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.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		ArrayList<Integer> res = new ArrayList<Integer>();
		int k;
		for (k = 40; k >= 0; k--) {
			if (n >= (1L << k) - 1) break;
		}
		for (int i = 1; i <= k; i++) res.add(i);
		n -= (1L << k) - 1;
		for (int i = k - 1; i >= 0; i--) {
			if (n < (1L << i)) continue;
			k++;
			res.add(i, k);
			n -= 1L << i;
		}
		System.out.println(2 * res.size());
		for (int x : res) System.out.print(x + " ");
		for (int i = 1; i <= res.size(); i++) System.out.print(i + " ");
		System.out.println();
	}
}