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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.StringTokenizer;

import javax.management.Query;

public class wwsdwq {
	public static void main (String [] args) throws NumberFormatException, IOException {
		BufferedReader  br= new BufferedReader(new InputStreamReader( System.in));
		Scanner sc =new Scanner(System .in);
		int n=sc.nextInt();
		Integer[] x=new Integer[n];
		for(int i=0;i<n;i++) {
			x[i]=sc.nextInt();
		}
		Arrays.sort(x);
		int c=0;
		int s=n-1;
		int i=0;
		while(c<n) {
			System.out.print(x[i]+" ");
			c++;
			if(c<n) {
				System.out.print(x[s-i]+" ");
			}
			else
				return;
			i++;
			c++;
		}
	}
}