5. (19 pts) Consider the following grammar for simple assignment statements: AssignSimt Var-E Var Index id | id [ Index ] Var nr E+EIE-EIE EIE/EI(E) (a) (12 pts) Build a parse tree for each of the following assignment statements: a[2] b + 1 (b) (7 pts) Rewrite the grammar so that it allows multi-dimensional arrays (instead of just one index, allow a list of indices separated by commas). For instance, each of the following should be a valid string under the new grammar m[5,3] = x y = p[i+1,j,k-1]