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 javax.xml.parsers.DocumentBuilder;
import java.io.*;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int quant = nextInt();
        int mas[] = new int[quant];
        for (int i = 0; i < quant; i++) {
            mas[i] = nextInt();
        }
        Arrays.sort(mas);
        for (int i = 0; i < quant; i++) {
            if (i % 2 == 0) {
                System.out.print(mas[(quant-  1)/ 2 - i / 2] + " ");
            } else {
                System.out.print(mas[quant - 1- i / 2] + " ");
            }
        }
    }


    static BufferedReader br;
    static StringTokenizer st;

    static String nextToken() {
        try {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        return st.nextToken();
    }

    static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    static long nextLong() {
        return Long.parseLong(nextToken());
    }

    static double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    static String next() {
        return nextToken();
    }
}