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>
#define m_max 1000100
int main(void){
    int n;
    scanf("%d",&n);
    int collatz[m_max];
    for(int i=0;i<m_max;i++)
    {
        collatz[i] = 0;
    }
    
    int count = 1;
    while(1)
    {
        if(n%2)
        {
            if(collatz[3*n+1]>0)
            {
                printf("%d\n",count+1);
                return 0;
            }
            else
            {
                collatz[3*n+1] = count;
                count++;
                n = 3*n+1;
            }
        }
        else
        {
            if(collatz[n/2]>0)
            {
                printf("%d\n",count+1);
                return 0;
            }
            else
            {
                collatz[n/2] = count;
                count++;
                n /= 2;
            }
        }
    }
}