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.lang.reflect.Array;
import java.util.*;

public class Main {

    public static void main (String[] args) throws IOException {
        int n = sc.nextInt();

        Integer[] arr = nextArr(n);
        Arrays.sort(arr);

        Integer[] zSorted = new Integer[n];
        int i1 = 0;
        int i2 = arr.length-1;
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0)
                zSorted[i] = arr[i1];
            else
                zSorted[i] = arr[arr.length-1-i1++];
        }


        pw.print(zSorted[0]);
        for (int i = 1; i < n; i++)
            pw.print(" " + zSorted[i]);
        pw.close();
    }



    public static Integer[] nextArr (int n) throws IOException {
        Integer[] arr = new Integer[n];
        for (int i = 0; i < n; i++)
            arr[i] = sc.nextInt();
        return arr;
    }


    static class Scanner
    {
        StringTokenizer st;
        BufferedReader br;

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

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

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

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

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

        public double nextDouble() throws IOException
        {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if(x.charAt(0) == '-')
            {
                neg = true;
                start++;
            }
            for(int i = start; i < x.length(); i++)
                if(x.charAt(i) == '.')
                {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                }
                else
                {
                    sb.append(x.charAt(i));
                    if(dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg?-1:1);
        }

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


    }

    static PrintWriter pw = new PrintWriter(System.out);
    static Scanner sc = new Scanner(System.in);
}
 			 		    	 					 	 		 	 		 		