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)

INF, MOD = float("inf"), 1e9 + 7
MAX, MIN = -INF, INF
dx1, dy1, dx2, dy2 = [-1, 0, 1, 0], [0, -1, 0, 1], [-1, 0, 1, -1, 1, -1, 0, 1], [-1, -1, -1, 0, 0, 1, 1, 1]

def get_int():
    return int(input())

def get_int_list():
    return list(map(int, input().split()))

def mins(x, y):
    x = min(x, y)

def maxs(x, y):
    x = max(x, y)

while(True):
    try:
        n = int(input())
        a = []
        a.append(n)
        while(True):
            x = 3 * a[len(a) - 1] + 1 if a[len(a) - 1] % 2 else int(a[len(a) - 1] / 2)
            if x in a:
                print(len(a) + 1)
                break
            a.append(x)
    except EOFError:
        exit()