Analysis brackets above AND below the staff

[Ivan Kuznetsov]

I would like to put analysis brackets above and below the staff
over the _same_ group of notes.

I started with an example at:

  https://lilypond.org/doc/v2.25/Documentation/notation/analysis-brackets

which has two brackets over the same group of notes, both above the staff.

Below is my minimum working example, with two analysis brackets
above the staff.  How would I tweak this to make the
second analysis bracket below the staff?


I imagine, somewhere I need to add something like this command:

     \override HorizontalBracket.direction = #UP

but I cannot figure out exactly what command should be used and where.

Thank you very much for your help.

\version "2.24.1"

\score {
  \layout {
    \context {
      \Voice
      \consists "Horizontal_bracket_engraver"
    }
  }

  {
     \override HorizontalBracket.direction = #UP

      c''2
        -\tweak HorizontalBracketText.text  "b"
        \startGroup


          -\tweak HorizontalBracketText.text "a"
        \startGroup

      <g' g''>2
        \stopGroup
        \stopGroup

}