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.Arrays;
import java.util.Scanner;

public class B {

	public static int I(String s) {
		return Integer.parseInt(s);
	}

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int N = I(in.nextLine());
		String[] s = in.nextLine().split("\\s+");
		int[] n = new int[N];
		for (int i = 0; i < N; i++)
			n[i] = I(s[i]);
		Arrays.sort(n);
		int[] m = new int[N];
		for (int i = 0, j = N - 1, k = 0; k < N;) {
			m[k++] = n[i++];
			if (j > i)
				m[k++] = n[j--];
		}

		StringBuilder sb = new StringBuilder(Integer.toString(m[0]));
		for (int i = 1; i < N; i++)
			sb.append(" ").append(Integer.toString(m[i]));
		System.out.println(sb.toString());
		in.close();
	}
}