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.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Achill {
    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            int n = sc.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; ++i) {
                a[i] = sc.nextInt();
            }
            Arrays.sort(a);
            int[] b = new int[n];
            boolean flag = true;
            for(int i = 0, k = 0; i < n; ++i)
            {
                b[i] = a[flag ? k : n-1-k];
                k += i % 2;
                flag = !flag;
            }
            Arrays.stream(b).forEach(item -> System.out.print(item + " "));
        }
    }
}
