Oscar Rondon added file main/revtex4-1.cls  about 9 years ago

Commit id: dc0674414bb362964f67a114b98cc24c714208c0

deletions | additions      

         

%%  %% 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:[email protected]  %%   %% See the REVTeX 4 README file for restrictions and more information.  %%   \NeedsTeXFormat{LaTeX2e}[1996/12/01]%  \ProvidesClass{revtex4-1}  [2010/07/25/20:33:00 4.1r (http://publish.aps.org/revtex4/ for documentation)]% \fileversion  \let\class@name\@gtempa  \GenericInfo{}{\space  Copyright (c) 2009 The American Physical Society.^^J  mailto:[email protected]^^J  Licensed under the LPPL:^^Jhttp://www.ctan.org/tex-archive/macros/latex/base/lppl.txt^^J  Arthur Ogawa ^^J  Based on work by David Carlisle %  \@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%  [2010/07/25/20:33:00 4.1r 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 \def\class@info#1{\ClassInfo{\class@name}{#1}}%  \def\obsolete@command#1{%  \class@warn@end{Command \string#1\space is obsolete.^^JPlease remove from your document}%  \global\let#1\@empty  #1%  }%  \def\replace@command#1#2{%  \class@warn@end{Command \string#1\space is obsolete;^^JUse \string#2\space instead}%  \global\let#1#2%  #1%  }%  \def\replace@environment#1#2{%  \class@warn@end{Environment #1 is obsolete;^^JUse #2 instead}%  \glet@environment{#1}{#2}%  \@nameuse{#1}%  }%  \def\incompatible@package#1{%  \@ifpackageloaded{#1}{%  \def\@tempa{I cannot continue.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  \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:}}%  \def\@@endlink@hypertext{\special{html:}}%  }{%  \def\@@startlink@hypertext#1{%  \leavevmode  \pdfstartlink\pdfstartlink@attr  user{/Subtype/Link/A<>}%  \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%  [2010/07/25/20:33:00 4.1r 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%  [2010/07/25/20:33:00 4.1r 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 [email protected]\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 = "4.1r",  %%% date = "2010/07/25",  %%% time = "20:33:00 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\ext@video{lov}%  \def\fname@video{Video}%  \def\lovname{List of Videos}%  \def\fps@video{tbp}%  \def\ftype@video{4}%  \def\fnum@video{\fname@video~\thevideo}%  \appdef\document@inithook{%  \@ifxundefined\c@float@type{}{%  \global\setcounter{float@type}{8}%  }%  }%  \expandafter\newbox\csname fbox@\ftype@video\endcsname  \expandafter\setbox\csname fbox@\ftype@video\endcsname\hbox{}%  \let\theHvideo\thevideo  \def\listofvideos{\print@toc{lov}}%  \let\l@video\l@figure  \appdef\class@documenthook{%  \do@if@floats{video}{.vdx}%  }%  \appdef\class@enddocumenthook{%  \printvideos\relax  }%  \newcommand\printvideos{%  \@ifstar{\true@sw}{\floatp@sw{\true@sw}{\false@sw}}%  {%  \print@float{video}{\oneapage}%  }{%  \print@float{video}{}%  }%  }%  \def\endtabular@hook{}%  \appdef\document@inithook{%  \@ifpackageloaded{dcolumn}{%  \expandafter\@ifnotrelax\csname NC@find@d\endcsname{}{%  \newcolumntype{d}{D{.