%Paper: 
%From: NARDI@mail.physics.lsa.umich.edu
%Date: Wed, 9 Sep 92 13:07 EDT


%%%%%%%%%%%%%%%%%%%%%%%   MACROS    %%%%%%%%%%%%%%%%%%%%%%%

\def\pmb#1{\setbox0=\hbox{#1}%
  \hbox{\kern-.025em\copy0\kern-\wd0
  \kern.05em\copy0\kern-\wd0
  \kern-0.025em\raise.0433em\box0} }

\def \mapright#1{\smash{\mathop{\longrightarrow}\limits^{#1}}}
\def\half {{1\over 2}}
\def\eps{\tens{\hbox{\mm \char'42}}_{\hskip -5pt\infty}}
\catcode`@=11
\def\leftrightarrowfill{$\m@th\mathord\leftarrow \mkern-6mu
  \cleaders\hbox{$\mkern-2mu \mathord- \mkern-2mu$}\hfill
  \mkern-6mu \mathord\rightarrow$}
\def\overleftrightarrow#1{\vbox{\ialign{##\crcr
     \leftrightarrowfill\crcr\noalign{\kern-1pt\nointerlineskip}
     $\hfil\displaystyle{#1}\hfil$\crcr}}}
\catcode`@=12
\def\tens{\overleftrightarrow}

\def\approxge{\hbox {\hfil\raise .4ex\hbox{$>$}\kern-.75 em
\lower .7ex\hbox{$\sim$}\hfil}}
\def\approxle{\hbox {\hfil\raise .4ex\hbox{$<$}\kern-.75 em
\lower .7ex\hbox{$\sim$}\hfil}}

%\def \section
%      #1          {\vbox{\smallskip\bigskip\noindent{\bf #1}\medskip}
%                   \nobreak}
\def \abstract#1 {\vskip 0.5truecm\sepline\vskip 0.5truecm
$$\vbox{\hsize=15truecm\noindent #1}$$}
\def \SISSA#1#2 {\vfil\vfil\centerline{Ref. S.I.S.S.A. #1 CM (#2)}}
\def \PACS#1 {\vfil\line{\hfil\hbox to 15truecm{PACS numbers: #1 \hfil}\hfil}}

\def \hfigure
     #1#2#3       {\midinsert \vskip #2 truecm $$\vbox{\hsize=14.5truecm
             \seven\baselineskip=10pt\noindent {\bcp \noindent Figure  #1}.
                   #3 } $$ \vskip -20pt \endinsert }

\def \hfiglin
     #1#2#3       {\midinsert \vskip #2 truecm $$\vbox{\hsize=14.5truecm
              \seven\baselineskip=10pt\noindent {\bcp \hfil\noindent
                   Figure  #1}. #3 \hfil} $$ \vskip -20pt \endinsert }

\def \vfigure
     #1#2#3#4     {\dimen0=\hsize \advance\dimen0 by -#3truecm
                   \midinsert \vbox to #2truecm{ \seven
                   \parshape=1 #3truecm \dimen0 \baselineskip=10pt \vfill
                   \noindent{\bcp Figure #1} \pretolerance=6500#4 \vfill }
                   \endinsert }

\def\hfigureps#1#2#3#4{
\midinsert
      \vskip #2 truecm
      \special{#4}
      $$
         \vbox{
            \hsize=14.5truecm \seven\baselineskip=10pt\noindent
            {\bcp \noindent Figure  #1}. #3
         }
      $$
      \vskip -10pt
\endinsert
}
%
% definizione di
\def \ref
     #1#2         {\smallskip \item{[#1]}#2}
\def \sepline     {\medskip\centerline{\vbox{\hrule width5truecm}} \medskip}
\def \tabrule     {\noalign{\vskip 5truept \hrule\vskip 5truept} }
\def \tabrul2     {\noalign{\vskip 5truept \hrule \vskip 2truept \hrule
                   \vskip 5truept} }

% \def \footnoterule{\kern-3pt \hrule width 0truein \kern2.6pt}

% \pageno=0
\footline={\ifnum\pageno>0 \tenrm \hss \folio \hss \fi }

\def\today
 {\count10=\year\advance\count10 by -1900 \number\day--\ifcase
  \month \or Jan\or Feb\or Mar\or Apr\or May\or Jun\or
             Jul\or Aug\or Sep\or Oct\or Nov\or Dec\fi--\number\count10}

\def\hour{\count10=\time\count11=\count10
\divide\count10 by 60 \count12=\count10
\multiply\count12 by 60 \advance\count11 by -\count12\count12=0
\number\count10 :\ifnum\count11 < 10 \number\count12\fi\number\count11}

\def\draft{
   \baselineskip=20pt
   \def\makeheadline{\vbox to 10pt{\vskip-22.5pt
   \line{\vbox to 8.5pt{}\the\headline}\vss}\nointerlineskip}
   \headline={\hfill \seven {\bcp Draft version}: today is \today\ at \hour
              \hfill}
          }

%
% Max -macros
%

%
\catcode`@=11
%
%------------------------- comandi riservati ---------------------------
%
\def\b@lank{ }

\newif\if@simboli
\newif\if@riferimenti

\newwrite\file@simboli
\def\simboli{
    \immediate\write16{ !!! Genera il file \jobname.SMB }
    \@simbolitrue\immediate\openout\file@simboli=\jobname.smb}

\newwrite\file@ausiliario
\def\riferimentifuturi{
    \immediate\write16{ !!! Genera il file \jobname.AUX }
    \@riferimentitrue\openin1 \jobname.aux
    \ifeof1\relax\else\closein1\relax\input\jobname.aux\fi
    \immediate\openout\file@ausiliario=\jobname.aux}

\newcount\eq@num\global\eq@num=0
\newcount\sect@num\global\sect@num=0

\newif\if@ndoppia
\def\numerazionedoppia{\@ndoppiatrue\gdef\la@sezionecorrente{\the\sect@num}}

\def\se@indefinito#1{\expandafter\ifx\csname#1\endcsname\relax}
\def\spo@glia#1>{} % si applica a \meaning\xxxxx; butta via tutto quello
                   % che produce \meaning fino al carattere >
                   % (v. manuale TeX, pag. 382, \strip#1>{}).

\newif\if@primasezione
\@primasezionetrue

\def\s@ection#1\par{\immediate
    \write16{#1}\if@primasezione\global\@primasezionefalse\else\goodbreak
    \vskip\spaziosoprasez\fi\noindent
    {\bf#1}\nobreak\vskip\spaziosottosez\nobreak\noindent}
%
%------------------------------ a disp. dell'utente:  sezioni -------------

\def\sezpreset#1{\global\sect@num=#1
    \immediate\write16{ !!! sez-preset = #1 }   }

\def\spaziosoprasez{50pt plus 60pt}
\def\spaziosottosez{15pt}

\def\sref#1{\se@indefinito{@s@#1}\immediate\write16{ ??? \string\sref{#1}
    non definita !!!}
    \expandafter\xdef\csname @s@#1\endcsname{??}\fi\csname @s@#1\endcsname}

\def\autosez#1#2\par{
    \global\advance\sect@num by 1\if@ndoppia\global\eq@num=0\fi
    \xdef\la@sezionecorrente{\the\sect@num}
    \def\usa@getta{1}\se@indefinito{@s@#1}\def\usa@getta{2}\fi
    \expandafter\ifx\csname @s@#1\endcsname\la@sezionecorrente\def
    \usa@getta{2}\fi
    \ifodd\usa@getta\immediate\write16
      { ??? possibili riferimenti errati a \string\sref{#1} !!!}\fi
    \expandafter\xdef\csname @s@#1\endcsname{\la@sezionecorrente}
    \immediate\write16{\la@sezionecorrente. #2}
    \if@simboli
      \immediate\write\file@simboli{ }\immediate\write\file@simboli{ }
      \immediate\write\file@simboli{  Sezione
                                  \la@sezionecorrente :   sref.   #1}
      \immediate\write\file@simboli{ } \fi
    \if@riferimenti
      \immediate\write\file@ausiliario{\string\expandafter\string\edef
      \string\csname\b@lank @s@#1\string\endcsname{\la@sezionecorrente}}\fi
    \goodbreak\vskip 48pt plus 60pt
% \noindent{\lltitle\the\sect@num.\quad  #2} % escluso per prD (I.,II.,III)
% \par\nobreak\vskip 15pt \nobreak\noindent}
\centerline{\lltitle #2}                     %  per prD.
\par\nobreak\vskip 15pt \nobreak\noindent}

\def\semiautosez#1#2\par{
    \gdef\la@sezionecorrente{#1}\if@ndoppia\global\eq@num=0\fi
    \if@simboli
      \immediate\write\file@simboli{ }\immediate\write\file@simboli{ }
      \immediate\write\file@simboli{  Sezione ** : sref.
          \expandafter\spo@glia\meaning\la@sezionecorrente}
      \immediate\write\file@simboli{ }\fi
\noindent\lltitle \s@ection#2 \par}

%------------------------------ a disp. dell'utente:  equazioni -----------

\def\eqpreset#1{\global\eq@num=#1
     \immediate\write16{ !!! eq-preset = #1 }     }

\def\eqref#1{\se@indefinito{@eq@#1}
    \immediate\write16{ ??? \string\eqref{#1} non definita !!!}
    \expandafter\xdef\csname @eq@#1\endcsname{??}
    \fi\csname @eq@#1\endcsname}

\def\eqlabel#1{\global\advance\eq@num by 1
    \if@ndoppia\xdef\il@numero{\la@sezionecorrente.\the\eq@num}
       \else\xdef\il@numero{\the\eq@num}\fi
    \def\usa@getta{1}\se@indefinito{@eq@#1}\def\usa@getta{2}\fi
    \expandafter\ifx\csname @eq@#1\endcsname\il@numero\def\usa@getta{2}\fi
    \ifodd\usa@getta\immediate\write16
       { ??? possibili riferimenti errati a \string\eqref{#1} !!!}\fi
    \expandafter\xdef\csname @eq@#1\endcsname{\il@numero}
    \if@ndoppia
       \def\usa@getta{\expandafter\spo@glia\meaning
       \la@sezionecorrente.\the\eq@num}
       \else\def\usa@getta{\the\eq@num}\fi
    \if@simboli
       \immediate\write\file@simboli{  Equazione
            \usa@getta :  eqref.   #1}\fi
    \if@riferimenti
       \immediate\write\file@ausiliario{\string\expandafter\string\edef
       \string\csname\b@lank @eq@#1\string\endcsname{\usa@getta}}\fi}

\def\autoeqno#1{\eqlabel{#1}\eqno(\csname @eq@#1\endcsname)}
\def\autoleqno#1{\eqlabel{#1}\leqno(\csname @eq@#1\endcsname)}
\def\eqrefp#1{(\eqref{#1})}

%%%%%%%%%%%%%%%%%%%%%    abbreviazioni       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\eq{\autoeqno}
\def\req{\eqrefp}
\def\chap{\autosez}        % #1 per il numero (scritto)     #2 per il titolo
\def\nochap{\semiautosez}  % #1 per il numero (non scritto) #2 per il titolo


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%--------------- bibliografia automatica: riservati ----------------------

\newcount\cit@num\global\cit@num=0

\newwrite\file@bibliografia
\newif\if@bibliografia
\@bibliografiafalse

\def\lp@cite{[}
\def\rp@cite{]}
\def\trap@cite#1{\lp@cite #1\rp@cite}
\def\lp@bibl{[}
\def\rp@bibl{]}
\def\trap@bibl#1{\lp@bibl #1\rp@bibl}

\def\refe@renza#1{\if@bibliografia\immediate        % scrive su .BIB
    \write\file@bibliografia{
    \string\item{\trap@bibl{\cref{#1}}}\string
    \bibl@ref{#1}\string\bibl@skip}\fi}

\def\ref@ridefinita#1{\if@bibliografia\immediate\write\file@bibliografia{
    \string\item{?? \trap@bibl{\cref{#1}}} ??? tentativo di ridefinire la
      citazione #1 !!! \string\bibl@skip}\fi}

\def\bibl@ref#1{\se@indefinito{@ref@#1}\immediate
    \write16{ ??? biblitem #1 indefinito !!!}\expandafter\xdef
    \csname @ref@#1\endcsname{ ??}\fi\csname @ref@#1\endcsname}

\def\c@label#1{\global\advance\cit@num by 1\xdef            % assegna il numero
   \la@citazione{\the\cit@num}\expandafter
   \xdef\csname @c@#1\endcsname{\la@citazione}}

\def\bibl@skip{\vskip +4truept}

%------------------------ bibl. automatica: a disp. dell'utente ------------

\def\stileincite#1#2{\global\def\lp@cite{#1}\global   %  Definisce le parentesi
    \def\rp@cite{#2}}                                 %  nelle citazioni
\def\stileinbibl#1#2{\global\def\lp@bibl{#1}\global   %  Definisce le parentesi
    \def\rp@bibl{#2}}                                 %  nella bibliografia

\def\citpreset#1{\global\cit@num=#1
    \immediate\write16{ !!! cit-preset = #1 }    }

\def\autobibliografia{\global\@bibliografiatrue\immediate
    \write16{ !!! Genera il file \jobname.BIB}\immediate
    \openout\file@bibliografia=\jobname.bib}

\def\cref#1{\se@indefinito                  % se indefinito definisce
   {@c@#1}\c@label{#1}\refe@renza{#1}\fi\csname @c@#1\endcsname}

\def\cite#1{\trap@cite{\cref{#1}}}                  %  [5]
\def\ccite#1#2{\trap@cite{\cref{#1},\cref{#2}}}     %  [5,6]
\def\ncite#1#2{\trap@cite{\cref{#1}--\cref{#2}}}    %  [5-8] senza definire
\def\upcite#1{$^{\,\trap@cite{\cref{#1}}}$}               % ^[5]
\def\upccite#1#2{$^{\,\trap@cite{\cref{#1},\cref{#2}}}$}  % ^[5,6]
\def\upncite#1#2{$^{\,\trap@cite{\cref{#1}-\cref{#2}}}$}  % ^[5-8] senza def.
\def\Rcite#1{Ref. \cref{#1}}
\def\Rccite#1#2{Refs. \cref{#1},\cref{#2} }
\def\clabel#1{\se@indefinito{@c@#1}\c@label           % sola definizione
    {#1}\refe@renza{#1}\else\c@label{#1}\ref@ridefinita{#1}\fi}
\def\cclabel#1#2{\clabel{#1}\clabel{#2}}                     % def. doppia
\def\ccclabel#1#2#3{\clabel{#1}\clabel{#2}\clabel{#3}}       % def. tripla

\def\biblskip#1{\def\bibl@skip{\vskip #1}}           % spaziatura nella bibl.

