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 q2 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n =sc.nextInt();
        int a[] =new int[n+1];
        for(int i=1;i<=n;i++)
        {
            a[i] = sc.nextInt();
        }
        Arrays.sort(a,1,n+1) ;
        int t[] =new int[n+1];
       int k=n;
        for(int i =2;i<=n;i=i+2)
        {
            t[i] = a[k];
            k--;
        }
        //int s=1;
         k=1;
        for(int i=1;i<=n;i=i+2)
        {  //if(i+1<n+1)
            //{
                //if(a[i]<=t[i+1])
                t[i]=a[k];k++;
               // else {s=-1;break;}
            //}
            /*else
            {
                t[i]=a[k];
            }*/

        }
       
        
        {
            int s=1;
            for(int i=2;i<=n-1;i=i+2)
                
            {
                if(!(t[i]>=t[i-1]&&t[i]>=t[i+1]))
                {
                    s=-1;
                    break;
                }
            }
            if(n%2==0&&t[n]<t[n-1])
                s=-1;
            if(s==-1)
                System.out.println("Impossible");
            else
                
            
            for(int i=1;i<=n;i++)
                System.out.print(t[i]+" ");
        }
            
    }
    
}
