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 <iostream>
#include <cmath>
using namespace std;

int p[202], q[202], cnt;
long long n;

void solve(long long n){
    if (!n) return;
    if (~n&1) 
        q[++q[0]] = cnt++, solve(n-1);
    else
        p[++p[0]] = cnt++, solve(n>>1);
}

int main(){
   	cin>>n;
	solve(n); 
	cout<<cnt+100<<endl;
    for (int i = 1; i <= q[0]; ++i) 
		cout<<cnt-q[i]<<" ";
    for (int i = p[0]; i; --i) 
    	cout<<cnt-p[i]<<" ";
    for (int i = 1; i <= 100; ++i) 
    	cout<<i<<" ";
    cout<<endl;;
    return 0;
}