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;
 
long long n; int h1=1001,r1=1000,h2=2001,r2=2000,stp,a[105],ans[10005];
void solve(long long n){
	if (n==1 || n%2==0){
		if (n>1) solve(n-1);
		stp++;
		ans[++r1]=stp; ans[--h2]=stp;
	} else{
		solve(n/2);
		stp++; ans[++r1]=stp; ans[++r2]=stp;
	}
}
int main(){
	scanf("%lld",&n); solve(n);int i;
	printf("%d\n",r1-h1+r2-h2+2);
	for (i=h1; i<=r1; i++) printf("%d ",ans[i]);
	for (i=h2; i<=r2; i++) printf("%d ",ans[i]);
	return 0;
}