\def\insertbibliografia{\if@bibliografia             % scrive la bibliografia
    \immediate\write\file@bibliografia{ }
    \immediate\closeout\file@bibliografia
    \catcode`@=11\input\jobname.bib\catcode`@=12\fi}

%--------- per comporre il file con la bibliografia --------------

\def\commento#1{\relax}
\def\biblitem#1#2\par{\expandafter\xdef\csname @ref@#1\endcsname{#2}}

% ricordare: una lista in chiaro della bibliografia si
% ottiene eseguendo $ TEX BIBLIST

%------------------------------ F I N E ---------------------------------
\catcode`@=12
%---------------------- P E R  L A  P A G I N A  ------------------------

%  Fissa i parametri della pagina

\magnification=1200
\topskip 20pt
\def\interlinea{\baselineskip=16pt}
% \def\interlinea{\baselineskip=22pt}                     % for proofs
\def\standardpage{\vsize=20.7truecm\voffset=+1.truecm
                  \hsize=15.truecm\hoffset=+10truemm
%                  \hsize=14.truecm\hoffset=+15truemm   % for proofs
                  \parindent=1.2truecm}

\tolerance 100000
\biblskip{+8truept}                        % spaziatura nella bibliografia
\def\hbup{\hfill\break\baselineskip 16pt}  % spaziatura fra i vari items

%------------------------- P E R  L E  N O T E --------------------------

\global\newcount\notenumber \global\notenumber=0
\def\note #1 {\global\advance\notenumber by1 \baselineskip 10pt
              \footnote{$^{\the\notenumber}$}{\nine #1} \interlinea}
\def\clearnotenumber{\notenumber=0}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%  Fonts......

\font\text=cmr10
\font\scal=cmsy5
\font\bcal=cmsy10 scaled \magstep3   %  big calligrafic
\font\it=cmti10
\font\name=cmssi10 scaled \magstep1
\font\lname=cmssi9
\font\btitle=cmbx10 scaled \magstep4     %%%%%%%%%%%
\font\title=cmbx10 scaled \magstep3      %   per titoli normali
% \font\ltitle=cmbx10 scaled \magstep2
\font\ltitle=cmbx12 scaled \magstep1
\font\lltitle=cmbx12 scaled \magstep1
% \font\lltitle=cmbx10 scaled \magstep1    %%%%%%%%%%%
\font\bmtitle=cmmi12                      %%%%%%%%%%%
\font\mtitle=cmmi12 %  scaled \magstep1     %   per titoli in matematico
\font\lmtitle=cmmi12                     %%%%%%%%%%%
\font\itltitle=cmti10 scaled \magstep2   %   per titoli in italico
\font\ittitle=cmti10 scaled \magstep3    %   per titoli in italico
\font\subtitle=cmbx10 scaled \magstep1
\font\abs=cmti10 scaled \magstep1        %    per l' abstract

\font\mb=cmmib10
\font\seven=cmr7                         %  per note e captions
\font\eight=cmr8                         %  per note e captions
\font\nine=cmr9                         %  per note e captions
\font\bcp=cmbx7
\font\icp=cmmi7
\font\bb=cmbx12 scaled \magstep1
\font\bl=cmbx12

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% NUMERAZIONE AUTOMATICA DELLE FORMULE.
% Istruzioni dell'automacro:

%   \eqlabel{pippo}:     aumenta di 1 il contatore delle equazioni.
%   \eqref{pippo}:       richiama il numero associato a pippo.
%   \autoeqno:           e' definito come
%                        "\eqlabel{pippo}\eqno(\eqref{pippo})".
%   \autosez{mike}:  aumenta di uno il contatore delle sezioni
%                        e azzera il contatore delle equazioni.
%   \sref{mike}:         richiama il numero associato a mike.
%    per cominciare una sezione: \autosez{1} titolo \par

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    queste istruzioni sono riportate nell' automacro !!!

%    \def\eq{\autoeqno}       % per numerare le equazioni
%    \def\req#1{(\eqref{#1})} % per richiamare le equazioni

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%% maggiore-circa,  minore-circa

\def\gtrsim{\ \rlap{\raise 2pt \hbox{$>$}}{\lower 2pt \hbox{$\sim$}}\ }
\def\lesssim{\ \rlap{\raise 2pt \hbox{$<$}}{\lower 2pt \hbox{$\sim$}}\ }

%%%%%% definizioni generali

\def\salta{\vskip 2pt}
\def\mn{\medskip\noindent}
\def\bs{\bigskip}
\def\hb{\hfil\break}
\def\no{\noindent}

\def\scs{\scriptstyle}
\def\scss{\scriptscriptstyle}
\def\ph#1{\phantom#1}
\def\o{\over}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%  definizioni per la bibliografia

\def\ea{{\it et.al.}}
\def\ib{{\it ibid.\ }}

\def\npb#1{Nucl. Phys. {\bf B#1},}
\def\plb#1{Phys. Lett. {\bf B#1},}
\def\prd#1{Phys. Rev. {\bf D#1},}
\def\prl#1{Phys. Rev. Lett. {\bf #1},}
\def\zpc#1{Z. Phys. {\bf C#1},}
\def\prep#1{Phys. Rep. {\bf #1},}
\def\rmp{Rev. Mod. Phys. }
\def\ijmpa{Int. Jour. Mod. Phys. A }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \autobibliografia    %  per il file BIBL.TEX
\stileincite{}{}     %  Definisce le parentesi nelle citazioni
\numerazionedoppia   % avverte che ci sono vari capitoli

\interlinea
\standardpage
\text                %  font per il testo

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\scs#1{{\scriptstyle #1}}
\def\scss#1{{\scriptscriptstyle #1}}
\def\ph#1{\phantom{#1}}
\def\o{\over}
\def\half{{1\over 2}}

%    FITDEF.TEX


\def\clel{c_L^{e}}
\def\slel{s_L^{e}}
\def\crel{c_R^{e}}
\def\srel{s_R^{e}}

\def\clmu{c_L^{\mu}}
\def\slmu{s_L^{\mu}}
\def\crmu{c_R^{\mu}}
\def\srmu{s_R^{\mu}}

\def\cltau{c_L^{\tau}}
\def\sltau{s_L^{\tau}}
\def\crtau{c_R^{\tau}}
\def\srtau{s_R^{\tau}}

\def\clu{c_L^{u}}
\def\slu{s_L^{u}}
\def\cru{c_R^{u}}
\def\sru{s_R^{u}}

\def\cld{c_L^{d}}
\def\sld{s_L^{d}}
\def\crd{c_R^{d}}
\def\srd{s_R^{d}}

\def\cls{c_L^{s}}
\def\sls{s_L^{s}}
\def\crs{c_R^{s}}
\def\srs{s_R^{s}}

\def\clc{c_L^{c}}
\def\slc{s_L^{c}}
\def\crc{c_R^{c}}
\def\src{s_R^{c}}

\def\clb{c_L^{b}}
\def\slb{s_L^{b}}
\def\crb{c_R^{b}}
\def\srb{s_R^{b}}

\def\clnue{c_L^{\nu_e}}
\def\slnue{s_L^{\nu_e}}
\def\crnue{c_R^{\nu_e}}
\def\srnue{s_R^{\nu_e}}

\def\clnumu{c_L^{\nu_\mu}}
\def\slnumu{s_L^{\nu_\mu}}
\def\crnumu{c_R^{\nu_\mu}}
\def\srnumu{s_R^{\nu_\mu}}

\def\clnutau{c_L^{\nu_\tau}}
\def\slnutau{s_L^{\nu_\tau}}
\def\crnutau{c_R^{\nu_\tau}}
\def\srnutau{s_R^{\nu_\tau}}

\def\kud{\kappa_{ud}}
\def\kus{\kappa_{us}}
\def\kcd{\kappa_{cd}}
\def\kcs{\kappa_{cs}}

%    BOTDEF.TEX

\def\A{{\cal A}}
\def\ww{M^2_W}
\def\zz{M^2_Z}
\def\zzo{M^2_{Z_0}}
\def\zzp{M^2_{Z^\prime}}
\def\ss{s^2_w}
\def\cc{c^2_w}
\def\G{{\cal G_{\rm SM}}}
\def\E{{\rm E}_6}
\def\sb{s_{\beta}}
\def\cb{c_{\beta}}

\def\N{{\hbox{\scal N}}}
\def\K{{\hbox{\scal K}}}

\def\pr{\prime}
\def\nubar{{\buildrel (-) \over \nu}}
\def\numubar{{\buildrel (-) \over {\nu_\mu}}}

%    LFC.TEX

\font\mbf=cmmib10  scaled \magstep1      %  boldface mathematic and italic.
\def\bfchi{{\hbox{\mbf\char'037}}}
\def\bftau{{\hbox{\mbf\char'034}}}
\def\bflambda{{\hbox{\mbf\char'025}}}
\def\bfmu{{\hbox{\mbf\char'026}}}
\def\bfepsilon{{\hbox{\mbf\char'017}}}
\def\bfe{{\hbox{\mbf\char'145}}}
\def\bfu{{\hbox{\mbf\char'165}}}
\def\bfF{{\hbox{\mbf\char'106}}}
\def\bfC{{\hbox{\mbf\char'103}}}
\def\bfS{{\hbox{\mbf\char'123}}}
\def\bfa{{\hbox{\mbf\char'141}}}

\font\bigm=cmmi12            %  big mathematic and italic.
\def\bchi{{\hbox{\bigm\char'037}}}
\def\btau{{\hbox{\bigm\char'034}}}
\def\blambda{{\hbox{\bigm\char'025}}}
\def\bmu{{\hbox{\bigm\char'026}}}
\def\bepsilon{{\hbox{\bigm\char'017}}}
\def\be{{\hbox{\bigm\char'145}}}
\def\bu{{\hbox{\bigm\char'165}}}
\def\bF{{\hbox{\bigm\char'106}}}
\def\bC{{\hbox{\bigm\char'103}}}
\def\bS{{\hbox{\bigm\char'123}}}
\def\ba{{\hbox{\bigm\char'141}}}

%%%%%%%%%%%%%%%%%%%%%%%   PAPER    %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%   PAPER    %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%   PAPER    %%%%%%%%%%%%%%%%%%%%%%%

\autobibliografia
% \pageno=1                    % for proofs
\pageno=0
\vsize=23.8truecm
\hsize=15.7truecm
\voffset=-1.truecm
\hoffset=+6truemm
\baselineskip 14pt
\rightline{UM-TH 92--19}\par\noindent

\bs\bs\bs
\centerline{\ltitle   Z$^{\displaystyle\bf \prime}$,
new fermions and flavor changing processes.}
\medskip
\medskip
\centerline{\ltitle
   Constraints on E$_{\, \displaystyle\bf 6}\,$ models from
\bfmu $\ \longrightarrow$ \bfe\bfe\bfe.}
% \bmu $\ \rightarrow$ \be\be\be.}
%   {\bmtitle \bf $\mu\rightarrow eee$}.}
\bs\bs
\bs\bs                                   %    !!!!!!!!!!!!!!!!!!
                 \centerline{Enrico Nardi}
\bs
\centerline{\it Randall Laboratory of Physics, University of Michigan,
           Ann Arbor, MI 48109--1120}
\vskip 1truecm                             %    !!!!!!!!!!!!!!!!!!!

\medskip
\centerline  { \bf {\abs Abstract}}      %    !!!!!!!!!!!!!!!!!!!
\bs

% \baselineskip 20pt                         %    !!!!!!!!!!!!!!!!!!!

\noindent
We study a new class of flavor changing interactions, which can arise
in models based on extended gauge groups (rank $>$4) when new charged
fermions are present together with a new neutral gauge boson. We
discuss the cases in which the flavor changing couplings in the new
neutral current coupled to the $Z^\prime$ are theoretically expected
to be large, implying that the observed suppression of neutral flavor
changing transitions must be provided by heavy $Z^\prime$ masses
together with small $Z$-$Z^\prime$ mixing angles. Concentrating on
E$_6$ models, we show how the tight experimental limit on $\mu
\rightarrow eee$ implies serious constraints on the $Z^\prime$ mass
and mixing angle. We conclude that if the value of the flavor changing
parameters is assumed to lie in a theoretically natural range, in most
cases the presence of a $Z^\prime$ much lighter than 1 TeV is
unlikely.
\bs
\noindent
PACS number(s): 13.10.+q,12.10.Dm,12.15.Cc,14.60.Jj
\vfill
\noindent
--------------------------------------------\phantom{-} \hb
\leftline{E-mail: nardi@umiphys.bitnet}
\bigskip
\leftline{UM-TH 92--19}
                   \bigskip
\centerline{August 1992}

\bs\bs
\eject
%              \bye

\standardpage                            %    !!!!!!!!!!!!!!!!!!!!!!!!
\interlinea                              %    !!!!!!!!!!!!!!!!!!!!!!!!
\null

\chap{Int} I. Introduction

The large set of accurate measurements performed during the last few
years has established that the standard electroweak theory provides an
excellent description of the particle physics phenomena up to about
100 GeV. It should also be stressed that the present theory
accommodates in a satisfactory way the whole spectrum of known
particles, and only two states, the top--quark and the Higgs scalar
that are necessary for the consistency of the model, have not been
discovered yet.
Another feature of the standard model (SM) that explains in a
satisfactory way a large set of experimental limits on rare processes,
is the Glashow-Iliopoulos-Maiani % (GIM)
suppression of flavor changing
neutral currents (FCNC) in the quark sector, together with the absence
of lepton flavor violating (LFV) currents.
All these features are quite peculiar of the SM, and in general most
of its possible extensions
predict a larger spectrum of states as well as larger rates for
FCNC processes.
Clearly the direct detection of any new unconventional particle would
be a major breakthrough towards the identification of a
new and more fundamental theory, but at the same time it is not
unlikely that some hints on the existence of new physics will come
from the observation of rare processes at rates larger than
what expected in the standard theory.

