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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const mod = 1000000007

// 1MB
const ioBufferSize = 1 * 1024 * 1024

var sc = func() *bufio.Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Buffer(make([]byte, ioBufferSize), ioBufferSize)
	sc.Split(bufio.ScanWords)
	return sc
}()

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

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

func main() {
	s := nextInt()
	already := map[int]bool{}
	already[s] = true

	i := 1
	for {
		i++
		s = f(s)
		if already[s] {
			fmt.Println(i)
			return
		}
		already[s] = true
	}
}