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
//package CF;
import java.io.*;
import java.util.*;
public class A{

    public static void main(String[] args) throws Exception {
	Scanner bf = new Scanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	int n = bf.nextInt();
	int [] a = new int[n];
	for (int i = 0; i < n; i++)
	{
	    a[i] = bf.nextInt();
	}
	Arrays.sort(a);
	int i,j;
        for ( i = 0, j = a.length-1; i<j ; i++,j--)
	{
	    out.print(a[i]+" ");
	    out.print(a[j]+" ");
	}
        out.println(i==j?a[i]:"");
	out.flush();
	out.close();

    }

    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
	{
	    String x = next();
	    StringBuilder sb = new StringBuilder("0");
	    double res = 0, f = 1;
	    boolean dec = false, neg = false;
	    int start = 0;
	    if(x.charAt(0) == '-')
	    {
		neg = true;
		start++;
	    }
	    for(int i = start; i < x.length(); i++)
		if(x.charAt(i) == '.')
		{
		    res = Long.parseLong(sb.toString());
		    sb = new StringBuilder("0");
		    dec = true;
		}
		else
		{
		    sb.append(x.charAt(i));
		    if(dec)
			f *= 10;
		}
	    res += Long.parseLong(sb.toString()) / f;
	    return res * (neg?-1:1);
	}

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

}