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: Accepted)

def f(n):
    if n%2==0:
        return n/2
    else:
        return 3*n+1
s = int(input())
a=[0]*1000001
get_ans = False
ans = 0
for i in range(2,1000001):
    #aiを保存しながら進む&見つかったら進まなくてよい
    if i==2:
        a[1] = s
        a[2] = f(s)
        if a[1]==a[2]:
            ans = 2
            break
    else:
        a[i]=f(a[i-1])
        for j in range(1,i):
            if a[i]==a[j]:
                ans = i
                get_ans = True
                break
    if get_ans:
        break
print(ans)