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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class zsort {
	public static void main(String []args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n =Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		ArrayList <Integer> le=new ArrayList<Integer>();
		for(int i=0;i<n;i++) {
			le.add(Integer.parseInt(st.nextToken()));
		}
		Collections.sort(le);
		int [] arr=new int[n];
		int c=0;
		for(int i=0;i<n;i++) {
			if(i==0) {
				arr[i]=le.get(c);
				c++;
			}
			else if(i%2==1) {
				arr[i]=le.get(le.size()-c);
				
			}else {
				arr[i]=le.get(c);
				c++;

			}
		}
		for(int i=0;i<n;i++) {
			if(i==n-1) {
				System.out.print(arr[i]);
			}else {
				System.out.print(arr[i]+" ");
			}
			
		}
	}
}
