From 1ede6fca8198bebb44106abace1cde6e5aa8e57f Mon Sep 17 00:00:00 2001
From: ottjk <joshott16@gmail.com>
Date: Sun, 7 Jan 2024 14:16:36 -0500
Subject: removed unused latex stuff

---
 texmf/tex/latex/revtex/revtex4.cls | 7670 ------------------------------------
 1 file changed, 7670 deletions(-)
 delete mode 100644 texmf/tex/latex/revtex/revtex4.cls

(limited to 'texmf/tex/latex/revtex/revtex4.cls')

diff --git a/texmf/tex/latex/revtex/revtex4.cls b/texmf/tex/latex/revtex/revtex4.cls
deleted file mode 100644
index bd6244a..0000000
--- a/texmf/tex/latex/revtex/revtex4.cls
+++ /dev/null
@@ -1,7670 +0,0 @@
-%%
-%% This is file `revtex4-2.cls',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% revtex4-2.dtx  (with options: `kernel')
-%% ltxutil.dtx  (with options: `kernel')
-%% ltxfront.dtx  (with options: `kernel')
-%% ltxgrid.dtx  (with options: `kernel')
-%% revtex4-2.dtx  (with options: `options')
-%% ltxutil.dtx  (with options: `options')
-%% ltxfront.dtx  (with options: `options')
-%% ltxgrid.dtx  (with options: `options')
-%% revtex4-2.dtx  (with options: `package')
-%% 
-%% This file is part of the APS files in the REVTeX 4 distribution.
-%% For the version number, search on the string 
-%% Original version by David Carlisle
-%% Modified by Arthur Ogawa (mailto:arthur_ogawa at sbcglobal dot net)
-%% 
-%% Version (4.2a, unreleased)
-%% Modified by Aptara on behalf of American Physical Society and American Institute of Physics
-%% 
-%% Version (4.2b,4.2c)
-%% Modified by Mark Doyle, American Physical Society (mailto:revtex at aps.org)
-%% 
-%% Version (4.2d,4.2e)
-%% Modified by Phelype Oleinik for the American Physical Society (mailto:phelype.oleinik at latex-project.org)
-%% 
-%% Copyright (c) 2019--2020 American Physical Society.
-%% https://journals.aps.org/revtex/
-%% mailto:revtex@aps.org
-%% 
-%% See the REVTeX 4.2 README-REVTEX file for restrictions and more information.
-%% 
-\NeedsTeXFormat{LaTeX2e}[1996/12/01]%
-\ProvidesClass{revtex4-2}
- [2020/10/03 4.2e (https://journals.aps.org/revtex/ for documentation)]% \fileversion
-\let\class@name\@gtempa
-\GenericInfo{}{\space
- Copyright (c) 2019 American Physical Society.^^J
- mailto:revtex@aps.org^^J
- Licensed under the LPPL:^^Jhttp://www.ctan.org/tex-archive/macros/latex/base/lppl.txt^^J
- Arthur Ogawa <arthur_ogawa at sbcglobal dot net>^^J
- Based on work by David Carlisle <david at dcarlisle.demon.co.uk>^^J
- Version (4.2d,4.2e): Modified by Mark Doyle and Phelype Oleinik^^J
- \@gobble
-}%
-\if@compatibility
-  \edef\reserved@a{\errhelp{%
-   Change your \string\documentstyle\space statement to
-   \string\documentclass\space and rerun.
-  }}\reserved@a
-  \errmessage{You cannot run \class@name\space in compatability mode}%
-  \expandafter\@@end
-\fi
-\typeout{%
-ltxutil%
- [2020/10/03 4.2e utilities package (portions licensed from W. E. Baxter web at superscript.com)]% \fileversion
-}%
-\def\class@err#1{\ClassError{\class@name}{#1}\@eha}%
-\def\class@warn#1{\ClassWarningNoLine{\class@name}{#1}}%
-\def\class@info#1{\ClassInfo{\class@name}{#1}}%
-\def\obsolete@command#1{%
- \class@warn@end{Command \string#1\space is obsolete.^^JPlease remove from your document}%
- \global\let#1\@empty
- #1%
-}%
-\def\replace@command#1#2{%
- \class@warn@end{Command \string#1\space is obsolete;^^JUse \string#2\space instead}%
- \global\let#1#2%
- #1%
-}%
-\def\replace@environment#1#2{%
- \class@warn@end{Environment #1 is obsolete;^^JUse #2 instead}%
- \glet@environment{#1}{#2}%
- \@nameuse{#1}%
-}%
-\def\incompatible@package#1{%
- \@ifpackageloaded{#1}{%
-  \def\@tempa{I cannot continue. You must remove the \string\usepackage\ statement that caused that package to be loaded.}%
-  \ClassError{\class@name}{The #1 package cannot be used with \class@name}%
-  \@tempa\stop
- }{%
-  \class@info{#1 was not loaded (OK!)}%
- }%
-}%
-\def\class@warn@end#1{%
- \gappdef\class@enddocumenthook{\class@warn{#1}}%
-}%
-\ifx\undefined\class@name
- \def\class@name{ltxutil}%
- \class@warn{You should define the class name before reading in this package. Using default}%
-\fi
-\def\t@{to}%
-\dimendef\dimen@iii\thr@@
-\def\halignt@{\halign\t@}%
-\chardef\f@ur=4\relax
-\chardef\cat@letter=11\relax
-\chardef\other=12\relax
-\def\let@environment#1#2{%
- \expandafter\let
- \csname#1\expandafter\endcsname\csname#2\endcsname
- \expandafter\let
- \csname end#1\expandafter\endcsname\csname end#2\endcsname
-}%
-\def\glet@environment#1#2{%
- \global\expandafter\let
- \csname#1\expandafter\endcsname\csname#2\endcsname
- \global\expandafter\let
- \csname end#1\expandafter\endcsname\csname end#2\endcsname
-}%
-\newcommand\tracingplain{%
- \tracingonline\z@\tracingcommands\z@\tracingstats\z@
- \tracingpages\z@\tracingoutput\z@\tracinglostchars\@ne
- \tracingmacros\z@\tracingparagraphs\z@\tracingrestores\z@
- \showboxbreadth5\showboxdepth3\relax %\errorstopmode
- }%
-\newcommand\traceoutput{%
- \appdef\@resetactivechars{\showoutput}%
-}%
-\newcommand\say[1]{\typeout{<\noexpand#1=\meaning#1>}}%
-\newcommand\saythe[1]{\typeout{<\noexpand#1=\the#1>}}%
-\def\fullinterlineskip{\prevdepth\z@}%
-\countdef\count@i\@ne
-\countdef\count@ii\tw@
-\long\def\prepdef#1#2{%
- \@ifxundefined#1{\toks@{}}{\toks@\expandafter{#1}}%
- \toks@ii{#2}%
- \edef#1{\the\toks@ii\the\toks@}%
-}%
-\long\def\appdef#1#2{%
- \@ifxundefined#1{\toks@{}}{\toks@\expandafter{#1}}%
- \toks@ii{#2}%
- \edef#1{\the\toks@\the\toks@ii}%
-}%
-\long\def\gappdef#1#2{%
- \@ifxundefined#1{\toks@{}}{\toks@\expandafter{#1}}%
- \toks@ii{#2}%
- \global\edef#1{\the\toks@\the\toks@ii}%
-}%
-\long\def\appdef@val#1#2{%
- \appdef#1{{#2}}%
-}%
-\long\def\appdef@e#1#2{%
- \expandafter\appdef
- \expandafter#1%
- \expandafter{#2}%
-}%
-\long\def\appdef@eval#1#2{%
- \expandafter\appdef@val
- \expandafter#1%
- \expandafter{#2}%
-}%
-\toksdef\toks@ii=\tw@
-\long\def\@ifxundefined#1{\@ifx{\undefined#1}}%
-\long\def\@ifnotrelax#1#2#3{\@ifx{\relax#1}{#3}{#2}}%
-\long\def\@argswap#1#2{#2#1}%
-\long\def\@argswap@val#1#2{#2{#1}}%
-\def\@ifxundefined@cs#1{\expandafter\@ifx\expandafter{\csname#1\endcsname\relax}}%
-\ifx\IfFormatAtLeastTF\undefined
-  \def\rvtx@ifformat@geq{\@ifl@t@r\fmtversion}%
-\else
-  \let\rvtx@ifformat@geq\IfFormatAtLeastTF
-\fi
-\def\@boolean#1#2{%
-  \long\def#1{%
-    #2% \if<something>
-      \expandafter\true@sw
-    \else
-      \expandafter\false@sw
-    \fi
-  }%
-}%
-\def\@boole@def#1#{\@boolean{#1}}% Implicit #2
-\def\@booleantrue#1{\let#1\true@sw}%
-\def\@booleanfalse#1{\let#1\false@sw}%
-\@boole@def\@ifx#1{\ifx#1}%
-\@boole@def\@ifx@empty#1{\ifx\@empty#1}%
-\@boole@def\@if@empty#1{\if!#1!}%
-\def\@if@sw#1#2{#1\expandafter\true@sw\else\expandafter\false@sw#2}%
-\@boole@def\@ifdim#1{\ifdim#1}%
-\@boole@def\@ifeof#1{\ifeof#1}%
-\@boole@def\@ifhbox#1{\ifhbox#1}%
-\@boole@def\@ifhmode{\ifhmode}%
-\@boole@def\@ifinner{\ifinner}%
-\@boole@def\@ifmmode{\ifmmode}%
-\@boole@def\@ifnum#1{\ifnum#1}%
-\@boole@def\@ifodd#1{\ifodd#1}%
-\@boole@def\@ifvbox#1{\ifvbox#1}%
-\@boole@def\@ifvmode{\ifvmode}%
-\@boole@def\@ifvoid#1{\ifvoid#1}%
-\long\def\true@sw#1#2{#1}%
-\long\def\false@sw#1#2{#2}%
-\long\def\loopuntil#1{#1{}{\loopuntil{#1}}}%
-\long\def\loopwhile#1{#1{\loopwhile{#1}}{}}%
-\def\@provide#1{%
- \@ifx{\undefined#1}{\true@sw}{\@ifx{\relax#1}{\true@sw}{\false@sw}}%
- {\def#1}{\def\j@nk}%
-}%
-\rvtx@ifformat@geq{2020-10-01}%
-  {%
-    \AddToHook{begindocument/before}{\document@inithook}%
-  }{%
-    \prepdef\document{%
-     \endgroup
-     \document@inithook
-     \true@sw{}%
-    }%
-  }
-\let\document@inithook\@empty
-\appdef\document@inithook{%
- \AtBeginDocument{\class@documenthook}%
-}%
-\AtEndDocument{%
- \class@enddocumenthook
-}%
-\let\class@documenthook\@empty
-\let\class@enddocumenthook\@empty
-\rvtx@ifformat@geq{2020-10-01}{%
-  % <definitions for newer LaTeX later>
-}{%
-  % <definitions for older LaTeX>
-\def\enddocument{%
- \let\AtEndDocument\@firstofone
- \@enddocumenthook
- \@checkend{document}%
- \clear@document
- \check@aux
- \deadcycles\z@
- \@@end
-}%
-\def\check@aux{\do@check@aux}%
-\def\do@check@aux{%
- \@if@sw\if@filesw\fi{%
-  \immediate\closeout\@mainaux
-  \let\@setckpt\@gobbletwo
-  \let\@newl@bel\@testdef
-  \@tempswafalse
-  \makeatletter
-  \input\jobname.aux\relax
- }{}%
- \@dofilelist
- \@ifdim{\font@submax >\fontsubfuzz\relax}{%
-  \@font@warning{%
-   Size substitutions with differences\MessageBreak
-   up to \font@submax\space have occured.\@gobbletwo
-  }%
- }{}%
- \@defaultsubs
- \@refundefined
- \@if@sw\if@filesw\fi{%
-  \@ifx{\@multiplelabels\relax}{%
-   \@if@sw\if@tempswa\fi{%
-    \@latex@warning@no@line{%
-     Label(s) may have changed.
-     Rerun to get cross-references right%
-    }%
-   }{}%
-  }{%
-    \@multiplelabels
-  }%
- }{}%
-}%
-}
-\rvtx@ifformat@geq{2020-10-01}{%
-  \AddToHook{enddocument}{\rvtx@enddocument@patch{}}%
-}{}
-\protected\long\def\rvtx@enddocument@patch#1#2\@checkend#3{%
-  \begingroup
-    \edef\x{\detokenize{#3}}%
-    \edef\y{\detokenize{document}}%
-  \expandafter\endgroup
-  \ifx\x\y
-    \expandafter\rvtx@enddocument@patch@end
-  \else
-    \expandafter\rvtx@enddocument@patch@more
-  \fi
-    {#1#2}{#3}}
-\def\rvtx@enddocument@patch@more#1#2{%
-  \rvtx@enddocument@patch{#1\@checkend{#2}}}
-\long\def\rvtx@enddocument@patch@end#1#2\clearpage#3\endgroup{%
-  \def\do@check@aux{#3\endgroup}%
-  #1%
-  \@checkend{#2}%
-  \clear@document
-  \check@aux}
-\def\check@aux{\do@check@aux}%
-\def\clear@document{%
- \clearpage
- \do@output@cclv{%
-  \Call@AfterLastShipout
- }%
-}%
-\appdef\class@documenthook{%
- \providecommand\Call@AfterLastShipout{}%
-}%
-\def\class@extension#1#2{%
- \IfFileExists{#1.#2}{%
-  \expandafter\class@extensionfile\csname ver@\@currname.\@currext\endcsname{#1}#2%
- }{%
-  \csname rtx@#1\endcsname
- }%
-}%
-\def\class@extensionfile#1#2#3{%
- \@pass@ptions#3\@unusedoptionlist{#2}%
- \global\let\@unusedoptionlist\@empty
- \expandafter\class@ext@hook\csname#2.#3-h@@k\endcsname#1{#2}#3%
-}%
-\def\class@ext@hook#1#2#3#4{%
- \@pushfilename@ltx
- \makeatletter
- \let\CurrentOption\@empty
- \@reset@ptions
- \let#1\@empty
- \xdef\@currname{#3}%
- \global\let\@currext#4%
- \global\let\@clsextension\@currext
- \input{#3.#4}%
- \@ifl@ter#4{#3}#2{%
-  \class@info{Class extension later than: #2}%
- }{%
-  \class@info{Class extension earlier: #2}%
-  \@@end
- }%
- #1%
- \let#1\@undefined
- \expandafter\@p@pfilename@ltx\@currnamestack@ltx\@nil
- \@reset@ptions
-}%
-\def\@pushfilename@ltx{%
- \xdef\@currnamestack@ltx{%
-  {\@currname}%
-  {\@currext}%
-  {\@clsextension}%
-  {\the\catcode`\@}%
-  \@currnamestack@ltx
- }%
-}%
-\def\@p@pfilename@ltx#1#2#3#4#5\@nil{%
- \gdef\@currname{#1}%
- \gdef\@currext{#2}%
- \gdef\@clsextension{#3}%
- \catcode`\@#4\relax
- \gdef\@currnamestack@ltx{#5}%
-}%
-\global\let\@currnamestack@ltx\@empty
-\def\flushing{%
-  \let\\\@normalcr
-  \leftskip\z@skip
-  \rightskip\z@skip
-  \@rightskip\z@skip
-  \parfillskip\@flushglue
-}%
-\expandafter\DeclareRobustCommand\expandafter\@centercr\expandafter{\@centercr}%
-\def\eqnarray@LaTeX{%
-   \stepcounter{equation}%
-   \def\@currentlabel{\p@equation\theequation}%
-   \global\@eqnswtrue
-   \m@th
-   \global\@eqcnt\z@
-   \tabskip\@centering
-   \let\\\@eqncr
-   $$\everycr{}\halign to\displaywidth\bgroup
-       \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
-      &\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
-      &\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
-         $\displaystyle{##}$\hfil\tabskip\@centering
-      &\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
-         \tabskip\z@skip
-      \cr
-}
-\long\def\eqnarray@fleqn@fixed{%
- \stepcounter{equation}\def\@currentlabel{\p@equation\theequation}%
- \global\@eqnswtrue\m@th\global\@eqcnt\z@
- \tabskip\ltx@mathindent
- \let\\=\@eqncr
- \setlength\abovedisplayskip{\topsep}%
- \ifvmode\addtolength\abovedisplayskip{\partopsep}\fi
- \addtolength\abovedisplayskip{\parskip}%
- \setlength\belowdisplayskip{\abovedisplayskip}%
- \setlength\belowdisplayshortskip{\abovedisplayskip}%
- \setlength\abovedisplayshortskip{\abovedisplayskip}%
- $$%
- \everycr{}%
- \halignt@\linewidth\bgroup
-  \hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
-  &\global\@eqcnt\@ne
-   \hskip\tw@\eqncolsep
-   \hfil${{}##{}}$\hfil
-  &\global\@eqcnt\tw@
-   \hskip\tw@\eqncolsep
-   $\displaystyle{##}$\hfil\tabskip\@centering
-  &\global\@eqcnt\thr@@\hb@xt@\z@\bgroup\hss##\egroup
-   \tabskip\z@skip
-  \cr
-}%
-\@ifx{\eqnarray\eqnarray@LaTeX}{%
- \class@info{Repairing broken LaTeX eqnarray}%
- \let\eqnarray\eqnarray@fleqn@fixed
- \newlength\eqncolsep
- \setlength\eqncolsep\z@
- \let\eqnarray@LaTeX\relax
- \let\eqnarray@fleqn@fixed\relax
-}{}%
-\def\ltx@mathindent{\@centering}%
-\def\set@eqnarray@skips{}%
-\def\prep@math{%
- \@ifvmode{\everypar{{\setbox\z@\lastbox}}}{}%
-}%
-\def\prep@math@patch{%
- \prepdef\equation{\prep@math}%
- \prepdef\eqnarray{\prep@math}%
-}%
-\def\footnote{\@ifnextchar[\ltx@xfootnote\ltx@yfootnote}%
-\def\ltx@xfootnote[#1]{%
- \ltx@def@footproc\ltx@footmark[#1]%
- \expandafter\ltx@foottext\expandafter{\the\csname c@\@mpfn\endcsname}%
-}%
-\def\ltx@yfootnote{%
- \ltx@stp@footproc\ltx@footmark
- \expandafter\ltx@foottext\expandafter{\the\csname c@\@mpfn\endcsname}%
-}%
-\def\footnotemark{\@ifnextchar[\ltx@xfootmark\ltx@yfootmark}%
-\def\ltx@xfootmark{\ltx@def@footproc\ltx@footmark}%
-\def\ltx@yfootmark{\ltx@stp@footproc\ltx@footmark}%
-\def\ltx@footmark#1{%
- \leavevmode
- \ifhmode\edef\@x@sf{\the\spacefactor}\nobreak\fi
- \begingroup
-  \expandafter\ltx@make@current@footnote\expandafter{\@mpfn}{#1}%
-  \expandafter\@argswap@val\expandafter{\Hy@footnote@currentHref}{\hyper@linkstart {link}}%
-   \@makefnmark
-  \hyper@linkend
- \endgroup
- \ifhmode\spacefactor\@x@sf\fi
- \relax
-}%
-\def\footnotetext{\@ifnextchar[\ltx@xfoottext\ltx@yfoottext}%
-\def\ltx@xfoottext{\ltx@def@footproc\ltx@foottext}%
-\def\ltx@yfoottext{\ltx@stp@footproc\ltx@foottext}%
-\long\def\ltx@foottext#1#2{%
- \begingroup
-  \expandafter\ltx@make@current@footnote\expandafter{\@mpfn}{#1}%
-  \@footnotetext{#2}%
- \endgroup
-}%
-\def\ltx@def@footproc#1[#2]{%
- \begingroup
-   \csname c@\@mpfn\endcsname #2\relax
-   \unrestored@protected@xdef\@thefnmark{\thempfn}%
- \expandafter\endgroup
- \expandafter#1%
- \expandafter{\the\csname c@\@mpfn\endcsname}%
-}%
-\def\ltx@stp@footproc#1{%
- \expandafter\stepcounter\expandafter{\@mpfn}%
- \protected@xdef\@thefnmark{\thempfn}%
- \expandafter#1%
- \expandafter{\the\csname c@\@mpfn\endcsname}%
-}%
-\appdef\class@documenthook{%
- \let\footnote@latex\footnote
- \@ifpackageloaded{hyperref}{}{%
-  \let\H@@footnotetext\@footnotetext
-  \def\@footnotetext{\H@@footnotetext}%
-  \let\H@@mpfootnotetext\@mpfootnotetext
-  \def\@mpfootnotetext{\H@@mpfootnotetext}%
- }%
-}%
-\def\ltx@make@current@footnote#1#2{%
-  \csname c@#1\endcsname#2\relax
-  \protected@edef\Hy@footnote@currentHref{\@currentHref-#1.\csname the#1\endcsname}%
-}%
-\def\thempfootnote@latex{{\itshape \@alph \c@mpfootnote }}%
-\def\ltx@thempfootnote{\@alph\c@mpfootnote}%
-\@ifx{\thempfootnote\thempfootnote@latex}{%
- \class@info{Repairing hyperref-unfriendly LaTeX definition of \string\mpfootnote}%
- \let\thempfootnote\ltx@thempfootnote
-}{}%
-\def\@makefnmark{%
- \hbox{%
-  \@textsuperscript{%
-   \normalfont\itshape\@thefnmark
-  }%
- }%
-}%
-\long\def\@footnotetext{%
- \insert\footins\bgroup
-  \make@footnotetext
-}%
-\long\def\@mpfootnotetext{%
- \minipagefootnote@pick
-  \make@footnotetext
-}%
-\long\def\make@footnotetext#1{%
-  \set@footnotefont
-  \set@footnotewidth
-  \@parboxrestore
-  \protected@edef\@currentlabel{%
-   \csname p@\@mpfn\endcsname\@thefnmark
-  }%
-  \color@begingroup
-   \@makefntext{%
-    \rule\z@\footnotesep\ignorespaces#1%
-    \@finalstrut\strutbox\vadjust{\vskip\z@skip}%
-   }%
-  \color@endgroup
- \minipagefootnote@drop
-}%
-\def\set@footnotefont{%
-  \reset@font\footnotesize
-  \interlinepenalty\interfootnotelinepenalty
-  \splittopskip\footnotesep
-  \splitmaxdepth\dp\strutbox
-}%
-\def\set@footnotewidth{\set@footnotewidth@one}%
-\def\robustify@contents{%
- \let \label \@gobble
