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.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.Arrays;

public class Main {

	private static StreamTokenizer inputReader = new StreamTokenizer(
			new BufferedReader(new InputStreamReader(System.in)));

	public static int nextInt() {
		int a = -1;
		try {
			inputReader.nextToken();
			a = (int) inputReader.nval;
		} catch (Exception e) {
		}
		return a;
	}
	
	public static void main(String[] args) {
		int numberOFItems = nextInt();
		int[] items = new int[numberOFItems];
		int[] sortedItems = new int[numberOFItems];
		
		for (int i = 0; i < numberOFItems; i++) {
			items[i] = nextInt();
		}
		
		Arrays.sort(items);
		int leftIndex = 0;
		int rightIndex = numberOFItems - 1;
		int index = 0;
		
		while (index < numberOFItems) {
			if (index % 2 != 0) {
				sortedItems[index] = items[rightIndex];
				rightIndex--;
			} else {
				sortedItems[index] = items[leftIndex];
				leftIndex++;
			}
			
			index++;
		}
		
		StringBuilder builder = new StringBuilder();
		
		for (int i = 0; i < numberOFItems; i++) {
			builder.append(sortedItems[i] + " ");
		}
		
		System.out.println(builder);

	}

}
