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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
class Solve{
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        long N = long.Parse(Console.ReadLine());
        List<int> act = new List<int>();
        N++;
        while(N > 0){
            if(N % 2 == 0){
                act.Add(2);
                N /= 2;
            }
            else{
                act.Add(1);
                N--;
            }
        }
        List<int> left = new List<int>();
        List<int> right = new List<int>();
        int count = 1;
        for(int i=act.Count-1;i>=0;i--){
            if(act[i] == 1){
                left.Add(count);
            }
            else{
                right.Add(count);
            }
            count++;
        }
        sb.Append((count*2-2)+"\n");
        for(int i=0;i<count-1;i++){
            sb.Append((i+1)+" ");
        }
        for(int i=left.Count-1;i>=0;i--){
            sb.Append(left[i]+" ");
        }
        for(int i=0;i<right.Count;i++){
            sb.Append(right[i]+" ");
        }
        sb.Append("\n");
    }
}