triplets across staves in piano scores

[Erich Neuwirth]

%% How can I put the last note of each triplet on the lower stave
%% on the upper stave of the piano staff?

\header{
        title = "Triplets across staves"
}


upper = \relative c' {

  \clef treble
  \key c \major
  \time 2/4
  c'2
}

lower = \relative c' {
  \clef bass
  \key c \major
  \time 2/4


        \tuplet 3/2 {g8 c  g'}
        \tuplet 3/2 {g,8 c  g'}

}

\score {
  <<
    \new PianoStaff  <<
     \new Staff = "upper" \upper
      \new Staff = "lower" \lower
        >>
 >>
 \layout {
    \context { \Staff \RemoveEmptyStaves }
  }
}
6

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