\input plain
% AMS-TEX VERSION 1.1
% COPYRIGHT (C) 1985 BY AMERICAN MATHEMATICAL SOCIETY
\catcode`\@=11
\ifx\amstexloaded@\relax\catcode`\@=\active
 \endinput\else\let\amstexloaded@\relax\fi
\def\W@{\immediate\write\sixt@@n}
\def\spaces@{\space\space\space\space\space}
\def\spaces@@{\spaces@\spaces@\spaces@\spaces@\spaces@}
\def\CR@{\W@{}\W@{\spaces@@ AmS-TeX - Version 1.1}\W@{}
\W@{COPYRIGHT 1985 - AMERICAN MATHEMATICAL SOCIETY ("AMS") - ALL RIGHTS
 RESERVED.}
\W@{USE OF A COPY OF AmS-TeX CONSTITUTES AN AGREEMENT TO THE TERMS OF A LEASE}
\W@{THEREOF FROM AMS TO THE LESSEE (i.e., THE ENTITY RECEIVING POSSESSION OF
 AN}
\W@{AUTHORIZED COPY OF AmS-TeX).  SUCH LEASE LIMITS USE TO NON-PROFIT,
 IN-HOUSE}
\W@{USES BY LESSEE.  ANY OTHER USE IS UNAUTHORIZED AND WILL RESULT IN
 TERMINATION}
\W@{OF SUCH LEASE ON NOTICE FROM AMS.}\W@{}
\W@{PLEASE ADDRESS REQUESTS FOR COMMERCIAL OR ADDITIONAL RIGHTS TO}
\W@{AMS, P.O. BOX 6248, PROVIDENCE, RI 02940, ATTN: EXECUTIVE DIRECTOR.}\W@{}}
\CR@
\everyjob{\CR@}
\toksdef\toks@@=2
\long\def\rightappend@#1\to#2{\toks@{\\{#1}}\toks@@
 =\expandafter{#2}\xdef#2{\the\toks@@\the\toks@}}
\newif\ifalloc@
\def\showallocations{{\def\\{\immediate\write-1}\alloclist@}\alloc@true}
\def\alloclist@{\empty}
\def\alloc@#1#2#3#4#5{\global\advance\count1#1by\@ne
 \ch@ck#1#4#2\allocationnumber=\count1#1
 \global#3#5=\allocationnumber
 \edef\appendit@{\string#5=\string#2\the\allocationnumber}%
 \expandafter\rightappend@\appendit@\to\alloclist@}
\newcount\m@ne
\m@ne-1
\newlinechar=`\^^J
\def\err@#1{\errmessage{AmS-TeX error: #1}}
\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\Err@#1{\errhelp\defaulthelp@\errmessage{AmS-TeX error: #1}}
\def\eat@#1{}
\newif\ifin@
\def\in@#1#2{\def\in@@##1#1##2##3\in@@{\ifx\in@##2\in@false\else\in@true\fi}%
 \in@@#2#1\in@\in@@}
\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\futureletnextat@{\futurelet\next\at@}
{\catcode`\@=\active
\lccode`\Z=`\@ \lccode`\I=`\I \lowercase
{\gdef@{\expandafter\csname futureletnextatZ\endcsname}\expandafter
 \gdef\csname atZ\endcsname
 {\ifcat\noexpand\next a\def\next{\csname atZZ\endcsname}\else
 \ifcat\noexpand\next0\def\next{\csname atZZ\endcsname}\else
 \ifcat\noexpand\next\relax\def\next{\csname atZZZ\endcsname}\else
 \def\next{\csname atZZZZ\endcsname}\fi\fi\fi\next}
\expandafter\gdef\csname atZZ\endcsname#1{\expandafter
 \ifx\csname #1Zat\endcsname\relax\def\next
 {\errhelp\expandafter=\csname athelpZ\endcsname
 \csname errZ\endcsname{Invalid use of \string@}}\else
 \def\next{\csname #1Zat\endcsname}\fi\next}
\expandafter\gdef\csname atZZZ\endcsname#1{\expandafter
 \ifx\csname \string#1ZZat\endcsname\relax\def\next
 {\errhelp\expandafter=\csname athelpZ\endcsname
 \csname errZ\endcsname{Invalid use of \string@}}\else
 \def\next{\csname \string#1ZZat\endcsname}\fi\next}
\expandafter\gdef\csname atZZZZ\endcsname#1{\errhelp
 \expandafter=\csname athelpZ\endcsname
 \csname errZ\endcsname{Invalid use of \string@}}}}
\def\atdef@#1{\expandafter\def\csname #1@at\endcsname}
\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{\futurelet\next\define@}
\def\define@{\ifcat\noexpand\next\relax
 \def\next@{\define@@}\else\errhelp\defahelp@
 \err@{\string\define\space must be followed by a control
 sequence}\def\next@{\def\garbage@}\fi\next@}
\def\undefined@{}
\def\preloaded@{}
\def\define@@#1{\ifx#1\relax\errhelp\defbhelp@
 \err@{\string#1\space is already defined}\def\next@{\def\garbage@}\else
 \expandafter\ifx\csname\expandafter\eat@\string
 #1@\endcsname\undefined@\errhelp\defbhelp@
 \err@{\string#1\space can't be defined}\def\next@{\def\garbage@}\else
 \expandafter\ifx\csname\expandafter\eat@\string#1\endcsname\relax
 \def\next@{\def#1}\else\errhelp\defbhelp@
 \err@{\string#1\space is already defined}\def\next@{\def\garbage@}\fi
 \fi\fi\next@}
\let\redefine\def
\def\predefine#1#2{\let#1#2}
\def\pagewidth#1{\hsize#1\relax}
\def\pageheight#1{\vsize#1\relax}
\def\hcorrection#1{\advance\hoffset#1\relax}
\def\vcorrection#1{\advance\voffset#1\relax}
\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?}
{\catcode`\@=\active
\gdef\@{\char'100 }}
\def\relaxnext@{\let\next\relax}
\atdef@-{\relaxnext@\leavevmode
 \def\next@{\ifx\next-\def\next-{\futurelet\next\nextii@}\else
  \def\next{\hbox{-}}\fi\next}%
 \def\nextii@{\ifx\next-\def\next-{\hbox{---}}\else
  \def\next{\hbox{--}}\fi\next}%
 \futurelet\next\next@}
\def\srdr@{\kern.16667em}
\def\drsr@{\kern.02778em}
\def\sldl@{\kern.02778em}
\def\dlsl@{\kern.16667em}
\atdef@"{\unskip\relaxnext@
 \def\next@{\ifx\next\space@\def\next. {\futurelet\next\nextii@}\else
  \def\next.{\futurelet\next\nextii@}\fi\next.}%
 \def\nextii@{\ifx\next`\def\next`{\futurelet\next\nextiii@}\else
  \ifx\next\lq\def\next\lq{\futurelet\next\nextiii@}\else\def\next
   ####1{\futurelet\next\nextiv@}\fi\fi\next}%
 \def\nextiii@{\ifx\next`\def\next`{\sldl@``}\else\ifx\next\lq
  \def\next\lq{\sldl@``}\else\def\next{\dlsl@`}\fi\fi\next}%
 \def\nextiv@{\ifx\next'\def\next'{\srdr@''}\else
  \ifx\next\rq\def\next\rq{\srdr@''}\else\def\next{\drsr@'}\fi\fi\next}%
 \futurelet\next\next@}
\def\flushpar{\par\noindent}
\def\textfontii{\the\textfont\tw@}
\def\lbrace@{\delimiter"4266308 }
\def\rbrace@{\delimiter"5267309 }
\def\{{\relax\ifmmode\lbrace@\else{\textfontii f}\spacefactor\@m\fi}
\def\}{\relax\ifmmode\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@{\string#1\space not allowed between paragraphs}}
\def\mathmodeerr@#1{\Err@{\string#1\space not allowed in math mode}}
\def\linebreak{\relax\ifmmode\mathmodeerr@\linebreak\else\ifhmode
 \unskip\unkern\break\else\vmodeerr@\linebreak\fi\fi}
\def\slash{\unskip/\penalty\exhyphenpenalty}
\newskip\saveskip@
\def\allowlinebreak{\relax\ifmmode\mathmodeerr@\allowlinebreak\else
 \ifhmode\saveskip@\lastskip\unskip
 \allowbreak\ifdim\saveskip@>\z@\hskip\saveskip@\fi
 \else\vmodeerr@\allowlinebreak\fi\fi}
\let\refskip@\relax
\def\nolinebreak{\relax\ifmmode\mathmodeerr@\nolinebreak\else
 \ifhmode\saveskip@\lastskip\unskip
 \nobreak\ifdim\saveskip@>\z@\hskip\saveskip@\refskip@\fi
 \else\vmodeerr@\nolinebreak\fi\fi}
\def\newline{\relaxnext@
 \def\next@{\relax\ifmmode\def\next@{\mathmodeerr@\newline}\else
  \ifhmode\ifx\next\par\def\next@{}\else\def\next@
  {\unskip\null\hfill\break}\fi\else
  \def\next@{\vmodeerr@\newline}\fi\fi\next@}%
 \futurelet\next\next@}
\def\dmatherr@#1{\Err@{\string#1\space not allowed in display math mode}}
\def\nondmatherr@#1{\Err@{\string#1\space not allowed in non-display math
 mode}}
\def\onlydmatherr@#1{\Err@{\string#1\space allowed only in display math mode}}
\def\nonmatherr@#1{\Err@{\string#1\space allowed only in math mode}}
\def\mathbreak{\relax\ifmmode\ifinner\break\else
 \dmatherr@\mathbreak\fi\else\nonmatherr@\mathbreak\fi}
\def\nomathbreak{\relax\ifmmode\ifinner\nobreak\else
 \dmatherr@\nomathbreak\fi\else\nonmatherr@\nomathbreak\fi}
\def\allowmathbreak{\relax\ifmmode\ifinner\allowbreak\else
 \dmatherr@\allowmathbreak\fi\else\nonmatherr@\allowmathbreak\fi}
\def\pagebreak{\relax\ifmmode
 \ifinner\nondmatherr@\pagebreak\else\postdisplaypenalty-\@M\fi
 \else\ifvmode\break\else\vadjust{\break}\fi\fi}
