Consider an ADT consisting of a set S of distinct integers and the following operations: - search(S,x) : Return true if x is in S and false otherwise. - insert (S,x) : Insert the element x into the set S. This operation has no effect if x is already in S. - delete (S,x) : Delete the element x from the set S. This operation has no effect if x is not in S. - min_difference(S): Given a set S with size of at least 2, return a pair of distinct integers (x,y), with x S,yS, with the minimum absolute difference, i.e. x,y,(x=yxyxy) Your task is to design a data structure to implement this ADT, such that all operations are performed in O(logn ) time, where n=S. You will do so by augmenting our familiar AVL tree. 1. Describe all information that will be stored in the nodes. 2. Provide pseudo-code for each required operation. 3. Justify why your algorithms are correct and why they achieve the required time bound