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
//package ladderB;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;

public class zSort {
public static void main(String[] args) throws IOException {
	BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
	in.readLine();
	String input[] =in.readLine().split(" ");
	int [] x=new int[input.length];
	for (int i = 0; i < x.length; i++) {
		x[i]=Integer.parseInt(input[i]);
	}
	Arrays.sort(x);
	ArrayList<Integer> output=new ArrayList<Integer>();
	for (int i = 0, j=x.length-1; i <=x.length/2 & j>=x.length/2; i++,j--) {
		output.add(x[i]);
		if(i!=x.length/2)
		output.add(x[j]);
	}
	for (int i = 0; i <output.size(); i++) {
		System.out.print(output.get(i)+ " ");
	}
}
}
