%%
%% This is file `ltxgrid.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% ltxgrid.dtx  (with options: `package,kernel')
%% 
%% This is a generated file;
%% altering it directly is inadvisable;
%% instead, modify the original source file.
%% See the URL in the file README-LTXGRID.tex.
%% 
%% License
%%    You may distribute this file under the conditions of the
%%    LaTeX Project Public License 1.3c or later
%%    (http://www.latex-project.org/lppl.txt).
%% 
%%    This file is distributed WITHOUT ANY WARRANTY;
%%    without even the implied warranty of MERCHANTABILITY
%%    or FITNESS FOR A PARTICULAR PURPOSE.
%% 
%%%  @LaTeX-file{
%%%     filename        = "ltxgrid.dtx",
%%%     version         = "4.2f",
%%%     date            = "2022/06/05",
%%%     author          = "Arthur Ogawa (mailto:arthur_ogawa at sbcglobal.net),
%%%                        Phelype Oleinik (mailto:phelype.oleinik at latex-project.org),
%%%                        commissioned by the American Physical Society.
%%%                        ",
%%%     copyright       = "Copyright (C) 1999, 2009 Arthur Ogawa,
%%%                        distributed under the terms of the
%%%                        LaTeX Project Public License 1.3c, see
%%%                        ftp://ctan.tug.org/macros/latex/base/lppl.txt
%%%                        ",
%%%     address         = "Arthur Ogawa,
%%%                        USA",
%%%     telephone       = "",
%%%     FAX             = "",
%%%     email           = "mailto colon arthur_ogawa at sbcglobal.net",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "latex, page grid, main vertical list",
%%%     supported       = "yes",
%%%     abstract        = "package to change page grid, MVL",
%%%  }
\NeedsTeXFormat{LaTeX2e}[1995/12/01]%
\ProvidesFile{%
ltxgrid%
.sty%
}%
 [2022/06/05 4.2f page grid package (portions licensed from W. E. Baxter web at superscript.com)]% \fileversion
\def\package@name{ltxgrid}%
\expandafter\PackageInfo\expandafter{\package@name}{%
 Page grid for \protect\LaTeXe,
 by A. Ogawa (arthur_ogawa at sbcglobal.net)%
}%
\RequirePackage{ltxutil}%
\newcounter{linecount}
\def\loop@line#1#2{%
 \par
 \hb@xt@\hsize{%
  \global\advance#1\@ne
  \edef\@tempa{\@ifnum{100>#1}{0}{}\@ifnum{10>#1}{0}{}\number#1}%
  \@tempa\edef\@tempa{\special{line:\@tempa}}\@tempa
  \vrule depth2.5\p@#2\leaders\hrule\hfil
 }%
}%
\def\lineloop#1{%
 \loopwhile{\loop@line\c@linecount{}\@ifnum{#1>\c@linecount}}%
}%
\def\linefoot#1{%
 \loop@line\c@linecount{%
  \footnote{%
   #1\special{foot:#1}\vrule depth2.5\p@\leaders\hrule\hfill
  }%
 }%
}%
\let\@@mark\mark
\let\@@topmark\topmark
\let\@@firstmark\firstmark
\let\@@botmark\botmark
\let\@@splitfirstmark\splitfirstmark
\let\@@splitbotmark\splitbotmark
\def\@themark{{}{}{}{}}%
\def\nul@mark{{}{}{}{}\@@nul}%
\def\set@mark@netw@#1#2#3#4#5#6#7{\gdef#1{{#6}{#7}{#4}{#5}}\do@mark}%
\def\set@marktw@#1#2#3#4#5#6{\gdef#1{{#2}{#6}{#4}{#5}}\do@mark}%
\def\set@markthr@@#1#2#3#4#5#6{\gdef#1{{#2}{#3}{#6}{#5}}\do@mark}%
\def\get@mark@@ne#1#2#3#4#5\@@nul{#1}%
\def\get@mark@tw@#1#2#3#4#5\@@nul{#2}%
\def\get@mark@thr@@#1#2#3#4#5\@@nul{#3}%
\def\get@mark@f@ur#1#2#3#4#5\@@nul{#4}%
\def\mark@netw@{\expandafter\set@mark@netw@\expandafter\@themark\@themark}%
\def\marktw@{\expandafter\set@marktw@\expandafter\@themark\@themark}%
\def\markthr@@{\expandafter\set@markthr@@\expandafter\@themark\@themark}%
\def\do@mark{\do@@mark\@themark\nobreak@mark}%
\def\do@@mark#1{%
 \begingroup
  \let@mark
  \@@mark{#1}%
 \endgroup
}%
\def\let@mark{%
 \let\protect\@unexpandable@protect
 \let\label\relax
 \let\index\relax
 \let\glossary\relax
}%
\def\nobreak@mark{%
 \@if@sw\if@nobreak\fi{\@ifvmode{\nobreak}{}}{}%
}%
\def\mark@envir{\markthr@@}%
\def\bot@envir{%
 \expandafter\expandafter
 \expandafter\get@mark@thr@@
 \expandafter\@@botmark
             \nul@mark
}%
\def\markboth{\mark@netw@}%
\def\markright{\marktw@}%
\def\leftmark{%
 \expandafter\expandafter
 \expandafter\get@mark@@ne
 \expandafter\saved@@botmark
             \nul@mark
}%
\def\rightmark{%
 \expandafter\expandafter
 \expandafter\get@mark@tw@
 \expandafter\saved@@firstmark
             \nul@mark
}%
\let\primitive@output\output
\long\def\@tempa#1\@@nil{#1}%
            \toks@
\expandafter\expandafter
\expandafter{%
\expandafter \@tempa
             \the\primitive@output
             \@@nil
             }%
\newtoks\output@latex
\output@latex\expandafter{\the\toks@}%
\let\output\output@latex
\primitive@output{\dispatch@output}%
\def\dispatch@output{%
 \let\par\@@par
 \expandafter\let\expandafter\output@procedure\csname output@\the\outputpenalty\endcsname
 \@ifnotrelax\output@procedure{}{%
  \expandafter\def\expandafter\output@procedure\expandafter{\the\output@latex}%
 }%
 \expandafter\@ifx\expandafter{\csname output@-\the\execute@message@pen\endcsname\output@procedure}{%
  \let\output@procedure\@message@saved
 }{}%
 \ltxgrid@info@sw{\class@info{\string\dispatch@output}\say\output@procedure\saythe\holdinginserts}{}%
 \outputdebug@sw{\output@debug}{}%
 \output@procedure
}%
\def\set@output@procedure#1#2{%
 \count@\outputpenalty\advance\count@-#2%
 \expandafter\let\expandafter#1\csname output@\the\count@\endcsname
}%
\def\output@debug{%
 \def\@tempa{\save@message}%
 \@ifx{\output@procedure\@tempa}{%
  \true@sw
 }{%
  \@ifnum{\outputpenalty=-\save@column@insert@pen}{%
   \@ifnum{\holdinginserts>\z@}%
  }{%
   \false@sw
  }%
 }%
 {}{\output@debug@}%
}%
\def\output@debug@{%
  \saythe\outputpenalty
  \saythe\interlinepenalty
  \saythe\brokenpenalty
  \saythe\clubpenalty
  \saythe\widowpenalty
  \saythe\displaywidowpenalty
  \saythe\predisplaypenalty
  \saythe\interdisplaylinepenalty
  \saythe\postdisplaypenalty
  \saythe\badness
  \say\thepagegrid
  \saythe\pagegrid@col
  \saythe\pagegrid@cur
  \saythe\insertpenalties
  \say\@@botmark
  \saythe\pagegoal
  \saythe\pagetotal
  \saythe{\badness\@cclv}%
  \say\@toplist
  \say\@botlist
  \say\@dbltoplist
  \say\@deferlist
  \trace@scroll{%
  \showbox\@cclv
  \showbox\@cclv@saved
  \showbox\pagesofar
  \showbox\csname col@1\endcsname
  \showbox\footsofar
  \showbox\footins
  \showbox\footins@saved
  \showlists
  }%
}%
\@ifxundefined{\outputdebug@sw}{%
 \@booleanfalse\outputdebug@sw
}{}%
\def\trace@scroll#1{\begingroup\showboxbreadth\maxdimen\showboxdepth\maxdimen\scrollmode#1\endgroup}%
\def\trace@box#1{\trace@scroll{\showbox#1}}%
\prepdef\@outputpage{\@outputpage@head}%
\let\@outputpage@head\@empty
\appdef\@outputpage{\@outputpage@tail}%
\let\@outputpage@tail\@empty
\def\show@box@size#1#2{%
 \show@box@size@sw{%
  \begingroup
   \setbox\z@\vbox{\unvcopy#2\hrule}%
   \class@info{Show box size: #1^^J%
    (\the\ht\z@\space X \the\wd\z@)
    \the\c@page\space\space\the\pagegrid@cur\space\the\pagegrid@col
   }%
  \endgroup
 }{}%
}%
\def\show@text@box@size{%
 \show@box@size{Text column}\@outputbox
 \tally@box@size@sw{%
  \@ifdim{\wd\@outputbox>\z@}{%
   \dimen@\ht\@outputbox\divide\dimen@\@twopowerfourteen
   \advance\dimen@-\dp\csname box@size@\the\pagegrid@col\endcsname
   \@ifdim{\dimen@>\z@}{%
    \advance\dimen@ \ht\csname box@size@\the\pagegrid@col\endcsname
    \global\ht\csname box@size@\the\pagegrid@col\endcsname\dimen@
    \show@box@size@sw{%
     \class@info{Column: \the\dimen@}%
    }{}%
   }{}%
  }{}%
  \global\dp\csname box@size@\the\pagegrid@col\endcsname\z@
 }{}%
}%
\def\show@pagesofar@size{%
 \show@box@size{Page so far}\pagesofar
 \dimen@\ht\pagesofar\divide\dimen@\@twopowerfourteen
 \global\dp\csname box@size@1\endcsname\dimen@
 \show@box@size@sw{%
  \class@info{Pagesofar: \the\dimen@}%
 }{}%
}%
\@booleanfalse\tally@box@size@sw
\@booleanfalse\show@box@size@sw
\expandafter\newbox\csname box@size@1\endcsname
\expandafter\setbox\csname box@size@1\endcsname\hbox{}%
\expandafter\newbox\csname box@size@2\endcsname
\expandafter\setbox\csname box@size@2\endcsname\hbox{}%
\def\total@text{%
 \@tempdima\the\ht\csname box@size@2\endcsname\divide\@tempdima\@twopowertwo\@tempcnta\@tempdima
 \@tempdimb\the\ht\csname box@size@1\endcsname\divide\@tempdimb\@twopowertwo\@tempcntb\@tempdimb
 \class@info{Total text: Column(\the\@tempcnta pt), Page(\the\@tempcntb pt)}%
}%
\def\natural@output{\toggle@insert{\output@holding}{\output@moving}}%
\output@latex{\natural@output}%
\def\output@holding{%
 \csname output@init@\bot@envir\endcsname
 \@if@exceed@pagegoal{\unvcopy\@cclv}{%
  \setbox\z@\vbox{\unvcopy\@cclv}%
  \outputdebug@sw{\trace@box\z@}{}%
  \dimen@\ht\@cclv\advance\dimen@-\ht\z@
  \dead@cycle@repair\dimen@
 }{%
  \dead@cycle
 }%
}%
\def\@if@exceed@pagegoal#1{%
 \begingroup
  \setbox\z@\vbox{#1}%
  \dimen@\ht\z@\advance\dimen@\dp\z@
  \outputdebug@sw{\saythe\dimen@}{}%
  \@ifdim{\dimen@>\pagegoal}{%
   \setbox\z@\vbox{\@@mark{}\unvbox\z@}%
   \splittopskip\topskip
   \splitmaxdepth\maxdepth
   \vbadness\@M
   \vfuzz\maxdimen
   \setbox\tw@\vsplit\z@ to\pagegoal
   \outputdebug@sw{\trace@scroll{\showbox\tw@\showbox\z@}}{}%
   \setbox\tw@\vbox{\unvbox\tw@}%
   \@ifdim{\ht\tw@=\z@}{%
    \ltxgrid@info{Found overly large chunk while preparing to move insertions. Attempting repairs}%
    \aftergroup\true@sw
   }{%
    \aftergroup\false@sw
   }%
 }{%
  \aftergroup\false@sw
 }%
 \endgroup
}%
\def\output@moving{%
 \set@top@firstmark
 \@ifnum{\outputpenalty=\do@newpage@pen}{%
  \setbox\@cclv\vbox{%
   \unvbox\@cclv
   \remove@lastbox
   \@ifdim{\ht\z@=\ht\@protection@box}{\box\lastbox}{\unskip}%
  }%
 }{}%
 \@cclv@nontrivial@sw{%
  \expandafter\output@do@prep\csname output@prep@\bot@envir \endcsname
  \@makecolumn\true@sw
  \expandafter\output@column@do\csname output@column@\thepagegrid\endcsname
  \protect@penalty\do@startcolumn@pen
  \clearpage@sw{%
   \protect@penalty\do@endpage@pen
  }{}%
  \expandafter\let\expandafter\output@post@\csname output@post@\bot@envir \endcsname
  \outputdebug@sw{\say\output@post@}{}%
  \@ifx{\output@post@\relax}{\output@post@document}{\output@post@}%
 }{%
  \void@cclv
 }%
 \set@colht
 \global\@mparbottom\z@
 \global\@textfloatsheight\z@
}%
\def\output@do@prep#1{%
