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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

class Main{

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int s = sc.nextInt();
		int[] f =new int[1000001];
		
		int[] cc = new int[1000000];
		for(int i = 1;i < 1000001;i++){
			if(i == 1){
				f[i] = s;
			}else if(f[i-1] % 2 == 0){
				f[i] = f[i-1] /2;
			}else{
				f[i] = 3*f[i-1] + 1;
			}
//			System.out.println(f[i]);

			if(cc[f[i]] > 0){
				System.out.println(i);
				return;
			}
			cc[f[i]]++;
			
		}
		
	}


}

class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return from - otherpair.from;
	}
}