For FEIE, can 2 physical Presence Periods be used In the Same tax Year, even if they don't over lap?

I have a 12 month physical presence period from April 13, 2016 to April 14, 2017 and another between August 3, 2017 to August 4, 2018.  Can I claim the qualifying days from Jan 1, 2016-April 13, 2016 and the days between August 3, 2017 and December 31, 2017?

 

Pub 54 says that 2 periods can overlap but doesn't say anything about a gap between 2 periods.