- \let \index \@gobble
- \let \glossary \@gobble
- \let\footnote \@gobble
- \def\({\string\(}%
- \def\){\string\)}%
- \def\\{\string\\}%
-}%
-\long\def\addtocontents#1#2{%
- \protected@write\@auxout{\robustify@contents}{\string \@writefile {#1}{#2}}%
-}%
-\def\addcontentsline#1#2#3{%
- \addtocontents{#1}{%
-  \protect\contentsline{#2}{#3}{\thepage}{}%
- }%
-}%
-\def\label#1{%
- \@bsphack
-  \protected@write\@auxout{}{%
-   \string\newlabel{#1}{{\@currentlabel}{\thepage}{}{}{}}%
-  }%
- \@esphack
-}%
-\def\ltx@contentsline#1{%
- \expandafter\@ifnotrelax\csname l@#1\endcsname{}{%
-  \expandafter\let\csname l@#1\endcsname\@gobbletwo
- }%
- \contentsline@latex{#1}%
-}%
-\appdef\document@inithook{%
- \let\contentsline@latex\contentsline
- \let\contentsline\ltx@contentsline
-}%
-\appdef\class@documenthook{%
- \prepdef\caption{\minipagefootnote@here}%
-}%
-\def\minipagefootnote@init{%
- \setbox\@mpfootins\box\voidb@x
-}%
-\def\minipagefootnote@pick{%
- \global\setbox\@mpfootins\vbox\bgroup
-  \unvbox\@mpfootins
-}%
-\def\minipagefootnote@drop{%
- \egroup
-}%
-\def\minipagefootnote@here{%
-    \par
-    \@ifvoid\@mpfootins{}{%
-      \vskip\skip\@mpfootins
-      \fullinterlineskip
-      \@ifinner{%
-       \vtop{\unvcopy\@mpfootins}%
-       {\setbox\z@\lastbox}%
-      }{}%
-      \unvbox\@mpfootins
-    }%
-}%
-\def\minipagefootnote@foot{%
- \@ifvoid\@mpfootins{}{%
-  \insert\footins\bgroup\unvbox\@mpfootins\egroup
- }%
-}%
-\def\endminipage{%
-    \par
-    \unskip
-    \minipagefootnote@here
-    \@minipagefalse   %% added 24 May 89
-  \color@endgroup
-  \egroup
-  \expandafter\@iiiparbox\@mpargs{\unvbox\@tempboxa}%
-}%
-\@booleantrue\floats@sw
-\let\@xfloat@LaTeX\@xfloat
-\def\@xfloat#1[#2]{%
-  \@xfloat@prep
-  \@nameuse{fp@proc@#2}%
-  \floats@sw{\@xfloat@LaTeX{#1}[#2]}{\@xfloat@anchored{#1}[]}%
-}%
-\def\@xfloat@prep{%
-  \ltx@footnote@pop
-  \def\@mpfn{mpfootnote}%
-  \def\thempfn{\thempfootnote}%
-  \c@mpfootnote\z@
-  \let\H@@footnotetext\H@@mpfootnotetext
-}%
-\let\ltx@footnote@pop\@empty
-\def\@xfloat@anchored#1[#2]{%
- \def\@captype{#1}%
- \begin@float@pagebreak
-  \let\end@float\end@float@anchored
-  \let\end@dblfloat\end@float@anchored
-        \hsize\columnwidth
-        \@parboxrestore
-        \@floatboxreset
-  \minipagefootnote@init
-}%
-\def\end@float@anchored{%
-  \minipagefootnote@here
-  \par\vskip\z@skip
- \par
- \end@float@pagebreak
-}%
-\def\begin@float@pagebreak{\par\addvspace\intextsep}%
-\def\end@float@pagebreak{\par\addvspace\intextsep}%
-\def\@mpmakefntext#1{%
- \parindent=1em
- \noindent
- \hb@xt@1em{\hss\@makefnmark}%
- #1%
-}%
-\def\do@if@floats#1#2{%
- \floats@sw{}{%
-  \expandafter\newwrite
-              \csname#1write\endcsname
-  \expandafter\def
-              \csname#1@stream\endcsname{\jobname#2}%
-  \expandafter\immediate
-  \expandafter\openout
-              \csname#1write\endcsname
-              \csname#1@stream\endcsname\relax
-  \@ifxundefined\@float@LaTeX{%
-   \let\@float@LaTeX\@float
-   \let\@dblfloat@LaTeX\@dblfloat
-   \let\@float\write@float
-   \let\@dblfloat\write@floats
-  }{}%
-  \let@environment{#1@float}{#1}%
-  \let@environment{#1@floats}{#1*}%
-  \@ifxundefined@cs{#1@write}{}{%
-   \let@environment{#1}{#1@write}%
-  }%
- }%
-}%
-\def\triggerpar{\leavevmode\@@par}%
-\def\oneapage{\def\begin@float@pagebreak{\newpage}\def\end@float@pagebreak{\newpage}}%
-\def\print@float#1#2{%
- \lengthcheck@sw{%
-  \total@float{#1}%
- }{}%
- \@ifxundefined@cs{#1write}{}{%
-  \begingroup
-   \@booleanfalse\floats@sw
-   #2%
-   \raggedbottom
-   \def\array@default{v}% floats must
-   \let\@float\@float@LaTeX
-   \let\@dblfloat\@dblfloat@LaTeX
-   \let\trigger@float@par\triggerpar
-   \let@environment{#1}{#1@float}%
-   \let@environment{#1*}{#1@floats}%
-   \expandafter\prepdef\csname#1\endcsname{\trigger@float@par}%
-   \expandafter\prepdef\csname#1*\endcsname{\trigger@float@par}%
-   \@namedef{fps@#1}{h!}%
-   \expandafter\immediate
-   \expandafter\closeout
-               \csname#1write\endcsname
-   \everypar{%
-    \global\let\trigger@float@par\relax
-    \global\everypar{}\setbox\z@\lastbox
-    \@ifxundefined@cs{#1sname}{}{%
-     \begin@float@pagebreak
-     \expandafter\section
-     \expandafter*%
-     \expandafter{%
-                  \csname#1sname\endcsname
-                 }%
-    }%
-   }%
-   \input{\csname#1@stream\endcsname}%
-  \endgroup
-  \global\expandafter\let\csname#1write\endcsname\relax
- }%
-}%
-\chardef\@xvi=16\relax
-\mathchardef\@twopowerfourteen="4000
-\mathchardef\@twopowertwo="4
-\def\tally@float#1{%
- \begingroup
-  \@tempcnta\count\@currbox
-  \divide\@tempcnta\@xxxii
-  \multiply\@tempcnta\@xxxii
-  \advance\count\@currbox-\@tempcnta
-  \divide\@tempcnta\@xxxii
-  \@ifnum{\count\@currbox>\@xvi}{%
-   \advance\count\@currbox-\@xvi\@booleantrue\@temp@sw
-  }{%
-   \@booleanfalse\@temp@sw
-  }%
-  \show@box@size@sw{%
-   \class@info{Float #1
-    (\the\@tempcnta)[\@temp@sw{16+}{}\the\count\@currbox]^^J%
-    (\the\ht\@currbox+\the\dp\@currbox)X\the\wd\@currbox
-   }%
-  }{}%
- \endgroup
- \expandafter\let
- \expandafter\@tempa
-             \csname fbox@\csname ftype@#1\endcsname\endcsname
- \@ifnotrelax\@tempa{%
-  \@ifhbox\@tempa{%
-   \setbox\@tempboxa\vbox{\unvcopy\@currbox\hrule}%
-   \dimen@\ht\@tempboxa
-   \divide\dimen@\@twopowerfourteen
-   \@ifdim{\wd\@tempboxa<\textwidth}{%
-    \advance\dimen@\ht\@tempa
-    \global\ht\@tempa\dimen@
-   }{%
-    \advance\dimen@\dp\@tempa
-    \global\dp\@tempa\dimen@
-   }%
-  }{}%
- }{}%
-}%
-\def\total@float#1{%
- \expandafter\let
- \expandafter\@tempa
-             \csname fbox@\csname ftype@#1\endcsname\endcsname
- \@ifnotrelax\@tempa{%
-  \@ifhbox\@tempa{%
-   \@tempdima\the\ht\@tempa\divide\@tempdima\@twopowertwo\@tempcnta\@tempdima
-   \@tempdimb\the\dp\@tempa\divide\@tempdimb\@twopowertwo\@tempcntb\@tempdimb
-   \class@info{Total #1: Column(\the\@tempcnta pt), Page(\the\@tempcnta pt)}%
-  }{}%
- }{}%
-}%
-\def\write@float#1{\write@@float{#1}{#1}}%
-\def\endwrite@float{\@Esphack}%
-\def\write@floats#1{\write@@float{#1*}{#1}}%
-\def\endwrite@floats{\@Esphack}%
-\def\write@@float#1#2{%
-  \ifhmode
-     \@bsphack
-  \fi
-  \chardef\@tempc\csname#2write\endcsname
-  \toks@{\begin{#1}}%
-  \def\@tempb{#1}%
-  \expandafter\let\csname end#1\endcsname\endwrite@float
-  \catcode`\^^M\active
-  \@makeother\{\@makeother\}\@makeother\%
-  \write@floatline
-}%
-\begingroup
- \catcode`\[\the\catcode`\{\catcode`\]\the\catcode`\}\@makeother\{\@makeother\}%
- \gdef\float@end@tag#1\end{#2}#3\@nul[%
-  \def\@tempa[#2]%
-  \@ifx[\@tempa\@tempb][\end[#2]][\write@floatline]%
- ]%
- \obeylines%
- \gdef\write@floatline#1^^M[%
-  \begingroup%
-   \newlinechar`\^^M%
-   \toks@\expandafter[\the\toks@#1]\immediate\write\@tempc[\the\toks@]%
-  \endgroup%
-  \toks@[]%
-  \float@end@tag#1\end{}\@nul%
- ]%
-\endgroup
-\def\@alph#1{\ifcase#1\or a\or b\or c\or d\else\@ialph{#1}\fi}
-\def\@ialph#1{\ifcase#1\or \or \or \or \or e\or f\or g\or h\or i\or j\or
-  k\or l\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or
-  y\or z\or aa\or bb\or cc\or dd\or ee\or ff\or gg\or hh\or ii\or jj\or
-  kk\or ll\or mm\or nn\or oo\or pp\or qq\or rr\or ss\or tt\or uu\or
-  vv\or ww\or xx\or yy\or zz\else\@ctrerr\fi}
-\def\@startsection#1#2#3#4#5#6{%
- \@startsection@hook
- \if@noskipsec \leavevmode \fi
- \par
- \@tempskipa #4\relax
- \@afterindenttrue
- \ifdim \@tempskipa <\z@
-  \@tempskipa -\@tempskipa \@afterindentfalse
- \fi
- \if@nobreak
-  \everypar{}%
- \else
-  \addpenalty\@secpenalty\addvspace\@tempskipa
- \fi
- \@ifstar
-  {\@dblarg{\@ssect@ltx{#1}{#2}{#3}{#4}{#5}{#6}}}%
-  {\@dblarg{\@sect@ltx {#1}{#2}{#3}{#4}{#5}{#6}}}%
-}%
-\def\@startsection@hook{}%
-\class@info{Repairing broken LateX \string\@sect}%
-\def\@sect@ltx#1#2#3#4#5#6[#7]#8{%
-  \@ifnum{#2>\c@secnumdepth}{%
-    \def\H@svsec{\phantomsection}%
-    \let\@svsec\@empty
-  }{%
-    \H@refstepcounter{#1}%
-    \def\H@svsec{%
-     \phantomsection
-    }%
-    \protected@edef\@svsec{{#1}}%
-    \@ifundefined{@#1cntformat}{%
-     \prepdef\@svsec\@seccntformat
-    }{%
-     \expandafter\prepdef
-     \expandafter\@svsec
-                 \csname @#1cntformat\endcsname
-    }%
-  }%
-  \@tempskipa #5\relax
-  \@ifdim{\@tempskipa>\z@}{%
-    \begingroup
-      \interlinepenalty \@M
-      #6{%
-       \@ifundefined{@hangfrom@#1}{\@hang@from}{\csname @hangfrom@#1\endcsname}%
-       {\hskip#3\relax\H@svsec}{\@svsec}{#8}%
-      }%
-      \@@par
-    \endgroup
-    \@ifundefined{#1mark}{\@gobble}{\csname #1mark\endcsname}{#7}%
-    \addcontentsline{toc}{#1}{%
-      \@ifnum{#2>\c@secnumdepth}{%
-       \protect\numberline{}%
-      }{%
-       \protect\numberline{\csname the#1\endcsname}%
-      }%
-      #8}%
-  }{%
-    \def\@svsechd{%
-      #6{%
-       \@ifundefined{@runin@to@#1}{\@runin@to}{\csname @runin@to@#1\endcsname}%
-       {\hskip#3\relax\H@svsec}{\@svsec}{#8}%
-      }%
-      \@ifundefined{#1mark}{\@gobble}{\csname #1mark\endcsname}{#7}%
-      \addcontentsline{toc}{#1}{%
-        \@ifnum{#2>\c@secnumdepth}{%
-         \protect\numberline{}%
-        }{%
-         \protect\numberline{\csname the#1\endcsname}%
-        }%
-        #8}%
-    }%
-  }%
-  \@xsect{#5}%
-}%
-\def\@hang@from#1#2#3{\@hangfrom{#1#2}#3}%
-\def\@runin@to #1#2#3{#1#2#3}%
-\def\@ssect@ltx#1#2#3#4#5#6[#7]#8{%
-  \def\H@svsec{\phantomsection}%
-  \@tempskipa #5\relax
-  \@ifdim{\@tempskipa>\z@}{%
-    \begingroup
-      \interlinepenalty \@M
-      #6{%
-       \@ifundefined{@hangfroms@#1}{\@hang@froms}{\csname @hangfroms@#1\endcsname}%
-       {\hskip#3\relax\H@svsec}{#8}%
-      }%
-      \@@par
-    \endgroup
-    \@ifundefined{#1smark}{\@gobble}{\csname #1smark\endcsname}{#7}%
-    \addcontentsline{toc}{#1}{\protect\numberline{}#8}%
-  }{%
-    \def\@svsechd{%
-      #6{%
-       \@ifundefined{@runin@tos@#1}{\@runin@tos}{\csname @runin@tos@#1\endcsname}%
-       {\hskip#3\relax\H@svsec}{#8}%
-      }%
-      \@ifundefined{#1smark}{\@gobble}{\csname #1smark\endcsname}{#7}%
-      \addcontentsline{toc}{#1}{\protect\numberline{}#8}%
-    }%
-  }%
-  \@xsect{#5}%
-}%
-\def\@hang@froms#1#2{#1#2}%
-\def\@runin@tos #1#2{#1#2}%
-\def\init@hyperref{%
- \providecommand\phantomsection{}%
- \providecommand\hyper@makecurrent[1]{}%
- \providecommand\Hy@raisedlink[1]{}%
- \providecommand\hyper@anchorstart[1]{}%
- \providecommand\hyper@anchorend{}%
- \providecommand\hyper@linkstart[2]{}%
- \providecommand\hyper@linkend{}%
- \providecommand\@currentHref{}%
-}%
-\let\H@refstepcounter\refstepcounter
-\appdef\document@inithook{%
- \init@hyperref
-}%
-\def\sec@upcase#1{\relax{#1}}%
-\appdef\document@inithook{%
- \@ifpackageloaded{array}{\switch@array}{\switch@tabular}%
- \prepdef\endtabular{\endtabular@hook}%
- \@provide\endtabular@hook{}%
- \prepdef\endarray{\endarray@hook}%
- \@provide\endarray@hook{}%
- \providecommand\array@hook{}%
- \prepdef\@tabular{\tabular@hook}%
- \@provide\tabular@hook{}%
-}%
-\def\switch@tabular{%
- \let\@array@sw\@array@sw@array
- \@ifx{\@array\@array@LaTeX}{%
-  \@ifx{\multicolumn\multicolumn@LaTeX}{%
-   \@ifx{\@tabular\@tabular@LaTeX}{%
-    \@ifx{\@tabarray\@tabarray@LaTeX}{%
-     \@ifx{\array\array@LaTeX}{%
-      \@ifx{\endarray\endarray@LaTeX}{%
-       \@ifx{\endtabular\endtabular@LaTeX}{%
-        \@ifx{\@mkpream\@mkpream@LaTeX}{%
-         \@ifx{\@addamp\@addamp@LaTeX}{%
-          \@ifx{\@arrayacol\@arrayacol@LaTeX}{%
-           \@ifx{\@tabacol\@tabacol@LaTeX}{%
-            \@ifx{\@arrayclassz\@arrayclassz@LaTeX}{%
-             \@ifx{\@tabclassiv\@tabclassiv@LaTeX}{%
-              \@ifx{\@arrayclassiv\@arrayclassiv@LaTeX}{%
-               \@ifx{\@tabclassz\@tabclassz@LaTeX}{%
-                \@ifx{\@classv\@classv@LaTeX}{%
-                 \@ifx{\hline\hline@LaTeX}{%
-                  \@ifx{\@tabularcr\@tabularcr@LaTeX}{%
-                   \@ifx{\@xtabularcr\@xtabularcr@LaTeX}{%
-                    \@ifx{\@xargarraycr\@xargarraycr@LaTeX}{%
-                     \@ifx{\@yargarraycr\@yargarraycr@LaTeX}{%
-                      \true@sw
-                     }{%
-                      \false@sw
-                     }%
-                    }{%
-                     \false@sw
-                    }%
-                   }{%
-                    \false@sw
-                   }%
-                  }{%
-                   \false@sw
-                  }%
-                 }{%
-                  \false@sw
-                 }%
-                }{%
-                 \false@sw
-                }%
-               }{%
-                \false@sw
-               }%
-              }{%
-               \false@sw
-              }%
-             }{%
-              \false@sw
-             }%
-            }{%
-             \false@sw
-            }%
-           }{%
-            \false@sw
-           }%
-          }{%
-           \false@sw
-          }%
-         }{%
-          \false@sw
-         }%
-        }{%
-         \false@sw
-        }%
-       }{%
-        \false@sw
-       }%
-      }{%
-       \false@sw
-      }%
-     }{%
-      \false@sw
-     }%
-    }{%
-     \false@sw
-    }%
-   }{%
-    \false@sw
-   }%
-  }{%
-   \false@sw
-  }%
- }{%
-  \false@sw
- }%
- {%
-  \class@info{Patching LaTeX tabular.}%
- }{%
-  \class@info{Unrecognized LaTeX tabular. Please update this document class! (Proceeding with fingers crossed.)}%
- }%
- \let\@array\@array@ltx
- \let\multicolumn\multicolumn@ltx
- \let\@tabular\@tabular@ltx
- \let\@tabarray\@tabarray@ltx
- \let\array\array@ltx
- \let\endarray\endarray@ltx
- \let\endtabular\endtabular@ltx
- \let\@mkpream\@mkpream@ltx
- \let\@addamp\@addamp@ltx
- \let\@arrayacol\@arrayacol@ltx
- \let\@tabacol\@tabacol@ltx
- \let\@arrayclassz\@arrayclassz@ltx
- \let\@tabclassiv\@tabclassiv@ltx
- \let\@arrayclassiv\@arrayclassiv@ltx
- \let\@tabclassz\@tabclassz@ltx
- \let\@classv\@classv@ltx
- \let\hline\hline@ltx
- \let\@tabularcr\@tabularcr@ltx
- \let\@xtabularcr\@xtabularcr@ltx
- \let\@xargarraycr\@xargarraycr@ltx
- \let\@yargarraycr\@yargarraycr@ltx
-}%
-\def\switch@array{%
- \@ifpackageloaded{colortbl}{\let\switch@array@info\colortbl@message}{\let\switch@array@info\array@message}%
- \let\@array@sw\@array@sw@LaTeX
- \@ifx{\@array\@array@array}{%
-  \@ifx{\@tabular\@tabular@array}{%
-   \@ifx{\@tabarray\@tabarray@array}{%
-    \@ifx{\array\array@array}{%
-     \@ifx{\endarray\endarray@array}{%
-      \@ifx{\endtabular\endtabular@array}{%
-       \@ifx{\@mkpream\@mkpream@array}{%
-        \@ifx{\@classx\@classx@array}{%
-         \@ifx{\insert@column\insert@column@array}{%
-          \@ifx{\@arraycr\@arraycr@array}{%
-           \@ifx{\@xarraycr\@xarraycr@array}{%
-            \@ifx{\@xargarraycr\@xargarraycr@array}{%
-             \@ifx{\@yargarraycr\@yargarraycr@array}{%
-              \true@sw
-             }{%
-              \false@sw
-             }%
-            }{%
-             \false@sw
-            }%
-           }{%
-            \false@sw
-           }%
-          }{%
-           \false@sw
-          }%
-         }{%
-          \false@sw
-         }%
-        }{%
-         \false@sw
-        }%
-       }{%
-        \false@sw
-       }%
-      }{%
-       \false@sw
-      }%
-     }{%
-      \false@sw
-     }%
-    }{%
-     \false@sw
-    }%
-   }{%
-    \false@sw
-   }%
-  }{%
-   \false@sw
-  }%
- }{%
-  \false@sw
- }{%
-  \class@info{Patching array package.}%
- }{%
-  \switch@array@info
- }%
- \let\@array    \@array@array@new
- \let\@@array   \@array % Cosi fan tutti
- \let\@tabular  \@tabular@array@new
- \let\@tabarray \@tabarray@array@new
- \let\array     \array@array@new
- \let\endarray  \endarray@array@new
- \let\endtabular\endtabular@array@new
- \let\@mkpream  \@mkpream@array@new
- \let\@classx   \@classx@array@new
- \let\@arrayacol\@arrayacol@ltx
- \let\@tabacol  \@tabacol@ltx
- \let\insert@column\insert@column@array@new
- \expandafter\let\csname endtabular*\endcsname\endtabular % Cosi fan tutti
- \let\@arraycr  \@arraycr@new
- \let\@xarraycr \@xarraycr@new
- \let\@xargarraycr\@xargarraycr@new
- \let\@yargarraycr\@yargarraycr@new
-}%
-\def\array@message{%
