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.Arrays;

public class zsort {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader bu = new BufferedReader(new InputStreamReader(System.in));
		
		int l = Integer.parseInt(bu.readLine());
		String[] array = bu.readLine().split(" ");
		
		int[] a = new int[l];
		
		
		
		int c = 0;
		for (String s : array) {
			a[c] = Integer.parseInt(s);
			 
				
			c++;
		}
		
		array = null;
		
		Arrays.sort(a);
		

		//System.out.println(Arrays.toString(a));
		
		
		
		int[] na = new int[l];
		
		int end = l-1;
		int front = 0;
		
		PrintWriter out = new PrintWriter(System.out);
		
		for (int i = 0; i < l; i++) {
			int plus = i+1;
			if (plus % 2 == 0) {
				//System.out.println(end + " " + i);
				na[i] = a[end];
				end--;
				
			}else {
				na[i] = a[front];
				front++;
			}
		
			out.print(na[i] + " ");
		}
		
		out.close();
		
		

	}

}
