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 A {
	static int n;
	static int num[];
	public static int [] m1(int ind, int arr[],boolean taken[]){
		if(ind==n)
			return arr;
		int x= arr[ind-1];
		boolean even= ind%2==1;
		for(int i=0; i<n; i++){
			if(!taken[i])
				if(even){
					if(num[i]>=x){
						taken[i]=true;
						arr[ind]=num[i];
						int result[]=m1(ind+1, arr,taken);
						taken[i]=false;
						if(result!=null)
							return result;
					}
				}
				else if(num[i]<=x){
					taken[i]=true;;
					arr[ind]=num[i];
					int result[]=m1(ind+1, arr,taken);
					if(result!=null)
						return result;
					taken[i]=false;
				}
		}
		return null;
		
	}
	public static void main(String[] args) {
		
		Scanner sc= new Scanner (System.in);
		n= sc.nextInt();
		num= new int [n];
		for(int i=0;i<n; i++)
			num[i]=sc.nextInt();
		int result[]=null;
		int arr[]= new int [n];
		boolean taken[]= new boolean [n];
		for(int i=0; i<n; i++){
			arr[0]=num[i];
			taken[i]=true;
			result=m1(1,arr,taken);
			taken[i]=false;
			if(result!=null)
				break;
		}
		if(result==null)
			System.out.println("Impossible");
		else{
			StringBuilder sb= new StringBuilder("");
			sb.append(result[0]);
			for(int i=1; i<n; i++)
				sb.append(" "+result[i]);
			System.out.println(sb);
		}
			
	}

}
