Write a C++ class dfa for deterministic finite automata. The states are numbered 0,1,... and state 0 is always the start state. All states have two transitions for characters 0 and 1. The following member functions must be supported:

• typedef std::size_t State;
• typedef std::unordered_set StateSet;
• constructor dfa(std::size_t n = 1, const StateSet &F = StateSet()): returns a new dfa with n1 states and accepting state set F. All transitions go to state 0.
• std::size_t size() const: returns the number of states of this dfa;
• StateSet F() const: returns the accepting state set.
• State delta(State s, char x) const: returns (s,x)
• void add_transition(State source, char symbol, State dest): changes transition in state source on input symbol to state dest;
• State eval(const string & w) const: returns the final state of this dfa after reading input string w starting in state 0;
• bool accept(const string & w) const: returns true iff this dfa accepts input string w starting in state 0.

Also overload the input and output operators to allow reading and writing dfas. Use the following format for reading/writing dfas:

 n k // number of states and number of accepting states a1 ... ak // accepting states s_1 0 d1 // transitions for each state s_1 1 d2 ... s_n 0 d_{2n+1} s_n 1 d_{2n+2}

We use M to refer to the above description of a dfa M.