Suppose that the language is deterministic context$-$free. Then there is a deterministic PDA M that accepts the language. Create two copies of this machine, called M$$ and M$.$ Call any two states in these two PDAs "duals" if they are copies of the same state in M$.$ Construct a new PDA D as follows:

$$ The set of states of D is the union of the set of states of M$$ and the set of states of M$.$ The start state of M$$ is the start state of D and the accept states of M$$ are the accept states of D$.$

$$ The transitions are as in M$$ and M$$ with the exceptions that any transition from an accept state in M$$ goes to its dual in M$$ and all b transitions in M$$ are converted to c transitions.

What is the alphabet of the PDA D$?$