Question: 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 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.

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