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;

    class ABC116B
    {
        static void Main(string[] args)
        {
            Method(args);
        }

        static void Method(string[] args)
        {
            int s = int.Parse(Console.ReadLine());
            int a = s;
            int[] x = new int[10000];
            int m = 0;
            for(int i = 0; i < 10000; i++)
            {
                x[i] = 0;
            }
            x[a] = 1;

            for (int i = 2; i < 1000000; i++)
            {
                if(a%2 == 0)
                {
                    a /= 2;
                }
                else
                {
                    a = 3 * a + 1;
                }
                if(x[a] != 1)
                    x[a] = 1;
                else
                {
                    m = i;
                    break;
                }
            }

            Console.WriteLine(m);
        }
    }