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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <string>
using namespace std;
int f(int n) {	
	return (n % 2 == 0 ? n / 2 : 3 * n + 1);
}
int main() {
	int s;
	cin >> s;
	vector<int> a(0);
	int i = 1, add;
	while (true) {
		if (i == 1) {
			add = s;
		} else if (i > 1) {
			add = f(a[i-2]);
		}

		for (int j = 0; j < a.size(); j++) {
			if (a[j] == add) {
				cout << i << endl;
				return (0);
			}
		}
		a.push_back(add);
		i++;
	}
}