Please Help Me Find a Quick Transmigration Story!

One of the worlds is an ancient society where women hold power and men are beneath them! Before the heroine transmigrates, the original owner is in love with a man. After the heroine transmigrates, she falls out of love with him. The hero works at a pleasure house, but his true identity is actually the crown prince. The heroine works herself to the bone to study and pass the imperial exam as its top scorer for his sake.