help with cross-staff piano beams and stems

[Sepand Shahab]

Dear list members,

How can I rewrite the following simplified example so that each quarter note unit has just one beam across the top of the upper staff and the four-note chords share cross-staff stems?

Many thanks,

Sepand



\version "2.12.3"



upper = \relative c' {   \clef treble

s8 <d e>16 <d e> 

<d e> <d e> <d e> <d e> 

}


lower = \relative c, {   \clef bass

<c c'>8  <a'' b>16 <a b> 

<a b> <a b> <a b> <a b> 

}


\score {
  \new PianoStaff = "PianoStaff_pf" <<  
    \new Staff = "Staff_pfUpper" <<  \upper >>

    \new Staff = "Staff_pfLower" <<  \lower >>
    
  >>
}