% updatemarks.sty 
% Copyright 2023, 2024 Wenjian Chern.
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3c
% of this license or any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
% 
% The Current Maintainer of this work is Wenjian Chern.
%
% This work consists of the files updatemarks.sty and updatemarks.tex
%
\NeedsTeXFormat{LaTeX2e}
\@ifundefined{NewDocumentCommand}{\RequirePackage{xparse}}{}
\ProvidesExplPackage{updatemarks}{2024/02/19}{0.2e}{extract and update marks from box}
\RequirePackage{etoolbox}
\RequirePackage{updatemarks-nums}

\seq_new:N \g__updatemarks_seq
\box_new:N \l__updatemarks_r_box 
\cs_new_eq:NN \l__updatemarks_s_box \l_tmpa_box % this box is used for locally split
\tex_countdef:D \g_updatemarks_max_int 256 \exp_stop_f:
\tl_new:N \l__updatemarks_tl
\tl_new:N \g__updatemarks_saved_tl

%% basicly copy from \__mark_extract_and_handle_marks:nn of LaTeX kernel 
\cs_new_protected:Npn \__updatemarks_extract:nnn #1#2#3 % material, map of number, code 
  {
    \__updatemarks_extract:nn {#1}
      { \__updatemarks_extract_split:nn {#2} {#3} }
  }
\cs_new_protected:Npn \__updatemarks_extract:nn #1#2 % material, code
  {
    \group_begin:
    \dim_set_eq:NN \tex_splitmaxdepth:D \c_max_dim
    \int_set_eq:NN \tex_vbadness:D      \c_max_int
    \dim_set_eq:NN \tex_vfuzz:D         \c_max_dim
    \__updatemarks_prepare_and_extract:nn {#2} {#1}
    \group_end:
  }
% old mechanism
\cs_new_protected:Npn \__updatemarks_prepare_and_extract:nn #1#2 % code, material
  {
    \vbox_set_to_ht:Nnw \l__updatemarks_r_box { -.5 \c_max_dim }
      #2 \tex_unskip:D 
      \box_set_to_last:N \l__updatemarks_r_box
      \int_compare:nNnT { \tex_lastnodetype:D } < { 0 }
        {
          \box_if_vertical:NT \l__updatemarks_r_box
            {
              \vbox_set_to_ht:Nnn \l__updatemarks_r_box { -.5 \c_max_dim }
                { \vbox_unpack:N \l__updatemarks_r_box \tex_kern:D \c_zero_dim }
              \int_compare:nNnT { \tex_badness:D } > { 0 }
                { \vbox_unpack:N \l__updatemarks_r_box }
            }
        }
      \tex_kern:D \c_zero_dim
    \vbox_set_end:
    \int_compare:nNnTF { \tex_badness:D } > { 0 }
      {
        \vbox_set_split_to_ht:NNn \l__updatemarks_s_box \l__updatemarks_r_box \c_max_dim
        #1
      }
      { \msg_error:nn { updatemarks } { infinite-shrinkage } }
  }
% new mechanism, copy a LaTeX kernel command
\cs_if_exist:NT \__mark_prepare_and_extract:nn
  {
    \cs_gset_eq:NN \__updatemarks_prepare_and_extract:nn 
      \__mark_prepare_and_extract:nn
  }
\cs_new_protected:Npn \__updatemarks_extract_split:nn #1#2 % map of number, code 
  {
    #1 
      { 
        \tl_set:No \l_updatemarks_last_tl { \tex_splitbotmarks:D ##1 }
        \tl_if_empty:NTF \l_updatemarks_last_tl
          {
            \cs_undefine:N \l_updatemarks_first_tl
            \cs_undefine:N \l_updatemarks_last_tl
          }
          { 
            \tl_set:No \l_updatemarks_first_tl { \tex_splitfirstmarks:D ##1 } 
            \tl_if_empty:NT \l_updatemarks_first_tl
              { \cs_undefine:N \l_updatemarks_first_tl }
          }
        #2
      }
  }
\cs_new_protected:Npn \__updatemarks_extract_num:n #1 % number 
  {
    \tl_if_exist:NT \l_updatemarks_last_tl
      {
        \tl_if_exist:cF { g__updatemarks_first-#1_tl }
          { \tl_gset_eq:cN { g__updatemarks_first-#1_tl } \l_updatemarks_first_tl }
        \tl_gset_eq:cN { g__updatemarks_last-#1_tl } \l_updatemarks_last_tl
      }
  }
\cs_new_protected:Npn \__updatemarks_extract_for_reinsertion:nn #1#2 % material, map 
  {
    \__updatemarks_extract:nn {#1}
      {
        #2
          {
            \tl_if_empty:oF { \tex_splitbotmarks:D ##1 }
              { 
                \tl_if_empty:oF { \tex_splitfirstmarks:D ##1 }
                  {
                    \tl_gput_right:Nx \g__updatemarks_saved_tl
                      {
                        \tex_marks:D ##1
                          { \exp_not:N \exp_not:n { \tex_splitfirstmarks:D ##1 } }
                      }
                  }
                \tl_gput_right:Nx \g__updatemarks_saved_tl
                  {
                    \tex_marks:D ##1
                      { \exp_not:N \exp_not:n { \tex_splitbotmarks:D ##1 } }
                  }
              }
          }
      }
  }

