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)

var reader = require('readline').createInterface({
  input: process.stdin,
  output: process.stdout
});

var lines = [];
reader.on('line',(line) => {
          lines.push(line);
});

reader.on('close', () => {
          var s = lines[0];
  var a = [s];
  for (var i = 0; i < 1000010; i++){
    if (a[i] % 2 == 0){
     a.push( a[i] / 2 );
    } else {
      a.push( a[i]*3+1 );
    }
    for (var j = 0; j < i;j++){
      if (a[i] == a[j]){
         console.log(i+1);
        return;
      }
    }
  }
});