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.Arrays;
import java.util.Scanner;

public class Node
{
	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[] zsortedarr=new int[100000];
		for(int i=0;i<=(n-1)/2;i++)
		{
			zsortedarr[2*i]=arr[i];
			
		}
		if(n%2!=0)
		for(int i=0;i<(n-1)/2;i++)
		{
			zsortedarr[2*i+1]=arr[n/2+i+1];
			
		}
		else
			for(int i=0;i<=(n-1)/2;i++)
			{
				zsortedarr[2*i+1]=arr[n/2+i];
				
			}
			
		for(int i=0;i<n;i++)
			System.out.print(zsortedarr[i]+" ");
		
	}
}