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+% AMSTEXL.TEX VERSION 2.0
+% Copyright (C) 1990, 1991 American Mathematical Society
+% All rights reserved.
+\catcode`\@=11
+\ifx\amstexloaded@\relax\catcode`\@=\active
+ \endinput\else\let\amstexloaded@\relax\fi
+\def\W@{\immediate\write\sixt@@n}
+\def\CR@{\W@{}\W@{AmS-TeX - Version 2.0L\space\space[LamS-TeX subset]}\W@{}
+\W@{COPYRIGHT 1985, 1990 - AMERICAN MATHEMATICAL SOCIETY}
+\W@{Use of this macro package is not restricted provided}
+\W@{each use is acknowledged upon publication.}\W@{}}
+\CR@
+\everyjob{\CR@}
+\toksdef\toks@@=2
+\long\def\rightappend@#1\to#2{\toks@{\\{#1}}\toks@@\expandafter{#2}%
+ \xdef#2{\the\toks@@\the\toks@}\toks@{}\toks@@{}}
+\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\@ for a printed @?^^J
+I've ignored the character or group after @.}
+\def\atdef@#1{\expandafter\def\csname #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\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@}
+\let\redefine\def
+\def\predefine#1#2{\let#1#2}
+\def\undefine#1{\let#1\undefined}
+\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\pagebreak{\RIfM@
+ \ifinner\nondmatherr@\pagebreak\else\postdisplaypenalty-\@M\fi
+ \else\ifvmode\removelastskip\break\else\vadjust{\break}\fi\fi}
+\def\nopagebreak{\RIfM@
+ \ifinner\nondmatherr@\nopagebreak\else\postdisplaypenalty\@M\fi
+ \else\ifvmode\nobreak\else\vadjust{\nobreak}\fi\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\newpage{\vnonvmode@{\vfill\break}{\nonvmodeerr@\newpage}}
+\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}
+\def\topsmash{\top@true\bot@false\smash@}
+\def\botsmash{\top@false\bot@true\smash@}
+\newif\iftop@
+\newif\ifbot@
+\def\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
+\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@{\mathcode`\'="0027 \mathcode`\*="002A \mathcode`\.="613A
+ \mathcode`\-="002D \mathcode`\/="002F \mathcode`\:="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}}
+\def\varinjlim{\mathop{\vtop{\ialign{##\crcr
+ \hfil\rm lim\hfil\crcr\noalign{\nointerlineskip}\rightarrowfill\crcr
+ \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
+\def\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}
+\newif\ifinany@
+\newif\ifinalign@
+\newif\ifingather@
+\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@
+ \ifinany@\else\openup\jot\fi\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@
+ \ifinany@\else\openup\jot\fi\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@
+ \ifinany@\else\openup\jot\fi\ialign
+ \bgroup\hfil\strut@$\m@th\displaystyle{##}$\hfil\crcr}
+\def\endgathered{\crcr\egroup\egroup}
+\newif\iftagsleft@
+\def\TagsOnLeft{\global\tagsleft@true}
+\def\TagsOnRight{\global\tagsleft@false}