 \outputdebug@sw{\class@info{Prep: \string#1}}{}%
 \@ifx{#1\relax}{\output@prep@document}{#1}%
}%
\def\output@column@do#1{%
  \outputdebug@sw{\class@info{Output column: \string#1}}{}%
  \@ifx{#1\relax}{\output@column@one}{#1}%
}%
\def\void@cclv{\begingroup\setbox\z@\box\@cclv\endgroup}%
\def\remove@lastbox{\setbox\z@\lastbox}%
\def\@cclv@nontrivial@sw{%
 \@ifx@empty\@toplist{%
  \@ifx@empty\@botlist{%
   \@ifvoid\footins{%
    \@ifvoid\@cclv{%
     \false@sw
    }{%
     \setbox\z@\vbox{\unvcopy\@cclv}%
     \@ifdim{\ht\z@=\topskip}{%
      \setbox\z@\vbox\bgroup
       \unvbox\z@
       \remove@lastbox
       \dimen@\lastskip\unskip
       \@ifdim{\ht\z@=\ht\@protection@box}{%
        \advance\dimen@\ht\z@
        \@ifdim{\dimen@=\topskip}{%
         \aftergroup\true@sw
        }{%
         \aftergroup\false@sw
        }%
       }{%
        \aftergroup\false@sw
       }%
      \egroup
      {%
       \false@sw
      }{%
       \true@sw
      }%
     }{%
      \@ifdim{\ht\z@=\z@}{%
       \ltxgrid@info{Found trivial column. Discarding it}%
       \outputdebug@sw{\trace@box\@cclv}{}%
       \false@sw
      }{%
       \true@sw
      }%
     }%
    }%
   }{%
    \true@sw
   }%
  }{%
   \true@sw
  }%
 }{%
  \true@sw
 }%
}%
\def\protect@penalty#1{\protection@box\penalty-#1\relax}%
\newbox\@protection@box
\setbox\@protection@box\vbox to1986sp{\vfil}%
\def\protection@box{\nointerlineskip\copy\@protection@box}%
\def\dead@cycle@repair#1{%
 \expandafter\do@@mark
 \expandafter{%
              \@@botmark
             }%
 \unvbox\@cclv
 \nointerlineskip
 \vbox to#1{\vss}%
 \@ifnum{\outputpenalty<\@M}{\penalty\outputpenalty}{}%
}%
\def\dead@cycle@repair@protected#1{%
 \expandafter\do@@mark
 \expandafter{%
              \@@botmark
             }%
 \begingroup
  \unvbox\@cclv
  \remove@lastbox
  \nointerlineskip
  \advance#1-\ht\@protection@box
  \vbox to#1{\vss}%
  \protection@box % Reinsert protection box
  \@ifnum{\outputpenalty<\@M}{\penalty\outputpenalty}{}%
 \endgroup
}%
\def\dead@cycle{%
 \expandafter\do@@mark
 \expandafter{%
              \@@botmark
             }%
 \unvbox\@cclv
 \@ifnum{\outputpenalty<\@M}{\penalty\outputpenalty}{}%
}%
\def\output@init@document{%
 \ltxgrid@info@sw{\class@info{\string\output@init@document}}{}%
 \global\vsize\vsize
}%
\def\output@prep@document{%
 \ltxgrid@foot@info@sw{\class@info{\string\output@prep@document}\trace@scroll{\showbox\footins\showbox\footsofar}}{}%
 \@ifvoid\footsofar{%
 }{%
  \global\setbox\footins\vbox\bgroup
   \unvbox\footsofar
   \@ifvoid\footins{}{%
    \marry@baselines
    \unvbox\footins
   }%
  \egroup
  \ltxgrid@foot@info@sw{\trace@box\footins}{}%
 }%
}%
\def\output@post@document{}%
\let\@opcol\@undefined
\def\@makecolumn#1{%
 \ltxgrid@foot@info@sw{\class@info{\string\@makecolumn\string#1}}{}%
 \setbox\@outputbox\vbox\bgroup
  \boxmaxdepth\@maxdepth
  \@tempdima\dp\@cclv
  \unvbox\@cclv
  \vskip-\@tempdima
 \egroup
 \xdef\@freelist{\@freelist\@midlist}\global\let\@midlist\@empty
 \show@text@box@size
 \@combinefloats
 #1{%
  \@combineinserts\@outputbox\footins
 }{%
  \combine@foot@inserts\footsofar\footins
 }%
 \set@adj@colht\dimen@
 \count@\vbadness
 \vbadness\@M
 \setbox\@outputbox\vbox to\dimen@\bgroup
  \@texttop
  \dimen@\dp\@outputbox
  \unvbox\@outputbox
  \vskip-\dimen@
  \@textbottom
 \egroup
 \vbadness\count@
 \global\maxdepth\@maxdepth
}%
\let\@makespecialcolbox\@undefined
\def\@combineinserts#1#2{%
 \ltxgrid@foot@info@sw{\class@info{\string\@combineinserts\string#1\string#2}\trace@box#2}{}%
 \setbox#1\vbox\bgroup
  \unvbox#1%
  \@ifvoid{#2}{}{%
   \dimen@\ht#2\advance\dimen@\dp#2\advance\dimen@\skip#2%
   \show@box@size{Combining inserts}#2%
   \vskip\skip#2%
   \setbox\z@\vbox{\footnoterule}\dimen@i\ht\z@
   \color@begingroup
   \normalcolor
   \cleaders\box\z@\vskip\dimen@i\kern-\dimen@i
   \csname combine@insert@\the\pagegrid@col\endcsname#2%
   \color@endgroup
   \kern-\dimen@\kern\dimen@
  }%
 \egroup
 \ltxgrid@foot@info@sw{\trace@box#1}{}%
}%
\def\combine@insert@tw@#1{%
 \compose@footnotes@two#1\@ifvbox{#1}{\unvbox}{\box}#1%
}%
\def\combine@insert@@ne#1{%
 \compose@footnotes@one#1\@ifvbox{#1}{\unvbox}{\box}#1%
}%
\def\twocolumn@grid@setup{%
 \expandafter\let\csname combine@insert@1\endcsname\combine@insert@tw@
 \expandafter\let\csname combine@insert@2\endcsname\combine@insert@@ne
}%
\def\onecolumn@grid@setup{%
 \expandafter\let\csname combine@insert@1\endcsname\combine@insert@@ne
 \expandafter\let\csname combine@insert@2\endcsname\combine@insert@@ne
}%
\let\columngrid@setup\onecolumn@grid@setup
\columngrid@setup
\appdef\@floatplacement{%
 \global\@fpmin\@fpmin
}%
\mathchardef\pagebreak@pen=\@M
\expandafter\let\csname output@-\the\pagebreak@pen\endcsname\relax
\mathchardef\do@startcolumn@pen=10005
\@namedef{output@-\the\do@startcolumn@pen}{\do@startcolumn}%
\def\do@startcolumn{%
 \setbox\@cclv\vbox{\unvbox\@cclv\remove@lastbox\unskip}%
 \clearpage@sw{\@clearfloatplacement}{\@floatplacement}%
 \set@colht
 \@booleanfalse\pfloat@avail@sw
 \begingroup
  \@colht\@colroom
  \@booleanfalse\float@avail@sw
  \@tryfcolumn\test@colfloat
  \float@avail@sw{\aftergroup\@booleantrue\aftergroup\pfloat@avail@sw}{}%
 \endgroup
 \fcolmade@sw{%
  \setbox\@cclv\vbox{\unvbox\@outputbox\unvbox\@cclv}%
  \outputpenalty-\pagebreak@pen
  \dead@cycle
 }{%
  \begingroup
   \let\@elt\@scolelt
   \let\reserved@b\@deferlist\global\let\@deferlist\@empty\reserved@b
  \endgroup
  \clearpage@sw{%
   \outputpenalty\@M
  }{%
   \outputpenalty\do@newpage@pen
  }%
  \dead@cycle
 }%
 \check@deferlist@stuck\do@startcolumn
 \set@vsize
}%
\def\@scolelt#1{\def\@currbox{#1}\@addtonextcol}%
\def\test@colfloat#1{%
 \csname @floatselect@sw@\thepagegrid\endcsname#1{}{\@testtrue}%
 \@if@sw\if@test\fi{}{\aftergroup\@booleantrue\aftergroup\float@avail@sw}%
}%
\def\@addtonextcol{%
 \begingroup
  \@insertfalse
  \@setfloattypecounts
  \csname @floatselect@sw@\thepagegrid\endcsname\@currbox{%
   \@ifnum{\@fpstype=8 }{}{%
     \@ifnum{\@fpstype=24 }{}{%
       \@flsettextmin
       \@reqcolroom \ht\@currbox
       \advance \@reqcolroom \@textmin
       \advance \@reqcolroom \vsize % take into account split insertions
       \advance \@reqcolroom -\pagegoal
       \@ifdim{\@colroom>\@reqcolroom}{%
         \@flsetnum \@colnum
         \@ifnum{\@colnum>\z@}{%
            \@bitor\@currtype\@deferlist
            \@if@sw\if@test\fi{}{%
              \@addtotoporbot
            }%
         }{}%
       }{}%
     }%
   }%
  }{}%
  \@if@sw\if@insert\fi{}{%
    \@cons\@deferlist\@currbox
  }%
 \endgroup
}%
\mathchardef\do@startpage@pen=10006
\@namedef{output@-\the\do@startpage@pen}{\do@startpage}%
\def\do@startpage{%
 \setbox\@cclv\vbox{\unvbox\@cclv\remove@lastbox\unskip}%
 \clearpage@sw{\@clearfloatplacement}{\@dblfloatplacement}%
 \set@colht
 \@booleanfalse\pfloat@avail@sw
 \begingroup
  \@booleanfalse\float@avail@sw
  \@tryfcolumn\test@dblfloat
  \float@avail@sw{\aftergroup\@booleantrue\aftergroup\pfloat@avail@sw}{}%
 \endgroup
 \fcolmade@sw{%
  \global\setbox\pagesofar\vbox{\unvbox\pagesofar\unvbox\@outputbox}%
  \@output@combined@page
 }{%
  \begingroup
   \@booleanfalse\float@avail@sw
   \let\@elt\@sdblcolelt
   \let\reserved@b\@deferlist\global\let\@deferlist\@empty\reserved@b
  \endgroup
  \@ifdim{\@colht=\textheight}{% No luck...
   \pfloat@avail@sw{% ...but a float *was* available!
    \forcefloats@sw{%
     \ltxgrid@warn{Forced dequeueing of floats stalled}%
    }{%
     \ltxgrid@warn{Dequeueing of floats stalled}%
    }%
   }{}%
  }{}%
  \outputpenalty\@M
  \dead@cycle
 }%
 \check@deferlist@stuck\do@startpage
 \set@colht
}%
\def\@output@combined@page{%
 \@combinepage\true@sw
 \@combinedblfloats
 \@outputpage
 \global\pagegrid@cur\@ne
 \protect@penalty\do@startpage@pen
}%
\def\@sdblcolelt#1{\def\@currbox{#1}\@addtodblcol}%
\def\test@dblfloat#1{%
 \@if@notdblfloat{#1}{\@testtrue}{}%
 \@if@sw\if@test\fi{}{\aftergroup\@booleantrue\aftergroup\float@avail@sw}%
}%
\def\@if@notdblfloat#1{\@ifdim{\wd#1<\textwidth}}%
\@booleanfalse\forcefloats@sw
\def\@addtodblcol{%
 \begingroup
  \@if@notdblfloat{\@currbox}{%
   \false@sw
  }{%
   \@setfloattypecounts
   \@getfpsbit \tw@
   \@bitor \@currtype \@deferlist
   \@if@sw\if@test\fi{%
    \false@sw
   }{%
    \@ifodd\@tempcnta{%
     \aftergroup\@booleantrue\aftergroup\float@avail@sw
     \@flsetnum \@dbltopnum
     \@ifnum{\@dbltopnum>\z@}{%
       \@ifdim{\@dbltoproom>\ht\@currbox}{%
        \true@sw
       }{%
        \@ifnum{\@fpstype<\sixt@@n}{%
         \begingroup
          \advance \@dbltoproom \@textmin
          \@ifdim{\@dbltoproom>\ht\@currbox}{%
           \endgroup\true@sw
          }{%
           \endgroup\false@sw
          }%
        }{%
         \false@sw
        }%
       }%
     }{%
      \false@sw
     }%
    }{%
     \false@sw
    }%
   }%
  }%
  {%
   \@tempdima -\ht\@currbox
   \advance\@tempdima
    -\@ifx{\@dbltoplist\@empty}{\dbltextfloatsep}{\dblfloatsep}%
   \global \advance \@dbltoproom \@tempdima
   \global \advance \@colht \@tempdima
   \global \advance \@dbltopnum \m@ne
   \@cons \@dbltoplist \@currbox
  }{%
   \@cons \@deferlist \@currbox
  }%
 \endgroup
}%
\def\@tryfcolumn#1{%
  \global\@booleanfalse\fcolmade@sw
  \@ifx@empty\@deferlist{}{%
    \global\let\@trylist\@deferlist
    \global\let\@failedlist\@empty
    \begingroup
      \dimen@\vsize\advance\dimen@-\pagegoal\@ifdim{\dimen@>\z@}{%
       \advance\@fpmin-\dimen@
      }{}%
      \def\@elt{\@xtryfc#1}\@trylist
    \endgroup
    \fcolmade@sw{%
      \global\setbox\@outputbox\vbox{\vskip \@fptop}%
      \let \@elt \@wtryfc \@flsucceed
      \global\setbox\@outputbox\vbox{\unvbox\@outputbox
        \unskip \vskip \@fpbot
      }%
      \let \@elt \relax
      \xdef\@deferlist{\@failedlist\@flfail}%
      \xdef\@freelist{\@freelist\@flsucceed}%
    }{}%
  }%
}%
\def\@wtryfc #1{%
  \global\setbox\@outputbox\vbox{\unvbox\@outputbox
    \box #1\vskip\@fpsep
  }%
}%
\def\@xtryfc#1#2{%
  \@next\reserved@a\@trylist{}{}% trim \@trylist. Ugly!
