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>

#define ll long long

ll n;
int len = 0;
std::deque <int> dq;

void solve(ll n){
	if (n == 1){
		return;
	}
	solve(n >> 1);
	dq.push_back(++ len);
	if (n & 1){
		dq.push_front(++ len);
	}
}

int main(){
	scanf("%lld", &n);
	++ n;
	solve(n);
	printf("%d\n", len << 1);
	while ((int) dq.size()){
		printf("%d ", dq.front());
		dq.pop_front();
	}
	for (int i = 1; i <= len; ++ i){
		printf("%d ", i);
	}
	return printf("\n"), 0;
}