\def\nopagebreak{\relax\ifmmode
 \ifinner\nondmatherr@\nopagebreak\else\postdisplaypenalty\@M\fi
 \else\ifvmode\nobreak\else\vadjust{\nobreak}\fi\fi}
\def\nonvmodeerr@#1{\Err@{\string#1\space not allowed within a paragraph
 or in math}}
\def\vnonvmode@#1#2{\relaxnext@
 \def\next@{\ifx\next\par\def\next@{#1}\else
  \def\next@{#2}\fi\next@}%
 \ifvmode\def\next{#1}\else
 \def\next{\futurelet\next\next@}\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@}
\newdimen\captionwidth@
\captionwidth@\hsize
\advance\captionwidth@-1.5in
\newdimen\smallcaptionwidth@
\def\Invalid@#1{\def#1{\Err@{Invalid use of \string#1}}}
\Invalid@\caption
\Invalid@\captionwidth
\newif\ifmid@
\def\topspace{\mid@false\ins@}
\def\midspace{\mid@true\ins@}
\def\ins@#1{\relaxnext@
 \smallcaptionwidth@\captionwidth@\gdef\thespace@{#1}%
 \def\next@{\ifx\next\space@\def\next. {\futurelet\next\nextii@}\else
  \def\next.{\futurelet\next\nextii@}\fi\next.}%
 \def\nextii@{\ifx\next\caption\def\next\caption{\futurelet\next\nextiii@}%
  \else\let\next\nextiv@\fi\next}%
 \def\nextiv@{\vnonvmode@
  {\ifmid@\let\next\midinsert\else\let\next\topinsert\fi
  \next\vbox to\thespace@{}\endinsert}
  {\ifmid@\nonvmodeerr@\midspace\else\nonvmodeerr@\topspace\fi}}%
 \def\nextiii@{\ifx\next\captionwidth\let\next\nextv@
  \else\let\next\nextvi@\fi\next}%
 \def\nextv@\captionwidth##1##2{\smallcaptionwidth@##1\relax\nextvi@{##2}}%
 \def\nextvi@##1{\def\thecaption@{##1}%
  \def\next@{\ifx\next\space@\def\next. {\futurelet\next\nextvii@}\else
   \def\next.{\futurelet\next\nextvii@}\fi\next.}%
  \futurelet\next\next@}%
 \def\nextvii@{\vnonvmode@
  {\ifmid@\let\next\midinsert\else
  \let\next\topinsert\fi\next\vbox to\thespace@{}\nobreak\smallskip
  \setbox\z@\hbox{\noindent\ignorespaces\thecaption@\unskip}%
  \ifdim\wd\z@>\smallcaptionwidth@\centerline{\vbox{\hsize\smallcaptionwidth@
  \noindent\ignorespaces\thecaption@\unskip}}%
  \else\centerline{\box\z@}\fi\endinsert}
  {\ifmid@\nonvmodeerr@\midspace
  \else\nonvmodeerr@\topspace\fi}}%
 \futurelet\next\next@}
\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`\!=`\\
\lowercase{\gdef\comment@#1^^J{\comment@@#1!endcomment\comment@@@}%
\gdef\comment@@#1!endcomment{\futurelet\next\comment@@@}%
\gdef\comment@@@#1\comment@@@{\ifx\next\comment@@@\let
\next=\comment@\else\def\next{\oldcodes@\endlinechar=`\^^M\relax}%
 \fi\next}}}
\mathchardef\prime@="0230
\def\prime{{{}\prime@{}}}
\def\prim@s{\prime@\futurelet\next\pr@m@s}
\let\dsize\displaystyle
\let\tsize\textstyle
\let\ssize\scriptstyle
\let\sssize\scriptscriptstyle
\def\,{\relax\ifmmode\mskip\thinmuskip\relax\else\kern.16667em\fi}
\def\!{\relax\ifmmode\mskip-\thinmuskip\relax\else\kern-.16667em\fi}
\let\thinspace\,
\let\negthinspace\!
\def\medspace{\relax\ifmmode\mskip\medmuskip\relax\else\kern.222222em\fi}
\def\negmedspace{\relax\ifmmode\mskip-\medmuskip\relax\else\kern-.222222em\fi}
\def\thickspace{\relax\ifmmode\mskip\thickmuskip\relax\else\kern.27777em\fi}
\let\;\thickspace
\def\negthickspace{\relax\ifmmode\mskip-\thickmuskip\relax\else
 \kern-.27777em\fi}
\atdef@,{\relax\ifmmode\mskip.1\thinmuskip\else\leavevmode\null,\fi}
\atdef@!{\relax\ifmmode\mskip-.1\thinmuskip\else\leavevmode\null!\fi}
\atdef@.{\relax\ifmmode&&\else\leavevmode.\spacefactor3000 \fi}
\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{\relaxnext@
 \def\next@{\ifx\next\thickness\let\next@\nextii@\else
  \def\next@{\nextii@\thickness1}\fi\next@}%
 \def\nextii@\thickness##1##2##3{{##2\above##1\ex@##3}}%
 \futurelet\next\next@}
\def\fracwithdelims#1#2#3#4{{#3\overwithdelims#1#2#4}}
\def\thickfracwithdelims#1#2{\relaxnext@\def\ldelim@{#1}\def\rdelim@{#2}%
 \def\next@{\ifx\next\thickness\let\next@\nextii@\else
  \def\next@{\nextii@\thickness1}\fi\next@}%
 \def\nextii@\thickness##1##2##3{{##2\abovewithdelims
  \ldelim@\rdelim@##1\ex@##3}}%
 \futurelet\next\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}
\newif\iftop@
\newif\ifbot@
\def\topsmash{\top@true\bot@false\smash@}
\def\botsmash{\top@false\bot@true\smash@}
\def\smash{\top@true\bot@true\smash@}
\def\smash@{\relax\ifmmode\def\next{\mathpalette\mathsm@sh}\else
 \let\next\makesm@sh\fi\next}
\def\finsm@sh{\iftop@\ht\z@\z@\fi\ifbot@\dp\z@\z@\fi\box\z@}
\def\LimitsOnSums{\global\let\slimits@\displaylimits}
\def\NoLimitsOnSums{\global\let\slimits@\nolimits}
\LimitsOnSums
\let\DOTSI\relax
\let\DOTSB\relax
\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\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@\futurelet\next\ints@}
\def\iiint{\DOTSI\intno@\thr@@\futurelet\next\ints@}
\def\iiiint{\DOTSI\intno@4 \futurelet\next\ints@}
\def\idotsint{\DOTSI\intno@\z@\futurelet\next\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\multintlimits@{\intop\ifnum\intno@=\z@\intdots@\else\intkern@\fi
 \ifnum\intno@>\tw@\intop\intkern@\fi
 \ifnum\intno@>\thr@@\intop\intkern@\fi\intop}
\def\multint@{\int\ifnum\intno@=\z@\intdots@\else\intkern@\fi
 \ifnum\intno@>\tw@\int\intkern@\fi
 \ifnum\intno@>\thr@@\int\intkern@\fi\int}
\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@{\relaxnext@
 \def\next@{\ifx\next\limits\def\next\limits{\nolimits}\else
  \def\next{\nolimits}\fi\next}%
 \futurelet\next\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@{deg}}
\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{$##$\cr
 \hfil{\fam\z@ lim}\hfil\cr\noalign{\nointerlineskip}%
 {-}\mkern-6mu\cleaders\hbox{$\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{\to}\cr\noalign{\nointerlineskip\kern-\ex@}\cr}}}}
\def\varprojlim{\mathop{\vtop{\ialign{$##$\cr
 \hfil{\fam\z@ lim}\hfil\cr\noalign{\nointerlineskip}%
 {\leftarrow}\mkern-6mu\cleaders\hbox{$\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{-}\cr\noalign{\nointerlineskip\kern-\ex@}\cr}}}}
\def\varliminf{\mathop{\underline{\vrule height\z@ depth.2exwidth\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{$\fontdimen13 \tenex\z@
 \displaystyle{#1}$}}\fontdimen13 \tenex\buffer}
\def\topshave#1{\topsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}
\def\botshave#1{\botsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}
\Invalid@\\
\def\Let@{\relax\iffalse{\fi\let\\=\cr\iffalse}\fi}
\Invalid@\vspace
\def\vspace@{\def\vspace##1{\noalign{\vskip##1\relax}}}
\def\multilimits@{\bgroup\vspace@\Let@
 \baselineskip\fontdimen10 \scriptfont\tw@
 \advance\baselineskip\fontdimen12 \scriptfont\tw@
 \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
 \lineskiplimit\thr@@\fontdimen8 \scriptfont\thr@@
 \vbox\bgroup\ialign\bgroup\hfil$\scriptstyle{##}$\hfil\cr}
\def\Sb{_\multilimits@}
\def\endSb{\cr\egroup\egroup\egroup}
\def\Sp{^\multilimits@}
\let\endSp\endSb
\def\ialign{\everycr{}\tabskip\z@skip\halign}
\def\spreadlines#1{\ifmmode\ifinner\onlydmatherr@\spreadlines\else
 \openup#1\relax\fi\else\onlydmatherr@\spreadlines\fi}
\def\Mathstrut@{\setbox\z@\hbox{$($}\setbox\tw@\null\ht\tw@\ht\z@\dp\tw@\dp\z@
 \box\tw@}
\newdimen\spreadmlines@
\def\spreadmatrixlines#1{\ifmmode\ifinner\onlydmatherr@\spreadmatrixlines\else
 \spreadmlines@#1\relax\fi\else\onlydmatherr@\spreadmatrixlines\fi}
\def\matrix{\catcode`\^^I=4 {}\,\vcenter\bgroup\Let@\vspace@