  \@currtype \count #2%
  \divide\@currtype\@xxxii\multiply\@currtype\@xxxii
  \@bitor \@currtype \@failedlist
  \@testfp #2%
  #1#2%
  \@ifdim{\ht #2>\@colht   }{\@testtrue}{}%
  \@if@sw\if@test\fi{%
   \@cons\@failedlist #2%
  }{%
   \begingroup
     \gdef\@flsucceed{\@elt #2}%
     \global\let\@flfail\@empty
     \@tempdima\ht #2%
     \def \@elt {\@ztryfc#1}\@trylist
     \@ifdim{\@tempdima >\@fpmin}{%
       \global\@booleantrue\fcolmade@sw
     }{%
       \@cons\@failedlist #2%
     }%
   \endgroup
   \fcolmade@sw{%
     \let \@elt \@gobble
   }{}%
  }%
}%
\def\@ztryfc #1#2{%
  \@tempcnta \count#2%
  \divide\@tempcnta\@xxxii\multiply\@tempcnta\@xxxii
  \@bitor \@tempcnta {\@failedlist \@flfail}%
  \@testfp #2%
  #1#2%
  \@tempdimb\@tempdima
  \advance\@tempdimb \ht#2\advance\@tempdimb\@fpsep
  \@ifdim{\@tempdimb >\@colht}{%
    \@testtrue
  }{}%
  \@if@sw\if@test\fi{%
    \@cons\@flfail #2%
  }{%
    \@cons\@flsucceed #2%
    \@tempdima\@tempdimb
  }%
}%
\def\newpage@prep{%
  \if@noskipsec
    \ifx \@nodocument\relax
      \leavevmode
      \global \@noskipsecfalse
    \fi
  \fi
  \if@inlabel
    \leavevmode
    \global \@inlabelfalse
  \fi
  \if@nobreak \@nobreakfalse \everypar{}\fi
  \par
}%
\def \newpage {%
 \newpage@prep
 \do@output@MVL{%
  \vfil
  \penalty-\pagebreak@pen
 }%
}%
\def\clearpage{%
 \newpage@prep
 \do@output@MVL{%
  \vfil
  \penalty-\pagebreak@pen
  \global\@booleantrue\clearpage@sw
  \protect@penalty\do@startcolumn@pen
  \protect@penalty\do@endpage@pen
 }%
 \do@output@MVL{%
  \global\@booleanfalse\clearpage@sw
 }%
}%
\def\cleardoublepage{%
 \clearpage
 \@if@sw\if@twoside\fi{%
  \@ifodd\c@page{}{%
   \null\clearpage
  }%
 }{}%
}%
\@booleanfalse\clearpage@sw
\mathchardef\do@endpage@pen=10007
\@namedef{output@-\the\do@endpage@pen}{\csname end@column@\thepagegrid\endcsname}%
\mathchardef\do@newpage@pen=10001
\expandafter\let\csname output@-\the\do@newpage@pen\endcsname\relax
\def\@clearfloatplacement{%
 \global\@topnum     \maxdimen
 \global\@toproom    \maxdimen
 \global\@botnum     \maxdimen
 \global\@botroom    \maxdimen
 \global\@colnum     \maxdimen
 \global\@dbltopnum  \maxdimen
 \global\@dbltoproom \maxdimen
 \global\@textmin    \z@
 \global\@fpmin      \z@
 \let\@testfp\@gobble
 \appdef\@setfloattypecounts{\@fpstype16\advance\@fpstype\m@ne}%
}%
\let\@doclearpage\@undefined
\let\@makefcolumn\@undefined
\let\@makecol\@undefined
\def\clr@top@firstmark{%
 \global\let\saved@@topmark\@undefined
 \global\let\saved@@firstmark\@empty
 \global\let\saved@@botmark\@empty
}%
\clr@top@firstmark
\def\set@top@firstmark{%
 \@ifxundefined\saved@@topmark{\expandafter\gdef\expandafter\saved@@topmark\expandafter{\@@topmark}}{}%
 \@if@empty\saved@@firstmark{\expandafter\gdef\expandafter\saved@@firstmark\expandafter{\@@firstmark}}{}%
 \@if@empty\@@botmark{}{\expandafter\gdef\expandafter\saved@@botmark\expandafter{\@@botmark}}%
}%
\appdef\@outputpage@tail{%
 \clr@top@firstmark
}%
\def\@float#1{%
 \@ifnextchar[{%
  \@yfloat\width@float{#1}%
 }{%
  \@ifxundefined@cs{fps@#1}{}{\expandafter\let\expandafter\fps@\csname fps@#1\endcsname}%
  \expandafter\@argswap\expandafter{\expandafter[\fps@]}{\@yfloat\width@float{#1}}%
 }%
}%
\def\@dblfloat#1{%
 \@ifnum{\pagegrid@col=\@ne}{%
  \@float{#1}%
 }{%
  \@ifnextchar[{%
   \@yfloat\widthd@float{#1}%
  }{%
   \@ifxundefined@cs{fpsd@#1}{}{\expandafter\let\expandafter\fpsd@\csname fpsd@#1\endcsname}%
   \expandafter\@argswap\expandafter{\expandafter[\fpsd@]}{\@yfloat\widthd@float{#1}}%
  }%
 }%
}%
\def\@yfloat#1#2[#3]{%
 \@xfloat{#2}[#3]%
 \hsize#1\linewidth\hsize
 \let\set@footnotewidth\@empty
 \minipagefootnote@init
}%
\def\fps@{tbp}%
\def\fpsd@{tp}%
\def\width@float{\columnwidth}%
\def\widthd@float{\textwidth}%
\def\end@float{%
 \end@@float{%
  \check@currbox@count
 }%
}%
\def\end@dblfloat{%
 \@ifnum{\pagegrid@col=\@ne}{%
  \end@float
 }{%
  \end@@float{%
   \@iffpsbit\@ne{\global\advance\count\@currbox\m@ne}{}%
   \@iffpsbit\f@ur{\global\advance\count\@currbox-4\relax}{}%
   \global\wd\@currbox\textwidth % Klootch
   \check@currbox@count
  }%
 }%
}%
\def\end@@float#1{%
 \minipagefootnote@here
 \@endfloatbox
 #1%
 \@ifnum{\@floatpenalty <\z@}{%
  \@largefloatcheck
  \@cons\@currlist\@currbox
  \@ifnum{\@floatpenalty <-\@Mii}{%
   \do@output@cclv{\@add@float}%
  }{%
   \vadjust{\do@output@cclv{\@add@float}}%
   \@Esphack
  }%
 }{}%
}%
\newcommand\float@end@float{%
 \@endfloatbox
 \global\setbox\@currbox\float@makebox\columnwidth
 \let\@endfloatbox\relax
 \end@float
}%
\newcommand\float@end@ltx{%
 \end@@float{%
  \global\setbox\@currbox\float@makebox\columnwidth
  \check@currbox@count
 }%
}%
\newcommand\newfloat@float[3]{%
 \@namedef{ext@#1}{#3} %!
 \let\float@do=\relax
 \xdef\@tempa{\noexpand\float@exts{\the\float@exts \float@do{#3}}}%
 \@tempa
 \floatplacement{#1}{#2}%
 \@ifundefined{fname@#1}{\floatname{#1}{#1}}{} %!
 \expandafter\edef\csname ftype@#1\endcsname{\value{float@type}}%
 \addtocounter{float@type}{\value{float@type}} %!
 \restylefloat{#1}%
 \expandafter\edef\csname fnum@#1\endcsname{%
  \expandafter\noexpand\csname fname@#1\endcsname{} %!
  \expandafter\noexpand\csname the#1\endcsname
 }
 \@ifnextchar[%]
  {%
   \float@newx{#1}%
  }{%
   \@ifundefined{c@#1}{\newcounter{#1}\@namedef{the#1}{\arabic{#1}}}{}%
  }%
}%
\newcommand\newfloat@ltx[3]{%
 \@namedef{ext@#1}{#3}%
 \let\float@do=\relax
 \xdef\@tempa{\noexpand\float@exts{\the\float@exts \float@do{#3}}}%
 \@tempa
 \floatplacement{#1}{#2}%
 \@ifundefined{fname@#1}{\floatname{#1}{#1}}{}%
 \expandafter\edef\csname ftype@#1\expandafter\endcsname\expandafter{\the\c@float@type}%
 \addtocounter{float@type}{\value{float@type}}%
 \restylefloat{#1}%
 \expandafter\edef\csname fnum@#1\endcsname{%
  \expandafter\noexpand\csname fname@#1\endcsname{}%
  \expandafter\noexpand\csname the#1\endcsname
 }
 \@ifnextchar[%]
  {%
   \float@newx{#1}%
  }{%
   \@ifundefined{c@#1}{\newcounter{#1}\@namedef{the#1}{\arabic{#1}}}{}%
  }%
}%
\appdef\document@inithook{%
 \@ifxundefined\newfloat{}{%
  \@ifx{\float@end\float@end@float}{%
   \@ifx{\newfloat\newfloat@float}{\true@sw}{\false@sw}%
   }{\false@sw}%
   {%
    \class@warn{Repair the float package}%
    \let\float@end\float@end@ltx
    \let\newfloat\newfloat@ltx
   }{%
    \class@warn{Failed to patch the float package}%
   }%
 }%
}%
\def\@iffpsbit#1{%
 \begingroup
  \@tempcnta\count\@currbox
  \divide\@tempcnta#1\relax
  \@ifodd\@tempcnta{\aftergroup\true@sw}{\aftergroup\false@sw}%
 \endgroup
}%
\def\check@currbox@count{%
 \@ifnum{\count\@currbox>\z@}{%
  \count@\count\@currbox\divide\count@\sixt@@n\multiply\count@\sixt@@n
  \@tempcnta\count\@currbox\advance\@tempcnta-\count@
  \@ifnum{\@tempcnta=\z@}{%
   \ltxgrid@warn{Float cannot be placed}%
  }{}%
  \expandafter\tally@float\expandafter{\@captype}%
 }{%
 }%
}%
\providecommand\minipagefootnote@init{}%
\providecommand\minipagefootnote@here{}%
\providecommand\tally@float[1]{}%
\let\@specialoutput\@undefined
\def\@add@float{%
 \@pageht\ht\@cclv\@pagedp\dp\@cclv
 \unvbox\@cclv
 \@next\@currbox\@currlist{%
  \csname @floatselect@sw@\thepagegrid\endcsname\@currbox{%
   \@ifnum{\count\@currbox>\z@}{%
    \advance \@pageht \@pagedp
    \advance \@pageht \vsize \advance \@pageht -\pagegoal
    \@addtocurcol
   }{%
    \@addmarginpar
   }%
  }{%
   \@resethfps
   \@cons\@deferlist\@currbox
  }%
 }{\@latexbug}%
 \@ifnum{\outputpenalty<\z@}{%
  \@if@sw\if@nobreak\fi{%
   \nobreak
  }{%
   \addpenalty \interlinepenalty
  }%
 }{}%
 \set@vsize
}%
\let\@reinserts\@undefined
\def \@addtocurcol {%
   \@insertfalse
   \@setfloattypecounts
   \ifnum \@fpstype=8
   \else
     \ifnum \@fpstype=24
     \else
       \@flsettextmin
       \advance \@textmin \@textfloatsheight
       \@reqcolroom \@pageht
       \ifdim \@textmin>\@reqcolroom
         \@reqcolroom \@textmin
       \fi
       \advance \@reqcolroom \ht\@currbox
       \ifdim \@colroom>\@reqcolroom
         \@flsetnum \@colnum
         \ifnum \@colnum>\z@
           \@bitor\@currtype\@deferlist
           \if@test
           \else
             \@bitor\@currtype\@botlist
             \if@test
               \@addtobot
             \else
               \ifodd \count\@currbox
                 \advance \@reqcolroom \intextsep
                 \ifdim \@colroom>\@reqcolroom
                   \global \advance \@colnum \m@ne
                   \global \advance \@textfloatsheight \ht\@currbox
                   \global \advance \@textfloatsheight 2\intextsep
                   \@cons \@midlist \@currbox
                   \if@nobreak
                     \nobreak
                     \@nobreakfalse
                     \everypar{}%
                   \else
                     \addpenalty \interlinepenalty
                   \fi
                   \vskip \intextsep
                   \unvbox\@currbox %AO
                   \penalty\interlinepenalty
                   \vskip\intextsep
                   \ifnum\outputpenalty <-\@Mii \vskip -\parskip\fi
                   \outputpenalty \z@
                   \@inserttrue
