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.PrintStream;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

//TaskB
public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		Task task = new Task(scanner, System.out);
		task.solve();
		System.out.close();
	}

	static private class Task {
		private Scanner in;
		private PrintStream out;
		
		public Task(Scanner in, PrintStream out) {
			this.in = in;
			this.out = out;
		}
		
		public void solve() {
			int n = in.nextInt();
			List<Integer> ss = new ArrayList<Integer>(1000);
			
			for (int i = 0; i < n; i++) {
				ss.add(in.nextInt());
			}
			
			ss.sort(new Comparator<Integer>() {
				public int compare(Integer o1, Integer o2) {
					if (o1 < o2) return -1;
					else if (o1 > o2) return 1;
					else return 0;
				}
			});
			
			out.print(ss.get(0));
			
			for (int i = 1; i < (ss.size() % 2 == 0 ? n - 1 : n); i+=2) {
				out.print(" " + ss.get(i + 1) + " " + ss.get(i));
			}
			
			if (ss.size() % 2 == 0) {
				out.print(" " + ss.get(ss.size() - 1));
			}
			
			//1 3 2 2 5
		}
	}	 
}