- \class@info{Unrecognized array package. Please update this document class! (Proceeding with fingers crossed.)}%
-}%
-\def\colortbl@message{%
- \class@info{colortbl package is loaded. (Proceeding with fingers crossed.)}%
-}%
-\def\@array@sw@LaTeX{\@ifx{\\\@tabularcr}}%
-\def\@array@sw@array{\@ifx{\d@llarbegin\begingroup}}%
-\def\@tabular@LaTeX{%
- \leavevmode
- \hbox\bgroup$%
-  \let\@acol\@tabacol
-  \let\@classz\@tabclassz
-  \let\@classiv\@tabclassiv
-  \let\\\@tabularcr
-  \@tabarray
-}%
-\def\@tabular@ltx{%
-  \let\@acoll\@tabacoll
-  \let\@acolr\@tabacolr
-  \let\@acol\@tabacol
-  \let\@classz\@tabclassz
-  \let\@classiv\@tabclassiv
-  \let\\\@tabularcr
-  \@tabarray
-}%
-\def\@tabular@array{%
- \leavevmode
- \hbox\bgroup$%
-  \col@sep\tabcolsep
-  \let\d@llarbegin\begingroup
-  \let\d@llarend\endgroup
-  \@tabarray
-}%
-\def\@tabular@array@new{%
-  \let\@acoll\@tabacoll
-  \let\@acolr\@tabacolr
-  \let\@acol\@tabacol
-  \let\d@llarbegin\begingroup
-  \let\d@llarend\endgroup
-  \@tabarray
-}%
-\def\@tabarray@LaTeX{%
- \m@th\@ifnextchar[\@array{\@array[c]}%
-}%
-\def\@tabarray@ltx{%
- \m@th\@ifnextchar[\@array{\expandafter\@array\expandafter[\array@default]}%
-}%
-\def\@tabarray@array{%
- \@ifnextchar[{\@@array}{\@@array[c]}%
-}%
-\def\@tabarray@array@new{%
- \@ifnextchar[{\@@array}{\expandafter\@@array\expandafter[\array@default]}%
-}%
-\newcount\intertabularlinepenalty
-\intertabularlinepenalty=100
-\newcount\@tbpen
-\appdef\samepage{\intertabularlinepenalty\@M}%
-\def\@tabularcr@LaTeX{{\ifnum 0=`}\fi \@ifstar \@xtabularcr \@xtabularcr}%
-\def\@tabularcr@ltx{{\ifnum 0=`}\fi \@ifstar {\global \@tbpen \@M \@xtabularcr }{\global \@tbpen \intertabularlinepenalty \@xtabularcr }}%
-\def\@xtabularcr@LaTeX{\@ifnextchar [\@argtabularcr {\ifnum 0=`{\fi }\cr }}%
-\def\@xtabularcr@ltx{\@ifnextchar [\@argtabularcr {\ifnum 0=`{\fi }\cr \noalign {\penalty \@tbpen }}}%
-\def\@xargarraycr@LaTeX#1{\@tempdima #1\advance \@tempdima \dp \@arstrutbox \vrule \@height \z@ \@depth \@tempdima \@width \z@ \cr}%
-\def\@xargarraycr@ltx#1{\@tempdima #1\advance \@tempdima \dp \@arstrutbox \vrule \@height \z@ \@depth \@tempdima \@width \z@ \cr \noalign {\penalty \@tbpen }}%
-\def\@yargarraycr@LaTeX#1{\cr \noalign {\vskip #1}}%
-\def\@yargarraycr@ltx#1{\cr \noalign {\penalty \@tbpen \vskip #1}}%
-\def\@arraycr@array{%
- \relax
- \iffalse{\fi\ifnum 0=`}\fi
- \@ifstar \@xarraycr \@xarraycr
-}%
-\def\@arraycr@new{%
- \relax
- \iffalse{\fi\ifnum 0=`}\fi
- \@ifstar {\global \@tbpen \@M \@xarraycr }{\global \@tbpen \intertabularlinepenalty \@xarraycr }%
-}%
-\def\@xarraycr@array{%
- \@ifnextchar [%]
- \@argarraycr {\ifnum 0=`{}\fi\cr}%
-}%
-\def\@xarraycr@new{%
- \@ifnextchar [%]
- \@argarraycr {\ifnum 0=`{}\fi\cr \noalign {\penalty \@tbpen }}%
-}%
-\def\@xargarraycr@array#1{%
- \unskip
- \@tempdima #1\advance\@tempdima \dp\@arstrutbox
- \vrule \@depth\@tempdima \@width\z@
- \cr
-}%
-\def\@xargarraycr@new#1{%
- \unskip
- \@tempdima #1\advance\@tempdima \dp\@arstrutbox
- \vrule \@depth\@tempdima \@width\z@
- \cr
- \noalign {\penalty \@tbpen }%
-}%
-\def\@yargarraycr@array#1{%
- \cr
- \noalign{\vskip #1}%
-}%
-\def\@yargarraycr@new#1{%
- \cr
- \noalign{\penalty \@tbpen \vskip #1}%
-}%
-\def\array@LaTeX{%
- \let\@acol\@arrayacol
- \let\@classz\@arrayclassz
- \let\@classiv\@arrayclassiv
- \let\\\@arraycr
- \let\@halignto\@empty
- \@tabarray
-}%
-\def\array@ltx{%
- \@ifmmode{}{\@badmath$}%
- \let\@acoll\@arrayacol
- \let\@acolr\@arrayacol
- \let\@acol\@arrayacol
- \let\@classz\@arrayclassz
- \let\@classiv\@arrayclassiv
- \let\\\@arraycr
- \let\@halignto\@empty
- \@tabarray
-}%
-\def\array@array{%
- \col@sep\arraycolsep
- \def\d@llarbegin{$}\let\d@llarend\d@llarbegin\gdef\@halignto{}%
- \@tabarray
-}
-\def\array@array@new{%
- \@ifmmode{}{\@badmath$}%
- \let\@acoll\@arrayacol
- \let\@acolr\@arrayacol
- \let\@acol\@arrayacol
- \def\d@llarbegin{$}%
- \let\d@llarend\d@llarbegin
- \gdef\@halignto{}%
- \@tabarray
-}%
-\def\@array@LaTeX[#1]#2{%
-  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
-  \bgroup
-  \setbox\@arstrutbox\hbox{%
-    \vrule \@height\arraystretch\ht\strutbox
-           \@depth\arraystretch \dp\strutbox
-           \@width\z@}%
-  \@mkpream{#2}%
-  \edef\@preamble{%
-    \ialign \noexpand\@halignto
-      \bgroup \@arstrut \@preamble \tabskip\z@skip \cr}%
-  \let\@startpbox\@@startpbox \let\@endpbox\@@endpbox
-  \let\tabularnewline\\%
-    \let\par\@empty
-    \let\@sharp##%
-    \set@typeset@protect
-    \lineskip\z@skip\baselineskip\z@skip
-    \ifhmode \@preamerr\z@ \@@par\fi
-    \@preamble
-}%
-\def\@array@ltx[#1]#2{%
- \@nameuse{@array@align@#1}%
-  \set@arstrutbox
-  \@mkpream{#2}%
-  \prepdef\@preamble{%
-    \tabskip\tabmid@skip
-    \@arstrut
-  }%
-  \appdef\@preamble{%
-    \tabskip\tabright@skip
-    \cr
-    \array@row@pre
-  }%
-  \let\tabularnewline\\%
-  \let\par\@empty
-  \let\@sharp##%
-  \set@typeset@protect
-  \lineskip\z@skip\baselineskip\z@skip
-  \tabskip\tableft@skip\relax
-  \ifhmode \@preamerr\z@ \@@par\fi
-  \everycr{}%
-  \expandafter\halign\expandafter\@halignto\expandafter\bgroup\@preamble
-}%
-\def\set@arstrutbox{%
-  \setbox\@arstrutbox\hbox{%
-    \vrule \@height\arraystretch\ht\strutbox
-           \@depth\arraystretch \dp\strutbox
-           \@width\z@
-  }%
-}%
-\def\@array@array[#1]#2{%
-  \@tempdima \ht \strutbox
-  \advance \@tempdima by\extrarowheight
-  \setbox \@arstrutbox \hbox{\vrule
-             \@height \arraystretch \@tempdima
-             \@depth \arraystretch \dp \strutbox
-             \@width \z@}%
-  \begingroup
-  \@mkpream{#2}%
-  \xdef\@preamble{\noexpand \ialign \@halignto
-                  \bgroup \@arstrut \@preamble
-                          \tabskip \z@ \cr}%
-  \endgroup
-  \@arrayleft
-  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi \fi
-  \bgroup
-  \let \@sharp ##\let \protect \relax
-  \lineskip \z@
-  \baselineskip \z@
-  \m@th
-  \let\\\@arraycr \let\tabularnewline\\\let\par\@empty \@preamble
-}%
-\def\@array@array@new[#1]#2{%
-  \@tempdima\ht\strutbox
-  \advance\@tempdima by\extrarowheight
-  \setbox\@arstrutbox\hbox{%
-   \vrule \@height\arraystretch\@tempdima
-          \@depth \arraystretch\dp\strutbox
-          \@width \z@
-  }%
-  \begingroup
-   \@mkpream{#2}%
-   \xdef\@preamble{\@preamble}%
-  \endgroup
-  \prepdef\@preamble{%
-   \tabskip\tabmid@skip
-    \@arstrut
-  }%
-  \appdef\@preamble{%
-   \tabskip\tabright@skip
-   \cr
-   \array@row@pre
-  }%
-  \@arrayleft
-  \@nameuse{@array@align@#1}%
-  \m@th
-  \let\\\@arraycr
-  \let\tabularnewline\\%
-  \let\par\@empty
-  \let\@sharp##%
-  \set@typeset@protect
-  \lineskip\z@\baselineskip\z@
-  \tabskip\tableft@skip
-  \everycr{}%
-  \expandafter\halign\expandafter\@halignto\expandafter\bgroup\@preamble
-}%
-\def\endarray@LaTeX{%
- \crcr\egroup\egroup
-}%
-\def\endarray@ltx{%
- \crcr\array@row@pst\egroup\egroup
-}%
-\def\endarray@array{%
- \crcr \egroup \egroup \@arrayright \gdef\@preamble{}%
-}%
-\def\endarray@array@new{%
- \crcr\array@row@pst\egroup\egroup % Same as \endarray@ltx
- \@arrayright
- \global\let\@preamble\@empty
-}%
-\def\endtabular@LaTeX{%
- \crcr\egroup\egroup $\egroup
-}%
-\def\endtabular@ltx{%
- \endarray
-}%
-\def\endtabular@array{%
- \endarray $\egroup
-}%
-\def\endtabular@array@new{%
- \endarray
-}%
-\@namedef{endtabular*}{\endtabular}%
-\long\def\multicolumn@LaTeX#1#2#3{%
- \multispan{#1}\begingroup
-  \@mkpream{#2}%
-  \def\@sharp{#3}\set@typeset@protect
-  \let\@startpbox\@@startpbox\let\@endpbox\@@endpbox
-  \@arstrut \@preamble\hbox{}\endgroup\ignorespaces
-}%
-\long\def\multicolumn@ltx#1#2#3{%
- \multispan{#1}%
- \begingroup
-  \@mkpream{#2}%
-  \def\@sharp{#3}%
-  \set@typeset@protect
- %\let\@startpbox\@@startpbox\let\@endpbox\@@endpbox
-  \@arstrut
-  \@preamble
-  \hbox{}%
- \endgroup
- \ignorespaces
-}%
-\def\@array@align@t{\leavevmode\vtop\bgroup}%
-\def\@array@align@b{\leavevmode\vbox\bgroup}%
-\def\@array@align@c{\leavevmode\@ifmmode{\vcenter\bgroup}{$\vcenter\bgroup\aftergroup$\aftergroup\relax}}%
-\def\@array@align@v{%
- \@ifmmode{%
-  \@badmath
-  \vcenter\bgroup
- }{%
-  \@ifinner{%
-   $\vcenter\bgroup\aftergroup$
-  }{%
-   \@@par\bgroup
-  }%
- }%
-}%
-\def\array@default{c}%
-\def\array@row@rst{%
- \let\@array@align@v\@array@align@c
-}%
-\def\array@row@pre{}%
-\def\array@row@pst{}%
-\newcommand\toprule{\tab@rule{\column@font}{\column@fil}{\frstrut}}%
-\newcommand\colrule{\unskip\lrstrut\\\tab@rule{\body@font}{}{\frstrut}}%
-\newcommand\botrule{\unskip\lrstrut\\\noalign{\hline@rule}{}}%
-\def\hline@LaTeX{%
- \noalign{\ifnum0=`}\fi\hrule \@height \arrayrulewidth \futurelet
-   \reserved@a\@xhline
-}%
-\def\hline@ltx{%
- \noalign{%
-  \ifnum0=`}\fi
-  \hline@rule
-  \futurelet\reserved@a\@xhline
- % \noalign ended in \@xhline
-}%
-\def\@xhline@unneeded{%
- \say\reserved@a
- \ifx\reserved@a\hline
-  \vskip\doublerulesep
-  \vskip-\arrayrulewidth
- \fi
- \ifnum0=`{\fi}%
-}%
-\def\tab@rule#1#2#3{%
- \crcr
- \noalign{%
-  \hline@rule
-  \gdef\@arstrut@hook{%
-   \global\let\@arstrut@hook\@empty
-   #3%
-  }%
-  \gdef\cell@font{#1}%
-  \gdef\cell@fil{#2}%
- }%
-}%
-\def\column@font{}%
-\def\column@fil{}%
-\def\body@font{}%
-\def\cell@font{}%
-\def\frstrut{}%
-\def\lrstrut{}%
-\def\@arstrut@hline{%
- \relax
- \@ifmmode{\copy}{\unhcopy}\@arstrutbox@hline
- \@arstrut@hook
-}%
-\let\@arstrut@org\@arstrut
-\def\@arstrut@hook{%
- \global\let\@arstrut\@arstrut@org
-}%
-\newbox\@arstrutbox@hline
-\appdef\set@arstrutbox{%
-  \setbox\@arstrutbox@hline\hbox{%
-    \setbox\z@\hbox{$0^{0}_{}$}%
-    \dimen@\ht\z@\advance\dimen@\@arstrut@hline@clnc
-    \@ifdim{\dimen@<\arraystretch\ht\strutbox}{\dimen@=\arraystretch\ht\strutbox}{}%
-    \vrule \@height\dimen@
-           \@depth\arraystretch \dp\strutbox
-           \@width\z@
-  }%
-}%
-\def\hline@rule{%
- \hrule \@height \arrayrulewidth
- \global\let\@arstrut\@arstrut@hline
-}%
-\def\@arstrut@hline@clnc{2\p@}% % Klootch: magic number
-\def\tableft@skip{\z@skip}%
-\def\tabmid@skip{\z@skip}%\@flushglue
-\def\tabright@skip{\z@skip}%
-\def\tableftsep{\tabcolsep}%
-\def\tabmidsep{\tabcolsep}%
-\def\tabrightsep{\tabcolsep}%
-\def\cell@fil{}%
-\def\pbox@hook{}%
-\appdef\@arstrut{\@arstrut@hook}%
-\let\@arstrut@hook\@empty
-\def\@addtopreamble{\appdef\@preamble}%
-\def\@mkpream@LaTeX#1{%
-  \@firstamptrue\@lastchclass6
-  \let\@preamble\@empty
-  \let\protect\@unexpandable@protect
-  \let\@sharp\relax
-  \let\@startpbox\relax\let\@endpbox\relax
-  \@expast{#1}%
-  \expandafter\@tfor \expandafter
-    \@nextchar \expandafter:\expandafter=\reserved@a\do
-       {\@testpach\@nextchar
-    \ifcase \@chclass \@classz \or \@classi \or \@classii \or \@classiii
-      \or \@classiv \or\@classv \fi\@lastchclass\@chclass}%
-  \ifcase \@lastchclass \@acol
-      \or \or \@preamerr \@ne\or \@preamerr \tw@\or \or \@acol \fi
-}%
-\def\@mkpream@ltx#1{%
- \@firstamptrue
- \@lastchclass6
- \let\@preamble\@empty
- \let\protect\@unexpandable@protect
- \let\@sharp\relax
- \@expast{#1}%
- \expandafter\@tfor\expandafter\@nextchar\expandafter:\expandafter=\reserved@a
- \do{%
-  \expandafter\@testpach\expandafter{\@nextchar}%
-  \ifcase\@chclass
-   \@classz
-  \or
-   \@classi
-  \or
-   \@classii
-  \or
-   \@classiii
-  \or
-   \@classiv
-  \or
-   \@classv
-  \fi
-  \@lastchclass\@chclass
- }%
- \ifcase\@lastchclass
-  \@acolr % right-hand column
- \or
- \or
-  \@preamerr\@ne
- \or
-  \@preamerr\tw@
- \or
- \or
-  \@acolr % right-hand column
- \fi
-}%
-\def\insert@column@array{%
-   \the@toks \the \@tempcnta
-   \ignorespaces \@sharp \unskip
-   \the@toks \the \count@ \relax
-}%
-\def\insert@column@array@new{%
- \the@toks\the\@tempcnta
- \array@row@rst\cell@font
- \ignorespaces\@sharp\unskip
- \the@toks\the\count@
- \relax
-}%
-\def\@mkpream@relax{%
- \let\tableftsep   \relax
- \let\tabmidsep    \relax
- \let\tabrightsep  \relax
- \let\array@row@rst\relax
- \let\cell@font    \relax
- \let\@startpbox   \relax
-}%
-\def\@mkpream@array#1{%
-   \gdef\@preamble{}\@lastchclass 4 \@firstamptrue
-   \let\@sharp\relax \let\@startpbox\relax \let\@endpbox\relax
-   \@temptokena{#1}\@tempswatrue
-   \@whilesw\if@tempswa\fi{\@tempswafalse\the\NC@list}%
-   \count@\m@ne
-   \let\the@toks\relax
-   \prepnext@tok
-   \expandafter \@tfor \expandafter \@nextchar
-    \expandafter :\expandafter =\the\@temptokena \do
-   {\@testpach
-   \ifcase \@chclass \@classz \or \@classi \or \@classii
-     \or \save@decl \or \or \@classv \or \@classvi
-     \or \@classvii \or \@classviii
-     \or \@classx
-     \or \@classx \fi
-   \@lastchclass\@chclass}%
-   \ifcase\@lastchclass
-   \@acol \or
-   \or
-   \@acol \or
-   \@preamerr \thr@@ \or
-   \@preamerr \tw@ \@addtopreamble\@sharp \or
-   \or
-   \else  \@preamerr \@ne \fi
-   \def\the@toks{\the\toks}%
-}%
-\def\@mkpream@array@new#1{%
- \gdef\@preamble{}%
- \@lastchclass\f@ur
- \@firstamptrue
- \let\@sharp\relax
- \@mkpream@relax
- \@temptokena{#1}\@tempswatrue
- \@whilesw\if@tempswa\fi{\@tempswafalse\the\NC@list}%
- \count@\m@ne
- \let\the@toks\relax
- \prepnext@tok
- \expandafter\@tfor\expandafter\@nextchar\expandafter:\expandafter=\the\@temptokena
- \do{%
-  \@testpach
-  \ifcase\@chclass
-   \@classz
-  \or
-   \@classi
-  \or
-   \@classii
-  \or
-   \save@decl
-  \or
-  \or
-   \@classv
-  \or
-   \@classvi
-  \or
-   \@classvii
-  \or
-   \@classviii
-  \or
-   \@classx
-  \or
-   \@classx
-  \fi
-  \@lastchclass\@chclass
- }%
- \ifcase\@lastchclass
-  \@acolr % right-hand column
- \or
- \or
-  \@acolr % right-hand column
- \or
-  \@preamerr\thr@@
- \or
-  \@preamerr\tw@\@addtopreamble\@sharp
- \or
- \or
- \else
-  \@preamerr\@ne
- \fi
- \def\the@toks{\the\toks}%
-}%
-\appdef\@mkpream@relax{%
- \let\CT@setup       \relax
- \let\CT@color       \relax
- \let\CT@do@color    \relax
- \let\color          \relax
- \let\CT@column@color\relax
- \let\CT@row@color   \relax
- \let\CT@cell@color  \relax
-}%
-\def\@addamp@LaTeX{%
-  \if@firstamp\@firstampfalse\else\edef\@preamble{\@preamble &}\fi
-}%
-\def\@addamp@ltx{%
- \if@firstamp\@firstampfalse\else\@addtopreamble{&}\fi
-}%
-\def\@arrayacol@LaTeX{%
- \edef\@preamble{\@preamble \hskip \arraycolsep}%
-}%
-\def\@arrayacol@ltx{%
- \@addtopreamble{\hskip\arraycolsep}%
-}%
-\def\@tabacoll{%
- \@addtopreamble{\hskip\tableftsep\relax}%
-}%
-\def\@tabacol@LaTeX{%
- \edef\@preamble{\@preamble \hskip \tabcolsep}%
-}%
-\def\@tabacol@ltx{%
- \@addtopreamble{\hskip\tabmidsep\relax}%
-}%
-\def\@tabacolr{%
- \@addtopreamble{\hskip\tabrightsep\relax}%
-}%
-\def\@arrayclassz@LaTeX{%
- \ifcase \@lastchclass \@acolampacol \or \@ampacol \or
-   \or \or \@addamp \or
-   \@acolampacol \or \@firstampfalse \@acol \fi
- \edef\@preamble{\@preamble
-  \ifcase \@chnum
-     \hfil$\relax\@sharp$\hfil \or $\relax\@sharp$\hfil
-    \or \hfil$\relax\@sharp$\fi}%
-}%
-\def\@arrayclassz@ltx{%
- \ifcase\@lastchclass
-  \@acolampacol
- \or
-  \@ampacol
- \or
- \or
- \or
-  \@addamp
- \or
-  \@acolampacol
- \or
-  \@firstampfalse\@acoll
- \fi
- \ifcase\@chnum
-  \@addtopreamble{%
-   \hfil\array@row@rst$\relax\@sharp$\hfil
-  }%
- \or
-  \@addtopreamble{%
-   \array@row@rst$\relax\@sharp$\hfil
-  }%
- \or
-  \@addtopreamble{%
-   \hfil\array@row@rst$\relax\@sharp$%
-  }%
- \fi
-}%
-\def\@tabclassz@LaTeX{%
-  \ifcase\@lastchclass
-    \@acolampacol
-  \or
-    \@ampacol
-  \or
-  \or
-  \or
-    \@addamp
-  \or
-    \@acolampacol
-  \or
-    \@firstampfalse\@acol
-  \fi
-  \edef\@preamble{%
-    \@preamble{%
-      \ifcase\@chnum
-        \hfil\ignorespaces\@sharp\unskip\hfil
-      \or
-        \hskip1sp\ignorespaces\@sharp\unskip\hfil
-      \or
-        \hfil\hskip1sp\ignorespaces\@sharp\unskip
-      \fi}}%
-}%
-\def\@tabclassz@ltx{%
- \ifcase\@lastchclass
-  \@acolampacol
- \or
-  \@ampacol
- \or
- \or
- \or
-  \@addamp
- \or
-  \@acolampacol
- \or
-  \@firstampfalse\@acoll
- \fi
- \ifcase\@chnum
-  \@addtopreamble{%
-   {\hfil\array@row@rst\cell@font\ignorespaces\@sharp\unskip\hfil}%
-  }%
- \or
-  \@addtopreamble{%
-   {\cell@fil\hskip1sp\array@row@rst\cell@font\ignorespaces\@sharp\unskip\hfil}%
-  }%
- \or
-  \@addtopreamble{%
-   {\hfil\hskip1sp\array@row@rst\cell@font\ignorespaces\@sharp\unskip\cell@fil}%
