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 CPP):

Solution:
#include <iostream>
#include <deque>

using namespace std;

deque<int> seq(long long n) {
	if (n == 1) return {};
	if (n % 2 == 0) {
		auto s = seq(n / 2);
		s.push_back(s.size() + 1);
		return s;
	} else {
		auto s = seq(n - 1);
		s.push_front(s.size() + 1);
		return s;
	}
}

int main() {
	long long n;

	cin >> n;

	auto s = seq(n + 1);
	cout << s.size() * 2 << endl;
	for (int x: s) cout << s.size() + 1 - x << ' ';
	for (int i = s.size(); i >= 1; --i) cout << i << ' ';
	cout << endl;

	return 0;
}