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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

 
	public class Main{
		
		public static void main (String [] args) throws IOException{
			BufferedReader br = new BufferedReader( new InputStreamReader(System.in));
			PrintWriter out = new PrintWriter(System.out);
			int n = Integer.parseInt(br.readLine());
			StringTokenizer st = new StringTokenizer(br.readLine());
			int [] x = new int [n];
			for (int i = 0 ; i< n ; i++){
				x[i] = Integer.parseInt(st.nextToken());
			}
			Arrays.sort(x);
			int i ;
			if (n%2 ==0) i = n-2; else i =n-1;
			
			for (int  j =1 ; i>j ; i-=2 , j+=2){
				int temp = x[i];
				x[i] = x[j];
				x[j] = temp;
			}
			
			for (int k = 0 ; k< n ; k++)
				out.print(x[k]+" ");
			
			
			
			
			out.flush();
			out.close();
		}}
