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.text.*;
import java.util.*;



public class CodeForces8 {

		public static void main(String [] args)
		{
			
			Scanner sc = new Scanner(System.in);
			
			int n = sc.nextInt();
			long arr[] = new long [n];
			
			long arr2[] = new long [n];
			
			for(int i = 0 ; i < n ; i++)
				arr[i] = sc.nextLong();
			
			Arrays.sort(arr);
			int j = 0;
			int c = arr.length - 1;
			for(int i = 0 ; i < n ; i++)
			{
				if(i %2 == 0)
				{
					arr2[i] = arr[j];
					j++;
				}
				else
				{
					arr2[i] = arr[c];
					c--;
				}
			}

			
			for(int i = 0 ; i < n-1 ; i+=2)
			{
				if(arr2[i] > arr2[i+1])
				{
					System.out.println("Impossible");
					return;
				}
			}
			for(int i = 1 ; i < n-1 ; i+=2)
			{
				if(arr2[i] < arr2[i+1])
				{
					System.out.println("Impossible");
					return;
				}
			}
			
			for(int i = 0 ; i < n ; i++)
				System.out.print(arr2[i] + " ");

			
		
			
			
		}
	}