                 \fi
               \fi
               \if@insert
               \else
                 \@addtotoporbot
               \fi
             \fi
           \fi
         \fi
       \fi
     \fi
   \fi
   \if@insert
   \else
     \@resethfps
     \@cons\@deferlist\@currbox
   \fi
}%
\@twocolumnfalse
\let\@twocolumntrue\@twocolumnfalse
\def\@addmarginpar{%
 \@next\@marbox\@currlist{%
  \@cons\@freelist\@marbox\@cons\@freelist\@currbox
 }\@latexbug
 \setbox\@marbox\hb@xt@\columnwidth{%
  \csname @addmarginpar@\thepagegrid\endcsname{%
   \hskip-\marginparsep\hskip-\marginparwidth
   \box\@currbox
  }{%
   \hskip\columnwidth\hskip\marginparsep
   \box\@marbox
  }%
  \hss
 }%
 \setbox\z@\box\@currbox
    \@tempdima\@mparbottom
    \advance\@tempdima -\@pageht
    \advance\@tempdima\ht\@marbox
 \@ifdim{\@tempdima >\z@}{%
   \@latex@warning@no@line {Marginpar on page \thepage\space moved}%
 }{%
   \@tempdima\z@
 }%
    \global\@mparbottom\@pageht
    \global\advance\@mparbottom\@tempdima
    \global\advance\@mparbottom\dp\@marbox
    \global\advance\@mparbottom\marginparpush
    \advance\@tempdima -\ht\@marbox
    \global\setbox \@marbox
                   \vbox {\vskip \@tempdima
                          \box \@marbox}%
    \global \ht\@marbox \z@
    \global \dp\@marbox \z@
    \kern -\@pagedp
    \nointerlineskip
  \box\@marbox
    \nointerlineskip
    \hbox{\vrule \@height\z@ \@width\z@ \@depth\@pagedp}%
}%
\newenvironment{turnpage}{%
 \def\width@float{\textheight}%
 \def\widthd@float{\textheight}%
 \appdef\@endfloatbox{%
  \@ifxundefined\@currbox{%
   \ltxgrid@warn{Cannot rotate! Not a float}%
  }{%
   \setbox\@currbox\vbox to\textwidth{\vfil\unvbox\@currbox\vfil}%
   \global\setbox\@currbox\vbox{\rotatebox{90}{\box\@currbox}}%
  }%
 }%
}{%
}%
\def\rotatebox@dummy#1#2{%
 \ltxgrid@warn{You must load the graphics or graphicx package in order to use the turnpage environment}%
 #2%
}%
\appdef\document@inithook{%
 \@ifxundefined\rotatebox{\let\rotatebox\rotatebox@dummy}{}%
}%
\@namedef{output@-1073741824}{%
 \deadcycles\z@
 \void@cclv
}%
\mathchardef\save@column@pen=10016
\@namedef{output@-\the\save@column@pen}{\save@column}%
\let \@cclv@saved \@holdpg
\let \@holdpg \@undefined
\def\save@column{%
 \@ifvoid\@cclv@saved{%
  \set@top@firstmark
  \global\@topmark@saved\expandafter{\@@topmark}%
 }{}%
 \global\setbox\@cclv@saved\vbox{%
  \@ifvoid\@cclv@saved{}{%
   \unvbox\@cclv@saved
   \marry@baselines
  }%
  \unvbox\@cclv
  \lose@breaks
  \remove@lastbox
 }%
}%
\newtoks\@topmark@saved
\def\prep@cclv{%
 \void@cclv
 \setbox\@cclv\box\@cclv@saved
 \vbadness\@M
}%
\mathchardef\save@column@insert@pen=10017
\@namedef{output@-\the\save@column@insert@pen}{\toggle@insert{\savecolumn@holding}{\savecolumn@moving}}%
\def\savecolumn@holding{%
 \@if@exceed@pagegoal{\unvcopy\@cclv\remove@lastbox}{%
  \setbox\z@\vbox{\unvcopy\@cclv\remove@lastbox}%
  \outputdebug@sw{\trace@box\z@}{}%
  \dimen@\ht\@cclv\advance\dimen@-\ht\z@
  \dead@cycle@repair@protected\dimen@
 }{%
  \dead@cycle
 }%
}%
\def\savecolumn@moving{%
 \ltxgrid@info@sw{\class@info{\string\savecolumn@moving}}{}%
 \@cclv@nontrivial@sw{%
  \save@column
 }{%
  \void@cclv
 }%
 \@ifvoid\footins{}{%
  \ltxgrid@foot@info@sw{\class@info{\string\savecolumn@moving}\trace@scroll{\showbox\footins@saved\showbox\footins}}{}%
  \@ifvoid\footins@saved{%
   \global\setbox\footins@saved\box\footins
  }{%
   \global\setbox\footins@saved\vbox\bgroup
    \unvbox\footins@saved
    \marry@baselines
    \unvbox\footins
   \egroup
  }%
  \ltxgrid@foot@info@sw{\trace@box\footins@saved}{}%
  \protect@penalty\save@column@insert@pen
 }%
}%
\newbox\footins@saved
\newbox\footins@recovered
\newbox\column@recovered
\mathchardef\save@message@pen=10018
\@namedef{output@-\the\save@message@pen}{\save@message}%
\def\save@message{%
 \void@cclv
 \toks@\expandafter{\@@firstmark}%
 \expandafter\gdef\expandafter\@message@saved\expandafter{\the\toks@}%
 \expandafter\do@@mark\expandafter{\the\@topmark@saved}%
}%
\gdef\@message@saved{}%
\mathchardef\execute@message@pen=10019
\@namedef{output@-\the\execute@message@pen}{\@message@saved}%
\def\execute@message{%
 \@execute@message\save@column@pen
}%
\def\execute@message@insert#1{%
 \@execute@message\save@column@insert@pen{%
  \setbox \footins \box \footins@saved
  \ltxgrid@foot@info@sw{\class@info{\string\execute@message@insert}\trace@box\footins}{}%
  #1%
 }%
}%
\long\def\@execute@message#1#2{%
 \begingroup
  \dimen@\prevdepth\@ifdim{\dimen@<\z@}{\dimen@\z@}{}%
  \setbox\z@\vbox{%
   \protect@penalty#1%
   \protection@box
   \toks@{\prep@cclv#2}%
   \@@mark{\the\toks@}%
   \penalty-\save@message@pen
   \setbox\z@\null\dp\z@\dimen@\ht\z@-\dimen@
   \nointerlineskip\box\z@
   \penalty-\execute@message@pen
  }\unvbox\z@
 \endgroup
}%
\def\do@output@cclv{\execute@message}%
\def\do@output@MVL#1{%
 \@ifvmode{%
  \begingroup\execute@message{\unvbox\@cclv#1}\endgroup
 }{%
  \@ifhmode{%
   \vadjust{\execute@message{\unvbox\@cclv#1}}%
  }{%
   \@latexerr{\string\do@output@MVL\space cannot be executed in this mode!}\@eha
  }%
 }%
}%
\def\lose@breaks{%
 \loopwhile{%
  \count@\lastpenalty
  \@ifnum{\count@=\@M}{%
   \unpenalty\true@sw
  }{%
   \false@sw
  }%
 }%
}%
\def\removestuff{\do@output@MVL{\unskip\unpenalty}}%
\def\removephantombox{%
 \vadjust{%
  \execute@message{%
   \unvbox\@cclv
   \remove@lastbox
   \unskip
   \unskip
   \unpenalty
   \penalty\predisplaypenalty
   \vskip\abovedisplayskip
  }%
 }%
}%
\def\addstuff#1#2{\edef\@tempa{\noexpand\do@output@MVL{\noexpand\@addstuff{#1}{#2}}}\@tempa}%
\def\@addstuff#1#2{%
 \skip@\lastskip\unskip
 \count@\lastpenalty\unpenalty
 \@if@empty{#1}{}{\penalty#1\relax}%
 \@ifnum{\count@=\z@}{}{\penalty\count@}%
 \vskip\skip@
 \@if@empty{#2}{}{\vskip#2\relax}%
}%
\def\replacestuff#1#2{\edef\@tempa{\noexpand\do@output@MVL{\noexpand\@replacestuff{#1}{#2}}}\@tempa}%
\def\@replacestuff#1#2{%
 \skip@\lastskip\unskip
 \count@\lastpenalty\unpenalty
 \@if@empty{#1}{}{%
 \@ifnum{\count@>\@M}{}{%
   \@ifnum{\count@=\z@}{\count@=#1\relax}{%
    \@ifnum{\count@<#1\relax}{}{%
     \count@=#1\relax
    }%
   }%
 }%
 }%
 \@ifnum{\count@=\z@}{}{\penalty\count@}%
 \@if@empty{#2}{}{%
  \@tempskipa#2\relax
  \@ifdim{\z@>\@tempskipa}{%
   \advance\skip@-\@tempskipa
  }{%
   \@ifdim{\skip@>\@tempskipa}{}{%
    \skip@\@tempskipa
   }%
  }%
 }%
 \vskip\skip@
}%
\def\move@insertions{\global\holdinginserts\z@}%
\def\hold@insertions{\global\holdinginserts\@ne}%
\hold@insertions
\def\toggle@insert#1#2{%
 \@ifnum{\holdinginserts>\z@}{\move@insertions#1}{\hold@insertions#2}%
}%
\def\do@columngrid#1#2{%
 \par
 \expandafter\let\expandafter\@tempa\csname open@column@#1\endcsname
 \@ifx{\relax\@tempa}{%
  \ltxgrid@warn{Unknown page grid #1. No action taken}%
 }{%
  \do@output@MVL{\start@column{#1}{#2}}%
 }%
}%
\def\start@column#1#2{%
 \def\@tempa{#1}\@ifx{\@tempa\thepagegrid}{%
  \ltxgrid@info{Already in page grid \thepagegrid. No action taken}%
 }{%
  \expandafter\execute@message@insert
  \expandafter{%
               \csname shut@column@\thepagegrid\expandafter\endcsname
               \csname open@column@#1\endcsname{#2}%
               \set@vsize
             }%
 }%
}%
\def\thepagegrid{one}%
\newbox\pagesofar
\newbox\footsofar
\def\combine@foot@inserts#1#2{%
  \ltxgrid@info@sw{\class@info{\string\combine@foot@inserts\string#1\string#2}}{}%
  \@ifvoid#1{%
    \ltxgrid@foot@info@sw{\trace@box#2}{}\global\setbox#1\box#2%
  }{%
   \global\setbox#1\vbox\bgroup
    \ltxgrid@foot@info@sw{\trace@box#1}{}\unvbox#1%
    \@ifvoid#2{}{%
     \marry@baselines
     \ltxgrid@foot@info@sw{\trace@box#2}{}\unvbox#2%
    }%
   \egroup
  }%
  \ltxgrid@foot@info@sw{\trace@scroll{\showbox#1\showbox#2}}{}%
}%
\newcommand\onecolumngrid{\do@columngrid{one}{\@ne}}%
\let\onecolumn\@undefined
\def\open@column@one#1{%
 \ltxgrid@info@sw{\class@info{\string\open@column@one\string#1}}{}%
 \unvbox\pagesofar
 \@ifvoid{\footsofar}{}{%
  \insert\footins\bgroup\unvbox\footsofar\egroup
  \penalty\z@
 }%
 \gdef\thepagegrid{one}%
 \global\pagegrid@col#1%
 \global\pagegrid@cur\@ne
 \global\count\footins\@m
 \global\divide\count\footins\tw@
 \set@column@hsize\pagegrid@col
 \set@colht
}%
\def\shut@column@one{%
 \ltxgrid@info@sw{\class@info{\string\shut@column@one}}{}%
 \@makecolumn\false@sw
 \global\setbox\pagesofar\vbox\bgroup
  \recover@column\@outputbox\footsofar\column@recovered\footins@recovered
 \egroup
 \begingroup\setbox\z@\box\@outputbox\endgroup
 \combine@foot@inserts\footsofar\footins
 \set@colht
}%
\def\float@column@one{%
 \@makecolumn\true@sw
 \@outputpage
}%
\def\end@column@one{%
 \unvbox\@cclv\remove@lastbox
 \protect@penalty\do@newpage@pen
}%
\def\output@column@one{%
 \@outputpage
}%
\def\@addmarginpar@one{%
 \@if@sw\if@mparswitch\fi{%
  \@ifodd\c@page{\false@sw}{\true@sw}%
 }{\false@sw}{%
  \@if@sw\if@reversemargin\fi{\false@sw}{\true@sw}%
 }{%
  \@if@sw\if@reversemargin\fi{\true@sw}{\false@sw}%
 }%
}%
\def\@floatselect@sw@one#1{\true@sw}%
\def\onecolumngrid@push{%
 \do@output@MVL{%
  \@ifnum{\pagegrid@col=\@ne}{%