\cs_new_protected:Npn \updatemarks_extract:nN #1#2 % box material, seq 
  {
    \__updatemarks_extract:nnn {#1}
      { \seq_map_inline:Nn #2 }
      { \__updatemarks_extract_num:n {##1} }
  }
\cs_new_protected:Npn \updatemarks_extract_split:N #1 % seq 
  {
    \__updatemarks_extract_split:nn 
      { \seq_map_inline:Nn #1 }
      { \__updatemarks_extract_num:n {##1} }
  }
\cs_new_protected:Npn \updatemarks_extract:nNN #1#2#3
  {
    \tl_clear:N \g__updatemarks_saved_tl
    \__updatemarks_extract_for_reinsertion:nn {#1}
      { \seq_map_inline:Nn #2 }
    \tl_set_eq:NN #3 \g__updatemarks_saved_tl
  }
\cs_new_eq:NN \__updatemarks_extract_act:n ?
\cs_new_protected:Npn \updatemarks_extract_act:nNn #1#2#3 % material, seq, code 
  {
    \cs_set_protected:Npn \__updatemarks_extract_act:n ##1 {#3}
    \__updatemarks_extract:nnn {#1} 
      { \seq_map_inline:Nn #2 }
      { \__updatemarks_extract_act:n {##1} }
  }