+\TagsOnLeft
+\newif\ifmathtags@
+\def\TagsAsMath{\global\mathtags@true}
+\def\TagsAsText{\global\mathtags@false}
+\TagsAsText
+\def\tag#1$${\iftagsleft@\leqno\else\eqno\fi\maketag@#1\maketag@$$}
+\interdisplaylinepenalty\@M
+\def\allowdisplaybreaks{\RIfMIfI@
+ \onlydmatherr@\allowdisplaybreaks\else
+ \interdisplaylinepenalty\z@\fi\else\onlydmatherr@\allowdisplaybreaks\fi}
+\Invalid@\allowdisplaybreak
+\Invalid@\displaybreak
+\Invalid@\intertext
+\def\allowdisplaybreak@{\def\allowdisplaybreak{\crcr\noalign{\allowbreak}}}
+\def\displaybreak@{\def\displaybreak{\crcr\noalign{\break}}}
+\def\intertext@{\def\intertext##1{\crcr\noalign{\vskip\belowdisplayskip
+ \vbox{\normalbaselines\noindent##1}\vskip\abovedisplayskip}}}
+\newskip\centering@
+\centering@\z@ plus\@m\p@
+\def\align{\relax\ifingather@\DN@{\csname align (in
+ \expandafter\eat@\string\\gather)\endcsname}\else
+ \ifmmode\ifinner\DN@{\onlydmatherr@\align}\else
+ \let\next@\align@\fi
+ \else\DN@{\onlydmatherr@\align}\fi\fi\next@}
+\newhelp\andhelp@
+{An extra & here is so disastrous that you should probably exit^^J
+and fix things up.}
+\newif\iftag@
+\newcount\and@
+\def\Tag@{\iftag@\else\errhelp\andhelp@\err@{Extra & on this line}\fi}
+\newdimen\lwidth@
+\newdimen\rwidth@
+\newdimen\maxlwidth@
+\newdimen\maxrwidth@
+\newdimen\totwidth@
+\def\displ@y@{\global\dt@ptrue\openup\jot
+ \everycr{\noalign{\global\tag@false\global\and@\z@\ifdt@p\global\dt@pfalse
+ \vskip-\lineskiplimit\vskip\normallineskiplimit\else
+ \penalty\interdisplaylinepenalty\fi}}}
+\def\black@#1{\noalign{\ifdim#1>\displaywidth
+ \dimen@\prevdepth\nointerlineskip
+ \vskip-\ht\strutbox@\vskip-\dp\strutbox@
+ \vbox{\noindent\hbox to#1{\strut@\hfill}}%
+ \prevdepth\dimen@
+ \fi}}
+\newdimen\lineht@
+\expandafter\def\csname align (in \expandafter\eat@\string\\gather)\endcsname
+ #1\endalign{\vcenter{\align@#1\endalign}}
+\Invalid@\endalign
+\newif\ifxat@
+\def\alignat{\RIfMIfI@\DN@{\onlydmatherr@\alignat}\else
+ \DN@{\csname alignat \endcsname}\fi\else
+ \DN@{\onlydmatherr@\alignat}\fi\next@}
+\newif\ifmeasuring@
+\newbox\savealignat@
+\Invalid@\endalignat
+\def\xalignat{\RIfMIfI@
+ \DN@{\onlydmatherr@\xalignat}\else
+ \DN@{\csname xalignat \endcsname}\fi\else
+ \DN@{\onlydmatherr@\xalignat}\fi\next@}
+\Invalid@\endxalignat
+\def\xxalignat{\RIfMIfI@
+ \DN@{\onlydmatherr@\xxalignat}\else\DN@{\csname xxalignat
+ \endcsname}\fi\else
+ \DN@{\onlydmatherr@\xxalignat}\fi\next@}
+\expandafter\def\csname xxalignat \endcsname#1#2\endxxalignat{\inany@true
+ \vspace@\allowdisplaybreak@\displaybreak@\intertext@
+ \displ@y\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
+ \xxattag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
