\catcode`\@=11
\def\W@{\immediate\write\sixt@@n}
\ifx\amstexloaded@\relax
 \W@{! lamstbls.tex cannot be used with amstex.tex}\let\relax\end\fi\relax
\toksdef\toks@@=2
\def\alloc@#1#2#3#4#5{\global\advance\count1#1by\@ne
 \ch@ck#1#4#2\allocationnumber=\count1#1
 \global#3#5=\allocationnumber}
\newcount\count@@
\newcount\count@@@
\def\FN@{\futurelet\next}
\def\DN@{\def\next@}
\def\DNii@{\def\nextii@}
\def\RIfM@{\relax\ifmmode}
\def\RIfMIfI@{\relax\ifmmode\ifinner}
\def\setboxz@h{\setbox\z@\hbox}
\def\wdz@{\wd\z@}
\def\boxz@{\box\z@}
\def\height{height}
\def\width{width}
\def\depth{depth}
\def\iterate{\body\expandafter\iterate\else\fi}
\newlinechar=`\^^J
\newhelp\defaulthelp@{Sorry, I already gave what help I could...^^J
Maybe you should try asking a human?^^J
An error might have occurred before I noticed any problems.^^J
``If all else fails, read the instructions.''}
\def\eat@#1{}
\def\space@.{\futurelet\space@\relax}
\space@. %
\newhelp\athelp@
{Only certain combinations beginning with @ make sense to me.^^J
Perhaps you wanted \string\@\space for a printed @?^^J
I've ignored the character or group after @.}
\def\atdef@#1{\expandafter\def\csname\string#1@at\endcsname}
\newhelp\defahelp@{If you typed \string\define\space cs instead of
\string\define\string\cs\space^^J
I've substituted an inaccessible control sequence so that your^^J
definition will be completed without mixing me up too badly.^^J
If you typed \string\define{\string\cs} the inaccessible control sequence^^J
was defined to be \string\cs, and the rest of your^^J
definition appears as input.}
\newhelp\defbhelp@{I've ignored your definition, because it might^^J
conflict with other uses that are important to me.}
\def\define@{\FN@\define@@}
\def\err@#1{\errmessage{LamS-TeX error: #1}}
\def\define@@{\ifcat\noexpand\next\relax
 \expandafter\define@@@\else\errhelp\defahelp@
 \err@{\noexpand\define must be followed by a control
 sequence}\expandafter\def\expandafter\nextii@\fi}
\def\undefined@@@@@@@@@@{}
\def\preloaded@@@@@@@@@@{}
\def\next@@@@@@@@@@{}
\def\define@@@#1{\ifx#1\relax\errhelp\defbhelp@
 \err@{\noexpand#1is already defined}\DN@{\DNii@}\else
 \expandafter\ifx\csname\expandafter\eat@\string
 #1@@@@@@@@@@\endcsname\undefined@@@@@@@@@@\errhelp\defbhelp@
 \err@{\noexpand#1can't be defined}\DN@{\DNii@}\else
 \expandafter\ifx\csname\expandafter\eat@\string#1\endcsname\relax
 \global\let#1\undefined\DN@{\def#1}\else\errhelp\defbhelp@
 \err@{\noexpand#1is already defined}\DN@{\DNii@}\fi
 \fi\fi\next@}
\def\undefine#1{\let#1\undefined}
\def\WT@#1{\expandafter\let\csname\expandafter\eat@\string#1 \endcsname=#1%
 \xdef\next@{\def\noexpand#1{\noexpand\NX@\expandafter\noexpand
  \csname\expandafter\eat@\string#1 \endcsname}}%
 \next@}
\def\predefine#1{\def\tdf@{#1}\afterassignment\wtdef@\let\tdf@@}
\def\redefine#1{\def\tdf@{#1}\afterassignment\wtdef@\def\tdf@@}
\def\define#1{\define@#1{}\redefine#1}
\def\wtdef@{\expandafter\let\tdf@\tdf@@\expandafter\WT@\tdf@}
\def\tie{\unskip\nobreak\ }
\let\graveaccent\`
\let\acuteaccent\'
\let\tildeaccent\~
\let\hataccent\^
\let\underscore\_
\let\B\=
\let\D\.
\let\ic@\/
\def\/{\unskip\ic@}
\def\textfonti{\the\textfont\@ne}
\def\t#1#2{{\edef\next@{\the\font}\textfonti\accent"7F \next@#1#2}}
\def~{\unskip\nobreak\ \ignorespaces}
\def\.{.\spacefactor\@m}
\atdef@;{\leavevmode\null;}
\atdef@:{\leavevmode\null:}
\atdef@?{\leavevmode\null?}
\def\@{\char64 }
\atdef@-{\leavevmode
 \DN@{\ifx\next-\DN@-{\FN@\nextii@}\else
  \DN@{\leavevmode\hbox{-}}\fi\next@}%
 \DNii@{\ifx\next-\DN@-{\leavevmode\hbox{---}}\else
  \DN@{\leavevmode\hbox{--}}\fi\next@}%
 \FN@\next@}
\def\srdr@{\kern.16667em}
\def\drsr@{\kern.02778em}
\def\sldl@{\kern.02778em}
\def\dlsl@{\kern.16667em}
\def\textfontii{\the\textfont\tw@}
\def\lbrace@{\delimiter"4266308 }
\def\rbrace@{\delimiter"5267309 }
\def\{{\RIfM@\lbrace@\else{\textfontii f}\spacefactor\@m\fi}
\def\}{\RIfM@\rbrace@\else
 \let\@sf\empty\ifhmode\edef\@sf{\spacefactor\the\spacefactor}\fi
 {\textfontii g}\@sf\relax\fi}
\let\lbrace\{
\let\rbrace\}
\def\AmSTeX{{\textfontii A}\kern-.1667em\lower.5ex\hbox
 {\textfontii M}\kern-.125em{\textfontii S}-\TeX}
\def\vmodeerr@#1{\Err@{\noexpand#1not allowed between paragraphs}}
\def\mathmodeerr@#1{\Err@{\noexpand#1not allowed in math mode}}
\def\slash{\unskip/\penalty\exhyphenpenalty}
\newskip\saveskip@
\def\dmatherr@#1{\Err@{\noexpand#1not allowed in display math mode}}
\def\nondmatherr@#1{\Err@{\noexpand#1not allowed in non-display math
 mode}}
\def\onlydmatherr@#1{\Err@{\noexpand#1allowed only in display math mode}}
\def\nonmatherr@#1{\Err@{\noexpand#1allowed only in math mode}}
\def\mathbreak{\RIfMIfI@\break\else
 \dmatherr@\mathbreak\fi\else\nonmatherr@\mathbreak\fi}
\def\nomathbreak{\RIfMIfI@\nobreak\else
 \dmatherr@\nomathbreak\fi\else\nonmatherr@\nomathbreak\fi}
\def\allowmathbreak{\RIfMIfI@\allowbreak\else
 \dmatherr@\allowmathbreak\fi\else\nonmatherr@\allowmathbreak\fi}
\def\nonvmodeerr@#1{\Err@{\noexpand#1not allowed within a paragraph
 or in math}}
\def\vnonvmode@#1#2{\DNii@{\ifx\next\par\DN@{#1}\else
 \DN@{#2}\fi\next@}%
 \ifvmode\DN@{#1}\else
 \DN@{\FN@\nextii@}\fi\next@}
\def\smallpagebreak{\vnonvmode@\smallbreak{\nonvmodeerr@\smallpagebreak}}
\def\medpagebreak{\vnonvmode@\medbreak{\nonvmodeerr@\medpagebreak}}
\def\bigpagebreak{\vnonvmode@\bigbreak{\nonvmodeerr@\bigpagebreak}}
\def\NoBlackBoxes{\global\overfullrule\z@}
\def\BlackBoxes{\global\overfullrule5\p@}
\def\Invalid@#1{\def#1{\Err@{\Invalid@@\string#1}}}
\def\Invalid@@{Invalid use of }
\def\newcodes@{\catcode`\\=12 \catcode`\{=12 \catcode`\}=12 \catcode`\#=12
 \catcode`\%=12\relax}
\def\oldcodes@{\catcode`\\=0 \catcode`\{=1 \catcode`\}=2 \catcode`\#=6
 \catcode`\%=14\relax}
\def\comment{\newcodes@\endlinechar=10 \comment@}
{\lccode`\0=`\\
\lowercase{\gdef\comment@#1^^J{\comment@@#10endcomment\comment@@@}%
\gdef\comment@@#10endcomment{\FN@\comment@@@}%
\gdef\comment@@@#1\comment@@@{\ifx\next\comment@@@\let\next@\comment@
 \else\def\next@{\oldcodes@\endlinechar=`\^^M\relax}%
 \fi\next@}}}
\def\pr@m@s{\ifx'\next\DN@##1{\prim@s}\else\let\next@\egroup\fi\next@}
\def\prime{{\null\prime@\null}}
\mathchardef\prime@="0230
\let\dsize\displaystyle
\let\tsize\textstyle
\let\ssize\scriptstyle
\let\sssize\scriptscriptstyle
\def\,{\RIfM@\mskip\thinmuskip\relax\else\kern.16667em\fi}
\def\!{\RIfM@\mskip-\thinmuskip\relax\else\kern-.16667em\fi}
\let\thinspace\,
\let\negthinspace\!
\def\medspace{\RIfM@\mskip\medmuskip\relax\else\kern.222222em\fi}
\def\negmedspace{\RIfM@\mskip-\medmuskip\relax\else\kern-.222222em\fi}
\def\thickspace{\RIfM@\mskip\thickmuskip\relax\else\kern.27777em\fi}
\let\;\thickspace
\def\negthickspace{\RIfM@\mskip-\thickmuskip\relax\else
 \kern-.27777em\fi}
\atdef@,{\RIfM@\mskip.1\thinmuskip\else\leavevmode\null,\fi}
\atdef@!{\RIfM@\mskip-.1\thinmuskip\else\leavevmode\null!\fi}
\atdef@.{\leavevmode.\spacefactor3000 }
\def\and{\DOTSB\;\mathchar"3026 \;}
\def\implies{\DOTSB\;\Longrightarrow\;}
\def\impliedby{\DOTSB\;\Longleftarrow\;}
\def\frac#1#2{{#1\over#2}}
\def\dfrac#1#2{{\displaystyle{#1\over#2}}}
\def\tfrac#1#2{{\textstyle{#1\over#2}}}
\newdimen\ex@
\ex@.2326ex
\Invalid@\thickness
\def\thickfrac{\DN@{\ifx\next\thickness\let\next@\nextii@\else
 \DN@{\nextii@\thickness1}\fi\next@}%
 \DNii@\thickness##1##2##3{{##2\above##1\ex@##3}}%
 \FN@\next@}
\def\fracwithdelims#1#2#3#4{{#3\overwithdelims#1#2#4}}
\def\thickfracwithdelims#1#2{\def\ldelim@{#1}\def\rdelim@{#2}%
 \DN@{\ifx\next\thickness\let\next@\nextii@\else
 \DN@{\nextii@\thickness1}\fi\next@}%
 \DNii@\thickness##1##2##3{{##2\abovewithdelims
 \ldelim@\rdelim@##1\ex@##3}}%
 \FN@\next@}
\def\binom#1#2{{#1\choose#2}}
\def\dbinom#1#2{{\displaystyle{#1\choose#2}}}
\def\tbinom#1#2{{\textstyle{#1\choose#2}}}
\def\:{\nobreak\hskip.1111em\mathpunct{}\nonscript\mkern-\thinmuskip{:}\hskip
 .3333emplus.0555em\relax}
\def\snug{\unskip\kern-\mathsurround}
\define\topsmash{\top@true\bot@false\smash@}
\define\botsmash{\top@false\bot@true\smash@}
\newif\iftop@
\newif\ifbot@
\undefine\smash
\define\smash{\top@true\bot@true\smash@}
\def\smash@{\RIfM@\expandafter\mathpalette\expandafter\mathsm@sh\else
 \expandafter\makesm@sh\fi}
\def\finsm@sh{\iftop@\ht\z@\z@\fi\ifbot@\dp\z@\z@\fi\leavevmode\boxz@}
\def\LimitsOnSums{\global\let\slimits@\displaylimits}
\def\NoLimitsOnSums{\global\let\slimits@\nolimits}
\LimitsOnSums
\catcode`\"=12
\mathchardef\coprod@="1360       \def\coprod{\DOTSB\coprod@\slimits@}
\mathchardef\bigvee@="1357       \def\bigvee{\DOTSB\bigvee@\slimits@}
\mathchardef\bigwedge@="1356     \def\bigwedge{\DOTSB\bigwedge@\slimits@}
\mathchardef\biguplus@="1355     \def\biguplus{\DOTSB\biguplus@\slimits@}
\mathchardef\bigcap@="1354       \def\bigcap{\DOTSB\bigcap@\slimits@}
\mathchardef\bigcup@="1353       \def\bigcup{\DOTSB\bigcup@\slimits@}
\mathchardef\prod@="1351         \def\prod{\DOTSB\prod@\slimits@}
\mathchardef\sum@="1350          \def\sum{\DOTSB\sum@\slimits@}
\mathchardef\bigotimes@="134E    \def\bigotimes{\DOTSB\bigotimes@\slimits@}
\mathchardef\bigoplus@="134C     \def\bigoplus{\DOTSB\bigoplus@\slimits@}
\mathchardef\bigodot@="134A      \def\bigodot{\DOTSB\bigodot@\slimits@}
\mathchardef\bigsqcup@="1346     \def\bigsqcup{\DOTSB\bigsqcup@\slimits@}
\def\LimitsOnInts{\global\let\ilimits@\displaylimits}
\def\NoLimitsOnInts{\global\let\ilimits@\nolimits}
\NoLimitsOnInts
\def\int{\DOTSI\intop\ilimits@}
\def\oint{\DOTSI\ointop\ilimits@}
\def\intic@{\mathchoice{\hskip.5em}{\hskip.4em}{\hskip.4em}{\hskip.4em}}
\def\negintic@{\mathchoice
 {\hskip-.5em}{\hskip-.4em}{\hskip-.4em}{\hskip-.4em}}
\def\intkern@{\mathchoice{\!\!\!}{\!\!}{\!\!}{\!\!}}
\def\intdots@{\mathchoice{\plaincdots@}
 {{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}
 {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}
 {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
\newcount\intno@
\def\iint{\DOTSI\intno@\tw@\FN@\ints@}
\def\iiint{\DOTSI\intno@\thr@@\FN@\ints@}
\def\iiiint{\DOTSI\intno@4 \FN@\ints@}
\def\idotsint{\DOTSI\intno@\z@\FN@\ints@}
\def\ints@{\findlimits@\ints@@}
\newif\iflimtoken@
\newif\iflimits@
\def\findlimits@{\limtoken@true\ifx\next\limits\limits@true
 \else\ifx\next\nolimits\limits@false\else
 \limtoken@false\ifx\ilimits@\nolimits\limits@false\else
 \ifinner\limits@false\else\limits@true\fi\fi\fi\fi}
\def\multint@{\int\ifnum\intno@=\z@\intdots@
 \else\intkern@\fi
 \ifnum\intno@>\tw@\int\intkern@\fi
 \ifnum\intno@>\thr@@\int\intkern@\fi
 \int}
\def\multintlimits@{\intop\ifnum\intno@=\z@\intdots@\else\intkern@\fi
 \ifnum\intno@>\tw@\intop\intkern@\fi
 \ifnum\intno@>\thr@@\intop\intkern@\fi\intop}
\def\ints@@{\iflimtoken@
 \def\ints@@@{\iflimits@\negintic@\mathop{\intic@\multintlimits@}\limits
  \else\multint@\nolimits\fi
  \eat@}
 \else
 \def\ints@@@{\iflimits@\negintic@
  \mathop{\intic@\multintlimits@}\limits\else
  \multint@\nolimits\fi}\fi\ints@@@}
\def\LimitsOnNames{\global\let\nlimits@\displaylimits}
\def\NoLimitsOnNames{\global\let\nlimits@\nolimits@}
\LimitsOnNames
\def\nolimits@{\DN@{\ifx\next\limits\DN@\limits{\nolimits}\else
  \let\next@\nolimits\fi\next@}%
 \FN@\next@}
\def\newmcodes@{\mathcode39="0027 \mathcode42="002A \mathcode46="613A
 \mathcode45="002D \mathcode47="002F \mathcode58="603A }
\def\operatorname#1{\mathop{\newmcodes@\kern\z@\fam\z@#1}\nolimits@}
\def\operatornamewithlimits#1{\mathop{\newmcodes@\kern\z@\fam\z@#1}\nlimits@}
\def\qopname@#1{\mathop{\fam\z@#1}\nolimits@}
\def\qopnamewl@#1{\mathop{\fam\z@#1}\nlimits@}
\def\arccos{\qopname@{arccos}}
\def\arcsin{\qopname@{arcsin}}
\def\arctan{\qopname@{arctan}}
\def\arg{\qopname@{arg}}
\def\cos{\qopname@{cos}}
\def\cosh{\qopname@{cosh}}
\def\cot{\qopname@{cot}}
\def\coth{\qopname@{coth}}
\def\csc{\qopname@{csc}}
\def\deg{\qopname@{deg}}
\def\det{\qopnamewl@{det}}
\def\dim{\qopname@{dim}}
\def\exp{\qopname@{exp}}
\def\gcd{\qopnamewl@{gcd}}
\def\hom{\qopname@{hom}}
\def\inf{\qopnamewl@{inf}}
\def\injlim{\qopnamewl@{inj\,lim}}
\def\ker{\qopname@{ker}}
\def\lg{\qopname@{lg}}
\def\lim{\qopnamewl@{lim}}
\def\liminf{\qopnamewl@{lim\,inf}}
\def\limsup{\qopnamewl@{lim\,sup}}
\def\ln{\qopname@{ln}}
\def\log{\qopname@{log}}
\def\max{\qopnamewl@{max}}
\def\min{\qopnamewl@{min}}
\def\Pr{\qopnamewl@{Pr}}
\def\projlim{\qopnamewl@{proj\,lim}}
\def\sec{\qopname@{sec}}
\def\sin{\qopname@{sin}}
\def\sinh{\qopname@{sinh}}
\def\sup{\qopnamewl@{sup}}
