$7.$ In coins$-$in$-$a$-$line game, there are an even number, N$,$ of coins placed in a line. Two

players, Aynur and Fatih, take turns removing one of the coins from either end of the

remaining line of coins. That is$,$ when it is a players turn, he or she removes the coin

at the left or right end of the line of coins and adds that coin to his or her collection.

The player who removes a set of coins with larger total value than the other player

wins, where we assume that both Aynur and Fatih know the value of each coin in some

common currency, such as dollars. See the following figure:

Design a dynamic programming algorithm that determine optimal strategy for the first

player $($Aynur$)$ who plays first. Assume that the second player $($Fatih$)$ always choose

the better coin $($i$.$e$.$ uses a greedy strategy$).$