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)

class CalcService
  def initialize(s)
    @s = s
    @memo = {}
  end

  def execute
    j = 1
    answer = {}
    ans = 0
    while true do
      ans = a(j)
      answer[ans] ||= []
      answer[ans] << j
      break if answer[ans].length > 1
      j += 1
    end
    puts j
  end

  def a (i)
    return @s if i == 1
    f(a(i-1))
  end

  def f (n)
    return @memo[n] if @memo.key?(n)
    if n % 2 == 0
      return n/2
    else
      return 3*n + 1
    end
  end
end
s = gets.to_i
CalcService.new(s).execute