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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys


inint = lambda: int(sys.stdin.readline())
inintm = lambda: map(int, sys.stdin.readline().split())
inintl = lambda: list(inintm())
instrm = lambda: map(str, sys.stdin.readline().split())
instrl = lambda: list(instrm())

s = inint()

a = [s]
al = [s]


for i in range(1, 1000001):
    if a[i-1] % 2 == 0:
        if a[i-1]//2 not in al:
            al.append(a[i-1]//2)
            a.append(a[i-1]//2)
        else:
            print(i+1)
            break
    else:
        if a[i-1]*3+1 not in al:
            al.append(a[i-1]*3+1)
            a.append(a[i-1]*3+1)
        else:
            print(i+1)
            break