+ \Let@\xxattag@{#1}\tabskip\z@skip\halign to\displaywidth
+ {\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
+\def\xxattag@#1{\toks@{\tabskip\z@skip\hfil\strut@
+ $\m@th\displaystyle{\the\hashtoks@}$&%
+ $\m@th\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\centering@&}%
+ \atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
+ \toks@=\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\the\hashtoks@}$%
+ \tabskip\z@skip&$\m@th\displaystyle{{}\the\hashtoks@}$\hfil
+ \tabskip\centering@}\advance\atcount@\m@ne\repeat
+ \edef\preamble@{\the\toks@\tabskip\z@skip}\edef\preamble@@{\preamble@}}
+\Invalid@\endxxalignat
+\newdimen\gwidth@
+\newdimen\gmaxwidth@
+\def\gmeasure@#1\endgather{\global\gwidth@\z@\global\gmaxwidth@\z@
+ \setbox\z@\vbox{\Let@
+ \halign{\setboxz@h{$\m@th\displaystyle{##}$}\global\gwidth@\wdz@
+ \ifdim\gwidth@>\gmaxwidth@\global\gmaxwidth@\gwidth@\fi
+ &\eat@{##}\crcr#1\crcr}}}
+\expandafter\def\csname gather \space\endcsname#1\endgather
+ {\gmeasure@#1\endgather\tabskip\centering@
+ \halign to\displaywidth{\hfil\strut@\setboxz@h{$\m@th\displaystyle{##}$}%
+ \global\gwidth@\wdz@\boxz@\hfil&
+ \setboxz@h{\strut@{\maketag@##\maketag@}}%
+ \dimen@\displaywidth\advance\dimen@-\gwidth@
+ \ifdim\dimen@>\tw@\wdz@\llap{\boxz@}\else
+ \llap{\vtop{\normalbaselines\null\boxz@}}\fi
+ \tabskip\z@skip\crcr#1\crcr\black@\gmaxwidth@}}
+\newdimen\glineht@
+\expandafter\def\csname gather \endcsname#1\endgather{\gmeasure@#1\endgather
+ \ifdim\gmaxwidth@>\displaywidth\let\gdisplaywidth@\gmaxwidth@\else
+ \let\gdisplaywidth@\displaywidth\fi\tabskip\centering@\halign to\displaywidth
+ {\hfil\strut@\setboxz@h{$\m@th\displaystyle{##}$}%
+ \global\gwidth@\wdz@\global\glineht@\ht\z@\boxz@\hfil&\kern-\gdisplaywidth@
+ \setboxz@h{\strut@{\maketag@##\maketag@}}%
+ \dimen@\displaywidth\advance\dimen@-\gwidth@
+ \ifdim\dimen@>\tw@\wdz@\rlap{\boxz@}\else
+ \rlap{\vbox{\normalbaselines\boxz@\vbox to\glineht@{}}}\fi
+ \tabskip\gdisplaywidth@\crcr#1\crcr\black@\gmaxwidth@}}
+\newif\ifctagsplit@
+\def\CenteredTagsOnSplits{\global\ctagsplit@true}
+\def\TopOrBottomTagsOnSplits{\global\ctagsplit@false}
+\TopOrBottomTagsOnSplits
+\def\split{\relax\ifinany@\let\next@\insplit@\else
+ \ifmmode\ifinner\def\next@{\onlydmatherr@\split}\else
+ \let\next@\outsplit@\fi\else
+ \def\next@{\onlydmatherr@\split}\fi\fi\next@}
+\def\insplit@{\global\setbox9=\vbox\bgroup\vspace@\Let@\ialign\bgroup
+ \hfil\strut@$\m@th\displaystyle{##}$&$\m@th\displaystyle{{}##}$\hfill\crcr}
+\def\endsplit{\crcr\egroup\egroup\iftagsleft@\expandafter\lendsplit@\else
+ \expandafter\rendsplit@\fi}
+\def\rendsplit@{\global\setbox\@ne\vbox
+ {\unvcopy9 \global\setbox\thr@@\lastbox\unskip}%
+ \setboxz@h{\unhcopy\thr@@\unskip\global\setbox\thr@@\lastbox
