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 5.4.1) (judge verdict: Wrong Answer)

#include "stdio.h"

unsigned long long int my_f(unsigned long long int N){
  if (N%2==0) {
    return N/2;
  }
  return 3*N+1;
}

int main(int argc, char const *argv[]) {
  unsigned long long int S;
  int c_f=0;
  int c_t=0;
  scanf("%llu", &S);
  long int i=1;
  while (S!=1) {
    S=my_f(S);
    if (S==2) {c_t=1;}
    if (S==4) {c_f=1;}
    i++;
  }
  if (c_f==1) {
    i=i+1;
  }else if(c_t==1){
    i=i+2;
  }else{
    i=i+3;
  }
  printf("%ld", i);
  return 0;
}