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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

const collatz = (n) => {
  if (n % 2 === 0) {
    n /= 2
  } else {
    n = 3 * n + 1
  }

  return n
}

const main = stdin => {
  const input = stdin.trim().split('\n')
  const s = parseInt(input[0])

  if (s === 1 || s === 2 || s === 4) {
    console.log(4)
    return
  }

  let tmp = s
  let first = 0
  let second = 0
  for (let i = 1; ; i++) {
    if (tmp === 4 && first === 0) {
      first = i
    } else if (tmp === 4 && first !== 0) {
      second = i
      break
    }
    tmp = collatz(tmp)
  }

  console.log(second)
}
// 標準入力
main(require("fs").readFileSync("/dev/stdin", "utf8"))