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.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.Function;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class Main{
	
public static  void main(String[]args) throws IOException{
	BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    int n=Integer.parseInt(br.readLine());
    String x=br.readLine();
    String[]tmp=x.split(" ");
    int[]arr=new int[tmp.length];
    for(int i=0;i<tmp.length;i++){
    	arr[i]=Integer.parseInt(tmp[i]);
    }Arrays.sort(arr);
    int[]result=new int[arr.length];
    int j=arr.length-1;
    int y=0;
    for(int i=0;y<j;i++){
    	result[i++]=arr[y++];
    	result[i]=arr[j--];
    }
    if(n%2!=0){
    	result[result.length-1]=arr[arr.length/2];
    }
    for(int i=0;i<result.length;i++){
    	System.out.print(result[i]+" ");
    }
}
}