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.InputStreamReader;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.io.*;
import java.util.*;

public class Main{
    public static void main(String[]  args)throws  Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in) );
        PrintWriter pr = new PrintWriter(System.out);
        StringTokenizer st;
        PriorityQueue<Integer> Q = new PriorityQueue<>();
        int x =Integer.parseInt(br.readLine());
        st= new StringTokenizer(br.readLine());
        for (int i = 0; i <x ; i++) {
            Q.add(Integer.parseInt(st.nextToken()));
        }
        int[] A = new int[x];
        for (int i = 0; i <x ; i++) {
            A[i]=Q.poll();
        }
        for (int i = 1; i <x-1 ; i+=2) {
            int temp = A[i];
            A[i]=A[i+1];
            A[i+1]=temp;
        }

       if(x%2==0) {
            if (A[A.length - 1]<A[A.length-2]){
                int temp = A[A.length-1];
                A[A.length-1]=A[A.length-2];
                A[A.length-2]=temp;
            }
        }
        for (int i = 0; i <x ; i++) {
            pr.print(A[i]+" ");
        }
pr.close();

    }
}