\bool_new:N \l_updatemarks_nonempty_bool 
\tl_new:N \l__updatemarks_saved_tl
\cs_new_protected:Npn \updatemarks_save:Nnn #1#2#3 % seq, pos, value 
  { 
    \bool_if:NTF \l_updatemarks_nonempty_bool
      {
        \seq_map_inline:Nn #1
          {
            \tl_set:No \l__updatemarks_saved_tl { #3 {##1} }
            \tl_if_empty:NF \l__updatemarks_saved_tl
              { \tl_gset_eq:cN { g__updatemarks_#2-##1_tl } \l__updatemarks_saved_tl }
          }
      }
      {
        \seq_map_inline:Nn #1 
          {
            \tl_gset:co { g__updatemarks_#2-##1_tl } { #3 {##1} } 
          }
      }
  }
\cs_new_protected:Npn \updatemarks_save_e:Nnn #1#2#3 % seq, pos, value 
  { 
    \bool_if:NTF \l_updatemarks_nonempty_bool
      {
        \seq_map_inline:Nn #1
          {
            \tl_set:Nx \l__updatemarks_saved_tl { #3 {##1} }
            \tl_if_empty:NF \l__updatemarks_saved_tl
              { \tl_gset_eq:cN { g__updatemarks_#2-##1_tl } \l__updatemarks_saved_tl }
          }
      }
      {
        \seq_map_inline:Nn #1 
          {
            \tl_gset:cx { g__updatemarks_#2-##1_tl } { #3 {##1} } 
          }
      }
  }
\cs_new_eq:NN \updatemarks_save_x:Nnn \updatemarks_save_e:Nnn 
\cs_new_protected:Npn \updatemarks_alias:Nnn #1#2#3 % seq, pos1, pos2
  {
    \bool_if:NTF \l_updatemarks_nonempty_bool
      {
        \seq_map_inline:Nn #1
          {
            \tl_set_eq:Nc \l__updatemarks_saved_tl { g__updatemarks_#3-##1_tl }
            \tl_if_empty:NF \l__updatemarks_saved_tl
              { \tl_gset_eq:cN { g__updatemarks_#2-##1_tl } \l__updatemarks_saved_tl }
          }
      }
      {
        \seq_map_inline:Nn #1
          { \tl_gset_eq:cc { g__updatemarks_#2-##1_tl } { g__updatemarks_#3-##1_tl } }
      }
  }
\cs_new_protected:Npn \updatemarks_remove:Nn #1#2 % seq, pos
  { \seq_map_inline:Nn #1 { \cs_undefine:c { g__updatemarks_#2-##1_tl } } }
\cs_new:Npn \updatemarks_value:nn #1#2 % pos, number
  {
    \tl_if_exist:cTF { g__updatemarks_#1- \int_eval:n {#2} _tl }
      { \exp_not:v { g__updatemarks_#1- \int_eval:n {#2} _tl } } { }
  }


\cs_new_protected:Npn \updatemarks_update:N #1 % seq 
  {
    \seq_if_empty:NF #1
      {
        \seq_map_inline:Nn #1
          {
            \tl_if_exist:cT { g__updatemarks_last-##1_tl }
              {
                \tl_if_exist:cT { g__updatemarks_first-##1_tl }
                  { \tex_marks:D ##1 { \exp_not:v { g__updatemarks_first-##1_tl } } }
                \tex_marks:D ##1 { \exp_not:v { g__updatemarks_last-##1_tl } } 
              }
            \cs_undefine:c { g__updatemarks_first-##1_tl }
            \cs_undefine:c { g__updatemarks_last-##1_tl }
          }
        \if@nobreak\ifvmode\nobreak\fi\fi
      }
  }
\cs_new_protected:Npn \__updatemarks_gput:Nn #1#2
  {
    \group_begin:
    \cs_set_eq:NN \MarkClass \__updatemarks_class_num:n 
    \cs_set_eq:NN \MaxClass \g_updatemarks_max_int
    \parserange_use_delimiter:n { -> }
    \parserange_check:
    \parserange_set_to_int:n { \__updatemarks_maybe_class:n {##1} }
    \parserange:nnnN { 0 } { \g_updatemarks_max_int } {#2} \g__updatemarks_seq
    \seq_gset_eq:NN #1 \g__updatemarks_seq
    \seq_gremove_duplicates:N #1
    \group_end:
  }
\cs_new_protected:Npn \updatemarks_parse_classes:Nn { \__updatemarks_gput:Nn }

\cs_new:Npn \__updatemarks_class_num:n #1 
  { 
    \cs_if_exist_use:cF { c__mark_class_ #1 _mark }
      { -1 \msg_expandable_error:nnn { updatemarks } { unknown-class } {#1} }
  }
\cs_new:Npn \__updatemarks_maybe_class:n #1
  { 
    \tl_if_head_eq_meaning:nNTF {#1} [ % ]
      { \__updatemarks_maybe_class_aux:w #1 } {#1}
  }
\cs_new:Npn \__updatemarks_maybe_class_aux:w [#1] { \__updatemarks_class_num:n {#1} }


