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.*;
import java.util.*;

public class Problem652B {

	
	static public void main(String[] args) throws java.lang.Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		
		int size;
		List<Integer> available = new ArrayList<Integer>();
		String[] temp = in.readLine().split(" ");
		size = Integer.parseInt(temp[0]);
		temp = in.readLine().split(" ");
		
		int[] res = new int[size];
		
		for(int i = 0; i < size; i++){
			available.add(Integer.parseInt(temp[i]));
		}
		
		Collections.sort(available);
		
		for(int i = 0; i < size; i++){
			if(i == 0 || i % 2 == 0){
				res[i] = available.get(0);
				available.remove(0);
			} else {
				res[i] = available.get(available.size() - 1);
				available.remove(available.size() - 1);
			}
		}
		
		for(int i = 0; i < size; i++){
			System.out.print(res[i] + " ");
		}
		
		System.out.println();
		
	}
}
