When search will work, why not use it for a try?
Search all the time from 00:00:00 to 23:59:59, you can easily got AC in 0.031sec...:)

Also, there exist a algorithm use only O(1):
  Because all change in liner,the max ans must be in one of the 8 time.
  But take care that the "eariest" time may not be any of them, it can be an earier such as 00:00:00...