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The NSA needs more friends

You successfully helped the NSA find friends! Congratulations!

Emboldened by your success, the NSA has decided to try and widen its net even more and has asked you to make some changes to your friend-finding program.

The problem

Instead of using a social network database where friend relationships are commutative and undirected, they would like you to use a social network database with directed relationships, where users "follow" other users instead. In this case, just because user A follows user B, user B doesn't necessarily follow user A.

They still want you to find good groups of friends, but the requirement is relaxed; not every user needs to be following every other user in the group directly. Instead, it is sufficient if every user is following every other user in the group transitively and indirectly. To be specific, if user A is following user B, and user B is following user C, then we can say user A is indirectly following user C. There's no limit to this chain of transitive relationships, but every user in a group must have a chain of directed transitive "following" relationships to every other user in the group.

Input format

Your program is still expected to take a --minimal-group-size=N argument, where N will be the smallest allowed amount of people in a group.

Your program should then read from stdin a JSON array of following relationships, where a following relationship is a size-2 array of names, the first element being the follower, and the second element being the followee.


./run --minimal-group-size=4


[["Edward Snowden", "Laura Poitras"],
 ["James Comey", "Keith Alexander"],
 ["Keith Alexander", "Michael Hayden"],
 ["Michael Hayden", "James Clapper"],
 ["James Clapper", "James Comey"],
 ["Keith Alexander", "Jeff Wendling"]]

Output format

You should then output a JSON array of arrays, where the internal arrays are lists of names of friends that are all friends with each other. The internal arrays should be at least of length N.



[["James Comey", "Keith Alexander", "Michael Hayden",
  "James Clapper"]]