From what I remember, it was about a girl who I think had the task of save the Yandere male lead. I remember the female lead transmigrated as the ML teacher that his (step)mom hired. The teacher was supposed to be trash but since our FL transmigrated to this body, things changed. They live in a mansion with some servants. His dad, (step)mom and (step)brother live somewhere else. Anyway... I also remember that around the end of the 1st arc, she went to a fair with the ML. Our FL saw something falling from the sky (a falling dog) that was about to hit our ML and she push him, saving him. She on the other hand ends up in a coma (I think the system said she would be put in hibernation or something). Anyway, when she wakes up some years have passed and our ML confessed his love towards her (his teacher).