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.Scanner;
import java.util.Arrays;

public class MainClass {
    public static Scanner input = new Scanner(System.in);

    public static void main(String[] args) {
        int inputArray[] = new int[input.nextInt()];
        int answerArray[] = new int[inputArray.length];
        for (int i = 0; i < inputArray.length; i++) inputArray[i] = input.nextInt();
        Arrays.sort(inputArray);
        int j = 0, k = (inputArray.length % 2 == 0 ? inputArray.length / 2 : inputArray.length / 2 + 1);
        for (int i = 0; i < inputArray.length; i++) {
            if (i % 2 != 0)
                answerArray[i] = inputArray[k++];
            else
                answerArray[i] = inputArray[j++];
        }
        for (int i = 0; i < inputArray.length; i++) System.out.print(answerArray[i] + " ");
    }
}