Need to split right bracket at side of matrix into three smaller brackets

Question

To the right of this matrix I have a big right curly bracket with the text "2m terms" that spans the height of the matrix. I need to replace this right bracket with three smaller ones that together span the height of the matrix.

\documentclass[a4paper,12pt,times,numbered,print,index]{article}   
\RequirePackage[left=37mm,right=30mm,top=35mm,bottom=30mm]{geometry}
\RequirePackage{libertine} 
\RequirePackage[small,bf,labelsep=space,
    tableposition=top]{caption} 
\usepackage{multirow}  
\usepackage{subfig,amsfonts,amsmath,amssymb,braket}
\usepackage{algorithm}% http://ctan.org/pkg/algorithms
\usepackage{algpseudocode}% http://ctan.org/pkg/algorithmicx

\begin{document}

\newcolumntype{C}[1]{>{\centering\arraybackslash$}p{#1}<{$}}

\def\rot#1{\rotatebox{90}{#1}}

\begin{figure}
\centering
\[
  \setcounter{MaxMatrixCols}{20}
  \begin{array}{@{}r@{}}
    \overbrace{\begin{array}{@{}*{6}{C{1.5em}}@{}}
      &&&&&&
    \end{array}}^{\text{$m$ terms}}
    \overbrace{\begin{array}{@{}*{6}{C{1.5em}}@{}}
      &&&&&&
    \end{array}}^{\text{$m$ terms}} \hspace*{30pt}\\[-.5\normalbaselineskip]



    % \overbrace{\begin{array}{@{}*{5}{C{1.5em}}@{}}
    %   &&&&
    % \end{array}}^{\text{Columns: $0$ to $\frac{m}{2}-1$}}
    % \overbrace{\begin{array}{@{}*{5}{C{1.5em}}@{}}
    %   &&&&
    % \end{array}}^{\text{Columns: $\frac{m}{2}$ to $m$}} \hspace*{25pt}\\[-.5\normalbaselineskip]


  H_{ab} = 
  \left.\hspace*{-\nulldelimiterspace}
    \left[\begin{array}{@{}*{12}{C{1.5em}}@{}}
        \underset{1}\leftarrow  & \cdots       & \cdots & \cdots     & \cdots    & \cdots  & \cdots  & \cdots   & \cdots        & \cdots        & \cdots  & \cdots     \\
        \vdots  & \cdots        & \cdots       & \cdots   & \cdots    & \cdots          & \underset{2}\rightarrow & \cdots   & \cdots        & \cdots        & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots       & \cdots   & \cdots    & \cdots          & \cdots            & \cdots  & \cdots      & \cdots        & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots      & \cdots    & \cdots    & \cdots          & \cdots            & \underset{5}\rightarrow & \cdots & \cdots       & \cdots  & \vdots \\
        \vdots  & \underset{6}\leftarrow  & \cdots & \cdots         & \cdots    & \cdots          & \cdots            & \cdots   & \cdots     & \cdots        & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots         & \cdots & \cdots    & \cdots          & \cdots            & \cdots        & \cdots  & \cdots      & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots         & \cdots & \cdots    & \cdots          & \cdots    & \cdots        & \underset{9}\rightarrow & \cdots & \cdots  & \vdots \\
        \vdots  & \cdots        & \underset{10}\leftarrow & \cdots& \cdots    & \cdots          & \cdots            & \cdots        & \cdots    & \cdots    & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots          & \ddots & \ddots    & \cdots          & \ddots            & \ddots        & \ddots   & \cdots     & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots          & \cdots & \ddots    & \ddots          & \ddots            & \ddots        & \ddots   & \ddots     & \cdots  & \vdots \\
        \vdots  & \cdots        & \cdots          & \cdots & \cdots    & \underset{m-3}\leftarrow & \cdots            & \cdots   & \cdots     & \cdots        & \cdots  & \vdots \\
        \vdots  & \cdots     & \cdots          & \cdots & \cdots    & \cdots          & \cdots    & \cdots   & \cdots   & \cdots     & \cdots  & \underset{m-2}\rightarrow \\
        \cdots  & \cdots        & \cdots         & \cdots  & \cdots    & \cdots          & \cdots & \cdots   & \cdots        & \cdots        & \cdots  & \cdots            \\ 
    \end{array}\right]\right\} \rotatebox[origin=c]{-90}{\scriptsize $2m$ terms}
  \end{array}
\]

\end{figure}
\end{document}

How can I change the bracket on the right to three smaller brackets?