-  }%
- \fi
-}%
-\def\@tabclassiv@LaTeX{%
- \@addtopreamble\@nextchar
-}%
-\def\@tabclassiv@ltx{%
- \expandafter\@addtopreamble\expandafter{\@nextchar}%
-}%
-\def\@arrayclassiv@LaTeX{%
- \@addtopreamble{$\@nextchar$}%
-}%
-\def\@arrayclassiv@ltx{%
- \expandafter\@addtopreamble\expandafter{\expandafter$\@nextchar$}%
-}%
-\def\@classv@LaTeX{%
- \@addtopreamble{\@startpbox{\@nextchar}\ignorespaces
- \@sharp\@endpbox}%
-}%
-\def\@classv@ltx{%
- \expandafter\@addtopreamble
- \expandafter{%
- \expandafter \@startpbox
- \expandafter {\@nextchar}%
- \pbox@hook\array@row@rst\cell@font\ignorespaces\@sharp\@endpbox
- }%
-}%
-\def\@classx@array{%
-  \ifcase \@lastchclass
-  \@acolampacol \or
-  \@addamp \@acol \or
-  \@acolampacol \or
-  \or
-  \@acol \@firstampfalse \or
-  \@addamp
-  \fi
-}%
-\def\@classx@array@new{%
- \ifcase \@lastchclass
-  \@acolampacol
- \or
-  \@addamp \@acol
- \or
-  \@acolampacol
- \or
- \or
-  \@firstampfalse\@acoll
- \or
-  \@addamp
- \fi
-}%
-\def\@xbitor@LaTeX #1{\@tempcntb \count#1
-   \ifnum \@tempcnta =\z@
-   \else
-     \divide\@tempcntb\@tempcnta
-     \ifodd\@tempcntb \@testtrue\fi
-   \fi}%
-\def\@xbitor@ltx#1{%
- \@tempcntb\count#1\relax
- \@ifnum{\@tempcnta=\z@}{}{%
-  \divide\@tempcntb\@tempcnta
-  \@ifodd\@tempcntb{\@testtrue}{}%
- }%
-}%
-\@ifx{\@xbitor\@xbitor@LaTeX}{%
-  \class@info{Repairing broken LaTeX \string\@xbitor}%
-}{%
-  \class@info{Unrecognized LaTeX \string\@xbitor. Please update this document class! (Proceeding with fingers crossed.)}%
-}%
-\let\@xbitor\@xbitor@ltx
-\newcommand*\@gobble@opt@one[2][]{}%
-\def\@starttoc#1{%
-  \begingroup
-    \toc@pre
-    \makeatletter
-    \@input{\jobname.#1}%
-    \if@filesw
-      \expandafter\newwrite\csname tf@#1\endcsname
-      \immediate\openout \csname tf@#1\endcsname \jobname.#1\relax
-    \fi
-    \@nobreakfalse
-    \toc@post
-  \endgroup
-}%
-\def\toc@pre{}%
-\def\toc@post{}%
-\def\toc@@font{}%
-\def\ltxu@dotsep{\z@}%
-\let\tocdim@section       \leftmargini
-\let\tocdim@subsection    \leftmarginii
-\let\tocdim@subsubsection \leftmarginiii
-\let\tocdim@paragraph     \leftmarginiv
-\let\tocdim@appendix      \leftmarginv
-\let\tocdim@pagenum       \leftmarginvi
-\def\toc@pre@auto{%
-  \toc@@font
-  \@tempdima\z@
-  \toc@setindent\@tempdima{section}%
-  \toc@setindent\@tempdima{subsection}%
-  \toc@setindent\@tempdima{subsubsection}%
-  \toc@setindent\@tempdima{paragraph}%
-  \toc@letdimen{appendix}%
-  \toc@letdimen{pagenum}%
-}%
-\def\toc@post@auto{%
-  \if@filesw
-   \begingroup
-    \toc@writedimen{section}%
-    \toc@writedimen{subsection}%
-    \toc@writedimen{subsubsection}%
-    \toc@writedimen{paragraph}%
-    \toc@writedimen{appendix}%
-    \toc@writedimen{pagenum}%
-   \endgroup
-  \fi
-}%
-\def\toc@setindent#1#2{%
- \csname tocdim@#2\endcsname\tocdim@min\relax
- \@ifundefined{tocmax@#2}{\@namedef{tocmax@#2}{\z@}}{}%
- \advance#1\@nameuse{tocmax@#2}\relax
- \expandafter\edef\csname tocleft@#2\endcsname{\the#1}%
-}%
-\def\toc@letdimen#1{%
- \csname tocdim@#1\endcsname\tocdim@min\relax
- \@ifundefined{tocmax@#1}{\@namedef{tocmax@#1}{\z@}}{}%
- \expandafter\let\csname tocleft@#1\expandafter\endcsname\csname tocmax@#1\endcsname
-}%
-\def\toc@writedimen#1{%
- \immediate\write\@auxout{%
-  \gdef\expandafter\string\csname tocmax@#1\endcsname{%
-   \expandafter\the\csname tocdim@#1\endcsname
-  }%
- }%
-}%
-\def\l@@sections#1#2#3#4{%
- \begingroup
-  \everypar{}%
-  \set@tocdim@pagenum\@tempboxa{#4}%
-  \global\@tempdima\csname tocdim@#2\endcsname
-  \leftskip\csname tocleft@#2\endcsname\relax
-  \dimen@\csname tocleft@#1\endcsname\relax
-  \parindent-\leftskip\advance\parindent\dimen@
-  \rightskip\tocleft@pagenum plus 1fil\relax
-  \skip@\parfillskip\parfillskip\z@
-  \let\numberline\numberline@@sections
-  \@nameuse{l@f@#2}%
-  \ignorespaces#3\unskip\nobreak\hskip\skip@
-  \hb@xt@\rightskip{\hfil\unhbox\@tempboxa}\hskip-\rightskip\hskip\z@skip
-  \expandafter\par
-  \expandafter\aftergroup\csname tocdim@#2%
-  \expandafter\endcsname
-  \expandafter\endgroup
-              \the\@tempdima\relax
-}%
-\def\set@tocdim@pagenum#1#2{%
- \setbox#1\hbox{\ignorespaces#2}%
- \@ifdim{\tocdim@pagenum<\wd#1}{\global\tocdim@pagenum\wd#1}{}%
-}%
-\def\numberline@@sections#1{%
- \leavevmode\hb@xt@-\parindent{%
-  \hfil
-  \@if@empty{#1}{}{%
-   \setbox\z@\hbox{#1.\kern\ltxu@dotsep}%
-   \@ifdim{\@tempdima<\wd\z@}{\global\@tempdima\wd\z@}{}%
-   \unhbox\z@
-  }%
- }%
- \ignorespaces
-}%
-\def\tocdim@min{\z@}%
-\def\list#1#2{%
-  \ifnum \@listdepth >5\relax
-    \@toodeep
-  \else
-    \global\advance\@listdepth\@ne
-  \fi
-  \rightmargin\z@
-  \listparindent\z@
-  \itemindent\z@
-  \csname @list\romannumeral\the\@listdepth\endcsname
-  \def\@itemlabel{#1}%
-  \let\makelabel\@mklab
-  \@nmbrlistfalse
-  #2\relax
-  \@trivlist
-  \parskip\parsep
-  \set@listindent
-  \ignorespaces
-}%
-\def\set@listindent@parshape{%
- \parindent\listparindent
- \advance\@totalleftmargin\leftmargin
- \advance\linewidth-\rightmargin
- \advance\linewidth-\leftmargin
- \parshape\@ne\@totalleftmargin\linewidth
-}%
-\def\set@listindent@{%
- \parindent\listparindent
- \advance\@totalleftmargin\leftmargin
- \advance\rightskip\rightmargin
- \advance\leftskip\@totalleftmargin
-}%
-\let\set@listindent\set@listindent@parshape
-\providecommand\href[0]{\begingroup\@sanitize@url\@href}%
-\def\@href#1{\@@startlink{#1}\endgroup\@@href}%
-\def\@@href#1{#1\@@endlink}%
-\providecommand \url  [0]{\begingroup\@sanitize@url \@url }%
-\def \@url #1{\endgroup\@href {#1}{\URL@prefix#1}}%
-\providecommand \URL@prefix [0]{URL }%
-\providecommand\doi[0]{\begingroup\@sanitize@url\@doi}%
-\def\@doi#1{\endgroup\@@startlink{\doibase#1}doi:\discretionary {}{}{}#1\@@endlink }%
-\providecommand \doibase [0]{https://doi.org/}%
-\providecommand \@sanitize@url[0]{\chardef\cat@space\the\catcode`\ \@sanitize\catcode`\ \cat@space}%
-\def\@@startlink#1{}%
-\def\@@endlink{}%
-\@ifxundefined \pdfoutput {\true@sw}{\@ifnum{\z@=\pdfoutput}{\true@sw}{\false@sw}}%
-{%
- \def\@@startlink@hypertext#1{\leavevmode\special{html:<a href="#1">}}%
- \def\@@endlink@hypertext{\special{html:</a>}}%
-}{%
- \def\@@startlink@hypertext#1{%
-  \leavevmode
-  \pdfstartlink\pdfstartlink@attr
-   user{/Subtype/Link/A<</Type/Action/S/URI/URI(#1)>>}%
-  \relax
- }%
- \def\@@endlink@hypertext{\pdfendlink}%
- \def\pdfstartlink@attr{attr{/Border[0 0 1 ]/H/I/C[0 1 1]}}%
-}%
-\def\hypertext@enable@ltx{%
- \let\@@startlink\@@startlink@hypertext
- \let\@@endlink\@@endlink@hypertext
-}%
-\def\href@Hy{\hyper@normalise \href@ }%
-\def\href@Hy@ltx{\@ifnextchar\bgroup\Hy@href{\hyper@normalise\href@}}%
-\def\Hy@href#{\hyper@normalise\href@}%
-\begingroup
-  \endlinechar=-1 %
-  \catcode`\^^A=14 %
-  \catcode`\^^M\active
-  \catcode`\%\active
-  \catcode`\#\active
-  \catcode`\_\active
-  \catcode`\$\active
-  \catcode`\&\active
-  \gdef\hyper@normalise@ltx{^^A
-    \begingroup
-    \catcode`\^^M\active
-    \def^^M{ }^^A
-    \catcode`\%\active
-    \let%\@percentchar
-    \let\%\@percentchar
-    \catcode`\#\active
-    \def#{\hyper@hash}^^A
-    \def\#{\hyper@hash}^^A
-    \@makeother\&^^A
-    \edef&{\string&}^^A
-    \edef\&{\string&}^^A
-    \edef\textunderscore{\string_}^^A
-    \let\_\textunderscore
-    \catcode`\_\active
-    \let_\textunderscore
-    \let~\hyper@tilde
-    \let\~\hyper@tilde
-    \let\textasciitilde\hyper@tilde
-    \let\\\@backslashchar
-    \edef${\string$}^^A
-    \Hy@safe@activestrue
-    \hyper@n@rmalise
-  }^^A
-  \catcode`\#=6 ^^A
-  \gdef\Hy@ActiveCarriageReturn@ltx{^^M}^^A
-  \gdef\hyper@n@rmalise@ltx#1#2{^^A
-    \def\Hy@tempa{#2}^^A
-    \ifx\Hy@tempa\Hy@ActiveCarriageReturn
-      \Hy@ReturnAfterElseFi{^^A
-        \hyper@@normalise{#1}^^A
-      }^^A
-    \else
-      \Hy@ReturnAfterFi{^^A
-        \hyper@@normalise{#1}{#2}^^A
-      }^^A
-    \fi
-  }^^A
-  \gdef\hyper@@normalise@ltx#1#2{^^A
-    \edef\Hy@tempa{^^A
-      \endgroup
-      \noexpand#1{\Hy@RemovePercentCr#2%^^M\@nil}^^A
-    }^^A
-    \Hy@tempa
-  }^^A
-  \gdef\Hy@RemovePercentCr@ltx#1%^^M#2\@nil{^^A
-    #1^^A
-    \ifx\limits#2\limits
-    \else
-      \Hy@ReturnAfterFi{^^A
-        \Hy@RemovePercentCr #2\@nil
-      }^^A
-    \fi
-  }^^A
-\endgroup
-\def\switch@hyperref@href{%
- \expandafter\@ifx\expandafter{\csname href \endcsname\href@Hy}{
-  \class@info{Repairing hyperref 6.75r \string\href}%
-  \let\hyper@normalise\hyper@normalise@ltx
-  \let\hyper@@normalise\hyper@@normalise@ltx
-  \let\hyper@n@rmalise\hyper@n@rmalise@ltx
-  \let\Hy@ActiveCarriageReturn\Hy@ActiveCarriageReturn@ltx
-  \let\Hy@RemovePercentCr\Hy@RemovePercentCr@ltx
-  \let\href\href@Hy@ltx
- }{}%
-}%
-\appdef\document@inithook{\switch@hyperref@href}%
-\def\typeout@org#1{%
- \begingroup
-  \set@display@protect
-  \immediate\write\@unused{#1}%
- \endgroup
-}%
-\long\def\typeout@ltx#1{%
- \begingroup
-  \set@display@protect
-  \immediate\write\@unused{#1}%
- \endgroup
-}%
-\@ifx{\typeout\typeout@org}{%
- \let\typeout\typeout@ltx
- \true@sw
-}{%
- \rvtx@ifformat@geq{2020-10-01}%
-   {\true@sw}{\false@sw}%
-}%
- {\class@info{Making \string\typeout\space \string\long}}%
- {}%
-\typeout{%
-ltxfront%
- [2020/10/03 4.2e frontmatter package (AO,DPC,MD)]% \fileversion
-}%
-\appdef\class@documenthook{\frontmatter@init}%
-\let\frontmatter@init\@empty
-\newcommand\frontmatter@title[2][]{%
- \def\@title{#2}%
- \def\@shorttitle{#1}%
- \let\@AF@join\@title@join
-}%
-\appdef\frontmatter@init{%
- \def\@title{\class@warn{No title}}%
- \let\@shorttitle\@empty
- \let\@title@aux\@title@aux@cleared
-}%
-\def\@title@join{\expandafter\@title@join@\@title@aux}%
-\def\@title@join@#1#2{%
- \def\@title@aux{{\@join{\@separator}{#1}{#2}}}%
-}%
-\def\@title@aux@cleared{{}}%
-\newcounter{affil}%
-\newcounter{collab}%
-\appdef\frontmatter@init{%
- \c@affil\z@
- \c@collab\z@
-}%
-\newcommand\frontmatter@author{% implicit #1
- \@author@def{}% implicit #2
-}%
-\def\collaboration{% implicit #1
- \@author@def{\@booleantrue\collaboration@sw}% implicit #2
-}%
-\appdef\frontmatter@init{%
- \@booleanfalse\collaboration@sw
-}%
-\def\@author@cleared{{}{}{}}%
-\def\@author@gobble#1#2#3{}%
-\def\@author@init{%
- \let\@author\@author@cleared
- \@booleanfalse\collaboration@sw
-}%
-\def\@authorclear@sw{\@ifx{\@author\@author@cleared}}%
-\appdef\frontmatter@init{%
- \@author@init
-}%
-\def\@author@def#1#2{%
- \frontmatterverbose@sw{\typeout{\string\author\space\string\collaboration}}{}%
- \move@AU\move@AF\move@AUAF
- \let\@AF@join\@author@join
- #1%
- \def\@author{{#2}{}}%
-}%
-\def\@author@join@#1#2#3{%
-  \def\@author{{#1}{\@join{\@separator}{#2}{#3}}}%
-}%
-\def\@author@join{\expandafter\@author@join@\@author}%
-\def\move@AU{%
- \@authorclear@sw{}{%
-  \collaboration@sw{%
-   \advance\c@collab\@ne
-   \@argswap{\CO@grp\CO@opr}%
-  }{%
-   \@argswap{\AU@grp\AU@opr}%
-  }%
-   {%
-    \expandafter\@argswap@val
-    \expandafter{\@author}%
-     {\expandafter\@argswap@val\expandafter{\the\c@collab}{\add@AUCO@grp}}%
-   }%
- }%
- \@author@init
-}%
-\def\add@AUCO@grp#1#2#3#4{%
- \appdef#3{#4{#1}#2}%
- \frontmatterverbose@sw{\say#3}{}%
-}%
-\def\@author@finish{%
- \frontmatterverbose@sw{\typeout{\string\@author@finish}}{}%
- \move@AU\move@AF
- \@ifx{\AU@grp\@empty}{%
-  \@ifx{\CO@grp\@empty}%
- }{%
-  \false@sw
- }%
- {}{%
-  \@ifx{\AF@grp\@empty}{%
-   \begingroup
-    \let\href\@secondoftwo
-    \let\AU@opr\@secondofthree
-    \let\CO@opr\@secondofthree
-    \let\footnote\@gobble
-    \@ifx{\CO@grp\@empty}{%
-     \class@warn{Assuming \string\noaffiliation\space for authors}%
-     \frontmatterverbose@sw{\say\AU@grp}%
-    }{%
-     \class@warn{Assuming \string\noaffiliation\space for collaboration}%
-     \frontmatterverbose@sw{\say\CO@grp}{}%
-    }%
-   \endgroup
-   \@affil@none\move@AF
-  }{}%
- }%
- \move@AUAF
-}%
-\def\@secondofthree#1#2#3{#2}%
-\def\@join#1#2#3{%
-  \@if@empty{#2}{#3}{#2#1#3}%
-}%
-\def\@separator{;\space}%
-\let\surname\@firstofone
-\let\firstname\@firstofone
-\newcommand\frontmatter@and{\class@err{\protect\and\space is not supported}}
-\def\cat@comma@active{\catcode`\,\active}%
-{\cat@comma@active\gdef,{\active@comma}}%
-\def\active@comma{,\penalty-300\relax}%
-\newcommand\affiliation{%
- \frontmatterverbose@sw{\typeout{\string\affiliation}}{}%
- \move@AU\move@AF
- \begingroup
-  \cat@comma@active
-  \@affiliation
-}%
-\def\@affiliation#1{%
- \endgroup
- \let\@AF@join\@affil@join
- \@affil@def{#1}%
-}%
-\newcommand\frontmatter@noaffiliation{%
- \frontmatterverbose@sw{\typeout{\string\noaffiliation}}{}%
- \move@AU\move@AF
- \@affil@none\move@AF
- \move@AUAF
-}%
-\def\blankaffiliation{{}}%
-\def\@affil@cleared{{{}}{}}%
-\def\@affil@nil{{\relax}{}}%
-\appdef\frontmatter@init{%
- \@affil@init
-}%
-\def\@affil@none{%
- \let\@affil\@affil@nil
-}%
-\def\@affil@init{%
- \let\@affil\@affil@cleared
-}%
-\def\@affilclear@sw{\@ifx{\@affil\@affil@cleared}}%
-\def\@affil@def#1{%
- \def\@affil{{#1}{}}%
-}%
-\def\@affil@join@#1#2#3{%
-  \def\@affil{{#1}{\@join{\@separator}{#2}{#3}}}%
-}%
-\def\@affil@join{\expandafter\@affil@join@\@affil}%
-\def\move@AF{%
- \@affilclear@sw{}{%
-  \@booleanfalse\temp@sw
-  \let\@tempd\@empty
-  \@affils@sw{%
-    \expandafter\@affil@addr@def\expandafter\@tempa\@affil
-    \def\AFF@opr{\@affil@match\@tempa}%
-    \@AFF@list
-  }{}\temp@sw
-  {%
-   \expandafter\@affil@aux@def\expandafter\@tempb\@affil
-   \@ifx{\@tempb\@empty}{}{%
-    \@ifx{\@tempb\@tempd}{}{%
-     \class@warn{%
-      Ancillary information for \@tempa\space must not be different!
-      Please put all of it on the first instance%
-     }%
-    }%
-   }%
-  }%
-  {%
-   \@ifx{\@affil\@affil@nil}{%
-    \def\@tempc{0}%
-    \@argswap@val{0}%
-   }{%
-    \advance\c@affil\@ne
-    \expandafter\def\expandafter\@tempc\expandafter{\the\c@affil}%
-    \expandafter\@argswap@val\expandafter{\the\c@affil}%
-   }%
-   {%
-    \expandafter\@argswap@val\expandafter{\the\c@collab}{%
-     \expandafter\@argswap@val\expandafter{\@affil}{%
-      \add@list@val@val@val\@AFF@list\AFF@opr
-     }%
-    }%
-   }%
-  }%
-  \appdef@eval\AF@grp\@tempc
-  \frontmatterverbose@sw{\say\AF@grp}{}%
-  \@affil@init
- }%
-}%
-\def\@affil@addr@def#1#2#3{%
- \def#1{#2}%
-}%
-\def\@affil@aux@def#1#2#3{%
- \def#1{#3}%
-}%
-\def\add@list@val@val@val#1#2#3#4#5{%
- \appdef#1{#2{#5}{#4}#3}%
- \frontmatterverbose@sw{\say#1}{}%
-}%
-\def\@affil@match#1#2#3#4#5{%
- \temp@sw{}{%
-  \def\@tempifx{#4}%
-  \@ifx{\@tempifx#1}{%
-   \groupauthors@sw{%
-    \@ifnum{#3=\c@collab}{%
-     \true@sw
-    }{%
-     \false@sw
-    }%
-   }{%
-    \true@sw
-   }%
-  }{%
-   \false@sw
-  }%
-  {%
-   \@booleantrue\temp@sw
-   \def\@tempc{#2}%
-   \def\@tempd{#5}%
-  }{%
-  }%
- }%
-}%
-\def\move@AUAF{%
- \frontmatterverbose@sw{\say\AU@grp\say\AF@grp\say\CO@grp}{}%
- \@ifx{\AF@grp\@empty}{%
-    \@ifx{\@empty\CO@grp}{%
-    }{%
-     \appdef     \@AAC@list{\AF@opr{{0}}}%
-     \appdef@e   \@AAC@list{\CO@grp}%
-     \appdef@e   \@AFG@list{\CO@grp}%
-     \let\CO@grp\@empty
-    }%
- }{%
-      \appdef     \@AAC@list{\AF@opr}%
-      \appdef@eval\@AAC@list{\AF@grp}%
-      \appdef@e   \@AAC@list{\AU@grp}%
-    \@ifx{\@empty\AU@grp}{%
-     \@ifx{\@empty\CO@grp}%
-    }{%
-     \false@sw
-    }%
-    {%
-    }{%
-      \@booleanfalse\temp@sw
-      \def\AFG@opr{\x@match\AF@grp}%
-      \let\CO@opr\@author@gobble
-      \@AFG@list
-      \temp@sw{}{%
-        \appdef     \@AFG@list{\AFG@opr}%
-        \appdef@eval\@AFG@list{\AF@grp}%
-      }%
-     \@ifx{\@empty\CO@grp}{}{%
-       \appdef@e   \@AAC@list{\CO@grp}%
-       \appdef@e   \@AFG@list{\CO@grp}%
-       \let\CO@grp\@empty
-     }%
-    }%
-    \let\CO@grp\@empty
-    \let\AU@grp\@empty
-    \let\AF@grp\@empty
- }%
- \frontmatterverbose@sw{\say\@AAC@list\say\@AFG@list}{}%
-}%
-\appdef\frontmatter@init{%
- \let\AU@grp\@empty
- \let\CO@grp\@empty
- \let\AF@grp\@empty
- \let\@AAC@list\@empty
- \let\@AFG@list\@empty
- \let\@AFF@list\@empty
-}%
-\appdef\frontmatter@init{%
- \let\@AF@join\@AF@join@error
-}%
-\def\@AF@join@error#1{%
- \class@warn{%
-  \string\email, \string\homepage, \string\thanks, or \string\altaffiliation\space
-  appears in wrong context.
