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;

/**
 * Mar 25, 2016 | 2:41:49 PM
 * <pre>
 * <u>Description</u>
 *
 * </pre>
 *
 * @author Essiennta Emmanuel (colourfulemmanuel@gmail.com)
 */
public class ProblemB{

    public int[] solve(int[] a){
        Arrays.sort(a);
        int[] ans = new int[a.length];
        for (int i = 0, j = 0; i < a.length; i += 2, j++)
            ans[i] = a[j];
        for (int i = 1, j = a.length - 1; i < a.length; i += 2, j--)
            ans[i] = a[j];
        return ans;
    }

    public static void main(String[] args){
        try (Scanner sc = new Scanner(System.in)) {
            int[] a = new int[sc.nextInt()];
            for (int i = 0; i < a.length; i++)
                a[i] = sc.nextInt();
            int[] solve = new ProblemB().solve(a);
            for (int x : solve)
                System.out.print(x + " ");
            System.out.println();
        }
    }
}
