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

public class b {

    private void solve() throws IOException {
        int n = nextInt();
        int[] a = new int[n];

        for(int i = 0; i < n; ++i) {
            a[i] = nextInt(); 
        }

        Arrays.sort(a);

        int[] b = new int[n]; 
        for(int i = 0, j = n -1, k = 0; i <= j; ++i, --j, k += 2) {
            b[k] = a[i];
            if(i < j) {
                b[k + 1] = a[j];
            }
        }
        
        for(int i : b) {
            System.out.print(i + " "); 
        }
    }

    static void debug(Object...o) {
        System.err.println(Arrays.deepToString(o));
    }

    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

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

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

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

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

    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }

    private void run() throws IOException {
        //br = new BufferedReader(new FileReader("b.in"));
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        //out = new PrintWriter("b.out");
        solve();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new b().run();
    }
}
