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.util.Arrays;
import java.util.StringTokenizer;
public class zsort {
public static void main(String[]args) throws IOException {
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	String line = br.readLine() ;
	StringTokenizer st = new StringTokenizer(line);
	int n=Integer.parseInt(st.nextToken());
	int []v=new int[n];
	line = br.readLine() ;
	st = new StringTokenizer(line);

	for(int i=0;i<n;i++) {
		v[i]=Integer.parseInt(st.nextToken());
	}
	Arrays.sort(v);
	int count=v.length-1;
	if(n>1) {
	System.out.print(v[0]+" "+v[count]);
	count --;
	for(int i=1;i<count;i++) {
		System.out.print(" "+v[i]+" "+v[count]);
		count--;
	}
	if(v.length%2==1)
		System.out.print(" "+v[v.length/2]);
}
	else
		System.out.println(v[0]);
	}
}
