Documentation

Starting from a positive integer \(n\), we can have a sequence of numbers such that at each step, the next number is \(3n+1\) if \(n\) is odd, or \(\frac{n}{2}\) if \(n\) is even. The Collatz conjecture states that this sequence will always end at 1 after a finite number of steps.

Using the Writer monad, count the number of these steps for a given positive integer \(n\).

Examples

>>> collatz 1
0

>>> collatz 2
1

>>> collatz 31
106

Hint