At an airport, multiple servicing teams are tasked with servicing planes in a specific sequence determined by their departure schedules. A bell signals when planes are allowed to depart, impacting all teams simultaneously. When the bell rings, teams may continue servicing the planes they are currently working on but cannot start servicing the next plane until the current one has been fully serviced and departed. The following constraints apply:The bell indicates when planes are cleared for departure, affecting all teams simultaneously.Teams can finish servicing their current plane even after the bell rings, but they cannot begin work on the next plane until the current one departs.Each team can handle only one plane at a time and must wait for the previous plane's departure before starting on the next.The goal is to maximize the efficiency of the servicing teams by strategically scheduling the bell rings to optimize the total working hours of each team. Assume you have three teams prove it is NP$-$complete problem. Show first it is NP$,$ then show It is NP$-$hard. Apply the prove to both directions