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.Diagnostics;
using System.Linq;

namespace ConsoleApp1
{
    using static Util;

    internal class Program
    {


        static void Main(string[] args)
        {
            var s = ReadLong();

            var hashN = new HashSet<long>();
            var cnt = 1;
            var m = s;
            hashN.Add(s);
            while (true)
            {
                cnt++;
                m = fn(m);
                if (hashN.Contains(m))
                {
                    break;
                }
                hashN.Add(m);
            }

            Console.WriteLine(cnt);
#if DEBUG
            Console.Read();
#endif
        }

        public static long fn(long n)
        {
            if (n % 2 == 0)
                return f1(n);
            else
                return f2(n);
        }

        public static long f1(long n)
        {
            return n / 2;
        }

        public static long f2(long n)
        {
            return 3*n +1;
        }

    }

    public static class Util
    {
        public static long[] ReadLongs() 
        {
            return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        }
        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }

    }
}