Original tree: 
(0)
   umbc(0)
      csee(0)
         full(6)
         associate(8)
         assistant(5)
         lecturer(6)
      math(0)
         full(6)
         assistant(3)
   umcp(0)
      cs(50)
      math(20)
After percolating sizes : 
(104)
   umbc(34)
      csee(25)
         full(6)
         associate(8)
         assistant(5)
         lecturer(6)
      math(9)
         full(6)
         assistant(3)
   umcp(70)
      cs(50)
      math(20)