\seq_new:N \g_updatemarks_seq 
\NewDocumentCommand \ExtractMarks { s o +m }
  {
    \tl_if_novalue:nTF {#2}
      {
        \updatemarks_extract:nN 
          { 
            \bool_if:nTF {#1} { #3 }
              {
                \if_hbox:N #3 \hbox_unpack:N #3 \scan_stop: \fi:
                \if_vbox:N #3 \vbox_unpack:N #3 \scan_stop: \fi:
              }
          } 
          \g_updatemarks_seq
      }
      {
        \seq_gclear:N \g__updatemarks_seq
        \__updatemarks_gput:Nn \g__updatemarks_seq {#2}
        \updatemarks_extract:nN 
          { 
            \bool_if:nTF {#1} { #3 }
              {
                \if_hbox:N #3 \hbox_unpack:N #3 \scan_stop: \fi:
                \if_vbox:N #3 \vbox_unpack:N #3 \scan_stop: \fi:
              }
          } 
          \g__updatemarks_seq
      }
  }
\NewDocumentCommand \ExtractMarksTo { s o +m m }
  {
    \tl_if_novalue:nTF {#2}
      {
        \updatemarks_extract:nNN
          { 
            \bool_if:nTF {#1} { #3 }
              {
                \if_hbox:N #3 \hbox_unpack:N #3 \scan_stop: \fi:
                \if_vbox:N #3 \vbox_unpack:N #3 \scan_stop: \fi:
              }
          } 
          \g_updatemarks_seq #4
      }
      {
        \seq_gclear:N \g__updatemarks_seq
        \__updatemarks_gput:Nn \g__updatemarks_seq {#2}
        \updatemarks_extract:nNN
          { 
            \bool_if:nTF {#1} { #3 }
              {
                \if_hbox:N #3 \hbox_unpack:N #3 \scan_stop: \fi:
                \if_vbox:N #3 \vbox_unpack:N #3 \scan_stop: \fi:
              }
          } 
          \g__updatemarks_seq #4
      }
  }
\NewDocumentCommand \ExtractSplitMarks { o }
  {
    \tl_if_novalue:nTF {#1}
      { \updatemarks_extract_split:N \g_updatemarks_seq }
      {
        \seq_gclear:N \g__updatemarks_seq
        \__updatemarks_gput:Nn \g__updatemarks_seq {#1}
        \updatemarks_extract_split:N \g__updatemarks_seq
      }
  }
\NewDocumentCommand \UpdateMarks { o }
  {
    \tl_if_novalue:nTF {#1}
      { \updatemarks_update:N \g_updatemarks_seq }
      {
        \seq_gclear:N \g__updatemarks_seq
        \__updatemarks_gput:Nn \g__updatemarks_seq {#1}
        \updatemarks_update:N \g__updatemarks_seq
      }
  }
\cs_new_protected:Npn \AddToUpdateMarksList 
  { \__updatemarks_gput:Nn \g_updatemarks_seq }
\cs_new_protected:Npn \SetUpdateMarksList 
  { 
    \seq_gclear:N \g_updatemarks_seq 
    \AddToUpdateMarksList 
  }
\cs_new_protected:Npn \RemoveFromUpdateMarksList #1
  {
    \__updatemarks_gput:Nn \g__updatemarks_seq {#1}
    % to support old expl3, do not use \seq_map_tokens:Nn
    \seq_map_inline:Nn \g__updatemarks_seq 
      { \seq_gremove_all:Nn \g_updatemarks_seq {##1} }
  }
\cs_new_protected:Npn \AddAllocatedToUpdateMarksList
  {
    \int_step_inline:nnn { 0 } { \g_updatemarks_max_int }
      { \seq_gput_right:Nn \g_updatemarks_seq {##1} }
    \seq_gremove_duplicates:N \g_updatemarks_seq
  }

