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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.PrintWriter
val pw = PrintWriter(System.out)

fun main(args : Array<String>) {
    func()
    pw.flush()
}

fun func() {
    val s = nextInt()
    val nums = mutableMapOf(s to 1)

    var num = s
    var index = 2

    while (true) {
        if (num % 2 == 0) {
            num /= 2
        } else {
            num = 3 * num + 1
        }

        if (nums[num] == null) {
            nums[num] = index
        } else {
            println(index)
            return
        }

        index++
    }
}

fun next() = readLine()!!
fun nextInt() = next().toInt()

fun println(value : Any) {
    pw.println(value)
}