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.io.*;
import java.util.*;

public class Main {




    public static void main(String[] args) throws IOException, InterruptedException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = Integer.parseInt(br.readLine());

        StringTokenizer st1 = new StringTokenizer(br.readLine());

        Integer arr[] = new Integer[n];

        for(int i = 0 ; i < n ; i++)
        {
            arr[i] = Integer.parseInt(st1.nextToken());
        }

        Arrays.sort(arr);

        int newArr[] = new int [n];

        for(int i = 0 , j = arr.length - 1 , k = 0 ; i <= j ; i++ , j-- )
        {
            if(i != j) {
                newArr[k++] = arr[i];
                newArr[k++] = arr[j];
            }
            else
            {
                newArr[k++] = arr[i];
            }

        }
        boolean flag = true;

        for(int i = 0 ; i < n - 1 ; i++)
        {
            if(i % 2 == 0)
            {
                if(newArr[i] > newArr[i+1])
                {
                    flag = false;
                    break;
                }
            }
            else
            {
                if(newArr[i] < newArr[i+1])
                {
                    flag = false;
                    break;
                }
            }
        }

        if(flag)
        {
            for(int i = 0 ; i < n ; i++)
            {
                out.print(newArr[i] + " ");
            }
            out.println();
        }
        else
        {
            out.println("Impossible");
        }


        out.flush();
        out.close();

    }

}


