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>
using namespace std;
const int N=65;
long long n;
int m,vi[N],a[205];
int main(){
	scanf("%lld",&n);
	for(;(1LL<<m)-1<=n;m++);

	--m;
	int cnt=m;
	n-=(1LL<<m)-1;
	for(int i=m;~i;i--)
		if(n>>i&1)	vi[i]=1,++cnt;

	int x=cnt;
	printf("%d\n",cnt*2);
	if(vi[0])	printf("%d ",cnt--); 
	for(int i=1;i<=m;i++){
		printf("%d ",i);
		if(vi[i])	printf("%d ",cnt--);
	}
	for(int i=1;i<=x;i++)	printf("%d ",i);
}