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.Arrays;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
    public static void main(String[] args) throws Exception {

        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n= sc.nextInt();
        int [] x=new int[n];
        for(int i=0 ;i<n;i++) {
        	x[i]=sc.nextInt();
        }
        Arrays.sort(x);
        int [] y=new int [n];
        int j=n-1;
        int i=0;
        for(int c=0;c<n;c++) {
        	if(c%2==0) {
        	y[c]=x[i++];
        	}
        	else {
        		y[c]=x[j--];
        	}	
        }
        
        for(int m=0; m<n;m++)
        	out.print(y[m]+" ");
		

        out.flush();

    }

       

    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);}

    }

}