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 N 210
#define ll long long
using namespace std;
int n,f[N],a[N];
ll s;

int main(){
	scanf("%lld",&s);
	for (n=0;s;)
		if (!(s&1))
			s--,a[++n]=0;
		else
			s>>=1,a[++n]=1;
	int h=1,r=n;
	for (int i=1;i<=n;i++)
		if (a[i])
			f[r--]=n-i+1;
		else
			f[h++]=n-i+1;
	printf("%d\n",n*2);
	for (int i=1;i<=n;i++)
		printf("%d ",f[i]);
	for (int i=1;i<n;i++)
		printf("%d ",i);
	printf("%d\n",n);
	return 0;
}