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Problem 475

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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, 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.

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音乐节

12n个音乐家参加了一场音乐节。第一天，他们组成了3n个四重奏，演奏了一整天。

这一天的演奏简直是场灾难，总之，在当天结束的时候，所有的音乐家都决定不再和这一天一同演奏四重奏的其它音乐家合作。

第二天，他们组成了4n个三重奏，每位音乐家都避开了第一天的合作者。

记f(12n)为这12n位音乐家组成三重奏的方法数。

已知f(12) = 576，f(24) mod 1 000 000 007 = 509089824。

求f(600) mod 1 000 000 007。

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