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 <bits/stdc++.h>

int main() {
	long long n;
	std::cin >> n, ++n;
	std::vector<int> bit;
	std::list<int> ans;
	while (n) 
		bit.push_back(n & 1), n >>= 1;
	int cur = 0;
	for (int i = (int)(bit.size()) - 2; i >= 0; --i) {
		ans.push_back(++cur);
		if (bit[i]) ans.push_front(++cur);
	}
	for (int i = 1; i <= cur; ++i) ans.push_back(i);
	std::cout << ans.size() << std::endl;
	for (auto x : ans) std::cout << x << " ";
	std::cout << std::endl;
}