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
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) a[i] = sc.nextInt();
		zSort(a);
		for (int i = 0; i < n; i++) System.out.print(a[i] + " ");
	}
	
	public static void zSort(int[] a) {
		Arrays.sort(a);
		// 1, 2, 2, 3, 5 -> 1, 5, 2, 3, 2
		int j = 1;
		for (int i = 2; i < a.length; i+=2) {
			if (a[i] > a[i-1]) {
				int tmp = a[j];
				a[j] = a[i];
				a[i] = tmp;
				j += 2;
			}
		}
	}
}
 			       			  	  	 		 					 	