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.util.*;
public class Zsort652B 
{

	public static void main(String[] args) 
	{
		Scanner sc = new Scanner (System.in);
		int n = sc.nextInt();
		int[] arr = new int [n];
		for(int i = 0 ; i<n ; i++)
		{
			arr[i]=sc.nextInt();
		}
		Arrays.sort(arr);
		int[]a = new int[(int)Math.ceil( n / 2.0)];
		int [] b = new int[n-(int)Math.ceil( n / 2.0)];
		int j =0;
		for(int i = 0 ; i <(int)Math.ceil( n / 2.0);i++)
		{
			a[i]=arr[j++];
		}
		for(int i = 0 ; i< n-(int)Math.ceil( n / 2.0);i++)
		{
			b[i]=arr[j++];
		}
		
		for(int i=0,k=0,l = 0 ; i<n ; i++)
		{
			if(i%2==0)
				arr[i]=a[k++];
			else
				arr[i]=b[l++];
		}
		for(int i = 0 ; i<n ; i++)
		{
			System.out.print(arr[i]);
			if(i!=n-1)System.out.print(" ");
		}
		
		
	}

}
