I want a strong female lead, not a crybaby....i hate the jealous type of girl

Strong female characters with troubled pasts! I just love it when some bullying person says something the main character actually experienced and I would be like you don't know anything and I cant wait till she puts you down! 😛

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the calm, troubled type like punpun from oyasumi punpun...you know, the type of character who is really troubled and agitated but this depression and agitation gives him/her substance and makes him/her unorthodoxly perceptive of their surroundings and therefore most of the side characters cant help but be attracted to this character's complexity.
that type of character.
another excellent manga with a main character befitting the above description would be river's edge

Most characters that I fancy are the types who have strong sense of humor, they aren't wimpy (unless it is Hiyori from Hiyokoi), aren't easily affected by the changes around them, do not cheat on their lovers, good in martial arts and FIERCE.
Examples : Ayuzawa Misaki, Kurosaki Mafuyu, Gintoki and Katsura (from Gintama)