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.io.PrintWriter;
import java.util.*;
public class Zsort {

	public static void main(String[] args) throws IOException{
		// TODO Auto-generated method stub
		Scanner sc = new Scanner (System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		int arr [] = new int [n];
		
		for (int i = 0 ; i  <  arr.length ; i++) arr[i] = sc.nextInt();
		
		Arrays.sort(arr);
		
		int i = 0;
		int q = arr.length -1;
		
		while (i <= q) {
			System.out.print(arr[i++] + " ");
			if (i <= q)
				System.out.print(arr[q--] + " ");
		}
	}

}
