Below, we address the main concerns raised in the reviews

We thank the reviewers for their comments and suggestions. We will incorporate the suggestions in our revised version. Below, we address the main concerns raised in the reviews. The work of Morris et al. [2019] was one of our main inspirations. We note that the time complexity of Morris et al. can probably be improved to Nevertheless, we admit that trying to prove our results without using it is an intriguing question.