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 {
	
	public static void main(String[] args) {
		
		// similar to median finding. Sort & alternate largest/smallest

		Scanner in = new Scanner(System.in);
		String str = in.nextLine();
		int n = Integer.parseInt(str);
		
		int[] arr = new int[n];
		for (int i = 0; i < n; i++){
			arr[i] = in.nextInt();
//			System.out.println(arr[i]);
		}
		
		Arrays.sort(arr);
		
		int[] newArr = new int[n];
		int start = 0;
		int end = n-1;
		for (int i = 0; i < n; i++){
			if((i+1) % 2 == 0 ){ //even
				newArr[i] = arr[end];
				if ((i-1) > 0 && newArr[i] < newArr[i-1]){
					System.out.println("Impossible");
					return;
				}		
				end--;
			}
			else{ // odd
				newArr[i] = arr[start];
				if ((i-1) > 0 && newArr[i] > newArr[i-1]){
					System.out.println("Impossible");
					return;
				}	
				start++;
			}
		}
		for (int i = 0; i < n; i++){
			System.out.print(newArr[i] + " ");
		}
	
		
	}
}
