Consider the following toy. Successive marbles are dropped into the toy at 0 or 1, corresponding to the bits of an input string x {0,1}^.

The levers at a,b and c cause a marble to fall left in the indicated position, but when the marble hits a lever, the lever moves so that the next marble goes in the opposite direction. The levers start in the indicated position. The string x is accepted if its last marble falls out of the toy at A and is rejected otherwise. Design a DFA that simulates this toy.