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
//z -sorting
//anshumansrivastava80@gmail.com

import java.util.Scanner;
public class B
{
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int N = s.nextInt();
		long[] inpu = new long[N+1];

		for(int i=1;i<=N;i++)
		{
			inpu[i] = s.nextLong();
		}

		insort(inpu);

		if(N%2==0)
			for(int i=1;i<N/2+1;i++)
			{
				System.out.print(inpu[i]+" "+inpu[N/2+i]+" ");
			}
		else
		{
			for(int i=1;i<N/2+1;i++)
			{
				System.out.print(inpu[i]+" "+inpu[(N+1)/2+i]+" ");
			}
			System.out.print(inpu[N/2+1]);
		}
		System.out.println("");		

	}

	public static void insort(long[] ary)
	{
		for (int i=1;i<ary.length;i++)
			for(int j=i;j>1;j--)
				if(ary[j]<ary[j-1])
				{
					long k = ary[j];
					ary[j]= ary[j-1];
					ary[j-1] = k;
				}
				else 
					break;
	}
}