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.*;
import java.util.*;
import java.awt.Point;

public class Edu10_B {
	public static void main(String[] args) throws IOException {
		BufferedInputStream bis = new BufferedInputStream(System.in);
		BufferedReader br = new BufferedReader(new InputStreamReader(bis));
		PrintWriter out = new PrintWriter(System.out);
		String line;
		StringTokenizer st;
		while ((line = br.readLine()) != null && !line.equals("")) {
			int n = Integer.parseInt(line.trim());
			int [] nums = new int[n];
			st = new StringTokenizer(br.readLine());
			for (int i = 0; i < nums.length; i++) {
				nums[i] = Integer.parseInt(st.nextToken());
			}
			Arrays.sort(nums);
			StringBuilder sb = new StringBuilder("");
			int [] res = new int[n];
			int [] cnts = {1, 0};
			int ind = 0;
			for(int i = n-1;i >= 0;i--) {
				if(n-i > n/2 && ind == 0)
					ind++;
				res[cnts[ind]] = nums[i];
				cnts[ind] += 2;
			}
			for(int i = 0;i < n;i++)
				sb.append(res[i]+" ");
			out.println(sb);
		}
		out.close();
	}
}