 \normalbaselines\openup\spreadmlines@\m@th\ialign
 \bgroup\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr
 \Mathstrut@\crcr\noalign{\kern-\baselineskip}}
\def\endmatrix{\crcr\Mathstrut@\crcr\noalign{\kern-\baselineskip}\egroup
 \egroup\,\catcode`\^^I=10 }
\def\format{\crcr\egroup\iffalse{\fi\ifnum`}=0 \fi\format@}
\def\format@#1\\{\def\preamble@{#1}%
 \def\c{\hfil$\the\hashtoks@$\hfil}%
 \def\r{\hfil$\the\hashtoks@$}%
 \def\l{$\the\hashtoks@$\hfil}%
 \setbox\z@\hbox{\xdef\Preamble@{\preamble@}}\ifnum`{=0 \fi\iffalse}\fi
 \ialign\bgroup\span\Preamble@\crcr}
\def\smallmatrix{{}\,\vcenter\bgroup\vspace@\Let@
 \baselineskip9\ex@\lineskip\ex@
 \m@th\ialign\bgroup\hfil$\scriptstyle{##}$\hfil&&\thickspace\hfil
 $\scriptstyle{##}$\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{$\mkern\strip@#1 \dotsspace@.\mkern\strip@#1 \dotsspace@$}\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{$\mkern\strip@#1 \dotsspace@.\mkern\strip@#1 \dotsspace@$}\hfill}
\def\innerhdotsfor#1\after#2{\spaceinnerhdots\@ne\for#1\after{#2}}
\def\enabletabs{\catcode`\^^I=4 \enabletabs@}
\def\enabletabs@#1\disabletabs{#1\catcode`\^^I=10 }
\def\EnableTabs{\catcode`\^^I=4 }
\def\DisableTabs{\catcode`\^^I=10 }
\def\cases{\bgroup\spreadmlines@\jot\left\{\,\matrix\format\l&\quad\l\\}
\def\endcases{\endmatrix\right.\egroup}
\newif\ifinalign@
\newif\ifingather@
\newif\ifinany@
\newbox\strutbox@
\setbox\strutbox@\hbox{\vrule height8\p@ depth3\p@ width\z@}
\def\strut@{\copy\strutbox@}
\def\topaligned{{}\,\vtop\aligned@}
\def\botaligned{{}\,\vbox\aligned@}
\def\aligned{{}\,\vcenter\aligned@}
\def\aligned@{\bgroup\vspace@\Let@
 \ifinany@\else\openup\jot\fi\m@th\ialign
 \bgroup\hfil\strut@$\displaystyle{##}$&$\displaystyle{{}##}$\hfil\crcr}
\def\endaligned{\crcr\egroup\egroup}
\let\endtopaligned\endaligned
\let\endbotaligned\endaligned
\newcount\atcount@
\newtoks\hashtoks@
\hashtoks@{#}
\def\alignedat#1{{}\,\vcenter\bgroup\doat@{#1}\vspace@\Let@
 \ifinany@\else\openup\jot\fi\m@th\ialign\bgroup\span\preamble@@\crcr}
\def\doat@#1{\toks@{\hfil\strut@$\displaystyle{\the\hashtoks@}$&$\displaystyle
 {{}\the\hashtoks@}$\hfil}\atcount@#1\relax\advance\atcount@\m@ne
 \loop\ifnum\atcount@>\z@\toks@=\expandafter{\the\toks@&\hfil$\displaystyle
 {\the\hashtoks@}$&$\displaystyle{{}\the\hashtoks@}$\hfil}\advance
 \atcount@\m@ne\repeat\xdef\preamble@{\the\toks@}\xdef\preamble@@{\preamble@}}
\let\endalignedat\endaligned
\def\gathered{{}\,\vcenter\bgroup\vspace@\Let@
 \ifinany@\else\openup\jot\fi\m@th\ialign
 \bgroup\hfil\strut@$\displaystyle{##}$\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\tagform@#1{\hbox{\rm(\ignorespaces#1\unskip)}}
\def\thetag{\leavevmode\tagform@}
\def\tag#1$${\iftagsleft@\leqno\else\eqno\fi\maketag@#1\maketag@$$}
\def\maketag@{\relaxnext@
 \def\next@{\ifx\next"\let\next@\nextii@\else\let\next@\nextiii@\fi\next@}%
 \def\nextii@"##1"##2\maketag@{\hbox{\rm##1}}%
 \def\nextiii@##1\maketag@{\ifmathtags@\tagform@{$##1$}\else
  \tagform@{##1}\fi}%
 \futurelet\next\next@}
\interdisplaylinepenalty\@M
\def\allowdisplaybreaks{\ifmmode\ifinner\onlydmatherr@\allowdisplaybreaks\else
 \interdisplaylinepenalty\z@\fi\else\onlydmatherr@\allowdisplaybreaks\fi}
\def\allowdisplaybreak@{\def\allowdisplaybreak{\noalign{\allowbreak}}}
\def\displaybreak@{\def\displaybreak{\noalign{\break}}}
\def\intertext@{\def\intertext##1{\noalign{\vskip\abovedisplayskip
 \vbox{\normalbaselines\noindent##1}\vskip\belowdisplayskip}}}
\newskip\centering@
\centering@\z@ plus\@m\p@
\def\align{\relaxnext@\ifingather@\let\next\galign@\else
 \ifmmode\ifinner\def\next{\onlydmatherr@\align}\else
 \let\next\align@\fi\else
 \def\next{\onlydmatherr@\align}\fi\fi\next}
\newcount\and@
\def\align@{\inalign@true\inany@true
 \def\tag{\ifnum\and@=\z@\def\next{&&}\else\def\next{&}\fi\next}%
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \iftagsleft@\let\next\lalign@\else\let\next\ralign@\fi\next}
\newdimen\lwidth@
\newdimen\rwidth@
\newdimen\maxlwidth@
\newdimen\maxrwidth@
\newdimen\totwidth@
\def\measure@#1\endalign{\lwidth@\z@\rwidth@\z@
 \maxlwidth@\z@\maxrwidth@\z@\and@\z@
 \setbox\@ne\vbox{\everycr{\noalign{\global\and@\z@}}\Let@
 \halign{\setbox\z@\hbox{$\displaystyle{\everycr{}##}$}%
 \global\lwidth@\wd\z@
 \ifdim\lwidth@>\maxlwidth@\global\maxlwidth@\lwidth@\fi
 \global\advance\and@\@ne
 &\setbox\z@\hbox{$\displaystyle{{}\everycr{}##}$}\global\rwidth@\wd\z@
 \ifdim\rwidth@>\maxrwidth@\global\maxrwidth@\rwidth@\fi
 \global\advance\and@\@ne
 &\eat@{\everycr{}##}\crcr#1\crcr}}\totwidth@\maxlwidth@
 \advance\totwidth@\maxrwidth@}
\def\displ@y@{\global\dt@ptrue\openup\jot\m@th
 \everycr{\noalign{\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\strut@}}%
 \prevdepth\dimen@\fi}}
\def\ralign@#1\endalign{\measure@#1\endalign\and@\z@
 \ifingather@\everycr{\noalign{\global\and@\z@}}\else\displ@y@\fi\Let@
 \tabskip\centering@\halign to\displaywidth
 {\hfil\strut@\setbox\z@\hbox{$\displaystyle{\everycr{}##}$}%
 \global\lwidth@\wd\z@\box\z@\global\advance\and@\@ne
 \tabskip\z@skip&\setbox\z@\hbox{$\displaystyle{{}\everycr{}##}$}%
 \global\rwidth@\wd\z@\box\z@\hfill\global\advance\and@\@ne
 \tabskip\centering@&\setbox\z@\hbox{\everycr{}\strut@\maketag@##\maketag@}%
 \dimen@\displaywidth\advance\dimen@-\totwidth@
 \divide\dimen@\tw@\advance\dimen@\maxrwidth@\advance\dimen@-\rwidth@
 \ifdim\dimen@>\tw@\wd\z@\llap{\box\z@}\else
 \llap{\vtop{\normalbaselines\null\box\z@}}\fi
 \tabskip\z@skip\crcr#1\crcr\black@\totwidth@}}
\newdimen\lineht@
\def\lalign@#1\endalign{\measure@#1\endalign\and@\z@
 \ifdim\totwidth@>\displaywidth\let\displaywidth@\totwidth@\else
 \let\displaywidth@\displaywidth\fi
 \ifingather@\everycr{\noalign{\global\and@\z@}}\else\displ@y@\fi\Let@
 \tabskip\centering@\halign to\displaywidth
 {\hfil\strut@\setbox\z@\hbox{$\displaystyle{\everycr{}##}$}%
 \global\lwidth@\wd\z@\global\lineht@\ht\z@\box\z@\global\advance\and@\@ne
 \tabskip\z@skip&\setbox\z@\hbox{$\displaystyle{{}\everycr{}##}$}%
 \global\rwidth@\wd\z@\ifdim\ht\z@>\lineht@\global\lineht@\ht\z@\fi
 \box\z@\hfil\global\advance\and@\@ne
 \tabskip\centering@&\kern-\displaywidth@
 \setbox\z@\hbox{\everycr{}\strut@\maketag@##\maketag@}%
 \dimen@\displaywidth\advance\dimen@-\totwidth@
 \divide\dimen@\tw@\advance\dimen@\maxlwidth@\advance\dimen@-\lwidth@
 \ifdim\dimen@>\tw@\wd\z@\rlap{\box\z@}\else
 \rlap{\vbox{\normalbaselines\box\z@\vbox to\lineht@{}}}\fi
 \tabskip\displaywidth@\crcr#1\crcr\black@\totwidth@}}
\def\galign@#1\endalign{\vcenter{\m@th\align@#1\endalign}}
\newbox\savealignat@
\newif\ifxat@
\newif\ifmeasuring@
\def\alignat{\relaxnext@\ifmmode\ifinner\def\next{\onlydmatherr@\alignat}\else
 \let\next\alignat@\fi\else\def\next{\onlydmatherr@\alignat}\fi\next}
\def\alignat@#1#2\endalignat{\inany@true\xat@false
 \def\tag{\xdef\tag@{}\count@#1\relax\multiply\count@\tw@
 \loop\ifnum\count@>\and@\xdef\tag@{&\tag@}\advance\count@\m@ne\repeat\tag@}%
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y@\measuring@true\setbox\savealignat@\hbox{$\displaystyle\Let@
 \attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
 \measuring@false\Let@
 \attag@{#1}\tabskip\centering@\halign to\displaywidth
