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.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class zsort1
{
    static Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    public static void main(String[] args)
    {
        int n=sc.nextInt();
        int ar[]=new int[n];
        for (int i = 0; i <n ; i++) {
            ar[i]=sc.nextInt();
        }
        int res[]=new int[n];
        Arrays.sort(ar);
        int l=0,r=ar.length-1,j=0;
        while (l<=r)
        {
            res[j++]=ar[l];
            if(l!=r)
                res[j++]=ar[r];
            l++;
            r--;
        }
        for (int i = 0; i <n ; i++) {
            System.out.print(res[i]+" ");
        }
    }
}
