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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main(){
  int s;
  cin >> s;
  
  int m = 0;
  vector<int> a;
  a.push_back(s);
  for (int i=1 ; ; i++){
    if (a.at(a.size()-1)%2 == 0)
      a.push_back(a.at(a.size()-1)/2);
    else
      a.push_back(3*a.at(a.size()-1) + 1);
    for (int j=0 ; j<a.size()-1 ; j++){
      if (a.at(a.size()-1) == a.at(j)){
        m = i+1;
        break;
      }
    }
    if (m != 0)
      break;
  }
  
  cout << m << endl;
}