The aim of this paper is to analyze a new class of
FCNC interactions that are generally
present in most of the extensions of the
SM which predict one (or more) additional neutral gauge boson
$Z_1$ together with
new charged fermions, and that are induced by $Z_1$ interactions.
In general the $Z_1$ is expected to be mixed with the standard
$Z_0$, and as a consequence both the resulting mass eigenstates,
that we will denote  as $Z$ and $Z^\pr$, will have flavor
changing couplings to the known charged fermions.

In particular we will concentrate on
LFV interactions, which are strictly forbidden in the SM,
and we will show that they could provide a clear signature
for this kind of new physics. In turn, the existing limits on LFV processes
imply serious constraints for several interesting models.
To stress the power of these constraints we will apply them to
a class of E$_6$ grand unified theories (GUTs),
which are a well known example of
theories where additional fermions and new neutral gauge bosons are
simultaneously present, and provide a good
frame for illustrating the kind of effects that we
want to explore. In an attempt of quantifying the constraints, we
will assume for the relevant E$_6$ LFV couplings
a range of values that we believe is theoretically natural,
and we will then turn the existing limits on LFV decays into
limits on the $Z^\prime$ parameters.
Though model dependent, our bounds turn out to be
much tighter than the present
limits obtained from direct searches at colliders [\cite{zp-direct}]
or as derived from the analysis of other $Z^\prime$ indirect effects
[\cite{fit6}\clabel{l-luo}--\cite{zp-new}].

The interesting possibility of violating
the conservation of lepton family number
as a consequence of $Z_1$
interactions was already briefly analyzed in [\cite{zp-fc}]
for a general class of extended electroweak models.
It was shown that LFV decays of the standard neutral gauge boson
like $Z  \rightarrow \ell_i \ell_j$, ($i\ne j$,
hereafter understood) can be induced by the presence of a $Z_1$ \
$i)$ if a sizeable mixing with the $Z_1$ is present, and \
$ii)$ if the new neutral gauge boson do not couple universally to the
fermion generations.
While the first condition is a natural feature of extended gauge models,
it could seem that the second one is somewhat more difficult to realize.
However, we will show that both these conditions are naturally satisfied
in extended gauge models that, like E$_6$, predict also new charged
fermions. This was already noted in a recent paper [\cite{fit6}],
where the consequences of the simultaneous presence of new neutral gauge bosons
and new fermions were analyzed, and a general formalism for taking
into account their combined effects was outlined.

In models like E$_6$, where several new neutral leptons are present
and a quite general form for the corresponding mass matrices and mixing
patterns is possible, LFV processes like $Z \rightarrow \ell_i
\ell_j$ arise naturally due to the contributions of loop
diagrams [\cite{e6-fcloop}]. A $Z_0\ell_i \ell_j$ vertex for
the gauge eigenstate $Z_0$ boson can however
appear already at the tree level, due to the presence of new exotic
charged leptons that could be mixed with the standard ones. A general
discussion of this kind of flavor changing vertices is given
e.g. in [\cite{ll1}], while the particular case of E$_6$ models is
analyzed in [\cite{e6-fcrizzo}].
The interest of considering flavor changing $Z_1$ interactions
stems from the fact that while in general the $Z_0$ flavor changing vertices
are strongly suppressed as the ratio between the masses of the known
and of the knew fermions, in some class of models no suppression factors are
expected for the $Z_1 f_i f_j$ vertices.
Then, in the context of these models, the
new interactions due to the additional gauge boson
could well represent the main source of flavor changing transitions.

In Sec. II
we will first review the essential formalism for dealing with
gauge boson and fermion mixing effects [\cite{fit6}] and
we will also
discuss the theoretical expectations  for the various flavor changing
parameters.
In Sec. III we will concentrate on E$_6$ models. We will confront the
theoretical expression for the decay
$\mu \rightarrow eee$ with the extremely stringent experimental limit
$Br(\mu^+ \rightarrow e^+e^+e^-) < 1\cdot 10^{-12}$
obtained by the SINDRUM collaboration [\cite{sindrum}],
and we will derive constraints on the mass of the new gauge boson
and on the
$Z_0$--$Z_1$ mixing angle as a function of the LFV parameters.
Finally, in Sec. IV we will draw our conclusions.


\chap{Form} {II. Z$^{\displaystyle\bf \prime}$ and new fermion effects.
           Formalism}

\nobreak
\bigskip
\nobreak
We will now review the formalism for describing the combined effects due
to the presence of a new neutral gauge boson, and of new fermions that
could be mixed with the known ones. We will follow closely the presentation
given in [\cite{fit6}] concentrating mainly on
the charged fermions sector and on flavor changing effects, and
we refer to [\cite{fit6}] for a more general discussion.
We will assume a low energy gauge group of the form
$\G\times U_1(1)$, where  $\G = SU(2)_L \times U(1)_Y \times
SU(3)_C$ is the usual SM gauge group.
Then in the gauge basis, the corresponding neutral current Lagrangian
reads

$$
-{\cal L}_{\rm NC}=eJ^\mu_{\rm em}A_\mu +
g_0 J_0^\mu Z_{0 \mu} + g_1 J_1^\mu Z_{1 \mu}.
\eq{2.1}
$$
\mn
In \req{2.1} $Z_0$ is the SM neutral gauge boson,
which couples with strength

$$
g_0 =(4\sqrt{2} G_F M^2_{Z_0})^{1/2}
\eq{2.2}
$$
to the usual combination of the neutral isospin and electromagnetic
currents
$$
J^\mu_0=J^\mu_3-s^2_W J^\mu_{\rm em}
\eq{2.3}
$$
where $s^2_W=\sin^2\theta_W$ is the weak mixing angle.
The new $Z_1$ corresponds to the additional $U_1(1)$ factor,
and couples to the new $J_1$ current with strength $g_1$.
In particular, if we assume that the $U_1(1)$ originates at low energy
from a GUT based on a $simple$ group,
then the $q_1(f)$ charges of the fermions are
fixed by the gauge group.
Normalizing the new generator $Q_1$
to the hypercharge axis $Y/2$ and assuming a similar renormalization
group evolution for the two abelian couplings $g_1$ and $g_{\scss Y}$
down to the electroweak scale, the
coupling strength of the new interaction can be written as
$$
g_1 \simeq g_0 s_W.
\eq{2.4}
$$
In general, after spontaneous symmetry breaking
the $Z_0$--$Z_1$ mass matrix turns out to be non diagonal.
The  $Z$ and $Z^\pr$ gauge bosons mass eigenstates
then correspond to two orthogonal combinations of
$Z_0$ and $Z_1$ that we will parametrize in term of
an angle $\phi$.
As a result, the currents that couple with strength $g_0$ to the physical
$Z$ and $Z^\prime$ are:
$$
\pmatrix{ J^\mu_Z \cr J^\mu_{Z^\prime} } =
\pmatrix{c_\phi&s_\phi\cr -s_\phi&c_\phi\cr}
\pmatrix{ J^\mu_0 \cr s_W J^\mu_1 }.
\eq{2.5}
$$
\mn
We see that the main effects of the presence of the new gauge boson
are the additional contribution to NC amplitudes,
described by the third term in the Lagrangian
\req{2.1}, and the mixing between the $J_0$ and $J_1$
currents in \req{2.5}.
We will not discuss additional indirect effects, as e.g. the shifts
induced by $Z_0$--$Z_1$ mixing in
the value of the weak mixing angle $s_W$  and in the overall coupling
strength $g_0$ when expressed as a function of the $Z$ mass
[\cite{fit6}-\cite{zp-new}],
since they are irrelevant for the present analysis.

We now discuss the form of the two currents $J_0$ and $J_1$,
and in particular the effects that could originate
from the presence of additional charged fermions.
We will henceforth denote as {\it new}, possible degrees
of freedom in addition to the standard 15 {\it known} fermions per generation.
Since no new fermions have been directly observed yet, the new
states must be rather heavy, and $m_{\rm new}\gtrsim M_Z/2$ can be
taken as the present model independent limit on the new masses.
Accordingly, we will denote the corresponding mass eigenstates as {\it
heavy}, while the known mass eigenstates will be labeled as {\it
light}.
In the presence of additional fermions, the light mass eigenstates
will correspond to superpositions of the known and new
states. Conservation of the electric and color charges forbids
a mixing between gauge eigenstates with different
$U(1)_{\rm em}$ and $SU(3)_{\rm c}$ quantum numbers,
and, in turn, this implies that
the electromagnetic and color currents of the
light mass eigenstates are not modified in the presence of the new
states.
However, the neutral isospin generator $T_3$ and the new generator $Q_1$ are
spontaneously broken, then a mixing between
gauge eigenstates with different $t_3$ and $q_1$ eigenvalues
is allowed, and as a result the couplings
of the light mass eigenstates to the $Z_0$ and $Z_1$ will be affected.

Since in the gauge currents chirality is conserved too,
it is convenient to group the fermions
with the same electric charge
and chirality $\alpha=L,R$
in a column vector of the known ($\cal K$) and new ($\cal N$) gauge
eigenstates  $\Psi^{o}_\alpha=(\Psi^o_{\K}, \Psi^o_{\N})_\alpha^T$.
The relation between the gauge eigenstates $\Psi^o_\alpha$
and the corresponding light and heavy mass eigenstates
$\Psi_\alpha=(\Psi_l,\Psi_h)_\alpha^T$
is then given by a unitary transformation
$$
\pmatrix{\Psi^o_{\K}\cr\Psi^o_{\N}}_\alpha = U_\alpha
\pmatrix{\Psi_l\cr\Psi_h}_\alpha \qquad{\rm where}\qquad
U_\alpha = \pmatrix{A &G\cr F & H}_\alpha ,
\qquad  \alpha=L,R.
\eq{2.6}
$$
\mn
The submatrices $A$ and $F$ describe the overlap of the light
eigenstates with the known and the new states respectively, and
from the unitarity of $U$ we have
$$
A^\dagger A+F^\dagger F=A A^\dagger +G G^\dagger =I.
\eq{2.7}
$$
Note that we have not introduced an extra index to
label the electric charge; nevertheless we will
treat $\Psi^o_\alpha$ and $\Psi_\alpha$
as vectors corresponding to a definite value of $q_{\rm em}$.

In terms of the fermion mass eigenstates
the neutral current  corresponding to a (broken)
generator ${\cal Q}$ reads
$$
J^\mu_{\cal Q} =\sum_{\alpha=L,R}
\bar\Psi_{\alpha} \gamma^\mu U^\dagger_\alpha {\cal Q}_\alpha
U_\alpha\Psi_{\alpha},
\eq{2.8}
$$
\mn
where ${\cal Q}_\alpha$ represents a generic diagonal
matrix of the charges for the chiral fermions.
Here we have to consider only the mixing effects in $J_3$
appearing in \req{2.3}
and in $J_1$,  since the term
proportional to $J_{\rm em}$ in $J_0$
is not modified by fermion mixing.
Hence in \req{2.8} ${\cal Q}=T_3,\, Q_1$ and
the elements of the corresponding matrices  are given by the
eigenvalues $t_3$ and $q_1$.

{}From \req{2.8} we see that if in one subspace of states with equal
electric charge and chirality
the matrix ${\cal Q}_\alpha$ is proportional to the identity,
then $U_\alpha^\dagger {\cal Q}_\alpha U_\alpha ={\cal Q}_\alpha$ and
for these fermions the corresponding current is not modified
in going to the base of the mass eigenstates.
In the SM for example, for a given electric
charge and chirality the $t_3$ eigenvalues of the fermions
are indeed the same,
and this implies in particular the absence (at the tree level)
of FCNC.                % (GIM mechanism).
In models with new fermions in contrast, the diagonal
matrices ${\cal Q}_\alpha$ have the general form
${\cal Q}_\alpha =
{\rm diag} ({\cal Q}^{\K}_\alpha,\, {\cal Q}^{\N}_\alpha )$
and do not commute with $U$.

To put in evidence the indirect effects
of fermion mixings in the couplings of the light mass eigenstates,
we now project \req{2.8} on the light components $\Psi_l$, obtaining
$$
J^\mu_{l{\cal Q}}
               =\sum_{\alpha=L,R}
\bar \Psi_{l\alpha} \gamma^\mu \left[
A^\dagger_\alpha {\cal Q}_\alpha^{\K}
A_\alpha +
F^\dagger_\alpha {\cal Q}^{\N}_\alpha F_\alpha \right]
\Psi_{l\alpha}.                   \eq{2.9}
$$
\mn
This equation is quite general, and describes
the effects of fermion mixings
in the neutral--currents of light--states for a wide class of models.
If the gauge group is generation independent, all the known states appearing
in one vector $\Psi^o_\alpha$ have the same eigenvalues with respect to
the generators of the gauge symmetry, and hence
we have ${\cal Q}^{\K}_\alpha= q_\alpha^{\K}I$ with
$q_\alpha^{\K}=t_3(f^{\K}_\alpha)$, $q_1(f^{\K}_\alpha)$.
The same is not true in general for the new states;
however, if we consider the particular case when
the mixing is with only one type of new fermions
with the same $q_\alpha^\N$ charges, then we have
${\cal Q}^{\N}_\alpha= q_\alpha^{\N}I$ as well.
Under these conditions, and by means of the unitarity relation \req{2.7},
\req{2.9} reduces to the simple form
$$
J^\mu_{l{\cal Q}}
               =\sum_{\alpha=L,R}
\bar \Psi_{l\alpha} \gamma^\mu \left[ q_\alpha^{\K} I +
(q_\alpha^{\N} - q_\alpha^{\K})
F^\dagger_\alpha F_\alpha \right]\Psi_{l\alpha}. \eq{2.10}
$$
\mn
We will restrict ourself to this equation, which is general
enough for describing the mixing with the additional charged fermions
in $\E$, and we refer to [\cite{fit6}] for a discussion of more general cases.

