Gokutsuma Days: Gokudou Sankyoudai ni Semaretemasu

One day Sakura, a socially withdrawn otaku, saves the life of the Amogumi’s leader. How in the world did she become the highest ranking wife?!
The leader declares to the three grandsons that, “The person who defeats Sakura-san will become the next leader.”
The eldest son is weak but kind, the second son seems fierce and aggressive, and the third son is a level-headed intellectual. The three of them are all highly skilled and stubborn in their own ways…
How is this shut-in the ultimate wife?! Jeez, no thank you. “Yakuza Harem,” start!