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 Solve2 {
 
  public static void main(String[] args) {
	Scanner scanner = new Scanner(System.in);
	int n = scanner.nextInt();
    int[] arr = new int[n];
    for(int i = 0; i < n; i++)
	  arr[i] = scanner.nextInt();
    Arrays.sort(arr);
	int[] res = new int[n];
	int a = 0;
	int b = n - 1;
	for(int i = 0; i < n; i++) {
	  if (i % 2 == 0) {
	    res[i] = arr[a++];
	  } else {
	    res[i] = arr[b--];
	  }
	}
	for(int i = 0; i < n; i++)
	  System.out.print(res[i]+ " ");
  }
}
