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Music festival

Problem 475 Published on Sunday, 8th June 2014, 10:00 am; Solved by 330;
Difficulty rating: 50%

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, each musician avoiding his 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) mod 1 000 000 007 = 509089824.

Find f(600) mod 1 000 000 007.