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 v5.12) (judge verdict: Accepted)

'use strict'

function Main(input) {
  const lines = input.split('\n').map(Number)
  const S = lines[0]

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

  let arr = [S]
  for (let i = 1; ; i++) {
    const val = f(arr[i - 1])
    const exists = arr.some(v => v === val)
    if (exists) {
      console.log(i + 1)
      return
    }
    arr[i] = val
  }
}

Main(require('fs').readFileSync('/dev/stdin', 'utf8'))