Problem: We will call a string x good if it satisfies the following condition:

* Condition: x can be represented as a concatenation of two copies of another string y of length at least 1.



For example, `aa` and `bubobubo` are good; an empty string, `a`, `abcabcabc` and `abba` are not good.

Eagle and Owl created a puzzle on good strings. Find one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.

* 1 ≤ |s| ≤ 200
* Each character of s is one of the 100 characters represented by the integers 1 through 100.
* Among the 2^{|s|} subsequences of s, exactly N are good strings.

Constraints

* 1 ≤ N ≤ 10^{12}

Input

Input is given from Standard Input in the following format:


N


Output

In the first line, print |s|, the length of s. In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Examples

Input

7


Output

4
1 1 1 1


Input

299


Output

23
32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Scanner;

public class Main {
  static Scanner sc = new Scanner(System.in);

  public static void main(String[] args) {
    long N = sc.nextLong();
    ArrayList<Integer> first = new ArrayList<>();
    ArrayList<Integer> second = new ArrayList<>();
    for (int i = 1; (1L << i) - 1 <= N; i++) {
      first.add(i);
      second.add(i);
    }
    N -= (1L << first.size()) - 1;
    while (N > 0) {
      int a = first.size() + 1;
      first.add(a);
      for (int i = 0; ; i++) {
        if ((1L << (i + 1)) > N) {
          second.add(i, a);
          N -= (1L << (i));
          break;
        }
      }
    }

    System.out.println(first.size() * 2);
    for (int i = 0; i < first.size(); i++) {
      System.out.print(first.get(i) + " ");
    }
    for (int i = 0; i < first.size(); i++) {
      System.out.print(second.get(i) + (i == first.size() - 1 ? "\n" : " "));
    }
  }

}