\def\tan{\qopname@{tan}}
\def\tanh{\qopname@{tanh}}
\define\varinjlim{\mathop{\vtop{\ialign{##\crcr
 \hfil\rm lim\hfil\crcr\noalign{\nointerlineskip}\rightarrowfill\crcr
 \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
\define\varprojlim{\mathop{\vtop{\ialign{##\crcr
 \hfil\rm lim\hfil\crcr\noalign{\nointerlineskip}\leftarrowfill\crcr
 \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
\def\varliminf{\mathop{\underline{\vrule\height\z@\depth.2ex\width\z@
 \hbox{\rm lim}}}}
\def\varlimsup{\mathop{\overline{\hbox{\rm lim}}}}
\newdimen\buffer@
\buffer@\fontdimen13 \tenex
\newdimen\buffer
\buffer\buffer@
\def\ChangeBuffer#1{\fontdimen13 \tenex#1\relax
 \global\buffer\fontdimen13 \tenex}
\def\ResetBuffer{\fontdimen13 \tenex\buffer@\global\buffer\buffer@}
\def\shave#1{\mathop{\hbox{$\m@th\fontdimen13 \tenex\z@
 \displaystyle{#1}$}}\fontdimen13 \tenex\buffer}
\def\topshave#1{\mathop{\topsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}}
\def\botshave#1{\mathop{\botsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}}
\Invalid@\\
\def\Let@{\relax\iffalse{\fi\let\\\cr\iffalse}\fi}
\Invalid@\vspace
\def\vspace@{\def\vspace##1{\crcr\noalign{\vskip##1\relax}}}
\def\multilimits@{\bgroup\vspace@\Let@
 \baselineskip\fontdimen10 \scriptfont\tw@
 \advance\baselineskip\fontdimen12 \scriptfont\tw@
 \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
 \lineskiplimit\lineskip
 \vbox\bgroup\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil\crcr}
\def\Sb{_\multilimits@}
\def\endSb{\crcr\egroup\egroup\egroup}
\def\Sp{^\multilimits@}
\let\endSp\endSb
\def\spreadlines#1{\RIfMIfI@\onlydmatherr@\spreadlines\else
 \openup#1\relax\fi\else\onlydmatherr@\spreadlines\fi}
\def\Mathstrut@{\copy\Mathstrutbox@}
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@\null
\setbox\z@\hbox{$\m@th($}
\ht\Mathstrutbox@\ht\z@
\dp\Mathstrutbox@\dp\z@
\newdimen\spreadmlines@
\def\spreadmatrixlines#1{\RIfMIfI@
 \onlydmatherr@\spreadmatrixlines\else
 \spreadmlines@#1\relax\fi\else\onlydmatherr@\spreadmatrixlines\fi}
\def\matrix{\null\,\vcenter\bgroup\Let@\vspace@
 \normalbaselines\openup\spreadmlines@\ialign
 \bgroup\hfil$\m@th##$\hfil&&\quad\hfil$\m@th##$\hfil\crcr
 \Mathstrut@\crcr\noalign{\kern-\baselineskip}}
\def\endmatrix{\crcr\Mathstrut@\crcr\noalign{\kern-\baselineskip}\egroup
 \egroup\,}
\def\format{\crcr\egroup\iffalse{\fi\ifnum`}=0 \fi\format@}
\newtoks\hashtoks@
\hashtoks@{#}
\def\format@#1\\{\def\preamble@{#1}%
 \def\l{$\m@th\the\hashtoks@$\hfil}%
 \def\c{\hfil$\m@th\the\hashtoks@$\hfil}%
 \def\r{\hfil$\m@th\the\hashtoks@$}%
 \edef\Preamble@{\preamble@}\ifnum`{=0 \fi\iffalse}\fi
 \ialign\bgroup\span\Preamble@\crcr}
\def\smallmatrix{\null\,\vcenter\bgroup\vspace@\Let@
 \baselineskip9\ex@\lineskip\ex@
 \ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil&&\thickspace\hfil
 $\m@th\scriptstyle{##}$\hfil\crcr}
\def\endsmallmatrix{\crcr\egroup\egroup\,}
\def\pmatrix{\left(\matrix}
\def\endpmatrix{\endmatrix\right)}
\def\bmatrix{\left[\matrix}
\def\endbmatrix{\endmatrix\right]}
\def\vmatrix{\left|\matrix}
\def\endvmatrix{\endmatrix\right|}
\def\Vmatrix{\left\|\matrix}
\def\endVmatrix{\endmatrix\right\|}
\def\hdots{\mathinner{\ldotp\ldotp\ldotp}}
\newmuskip\dotsspace@
\dotsspace@1.5mu
\def\strip@#1 {#1}
\def\spacehdots#1\for#2{\multispan{#2}\xleaders
 \hbox{$\m@th\mkern\strip@#1 \dotsspace@.\mkern\strip@#1 \dotsspace@$}\hfill}
\def\hdotsfor#1{\spacehdots\@ne\for{#1}}
\def\multispan@#1{\omit\mscount#1\unskip\loop\ifnum\mscount>\@ne\sp@n\repeat}
\def\spaceinnerhdots#1\for#2\after#3{\multispan@{\strip@#2 }#3\xleaders
 \hbox{$\m@th\mkern\strip@#1 \dotsspace@.\mkern\strip@#1 \dotsspace@$}\hfill}
\def\innerhdotsfor#1\after#2{\spaceinnerhdots\@ne\for#1\after{#2}}
\def\cases{\bgroup\spreadmlines@\jot\left\{\,\matrix\format\l&\quad\l\\}
\def\endcases{\endmatrix\right.\egroup}
\def\strut@{\copy\strutbox@}
\newbox\strutbox@
\setbox\strutbox@\hbox{\vrule\height8\p@\depth3\p@\width\z@}
\def\topaligned{\null\,\vtop\aligned@}
\def\botaligned{\null\,\vbox\aligned@}
\def\aligned{\null\,\vcenter\aligned@}
\def\aligned@{\bgroup\vspace@\Let@
 \openup\jot\ialign
 \bgroup\hfil\strut@$\m@th\displaystyle{##}$&
 $\m@th\displaystyle{{}##}$\hfil\crcr}
\def\endaligned{\crcr\egroup\egroup}
\let\endtopaligned\endaligned
\let\endbotaligned\endaligned
\def\alignedat#1{\null\,\vcenter\bgroup\doat@{#1}\vspace@\Let@
 \openup\jot\ialign\bgroup\span\preamble@@\crcr}
\newcount\atcount@
\def\doat@#1{\toks@{\hfil\strut@$\m@th
 \displaystyle{\the\hashtoks@}$&$\m@th\displaystyle
 {{}\the\hashtoks@}$\hfil}%
 \atcount@#1\relax\advance\atcount@\m@ne
 \loop\ifnum\atcount@>\z@\toks@=\expandafter{\the\toks@&\hfil$\m@th
 \displaystyle{\the\hashtoks@}$&$\m@th
 \displaystyle{{}\the\hashtoks@}$\hfil}\advance\atcount@\m@ne\repeat
 \edef\preamble@{\the\toks@}\edef\preamble@@{\preamble@}}
\let\endalignedat\endaligned
\def\gathered{\null\,\vcenter\bgroup\vspace@\Let@
 \openup\jot\ialign
 \bgroup\hfil\strut@$\m@th\displaystyle{##}$\hfil\crcr}
\def\endgathered{\crcr\egroup\egroup}
\def\bmod{\mskip-\medmuskip\mkern5mu\mathbin{\fam\z@ mod}\penalty900
 \mkern5mu\mskip-\medmuskip}
\def\pmod#1{\allowbreak\ifinner\mkern8mu\else\mkern18mu\fi
 ({\fam\z@ mod}\,\,#1)}
\def\pod#1{\allowbreak\ifinner\mkern8mu\else\mkern18mu\fi(#1)}
\def\mod#1{\allowbreak\ifinner\mkern12mu\else\mkern18mu\fi{\fam\z@ mod}\,\,#1}
\newcount\cfraccount@
\def\cfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut
 \iffalse{\fi\def\\{\over\displaystyle}\iffalse}\fi}
\def\lcfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut
 \iffalse{\fi\def\\{\hfill\over\displaystyle}\iffalse}\fi}
\def\rcfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut\hfill
 \iffalse{\fi\def\\{\over\displaystyle}\iffalse}\fi}
\def\endcfrac{\gloop@\ifnum\cfraccount@>\z@\global\advance\cfraccount@\m@ne
 \egroup\hskip-\nulldelimiterspace\egroup\repeat}
\def\binrel@#1{\setboxz@h{\thinmuskip0mu
  \medmuskip\m@ne mu\thickmuskip\@ne mu$#1\m@th$}%
 \setbox\tw@\hbox{\thinmuskip0mu\medmuskip\m@ne mu\thickmuskip
  \@ne mu${}#1{}\m@th$}%
 \setbox\tw@\hbox{\hskip\wd\tw@\hskip-\wdz@}}
\def\overset#1\to#2{\binrel@{#2}\ifdim\wd\tw@<\z@
 \mathbin{\mathop{\kern\z@#2}\limits^{#1}}\else\ifdim\wd\tw@>\z@
 \mathrel{\mathop{\kern\z@#2}\limits^{#1}}\else
 {\mathop{\kern\z@#2}\limits^{#1}}{}\fi\fi}
\def\underset#1\to#2{\binrel@{#2}\ifdim\wd\tw@<\z@
 \mathbin{\mathop{\kern\z@#2}\limits_{#1}}\else\ifdim\wd\tw@>\z@
 \mathrel{\mathop{\kern\z@#2}\limits_{#1}}\else
 {\mathop{\kern\z@#2}\limits_{#1}}{}\fi\fi}
\def\oversetbrace#1\to#2{\overbrace{#2}^{#1}}
\def\undersetbrace#1\to#2{\underbrace{#2}_{#1}}
\def\sideset#1\and#2\to#3{%
 \setboxz@h{$\dsize{\vphantom{#3}}#1{#3}\m@th$}%
 \setbox\tw@\hbox{$\dsize{#3}#2\m@th$}%
 \hskip\wdz@\hskip-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wdz@
  {\vphantom{#3}}#1{#3}#2}}
\def\rightarrowfill@#1{$#1\m@th\mathord-\mkern-6mu\cleaders
 \hbox{$#1\mkern-2mu\mathord-\mkern-2mu$}\hfill
 \mkern-6mu\mathord\rightarrow$}
\def\leftarrowfill@#1{$#1\m@th\mathord\leftarrow\mkern-6mu\cleaders
 \hbox{$#1\mkern-2mu\mathord-\mkern-2mu$}\hfill\mkern-6mu\mathord-$}
\def\leftrightarrowfill@#1{$#1\m@th\mathord\leftarrow\mkern-6mu\cleaders
 \hbox{$#1\mkern-2mu\mathord-\mkern-2mu$}\hfill
 \mkern-6mu\mathord\rightarrow$}
\def\overrightarrow{\mathpalette\overrightarrow@}
\def\overrightarrow@#1#2{\vbox{\ialign{##\crcr\rightarrowfill@#1\crcr
 \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#1#2\hfil$\crcr}}}
\let\overarrow\overrightarrow
\def\overleftarrow{\mathpalette\overleftarrow@}
\def\overleftarrow@#1#2{\vbox{\ialign{##\crcr\leftarrowfill@#1\crcr
 \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#1#2\hfil$\crcr}}}
\def\overleftrightarrow{\mathpalette\overleftrightarrow@}
\def\overleftrightarrow@#1#2{\vbox{\ialign{##\crcr\leftrightarrowfill@#1\crcr
 \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#1#2\hfil$\crcr}}}
\def\underrightarrow{\mathpalette\underrightarrow@}
\def\underrightarrow@#1#2{\vtop{\ialign{##\crcr$\m@th\hfil#1#2\hfil$\crcr
 \noalign{\nointerlineskip}\rightarrowfill@#1\crcr}}}
\let\underarrow\underrightarrow
\def\underleftarrow{\mathpalette\underleftarrow@}
\def\underleftarrow@#1#2{\vtop{\ialign{##\crcr$\m@th\hfil#1#2\hfil$\crcr
 \noalign{\nointerlineskip}\leftarrowfill@#1\crcr}}}
\def\underleftrightarrow{\mathpalette\underleftrightarrow@}
\def\underleftrightarrow@#1#2{\vtop{\ialign{##\crcr$\m@th\hfil#1#2\hfil$\crcr
 \noalign{\nointerlineskip}\leftrightarrowfill@#1\crcr}}}
\let\DOTSI\relax
\let\DOTSB\relax
\let\DOTSX\relax
\newif\ifmath@
{\uccode`7=`\\ \uccode`8=`m \uccode`9=`a \uccode`0=`t \uccode`!=`h
 \uppercase{\gdef\math@#1#2#3#4#5#6\math@{\global\math@false\ifx 7#1\ifx 8#2%
 \ifx 9#3\ifx 0#4\ifx !#5\xdef\meaning@{#6}\global\math@true\fi\fi\fi\fi\fi}}}
\newif\ifmathch@
{\uccode`7=`c \uccode`8=`h \uccode`9=`\"
 \uppercase{\gdef\mathch@#1#2#3#4#5#6\mathch@{\global\mathch@false
  \ifx 7#1\ifx 8#2\ifx 9#5\global\mathch@true\xdef\meaning@{9#6}\fi\fi\fi}}}
\newcount\classnum@
\def\getmathch@#1.#2\getmathch@{\classnum@#1 \divide\classnum@4096
 \ifcase\number\classnum@\or\or\gdef\thedots@{\dotsb@}\or
 \gdef\thedots@{\dotsb@}\fi}
\newif\ifmathbin@
{\uccode`4=`b \uccode`5=`i \uccode`6=`n
 \uppercase{\gdef\mathbin@#1#2#3{%
  \DNii@##1\mathbin@{\ifx\space@\next\global\mathbin@true\fi}%
 \global\mathbin@false\DN@##1\mathbin@{}%
 \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
\newif\ifmathrel@
{\uccode`4=`r \uccode`5=`e \uccode`6=`l
 \uppercase{\gdef\mathrel@#1#2#3{%
  \DNii@##1\mathrel@{\ifx\space@\next\global\mathrel@true\fi}%
 \global\mathrel@false\DN@##1\mathrel@{}%
 \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
\newif\ifmacro@
{\uccode`5=`m \uccode`6=`a \uccode`7=`c
 \uppercase{\gdef\macro@#1#2#3#4\macro@{\global\macro@false
  \ifx 5#1\ifx 6#2\ifx 7#3\global\macro@true
  \xdef\meaning@{\macro@@#4\macro@@}\fi\fi\fi}}}
\def\macro@@#1->#2\macro@@{#2}
\newif\ifDOTS@
\newcount\DOTSCASE@
{\uccode`6=`\\ \uccode`7=`D \uccode`8=`O \uccode`9=`T \uccode`0=`S
 \uppercase{\gdef\DOTS@#1#2#3#4#5{\global\DOTS@false\DN@##1\DOTS@{}%
  \ifx 6#1\ifx 7#2\ifx 8#3\ifx 9#4\ifx 0#5\let\next@\DOTS@@\fi\fi\fi\fi\fi
  \next@}}}
{\uccode`3=`B \uccode`4=`I \uccode`5=`X
 \uppercase{\gdef\DOTS@@#1{%
  \DNii@##1\DOTS@{\ifx\space@\next\global\DOTS@true\fi}%
  \DN@{\FN@\nextii@}%
  \ifx 3#1\global\DOTSCASE@\z@\else
  \ifx 4#1\global\DOTSCASE@\@ne\else
  \ifx 5#1\global\DOTSCASE@\tw@\else\DN@##1\DOTS@{}%
  \fi\fi\fi\next@}}}
\newif\ifnot@
{\uccode`5=`\\ \uccode`6=`n \uccode`7=`o \uccode`8=`t
 \uppercase{\gdef\not@#1#2#3#4{%
  \DNii@##1\not@{\ifx\space@\next\global\not@true\fi}%
 \global\not@false\DN@##1\not@{}%
 \ifx 5#1\ifx 6#2\ifx 7#3\ifx 8#4\DN@{\FN@\nextii@}\fi\fi\fi
 \fi\next@}}}
\newif\ifkeybin@
\def\dots{\RIfM@\expandafter\mdots@\else\expandafter\tdots@\fi}
\def\mdots@{\FN@\mdots@@}
\def\mdots@@{\gdef\thedots@{\dotso@}%
 \ifx\next\boldkey\gdef\thedots@\boldkey{\boldkeydots@}\else
 \ifx\next\boldsymbol\gdef\thedots@\boldsymbol{\boldsymboldots@}\else
 \ifx,\next\gdef\thedots@{\dotsc}%
 \else\ifx\not\next\gdef\thedots@{\dotsb@}%
 \else\keybin@
 \ifkeybin@\gdef\thedots@{\dotsb@}%
 \else\xdef\meaning@{\meaning\next..........}\xdef\meaning@@{\meaning@}%
  \expandafter\math@\meaning@\math@
  \ifmath@
   \expandafter\mathch@\meaning@\mathch@
   \ifmathch@\expandafter\getmathch@\meaning@\getmathch@\fi
  \else\expandafter\macro@\meaning@@\macro@
  \ifmacro@
   \expandafter\not@\meaning@\not@\ifnot@\gdef\thedots@{\dotsb@}%
  \else\expandafter\DOTS@\meaning@\DOTS@
  \ifDOTS@
   \ifcase\number\DOTSCASE@\gdef\thedots@{\dotsb@}%
    \or\gdef\thedots@{\dotsi}\else\fi
  \else\expandafter\math@\meaning@\math@
  \ifmath@\expandafter\mathbin@\meaning@\mathbin@
  \ifmathbin@\gdef\thedots@{\dotsb@}%
  \else\expandafter\mathrel@\meaning@\mathrel@
  \ifmathrel@\gdef\thedots@{\dotsb@}%
  \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
 \thedots@}
\def\plainldots@{\mathinner{\ldotp\ldotp\ldotp}}
\def\plaincdots@{\mathinner{\cdotp\cdotp\cdotp}}
\def\dotsi{\!\plaincdots@}
\let\dotsb@\plaincdots@
\newif\ifextra@
\newif\ifrightdelim@
\def\rightdelim@{\global\rightdelim@true
 \ifx\next)\else
 \ifx\next]\else
 \ifx\next\rbrack\else
 \ifx\next\}\else
 \ifx\next\rbrace\else
 \ifx\next\rangle\else
 \ifx\next\rceil\else
 \ifx\next\rfloor\else
 \ifx\next\rgroup\else
 \ifx\next\rmoustache\else
