Honestly... When I saw Yui making a video of the rap battle, the first thing that occured to me was that her "move" would be blackmailing Hachiman into the relationship.
In any event, the moment Yui took her phone out, I could see Hachiman rue it later.
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Those who forget about the past are condemned to repeat it - Santayana
Sidenote: I'm seemingly too dumb for my current keyboard, so if you see the same character twice in a row, when it doesn't belong there just ignore it.