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

func a(i int, s int) int{
  if i == 1{
    return s
  }else{
    return f(a(i-1, s))
  }
}

func main(){
  var s int
  fmt.Scan(&s)
  for i := 1; i<=1000000; i++{
    for j:=1; j<i; j++{
      if a(i,s) == a(j,s){
        fmt.Print(i)
        return
      }
    }
  }
}