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.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class m {

	public static void main(String[] args) throws IOException, InterruptedException {
		PrintWriter pw = new PrintWriter(System.out);
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		st = new StringTokenizer(br.readLine());
		int[] l = new int[n];
		for (int i=0;i<n;i++) {
			l[i]=Integer.parseInt(st.nextToken());
		}
		int tmp;
		for (int i=1;i<n;i++) {
			if (i%2!=0) {
				if (l[i]<l[i-1]) {
					tmp = l[i];
					l[i]=l[i-1];
					l[i-1]=tmp;
				}
			}
			else {
				if (l[i]>l[i-1]) {
					tmp = l[i];
					l[i]=l[i-1];
					l[i-1]=tmp;
				}
			}
		}
		for (int i=0;i<n;i++) {
			if (i==n-1) {
				pw.print(l[i]);
				break;
			}	
			pw.print(l[i]+" ");
		}
		pw.flush();pw.close();
	}
	
}
