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.*;

public class B {

    public static void main(String[] args) {
    	Scanner s = new Scanner(System.in);
    	int n = s.nextInt();
    	int[] arr = new int[n];
    	for(int i=0; i<n; i++)
    		arr[i] = s.nextInt();
    	Arrays.sort(arr);
    	int[] newarr = new int[n];
    	int j=0;
    	for(int i=0; i<n; i+=2)
    		newarr[i] = arr[j++];
    	j=n-1;
    	for(int i=1; i<n; i+=2)
    		newarr[i] = arr[j--];
    	for(int i=0; i<n; i++) System.out.print(newarr[i] + " ");
    	System.out.println();
    }
}
