long total = aggr.treeAggregate(root);
    if (range.hasLowerBound()) {
      total -= aggregateBelowRange(aggr, root);
    }
    if (range.hasUpperBound()) {
      total -= aggregateAboveRange(aggr, root);
    }
    return total;
  }

  private long aggregateBelowRange(Aggregate aggr, @CheckForNull AvlNode<E> node) {
    if (node == null) {
      return 0;
    }

    long total = aggr.treeAggregate(root);
    if (range.hasLowerBound()) {
      total -= aggregateBelowRange(aggr, root);
    }
    if (range.hasUpperBound()) {
      total -= aggregateAboveRange(aggr, root);
    }
    return total;
  }

  private long aggregateBelowRange(Aggregate aggr, @CheckForNull AvlNode<E> node) {
    if (node == null) {
      return 0;
    }