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;

public class Problem4 {
    public static void main(String[]args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());
        Integer[] arr = new Integer[n];
        String line = reader.readLine();
        String[] split = line.split(" ");
        for(int i=0; i<n; i++){
            arr[i] = Integer.parseInt(split[i]);
        }
        Arrays.sort(arr);
        Integer[] output = new Integer[n];
        int c = 0;
        int i = 0;
        int j = n-1;
        while(i<j){
                output[c++] = arr[i++];
                if(i != j)
                    output[c++] = arr[j--];
        }
        if(i == j && c<n)
            output[n-1] = arr[i];

        System.out.print(output[0]);
        for(int I=1; I<n; I++){
            System.out.print(" "+output[I]);
        }
        System.out.println();
    }
}
