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.*;
import java.util.StringTokenizer;

public class zsort
        {
            static class Scanner{
                StringTokenizer st;
                BufferedReader br;
                public Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
                public Scanner(String file) throws Exception {br = new BufferedReader(new FileReader(file));}
                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(3000);}
            }
            public static void main(String[]args) throws IOException {
                Scanner sc = new Scanner(System.in);
                int n = sc.nextInt();
                int[]x=new int[n];
                for (int i=0;i<n;i++){
                    x[i]=sc.nextInt();
                }
                for (int i=0;i<n;i+=2){
                    int min = x[i];
                    int m=i;
                    int max=x[i];
                    int ma=i;
                    for (int j=i;j<n;j++){
                        if(x[j]<min){
                            min=x[j];
                            m=j;
                        }
                        if (x[j]>max){
                            max=x[j];
                            ma=j;
                        }

                    }
                    int t=x[i];
                    x[i]=min;
                    x[m]=t;
                    if(t!=max){
                    t=x[i+1];
                    x[i+1]=max;
                    x[ma]=t;}
                }

            for (int i=0;i<n;i++)
                System.out.print(x[i]+" ");


            }
}
