Collatz Sequence Length

Given a positive integer $n$, compute the length of the Collatz sequence starting from $n$ until it reaches 1. The Collatz sequence is defined as follows:

1. If $n = 1$, the sequence terminates.
2. If $n$ is even, the next term is $\frac{n}{2}$.
3. If $n$ is odd and $n > 1$, the next term is $3n + 1$.

Use memoization to optimize the computation for large values of $n$. Your program should read a single integer from standard input and output the length of the sequence to standard output.

inputFormat

A single positive integer $n$ provided via standard input.

outputFormat

Output the number of terms in the Collatz sequence starting from $n$ until it reaches 1, printed to standard output.## sample

13

10