3. Your client would like to save some money by cutting their HR budget in half. Essentially, this means pairing offices from among their satellite campuses around the world and providing an HR office at one of the two campuses in the pair. With cutting their staff, they want to make sure the HR offices are responsive to the questions and services requested of them. One measure of responsiveness is the difference in times zones between two paired campuses. Presumably, if two campuses are in time zones very far apart, then the HR office that serves both campuses will be closed during part of the work day of the other. We will identify a time zone for campus i, UTC, as an integer between -11 and 12 inclusive, which represents the difference in hours from a particular time zone called Coordinated Universal Time (or UTC). The "distance" between two campuses i and j is the minimum of {|UTC;- UTCI, 24 - JUTC-UTC|}. You want to present a plan that pairs campuses together in such a way that the total of these distances is minimized. Example: Given these 6 campuses and their UTC values, the best pairing and total distance is given. A: -3; B: 11; C: -10; D: -5; E: 4; F: 4 The best pairing is D and A, E and F, B and C with a total distance of 5. a) Design an algorithm that, given a set of n campuses (assume n is even) and each UTC, lists the ideal pairs and the total distance between the pairs. b) Analyze the running time of this algorithm. State the most descriptive running time of your algorithm and explain where that running time comes from--which critical steps take how much time