- }%
-}%
-\def\sanitize@url{%
- \@makeother\%%
- \@makeother\~%
- \@makeother\_%
-}%
-\newcommand*\email[1][]{\begingroup\sanitize@url\@email{#1}}%
-\def\@email#1#2{%
- \endgroup
- \@AF@join{#1\href{mailto:#2}{#2}}%
-}%
-\newcommand*\homepage[1][]{\begingroup\sanitize@url\@homepage{#1}}%
-\def\@homepage#1#2{%
- \endgroup
- \@AF@join{#1\href{#2}{#2}}%
-}%
-\appdef\class@documenthook{%
- \providecommand\href[1]{}%
-}%
-\def\frontmatter@thanks{% implicit #1
-  \@AF@join
-}%
-\newcommand*\altaffiliation[2][]{%
-  \@AF@join{#1#2}%
-}%
-\def\set@listcomma@list#1{%
-  \expandafter\@reset@ac\expandafter#1#1{0}\@reset@ac{%
-   \let\@listcomma\relax
-  }{%
-   \let\@listcomma\@listcomma@comma
-  }%
-}%
-\def\set@listcomma@count#1{%
-  \@ifnum{#1=\tw@}{%
-    \let\@listcomma\relax
-  }{%
-    \let\@listcomma\@listcomma@comma
-  }%
-}%
-\def\@reset@ac#1#2#3\@reset@ac{%
-  \def#1{#3}%
-  \@tempcnta#2\relax
-  \@ifnum{#2=\tw@}%
-}%
-\def\@listand{\@ifnum{\@tempcnta=\tw@}{\andname\space}{}}%
-\def\@listcomma@comma{\@ifnum{\@tempcnta>\@ne}{,}{}}%
-\def\@listcomma@comma@UK{\@ifnum{\@tempcnta>\tw@}{,}{}}%
-\def\@collaboration@gobble#1#2#3{}%
-\def\doauthor#1#2#3{%
-  \ignorespaces#1\unskip\@listcomma
-  \begingroup
-   #3%
-  \@if@empty{#2}{\endgroup{}{}}{\endgroup{\comma@space}{}\frontmatter@footnote{#2}}%
-  \space \@listand
-}%
-\def\x@match#1#2{%
- \temp@sw{}{%
-  \def\@tempifx{#2}%
-  \@ifx{\@tempifx#1}{%
-    \@booleantrue\temp@sw
-  }{%
-  }%
- }%
-}%
-\def\y@match#1#2#3{%
- \temp@sw{}{%
-  \def\@tempifx{#3}%
-  \@ifx{\@tempifx#1}{%
-    \@booleantrue\temp@sw
-    \def\@tempb{#2}%
-  }{%
-  }%
- }%
-}%
-\def\frontmatter@footnote#1{%
- \begingroup
-  \@booleanfalse\temp@sw
-  \def\@tempa{#1}%
-  \let\@tempb\@empty
-  \def\@TBN@opr{\y@match\@tempa}%
-  \@FMN@list
-  \temp@sw{%
-   \expandafter\frontmatter@footnotemark
-   \expandafter{\@tempb}%
-  }{%
-   \stepcounter\@mpfn
-   \expandafter\expandafter
-   \expandafter\frontmatter@foot@mark
-   \expandafter\expandafter
-   \expandafter{%
-   \expandafter \the\csname c@\@mpfn\endcsname
-               }{#1}%
-  }%
- \endgroup
-}%
-\def\frontmatter@foot@mark#1#2{%
- \frontmatter@footnotemark{#1}%
- \g@addto@macro\@FMN@list{\@TBN@opr{#1}{#2}}%
-}%
-\appdef\frontmatter@init{%
- \global\let\@FMN@list\@empty
-}%
-\def\frontmatter@footnotemark#1{%
- \leavevmode
- \ifhmode\edef\@x@sf{\the\spacefactor}\nobreak\fi
-  \begingroup
-   \hyper@linkstart {link}{frontmatter.#1}%
-    \csname c@\@mpfn\endcsname#1\relax
-    \def\@thefnmark{\frontmatter@thefootnote}%
-    \@makefnmark
-   \hyper@linkend
-  \endgroup
- \ifhmode\spacefactor\@x@sf\fi
- \relax
-}%
-\def\keywords#1{%
-  \aftermaketitle@chk{\keywords}%
-  \gdef\@keywords{#1}%
-}%
-\appdef\frontmatter@init{%
- \let\@keywords\@empty
-}%
-\newcommand*\frontmatter@date[2][\Dated@name]{\def\@date{#1#2}}%
-\def\@date{}%
-\newcommand*\received[2][\Received@name]{\def\@received{#1#2}}%
-\def\@received{}%
-\newcommand*\revised[2][\Revised@name]{\def\@revised{#1#2}}%
-\def\@revised{}%
-\newcommand*\accepted[2][\Accepted@name]{\def\@accepted{#1#2}}%
-\def\@accepted{}%
-\newcommand*\published[2][\Published@name]{\def\@published{#1#2}}%
-\def\@published{}%
-\def\pacs#1{%
-  \aftermaketitle@chk{\pacs}%
-  \gdef\@pacs{#1}%
-}%
-\appdef\frontmatter@init{%
- \let\@pacs\@empty
-}%
-\def\preprint#1{\gappdef\@preprint{\preprint{#1}}}%
-\appdef\frontmatter@init{%
- \let\@preprint\@empty
-}%
-\newbox\absbox
-\def\toclevel@abstract{1}%
-\def\addcontents@abstract{%
- \phantomsection
- \expandafter\def\csname Parent0\endcsname{section*.2}%
- \expandafter\@argswap@val\expandafter{\abstractname}{\addcontentsline{toc}{abstract}}%
-}%
-\newenvironment{frontmatter@abstract}{%
-  \aftermaketitle@chk{\begin{abstract}}%
-  \global\setbox\absbox\vbox\bgroup
-   \color@begingroup
-   \columnwidth\textwidth
-   \hsize\columnwidth
-   \@parboxrestore
-   \def\@mpfn{mpfootnote}\def\thempfn{\thempfootnote}\c@mpfootnote\z@
-   \let\@footnotetext\frontmatter@footnotetext
-   \minipagefootnote@init
-   \let\set@listindent\set@listindent@
-   \let\@listdepth\@mplistdepth \@mplistdepth\z@
-   \let@environment{description}{frontmatter@description}%
-   \@minipagerestore
-   \@setminipage
-    \frontmatter@abstractheading
-    \frontmatter@abstractfont
-    \let\footnote\mini@note
-    \expandafter\everypar\expandafter{\the\everypar\addcontents@abstract\everypar{}}%
-}{%
-    \par
-    \unskip
-    \minipagefootnote@here
-    \@minipagefalse   %% added 24 May 89
-    \color@endgroup
-  \egroup
-}%
-\long\def\frontmatter@footnotetext#1{%
-  \minipagefootnote@pick
-    \set@footnotefont
-    \set@footnotewidth
-    \@parboxrestore
-    \protected@edef\@currentlabel{\csname p@\@mpfn\endcsname\@thefnmark}%
-    \color@begingroup
-      \frontmatter@makefntext{%
-        \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox\vadjust{\vskip\z@skip}%
-      }%
-    \color@endgroup
-  \minipagefootnote@drop
-}%
-\def\ltx@no@footnote{%
- \let\ltx@xfootnote\ltx@no@xfootnote\let\ltx@yfootnote\ltx@no@yfootnote
- \let\ltx@xfootmark\ltx@no@xfootmark\let\ltx@yfootmark\ltx@no@yfootmark
- \let\ltx@xfoottext\ltx@no@xfoottext\let\ltx@yfoottext\ltx@no@yfoottext
-}%
-\def\ltx@no@xfootnote[#1]#2{\ltx@no@footwarn\footnote}%
-\def\ltx@no@yfootnote#1{\ltx@no@footwarn\footnote}%
-\def\ltx@no@xfootmark[#1]{\ltx@no@footwarn\footnotemark}%
-\def\ltx@no@yfootmark{\ltx@no@footwarn\footnotemark}%
-\def\ltx@no@xfoottext[#1]#2{\ltx@no@footwarn\footnotetext}%
-\def\ltx@no@yfoottext#1{\ltx@no@footwarn\footnotetext}%
-\def\ltx@no@footwarn#1{%
- \class@warn{%
-  The \string#1\space command is not legal on the title page;
-  using \string\thanks\space instead might suit you: consult the manual for details%
- }%
-}%
-\def\frontmatter@abstractheading{%
- \begingroup
-  \centering\large
-  \abstractname
-  \par
- \endgroup
-}%
-\def\frontmatter@abstractfont{}%
-\newenvironment{frontmatter@description}{%
- \list{}{%
-  \leftmargin\z@
-  \labelwidth\z@
-  \itemindent\z@
-  \let\makelabel\frontmatter@descriptionlabel
- }%
-}{%
- \endlist
-}%
-\def\frontmatter@descriptionlabel#1{%
- \hspace\labelsep
- \normalfont\bfseries
- #1:%
-}%
-\def\frontmatter@abstractwidth{\textwidth}
-\def\frontmatter@abstract@produce{%
-  \par
-  \preprintsty@sw{%
-   \do@output@MVL{%
-    \vskip\frontmatter@preabstractspace
-    \vskip200\p@\@plus1fil
-    \penalty-200\relax
-    \vskip-200\p@\@plus-1fil
-   }%
-  }{%
-   \addvspace{\frontmatter@preabstractspace}%
-  }%
-   \begingroup
-    \dimen@\baselineskip
-    \setbox\z@\vtop{\unvcopy\absbox}%
-    \advance\dimen@-\ht\z@\advance\dimen@-\prevdepth
-    \@ifdim{\dimen@>\z@}{\vskip\dimen@}{}%
-   \endgroup
-   \begingroup
-    \prep@absbox
-    \unvbox\absbox
-    \post@absbox
-   \endgroup
-  \@ifx{\@empty\mini@notes}{}{\mini@notes\par}%
-  \addvspace\frontmatter@postabstractspace
-}%
-\appdef\frontmatter@init{\let\mini@notes\@empty}%
-\let\prep@absbox\@empty
-\let\post@absbox\@empty
-\def\frontmatter@preabstractspace{.5\baselineskip}
-\def\frontmatter@postabstractspace{.5\baselineskip}
-\newenvironment{frontmatter@titlepage}{%
-      \twocolumn@sw{\onecolumngrid}{\newpage}%
-      \thispagestyle{titlepage}%
-      \setcounter{page}\@ne
-}{%
-     \twocolumn@sw{\twocolumngrid}{\newpage}%
-     \twoside@sw{}{%
-        \setcounter{page}\@ne
-     }%
-}%
-\def\frontmatter@maketitle{%
-  \@author@finish
-  \title@column\titleblock@produce
-  \suppressfloats[t]%
-  \let\and\relax
-  \let\affiliation\@gobble
-  \let\author\@gobble
-  \let\@AAC@list\@empty
-  \let\@AFF@list\@empty
-  \let\@AFG@list\@empty
-  \let\@AF@join\@AF@join@error
-  \let\email\@gobble
-  \let\@address\@empty
-  \let\maketitle\relax
-  \let\thanks\@gobble
-  \let\abstract\@undefined\let\endabstract\@undefined
-  \titlepage@sw{%
-   \vfil
-   \clearpage
-  }{}%
-}%
-\def\maketitle@Hy{%
-  \let\Hy@saved@footnotemark\@footnotemark
-  \let\Hy@saved@footnotetext\@footnotetext
-  \let\@footnotemark\H@@footnotemark
-  \let\@footnotetext\H@@footnotetext
-  \@ifnextchar[%]
-   \Hy@maketitle@optarg
-   {%
-    \HyOrg@maketitle
-    \Hy@maketitle@end
-   }%
-}%
-\appdef\class@documenthook{%
-  \@ifx{\maketitle\maketitle@Hy}{%
-   \class@info{Taking \string\maketitle\space back from hyperref}%
-   \let\maketitle\frontmatter@maketitle
-  }{%
-  }%
-}%
-\def\titleblock@produce{%
- \begingroup
-  \ltx@footnote@pop
-  \def\@mpfn{mpfootnote}%
-  \def\thempfn{\thempfootnote}%
-  \c@mpfootnote\z@
-  \let\@makefnmark\frontmatter@makefnmark
-  \frontmatter@setup
-  \thispagestyle{titlepage}\label{FirstPage}%
-  \frontmatter@title@produce
-  \groupauthors@sw{%
-   \frontmatter@author@produce@group
-  }{%
-   \frontmatter@author@produce@script
-  }%
-  \frontmatter@RRAPformat{%
-   \expandafter\produce@RRAP\expandafter{\@date}%
-   \expandafter\produce@RRAP\expandafter{\@received}%
-   \expandafter\produce@RRAP\expandafter{\@revised}%
-   \expandafter\produce@RRAP\expandafter{\@accepted}%
-   \expandafter\produce@RRAP\expandafter{\@published}%
-  }%
-  \frontmatter@abstract@produce
-  \@ifx@empty\@pacs{}{%
-   \@pacs@produce\@pacs
-  }%
-  \@ifx@empty\@keywords{}{%
-   \@keywords@produce\@keywords
-  }%
-  \par
-  \frontmatter@finalspace
- \endgroup
-}%
-\def\toclevel@title{0}%
-\def\frontmatter@title@produce{%
- \begingroup
-  \frontmatter@title@above
-  \frontmatter@title@format
-  \@title
-  \unskip
-  \phantomsection\expandafter\@argswap@val\expandafter{\@title}{\addcontentsline{toc}{title}}%
-  \@ifx{\@title@aux\@title@aux@cleared}{}{%
-   \expandafter\frontmatter@footnote\expandafter{\@title@aux}%
-  }%
-  \par
-  \frontmatter@title@below
- \endgroup
-}%
-\appdef\let@mark{\let\\\relax}%
-\def\frontmatter@title@above{}%
-\def\frontmatter@title@format{}%
-\def\frontmatter@title@below{\addvspace{\baselineskip}}%
-\def\frontmatter@author@produce@script{%
-  \begingroup
-    \let\@author@present\@author@present@script
-    \frontmatterverbose@sw{\typeout{\string\frontmatter@author@produce@script:}\say\@AAC@list\say\@AFF@list\say\@AFG@list}{}%
-    \let\AU@temp\@empty
-    \@tempcnta\z@
-    \let\AF@opr \@gobble
-    \def\AU@opr{\@author@count\@tempcnta}%
-    \def\CO@opr{\@collaboration@count\AU@temp\@tempcnta}%
-    \@AAC@list
-    \expandafter\CO@opr\@author@cleared
-    \begingroup
-     \frontmatter@authorformat
-     \let\AF@opr \@affilID@def
-     \let\AU@opr \@author@present
-     \def\CO@opr{\@collaboration@present\AU@temp}%
-     \set@listcomma@list\AU@temp
-     \@AAC@list
-     \unskip\unskip
-     \par
-    \endgroup
-    \begingroup
-     \frontmatter@above@affiliation@script
-     \let\AFF@opr \@affil@script
-     \@AFF@list
-     \frontmatter@footnote@produce
-     \par
-    \endgroup
-  \endgroup
-}%
-\def\@author@count#1{%
- \advance#1\@ne
- \@author@gobble
-}%
-\def\@collaboration@present#1#2#3#4{%
- \par
- \begingroup
-  \frontmatter@collaboration@above
-  \@affilID@def{}%
-  \@tempcnta\z@
-  \@author@present{}{(\ignorespaces#3\unskip)}{#4}%
-  \par
- \endgroup
- \set@listcomma@list#1%
-}%
-\def\frontmatter@collaboration@above{}%
-\def\@collaboration@count#1#2{%
- \appdef@eval#1{\the#2}#2\z@
- \@author@gobble
-}%
-\def\@affilID@def{\def\@affilID@temp}%
-\let\@affilID@temp\@empty
-\def\affil@script#1#2#3{%
- \def\@tempifx{#1}\@ifx{\@tempifx\@tempa}{%
-  \@if@empty{#2}{}{%
-   \par
-   \begingroup
-    \def\@thefnmark{#1}\@makefnmark\ignorespaces
-    #2%
-    \@if@empty{#3}{}{\frontmatter@footnote{#3}}%
-    \par
-   \endgroup
-  }%
- }{}%
-}%
-\def\@affil@script#1#2#3#4{%
- \@ifnum{#1=\z@}{}{%
-  \par
-  \begingroup
-   \frontmatter@affiliationfont
-   \@ifnum{\c@affil<\affil@cutoff}{}{%
-    \def\@thefnmark{#1}\@makefnmark
-   }%
-   \ignorespaces#3%
-   \@if@empty{#4}{}{\frontmatter@footnote{#4}}%
-   \par
-  \endgroup
- }%
-}%
-\let\affil@cutoff\@ne
-\def\@author@present@script#1#2#3{%
- \begingroup
-  \gdef\comma@space{\textsuperscript{,\,}}%
-  \doauthor{#2}{#3}{\@affil@present@script}%
- \endgroup
- \advance\@tempcnta\m@ne
-}%
-\def\@affilcomma#1#2{%
- \@ifx{\z@#1}{%
-  \@ifx{\relax#2}{}{%
-   \@affilcomma{#2}%
-  }%
- }{%
-  #1%
-  \@ifx{\relax#2}{}{%
-   \@ifx{\z@#2}{%
-    \@affilcomma
-   }{%
-    ,\,\@affilcomma{#2}%
-   }%
-  }%
- }%
-}%
-\def\@affil@present@script{%
- \let\@tempa\@empty
- \expandafter\@affil@present@script@\@affilID@temp\relax
-}%
-\def\@affil@present@script@#1{%
- \@ifx{\relax#1}{%
-  \@ifx{\@tempa\@empty}{%
-   \aftergroup\false@sw
-  }{%
-   \textsuperscript{\expandafter\@affilcomma\@tempa\relax\relax}%
-   \aftergroup\true@sw
-  }%
- }{%
-  \@ifnum{#1=\z@}{}{\appdef\@tempa{{#1}}}%
-  \@affil@present@script@
- }%
-}%
-\@provide\@author@parskip{\z@skip}%
-\def\frontmatter@author@produce@group{%
-  \begingroup
-    \let\@author@present\@author@present@group
-    \frontmatter@authorformat
-    \frontmatterverbose@sw{\typeout{\string\frontmatter@author@produce@group:}\say\@AAC@list\say\@AFF@list\say\@AFG@list}{}%
-    \let\AU@temp\@empty
-    \set@listcomma@list\AU@temp
-    \def\CO@opr{\@collaboration@present\AU@temp}%
-    \let\AFG@opr \affils@present@group
-    \let\@listcomma\relax
-    \@AFG@list
-    \frontmatter@footnote@produce
-    \par
-  \endgroup
-  \frontmatter@authorbelow
-}%
-\@provide\frontmatter@authorbelow{}%
-\def\affils@present@group#1{%
- \begingroup
-   \def\AF@temp{#1}%
-   \@tempcnta\z@
-   \let\AU@opr \@undefined
-   \let\CO@opr \@undefined
-   \def\AF@opr{\@affilID@count\AF@temp\@tempcnta}%
-   \@AAC@list
-   \@ifnum{\@tempcnta=\z@}{}{%
-    \begingroup
-     \frontmatter@above@affilgroup
-     \set@listcomma@count\@tempcnta
-     \let\AU@opr \@undefined
-     \let\CO@opr \@undefined
-     \def\AF@opr{\@affilID@match\AF@temp}%
-     \@AAC@list
-    \endgroup
-    \begingroup
-     \par
-     \frontmatter@above@affiliation
-     \frontmatter@affiliationfont
-     \let\\\frontmatter@addressnewline
-     \@tempcnta\z@
-     \@tfor\AF@temp:=#1\do{%
-      \expandafter\@ifx\expandafter{\expandafter\z@\AF@temp}{}{%
-       \advance\@tempcnta\@ne
-      }%
-     }%
-     \@ifnum{\@tempcnta=\tw@}{%
-      \let\@listcomma\relax
-     }{}%
-     \def@after@address
-     \runinaddress@sw{%
-     }{%
-      \tightenlines@sw{}{%
-       \parskip\z@
-      }%
-      \appdef\after@address\par
-     }%
-     \let\AFF@opr \@affil@group
-     \do@affil@fromgroup\@AFF@list#1\relax
-    \endgroup
-   }%
-   \par
- \endgroup
-}%
-\def\def@after@address{\def\after@address{\@listcomma\ \@listand}}%
-\def\def@after@address@empty{\let\after@address\@empty}%
-\def\@affilID@count#1#2#3{%
-  \def\@tempifx{#3}%
-  \@ifx{\@tempifx#1}{%
-    \def\AU@opr{\@author@count#2}%
-  }{%
-    \let\AU@opr \@author@gobble
-  }%
-  \let\CO@opr \@collaboration@gobble
-}%
-\def\@affilID@match#1#2{%
- \def\@tempifx{#2}%
- \@ifx{\@tempifx#1}{%
-   \let\AU@opr \@author@present
- }{%
-   \let\AU@opr \@author@gobble
- }%
-  \let\CO@opr \@collaboration@gobble
-}%
-\def\do@affil@fromgroup#1#2{%
-  \@ifx{\relax#2}{}{%
-    \count@#2\relax
-    \@ifnum{\z@=\count@}{}{#1}%
-    \do@affil@fromgroup#1%
-  }%
-}%
-\def\@affil@group#1#2#3#4{%
-  \@ifnum{#1=\count@}{%
-   \def\@tempa{#3}%
-   \@ifx{\@tempa\blankaffiliation}{}{%
-    #3%
-    \@if@empty{#4}{}{%
-     \frontmatter@footnote{#4}%
-    }%
-    \after@address
-   }%
-   \advance\@tempcnta\m@ne
-  }{}%
-}%
-\def\@author@present@group#1#2#3{%
-  \gdef\comma@space{\gdef\comma@space{\textsuperscript{,\,}}}%
-  \doauthor{#2}{#3}{\@affil@present@group}%
-  \advance\@tempcnta\m@ne
-}%
-\def\@affil@present@group{%
- \aftergroup\false@sw
-}%
-\def\@pacs@produce#1{%
- \showPACS@sw{%
-  \begingroup
-   \frontmatter@PACS@format
-   \@pacs@name#1\par
-  \endgroup
- }{%
-  \@if@empty{#1}{}{%
-   \class@warn{\PACS@warn}%
-  }%
- }%
-}%
-\def\PACS@warn{If you want your PACS to appear in your output, use document class option showpacs}%
-\def\@keywords@produce#1{%
- \showKEYS@sw{%
-  \begingroup
-   \frontmatter@keys@format
-   \@keys@name#1\par
-  \endgroup
- }{%
-  \@if@empty{#1}{}{%
-   \class@warn{If you want your keywords to appear in your output, use document class option showkeys}%
-  }%
- }%
-}%
-\def\frontmatter@footnote@produce@footnote{%
- \let\@TBN@opr\present@FM@footnote
- \@FMN@list
- \global\let\@FMN@list\@empty
-}%
-\def\present@FM@footnote#1#2{%
- \begingroup
-  \csname c@\@mpfn\endcsname#1\relax
-  \def\@thefnmark{\frontmatter@thefootnote}%
-  \frontmatter@footnotetext{#2}%
- \endgroup
-}%
-\def\frontmatter@footnote@produce@endnote{%
-}%
-\appdef\frontmatter@init{%
- \@ifxundefined\title@column         {\let\title@column\@empty}{}%
- \@ifxundefined\preprintsty@sw       {\@booleanfalse\preprintsty@sw}{}%
- \@ifxundefined\frontmatter@footnote@produce{\let\frontmatter@footnote@produce\frontmatter@footnote@produce@footnote}{}%
- \@ifxundefined\do@output@MVL        {\let\do@output@MVL\@firstofone}{}%
- \@ifxundefined\comma@space          {\let\comma@space\@empty}{}%
-}%
-\def\frontmatter@thefootnote{%
- \altaffilletter@sw{\@alph}{\@fnsymbol}{\csname c@\@mpfn\endcsname}%
-}%
-\@ifx{\altaffilletter@sw\@undefined}{\@booleantrue\altaffilletter@sw}{}%
-\def\frontmatter@makefnmark{%
- \@textsuperscript{%
-  \normalfont\@thefnmark
- }%
-}%
-\long\def\frontmatter@makefntext#1{%
- \parindent 1em
- \noindent
- \Hy@raisedlink{\hyper@anchorstart{frontmatter.\expandafter\the\csname c@\@mpfn\endcsname}\hyper@anchorend}%
- \@makefnmark
- #1%
-}%
-\def\frontmatter@setup{}%
-\def\frontmatter@RRAPformat#1{%
- \removelastskip
- \begingroup
-  \frontmatter@RRAP@format
-  #1\par
- \endgroup
-}%
-\def\punct@RRAP{; }%
-\def\produce@RRAP#1{%
-  \@if@empty{#1}{}{%
-   \@ifvmode{\leavevmode}{\unskip\punct@RRAP\ignorespaces}%
-   #1%
-  }%
-}%
-\def\frontmatter@authorformat{}%
-\def\frontmatter@above@affilgroup{}%
-\def\frontmatter@above@affiliation{}%
-\def\frontmatter@above@affiliation@script{}%