 \ifx\next\right\else
 \ifx\next\bigr\else
 \ifx\next\biggr\else
 \ifx\next\Bigr\else
 \ifx\next\Biggr\else\global\rightdelim@false
 \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
\def\extra@{%
 \global\extra@false\rightdelim@\ifrightdelim@\global\extra@true
 \else\ifx\next$\global\extra@true
 \else\xdef\meaning@{\meaning\next..........}%
 \expandafter\macro@\meaning@\macro@\ifmacro@
 \expandafter\DOTS@\meaning@\DOTS@
 \ifDOTS@
 \ifnum\DOTSCASE@=\tw@\global\extra@true
 \fi\fi\fi\fi\fi}
\newif\ifbold@
\def\dotso@{%
 \ifbold@
  \let\next\delayed@
  \DNii@{\extra@\plainldots@\ifextra@\,\fi}%
 \else
  \DNii@{\DN@{\extra@\plainldots@\ifextra@\,\fi}\FN@\next@}%
 \fi
 \nextii@}
\def\ldots{\DN@{\extrap@\plainldots@}%
 \FN@\next@}
\def\cdots{\DN@{\extrap@\plaincdots@}%
 \FN@\next@}
\let\dotso\ldots
\let\dotsb\cdots
\let\dotsm\dotsb
\def\cdot{\mathchar"2201 }
\def\longrightarrow{\DOTSB\relbar\joinrel\rightarrow}
\def\Longrightarrow{\DOTSB\Relbar\joinrel\Rightarrow}
\def\longleftarrow{\DOTSB\leftarrow\joinrel\relbar}
\def\Longleftarrow{\DOTSB\Leftarrow\joinrel\Relbar}
\def\longleftrightarrow{\DOTSB\leftarrow\joinrel\rightarrow}
\def\Longleftrightarrow{\DOTSB\Leftarrow\joinrel\Rightarrow}
\def\mapsto{\DOTSB\mapstochar\rightarrow}
\def\longmapsto{\DOTSB\mapstochar\longrightarrow}
\def\hookrightarrow{\DOTSB\lhook\joinrel\rightarrow}
\def\hookleftarrow{\DOTSB\leftarrow\joinrel\rhook}
\def\doteq{\DOTSB\buildrel\textstyle.\over=}
\def\iff{\DOTSB\;\Longleftrightarrow\;}
\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\rm...}\vss}}}}
\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\rm....}\vss}}}}
\def\sphat{^{\mathchoice{}{}%
 {\,\,\botsmash{\hbox{\lower4\ex@\hbox{$\m@th\widehat{\null}$}}}}%
 {\,\botsmash{\hbox{\lower3\ex@\hbox{$\m@th\hat{\null}$}}}}}}
\def\spcheck{^\vee}
\def\sptilde{^\sim}
\def\spacute{^{\!\botsmash{\hbox{\lower\@ne ex\hbox{\'{}}}}}}
\def\spgrave{^{\mathchoice{}{}{}{\!}%
 \botsmash{\hbox{\lower\@ne ex\hbox{\`{}}}}}}
\def\spdot{^{\hbox{\raise\ex@\hbox{\rm.}}}}
\def\spddot{^{\hbox{\raise\ex@\hbox{\rm..}}}}
\def\spdddot{^{\hbox{\raise\ex@\hbox{\rm...}}}}
\def\spddddot{^{\hbox{\raise\ex@\hbox{\rm....}}}}
\def\spbreve{^{\!\botsmash{\hbox{\lower4\ex@\hbox{\u{}}}}}}
\def\spbar{^-}
\def\spvec{^\rightarrow}
\def\textonlyfont@#1#2{\def#1{\RIfM@
 \Err@{Use \noexpand#1only in text}\else#2\fi}}
\textonlyfont@\rm\tenrm
\textonlyfont@\it\tenit
\textonlyfont@\sl\tensl
\textonlyfont@\bf\tenbf
\def\oldnos#1{\RIfM@{\mathcode`\,="013B \fam\@ne#1}\else
 \leavevmode\hbox{$\m@th\mathcode`\,="013B \fam\@ne#1$}\fi}
\def\text{\RIfM@\expandafter\text@\else\expandafter\text@@\fi}
\def\text@@#1{\leavevmode\hbox{#1}}
\def\mathhexbox@#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
\def\dag{{\mathhexbox@279}}
\def\ddag{{\mathhexbox@27A}}
\def\S{{\mathhexbox@278}}
\def\P{{\mathhexbox@27B}}
\newif\iffirstchoice@
\firstchoice@true
\def\text@#1{\mathchoice
 {\hbox{\everymath{\displaystyle}\def\textfonti{\the\textfont\@ne}%
  \def\textfontii{\the\textfont\tw@}\textdef@@ T#1}}
 {\hbox{\firstchoice@false
  \everymath{\textstyle}\def\textfonti{\the\textfont\@ne}%
  \def\textfontii{\the\textfont\tw@}\textdef@@ T#1}}
 {\hbox{\firstchoice@false
  \everymath{\scriptstyle}\def\textfonti{\the\scriptfont\@ne}%
  \def\textfontii{\the\scriptfont\tw@}\textdef@@ S\rm#1}}
 {\hbox{\firstchoice@false
  \everymath{\scriptscriptstyle}\def\textfonti
  {\the\scriptscriptfont\@ne}%
  \def\textfontii{\the\scriptscriptfont\tw@}\textdef@@ s\rm#1}}}
\def\textdef@@#1{\textdef@#1\rm\textdef@#1\bf\textdef@#1\sl\textdef@#1\it}
\def\rmfam{0}
\def\textdef@#1#2{%
 \DN@{\csname\expandafter\eat@\string#2fam\endcsname}%
 \if S#1\edef#2{\the\scriptfont\next@\relax}%
 \else\if s#1\edef#2{\the\scriptscriptfont\next@\relax}%
 \else\edef#2{\the\textfont\next@\relax}\fi\fi}
\scriptfont\itfam\tenit \scriptscriptfont\itfam\tenit
\scriptfont\slfam\tensl \scriptscriptfont\slfam\tensl
\newif\iftopfolded@
\newif\ifbotfolded@
\def\topfoldedtext{\topfolded@true\botfolded@false\foldedtext@}
\def\botfoldedtext{\botfolded@true\topfolded@false\foldedtext@}
\def\foldedtext{\topfolded@false\botfolded@false\foldedtext@}
\Invalid@\foldedwidth
\def\foldedtext@{%
 \DN@{\ifx\next\foldedwidth\let\next@\nextii@\else
  \DN@{\nextii@\foldedwidth{.3\hsize}}\fi\next@}%
 \DNii@\foldedwidth##1##2{\setbox\z@\vbox
  {\normalbaselines\hsize##1\relax
  \tolerance1600 \noindent\ignorespaces##2}\ifbotfolded@\boxz@\else
  \iftopfolded@\vtop{\unvbox\z@}\else\vcenter{\boxz@}\fi\fi}%
 \FN@\next@}
\def\bold{\RIfM@\expandafter\bold@\else
 \expandafter\nonmatherr@\expandafter\bold\fi}
\def\bold@#1{{\bold@@{#1}}}
\def\bold@@#1{\fam\bffam\relax#1}
\def\slanted{\RIfM@\expandafter\slanted@\else
 \expandafter\nonmatherr@\expandafter\slanted\fi}
\def\slanted@#1{{\slanted@@{#1}}}
\def\slanted@@#1{\fam\slfam\relax#1}
\def\rom{\RIfM@\expandafter\rom@\else
 \expandafter\nonmatherr@\expandafter\rom\fi}
\def\rom@#1{{\rom@@{#1}}}
\def\rom@@#1{\fam\rmfam\relax#1}
\def\italic{\RIfM@\expandafter\italic@\else
 \expandafter\nonmatherr@\expandafter\italic\fi}
\def\italic@#1{{\italic@@{#1}}}
\def\italic@@#1{\fam\itfam\relax#1}
\def\Cal{\RIfM@\expandafter\Cal@\else
 \expandafter\nonmatherr@\expandafter\Cal\fi}
\def\Cal@#1{{\Cal@@{#1}}}
\def\Cal@@#1{\noaccents@\fam\tw@#1}
\comment
\mathchardef\Gamma="0000
\mathchardef\Delta="0001
\mathchardef\Theta="0002
\mathchardef\Lambda="0003
\mathchardef\Xi="0004
\mathchardef\Pi="0005
\mathchardef\Sigma="0006
\mathchardef\Upsilon="0007
\mathchardef\Phi="0008
\mathchardef\Psi="0009
\mathchardef\Omega="000A
\mathchardef\varGamma="0100
\mathchardef\varDelta="0101
\mathchardef\varTheta="0102
\mathchardef\varLambda="0103
\mathchardef\varXi="0104
\mathchardef\varPi="0105
\mathchardef\varSigma="0106
\mathchardef\varUpsilon="0107
\mathchardef\varPhi="0108
\mathchardef\varPsi="0109
\mathchardef\varOmega="010A
\endcomment
\newif\ifmsamloaded@
\newif\ifmsbmloaded@
\newif\ifeufmloaded@
\let\alloc@@\alloc@
\def\hexnumber@#1{\ifcase#1 0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or 8\or
 9\or A\or B\or C\or D\or E\or F\fi}
\edef\bffam@{\hexnumber@\bffam}
\def\loadmsam{\msamloaded@true
 \font\tenmsa=msam10
 \font\sevenmsa=msam7
 \font\fivemsa=msam5
 \alloc@@8\fam\chardef\sixt@@n\msafam
 \textfont\msafam=\tenmsa
 \scriptfont\msafam=\sevenmsa
 \scriptscriptfont\msafam=\fivemsa
 \edef\msafam@{\hexnumber@\msafam}%
 \mathchardef\dabar@"0\msafam@39
 \def\dashrightarrow{\mathrel{\dabar@\dabar@\mathchar"0\msafam@4B}}%
 \def\dashleftarrow{\mathrel{\mathchar"0\msafam@4C\dabar@\dabar@}}%
 \let\dasharrow\dashrightarrow
 \def\ulcorner{\delimiter"4\msafam@70\msafam@70 }
 \def\urcorner{\delimiter"5\msafam@71\msafam@71 }
 \def\llcorner{\delimiter"4\msafam@78\msafam@78 }
 \def\lrcorner{\delimiter"5\msafam@79\msafam@79 }
 \def\yen{{\mathhexbox@\msafam@55 }}
 \def\checkmark{{\mathhexbox@\msafam@58 }}
 \def\circledR{{\mathhexbox@\msafam@72 }}
 \def\maltese{{\mathhexbox@\msafam@7A }}}
\def\loadmsbm{\msbmloaded@true
 \font\tenmsb=msbm10
 \font\sevenmsb=msbm7
 \font\fivemsb=msbm5
 \alloc@@8\fam\chardef\sixt@@n\msbfam
 \textfont\msbfam=\tenmsb
 \scriptfont\msbfam=\sevenmsb
 \scriptscriptfont\msbfam=\fivemsb
 \edef\msbfam@{\hexnumber@\msbfam}}
\def\widehat#1{\ifmsbmloaded@
 \setboxz@h{$\m@th#1$}\ifdim\wdz@>\tw@ em\mathaccent"0\msbfam@5B{#1}\else
  \mathaccent"0362{#1}\fi
 \else\mathaccent"0362{#1}\fi}
\def\widetilde#1{\ifmsbmloaded@
 \setboxz@h{$\m@th#1$}\ifdim\wdz@>\tw@ em\mathaccent"0\msbfam@5D{#1}\else
  \mathaccent"0365{#1}\fi
 \else\mathaccent"0365{#1}\fi}
\def\newsymbol#1#2#3#4#5{\define#1{}\let\next@\relax
 \ifnum#2=\@ne\ifmsamloaded@\let\next@\msafam@\fi\else
 \ifnum#2=\tw@\ifmsbmloaded@\let\next@\msbfam@\fi\fi\fi
 \ifx\next@\relax
  \ifnum#2>\tw@\Err@{\Invalid@@\string\newsymbol}\else
  \ifnum#2=\@ne\Err@{You must first \string\loadmsam}\else
   \Err@{You must first \string\loadmsbm}\fi\fi
 \else
  \mathchardef#1="#3\next@#4#5
 \fi}
\def\UseAMSsymbols{\input amssym.tex\relax}
\def\Bbb{\RIfM@\expandafter\Bbb@\else
 \expandafter\nonmatherr@\expandafter\Bbb\fi}
\def\Bbb@#1{{\Bbb@@{#1}}}
\def\Bbb@@#1{\noaccents@\fam\msbfam\relax#1}
\def\loadeufm{\eufmloaded@true
 \font\teneufm=eufm10
 \font\seveneufm=eufm7
 \font\fiveeufm=eufm5
 \alloc@@8\fam\chardef\sixt@@n\eufmfam
 \textfont\eufmfam=\teneufm
 \scriptfont\eufmfam=\seveneufm
 \scriptscriptfont\eufmfam=\fiveeufm}
\def\frak{\RIfM@\expandafter\frak@\else
 \expandafter\nonmatherr@\expandafter\frak\fi}
\def\frak@#1{{\frak@@{#1}}}
\def\frak@@#1{\fam\eufmfam\relax#1}
\let\goth\frak
\newif\ifcmmibloaded@
\newif\ifcmbsyloaded@
\def\loadbold{\cmmibloaded@true\cmbsyloaded@true
 \font\tencmmib=cmmib10
 \font\sevencmmib=cmmib7
 \font\fivecmmib=cmmib5
 \alloc@@8\fam\chardef\sixt@@n\cmmibfam
 \textfont\cmmibfam=\tencmmib
 \scriptfont\cmmibfam=\sevencmmib
 \scriptscriptfont\cmmibfam=\fivecmmib
 \edef\cmmibfam@{\hexnumber@\cmmibfam}%
 \font\tencmbsy=cmbsy10
 \font\sevencmbsy=cmbsy7
 \font\fivecmbsy=cmbsy5
 \alloc@@8\fam\chardef\sixt@@n\cmbsyfam
 \textfont\cmbsyfam=\tencmbsy
 \scriptfont\cmbsyfam=\sevencmbsy
 \scriptscriptfont\cmbsyfam=\fivecmbsy
 \edef\cmbsyfam@{\hexnumber@\cmbsyfam}}
\def\mathchari@#1#2#3{\ifcmmibloaded@\mathchar"#1\cmmibfam@#2#3 \else
 \Err@{First bold symbol font not loaded}\fi}
\def\mathcharii@#1#2#3{\ifcmbsyloaded@\mathchar"#1\cmbsyfam@#2#3 \else
 \Err@{Second bold symbol font not loaded}\fi}
\def\boldsymbol#1{%
 \DN@{\Err@{You can't use \string\boldsymbol\space with \string#1}#1}%
 \ifcat\noexpand#1A%
   \let\next@\relax
  \ifcmmibloaded@{\fam\cmmibfam#1}\else\Err@{First bold symbol
   font not loaded}\fi
 \else
  \xdef\meaning@{\meaning#1.........}%
  \expandafter\math@\meaning@\math@
  \ifmath@
   \expandafter\mathch@\meaning@\mathch@
   \ifmathch@
    \expandafter\boldsymbol@@\meaning@\boldsymbol@@
   \fi
  \else
   \expandafter\macro@\meaning@\macro@
   \expandafter\delim@\meaning@\delim@
   \ifdelim@
    \expandafter\delim@@\meaning@\delim@@
   \else
    \boldsymbol@{#1}%
   \fi
  \fi
 \fi
 \next@}
\def\mathhexboxii@#1#2{\ifcmbsyloaded@\mathhexbox@{\cmbsyfam@}{#1}{#2}\else
  \Err@{Second bold symbol font not loaded}\fi}
\def\boldsymbol@#1{\let\next@\relax\let\next#1%
 \ifx\next\cdot\mathcharii@201 \else
 \ifx\next\prime{{\null\mathcharii@030 \null}}\else
 \ifx\next\lbrack\mathchar"4\bffam@5B \else
 \ifx\next\rbrack\mathchar"5\bffam@5D \else
 \ifx\next\{\mathcharii@466 \else
 \ifx\next\lbrace\mathcharii@466 \else
 \ifx\next\}\mathcharii@567 \else
 \ifx\next\rbrace\mathcharii@567 \else
 \ifx\next\surd{{\mathcharii@170}}\else
 \ifx\next\S{{\mathhexboxii@78}}\else
 \ifx\next\P{{\mathhexboxii@7B}}\else
 \ifx\next\dag{{\mathhexboxii@79}}\else
 \ifx\next\ddag{{\mathhexboxii@7A}}\else
 \DN@{\Err@{You can't use \string\boldsymbol\space with \string#1}#1}%
 \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
\def\boldsymbol@@#1.#2\boldsymbol@@{\classnum@#1 \count@@@\classnum@
 \divide\classnum@4096 \count@\classnum@
 \multiply\count@4096 \advance\count@@@-\count@ \count@@\count@@@
 \divide\count@@@\@cclvi \count@\count@@
 \multiply\count@@@\@cclvi \advance\count@@-\count@@@
 \divide\count@@@\@cclvi
 \multiply\classnum@4096 \advance\classnum@\count@@
 \ifnum\count@@@=\z@
  \count@"\bffam@ \multiply\count@\@cclvi
  \advance\classnum@\count@
  \DN@{\mathchar\number\classnum@}%
 \else
  \ifnum\count@@@=\@ne
   \ifcmmibloaded@
   \count@"\cmmibfam@ \multiply\count@\@cclvi
   \advance\classnum@\count@
   \DN@{\mathchar\number\classnum@}%
   \else\DN@{\Err@{First bold symbol font not loaded}}\fi
  \else
   \ifnum\count@@@=\tw@
  \ifcmbsyloaded@
    \count@"\cmbsyfam@ \multiply\count@\@cclvi
    \advance\classnum@\count@
    \DN@{\mathchar\number\classnum@}%
  \else\DN@{\Err@{Second bold symbol font not loaded}}\fi
  \fi
 \fi
\fi}
\newif\ifdelim@
\newcount\delimcount@
{\uccode`6=`\\ \uccode`7=`d \uccode`8=`e \uccode`9=`l
 \uppercase{\gdef\delim@#1#2#3#4#5\delim@
  {\delim@false\ifx 6#1\ifx 7#2\ifx 8#3\ifx 9#4\delim@true
   \xdef\meaning@{#5}\fi\fi\fi\fi}}}
\def\delim@@#1"#2#3#4#5#6\delim@@{\if#32%
\let\next@\relax
 \ifcmbsyloaded@
 \mathcharii@#2#4#5 \else\Err@{Second bold family not loaded}\fi\fi}
\def\vert{\delimiter"026A30C }
\def\Vert{\delimiter"026B30D }
\let\|\Vert
\def\backslash{\delimiter"026E30F }
\def\boldkeydots@#1{\bold@true\let\next=#1\let\delayed@=#1\mdots@@
 \boldkey#1\bold@false}  % = required!
