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.lang.*;
import java.io.*;

public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] arr=new int[n];
		for(int i=0;i<n;i++){
		    arr[i]=sc.nextInt();
		}
		Arrays.sort(arr);
		int[] brr=new int[n];
		if(n%2!=0){
		    
		    brr[n-1]=arr[n/2];
		}
		    int idx=0;
		    for(int i=0,j=n-1;i<j;i++,j--){
		        brr[idx++]=arr[i];
		        brr[idx++]=arr[j];
		    }
		    boolean f=true;
		    for(int i=1;i<n;i+=2){
		        if(brr[i]>=brr[i-1]){
		            continue;
		        }
		        else{
		            f=false;
		            break;
		        }
		    }
		    if(f==false){
		        System.out.println("Impossible");
		    }
		    else{
		        for(int i=2;i<n;i+=2){
		            if(brr[i]<=brr[i-1]){
		                continue;
		            }
		            else{
		                f=false;
		                break;
		            }
		        }
		        if(f==false){
		        System.out.println("Impossible");
		    }
		    else{
		        for(int i=0;i<n;i++){
		            System.out.print(brr[i]+" ");
		        }
		        System.out.println();
		    }
		        
		    }
		
		
	}
}

