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 Atcoder
{
    class Atcoderrrrrrr
    {
        static void Main(string[] args)
        {
            string s = Console.ReadLine();
            List<int> ls = new List<int>();
            int obj = 0;int ans = 0;
            for(int i = 1;i<=1000000;i++){
                if(i == 1){
                    obj = int.Parse(s);
                    ls.Add(int.Parse(s));
                }else{
                    obj = Func(obj);
                    if(ls.Contains(obj)){
                        ans = i;
                        break;
                    }
                    ls.Add(obj);
                }
            }
            Console.WriteLine(ans);
        }

        static public int Func(int n){
            if(n%2 == 0){
                return n/2;
            }else{
                return (3*n)+1;
            }
        }
    }
}