\def\boldsymboldots@#1{\bold@true\let\next#1\let\delayed@#1\mdots@@
 \boldsymbol#1\bold@false}

%%\newif\ifeufbloaded@
%%\def\loadeufb{\eufbloaded@true
%% \font\teneufb=eufb10
%% \font\seveneufb=eufb7
%% \font\fiveeufb=eufb5
%% \alloc@@8\fam\chardef\sixt@@n\eufbfam
%% \textfont\eufbfam=\teneufb
%% \scriptfont\eufbfam=\seveneufb
%% \scriptscriptfont\eufbfam=\fiveeufb
%% \edef\eufbfam@{\hexnumber@\eufbfam}}

%%\newif\ifeusmloaded@
%%\def\loadeusm{\eusmloaded@true
%% \font\teneusm=eusm10
%% \font\seveneusm=eusm7
%% \font\fiveeusm=eusm5
%% \alloc@@8\fam\chardef\sixt@@n\eusmfam
%% \textfont\eusmfam=\teneusm
%% \scriptfont\eusmfam=\seveneusm
%% \scriptscriptfont\eusmfam=\fiveeusm
%% \edef\eusmfam@{\hexnumber@\eusmfam}}

%%\newif\ifeusbloaded@
%%\def\loadeusb{\eusbloaded@true
%% \font\teneusb=eusb10
%% \font\seveneusb=eusb7
%% \font\fiveeusb=eusb5
%% \alloc@@8\fam\chardef\sixt@@n\eusbfam
%% \textfont\eusbfam=\teneusb
%% \scriptfont\eusbfam=\seveneusb
%% \scriptscriptfont\eusbfam=\fiveeusb
%% \edef\eusbfam@{\hexnumber@\eusbfam}}

%%\newif\ifeurmloaded@
%%\def\loadeurm{\eurmloaded@true
%% \font\teneurm=eurm10
%% \font\seveneurm=eurm7
%% \font\fiveeurm=eurm5
%% \alloc@@8\fam\chardef\sixt@@n\eurmfam
%% \textfont\eurmfam=\teneurm
%% \scriptfont\eurmfam=\seveneurm
%% \scriptscriptfont\eurmfam=\fiveeurm
%% \edef\eurmfam@{\hexnumber@\eurmfam}}

%%\newif\ifeurbloaded@
%%\def\loadeurb{\eurbloaded@true
%% \font\teneurb=eurb10
%% \font\seveneurb=eurb7
%% \font\fiveeurb=eurb5
%% \alloc@@8\fam\chardef\sixt@@n\eurbfam
%% \textfont\eurbfam=\teneurb
%% \scriptfont\eurbfam=\seveneurb
%% \scriptscriptfont\eurbfam=\fiveeurb
%% \edef\eurbfam@{\hexnumber@\eurbfam}}

\def\accentclass@{7}
\def\noaccents@{\def\accentclass@{0}}
\def\makeacc@#1#2{\def#1{\mathaccent"\accentclass@#2 }}
\makeacc@\hat{05E}
\makeacc@\check{014}
\makeacc@\tilde{07E}
\makeacc@\acute{013}
\makeacc@\grave{012}
\makeacc@\dot{05F}
\makeacc@\ddot{07F}
\makeacc@\breve{015}
\makeacc@\bar{016}
\def\vec{\mathaccent"017E }
\newcount\skewcharcount@
\newcount\familycount@
\def\theskewchar@{\familycount@\@ne
 \global\skewcharcount@\the\skewchar\textfont\@ne
 \ifnum\fam>\m@ne\ifnum\fam<16
  \global\familycount@\the\fam\relax
  \global\skewcharcount@\the\skewchar\textfont\the\fam\relax\fi\fi
 \ifnum\skewcharcount@>\m@ne
  \ifnum\skewcharcount@<128
  \multiply\familycount@256
  \global\advance\skewcharcount@\familycount@
  \global\advance\skewcharcount@28672
  \mathchar\skewcharcount@\else
  \global\skewcharcount@\m@ne\fi\else
 \global\skewcharcount@\m@ne\fi}
\newcount\pointcount@
\def\getpoints@#1.#2\getpoints@{\pointcount@#1 }
\newdimen\accentdimen@
\newcount\accentmu@
\def\dimentomu@{\multiply\accentdimen@ 100
 \expandafter\getpoints@\the\accentdimen@\getpoints@
 \multiply\pointcount@18
 \divide\pointcount@\@m
 \global\accentmu@\pointcount@}
\def\Makeacc@#1#2{\def#1{\RIfM@\DN@{\mathaccent@
 {"\accentclass@#2 }}\else\DN@{\nonmatherr@{#1}}\fi\next@}}
\def\unbracefonts@{\let\Cal@\Cal@@\let\rom@\rom@@\let\bold@\bold@@
 \let\slanted@\slanted@@}
\def\mathaccent@#1#2{\ifnum\fam=\m@ne\xdef\thefam@{1}\else
 \xdef\thefam@{\the\fam}\fi
 \accentdimen@\z@
 \setboxz@h{\unbracefonts@$\m@th\fam\thefam@\relax#2$}%
 \ifdim\accentdimen@=\z@\DN@{\mathaccent#1{#2}}%
  \setbox\tw@\hbox{\unbracefonts@$\m@th\fam\thefam@\relax#2\theskewchar@$}%
  \setbox4=\hbox{$\m@th\ifnum\skewcharcount@=\m@ne\else
   \mathchar\skewcharcount@\fi$}%
  \global\accentdimen@\wd\tw@\global\advance\accentdimen@-\wdz@
  \global\advance\accentdimen@-\wd4
  \global\multiply\accentdimen@\tw@
  \dimentomu@\global\advance\accentmu@\@ne
 \else\DN@{{\mathaccent#1{#2\mkern\accentmu@ mu}%
    \mkern-\accentmu@ mu}{}}\fi
 \next@}
\Makeacc@\Hat{05E}
\Makeacc@\Check{014}
\Makeacc@\Tilde{07E}
\Makeacc@\Acute{013}
\Makeacc@\Grave{012}
\Makeacc@\Dot{05F}
\Makeacc@\Ddot{07F}
\Makeacc@\Breve{015}
\Makeacc@\Bar{016}
\def\Vec{\RIfM@\DN@{\mathaccent@{"017E }}\else
 \DN@{\nonmatherr@\Vec}\fi\next@}
\def\sqrt#1{\radical"270370 {#1}}
\let\underline@\underline
\let\overline@\overline
\def\underline#1{\underline@{#1}}
\def\overline#1{\overline@{#1}}
\Invalid@\leftroot
\Invalid@\uproot
\newcount\uproot@
\newcount\leftroot@
\def\plainroot@#1\of#2{\setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#1}$}%
 \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
 {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
\def\r@@t#1#2{\setboxz@h{$\m@th#1\sqrt{#2}$}%
 \dimen@\ht\z@\advance\dimen@-\dp\z@
 \setbox\tw@\hbox{$\m@th#1\mskip\uproot@ mu$}\advance\dimen@ by1.667\wd\tw@
 \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
 \mkern-10mu\mkern\leftroot@ mu\boxz@}
\def\boxed#1{\setboxz@h{$\m@th\displaystyle{#1}$}\dimen@.4\ex@
 \advance\dimen@3\ex@\advance\dimen@\dp\z@
 \hbox{\lower\dimen@\hbox{%
 \vbox{\hrule\height.4\ex@
 \hbox{\vrule\width.4\ex@\hskip3\ex@\vbox{\vskip3\ex@\boxz@\vskip3\ex@}%
 \hskip3\ex@\vrule\width.4\ex@}\hrule\height.4\ex@}%
 }}}
\newdimen\minaw@
\minaw@11.11128\ex@
\def\pmb{\RIfM@\expandafter\mathpalette\expandafter\pmb@\else
 \expandafter\pmb@@\fi}
\def\pmb@@#1{\leavevmode\setboxz@h{#1}\kern-.025em\copy\z@\kern-\wdz@
 \kern-.05em\copy\z@\kern-\wdz@\kern-.025em\raise.0433em\boxz@}
\def\binrel@@#1{\ifdim\wd2<\z@\mathbin{#1}\else\ifdim\wd\tw@>\z@
 \mathrel{#1}\else{#1}\fi\fi}
\newdimen\pmbraise@
\def\pmb@#1#2{\setbox4=\hbox{$\m@th#1{#2}$}%
 \setbox6=\hbox{$\m@th#1\mkern.7794mu$}\pmbraise@\wd6
 \binrel@{#2}\binrel@@{\mkern-.45mu\copy4 \kern-\wd4
 \mkern-.9mu\copy4 \kern-\wd4 \mkern-.45mu\raise\pmbraise@\box4}}
%\loadmsam
%\loadmsbm
%\loadeufm
\let\proclaim\undefined
\Invalid@\=
\let\+\relax
\Invalid@\+
\let\>\undefined
\let\cal\undefined
\let\mit\undefined
\let\oldstyle\undefined
\def\Err@#1{\errhelp\defaulthelp@\err@{#1}}
{\catcode`\@=\active
 \edef\next{\gdef\noexpand@{\futurelet\noexpand\next
  \csname at\string@\endcsname}}
 \next
}
\def\at@{\ifcat\noexpand\next a\let\next@\at@@\else
 \ifcat\noexpand\next0\let\next@\at@@\else
 \ifcat\noexpand\next\relax\let\next@\at@@\else
 \let\next@\at@@@\fi\fi\fi\next@}
\def\at@@@{\errhelp\athelp@\err@{Invalid use of @}}
\def\at@@#1{\expandafter
 \ifx\csname\string#1@at\endcsname\relax\let\next@\at@@@\else
 \DN@{\csname\string#1@at\endcsname}\fi\next@}
\let\lkerns@\relax
\def\nolinebreak{\RIfM@\mathmodeerr@\nolinebreak\else
 \ifhmode\saveskip@\lastskip\unskip
 \nobreak\ifdim\saveskip@>\z@\hskip\saveskip@\fi\lkerns@
 \else\vmodeerr@\nolinebreak\fi\fi}
\def\allowlinebreak{\RIfM@\mathmodeerr@\allowlinebreak\else
 \ifhmode\saveskip@\lastskip\unskip
 \allowbreak\ifdim\saveskip@>\z@\hskip\saveskip@\fi\lkerns@
 \else\vmodeerr@\allowlinebreak\fi\fi}
\def\linebreak{\RIfM@\mathmodeerr@\linebreak\else
 \ifhmode\unskip\unkern\break\lkerns@
 \else\vmodeerr@\linebreak\fi\fi}
\let\nkerns@\relax
\def\newline{\RIfM@\mathmodeerr@\newline\else
 \ifhmode\unskip\unkern\null\hfill\break\nkerns@
 \else\vmodeerr@\newline\fi\fi}%
\def\newbox@{\alloc@@4\box\chardef\insc@unt}
\def\accentedsymbol#1#2{\expandafter\newbox@\csname\exstring@#1@box\endcsname
 \setbox\csname\exstring@#1@box\endcsname\hbox{$\m@th#2$}%
 \define#1{\copy\csname\exstring@#1@box\endcsname{}}}
\def\loop#1\repeat{\def\iterate{#1\relax\expandafter\iterate\fi}%
 \iterate\let\iterate\relax}
\def\gloop@#1\repeat{\gdef\body{#1}\iterate}
\def\tdots@{\unskip
 \DN@{$\m@th\mathinner{\ldotp\ldotp\ldotp}\,
   \ifx\next,\,$\else\ifx\next.\,$\else\ifx\next;\,$\else\ifx\next:\,$\else
   \ifx\next?\,$\else\ifx\next!\,$\else$ \fi\fi\fi\fi\fi\fi}%
 \ \FN@\next@}
\def\extrap@#1{%
 \ifx\next,\DN@{#1\,}\else
 \ifx\next;\DN@{#1\,}\else
 \ifx\next.\DN@{#1\,}\else\extra@
 \ifextra@\DN@{#1\,}\else
 \let\next@#1\fi\fi\fi\fi\next@}
\def\dotsc{\DN@{\ifx\next;\plainldots@\,\else
  \ifx\next.\plainldots@\,\else\extra@\plainldots@
  \ifextra@\,\fi\fi\fi}%
 \FN@\next@}
\def\keybin@{\keybin@true
 \ifx\next+\else\ifx\next=\else\ifx\next<\else\ifx\next>\else\ifx\next-\else
 \ifx\next*\else\ifx\next:\else\keybin@false\fi\fi\fi\fi\fi\fi\fi}
\font\tensmc=cmcsc10
\textonlyfont@\smc\tensmc
\def\boldkey#1{\ifcat\noexpand#1A%
  \ifcmmibloaded@{\fam\cmmibfam#1}\else
   \Err@{First bold symbol font not loaded}\fi
 \else
 \ifx#1!\mathchar"5\bffam@21 \else
 \ifx#1(\mathchar"4\bffam@28 \else\ifx#1)\mathchar"5\bffam@29 \else
 \ifx#1+\mathchar"2\bffam@2B \else\ifx#1:\mathchar"3\bffam@3A \else
 \ifx#1;\mathchar"6\bffam@3B \else\ifx#1=\mathchar"3\bffam@3D \else
 \ifx#1?\mathchar"5\bffam@3F \else\ifx#1[\mathchar"4\bffam@5B \else
 \ifx#1]\mathchar"5\bffam@5D \else
 \ifx#1,\mathchari@63B \else
 \ifx#1-\mathcharii@200 \else
 \ifx#1.\mathchari@03A \else
 \ifx#1/\mathchari@03D \else
 \ifx#1<\mathchari@33C \else
 \ifx#1>\mathchari@33E \else
 \ifx#1*\mathcharii@203 \else
 \ifx#1|\mathcharii@06A \else
 \ifx#10\bold0\else\ifx#11\bold1\else\ifx#12\bold2\else\ifx#13\bold3\else
 \ifx#14\bold4\else\ifx#15\bold5\else\ifx#16\bold6\else\ifx#17\bold7\else
 \ifx#18\bold8\else\ifx#19\bold9\else
  \Err@{\string\boldkey\space can't be used with #1}%
 \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
 \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
\def\root{%
  \DN@{\ifx\next\uproot\let\next@\nextii@\else
   \ifx\next\leftroot\let\next@\nextiii@\else
   \let\next@\plainroot@\fi\fi\next@}%
  \DNii@\uproot##1{\uproot@##1\relax\FNSS@\nextiv@}%
  \def\nextiv@{\ifx\next\leftroot\let\next@\nextv@\else
   \let\next@\plainroot@\fi\next@}%
  \def\nextv@\leftroot##1{\leftroot@##1\relax\plainroot@}%
  \def\nextiii@\leftroot##1{\leftroot@##1\relax\FNSS@\nextvi@}%
  \def\nextvi@{\ifx\next\uproot\let\next@\nextvii@\else
   \let\next@\plainroot@\fi\next@}%
  \def\nextvii@\uproot##1{\uproot@##1\relax\plainroot@}%
  \bgroup\uproot@\z@\leftroot@\z@
 \FNSS@\next@}
\def\arabic#1{#1}
\def\alph#1{\count@#1\relax\advance\count@96 \ifnum\count@>122
 \Err@{\string\alph\space can't be used for numbers > 26}\else\char\count@\fi}
\def\Alph#1{\count@#1\relax\advance\count@64 \ifnum\count@>90
 \Err@{\string\Alph\space can't be used for numbers > 26}\else\char\count@\fi}
\def\roman#1{\romannumeral#1\relax}
\def\Roman#1{\uppercase\expandafter{\romannumeral#1}}
\def\fnsymbol#1{\count@#1\relax
 \count@@\count@
 \advance\count@\m@ne\divide\count@7
 \count@@@\count@\advance\count@@@\@ne
 \multiply\count@7 \advance\count@@-\count@
 \count@\count@@@
 {\loop
  \ifcase\count@@\or*\or\dag\or\ddag\or\P\or\S\or\text{$\|$}\or\#\fi
  \advance\count@\m@ne\ifnum\count@>\z@\repeat}}
\def\cardnine@#1{\ifcase#1\or one\or two\or three\or four\or five\or
 six\or seven\or eight\or nine\fi}
\newcount\ten@
\ten@10
\def\cardinal#1{\count@#1\relax
 \ifnum\count@>99 \number\count@
 \else
  \ifnum\count@=\z@ zero%
  \else
   \ifnum\count@<\ten@\cardnine@\count@
   \else
    \ifnum\count@<20
     \advance\count@-\ten@
     \ifcase\count@ ten\or eleven\or twelve\or thirteen\or fourteen\or
      fifteen\or sixteen\or seventeen\or eighteen\or nineteen\fi
    \else
     \count@@\count@\count@@@\count@@
     \divide\count@\ten@\multiply\count@\ten@
     \advance\count@@@-\count@\divide\count@\ten@
     \ifcase\count@\or\or twenty\or thirty\or forty\or fifty\or sixty\or
      seventy\or eighty\or ninety\fi
     \ifnum\count@@@=\z@\else-\cardnine@\count@@@\fi
    \fi
   \fi
  \fi
 \fi}
\def\ordnine@#1{\ifcase#1\or first\or second\or third\or fourth\or fifth\or
 sixth\or seventh\or eighth\or ninth\fi}
\newcount\count@@@@
\def\ordsuffix@{\count@@@@\count@
 \divide\count@\ten@
 \count@@@\count@\count@@\count@
 \divide\count@@\ten@\multiply\count@@\ten@
 \advance\count@@@-\count@@
 \ifnum\count@@@=\@ne th%
 \else
  \count@@@\count@@@@
  \count@@\count@@@@
  \divide\count@@\ten@\multiply\count@@\ten@
  \advance\count@@@-\count@@
  \ifcase\count@@@ th\or st\or nd\or rd\else th\fi
 \fi}
\def\nordinal#1{\count@#1\relax\number\count@\ordsuffix@}
\def\spordinal#1{\count@#1\relax\number\count@$^{\text{\ordsuffix@}}$}
\def\ordinal#1{\count@#1\relax
 \ifnum\count@>99 \number\count@\ordsuffix@
 \else
   \ifnum\count@=\z@ zeroth%
  \else
    \ifnum\count@<\ten@\ordnine@\count@
    \else
     \ifnum\count@<20 \advance\count@-\ten@
      \ifcase\count@ tenth\or eleventh\or twelfth\or thirteenth\or
       fourteenth\or fifteenth\or sixteenth\or seventeenth\or eighteenth\or
       nineteenth\fi
     \else
      \count@@\count@
      \divide\count@\ten@\multiply\count@\ten@
      \count@@@\count@@\advance\count@@@-\count@
      \divide\count@\ten@
      \ifcase\count@\or\or twent\or thirt\or fort\or fift\or sixt\or sevent\or
       eight\or ninet\fi
      \ifnum\count@@@=\z@ ieth\else y-\ordnine@\count@@@\fi
     \fi
    \fi
  \fi
 \fi}
\font\tensmc=cmcsc10
\textonlyfont@\smc\tensmc
\newtoks\noexpandtoks@
\noexpandtoks@{\let\arabic\relax\let\alph\relax\let\Alph\relax
 \let\roman\relax\let\Roman\relax\let\fnsymbol\relax\let\rm\relax
 \let\it\relax\let\bf\relax\let\sl\relax\let\smc\relax
 \let\/\relax\let\null\relax}
\def\noexpands@{\the\noexpandtoks@}
\def\protect#1{\global\noexpandtoks@
 \expandafter{\the\noexpandtoks@\let#1\relax}}
\Invalid@\label
\Invalid@\pagelabel
\newread\laxread@
\def\Finit@#1#2\Finit@{\let\nextii@#1\def\nextiii@{#2}}
\catcode`\~=11
