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: Wrong Answer)

using System;
public class Program {
  public static void Main() {
    int[] array = new int[1000000];
    array[0] = int.Parse(Console.ReadLine());
    for (int i = 1; i < array.Length; i++) {
    	array[i] = F(array[i-1]);
      	if (array[i] == 4) {
          Console.WriteLine(i + 4);
          return;
        }
    }
  }
  
  public static int F(int n) {
    if (n % 2 == 0) {
      return n / 2;
    } else {
      return 3*n + 1;
    }
  }
}