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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.Arrays;

public class Main {

    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pr = new PrintWriter(System.out);
        int n = Integer.parseInt(br.readLine());
        String tokens[] = br.readLine().split("\\s+");
        int aArray[] = new int[n];

        for (int i = 0; i < n; ++i)
            aArray[i] = Integer.parseInt(tokens[i]);

        Arrays.sort(aArray);
        for (int i = 1; i < n - 1; i += 2) {
            int temp = aArray[i];
            aArray[i] = aArray[i + 1];
            aArray[i + 1] = temp;
        }
        for (int i = 0; i < n; i++)
            pr.print(aArray[i] + " ");
        

        pr.flush();
        pr.close();

    }
}
