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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Codef{
    public static void main(String[] args) throws IOException{
        BufferedReader vod=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(vod.readLine());
        StringTokenizer s=new StringTokenizer(vod.readLine());
        int[] ar=new int[n];
        for (int i=0; i<n; i++)
            ar[i]=Integer.parseInt(s.nextToken());
        Arrays.sort(ar);
        for (int i=0; i<n/2; i++){
            System.out.print(ar[i]+" "+ar[n-i-1]+" ");
        }
        if (n%2!=0)
            System.out.print(ar[n/2]);
    }
}