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
using namespace std;
int main(){
	ll n;
	cin>>n;n++;
	int *a=new int[400],now=0;
	a+=200;
	for(int i=40;~i;i--){
		if(now){
			*(a+now-1)=now;
			now++;
		}
		if(n>>i&1){
			if(!now){
				now=1;continue;
			}
			a--;
			*a=now++;
		}
	}
	cout<<2*now-2<<'\n';
	for(int i=0;i<now-1;i++)
		cout<<*(a+i)<<' ';
	for(int i=1;i<now;i++)
		cout<<i<<' ';
	cout<<'\n';
	return 0;
}