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Shortest judge solution: 774 bytes. Shortest team solution (during contest): 678 bytes.

This was one of the simplest problems, though I underestimated how intimidating it looks. The main idea is to realize that because both rotations and reflections of pieces are allowed, the geometry of the problem is completely irrelevant. That is, it suffices to check if there is an infinite chain of pieces P₁ , P₂ , . . . such that P_i can be connected to P_i+1 . If such a chain exists then using rotations and reflections it can always be laid out in such a way that only the adjacent pieces touch each other (e.g. you can make it so that you always go upwards or to the right). If such a chain doesn’t exist then clearly the answer is “bounded”.

This reduces the problem to checking for cycles in a graph that consists of the n ≤ 40 000 pieces. This is however still too much, but there is one small additional trick: only the connections matter, so you can consider the graph consisting only of 2 · 2⁶ nodes A+, A−, . . . , Z +, Z −.