\def\getparts@ @#1~#2~#3~#4~#5~#6{\def\nextiv@{#1}%
 \def\nextiii@{#2~#3~#4~#5~}\count@#6\relax}
\newif\ifreferr@
\referr@true
\def\RefErrors{\global\referr@true}
\def\RefWarnings{\global\referr@false}
\setbox\z@\hbox{\global\count@=`^^30}
\ifnum\count@=48 \let\versionthree@\relax\fi
\def\nolabel@#1#2#3{\expandafter\ifx\csname#2@L\endcsname\relax
 \ifreferr@\Err@{No \noexpand\label found for #2}\else
 \W@{Warning: No \noexpand\label found for #2.}%
 \ifx\versionthree@\relax\W@{l.\number\inputlineno\space ... \string#1{#2}}\fi
 \fi#3\else}
\def\csL@#1{{\noexpands@\xdef\Next@{\csname#1@L\endcsname}}}
\define\ref#1{\nolabel@\ref{#1}\relax
 \DNii@##1~##2\nextii@{##1}%
 \csL@{#1}\expandafter\nextii@\Next@\nextii@\fi}
\define\Ref#1{\nolabel@\Ref{#1}\relax
 \DNii@##1~##2~##3\nextii@{##2}%
 \csL@{#1}\expandafter\nextii@\Next@\nextii@\fi}
\define\nref#1{\nolabel@\nref{#1}\relax
 \DNii@##1~##2~##3~##4\nextii@{##3}%
 \csL@{#1}\expandafter\nextii@\Next@\nextii@\fi}
\define\pref#1{\nolabel@\pref{#1}\relax
 \DNii@##1~##2~##3~##4~##5\nextii@{##4}%
 \csL@{#1}\expandafter\nextii@\Next@\nextii@\fi}
\def\Evaluatenref#1{\nolabel@\Evaluatenref{#1}{\gdef\Nref{-10000 }}%
 \DNii@##1~##2~##3~##4\nextii@{\DNii@{##3}}%
 \csL@{#1}\expandafter\nextii@\Next@\nextii@
 \xdef\Nref{\nextii@}\fi}
\def\Evaluatepref#1{\nolabel@\Evaluatepref{#1}{\global\let\Pref\empty}%
 \DNii@##1~##2~##3~##4~##5\nextii@{\DNii@{##4}}%
 \csL@{#1}\expandafter\nextii@\Next@\nextii@
 \xdef\Pref{\nextii@}\fi}
\def\readlax#1{\immediate\openin\laxread@=#1.lax\relax
 \ifeof\laxread@\W@{}\W@{File #1.lax not found.}\W@{}\fi
 {\endlinechar\m@ne\noexpands@\catcode`\@=11 \catcode`\~=11
  \loop\ifeof\laxread@\else
   \read\laxread@ to\nextv@
   \ifx\nextv@\empty
   \else
    \expandafter\Finit@\nextv@\Finit@
    \ifx\nextii@ F%
    \else
     \expandafter\getparts@\nextv@
     \expandafter\ifx\csname\nextiv@ @L\endcsname\relax
      \edef\next@{\gdef\csname\nextiv@ @L\endcsname
       {\nextiii@\ifnum\count@=\@ne0\else2\fi}}%
      \next@
     \else
      \Err@{Label \nextiv@\space in #1.lax already used}%
     \fi
    \fi
   \fi
  \repeat}%
 \immediate\closein\laxread@}
\catcode`\~=\active
\def\tbldocstyle#1{\input #1.stt\relax}
\newwrite\writedata@
\newif\ifshow@
\pageno\z@
\def\document{\immediate\openout\writedata@=\jobname.dat
 \global\font\t@nrm=cmr10
 \global\topskip\z@
 \global\output{\ifshow@\else\advancepageno\fi
 \shipout\vbox{\vbox to\vsize{\unvbox255 }%
 \baselineskip2pc
 \ifshow@
 \line{\hfil\t@nrm File [\jobname], Subtable \number\count@@\hfil}%
 \else
 \line{\hfil\t@nrm File [\jobname], \#\number\pageno\hfil}\fi}%
 }}
\def\bye{\par\vfill\supereject\ifproofing@\W@{}\W@{CAUTION:  PROOFING ON !!!}
 \W@{CAUTION:  PROOFING ON !!!}
 \W@{CAUTION:  PROOFING ON !!!}\W@{}\fi\end}
\let\enddocument\bye
\def\exstring@{\expandafter\eat@\string}
\def\unpurge#1{\input #1\relax}
\def\purge#1{\input #1.tox\relax}
\def\East#1#2{\setboxz@h{$\m@th\ssize\;{#1}\;\;$}%
 \setbox\tw@\hbox{$\m@th\ssize\;{#2}\;\;$}\setbox4=\hbox{$\m@th#2$}%
 \dimen@\minaw@
 \ifdim\wdz@>\dimen@\dimen@\wdz@\fi\ifdim\wd\tw@>\dimen@\dimen@\wd\tw@\fi
 \ifdim\wd4 >\z@
  \mathrel{\mathop{\hbox to\dimen@{\rightarrowfill}}\limits^{#1}_{#2}}%
 \else
  \mathrel{\mathop{\hbox to\dimen@{\rightarrowfill}}\limits^{#1}}%
 \fi}
\def\West#1#2{\setboxz@h{$\m@th\ssize\;\;{#1}\;$}%
 \setbox\tw@\hbox{$\m@th\ssize\;\;{#2}\;$}\setbox4=\hbox{$\m@th#2$}%
 \dimen@\minaw@
 \ifdim\wdz@>\dimen@\dimen@\wdz@\fi\ifdim\wd\tw@>\dimen@\dimen@\wd\tw@\fi
 \ifdim\wd4 >\z@
  \mathrel{\mathop{\hbox to\dimen@{\leftarrowfill}}\limits^{#1}_{#2}}%
 \else
  \mathrel{\mathop{\hbox to\dimen@{\leftarrowfill}}\limits^{#1}}%
 \fi}

\newif\ifproofing@
\def\proofing{\global\proofing@true
 \W@{}\W@{CAUTION:  PROOFING ON !!!}
 \W@{CAUTION:  PROOFING ON !!!}
 \W@{CAUTION:  PROOFING ON !!!}\W@{}}

\Invalid@\paste
\newtoks\ET@
\def\everytable#1{\ET@{#1}}
\def\VTW@{.4\p@}
\def\vtablelines(#1){\def\VTW@{#1}}
\def\HTW@{.4\p@}
\def\htablelines(#1){\def\HTW@{#1}}
\def\Ls@{\z@}
\def\Rs@{\z@}
\def\sides{\def\Ls@{\VTW@}\def\Rs@{\VTW@}}
\def\Sides(#1#2;#3#4){\if#1*\def\Ls@{\VTW@}\else\def\Ls@{#1#2}\fi
 \if#3*\def\Rs@{\VTW@}\else\def\Rs@{#3#4}\fi}
\newif\ifTW@
\newif\ifTWG@
\newif\ifTWL@
\def\tablewidth(#1#2){\TW@true\TWG@false\TWL@false\if#1+\TWG@true
 \def\TW@{#2}\else\if#1-\TWL@true\def\TW@{#2}\else\def\TW@{#1#2}\fi\fi}
\newbox\LBX@
\newbox\RBX@
\def\table{\the\ET@\edef\PRF@{\the\font}\MS@\MNBL@\edef\TF@{\the\font}%
 \begingroup\catcode`\&\active\catcode`\"\active\catcode`\|\active
 \expandafter\let\csname +\endcsname\relax\csname table \endcsname}
\def\MNBL@{\xdef\NBL@{\lineskip\the\lineskip\baselineskip\the\baselineskip
 \lineskiplimit\the\lineskiplimit}}
\expandafter\newbox\csname table0\endcsname
\expandafter\newbox\csname table1\endcsname
\expandafter\newbox\csname table2\endcsname
\expandafter\newbox\csname table3\endcsname
\expandafter\newbox\csname table4\endcsname
\expandafter\newbox\csname table5\endcsname
\expandafter\newbox\csname table6\endcsname
\expandafter\newbox\csname table7\endcsname
\expandafter\newbox\csname table8\endcsname
\expandafter\newbox\csname table9\endcsname
\newif\ifstoring@
\def\storetable#1{\storing@true\count@#1\relax
 \edef\thetable@{\number\count@}\table}
\def\usetable#1{\count@#1\relax\copy\csname table\number\count@\endcsname}
\def\showstored#1{%
 \ifvoid\csname table#1\endcsname
  \Err@{No table stored in location #1}%
 \else
  \count@@=#1\relax\DN@{\csname table#1\endcsname}%
  \dimen@\ht\next@ \advance\dimen@\dp\next@
  \ifdim\dimen@>\vsize\Err@{Subtable bigger than \string\vsize: height
   \the\ht\next@, depth \the\dp\next@}\fi
  \count@\pageno \pageno\z@
  \hrule\height\z@\vskip\vsize\noindent\smash{\copy\next@}%
  \show@true\eject \pageno\count@ \show@false
 \fi}
\def\cleartable#1{\count@#1\relax
 \global\setbox\csname table\number\count@\endcsname\box\voidb@x}
\newdimen\FSH
\newdimen\FSD
\newdimen\HT@
\newdimen\DP@
\newdimen\EH@
\newdimen\ED@
\EH@\z@
\ED@\z@
\newif\ifHD@
\newif\ifEH@
\newif\ifED@
\def\HD(#1#2;#3#4){\HD@true
 \if#1+\EH@#2\relax\EH@true\else\EH@#1#2\relax\EH@false\fi
 \if#3+\ED@#4\relax\ED@true\else\ED@#3#4\relax\ED@false\fi}
\def\MS@{{\setboxz@h{\count@\z@\loop\char\count@\ifnum\count@<127
  \advance\count@\@ne\repeat}%
 \global\HT@\ht\z@\global\DP@\dp\z@
 \ifHD@
  \ifEH@\dimen@\HT@\advance\dimen@\EH@\else\dimen@\EH@\fi
  \ifED@\dimen@ii\DP@\advance\dimen@ii\ED@\else\dimen@ii\ED@\fi
 \else
  \dimen@\HT@\dimen@ii\DP@
 \fi
 \global\FSH\dimen@ \global\FSD\dimen@ii
 \xdef\FS@{\leavevmode\vrule\height\the\dimen@\depth\the\dimen@ii\width\z@}%
 \xdef\FS@@{\leavevmode\vrule\height\the\ht\z@\depth\the\dp\z@\width\z@}%
 \global\let\FS\FS@}}
\def\showstrutdims{\MS@
 \immediate\write\sixt@@n{Strut height = \the\HT@; strut depth = \the\DP@}}
\newif\ifLG@
\newcount\CN@
\newcount\CT@
\newcount\SCT@
\newif\ifFS@
\def\LGL@{}
\def\RGL@{}
\def\LSL@{}
\def\RSL@{}
\let\T@B=&
\newcount\DCC@
\newcount\DLC@
\newif\ifNS@
\newif\ifAD@
\def\alldq{\AD@true}
\newskip\FT@
\newskip\LT@
\def\tss{\Err@{\string\tss\space doesn't follow a \string\table}}
\def\sss{\Err@{\string\sss\space doesn't follow a \string\tss...\string\\}}
{
\catcode`\&\active \catcode`\|\active \catcode`\"\active
\gdef\pretss@#1{{\let&0\let|0\let\rt0\let\s0\let\g0\let\|0%
 \let\p0\let\P0\let\d0\let\$0%
 \let\next@0%
 \def\l{\l@\next@}\def\c{\c@\next@}\def\r{\r@\next@}%
 \def\L{\L@}\def\C{\C@}\def\R{\R@}%
 \let\lmath@0\let\cmath@0\let\rmath@0\let\lMath@0\let\cMath@0\let\rMath@0%
 \def\lmath{\lmath@\next@}\def\cmath{\cmath@\next@}\def\rmath{\rmath@\next@}%
 \def\lMath{\lMath@\next@}\def\cMath{\cMath@\next@}\def\rMath{\rMath@\next@}%
 \def~{\s1\ignorespaces}%
 \let\LP@0\let\CP@0\let\RP@0%
 \let\lP@0\let\cP@0\let\rP@0%
 \ifAD@
  \def\l@{\lP@\next@}\def\c@{\cP@\next@}\def\r@{\rP@\next@}%
  \def\L@{\LP@}\def\C@{\CP@}\def\R@{\RP@}\def"{}%
  \def\"##1{\ifx##1\l\noexpand\l@\next@\else\ifx##1\c\noexpand\c@\next@\else
   \ifx##1\r\noexpand\r@\next@\else\ifx##1\L\noexpand\L@\else
   \ifx##1\C\noexpand\C@\else\ifx##1\R\noexpand\R@\else##1\fi\fi\fi\fi\fi\fi}%
 \else
  \let\l@0\let\c@0\let\r@0\let\L@0\let\C@0\let\R@0\def\"{}%
  \def"##1{\ifx##1\l\lP@\next@\else\ifx##1\c\cP@\next@\else
   \ifx##1\r\rP@\next@\else\ifx##1\L\LP@\else\ifx##1\C\CP@\else\ifx##1\R\RP@
   \else##1\fi\fi\fi\fi\fi\fi}%
 \fi
 \xdef\PPR@{#1}}}
\expandafter\gdef\csname table \endcsname#1\tss#2\\{\pretss@{#2}%
 {\let&0\let|0\let\rt0\let\s0\let\g0\let\|0%
  \let\p0\let\P0\let\d0\let\$0%
  \let\next@0%
  \let\l@0\let\c@0\let\r@0%
  \let\L@0\let\C@0\let\R@0%
  \let\lmath@0\let\cmath@0\let\rmath@0\let\lMath@0\let\cMath@0\let\rMath@0%
  \let\LP@0\let\CP@0\let\RP@0%
  \let\lP@0\let\cP@0\let\rP@0%
  \gdef\PR@{}%
  \expandafter\SC@\PPR@\rt Z%
 }%
 \gdef\SS@{B}\gdef\LS@{B}\catcode`\"12
 \FN@\dt@}
\gdef\SC@#1\rt{\xdef\PR@{\PR@#1}\FN@\SC@@}
\gdef\SC@@{\ifx\next Z\DNii@ Z{}\else\let\nextii@\SC@@@\fi\nextii@}
\gdef\SC@@@#1#2{\count@#1\relax\loop\ifnum\count@>\z@
 \xdef\PR@{\PR@#2}\advance\count@\m@ne\repeat\SC@}
\catcode`\"12
\gdef\dt@{\ifx\next\space@\DN@. {\FN@\dt@@}\else
 \DN@.{\FN@\dt@@}\fi\next@.}
\gdef\dt@@{\NS@true\ifx\next\sss\expandafter\dt@@@\else
 \expandafter\dt@@@@\fi}
\gdef\dt@@@\sss#1\\{%
 {\let\t0\let\m0\let\b0%
  \if Z#1Z%
  \else
   \def\t{\global\NS@false\gdef\LS@{T}}%
   \def\m{\global\NS@false\gdef\LS@{M}}%
   \def\b{\gdef\LS@{B}}%
   \setboxz@h{#1}%
   \def\t{T}\def\m{M}\def\b{B}\xdef\SS@{#1}%
 \fi}%
 \dt@@@@}
\gdef\dt@@@@{%
 {\DN@{}%
  \let\l@\LG@false\let\c@\LG@false\let\r@\LG@false
  \let\lP@\LG@false\let\cP@\LG@false\let\rP@\LG@false
  \let\lmath@\LG@false\let\cmath@\LG@false\let\rmath@\LG@false
  \let\lMath@\LG@false\let\cMath@\LG@false\let\rMath@\LG@false
  \def\L@##1{\LG@false}\def\C@##1{\LG@false}\def\R@##1{\LG@false}%
  \def\LP@##1{\LG@false}\def\CP@##1{\LG@false}\def\RP@##1{\LG@false}%
  \def\p(##1){\LG@false}\def\P(##1)##2{\LG@false}%
  \def\d##1{\LG@false}\def\$##1{\LG@false}%
  \def&{\LG@true\FS@false\global\LT@\z@\global\advance\CN@\@ne}%
  \def\|(##1){\LG@true\FS@false\global\LT@\z@\global\advance\CN@\@ne}%
  \def\g(##1){\dimen@##1\relax
   \ifLG@\xdef\LGL@{\LGL@ Z\the\CN@"\the\dimen@}\else
   \xdef\RGL@{\RGL@ Z\the\CN@"\the\dimen@}\fi}%
  \def\s##1{%
   \ifLG@
    \ifFS@\global\FT@\z@ plus##1fil minus##1fil\FS@false\fi
    \xdef\LSL@{\LSL@ Z\the\CN@"##1}%
   \else
    \global\LT@\z@ plus##1fil minus##1fil
    \xdef\RSL@{\RSL@ Z\the\CN@"##1}%
   \fi
   \global\advance\SCT@##1\relax}%
  \CN@\@ne\LG@true\FS@true\SCT@\z@\FT@\z@\relax\LT@\z@\relax
  \setboxz@h{\PR@}%
  \global\CT@\CN@
  \def\l@{\LB@{\the\hashtoks@}}\def\c@{\CB@{\the\hashtoks@}}%
  \def\r@{\RB@{\the\hashtoks@}}%
  \def\lP@{\LBP@{\the\hashtoks@}}\def\cP@{\CBP@{\the\hashtoks@}}%
  \def\rP@{\RBP@{\the\hashtoks@}}%
  \let\lmath@\l@\let\cmath@\c@\let\rmath@\r@
  \let\lMath@\l@\let\cMath@\c@\let\rMath@\r@
  \def\L@##1{\l@}\def\C@##1{\c@}\def\R@##1{\r@}%
  \def\LP@##1{\l@}\def\CP@##1{\c@}\def\RP@##1{\r@}%
  \def\p(##1){\PB@{##1}{\the\hashtoks@}}%
  \def\P(##1)##2{\PB@{##1}{\the\hashtoks@}}%
  \def\d##1{\DB@{\the\hashtoks@}}\def\$##1{\DL@{\the\hashtoks@}}%
  \def&{\T@B\csname table \space\space\space\endcsname\the\hashtoks@\T@B}%
  \def\|(##1){\T@B\VR@@{##1}\the\hashtoks@\T@B}%
  \let\LB@0\let\CB@0\let\RB@0%
  \let\LBP@0\let\CBP@0\let\RBP@0%
  \let\PB@0%
  \let\DB@0\let\DL@0%
  \expandafter\let\csname table \space\space\space\endcsname0%
  \let\VR@@0%
  \let\g0\let\s0%
  \xdef\pR@@{\PR@}%
  \def\lmath@{\MLB@{\the\hashtoks@}\ignorespaces}%
  \def\cmath@{\MCB@{\the\hashtoks@}\ignorespaces}%
  \def\rmath@{\MRB@{\the\hashtoks@}\ignorespaces}%
  \def\lMath@{\CMLB@{\the\hashtoks@}\ignorespaces}%
  \def\cMath@{\CMCB@{\the\hashtoks@}\ignorespaces}%
  \def\rMath@{\CMRB@{\the\hashtoks@}\ignorespaces}%
  \def\L@##1{\CLB@{##1}{\the\hashtoks@}\ignorespaces}%
  \def\C@##1{\CCB@{##1}{\the\hashtoks@}\ignorespaces}%
  \def\R@##1{\CRB@{##1}{\the\hashtoks@}\ignorespaces}%
  \def\LP@##1{\CLBP@{##1}{\the\hashtoks@}\ignorespaces}%
  \def\CP@##1{\CCBP@{##1}{\the\hashtoks@}\ignorespaces}%
  \def\RP@##1{\CRBP@{##1}{\the\hashtoks@}\ignorespaces}%
  \def\p(##1){\PB@{##1}{\the\hashtoks@}}%
  \def\P(##1)##2{\CPB@{##1}{##2}{\the\hashtoks@}}%
  \def\d##1{\DBB@{##1}{\the\hashtoks@}}%
  \def\$##1{\DLL@{##1}{\the\hashtoks@}}%
  \def&{\T@B\csname table \space\space\space\endcsname\the\hashtoks@\T@B}%
  \def\|(##1){\T@B\VR@@{##1}\the\hashtoks@\T@B}%
  \let\LB@0\let\CB@0\let\RB@0%
  \let\PB@0\let\CPB@0%
  \let\DBB@0%
  \let\DLL@0%
  \let\CLB@0\let\CCB@0\let\CRB@0%
  \let\CLBP@0\let\CCBP@0\let\CRBP@0%
  \let\MLB@0\let\MCB@0\let\MRB@0%
  \let\CMLB@0\let\CMCB@0\let\CMRB@0%
  \expandafter\let\csname table \space\space\space\endcsname0%
  \let\VR@@0%
  \let\g0\let\s0%
  \xdef\PR@@{\PR@}%
  \def&##1##2{%
   \ifx##1\s
    \T@B\tabskip\z@\noexpand\relax
    \csname table \space\space\space\endcsname\the\hashtoks@
    \tabskip\z@ plus##2fil minus##2fil\T@B
   \else
    \T@B\tabskip\z@\noexpand\relax
    \csname table \space\space\space\endcsname\the\hashtoks@\T@B
   \ifx##1\L@\L@{##2}\else\ifx##1\C@\C@{##2}\else\ifx##1\R@\R@{##2}\else
