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: Accepted)

#include <stdio.h>

int collatz(int n){
  if(n%2==0) return n/2;
  else return 3*n+1;
}

int main(){
  int s;
  scanf("%d",&s);
  int i,m;
  int visited[100001];
  for(i=0;i<100001;i++) visited[i]=0;
  visited[s]=1;

  i=2;
  while(1){
    s=collatz(s);
    if(visited[s]==1){
      m=i;
      break;
    }else{
      visited[s]=1;
      i++;
    }
  }

  printf("%d\n",m);
  return 0;
}