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: Runtime Error)

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>

bool in_judge(std::vector<int> &a){
	int n = a.size();
	for(int i=0; i<n-1; i++){
		if(a[i]==a[n-1]){
			return true;
		}
	}
	return false;
}

int main(){
	int s;
	std::cin >> s;
	std::vector<int> a(1, s);
	for(int i=1; ; i++){
		if(a[i-1]%2==0){
			a.push_back(a[i-1] / 2);
		}else{
			a.push_back(3*a[i-1] + 1);
		}
		if(in_judge(a)){
			std::cout << i+1 <<std::endl;
			return 9;
		}
	}

	return 0;
}