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)

from sys import stdin

def func(n):
    if n % 2:
        ret = 3 * n + 1
    else:
        ret = n // 2
    return ret

def main():
    S = int(input())

    a = [0, S]
    for _ in range(2, 100):
        n = func(a[-1])
        a.append(n)
        if n == 1:
            a.append(4)
            break

    for i, n in enumerate(a):
        try:
            m = a.index(n, i + 1)
            print(m)
            break
        except:
            pass

input = lambda: stdin.readline()
main()