-\def\frontmatter@affiliationfont{\itshape\selectfont}%
-\def\frontmatter@RRAP@format{}%
-\def\frontmatter@PACS@format{}%
-\def\frontmatter@keys@format{}%
-\def\frontmatter@finalspace{\addvspace{18\p@}}
-\def\frontmatter@addressnewline{%
-  \@ifhmode{\skip@\lastskip\unskip\unpenalty\break\hskip\skip@}{}%
-  % was: \vskip-.5ex
-}%
-\def\frontmatter@preabstractspace{5.5\p@}
-\def\frontmatter@postabstractspace{6.5\p@}
-\def\aftermaketitle@chk#1{%
-  \@ifx{\maketitle\relax}{%
-    \class@err{\protect#1 must be used before \protect\maketitle}%
-  }{}%
-}%
-\def\ps@titlepage{\ps@empty}%
-\def\volumeyear#1{\gdef\@volumeyear{#1}}%
-\def\@volumeyear{}%
-\def\volumenumber#1{\gdef\@volumenumber{#1}}%
-\def\@volumenumber{}%
-\def\issuenumber#1{\gdef\@issuenumber{#1}}%
-\def\@issuenumber{}%
-\def\eid#1{\gdef\@eid{#1}}%
-\def\@eid{}%
-\def\startpage#1{\gdef\@startpage{#1}\c@page#1\relax}%
-\def\@startpage{\pageref{FirstPage}}%
-\def\endpage#1{\gdef\@endpage{#1}}%
-\def\@endpage{\pageref{LastPage}}%
-\def\print@toc#1{%
- \begingroup
-  \expandafter\section
-  \expandafter*%
-  \expandafter{%
-              \csname#1name\endcsname
-              }%
-  \let\appendix\appendix@toc
-  \@starttoc{#1}%
- \endgroup
-}%
-\def\appendix@toc{}%
-\def\Dated@name{Dated }%
-\def\Received@name{Received }%
-\def\Revised@name{Revised }%
-\def\Accepted@name{Accepted }%
-\def\Published@name{Published }%
-\appdef\robustify@contents{%
- \let\thanks\@gobble\let\class@warn\@gobble
- \def\begin{\string\begin}\def\end{\string\end}%
-}%
-\@ifxundefined\frontmatter@syntax@sw{\@booleantrue\frontmatter@syntax@sw}{}%
-\frontmatter@syntax@sw{%
- \let\title         \frontmatter@title
- \let\author        \frontmatter@author
- \let\date          \frontmatter@date
- \@ifxundefined\@maketitle{%
-  \let\maketitle    \frontmatter@maketitle
-  \@booleantrue     \titlepage@sw
- }{%
-  \let\@maketitle   \frontmatter@maketitle
-  \prepdef\maketitle\@author@finish
- }%
- \let\noaffiliation \frontmatter@noaffiliation
- \let\thanks@latex  \thanks
- \let\thanks        \frontmatter@thanks
- \let\and@latex     \and
- \let\and           \frontmatter@and
- \let@environment{titlepage}{frontmatter@titlepage}%
- \let@environment{abstract}{frontmatter@abstract}%
-}{%
- \let\noaffiliation\@empty
-}%
-\typeout{%
-ltxgrid%
- [2020/10/03 4.2e page grid package (portions licensed from W. E. Baxter web at superscript.com)]% \fileversion
-}%
-\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}%
-}%
-\let\setup@hook\@empty
-\appdef\document@inithook{%
- \switch@longtable
- \let\LT@makecaption\LT@makecaption@rtx
-}%
-\def\LT@makecaption@rtx#1#2#3{%
-  \LT@mcol\LT@cols c{%
-    \hbox to\z@{%
-     \hss
-     \parbox[t]\LTcapwidth{%
-      \sbox\@tempboxa{#1{#2: }#3\unskip\nobreak\vrule\@width\z@\@height\z@\@depth .5\baselineskip}%
-      \ifdim\wd\@tempboxa>\hsize
-        #1{#2: }#3\unskip\nobreak\vrule\@width\z@\@height\z@\@depth .5\baselineskip
-      \else
-        \hbox to\hsize{\hfil\box\@tempboxa\hfil}%
-      \fi
-      \endgraf
-     }%
-     \hss
-    }%
-  }%
-}%
-\def\protectdef@boldmath{%
- \expandafter\@ifnotrelax\csname boldmath \endcsname{}{%
-  \class@info{Robustifying \string\LaTeX's \string\boldmath\space command}%
-  \expandafter\let\csname boldmath \endcsname\boldmath
-  \expandafter\def\expandafter\boldmath\expandafter{\expandafter\protect\csname boldmath \endcsname}%
- }%
-}%
-\appdef\document@inithook{%
- \protectdef@boldmath
-}%
-\DeclareOption{checkin}{%
-  \@booleantrue\dateinRH@sw
-  \@booleantrue\preprintsty@sw
-  \def\@pointsize{12}%
-  \@booleantrue\showPACS@sw
-  \@booleantrue\showKEYS@sw
-  \def\fp@proc@h{\allow@breaking@tables}%
-  \def\fp@proc@H{\allow@breaking@tables}%
-}%
-\@booleanfalse\dateinRH@sw
-\def\checkindate{\dateinRH@sw{{\tiny(\today)}}{}}%
-\def\allow@breaking@tables{%
- \def\array@default{v}% tabular can break over pages
- \@booleanfalse\floats@sw % table can break over pages
-}%
-\DeclareOption{preprint}{%
- \@booleantrue\preprintsty@sw
- \ExecuteOptions{12pt}%
-}%
-\DeclareOption{reprint}{%
-\@booleanfalse\preprintsty@sw
-\@booleantrue\twocolumn@sw
- \ExecuteOptions{10pt}%
-}%
-\DeclareOption{manuscript}{%
- \class@warn{Document class option manuscript is obsolete; use preprint instead}%
- \ExecuteOptions{preprint}%
-}%
-\@booleanfalse\preprintsty@sw
-\DeclareOption{showpacs}{%
-  \@booleantrue\showPACS@sw
-}%
-\DeclareOption{noshowpacs}{%
-  \@booleanfalse\showPACS@sw
-}%
-\DeclareOption{showkeys}{%
-  \@booleantrue\showKEYS@sw
-}%
-\DeclareOption{noshowkeys}{%
-  \@booleanfalse\showKEYS@sw
-}%
-\@booleanfalse\showPACS@sw
-\@booleanfalse\showKEYS@sw
-\DeclareOption{balancelastpage}{%
-  \@booleantrue\balancelastpage@sw
-}%
-\DeclareOption{nobalancelastpage}{%
-  \@booleanfalse\balancelastpage@sw
-}%
-\@booleantrue\balancelastpage@sw
-\DeclareOption{nopreprintnumbers}{\@booleanfalse\preprint@sw}%
-\DeclareOption{preprintnumbers}{\@booleantrue\preprint@sw}%
-\appdef\setup@hook{%
- \@ifxundefined\preprint@sw{\let\preprint@sw\preprintsty@sw}{}%
-}%
-\DeclareOption{hyperref}{%
- \class@warn{Class option "hyperref" is no longer supported.^^JEmploy \string\usepackage{hyperref} instead}%
-}%
-\DeclareOption{10pt}{\def\@pointsize{10}}%
-\DeclareOption{11pt}{\def\@pointsize{11}}%
-\DeclareOption{12pt}{\def\@pointsize{12}}%
-\let\@pointsize\@undefined
-\DeclareOption{a4paper}{%
-    \setlength\paperheight {297mm}%
-    \setlength\paperwidth  {210mm}%
-}%
-\DeclareOption{a5paper}{%
-    \setlength\paperheight {210mm}%
-    \setlength\paperwidth  {148mm}%
-}%
-\DeclareOption{b5paper}{%
-    \setlength\paperheight {250mm}%
-    \setlength\paperwidth  {176mm}%
-}%
-\DeclareOption{letterpaper}{%
-    \setlength\paperheight {11in}%
-    \setlength\paperwidth  {8.5in}%
-}%
-\DeclareOption{legalpaper}{%
-    \setlength\paperheight {14in}%
-    \setlength\paperwidth  {8.5in}%
-}%
-\DeclareOption{executivepaper}{%
-    \setlength\paperheight {10.5in}%
-    \setlength\paperwidth  {7.25in}%
-}%
-\DeclareOption{landscape}{%
-    \setlength\@tempdima   {\paperheight}%
-    \setlength\paperheight {\paperwidth}%
-    \setlength\paperwidth  {\@tempdima}%
-}%
-\ds@letterpaper
-\DeclareOption{bibnotes}{\let\frontmatter@footnote@produce\frontmatter@footnote@produce@endnote}%
-\DeclareOption{nobibnotes}{\let\frontmatter@footnote@produce\frontmatter@footnote@produce@footnote}%
-\let\frontmatter@footnote@produce\frontmatter@footnote@produce@footnote
-\appdef\class@enddocumenthook{\auto@bib}%
-\DeclareOption{footinbib}{\@booleantrue\footinbib@sw}
-\DeclareOption{nofootinbib}{\@booleanfalse\footinbib@sw}
-\@booleanfalse\footinbib@sw
-\DeclareOption{altaffilletter}{\@booleantrue\altaffilletter@sw}%
-\DeclareOption{altaffilsymbol}{\@booleanfalse\altaffilletter@sw}%
-\@booleanfalse\altaffilletter@sw
-\DeclareOption{superbib}{%
- \let\place@bibnumber\place@bibnumber@sup
-}%
-\def\place@bibnumber{\NATx@bibnumfmt}%
-\def\place@bibnumber@sup#1{\textsuperscript{#1}}%
-\def\place@bibnumber@inl#1{[#1]}%
-\DeclareOption{citeautoscript}{\@booleantrue\citeautoscript@sw}%
-\@booleanfalse\citeautoscript@sw
-\DeclareOption{longbibliography}{\@booleantrue\longbibliography@sw}%
-\DeclareOption{nolongbibliography}{\@booleanfalse\longbibliography@sw}%
-\@booleantrue\longbibliography@sw
-\DeclareOption{eprint}{\@booleantrue\eprint@enable@sw}%
-\DeclareOption{noeprint}{\@booleanfalse\eprint@enable@sw}%
-\@booleantrue\eprint@enable@sw
-\@booleanfalse\twoside@sw
-\appdef\document@inithook{%
- \twoside@sw{\@twosidetrue}{\@twosidefalse}%
-}%
-\DeclareOption{twoside}{\@booleantrue \twoside@sw\@mparswitchfalse}%
-\DeclareOption{oneside}{\@booleanfalse\twoside@sw\@mparswitchtrue}%
-\DeclareOption{onecolumn}{\@booleanfalse\twocolumn@sw}%
-\DeclareOption{twocolumn}{\@booleantrue\twocolumn@sw}%
-\@booleanfalse\twocolumn@sw
-\def\select@column@grid{%
- \twocolumn@sw{%
-  \twocolumn@grid@setup
-  \open@twocolumn
- }{%
-  \onecolumn@grid@setup
- }%
-}%
-\appdef\class@documenthook{%
- \select@column@grid
-}%
-\appdef\setup@hook{%
- \let\clearpage@ltx\clearpage
- \prepdef\clear@document{\let\clearpage\clearpage@ltx\let\clear@document\@empty\close@column}%
- \appdef\class@documenthook{%
-  \appdef\class@enddocumenthook{%
-   \let\clearpage\clear@document
-  }%
- }%
-}%
-\DeclareOption{author-year}{\@booleantrue\authoryear@sw}%
-\DeclareOption{numerical}{\@booleanfalse\authoryear@sw}%
-\@booleanfalse\authoryear@sw
-\DeclareOption{galley}{%
-  \ExecuteOptions{onecolumn}%
-  \@booleantrue\galley@sw
-  \@booleanfalse\preprintsty@sw
-  \appdef\setup@hook{%
-    \advance\textwidth-\columnsep
-    \textwidth.5\textwidth
-  }%
-}%
-\@booleanfalse\galley@sw
-\DeclareOption{raggedbottom}{\@booleantrue\raggedcolumn@sw}
-\DeclareOption{flushbottom}{\@booleanfalse\raggedcolumn@sw}
-\@booleanfalse\raggedcolumn@sw
-\appdef\setup@hook{%
- \raggedcolumn@sw{\raggedbottom}{\flushbottom}%
-}%
-\DeclareOption{tightenlines}{\@booleantrue\tightenlines@sw}
-\@booleanfalse\tightenlines@sw
-\@booleanfalse\lengthcheck@sw
-\DeclareOption{lengthcheck}{%
- \@booleantrue\lengthcheck@sw
- \ExecuteOptions{reprint}%
-}%
-\appdef\setup@hook{%
- \lengthcheck@sw{\@booleantrue\tally@box@size@sw}{}%
-}%
-\appdef\setup@hook{%
- \draft@sw{\overfullrule 5\p@}{\overfullrule\z@}%
-}%
-\DeclareOption{draft}{\@booleantrue\draft@sw}%
-\DeclareOption{final}{\@booleanfalse\draft@sw}%
-\@booleanfalse\draft@sw
-\appdef\setup@hook{%
- \eqsecnum@sw{%
-  \@addtoreset{equation}{section}%
-  \def\theequation@prefix{\arabic{section}.}%
- }{}%
-}%
-\DeclareOption{eqsecnum}{\@booleantrue\eqsecnum@sw}%
-\@booleanfalse\eqsecnum@sw
-\appdef\setup@hook{%
- \setup@secnums
-}%
-\DeclareOption{secnumarabic}{%
- \def\setup@secnums{\secnums@arabic}%
-}%
-\def\setup@secnums{\secnums@rtx}%
-\DeclareOption{fleqn}{%
- \input{fleqn.clo}%
-}%
-\DeclareOption{floats}{\@booleantrue\floats@sw\@booleanfalse\floatp@sw}
-\DeclareOption{endfloats}{\@booleanfalse\floats@sw\@booleanfalse\floatp@sw}
-\DeclareOption{endfloats*}{\@booleanfalse\floats@sw\@booleantrue\floatp@sw}
-\@booleantrue\floats@sw
-\@booleantrue\floatp@sw
-\DeclareOption{titlepage}{\@booleantrue\titlepage@sw}
-\DeclareOption{notitlepage}{\@booleanfalse\titlepage@sw}
-\@booleanfalse\titlepage@sw
-\def\change@society#1{%
- \def\@tempa{#1}%
- \@ifxundefined\@society{%
-  \class@info{Selecting society \@tempa}%
-  \let\@society\@tempa
- }{%
-  \@ifx{\@tempa\@society}{}{%
-   \class@warn{Conflicting society \@tempa<>\@society; not selected}%
-  }%
- }%
-}%
-\def\change@journal#1{%
- \def\@tempa{#1}%
- \@ifxundefined\@journal{%
-  \class@info{Selecting journal \@tempa}%
-  \let\@journal\@tempa
- }{%
-  \@ifx{\@tempa\@journal}{}{%
-   \class@warn{Conflicting journal \@tempa<>\@journal; not selected}%
-  }%
- }%
-}%
-\DeclareOption{osa}{\change@society{osa}\let\@journal\@undefined}%
-\DeclareOption{osameet}{\change@society{osa}\def\@journal{osameet}}%
-\DeclareOption{opex}{\change@society{osa}\def\@journal{opex}}%
-\DeclareOption{tops}{\change@society{osa}\def\@journal{tops}}%
-\DeclareOption{josa}{\change@society{osa}\def\@journal{josa}}%
-\let\rtx@require@packages\@empty
-\appdef\rtx@require@packages{%
- \RequirePackage[overload]{textcase}%
-}%
-\DeclareOption{amsfonts}{%
-  \def\class@amsfonts{\RequirePackage{amsfonts}}%
-}%
-\DeclareOption{noamsfonts}{%
-  \let\class@amsfonts\@empty
-}%
-\appdef\rtx@require@packages{%
- \@ifxundefined\class@amsfonts{}{\class@amsfonts}%
-}%
-\DeclareOption{amssymb}{%
-  \def\class@amssymb{\RequirePackage{amssymb}}%
-}%
-\DeclareOption{noamssymb}{%
-  \let\class@amssymb\@empty
-}%
-\appdef\rtx@require@packages{%
- \@ifxundefined\class@amssymb{}{\class@amssymb}%
-}%
-\DeclareOption{amsmath}{%
-  \def\class@amsmath{\RequirePackage{amsmath}[\ver@amsmath@prefer]}%
-}%
-\DeclareOption{noamsmath}{%
-  \let\class@amsmath\@empty
-}%
-\appdef\rtx@require@packages{%
- \preserve@LaTeX
- \@ifxundefined\class@amsmath{}{\class@amsmath}%
- \appdef\class@enddocumenthook{\test@amsmath@ver}%
-}%
-\appdef\preserve@LaTeX{%
- \let\@ifl@aded@LaTeX\@ifl@aded
- \let\@ifpackageloaded@LaTeX\@ifpackageloaded
- \let\@pkgextension@LaTeX\@pkgextension
- \let\@ifpackagelater@LaTeX\@ifpackagelater
- \let\@ifl@ter@LaTeX\@ifl@ter
- \let\@ifl@t@r@LaTeX\@ifl@t@r
- \let\@parse@version@LaTeX\@parse@version
-}%
-\appdef\restore@LaTeX{%
- \let\@ifl@aded\@ifl@aded@LaTeX
- \let\@ifpackageloaded\@ifpackageloaded@LaTeX
- \let\@pkgextension\@pkgextension@LaTeX
- \let\@ifpackagelater\@ifpackagelater@LaTeX
- \let\@ifl@ter\@ifl@ter@LaTeX
- \let\@ifl@t@r\@ifl@t@r@LaTeX
- \let\@parse@version\@parse@version@LaTeX
-}%
-\def\test@amsmath@ver{%
- \begingroup
-  \restore@LaTeX
-  \@ifpackageloaded{amsmath}{%
-   \@ifpackagelater{amsmath}{\ver@amsmath@prefer}{}{%
-     \class@warn{%
-      You have loaded amsmath, version "\csname ver@amsmath.sty\endcsname",\MessageBreak
-      but this class requires version "\ver@amsmath@prefer", or later.\MessageBreak
-      Please update your LaTeX installation.
-     }%
-   }%
-  }{%
-  }%
- \endgroup
-}%
-\def\ver@amsmath@prefer{2000/01/15 v2.05 AMS math features}%
-\DeclareOption{byrevtex}{\@booleantrue\byrevtex@sw}%
-\@booleanfalse\byrevtex@sw
-\DeclareOption{floatfix}{\@booleantrue\force@deferlist@sw}%
-\DeclareOption{nofloatfix}{\@booleanfalse\force@deferlist@sw}%
-\@booleanfalse\force@deferlist@sw
-\gdef\@fltovf{%
- \@latex@error{%
-  Too many unprocessed floats%
-  \force@deferlist@sw{}{; try class option [floatfix]}%
- }\@ehb
-}%
-\def\@fltstk{%
- \@latex@warning{%
-  A float is stuck (cannot be placed)%
-  \force@deferlist@sw{}{; try class option [floatfix]}%
- }%
-}%
-\DeclareOption{ltxgridinfo}{%
- \@booleantrue\ltxgrid@info@sw
-}%
-\DeclareOption{outputdebug}{%
- \@booleantrue\outputdebug@sw
- \@booleantrue\ltxgrid@info@sw
- \@booleantrue\ltxgrid@foot@info@sw
- \traceoutput
-}%
-\DeclareOption{raggedfooter}{\@booleanfalse\textheight@sw}%
-\DeclareOption{noraggedfooter}{\@booleantrue\textheight@sw}%
-\DeclareOption{frontmatterverbose}{\@booleantrue\frontmatterverbose@sw}%
-\@booleanfalse\frontmatterverbose@sw
-\DeclareOption{linenumbers}{%
- \appdef
- \class@documenthook{%
-  \RequirePackage{lineno}[2005/11/02 v4.41]%
-  \linenumbersep4pt\relax
-  \linenumbers\relax
- }%
-}%
-\DeclareOption{nomerge}{%
- \appdef\setup@hook{%
-  \@ifnum{\NAT@merge>\z@}{\let\NAT@merge\z@}{}%
- }%
-}%
-\def\@parse@class@options@society{%
- \edef\@tempa{\@ptionlist{\@currname.\@currext}}%
- \expandafter\@for\expandafter\CurrentOption\expandafter:\expandafter=\@tempa\do{%
-  \expandafter\@ifnotrelax\csname ds@\CurrentOption\endcsname{}{%
-   \IfFileExists{\CurrentOption\substyle@post.\substyle@ext}{%
-    \expandafter\change@society\expandafter{\CurrentOption}%
-    \expandafter\let\csname ds@\CurrentOption\endcsname\@empty
-   }{}%
-  }%
- }%
-}%
-\def\@parse@class@options@#1{%
- \edef\@tempa{\@ptionlist{\@currname.\@currext}}%
- \expandafter\@for\expandafter\CurrentOption\expandafter:\expandafter=\@tempa\do{%
-  \expandafter\@ifnotrelax\csname ds@\CurrentOption\endcsname{%
-   \begingroup\csname ds@\CurrentOption\endcsname
-    \@ifxundefined#1{%
-     \endgroup
-    }{%
-     \expandafter\endgroup\expandafter\def\expandafter#1\expandafter{#1}%
-    }%
-  }{}%
- }%
-}%
-\def\@parse@class@options@journal{%
- \edef\@tempa{\@ptionlist{\@currname.\@currext}}%
- \expandafter\@for\expandafter\CurrentOption\expandafter:\expandafter=\@tempa\do{%
-  \expandafter\@ifnotrelax\csname ds@\CurrentOption\endcsname{%
-   \begingroup
-    \csname ds@\CurrentOption\endcsname
-    \@ifxundefined\@journal{%
-     \endgroup
-    }{%
-     \expandafter\endgroup\expandafter\def\expandafter\@journal\expandafter{\@journal}%
-    }%
-  }{}%
- }%
-}%
-\def\@parse@class@options{%
- \edef\@tempa{\@ptionlist{\@currname.\@currext}}%
- \expandafter\@for\expandafter\CurrentOption\expandafter:\expandafter=\@tempa\do{%
-  \expandafter\@ifnotrelax\csname ds@\CurrentOption\endcsname{%
-   \begingroup
-    \csname ds@\CurrentOption\endcsname
-    \@ifxundefined\@pointsize{%
-     \endgroup
-    }{%
-     \expandafter\endgroup\expandafter\def\expandafter\@pointsize\expandafter{\@pointsize}%
-    }%
-  }{%
-   \IfFileExists{\CurrentOption\substyle@post.\substyle@ext}{%
-    \expandafter\change@society\expandafter{\CurrentOption}%
-    \expandafter\let\csname ds@\CurrentOption\endcsname\@empty
-   }{}%
-  }%
- }%
-}%
-\DeclareOption{hypertext}{\hypertext@enable@ltx}%
-\appdef\document@inithook{\@ifpackageloaded{hyperref}{\hypertext@enable@ltx}{}}%
-\DeclareOption{frontmatterverbose}{\@booleantrue\frontmatterverbose@sw}%
-\@booleanfalse\frontmatterverbose@sw
-\DeclareOption{inactive}{\@booleanfalse\frontmatter@syntax@sw}%
-\@booleantrue\frontmatter@syntax@sw
-\@booleanfalse\runinaddress@sw
-\@booleantrue\@affils@sw
-\@booleanfalse\groupauthors@sw
-\DeclareOption{groupedaddress}{\clo@groupedaddress}%
-\def\clo@groupedaddress{%
- \@booleantrue\groupauthors@sw
- \@booleantrue\@affils@sw
- \@booleanfalse\runinaddress@sw
-}%
-\DeclareOption{unsortedaddress}{\clo@unsortedaddress}%
-\def\clo@unsortedaddress{%
- \@booleantrue\groupauthors@sw
- \@booleanfalse\@affils@sw
- \@booleanfalse\runinaddress@sw
-}%
-\DeclareOption{runinaddress}{\clo@runinaddress}%
-\def\clo@runinaddress{%
- \@booleantrue\groupauthors@sw
- \@booleantrue\@affils@sw
- \@booleantrue\runinaddress@sw
-}%
-\DeclareOption{superscriptaddress}{\clo@superscriptaddress}%
-\def\clo@superscriptaddress{%
- \@booleanfalse\groupauthors@sw
- \@booleantrue\@affils@sw
- \@booleanfalse\runinaddress@sw
-}%
-%%%  @LaTeX-file{
-%%%     filename        = "revtex4-2.dtx",
-%%%     version         = "4.2e",
-%%%     date            = "2020/10/03",
-%%%     author          = "Mark Doyle (mailto: revtex at aps.org), Arthur Ogawa (mailto:arthur_ogawa at sbcglobal.net),
-%%%                        commissioned by the American Physical Society.