 {\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\def\xalignat{\relaxnext@\ifmmode\ifinner
 \def\next{\onlydmatherr@\xalignat}\else\let\next\xalignat@\fi\else
 \def\next{\onlydmatherr@\xalignat}\fi\next}
\def\xalignat@#1#2\endxalignat{\inany@true\xat@true
 \def\tag{\def\tag@{}\count@#1\relax\multiply\count@\tw@
 \loop\ifnum\count@>\and@\xdef\tag@{&\tag@}\advance\count@\m@ne\repeat\tag@}%
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y@\measuring@true\setbox\savealignat@\hbox{$\displaystyle\Let@
 \attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
 \measuring@false\Let@
 \attag@{#1}\tabskip\centering@\halign to\displaywidth
 {\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\def\attag@#1{\let\Maketag@\maketag@\let\maketag@=0
 \ifmeasuring@\def\llap@##1{\setbox\z@\hbox{##1}\hbox to\tw@\wd\z@{}}%
 \def\rlap@##1{\setbox\z@\hbox{##1}\hbox to\tw@\wd\z@{}}\else
 \let\llap@\llap\let\rlap@\rlap\fi
 \toks@{\hfil\strut@$\displaystyle{\everycr{}\the\hashtoks@}$\tabskip\z@skip
 \global\advance\and@\@ne&$\displaystyle{{}\everycr{}\the\hashtoks@}$%
 \hfil\ifxat@\tabskip\centering@\fi\global\advance
 \and@\@ne}\iftagsleft@
 \toks@@{\tabskip\centering@&\kern-\displaywidth
 \rlap@{\everycr{}\maketag@\the\hashtoks@\maketag@}%
 \global\advance\and@\@ne\tabskip\displaywidth}\else
 \toks@@{\tabskip\centering@&\llap@{\everycr{}\maketag@
 \the\hashtoks@\maketag@}\global\advance\and@\@ne\tabskip\z@skip}\fi
 \atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
 \toks@=\expandafter{\the\toks@&\hfil$\displaystyle{\everycr{}%
 \the\hashtoks@}$\global\advance\and@\@ne
 \tabskip\z@skip&$\displaystyle{{}\everycr{}\the\hashtoks@}$\hfil\ifxat@
 \tabskip\centering@\fi\global\advance\and@\@ne}\advance\atcount@\m@ne\repeat
 \xdef\preamble@{\the\toks@\the\toks@@}\xdef\preamble@@{\preamble@}%
 \let\maketag@\Maketag@}
\def\xxalignat{\relaxnext@\ifmmode\ifinner
 \def\next{\onlydmatherr@\xxalignat}\else\let\next\xxalignat@\fi\else
 \def\next{\onlydmatherr@\xxalignat}\fi\next}
\def\xxalignat@#1#2\endxxalignat{\inany@true
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y\setbox\savealignat@\hbox{$\displaystyle\Let@
 \xxattag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
 \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@
 $\displaystyle{\the\hashtoks@}$&%
 $\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\centering@&}%
 \atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
 \toks@=\expandafter{\the\toks@&\hfil$\displaystyle{\the\hashtoks@}$%
 \tabskip\z@skip&$\displaystyle{{}\the\hashtoks@}$\hfil
 \tabskip\centering@}\advance\atcount@\m@ne\repeat
 \xdef\preamble@{\the\toks@\tabskip\z@skip}\xdef\preamble@@{\preamble@}}
\newdimen\gwidth@
\newdimen\gmaxwidth@
\def\gmeasure@#1\endgather{\gwidth@\z@\gmaxwidth@\z@\setbox\@ne\vbox{\Let@
 \halign{\setbox\z@\hbox{$\displaystyle{##}$}\global\gwidth@\wd\z@
 \ifdim\gwidth@>\gmaxwidth@\global\gmaxwidth@\gwidth@\fi
 &\eat@{##}\crcr#1\crcr}}}
\def\gather{\relaxnext@\ifmmode\ifinner\def\next{\onlydmatherr@\gather}\else
 \ingather@true\inany@true\def\tag{&}%
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y\Let@
 \iftagsleft@\let\next\lgather@\else\let\next\rgather@\fi\fi
 \else\def\next{\onlydmatherr@\gather}\fi\next}
\def\rgather@#1\endgather{\gmeasure@#1\endgather\tabskip\centering@
 \halign to\displaywidth{\hfil\strut@\setbox\z@\hbox{$\displaystyle{##}$}%
 \global\gwidth@\wd\z@\box\z@\hfil&
 \setbox\z@\hbox{\strut@{\maketag@##\maketag@}}%
 \dimen@\displaywidth\advance\dimen@-\gwidth@
 \ifdim\dimen@>\tw@\wd\z@\llap{\box\z@}\else
 \llap{\vtop{\normalbaselines\null\box\z@}}\fi
 \tabskip\z@skip\crcr#1\crcr\black@\gmaxwidth@}}
\newdimen\glineht@
\def\lgather@#1\endgather{\gmeasure@#1\endgather
 \ifdim\gmaxwidth@>\displaywidth\let\gdisplaywidth@\gmaxwidth@\else
 \let\gdisplaywidth@\displaywidth\fi\tabskip\centering@\halign to\displaywidth
 {\hfil\strut@\setbox\z@\hbox{$\displaystyle{##}$}%
 \global\gwidth@\wd\z@\global\glineht@\ht\z@\box\z@\hfil&\kern-\gdisplaywidth@
 \setbox\z@\hbox{\strut@{\maketag@##\maketag@}}%
 \dimen@\displaywidth\advance\dimen@-\gwidth@
 \ifdim\dimen@>\tw@\wd\z@\rlap{\box\z@}\else
 \rlap{\vbox{\normalbaselines\box\z@\vbox to\glineht@{}}}\fi
 \tabskip\gdisplaywidth@\crcr#1\crcr\black@\gmaxwidth@}}
\newif\ifctagsplit@
\def\CenteredTagsOnSplits{\global\ctagsplit@true}
\def\TopOrBottomTagsOnSplits{\global\ctagsplit@false}
\def\split{\relaxnext@\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\outsplit@#1$${\align\insplit@#1\endalign$$}
\def\insplit@{\global\setbox\z@\vbox\bgroup\vspace@\Let@\m@th\ialign\bgroup
 \hfil\strut@$\displaystyle{##}$&$\displaystyle{{}##}$\hfill\crcr}
\def\endsplit{\crcr\egroup\egroup\iftagsleft@\let\next\lendsplit@\else
 \let\next\rendsplit@\fi\next}
\def\rendsplit@{\global\setbox9\vbox
 {\unvcopy\z@\global\setbox8\lastbox\unskip}%
 \setbox\@ne\hbox{\unhcopy8\unskip\global\setbox\tw@\lastbox
 \unskip\global\setbox\thr@@\lastbox}%
 \global\setbox7\hbox{\unhbox\tw@\unskip}%
 \ifinalign@
  \ifctagsplit@\gdef\split@{\hbox to\wd\thr@@{}&
  \vcenter{\vbox{\moveleft\wd\thr@@\box\z@}}}\else
  \gdef\split@{&\vbox{\moveleft\wd\thr@@\box9}\crcr
  \box\thr@@&\box7}\fi
 \else
  \ifctagsplit@\gdef\split@{\vcenter{\box\z@}}\else
  \gdef\split@{\box9\crcr\hbox{\box\thr@@\box7}}\fi
 \fi\split@}
\def\lendsplit@{\global\setbox9\vtop{\unvcopy\z@}%
 \setbox\@ne\vbox{\unvcopy\z@\global\setbox8\lastbox}%
 \setbox\@ne\hbox{\unhcopy8\unskip\setbox\tw@\lastbox
 \unskip\global\setbox\thr@@\lastbox}%
 \ifinalign@
  \ifctagsplit@\gdef\split@{\hbox to\wd\thr@@{}&
  \vcenter{\vbox{\moveleft\wd\thr@@\box9}}}\else
  \gdef\split@{\hbox to\wd\thr@@{}&\vbox{\moveleft\wd\thr@@\box9}}\fi
 \else
  \ifctagsplit@\gdef\split@{\vcenter{\box9}}\else
  \gdef\split@{\box9}\fi
 \fi\split@}
\newdimen\multlinegap@
\multlinegap@1em
\newdimen\multlinetaggap@
\multlinetaggap@1em
\def\MultlineGap#1{\global\multlinegap@#1\relax}
\def\multlinegap#1{\relax\ifmmode\ifinner\onlydmatherr@\multlinegap\else
 \multlinegap@#1\relax\fi\else\onlydmatherr@\multlinegap\fi}
\def\nomultlinegap{\multlinegap{\z@}}
\newbox\mtagbox@
\newif\iftagin@
\def\tagin@#1{\tagin@false\in@\tag{#1}\ifin@\tagin@true\fi}
\newdimen\ltwidth@
\newdimen\rtwidth@
\newdimen\mwidth@
\newdimen\mlineht@
\newif\ifzerocr@
\newif\ifonecr@
\def\lmmeasure@#1\endmultline{\m@th\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\@ne\vbox{\Let@\halign{\setbox\z@\hbox
 {$\everycr{}\displaystyle{}##$}\ifonecr@\global\mwidth@\wd\z@
 \global\mlineht@\ht\z@\fi\crcr#1\crcr}}}
\def\rmmeasure@#1\endmultline{\m@th
 \def\shoveleft##1{##1}\def\shoveright##1{##1}%
 \setbox\@ne\vbox{\Let@\halign{\setbox\z@\hbox
 {$\everycr{}\displaystyle{}##$}\global\mwidth@\wd\z@
 \crcr#1\crcr}}}
\def\multline{\relaxnext@\ifmmode\ifinner
 \def\next{\onlydmatherr@\multline}\else\let\next\multline@\fi\else
 \def\next{\onlydmatherr@\multline}\fi\next}
\def\multline@#1$${\inany@true\vspace@\allowdisplaybreak@\displaybreak@
 \tagin@{#1}\iftagsleft@\def\next{\lmultline@#1$$}\else
 \def\next{\rmultline@#1$$}\fi\next}
\def\lmultline@#1$${\iftagin@\def\next{\lmultline@@#1$$}\else
