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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main {

	
	public static void main(String[] args) throws IOException 
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] a = new int[n], b = new int[n];
		for(int i = 0; i < n; ++i)
			a[i] = sc.nextInt();
		shuffle(a);
		Arrays.sort(a);
		int k = n - 1;
		for(int i = 1; i < n; i += 2)
			b[i] = a[k--];
		for(int i = 0; i < n; i += 2)
			b[i] = a[k--];
		for(int i = 0; i < n; ++i)
			out.print(b[i] + " ");
		
		out.flush();
		out.close();

	}
	
	static void shuffle(int[] a)
	{
		int n = a.length;
		for(int i = 0; i < n; ++i)
		{
			int r = (int)(Math.random() * (n-i)) + i;
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}
	
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}

		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}

		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}

		public boolean ready() throws IOException {return br.ready();}


	}
}