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.Scanner;

public class Code {
	public static void main(String []args){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		long a[]=new long[n];
		for(int i=0;i<n;i++){
			a[i]=s.nextLong();
		}
		int t1=0,t2=0;
		long min,max;
		for(int i=0;i<n-1;i++){
			min=a[i];
			max=a[i];
			t1=t2=i;
			for(int j=i+1;j<n;j++){
				if(i%2==0&&min>=a[j]){
					min=a[j];
					t1=j;
				}
				else if(i%2!=0&&max<=a[j]){
					max=a[j];
					t2=j;
				}
			}
			if(i%2==0){
				a[t1]=a[i];
				a[i]=min;
				
			}else{
				a[t2]=a[i];
				a[i]=max;
			}
			
		}

		for(int i=0;i<n;i++)
			System.out.print(a[i]+" ");
	}
	
}
