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.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class zSort {
	public static long[] mergesort(long [] a,int start,int end) {
			if (start==end) return new long [] {a[start]};
			int mid =(start+end)/2;
			long left[]=mergesort(a,start,mid);
			long right[]=mergesort(a,mid+1,end);
			long []res=new long [end-start+1];
			int i=0;
			int j=0;
			int idx=0;
			while(i<left.length&&j<right.length) {
				if(left[i]<=right[j]) 
					res[idx++]=left[i++];
					else {
						res[idx++]=right[j++];
				}}
			while(i<left.length) res[idx++]=left[i++];
			while(j<right.length) res[idx++]=right[j++];
			return res;
}
	public static void main(String []args) throws IOException {
 		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter pw =new PrintWriter(System.out);
 		int x=Integer.parseInt(br.readLine());
 		StringTokenizer s=new StringTokenizer(br.readLine());
 		
 		long a[]=new long[x];
 		
 		for(int i=0;s.hasMoreTokens();i++) 
 			a[i]=Long.parseLong(s.nextToken()); 
 		a=mergesort(a,0,x-1);
 		for(int i=1;i<a.length-1;i+=2) {
 			long temp=a[i];
 			a[i]=a[i+1];
 			a[i+1]=temp;
 		}
 		for(long i:a)
 			pw.print(i+" ");
 		pw.flush();}}
