 If you liked
Matantei Loki Ragnarok
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 ...then you might like
Code:Breaker
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Similar:
1. Annoying girl enters main character's life.
2. Main character protects said annoying girl.
3. Main character starts to "like" the annoying girl.
Differences:
Mythical Detective Loki - Girl doesn't possess any powers (based in mystery with super natural with norse gods).
Code:Breaker - Girl possesses a power (based in super natural with government).