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In both of these series, an innocent person is forced into the position of a serial killer, in Tengoku to Jigoku it's through body-swapping, and in Psychopath Diary it's through amnesia. They also both include police investigation and a bit of mystery.
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Both have a character that's an outsider arriving at a place that holds secrets. Both are thrillers with mystery and psychological elements. Both have unsettling characters.
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Both are light, easy to watch dramas. They both have people teaming up to do detective work in ancient times.