   \global\let\restorecolumngrid\@empty
  }{%
   \xdef\restorecolumngrid{%
    \noexpand\start@column{\thepagegrid}{\the\pagegrid@col}%
   }%
   \start@column{one}{\@ne}%
  }%
 }%
}%
\def\onecolumngrid@pop{%
 \do@output@MVL{\restorecolumngrid}%
}%
\newcommand\twocolumngrid{\do@columngrid{mlt}{\tw@}}%
\let\twocolumn\@undefined
\let\@topnewpage\@undefined
\def\open@column@mlt#1{%
 \ltxgrid@info@sw{\class@info{\string\open@column@mlt\string#1}}{}%
 \@ifvoid{\footsofar}{}{%
  \insert\footins\bgroup\unvbox\footsofar\egroup
 }%
 \gdef\thepagegrid{mlt}%
 \global\pagegrid@col#1%
 \global\pagegrid@cur\@ne
 \global\count\footins\@m
 \set@column@hsize\pagegrid@col
 \set@colht
}%
\def\shut@column@mlt{%
 \ltxgrid@info@sw{\class@info{\string\shut@column@mlt}}{}%
 \@cclv@nontrivial@sw{%
  \@makecolumn\false@sw
  \@ifnum{\pagegrid@cur<\pagegrid@col}{%
   \expandafter\global\expandafter\setbox\csname col@\the\pagegrid@cur\endcsname\box\@outputbox
   \global\advance\pagegrid@cur\@ne
  }{}%
 }{%
  \void@cclv
 }%
 \@ifnum{\pagegrid@cur>\@ne}{%
  \csname balance@\the\pagegrid@col\endcsname
  \grid@column\@outputbox{}%
  \@combinepage\false@sw
  \@combinedblfloats
  \global\setbox\pagesofar\box\@outputbox
  \show@pagesofar@size
 }{}%
 \set@colht
}%
\def\float@column@mlt{%
  \@output@combined@page
}%
\def\end@column@mlt{%
 \@ifx@empty\@toplist{%
  \@ifx@empty\@botlist{%
   \@ifx@empty\@dbltoplist{%
    \@ifx@empty\@deferlist{%
     \@ifnum{\pagegrid@cur=\@ne}{%
      \false@sw
     }{%
      \true@sw
     }%
    }{%
     \true@sw
    }%
   }{%
    \true@sw
   }%
  }{%
   \true@sw
  }%
 }{%
  \true@sw
 }%
 % true = kick out a column and try again
 {%
  \@cclv@nontrivial@sw{%
   \unvbox\@cclv\remove@lastbox
  }{%
   \unvbox\@cclv\remove@lastbox\unskip\null
  }%
  \protect@penalty\do@newpage@pen
  \protect@penalty\do@endpage@pen
 }{%
  \unvbox\@cclv\remove@lastbox
 }%
}%
\def\output@column@mlt{%
 \@ifnum{\pagegrid@cur<\pagegrid@col}{%
  \expandafter\global\expandafter\setbox\csname col@\the\pagegrid@cur\endcsname\box\@outputbox
  \global\advance\pagegrid@cur\@ne
 }{%
  \set@adj@colht\dimen@
  \grid@column\@outputbox{}%
  \@output@combined@page
 }%
}%
\let\@outputdblcol\@undefined
\def\@floatselect@sw@mlt#1{\@if@notdblfloat{#1}}%
\def\@addmarginpar@mlt{% emits a boolean
 \@ifnum{\pagegrid@cur=\@ne}%
}%
\def\set@footnotewidth@one{%
 \hsize\columnwidth
 \linewidth\hsize
}%
\def\set@footnotewidth@two{\set@footnotewidth@mlt\tw@}%
\def\set@footnotewidth@mlt#1{%
 \hsize\textwidth
 \advance\hsize\columnsep
 \divide\hsize#1%
 \advance\hsize-\columnsep
 \linewidth\hsize
}%
\def\compose@footnotes@one#1{%
 \ltxgrid@foot@info@sw{\class@info{\string\compose@footnotes@one\string#1}\trace@box#1}{}%
}%
\let\compose@footnotes\compose@footnotes@one
\def\compose@footnotes@two#1{%
 \ltxgrid@foot@info@sw{\class@info{\string\compose@footnotes@two\string#1}\trace@box#1}{}%
 \setbox\z@\box\@tempboxa
 \let\recover@column\recover@column@null
 \let\marry@baselines\@empty
 \balance@two#1\@tempboxa
 \global\setbox#1\hbox to\textwidth{\box#1\hfil\box\@tempboxa}%
 \ltxgrid@foot@info@sw{\trace@box#1}{}%
}%
\let\pagegrid@cur\col@number
\let\col@number\@undefined
\newcount\pagegrid@col
\pagegrid@cur\@ne
\expandafter\let\csname col@\the\pagegrid@cur\endcsname\@leftcolumn
\let\@leftcolumn\@undefined
\pagegrid@col\tw@
\def\pagegrid@init{%
 \advance\pagegrid@cur\@ne
 \@ifnum{\pagegrid@cur<\pagegrid@col}{%
  \csname newbox\expandafter\endcsname\csname  col@\the\pagegrid@cur\endcsname
  \pagegrid@init
 }{%
 }%
}%
\appdef\class@documenthook{%
 \pagegrid@init
}%
\def\grid@column#1#2{%
 \ltxgrid@info@sw{\class@info{\string\grid@column\string#1}}{}%
 \global\setbox#1\vbox\bgroup
  \hb@xt@\textwidth\bgroup
   \vrule\@height\z@\@width\z@\@if@empty{#2}{}{\@depth#2}%
   \pagegrid@cur\@ne
   \@ifnum{\pagegrid@cur<\pagegrid@col}{\loopwhile{\append@column@\pagegrid@cur\pagegrid@col}}{}%
   \box@column#1%
  \egroup
  \vskip\z@skip
 \egroup
}%
\def\append@column@#1#2{%
 \expandafter\box@column\csname col@\the#1\endcsname
 \hfil\vrule\@width\columnseprule\hfil
 \advance#1\@ne
 \@ifnum{#1<#2}%
}%
\def\box@column#1{%
 \ltxgrid@info@sw{\class@info{\string\box@column\string#1}}{}%
 \raise\topskip
 \hb@xt@\columnwidth\bgroup
  \dimen@\ht#1\@ifdim{\dimen@>\@colht}{\dimen@\@colht}{}%
  \count@\vbadness\vbadness\@M
  \dimen@ii\vfuzz\vfuzz\maxdimen
  \ltxgrid@info@sw{\saythe\@colht\saythe\dimen@}{}%
  \vtop to\dimen@\bgroup
   \hrule\@height\z@
   \unvbox#1%
   \raggedcolumn@skip
  \egroup
  \vfuzz\dimen@ii
  \vbadness\count@
  \hss
 \egroup
}%
\def\marry@baselines{%
 \begingroup
  \setbox\z@\lastbox
  \@ifvoid{\z@}{%
   \endgroup
  }{%
   \aftergroup\kern
   \aftergroup-%
   \expandafter\box\expandafter\z@\expandafter\endgroup\the\dp\z@\relax
  }%
 \vskip\marry@skip\relax
}%
\gdef\marry@skip{\z@skip}%
\def\set@marry@skip{%
 \begingroup
  \skip@\baselineskip\advance\skip@-\topskip
  \@ifdim{\skip@>\z@}{%
   \xdef\marry@skip{\the\skip@}%
  }{}%
 \endgroup
}%
\appdef\document@inithook{%
 \@ifxundefined\raggedcolumn@sw{\@booleanfalse\raggedcolumn@sw}{}%
}%
\def\raggedcolumn@skip{%
 \vskip\z@\raggedcolumn@sw{\@plus.0001fil\@minus.0001fil}{}\relax
}%
\def\@combinepage#1{%
 \ltxgrid@foot@info@sw{\class@info{\string\@combinepage\string#1}}{}%
 \@ifvoid\pagesofar{}{%
  \setbox\@outputbox\vbox{%
   \unvbox\pagesofar
   \marry@baselines
   \unvbox\@outputbox
  }%
 }%
 #1{%
  \@ifvoid\footsofar{}{%
   \show@box@size{Combining page footnotes}\footsofar
   \setbox\footins\box\footsofar
   \compose@footnotes
   \@combineinserts\@outputbox\footins
  }%
 }{%
 }%
}%
\def \@cflt{%
 \let \@elt \@comflelt
 \setbox\@tempboxa \vbox{}%
 \@toplist
 \setbox\@outputbox \vbox{%
  \boxmaxdepth \maxdepth
  \unvbox\@tempboxa\unskip
  \topfigrule\vskip \textfloatsep
  \unvbox\@outputbox
 }%
 \let\@elt\relax
 \xdef\@freelist{\@freelist\@toplist}%
 \global\let\@toplist\@empty
}%
\def \@cflb {%
 \let\@elt\@comflelt
 \setbox\@tempboxa \vbox{}%
 \@botlist
 \setbox\@outputbox \vbox{%
  \unvbox\@outputbox
  \vskip \textfloatsep\botfigrule
  \unvbox\@tempboxa\unskip
 }%
 \let\@elt\relax
 \xdef\@freelist{\@freelist\@botlist}%
 \global \let \@botlist\@empty
}%
\def\@combinedblfloats{%
 \@ifx@empty\@dbltoplist{}{%
  \setbox\@tempboxa\vbox{}%
  \let\@elt\@comdblflelt\@dbltoplist
  \let\@elt\relax\xdef\@freelist{\@freelist\@dbltoplist}%
  \global\let\@dbltoplist\@empty
  \setbox\@outputbox\vbox{%
   %\boxmaxdepth\maxdepth   %% probably not needed, CAR
   \unvbox\@tempboxa\unskip
   \@ifnum{\@dbltopnum>\m@ne}{\dblfigrule}{}%FIXME: how is \@dbltopnum maintained?
   \vskip\dbltextfloatsep
   \unvbox\@outputbox
  }%
 }%
}%
\def\set@column@hsize#1{%
 \pagegrid@col#1%
 \global\columnwidth\textwidth
 \global\advance\columnwidth\columnsep
 \global\divide\columnwidth\pagegrid@col
 \global\advance\columnwidth-\columnsep
 \global\hsize\columnwidth
 \global\linewidth\columnwidth
 \skip@\baselineskip\advance\skip@-\topskip
 \@ifnum{\pagegrid@col>\@ne}{\set@marry@skip}{}%
}%
\def\set@colht{%
 \set@adj@textheight\@colht
 \global\let\enlarge@colroom\@empty
 \set@colroom
}%
\def\set@adj@textheight#1{%
 \ltxgrid@info@sw{\class@info{\string\set@adj@textheight\string#1}\saythe\textheight}{}%
 #1\textheight
 \def\@elt{\adj@page#1}%
 \@booleantrue\firsttime@sw\@dbltoplist
 \let\@elt\relax
 \global#1#1\relax
 \ltxgrid@info@sw{\saythe#1}{}%
}%
\def\set@colroom{%
 \ltxgrid@info@sw{\class@info{\string\set@colroom}}{}%
 \set@adj@colht\@colroom
 \@if@empty\enlarge@colroom{}{%
  \global\advance\@colroom\enlarge@colroom\relax
  \ltxgrid@info@sw{\saythe\@colroom}{}%
 }%
 \@ifdim{\@colroom>\topskip}{}{%
  \ltxgrid@info{Not enough room: \string\@colroom=\the\@colroom; increasing to \the\topskip}%
  \@colroom\topskip
 }%
 \global\@colroom\@colroom
 \set@vsize
}%
\def\set@vsize{%
 \global\vsize\@colroom
 \ltxgrid@info@sw{\class@info{\string\set@vsize\string\vsize=\string\colroom}\saythe\vsize}{}%
}%
\def\set@adj@colht#1{%
 #1\@colht
 \ltxgrid@info@sw{\class@info{\string\set@adj@colht\string#1-\string\pagesofar}\saythe#1}{}%
 \@ifvoid\pagesofar{}{%
  \advance#1-\ht\pagesofar\advance#1-\dp\pagesofar
  \ltxgrid@info@sw{\class@info{\string\pagesofar}\saythe#1}{}%
 }%
 \def\@elt{\adj@column#1}%
 \@booleantrue\firsttime@sw\@toplist
 \@booleantrue\firsttime@sw\@botlist
 \let\@elt\relax
}%
\def\adj@column#1#2{%
 \advance#1-\ht#2%
 \advance#1-\firsttime@sw{\textfloatsep\@booleanfalse\firsttime@sw}{\floatsep}%
 \ltxgrid@info@sw{\class@info{\string\adj@column\string#1-\string#2}\saythe#1}{}%
}%
\def\adj@page#1#2{%
 \advance#1-\ht#2%
 \advance#1-\firsttime@sw{\dbltextfloatsep\@booleanfalse\firsttime@sw}{\dblfloatsep}%
 \ltxgrid@info@sw{\class@info{\string\adj@page\string#1-\string#2}\saythe#1}{}%
}%
\def\set@adj@box#1#2{%
 \@ifvoid#2{}{%
  \advance#1-\ht#2\advance#1-\dp#2%
  \@booleantrue\temp@sw
  \ltxgrid@foot@info@sw{\class@info{\string\set@adj@box\string#2}\saythe#1}{}%
 }%
}%
\appdef\@outputpage@tail{%
 \set@colht          % FIXME: needed?
 \@floatplacement    % FIXME: needed?
 \@dblfloatplacement % FIXME: needed?
