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

public class ECR10B {

	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		int n=in.nextInt();
		int[] a=new int[n];
		for(int i=0;i<n;i++) a[i]=in.nextInt();
		Arrays.sort(a);
		
		int[] b=new int[n];
		int p=0,q=n-1,j=0;
		while(p<q){
			b[j++]=a[p++];
			b[j++]=a[q--];
		}
		if(n%2==1)
			b[j]=a[p];
		boolean f=true;
		for(int i=0;i<n&&f;i++){
			if(i%2==1&&i>0&&b[i]<b[i-1]){
				f=false;
			}else if(i%2==0&&i>0&&b[i]>b[i-1]){
				f=false;
			}
		}
		PrintWriter out=new PrintWriter(System.out);
		if(!f){
			out.print("Impossible");
		}else{
			for(int i=0;i<n;i++)
				out.print(b[i]+" ");
		}
		out.flush();
		out.close();
	}
	static class FastScanner{
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(){br=new BufferedReader(new InputStreamReader(System.in));}
		String nextToken(){
			while(st==null||!st.hasMoreElements())
				try{st=new StringTokenizer(br.readLine());}catch(Exception e){}
			return st.nextToken();
		}
		int nextInt(){return Integer.parseInt(nextToken());}
		long nextLong(){return Long.parseLong(nextToken());}
		double nextDouble(){return Double.parseDouble(nextToken());}
	}

}
