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.Arrays;
import java.util.Scanner;

/**
 * Created by Ashiq on 6/10/2016.
 */
public class Zsort {
    public static void main(String[] args) {
        int ara[];
        Scanner s=new Scanner(System.in);
        int a=s.nextInt();
        ara=new int[a];
        for (int i = 0; i < ara.length; i++) {

            ara[i]=s.nextInt();
        }
        Arrays.sort(ara);
        int []ans=new int[a+1];
        int k=0;
        for( int n=1;n<=a;n+=2)
        {
            ans[n]=ara[k];
            k++;
        }
        for( int n=2;n<=a;n+=2)
        {
            ans[n]=ara[k];
            k++;
        }
        for (int i = 1; i < ans.length; i++) {
            System.out.print(ans[i]+" ");

        }
    }
}
