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>
#include <stdlib.h>

int data[100000] = {0};

int f(int n) {
	if ((n & 1) == 0) {
		//printf("%d\n",n/2);
		return n/2;
	}
	//printf("%d\n",(3*n) + 1);
	return (3 * n) + 1;
}

int comp(int i) {
	int org_i = i;
	while(1) {
		i--;
		if(i < 0) {
			break;
		}
	//	printf("c %d %d\n", data[org_i], data[i]);
		if (data[org_i] == data[i]) {
			return 1;
		}
	}
	return 0;
}

int main()
{
	int n_in;
	int i = 0;
	int result = 0;
	scanf("%d", &n_in);

	data[i] = n_in;
	while(1) {
		i++;
		data[i] = f(data[i-1]);
		result = comp(i);
		if (result == 1) {
			break;
		}
	}
	printf("%d\n",i+1);
	return 0;
}