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.StringTokenizer;

public class Problem652B
{
	public static void main(String[] args) throws IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] a = new int[n];
		StringTokenizer st = new StringTokenizer(br.readLine());
		for(int i=0 ; i<n ; i++)
		{
			a[i] = Integer.parseInt(st.nextToken());
		}
		Arrays.sort(a);		//sort whole array
		int[] b = new int[n];
		int k = n/2;		//half size of array
		
		for(int i=0 ; i<n-k ; i++)
		{
			b[2*i] = a[i];			//insert lower half to odd indices of b
		}
		
		for(int i=0 ; i<k ; i++)
		{
			b[2*i+1] = a[n-k+i];	//insert upper half to even indices of b
		}
		
		//it is always possible to z-sort arrays
		for(int i=0 ; i<n ; i++)
		{
			System.out.print(b[i]+" ");
		}
	}
}
