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 static System.Console;
using System.Collections.Generic;
using System.Linq;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var s = int.Parse(ReadLine());
            var list = new List<int>();
            var hashSet = new HashSet<int>();
            list.Add(s);
            hashSet.Add(s);
            int cnt = 1;

            while (true)
            {
                if (list[list.Count() - 1] % 2 == 0)
                {
                    cnt++;
                    int a = list[list.Count() - 1] / 2;
                    list.Add(a);
                    if (hashSet.Add(a) == false)
                    {
                        break;
                    }
                }
                else
                {
                    cnt++;
                    int a = 3 * list[list.Count() - 1] + 1;
                    list.Add(a);
                    if(hashSet.Add(a) == false)
                    {
                        break;
                    }
                }
            }

            WriteLine(cnt);
        }
    }
}