Suppose we implement the tree-based union-find data structure, but we don’t use the union-by-size heuristic nor the path-compression heuristic. Show that the total running time for performing a sequence of n union and find operations, starting with n singleton sets, is Θ(n²) in this case. That is, provide a proof that it is O(n²) and an example that requires Ω(n²) time.