In this game, there is a stack of n bricks. The ith brick in the stack is worth v[i] points (where v[0] is the value of the top brick). The players take turns removing either 1, 2, 3 or 4 bricks from the top of the stack. The player that removes a brick earns the number of points associated with the brick. The game ends when all the bricks have been removed, and the winner is the player who has earned the most points. For example, if v = [1, 1, 3, 4] and Smoov is the first player to move, then Smoov's optimal strategy is to take just the first brick (earning 1 point). Curly's optimal strategy is then to take the next two bricks (earning 4 points). Smoov then finishes by taking the last brick (earning 4 more points). Therefore, the maximum score Smoov can earn is 5. Assume that Smoov takes the first turn and that both Smoov and Curly play optimally. Given the list v of the values of the bricks (all integers greaterthanorequalto 0), output the maximum score Smoov can earn. (a) Define the subproblems to be solved in English. Solution: Let s_i denote the optimum score for whoever's turn it is when v_i is the top remaining brick. The subproblems are to compute s_i for each i from n - 1 to 0. (b) Define an appropriate recurrence for the subproblems. Solution: s_i = {0, i greaterthanorequalto n v[i] + max (min(s_i+2, s_i+3), v[i + 1] + min(s_i+3, s_i+4)), i < n For the particular input v = [1, 2, 0, 8, 0, 3, 3, 2], compute s_i for 0 lessthanorequalto i lessthanorequalto 7.