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;

namespace B___Collatz_Problem
{
    class Program
    {
        static void Main(string[] args)
        {
            var s = int.Parse(Console.ReadLine());
            var a = new List<int> { s };
            for (var i = 1; i < 1000000; i++)
            {
                if (a[i - 1] % 2 == 0)
                {
                    a.Add(a[i - 1] / 2);
                }
                else
                {
                    a.Add(3 * a[i - 1] + 1);
                }
                for (var j = 0; j < a.Count - 1; j++)
                {
                    for (var k = 1; k < a.Count; k++)
                    {
                        if (a[j] == a[k] && j < k)
                        {
                            Console.WriteLine(k + 1);
                            return;
                        }
                    }
                }
            }
        }
    }
}