In the hierarchy, there are minimum equivalent problems in which the proof of equivalence comes by comparing their functions in the minimum sense. For example, in the minimum circuit problem, we are given a circuit C where there is no circuit C with fewer gates that computes the same function as C. Where would this minimum circuit problem be in the hierarchy (either the lower part or the higher part)? Provide your reasoning in the answer. (30 pts). Explain when and how the collapse of the hierarchy happens (10 pts)