}%
\begingroup
 \catcode`\1=\cat@letter
 \catcode`\2=\cat@letter
 \toks@{%
  \setbox\footins\box\footsofar
  \balance@two\col@1\@outputbox
  \global\setbox\col@1\box\col@1
  \global\setbox\@outputbox\box\@outputbox
  \combine@foot@inserts\footsofar\footins
 }%
 \aftergroup\def\aftergroup\balance@2\expandafter
\endgroup\expandafter{\the\toks@}%
\def\balance@two#1#2{%
 \ltxgrid@info@sw{\class@info{\string\balance@two\string#1\string#2}}{}%
 \outputdebug@sw{\trace@scroll{\showbox#1\showbox#2}}{}%
 \setbox\thr@@\copy\footsofar
 \setbox\@ne\vbox\bgroup
  \@ifvoid{#1}{}{%
   \recover@column#1\footsofar\column@recovered\footins@recovered
   \@ifvoid{#2}{}{\marry@baselines}%
  }%
  \@ifvoid{#2}{}{%
   \recover@column#2\footsofar\column@recovered\footins@recovered
  }%
 \egroup
 \outputdebug@sw{\trace@scroll{\showbox\@ne}}{}%
 \ltxgrid@foot@info@sw{\trace@scroll{\showbox\footsofar}}{}%
 \dimen@\ht\@ne\divide\dimen@\tw@
 \dimen@i\dimen@
 \vbadness\@M
 \vfuzz\maxdimen
 \splittopskip\topskip
 \loopwhile{%
  \setbox\z@\copy\@ne\setbox\tw@\vsplit\z@ to\dimen@
  \remove@depth\z@\remove@depth\tw@
  \dimen@ii\ht\tw@\advance\dimen@ii-\ht\z@
  \dimen@i=.5\dimen@i
  \ltxgrid@info@sw{\saythe\dimen@\saythe\dimen@i\saythe\dimen@ii}{}%
  \@ifdim{\dimen@ii<.5\p@}{%
   \@ifdim{\dimen@ii>-.5\p@}%
  }{%
   \false@sw
  }%
  {%
   \true@sw
  }{%
   \@ifdim{\dimen@i<.5\p@}%
  }%
  {%
   \false@sw
  }%
  {%
   \advance\dimen@\@ifdim{\dimen@ii<\z@}{}{-}\dimen@i
   \true@sw
  }%
 }%
 \ltxgrid@info@sw{\saythe\dimen@\saythe\dimen@i\saythe\dimen@ii}{}%
 \@ifdim{\ht\z@=\z@}{%
  \@ifdim{\ht\tw@=\z@}%
 }{%
  \true@sw
 }%
 {%
 }{%
  \ltxgrid@info{Unsatifactorily balanced columns: giving up}%
  \setbox\tw@\box#1%
  \setbox\z@ \box#2%
  \global\setbox\footsofar\box\thr@@
 }%
 \setbox\tw@\vbox{\unvbox\tw@\vskip\z@skip}%
 \setbox\z@ \vbox{\unvbox\z@ \vskip\z@skip}%
 \set@colht
 \dimen@\ht\z@\@ifdim{\dimen@<\ht\tw@}{\dimen@\ht\tw@}{}%
 \@ifdim{\dimen@>\@colroom}{\dimen@\@colroom}{}%
 \ltxgrid@info@sw{\saythe{\ht\z@}\saythe{\ht\tw@}\saythe\@colroom\saythe\dimen@}{}%
 \setbox#1\vbox to\dimen@{\unvbox\tw@\unskip\raggedcolumn@skip}%
 \setbox#2\vbox to\dimen@{\unvbox\z@ \unskip\raggedcolumn@skip}%
 \outputdebug@sw{\trace@scroll{\showbox#1\showbox#2}}{}%
}%
\def\remove@depth#1{%
  \setbox#1\vbox\bgroup
   \unvcopy#1%
   \setbox\z@\vbox\bgroup
    \unvbox#1%
    \setbox\z@\lastbox
    \aftergroup\kern\aftergroup-\expandafter
   \egroup
   \the\dp\z@\relax
  \egroup
}%
\def\recover@column#1#2#3#4{%
 \ltxgrid@info@sw{\class@info{\string\recover@column\string#1\string#2\string#3\string#4}}{}%
 \setbox#4\vbox{\unvcopy#1}%
 \ltxgrid@foot@info@sw{\trace@scroll{\showbox#4}}{}%
 \dimen@\ht#4%
 \ltxgrid@foot@info@sw{\saythe\dimen@}{}%
 \setbox#4\vbox\bgroup
  \unvbox#4\unskip
  \dimen@i\lastkern\unkern\advance\dimen@i\lastkern
  \@ifdim{\dimen@i=\z@}{%
   \dimen@i\lastkern\unkern
   \ltxgrid@foot@info@sw{\saythe\dimen@i}{}%
   \aftergroup\dimen@i
   \expandafter\egroup\the\dimen@i\relax
  }{%
   \egroup
  }%
 \@ifdim{\dimen@i<\z@}{%
  \advance\dimen@\dimen@i
  \ltxgrid@foot@info@sw{\saythe\dimen@i\saythe\dimen@}{}%
  \splittopskip\z@skip
  \global\setbox#3\vsplit#4 to\dimen@
  \global\setbox#4\vbox{\unvbox#4}%
  \ltxgrid@foot@info@sw{\trace@scroll{\showbox#1\showbox#2\showbox#3\showbox#4}}{}%
  \global\setbox#2\vbox\bgroup\unvbox#2\vskip\z@skip\unvbox#4\egroup
 }{%
  \setbox#3\box#4%
  \ltxgrid@foot@info@sw{\trace@scroll{\showbox#1\showbox#2\showbox#3\showbox#4}}{}%
 }%
 \unvbox#3%
 \loopwhile{\dimen@\lastskip\@ifdim{\dimen@>\z@}{\unskip\true@sw}{\false@sw}}%
}%
\def\recover@column@null#1#2#3#4{%
 \unvcopy#1%
}%
\rvtx@ifformat@geq{2020/10/01}%
  {%
    \AddToHook{begindocument}{%
      \open@column@one\@ne
      \set@colht
      \@floatplacement
      \@dblfloatplacement
    }%
  }{%
    \prepdef\@begindocumenthook{%
     \open@column@one\@ne
     \set@colht
     \@floatplacement
     \@dblfloatplacement
    }%
  }
\def\longtable@longtable{%
 \par
 \ifx\multicols\@undefined\else\ifnum\col@number>\@ne\@twocolumntrue\fi\fi
 \if@twocolumn\LT@err{longtable not in 1-column mode}\@ehc\fi
 \begingroup
 \@ifnextchar[\LT@array{\LT@array[x]}%
}%
\def\longtable@new{%
 \par
  \@ifnextchar[\LT@array{\LT@array[x]}%
}%
\def\endlongtable@longtable{%
  \crcr
  \noalign{%
    \let\LT@entry\LT@entry@chop
    \xdef\LT@save@row{\LT@save@row}}%
  \LT@echunk
  \LT@start
  \unvbox\z@
  \LT@get@widths
  \if@filesw
    {\let\LT@entry\LT@entry@write\immediate\write\@auxout{%
      \gdef\expandafter\noexpand
        \csname LT@\romannumeral\c@LT@tables\endcsname
          {\LT@save@row}}}%
  \fi
  \ifx\LT@save@row\LT@@save@row
  \else
    \LT@warn{Column \@width s have changed\MessageBreak
             in table \thetable}%
    \LT@final@warn
  \fi
  \endgraf\penalty -\LT@end@pen
  \endgroup
  \global\@mparbottom\z@
  \pagegoal\vsize
  \endgraf\penalty\z@\addvspace\LTpost
  \ifvoid\footins\else\insert\footins{}\fi
}%
\def\endlongtable@new{%
  \crcr
  \noalign{%
   \let\LT@entry\LT@entry@chop
   \xdef\LT@save@row{\LT@save@row}%
  }%
  \LT@echunk
  \LT@start
  \unvbox\z@
  \LT@get@widths
  \@if@sw\if@filesw\fi{%
   {%
    \let\LT@entry\LT@entry@write
    \immediate\write\@auxout{%
     \gdef\expandafter\noexpand\csname LT@\romannumeral\c@LT@tables\endcsname
     {\LT@save@row}%
    }%
   }%
  }{}%
  \@ifx{\LT@save@row\LT@@save@row}{}{%
   \LT@warn{%
    Column \@width s have changed\MessageBreak in table \thetable
   }\LT@final@warn
  }%
  \endgraf
  \nobreak
  \box\@ifvoid\LT@lastfoot{\LT@foot}{\LT@lastfoot}%
 \global\@mparbottom\z@
 \endgraf
 \LT@post
}%
\def\LT@start@longtable{%
  \let\LT@start\endgraf
  \endgraf\penalty\z@\vskip\LTpre
  \dimen@\pagetotal
  \advance\dimen@ \ht\ifvoid\LT@firsthead\LT@head\else\LT@firsthead\fi
  \advance\dimen@ \dp\ifvoid\LT@firsthead\LT@head\else\LT@firsthead\fi
  \advance\dimen@ \ht\LT@foot
  \dimen@ii\vfuzz
  \vfuzz\maxdimen
    \setbox\tw@\copy\z@
    \setbox\tw@\vsplit\tw@ to \ht\@arstrutbox
    \setbox\tw@\vbox{\unvbox\tw@}%
  \vfuzz\dimen@ii
  \advance\dimen@ \ht
        \ifdim\ht\@arstrutbox>\ht\tw@\@arstrutbox\else\tw@\fi
  \advance\dimen@\dp
        \ifdim\dp\@arstrutbox>\dp\tw@\@arstrutbox\else\tw@\fi
  \advance\dimen@ -\pagegoal
  \ifdim \dimen@>\z@\vfil\break\fi
      \global\@colroom\@colht
  \ifvoid\LT@foot\else
    \advance\vsize-\ht\LT@foot
    \global\advance\@colroom-\ht\LT@foot
    \dimen@\pagegoal\advance\dimen@-\ht\LT@foot\pagegoal\dimen@
    \maxdepth\z@
  \fi
  \ifvoid\LT@firsthead\copy\LT@head\else\box\LT@firsthead\fi
\nobreak
  \output{\LT@output}%
}%
\def\LT@start@new{%
 \let\LT@start\endgraf
 \endgraf
 \markthr@@{}%
 \LT@pre
 \@ifvoid\LT@firsthead{\LT@top}{\box\LT@firsthead\nobreak}%
 \mark@envir{longtable}%
}%
\def\LT@end@hd@ft@longtable#1{%
 \LT@echunk
 \ifx\LT@start\endgraf
  \LT@err{Longtable head or foot not at start of table}{Increase LTchunksize}%
 \fi
 \setbox#1\box\z@
 \LT@get@widths\LT@bchunk
}%
\def\LT@end@hd@ft@new#1{%
 \LT@echunk
 \@ifx{\LT@start\endgraf}{%
  \LT@err{Longtable head or foot not at start of table}{Increase LTchunksize}%
 }%
 \global\setbox#1\box\z@
 \LT@get@widths
 \LT@bchunk
}%
\def\LT@array@longtable[#1]#2{%
  \refstepcounter{table}\stepcounter{LT@tables}%
  \if l#1%
    \LTleft\z@ \LTright\fill
  \else\if r#1%
    \LTleft\fill \LTright\z@
  \else\if c#1%
    \LTleft\fill \LTright\fill
  \fi\fi\fi
  \let\LT@mcol\multicolumn
  \let\LT@@tabarray\@tabarray
  \let\LT@@hl\hline
  \def\@tabarray{%
    \let\hline\LT@@hl
    \LT@@tabarray}%
  \let\\\LT@tabularcr\let\tabularnewline\\%
  \def\newpage{\noalign{\break}}%
  \def\pagebreak{\noalign{\ifnum`}=0\fi\@testopt{\LT@no@pgbk-}4}%
  \def\nopagebreak{\noalign{\ifnum`}=0\fi\@testopt\LT@no@pgbk4}%
  \let\hline\LT@hline \let\kill\LT@kill\let\caption\LT@caption
  \@tempdima\ht\strutbox
  \let\@endpbox\LT@endpbox
  \ifx\extrarowheight\@undefined
    \let\@acol\@tabacol
    \let\@classz\@tabclassz \let\@classiv\@tabclassiv
    \def\@startpbox{\vtop\LT@startpbox}%
    \let\@@startpbox\@startpbox
    \let\@@endpbox\@endpbox
    \let\LT@LL@FM@cr\@tabularcr
  \else
    \advance\@tempdima\extrarowheight
    \col@sep\tabcolsep
    \let\@startpbox\LT@startpbox\let\LT@LL@FM@cr\@arraycr
  \fi
  \setbox\@arstrutbox\hbox{\vrule
    \@height \arraystretch \@tempdima
    \@depth \arraystretch \dp \strutbox
    \@width \z@}%
  \let\@sharp##\let\protect\relax
   \begingroup
    \@mkpream{#2}%
    \xdef\LT@bchunk{%
       \global\advance\c@LT@chunks\@ne
       \global\LT@rows\z@\setbox\z@\vbox\bgroup
       \LT@setprevdepth
       \tabskip\LTleft \noexpand\halign to\hsize\bgroup
      \tabskip\z@ \@arstrut \@preamble \tabskip\LTright \cr}%
  \endgroup
  \expandafter\LT@nofcols\LT@bchunk&\LT@nofcols
  \LT@make@row
  \m@th\let\par\@empty
  \everycr{}\lineskip\z@\baselineskip\z@
  \LT@bchunk}%
\def\LT@LR@l{\LTleft\z@   \LTright\fill}%
\def\LT@LR@r{\LTleft\fill \LTright\z@  }%
\def\LT@LR@c{\LTleft\fill \LTright\fill}%
\def\LT@array@new[#1]#2{%
 \refstepcounter{table}\stepcounter{LT@tables}%
 \table@hook
 \LTleft\fill \LTright\fill
 \csname LT@LR@#1\endcsname
