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)

s = int(input())

a = []
a.append(s)
b = {}

ans = 1000000
for i in range(1, 1000000):
    if a[i - 1] % 2 == 0:
        a.append(int(a[i - 1] / 2))
        if a[i - 1] in b:
            b[a[i - 1]] = b[a[i - 1]] + 1
            if b[a[i - 1]] > 1:
                ans = i
                break
        else:
            b[a[i - 1]] = 1
    else:
        a.append(3 * a[i - 1] + 1)
        if a[i - 1] in b:
            b[a[i - 1]] = b[a[i - 1]] + 1
            if b[a[i - 1]] > 1:
                ans = i
                break
        else:
            b[a[i - 1]] = 1

print(ans)