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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.ComponentModel.DataAnnotations;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            long m = long.Parse(Console.ReadLine());
            long[] list = new long[1000000];
            for (int i = 0; i < 1000000; i++)
            {
                if (i == 0)
                {
                    list[i] = m;
                }
                else
                {
                    if (list[i - 1] % 2 == 0)
                    {
                        long add = list[i - 1] / 2;
                        if (list.Contains(add))
                        {
                            Console.WriteLine(i + 1);
                            return;
                        }
                        list[i] = add;
                    }
                    else
                    {
                        long add = list[i - 1] * 3 + 1;
                        if (list.Contains(add))
                        {
                            Console.WriteLine(i + 1);
                            return;
                        }
                        list[i] = add;
                    }
                }
                
            }
        }
    }
}
// 文字列の入力
//string s = Console.ReadLine();

// 整数の入力
//long n = long.Parse(Console.ReadLine());

// 文字列配列の入力
//string[] inputStrArray = Console.ReadLine().Split(' ');

// 整数配列の入力
//long[] inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();


//Console.WriteLine(ans);