+ \unskip\global\setbox5=\lastbox}%
+ \global\setbox7=\hbox{\unhbox\thr@@\unskip}%
+ \ifinalign@\ifctagsplit@
+ \gdef\split@{\hbox to\wd5 {}&
+ \vcenter{\vbox{\moveleft\wd5 \box9}}}%
+ \else\gdef\split@{&\vbox{\moveleft\wd5 \box\@ne}\crcr
+ \box5 &\box7}\fi
+ \else
+ \ifctagsplit@\gdef\split@{\vcenter{\box9}}\else
+ \gdef\split@{\box\@ne\crcr\hbox{\box\thr@@\box7}}\fi
+ \fi
+ \split@}
+\def\lendsplit@{\global\setbox\@ne\vtop{\unvcopy9}%
+ \setbox\z@\vbox{\unvcopy9 \global\setbox\thr@@\lastbox}%
+ \setboxz@h{\unhcopy\thr@@\unskip\setbox\z@\lastbox
+ \unskip\global\setbox\thr@@\lastbox}%
+ \ifinalign@\ifctagsplit@
+ \gdef\split@{\hbox to\wd\thr@@{}&
+ \vcenter{\vbox{\moveleft\wd\thr@@\box\@ne}}}%
+ \else
+ \gdef\split@{\hbox to\wd\thr@@{}&\vbox{\moveleft\wd\thr@@\box\@ne}}\fi
+ \else
+ \ifctagsplit@\gdef\split@{\vcenter{\box\@ne}}\else
+ \gdef\split@{\box\@ne}\fi
+ \fi\split@}
+\def\outsplit@#1$${\align\insplit@#1\endalign$$}
+\newdimen\multlinegap@
+\multlinegap@1em
+\newdimen\multlinetaggap@
+\multlinetaggap@1em
+\def\MultlineGap#1{\global\multlinegap@#1\relax}
+\def\multlinegap#1{\RIfMIfI@\onlydmatherr@\multlinegap\else
+ \multlinegap@#1\relax\fi\else\onlydmatherr@\multlinegap\fi}
+\def\nomultlinegap{\multlinegap{\z@}}
+\def\multline{\RIfMIfI@
+ \DN@{\onlydmatherr@\multline}\else
+ \DN@{\multline@}\fi\else
+ \DN@{\onlydmatherr@\multline}\fi\next@}
+\newif\iftagin@
+\def\multline@#1$${\inany@true\vspace@\allowdisplaybreak@\displaybreak@
+ \tagin@{#1}\iftagsleft@\DN@{\multline@l#1$$}\else
+ \DN@{\multline@r#1$$}\fi\next@}
+\newdimen\mwidth@
+\def\rmmeasure@#1\endmultline{%
+ \def\shoveleft##1{##1}\def\shoveright##1{##1}%
+ \setbox\z@\vbox{\Let@\halign{\setboxz@h
+ {$\m@th\@lign\displaystyle{}##$}\global\mwidth@\wdz@
+ \crcr#1\crcr}}}
+\newdimen\mlineht@
+\newif\ifzerocr@
+\newif\ifonecr@
+\def\lmmeasure@#1\endmultline{\global\zerocr@true\global\onecr@false
+ \everycr{\noalign{\ifonecr@\global\onecr@false\fi
+ \ifzerocr@\global\zerocr@false\global\onecr@true\fi}}%
+ \def\shoveleft##1{##1}\def\shoveright##1{##1}%
+ \setbox\z@\vbox{\Let@\halign{\setboxz@h
+ {$\m@th\@lign\displaystyle{}##$}\ifonecr@\global\mwidth@\wdz@
+ \global\mlineht@\ht\z@\fi\crcr#1\crcr}}}
+\newbox\mtagbox@
+\newdimen\ltwidth@
+\newdimen\rtwidth@
+\def\multline@l#1$${\iftagin@\DN@{\lmultline@@#1$$}\else
+ \DN@{\setbox\mtagbox@\null\ltwidth@\z@\rtwidth@\z@
+ \lmultline@@@#1$$}\fi\next@}
+\def\lmultline@@#1\endmultline\tag#2$${%
+ \setbox\mtagbox@\hbox{\maketag@#2\maketag@}%
+ \lmmeasure@#1\endmultline\dimen@\mwidth@\advance\dimen@\wd\mtagbox@
+ \advance\dimen@\multlinetaggap@
+ \ifdim\dimen@>\displaywidth\ltwidth@\z@\else\ltwidth@\wd\mtagbox@\fi
+ \lmultline@@@#1\endmultline$$}
+\def\lmultline@@@{\displ@y