\cs_new_protected:Npn \__updatemarks_get_all_classes:
  {
    \seq_map_inline:Nn \g__mark_classes_seq
      { 
        \seq_gput_right:Nx \g_updatemarks_classes_seq 
          { \int_value:w \__updatemarks_class_num:n {##1} } 
      }
  }
\seq_new:N \g_updatemarks_classes_seq
\cs_if_exist:NTF \g__mark_classes_seq
  { 
    \hook_gput_code:nnn { begindocument/end } { updatemarks }
      {
        \__updatemarks_get_all_classes: 
        \AddAllocatedToUpdateMarksList
      }
  }
  { 
    \AtBeginDocument { \AddAllocatedToUpdateMarksList }
  }

\msg_new:nnn { updatemarks } { unknown-class } { Unknown~mark~class~`#1'. }
\msg_new:nnn { updatemarks } { infinite-shrinkage }
  { Infinite~shrinkage~found~when~extracting~marks. }


\cs_new_protected:Npn \savemarks@of #1 #2 #3
  {
    \bool_if:cT { l__updatemarks_#1_bool }
      { \updatemarks_save:Nnn \g_updatemarks_seq {#2} {#3} }
  }
\cs_new_protected:Npn \removemarks@of #1 #2
  {
    \bool_if:cT { l__updatemarks_#1_bool }
      { \updatemarks_remove:Nn \g_updatemarks_seq {#2} }
  }
\cs_new_protected:Npn \updatemarks@of #1
  { 
    \bool_if:cT { l__updatemarks_#1_bool }
      { \updatemarks_update:N \g_updatemarks_seq }
  }
\cs_new_protected:Npn \extractmarks@of #1 #2
  {
    \bool_if:cT { l__updatemarks_#1_bool }
      { \updatemarks_extract:nN { #2 } \g_updatemarks_seq }
  }
\cs_new_protected:Npn \extractsplitmarks@of #1
  {
    \bool_if:cT { l__updatemarks_#1_bool }
      { \updatemarks_extract_split:N \g_updatemarks_seq }
  }
% \let\updatemarks@@imakebox\@imakebox
% % savebox and makebox 
% \cs_if_exist:NF \updatemarks@makebox@patch
%   {
%     \patchcmd \@imakebox { \hb@xt@ } { \extractmarks@of{makebox}\hb@xt@ }
%       { } { \ERROR }
%     \patchcmd \@imakebox { \@end@tempboxa } { \updatemarks@of{makebox}\@end@tempboxa }
%       { } { \ERROR }
%   }
\let\updatemarks@endminipage\endminipage
% minipage 
\cs_if_exist_use:NF \updatemarks@minipage@patch
  {
    \patchcmd \endminipage 
      { \color@endgroup\egroup } 
      { \color@endgroup\egroup\extractmarks@of{minipage}{\unvcopy\@tempboxa} } 
      { } { \ERROR }
    \apptocmd \endminipage { \updatemarks@of{minipage} } { } { \ERROR }
  }
% tcolorbox
\cs_if_exist:NTF \updatemarks@tcolorbox@patch { \use_none:n } 
  { \tl_const:Nn \updatemarks@tcolorbox@patch }
  {
    \tcbset{updatemarks/.is~choice,
      updatemarks/true/.code=\bool_set_true:N \l__updatemarks_tcolorbox_bool,
      updatemarks/false/.code=\bool_set_false:N \l__updatemarks_tcolorbox_bool,
      updatemarks/.default=true}
    \patchcmd \tcbox@inner@hbox { \tcbdimto }
      { \extractmarks@of{tcolorbox}{\unhcopy\tcb@upperbox}\tcbdimto }
      { } { \ERROR }
    \let\endtcb@lrbox=\updatemarks@endminipage
    \patchcmd \endtcb@lrbox 
      { \color@endgroup\egroup } 
      { \color@endgroup\egroup\extractmarks@of{tcolorbox}{\unvcopy\@tempboxa} } 
      { } { \ERROR }
    \let\endtcb@savebox=\endtcb@lrbox
    \patchcmd \tcb@drawing@env@end { \csname }
      { \updatemarks@of{tcolorbox}\csname } { } { \ERROR }
    % breakable library
    \ifdefined \tcb@vsplit@upper 
      \apptocmd \tcb@vsplit@upper { \extractsplitmarks@of{tcolorbox} } { } { \ERROR }
      \apptocmd \tcb@vsplit@lower { \extractsplitmarks@of{tcolorbox} } { } { \ERROR }
      \patchcmd \tcb@split@start { \iftcb@final@box }
        { \iftcb@final@box 
          \extractmarks@of{tcolorbox}{\unvcopy\tcb@upperbox\unvcopy\tcb@lowerbox} } 
        { } { \ERROR }
      \patchcmd \tcb@split@start 
        { \tcb@comp@h@page\tcb@check@for@final@box\iftcb@final@box }
        { \tcb@comp@h@page\tcb@check@for@final@box\iftcb@final@box 
          \extractmarks@of{tcolorbox}{\unvcopy\tcb@upperbox\unvcopy\tcb@lowerbox}}
        { } { \ERROR }
      \patchcmd \tcb@split@USL { \iftcb@final@box }
        { \iftcb@final@box 
          \extractmarks@of{tcolorbox}{\unvcopy\tcb@totalupperbox 
            \iftcb@lowerspace\unvcopy\tcb@totallowerbox\fi } 
        } 
        { } { \ERROR }
      \patchcmd \tcb@split@SL@displayed { \iftcb@final@box }
        { \iftcb@final@box 
          \extractmarks@of{tcolorbox}{\unvcopy\tcb@totallowerbox} } 
        { } { \ERROR }
      \patchcmd \tcb@split@L { \iftcb@final@box }
        { \iftcb@final@box 
          \extractmarks@of{tcolorbox}{\unvcopy\tcb@totallowerbox} } 
        { } { \ERROR }
    \fi 
  }
% multicol 
\cs_if_exist:NTF \updatemarks@multicol@patch { \use_none:n }
  { \tl_const:Nn \updatemarks@multicol@patch }
  {
    %% the patch is used to extract marks
    \tl_set:No \set@keptmarks 
      { \set@keptmarks \extractsplitmarks@of{multicol} }

