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: Wrong Answer)

s = gets.to_i

def f(n)
  ret = 0
  if n.even?
    ret = n /2
  else
    ret = 3 * n + 1
  end
  ret
end


list = []
list[0] = s
i = 1
loop do
  v = f(list[i-1])
  list[i] = v
  break if v == 4
  i += 1
end

ans = 10000000
for i in 0..(list.size - 2) do
  for j in (i+1)..(list.size - 1) do
    v1 = list[i]
    v2 = list[j]
    if v1 == v2 && j < ans
      ans = j
    end
  end
end

if ans == 10000000
  ans = list.size + 3
end

puts ans