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Regarding "Saya-chan-sensei", which characters called her that? Yuu is the first character I remember doing it, back in episode 2, which makes sense given later revelations. On the other hand, given her role as the friendly guidance counselor, it makes more sense for her to try to foster that kind of relationship with the students than in most series...
This might be silly, but should we separate character tropes for the OVA and character tropes for the anime? It could be confusing otherwise.
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How well does it match the trope?