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<cstdio>
int main(){
	long long n,s,f[107];
	int p=1,a[107];
	scanf("%lld",&n);
	f[0]=1;
	for(;n;++p){
		s=0;
		int q=0;
		while(s+f[q]<=n&&q<p)s+=f[q++];
		for(int i=p;i>q;--i)a[i]=a[i-1],f[i]=f[i-1];
		a[q]=p,f[q]=s;
		n-=s;
	}
	printf("%d\n",p*2-2);
	for(int i=1;i<p;++i)printf("%d ",i);
	for(int i=1;i<p;++i)printf("%d ",a[i]);
	return 0;
}