 \def\next{\setbox\mtagbox@\null\ltwidth@\z@\rtwidth@\z@
 \lmultline@@@#1$$}\fi\next}
\def\lmultline@@#1\endmultline\tag#2$${\rtwidth@\z@
 \setbox\mtagbox@\hbox{\maketag@#2\maketag@}%
 \lmmeasure@#1\endmultline\dimen@\mwidth@\advance\dimen@\wd\mtagbox@
 \advance\dimen@\multlinetaggap@
 \ifdim\dimen@>\displaywidth\ltwidth@\z@\else\ltwidth@\wd\mtagbox@\fi
 \lmultline@@@#1\endmultline$$}
\def\lmultline@@@{\displ@y
 \def\shoveright##1{##1\hfilneg\hskip\multlinegap@}%
 \def\shoveleft##1{\setbox\z@\hbox{$\displaystyle{}##1$}%
  \setbox\@ne\hbox{$\displaystyle##1$}%
  \hfilneg\iftagin@\ifdim\ltwidth@>\z@\hskip\ltwidth@\hskip\multlinetaggap@\fi
  \else\hskip\multlinegap@\fi\hskip.5\wd\@ne\hskip-.5\wd\z@##1}%
  \halign\bgroup\Let@\hbox to\displaywidth
  {\strut@$\displaystyle\hfil{}##\hfil$}\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\rmultline@#1$${\iftagin@\def\next{\rmultline@@#1$$}\else
 \def\next{\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{\setbox\z@\hbox{$\displaystyle{}##1$}%
  \setbox\@ne\hbox{$\displaystyle##1$}%
  \hfilneg\hskip\multlinegap@\hskip.5\wd\@ne\hskip-.5\wd\z@##1}%
 \halign\bgroup\Let@\hbox to\displaywidth
 {\strut@$\displaystyle\hfil{}##\hfil$}\crcr
 \hfilneg\hskip\multlinegap@}
\def\endmultline{\iftagsleft@\let\next\lendmultline@\else
 \let\next\rendmultline@\fi\next}
\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\mod#1{\allowbreak\ifinner\mkern12mu\else\mkern18mu\fi{\fam\z@ mod}\,\,#1}
\def\pod#1{\allowbreak\ifinner\mkern8mu\else\mkern18mu\fi(#1)}
\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)}
\newcount\cfraccount@
\def\gloop@#1\repeat{\gdef\body{#1}\iterate}
\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\hfill}\iffalse}\fi}
\def\endcfrac{\gloop@\ifnum\cfraccount@>\z@\global\advance\cfraccount@\m@ne
 \egroup\hskip-\nulldelimiterspace\egroup\repeat}
\def\binrel@#1{\setbox\z@\hbox{\thinmuskip0mu
 \medmuskip\m@ne mu\thickmuskip\@ne mu$#1\m@th$}%
 \setbox\@ne\hbox{\thinmuskip0mu\medmuskip\m@ne mu\thickmuskip
 \@ne mu${}#1{}\m@th$}%
 \setbox\tw@\hbox{\hskip\wd\@ne\hskip-\wd\z@}}
\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{%
 \setbox\@ne\hbox{$\dsize{\vphantom{#3}}#1{#3}\m@th$}%
 \setbox\tw@\hbox{$\dsize{#3}#2\m@th$}%
 \kern\wd\@ne\kern-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wd\@ne
 {\vphantom{#3}}#1{#3}#2}}
\def\overrightarrow{\mathpalette\overrightarrow@}
\def\overrightarrow@#1#2{\vbox{\ialign{$##$\cr
 #1{-}\mkern-6mu\cleaders\hbox{$#1\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{\to}\cr\noalign{\kern-\ex@\nointerlineskip}\hfil#1#2\hfil\cr}}}
\let\overarrow\overrightarrow
\def\overleftarrow{\mathpalette\overleftarrow@}
\def\overleftarrow@#1#2{\vbox{\ialign{$##$\cr
 #1{\leftarrow}\mkern-6mu\cleaders\hbox{$#1\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{-}\cr\noalign{\kern-\ex@\nointerlineskip}\hfil#1#2\hfil\cr}}}
\def\overleftrightarrow{\mathpalette\overleftrightarrow@}
\def\overleftrightarrow@#1#2{\vbox{\ialign{$##$\cr
 #1{\leftarrow}\mkern-6mu\cleaders\hbox{$#1\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{\to}\cr\noalign{\kern-\ex@\nointerlineskip}\hfil#1#2\hfil\cr}}}
\def\underrightarrow{\mathpalette\underrightarrow@}
\def\underrightarrow@#1#2{\vtop{\ialign{$##$\cr
 \hfil#1#2\hfil\cr\noalign{\nointerlineskip}%
 #1{-}\mkern-6mu\cleaders\hbox{$#1\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{\to}\cr}}}
\let\underarrow\underrightarrow
\def\underleftarrow{\mathpalette\underleftarrow@}
\def\underleftarrow@#1#2{\vtop{\ialign{$##$\cr
 \hfil#1#2\hfil\cr\noalign{\nointerlineskip}#1{\leftarrow}\mkern-6mu
 \cleaders\hbox{$#1\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{-}\cr}}}
\def\underleftrightarrow{\mathpalette\underleftrightarrow@}
\def\underleftrightarrow@#1#2{\vtop{\ialign{$##$\cr
 \hfil#1#2\hfil\cr\noalign{\nointerlineskip}#1{\leftarrow}\mkern-6mu
 \cleaders\hbox{$#1\mkern-2mu{-}\mkern-2mu$}\hfill
 \mkern-6mu{\to}\cr}}}
\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{%
  \def\next@##1\mathbin@{\ifx\space@\next\global\mathbin@true\fi}%
 \global\mathbin@false\def\next##1\mathbin@{}%
 \ifx 4#1\ifx 5#2\ifx 6#3\def\next{\futurelet\next\next@}\fi\fi\fi\next}}}
\newif\ifmathrel@
{\uccode`4=`r \uccode`5=`e \uccode`6=`l
 \uppercase{\gdef\mathrel@#1#2#3{%
  \def\next@##1\mathrel@{\ifx\space@\next\global\mathrel@true\fi}%
 \global\mathrel@false\def\next##1\mathrel@{}%
 \ifx 4#1\ifx 5#2\ifx 6#3\def\next{\futurelet\next\next@}\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\def\next##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}}}
\let\DOTSX\relax
{\uccode`3=`B \uccode`4=`I \uccode`5=`X
 \uppercase{\gdef\DOTS@@#1{%
  \def\next{\futurelet\next\next@}%
  \def\next@##1\DOTS@{\ifx\space@\next\global\DOTS@true\fi}%
  \ifx 3#1\global\DOTSCASE@\z@\else
  \ifx 4#1\global\DOTSCASE@\@ne\else
  \ifx 5#1\global\DOTSCASE@\tw@\else\def\next##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{%
  \def\next@##1\not@{\ifx\space@\next\global\not@true\fi}%
 \global\not@false\def\next##1\not@{}%
 \ifx 5#1\ifx 6#2\ifx 7#3\ifx 8#4\def\next{\futurelet\next\next@}\fi\fi\fi\fi
 \next}}}
\newif\ifkeybin@
\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}
\def\dots{\ifmmode\let\next\mdots@\else\let\next\tdots@\fi\next}
\def\tdots@{\unskip\relaxnext@
 \def\next@{$\mathinner{\ldotp\ldotp\ldotp}\,
   \ifx\next,$\else\ifx\next.\,$\else\ifx\next;\,$\else\ifx\next:\,$\else
   \ifx\next?\,$\else\ifx\next!\,$\else$ \fi\fi\fi\fi\fi\fi}%
 \ \futurelet\next\next@}
\def\mdots@{\futurelet\next\mdots@@}
\def\mdots@@{\gdef\thedots@{\dotso@}%
 \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
  \thedots@}
\def\plainldots@{\mathinner{\ldotp\ldotp\ldotp}}
\def\plaincdots@{\mathinner{\cdotp\cdotp\cdotp}}
\def\dotsi{\!\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$\global\extra@true\else
 \xdef\meaning@{\meaning\next.........}%
 \expandafter\macro@\meaning@\macro@
 \ifmacro@\expandafter\DOTS@\meaning@\DOTS@
 \ifDOTS@
 \ifnum\DOTSCASE@=\tw@\global\extra@true\fi\fi\fi\fi\fi}
\def\extrap@#1{%
 \ifx\next,\def\next{#1\,}\else
 \ifx\next;\def\next{#1\,}\else
 \ifx\next.\def\next{#1\,}\else\extra@
 \ifextra@\def\next{#1\,}\else
 \let\next#1\fi\fi\fi\fi\next}
\def\ldots{\relaxnext@
 \def\next@{\extrap@\plainldots@}%
 \futurelet\next\next@}
\def\cdots{\relaxnext@
 \def\next@{\extrap@\plaincdots@}%
 \futurelet\next\next@}
\let\dotsb@\plaincdots@
\let\dotsb\cdots
\def\dotso@{%
 \def\next@{\extra@\plainldots@\ifextra@\,\fi}%
 \futurelet\next\next@}
\def\dotso{\relaxnext@
 \def\next@{\extrap@\plainldots@}%
 \futurelet\next\next@}
\def\dotsc{\relaxnext@
 \def\next@{%
  \ifx\next;\plainldots@\,\else
  \ifx\next.\plainldots@\,\else\extra@\plainldots@
  \ifextra@\,\fi\fi\fi}%
 \futurelet\next\next@}
\def\cdot{\relax\mathchar"2201 }
\let\dotsm\dotsb
\def\longrightarrow{\DOTSB\relbar\joinrel\rightarrow}
\def\Longrightarrow{\DOTSB\Relbar\joinrel\Rightarrow}
\def\longleftarrow{\DOTSB\leftarrow\joinrel\relbar}
\def\Longleftarrow{\DOTSB\Leftarrow\joinrel\Relbar}
\def\longleftrightarrow{\DOTSB\leftarrow\joinrel\rightarrow}
\def\Longleftrightarrow{\DOTSB\Leftarrow\joinrel\Rightarrow}
