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 ProB {
	static int n;
	static int[] aa=new int[1005];
	static int[] bb=new int[1005];

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		n=in.nextInt();
		for(int i=1;i<=n;i++)
			aa[i]=in.nextInt();
		Arrays.sort(aa,1,n+1);;
		for(int i=0;i<n/2;i++)
			bb[(i+1)*2]=aa[n-i];
		for(int i=1;i<=n-n/2;i++)
			bb[i*2-1]=aa[i];
		for(int i=1;i<=n;i++)
			System.out.print(bb[i]+" ");
	}
}
