Different time signatures

[Dmitry Rutsky]

How can I get different time signatures on different staffs? Why example I am 
sending doesn't work?

        --- Dmitry Rutsky

RH = \notes \relative c
{
   \time 4/4
   c4 f g c
   \bar "|."
}

LH = \notes \relative c
{
   \time 12/8
   c8 d e f g a b c
}

\score
{
   \context PianoStaff
   <
      \context Staff = up \RH
      \context Staff = down \LH
   >

   \paper
   {
   }
}