Double Invasion: a Room That You Can't Get Out of Without Having Sex

Two male protagonists/amnesia/imprisonment/superpowers/fighting of wits/falling in love and killing each other I lost my memory and was imprisoned in a pure white secret room. I was required to fill out a one-page "questionnaire" every day. If I didn't fill it out well, I would have to receive forced "treatment" from a man. In order to escape, I was obedient on the surface and pretended to be sinking, but in fact I was working hard step by step and began to solve the puzzle...