Design an implementation of an Abstract Data Type consisting of a set with the following operations: insert(S, x) Insert x into the set S. delete(S, x) Delete x fromthe set S. member(S, x) Return true if x ∈ S, false otherwise. position(S, x) Return the number of elements of S less than x. concatenate(S, T) Set S to the union of S and T, assuming every element in S is smaller than every element of T. All operations involving n-element sets are to take time O(log n).

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