+ \def\shoveright##1{##1\hfilneg\hskip\multlinegap@}%
+ \def\shoveleft##1{\setboxz@h{$\m@th\displaystyle{}##1$}%
+ \setbox\tw@\hbox{$\m@th\displaystyle##1$}%
+ \hfilneg
+ \iftagin@
+ \ifdim\ltwidth@>\z@\hskip\ltwidth@\hskip\multlinetaggap@\fi
+ \else\hskip\multlinegap@\fi\hskip.5\wd\tw@\hskip-.5\wdz@##1}%
+ \halign\bgroup\Let@\hbox to\displaywidth
+ {\strut@$\m@th\displaystyle\hfil{}##\hfil$}\crcr
+ \hfilneg
+ \iftagin@
+ \ifdim\ltwidth@>\z@
+ \box\mtagbox@\hskip\multlinetaggap@
+ \else
+ \rlap{\vbox{\normalbaselines\hbox{\strut@\box\mtagbox@}%
+ \vbox to\mlineht@{}}}\fi
+ \else\hskip\multlinegap@\fi}
+\def\multline@r#1$${\iftagin@\DN@{\rmultline@@#1$$}\else
+ \DN@{\setbox\mtagbox@\null\ltwidth@\z@\rtwidth@\z@
+ \rmultline@@@#1$$}\fi\next@}
+\def\rmultline@@#1\endmultline\tag#2$${\ltwidth@\z@
+ \setbox\mtagbox@\hbox{\maketag@#2\maketag@}%
+ \rmmeasure@#1\endmultline\dimen@\mwidth@\advance\dimen@\wd\mtagbox@
+ \advance\dimen@\multlinetaggap@
+ \ifdim\dimen@>\displaywidth\rtwidth@\z@\else\rtwidth@\wd\mtagbox@\fi
+ \rmultline@@@#1\endmultline$$}
+\def\rmultline@@@{\displ@y
+ \def\shoveright##1{##1\hfilneg\iftagin@\ifdim\rtwidth@>\z@
+ \hskip\rtwidth@\hskip\multlinetaggap@\fi\else\hskip\multlinegap@\fi}%
+ \def\shoveleft##1{\setboxz@h{$\m@th\displaystyle{}##1$}%
+ \setbox\tw@\hbox{$\m@th\displaystyle##1$}%
+ \hfilneg\hskip\multlinegap@\hskip.5\wd\tw@\hskip-.5\wdz@##1}%
+ \halign\bgroup\Let@\hbox to\displaywidth
+ {\strut@$\m@th\displaystyle\hfil{}##\hfil$}\crcr
+ \hfilneg\hskip\multlinegap@}
+\def\endmultline{\iftagsleft@\expandafter\lendmultline@\else
+ \expandafter\rendmultline@\fi}
+\def\lendmultline@{\hfilneg\hskip\multlinegap@\crcr\egroup}
+\def\rendmultline@{\iftagin@
+ \ifdim\rtwidth@>\z@
+ \hskip\multlinetaggap@\box\mtagbox@
+ \else\llap{\vtop{\normalbaselines\null\hbox{\strut@\box\mtagbox@}}}\fi
+ \else\hskip\multlinegap@\fi
+ \hfilneg\crcr\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\global\advance\cfraccount@\@ne\strut
+ \iffalse{\fi\def\\{\over\displaystyle}\iffalse}\fi}
+\def\lcfrac{\bgroup\bgroup\global\advance\cfraccount@\@ne\strut
+ \iffalse{\fi\def\\{\hfill\over\displaystyle}\iffalse}\fi}
+\def\rcfrac{\bgroup\bgroup\global\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}
+\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
+\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 \skewchar\tencmmib='177
+ \font@\sevencmmib=cmmib7 \skewchar\sevencmmib='177
+ \font@\fivecmmib=cmmib5 \skewchar\fivecmmib='177
+ \alloc@@8\fam\chardef\sixt@@n\cmmibfam
+ \textfont\cmmibfam=\tencmmib
+ \scriptfont\cmmibfam=\sevencmmib
+ \scriptscriptfont\cmmibfam=\fivecmmib
+ \edef\cmmibfam@{\hexnumber@\cmmibfam}%
+ \font@\tencmbsy=cmbsy10 \skewchar\tencmbsy='60
