Carry out the algorithm presented to get the minimal DFA equivalent to the twelve-state DFA drawn below. This DFA has alphabet {0, 1} and determines whether a string represents a number in binary that is divisible by twelve. The state set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. On input 0, the machine goes from state i to state 2i. On input 1, the machine goes from state i to state (2i 1). Give each of the equivalence relations produced by the algorithm and demonstrate that your last one is really the last one. Draw the resulting minimal DFA.