A few consideration are now in order.
In \req{2.10} the first term $q_\alpha^{\K}I $
inside the square brackets gives the couplings of a particular
light fermion in the absence of
mixing effects. The second term represents the
modifications due to fermion mixings.
The matrix $F^\dagger F$ appearing in this term
is in general not diagonal, and
while the magnitude of the diagonal elements will affect
the strength of the flavor diagonal couplings of the mass
eigenstates, the off diagonal terms will induce FCNC.
Clearly whenever the coefficient
$(q_\alpha^{\N} - q_\alpha^{\K})$ vanishes, the mixing effects are
absent.
When $t_3(f_\alpha^{\N}) \ne t_3(f_\alpha^{\K})$
the $J_0$ current is modified, and then the
existing low--energy and on--resonance NC data
as well as the current limits on rare processes,
can be used to constrain directly the corresponding
elements of $F^\dagger F$.
Model independent limits on the diagonal elements $(F^\dagger F)_{ii}$
affecting $Z_0$ interactions
were first given in [\cite{ll1}] and subsequently updated in
[\cite{fit}], and the most recent limits in the frame
of $\E$ models can be found in [\cite{fit6}].
Bounds on the off diagonal terms
$(F^\dagger F)_{i\ne j}$ have been given in [\cite{ll1}] as well.
All these limits turn out to be very stringent, usually at the level
of 1\% or better.
In contrast, if $t_3(f_\alpha^{\N}) = t_3(f_\alpha^{\K})$
the $J_0$ current is not modified, but since in general
we still have $q_1(f_\alpha^{\N}) \ne q_1(f_\alpha^{\K})$,
sizable effects could indeed be present in $J_1$.
We stress that the present experimental data
cannot be used to set limits on these mixings,
since they only affect a new hypothetical interaction,
and we can only rely on theoretical speculations to estimate
their magnitude.

According to these considerations it is clear that from a phenomenological
point of view
it is convenient to classify possible new fermions
in terms of their transformation properties under $SU(2)_L$.
Since we are only interested in fermions with conventional electric
charges, the new states must be singlets or doublets of weak--isospin.
A rather heterodox exception is that of a gauge triplet of
fermions [\cite{salati-trip}], but we will not consider this
possibility here.
According to the nomenclature in use [\cite{fit6},\cite{ll1},\cite{fit}],
we denote the particles with unconventional isospin assignments
(left--handed singlets or right--handed doublets) as {\it exotic} fermions.
All the standard fermions, as well as all the new states
that have conventional $SU(2)_L$ assignments, are referred to
as {\it ordinary}.
For example mirror fermions, having opposite $SU(2)_L$ assignments from
those of the known fermions, are exotic.
Sequential fermions are simply repetition of the new fermions.
They could be present in a complete new family or as components of
large fermion representations and are clearly classified as ordinary.
In this paper we will mainly concentrate on
vector multiplets of new fermions for which the L and R components
have the same $SU(2)_L$ transformation properties,
and hence always contain both ordinary and exotic states.
{}From the previous discussion, we see that while ordinary--exotic fermion
mixings are tightly constrained
due to the effects induced in the $J_0$ current,
no limits can be given for the ordinary--ordinary
mixings, since they affect only $J_1$.

This classification is also very convenient
for discussing  the possible form of the fermion mass matrices
and the expected magnitude of the mixings between the known and the
new fermions.
To give an example, let us introduce for each fermion family
a vector gauge singlet of new fermions
$({X^o_{\scss E}}_L,{X^o_{\scss O}}_R)_i$
($E$ = exotic, $O$ = ordinary, $i=1,2,3$)
with the same electric and color
charges than the  known fermions $({f^o_{\scss O}}_L,{f^o_{\scss
O}}_R)_i$. Then in the gauge eigenstate basis
the mass term reads
$$
{\cal L}_{\rm mass}=
{(\bar {f^o_{\scss O}}, \bar {X^o_{\scss E}})}_L \>
{\cal M} \> {f^o_{\scss O} \choose  X^o_{\scss O}}_R
+ {\rm h.c.}
\eq{2.11}
$$
where e.g. $f^o = (f^o_1,f^o_2,f^o_3)^T$ etc..
The non diagonal mass matrix ${\cal M}$ takes the form
$$
{\cal M} = \pmatrix{D &D^\pr\cr S^\pr &S},
\eq{2.12}
$$
\mn
where $D$ and $D^\pr$ are $3\times3$ matrices generated by
vacuum expectation values (vevs)
of doublets multiplied by Yukawa couplings, while
$S$ and $S^\pr$ are generated by vevs of singlets.
As a general rule, while the mass terms
which couple ordinary L-fermions to ordinary R-fermions
(or exotic L-fermions to exotic R-fermions)
arise from vevs of Higgs doublets, the entries
which couple ordinary fermions to the exotic ones are generated
by vevs of singlets.
Then in general Higgs singlets
are responsible for the large masses of new
heavy fermions in vector multiplets and,
in most cases, also contribute to the mass
of the new heavy gauge boson; hence it is natural to
assume $S,S^\pr \sim \Lambda \gg D,D^\pr$.

The diagonal mass matrix M is obtained via a biunitary transformation
acting on the L and R sectors:
$$
\def\oe{\scss{O{\rm-}E}}
\def\oo{\scss{O{\rm-}O}}
\eqalign{
{\rm M}^2
%&=U_L^{\scss {O-E}}({\cal M}{\cal M}^\dagger) {U_L^{\scss OE}}^\dagger \cr
%&=U_R^{\scss {OO}({\cal M}^\dagger{\cal M}) {U_R^{\scss O-O}}^\dagger.  \cr
&=U_L^{\oe}({\cal M}{\cal M}^\dagger) {U_L^{\oe}}^\dagger \cr
&=U_R^{\oo}({\cal M}^\dagger{\cal M}) {U_R^{\oo}}^\dagger.  \cr
} \eq{2.13}
$$
Since $D/\Lambda$, $D^\pr/\Lambda\sim \varepsilon \ll 1\,$,
the order of magnitude of the different entries in
${\cal M}{\cal M}^\dagger $ and ${\cal M}^\dagger {\cal M}$ is

$$
\eqlabel{2.14} \eqlabel{2.15}
\eqalignno{
{\cal M}{\cal M}^\dagger &
% =\pmatrix{|D|^2+|D^\pr|^2 &DS^{\pr\dagger}+D^\pr S^\dagger \cr
%         S^\pr D^\dagger+SD^{\pr\dagger} &|S|^2+|S^\pr|^2 \cr}
\sim \Lambda^2 \pmatrix{\varepsilon^2 &\varepsilon \cr
              \varepsilon   &1       \cr}     &\req{2.14}\cr
{\cal M}^\dagger{\cal M} &
% &=\pmatrix{|D|^2+|S^\pr|^2 &D^{\dagger}D^\pr+S^{\pr\dagger}S \cr
%         D^{\pr\dagger}D+S^\dagger S^{\pr}&|D^\pr|^2+|S|^2 \cr}
\sim \phantom{\Lambda}\pmatrix{\Lambda^2 &\Lambda^2 \cr
              \Lambda^2 &\Lambda^2 \cr}.             &\req{2.15}\cr }
$$

Given the form of
${\cal M}{\cal M}^\dagger$ in  \req{2.14}
and keeping in mind the expression \req{2.6} for
the matrices  $U$,
we see that for the matrix
describing the ordinary--exotic mixings in \req{2.13}
it is natural to expect that the
submatrices $F$ and $G$
would acquire an overall suppression factor
$\varepsilon$, of the order of the ratio of the light to heavy mass
scale. In contrast, since all the entries in \req{2.15} are of the
same order of magnitude, such a suppression is not present for the
ordinary-ordinary $F$ and $G$ mixing terms.
Now, since it is precisely $F^\dagger F$
in \req{2.10} which affects the flavor
diagonal couplings and also induces  FCNC,
the suppression of the ordinary--exotic mixings
explains in a natural way the non--observations of these effects
in the $Z_0$ interactions.
On the other hand for the ordinary--ordinary mixings
there is no reason to expect the elements of
$F^\dagger F$ to be particularly small,
and accordingly flavor changing processes can be expected to occur
at a sizeable rate in $Z_1$ interactions.

Written explicitly, the flavor diagonal chiral couplings of a
light $f$ fermion to the $Z_0$ and $Z_1$ gauge bosons are
$$
\eqalign{
\varepsilon_{0\alpha}^f &= t_3(f_\alpha) - s^2_W q_{\rm em}(f)
\ + \ [t_3(f^{\N}_\alpha) - t_3(f^{\K}_\alpha)] \,
(F_\alpha^\dagger F_\alpha)_{ff}
\cr
\varepsilon_{1\alpha}^f &= q_1(f_\alpha) \ + \
[q_1(f^{\N}_\alpha) - q_1(f^{\K}_\alpha)] \,
(F_\alpha^\dagger F_\alpha)_{ff},
\qquad\qquad\qquad \alpha=L,R.  \cr
}
\eq{2.16}
$$
while the $f_i\,f_j$ flavor changing couplings read
$$
\eqalign{
\kappa_{0\alpha}^{ij} &= [t_3(f^{\N}_\alpha) - t_3(f^{\K}_\alpha)]
\, (F_\alpha^\dagger F_\alpha)_{ij}
\cr
\kappa_{1\alpha}^{ij} &= [q_1(f^{\N}_\alpha) - q_1(f^{\K}_\alpha)]
\, (F_\alpha^\dagger F_\alpha)_{ij},
\qquad\qquad\qquad \alpha=L,R.  \cr
}
\eq{2.17}
$$
The corresponding couplings
to the physical $Z$ and $Z^\prime$ bosons, that we will denote as
$\varepsilon_\alpha^f$, $\varepsilon_\alpha^{\pr\,f}$
and
$\kappa^{ij}_\alpha$, $\kappa_\alpha^{\pr\, ij}$,
can be readily obtained via the transformation \req{2.5}.
For the flavor changing couplings we have for example
$$
\eqalign{
\kappa^{ij}_\alpha &=c_\phi\, \kappa^{ij}_{0 \alpha} +
s_\phi s_w \, \kappa^{ij}_{1 \alpha}          \cr
\kappa_\alpha^{\pr\, ij} &=-s_\phi \, \kappa^{ij}_{0 \alpha}
 + c_\phi s_w \, \kappa^{ij}_{1 \alpha}
\qquad \qquad \qquad \qquad  \alpha=L,R, \cr }
\eq{2.18}
$$
\mn
and analogous expressions hold for
$\varepsilon_\alpha^f$ and $\varepsilon_\alpha^{\pr\,f}$ too.
In terms of the flavor non--diagonal couplings \req{2.18},
the FCNC Lagrangian for the light $f^i$ and $f^j$ fermions
in the mass eigenstate basis finally reads
$$
-{\cal L}_{\rm FC}^{ij}=
g_0 \sum_{\alpha=L,R} \left(
\bar{f^i_\alpha}\gamma^\mu \, \kappa^{ij}_\alpha \, f^j_\alpha \, Z_\mu
\ + \
\bar{f^i_\alpha} \gamma^\mu \, \kappa^{\pr ij}_\alpha \,
f^j_\alpha Z^\pr_\mu\right).
\eq{2.19}
$$

{}From the first equation in \req{2.18} we see that
even in the case when only ordinary--ordinary mixing effects
are present and hence $\kappa^{ij}_{0 \alpha} = 0$,
the $Z$ boson can still mediate flavor changing transitions,
suppressed now by a factor proportional to the $Z_0$--$Z_1$
mixing [\cite{zp-fc}].
However, for several models the existing limits on $\phi$ are rather
stringent: $|\phi| \lesssim 0.02$ [\cite{fit6}-\cite{zp-new}] and
then we can expect that if the $Z^\pr$ is not too heavy, FCNC
processes would be mainly induced by $Z^\pr$ exchange.

\chap{Constr}III. Constraints on E$_{\displaystyle\bf 6}$ models from
\bfmu $\ \rightarrow$ \bfe\bfe\bfe.

In the previous section
we have shown that in the presence of new charged fermions
the new neutral current $J_1$ could induce sizeable
flavor changing transitions either via $Z^\pr$
interactions, or as a consequence of a non--vanishing $Z_0$--$Z_1$ mixing.
This kind of new  physics
would manifest itself in affecting the rates for several
processes which are forbidden or highly suppressed in the SM.
In the quark sector it could enhance the branchings for the
leptonic decays of mesons like $K^0$, $D^0$, $B^0\rightarrow \ell^+\ell^-$,
and it would also affect the neutral meson mixings and mass
differences.
In the lepton sector it would induce
several LFV neutrinoless $\tau$ decay modes like
$\tau \rightarrow
eee$, $\mu\mu\mu$, $\mu ee$, $e\mu\mu$, $\mu \pi$, $\mu \rho$
which are all constrained at the level of
$\lesssim$ few$\times 10^{-5}$ [\cite{pdg92}],
but in particular it would also give rise to the decay
$\mu \rightarrow eee $ for which the existing
limit [\cite{sindrum}] is
% obtained by the SINDRUM collaboration
much more stringent:

$$
Br(\mu^+\rightarrow e^+e^+e^-)<1.0\cdot 10^{-12} \hskip 1truecm
({\rm at\quad} 90\% \, c.l.\,) .
\eq{3.1}
$$
\mn
Given the LFV Lagrangian \req{2.19}, the expression for this
decay rate relative to the charged current decay $\mu \rightarrow
\nu e\bar\nu $ is

\def\e{{\varepsilon}}
\def\ep{{\varepsilon^\prime}}
\def\k{{\kappa}}
\def\kp{{\kappa^\prime}}
$$
\eqlabel{3.2}
\eqalignno{
{Br(\mu\rightarrow eee) \o Br(\mu\rightarrow \nu e\bar\nu)} &=
2\Bigl[3(\e_R^2+\e_L^2)(\k_R^2+\k_L^2)+
(\e_R^2-\e_L^2)(\k_R^2-\k_L^2)\Bigr]  +                 \cr
2({M^2_Z\o M^2_{Z^\pr}})^2&\Bigl[3(\ep_R^2+\ep_L^2)(\kp_R^2+\kp_L^2)+
(\ep_R^2-\ep_L^2)(\kp_R^2-\kp_L^2)\Bigr] +         &\req{3.2}     \cr
4{M^2_Z\o M^2_{Z^\pr}}
\bigl[3(\e_R\ep_R  &+\e_L\ep_L)(\k_R\kp_R+\k_L\kp_L)+
(\e_R\ep_R-\e_L\ep_L)(\k_R\kp_R-\k_L\kp_L)\bigr]      \cr}
$$
where for $\k_{R,L}$ and $\kp_{R,L}$ defined in \req{2.18}
we have dropped the indices $i=e$ and $j=\mu$, and
$\e_{R,L}$ and $\ep_{R,L}$ refer to the electron couplings.

