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 <map>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define N 506
using namespace std;
int m,p1,p2,a[N],b[N],ans[N];long long n;
int main()
{
	scanf("%lld",&n);n++;m=100;
	while(n>1){
		if(n&1)n--,a[++p1]=m--;
		else n>>=1,b[++p2]=m--;
	}
	printf("%d\n",2*(p1+p2));
	for(int i=1;i<=p1;i++)printf("%d ",a[i]);
	for(int i=p2;i>=1;i--)printf("%d ",b[i]);
	for(int i=100-p1-p2+1;i<=100;i++)printf("%d ",i);puts("");
}