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.*;
import java.util.*;

public class practice652b {
	public static void main(String[] args) throws Exception {
		
//		BufferedReader f = new BufferedReader(new  FileReader (new  File("sample.txt")));	
//		PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("sample.txt")));
//		StringTokenizer st = new StringTokenizer(f.readLine());

		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));	
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		StringTokenizer st = new StringTokenizer(f.readLine());

		int n = Integer.parseInt(st.nextToken());
		
		int[] arr = new int[n];
		
		st = new StringTokenizer(f.readLine());
		for (int i = 0; i < n; i++) {
			arr[i] = Integer.parseInt(st.nextToken());
		}
 
		Arrays.sort(arr);
		
		int i = 0;
		int j = n-1;
		
		while(j >= i) {
			if (i != 0) {
				out.print(" ");
			}
			if (j != i) {
				out.print(arr[i] + " " + arr[j]);
			} else {
				out.print(arr[i]);
			}
			i++;
			j--;
		}
		
		out.close();
	}
}


