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.math.*;
import java.util.*;
import java.awt.Frame;
import java.io.*;


public class Main{
	static BigInteger zero = BigInteger.ZERO;
	public static void main(String[] args){
		Scanner cin = new Scanner (new BufferedInputStream(System.in));		
		int n = cin.nextInt();
		int[] a = new int[n];
		for(int i = 0; i < n; i++)
			a[i] = cin.nextInt();
		
		Arrays.sort(a);

//		for(int i = 0; i < n; i++)
//			System.out.print(""+a[i]+' ');
//		System.out.println();
		
		System.out.print(a[0]);
		for(int i = 1, j = n-1; ; ){
			if(j < i) break;
			System.out.print(" "+a[j--]);
			if(j < i) break;
			System.out.print(" "+a[i++]);
		}
		System.out.println();
	}
}
	   	 			 	    	  	    		  		 	