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>
#include<stdlib.h>
#include<string.h>
#include<math.h>

#define MAX(p,q) ((p>q)?(p):(q))
#define MIN(p,q) ((p<q)?(p):(q))

#define REP(i,n) for(i=1;i<n;i++)

int gcd(int a,int b);

int main(void)
{
  int a[10000000];
  int s;
  scanf("%d",&s);
  int i,j;
  a[0]=s;
  REP(i,1000000)
  {
    if(i%2==0) a[i]=a[i-1]/2;
    else a[i]=3*a[i-1]+1;
    REP(j,i)
    {
      if(a[i]==a[j])
      {
        printf("%d",i);
        break;
      }
    }
    if(a[i]==a[j]) break;
  }
  
  return 0;
}

int gcd(int a,int b)
{
  int max,min,tmp;
  max = MAX(a,b);
  min = MIN(a,b);
  if(max%min==0) return min;
  else
  {
    tmp = min;
    min = max%min;
    max = tmp;
    return gcd(max,min);
  }
}