As a first result, by confronting  \req{3.1} and \req{3.2}
we can derive the limits on the $Z\mu e$ LFV vertices.
Assuming  that the $Z^\pr$ is completely decoupled from the
low energy physics ($M_{Z^\pr}\rightarrow \infty$ and $\phi
\rightarrow 0$) and taking $s^2_W=0.23$, we obtain:
$$
\eqalign{
|\k^{e\mu}_L| &< 1.1\cdot 10^{-6}  \cr
|\k^{e\mu}_R| &< 1.2\cdot 10^{-6}.  \cr}
\eq{3.3}
$$
As we have discussed, if these couplings do originate from
some kind of mixing of the electron and muon
with heavy exotic leptons,
we expect them to be strongly suppressed, e.g. by a
factor of the order $m^2_\mu/M^2_Z\sim 10^{-6}$ or smaller, and
then we see that the existence of FCNC induced by
ordinary--exotic mixings does not conflict with the stringent limits in
\req{3.3}.

Now, in order to study the effects of the $Z^\pr$ flavor changing vertices,
we first need to fix the $q_1$ charges of the fermions, which
in turn determine the coefficient of the flavor changing
mixings.
This can be done by choosing a specific GUT,
and we will carry out our analysis in the frame of E$_6$.
Since E$_6$ has rank 6, while the
SM gauge group $\G$ has rank 4, the breaking of $\E$ to the SM will
lead to extra $Z^\pr$s. We will consider the possibility that
either $\E$ breaks directly to rank 5, or that one of the two extra
$Z^\pr$s is heavy enough so that its effects on the low energy physics
are negligible, and in these cases the formalism developed in
the previous section can be straightforwardly applied.
We will choose the  embedding of $\G$ into $\E$ trough the
maximal subalgebra chain
$
\E \rightarrow \ U(1)_{\psi} \times SO(10)
\rightarrow \ U(1)_{\chi} \times SU(5)\rightarrow \G
$,
then an effective extra $U_1(1)$ could arise
at low energy as a combination of the $U(1)_\psi$ and
$U(1)_\chi$ factors.
We will parametrize this combination in terms of an
angle $\beta$, and this will define an entire
class of $Z^\pr$ models in which each fermion $f$ is coupled
to the new boson through the effective charge
$$
q_1(f)=q_\psi(f) \sin\beta + q_\chi(f) \cos\beta .
\eq{3.4}
$$
Particular cases that are commonly studied in the literature
[\cite{fit6}--\cite{zp-new},\cite{rizzo-e6}]
correspond to $\sin\beta=-\sqrt{5/8}$, 0, 1
and are respectively denoted $Z_\eta$, $Z_\chi$ and $Z_\psi$ models.
$Z_\psi$ occurs in $\E\to$ SO(10), while
$Z_\eta$ occurs in superstring models when
$\E$ directly breaks down to rank 5.
As we will see this model plays a peculiar role in the present analysis,
since it evades completely the kind of constraints that we are investigating.
Finally, a $Z_\chi$ boson occurs in SO(10)$\to$ SU(5) and
couples to the conventional fermions in the same way
than the $Z^\pr$ present in SO(10) GUTs,
however since SO(10) does not contain additional charged fermions, the
kind of flavor changing effects that we are studying here is absent.
In contrast, new charged quarks and leptons are present
in $\E$. In the GUTs based on this gauge group
the fermions are assigned to the
fundamental {\bf 27} representation that contains,
beyond the standard 15 degrees of freedom,
12 additional states for each generation,
among which we have a vector doublet of new leptons
$(N\> E^-)_L^T$, $(E^+ \> N^c)_L^T$ on which we will now concentrate.

The chiral couplings of the leptons to the $Z_1$ and the coefficient
of the LFV term, are determined by the $q_\psi$ and $q_\chi$
charges of the new and known states, which are
$$
\eqlabel{3.8}
\eqalignno{
q_\psi(E_L)=-q_\psi(E_R)=-{1\o 3}\sqrt{5\o 2} \hskip 1.2truecm
&q_\chi(E_L)=q_\chi(E_R)=-{1\o 3}\sqrt{3\o 2}   & \cr
q_\psi(e_L)=-q_\psi(e_R)={1\o 6}\sqrt{5\o 2}  \hskip 1.8truecm
&q_\chi(e_L)=3q_\chi(e_R)={1\o 2}\sqrt{3\o 2}.   & \req{3.8} \cr
}
$$
With respect to the $SU(2)_L$ transformation properties, the $E^+_L$ heavy
leptons are exotic, and than the mixing of their CP conjugate states
$E^-_R$ with $e_R$, $\mu_R$ and $\tau_R$ are constrained by $Z_0$
interactions.
{}From \req{3.3} we have for example
$$
(F_R^\dagger F_R)_{e\mu} < 2.4\cdot 10^{-6},
\eq{3.5}
$$
while the 90\% c.l. limits on the flavor diagonal mixings given in
[\cite{fit6}] are respectively
$$
\eqlabel{3.6}
\eqlabel{3.7}
\eqalignno{
(F_R^\dagger F_R)_{ee} &< 1.3\cdot 10^{-2}     & \req{3.6} \cr
(F_R^\dagger F_R)_{\mu\mu} &< 1.1\cdot 10^{-2}. & \req{3.7} \cr
}
$$
\mn
Due to the tight bound \req{3.5} it is reasonable to
neglect the LFV couplings in the R-sector and
(conservatively) set $\k_R^{e\mu}=\kp_R^{e\mu}=0$ in \req{3.2}.
According to \req{3.6}, it is also justified to
neglect the effects of the fermion mixings in the
flavor diagonal couplings of the R-electrons.

In contrast, the $E^-_L$ leptons are ordinary, and no bounds exist
on their mixing with the light leptons.
We will still neglect the diagonal term
$(F_L^\dagger F_L)_{ee}$ since it is reasonable to
expect that if this term were so large as to spoil the approximation
$\e_{1\alpha}^f\simeq q_1(f_\alpha)$
the value of the off-diagonal term
$(F_L^\dagger F_L)_{e\mu}$ would also be large,
possibly leading to even stronger limits than the ones
derived here.

Due to the approximations made, for each value of the parameter
$\beta$ in \req{3.4}
the branching ratio \req{3.2} depends on the values of
$M_Z^\pr$, $\phi$ and ${\cal F}_{e\mu}\equiv(F_L^\dagger F_L)_{e\mu}$.
However, it is easy to see that since the gauge boson mixing effects in the
diagonal electron couplings are in any case very small,
being $|\phi| \lesssim 0.02$ [\cite{fit6}-\cite{zp-new}],
the relevant variables are actually only two, namely
${\cal F}_{e\mu} \cdot (M_Z^2/M_{Z^\pr}^2)$ and
${\cal F}_{e\mu} \cdot \phi$.
Moreover once the Higgs sector of the model
is specified, $M_{Z^\pr}$ and $\phi$ are
no more independent quantities.
For example an approximate relation that holds for
small mixings and when $M_{Z^\pr}$ ($\gg M_Z$)
originates from a large Higgs singlet vev [\cite{l-luo}] reads
$$
\phi \simeq - {M_Z^2\o M^2_{Z^\pr}} s_W
{\sum_i t_3^i q_1^i |\langle\phi^i\rangle|^2
\o
\sum_i {t_3^i}^2 |\langle\phi^i\rangle|^2 },
\eq{3.9}
$$
and in this case the branching ratio \req{3.2}
is in practice only a function of \break
${\cal F}_{e\mu}\cdot(M^2_Z/ M_{Z^\pr}^2)$.

As in the SM for the Cabibbo-Kobayashi-Maskawa (CKM) matrix,
also in $\E$ we don't have a clue for predicting
the values of the fermion mixing parameters.
Without attempting to push too far an analogy between
the mixings we are interested in
% $U^\dagger_L U_L$
and the CKM matrix,
we will merely note that both these cases involve mixings among ordinary
fermions, and that we do not expect in the present case any
additional suppression factor. We also note that
all the CKM matrix elements are $> 10^{-3}$ and that in particular
the mixing between the first and the second generation is rather
large.
We will then assume that the LFV term ${\cal F}_{e\mu}$
lies in the range $10^{-2}$--$10^{-4}$. Under this assumption
the presence of a too light $Z^\pr$
as well as a too large amount of $Z_0$--$Z_1$ mixing will
clearly conflict with the limit \req{3.1}.
The bounds that can be derived in this way are indeed very strong,
but obviously they cannot replace the
direct [\cite{zp-direct}] or indirect [\cite{fit6}-\cite{zp-new}]
limits on the $Z^\pr$
parameters, since for very small values of the
LFV $Z^\pr$ couplings
(${\cal F}_{e\mu} \lesssim 10^{-6}$)
they would in fact be weaker.
We will nevertheless present our
constraints in the form of numerical limits on $M_{Z^\pr}$ and $\phi$,
since, in doing so, the strength of the arguments that have been
discussed here is put in clear evidence.

Our results are collected in Figs. 1 and 2.
Figure 1 shows the bounds on $M_Z^\pr$,
the thick solid line depicts the bounds obtained
for ${\cal F}_{e\mu} = 10^{-2}$ and by setting the
gauge boson mixing angle $\phi$ to zero. The decay $\mu\rightarrow
eee$ is due only to $Z^\pr$ exchange in this case.
The limits for different values of
${\cal F}_{e\mu}$ can be red off this line as well,
by assuming for the vertical axis units of
of GeV$\cdot [100{\cal F}_{e\mu}]^{1\o 2}$.
The thick dashed line, drawn here for convenience, shows
the bounds corresponding to $\phi=0$ and
${\cal F}_{e\mu} = 10^{-3}$, vertical units are again
in GeV in this case.
We see that for ${\cal F}_{e\mu}> 10^{-3}$
a $Z^\pr$ below 1 TeV would be excluded for most of the values
of $\beta$. Also, it is clear that
${\cal F}_{e\mu}\simeq  10^{-4}$ still leads to significative
bounds, being $M_{Z^\pr}$ constrained to values $\gtrsim 400$GeV
for large part of the $\sin\beta$ axis.

To study the possible effects on these results
 of a non vanishing
mixing angle $\phi$, i.e. when both the $Z^\pr$ and $Z$ bosons
contribute to the decay, we have used \req{3.9}
assuming two doublets of Higgs fields $h_{N^c}$ and $h_N$
with vevs $\bar v$  and $v$.
Since $\bar v$  and $v$ give mass respectively to the
$t$ and $b$ quarks, $\sigma \equiv {\bar v}^2/v^2 > 1$ is
theoretically preferred.
The bounds on $M_{Z^\pr}$ obtained by allowing
for a $Z_0$--$Z_1$ mixing consistent with this minimal Higgs
sector are shown Fig. 1 by the dotted and dot-dashed lines,
which correspond to $\sigma = 1$ and $\infty$ respectively.
It is apparent that by allowing for a non vanishing
value of $\phi$, the limits on the $Z^\pr$ mass are only slightly affected.

Figure 2 depicts the constraints on the $Z_0$--$Z_1$ mixing angle
$\phi$. The solid line shows the bounds obtained by
assuming ${\cal F}_{e\mu} = 10^{-2}$ and taking
the limit $M_{Z^\pr} \rightarrow \infty$.
In this case the decay $\mu \rightarrow eee$ is mediated only by
the $Z$ boson, and is due to the mixing between the $Z_0$ and the $Z_1$.
The dotted line shows the bounds for
${\cal F}_{e\mu} = 10^{-3}$ in the same limit.
The limits for different choices of ${\cal F}_{e\mu}$
are easily obtained from the solid [dashed] lines by rescaling
the vertical units by
$(10^2 {\cal F}_{e\mu})^{-1}$ \ [$(10^3 {\cal F}_{e\mu})^{-1}$].

The dotted ($\sigma=1$) and dot--dashed lines ($\sigma=\infty$)
enclose the regions of the limits obtained assuming a minimal Higgs
sector. In this case the value of $M_{Z^\pr}$ is
finite and consistent, according to \req{3.9},
with the values of $\phi$ at the bound.
We see that with this additional constraint
significant limits are found
for ${\cal F}_{e\mu} = 10^{-4}$ as well.

{}From Fig. 2 it is apparent that for a minimal Higgs sector
the limits on $\phi$ are significantly tighter
than in the $M_{Z^\pr} \rightarrow \infty$ limit, showing that
\req{3.1} in first place gives direct constraints on
the $Z^\pr$ mass, while the bounds on the $Z_0$--$Z_1$ mixing
obtained independently of $M_{Z^\pr}$ are weaker.
We note that this
behaviour is opposite to what is encountered in deriving
limits on the $Z^\pr$ parameters from precise electroweak data
[\cite{fit6}-\cite{zp-new}],
where in fact the best bounds on the $Z^\pr$ mass are obtained
from the tight limits on $\phi$ implied by the LEP measurements.

{}From Figs. 1 and 2 it is apparent that for the $\eta$ model,
corresponding to $\sin \beta=-\sqrt{5/8}$, both the
$Z^\pr$ mass and the $Z_0$--$Z_1$ mixing angle are not
constrained by the present analysis. This is due to the fact
that in this model, for the
ordinary--ordinary fermion mixings  besides
$t_3^\K=t_3^\N$ we also have $q_\eta^\K=q_\eta^\N$,
implying that both the coefficients of the $F_L^\dagger F_L$ term
in the $J_3$ and in the $J_1$ currents vanish.
This happens also in the quark sector and in the neutral sector,
hence the unsuppressed flavor
changing vertices are completely absent for the $Z_\eta$ boson,
and this insures that
besides the decay $\mu \rightarrow eee$ no other
processes can be found for implementing this kind of
constraints for the $\eta$ model.
The reason for this can be understood by considering
the decomposition $\E \rightarrow SU(6)\times SU(2)_I$,
where $SU(6)$ contains the SM group, while the
$SU(2)_I$ is ``inert" in the sense that $I_{3I}$ does not
contribute to the $Q_{\rm em}$ generator
[\cite{rosner86},\cite{slansky}].
% [D. London and J.L. Rosner, prd 34 (1986) 1530]
$I_{3I}$ corresponds to
$\beta=\arctan\sqrt{3/5}$ in \req{3.4} and is orthogonal to $Q_\eta$
[$\beta=\arctan(-\sqrt{5/3})$]
which is then contained in the $SU(6)$ factor as well.
The fermions in the {\bf 27} of $\E$ with the same SM quantum numbers
($q_{\rm em}$, $t_3$, color) form multiplets (singlets and doublets) of
$SU(2)_I$ and clearly these multiplets also carry definite values of
the $Q_\eta$ charge. All the ordinary fermions with the same
color and electric charges, being members of the same $SU(2)_I$
multiplet,  have also the same $q_\eta$, and this
implies the absence of both the diagonal and the flavor changing
ordinary--ordinary mixing effects.
In contrast ordinary--exotic fermion mixing could still give rise to FCNC
also in the $\eta$ model,
but as already discussed the corresponding transitions are expected to be
largely suppressed, and do not imply any useful constraint.

