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"
	"io"
	"os"
	"strconv"
)

var sc = NewScanner(os.Stdin, 1000000)

var a []int

func main() {
	exist := map[int]bool{}

	var tmp int
	var res int
	s := sc.readInt()
	count := 0
	a = append(a, s)
	exist[s] = true
	count++

	for {
		if a[count-1]%2 == 0 {
			tmp = int(a[count-1] / 2)
		} else {
			tmp = a[count-1]*3 + 1
		}
		a = append(a, tmp)
		_, ok := exist[tmp]
		if ok {
			res = count + 1
			break
		}
		exist[tmp] = true
		count++
	}
	fmt.Println(res)
}

type Scanner struct {
	*bufio.Scanner
}

func (scn *Scanner) readInt() int {
	scn.Scanner.Scan()
	i, _ := strconv.Atoi(scn.Scanner.Text())
	return i
}

func NewScanner(r io.Reader, bufSize int) *Scanner {
	buf := make([]byte, bufSize)
	scn := bufio.NewScanner(r)
	scn.Buffer(buf, bufSize)
	scn.Split(bufio.ScanWords)
	return &Scanner{scn}
}