%% This is file `revtex4-1.cls',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% revtex4-1.dtx  (with options: `kernel')
%% ltxutil.dtx  (with options: `kernel')
%% ltxfront.dtx  (with options: `kernel')
%% ltxgrid.dtx  (with options: `kernel')
%% revtex4-1.dtx  (with options: `options')
%% ltxutil.dtx  (with options: `options')
%% ltxfront.dtx  (with options: `options')
%% ltxgrid.dtx  (with options: `options')
%% revtex4-1.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)
%%
%% Copyright (c) 2009 The American Physical Society.
%% http://publish.aps.org/revtex4/
%% mailto:revtex4@aps.org
%%
%% See the REVTeX 4 README file for restrictions and more information.
%%
\NeedsTeXFormat{LaTeX2e}[1996/12/01]%
\ProvidesClass{revtex4-1}
              [2010/02/25/18:00:00 4.1p (http://publish.aps.org/revtex4/ for documentation)]% \fileversion
              \let\class@name\@gtempa
              \GenericInfo{}{\space
                Copyright (c) 2009 The 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>%
                \@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%
                [2010/02/25/18:00:00 4.1p 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                \class@warn@end{Command \string#1\space is obsolete.^^JPlease remove from your document}%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}}%
              \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}%
              }%
              \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
              \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
                  }%
                }{}%
              }%
              \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]{http://dx.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}{%
                                                     \class@info{Making \string\typeout\space \string\long}%
                                                     \let\typeout\typeout@ltx
                                                   }{}%
                                                   \typeout{%
                                                     ltxfront%
                                                     [2010/02/25/18:00:00 4.1p frontmatter package (AO,DPC)]% \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%
                                                                            [2010/02/25/18:00:00 4.1p 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%
                                                                                  }%
                                                                                  \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\@vspace@org #1{%
                                                                                        \ifvmode
                                                                                        \vskip #1
                                                                                        \vskip\z@skip
                                                                                        \else
                                                                                        \@bsphack
                                                                                        \vadjust{\@restorepar
                                                                                          \vskip #1
                                                                                          \vskip\z@skip
                                                                                        }%
                                                                                        \@esphack
                                                                                        \fi
                                                                                      }%
                                                                                      \def\@vspace@ltx#1{%
                                                                                        \@ifvmode{%
                                                                                          \vskip#1\vskip\z@skip
                                                                                        }{%
                                                                                          \@bsphack
                                                                                          \ex@vadjust@ltx{%
                                                                                            \@restorepar
                                                                                            \nobreak
                                                                                            \vskip#1\vskip\z@skip
                                                                                          }%
                                                                                          \@esphack
                                                                                        }%
                                                                                      }%
                                                                                      \def\@vspacer@org#1{%
                                                                                        \ifvmode
                                                                                        \dimen@\prevdepth
                                                                                        \hrule \@height\z@
                                                                                        \nobreak
                                                                                        \vskip #1
                                                                                        \vskip\z@skip
                                                                                        \prevdepth\dimen@
                                                                                        \else
                                                                                        \@bsphack
                                                                                        \vadjust{\@restorepar
                                                                                          \hrule \@height\z@
                                                                                          \nobreak
                                                                                          \vskip #1
                                                                                          \vskip\z@skip}%
                                                                                        \@esphack
                                                                                        \fi
                                                                                      }%
                                                                                      \def\@vspacer@ltx#1{%
                                                                                        \@ifvmode{%
                                                                                          \dimen@\prevdepth
                                                                                          \hrule\@height\z@
                                                                                          \nobreak
                                                                                          \vskip#1\vskip\z@skip
                                                                                          \prevdepth\dimen@
                                                                                        }{%
                                                                                          \@bsphack
                                                                                          \ex@vadjust@ltx{%
                                                                                            \@restorepar
                                                                                            \hrule\@height\z@
                                                                                            \nobreak
                                                                                            \vskip#1\vskip\z@skip
                                                                                          }%
                                                                                          \@esphack
                                                                                        }%
                                                                                      }%
                                                                                      \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
                                                                                        }%
                                                                                      }%
                                                                                      \long\def\end@line@org{%
                                                                                        \let\reserved@e\relax
                                                                                        \let\reserved@f\relax
                                                                                        \@ifstar{%
                                                                                          \let\reserved@e\vadjust
                                                                                          \let\reserved@f\nobreak
                                                                                          \@xnewline
                                                                                        }%
                                                                                        \@xnewline
                                                                                      }%
                                                                                      \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\@newline@org[#1]{%
                                                                                        \let\reserved@e\vadjust
                                                                                        \@gnewline{\vskip#1}%
                                                                                      }%
