Write a data structure that represents a priority queue that provides constant time lookup for the largest element, but has logarithmic time complexity for adding and removing elements. A queue inserts new elements at the end and removes elements from the top. By default, the queue should use operator< to compare elements, but it should be possible for the user to provide a comparison function object that returns true if the first argument is less than the second. The implementation must provide at least the following operations:

push() to add a new element
pop() to remove the top element
top() to provide access to the top element
size() to indicate the number of elements in the queue
empty() to indicate whether the queue is empty