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)

function Main(input){
  const s = parseInt(input);
  var arr = [s];
  
  var flag = true;
  var idx = -1;
  do{
    var _f = f(arr[arr.length - 1]);
    idx = arr.findIndex(elem => elem === _f);
    if(idx < 0){
      arr.push(_f);
    }else{
      flag = false;
    }
  }while(flag)
  
  console.log(arr.length + 1);
}

function f(num) {
  if(num % 2 == 0){
    return num / 2;
  }else{
    return 3 * num + 1;
  }
}

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