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 Ruby (2.3.3) (judge verdict: Accepted)

def func(n)
  if n.even?
    (n / 2)
  else
    (3 * n + 1)
  end
end

s = gets.chomp.to_i
n = 1_000_000

a = []
a[0] = s

flg = 0
(1..(n - 1)).each do |i|
  a[i] = func(a[i - 1])
  (0..(i - 1)).each do |j|
    if a[i] == a[j]
      puts (i + 1)
      flg = 1
      break
    end
  end
  break if flg == 1
end