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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleAppAtCoderBeginnerContest116B
{
    class Program
    {
        public static List<int> sequence= new List<int>();
        static int counter;

        static void Main(string[] args)
        {
            // 整数の入力
            int s = int.Parse(Console.ReadLine());// 初項S

            sequence.Add(s);
            int temp = counter;
            int next_s=progresson(s);
            //Console.WriteLine("next_s:"+next_s);
            while (temp != counter)
            {
                temp = counter;
                next_s=progresson(next_s);
                
            }
                 Console.WriteLine(counter+2);
        }

        public static int progresson(int number)
        {
            int s=number;
            int num;

            if (s % 2 == 1)// 奇数
            {
                num = 3 * s + 1;
                if (sequence.Contains(num) == false)
                    {
                        sequence.Add(num);
                        counter++;
                    }
            }
            else// 偶数
            {
                num = s / 2;
                if (sequence.Contains(num) == false)
                    {
                        sequence.Add(num);
                        counter++;
                    }
            }
            return num;
        }
    }
}