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 edu10A 
{
	public static void main(String[] args) 
	{
		Scanner sc = new Scanner(System.in);
		int [] arr = new int[1005];
		int [] ans = new int [1005];
		int n, x, y=0;
		
		for(int i=0; i<1004; i++) ans[i] = 0;
		
		n = sc.nextInt();
		for(int i=0; i<n; i++) arr[i] = sc.nextInt();
		Arrays.sort(arr, 0, n);
		
		if(n % 2 != 0) x = n/2+1;
		else x = n/2;
		
		for(int i=1; i<n; i+=2) ans[i] = arr[x++];
		for(int i=0; i<n; i+=2) ans[i] = arr[y++];
		
		for(int i=1; i<n; i++)
		{
			if((i%2 !=0 && ans[i]< ans[i-1]) || (i%2 == 0 && ans[i]>ans[i-1]))
			{
				System.out.println("Impossible");
				return;
			}
		}
		
		for(int i=0; i<n; i++) System.out.println(ans[i]);
	}
}
