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 <stdio.h>
#include <algorithm>
#include <vector>
#include <iostream>
#include <map>
using namespace std;

int main()
{
	int S;
  	cin >> S;
  	int i = 2;
  	vector<int> A;
  	A.push_back(S);
  	map<int, int> num;
  	int answer=0;
  	int n = 0;
  	while(1){
      	n = A[i-2];
    	if(n%2){
        	A.push_back(n*3+1);
      		if(num.find(n*3+1) != num.end()){
              answer = i;
              break;
            }
      		num[n*3+1] = 1;
        } else {
    		A.push_back(n/2);
      		if(num.find(n/2) != num.end()){
              answer = i;
              break;
            }
      		num[n/2] = 1;
        }
      	i++;
    }
	cout << answer << endl;

}