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 main(void){
int a[100000] = {};
int n,i,s,m,j;
scanf ("%d",&s);
a[0] = s;
n = 0;
for (i = 0;i < 1000;i++)
{
    if (a[i]%2 != 0)
    {
        a[i+1] = (3*a[i])+1;
    }
    else
    {
        a[i+1] = a[i]/2;
    }
}
for (i = 0;i < 1000;i++)
{
    for (j = i+1;j < 1000;j++)
    {
        if (a[i] == a[j])
        break;
    }
if (a[i] == a[j])
break;
}
printf ("%d",j+1);
    return 0;
}