Jeddah Municipality has decided to build a network of national hospitals to treat infectious diseases. A special task force is constituted which is tasked to investigate possible locations for these new hospitals. The task force has done its job and come back with a list of potential sites. Each of these hospitals has an associated cost and will provide coverage to some number of nearby districts within Jeddah. We can represent each potential hospital site as having: a name (string), cost to build the hospital (int) and a set of districts to be covered (Set of strings). Jeddah Municipality is interested in providing health care to all, but they do not have funds to build an unlimited number of hospitals. The goal is to provide coverage to as many districts as possible using the available funds. For example, suppose Jeddah Municipality has the following districts: Al-Aziziya, Ar-Rihab, Mosharafa, Al-Faysaliya, Bani Malik, An-Naseem, Al-Balad, Al-Salam, Al- Makarona, As-Salmiya, Al-Gozain, Al-Hamdaniya Suppose that these are the possible hospital sites: Site 1: Covers Al-Aziziya, Ar-Rihab, Mosharafa, Al-Faysaliya. Cost: SARS 20,000,000. Site 2: Covers Ar-Rihab, Bani Malik, An-Naseem, Al-Balad. Cost: SARS 50,000,000. Site 3: Covers Al-Balad, Al-Salam, Al-Makarona, As-Salmiya, Al-Gozain. Cost: SARS 40,000,000. Site 4: Covers As-Salmiya, Al-Gozain, Al-Hamdaniya. Cost: SARS 10,000,000. Site 5: Covers Mosharafa, Al-Faysaliya, An-Naseem, Al-Balad. Cost: SARS 30,000,00. Site 6: Covers Al-Balad, Al-Salam, Al-Hamdaniya. Cost: SARS 10,000,000. Site 7: Covers AI-Balad, Mosharafa, Al-Salam, Al-Makarona, As-Salmiya. Cost: SARS 60,000,000. Site 8: Covers Ar-Rihab, Bani Malik, Al-Makarona, As-Salmiya, Al-Balad. Cost: SARS 50,000,000. If you build Site 1 and Site 2, you have provi Faysaliya, Bani Malik, An-Naseem, and Al-Balad a total of seven districts, at a cost of SARS 70,000,000. (Notice that both Site 1 and Site 2 provide coverage to Ar-Rihab, so even though Site 1 and Site 2 cover four districts each, only seven total districts end up covered). Adding in Site 5 would add in a cost of SARS 50,000,000 without actually providing any new coverage, since all four of the cities it services are already covered. coverage to Al-Aziziya, Ar-Rihab, sharafa, Al- Your task is to write a recursive function that takes as input a list of possible hospital sites and an amount of funds available, and then returns a list of hospitals that should be built to provide coverage to the maximum number of cities. It is important to note that multiple hospitals could provide coverage to the same district. However, when you count up the total number of districts covered, you do not double-count a district. A sample run: Suppose total available funds (budget) are: SARS 80,000,000. The optimal coverage is [Site 1, Site 4, Site 5, Site 6] which covers 11 districts.