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 <cstdio>
#include <vector>
int main() {
	long long n;
	scanf("%lld", &n);
	n++;
	
	int all = 100;
	
	std::vector <int> p, q;
	while(n > 1) {
		if(n & 1) {
			p.push_back(all--);
			n--;
		}
		else {
			q.push_back(all--);
			n >>= 1;
		}
	}
	
	int sz = p.size() + q.size();
	printf("%d\n", sz + 100);
	for(int i = 0; i < p.size(); i++)
		printf("%d ", p[i]);
	for(int i = q.size() - 1; ~i; --i)
		printf("%d ", q[i]);
	for(int i = 1; i <= 100; i++)
		printf("%d ", i);
	return 0;
}