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 <stdio.h>
#include <vector>

using namespace std;

int S;
vector<int> seq;

int func(int n)
{
	if (n % 2 == 0) return n / 2;
	else return 3 * n + 1;
}

bool check()
{
	int n = seq.size();

	for (int i = 1; i < n; i++)
	{
		if (seq[n - 1] == seq[n - 1 - i]) return true;
	}

	return false;
}

int main()
{
	scanf("%d", &S);
	seq.push_back(S);

	while (check() == false)
	{
		seq.push_back(func(seq[seq.size() - 1]));
	}

	printf("%d", seq.size());

	return 0;
}