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;

public class ZSort2 {
    public static void main(String[]args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);

        int n=Integer.parseInt(br.readLine());
        int[]arr=new int[n];
        String []input=br.readLine().split(" ");
        for(int i=0;i<n;i++){
            arr[i]=Integer.parseInt(input[i]);
        }
        Arrays.sort(arr);
        int[]temp=new int[n];
//        temp[0]=arr[0];
        int k=0;
        int m=1;
        if(n%2==0) {
            for (int j = 0; j <n/2;j++){
//                System.out.println("j= "+j);
                temp[k]=arr[j];
//                if(k>0)
//                    temp[++k]=arr[n-(k-1)];
//                else
                    temp[++k]=arr[n-m] ;
//                temp[++k]=arr[n-k];
//                System.out.println("k= "+k+" arr[n-k]= "+arr[n-k]);
                k++;
                m++;
            }
        }
        else{
            for (int j =0; j <(n/2);j++){

                temp[k]=arr[j];
//                if(k>0)
//                temp[++k]=arr[n-(k-1)];
//                else
                    temp[++k]=arr[n-m] ;
//                pw.print("j= "+j+" arr[j]= "+arr[j]+"arr[n-k]= "+temp[k]);
                k++;
                m++;
            }
//            pw.println("arr[n/2]= "+arr[n/2]);
            temp[n-1]=arr[n/2];
        }
        for(int l=0;l<n;l++){
            pw.print(temp[l]+" ");
        }





pw.close();
    }

}
