Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

7

Sample Output 1

4
1 1 1 1

There are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.

Sample Input 2

299

Sample Output 2

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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <iomanip>
#include <queue>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
using namespace std;

#define INF (1ll<<60)


long long M = 1000000007;


int main(int argc, char const *argv[]) {
    long long n;cin>>n;
    n++;
    deque<int> dq;
    int k = 0;
    while(n>>k > 0)k++;
    k-=2;
    int l = 1;
    for(;k>-1;k--){
        dq.push_back(l);
        l++;
        if((n>>k)%2==1){
            dq.push_front(l);
            l++;
        }
    }
    cout<<2*(l-1)<<endl;
    for(int i=1;i<l;++i)cout<<i<<" ";
    for(int i:dq)cout<<i<<" ";
    cout<<endl;
    return 0;
}