According to this discussion, if an additional $Z^\pr$
with a mass of a few hundreds GeV is found together with new fermions
that could fit in the {\bf 27} of $\E$,
the observed absence of unsuppressed FCNC would suggest that
it could most probably be a $Z_\eta$.

\chap{Conclusions}   {IV. Conclusions}

We have carried out an analysis of models that predict a new
neutral gauge boson and new charged fermions from the point of view
of FCNC processes.
We have argued that in most of these models
unsuppressed flavor changing couplings of the light fermions to the
new $Z^\pr$
can be present as a consequence of a mixing between the known
and the new charged fermions.
By assuming that these flavor changing vertices should not be
unnaturally small,
we have inferred that the observed suppression of FCNC processes
can still be explained in a natural way if
the new gauge boson is sufficiently heavy
and almost unmixed with the standard $Z$.
Also we have attempted a semi-quantitative analysis
of this kind of new physics in the frame of $\E$ models,
by confronting the theoretical expectations for the LFV effects
with the extremely
stringent limits on the $\mu \rightarrow eee$ decay mode.
Our conclusions are that the existence of $Z^\pr$ bosons from $\E$
much lighter than 1 TeV is unlikely, with the noticeable
exception of the superstring inspired $\eta$ model which
evades completely our constraints.
At the same time, our analysis suggests that
the observation of FCNC processes at rates larger
than the SM predictions could be interpreted as a hint for the
simultaneous presence of additional gauge bosons and new charged fermions.
Indeed these new states could manifest themselves indirectly via this kind of
flavor changing effects well before they are directly produced.


\vfill\eject

%%%%%%%%%%%%%%%%%%%%%%%%%   REFERENCES    %%%%%%%%%%%%%%%%%%%%%%%

\null
\baselineskip 8pt
\centerline{\title References}
\vskip .8truecm

\biblitem{zp-fc}
T.K. Kuo and N. Nakagawa, \prd{32} 306 (1985).\par

\biblitem{e6-fcloop}
J. Bernabeu \ea, \plb{187} 303 (1987). \par

\biblitem{e6-fcrizzo}
G.Eilam and T.G. Rizzo, \plb{188} 91 (1987). \par

\biblitem{salati-trip}
B.W. Lee, \prd{6} 1188 (1972); \hbup
J. Prentki and B. Zumino, \npb{47} 99 (1972); \hbup
P. Salati, \plb{253} 173 (1991). \par

\biblitem{zp-direct}
CDF Collaboration, F. Abe \ea, \prl{67} 2609 (1991); \ib {\bf 68},
1463 (1992). \par

\biblitem{fit6}
E. Nardi, E. Roulet and D. Tommasini,
Report No. FERMILAB PUB-92/127-A 1992,
to appear in \prd{46} (1 october 1992). \par

\biblitem{l-luo}
P. Langacker and M. Luo, \prd{45} 278 (1992). \par

\biblitem{zp-new}
J. Layssac, F.M. Renard and C. Verzegnassi, \zpc{53} 97 (1992); \hbup
M.C. Gonzalez Garc\'\i a and J.W.F. Valle; \plb{259} 365 (1991); \hbup
% ======= Improved bounds on extended gauge models from new LEP data
G. Altarelli et al., \plb{263} 459 (1991); \hbup
% =====  Correlation between M(Z-prime) and m(t) bounds. 1. NC data
F.del Aguila, J.M. Moreno and M. Quir\'os, \npb{361} 45 (1991); \hbup
% ======  Correlation between M(Z-prime) and m(t) bounds. 2. All data
F. del Aguila, W. Hollik, J.M. Moreno and M. Quir\'os, \ib {\bf B372}
 3 (1992). \par

\biblitem{rizzo-direct}
P. Langacker and M. Luo, in ref. [\cite{zp-new}];  \hbup
T.G. Rizzo; talk given at the 15$^{th}$ Johns Hopkins
Workshop on Current Problems in Particle Theory, Baltimore, MD, August
26-28 1991; ANL-HEP-CP-91-85. \par

\biblitem{fit}
E. Nardi, E. Roulet and D. Tommasini.
Report no. FERMILAB Pub-91/207-A,
to appear in \npb{}; \hbup
E. Nardi, E. Roulet and D. Tommasini;
Contributed to Int. Workshop on Electroweak Physics beyond the Standard
Model, Valencia, Spain, Oct 2-5, 1991
[Fermilab Report No. Conf-91/335-A 1991 (unpublished)]. \par

\biblitem{ll1}
P. Langacker and D. London, \prd{38} (1988) 886.\par

\biblitem{ll2}
P. Langacker and D. London, \prd{38} (1988) 907.\par

\biblitem{slansky}
For a review on the group E$_6$, see R. Slansky; \prep{79} (1981) 1. \par

\biblitem{pdg92}
Particle Data Group, J.J. Hern\'andez {\it et al.},
\prd {\bf 45} Part. II (1992). \par

\biblitem{sindrum}
SINDRUM collaboration, U. Bellgardt \ea, \npb{299}
(1988) 1. \par

\biblitem{rizzo-e6}
J.L. Hewett and T.G. Rizzo, \prep{183} (1989) 195, and references
therein. \par

\biblitem{rosner86}
D. London and J.L. Rosner, \prd{34} (1986) 1530. \par

\interlinea


%%%%%%%%%%%%%%%%%%%%%%%%%   FIGURE CAPTIONS %%%%%%%%%%%%%%%%%%%%%%%

\insertbibliografia
\vfill\eject

\centerline{\lltitle Figure captions}
\bigskip
\baselineskip 14pt

\medskip\noindent
Fig. 1:
Limits on $M_{Z^\pr}$ for a general $\E$ neutral gauge boson, as a
function of $\sin\beta$ and for different values of
the lepton flavor violating term ${\cal F}_{e\mu}\equiv(F_L^\dagger
F_L)_{e\mu}$.
The thick solid line is obtained by setting
the $Z_0$--$Z_1$ mixing angle $\phi$ to zero, and assuming
${\cal F}_{e\mu}=10^{-2}$.
The limits for different values of ${\cal F}_{e\mu}$
can be read off this line by assuming for the vertical axis units of
GeV$\cdot (100 {\cal F}_{e\mu})^{1\o 2}$. The thick dashed line
depicts the limits corresponding to ${\cal
F}_{e\mu}=10^{-3}$ (vertical units in GeV). The bounds obtained by
allowing for a non-vanishing $Z_0$--$Z_1$ mixing, consistent
with the values of $M_Z^\pr$ when a minimal Higgs sector is assumed, are also
shown. The dotted lines correspond to equal vevs of the two Higgs
doublets present in the model, {\it i.e.}
$\sigma\equiv {\bar v}/v=1$ while the dot--dashed lines
correspond to $\sigma=\infty$.

\bs\bs\bs
\medskip\noindent
Fig. 2:
Limits on the $Z_0$--$Z_1$ mixing angle $\phi$ for a general $Z_1$
from $\E$, as a function of $\sin\beta$ and for different values of
the lepton flavor violating term ${\cal F}_{e\mu}\equiv(F_L^\dagger
F_L)_{e\mu}$. The thick solid and dashed lines
are obtained in the
limit $M_{Z^\pr}\rightarrow \infty$ assuming
${\cal F}_{e\mu}=10^{-2}$ and
${\cal F}_{e\mu}=10^{-3}$ respectively. Limits for different values of
${\cal F}_{e\mu}$ can be obtained from these lines by rescaling the
vertical units by $(10^2 {\cal F}_{e\mu})^{-1}$ and $(10^3 {\cal
F}_{e\mu})^{-1}$ respectively. The dotted $(\sigma=1)$ and dot-dashed
$(\sigma=\infty)$ lines show the limits obtained for a finite $Z^\pr$
mass and assuming a minimal Higgs sector. In this case the bounds are
tighter and are essentially determined by the corresponding limits on
$M_{Z^\pr}$ through eq. \req{3.9}.  Also the limits corresponding to
${\cal F}_{e\mu}=10^{-4}$ are shown in this case.

