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 a[50],ans[100];
int main(){
	long long n;
	scanf("%lld",&n);n++;
	int m=0,t=0;
	for (;n>1;n>>=1) m+=(a[++t]=n&1);
	int l=m+1,r=m;
	for (int i=t,j=0;i;i--){
		ans[++r]=++j;
		if (a[i]) ans[--l]=++j;
	}
	printf("%d\n",r*2);
	for (int i=1;i<=r;i++) printf("%d ",ans[i]);
	for (int i=1;i<=r;i++) printf("%d ",i);
}