How to factorize $n(n+1)(n+2)(n+3)+1$? How to factorize $n(n+1)(n+2)(n+3)+1$ ?

It's turned into the lowest power of $n$ ever possible but the question wants me to factorize it.

How can I do that ?
$$n(n+3)=n^2+3n$$

and $$(n+1)(n+2)=n^2+3n+2$$

$$\implies n(n+1)(n+2)(n+3)=(n^2+3n)[(n^2+3n)+2]+1=[(n^2+3n)+1]^2$$
Just by running it through Wolfram, I think the simplest way to write it is $(n^2+3n+1)^2$. Many of the other ways still had a "$+1$" at the end of them.