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>
#define MAX 1000000
int f(int a);

int main() {
    int i, j, s, a[MAX];
    if (scanf("%d", &s) == -1) return -1;
    a[0] = s;
    for (i = 1; i < MAX; i++) {
        a[i] =f(a[i-1]);
        for (j = 0; j < i; j++) {
            if (a[i] == a[j]) {
                printf("%d\n", i+1);
                return 0;
            }
        }
    }
    return 0;
}

int f(int a) {
    if (a % 2 == 0) return a / 2;
    return 3 * a + 1;
}