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.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	static Scanner in =  new Scanner(System.in);
	static int n;
	static int[] v;
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
	public static void main(String[] args) throws IOException
	{
		n=in.nextInt();
		v=new int[n+1];
		for(int i=1;i<=n;i++)v[i]=in.nextInt();
		Arrays.sort(v);
		for(int i=2;i<n;i+=2)
		{
			int aux = v[i];
			v[i]=v[i+1];
			v[i+1]=aux;
		}
		for(int i=1;i<=n;i++)out.write(v[i]+" ");
		out.flush();
	}
}
