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>

typedef long long LL;

std::vector<int> p; int tot;
void solve(LL n) {
	if (!n) return;
	if (n & 1) solve(n >> 1), p.push_back(++tot);
	else solve(n - 1), p.insert(p.begin(), ++tot);
}
int main() {
	std::ios::sync_with_stdio(0), std::cin.tie(0);
	LL n; std::cin >> n, solve(n);
	std::cout << (p.size() << 1) << '\n';
	for (int i : p) std::cout << i << ' ';
	for (int i = 1; i <= tot; ++i) std::cout << i << ' ';
	std::cout << '\n';
	return 0;
}