Design (in detail) and analyze a data structure that will hold a set of n weighted intervals of the real line, that is, a set of triples (a, b, w) such that a, b and a < b and w is a positive integer. Think of a as the left endpoint and b the right endpoint of a segment of the real line. A query to this data structure will consist of a value z and will ask for the heaviest interval containing z. You data structure should require O(nlogn) preprocessing time, and then O(logn) time to process a query.