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.util.Arrays;

public class Main {
	
	
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String s;
		s = br.readLine();
		int n = Integer.parseInt(s);
		s = br.readLine();
		String[] sArr = s.split(" ");
		int[] arr = new int[n];
		for(int i=0;i<n;i++)
			arr[i] = Integer.parseInt(sArr[i]);
		Arrays.sort(arr);
		int start=0;
		int end=arr.length-1;
		int[] out = new int[n];
		int i=0;
		boolean ok = true;
		while(start<=end && i<out.length)
		{
			//if(arr[start])
			out[i++] = arr[start++];
			if(i<out.length)
				out[i++] = arr[end--];
		}
		
		for(int k=0;k<out.length;k++)
		{
			System.out.print(out[k]);
			if(k !=out.length-1)
				System.out.print(" ");
		}
	}

}