\def\mapsto{\DOTSB\mapstochar\rightarrow}
\def\longmapsto{\DOTSB\mapstochar\longrightarrow}
\def\hookrightarrow{\DOTSB\lhook\joinrel\rightarrow}
\def\hookleftarrow{\DOTSB\leftarrow\joinrel\rhook}
\def\doteq{\DOTSB\buildrel\textstyle.\over=}
\def\iff{\DOTSB\;\Longleftrightarrow\;}
\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\tenrm...}\vss}}}}
\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\tenrm....}\vss}}}}
\def\sphat{^{\mathchoice{}{}{\,\,\botsmash{\hbox{\lower 4\ex@\hbox
 {$\widehat{\null}$}}}}{\,\botsmash{\hbox{\lower3\ex@\hbox
 {$\hat{\null}$}}}}}}
\def\spcheck{^\vee}
\def\sptilde{^\sim}
\def\spacute{^{\!\botsmash{\hbox{\lower\@ne ex\hbox{\'{}}}}}}
\def\spgrave{^{\mathchoice{}{}{}{\!}%
 \botsmash{\hbox{\lower\@ne ex\hbox{\`{}}}}}}
\def\spdot{^{\hbox{\raise\ex@\hbox{\tenrm.}}}}
\def\spddot{^{\hbox{\raise\ex@\hbox{\tenrm..}}}}
\def\spdddot{^{\hbox{\raise\ex@\hbox{\tenrm...}}}}
\def\spddddot{^{\hbox{\raise\ex@\hbox{\tenrm....}}}}
\def\spbreve{^{\!\botsmash{\hbox{\lower4\ex@\hbox{\u{}}}}}}
\def\spbar{^-}
\def\spvec{^\rightarrow}
\def\textfont@#1#2{\def#1{\relax\ifmmode
 \Err@{Use \string#1\space only in text}\else#2\fi}}
\textfont@\rm\tenrm
\textfont@\it\tenit
\textfont@\sl\tensl
\textfont@\bf\tenbf
\textfont@\smc\tensmc
\def\oldnos#1{\ifmmode{\mathcode`\,="013B \fam\@ne#1}\else
  \leavevmode\hbox{$\mathcode`\,="013B \fam\@ne#1$}\fi}
\def\text{\relaxnext@\ifmmode\let\next\text@\else\let\next\text@@\fi\next}
\def\text@@#1{\leavevmode\hbox{#1}}
\def\mathhexbox@#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
\def\dag{{\mathhexbox@279}}
\def\ddag{{\mathhexbox@27A}}
\def\S{{\mathhexbox@278}}
\def\P{{\mathhexbox@27B}}
\newcount\footmarkcount@
\footmarkcount@\z@
\newcount\footmarkcount@@
\def\text@#1{\footmarkcount@@\footmarkcount@\mathchoice
 {\hbox{\everymath{\displaystyle}\def\textfonti{\the\textfont\@ne}%
  \def\textfontii{\the\textfont\tw@}\textdef@@ T#1}}
 {\hbox{\everymath{\textstyle}\def\textfonti{\the\textfont\@ne}%
  \def\textfontii{\the\textfont\tw@}\textdef@@ T#1}}
 {\hbox{\everymath{\scriptstyle}\def\textfonti{\the\scriptfont\@ne}%
  \def\textfontii{\the\scriptfont\tw@}\textdef@@ S\rm#1}}
 {\hbox{\everymath{\scriptscriptstyle}\def\textfonti
  {\the\scriptscriptfont\@ne}%
  \def\textfontii{\the\scriptscriptfont\tw@}\textdef@@ s\rm#1}}%
  \advance\footmarkcount@-\footmarkcount@@
  \divide\footmarkcount@4 \global\advance\footmarkcount@\footmarkcount@@}
\def\textdef@@#1{\textdef@#1\rm\textdef@#1\bf\textdef@#1\sl\textdef@#1\it}
\def\rmfam{0}
\def\textdef@#1#2{%
 \def\next{\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@{\relaxnext@
 \def\next@{\ifx\next\foldedwidth\let\next\nextii@\else
  \def\next{\nextii@\foldedwidth{.3\hsize}}\fi\next}%
 \def\nextii@\foldedwidth##1##2{\setbox\z@\vbox
  {\normalbaselines\hsize##1\relax
  \tolerance1600 \noindent\ignorespaces##2}\ifbotfolded@\box\z@\else
  \iftopfolded@\vtop{\unvbox\z@}\else\vcenter{\box\z@}\fi\fi}%
 \futurelet\next\next@}
\mathcode`\0="0030
\mathcode`\1="0031
\mathcode`\2="0032
\mathcode`\3="0033
\mathcode`\4="0034
\mathcode`\5="0035
\mathcode`\6="0036
\mathcode`\7="0037
\mathcode`\8="0038
\mathcode`\9="0039
\def\Cal{\relaxnext@\ifmmode\let\next\Cal@\else
 \def\next{\Err@{Use \string\Cal\space only in math mode}}\fi\next}
\def\Cal@#1{{\Cal@@{#1}}}
\def\Cal@@#1{\noaccents@\fam\tw@#1}
\def\bold{\relaxnext@\ifmmode\let\next\bold@\else
 \def\next{\Err@{Use \string\bold\space only in math mode}}\fi\next}
\def\bold@#1{{\bold@@{#1}}}
\def\bold@@#1{\fam\bffam#1}
\def\slanted{\relaxnext@\ifmmode\let\next\slanted@\else
 \def\next{\Err@{Use \string\slanted\space only in math mode}}\fi\next}
\def\slanted@#1{{\slanted@@{#1}}}
\def\slanted@@#1{\fam\slfam#1}
\def\roman{\relaxnext@\ifmmode\let\next\roman@\else
 \def\next{\Err@{Use \string\roman\space only in math mode}}\fi\next}
\def\roman@#1{{\roman@@{#1}}}
\def\roman@@#1{\fam\rmfam#1}
\def\italic{\relaxnext@\ifmmode\let\next\italic@\else
 \def\next{\Err@{Use \string\italic\space only in math mode}}\fi\next}
\def\italic@#1{{\italic@@{#1}}}
\def\italic@@#1{\fam\itfam#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
\def\hexnumber@#1{\ifnum#1<10 \number#1\else
 \ifnum#1=10 A\else\ifnum#1=11 B\else\ifnum#1=12 C\else
 \ifnum#1=13 D\else\ifnum#1=14 E\else\ifnum#1=15 F\fi\fi\fi\fi\fi\fi\fi}
\def\bffam@{\hexnumber@\bffam}
\mathchardef\boldGamma="0\bffam@00
\mathchardef\boldDelta="0\bffam@01
\mathchardef\boldTheta="0\bffam@02
\mathchardef\boldLambda="0\bffam@03
\mathchardef\boldXi="0\bffam@04
\mathchardef\boldPi="0\bffam@05
\mathchardef\boldSigma="0\bffam@06
\mathchardef\boldUpsilon="0\bffam@07
\mathchardef\boldPhi="0\bffam@08
\mathchardef\boldPsi="0\bffam@09
\mathchardef\boldOmega="0\bffam@0A
%\font\tenmsx=msxm10
%\font\sevenmsx=msxm7
%\font\fivemsx=msxm5
%\font\tenmsy=msym10
%\font\sevenmsy=msym7
%\font\fivemsy=msym5
\newfam\msxfam
\newfam\msyfam
%\textfont\msxfam=\tenmsx
%\scriptfont\msxfam=\sevenmsx
%\scriptscriptfont\msxfam=\fivemsx
%\textfont\msyfam=\tenmsy
%\scriptfont\msyfam=\sevenmsy
%\scriptscriptfont\msyfam=\fivemsy
\def\msx@{\hexnumber@\msxfam}
\def\msy@{\hexnumber@\msyfam}
\mathchardef\boxdot="2\msx@00
\mathchardef\boxplus="2\msx@01
\mathchardef\boxtimes="2\msx@02
\mathchardef\square="0\msx@03
\mathchardef\blacksquare="0\msx@04
\mathchardef\centerdot="2\msx@05
\mathchardef\lozenge="0\msx@06
\mathchardef\blacklozenge="0\msx@07
\mathchardef\circlearrowright="3\msx@08
\mathchardef\circlearrowleft="3\msx@09
%\mathchardef\rightleftharpoons="3\msx@0A
\mathchardef\leftrightharpoons="3\msx@0B
\mathchardef\boxminus="2\msx@0C
\mathchardef\Vdash="3\msx@0D
\mathchardef\Vvdash="3\msx@0E
\mathchardef\vDash="3\msx@0F
\mathchardef\twoheadrightarrow="3\msx@10
\mathchardef\twoheadleftarrow="3\msx@11
\mathchardef\leftleftarrows="3\msx@12
\mathchardef\rightrightarrows="3\msx@13
\mathchardef\upuparrows="3\msx@14
\mathchardef\downdownarrows="3\msx@15
\mathchardef\upharpoonright="3\msx@16
\let\restriction\upharpoonright
\mathchardef\downharpoonright="3\msx@17
\mathchardef\upharpoonleft="3\msx@18
\mathchardef\downharpoonleft="3\msx@19
\mathchardef\rightarrowtail="3\msx@1A
\mathchardef\leftarrowtail="3\msx@1B
\mathchardef\leftrightarrows="3\msx@1C
\mathchardef\rightleftarrows="3\msx@1D
\mathchardef\Lsh="3\msx@1E
\mathchardef\Rsh="3\msx@1F
\mathchardef\rightsquigarrow="3\msx@20
\mathchardef\leftrightsquigarrow="3\msx@21
\mathchardef\looparrowleft="3\msx@22
\mathchardef\looparrowright="3\msx@23
\mathchardef\circeq="3\msx@24
\mathchardef\succsim="3\msx@25
\mathchardef\gtrsim="3\msx@26
\mathchardef\gtrapprox="3\msx@27
\mathchardef\multimap="3\msx@28
\mathchardef\therefore="3\msx@29
\mathchardef\because="3\msx@2A
\mathchardef\doteqdot="3\msx@2B
\let\Doteq\doteqdot
\mathchardef\triangleq="3\msx@2C
\mathchardef\precsim="3\msx@2D
\mathchardef\lesssim="3\msx@2E
\mathchardef\lessapprox="3\msx@2F
\mathchardef\eqslantless="3\msx@30
\mathchardef\eqslantgtr="3\msx@31
\mathchardef\curlyeqprec="3\msx@32
\mathchardef\curlyeqsucc="3\msx@33
\mathchardef\preccurlyeq="3\msx@34
\mathchardef\leqq="3\msx@35
\mathchardef\leqslant="3\msx@36
\mathchardef\lessgtr="3\msx@37
