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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = scanner.nextInt();
        }
        Arrays.sort(array);
        int[] cloneArray = new int[size];
        for (int i = 0; i < size; i++){
            cloneArray[i] = array[size - (i+1)];
        }
        ArrayList<Integer> result = new ArrayList<>();
        int i = 0;
        while (i < (double) size / 2) {
            result.add(array[i]);
            result.add(cloneArray[i]);
            i++;
        }
        if (size % 2 != 0) result.remove(size);

        for (int x : result) {
            System.out.print(x + " ");
        }

    }
}