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 AtCoderABC052B
{
    class Program
    {
        static void Main()
        {
            int S = int.Parse(Console.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;
                    }
                }
            }
            Console.WriteLine(cnt);
        }
    }
}