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

import (
        "fmt"
)

func solution(s int) int {
        memo := make(map[int]bool, 0)
        memo[s] = true
        i := 2
        b := s
        for {
                a := helper(b)
                i++
                b = a
                if memo[a] {
                        break
                } else {
                        memo[a] = true
                }
        }
        return i - 1
}

func helper(n int) int {
        if n%2 == 0 {
                return n / 2
        }
        return 3*n + 1
}

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