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>
#include <math.h>
#include <stdlib.h>
//25min
int main(void){
  int s;
  int a[100001];

  scanf("%d", &s);

  a[1] = s;
  int i = 2;
  while(s % 1 == 0){
    if(s % 2 == 0){
      a[i] = s / 2;
    }else{
      a[i] = 3 * s + 1;
    }
    //printf("a[%d]=%d\n",i,a[i]);

    //i++;
    for(int j = i - 1; j > 0; j--){
      if(a[j] == a[i]){
	printf("%d\n", i);
	return 0;
      }
    }
    s = a[i];
    i++;
  }
  
  return 0;
}