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.Arrays;

public class Main {
    public static void main(String args[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());
        String[] str = br.readLine().split(" ");
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) arr[i] = Integer.parseInt(str[i]);

        int[] ans = solve(arr, n);
        for (int i = 0; i < n; i++) System.out.print(ans[i] + " ");
        System.out.println("");
    }

    public static int[] solve(int[] array, int arrayLength) {
        Arrays.sort(array);
        int[] res = new int[arrayLength];
        int index = 0;
        for (int i = 0; i < arrayLength / 2; i++) {

            res[index] = array[i];
            res[index + 1] = array[arrayLength - 1 - i];
            index += 2;
        }
        if (arrayLength % 2 != 0) res[arrayLength - 1] = array[arrayLength / 2];
        return res;
    }
}