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 zsort {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader b=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(b.readLine());
		String[] in=b.readLine().split(" ");
		int l=0;
		int r=t-1;
		int[] nums=new int[t];
		for(int i=0;i<t;i++){
			nums[i]=Integer.parseInt(in[i]);
		}
		Arrays.sort(nums);
		int[] ans=new int[t];
		int j=0;
		while(l<r){
			ans[j]=nums[l];
			j++;
			ans[j]=nums[r];
			j++;
			l++;
			r--;
		}
		if(l==r){
			ans[j]=nums[l];
		}
		PrintWriter out =new PrintWriter(System.out);
		out.print(ans[0]);
		for(int i=1;i<t;i++){
			out.print(" "+ans[i]);
		}
		out.close();
	}

}