 \let\LT@mcol\multicolumn
 \let\LT@@hl\hline
 \prepdef\@tabarray{\let\hline\LT@@hl}%
 \let\\\LT@tabularcr
 \let\tabularnewline\\%
 \def\newpage{\noalign{\break}}%
 \def\pagebreak{\noalign{\ifnum`}=0\fi\@testopt{\LT@no@pgbk-}4}%
 \def\nopagebreak{\noalign{\ifnum`}=0\fi\@testopt\LT@no@pgbk4}%
 \let\hline\LT@hline
 \let\kill\LT@kill
 \let\caption\LT@caption
 \@tempdima\ht\strutbox
 \let\@endpbox\LT@endpbox
 \@ifxundefined\extrarowheight{%
  \let\@acol\@tabacol
  \let\@classz\@tabclassz
  \let\@classiv\@tabclassiv
  \def\@startpbox{\vtop\LT@startpbox}%
  \let\@@startpbox\@startpbox
  \let\@@endpbox\@endpbox
  \let\LT@LL@FM@cr\@tabularcr@LaTeX
  \let\@xtabularcr\@xtabularcr@LaTeX
 }{%
  \advance\@tempdima\extrarowheight
  \col@sep\tabcolsep
  \let\@startpbox\LT@startpbox
  \let\LT@LL@FM@cr\@arraycr@array
 }%
 \let\@acoll\@tabacoll
 \let\@acolr\@tabacolr
 \let\@acol\@tabacol
 \setbox\@arstrutbox\hbox{%
  \vrule
  \@height \arraystretch \@tempdima
  \@depth \arraystretch \dp \strutbox
  \@width \z@
 }%
 \let\@sharp##%
 \let\protect\relax
 \begingroup
  \@mkpream{#2}%
  \@mkpream@relax
  \edef\@preamble{\@preamble}%
  \prepdef\@preamble{%
   \global\advance\c@LT@chunks\@ne
   \global\LT@rows\z@
   \setbox\z@\vbox\bgroup
    \LT@setprevdepth
    \tabskip\LTleft
    \halign to\hsize\bgroup
     \tabskip\z@
     \@arstrut
  }%
  \appdef\@preamble{%
     \tabskip\LTright
     \cr
  }%
  \global\let\LT@bchunk\@preamble
 \endgroup
 \expandafter\LT@nofcols\LT@bchunk&\LT@nofcols
 \LT@make@row
 \m@th
 \let\par\@empty
 \everycr{}%
 \lineskip\z@
 \baselineskip\z@
 \LT@bchunk
}%
\appdef\table@hook{}%
\def\switch@longtable{%
 \@ifpackageloaded{longtable}{%
  \@ifx{\longtable\longtable@longtable}{%
   \@ifx{\endlongtable\endlongtable@longtable}{%
    \@ifx{\LT@start\LT@start@longtable}{%
     \@ifx{\LT@end@hd@ft\LT@end@hd@ft@longtable}{%
      \@ifx{\LT@array\LT@array@longtable}{%
       \true@sw
      }{\false@sw}%
     }{\false@sw}%
    }{\false@sw}%
   }{\false@sw}%
  }{\false@sw}%
  {%
   \class@info{Patching longtable package}%
  }{%
   \class@info{Patching unrecognized longtable package. (Proceeding with fingers crossed)}%
  }%
  \let\longtable\longtable@new
  \let\endlongtable\endlongtable@new
  \let\LT@start\LT@start@new
  \let\LT@end@hd@ft\LT@end@hd@ft@new
  \let\LT@array\LT@array@new
  \newenvironment{longtable*}{%
   \onecolumngrid@push
   \longtable
  }{%
   \endlongtable
   \onecolumngrid@pop
  }%
 }{}%
}%
\def\LT@pre{\penalty\z@\vskip\LTpre}%
\def\LT@bot{\nobreak\copy\LT@foot\vfil}%
\def\LT@top{\copy\LT@head\nobreak}%
\def\LT@post{\penalty\z@\addvspace\LTpost\mark@envir{\curr@envir}}%
\def\LT@adj{%
 \setbox\z@\vbox{\null}\dimen@-\ht\z@
 \setbox\z@\vbox{\unvbox\z@\LT@bot}\advance\dimen@\ht\z@
 \global\advance\vsize-\dimen@
}%
\def\output@init@longtable{\LT@adj}%
\def\output@prep@longtable{\setbox\@cclv\vbox{\unvbox\@cclv\LT@bot}}%
\def\output@post@longtable{\LT@top}%
\let\output@init@theindex\@empty
\let\output@prep@theindex\@empty
\def\output@post@theindex{%
 \@ifodd\c@page{}{%
  \@ifnum{\pagegrid@cur=\@ne}{%
  }%
 }%
}%
\def\check@aux{\do@output@MVL{\do@check@aux}}%
\def\check@deferlist@stuck#1{%
 \@ifx{\@deferlist@postshipout\@empty}{}{%
  \@ifx{\@deferlist@postshipout\@deferlist}{%
   \@fltstk
   \clearpage@sw{%
    \ltxgrid@warn{Deferred float stuck during \string\clearpage\space processing}%
   }{%
    \force@deferlist@stuck#1%
   }%
  }{%
  }%
  \global\let\@deferlist@postshipout\@empty
 }%
}%
\def\@fltstk{%
 \@latex@warning{A float is stuck (cannot be placed without \string\clearpage)}%
}%
\appdef\@outputpage@tail{%
 \global\let\@deferlist@postshipout\@deferlist
}%
\def\@next#1#2{%
 \@ifx{#2\@empty}{\false@sw}{%
  \expandafter\@xnext#2\@@#1#2%
  \true@sw
 }%
}%
\def\@xnext\@elt#1#2\@@#3#4{%
 \def#3{#1}%
 \gdef#4{#2}%
 \def\@tempa{#4}\def\@tempb{\@freelist}%
 \@ifx{\@tempa\@tempb}{%
  \@ifx{#4\@empty}{%
   \force@deferlist@empty%{Float register pool exhausted}%
  }{}%
 }{}%
}%
\def\force@deferlist@stuck#1{%
 \force@deferlist@sw{%
  \@booleantrue\clearpage@sw
  \@booleantrue\forcefloats@sw
  #1%
 }{%
 }%
}%
\def\force@deferlist@empty{%
 \force@deferlist@sw{%
  \penalty-\pagebreak@pen
  \protect@penalty\do@forcecolumn@pen
 }{%
 }%
}%
\@booleanfalse\force@deferlist@sw
\mathchardef\do@forcecolumn@pen=10009
\@namedef{output@-\the\do@forcecolumn@pen}{\do@forcecolumn}%
\def\do@forcecolumn{%
 \@booleantrue\clearpage@sw
 \@booleantrue\forcefloats@sw
 \do@startcolumn
}%
\def\enlargethispage{%
 \@ifstar{%
  \@enlargethispage{}%
 }{%
  \@enlargethispage{}%
 }%
}%
\def\@enlargethispage#1#2{%
 \begingroup
  \dimen@#2\relax
  \edef\@tempa{#1}%
  \edef\@tempa{\noexpand\@@enlargethispage{\@tempa}{\the\dimen@}}%
  \expandafter\do@output@MVL\expandafter{\@tempa}%
 \endgroup
}%
\def\@@enlargethispage#1#2{%
 \def\@tempa{one}%
 \@ifx{\thepagegrid\@tempa}{%
  \true@sw
 }{%
  \def\@tempa{mlt}%
  \@ifx{\thepagegrid\@tempa}{%
   \@ifnum{\pagegrid@cur=\@ne}{%
    \gdef\enlarge@colroom{#2}%
    \true@sw
   }{%
    \ltxgrid@warn{Too late to enlarge this page; move the command to the first column.}%
    \false@sw
   }%
  }{%
   \ltxgrid@warn{Unable to enlarge a page of this kind.}%
   \false@sw
  }%
 }%
 {%
  \class@info{Enlarging page \thepage\space by #2}%
  \global\advance\@colroom#2\relax
  \set@vsize
 }{%
 }%
}%
\let\enlarge@colroom\@empty
\let\@kludgeins\@undefined
\@booleantrue\textheight@sw
\prepdef\@outputpage@head{%
 \textheight@sw{%
  \count@\vbadness\vbadness\@M
  \dimen@\vfuzz\vfuzz\maxdimen
  \setbox\@outputbox\vbox to\textheight{\unvbox\@outputbox}%
  \vfuzz\dimen@
  \vbadness\count@
 }{}%
}%
\appdef\@outputpage@head{%
 \@ifx{\LS@rot\@undefined}{}{\LS@rot}%
}%
\def\ltxgrid@info{%
 \ltxgrid@info@sw{\class@info}{\@gobble}%
}%
\@booleanfalse\ltxgrid@info@sw
\def\ltxgrid@warn{%
 \ltxgrid@warn@sw{\class@warn}{\@gobble}%
}%
\@booleantrue\ltxgrid@warn@sw
\@booleanfalse\ltxgrid@foot@info@sw
\def\def@next@handler#1#2#3{%
 \advance#1\@ne\mathchardef#2\the#1%
 \expandafter\def\csname output@-\the#1\endcsname{#3}%
}%
\def\def@line@handler#1#2{%
 \begingroup
  \@tempcnta\int@parpenalty
  \advance\@tempcnta-#1%
  \aftergroup\def
  \expandafter\aftergroup\csname output@-\the\@tempcnta\endcsname
 \endgroup{#2}%
}%
\mathchardef\int@parpenalty11012
\def@line@handler\z@{\@handle@line@ltx{}{}{}}%
\def@line@handler\@ne{\@handle@line@ltx{}{}{\brokenpenalty@ltx}}%
\def@line@handler\tw@{\@handle@line@ltx{}{\clubpenalty@ltx}{}}%
\def@line@handler\thr@@{\@handle@line@ltx{\clubpenalty@ltx}{}{\brokenpenalty@ltx}}%
\def@line@handler\f@ur{\@handle@line@ltx{\widowpenalty@ltx}{}{}}%
\def@line@handler{5}{\@handle@line@ltx{\widowpenalty@ltx}{}{\brokenpenalty@ltx}}%
\def@line@handler{6}{\@handle@line@ltx{\widowpenalty@ltx}{\clubpenalty@ltx}{}}%
\def@line@handler{7}{\@handle@line@ltx{\widowpenalty@ltx}{\clubpenalty@ltx}{\brokenpenalty@ltx}}%
\def@line@handler{8}{\@handle@line@ltx{\displaywidowpenalty@ltx}{}{}}%
\def@line@handler{9}{\@handle@line@ltx{\displaywidowpenalty@ltx}{}{\brokenpenalty@ltx}}%
\def@line@handler{10}{\@handle@line@ltx{\displaywidowpenalty@ltx}{\clubpenalty@ltx}{}}%
\def@line@handler{11}{\@handle@line@ltx{\displaywidowpenalty@ltx}{\clubpenalty@ltx}{\brokenpenalty@ltx}}%
\def\@handle@line@ltx#1#2#3{%
 \@@handle@line@ltx
 \@tempcnta\lastpenalty
 \@tempcntb\interlinepenalty@ltx\relax
 \@if@empty{#1}{}{\advance\@tempcntb#1\relax}%
 \@if@empty{#2}{}{\advance\@tempcntb#2\relax}%
 \@if@empty{#3}{}{\advance\@tempcntb#3\relax}%
 \penalty\@ifnum{\@tempcnta<\@tempcntb}{\@tempcntb}{\@tempcnta}%
}%
\let\@@handle@line@ltx\@empty
\@tempcnta\int@parpenalty
\def@next@handler\@tempcnta\int@postparpenalty{\reset@queues@ltx\handle@par@ltx}%
\def@next@handler\@tempcnta\int@vadjustpenalty{\handle@vadjust@ltx}%
\def@next@handler\@tempcnta\int@whatsitpenalty{\handle@whatsit@ltx}%
\def@next@handler\@tempcnta\int@predisplaypenalty{\reset@queues@ltx\@handle@display@ltx{\predisplaypenalty@ltx}}%
\def@next@handler\@tempcnta\int@interdisplaylinepenalty{\@handle@display@ltx{\interdisplaylinepenalty@ltx}}%
\def@next@handler\@tempcnta\int@postdisplaypenalty{\@handle@display@ltx{\postdisplaypenalty@ltx}}%
\def\@handle@display@ltx#1{%
 \@@handle@display@ltx
 \@tempcnta\lastpenalty
 \@tempcntb#1%
 \penalty\@ifnum{\@tempcnta<\@tempcntb}{\@tempcntb}{\@tempcnta}%
}%
\let\@@handle@display@ltx\@empty
\def\handle@par@ltx{}%
\def\set@linepenalties{%
 \expandafter\def\expandafter\interlinepenalty@ltx\expandafter{\the\interlinepenalty}%
 \interlinepenalty-\int@parpenalty
 \expandafter\def\expandafter\brokenpenalty@ltx\expandafter{\the\brokenpenalty}%
 \brokenpenalty\@ne
 \expandafter\def\expandafter\clubpenalty@ltx\expandafter{\the\clubpenalty}%
 \clubpenalty\tw@
 \expandafter\def\expandafter\widowpenalty@ltx\expandafter{\the\widowpenalty}%
 \widowpenalty\f@ur
 \expandafter\def\expandafter\displaywidowpenalty@ltx\expandafter{\the\displaywidowpenalty}%
 \displaywidowpenalty8\relax
}%
\def\restore@linepenalties{%
 \interlinepenalty\interlinepenalty@ltx
 \brokenpenalty\brokenpenalty@ltx
 \clubpenalty\clubpenalty@ltx