    %% the patch is used for boxmulticols
    \patchcmd \endmulticols { \page@sofar }
      { \updatemarks@of{multicol}\page@sofar }
      { } { \ERROR }

    %% the patch is used for middle page to remove unnecessary extract
    \patchcmd \multi@column@out { \let\topmark\kept@topmark }
      { 
        \let\topmark\kept@topmark 
        \removemarks@of{multicol}{first}
        \removemarks@of{multicol}{last}
      }
      { } { \ERROR }
    
    %% the patch is used for final page
    \patchcmd \balance@columns@out { \page@sofar }
      { \updatemarks@of{multicol}\page@sofar }
      { } { \ERROR }

    %% these patches are used to update marks after forced break 
    \patchcmd \balance@columns@out { \unvbox\colbreak@box }
      { \extractmarks@of{multicol}{\unvcopy\colbreak@box}\unvbox\colbreak@box }
      { } { \ERROR }
    \patchcmd \balance@columns@out { \unvbox\@cclv }
      { \extractmarks@of{multicol}{\unvcopy\@cclv}\unvbox\@cclv }
      { } { \ERROR }
    \patchcmd \balance@columns { \get@keptmarks\mult@box }
      { \if@boxedmulticols\get@keptmarks\mult@box\fi }
      { } { }

    % patches of new mark mechanism 
    \updatemarks@multicolnewmark@patch
  }
\cs_if_exist:NTF \updatemarks@adjmulticol@patch { \use_none:n }
  { \tl_const:Nn \updatemarks@adjmulticol@patch }
  {
    \patchcmd \adjmc@process@ne@column { \unvbox }
      { \extractmarks@of{multicol}{\unvcopy\mult@box}\unvbox }
      { } { \ERROR }
    \updatemarks@adjmulticolnewmark@patch
  }
\cs_if_exist:NTF \updatemarks@paracol@patch { \use_none:n }
  { \tl_const:Nn \updatemarks@paracol@patch }
  {
    \updatemarks@paracolnewmark@patch 
  }

