Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

7

Sample Output 1

4
1 1 1 1

There are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.

Sample Input 2

299

Sample Output 2

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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

int main() {
	long long n;
	scanf("%lld", &n);

	vector <int> q;
	n--;

	int val = 63-__builtin_clzll(n);

	//printf("%d\n", val);

	for (int i = 0; i <= val; ++i) {
		if(n&(1LL<<i)) {
			q.push_back(0);
		} else {
			q.push_back(1);
		}
	}
	reverse(q.begin(), q.end());


	deque <int> ans;
	int cnt = 1;
	for (int i = 0; i < q.size(); ++i) {
		//printf("%d\n", q[i]);
		if(q[i] == 0) {
			ans.push_back(cnt++);
			//if(i != 0) {
				ans.push_front(cnt++);
			//}
		} else {
			ans.push_back(cnt++);
		}
	}
	printf("%lu\n", 2*ans.size());
	for (int x: ans) {
		printf("%d ", x);
	}
	sort(ans.begin(), ans.end());
	for (int x: ans) {
		printf("%d ", x);
	}
}