Energy conversion efficiency of the steam engine.

The path followed by water in steam engines can be described as the following:

From A to B: Liquid water is compressed in pump, it receives a work $ W_{A rightarrow B} $.

From B to C: Water is heated in a boiler where it receives heat $ Q $ without any work, and from where it gets out as vapor.

From C to D: In the turbine, water gives the amount of work $ W_{C rightarrow D} $ without gaining or losing heat.

From D to A: Water is cooled in a condenser, without work transfer, where it goes back to its original state and properties, to go the pump again to get compressed and so on…

Q: What is the energy conversion efficiency $ eta $ of the steam engine?

We know that it is the ratio of the useful output energy and the input energy.

In this case, the output energy is the work $ W_{C rightarrow D} $ done by the water during the phase $ C rightarrow D $ , and the input is the work of compression $ W_{A rightarrow B} $ and the heat Q.

In the solution of the problem, the energy conversion efficiency is expressed as: $$ eta = frac{W_{A rightarrow B} + W_{C rightarrow D} }{Q} $$

Can you explain to me why it is not: $ eta = frac{W_{C rightarrow D} }{Q + W_{A rightarrow B} } $ ?

Thank you.