\vfill\eject
\bye

%%%%%%%%%%%%%%%%%%%%%%%%%   FIG. 1  and FIG. 2 %%%%%%%%%%%%%%%%%%%%%%%

%!PS-Adobe-1.0
%%EndComments
save 50 dict begin /psplot exch def
/StartPSPlot
   {newpath 0 0 moveto 0 setlinewidth 0 setgray 1 setlinecap
    1 setlinejoin 72 300 div dup scale}def
/pending {false} def
/finish {pending {currentpoint stroke moveto /pending false def} if} def
/r {finish newpath moveto} def
/d {lineto /pending true def} def
/l {finish 4 2 roll moveto lineto currentpoint stroke moveto} def
/p {finish newpath moveto currentpoint lineto currentpoint stroke moveto} def
/e {finish gsave showpage grestore newpath 0 0 moveto} def
/lw {finish setlinewidth} def
/lt0 {finish [] 0 setdash} def
/lt1 {finish [3 5] 0 setdash} def
/lt2 {finish [20 10] 0 setdash} def
/lt3 {finish [60 10] 0 setdash} def
/lt4 {finish [3 10 20 10] 0 setdash} def
/lt5 {finish [3 10 60 10] 0 setdash} def
/lt6 {finish [20 10 60 10] 0 setdash} def
/EndPSPlot {clear psplot end restore}def
% end fixed prolog
StartPSPlot
%%EndProlog
%%Page: 1 1
   4 lw lt0 2050  500 r 2050 3100 d 2050  500 r 2018  500 d 2050  630 r
 2018  630 d 2050  760 r 1986  760 d 2050  890 r 2018  890 d 2050 1020 r
 2018 1020 d 2050 1150 r 2018 1150 d 2050 1280 r 1986 1280 d 2050 1410 r
 2018 1410 d 2050 1540 r 2018 1540 d 2050 1670 r 2018 1670 d 2050 1800 r
 1986 1800 d 2050 1930 r 2018 1930 d 2050 2060 r 2018 2060 d 2050 2190 r
 2018 2190 d 2050 2320 r 1986 2320 d 2050 2450 r 2018 2450 d 2050 2580 r
 2018 2580 d 2050 2710 r 2018 2710 d 2050 2840 r 1986 2840 d 2050 2970 r
 2018 2970 d 2050 3100 r 2018 3100 d 2114  714 r 2114  750 d 2128  764 r
 2130  762 d 2132  764 d 2130  766 d 2128  764 d 2090  788 r 2092  782 d
 2096  780 d 2102  780 d 2106  782 d 2108  788 d 2108  796 d 2106  802 d
 2102  804 d 2096  804 d 2092  802 d 2090  796 d 2090  788 d 2092  784 d
 2096  782 d 2102  782 d 2106  784 d 2108  788 d 2108  796 r 2106  800 d
 2102  802 d 2096  802 d 2092  800 d 2090  796 d 2108  788 r 2110  782 d
 2112  780 d 2116  778 d 2124  778 d 2128  780 d 2130  782 d 2132  788 d
 2132  796 d 2130  802 d 2128  804 d 2124  806 d 2116  806 d 2112  804 d
 2110  802 d 2108  796 d 2108  788 r 2110  784 d 2112  782 d 2116  780 d
 2124  780 d 2128  782 d 2130  784 d 2132  788 d 2132  796 r 2130  800 d
 2128  802 d 2124  804 d 2116  804 d 2112  802 d 2110  800 d 2108  796 d
 2114 1234 r 2114 1270 d 2128 1284 r 2130 1282 d 2132 1284 d 2130 1286 d
 2128 1284 d 2094 1316 r 2132 1316 d 2090 1318 r 2132 1318 d 2090 1318 r
 2120 1296 d 2120 1328 d 2132 1310 r 2132 1324 d 2090 1798 r 2092 1792 d
 2098 1788 d 2108 1786 d 2114 1786 d 2124 1788 d 2130 1792 d 2132 1798 d
 2132 1802 d 2130 1808 d 2124 1812 d 2114 1814 d 2108 1814 d 2098 1812 d
 2092 1808 d 2090 1802 d 2090 1798 d 2092 1794 d 2094 1792 d 2098 1790 d
 2108 1788 d 2114 1788 d 2124 1790 d 2128 1792 d 2130 1794 d 2132 1798 d
 2132 1802 r 2130 1806 d 2128 1808 d 2124 1810 d 2114 1812 d 2108 1812 d
 2098 1810 d 2094 1808 d 2092 1806 d 2090 1802 d 2128 2300 r 2130 2298 d
 2132 2300 d 2130 2302 d 2128 2300 d 2094 2332 r 2132 2332 d 2090 2334 r
 2132 2334 d 2090 2334 r 2120 2312 d 2120 2344 d 2132 2326 r 2132 2340 d
 2128 2820 r 2130 2818 d 2132 2820 d 2130 2822 d 2128 2820 d 2090 2844 r
 2092 2838 d 2096 2836 d 2102 2836 d 2106 2838 d 2108 2844 d 2108 2852 d
 2106 2858 d 2102 2860 d 2096 2860 d 2092 2858 d 2090 2852 d 2090 2844 d
 2092 2840 d 2096 2838 d 2102 2838 d 2106 2840 d 2108 2844 d 2108 2852 r
 2106 2856 d 2102 2858 d 2096 2858 d 2092 2856 d 2090 2852 d 2108 2844 r
 2110 2838 d 2112 2836 d 2116 2834 d 2124 2834 d 2128 2836 d 2130 2838 d
 2132 2844 d 2132 2852 d 2130 2858 d 2128 2860 d 2124 2862 d 2116 2862 d
 2112 2860 d 2110 2858 d 2108 2852 d 2108 2844 r 2110 2840 d 2112 2838 d
 2116 2836 d 2124 2836 d 2128 2838 d 2130 2840 d 2132 2844 d 2132 2852 r
 2130 2856 d 2128 2858 d 2124 2860 d 2116 2860 d 2112 2858 d 2110 2856 d
 2108 2852 d  150  500 r  150 3100 d  150  500 r  182  500 d  150  630 r
  182  630 d  150  760 r  214  760 d  150  890 r  182  890 d  150 1020 r
  182 1020 d  150 1150 r  182 1150 d  150 1280 r  214 1280 d  150 1410 r
  182 1410 d  150 1540 r  182 1540 d  150 1670 r  182 1670 d  150 1800 r
  214 1800 d  150 1930 r  182 1930 d  150 2060 r  182 2060 d  150 2190 r
  182 2190 d  150 2320 r  214 2320 d  150 2450 r  182 2450 d  150 2580 r
  182 2580 d  150 2710 r  182 2710 d  150 2840 r  214 2840 d  150 2970 r
  182 2970 d  150 3100 r  182 3100 d 2050  500 r  150  500 d 1954  500 r
 1954  532 d 1834  500 r 1834  564 d 1713  500 r 1713  532 d 1593  500 r
 1593  564 d 1473  500 r 1473  532 d 1353  500 r 1353  564 d 1232  500 r
 1232  532 d 1112  500 r 1112  564 d  992  500 r  992  532 d  872  500 r
  872  564 d  751  500 r  751  532 d  631  500 r  631  564 d  511  500 r
  511  532 d  391  500 r  391  564 d  270  500 r  270  532 d  150  500 r
  150  564 d 1818  320 r 1816  324 d 1810  330 d 1852  330 d 1812  328 r
 1852  328 d 1852  320 r 1852  338 d 1810  366 r 1812  360 d 1818  356 d
 1828  354 d 1834  354 d 1844  356 d 1850  360 d 1852  366 d 1852  370 d
 1850  376 d 1844  380 d 1834  382 d 1828  382 d 1818  380 d 1812  376 d
 1810  370 d 1810  366 d 1812  362 d 1814  360 d 1818  358 d 1828  356 d
 1834  356 d 1844  358 d 1848  360 d 1850  362 d 1852  366 d 1852  370 r
 1850  374 d 1848  376 d 1844  378 d 1834  380 d 1828  380 d 1818  378 d
 1814  376 d 1812  374 d 1810  370 d 1810  406 r 1812  400 d 1818  396 d
 1828  394 d 1834  394 d 1844  396 d 1850  400 d 1852  406 d 1852  410 d
 1850  416 d 1844  420 d 1834  422 d 1828  422 d 1818  420 d 1812  416 d
 1810  410 d 1810  406 d 1812  402 d 1814  400 d 1818  398 d 1828  396 d
 1834  396 d 1844  398 d 1848  400 d 1850  402 d 1852  406 d 1852  410 r
 1850  414 d 1848  416 d 1844  418 d 1834  420 d 1828  420 d 1818  418 d
 1814  416 d 1812  414 d 1810  410 d 1810  446 r 1812  440 d 1818  436 d
 1828  434 d 1834  434 d 1844  436 d 1850  440 d 1852  446 d 1852  450 d
 1850  456 d 1844  460 d 1834  462 d 1828  462 d 1818  460 d 1812  456 d
 1810  450 d 1810  446 d 1812  442 d 1814  440 d 1818  438 d 1828  436 d
 1834  436 d 1844  438 d 1848  440 d 1850  442 d 1852  446 d 1852  450 r
 1850  454 d 1848  456 d 1844  458 d 1834  460 d 1828  460 d 1818  458 d
 1814  456 d 1812  454 d 1810  450 d 1577  316 r 1579  318 d 1581  316 d
 1579  314 d 1577  314 d 1573  316 d 1571  318 d 1569  324 d 1569  332 d
 1571  338 d 1573  340 d 1577  342 d 1581  342 d 1585  340 d 1589  334 d
 1593  324 d 1595  320 d 1599  316 d 1605  314 d 1611  314 d 1569  332 r
 1571  336 d 1573  338 d 1577  340 d 1581  340 d 1585  338 d 1589  332 d
 1593  324 d 1607  314 r 1605  316 d 1605  320 d 1609  330 d 1609  336 d
 1607  340 d 1605  342 d 1605  320 r 1611  330 d 1611  338 d 1609  340 d
 1605  342 d 1601  342 d 1569  366 r 1571  360 d 1577  356 d 1587  354 d
 1593  354 d 1603  356 d 1609  360 d 1611  366 d 1611  370 d 1609  376 d
 1603  380 d 1593  382 d 1587  382 d 1577  380 d 1571  376 d 1569  370 d
 1569  366 d 1571  362 d 1573  360 d 1577  358 d 1587  356 d 1593  356 d
 1603  358 d 1607  360 d 1609  362 d 1611  366 d 1611  370 r 1609  374 d
 1607  376 d 1603  378 d 1593  380 d 1587  380 d 1577  378 d 1573  376 d
 1571  374 d 1569  370 d 1569  406 r 1571  400 d 1577  396 d 1587  394 d
 1593  394 d 1603  396 d 1609  400 d 1611  406 d 1611  410 d 1609  416 d
 1603  420 d 1593  422 d 1587  422 d 1577  420 d 1571  416 d 1569  410 d
 1569  406 d 1571  402 d 1573  400 d 1577  398 d 1587  396 d 1593  396 d
 1603  398 d 1607  400 d 1609  402 d 1611  406 d 1611  410 r 1609  414 d
 1607  416 d 1603  418 d 1593  420 d 1587  420 d 1577  418 d 1573  416 d
 1571  414 d 1569  410 d 1569  446 r 1571  440 d 1577  436 d 1587  434 d
 1593  434 d 1603  436 d 1609  440 d 1611  446 d 1611  450 d 1609  456 d
 1603  460 d 1593  462 d 1587  462 d 1577  460 d 1571  456 d 1569  450 d
 1569  446 d 1571  442 d 1573  440 d 1577  438 d 1587  436 d 1593  436 d
 1603  438 d 1607  440 d 1609  442 d 1611  446 d 1611  450 r 1609  454 d
 1607  456 d 1603  458 d 1593  460 d 1587  460 d 1577  458 d 1573  456 d
 1571  454 d 1569  450 d 1335  316 r 1337  318 d 1339  316 d 1337  314 d
 1335  314 d 1331  318 d 1329  324 d 1329  332 d 1331  338 d 1335  340 d
 1341  340 d 1345  338 d 1347  332 d 1347  326 d 1329  332 r 1331  336 d
 1335  338 d 1341  338 d 1345  336 d 1347  332 d 1349  336 d 1353  340 d
 1357  342 d 1363  342 d 1367  340 d 1369  338 d 1371  332 d 1371  324 d
 1369  318 d 1367  316 d 1363  314 d 1361  314 d 1359  316 d 1361  318 d
 1363  316 d 1351  338 r 1357  340 d 1363  340 d 1367  338 d 1369  336 d
 1371  332 d 1329  366 r 1331  360 d 1337  356 d 1347  354 d 1353  354 d
 1363  356 d 1369  360 d 1371  366 d 1371  370 d 1369  376 d 1363  380 d
 1353  382 d 1347  382 d 1337  380 d 1331  376 d 1329  370 d 1329  366 d
 1331  362 d 1333  360 d 1337  358 d 1347  356 d 1353  356 d 1363  358 d
 1367  360 d 1369  362 d 1371  366 d 1371  370 r 1369  374 d 1367  376 d
 1363  378 d 1353  380 d 1347  380 d 1337  378 d 1333  376 d 1331  374 d
 1329  370 d 1329  406 r 1331  400 d 1337  396 d 1347  394 d 1353  394 d
 1363  396 d 1369  400 d 1371  406 d 1371  410 d 1369  416 d 1363  420 d
 1353  422 d 1347  422 d 1337  420 d 1331  416 d 1329  410 d 1329  406 d
 1331  402 d 1333  400 d 1337  398 d 1347  396 d 1353  396 d 1363  398 d
 1367  400 d 1369  402 d 1371  406 d 1371  410 r 1369  414 d 1367  416 d
 1363  418 d 1353  420 d 1347  420 d 1337  418 d 1333  416 d 1331  414 d
 1329  410 d 1329  446 r 1331  440 d 1337  436 d 1347  434 d 1353  434 d
 1363  436 d 1369  440 d 1371  446 d 1371  450 d 1369  456 d 1363  460 d
 1353  462 d 1347  462 d 1337  460 d 1331  456 d 1329  450 d 1329  446 d
 1331  442 d 1333  440 d 1337  438 d 1347  436 d 1353  436 d 1363  438 d
 1367  440 d 1369  442 d 1371  446 d 1371  450 r 1369  454 d 1367  456 d
 1363  458 d 1353  460 d 1347  460 d 1337  458 d 1333  456 d 1331  454 d
 1329  450 d 1092  332 r 1130  332 d 1088  334 r 1130  334 d 1088  334 r
 1118  312 d 1118  344 d 1130  326 r 1130  340 d 1088  366 r 1090  360 d
 1096  356 d 1106  354 d 1112  354 d 1122  356 d 1128  360 d 1130  366 d
 1130  370 d 1128  376 d 1122  380 d 1112  382 d 1106  382 d 1096  380 d
 1090  376 d 1088  370 d 1088  366 d 1090  362 d 1092  360 d 1096  358 d
 1106  356 d 1112  356 d 1122  358 d 1126  360 d 1128  362 d 1130  366 d
 1130  370 r 1128  374 d 1126  376 d 1122  378 d 1112  380 d 1106  380 d
 1096  378 d 1092  376 d 1090  374 d 1088  370 d 1088  406 r 1090  400 d
 1096  396 d 1106  394 d 1112  394 d 1122  396 d 1128  400 d 1130  406 d
 1130  410 d 1128  416 d 1122  420 d 1112  422 d 1106  422 d 1096  420 d
 1090  416 d 1088  410 d 1088  406 d 1090  402 d 1092  400 d 1096  398 d
 1106  396 d 1112  396 d 1122  398 d 1126  400 d 1128  402 d 1130  406 d
 1130  410 r 1128  414 d 1126  416 d 1122  418 d 1112  420 d 1106  420 d
 1096  418 d 1092  416 d 1090  414 d 1088  410 d 1088  446 r 1090  440 d
 1096  436 d 1106  434 d 1112  434 d 1122  436 d 1128  440 d 1130  446 d
 1130  450 d 1128  456 d 1122  460 d 1112  462 d 1106  462 d 1096  460 d
 1090  456 d 1088  450 d 1088  446 d 1090  442 d 1092  440 d 1096  438 d
 1106  436 d 1112  436 d 1122  438 d 1126  440 d 1128  442 d 1130  446 d
 1130  450 r 1128  454 d 1126  456 d 1122  458 d 1112  460 d 1106  460 d
 1096  458 d 1092  456 d 1090  454 d 1088  450 d  848  318 r  868  314 d
  866  318 d  864  324 d  864  330 d  866  336 d  870  340 d  876  342 d
  878  342 d  884  340 d  888  336 d  890  330 d  890  324 d  888  318 d
  886  316 d  882  314 d  880  314 d  878  316 d  880  318 d  882  316 d
  864  330 r  866  334 d  870  338 d  876  340 d  878  340 d  884  338 d
  888  334 d  890  330 d  848  318 r  848  338 d  850  318 r  850  328 d
  848  338 d  848  366 r  850  360 d  856  356 d  866  354 d  872  354 d
  882  356 d  888  360 d  890  366 d  890  370 d  888  376 d  882  380 d
  872  382 d  866  382 d  856  380 d  850  376 d  848  370 d  848  366 d
  850  362 d  852  360 d  856  358 d  866  356 d  872  356 d  882  358 d
  886  360 d  888  362 d  890  366 d  890  370 r  888  374 d  886  376 d
  882  378 d  872  380 d  866  380 d  856  378 d  852  376 d  850  374 d
  848  370 d  848  406 r  850  400 d  856  396 d  866  394 d  872  394 d
  882  396 d  888  400 d  890  406 d  890  410 d  888  416 d  882  420 d
  872  422 d  866  422 d  856  420 d  850  416 d  848  410 d  848  406 d