+ \font@\sevencmbsy=cmbsy7 \skewchar\sevencmbsy='60
+ \font@\fivecmbsy=cmbsy5 \skewchar\fivecmbsy='60
+ \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 \noexpand\boldsymbol 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 \noexpand\boldsymbol 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}
+\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@{\global\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
+ \global\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@{\global\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
+ \global\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}$}\dimen@.4\ex@
+ \advance\dimen@3\ex@\advance\dimen@\dp\z@
+ \hbox{\lower\dimen@\hbox{%
+ \vbox{\hrule\height.4\ex@
+ \hbox{\vrule\width.4\ex@\hskip3\ex@\vbox{\vskip3\ex@\boxz@\vskip3\ex@}%
+ \hskip3\ex@\vrule\width.4\ex@}\hrule\height.4\ex@}%
+ }}}
+\newdimen\minaw@
+\minaw@11.11128\ex@
+\def\pmb{\RIfM@\expandafter\mathpalette\expandafter\pmb@\else
+ \expandafter\pmb@@\fi}
+\def\pmb@@#1{\leavevmode\setboxz@h{#1}\kern-.025em\copy\z@\kern-\wdz@
+ \kern-.05em\copy\z@\kern-\wdz@\kern-.025em\raise.0433em\boxz@}
+\def\binrel@@#1{\ifdim\wd\tw@<\z@\mathbin{#1}\else\ifdim\wd\tw@>\z@
+ \mathrel{#1}\else{#1}\fi\fi}
+\newdimen\pmbraise@
+\def\pmb@#1#2{\setbox4=\hbox{$\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}}
+\font\dummyft@=dummy
+\fontdimen1 \dummyft@=\z@
+\fontdimen2 \dummyft@=\z@
+\fontdimen3 \dummyft@=\z@
+\fontdimen4 \dummyft@=\z@
+\fontdimen5 \dummyft@=\z@
+\fontdimen6 \dummyft@=\z@
+\fontdimen7 \dummyft@=\z@
+\fontdimen8 \dummyft@=\z@
+\fontdimen9 \dummyft@=\z@
+\fontdimen10 \dummyft@=\z@
+\fontdimen11 \dummyft@=\z@
+\fontdimen12 \dummyft@=\z@
+\fontdimen13 \dummyft@=\z@
+\fontdimen14 \dummyft@=\z@
+\fontdimen15 \dummyft@=\z@
+\fontdimen16 \dummyft@=\z@
+\fontdimen17 \dummyft@=\z@
+\fontdimen18 \dummyft@=\z@
+\fontdimen19 \dummyft@=\z@
+\fontdimen20 \dummyft@=\z@
+\fontdimen21 \dummyft@=\z@
+\fontdimen22 \dummyft@=\z@
+\def\dodummy@{{\def\\##1{\global\let##1\dummyft@}\fontlist@}}
+\def\nopages@{\output={\setbox\z@\box255 \deadcycles\z@}%
+ \alloc@@5\toks\toksdef\@cclvi\output}
+\let\galleys\nopages@
+\newif\ifsyntax@
+\newcount\countxviii@
+\def\syntax{\syntax@true\dodummy@\countxviii@\count18
+ \loop\ifnum\countxviii@>\m@ne\textfont\countxviii@=\dummyft@
+ \scriptfont\countxviii@=\dummyft@\scriptscriptfont\countxviii@=\dummyft@
+ \advance\countxviii@\m@ne\repeat
+ \dummyft@\tracinglostchars\z@\nopages@\frenchspacing\hbadness\@M}
+\def\S@{S } \def\G@{G } \def\P@{P }
+\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}}
+\let\proclaim\undefined
+\let\=\undefined
+\let\>\undefined
+\let\cal\undefined
+\let\mit\undefined
+\let\oldstyle\undefined
+\catcode`\@=\active