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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class B_10 {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        int []a = new int[n+1];
        for (int i = 0; i <n ; i++) {
			a[i] = nextInt();
        }
        zigZag(a,n);
        for (int i = 0; i < n; i++) {
			System.out.print(a[i]+" ");
		}
        pw.close();
    }

    private static void zigZag(int[] arr, int n) {
        boolean flag = true;

        for (int i=0; i<=n-2; i++)
        {
            if (flag) 
            {
                if (arr[i] > arr[i+1]){
                	int tmp = arr[i];
            		arr[i]=arr[i+1];
            		arr[i+1]=tmp;
                }
            }
            else 
            {
                
                if (arr[i] < arr[i+1]){
                	int tmp = arr[i];
            		arr[i]=arr[i+1];
            		arr[i+1]=tmp;
                }
            }
            flag = !flag; 
            
        }		
	}


	private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
//    private static long nextLong() throws IOException {
//        return Long.parseLong(next());
//    }
//    private static double nextDouble() throws IOException {
//        return Double.parseDouble(next());
//    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}