How much can a non-dependant child covered by his parent's HDHP contribute to his own HSA?

I am 25 years old, a non-dependant, and covered under my mom's family HDHP (for the entire year). My dad is also covered under the same insurance plan.  Can I contribute $6750 to my own HSA (no matter what my parents contribute to their own HSAs), or is the $6750 limit shared between the three of us?