Removing empty staves in piano template with melody and lyrics

[muggle]

I'm using the template shown in the LilyPond manual with a few modifications:

\version "2.16.2"

\header{
  title =  \markup{"title"}
  subsubtitle = \markup{"subtitle"}
}

melody = \relative c'' {
  \clef treble
  \key c \major
  \time 4/4

  R1*16 a4 b c d
}

text = \lyricmode {
  Aaa Bee Cee Dee
}

upper = \relative c'' {
  \clef treble
  \key c \major
  \time 4/4

  c4 c c c c c c c c c c c c c c c c c c c
  c c c c c c c c c c c c c c c c c c c c c
  c c c c c c c c c c c c c c c c c c c c c
  c c c c c c
}

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

  c2 c c c c c c c c c c c c c c c c c c c c
  c c c c c c c c c c c c c
}

\score {
  <<
    \new Voice = "mel" { \autoBeamOff \melody }
    \new Lyrics \lyricsto mel \text
    \new PianoStaff <<
      \new Staff = "upper" \upper
      \new Staff = "lower" \lower
    >>
  >>
  \layout {
    \context { \Staff \RemoveEmptyStaves }
  }
  \midi { }
}

I know that the line "\context { \Staff \RemoveEmptyStaves }" makes any rest
bars invisible. My piano introduction is over 8 bars long, but some of these
rest bars still appear in the first line of the score - the rest are hidden.
Is there a way to hide these rest bars as well? I'm not concerned about the
lyrics at this point.



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