Draw the state diagram, this has nothing to do with the fact that L is not a CFL

Design a state transition diagrams for a (deterministic) Turing machine which recognizes the following language over A -la, b, cj: L {x | num(a,x)=max(num(b, a), num(c, a: = where num(a, x) denotes the number of occurrences of a in the string . Hint: First symbols b can be matched with symbols c to find which are more numerous (and the more numerous symbols are replaced by ""), and then symbols a are matched with "*