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;
ll n;
std::vector<int>ans,A,B;int y=1;
void solve(ll x){
	if(x==1){A=B={1};return;}
	if(x&1)solve(x>>1),++y,A.push_back(y);
		else solve(x-1),++y,A.insert(A.begin(),y);B.push_back(y);
}
int main(){
	scanf("%lld",&n);
	solve(n);
	ans=A;ans.insert(ans.end(),B.begin(),B.end());
	printf("%d\n",ans.size());
	for(int i:ans)printf("%d ",i);puts("");
	return 0;
}