   \ifx##1\LP@\LP@{##2}\else\ifx##1\CP@\CP@{##2}\else\ifx##1\RP@\RP@{##2}\else
   \ifx##1\p\p{##2}\else\ifx##1\P\P{##2}\else\ifx##1\d\d{##2}\else
   \ifx##1\$\${##2}\else##1##2\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}%
  \def\s##1{\tabskip\z@ plus##1fil minus##1fil\noexpand\relax\noexpand
   \ignorespaces}%
  \xdef\PR@@@{\PR@\empty}%
 }%
 \def\g(##1){\hskip##1\relax\ignorespaces}%
 \catcode`\&=4 \MC@\DV@\VT@}
}
\expandafter\newdimen\csname c-1l\endcsname
\expandafter\newdimen\csname c-2l\endcsname
\expandafter\newdimen\csname c-3l\endcsname
\expandafter\newdimen\csname c-4l\endcsname
\expandafter\newdimen\csname c-5l\endcsname
\expandafter\newdimen\csname c-6l\endcsname
\expandafter\newdimen\csname c-7l\endcsname
\expandafter\newdimen\csname c-8l\endcsname
\expandafter\newdimen\csname c-9l\endcsname
\expandafter\newdimen\csname c-10l\endcsname
\expandafter\newdimen\csname c-11l\endcsname
\expandafter\newdimen\csname c-12l\endcsname
\expandafter\newdimen\csname c-13l\endcsname
\expandafter\newdimen\csname c-14l\endcsname
\expandafter\newdimen\csname c-15l\endcsname
\expandafter\newdimen\csname c-16l\endcsname
\expandafter\newdimen\csname c-17l\endcsname
\expandafter\newdimen\csname c-18l\endcsname
\expandafter\newdimen\csname c-19l\endcsname
\expandafter\newdimen\csname c-20l\endcsname
\expandafter\newdimen\csname c-1c\endcsname
\expandafter\newdimen\csname c-2c\endcsname
\expandafter\newdimen\csname c-3c\endcsname
\expandafter\newdimen\csname c-4c\endcsname
\expandafter\newdimen\csname c-5c\endcsname
\expandafter\newdimen\csname c-6c\endcsname
\expandafter\newdimen\csname c-7c\endcsname
\expandafter\newdimen\csname c-8c\endcsname
\expandafter\newdimen\csname c-9c\endcsname
\expandafter\newdimen\csname c-10c\endcsname
\expandafter\newdimen\csname c-11c\endcsname
\expandafter\newdimen\csname c-12c\endcsname
\expandafter\newdimen\csname c-13c\endcsname
\expandafter\newdimen\csname c-14c\endcsname
\expandafter\newdimen\csname c-15c\endcsname
\expandafter\newdimen\csname c-16c\endcsname
\expandafter\newdimen\csname c-17c\endcsname
\expandafter\newdimen\csname c-18c\endcsname
\expandafter\newdimen\csname c-19c\endcsname
\expandafter\newdimen\csname c-20c\endcsname
\expandafter\newdimen\csname c-1r\endcsname
\expandafter\newdimen\csname c-2r\endcsname
\expandafter\newdimen\csname c-3r\endcsname
\expandafter\newdimen\csname c-4r\endcsname
\expandafter\newdimen\csname c-5r\endcsname
\expandafter\newdimen\csname c-6r\endcsname
\expandafter\newdimen\csname c-7r\endcsname
\expandafter\newdimen\csname c-8r\endcsname
\expandafter\newdimen\csname c-9r\endcsname
\expandafter\newdimen\csname c-10r\endcsname
\expandafter\newdimen\csname c-11r\endcsname
\expandafter\newdimen\csname c-12r\endcsname
\expandafter\newdimen\csname c-13r\endcsname
\expandafter\newdimen\csname c-14r\endcsname
\expandafter\newdimen\csname c-15r\endcsname
\expandafter\newdimen\csname c-16r\endcsname
\expandafter\newdimen\csname c-17r\endcsname
\expandafter\newdimen\csname c-18r\endcsname
\expandafter\newdimen\csname c-19r\endcsname
\expandafter\newdimen\csname c-20r\endcsname
\def\MC@{%
 \ifnum\CT@>20
  \count@\@cclv \advance\count@-\count11
  \divide\count@\thr@@ \advance\count@20
  \ifnum\count@<\CT@
   \Err@{You can't have more than \number\count@\space columns}%
  \else
   \mscount\CT@
   \loop\ifnum\mscount>20
    \advance\count11by\@ne\ch@ck1\insc@unt\dimen\allocationnumber=\count11
    \expandafter\dimendef\csname c-\number\mscount l\endcsname
     =\allocationnumber
    \advance\count11by\@ne\ch@ck1\insc@unt\dimen\allocationnumber=\count11
    \expandafter\dimendef\csname c-\number\mscount c\endcsname
     =\allocationnumber
    \advance\count11by\@ne\ch@ck1\insc@unt\dimen\allocationnumber=\count11
    \expandafter\dimendef\csname c-\number\mscount r\endcsname
     =\allocationnumber
   \advance\mscount\m@ne\repeat
  \fi
 \fi}
{
\catcode`\|\active
\gdef\DV@{\toks@{}\toks@@{}\mscount\CT@
 \loop\ifnum\mscount>\@ne
  \toks@=\expandafter{\the\toks@|\omit}\toks@@=\expandafter{\the\toks@@|}%
  \advance\mscount\m@ne\repeat
 \xdef\VV@{\the\toks@}\xdef\VV@@{\the\toks@@}%
 \mscount\CT@
 \loop\ifnum\mscount>\z@
  \global\csname c-\number\mscount l\endcsname\z@
  \global\csname c-\number\mscount c\endcsname\z@
  \global\csname c-\number\mscount r\endcsname\z@
  \advance\mscount\m@ne\repeat}
}
\Invalid@\endtable
\let\NX@\relax
\def\VT@{\begingroup\let\NX@\noexpand
 \noexpand\catcode`\|\active\catcode`\&\active\csname table \space\endcsname}
\newif\ifNM@
\newif\ifNY@
\newif\ifNZ@
\newif\ifSL@
\def\@@@#1\@@#2#3\@@@{\ifx\@@@@#2\else\global\SL@true\fi}

{\catcode`\@=\active \uccode`\Z=`\@
 \uppercase{\expandafter\gdef\csname ATZ\endcsname{\let@\relax}}}

{
\catcode`\&\active \catcode`\|\active
\expandafter\gdef\csname table \space\endcsname#1\endtable{%
 \global\NM@true\global\NY@true\global\NZ@true\global\SL@false
 \let\TF@0\let\\0\let\hd0%
 \let\l0\let\c0\let\r0\let\+0\let\=0%
 \let\ex@@0\let\exa@0\let\exb@0%
 \let\hls@0\let\hl@0%
 \let\hL@0\let\vs@0\let\body0\let\iterate0%
 \def\cf##1{\cf@{##1}}\let\cf@0\let\fam0%
 \let\usetable0\let\VTW@@0\let~0\AT@\let\PRX@0\let\PX@0%
 \let\$0\let\(0\let\)0%
 {\let\@@0\def\t{\@@}\def\m{\@@}\def\b{\@@}\def\yy{\@@}\def\vZ{\@@}%
  \let\vs0\let\vz0\let\xx0\let\hlyy0\let\hLyy0%
  \let\ex0\let\exa0\let\exb0\let\hl0\let\hls0\let\exs0\let\NS0\let\hL0%
  \let&0\let|0\def\|{}%
  \expandafter\xdef\csname table \space\space\endcsname{#1}%
  \xdef\next@{#1}\expandafter\@@@\next@\@@\@@@@\@@@
 }%
 \def\t{\global\NM@false\t@}\def\m{\global\NM@false\m@}%
 \def\b{\global\NM@false\b@}%
 \let\t@0\let\m@0\let\b@0\let\NM@false0%
 \def\vs(##1){\noalign{\vs@{##1}}}%
 \def\vz{\noalign{\vz@}}%
 \def\vZ{\noalign{\global\NZ@false}\vZ@}\let\vZ@0\let\NZ@false0\let\vz@0%
 \def\hd{\NX@\hd@}%
 \def\xx{\noexpand\omit\global\X@true\xx@}\let\xx@0\let\X@true0%
 \def\yy{\global\NY@false\yy@}\let\yy@0\let\NY@false0%
 \def\hl{\noalign{\hrule\height\HTW@\hl@}}%
 \def\hL(##1){\noalign{\hrule\height##1\hL@{##1}}}%
 \def\hlyy{\noalign{\global\NY@false}\hlyy@}\let\hlyy@0%
 \def\hLyy{\noalign{\global\NY@false}\hLyy@}\let\hLyy@0%
 \def\hls##1\\{\hls@##1\cr\PX@}%
 \def\ex(##1){\ex@@{##1}\omit\vrule\height##1\width\z@\VV@\\}%
 \def\exs(##1)##2\\{\PRX@{##1}\omit\vrule\height##1\width\z@##2\cr\PX@}%
 \def\exa{\noalign{\global\NY@false}\exa@}%
 \def\exb{\noalign{\global\NY@false}\exb@}%
 \def\NS##1\\{\NS@##1\cr\NS@@}\let\NS@0\let\NS@@0%
 \def&{\T@B\omit\T@B}\def|{\T@B ZZZ\T@B}\def\|(##1){\T@B Y\VP@##1;;)\T@B}%
 \expandafter\xdef\csname table \space\space\endcsname{#1\crcr\ex(\z@)}%
 \xdef\VT@@@@{#1}%
 \xdef\VT@@@@@{\VV@@}%
 \endgroup\DT@}
}
\expandafter\def\csname table \space\space\space\endcsname#1#2#3{%
 \if#1Z\hskip-\VTW@\vrule\width\VTW@\else
 \let\VTW@@\VTW@\hskip-#2\vrule\width#2\vrule\width#3\hskip-#3\fi}
\def\VR@@#1#2#3#4{\if#2Z\hskip-#1\vrule\width#1\else
 \def\VTW@@{#1}\hskip-#3\vrule\width#3\vrule\width#4\hskip-#4\fi}
\def\VP@#1#2){\if#1*\VP@@#1#2)\else\VP@@@#1#2)\fi}
\def\VP@@#1;#2#3){\if#2*{\VTW@@}{\VTW@@}\else\VP@@@@#2#3)\fi}
\def\VP@@@@#1;#2){\if Z#1Z{\VTW@@}{\z@}\else{\VTW@@}{#1}\fi}
\def\VP@@@#1;#2#3){\if#2*{#1}{\VTW@@}\else{#1}{\VP@@@@@#2#3)}\fi}
\def\VP@@@@@#1;#2){\if Z#1Z\z@\else#1\fi}
{
\lccode`\7=`\p \lccode`\8=`\t
\lowercase{\gdef\FD@#1{\DN@##178##2\next@{\edef\FD@@{##1}\xdef#1{##2}}%
 \expandafter\next@#1\next@}}
}
\newif\ifl@
\newif\ifc@
\newif\ifr@
\newif\ift@
\newif\ifm@
\newif\ifb@
\newif\ifX@
\newif\ifY@
\newif\ifE@
\newif\ifH@
\newcount\RN@
\newif\ifR@
\newdimen\EW@
\def\HLS@{}
\def\DLS@{}
\newif\ifOP@
\newif\ifS@
\newif\ifNH@
\newif\ifSP@
\newif\ifSC@
\def\showsecondpass{\SP@true}
\def\noshowsecondpass{\SP@false}
\def\showcolwidths{\SC@true}
\def\noshowcolwidths{\SC@false}
\newif\ifTMS@
\newbox\tablebox@
\def\IT@{"}
\newif\ifnote@
\newif\iffnote@
\def\DT@{\FN@\DT@@}
\Invalid@\note
\Invalid@\fnote
\def\DT@@{\global\note@false\global\fnote@false
 \ifx\next\note\global\note@true\else\ifx\next\fnote\global\fnote@true\fi\fi
 \DT@@@}
\def\DT@@@{{%
 \let\RUH@\RH@\edef\SSC@{\SS@}%
 \everycr{\noalign{\RUH@\GS@
  \if T\TSS@\global\TMS@true\else\if M\TSS@\global\TMS@true\else
   \global\TMS@false\fi\fi
  \ifE@\else\ifH@\else
   \global\advance\RN@\@ne\fi\fi
  \global\E@false\global\H@false
  \global\CN@\@ne}}%
 \S@true\NH@true
 \let\CFG@\relax\let\LCFG@\relax\let\RCFG@\relax
 \let\LFG@\relax\let\LLFG@\relax
 \let\RFG@\relax\let\RRFG@\relax
 \def\s##1{\ignorespaces}%
 \let\CWD@\CWD@@\let\LWD@\LWD@@\let\RWD@\RWD@@
 \def\l{\global\l@true}%
 \def\c{\hfill\global\c@true}%
 \def\r{\hfill\global\r@true}%
 \def\t@{\global\t@true}%
 \def\m@{\global\m@true}%
 \def\b@{\global\b@true}%
 \RN@\z@\R@false
 \ifTW@
  \ifTWG@\DN@{\halign spread\TW@}\else\ifTWL@
  \DN@{\halign spread-\TW@}\else\DN@{\halign to\TW@}\fi\fi
 \else
  \DN@{\halign}%
 \fi
 \global\setbox\@ne\vbox{\EW@\z@\offinterlineskip
  \let\=\relax\let\\\cr\tabskip\z@\tabskip\FT@\next@
  {\span\PR@@@\tabskip\z@\tabskip\LT@\cr\csname table \space\space\endcsname
  \crcr}}%
 {\def\LB@##1{\LFG@@\global\advance\CN@\@ne}%
  \def\CB@##1{\CFG@@\global\advance\CN@\@ne}%
  \def\RB@##1{\RFG@@\global\advance\CN@\@ne}%
  \def\PB@##1##2{\global\advance\CN@\@ne}%
  \def\DB@##1{\RFG@@\global\advance\CN@\@ne}%
  \def\DL@##1{\RFG@@\global\advance\CN@\@ne}%
  \let\LBP@\LB@\let\CBP@\CB@\let\RBP@\RB@
  \setbox\z@\vbox{\EW@\z@\let\\\cr\halign{\span\pR@@\cr\VT@@@@@\cr}}%
 }%
 \dimen@\z@\setbox\z@\vbox{\unvcopy\@ne\unpenalty
  \setbox\z@\lastbox\unskip\unpenalty\setbox\z@
  \hbox{\unhbox\z@\count@\CT@\multiply\count@\tw@\advance\count@\m@ne
  \def\CWS@{.}\loop\unskip\setbox\z@\lastbox\ifSC@\ifnum\count@=\@ne
  \xdef\CWS@{\the\wdz@\CWS@}\else
  \ifodd\count@\xdef\CWS@{; \the\wdz@\CWS@}\fi\fi\fi
  \global\advance\dimen@\wdz@\ifnum\count@>\z@
  \advance\count@\m@ne\repeat}}%
 \ifSC@
  \immediate\write\sixt@@n{}%
  {\lccode`\Z=`\#\lccode`\C=`\C
  \count@\pageno\advance\count@\@ne
  \lowercase{\message{Column widths of table Z\number\count@: \CWS@}}}%
  \immediate\write\sixt@@n{}%
 \fi
 \xdef\IT@{\IT@"}%
 \OP@false\ifNZ@\ifNS@\ifNM@\ifNY@\ifS@\ifNH@\OP@true\else
 \ifTW@\else\OP@true\fi\fi\fi\fi\fi\fi\fi
 \ifOP@
  \global\setbox\tablebox@\hbox{\boxz@\hbox to\Rs@{}\hbox to\Ls@{}}%
 \else
  \ifSP@\immediate\write\sixt@@n{Second pass for
   Table \string"\TN@\string"}%
  \fi
  \setbox\@ne\null
  \PRF@\edef\TF@{\the\font}\MS@\RN@\z@
  \ifTW@
   \ifnum\SCT@=\z@
    \Err@{You don't have any stretch in this table}\EW@\z@
   \else
    \ifTWG@\EW@\TW@\else\ifTWL@\EW@-\TW@\else
     \EW@\TW@\advance\EW@-\dimen@\fi\fi
    \divide\EW@\SCT@
   \fi
  \else
   \EW@\z@
  \fi
  \def\s##1{\hbox to##1\EW@{}\ignorespaces}%
  \FD@\HLS@\FD@\DLS@
  \R@true\let\CFG@\CFG@@\let\LCFG@\LCFG@@\let\RCFG@\RCFG@@
  \let\LFG@\LFG@@\let\LLFG@\LLFG@@\let\RFG@\RFG@@\let\RRFG@\RRFG@@
  \let\CWD@\relax\let\LWD@\relax\let\RWD@\relax\let\RUH@\UH@
  \edef\SS@{\SSC@}%
  \let\=\relax
  \global\setbox\tablebox@\hbox{%
   \vbox{\offinterlineskip\let\\\cr\halign{\tabskip\z@\span\PR@@\tabskip\z@\cr
   \VT@@@@\crcr}}\hbox to\Rs@{}\hbox to\Ls@{}}%
 \fi}%
 \setboxz@h{\unhbox\tablebox@\global\setbox\LBX@\lastbox
  \global\setbox\RBX@\lastbox}%
 \dimen@\ht\z@ \dimen@ii\dp\z@
 \global\setbox\tablebox@\hbox{\vrule\height\dimen@\depth\dimen@ii
  \width\wd\LBX@\hskip-\wd\LBX@
 \boxz@\hskip-\wd\RBX@\vrule\height\dimen@\depth\dimen@ii\width\wd\RBX@}%
 \global\TW@false\global\AD@false
 \gdef\TW@{\z@}\gdef\Ls@{\z@}\gdef\Rs@{\z@}\gdef\HLS@{}%
 \gdef\DLS@{}\gdef\LGL@{}\gdef\RGL@{}\gdef\LSL@{}\gdef\RSL@{}%
 \gdef\PR@{}\gdef\SS@{}\gdef\pR@@{}\gdef\PR@@{}\gdef\PR@@@{}\gdef\VV@{}%
 \gdef\VV@@{}%
 \expandafter\gdef\csname table \space\space\endcsname{}%
 \gdef\VT@@@@{}\gdef\VT@@@@@{}%
 \gdef\XHL@{}\gdef\XXL@{}\gdef\XXHL@{}\endgroup
 \ifstoring@
  \DN@{\global\setbox\csname table\thetable@\endcsname\box\tablebox@
  \global\storing@false}%
 \else
 \ifnote@\let\next@\donote@\else\iffnote@\let\next@\dofnote@\else
  \let\next@\writeit@\fi\fi
 \fi\next@}
\newbox\notebox@
\newbox\newnotebox@
\newif\iffirstnote@
\newif\iffirstfnote@
\firstnote@true
\firstfnote@true
\long\def\noteformat@#1{\global\setbox\newnotebox@
 \vbox{\hsize=\wd\tablebox@\null\noindent\rm #1\par\null}}
\long\def\noteformat@@#1{\noteformat@{\ignorespaces#1\unskip}%
 \iffirstnote@
  \global\setbox\notebox@\box\newnotebox@
 \else
  \global\setbox\notebox@
  \vbox{\box\notebox@\nointerlineskip\vskip-\baselineskip
   \box\newnotebox@}\fi
 \firstnote@false}
\long\def\donote@\note#1{\noteformat@@{#1}\FN@\morenote@}
\long\def\dofnote@\fnote#1{\fnoteformat@@{#1}\FN@\morenote@}
\let\fnoteformat@\noteformat@
\long\def\fnoteformat@@#1{\fnoteformat@{\ignorespaces#1\unskip}%
 \iffirstnote@
  \firstnote@false
  \iffirstfnote@
   \global\setbox\notebox@\box\newnotebox@
  \else
   \global\setbox\notebox@\vbox{\box\notebox@\nointerlineskip
   \vskip-\baselineskip\box\newnotebox@}%
  \fi
 \else
  \global\setbox\notebox@\vbox{\box\notebox@\nointerlineskip
  \iffirstfnote@\smallskip\fi
  \vskip-\baselineskip\box\newnotebox@}%
 \fi
 \firstfnote@false}
\def\morenote@{\ifx\next\space@\DN@. {\FN@\morenote@}\else
