Graph Coloring · Challenge problem

A conference has $2$ keynote speakers, who co-present one joint session together, plus $6$ breakout facilitators. Each facilitator has a separate private planning meeting with EACH keynote speaker individually ($12$ such meetings), in addition to the keynotes' own joint session ($1$ meeting), $13$ meetings in all. No person may be in two meetings during the same time period. What is the minimum number of periods needed to schedule every meeting?