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.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main {
	public static void main(String args[]) throws IOException {
		BufferedReader in;
		File f = new File("data.txt");
		StringBuilder out = new StringBuilder();
		if (f.exists()) {
			in = new BufferedReader(new FileReader(f));
		} else {
			in = new BufferedReader(new InputStreamReader(System.in));
		}
		int n = Integer.parseInt(in.readLine());
		int arr[] = readInts(in.readLine());
		Arrays.sort(arr);
		int a = 0;
		int b = arr.length-1;
		while(a<b){
			if(a>0)
				out.append(" ");
			out.append(arr[a]);
			out.append(" ");
			out.append(arr[b]);
			a++;
			b--;
		}
		if(a == b){
			out.append(" " + arr[a]);
		}
		System.out.print(out);
		
	}
	
	public static int[] readInts(String cad) {
		StringTokenizer token = new StringTokenizer(cad, " ");
		int arr[] = new int[token.countTokens()];
		int i = 0;
		while (token.hasMoreTokens())
			arr[i++] = Integer.parseInt(token.nextToken());
		return arr;
	}
}
