B'Your friend Kirchhoff is shocked with the current state of electronics design. "Ohmygosh! Watt is wrong with the field? All these circuits are inefficient! There 's so much capacity for improvement. The electrical engineers must not conduct their classes very well. It 's absolutely revolting" he said. The negativity just keeps flowing out of him, but even after complaining so many times he still hasn 't lepton the chance to directly change anything. "These circuits have too much total resistance. Wire they designed this way? It 's just causing a massive loss of resistors! Their entire field could conserve so much money if they just maximized the potential of their designs. Why can 't they just try alternative ideas?" The frequency of his protests about the electrical engineering department hertz your soul, so you have decided to take charge and help them yourself. You plan to create a program that will optimize the circuits while keeping the same circuit layout and maintaining the same effective resistance. A circuit has two endpoints, and is associated with a certain constant, R , called its effective resistance. The circuits we 'll consider will be formed from individual resistors joined together in series or in parallel, forming more complex circuits. The following image illustrates combining circuits in series or parallel. According to your friend Kirchhoff, the effective resistance can be calculated quite easily when joining circuits this way: Circuits will be represented by strings. Individual resistors are represented by an asterisk, "*". For more complex circuits, suppose s_1, s_2, ldots, s_k represent k ge 2 circuits. Then: For example, "(* P (* S *) P *)" represents the following circuit: Given a circuit, your task is to assign the resistances of the individual resistors such that they satisfy the following requirements: If there are n individual resistors, then you need to output the list r_1, r_2, ldots, r_n ( 0 '...