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 Python (3.4.3) (judge verdict: Wrong Answer)

s = int(input())

def collatz(s):
  if result[i-1] % 2 == 0:
    x = result[i-1]/2
  elif result[i-1] % 2 > 0:
    x = (3*int(result[i-1])) + 1
  return x

result = []
x = 0
c = 0
i = 0
tmp = []
while True:
  if s == 1:
    ans = [s]
    break
  elif i == 0:
    i += 1
    x = s
  elif c == 2:
    ans = [y for y, z in enumerate(result) if z == result[1]]
    break
  elif int(x) == 1:
    i = 1
    c += 1
    x = result[i]
    continue
  else:
    x = collatz(s)
    i += 1
  result.append(int(x))

print(sum(ans))