Music Festival
$12n$ musicians participate at a music festival. On the first day, they form $3n$ quartets and practice all day.
It is a disaster. At the end of the day, all musicians decide they will never again agree to play with any member of their quartet.
On the second day, they form $4n$ trios, with every musician avoiding any previous quartet partners.
Let $f(12n)$ be the number of ways to organize the trios amongst the $12n$ musicians.
You are given $f(12) = 576$ and $f(24) \bmod 1\,000\,000\,007 = 509089824$.
Find $f(600) \bmod 1\,000\,000\,007$.