Let us define a multiplication operation on three symbols a, b, c according to the following table; thus ab = b, ba = c, and so on. Notice that the multiplication operation defined by the table is neither associative nor commutative. a b C b b C b a a b C a a C C Find an efficient algorithm that examines a string of these symbols, say bbbbac, and decides whether or not it is possible to parenthesize the string in such a way that the value of the resulting expression is a. For example, on input bbbbac your algorithm should return yes because ((b(bb)) (ba)) c = a.