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.*;
import java.util.*;


public class Zsort {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] a = new int[n];
		int temp;
		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < a.length; i++) 
			a[i]= Integer.parseInt(st.nextToken());
		for (int i = 1; i < a.length; i++) {
			if (i%2==0) {
				if (a[i]>a[i-1]) {
					temp = a[i];
					a[i]=a[i-1];
					a[i-1]=temp;
					if(i>1)
						i=i-2;
				}
			} else {
				if (a[i]<a[i-1]) {
					temp = a[i];
					a[i]=a[i-1];
					a[i-1]= temp;
					if(i>1)
						i=i-2;
				}

			}
		}
		for (int i = 0; i < a.length; i++) {
			System.out.print(a[i] + " ");
			
		}
		
	}

}
