We consider the problem of maintaining a set S of integers under the following operations: Insert(S, x): This operation inserts element x into the set S. Delete50%Largest(S): This operation deletes the largest |S|/2 elements from the set S. Design a data structure (and explain the algorithms for Insert and Delete50%Largest) such that any sequence of n operations takes O(n) time, i.e. each operation takes constant amortized time. Define the potential function you use to do the amortized analysis. You may assume that the set S is empty at the start of the sequence.