// TreeSet variant allowing multiple elements which are considered
// equal by the comparator but not by eq().
// could be augmented to implement NavigableSet.
// All operations O(log n) with n being the number of _different_ elements.
sclass TreeSetWithDuplicates<A> implements Iterable<A> {
  TreeSet<Set<A>> internal;
  Comparator<A> comparator;
  int size;
  
  *(Comparator<A> *comparator) {
    internal = new TreeSet<Set<A>>((setA, setB) -> {
      ret comparator.compare(main first(setA), main first(setB));
    });
  }
  
  swappable Set<A> makeInternalSet() { ret new HashSet; }
  
  void add(A a) {
    Set<A> newSet = addAndReturnCollection(makeInternalSet(), a);
    Set<A> found = navigableSet_find(internal, newSet);
    if (found != null) {
      if (!found.add(a)) ret;
    } else
      internal.add(newSet);
    ++size;
  }
  
  void remove(A a) {
    Set<A> newSet = addAndReturnCollection(makeInternalSet(), a);
    Set<A> found = navigableSet_find(internal, newSet);
    if (found == null) ret;
    found.remove(a);
    if (empty(found)) internal.remove(found);
    --size;
  }
  
  A first() {
    ret main first(main first(internal));
  }
  
  public ItIt<A> iterator() {
    ret nestedIterator(internal, methodLambda0 iterator);
  }
  
  void addAll(Cl<? extends A> l) {
    fOr (A a : l) add(a);
  }
  
  public int size() { ret size; }
  
  // may return null
  Set<A> tiedForFirst() { ret first(internal); }
}