A factorial function

You will write your own factorial function with a loop, use it to count down a product, and find where factorials pass a million. The checker tests your work against math.factorial.

The idea. Start with 1, which is $0!$, and multiply by $1$, $2$, ... up to $n$. A product of $k$ numbers counting down from $n$ is $\dfrac{n!}{(n - k)!}$.

Your tasks.

1. Finish factorial(n): it must return $1$ for $n = 0$, and $n!$ for larger $n$.
2. Finish count_down(n, k): the product of the $k$ numbers $n$, $n - 1$, ..., using factorial and //.
3. Set first_big to the smallest $n$ for which $n!$ is more than $1000000$.