MO's with Expensive Operations

If $add$ and $remove$ take $O(f)$ time each, MO's total complexity becomes $O((n + q)\sqrt{n} \cdot f)$.

For example, if you're maintaining a sorted structure with $O(\log n)$ insert/delete: Total time: $O((n + q)\sqrt{n} \cdot \log n)$ This is still often better than $O(nq)$ naive approach.

But for tight limits, consider if a different technique (like merge sort tree or persistent segment tree) would be faster. The beauty of MO's is its flexibility. Any problem with efficient extend/shrink operations can use it.