 \ifx\next\note\DN@.{\donote@}\else\ifx\next\fnote
 \DN@.{\dofnote@}\else\DN@.{\writeit@}\fi\fi\fi\next@.}
\def\writeit@{\global\firstnote@true\global\firstfnote@true
 \dimen@\dp\tablebox@
 \setbox\tablebox@\hbox{\vbox{\box\tablebox@
  \ifvoid\notebox@
  \else
   \nointerlineskip\smallskip
   \MS@
   \ifdim\dimen@<\FSD\dimen@ii\FSD\advance\dimen@ii-\dimen@\vskip\dimen@ii\fi
  \box\notebox@\vskip-\baselineskip\fi}}%
 \immediate\write\writedata@
  {\the\ht\tablebox@\space\the\dp\tablebox@\space\the\wd\tablebox@}%
 \dimen@\ht\tablebox@ \advance\dimen@\dp\tablebox@
 \ifdim\dimen@>\vsize\Err@{Table bigger than \string\vsize; height
  \the\ht\tablebox@, depth \the\dp\tablebox@}\fi
 \hrule\height\z@
 \vskip\vsize
 \ifproofing@\else\special{beginpaste:}\fi
 \ht\tablebox@=\z@\dp\tablebox@=\z@\wd\tablebox@=\z@
 \noindent\box\tablebox@
 \ifproofing@\else\special{endpaste:}\fi
 \smash{\vrule\height1sp\width1sp\depth\z@}
\eject}
\newbox\TBX@
\def\es@{\crcr\egroup\egroup\let\FS@\relax}
\def\ls@{\let\=\es@\vbox\bgroup\NBL@\let\+\cr\everycr{}\halign
 \bgroup\ignorespaces##\unskip\FS@@\hfil\cr}
\def\cs@{\let\=\es@\vbox\bgroup\NBL@\let\+\cr\everycr{}\halign
 \bgroup\hfil\ignorespaces##\unskip\FS@@\hfil\cr}
\def\rs@{\let\=\es@\vbox\bgroup\NBL@\let\+\cr\everycr{}\halign
 \bgroup\hfil\ignorespaces##\unskip\FS@@\cr}
\def\FG@{\hskip\SSL@\EW@\hskip-\SSLL@\EW@}
\def\CLB@#1#2{%
 \if&#2&%
 \else
  \let\=\ls@\l@false\c@false\r@false\Y@false
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\global\X@false\SL@true\fi
  \ifSL@
   \t@false\m@false\b@false\setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip
    \FS@}\def\UPT@{L}\UP@
  \else
   \ifTMS@
    \t@false\m@false\b@false
    \setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip\FS@}\def\UPT@{L}\UP@
   \else
    \TF@#1\ignorespaces#2\unskip\FS@
   \fi
  \fi
  \hfil
  \ifc@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\def\LB@#1{\CLB@{}{#1}}
\def\MLB@#1{%
 \if&#1&%
 \else
  \ifX@
   \CB@{\TF@#1}\global\X@false
  \else
   \let\=\ls@\l@false\c@false\r@false\Y@false
   \ifSL@
    \t@false\m@false\b@false\setbox\TBX@\hbox{$#1$\FS@}\def\UPT@{L}\UP@
   \else
    \ifTMS@
     \t@false\m@false\b@false\setbox\TBX@\hbox{$#1$\FS@}\def\UPT@{L}\UP@
    \else
     $#1$\FS@
    \fi
   \fi
   \hfil
   \ifc@\hfill\fi
  \fi
 \fi
 \global\advance\CN@\@ne}
\def\CMLB@#1{%
 \if&#1&%
 \else
  \ifX@
   \CB@{\TF@#1}\global\X@false
  \else
   \let\=\ls@\l@false\c@false\r@false\Y@false
   \ifSL@
    \t@false\m@false\b@false\setbox\TBX@\hbox{$\displaystyle{#1}$\FS@}%
    \def\UPT@{L}\UP@
   \else
    \ifTMS@
     \t@false\m@false\b@false\setbox\TBX@\hbox{$\displaystyle{#1}$\FS@}%
     \def\UPT@{L}\UP@
    \else
     $\displaystyle{#1}$\FS@
    \fi
   \fi
   \hfil
   \ifc@\hfill\fi
  \fi
 \fi
 \global\advance\CN@\@ne}
\def\CLBP@#1#2{%
 \if&#2&%
 \else
  \let\=\ls@\l@false\c@false\r@false\Y@false\t@false\m@false\b@false
  \setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip\FS@}\LFG@\LLFG@\LWD@
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\global\X@false\fi
  \def\UPT@{L}\UP@
  \hfil
  \ifc@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\def\LBP@#1{\CLBP@{}{#1}}
\let\CLB@@\CLB@
\let\CLBP@@\CLBP@
\let\MLB@@\MLB@
\let\CMLB@@\CMLB@
\def\CCB@#1#2{%
 \if&#2&%
 \else
  \let\=\cs@\l@false\c@false\r@false\Y@false
  \hfil
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\global\X@false\SL@true\fi
  \ifSL@
   \t@false\m@false\b@false\setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip
   \FS@}\def\UPT@{C}\UP@
  \else
   \ifTMS@\t@false\m@false\b@false
    \setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip\FS@}\def\UPT@{C}\UP@
   \else
    \TF@#1\ignorespaces#2\unskip\FS@
   \fi
  \fi
  \hfil
  \ifl@\hfill\fi
  \ifc@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\def\CB@#1{\CCB@{}{#1}}
\def\MCB@#1{%
 \if&#1&%
 \else
  \ifX@
   \CB@{\TF@#1}\global\X@false
  \else
   \let\=\cs@\l@false\c@false\r@false\Y@false\hfil
   \ifSL@
    \t@false\m@false\b@false\setbox\TBX@\hbox{$#1$\FS@}\def\UPT@{C}\UP@
   \else
    \ifTMS@
     \t@false\m@false\b@false\setbox\TBX@\hbox{$#1$\FS@}\def\UPT@{C}\UP@
    \else
     $#1$\FS@
    \fi
   \fi
   \hfil
   \ifl@\hfill\fi
   \ifc@\hfill\fi
  \fi
 \fi
 \global\advance\CN@\@ne}
\def\CMCB@#1{%
 \if&#1&%
 \else
  \ifX@
   \CB@{\TF@#1}\global\X@false
  \else
   \let\=\cs@\l@false\c@false\r@false\Y@false\hfil
   \ifSL@
    \t@false\m@false\b@false\setbox\TBX@\hbox{$\displaystyle{#1}$\FS@}%
    \def\UPT@{C}\UP@
   \else
    \ifTMS@
     \t@false\m@false\b@false
     \setbox\TBX@\hbox{$\displaystyle{#1}$\FS@}\def\UPT@{C}\UP@
    \else
     $\displaystyle{#1}$\FS@
    \fi
   \fi
   \hfil
   \ifl@\hfill\fi
   \ifc@\hfill\fi
  \fi
 \fi
 \global\advance\CN@\@ne}
\def\CCBP@#1#2{%
 \if&#2&%
 \else
  \let\=\cs@\l@false\c@false\r@false\Y@false\t@false\m@false\b@false
  \setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip\FS@}\CFG@\hfil\LCFG@\CWD@
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\fi
  \def\UPT@{C}\UP@\RCFG@
  \ifX@\global\X@false\fi
  \hfil
  \ifl@\hfill\fi
  \ifc@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\def\CBP@#1{\CCBP@{}{#1}}
\let\CCB@@\CCB@
\let\CCBP@@\CCBP@
\let\MCB@@\MCB@
\let\CMCB@@\CMCB@
\def\CRB@#1#2{%
 \if&#2&%
 \else
  \let\=\rs@\l@false\c@false\r@false\Y@false\hfil
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\global\X@false\SL@true\fi
  \ifSL@
   \t@false\m@false\b@false\setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip
    \FS@}\def\UPT@{R}\UP@
  \else
   \ifTMS@
    \t@false\m@false\b@false
    \setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip\FS@}%
    \ifc@\hfill\fi
    \def\UPT@{R}\UP@
   \else
    \TF@#1\ignorespaces#2\unskip\FS@
   \fi
  \fi
  \ifc@\hfill\fi
  \ifl@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\def\RB@#1{\CRB@{}{#1}}
\def\MRB@#1{%
 \if&#1&%
 \else
  \ifX@
   \CB@{\TF@#1}\global\X@false
  \else
   \let\=\rs@\l@false\c@false\r@false\Y@false\hfil
   \ifSL@
    \t@false\m@false\b@false\setbox\TBX@\hbox{$#1$\FS@}\def\UPT@{R}\UP@
   \else
    \ifTMS@
     \t@false\m@false\b@false\setbox\TBX@\hbox{$#1$\FS@}%
     \ifc@\hfill\fi
     \def\UPT@{R}\UP@
    \else
     $#1$\FS@
    \fi
   \fi
   \ifc@\hfill\fi
   \ifl@\hfill\fi
  \fi
 \fi
 \global\advance\CN@\@ne}
\def\CMRB@#1{%
 \if&#1&%
 \else
  \ifX@
   \CB@{\TF@#1}\global\X@false
  \else
   \let\=\rs@\l@false\c@false\r@false\Y@false\hfil
   \ifSL@
    \t@false\m@false\b@false\setbox\TBX@\hbox{$\displaystyle{#1}$\FS@}%
    \def\UPT@{R}\UP@
   \else
    \ifTMS@
     \t@false\m@false\b@false\setbox\TBX@\hbox{$\displaystyle{#1}$\FS@}%
     \ifc@\hfill\fi
     \def\UPT@{R}\UP@
    \else
     $\displaystyle{#1}$\FS@
    \fi
   \fi
   \ifc@\hfill\fi
   \ifl@\hfill\fi
  \fi
 \fi
 \global\advance\CN@\@ne}
\def\RBP@#1{\CRBP@{}{#1}}
\def\CRBP@#1#2{%
 \if&#2&%
 \else
  \let\=\rs@\l@false\c@false\r@false\Y@false\t@false\m@false\b@false
  \setbox\TBX@\hbox{\TF@#1\ignorespaces#2\unskip\FS@}%
  \RFG@\hfil
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\fi
  \RWD@\def\UPT@{R}\UP@\RRFG@
  \ifX@\global\X@false\fi
  \ifc@\hfill\fi
  \ifl@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\let\CRB@@\CRB@
\let\CRBP@@\CRBP@
\let\MRB@@\MRB@
\let\CMRB@@\CMRB@
\def\UP@{%
 \ifR@
  \ifY@
   \ift@\def\CSS@{T}\else\ifm@\def\CSS@{M}\else\def\CSS@{B}\fi\fi
   \let\HLS@@\HLS@ \let\DLS@@\DLS@
   \dimen@\TRHT@ \advance\dimen@\TRDP@
   \AX@
   \count@\YC@
   \loop
    \ifnum\count@>\@ne \FD@\HLS@@ \advance\dimen@\FD@@\p@
    \FD@\DLS@@
    \ifnum\count@=\tw@ \FLD@\FD@@\p@ \else \advance\dimen@\FD@@\p@ \fi
    \advance\count@\m@ne\repeat
   \if\UPT@ P\else\ifc@\hfill\fi\if\UPT@ L\ifr@\hfill\fi\fi\fi
   \vbox to\TRHT@{%
    \vbox to\dimen@{%
     \if B\CSS@\vfill\fi
     \if M\CSS@\vskip\FLD@\vfill\fi
     \box\TBX@
     \if M\CSS@\vfill\fi
     \if T\CSS@\vfill\fi
     }\vss}%
  \else
   \ift@\def\CSS@{T}\else\ifm@\def\CSS@{M}\else\ifb@\def\CSS@{B}\else
    \if\TSS@ T\def\CSS@{T}\else\if\TSS@ M\def\CSS@{M}\else\def\CSS@{B}\fi\fi
   \fi\fi\fi
   \ifdim\TRHT@>\ht\TBX@
    \if\UPT@ P\else\ifc@\hfill\fi\if\UPT@ L\ifr@\hfill\fi\fi\fi
    \vbox to\TRHT@{%
     \if B\CSS@\vfill\fi
     \if M\CSS@\vfill\fi
     \if M\CSS@\dp\TBX@\z@\fi
     \box\TBX@
     \if M\CSS@\vfill\fi
     \if T\CSS@\vfill\fi}%
   \else
    \if\UPT@ P\let\next@\box\else\let\next@\unhbox\fi
    \next@\TBX@
   \fi
  \fi
 \else
  \ifY@
  \else
   \ifdim\ht\TBX@>\RHT@ \global\RHT@\ht\TBX@ \fi
   \ifdim\dp\TBX@>\RDP@ \global\RDP@\dp\TBX@ \fi
  \fi
  \if\UPT@ P\let\next@\box\else\let\next@\unhbox\fi
  \next@\TBX@
 \fi}
\def\DBB@#1#2{\DB@{\global\DCC@#1\relax#2}}
\let\DBB@@\DBB@
\def\DB@#1{%
 \if&#1&%
 \else
  \l@false\c@false\r@false\Y@false\t@false\m@false\b@false
  \setbox\TBX@\hbox{\TF@\ignorespaces#1\unskip\FS@}%
  \ifl@\else\ifc@\else\ifr@\else\setbox\TBX@\hbox{\TF@\DC@{#1}\FS@}\fi\fi\fi
  \RFG@
  \hfil
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\fi
  \RWD@\def\UPT@{R}\UP@\RRFG@
  \ifX@\global\X@false\fi
  \ifc@\hfill\fi
  \ifl@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\def\S@#1#2 #3\S@{#1#2}
\def\DC@#1{\expandafter\DC@@\S@#1 \S@..\DC@@}
\def\DC@@#1.#2.#3\DC@@{#1\setboxz@h{.}\dimen@\wdz@
 \setboxz@h{0}\advance\dimen@\DCC@\wdz@
 \hbox to\dimen@{\if Z#3Z\else.\fi#2\hss}}
\newif\ifD@
\newif\ifLP@
\let\(\relax
\let\)\relax
\def\DLL@#1#2{\DL@{\global\DLC@#1\relax#2}}
\let\DLL@@\DLL@
\def\DL@#1{%
 \if&#1&%
 \else
  \l@false\c@false\r@false\Y@false\t@false\m@false\b@false\D@false\LP@false
  \def\${\global\D@true\char'044\relax}%
  \def\({\global\LP@true}%
  \def\){\rlap)}%
  \setbox\TBX@\hbox{\TF@\ignorespaces#1\unskip\FS@}%
  \ifl@\else\ifc@\else\ifr@\else\setbox\TBX@\hbox{\TF@\DLA@{#1}\FS@}\fi\fi\fi
  \RFG@
  \hfil
  \ifX@\FG@\hskip\SLG@\hskip-\SLLG@\fi
  \RWD@\def\UPT@{R}\UP@\RRFG@\ifX@\global\X@false\fi
  \ifc@\hfill\fi
  \ifl@\hfill\fi
 \fi
 \global\advance\CN@\@ne}
\newdimen\DLG@
\DLG@=1em
\def\dollarspace(#1){\DLG@#1\relax}
\def\DLA@#1{\def\){\rlap)}\def\({}\let\$\relax\DLA@@#1..\DLA@@}
\newbox\DGB@
\newbox\PRB@
\def\DLA@@#1.#2.#3\DLA@@{\setbox\DGB@\hbox{0}\setbox\PRB@\hbox{.}%
 \setbox\tw@\hbox{,}%
 \dimen@\DLC@\wd\DGB@
 \count@\DLC@ \advance\count@\m@ne \divide\count@\thr@@
 \advance\dimen@\count@\wd\tw@
 \ifD@\char'044 \fi
 \kern\DLG@
 \ifLP@ \ifD@\setboxz@h{(}\kern-\wdz@\fi (\fi
 \hbox to\dimen@{\hfill#1}%
 \if Z#3Z\kern\tw@\wd\DGB@\kern\wd\PRB@\else.\fi
 #2\unskip}
\def\dollar{\char'044 }
\def\PB@#1#2{\CPB@{#1}{}{#2}}
\def\CPB@#1#2#3{%
 \if&#3&%
 \else
  \ifX@
   \CB@{\TF@#3}\global\X@false
  \else
   \l@false\c@false\r@false
   \setbox\TBX@\vbox{\TF@\NBL@\parskip\z@\edef\indent{\hskip\the\parindent}%
   \parindent\z@\parfillskip\z@ plus1fil\relax\hsize#1\relax
   \FS@@#2\ignorespaces#3\unskip\FS@@
   \ifc@\hfill\null\fi}%
   \def\UPT@{P}\UP@
  \fi
 \fi}
\let\PB@@\PB@
\let\CPB@@\CPB@
\newdimen\RHT@
\newdimen\RDP@
\newdimen\TRHT@
\newdimen\TRDP@
\newdimen\PRHT@
\newdimen\PRDP@
\newdimen\FRHT@
\newcount\YC@
\newdimen\FLD@
\def\AX@{%
 {\ifx\XHL@\empty
  \else
   \advance\YC@\RN@
   \DN@##1,##2"##3{\ifnum##1>\RN@\ifnum##1<\YC@
    \global\advance\dimen@##2\relax\fi\fi
    \ifnum##3=\m@ne\let\nextii@\relax\else\DNii@{\next@##3}\fi
    \nextii@}%
   \expandafter\next@\XHL@\m@ne
  \fi
 }}
\def\RH@{%
 \ifH@
  \dimen@\RHT@ \advance\dimen@\RDP@
  \xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}%
 \else\ifE@\else
  \xdef\HLS@{\HLS@\the\RHT@}\xdef\DLS@{\DLS@\the\RDP@}%
 \fi\fi
 \global\RHT@\z@\global\RDP@\z@}
\def\UH@{%
 \ifnum\RN@=\tw@ \global\FRHT@\FSH \fi
 \ifH@\else\ifE@\else
  \global\PRHT@\TRHT@ \global\PRDP@\TRDP@
  \ifx\HLS@\empty \else \FD@\HLS@ \global\TRHT@\FD@@\p@ \fi
  \ifx\DLS@\empty \else \FD@\DLS@ \global\TRDP@\FD@@\p@ \fi
 \fi\fi}
\def\CWD@@{%
 \ifX@\else
  \ifl@
   \ifdim\wd\TBX@>\csname c-\number\CN@ l\endcsname
    \global\csname c-\number\CN@ l\endcsname\wd\TBX@\fi
  \else\ifr@
   \ifdim\wd\TBX@>\csname c-\number\CN@ r\endcsname
    \global\csname c-\number\CN@ r\endcsname\wd\TBX@\fi
  \else
   \ifdim\wd\TBX@>\csname c-\number\CN@ c\endcsname
   \global\csname c-\number\CN@ c\endcsname\wd\TBX@\fi
  \fi\fi
 \fi}
\def\LWD@@{%
 \ifX@\else
  \ifr@
   \ifdim\wd\TBX@>\csname c-\number\CN@ r\endcsname
    \global\csname c-\number\CN@ r\endcsname\wd\TBX@\fi
  \else\ifc@
   \ifdim\wd\TBX@>\csname c-\number\CN@ c\endcsname
    \global\csname c-\number\CN@ c\endcsname\wd\TBX@\fi
  \else
   \ifdim\wd\TBX@>\csname c-\number\CN@ l\endcsname
    \global\csname c-\number\CN@ l\endcsname\wd\TBX@\fi
  \fi\fi
 \fi}
\def\RWD@@{%
 \ifX@\else
  \ifl@
   \ifdim\wd\TBX@>\csname c-\number\CN@ l\endcsname
    \global\csname c-\number\CN@ l\endcsname\wd\TBX@\fi
  \else\ifc@
   \ifdim\wd\TBX@>\csname c-\number\CN@ c\endcsname
    \global\csname c-\number\CN@ c\endcsname\wd\TBX@\fi
  \else
   \ifdim\wd\TBX@>\csname c-\number\CN@ r\endcsname
    \global\csname c-\number\CN@ r\endcsname\wd\TBX@\fi
  \fi\fi
 \fi}
\newif\ifLX@
\newif\ifCX@
\newif\ifRX@
\newdimen\FGD@
\def\CFG@@{%
 \ifdim \csname c-\number\CN@ l\endcsname > \csname c-\number\CN@ c\endcsname
  \ifdim \csname c-\number\CN@ l\endcsname > \csname c-\number\CN@ r\endcsname
