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;

/**
 * Created by NatchaS on 3/27/16.
 */
public class ZSort {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] A = new int[N];
        for(int i = 0; i < N; i++){
            A[i] = in.nextInt();
        }
        Arrays.sort(A);
        int[] Out = new int[N];
        int i = 0;
        int j = N-1;
        for(int c = 0; c < N; c++){
            if (c%2==0){
                Out[c] = A[i++];
            } else {
                Out[c] = A[j--];
            }
        }

        for(int k = 0; k < N; k++){
            System.out.format("%s ", Out[k]);
        }
    }
}
