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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


import java.util.StringTokenizer;



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

}
