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));
		int n=Integer.parseInt(br.readLine());
		StringTokenizer st=new StringTokenizer(br.readLine());
		int [] x=new int[n];
		for(int i=0;i<n;++i) {
			x[i]=Integer.parseInt(st.nextToken());
		}
		Arrays.sort(x);
		int []y=new int[n];
		int k;
		int j=k=(n+1)/2;
		int z=0;
		for(int i=0;i<k;i++) {
			y[z]=x[i];
			z=z+2;
		}
		z=1;
		for(int i=k;i<n;++i) {
			y[z]=x[i];
			z=z+2;
		}
		dis(y);
	}
	public static void dis(int[]y) {
		for(int i=0;i<y.length-1;++i) {
			System.out.print(y[i]+" ");
		}
		if(y.length>0)
			System.out.print(y[y.length-1]);
	}
}
