You pass a carnival booth and the man operating the booth asks you to try his game. He lays out an even number of coins, n, in an array. Each coin has an associated value v_1, .., v_n. In this game, you and the man take turns picking up either the first coin or the last coin in the array and adding it to your stash. The person with the most money at the end of the game wins. You are the first player to take a coin, and the game goes on until no coins remain. Give an algorithm to determine the maximum amount of money you will have in your stash if your opponent plays optimally