Otonashi Ayana

Ayana is a mysterious girl who gets encountered by all five protagonists; for the first time typically on the school's rooftop. She speaks enigmatically, in riddles, and frequently makes literary references and strange jokes that others find more unsettling than amusing. Her conversations are often about "The End Sky" (終ノ空 - Tsui no Sora), a concept that only she herself seems to truly understand.