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;

public class B652 {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int[] a = new int[n];
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = s.nextInt();
        }
        Arrays.sort(a); // ascending , for all elements

        int j=a.length-1;
        for (int i = 1; i < a.length; i+=2,j--) {
            res[i]=a[j];
        }

        j=0;
        for (int i = 0; i < a.length; i+=2,j++) {
            res[i]=a[j];
        }

        for(int cell:res) System.out.print(cell+" ");
    }

    static void swap(int[] arr,int index_a,int index_b)
    {
        int tmp = arr[index_a];
        arr[index_a] = arr[index_b];
        arr[index_b] = tmp;
    }
}
