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: Wrong Answer)

#include <iostream>
#include <vector>

using namespace std;

int main()
{
	// 入力
	int s;
	cin >> s;
	
	vector<int> a(1000000);
	
	int i = 0;
	int answer = 0;
	while (true)
	{
		if (i == 0)
		{
			a[i] = s;
			
			if (s == 1)
			{
				answer = i + 1;
				break;
			}
		}
		else {
			// 偶数
			if (a[i - 1] % 2 == 0)
			{
				a[i] = a[i - 1] / 2;
			}
			// 奇数
			else {
				a[i] = 3 * a[i - 1] + 1;
			}
			
			if (a[i - 1] == 1)
			{
				answer = i + 1;
				break;
			}
		}
		
		//cout << a[i] << " ";
		
		i++;
	}
	
	cout << answer << endl;
	
	return 0;
}