new Scanner(System.in);
	    int n=sc.nextInt();
	    int a[]=new int[n];
	    int r[]=new int[n];
	    for(int i=0;i<n;i++){
	    	a[i]=sc.nextInt();
	    }
	    Arrays.sort(a);
	    String x="";
	    int i=0;
	    int c=0;
	    int j=n-1;
	    while(c<n){
	    		if(c%2!=0){
	    			r[c]=a[j];
	    			j--;
	    			if(c>0&&r[c]<r[c-1]){
	    				System.out.println("Impossible");
	    	    		break;
	    			}
	    		}
	    		else{
	    			r[c]=a[i];
	    			i++;
	    			if(c>0&&r[c]>r[c-1]){
	    				System.out.println("Impossible");
	    	    		break;
	    			}
	    		}
	    		x+=r[c]+" ";
	    		c++;
	    	}
	    System.out.println(x);	
  }
	
}