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.Arrays;
import java.util.Scanner;

public class B652 {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int[] array = new int[a];
        for (int i = 0; i < array.length; i++) {
            array[i] = sc.nextInt();
        }
        Arrays.sort(array);

            for (int i = 0, j = array.length - 1; i <array.length / 2; i++, j--) {
                System.out.print(array[i] + " ");

                System.out.print(array[j] + " ");
            }
            if (array.length%2!=0)
            {
                System.out.println(array[(array.length/2)]);
            }
        }
    }

