Scala (scalaz) State monad - map over Option state type

How can I apply implement the following function?

def wrapIntoOption(state: State[S, A]): State[Option[S], Option[A]]

The bigger picture is this:

case class Engine(cylinders: Int)
case class Car(engineOpt: Option[Engine])

val engineOptLens = Lens.lensu((c, e) => c.copy(engineOpt = e), _.engineOpt)

def setEngineCylinders(count: Int): State[Engine, Int] = State { engine =>
  (engine.copy(cylinders = count), engine.cylinders)
}

def setEngineOptCylinders(count: Int): State[Option[Engine], Option[Int]] = {
  ??? // how to reuse setEngineCylinders?
}

def setCarCylinders(count: Int): State[Car, Option[Int]] = {
  engineOptLens.lifts(setEngineOptCylinders)
}

Is there nicer way to deal with Option properties?

One way to create the wrapIntoOption function would be to call run on the passed State[S, A] and convert the resulting (S, A) tuple into (Option[S], Option[A]).

import scalaz.State
import scalaz.std.option._
import scalaz.syntax.std.option._

def wrapIntoOption[S, A](state: State[S, A]): State[Option[S], Option[A]] =
  State(_.fold((none[S], none[A])){ oldState =>
    val (newState, result) = state.run(oldState)
    (newState.some, result.some)
  })

You could then define setEngineOptCylinders as :

def setEngineOptCylinders(count: Int): State[Option[Engine], Option[Int]] = 
  wrapIntoOption(setEngineCylinders(count))

Which you can use as :

scala> val (newEngine, oldCylinders) = setEngineOptCylinders(8).run(Engine(6).some)
newEngine: Option[Engine] = Some(Engine(8))
oldCylinders: Option[Int] = Some(6)