The torque produced by an engine has dimensional formula L2M1T-2. We may first guess that it depends

Question:

The torque produced by an engine has dimensional formula L2M1T-2. We may first guess that it depends on the engine's rotation rate (with dimensional formula L0M0T-1), and the volume of air displaced (with dimensional formula L3M0T0).
(a) Try to find a complete set of dimensionless products. What goes wrong?
(b) Adjust the guess by adding the density of the air (with dimensional formula L-3M1T0). Now find a complete set of dimensionless products.