\mathchardef\backprime="0\msx@38
\mathchardef\risingdotseq="3\msx@3A
\mathchardef\fallingdotseq="3\msx@3B
\mathchardef\succcurlyeq="3\msx@3C
\mathchardef\geqq="3\msx@3D
\mathchardef\geqslant="3\msx@3E
\mathchardef\gtrless="3\msx@3F
\mathchardef\sqsubset="3\msx@40
\mathchardef\sqsupset="3\msx@41
\mathchardef\vartriangleright="3\msx@42
\mathchardef\vartriangleleft ="3\msx@43
\mathchardef\trianglerighteq="3\msx@44
\mathchardef\trianglelefteq="3\msx@45
\mathchardef\bigstar="0\msx@46
\mathchardef\between="3\msx@47
\mathchardef\blacktriangledown="0\msx@48
\mathchardef\blacktriangleright="3\msx@49
\mathchardef\blacktriangleleft="3\msx@4A
\mathchardef\vartriangle="3\msx@4D
\mathchardef\blacktriangle="0\msx@4E
\mathchardef\triangledown="0\msx@4F
\mathchardef\eqcirc="3\msx@50
\mathchardef\lesseqgtr="3\msx@51
\mathchardef\gtreqless="3\msx@52
\mathchardef\lesseqqgtr="3\msx@53
\mathchardef\gtreqqless="3\msx@54
\mathchardef\Rrightarrow="3\msx@56
\mathchardef\Lleftarrow="3\msx@57
\mathchardef\veebar="2\msx@59
\mathchardef\barwedge="2\msx@5A
\mathchardef\doublebarwedge="2\msx@5B
%\mathchardef\angle="0\msx@5C
\mathchardef\measuredangle="0\msx@5D
\mathchardef\sphericalangle="0\msx@5E
\mathchardef\varpropto="3\msx@5F
\mathchardef\smallsmile="3\msx@60
\mathchardef\smallfrown="3\msx@61
\mathchardef\Subset="3\msx@62
\mathchardef\Supset="3\msx@63
\mathchardef\Cup="2\msx@64
\let\doublecup\Cup
\mathchardef\Cap="2\msx@65
\let\doublecap\Cap
\mathchardef\curlywedge="2\msx@66
\mathchardef\curlyvee="2\msx@67
\mathchardef\leftthreetimes="2\msx@68
\mathchardef\rightthreetimes="2\msx@69
\mathchardef\subseteqq="3\msx@6A
\mathchardef\supseteqq="3\msx@6B
\mathchardef\bumpeq="3\msx@6C
\mathchardef\Bumpeq="3\msx@6D
\mathchardef\lll="3\msx@6E
\let\llless\lll
\mathchardef\ggg="3\msx@6F
\let\gggtr\ggg
\mathchardef\circledS="0\msx@73
\mathchardef\pitchfork="3\msx@74
\mathchardef\dotplus="2\msx@75
\mathchardef\backsim="3\msx@76
\mathchardef\backsimeq="3\msx@77
\mathchardef\complement="0\msx@7B
\mathchardef\intercal="2\msx@7C
\mathchardef\circledcirc="2\msx@7D
\mathchardef\circledast="2\msx@7E
\mathchardef\circleddash="2\msx@7F
\def\ulcorner{\delimiter"4\msx@70\msx@70 }
\def\urcorner{\delimiter"5\msx@71\msx@71 }
\def\llcorner{\delimiter"4\msx@78\msx@78 }
\def\lrcorner{\delimiter"5\msx@79\msx@79 }
\def\yen{{\mathhexbox@\msx@55 }}
\def\checkmark{{\mathhexbox@\msx@58 }}
\def\circledR{{\mathhexbox@\msx@72 }}
\def\maltese{{\mathhexbox@\msx@7A }}
\mathchardef\lvertneqq="3\msy@00
\mathchardef\gvertneqq="3\msy@01
\mathchardef\nleq="3\msy@02
\mathchardef\ngeq="3\msy@03
\mathchardef\nless="3\msy@04
\mathchardef\ngtr="3\msy@05
\mathchardef\nprec="3\msy@06
\mathchardef\nsucc="3\msy@07
\mathchardef\lneqq="3\msy@08
\mathchardef\gneqq="3\msy@09
\mathchardef\nleqslant="3\msy@0A
\mathchardef\ngeqslant="3\msy@0B
\mathchardef\lneq="3\msy@0C
\mathchardef\gneq="3\msy@0D
\mathchardef\npreceq="3\msy@0E
\mathchardef\nsucceq="3\msy@0F
\mathchardef\precnsim="3\msy@10
\mathchardef\succnsim="3\msy@11
\mathchardef\lnsim="3\msy@12
\mathchardef\gnsim="3\msy@13
\mathchardef\nleqq="3\msy@14
\mathchardef\ngeqq="3\msy@15
\mathchardef\precneqq="3\msy@16
\mathchardef\succneqq="3\msy@17
\mathchardef\precnapprox="3\msy@18
\mathchardef\succnapprox="3\msy@19
\mathchardef\lnapprox="3\msy@1A
\mathchardef\gnapprox="3\msy@1B
\mathchardef\nsim="3\msy@1C
\mathchardef\napprox="3\msy@1D
\mathchardef\varsubsetneq="3\msy@20
\mathchardef\varsupsetneq="3\msy@21
\mathchardef\nsubseteqq="3\msy@22
\mathchardef\nsupseteqq="3\msy@23
\mathchardef\subsetneqq="3\msy@24
\mathchardef\supsetneqq="3\msy@25
\mathchardef\varsubsetneqq="3\msy@26
\mathchardef\varsupsetneqq="3\msy@27
\mathchardef\subsetneq="3\msy@28
\mathchardef\supsetneq="3\msy@29
\mathchardef\nsubseteq="3\msy@2A
\mathchardef\nsupseteq="3\msy@2B
\mathchardef\nparallel="3\msy@2C
\mathchardef\nmid="3\msy@2D
\mathchardef\nshortmid="3\msy@2E
\mathchardef\nshortparallel="3\msy@2F
\mathchardef\nvdash="3\msy@30
\mathchardef\nVdash="3\msy@31
\mathchardef\nvDash="3\msy@32
\mathchardef\nVDash="3\msy@33
\mathchardef\ntrianglerighteq="3\msy@34
\mathchardef\ntrianglelefteq="3\msy@35
\mathchardef\ntriangleleft="3\msy@36
\mathchardef\ntriangleright="3\msy@37
\mathchardef\nleftarrow="3\msy@38
\mathchardef\nrightarrow="3\msy@39
\mathchardef\nLeftarrow="3\msy@3A
\mathchardef\nRightarrow="3\msy@3B
\mathchardef\nLeftrightarrow="3\msy@3C
\mathchardef\nleftrightarrow="3\msy@3D
\mathchardef\divideontimes="2\msy@3E
\mathchardef\varnothing="0\msy@3F
\mathchardef\nexists="0\msy@40
\mathchardef\mho="0\msy@66
\mathchardef\thorn="0\msy@67
\mathchardef\beth="0\msy@69
\mathchardef\gimel="0\msy@6A
\mathchardef\daleth="0\msy@6B
\mathchardef\lessdot="3\msy@6C
\mathchardef\gtrdot="3\msy@6D
\mathchardef\ltimes="2\msy@6E
\mathchardef\rtimes="2\msy@6F
\mathchardef\shortmid="3\msy@70
\mathchardef\shortparallel="3\msy@71
\mathchardef\smallsetminus="2\msy@72
\mathchardef\thicksim="3\msy@73
\mathchardef\thickapprox="3\msy@74
\mathchardef\approxeq="3\msy@75
\mathchardef\succapprox="3\msy@76
\mathchardef\precapprox="3\msy@77
\mathchardef\curvearrowleft="3\msy@78
\mathchardef\curvearrowright="3\msy@79
\mathchardef\digamma="0\msy@7A
\mathchardef\varkappa="0\msy@7B
\mathchardef\hslash="0\msy@7D
%\mathchardef\hbar="0\msy@7E
\mathchardef\backepsilon="3\msy@7F
\def\Bbb{\relaxnext@\ifmmode\let\next\Bbb@\else
 \def\next{\Err@{Use \string\Bbb\space only in math mode}}\fi\next}
\def\Bbb@#1{{\Bbb@@{#1}}}
\def\Bbb@@#1{\noaccents@\fam\msyfam#1}
\newcount\skewcharcount@
\newcount\familycount@
\def\theskewchar@{\global\familycount@\@ne
 \global\skewcharcount@\the\skewchar\textfont\@ne
 \ifnum\fam>\m@ne\ifnum\fam<17
 \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 }
\def\accentfam@{7}
\def\noaccents@{\def\accentfam@{0}}
\def\makeacc@#1#2{\def#1{\mathaccent"\accentfam@#2 }}
\def\Makeacc@#1#2{\relaxnext@\def#1{\relax\ifmmode\def\next{\mathaccent@
 {"\accentfam@#2 }}\else\def\next{\Err@{Use
 \string#1\space only in math mode}}\fi\next}}
\makeacc@\hat{05E}           \Makeacc@\Hat{05E}
\makeacc@\check{014}         \Makeacc@\Check{014}
\makeacc@\tilde{07E}         \Makeacc@\Tilde{07E}
\makeacc@\acute{013}         \Makeacc@\Acute{013}
\makeacc@\grave{012}         \Makeacc@\Grave{012}
\makeacc@\dot{05F}           \Makeacc@\Dot{05F}
\makeacc@\ddot{07F}          \Makeacc@\Ddot{07F}
\makeacc@\breve{015}         \Makeacc@\Breve{015}
\makeacc@\bar{016}           \Makeacc@\Bar{016}
\def\vec{\mathaccent"017E }
\def\Vec{\relaxnext@\ifmmode\def\next{\mathaccent@{"017E }}\else
 \def\next{\Err@{Use \string\vec\space only in math mode}}\fi\next}
\newdimen\accentdimen@
\newcount\accentmu@
\def\unbracefonts@{\let\Cal@\Cal@@\let\rom@\rom@@\let\bold@\bold@@
 \let\slanted@\slanted@@}
\def\mathaccent@#1#2{\relaxnext@\ifnum\fam=\m@ne\xdef\thefam@{1}\else
 \xdef\thefam@{\the\fam}\fi
 \accentdimen@\z@
 \setbox\z@\hbox{\unbracefonts@$\fam\thefam@#2$}%
 \ifdim\accentdimen@=\z@\def\next{\mathaccent#1{#2}}%
 \setbox\@ne\hbox{\unbracefonts@$\fam\thefam@#2\theskewchar@$}%
 \setbox\tw@\hbox{$\ifnum\skewcharcount@=\m@ne\else
  \mathchar\skewcharcount@\fi$}%
 \global\accentdimen@\wd\@ne\global\advance\accentdimen@-\wd\z@
