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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main33 {
	public static void main(String[]args) throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		int x=sc.nextInt();
		int[]arr=new int[x];
		for(int i=0;i<x;i++) {
			arr[i]=sc.nextInt();
		}
		Arrays.sort(arr);
		int[]res=new int[x];
		 int j=0;int i=0;
		    while(j<x)
		    {
		        res[j]=arr[i];i++;j+=2;
		    }

		    j=1;
		    i=x-1;
		    while(j<x)
		    {
		        res[j]=arr[i];
		        i--;
		        j+=2;
		    }


		    for(i=1;i<x;i+=2)
		    {
		        if(res[i]<res[i-1])
		        {
		            out.println("Impossible");
		          //  return 0;
		        }
		    }

		    for(i=2;i<x;i+=2)
		    {
		        if(res[i]>res[i-1])
		        {
		            out.println("Impossible");
		          //  return 0;
		        }
		    }
//out.println(res[0]);
		for(int m=0;m<res.length;m++) {
			out.print(res[m]+" ");
			//out.println("hello");
		}
		out.flush();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(4000);
		}
	}
	 public static boolean containsSameValues(int[] array) {
	     if(array.length == 0) {
	         throw new IllegalArgumentException("Array is empty");
	     }
	     int first = array[0];
	     for(int i=0;i<array.length;i++) {
	         if(array[i] != first) {
	             return false;
	         }
	      }
	      return true;
	 }
}
