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 practice {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		ArrayList<Integer> a = new ArrayList<Integer>();
		for(int i = 0; i < n; i++) {
			a.add(s.nextInt());
		}
		Collections.sort(a);
		int ind=0;
		while(a.size()!=0) {
			System.out.print(a.get(ind)+" ");
			a.remove(ind);
			if(ind==0) {
				ind=a.size()-1;
			} else {
				ind=0;
			}
		}
	}
}
