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 abgupta on 3/19/17.
 */
public class C_652_B {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = readIntArray(in, n);

        Arrays.sort(a);

        int[] b = new int[n];

        for(int i=0;i<n;i++) {
            if (2*i >= n) break;
            b[2*i] = a[i];
        }

        for(int j=1;j<n;j++) {
            if (2*j-1>=n) break;
            b[2*j-1] = a[n-j];
        }

        for(int i=0;i<n;i++) {
            System.out.print(b[i]+ " ");
        }

    }

    private static int[] readIntArray(Scanner in, int n) {
        int[] a = new int[n];
        for(int i=0;i<n;i++)
            a[i] = in.nextInt();

        return a;
    }
}
