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 Zsort {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int arr[] = new int[n];
		for(int i=0;i<n;i++){
			arr[i] = sc.nextInt();
		}
		Arrays.sort(arr);
		
		int ans[] = new int[n];
		int start = 0;
		int end   = n-1;
		for(int i=0;i<n;i++){
			if(i%2 == 0)
				ans[i] = arr[start++];
			else
				ans[i] = arr[end--];
		}
		for(int i=0;i<n;i++)
			System.out.print(ans[i]+" ");
		System.out.println();
	}

}
