Problem:
Score : 200 points

Problem Statement

A sequence a=\{a_1,a_2,a_3,......\} is determined as follows:

The first term s is given as input.

Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.

a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.

Find the minimum integer m that satisfies the following condition:

There exists an integer n such that a_m = a_n (m > n).

Constraints

1 \leq s \leq 100

All values in input are integers.

It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum integer m that satisfies the condition.

Sample Input 1

8

Sample Output 1

5

a=\{8,4,2,1,4,2,1,4,2,1,......\}. As a_5=a_2, the answer is 5.

Sample Input 2

7

Sample Output 2

18

a=\{7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,......\}.

Sample Input 3

54

Sample Output 3

114

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var ir = new Resolver(new ConsoleReader());
            Console.WriteLine(ir.Resolve());
        }
    }

    public class Resolver
    {
        IInputReader InputReader { get; }
        public List<string> Messages { get; set; } = new List<string>();

        int s;

        public void ParseLines(){
            s = int.Parse(InputReader.ReadLine());
        }

        int myFunction(int n){
            if (n % 2 == 0) return n / 2;
            return 3 * n + 1;
        }


        public string Resolve()
        {
            int i = 1;
            var nums = new List<int>();
            nums.Add(s);

            while(true){
                i++;
                s = myFunction(s);
                if (nums.Contains(s)) break;
                nums.Add(s);
            }

            return i.ToString();
        }



        public Resolver(IInputReader inputReader)
        {
            InputReader = inputReader;
            ParseLines();
        }

    }

    public interface IInputReader
    {
        string ReadLine();
    }

    class ConsoleReader : IInputReader
    {
        string IInputReader.ReadLine()
        {
            return Console.ReadLine();
        }
    }
}