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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;

/**
 * Created by wannabe on 25.03.16.
 */
public class B {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		List<Integer> foo = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			foo.add(in.nextInt());
		}
		List<Integer> res = new ArrayList<>();
		int min, max;

		while (foo.size() > 1)  {
			int[] minMax = minMax(foo);
			min = foo.get(minMax[0]);
			max = foo.get(minMax[1]);
			res.add(min);
			res.add(max);
			foo.remove(minMax[0]);
			foo.remove(minMax[1] < minMax[0] ? minMax[1] : minMax[1] - 1);
		}
		if (!foo.isEmpty()) {
			res.add(foo.get(0));
		}

		for (int i = 0; i < res.size() - 1; i++) {
			if (i == 0 || (i > 1 && i % 2 == 0)) {
				if (res.get(i) > res.get(i + 1)) {
					System.out.println("Impossible");
					return;
				}
			} else {
				if (res.get(i) < res.get(i + 1)) {
					System.out.println("Impossible");
					return;
				}
			}
		}
		System.out.println(res.stream().map(String::valueOf).collect(Collectors.joining(" ")));

	}

	protected static int[] minMax(List<Integer> foo) {
		int min = foo.get(0), max = foo.get(0);
		int minI = 0, maxI = 0;
		for (int i = 0; i < foo.size(); i++) {
			int item = foo.get(i);
			if (item < min) {
				min = item;
				minI = i;
			}
			else if (item >= max) {
				max = item;
				maxI = i;
			}
		}
		return new int[]{minI, maxI};
	}
}