}{.}{-1}}%  }%  }{}%  }%  \def\toprule{\hline\hline}%  \def\colrule{\hline}%  \def\botrule{\hline\hline}%  \newenvironment{ruledtabular}{%  \def\array@default{v}%  \appdef\tabular@hook{\def\@halignto{to\hsize}}%  \let\tableft@skip@default\tableft@skip  \let\tableft@skip\tableft@skip@float  \let\tabmid@skip@default\tabmid@skip  \let\tabmid@skip\tabmid@skip@float  \let\tabright@skip@default\tabright@skip  \let\tabright@skip\tabright@skip@float  \let\array@row@pre@default\array@row@pre  \let\array@row@pre\array@row@pre@float  \let\array@row@pst@default\array@row@pst  \let\array@row@pst\array@row@pst@float  \appdef\array@row@rst{%  \let\array@row@pre\array@row@pre@default  \let\array@row@pst\array@row@pst@default  \let\tableft@skip\tableft@skip@default  \let\tabmid@skip\tabmid@skip@default  \let\tabright@skip\tabright@skip@default  \appdef\tabular@hook{\let\@halignto\@empty}%  }%  }{%  }%  \def\@makefntext#1{%  \def\baselinestretch{1}%  \parindent1em%  \noindent  \hb@[email protected]{%  \hss\@makefnmark  }%  #1%  \par  }%  \def\@makefnmark{%  \hbox{%  \@textsuperscript{%  \normalfont\@thefnmark  }%  }%  }%  \expandafter\DeclareRobustCommand  \expandafter\rev@citet  \expandafter{%  \expandafter\begingroup  \expandafter\rtx@swap@citea  \expandafter\g@bblefirsttoken  \csname citet \endcsname  }%  \expandafter\DeclareRobustCommand  \expandafter\rev@citealp  \expandafter{%  \expandafter\begingroup  \expandafter\rtx@swap@citea  \expandafter\g@bblefirsttoken  \csname citealp \endcsname  }%  \expandafter\DeclareRobustCommand  \expandafter\rev@citealpnum  \expandafter{%  \expandafter\begingroup  \expandafter\rtx@swap@citenum  \expandafter\g@bblefirsttoken  \csname citealp \endcsname  }%  \def\rtx@swap@citenum{%  \rtx@swap@citea  \let\@cite\NAT@citenum  \let\NAT@mbox\mbox  \let\citeyear\NAT@citeyear  \let\NAT@space\NAT@spacechar  }%  \def\g@bblefirsttoken{%  \expandafter\true@sw  \expandafter\@empty  }%  \newcommand\rtx@citesuper[3]{%  \ifNAT@swa  \leavevmode  \unskip  \textsuperscript{\normalfont#1}%  \if*#3*\else\ (#3)\fi  \else  #1%  \fi  \endgroup  }%  \def\@makefnmark@cite{\begingroup\NAT@swatrue\@cite{{\@thefnmark}}{}{}}%  \def\rtx@bibsection{%  \@ifx@empty\refname{%  \par  }{%  \expandafter\section\expandafter*\expandafter{\refname}%  \@nobreaktrue  }%  }%  \def\rtx@swap@citea{%  \let\NAT@def@citea\rtx@def@citea  \let\NAT@def@citea@close\rtx@def@citea@close  \let\NAT@def@citea@box\rtx@def@citea@box  }%  \def\rtx@def@citea{%  \def\@citea{\NAT@separator\NAT@space}%  \advance\c@NAT@ctr\@ne  \@ifnum{\count@>\tw@}{%  \@ifnum{\c@NAT@ctr=\count@}{\appdef\@citea{\NAT@conj\NAT@space}}{}%  }{%  \def\@citea{\NAT@space\NAT@conj\NAT@space}%  }%  }%  \def\rtx@def@citea@close{%  \rtx@def@citea  \prepdef\@citea{\NAT@@close}%  }%  \def\rtx@def@citea@box{%  \rtx@def@citea@close  \expandafter\def\expandafter\@citea\expandafter{\expandafter\NAT@mbox\expandafter{\@citea}}%  }%  \def\NAT@conj{and}%  \def\NAT@BibitemShut#1{%  \def\@bibstop{#1}%  \let\bibitem@Stop\bibitemStop  \let\bibitem@NoStop\bibitemNoStop  \@ifx{\bibitemShut\relax}{\let\@bibitemShut\@empty}{%  \expandafter\def\expandafter\@bibitemShut\expandafter{\bibitemShut}%  }%  }%  \def\BibitemShut@ltx#1{%  \unskip  \def\@bibstop{#1}%  \let\bibitem@Stop\bibitemStop  \let\bibitem@NoStop\bibitemNoStop  \@ifx{\bibitemShut\relax}{\let\@bibitemShut\@empty}{%  \expandafter\def\expandafter\@bibitemShut\expandafter{\bibitemShut}%  }%  }%  \newenvironment{thebibliography}{}{}%  \let\@listi\@empty  \appdef\rtx@require@packages{%  \RequirePackage[sort&compress]{natbib}[2009/11/07 8.31a (PWD, AO)]%  \let@environment{NAT@thebibliography}{thebibliography}%  \let@environment{thebibliography}{rtx@thebibliography}%  \let\bibliographystyle@latex\bibliographystyle  \let\NAT@citesuper\rtx@citesuper  \let\bibsection\rtx@bibsection  \let\NATx@bibsetnum\NAT@bibsetnum  \def\NAT@bibsetnum#1{%  \setlength{\topsep}{\z@}%  \NATx@bibsetnum{\ref{LastBibItem}}%  }%  \let\NATx@bibsetup\NAT@bibsetup  \def\NAT@bibsetup{%  \setlength{\labelwidth}{\z@}%  \setlength{\labelsep}{\z@}%  \setlength{\itemindent}{\z@}%  \setlength{\listparindent}{\z@}%  \setlength{\topsep}{\z@}%  \setlength{\parsep}{\z@}%  \NATx@bibsetup  }%  \let\bibpreamble\@empty  \def\newblock{\ }%  \let\NATx@bibnumfmt\bibnumfmt  \def\bibnumfmt{\place@bibnumber}%  \let\NAT@merge\thr@@  \let\NAT@citeyear\citeyear  \let\onlinecite\rev@citealp  \let\textcite\rev@citet  \@ifx{\BibitemShut\NAT@BibitemShut}{%  \class@info{Repairing natbib's \string\BibitemShut}%  \let\BibitemShut\BibitemShut@ltx  }{}%  \let\bibliographystyle@latex\bibliographystyle  \def\bibliographystyle{\@booleantrue\bibliographystyle@sw\def\@bibstyle}%  \@booleanfalse\bibliographystyle@sw  \def\NAT@bibitem@cont{%  \let\bibitem@Stop\bibitemContinue@Stop  \let\bibitem@NoStop\bibitemContinue  }%  \def\bibitemNoStop{%  \@ifx@empty\@bibitemShut{.\spacefactor\@mmm\space}{\@bibitemShut}%  }%  \def\bibitemContinue{%  \@ifx@empty\@bibitemShut{;\spacefactor\@mmm\space}{\@bibitemShut}%  }%  \def\bibitemContinue@Stop{%  \@ifx@empty\@bibitemShut{\spacefactor\@mmm\space}{\@bibitemShut}%  }%  }%  \DeclareRobustCommand\onlinecite{\@onlinecite}%  \DeclareRobustCommand\textcite{\@textcite}%  \let\bibliography@latex\bibliography  \def\bibliography#1{%  \auto@bib@empty  \begingroup  \let\auto@bib@innerbib\@empty  \@ifx@empty{\pre@bibdata}{%  \bibliography@latex{#1}%  }{%  \@if@empty{#1}{%  \expandafter\bibliography@latex\expandafter{\pre@bibdata}%  }{%  \expandafter\bibliography@latex\expandafter{\pre@bibdata,#1}%  }%  }%  \endgroup  }%  \let\pre@bibdata\@empty  \newenvironment{rtx@thebibliography}[1]{%  \NAT@thebibliography{#1}%  \let\@TBN@opr\present@bibnote  \@FMN@list  }{%  \auto@bib@innerbib  \edef\@currentlabel{\arabic{NAT@ctr}}%  \label{LastBibItem}%  \endNAT@thebibliography  \aftergroup\auto@bib@empty  }%  \def\present@bibnote#1#2{%  \item[%  \textsuperscript{%  \normalfont  \Hy@raisedlink{\hyper@anchorstart{frontmatter.