You have won a "Boston Sports Pass" as part of a student raffle! The pass works as follows, you get a free ticket to either one Bruins or one Celtics game each of thenweekends of the season. However, there is a catch. Every time you want to switch from one to the other, you have to pay aswitch fee. So if you get Celtics tickets the first three weekends, and then Bruins tickets the remaining weekends, you would pay the fee once. If you switched every weekend, you would pay the feen−1times. You can choose to start with whichever team you like without paying any fee. Unfortunately, because you are too busy studying, you determine you can’t go to any games. Fortunately, you can turn this into a nice chunk of change, as your sports-afficionado Algorithms instructor offers to buy the tickets off of you. He tells you how much he would pay you for each game, but he isn’t willing to pay the switch fee. Determine the maximum amount of profit you can make. To formalize, the input to the problem is 2n+ 1 numbers, C1,...,Cn, B1,...,Bn, S >0 where Ci is the amount you’d receive for choosing t.