How to overlap \leftHand and \rightHand in the same staff

[Disc Magnet]

I've written a Lilypond input file like this:

leftHand = \relative c' {
    c e g e
    d f a f
    e g b g
    f a c a
}

rightHand = \relative c'' {
    c2 c
    d d
    e e
    f f
}

\score {
    \new Staff {
        \time 4/4
        \tempo 4 = 120
        \leftHand
        \rightHand
    }
    \midi { }
    \layout{ }
}

Now this generates a score with 8 bars. However, what I want is a
score of 4 bars. I want the left hand and right hand to overlap in the
same staff. Thus the first bar should show c4 e4 g4 e4 relative to c'
as well as c2 c2 relative to c''. Similarly for the 2nd, 3rd and 4th
bars.

How can this be done?

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