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.ArrayList;
import java.util.Arrays;

public class oo2 {
    public static void main(String[] args) throws IOException {
        BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(r.readLine());
        String aa = r.readLine();
        String[] as = (aa.split(" "));
        int[] asi = new int[n];
        for (int a = 0; a < n; a++) {
            asi[a] = Integer.parseInt(as[a]);
        }
        ArrayList<Integer> itog = new ArrayList<>();
        Arrays.sort(asi);
        for (int a = 0; a < n/2+n%2; a++) {
            if (asi[a] != 0) {
                itog.add(asi[a]);
                asi[a] = 0;
            }
            if (asi[asi.length-1-a] != 0) {
                itog.add(asi[asi.length-1-a]);
                asi[asi.length-1-a] = 0;
            }
        }
        for (Integer a : itog)
            System.out.print(a+" ");
    }
}