   \DN@{\global\S@false\LX@true}%
   \FGD@ \csname c-\number\CN@ l\endcsname
   \advance\FGD@ -\csname c-\number\CN@ c\endcsname
  \else
   \DN@{\global\S@false\RX@true}%
   \FGD@ \csname c-\number\CN@ r\endcsname
   \advance\FGD@ -\csname c-\number\CN@ c\endcsname
  \fi
 \else
  \ifdim \csname c-\number\CN@ r\endcsname > \csname c-\number\CN@ c\endcsname
   \DN@{\global\S@false\RX@true}%
   \FGD@ \csname c-\number\CN@ r\endcsname
   \advance\FGD@ -\csname c-\number\CN@ c\endcsname
  \else
   \DN@{\CX@true}%
  \fi
 \fi
 \next@}
\def\LCFG@@{%
 \ifX@\else\ifRX@
  \ifl@\else\ifr@\else\hskip\FGD@\fi\fi
 \fi\fi}
\def\RCFG@@{%
 \ifX@\else\ifLX@
  \ifr@\else\ifl@\else\hskip\FGD@\fi\fi
 \fi\fi}
\def\LFG@@{%
 \ifdim\csname c-\number\CN@ c\endcsname > \csname c-\number\CN@ l\endcsname
  \ifdim\csname c-\number\CN@ c\endcsname > \csname c-\number\CN@ r\endcsname
   \DN@{\global\S@false\CX@true}%
   \FGD@ \csname c-\number\CN@ c\endcsname
   \advance\FGD@ -\csname c-\number\CN@ l\endcsname
  \else
   \DN@{\global\S@false\RX@true}%
   \FGD@ \csname c-\number\CN@ r\endcsname
   \advance\FGD@ -\csname c-\number\CN@ l\endcsname
  \fi
 \else
  \ifdim\csname c-\number\CN@ r\endcsname > \csname c-\number\CN@ l\endcsname
   \DN@{\global\S@false\RX@true}%
   \FGD@ \csname c-\number\CN@ r\endcsname
   \advance\FGD@ -\csname c-\number\CN@ l\endcsname
  \else
   \DN@{\LX@true}%
  \fi
 \fi
 \next@}
\def\RFG@@{%
 \ifdim\csname c-\number\CN@ c\endcsname > \csname c-\number\CN@ r\endcsname
  \ifdim\csname c-\number\CN@ c\endcsname > \csname c-\number\CN@ l\endcsname
   \DN@{\global\S@false\CX@true}%
   \FGD@ \csname c-\number\CN@ c\endcsname
   \advance\FGD@ -\csname c-\number\CN@ r\endcsname
  \else
   \DN@{\global\S@false\LX@true}%
   \FGD@ \csname c-\number\CN@ l\endcsname
   \advance\FGD@ -\csname c-\number\CN@ r\endcsname
  \fi
 \else
  \ifdim\csname c-\number\CN@ l\endcsname > \csname c-\number\CN@ r\endcsname
   \DN@{\global\S@false\LX@true}%
   \FGD@ \csname c-\number\CN@ l\endcsname
   \advance\FGD@ -\csname c-\number\CN@ r\endcsname
  \else
   \DN@{\RX@true}%
  \fi
 \fi
 \next@}
\def\LLFG@@{%
 \ifX@
 \else
  \ifCX@
   \ifr@\else\ifc@\else\hskip.5\FGD@\fi\fi
  \fi
  \ifRX@
   \ifr@\else\ifc@\else\hskip\FGD@\fi\fi
  \fi
 \fi}
\def\RRFG@@{%
 \ifX@
 \else
  \ifCX@
   \ifl@\else\ifc@\else\hskip.5\FGD@\fi\fi
  \fi
  \ifLX@
   \ifl@\else\ifc@\else\hskip\FGD@\fi\fi
  \fi
 \fi}
\def\XHL@{}
\def\vs@#1{\vskip#1\relax
 \dimen@=#1\relax\xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}}
\def\vz@{\dimen@\FSH \advance\dimen@\FSD \vskip-\dimen@
 \xdef\XHL@{\XHL@\the\RN@,-\the\dimen@"}}
\def\vZ@{\noalign
 {\dimen@\PRDP@ \advance\dimen@\TRHT@
  \xdef\XHL@{\XHL@\the\RN@,-\the\dimen@"}\vskip-\dimen@}%
 \relax\vrule\depth\PRDP@\height\z@\width\z@\ignorespaces}
\def\cf@#1{\noalign{#1\xdef\TF@{\the\font}\TF@\MS@}}%
\def\hd@(#1#2;#3#4){\relax
 \if#1+%
  \dimen@#2\relax \advance\dimen@\HT@
 \else
  \dimen@#1#2\relax
 \fi
 \if#3+%
  \dimen@ii#4\relax \advance\dimen@ii\DP@
 \else
  \dimen@ii#3#4\fi
 \vrule\height\dimen@\depth\dimen@ii\width\z@}
\def\hl@{\xdef\XHL@{\XHL@\the\RN@,\HTW@"}}
\def\hL@#1{\dimen@#1\relax\xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}}
\def\hls@{\noalign
 {\global\H@true
  \gdef\CLB@##1{\DH@}\gdef\CLBP@##1{\DH@}%
  \global\let\MLB@\DH@ \global\let\CMLB@\DH@
  \gdef\CCB@##1{\DH@}\gdef\CCBP@##1{\DH@}%
  \global\let\MCB@\DH@ \global\let\CMCB@\DH@
  \gdef\CRB@##1{\DH@}\gdef\CRBP@##1{\DH@}%
  \global\let\MRB@\DH@ \global\let\CMRB@\DH@
  \gdef\CPB@##1##2{\DH@}\gdef\DBB@##1{\DH@}\gdef\DLL@##1{\DH@}%
 }%
}
\def\PX@{\noalign
 {\global\let\CLB@\CLB@@ \global\let\CCB@\CCB@@ \global\let\CRB@\CRB@@
 \global\let\CLBP@\CLBP@@ \global\let\CCBP@\CCBP@@ \global\let\CRBP@\CRBP@@
 \global\let\MLB@\MLB@@ \global\let\MCB@\MCB@@ \global\let\MRB@\MRB@@
 \global\let\CMLB@\CMLB@@ \global\let\CMCB@\CMCB@@ \global\let\CMRB@\CMRB@@
 \global\let\CPB@\CPB@@ \global\let\DBB@\DBB@@ \global\let\DLL@\DLL@@
 }%
}
\let\HRH@\HTW@
\let\HRD@\z@
\let\LSG@\z@
\let\RSG@\z@
\let\LHG@\z@
\let\RHG@\z@
\def\DH@#1{\GLG@\GRG@\GSL@\GSR@
 \HP@{#1}%
 \HHDU@
 \hskip\LSG@
 \hskip\LHG@
 \leaders\hrule\height\HRH@\depth\HRD@\hfill
 \hskip\RHG@
 \hskip\RSG@
 \global\advance\CN@\@ne}
\def\HP@#1{\HP@@#1Y\HP@@}
\def\HP@@#1#2\HP@@{\if#1Y\let\HRH@\z@\else\HP@@@#1#2\HP@@@\fi}
\def\HP@@@#1#2Y\HP@@@{%
 \if#1+%
  \edef\LHG@{-\the\LG@}\edef\RHG@{-\the\RG@}%
 \else\if#1_%
   \global\NH@false\edef\LHG@{-\the\LG@}\edef\RHG@{-\the\RG@}%
   \dimen@=-\SL@ \EW@ \edef\LSG@{\the\dimen@}%
   \dimen@=-\SR@ \EW@ \edef\RSG@{\the\dimen@}%
 \else
  \HP@@@@#1#2:Y\HP@@@@
 \fi\fi}
\def\HP@@@@#1:#2#3\HP@@@@{\HP@@@@@#1;Y\HP@@@@@\if#2Y\else
 \HP@@@@@@#2#3\HP@@@@@@\fi}
\def\HP@@@@@#1#2;#3#4\HP@@@@@{\if#1*\else\def\HRH@{#1#2}\fi
 \if#3Y\else\HP@@@@@@@@#3#4\HP@@@@@@@@\fi}
\def\HP@@@@@@@@#1;Y\HP@@@@@@@@{\def\HRD@{#1}}
\def\HP@@@@@@#1#2:Y\HP@@@@@@{%
 \if#1+%
  \edef\LHG@{-\the\LG@}\edef\RHG@{-\the\RG@}%
 \else\if#1_%
  \global\NH@false\edef\LHG@{-\the\LG@}\edef\RHG@{-\the\RG@}%
  \dimen@=-\SL@ \EW@ \edef\LSG@{\the\dimen@}%
  \dimen@=-\SR@ \EW@ \edef\RSG@{\the\dimen@}%
 \else
  \HP@@@@@@@#1#2;Y\HP@@@@@@@
 \fi\fi}
\def\HP@@@@@@@#1;#2#3\HP@@@@@@@{\HP@@@@@@@@@#1YY\HP@@@@@@@@@
 \if#2Y\else\HP@@@@@@@@@@#2#3\HP@@@@@@@@@@\fi}
\def\HP@@@@@@@@@#1#2Y#3\HP@@@@@@@@@{%
 \if#1l%
  \dimen@=-\LG@
  \DN@{#2}\ifx\next@\empty\else\ifx\next@\space\else
   \advance\dimen@\next@\fi\fi
  \edef\LHG@{\the\dimen@}%
 \else\if#1L%
  \global\NH@false\edef\LHG@{-\the\LG@}%
  \dimen@=-\SL@ \EW@
  \DN@{#2}\ifx\next@\empty\else\ifx\next@\space
   \else\advance\dimen@\next@\fi\fi
  \edef\LSG@{\the\dimen@}%
 \else
  \HP@@@@@@@@@@@#1#2Y#3\HP@@@@@@@@@@@
 \fi\fi}
\def\HP@@@@@@@@@@@#1Y#2\HP@@@@@@@@@@@{\def\LHG@{#1}}
\def\HP@@@@@@@@@@#1#2;Y\HP@@@@@@@@@@{%
 \if#1r%
  \dimen@=-\RG@
  \DN@{#2}\ifx\next@\empty\else\ifx\next@\space\else
   \advance\dimen@\next@\fi\fi
  \edef\RHG@{\the\dimen@}%
 \else\if#1R%
  \global\NH@false\edef\RHG@{-\the\RG@}%
  \dimen@=-\SR@ \EW@
  \DN@{#2}\ifx\next@\empty\else\ifx\next@\space\else
   \advance\dimen@\next@\fi\fi
  \edef\RSG@{\the\dimen@}%
 \else
  \def\RHG@{#1#2}%
 \fi\fi}
\def\HHDU@{\ifdim\HRH@>\RHT@\global\RHT@\HRH@\fi
 \ifdim\HRD@>\RDP@\global\RDP@\HRD@\fi}
\def\GS@{\ifE@\else\ifH@\else\expandafter\GS@@\SS@\GS@@\fi\fi}
\def\TSS@{B}
\def\GS@@#1#2\GS@@{\gdef\TSS@{#1}\if T\LS@\gdef\SS@{#2T}\else
 \if M\LS@\gdef\SS@{#2M}\else\gdef\SS@{#2B}\fi\fi}
\newdimen\LG@
\newdimen\RG@
\def\GLG@{%
 \edef\next@{\def\noexpand\next@####1Z\the\CN@"####2Z####3\noexpand\next@
  {\global\noexpand\LG@\noexpand####2}%
  \noexpand\expandafter\noexpand\next@\LGL@ Z\the\CN@"\z@ Z\noexpand\next@}%
 \next@}
\def\GRG@{%
 \edef\next@{\def\noexpand\next@####1Z\the\CN@"####2Z####3\noexpand\next@
  {\global\noexpand\RG@\noexpand####2}%
  \noexpand\expandafter\noexpand\next@\RGL@ Z\the\CN@"\z@ Z\noexpand\next@}%
 \next@}
\newcount\SL@
\newcount\SR@
\def\GSL@{%
 \edef\next@{\def\noexpand\next@####1Z\the\CN@"####2Z####3\noexpand\next@
  {\global\noexpand\SL@####2}%
  \noexpand\expandafter\noexpand\next@\LSL@ Z\the\CN@"\z@ Z\noexpand\next@}%
 \next@}
\def\GSR@{%
 \edef\next@{\def\noexpand\next@####1Z\the\CN@"####2Z####3\noexpand\next@
  {\global\noexpand\SR@####2}%
  \noexpand\expandafter\noexpand\next@\RSL@ Z\the\CN@"\z@ Z\noexpand\next@}%
 \next@}
\newdimen\SLG@
\newcount\SSL@
\newdimen\SLLG@
\newcount\SSLL@
\def\ex@@#1{\noalign
 {\dimen@=#1\relax \xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}\global\E@true}}
\def\PRX@#1{\noalign
 {\dimen@=#1\relax \xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}\global\E@true}}
\def\NS@{\noalign{\global\let\FS@\relax}}
\def\NS@@{\noalign{\global\let\FS@\FS}}
\newdimen\XD@
\def\XXL@{}
\def\xx@#1{\GLG@\GSL@ \global\SSL@\SL@ \global\SLG@\LG@
 \advance\CN@#1\relax \advance\CN@\m@ne
 \GLG@\GSL@ \global\SLLG@\LG@ \global\SSLL@\SL@
 \mscount=#1\relax \multiply\mscount\tw@ \advance\mscount-\tw@
 \loop
 \ifnum\mscount>\@ne\sp@n\repeat
 \span
 {\mscount\CN@ \advance\mscount-#1\relax \advance\mscount\@ne
  \advance\CN@\m@ne
  \loop \xdef\XXL@{\XXL@"\the\mscount,\the\RN@}%
  \ifnum\mscount<\CN@\advance\mscount\@ne\repeat
 }%
 \FS@\ignorespaces}
{
\catcode`\|\active
\gdef\exa@(#1){\noalign
 {\dimen@#1\relax \xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}%
  \count@\@ne \advance\CT@\m@ne
  \toks@{\omit\vrule\height#1\width\z@}%
  \loop \XX@
  \ifXX@
   \global\toks@=\expandafter{\the\toks@\T@B\omit\T@B\omit}%
  \else
   \global\toks@=\expandafter{\the\toks@\T@B Z{}{}\T@B\omit}%
  \fi
  \ifnum\count@<\CT@ \advance\count@\@ne \repeat
 \global\E@true
 }%
 \the\toks@\\}
\gdef\exb@(#1){\noalign
 {\dimen@#1\relax \xdef\XHL@{\XHL@\the\RN@,\the\dimen@"}%
  \count@\@ne \advance\CT@\m@ne \advance\RN@\m@ne
  \toks@{\omit\vrule\height#1\width\z@}%
  \loop \XX@
   \ifXX@
    \global\toks@=\expandafter{\the\toks@\T@B\omit\T@B\omit}%
   \else
    \global\toks@=\expandafter{\the\toks@\T@B Z{}{}\T@B\omit}%
   \fi
  \ifnum\count@<\CT@\advance\count@\@ne\repeat
 \global\E@true
 }%
 \the\toks@\\}
\gdef\hlyy@{\noalign
 {\global\H@true
  \gdef\CLB@##1{\DH@}\gdef\CLBP@##1{\DH@}%
  \global\let\MLB@\DH@\global\let\CMLB@\DH@
  \gdef\CCB@##1{\DH@}\gdef\CCBP@##1{\DH@}%
  \global\let\MCB@\DH@\global\let\CMCB@\DH@
  \gdef\CRB@##1{\DH@}\gdef\CRBP@##1{\DH@}%
  \global\let\MRB@\DH@\global\let\CMRB@\DH@
  \gdef\CPB@##1##2{\DH@}\global\let\DBB@\DH@ \global\let\DLL@\DH@
  \count@\@ne \X@
  \ifXX@ \global\toks@{}\else\global\toks@{_}\fi
  \count@\tw@
  \loop \X@
   \ifXX@
    \global\toks@=\expandafter{\the\toks@\T@B Z{}{}\T@B}%
   \else
    \global\toks@=\expandafter{\the\toks@\T@B Z{}{}\T@B_}%
   \fi
  \ifnum\count@<\CT@\advance\count@\@ne\repeat
 }%
 \the\toks@\cr\PX@}
\gdef\hLyy@(#1){\noalign
 {\global\H@true
  \gdef\CLB@##1{\DH@}\gdef\CLBP@##1{\DH@}%
  \global\let\MLB@\DH@\global\let\CMLB@\DH@
  \gdef\CCB@##1{\DH@}\gdef\CCBP@##1{\DH@}%
  \global\let\MCB@\DH@\global\let\CMCB@\DH@
  \gdef\CRB@##1{\DH@}\gdef\CRBP@##1{\DH@}%
  \global\let\MRB@\DH@\global\let\CMRB@\DH@
  \gdef\CPB@##1##2{\DH@}\global\let\DBB@\DH@\global\let\DLL@\DH@
  \count@\@ne \X@
  \ifXX@\global\toks@{}\else\global\toks@{#1:_}\fi
  \count@\tw@
  \loop \X@
  \ifXX@
   \global\toks@=\expandafter{\the\toks@\T@B Z{}{}\T@B}%
  \else
   \global\toks@=\expandafter{\the\toks@\T@B Z{}{}\T@B#1:_}%
  \fi
  \ifnum\count@<\CT@\advance\count@\@ne\repeat
  }%
 \the\toks@\cr\PX@}
}
\newif\ifXX@
\def\XXHL@{}
\def\yy@#1{\global\Y@true\global\YC@#1\relax
 {\mscount\RN@ \advance\mscount\@ne
  \advance\RN@#1\relax \advance\RN@\m@ne
  \loop\xdef\XXHL@{\XXHL@"\the\CN@,\the\mscount}\ifnum\mscount<\RN@
   \advance\mscount\@ne\repeat
 }%
 \ignorespaces}
\def\X@{\edef\next@{\def\noexpand\next@####1"\the\count@,\the\RN@"####2####3%
 \noexpand\next@{\noexpand\ifnum####2=\m@ne\noexpand\global\noexpand\XX@false
 \noexpand\else\noexpand\global\noexpand\XX@true\noexpand\fi}%
 \noexpand\expandafter\noexpand\next@\XXHL@"\the\count@,\the\RN@"\m@ne
 \noexpand\next@}\next@\relax}
\def\XX@{\edef\next@{\def\noexpand\next@####1"\the\count@,\the\RN@"####2####3%
 \noexpand\next@{\noexpand\ifnum####2=\m@ne\noexpand\global\noexpand\XX@false
 \noexpand\else\noexpand\global\noexpand\XX@true\noexpand\fi}%
 \noexpand\expandafter\noexpand\next@\XXL@"\the\count@,\the\RN@"\m@ne
 \noexpand\next@}\next@\relax}
\def\tdefine#1{\define@#1{}\tredefine#1}
\def\tredefine#1{\def\tdf@{#1}\catcode`\&\active\catcode`\|\active
 \catcode`\"\active\afterassignment\tdef@\def\tdf@@}
\def\tdef@{\expandafter\let\tdf@\tdf@@
 \catcode`\&=4 \catcode`\|=12 \catcode`\"=12 }
\def\colwidth(#1){\hskip#1\null}
\def\dotleads{\Leads{5pt}.}
\def\Leads#1#2{\leaders\hbox to#1{\hfil#2\hfil}\hfill\null}
\predefine\Polishl\l
\predefine\PolishL\L
\predefine\tieaccent\t
\predefine\barunder\b
\predefine\umlaut\"
\predefine\cedilla\c
\predefine\dotunder\d
\WT@\*
\WT@\cong
\WT@\longleftarrow
\WT@\longmapsto
\WT@\longrightarrow
\WT@\mathstrut
\WT@\notin
\WT@\overbrace
\WT@\overleftarrow
\WT@\overrightarrow
\WT@\overleftrightarrow
\WT@\rightleftharpoons
\WT@\underleftarrow
\WT@\underrightarrow
\WT@\underleftrightarrow
\WT@\rightleftharpoons
\WT@\underbrace
\WT@\copyright
\WT@\dots
\WT@\frenchspacing
\WT@\nonfrenchspacing
\WT@\medspace
\WT@\;
\WT@\negmedspace
\WT@\thickspace
\WT@\negthickspace
\WT@\slanted
\WT@\rom
\WT@\italic
\WT@\frak
\WT@\goth
\WT@\Bbb
\WT@\Hat
\WT@\oldnos
\WT@\pmb
\def\vphantom{\relax\v@true\h@false\ph@nt}
\def\hphantom{\relax\v@false\h@true\ph@nt}
\def\phantom{\relax\v@true\h@true\ph@nt}
\WT@\vphantom
\WT@\hphantom
\WT@\phantom
{\catcode`\'=\active \gdef'{\NX@\wit@prime}%
 \gdef\wit@prime{^\bgroup\prim@s}}
\WT@\text
\WT@\Cal
\WT@\bold
\WT@\iint
\WT@\iiint
\WT@\iiiint
\WT@\idotsint
\WT@\{
\WT@\}
\WT@\,
\WT@\!
\WT@\ldots
\WT@\cdots
\WT@\dotsm
\WT@\dotso
\WT@\dotsc
\WT@\Hat
\WT@\Check
\WT@\Tilde
\WT@\Acute
\WT@\Grave
\WT@\Dot
\WT@\Ddot
\WT@\Breve
\WT@\Bar
\WT@\Vec
\WT@\nolimits@
\def\alloc@#1#2#3#4#5{\global\advance\count1#1by\@ne
 \ch@ck#1#4#2\allocationnumber=\count1#1
 \global#3#5=\allocationnumber
 \wlog{\string#5=\string#2\the\allocationnumber}}
\catcode`\@=\active