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.StringTokenizer;

public class AP {
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public Scanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }
    }

    public static void main(String[] args) throws IOException {
        PrintWriter pw = new PrintWriter(System.out);
        Scanner sc = new Scanner(System.in);
        int x = sc.nextInt();
        int[] y = new int[x];
        int temp;
        for (int i = 0; i < x; i++) {
            y[i] = sc.nextInt();
        }

        for (int i = 1; i < x; i++) {

            if (i % 2 != 0) {
                if (y[i] < y[i - 1]) {
                    temp = y[i - 1];
                    y[i - 1] = y[i];
                    y[i] = temp;
                }
            } else {
                if (y[i] > y[i - 1]) {
                    temp = y[i];
                    y[i] = y[i - 1];
                    y[i - 1] = temp;
                }
            }

        }for(int i=0;i<x;i++){
            System.out.print(y[i]+" ");
        }
    }
}