I'm looking for an isekai manga where the female main character got transported to another world and started her life from a village. She is overpowered, has high adaptability to survive, and is very good with mind games. It has a European medieval setting. One day, as she was on a cart with one of the villagers, two knights were yelling for help and running towards her as they were chased down by some thugs with a bit of better magical combat, and she saved them using her magical and strengthening prowess. After some time, a playboy masochistic captain from the capital came to the village to find her.
After refusing to return to the capital with that masochistic captain so many times, she reluctantly went with him and met the intimidating conniving cunning prince (second prince of the kingdom I think?). She then started to work for that prince in which her first mission was to help the prince's friend, who is a king of a neighboring kingdom, with cleaning out the scary concubines in his harem.
The female mc is one of those special other-worlders that if one appears in one kingdom, that kingdom will give her protection. There is another special other-worlder who came to visit the female mc, however, unlike the female mc, this one was ignorant of noble palace political etiquettes of this world due to the kingdom, who's protecting her, taught her noble girls' etiquette and lessons only instead of how this world works.
For the female mc's best protection, the prince had her be engaged to two captains of his kingdom and a captain from his friend's, the neighbor king, kingdom. The two captains: one is that same masochistic captain and the other is crazed on magical items captain. The neighbor kingdom's captain is known for his bloodied hair and body due to his crazy killing power.
I just couldn't forget this manga at all as I kept remembering what a team the female mc is with the prince. Both of them has such strong mentality. As the prime minister of that kingdom she's in said, she's the kitten under the big cat. So, I hope someone will be able to help me find this manga again.