#1}\hyper@anchorend}%  \begingroup  \csname c@\@mpfn\endcsname#1\relax  \frontmatter@thefootnote  \endgroup  }%  ]#2\par  }%  \def\write@bibliographystyle{%  \@ifxundefined\@bibstyle{}{%  \expandafter\bibliographystyle@latex\expandafter{\@bibstyle}%  \bibliographystyle@sw{}{\@bibdataout@rev}%  }%  \global\let\write@bibliographystyle\relax  }%  \AtEndDocument{\write@bibliographystyle}%  \def\rtx@@citetp[#1]{\@ifnextchar[{\rtx@citex[#1]}{\rtx@citex[][#1]}}%  \def\rtx@citex[#1][#2]#3{%  \begingroup  \def\@tempa{[#1][#2]{#3}}%  \@ifx{\@cite\NAT@citesuper}{%  \leavevmode  \skip@\lastskip  \unskip  \super@cite@let  }{%  \super@cite@end  }%  }%  \def\super@cite@let{%  \futurelet\@let@token\super@cite@check  }%  \def\super@cite@end{%  \aftergroup\@citex\expandafter\endgroup\@tempa  }%  \def\super@cite@check{%  \@ifx{\@let@token\@sptoken}{%  \super@cite@end  }{%  \super@cite@swap  }%  }%  \long\def\super@cite@swap#1{%  \expandafter\@ifx\expandafter{\csname rtx@automove#1\endcsname\@empty}{%  #1%  \super@cite@let  }{%  \super@cite@end  #1%  }%  }%  \expandafter\let\csname rtx@automove.\endcsname\@empty  \expandafter\let\csname rtx@automove,\endcsname\@empty  \expandafter\let\csname rtx@automove:\endcsname\@empty  \expandafter\let\csname rtx@automove;\endcsname\@empty  \appdef\class@documenthook{%  \citeautoscript@sw{%  \@ifx{\@cite\NAT@citesuper}{%  \let\NAT@@citetp\rtx@@citetp  }{}%  }{}%  }%  \def\mini@note{\save@note\mini@notes}%Implicit #2  \def\save@note#1#2{%  \stepcounter\@mpfn  \protected@xdef\@thefnmark{\thempfn}%  \@footnotemark  \expandafter\g@addto@macro  \expandafter#1%  \expandafter{%  \expandafter \@@footnotetext  \expandafter {\@thefnmark}{#2}%  }%  }%  \long\def\@@footnotetext#1{\def\@thefnmark{#1}\@footnotetext}%  \let\mini@notes\@empty  \def\rev@citemark#1{%  \expandafter\cite\expandafter{\@thefnmark}%  }%  \def\rev@endtext#1{%  \let\@endnotelabel\@thefnmark  \@endnotetext  }%  \def\endnote@ext{.end}%  \def\bibdata@app{Notes}%  \def\bibdata@ext{bib}%  \long\def\@endnotetext#1{%  \begingroup  \endnote@relax  \immediate\write\@bibdataout{%  @FOOTNOTE{%  \@endnotelabel,%  key="\@endnotelabel",%  note="#1"%  }%  }%  \endgroup  }%  \newwrite\@bibdataout  \def\endnote@relax{%  \let\label\relax \let\index\relax \let\glossary\relax  \let\cite \relax \let\ref \relax \let\pageref \relax  \let\( \relax \let\) \relax \let\\ \relax  \let~\relax  \let \protect \@unexpandable@protect  \newlinechar`\^^M%  \let\begin\relax \let\end\relax  }%  \appdef\class@documenthook{\@bibdataout@init}%  \def\@bibdataout@init{%  \immediate\openout\@bibdataout\pre@bibdata.\bibdata@ext\relax  }%  \def\@bibdataout@rev{%  \immediate\write\@bibdataout{%  @CONTROL{%  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'.