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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main {
         public static void main(String[]args) throws IOException{
        	 PrintWriter pw=new PrintWriter(System.out);
             BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
             String x3=br.readLine();
             StringTokenizer st=new StringTokenizer(x3);
             int n=Integer.parseInt(st.nextToken());
          /*   if(n==2 || n==3){
            	 pw.println("Impossible");
            	 
             }*/
             //else{
             String x2=br.readLine();
             StringTokenizer st2=new StringTokenizer(x2);
             int[]x=new int[n];
             int s=0;
             while(st2.hasMoreTokens()){
            	 x[s++]=Integer.parseInt(st2.nextToken());
             }
             Arrays.sort(x);
             boolean f=true;
             if(n%2!=0)
            	 n=n+1;
             for(int i=0;i<n/2;i++){
            	 int j=x.length-1-i;
            	 if(f==true)
            		 f=false;
            	 else
            		 pw.print(" ");
            	 pw.print(x[i]);
            	 pw.print(" ");
            	 if(j>i)
            	 pw.print(x[j]);
             }
             pw.close();
             
             //}
             }
}
