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.StringTokenizer;

public class zsort {

	public static void thezsort(int [] x ) {
		if (x.length==1) {
			return;
		}
		else if (x.length==2) {
			if (x[0]>x[1]) {
				int temp = x[0];
				int temp2 = x[1];
				x[0]=temp2;
				x[1]=temp;
				return;
			}
			else
				return;
		}
		else if (x.length>2) {
			for (int i=1;i<x.length;i++) {
				if ((i+1)%2==0) {
					if (x[i]<x[i-1]) {
						int u =i-1;
						int temp = x[u];
						int temp2 = x[i];
						x[u]=temp2;
						x[i]=temp;
					}
					
				}
				else {
					
					if (x[i]>x[i-1]&&i>1) {
						int u =i-1;
						int temp = x[u];
						int temp2 = x[i];
						x[u]=temp2;
						x[i]=temp;
					}
					
				}
			}
		}
		
	}
	
	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		PrintWriter out = new PrintWriter(System.out);		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));	
		StringTokenizer st = new StringTokenizer(br.readLine());
		 int y = Integer.parseInt(st.nextToken());
		 int [] x = new int [y];
		 st = new StringTokenizer(br.readLine());
		 for (int p=0;p<y;p++) {
			 x[p]=Integer.parseInt(st.nextToken());
		 }
thezsort(x);
for (int i=0;i<x.length;i++) {
	 out.print(x[i]+" ");
}
out.flush();
out.close();
	}

}