\AtBeginDocument{
  \@ifpackageloaded{tcolorbox}{\updatemarks@tcolorbox@patch}{}
  \@ifpackageloaded{multicol}{\updatemarks@multicol@patch}{}
  \@ifpackageloaded{adjmulticol}{\updatemarks@adjmulticol@patch}{}
  \@ifpackageloaded{paracol}{\updatemarks@paracol@patch}{}
} 


\keys_define:nn { updatemarks }
  {
%    makebox .bool_set:N = \l__updatemarks_makebox_bool ,
    minipage  .bool_set:N = \l__updatemarks_minipage_bool  ,
    tcolorbox .bool_set:N = \l__updatemarks_tcolorbox_bool ,
    multicol  .bool_set:N = \l__updatemarks_multicol_bool  ,
    multicols .bool_set:N = \l__updatemarks_multicol_bool  ,
    paracol   .bool_set:N = \l__updatemarks_paracol_bool   ,
  }

\cs_if_exist:NTF \ProcessKeyOptions
  { \ProcessKeyOptions [ updatemarks ] }
  {
    \RequirePackage{l3keys2e}
    \ProcessKeysOptions { updatemarks }
  }

\cs_if_free:NT \mark_new_class:n 
  {
    \providecommand \updatemarks@multicolnewmark@patch { }
    \providecommand \updatemarks@adjmulticolnewmark@patch { }
    \providecommand \updatemarks@paracolnewmark@patch { }
    \endinput 
  }

\tl_const:Nn \updatemarks@multicol@firstpage
  {
    \bool_if:NT \l__updatemarks_multicol_bool
      {
        \bool_set_false:N \l_updatemarks_nonempty_bool
        \updatemarks_save:Nnn \g_updatemarks_seq { top } { \tex_topmarks:D \use:n }
      }
  }
\tl_const:Nn \updatemarks@multicol@middlepage
  {
    \__mark_update_structure_alias:nn { previous-page } { page }
    \seq_map_inline:Nn \g__mark_classes_seq
      {
        \tl_gset_eq:cc { g__mark_page_top_#1_tl } { g__mark_page_last_#1_tl }

        \tl_set:Nx \l__updatemarks_tl
          { \updatemarks_value:nn { first } { \__updatemarks_class_num:n {#1} } }
        \tl_if_empty:NTF \l__updatemarks_tl
          { \tl_gset_eq:cc { g__mark_page_first_#1_tl } { g__mark_page_last_#1_tl } }
          { \tl_gset_eq:cN { g__mark_page_first_#1_tl } \l__updatemarks_tl }

        \tl_set:Nx \l__updatemarks_tl
          { \updatemarks_value:nn { last } { \__updatemarks_class_num:n {#1} } }
        \tl_if_empty:NF \l__updatemarks_tl
          { \tl_gset_eq:cN { g__mark_page_last_#1_tl } \l__updatemarks_tl }
      }
    \updatemarks_remove:Nn \g_updatemarks_seq { top }
    \updatemarks_remove:Nn \g_updatemarks_seq { first }
    \updatemarks_remove:Nn \g_updatemarks_seq { last }
  }

\providecommand \updatemarks@multicolnewmark@patch
  {
    \patchcmd \prep@keptmarks { \fi }
      { \updatemarks@multicol@firstpage\fi }
      { } { \ERROR }
    \patchcmd \multi@column@out
      { 
        \removemarks@of{multicol}{first}
        \removemarks@of{multicol}{last}
      }
      { }
      { } { \ERROR }
    \patchcmd \multi@column@out { \@makecol }
      { \@makecol\updatemarks@multicol@middlepage }
      { } { \ERROR }
  }

\providecommand \updatemarks@adjmulticolnewmark@patch { }
\providecommand \updatemarks@paracolnewmark@patch { }