[Community Puzzle] Mathematics for big ears

Coding Games and Programming Challenges to Code Better

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Created by @nicola,validated by @Jumpmaster,@The_ZimaBlue and @davilla.
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Hey there!

The first two tests are easily understandable, but I don’t understand the Klein test.
Why would (1,2) and (3,4) generate 4 solutions?
you can have () by combining either one with themselves, but where is the 4th possibility coming from?

The four permutations are: (), (1 2), (3 4) and (1 2)(3 4).

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Thanks @nicola !

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