-%%%                        ",
-%%%     copyright       = "Copyright (C) 1999, 2009 Arthur Ogawa, Version 4.2 Copyright (C) 2019 American Physical Society
-%%%                        distributed under the terms of the
-%%%                        LaTeX Project Public License 1.3c, see
-%%%                        ftp://ctan.tug.org/macros/latex/base/lppl.txt
-%%%                        ",
-%%%     address         = "Mark Doyle,
-%%%                        USA",
-%%%     telephone       = "",
-%%%     FAX             = "",
-%%%     email           = "mailto colon revtex at aps.org",
-%%%     codetable       = "ISO/ASCII",
-%%%     keywords        = "",
-%%%     supported       = "yes",
-%%%     abstract        = "",
-%%%  }
-\def\substyle@post{4-2}%
-\def\substyle@ext{rtx}%
-\DeclareOption*{\OptionNotUsed}%
-\def\@process@society#1{%
- \@ifxundefined\@society{%
-  \class@warn{No Society specified, using default society #1}%
-  \def\@society{#1}\let\@journal\@undefined
- }{}%
- \expandafter\input\expandafter{\@society\substyle@post.\substyle@ext}%
-}%
-\def\@process@journal#1{%
- \@ifxundefined\@journal{%
-  \class@warn{No journal specified, using default #1}%
-  \def\@journal{#1}%
- }{}%
- \expandafter\expandafter
- \expandafter\rtx@do@substyle
- \expandafter\expandafter
- \expandafter{\expandafter\@society\@journal}%
-}%
-\def\rtx@do@substyle#1{%
- \InputIfFileExists{#1\substyle@post.\substyle@ext}{}{\csname rtx@#1\endcsname}%
-}%
-\def\@process@pointsize#1{%
- \@ifxundefined\@pointsize{%
-  \def\@pointsize{#1}%
-  \class@warn{No type size specified, using default \@pointsize}%
- }{}%
- \expandafter\expandafter
- \expandafter\rtx@do@substyle
- \expandafter\expandafter
- \expandafter{\expandafter\@society\@pointsize pt}%
-}%
-  \def\ps@headings{%
-      \let\@oddfoot\@empty\let\@evenfoot\@empty
-      \def\@evenhead{\thepage\hfil\slshape\leftmark}%
-      \def\@oddhead{{\slshape\rightmark}\hfil\thepage}%
-      \let\@mkboth\markboth
-    \def\sectionmark##1{%
-      \markboth {\MakeUppercase{%
-        \ifnum \c@secnumdepth >\z@
-          \thesection\quad
-        \fi
-        ##1}}{}}%
-    \def\subsectionmark##1{%
-      \markright {%
-        \ifnum \c@secnumdepth >\@ne
-          \thesubsection\quad
-        \fi
-        ##1}}}%
-\def\ps@myheadings{%
-    \let\@oddfoot\@empty\let\@evenfoot\@empty
-    \def\@evenhead{\thepage\hfil\slshape\leftmark}%
-    \def\@oddhead{{\slshape\rightmark}\hfil\thepage}%
-    \let\@mkboth\@gobbletwo
-    \let\sectionmark\@gobble
-    \let\subsectionmark\@gobble
-    }%
-\def\ps@article{%
-    \def\@evenhead{\let\\\heading@cr\thepage\quad\checkindate\hfil{\leftmark}}%
-    \def\@oddhead{\let\\\heading@cr{\rightmark}\hfil\checkindate\quad\thepage}%
-    \def\@oddfoot{}%
-    \def\@evenfoot{}%
-    \let\@mkboth\markboth
-  \let\sectionmark\@gobble
-  \let\subsectionmark\@gobble
-}%
-\def\ps@article@final{%
-    \def\@evenhead{\let\\\heading@cr\thepage\quad\checkindate\hfil{\leftmark}}%
-    \def\@oddhead{\let\\\heading@cr{\rightmark}\hfil\checkindate\quad\thepage}%
-    \def\@oddfoot{}%
-    \def\@evenfoot{}%
-    \let\@mkboth\markboth
-    \def\sectionmark##1{%
-      \markboth{%
-       \MakeTextUppercase{%
-        \@ifnum{\c@secnumdepth >\z@}{\thesection\hskip 1em\relax}{}%
-         ##1%
-       }%
-       }{}%
-    }%
-    \def\subsectionmark##1{%
-      \markright {%
-        \@ifnum{\c@secnumdepth >\@ne}{\thesubsection\hskip 1em\relax}{}%
-         ##1%
-      }%
-    }%
-}%
-\def\heading@cr{\unskip\space\ignorespaces}%
-\def\ps@preprint{%
-  \def\@oddfoot{\hfil\thepage\quad\checkindate\hfil}%
-  \def\@evenfoot{\hfil\thepage\quad\checkindate\hfil}%
-  \def\@oddhead{}%
-  \def\@evenhead{}%
-  \let\@mkboth\@gobbletwo
-  \let\sectionmark\@gobble
-  \let\subsectionmark\@gobble
-}%
-\let\@oddhead\@empty
-\let\@evenhead\@empty
-\let\@oddfoot\@empty
-\let\@evenfoot\@empty
-\def\lastpage@putlabel{%
- \if@filesw
-  \begingroup
-    \advance\c@page\m@ne
-    \immediate\write\@auxout{\string\newlabel{LastPage}{{}{\thepage}{}{}{}}}%
-  \endgroup
- \fi
-}%
-\appdef\clear@document{%
- \do@output@cclv{%
-  \lastpage@putlabel
-  \tally@box@size@sw{\total@text}{}%
- }%
-}%
-\providecommand\write@column@totals{}%
-\appdef\rtx@require@packages{%
- \RequirePackage{url}%
-}%
-\appdef\document@inithook{%
- \incompatible@package{cite}%
- \incompatible@package{mcite}%
- \incompatible@package{multicol}%
-}%
-\def\labelenumi{\theenumi.}
-\def\theenumi{\arabic{enumi}}
-\def\labelenumii{(\theenumii)}
-\def\theenumii{\alph{enumii}}
-\def\p@enumii{\theenumi}
-\def\labelenumiii{\theenumiii.}
-\def\theenumiii{\roman{enumiii}}
-\def\p@enumiii{\theenumi(\theenumii)}
-\def\labelenumiv{\theenumiv.}
-\def\theenumiv{\Alph{enumiv}}
-\def\p@enumiv{\p@enumiii\theenumiii}
-\def\labelitemi{\textbullet}
-\def\labelitemii{\normalfont\bfseries\textendash}
-\def\labelitemiii{\textasteriskcentered}
-\def\labelitemiv{\textperiodcentered}
-\pagenumbering{arabic}
-\setcounter{topnumber}{2}
-\def\topfraction{.9}
-\setcounter{bottomnumber}{1}
-\def\bottomfraction{.9}
-\setcounter{totalnumber}{3}
-\def\textfraction{.1}
-\def\floatpagefraction{.9}
-\setcounter{dbltopnumber}{2}
-\def\dbltopfraction{.9}
-\def\dblfloatpagefraction{.9}
-\newenvironment{verse}{%
-  \let\\=\@centercr
-  \list{}{%
-    \itemsep\z@ \itemindent -1.5em\listparindent \itemindent
-    \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]%
-}{%
- \endlist
-}%
-\newenvironment{quotation}{%
-  \list{}{%
-    \listparindent 1.5em
-    \itemindent\listparindent
-    \rightmargin\leftmargin \parsep \z@ \@plus\p@}\item[]%
-}{%
- \endlist
-}%
-\newenvironment{quote}{%
-  \list{}{%
-  \rightmargin\leftmargin}\item[]%
-}{%
- \endlist
-}%
-\def\descriptionlabel#1{%
-  \hspace\labelsep \normalfont\bfseries #1\unskip:%
-}%
-\newenvironment{description}{%
- \list{}{%
-    \labelwidth\z@ \itemindent-\leftmargin
-    \let\makelabel\descriptionlabel
- }%
-}{%
- \endlist
-}%
-\newcounter{part}%
-\let\thepart\@undefined
-\newcounter{section}%
-\let\thesection\@undefined
-\newcounter{subsection}[section]%
-\let\thesubsection\@undefined
-\newcounter{subsubsection}[subsection]%
-\let\thesubsubsection\@undefined
-\newcounter{paragraph}[subsubsection]%
-\let\theparagraph\@undefined
-\newcounter{subparagraph}[paragraph]%
-\let\thesubparagraph\@undefined
-\def\secnums@rtx{%
- \@ifxundefined\thepart{%
-  \def\thepart{\Roman{part}}%
- }{}%
- \@ifxundefined\thesection{%
-  \def\thesection       {\Roman{section}}%
-  \def\p@section        {}%
- }{}%
- \@ifxundefined\thesubsection{%
-  \def\thesubsection    {\Alph{subsection}}%
-  \def\p@subsection     {\thesection\,}%
- }{}%
- \@ifxundefined\thesubsubsection{%
-  \def\thesubsubsection {\arabic{subsubsection}}%
-  \def\p@subsubsection  {\thesection\,\thesubsection\,}%
- }{}%
- \@ifxundefined\theparagraph{%
-  \def\theparagraph     {\alph{paragraph}}%
-  \def\p@paragraph      {\thesection\,\thesubsection\,\thesubsubsection\,}%
- }{}%
- \@ifxundefined\thesubparagraph{%
-  \def\thesubparagraph  {\arabic{subparagraph}}%
-  \def\p@subparagraph   {\thesection\,\thesubsection\,\thesubsubsection\,\theparagraph\,}%
- }{}%
-}%
-\def\secnums@arabic{%
- \@ifxundefined\thepart{%
-  \def\thepart          {\Roman{part}}%
- }{}%
- \@ifxundefined\thesection{%
-  \def\thesection       {\Roman{section}}%
-  \def\p@section        {}%
- }{}%
- \@ifxundefined\thesubsection{%
-  \def\thesubsection    {\thesection.\arabic{subsection}}%
-  \def\p@subsection     {}%
- }{}%
- \@ifxundefined\thesubsubsection{%
-  \def\thesubsubsection {\thesubsection.\arabic{subsubsection}}%
-  \def\p@subsubsection  {}%
- }{}%
- \@ifxundefined\theparagraph{%
-  \def\theparagraph     {\thesubsubsection.\arabic{paragraph}}%
-  \def\p@paragraph      {}%
- }{}%
- \@ifxundefined\thesubparagraph{%
-  \def\thesubparagraph  {\theparagraph.\arabic{subparagraph}}%
-  \def\p@subparagraph   {}%
- }{}%
-}%
-\newenvironment{acknowledgments}{%
- \acknowledgments@sw{%
-  \expandafter\section\expandafter*\expandafter{\acknowledgmentsname}%
- }{%
-  \par
-  \phantomsection
-  \addcontentsline{toc}{section}{\protect\numberline{}\acknowledgmentsname}%
- }%
-}{%
- \par
-}%
-\@booleantrue\acknowledgments@sw
-\newenvironment{acknowledgements}{%
- \replace@environment{acknowledgements}{acknowledgments}%
-}{%
- \endacknowledgments
-}%
-\def\part{\par
-   \addvspace{4ex}%
-   \@afterindentfalse
-   \secdef\@part\@spart}%
-\def\@part[#1]#2{%
- \@ifnum{\c@secnumdepth >\m@ne}{%
-        \refstepcounter{part}%
-        \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}%
- }{%
-      \addcontentsline{toc}{part}{#1}%
- }%
- \begingroup
-    \parindent \z@ \raggedright
-    \interlinepenalty\@M
-    \@ifnum{\c@secnumdepth >\m@ne}{%
-      \Large \bf \partname~\thepart%
-      \par\nobreak
-    }{}%
-    \huge \bf
-    #2%
-    \markboth{}{}\par
- \endgroup
-   \nobreak
-   \vskip 3ex
-   \@afterheading
-}%
-\def\@spart#1{{\parindent \z@ \raggedright
-    \interlinepenalty\@M
-    \huge \bf
-    #1\par}
-    \nobreak
-    \vskip 3ex
-    \@afterheading}
-\def\section{%
-  \@startsection
-    {section}%
-    {1}%
-    {\z@}%
-    {0.8cm \@plus1ex \@minus .2ex}%
-    {0.5cm}%
-    {\normalfont\small\bfseries}%
-}%
-\def\subsection{%
-  \@startsection
-    {subsection}%
-    {2}%
-    {\z@}%
-    {.8cm \@plus1ex \@minus .2ex}%
-    {.5cm}%
-    {\normalfont\small\bfseries}%
-}%
-\def\subsubsection{%
-  \@startsection
-    {subsubsection}%
-    {3}%
-    {\z@}%
-    {.8cm \@plus1ex \@minus .2ex}%
-    {.5cm}%
-    {\normalfont\small\itshape}%
-}%
-\def\paragraph{%
-  \@startsection
-    {paragraph}%
-    {4}%
-    {\parindent}%
-    {\z@}%
-    {-1em}%
-    {\normalfont\normalsize\itshape}%
-}%
-\def\subparagraph{%
-  \@startsection
-    {subparagraph}%
-    {5}%
-    {\parindent}%
-    {3.25ex \@plus1ex \@minus .2ex}%
-    {-1em}%
-    {\normalfont\normalsize\bfseries}%
-}%
-\def\theequation{%
- \theequation@prefix\arabic{equation}%
-}%
-\def\theequation@prefix{}%
-\setcounter{secnumdepth}{4}
-\lineskip 1pt
-\normallineskip 1pt
-\def\baselinestretch{1}%
-\@lowpenalty   51
-\@medpenalty  151
-\@highpenalty 301
-\@beginparpenalty -\@lowpenalty
-\@endparpenalty   -\@lowpenalty
-\@itempenalty     -\@lowpenalty
-\arraycolsep 3pt
-\tabcolsep 2pt
-\arrayrulewidth .4pt
-\doublerulesep 2pt
-\skip\@mpfootins = 0pt
-\fboxsep  = 3.0pt
-\fboxrule = 0.4pt
-\newenvironment{figure}
-               {\@float{figure}}
-               {\end@float}
-\newenvironment{figure*}
-               {\@dblfloat{figure}}
-               {\end@dblfloat}
-\def\listoffigures{\print@toc{lof}}%
-\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}%
-\newlength\abovecaptionskip
-\newlength\belowcaptionskip
-\setlength\abovecaptionskip{10\p@}
-\setlength\belowcaptionskip{2\p@}
-\long\def\@makecaption#1#2{%
-  \par
-  \vskip\abovecaptionskip
-  \begingroup
-   \small\rmfamily
-   \sbox\@tempboxa{%
-    \let\\\heading@cr
-    \@make@capt@title{#1}{#2}%
-   }%
-   \@ifdim{\wd\@tempboxa >\hsize}{%
-    \begingroup
-     \samepage
-     \flushing
-     \let\footnote\@footnotemark@gobble
-     \@make@capt@title{#1}{#2}\par
-    \endgroup
-   }{%
-     \global \@minipagefalse
-     \hb@xt@\hsize{\hfil\unhbox\@tempboxa\hfil}%
-   }%
-  \endgroup
-  \vskip\belowcaptionskip
-}%
-\def\@make@capt@title#1#2{%
- \@ifx@empty\float@link{\@firstofone}{\expandafter\href\expandafter{\float@link}}%
-  {#1}\@caption@fignum@sep#2%
-}%
-\def\@footnotemark@gobble{%
- \@footnotemark
- \@ifnextchar[{\@gobble@opt@i}{\@gobble}%
-}%
-\def\@gobble@opt@i[#1]#2{}%
-\def\@mpmakefntext#1{%
- \flushing
- \parindent=1em
- \noindent
- \hb@xt@1em{\hss\@makefnmark}%
- #1%
-}%
-\def\@caption@fignum@sep{. }%
-\def\setfloatlink{\def\float@link}%
-\let\float@link\@empty
-\newcounter{figure}
-\renewcommand \thefigure {\@arabic\c@figure}
-\def\fps@figure{tbp}
-\def\ftype@figure{1}
-\def\ext@figure{lof}
-\def\fnum@figure{\figurename~\thefigure}
-\expandafter\newbox\csname fbox@\ftype@figure\endcsname
-\expandafter\setbox\csname fbox@\ftype@figure\endcsname\hbox{}%
-\appdef\class@documenthook{%
- \do@if@floats{figure}{.fgx}%
-}%
-\appdef\class@enddocumenthook{%
- \printfigures\relax
-}%
-\newcommand\printfigures{%
- \@ifstar{\true@sw}{\floatp@sw{\true@sw}{\false@sw}}%
- {%
-  \print@float{figure}{\oneapage}%
- }{%
-  \print@float{figure}{}%
- }%
-}%
-\appdef\@xfloat@prep{%
- \appdef\@parboxrestore{\centering}%
-}%
-\newenvironment{table}
-               {\@float{table}}
-               {\end@float}
-\newenvironment{table*}
-               {\@dblfloat{table}}
-               {\end@dblfloat}
-\newcounter{table}
-\renewcommand\thetable{\@Roman\c@table}
-\def\fps@table{tbp}
-\def\ftype@table{2}
-\def\ext@table{lot}
-\def\fnum@table{\tablename~\thetable}
-\expandafter\newbox\csname fbox@\ftype@table\endcsname
-\expandafter\setbox\csname fbox@\ftype@table\endcsname\hbox{}%
-\def\listoftables{\print@toc{lot}}%
-\let\l@table\l@figure
-\def\table@hook{\small}%
-\def\squeezetable{\def\table@hook{\scriptsize}}%
-\appdef\@floatboxreset{\table@hook}%
-\def\set@table@environments{%
- \floats@sw{}{%
-  \let@environment{longtable@float}{longtable}%
-  \let@environment{longtable}{longtable@write}%
-  \let@environment{longtable*@float}{longtable*}%
-  \let@environment{longtable*}{longtable*@write}%
-  \let@environment{turnpage@float}{turnpage}%
-  \let@environment{turnpage}{turnpage@write}%
- }%
- \do@if@floats{table}{.tbx}%
-}%
-\appdef\document@inithook{%
- \set@table@environments
-}%
-\appdef\class@enddocumenthook{%
- \printtables\relax
-}%
-\newenvironment{longtable@write}{%
- \write@@float{longtable}{table}%
-}{%
- \endwrite@float
-}%
-\newenvironment{longtable*@write}{%
- \write@@float{longtable*}{table}%
-}{%
- \endwrite@float
-}%
-\newenvironment{turnpage@write}{%
- \immediate\write\tablewrite{\string\begin{turnpage}}%
-}{%
- \immediate\write\tablewrite{\string\end{turnpage}}%
-}%
-\newcommand\printtables{%
- \begingroup
-  \let@environment{longtable}{longtable@float}%
-  \let@environment{longtable*}{longtable*@float}%
-  \let@environment{turnpage}{turnpage@anchored}%
-  \prepdef\longtable{\trigger@float@par}%
-  \expandafter\prepdef\csname longtable*\endcsname{\trigger@float@par}%
-  \expandafter\prepdef\csname table@floats\endcsname{%
-   \onecolumngrid@push
-  }%
-  \expandafter\appdef\csname endtable@floats\endcsname{%
-   \onecolumngrid@pop
-  }%
-  \@ifstar{\true@sw}{\floatp@sw{\true@sw}{\false@sw}}%
-  {%
-   \print@float{table}{\oneapage}%
-  }{%
-   \print@float{table}{}%
-  }%
- \endgroup
-}%
-\newenvironment{turnpage@anchored}{%
- \onecolumngrid@push
- \setbox\z@\vbox to\textwidth\bgroup
-  \columnwidth\textheight
-}{%
-  \vfil
- \egroup
- \rotatebox{90}{\box\z@}%
- \onecolumngrid@pop
-}%
-\newenvironment{video}
- {\@float{video}}
- {\end@float}%
-\newenvironment{video*}
- {\@dblfloat{video}}
- {\end@dblfloat}%
-\newcounter{video}
-\renewcommand \thevideo {\@arabic\c@video}
-\def\ext@video{lov}%
-\def\fname@video{Video}%
-\def\lovname{List of Videos}%
-\def\fps@video{tbp}%
-\def\ftype@video{4}%
-\def\fnum@video{\fname@video~\thevideo}%
-\appdef\document@inithook{%
- \@ifxundefined\c@float@type{}{%
-  \global\setcounter{float@type}{8}%
- }%
-}%
-\expandafter\newbox\csname fbox@\ftype@video\endcsname
-\expandafter\setbox\csname fbox@\ftype@video\endcsname\hbox{}%
-\let\theHvideo\thevideo
-\def\listofvideos{\print@toc{lov}}%
-\let\l@video\l@figure
-\appdef\class@documenthook{%
- \do@if@floats{video}{.vdx}%
-}%
-\appdef\class@enddocumenthook{%
- \printvideos\relax
-}%
-\newcommand\printvideos{%
- \@ifstar{\true@sw}{\floatp@sw{\true@sw}{\false@sw}}%
- {%
-  \print@float{video}{\oneapage}%
- }{%
-  \print@float{video}{}%
- }%
-}%
-\def\endtabular@hook{}%
-\appdef\document@inithook{%
- \@ifpackageloaded{dcolumn}{%
-  \expandafter\@ifnotrelax\csname NC@find@d\endcsname{}{%
-   \newcolumntype{d}{D{.}{.}{-1}}%
-  }%
- }{}%
-}%
-\def\toprule{\hline\hline}%
-\def\colrule{\hline}%
-\def\botrule{\hline\hline}%
-\newenvironment{ruledtabular}{%
- \def\array@default{v}%
- \appdef\tabular@hook{\def\@halignto{to\hsize}}%
- \let\tableft@skip@default\tableft@skip
- \let\tableft@skip\tableft@skip@float
- \let\tabmid@skip@default\tabmid@skip
- \let\tabmid@skip\tabmid@skip@float
- \let\tabright@skip@default\tabright@skip
- \let\tabright@skip\tabright@skip@float
- \let\array@row@pre@default\array@row@pre
- \let\array@row@pre\array@row@pre@float
- \let\array@row@pst@default\array@row@pst
- \let\array@row@pst\array@row@pst@float
- \appdef\array@row@rst{%
-  \let\array@row@pre\array@row@pre@default
-  \let\array@row@pst\array@row@pst@default
-  \let\tableft@skip\tableft@skip@default
-  \let\tabmid@skip\tabmid@skip@default
-  \let\tabright@skip\tabright@skip@default
-  \appdef\tabular@hook{\let\@halignto\@empty}%
- }%
-}{%
-}%
-\def\@makefntext#1{%
-  \def\baselinestretch{1}%
-  \parindent1em%
-  \noindent
-  \hb@xt@1.8em{%
-   \hss\@makefnmark
-  }%
-  #1%
-  \par
-}%
-\def\@makefnmark{%
- \hbox{%
-  \@textsuperscript{%
-   \normalfont\@thefnmark
-  }%
- }%
-}%
-\expandafter\DeclareRobustCommand
-\expandafter\rev@citet
-\expandafter{%
- \expandafter\begingroup
-  \expandafter\rtx@swap@citea
-  \expandafter\g@bblefirsttoken
-              \csname citet \endcsname
-}%
-\expandafter\DeclareRobustCommand
-\expandafter\rev@citealp
-\expandafter{%
- \expandafter\begingroup
-  \expandafter\rtx@swap@citea
-  \expandafter\g@bblefirsttoken
-              \csname citealp \endcsname
-}%
-\expandafter\DeclareRobustCommand
-\expandafter\rev@citealpnum
-\expandafter{%
- \expandafter\begingroup
-  \expandafter\rtx@swap@citenum
-  \expandafter\g@bblefirsttoken
-              \csname citealp \endcsname
-}%
-\def\rtx@swap@citenum{%
-  \rtx@swap@citea
-  \let\@cite\NAT@citenum
-  \let\NAT@mbox\mbox
-  \let\citeyear\NAT@citeyear
-  \let\NAT@space\NAT@spacechar
-}%
-\def\g@bblefirsttoken{%
- \expandafter\true@sw
- \expandafter\@empty
-}%
-\newcommand\rtx@citesuper[3]{%
- \ifNAT@swa
-  \leavevmode
-  \unskip
-  \textsuperscript{\normalfont#1}%
-  \if*#3*\else\ (#3)\fi
- \else
-  #1%
- \fi
- \endgroup
-}%
-\def\@makefnmark@cite{\begingroup\NAT@swatrue\@cite{{\@thefnmark}}{}{}}%
-\def\rtx@bibsection{%
- \@ifx@empty\refname{%
-  \par
- }{%
-  \expandafter\section\expandafter*\expandafter{\refname}%
