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.BufferedInputStream;
import java.util.Scanner;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Collections;
import java.util.ArrayList;
import java.util.Queue;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.StringTokenizer;
import java.io.BufferedInputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.HashMap;
import java.util.Scanner;
public class Graph {
	static int count=0;
	static int [] mergesort(int [] in,int start, int end) {
		if(start == end) return new int [] {in[start]};
		int mid=(start+end)/2;
		int [] left =mergesort(in, start,mid);
		int [] right=mergesort(in, mid+1, end);
		int [] arr=new int[end-start+1];
		int i=0,j=0,p=0;
		while(i<left.length && j<right.length) {
			if(left[i]<=right[j]) arr[p++]=left [i++];
			else {
				arr[p++]=right[j++];
				count+=left.length-i;
			}
		}
		while(i<left.length) arr[p++]=left [i++];
		while(j<right.length) arr[p++]=right[j++];
		return arr;
			
	}
	public static void Bubble(int [] arr ) {
		
	}
	public static void main(String [] args) throws IOException {
		PrintWriter pw=new PrintWriter(System.out);
		Scanner sc=new Scanner(System.in);
		int x=sc.nextInt();
		Integer [] arr =new Integer [x];
		for(int i=0;i<x;i++) arr[i]=sc.nextInt();
		Arrays.sort(arr);
		int even=x-1;
		int odd=0;
		int [] order=new int [x];
		for(int i=0;i<x;i++)
			if(i%2==0)	order[i]=arr[odd++];
			else order[i]=arr[even--];
		for(int y:order) pw.print(y+" ");
		pw.flush();
		pw.close();
	}
	
	static class pair implements Comparable<pair>{
		String  name; int x,y ;
		public pair(String name , int x) {
			this.name=name; this.x=x;
		}
		
		public int compareTo(pair o) {
			if(!name.equals(o.name))
				return name.compareTo(o.name);
			return x-o.x;
		}
		public String toString() {
			return name +" "+x;
		}
	}
   static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	}