                                                                                      \def\@newline@ltx[#1]{%
                                                                                        \let\reserved@e\ex@vadjust@ltx
                                                                                        \@gnewline{\vskip#1}%
                                                                                      }%
                                                                                      \@ifx{\@vspace\@vspace@org}{%
                                                                                        \@ifx{\@vspacer\@vspacer@org}{%
                                                                                          \@ifx{\@no@pgbk\@no@pgbk@org}{%
                                                                                            \@ifx{\@newline\@newline@org}{%
                                                                                              \expandafter\@ifx\expandafter{\csname\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\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}%
                                                                                           \@booleanfalse\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        = "revtex4-1.dtx",
                                                                                           %%%     version         = "4.1p",
                                                                                           %%%     date            = "2010/02/25",
                                                                                           %%%     time            = "18:00:00 UT-8",
                                                                                           %%%     checksum        = "7177",
                                                                                           %%%     author          = "Arthur Ogawa (mailto:arthur_ogawa at sbcglobal.net),
                                                                                           %%%                        commissioned by the American Physical Society.
                                                                                           %%%                        ",
                                                                                           %%%     copyright       = "Copyright (C) 1999, 2009 Arthur Ogawa,
                                                                                           %%%                        distributed under the terms of the
                                                                                           %%%                        LaTeX Project Public License, see
                                                                                           %%%                        ftp://ctan.tug.org/macros/latex/base/lppl.txt
                                                                                           %%%                        ",
                                                                                           %%%     address         = "Arthur Ogawa,
                                                                                           %%%                        USA",
                                                                                           %%%     telephone       = "",
                                                                                           %%%     FAX             = "",
                                                                                           %%%     email           = "mailto colon arthur_ogawa at sbcglobal.net",
                                                                                           %%%     codetable       = "ISO/ASCII",
                                                                                           %%%     keywords        = "latex, page grid, main vertical list",
                                                                                           %%%     supported       = "yes",
                                                                                           %%%     abstract        = "package to change page grid, MVL",
                                                                                           %%%     docstring       = "The checksum field above generated by ltxdoc",
                                                                                           %%%  }
                                                                                           \def\substyle@post{4-1}%
                                                                                           \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\fps@video{tbp}%
                                                                                                                                                                                       \def\ftype@video{4}%
                                                                                                                                                                                       \def\ext@video{lov}%
                                                                                                                                                                                       \def\fnum@video{\fname@video~\thevideo}%
                                                                                                                                                                                       \def\fname@video{Video}%
                                                                                                                                                                                       \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{\def\@bibstyle}%
                                                                                                                                                                                         \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}%
                                                                                                                                                                                         }%
                                                                                                                                                                                         \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
                                                                                                                                                                                           \@bibdataout@rev
                                                                                                                                                                                         }%
                                                                                                                                                                                         \def\@bibdataout@rev{%
                                                                                                                                                                                           \immediate\write\@bibdataout{%
                                                                                                                                                                                             @CONTROL{%
                                                                                                                                                                                               REVTEX41Control%
                                                                                                                                                                                               \eprint@enable@sw{}{,eprint="}%
                                                                                                                                                                                             }%
                                                                                                                                                                                           }%
                                                                                                                                                                                           \if@filesw
                                                                                                                                                                                           \immediate\write\@auxout{\string\citation{REVTEX41Control}}%
                                                                                                                                                                                           \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{revsymb4-1}%
                                                                                                                                                                                         }%
                                                                                                                                                                                         \appdef\class@documenthook{\revsymb@inithook}%
                                                                                                                                                                                         \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
                                                                                                                                                                                         \setup@hook
                                                                                                                                                                                         \endinput
                                                                                                                                                                                         %%
                                                                                                                                                                                         %% End of file `revtex4-1.cls'.
                                                                                                                                                                                         
