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.*;
import java.io.*;
public class coco{
	public static void main(String[]args){
	Scanner sc=new Scanner(System.in);
	int n=sc.nextInt();
	int[]a=new int[n];
	for(int i=0;i<n;i++){
		a[i]=sc.nextInt();
		}
	Arrays.sort(a);
	int mid=a.length/2;
	int[]x=new int[n];
	int l=1;
	int t=0;
	for(int j=0;j<n-l;j++){
		x[j+t]=a[j];
		x[j+l]=a[mid];
		mid++;
		l+=1;
		t++;
		}
		int temp=0;
	if(a.length%2!=0&&a.length>2){
		temp=x[a.length-2];
		x[a.length-2]=a[a.length-1];
		x[a.length-1]=temp;}
	if(a.length==1){
		x[0]=a[0];
		}
	boolean flag=true;
	for(int k=0;k<n-1&&flag==false;k++){
		if(a[k+1]<a[k])
			flag=false;
		k++;
		}
	if((!flag))
		System.out.println("Impossible");
	else
		for(int m=0;m<n;m++){
			System.out.print(x[m]+" ");
			}
	}
}