-  \@nobreaktrue
- }%
-}%
-\def\rtx@swap@citea{%
- \let\NAT@def@citea\rtx@def@citea
- \let\NAT@def@citea@close\rtx@def@citea@close
- \let\NAT@def@citea@box\rtx@def@citea@box
-}%
-\def\rtx@def@citea{%
- \def\@citea{\NAT@separator\NAT@space}%
- \advance\c@NAT@ctr\@ne
- \@ifnum{\count@>\tw@}{%
-  \@ifnum{\c@NAT@ctr=\count@}{\appdef\@citea{\NAT@conj\NAT@space}}{}%
- }{%
-  \def\@citea{\NAT@space\NAT@conj\NAT@space}%
- }%
-}%
-\def\rtx@def@citea@close{%
- \rtx@def@citea
- \prepdef\@citea{\NAT@@close}%
-}%
-\def\rtx@def@citea@box{%
- \rtx@def@citea@close
- \expandafter\def\expandafter\@citea\expandafter{\expandafter\NAT@mbox\expandafter{\@citea}}%
-}%
-\def\NAT@conj{and}%
-\def\NAT@BibitemShut#1{%
- \def\@bibstop{#1}%
- \let\bibitem@Stop\bibitemStop
- \let\bibitem@NoStop\bibitemNoStop
- \@ifx{\bibitemShut\relax}{\let\@bibitemShut\@empty}{%
-  \expandafter\def\expandafter\@bibitemShut\expandafter{\bibitemShut}%
- }%
-}%
-\def\BibitemShut@ltx#1{%
- \unskip
- \def\@bibstop{#1}%
- \let\bibitem@Stop\bibitemStop
- \let\bibitem@NoStop\bibitemNoStop
- \@ifx{\bibitemShut\relax}{\let\@bibitemShut\@empty}{%
-  \expandafter\def\expandafter\@bibitemShut\expandafter{\bibitemShut}%
- }%
-}%
-\newenvironment{thebibliography}{}{}%
-\let\@listi\@empty
-\appdef\rtx@require@packages{%
- \RequirePackage[sort&compress]{natbib}[2009/11/07 8.31a (PWD, AO)]%
- \let@environment{NAT@thebibliography}{thebibliography}%
- \let@environment{thebibliography}{rtx@thebibliography}%
- \let\bibliographystyle@latex\bibliographystyle
- \let\NAT@citesuper\rtx@citesuper
-\let\bibsection\rtx@bibsection
-\let\NATx@bibsetnum\NAT@bibsetnum
-\def\NAT@bibsetnum#1{%
- \setlength{\topsep}{\z@}%
- \NATx@bibsetnum{\ref{LastBibItem}}%
-}%
-\let\NATx@bibsetup\NAT@bibsetup
-\def\NAT@bibsetup{%
- \setlength{\labelwidth}{\z@}%
- \setlength{\labelsep}{\z@}%
- \setlength{\itemindent}{\z@}%
- \setlength{\listparindent}{\z@}%
- \setlength{\topsep}{\z@}%
- \setlength{\parsep}{\z@}%
- \NATx@bibsetup
-}%
-\let\bibpreamble\@empty
-\def\newblock{\ }%
-\let\NATx@bibnumfmt\bibnumfmt
-\def\bibnumfmt{\place@bibnumber}%
-\let\NAT@merge\thr@@
-\let\NAT@citeyear\citeyear
-\let\onlinecite\rev@citealp
-\let\textcite\rev@citet
-\@ifx{\BibitemShut\NAT@BibitemShut}{%
- \class@info{Repairing natbib's \string\BibitemShut}%
- \let\BibitemShut\BibitemShut@ltx
-}{}%
-\let\bibliographystyle@latex\bibliographystyle
-\def\bibliographystyle{\@booleantrue\bibliographystyle@sw\def\@bibstyle}%
-\@booleanfalse\bibliographystyle@sw
-\def\NAT@bibitem@cont{%
- \let\bibitem@Stop\bibitemContinue@Stop
- \let\bibitem@NoStop\bibitemContinue
-}%
-\def\bibitemNoStop{%
- \@ifx@empty\@bibitemShut{.\spacefactor\@mmm\space}{\@bibitemShut}%
-}%
-\def\bibitemContinue{%
- \@ifx@empty\@bibitemShut{;\spacefactor\@mmm\space}{\@bibitemShut}%
-}%
-\def\bibitemContinue@Stop{%
- \@ifx@empty\@bibitemShut{\spacefactor\@mmm\space}{\@bibitemShut}%
-}%
-}%
-\DeclareRobustCommand\onlinecite{\@onlinecite}%
-\DeclareRobustCommand\textcite{\@textcite}%
-\let\bibliography@latex\bibliography
-\def\bibliography#1{%
- \auto@bib@empty
- \begingroup
-  \let\auto@bib@innerbib\@empty
-  \@ifx@empty{\pre@bibdata}{%
-   \bibliography@latex{#1}%
-  }{%
-   \@if@empty{#1}{%
-    \expandafter\bibliography@latex\expandafter{\pre@bibdata}%
-   }{%
-    \expandafter\bibliography@latex\expandafter{\pre@bibdata,#1}%
-   }%
-  }%
- \endgroup
-}%
-\let\pre@bibdata\@empty
-\newenvironment{rtx@thebibliography}[1]{%
- \NAT@thebibliography{#1}%
- \let\@TBN@opr\present@bibnote
- \@FMN@list
-}{%
- \auto@bib@innerbib
- \edef\@currentlabel{\arabic{NAT@ctr}}%
- \label{LastBibItem}%
- \endNAT@thebibliography
- \aftergroup\auto@bib@empty
-}%
-\def\present@bibnote#1#2{%
- \item[%
-  \textsuperscript{%
-   \normalfont
-   \Hy@raisedlink{\hyper@anchorstart{frontmatter.#1}\hyper@anchorend}%
-   \begingroup
-    \csname c@\@mpfn\endcsname#1\relax
-    \frontmatter@thefootnote
-   \endgroup
-  }%
- ]#2\par
-}%
-\def\write@bibliographystyle{%
- \@ifxundefined\@bibstyle{}{%
-  \expandafter\bibliographystyle@latex\expandafter{\@bibstyle}%
-  \bibliographystyle@sw{}{\@bibdataout@rev}%
- }%
- \global\let\write@bibliographystyle\relax
-}%
-\AtEndDocument{\write@bibliographystyle}%
-\def\rtx@@citetp[#1]{\@ifnextchar[{\rtx@citex[#1]}{\rtx@citex[][#1]}}%
-\def\rtx@citex[#1][#2]#3{%
- \begingroup
-  \def\@tempa{[#1][#2]{#3}}%
-  \@ifx{\@cite\NAT@citesuper}{%
-   \leavevmode
-   \skip@\lastskip
-   \unskip
-   \super@cite@let
-  }{%
-   \super@cite@end
-  }%
-}%
-\def\super@cite@let{%
- \futurelet\@let@token\super@cite@check
-}%
-\def\super@cite@end{%
- \aftergroup\@citex\expandafter\endgroup\@tempa
-}%
-\def\super@cite@check{%
- \@ifx{\@let@token\@sptoken}{%
-  \super@cite@end
- }{%
-  \super@cite@swap
- }%
-}%
-\long\def\super@cite@swap#1{%
- \expandafter\@ifx\expandafter{\csname rtx@automove#1\endcsname\@empty}{%
-  #1%
-  \super@cite@let
- }{%
-  \super@cite@end
-  #1%
- }%
-}%
-\expandafter\let\csname rtx@automove.\endcsname\@empty
-\expandafter\let\csname rtx@automove,\endcsname\@empty
-\expandafter\let\csname rtx@automove:\endcsname\@empty
-\expandafter\let\csname rtx@automove;\endcsname\@empty
-\appdef\class@documenthook{%
- \citeautoscript@sw{%
-  \@ifx{\@cite\NAT@citesuper}{%
-   \let\NAT@@citetp\rtx@@citetp
-  }{}%
- }{}%
-}%
-\def\mini@note{\save@note\mini@notes}%Implicit #2
-\def\save@note#1#2{%
-  \stepcounter\@mpfn
-  \protected@xdef\@thefnmark{\thempfn}%
-  \@footnotemark
-  \expandafter\g@addto@macro
-  \expandafter#1%
-  \expandafter{%
-  \expandafter \@@footnotetext
-  \expandafter {\@thefnmark}{#2}%
-              }%
-}%
-\long\def\@@footnotetext#1{\def\@thefnmark{#1}\@footnotetext}%
-\let\mini@notes\@empty
-\def\rev@citemark#1{%
- \expandafter\cite\expandafter{\@thefnmark}%
-}%
-\def\rev@endtext#1{%
- \let\@endnotelabel\@thefnmark
- \@endnotetext
-}%
-\def\endnote@ext{.end}%
-\def\bibdata@app{Notes}%
-\def\bibdata@ext{bib}%
-\long\def\@endnotetext#1{%
-  \begingroup
-    \endnote@relax
-    \immediate\write\@bibdataout{%
-     @FOOTNOTE{%
-      \@endnotelabel,%
-      key="\@endnotelabel",%
-      note="#1"%
-     }%
-    }%
-  \endgroup
-}%
-\newwrite\@bibdataout
-\def\endnote@relax{%
- \let\label\relax \let\index\relax \let\glossary\relax
- \let\cite \relax \let\ref  \relax \let\pageref \relax
- \let\(    \relax \let\)    \relax \let\\       \relax
- \let~\relax
- \let \protect \@unexpandable@protect
- \newlinechar`\^^M%
- \let\begin\relax \let\end\relax
-}%
-\appdef\class@documenthook{\@bibdataout@init}%
-\def\@bibdataout@init{%
- \immediate\openout\@bibdataout\pre@bibdata.\bibdata@ext\relax
-}%
-\def\@bibdataout@rev{%
- \immediate\write\@bibdataout{%
-  @CONTROL{%
-   REVTEX42Control%
-   \eprint@enable@sw{}{,eprint="1"}%
-  }%
- }%
- \if@filesw
-  \immediate\write\@auxout{\string\citation{REVTEX42Control}}%
- \fi
-}%
-\def\printendnotes{%
- \class@warn{The \string\printendnotes\space command no longer serves any function. Please remove it from your document.}%
-}%
-\def\make@footnote@endnote{%
- \footinbib@sw{%
-  \authoryear@sw{}{%
-   \ltx@footnote@push
-   \def\thempfn{Note\thefootnote}%
-   \let\ltx@footmark\rev@citemark
-   \let\ltx@foottext\rev@endtext
-  }%
- }{}%
-}%
-\def\ltx@footnote@push{%
- \let\ltx@footmark@latex\ltx@footmark
- \let\ltx@foottext@latex\ltx@foottext
- \let\thempfn@latex\thempfn
- \def\ltx@footnote@pop{%
-  \let\ltx@footmark\ltx@footmark@latex
-  \let\ltx@foottext\ltx@foottext@latex
-  \let\thempfn\thempfn@latex
- }%
-}%
-\appdef\class@documenthook{%
- \make@footnote@endnote
-}%
-\def\auto@bib{%
- \@ifx@empty\@FMN@list{%
-  \footinbib@sw{%
-   \@ifnum{\csname c@\@mpfn\endcsname>\z@}{%
-    \true@sw
-   }{%
-    \test@bbl@sw
-   }%
-  }{%
-   \test@bbl@sw
-  }%
- }{%
-  \true@sw
- }%
- {%
-  \bibliography{}%
- }{}%
-}%
-\def\auto@bib@empty{%
- \let\auto@bib\@empty
-}%
-\def\test@bbl@sw{%
- \setbox\z@\vbox\bgroup
-  \let\providecommand\providecommand@j@nk
-  \let\bibfield\@gobbletwo
-  \let\bibinfo\@gobbletwo
-  \let\translation\@gobble
-  \let\BibitemOpen\@empty
-  \let\bibitemStop\@empty
-  \let\bibitemNoStop\@empty
-  \let\EOS\@empty
-  \let\BibitemShut\@gobble
-  \let\bibAnnoteFile\@gobbletwo
-  \let\bibAnnote\@gobblethree
-  \let\textbf\@gobble
-  \let\emph\@gobble
-  \@booleanfalse\bibitem@sw
-  \let\bibitem\bibitem@set
-  \auto@bib@innerbib
-  \bibitem@sw{\aftergroup\true@sw}{\aftergroup\false@sw}%
- \egroup
-}%
-\newcommand\bibitem@set[1][]{%
- \bibitem@sw{}{%
-  \@booleantrue\bibitem@sw
-  \aftergroup\@booleantrue\aftergroup\bibitem@sw
- }%
-}%
-\def\auto@bib@innerbib{%
- \begingroup
-  \let@environment{thebibliography}{thebibliography@nogroup}%
-  \bibliography{}%
- \endgroup
-}%
-\def\thebibliography@nogroup#1{%
- \endgroup
- \def\@currenvir{thebibliography}%
-}%
-\def\endthebibliography@nogroup{\begingroup}%
-\long\def \@gobblethree #1#2#3{}%
-\def\providecommand@j@nk#1[#2]{%
- \@ifnum{#2=\z@}{\def\j@nk}{%
-  \@ifnum{#2=\@ne}{\def\j@nk##1}{%
-   \@ifnum{#2=\tw@}{\def\j@nk##1##2}{%
-    \@ifnum{#2=\thr@@}{\def\j@nk##1##2##3}{%
-    }%
-   }%
-  }%
- }%
-}%
-\def\thepage{\@arabic\c@page}%
-\appdef\setup@hook{%
- \tabbingsep \labelsep
- \leftmargin\leftmargini
- \labelwidth\leftmargin\advance\labelwidth-\labelsep
- \let\@listi\@listI
- \@listi
-}%
-\appdef\class@documenthook{%
- \global\c@page\@ne
- \def\curr@envir{document}%
- \mark@envir{\curr@envir}%
-}%
-\def\open@onecolumn{%
- \open@column@one\@ne
- \set@colht
- \@floatplacement
- \@dblfloatplacement
-}%
-\def\open@twocolumn{%
- \open@column@mlt\tw@
- \set@colht
- \@floatplacement
- \@dblfloatplacement
- \sloppy
- \let\set@listindent\set@listindent@
-}%
-\def\appendix{%
- \par
- \setcounter{section}\z@
- \setcounter{subsection}\z@
- \setcounter{subsubsection}\z@
- \def\thesubsection{\arabic{subsection}}%
- \def\thesubsubsection{\alph{subsubsection}}%
- \@addtoreset{equation}{section}%
- \def\theequation@prefix{\thesection}%
- \addtocontents{toc}{\protect\appendix}%
- \@ifstar{%
-  \def\thesection{\unskip}%
-  \def\theequation@prefix{A.}%
- }{%
-  \def\thesection{\Alph{section}}%
- }%
-}%
-\def\title@column#1{%
- \minipagefootnote@init
- #1%
- \minipagefootnote@foot
-}%
-\def\close@column{%
- \newpage
-}%
-\def\galley@outdent{\rightmargin-\columnwidth\advance\rightmargin-\columnsep}%
-\let\widetext@outdent\@empty
-\newenvironment{widetext@galley}{%
-  \list{}{%
-    \topsep        \z@skip
-    \listparindent \parindent
-    \itemindent    \parindent
-    \leftmargin    \z@
-    \parsep        \z@\@plus\p@
-    \widetext@outdent
-    \relax
-  }%
-  \item\relax
-}{
-  \endlist
-}%
-\def\title@column@grid#1{%
- \minipagefootnote@init
-  \onecolumngrid
-  \begingroup
-   \let\@footnotetext\frontmatter@footnotetext
-   \ltx@no@footnote
-   #1%
-  \endgroup
-  \twocolumngrid
- \minipagefootnote@foot
-}%
-\def\close@column@grid{%
- \balancelastpage@sw{%
-  \onecolumngrid
- }{}%
-}%
-\newenvironment{widetext@grid}{%
-  \par\ignorespaces
-  \setbox\widetext@top\vbox{%
-   \hb@xt@\hsize{%
-    \leaders\hrule\hfil
-    \vrule\@height6\p@
-   }%
-  }%
-  \setbox\widetext@bot\hb@xt@\hsize{%
-    \vrule\@depth6\p@
-    \leaders\hrule\hfil
-  }%
-  \onecolumngrid
-  \vskip10\p@
-  \dimen@\ht\widetext@top\advance\dimen@\dp\widetext@top
-  \cleaders\box\widetext@top\vskip\dimen@
-  \vskip6\p@
-  \prep@math@patch
-}{%
-  \par
-  \vskip6\p@
-  \setbox\widetext@bot\vbox{%
-   \hb@xt@\hsize{\hfil\box\widetext@bot}%
-  }%
-  \dimen@\ht\widetext@bot\advance\dimen@\dp\widetext@bot
-  \cleaders\box\widetext@bot\vskip\dimen@
-  \vskip8.5\p@
-  \twocolumngrid\global\@ignoretrue
-  \@endpetrue
-}%
-\newbox\widetext@top
-\newbox\widetext@bot
-\def\set@page@grid{%
- \twocolumn@sw{%
-  \let\set@footnotewidth\set@footnotewidth@two
-  \let\compose@footnotes\compose@footnotes@two
-  \let@environment{widetext}{widetext@grid}%
-  \let\title@column\title@column@grid
-  \let\close@column\close@column@grid
- }{%
-  \let@environment{widetext}{widetext@galley}%
-  \preprintsty@sw{%
-  }{%
-   \galley@sw{%
-    \let\widetext@outdent\galley@outdent
-   }{}%
-  }%
- }%
-}%
-\appdef\setup@hook{\set@page@grid}%
-\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
-\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
-\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
-\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
-\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
-\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
-\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
-\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
-\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
-\def\today{\ifcase\month\or
-  January\or February\or March\or April\or May\or June\or
-  July\or August\or September\or October\or November\or December\fi
-  \space\number\day, \number\year}
-\def\partname{Part}
-\def\tocname{Contents}
-\def\lofname{List of Figures}
-\def\lotname{List of Tables}
-\def\refname{References}
-\def\indexname{Index}
-\def\figurename{FIG.}
-\def\figuresname{Figures}%
-\def\tablename{TABLE}
-\def\tablesname{Tables}%
-\def\abstractname{Abstract}
-\def\appendixesname{Appendixes}%
-\def\appendixname{Appendix}%
-\def\acknowledgmentsname{Acknowledgments}
-\def\journalname{??}
-\def\copyrightname{??}
-\def\andname{and}
-\def\@pacs@name{PACS numbers: }%
-\def\@keys@name{Keywords: }%
-\def\ppname{pp}
-\def\numbername{number}
-\def\volumename{volume}
-\def\Dated@name{Dated: }%
-\def\Received@name{Received }%
-\def\Revised@name{Revised }%
-\def\Accepted@name{Accepted }%
-\def\Published@name{Published }%
-\def\address{\replace@command\address\affiliation}%
-\def\altaddress{\replace@command\altaddress\altaffiliation}%
-\newenvironment{references}{%
- \class@warn@end{The references environment is not supported; use thebibliography instead.}
- \gdef\references{\thebibliography{}}\references
-}{%
- \endthebibliography
-}%
-\def\draft{%
- \class@warn@end{Command \string\draft\space is obsolete;^^JInvoke option draft instead.}%
- \@booleantrue\draft@sw
-}%
-\def\tighten{%
- \class@warn@end{Command \string\tighten\space is obsolete;^^JInvoke option tightenlines instead.}%
- \@booleantrue\tightenlines@sw
-}%
-\def\tableline{%
- \noalign{%
-  \class@warn@end{Command \string\tableline\space is obsolete;^^JUse \string\colrule\space instead.}%
-  \global\let\tableline\colrule
- }%
- \tableline
-}%
-\def\case{\replace@command\case\frac}%
-\def\slantfrac{\replace@command\slantfrac\frac}%
-\def\tablenote{\replace@command\tablenote\footnote}%
-\def\tablenotemark{\replace@command\tablenotemark\footnotemark}%
-\def\tablenotetext{\replace@command\tablenotetext\footnotetext}%
-\DeclareRobustCommand\REV@text[1]{%
- \relax
- \ifmmode
-  \mathchoice
-   {\hbox{{\everymath{\displaystyle     }#1}}}%
-   {\hbox{{\everymath{\textstyle        }#1}}}%
-   {\hbox{{\everymath{\scriptstyle      }\let\f@size\sf@size\selectfont#1}}}%
-   {\hbox{{\everymath{\scriptscriptstyle}\let\f@size\ssf@size\selectfont#1}}}%
-  \glb@settings
- \else
-  \mbox{#1}%
- \fi
-}%
-\DeclareRobustCommand\REV@bbox[1]{%
- \relax
- \ifmmode
-  \mathchoice
-   {\hbox{{\everymath{\displaystyle     }\boldmath$#1$}}}%
-   {\hbox{{\everymath{\textstyle        }\boldmath$#1$}}}%
-   {\hbox{{\everymath{\scriptstyle      }\boldmath$#1$}}}%
-   {\hbox{{\everymath{\scriptscriptstyle}\boldmath$#1$}}}%
-  \glb@settings
- \else
-  \mbox{#1}%
- \fi
-}%
-\DeclareRobustCommand\REV@bm[1]{%
- \class@warn@end{To use \string\bm, please load the bm package!}%
- \global\let\bm\relax
-}%
-\def\FL{\obsolete@command\FL}%
-\def\FR{\obsolete@command\FR}%
-\def\narrowtext{\obsolete@command\narrowtext}%
-\def\mediumtext{\obsolete@command\mediumtext}%
-\newenvironment{quasitable}{%
- \let@environment{tabular}{longtable}%
-}{%
-}%
-\let\text\REV@text
-\let\bm\REV@bm
-\appdef\setup@hook{%
- \providecommand\bibinfo[2]{#2}%
- \providecommand\eprint[2][]{#2}%
-}%
-\def\bbox#1{%
- \class@warn@end{\string\bbox\space is obsolete,^^Jload the bm package and use \string\bm\space instead.}%
- \global\let\bbox\relax
-}%
-\newenvironment{mathletters}{%
- \class@warn@end{Environment {mathletters} is obsolete;^^Jload the amsmath package and use {subequations}!}%
- \global\let\mathletters\@empty
-}{%
-}%
-\def\eqnum#1{%
- \class@warn@end{\string\eqnum\space is obsolete, load the amsmath package and use \string\tag!}%
- \global\let\eqnum\@gobble
-}%
-\appdef\rtx@require@packages{%
- \RequirePackage{revsymb4-2}%
-}%
-\appdef\class@documenthook{\revsymb@inithook}%
-%%
-\def\@startflt#1{%
-  \begingroup
-    %\toc@pre
-    \makeatletter
-    \@input{\jobname.#1}%
-    \if@filesw
-      \expandafter\newwrite\csname tf@#1\endcsname
-      \immediate\openout \csname tf@#1\endcsname \jobname.#1\relax
-    \fi
-    \@nobreakfalse
-    %\toc@post
-  \endgroup
-}%
-\def\att@TOC{toc}%
-\def\print@toc#1{%
- \begingroup
-  \expandafter\section
-  \expandafter*%
-  \expandafter{%
-              \csname#1name\endcsname
-              }%
-  \let\appendix\appendix@toc
-  \def\tempa{#1}%
-  \ifx\tempa\att@TOC%%
-  \@starttoc{#1}%
-  \else%%
-  \@startflt{#1}%%
-  \fi%%
- \endgroup
-}%
-%%
-\def\@LN@LLerror@org{%
- \PackageError{lineno}{%
-  \string\linelabel\space without \string\linenumbers
- }{%
-  Just see documentation. (New feature v4.11)%
- }%
- \@gobble
-}%
-\def\@LN@LLerror@ltx{%
- \PackageWarning{lineno}{%
-  To make the \string\linelabel\space command work, you must issue the \string\linenumbers\ command
- }%
- \@gobble
-}%
-\appdef\class@documenthook{%
- \@ifx{\@LN@LLerror\@LN@LLerror@org}{%
-  \class@info{Overriding \string\@LN@LLerror}%
-  \let\@LN@LLerror\@LN@LLerror@ltx
- }{}%
- \@ifpackageloaded{lineno}{%
-  \@ifxundefined{\set@linepenalties}{}{%
-   \def\prep@absbox{\set@linepenalties}%
-   \def\post@absbox{\let\@LN@parpgbrk\@empty\@linenumberpar}%
-  }%
- }{}%
-}%
-\appdef\rtx@require@packages{%
- \InputIfFileExists{\jobname.rty}{}{}%
-}%
-\@parse@class@options@society
-\@process@society{aps}%
-\@parse@class@options@\@journal
-\expandafter\@process@journal\expandafter{\@journal@default}%
-\@parse@class@options@\@pointsize
-\expandafter\@process@pointsize\expandafter{\@pointsize@default}%
-\@options
-\rtx@require@packages
-\appdef\setup@hook{\normalsize}%
-\setup@hook
-\endinput
-%%
-%% End of file `revtex4-2.cls'.
-- 
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