 \global\advance\accentdimen@-\wd\tw@
 \global\multiply\accentdimen@\tw@
 \dimentomu@\accentdimen@\accentmu@\global\advance\accentmu@\@ne\else
 \def\next{{\mathaccent#1{#2\mkern\accentmu@ mu}\mkern-\accentmu@ mu}{}}\fi
 \next}
\def\dimentomu@#1#2{\multiply#1 100
 \expandafter\getpoints@\the#1\getpoints@
 \multiply\pointcount@18
 \divide\pointcount@\@m
 \global#2\pointcount@}
\def\newbox@{\alloc@4\box\chardef\insc@unt}
\def\accentedsymbol#1#2{\expandafter\newbox@\csname\expandafter
 \eat@\string#1@box\endcsname
 \expandafter\setbox\csname\expandafter\eat@
 \string#1@box\endcsname\hbox{$#2$}\define
 #1{\expandafter\copy\csname\expandafter\eat@\string#1@box\endcsname{}}}
\def\sqrt#1{\radical"270370 {#1}}
\let\underline@\underline
\let\overline@\overline
\def\underline#1{\underline@{#1}}
\def\overline#1{\overline@{#1}}
\Invalid@\leftroot
\Invalid@\uproot
\newcount\uproot@
\newcount\leftroot@
\def\root{\relaxnext@
 \def\next@{\ifx\next\uproot\let\next\nextii@\else
  \ifx\next\leftroot\let\next\nextiii@\else
  \let\next\plainroot@\fi\fi\next}%
 \def\nextii@\uproot##1{\uproot@##1\relax\futurelet\next\nextiv@}%
 \def\nextiv@{\ifx\next\space@\def\next. {\futurelet\next\nextv@}\else
  \def\next.{\futurelet\next\nextv@}\fi\next.}%
 \def\nextv@{\ifx\next\leftroot\let\next\nextvi@\else
  \let\next\plainroot@\fi\next}%
 \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
 \def\nextiii@\leftroot##1{\leftroot@##1\relax\futurelet\next\nextvii@}%
 \def\nextvii@{\ifx\next\space@
  \def\next. {\futurelet\next\nextviii@}\else
  \def\next.{\futurelet\next\nextviii@}\fi\next.}%
 \def\nextviii@{\ifx\next\uproot\let\next\nextix@\else
  \let\next\plainroot@\fi\next}%
 \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
\bgroup\uproot@\z@\leftroot@\z@\futurelet\next\next@}
\def\plainroot@#1\of#2{\setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#1}$}%
 \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
 {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1\sqrt{#2}$}%
 \dimen@\ht\z@\advance\dimen@-\dp\z@
 \setbox1\hbox{$\m@th#1\mskip\uproot@ mu$}\advance\dimen@ by1.667\wd\@ne
 \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
 \mkern-10mu\mkern\leftroot@ mu\box\z@}
\def\boxed#1{\setbox\z@\hbox{$\displaystyle{#1}$}\hbox{\lower.4\ex@
 \hbox{\lower3\ex@\hbox{\lower\dp\z@\hbox{\vbox{\hrule height.4\ex@
 \hbox{\vrule width.4\ex@\hskip3\ex@\vbox{\vskip3\ex@\box\z@\vskip3\ex@}%
 \hskip3\ex@\vrule width.4\ex@}\hrule height.4\ex@}}}}}}
\let\ampersand@\relax
\newdimen\bigaw@
\newdimen\minaw@
\minaw@11.11128\ex@
\newdimen\minCDaw@
\minCDaw@2.5pc
\newif\ifCD@
\def\minCDarrowwidth#1{\relax\ifmmode\ifinner\onlydmatherr@\minCDarrowwidth
 \else\minCDaw@#1\relax\fi\else\onlydmatherr@\minCDarrowwidth\fi}
\def\CD{\bgroup\vspace@\relax\iffalse{\fi\let\ampersand@&\iffalse}\fi
 \CD@true\vcenter\bgroup\Let@\tabskip\z@skip\baselineskip20\ex@
 \lineskip3\ex@\lineskiplimit3\ex@\halign\bgroup
 &\hfill$\m@th##$\hfill\cr}
\def\endCD{\cr\egroup\egroup\egroup}
\atdef@>#1>#2>{\ampersand@\setbox\z@\hbox{$\ssize
 \;{#1}\;\;$}\setbox\@ne\hbox{$\ssize\;{#2}\;\;$}\setbox\tw@
 \hbox{$#2$}\ifCD@
 \global\bigaw@\minCDaw@\else\global\bigaw@\minaw@\fi
 \ifdim\wd\z@>\bigaw@\global\bigaw@\wd\z@\fi
 \ifdim\wd\@ne>\bigaw@\global\bigaw@\wd\@ne\fi
 \ifCD@\hskip.5em\fi
 \ifdim\wd\tw@>\z@
 \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill}}\limits^{#1}_{#2}}\else
 \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill}}\limits^{#1}}\fi
 \ifCD@\hskip.5em\fi\ampersand@}
\atdef@<#1<#2<{\ampersand@\setbox\z@\hbox{$\ssize
 \;\;{#1}\;$}\setbox\@ne\hbox{$\ssize\;\;{#2}\;$}\setbox\tw@
 \hbox{$#2$}\ifCD@
 \global\bigaw@\minCDaw@\else\global\bigaw@\minaw@\fi
 \ifdim\wd\z@>\bigaw@\global\bigaw@\wd\z@\fi
 \ifdim\wd\@ne>\bigaw@\global\bigaw@\wd\@ne\fi
 \ifCD@\hskip.5em\fi
 \ifdim\wd\tw@>\z@
 \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill}}\limits^{#1}_{#2}}\else
 \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill}}\limits^{#1}}\fi
 \ifCD@\hskip.5em\fi\ampersand@}
\atdef@ A#1A#2A{\llap{$\vcenter{\hbox
 {$\ssize#1$}}$}\Big\uparrow\rlap{$\vcenter{\hbox{$\ssize#2$}}$}&&}
\atdef@ V#1V#2V{\llap{$\vcenter{\hbox
 {$\ssize#1$}}$}\Big\downarrow\rlap{$\vcenter{\hbox{$\ssize#2$}}$}&&}
\atdef@={&\hskip.5em\mathrel
 {\vbox{\hrule width\minCDaw@\vskip3\ex@\hrule width
 \minCDaw@}}\hskip.5em&}
\atdef@|{\Big\Vert&&}
\atdef@@\vert{\Big\Vert&&}
\def\pretend#1\haswidth#2{\setbox\z@\hbox{$\scriptstyle{#2}$}\hbox
 to\wd\z@{\hfill$\scriptstyle{#1}$\hfill}}
\def\pmb{\relaxnext@\ifmmode\def\next{\mathpalette\pmb@}\else
 \let\next\pmb@@\fi\next}
\def\pmb@@#1{\leavevmode\setbox\z@\hbox{#1}\kern-.025em\copy\z@\kern-\wd\z@
 \kern-.05em\copy\z@\kern-\wd\z@\kern-.025em\raise.0433em\box\z@}
\def\binrel@@#1{\ifdim\wd2<\z@\mathbin{#1}\else\ifdim\wd\tw@>\z@
 \mathrel{#1}\else{#1}\fi\fi}
\newdimen\pmbraise@
\def\pmb@#1#2{\setbox\thr@@\hbox{$\m@th#1{#2}$}%
 \setbox4\hbox{$\m@th#1\mkern.7794mu$}\pmbraise@\wd4
 \divide\pmbraise@18
 \binrel@{#2}\binrel@@{\mkern-.45mu\copy\thr@@\kern-\wd\thr@@
 \mkern-.9mu\copy\thr@@\kern-\wd\thr@@\mkern-.45mu\raise\pmbraise@\box\thr@@}}
\def\documentstyle#1{\input #1.sty}
\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\fontlist@{\\{\tenrm}\\{\sevenrm}\\{\fiverm}\\{\teni}\\{\seveni}%
 \\{\fivei}\\{\tensy}\\{\sevensy}\\{\fivesy}\\{\tenex}\\{\tenbf}\\{\sevenbf}%
 \\{\fivebf}\\{\tensl}\\{\tenit}%
 %\\{\tenmsx}\\{\sevenmsx}\\{\fivemsx}\\{\tenmsy}\\{\sevenmsy}\\{\fivemsy}%
 }
\def\font@#1=#2 {\rightappend@#1\to\fontlist@\font#1=#2 }
\def\dodummy@{{\def\\##1{\global\let##1\dummyft@}\fontlist@}}
\newif\ifsyntax@
\newif\ifgalleys@
\newcount\countxviii@
\def\newtoks@{\alloc@5\toks\toksdef\@cclvi}
\def\nopages@{\output={\setbox\z@\box255 \deadcycles\z@}\newtoks@\output}
\def\syntax{\syntax@true\dodummy@\countxviii@\count18
 \loop\ifnum\countxviii@>\z@\textfont\countxviii@=\dummyft@
 \scriptfont\countxviii@=\dummyft@\scriptscriptfont\countxviii@=\dummyft@
 \advance\countxviii@\m@ne\repeat
 \dummyft@\tracinglostchars\z@\nopages@\frenchspacing\hbadness\@M}
\def\galleys{\galleys@true\nopages@}
\def\S@{S } \def\G@{G } \def\P@{P }
\newif\ifbadans@
\def\printoptions{\immediate\write\sixt@@n{Do you want S(yntax check),
  G(alleys) or P(ages)?^^JType S, G or P, follow by <return>: }\loop
 \read\m@ne to\ans@
 \xdef\next{\def\noexpand\Ans@{\ans@}}%
 \uppercase\expandafter{\next}%
 \ifx\Ans@\S@\badans@false\syntax\else
 \ifx\Ans@\G@\badans@false\galleys\else
 \ifx\Ans@\P@\badans@false\else
 \badans@true\fi\fi\fi
 \ifbadans@\immediate\write\sixt@@n{Type S, G or P, follow by <return>: }%
 \repeat}
\def\alloc@#1#2#3#4#5{\global\advance\count1#1by\@ne
 \ch@ck#1#4#2\allocationnumber=\count1#1
 \global#3#5=\allocationnumber
 \ifalloc@\wlog{\string#5=\string#2\the\allocationnumber}\fi}
\def\document{\def\alloclist@{\empty}\def\fontlist@{\empty}}
\let\enddocument\bye
\let\plainproclaim\proclaim
\let\plainfootnote\footnote
\let\proclaim\undefined
\let\footnote\undefined
\let\=\undefined
\let\>\undefined
\let\cal\undefined
\let\mit\undefined
\let\oldstyle\undefined
\catcode`\@=\active
\def\Fmtname{amstex}\def\Fmtversion{1.0}
