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.*;

public class Solution {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] array = new int[n];
		for(int i = 0; i < n; i++) {
			array[i] = scanner.nextInt();
		}
		Arrays.sort(array);
		int currentOffset = 0;
		boolean start = true;
		while(!exitCondition(n, start, currentOffset)) {
			int index = (start) ? currentOffset : (n-1) - currentOffset;
			System.out.print(array[index] + " ");
			start = !start;
			if(start == true) {
				currentOffset++;
			}
		}
	}
	
	private static boolean exitCondition(int n, boolean start, int currentOffset) {
		if(n%2 == 1) {
			return !start && (currentOffset == Math.floor((double) n / 2));
		} else {
			return start && (currentOffset == n/2);
		}
	}
}