 \widowpenalty\widowpenalty@ltx
 \displaywidowpenalty\displaywidowpenalty@ltx
 \relax
}%
\def\set@displaypenalties#1{%
 \expandafter\def\expandafter\predisplaypenalty@ltx\expandafter{\the\predisplaypenalty}%
 \expandafter\def\expandafter\interdisplaylinepenalty@ltx\expandafter{\the\interdisplaylinepenalty}%
 \expandafter\def\expandafter\postdisplaypenalty@ltx\expandafter{\the\postdisplaypenalty}%
 \@ifhmode{\predisplaypenalty-\int@predisplaypenalty\relax}{}%
 #1{\interdisplaylinepenalty-\int@interdisplaylinepenalty\relax}{}%
 #1{\postdisplaypenalty-\int@postdisplaypenalty\relax}{}%
}%
\def\enqueue@whatsit@ltx#1{%
 \gappdef\g@whatsit@queue{{#1}}%
 \vadjust{\penalty-\int@whatsitpenalty}%
}%
\def\handle@whatsit@ltx{%
 \unvbox\@cclv
 \g@pop@ltx\g@whatsit@queue\@tempa
 \expandafter\do@whatsit\expandafter{\@tempa}%
}%
\def\do@whatsit#1{}%
\def\g@pop@ltx#1#2{%
 \expandafter\@g@pop@ltx#1{}{}\@@#1#2%
}%
\def\@g@pop@ltx#1#2\@@#3#4{%
 \gdef#3{#2}%
 \def#4{#1}%
}%
\let\vspace@ltx\vspace
\let\pagebreak@ltx\pagebreak
\let\nopagebreak@ltx\nopagebreak
\let\endline@ltx\\
\let\@arrayparboxrestore@ltx\@arrayparboxrestore
\def\@tempa#1{%
\def\@vspace@org ##1{%
  \ifvmode
    #1% \vskip #1
    \vskip\z@skip
   \else
     \@bsphack
     \vadjust{\@restorepar
              #1% \vskip #1
              \vskip\z@skip
              }%
     \@esphack
   \fi
}%
\def\@vspace@ltx##1{%
 \@ifvmode{%
  #1% \vskip #1
  \vskip\z@skip
 }{%
  \@bsphack
  \ex@vadjust@ltx{%
   \@restorepar
   \nobreak
   #1% \vskip #1
   \vskip\z@skip
  }%
  \@esphack
 }%
}%
\def\@vspacer@org##1{%
  \ifvmode
    \dimen@\prevdepth
    \hrule \@height\z@
    \nobreak
    #1%\vskip #1
    \vskip\z@skip
    \prevdepth\dimen@
  \else
    \@bsphack
    \vadjust{\@restorepar
             \hrule \@height\z@
             \nobreak
             #1%\vskip #1
             \vskip\z@skip}%
    \@esphack
\fi
}%
\def\@vspacer@ltx##1{%
 \@ifvmode{%
  \dimen@\prevdepth
  \hrule\@height\z@
  \nobreak
  #1%\vskip#1
  \vskip\z@skip
  \prevdepth\dimen@
 }{%
  \@bsphack
  \ex@vadjust@ltx{%
   \@restorepar
   \hrule\@height\z@
   \nobreak
   #1%\vskip#1
   \vskip\z@skip
  }%
  \@esphack
 }%
}%
}
\rvtx@ifformat@geq{2020/10/01}%
  {\@tempa{\@vspace@calcify{#1}}}%
  {\@tempa{\vskip #1 }}%
\def\@no@pgbk@org #1[#2]{%
  \ifvmode
    \penalty #1\@getpen{#2}%
  \else
    \@bsphack
    \vadjust{\penalty #1\@getpen{#2}}%
    \@esphack
  \fi
}%
\def\@no@pgbk@ltx#1[#2]{%
 \@ifvmode{%
  \penalty#1\@getpen{#2}%
 }{%
  \@bsphack
  \ex@vadjust@ltx{%
   \penalty#1\@getpen{#2}%
  }%
  \@esphack
 }%
}%
\rvtx@ifformat@geq{2020/02/02}%
{\protected}{\long}\def\end@line@org{%
 \let\reserved@e\relax
 \let\reserved@f\relax
 \@ifstar{%
  \let\reserved@e\vadjust
  \let\reserved@f\nobreak
  \@xnewline
 }%
 \@xnewline
}%
\rvtx@ifformat@geq{2020/02/02}%
{\protected}{\long}\def\end@line@ltx{%
 \let\reserved@e\relax
 \let\reserved@f\relax
 \@ifstar{%
  \let\reserved@e\ex@vadjust@ltx
  \let\reserved@f\nobreak
  \@xnewline
 }{%
  \@xnewline
 }%
}%
\def\@tempa#1{%
  \def\@newline@org[##1]{%
   \let\reserved@e\vadjust
   \@gnewline{#1}% \vskip#1
  }%
  \def\@newline@ltx[##1]{%
   \let\reserved@e\ex@vadjust@ltx
   \@gnewline{#1}% \vskip#1
  }%
}
\rvtx@ifformat@geq{2020/10/01}%
  {\@tempa{\@vspace@calcify{#1}}}%
  {\@tempa{\vskip #1}}%
 \@ifx{\@vspace\@vspace@org}{%
  \@ifx{\@vspacer\@vspacer@org}{%
   \@ifx{\@no@pgbk\@no@pgbk@org}{%
    \@ifx{\@newline\@newline@org}{%
     \expandafter\@ifx\expandafter{%
       \csname\rvtx@ifformat@geq{2020/02/02}%
         {\expandafter\@gobble\string\\}%
         {\expandafter\@gobble\string\\ }\endcsname
       \end@line@org
     }{%
       \true@sw
     }{\false@sw}%
    }{\false@sw}%
   }{\false@sw}%
  }{\false@sw}%
 }{\false@sw}%
 {%
  \class@info{Overriding \string\@vspace, \string\@vspacer, \string\@no@pgbk, \string\@newline, and \string\\ }%
  \let\@normalcr\end@line@ltx
  \expandafter\let
    \csname\rvtx@ifformat@geq{2020/02/02}%
      {\expandafter\@gobble\string\\}%
      {\expandafter\@gobble\string\\ }\endcsname\@normalcr
  \let\@newline\@newline@ltx
  \let\@vspace\@vspace@ltx
  \let\@vspacer\@vspacer@ltx
  \let\@no@pgbk\@no@pgbk@ltx
 }{%
  \class@warn{%
   Failed to recognize \string\@vspace, \string\@vspacer, \string\@no@pgbk, \string\@newline, and \string\\;
   no patches applied. Please get a more up-to-date class,
  }%
 }%
\let\ex@vadjust@ltx\vadjust
\def\enqueue@vadjust@ltx#1{%
 \gappdef\g@vadjust@queue{{#1}}%
 \vadjust{\penalty-\int@vadjustpenalty}%
}%
\def\handle@vadjust@ltx{%
 \unvbox\@cclv
 \g@pop@ltx\g@vadjust@queue\@tempa
 \expandafter\gappdef\expandafter\g@vadjust@line\expandafter{\@tempa}%
}%
\let\g@vadjust@line\@empty
\def\reset@queues@ltx{%
 \global\let\g@whatsit@queue\@empty
 \global\let\g@vadjust@queue\@empty
}%
\newcommand\linenomathWithnumbers@LN{%
  \ifLineNumbers
    \ifnum\interlinepenalty>-\linenopenaltypar
      \global\holdinginserts\thr@@
      \advance\interlinepenalty \linenopenalty
     \ifhmode
      \advance\predisplaypenalty \linenopenalty
     \fi
      \advance\postdisplaypenalty \linenopenalty
      \advance\interdisplaylinepenalty \linenopenalty
    \fi
  \fi
  \ignorespaces
}%
\newcommand\linenomathNonumbers@LN{%
  \ifLineNumbers
    \ifnum\interlinepenalty>-\linenopenaltypar
      \global\holdinginserts\thr@@
      \advance\interlinepenalty \linenopenalty
     \ifhmode
      \advance\predisplaypenalty \linenopenalty
     \fi
    \fi
  \fi
  \ignorespaces
}%
\def\endlinenomath@LN{%
  \ifLineNumbers
   \global\holdinginserts\@LN@outer@holdins
  \fi
  \global\@ignoretrue
}
\def\linenumberpar@LN{%
  \ifvmode \@@@par \else
    \ifinner \@@@par \else
      \xdef\@LN@outer@holdins{\the\holdinginserts}%
      \advance \interlinepenalty \linenopenalty
      \linenoprevgraf \prevgraf
      \global \holdinginserts \thr@@
      \@@@par
      \ifnum\prevgraf>\linenoprevgraf
        \penalty-\linenopenaltypar
      \fi
      \@LN@parpgbrk
      \global\holdinginserts\@LN@outer@holdins
      \advance\interlinepenalty -\linenopenalty
    \fi
  \fi
}%
\appdef\class@documenthook{%
 \@ifpackageloaded{lineno}{%
  \@ifx{\linenomathWithnumbers\linenomathWithnumbers@LN}{%
   \@ifx{\linenomathNonumbers\linenomathNonumbers@LN}{%
    \@ifx{\endlinenomath\endlinenomath@LN}{%
     \@ifx{\linenumberpar\linenumberpar@LN}{%
      \true@sw
     }{\false@sw}%
    }{\false@sw}%
   }{\false@sw}%
  }{\false@sw}%
  {%
   \class@info{Overriding lineo.sty, restoring output routine,}%
   \let\linenumberpar\linenumberpar@ltx
   \let\endlinenomath\endlinenomath@ltx
   \expandafter\let\csname endlinenomath*\endcsname\endlinenomath@ltx
   \let\linenomathWithnumbers\linenomathWithnumbers@ltx
   \let\linenomathNonumbers\linenomathNonumbers@ltx
   \let\ex@vadjust@ltx\ex@vadjust@line
   \let\@LN@postlabel\enqueue@whatsit@ltx
   \let\do@whatsit\write@linelabel
   \let\handle@par@ltx\handle@par@LN
   \let\@@handle@line@ltx\Make@LineNo@ltx
   \let\@@handle@display@ltx\Make@LineNo@ltx
   \output@latex{\natural@output}%
   \let\vspace\vspace@ltx
   \let\pagebreak\pagebreak@ltx
   \let\nopagebreak\nopagebreak@ltx
   \let\@arrayparboxrestore\@arrayparboxrestore@ltx
   \let\\\endline@ltx
   \appdef\set@footnotefont{%
    \let\par\@@@par
    \let\@@par\@@@par
   }%
   \@if@sw\ifLineNumbers\fi{%
    \class@info{Reinvoke \string\linenumbers}%
    \let\@@par\linenumberpar
    \@ifx{\@par\linenumberpar@LN}{\let\@par\linenumberpar}{}%
    \@ifx{\par\linenumberpar@LN}{\let\par\linenumberpar}{}%
   }{%
    \class@info{Line numbering not turned on yet}%
   }%
  }{%
   \class@warn{Failed to recognize lineno.sty procedures; no patches applied. Please get a more up-to-date class.}%
  }%
 }{%
 }%
}%
\def\linenumberpar@ltx{\@ifvmode{\@@@par}{\@linenumberpar}}%
\def\@linenumberpar{%
   \linenoprevgraf\prevgraf
   \set@linepenalties
   \@@@par
   \@ifnum{\prevgraf>\linenoprevgraf}{
    \penalty-\int@postparpenalty
   }{}%
   \@LN@parpgbrk
   \restore@linepenalties
}%
\newcommand\linenomathWithnumbers@ltx{\@linenomathnumbers@ltx\true@sw}%
\newcommand\linenomathNonumbers@ltx{\@linenomathnumbers@ltx\false@sw}%
\def\@linenomathnumbers@ltx#1{%
 \@if@sw\ifLineNumbers\fi{%
   \set@linepenalties
   \set@displaypenalties#1%
 }{}%
 \ignorespaces
}%
\def\endlinenomath@ltx{%
 \global\@ignoretrue
}%
\def\handle@par@LN{%
 \Make@LineNo@ltx
 \@tempcnta\lastpenalty
 \@ifnum{\@tempcnta=\z@}{}{%
  \expandafter\gdef
  \expandafter\@LN@parpgbrk
  \expandafter{%
   \expandafter\penalty
               \the\@tempcnta
   \global\let\@LN@parpgbrk\@LN@screenoff@pen
  }%
 }%
}%
\def\Make@LineNo@ltx{%
 \@LN@maybe@normalLineNumber
 \boxmaxdepth\maxdimen\setbox\z@\vbox{\unvbox\@cclv}%
 \@tempdima\dp\z@
 \unvbox\z@
 \sbox\@tempboxa{\hb@xt@\z@{\makeLineNumber}}%
 \ht\@tempboxa\z@
 \@LN@depthbox
 \stepLineNumber
 \g@vadjust@line
 \global\let\g@vadjust@line\@empty
}%
\def\write@linelabel#1{%
 \protected@write\@auxout{}{%
  \string\newlabel{#1}{{\theLineNumber}{\thepage}{}{}{}}%
 }%
}%
\def\ex@vadjust@line{%
 \@if@sw\ifLineNumbers\fi{\enqueue@vadjust@ltx}{\vadjust}%
}%
\endinput
%%
%% End of file `ltxgrid.sty'.
