The Beginning of finding out about the Red Eye
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After defeating Rorozaki, Asahi, father of Satan and Yami made a daycare on the land which had the Black eyed Service centre. To gain the public's trust they had to make some rules, like there would be 5 rooms with 2 people in each room, Each room has an age group, like 1 and 2 years in room 2, all the workers were taken from the island and had all their contact and information about them. The incharge or owner of that daycare, the sunrise daycare, was Aika Nohara, the girl Satan and Yami met at the red ice tree island. While Asahi's people were trying to find out where the other evil organization was, at that time Satan thought of finding out about that red eye, to hide it and to make people think that they are safe Satan wore an eye-patch on his left eye. Then he remembered that Rorozaki was saying something that was connected to lucifer, trying to find out about it Satan asked his father to get books related to demon mythology.
Note : The Universe Satan and Yami live is completely different from our universe.
After that Satan thought of practicing with Yami to find out about the eye.