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.*;

public class solve {

	public static void main(String[] args) {

		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int c= 0 ; 
		int arr[] = new int[n];
		for(int i=0;i<n;i++)
			arr[i]=in.nextInt();
		Arrays.sort(arr);
	int k= 1; 
	int i=0;
	int l = n-1 ;
	
	while(c<n){
		if(k%2==1){
			System.out.print(arr[i]+" ");
		i++;}
		else if(k%2==0){
			System.out.print(arr[l]+" ");
		l--;}
		k++;c++;
		
		
		
	}
	


	}

}
