3 voices in piano staff - middle voice autochange: howto?

[Frédéric Bron]

I would like to have a piano staff with one voice on the upper staff,
one voice on the lower staff and one voice automatically switching
between the two staffs.
Is it possible?

I tried this but without success:

\version "2.12.3"
\include "english.ly"
\score {
        \new PianoStaff <<
                \new Staff = "up" { \clef "treble"
                        \relative c'' { \voiceOne c4 d e f \oneVoice f e d c }
                }
                \new Staff = "down" { \clef "bass"
                        \relative c { \voiceTwo c d e f \voiceOne f e d c }
                }
                \autochange {
                        \relative c' { c d e f \voiceTwo a, g f e }
                }
        >>
}

I also tried without \voiceOne, \oneVoice, \voiceTwo but did not get
anything correct.

Thanks,

Frédéric