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) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
}


class Task {


    public void solve(InputReader in, OutputWriter out) {
        int n = in.nextInt();
        int tab[] = new int[n];
        for(int i=0;i<n;i++) {
            tab[i] = in.nextInt();
        }
        Arrays.sort(tab);
        int result[] = new int[n];
        int j = 0;
        for(int i=0;i<n;i+=2) {
            result[i] = tab[j++];
        }
        int k = n - 1;
        for(int i=1;i<n;i+=2) {
            result[i] = tab[k--];
        }
        for(int i=0;i<n;i++) {
            out.print(result[i] + " ");
        }
    }
}


class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
    public boolean hasNext() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                String line = reader.readLine();
                if ( line == null ) {
                    return false;
                }
                tokenizer = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }

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

    public double nextDouble() { return Double.parseDouble(next());}
}
class OutputWriter {
    private final PrintWriter writer;
    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }
    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }
    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if ( i != 0 ) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }
    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }
    public void close() {
        writer.close();
    }
}