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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>

int main(int argc, char *argv[])
{
    long long s, a[(int)1e6];
    int i, j;

    scanf("%lld", &s);

    a[0] = s;

    for (i = 1; i < (int)1e6; i++) {
        if (a[i - 1] % 2) {
            a[i] = 3 * a[i - 1]+ 1;
        } else {
            a[i] = a[i - 1] / 2;
        }
    }

    for (i = 1; i < (int)1e6; i++) {
        for (j = 0; j < i; j++) {
            if (a[i] == a[j]) {
                printf("%d\n", i + 1);
                return 0;
            }
        }
    }

    return 0;
}