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 Go (1.6) (judge verdict: Accepted)

// Package main provides
//
// File:  b.go
// Author: ymiyamoto
//
// Created on Tue Jan 22 16:26:07 2019
//
package main

import "fmt"

func main() {
	var s int
	fmt.Scan(&s)

	arr := []int{s}
	for s != 1 {
		if s%2 == 0 {
			s /= 2
		} else {
			s = 3*s + 1
		}
		arr = append(arr, s)
	}

	arr = append(arr, []int{4, 2, 1}...)
	for i := range arr {
		for j := i + 1; j < len(arr); j++ {
			if arr[i] == arr[j] {
				fmt.Println(j + 1)
				return
			}
		}
	}

}