  850  402 d  852  400 d  856  398 d  866  396 d  872  396 d  882  398 d
  886  400 d  888  402 d  890  406 d  890  410 r  888  414 d  886  416 d
  882  418 d  872  420 d  866  420 d  856  418 d  852  416 d  850  414 d
  848  410 d  848  446 r  850  440 d  856  436 d  866  434 d  872  434 d
  882  436 d  888  440 d  890  446 d  890  450 d  888  456 d  882  460 d
  872  462 d  866  462 d  856  460 d  850  456 d  848  450 d  848  446 d
  850  442 d  852  440 d  856  438 d  866  436 d  872  436 d  882  438 d
  886  440 d  888  442 d  890  446 d  890  450 r  888  454 d  886  456 d
  882  458 d  872  460 d  866  460 d  856  458 d  852  456 d  850  454 d
  848  450 d  613  338 r  615  336 d  617  338 d  615  340 d  613  340 d
  609  338 d  607  334 d  607  328 d  609  322 d  613  318 d  617  316 d
  625  314 d  637  314 d  643  316 d  647  320 d  649  326 d  649  330 d
  647  336 d  643  340 d  637  342 d  635  342 d  629  340 d  625  336 d
  623  330 d  623  328 d  625  322 d  629  318 d  635  316 d  607  328 r
  609  324 d  613  320 d  617  318 d  625  316 d  637  316 d  643  318 d
  647  322 d  649  326 d  649  330 r  647  334 d  643  338 d  637  340 d
  635  340 d  629  338 d  625  334 d  623  330 d  607  366 r  609  360 d
  615  356 d  625  354 d  631  354 d  641  356 d  647  360 d  649  366 d
  649  370 d  647  376 d  641  380 d  631  382 d  625  382 d  615  380 d
  609  376 d  607  370 d  607  366 d  609  362 d  611  360 d  615  358 d
  625  356 d  631  356 d  641  358 d  645  360 d  647  362 d  649  366 d
  649  370 r  647  374 d  645  376 d  641  378 d  631  380 d  625  380 d
  615  378 d  611  376 d  609  374 d  607  370 d  607  406 r  609  400 d
  615  396 d  625  394 d  631  394 d  641  396 d  647  400 d  649  406 d
  649  410 d  647  416 d  641  420 d  631  422 d  625  422 d  615  420 d
  609  416 d  607  410 d  607  406 d  609  402 d  611  400 d  615  398 d
  625  396 d  631  396 d  641  398 d  645  400 d  647  402 d  649  406 d
  649  410 r  647  414 d  645  416 d  641  418 d  631  420 d  625  420 d
  615  418 d  611  416 d  609  414 d  607  410 d  607  446 r  609  440 d
  615  436 d  625  434 d  631  434 d  641  436 d  647  440 d  649  446 d
  649  450 d  647  456 d  641  460 d  631  462 d  625  462 d  615  460 d
  609  456 d  607  450 d  607  446 d  609  442 d  611  440 d  615  438 d
  625  436 d  631  436 d  641  438 d  645  440 d  647  442 d  649  446 d
  649  450 r  647  454 d  645  456 d  641  458 d  631  460 d  625  460 d
  615  458 d  611  456 d  609  454 d  607  450 d  367  314 r  379  314 d
  375  314 r  371  316 d  367  320 d  367  324 d  373  334 d  373  338 d
  371  340 d  367  342 d  371  316 r  369  320 d  369  324 d  373  334 d
  367  342 r  373  342 d  379  340 d  389  332 d  393  330 d  399  328 d
  409  328 d  379  340 r  389  330 d  393  328 d  399  326 d  409  326 d
  367  366 r  369  360 d  375  356 d  385  354 d  391  354 d  401  356 d
  407  360 d  409  366 d  409  370 d  407  376 d  401  380 d  391  382 d
  385  382 d  375  380 d  369  376 d  367  370 d  367  366 d  369  362 d
  371  360 d  375  358 d  385  356 d  391  356 d  401  358 d  405  360 d
  407  362 d  409  366 d  409  370 r  407  374 d  405  376 d  401  378 d
  391  380 d  385  380 d  375  378 d  371  376 d  369  374 d  367  370 d
  367  406 r  369  400 d  375  396 d  385  394 d  391  394 d  401  396 d
  407  400 d  409  406 d  409  410 d  407  416 d  401  420 d  391  422 d
  385  422 d  375  420 d  369  416 d  367  410 d  367  406 d  369  402 d
  371  400 d  375  398 d  385  396 d  391  396 d  401  398 d  405  400 d
  407  402 d  409  406 d  409  410 r  407  414 d  405  416 d  401  418 d
  391  420 d  385  420 d  375  418 d  371  416 d  369  414 d  367  410 d
  367  446 r  369  440 d  375  436 d  385  434 d  391  434 d  401  436 d
  407  440 d  409  446 d  409  450 d  407  456 d  401  460 d  391  462 d
  385  462 d  375  460 d  369  456 d  367  450 d  367  446 d  369  442 d
  371  440 d  375  438 d  385  436 d  391  436 d  401  438 d  405  440 d
  407  442 d  409  446 d  409  450 r  407  454 d  405  456 d  401  458 d
  391  460 d  385  460 d  375  458 d  371  456 d  369  454 d  367  450 d
  126  324 r  128  318 d  132  316 d  138  316 d  142  318 d  144  324 d
  144  332 d  142  338 d  138  340 d  132  340 d  128  338 d  126  332 d
  126  324 d  128  320 d  132  318 d  138  318 d  142  320 d  144  324 d
  144  332 r  142  336 d  138  338 d  132  338 d  128  336 d  126  332 d
  144  324 r  146  318 d  148  316 d  152  314 d  160  314 d  164  316 d
  166  318 d  168  324 d  168  332 d  166  338 d  164  340 d  160  342 d
  152  342 d  148  340 d  146  338 d  144  332 d  144  324 r  146  320 d
  148  318 d  152  316 d  160  316 d  164  318 d  166  320 d  168  324 d
  168  332 r  166  336 d  164  338 d  160  340 d  152  340 d  148  338 d
  146  336 d  144  332 d  126  366 r  128  360 d  134  356 d  144  354 d
  150  354 d  160  356 d  166  360 d  168  366 d  168  370 d  166  376 d
  160  380 d  150  382 d  144  382 d  134  380 d  128  376 d  126  370 d
  126  366 d  128  362 d  130  360 d  134  358 d  144  356 d  150  356 d
  160  358 d  164  360 d  166  362 d  168  366 d  168  370 r  166  374 d
  164  376 d  160  378 d  150  380 d  144  380 d  134  378 d  130  376 d
  128  374 d  126  370 d  126  406 r  128  400 d  134  396 d  144  394 d
  150  394 d  160  396 d  166  400 d  168  406 d  168  410 d  166  416 d
  160  420 d  150  422 d  144  422 d  134  420 d  128  416 d  126  410 d
  126  406 d  128  402 d  130  400 d  134  398 d  144  396 d  150  396 d
  160  398 d  164  400 d  166  402 d  168  406 d  168  410 r  166  414 d
  164  416 d  160  418 d  150  420 d  144  420 d  134  418 d  130  416 d
  128  414 d  126  410 d  126  446 r  128  440 d  134  436 d  144  434 d
  150  434 d  160  436 d  166  440 d  168  446 d  168  450 d  166  456 d
  160  460 d  150  462 d  144  462 d  134  460 d  128  456 d  126  450 d
  126  446 d  128  442 d  130  440 d  134  438 d  144  436 d  150  436 d
  160  438 d  164  440 d  166  442 d  168  446 d  168  450 r  166  454 d
  164  456 d  160  458 d  150  460 d  144  460 d  134  458 d  130  456 d
  128  454 d  126  450 d 2050 3100 r  150 3100 d 1954 3100 r 1954 3068 d
 1834 3100 r 1834 3036 d 1713 3100 r 1713 3068 d 1593 3100 r 1593 3036 d
 1473 3100 r 1473 3068 d 1353 3100 r 1353 3036 d 1232 3100 r 1232 3068 d
 1112 3100 r 1112 3036 d  992 3100 r  992 3068 d  872 3100 r  872 3036 d
  751 3100 r  751 3068 d  631 3100 r  631 3036 d  511 3100 r  511 3068 d
  391 3100 r  391 3036 d  270 3100 r  270 3068 d  150 3100 r  150 3036 d
   1 lw 2230  640 r 2272  640 d 2230  642 r 2272  642 d 2242  654 r 2258  654 d
 2230  634 r 2230  666 d 2240  666 d 2230  664 d 2250  642 r 2250  654 d
 2272  634 r 2272  648 d 2230  680 r 2232  678 d 2234  680 d 2232  682 d
 2230  680 d 2244  680 r 2272  680 d 2244  682 r 2272  682 d 2244  674 r
 2244  682 d 2272  674 r 2272  688 d 2244  710 r 2246  706 d 2248  704 d
 2252  702 d 2256  702 d 2260  704 d 2262  706 d 2264  710 d 2264  714 d
 2262  718 d 2260  720 d 2256  722 d 2252  722 d 2248  720 d 2246  718 d
 2244  714 d 2244  710 d 2246  706 r 2250  704 d 2258  704 d 2262  706 d
 2262  718 r 2258  720 d 2250  720 d 2246  718 d 2248  720 r 2246  722 d
 2244  726 d 2246  726 d 2246  722 d 2260  704 r 2262  702 d 2266  700 d
 2268  700 d 2272  702 d 2274  708 d 2274  718 d 2276  724 d 2278  726 d
 2268  700 r 2270  702 d 2272  708 d 2272  718 d 2274  724 d 2278  726 d
 2280  726 d 2284  724 d 2286  718 d 2286  706 d 2284  700 d 2280  698 d
 2278  698 d 2274  700 d 2272  706 d 2268  740 r 2270  738 d 2272  740 d
 2270  742 d 2268  740 d 2238  796 r 2236  800 d 2230  806 d 2272  806 d
 2232  804 r 2272  804 d 2272  796 r 2272  814 d  222  791 r  264  765 d
  222  793 r  264  767 d  222  767 r  232  765 d  222  765 d  222  793 d
  264  765 r  264  793 d  254  793 d  264  791 d  264  801 r  260  804 d
  259  806 d  260  809 d  263  809 d  268  807 d  276  805 d  259  806 r
  260  807 d  263  807 d  268  806 d  276  804 d  268  807 r  263  810 d
  260  812 d  259  815 d  259  817 d  260  819 d  262  821 d  265  821 d
  271  819 d  284  816 d  259  817 r  262  819 d  265  819 d  271  818 d
  284  815 d  222 1800 r  264 1774 d  222 1802 r  264 1776 d  222 1776 r
  232 1774 d  222 1774 d  222 1802 d  264 1774 r  264 1802 d  254 1802 d
  264 1800 d  259 1810 r  259 1813 d  260 1815 d  262 1816 d  282 1825 d
  284 1827 d  259 1813 r  262 1815 d  282 1824 d  283 1825 d  284 1827 d
  284 1830 d  259 1831 r  262 1830 d  266 1826 d  277 1814 d  282 1810 d
  284 1809 d  222 2996 r  264 2970 d  222 2998 r  264 2972 d  222 2972 r
  232 2970 d  222 2970 d  222 2998 d  264 2970 r  264 2998 d  254 2998 d
  264 2996 d  251 3023 r  284 3016 d  251 3024 r  284 3015 d  264 3006 r
  260 3009 d  259 3011 d  260 3014 d  263 3014 d  269 3012 d  271 3012 d
  274 3014 d  275 3016 d  275 3020 d  274 3022 d  271 3026 d  259 3011 r
  260 3012 d  263 3012 d  269 3011 d  271 3011 d  274 3012 d  275 3014 d
  276 3016 d  276 3018 d  275 3022 d  271 3026 d  268 3028 d  263 3030 d
  259 3032 d  242 3072 r  246 3078 d  250 3072 d  236 3066 r  246 3076 d
  256 3066 d  246 3042 r  246 3076 d  242  521 r  246  515 d  250  521 d
  236  527 r  246  517 d  256  527 d  246  517 r  246  551 d  222  591 r
  264  565 d  222  593 r  264  567 d  222  567 r  232  565 d  222  565 d
  222  593 d  264  565 r  264  593 d  254  593 d  264  591 d  251  618 r
  284  611 d  251  619 r  284  610 d  264  601 r  260  604 d  259  606 d
  260  609 d  263  609 d  269  607 d  271  607 d  274  609 d  275  611 d
  275  615 d  274  617 d  271  621 d  259  606 r  260  607 d  263  607 d
  269  606 d  271  606 d  274  607 d  275  609 d  276  611 d  276  613 d
  275  617 d  271  621 d  268  623 d  263  625 d  259  627 d  346 2205 r
  348 2204 d  350 2201 d  350 2198 d  347 2197 d  344 2197 d  341 2198 d
  339 2201 d  337 2207 d  337 2218 d  341 2215 d  344 2214 d  353 2211 d
  360 2208 d  362 2207 d  365 2204 d  367 2200 d  367 2196 d  365 2193 d
  362 2193 d  361 2194 d  361 2196 d  362 2197 d  355 2203 r  354 2204 d
  353 2207 d  353 2214 d  351 2217 d  348 2218 d  357 2215 d  371 2218 r
  370 2221 d  369 2224 d  367 2226 d  366 2227 d  364 2226 d  363 2224 d
  363 2222 d  364 2219 d  367 2218 d  369 2217 d  372 2217 d  373 2218 d
  374 2219 d  375 2220 d  375 2222 d  374 2224 d  372 2226 d  363 2222 r
  364 2220 d  367 2219 d  369 2218 d  372 2218 d  374 2219 d  363 2235 r
  381 2229 d  363 2235 r  381 2230 d  367 2235 r  371 2234 d  373 2234 d
  375 2235 d  375 2237 d  374 2239 d  372 2240 d  369 2242 d  363 2244 r
  372 2241 d  374 2241 d  375 2243 d  374 2245 d  372 2246 d  363 2245 r
  372 2242 d  374 2242 d  375 2243 d  350 2252 r  350 2277 d  358 2252 r
  358 2277 d  343 2290 r  341 2293 d  337 2297 d  367 2297 d  339 2296 r
  367 2296 d  367 2290 r  367 2303 d  337 2322 r  339 2318 d  343 2315 d
  350 2314 d  354 2314 d  361 2315 d  365 2318 d  367 2322 d  367 2325 d
  365 2329 d  361 2332 d  354 2333 d  350 2333 d  343 2332 d  339 2329 d
  337 2325 d  337 2322 d  339 2319 d  340 2318 d  343 2317 d  350 2315 d
  354 2315 d  361 2317 d  364 2318 d  365 2319 d  367 2322 d  367 2325 r
  365 2328 d  364 2329 d  361 2331 d  354 2332 d  350 2332 d  343 2331 d
  340 2329 d  339 2328 d  337 2325 d  332 2340 r  332 2355 d  325 2361 r
  326 2362 d  327 2361 d  326 2360 d  325 2360 d  323 2361 d  322 2362 d
  322 2364 d  322 2368 d  322 2370 d  323 2371 d  325 2372 d  327 2372 d
  328 2371 d  330 2369 d  332 2364 d  332 2363 d  334 2361 d  337 2360 d
  339 2360 d  322 2368 r  322 2369 d  323 2370 d  325 2371 d  327 2371 d
  328 2370 d  330 2368 d  332 2364 d  337 2360 r  337 2361 d  337 2363 d
  338 2367 d  338 2369 d  337 2371 d  337 2372 d  337 2363 r  339 2367 d
  339 2370 d  338 2371 d  337 2372 d  335 2372 d 1489 2140 r 1491 2139 d
 1493 2136 d 1493 2133 d 1490 2132 d 1487 2132 d 1484 2133 d 1482 2136 d
 1480 2142 d 1480 2153 d 1484 2150 d 1487 2149 d 1496 2146 d 1503 2143 d
 1505 2142 d 1508 2139 d 1510 2135 d 1510 2131 d 1508 2128 d 1505 2128 d
 1504 2129 d 1504 2131 d 1505 2132 d 1498 2138 r 1497 2139 d 1496 2142 d
 1496 2149 d 1494 2152 d 1491 2153 d 1500 2150 d 1514 2153 r 1513 2156 d
 1512 2159 d 1510 2161 d 1509 2162 d 1507 2161 d 1506 2159 d 1506 2157 d
 1507 2154 d 1510 2153 d 1512 2152 d 1515 2152 d 1516 2153 d 1517 2154 d
 1518 2155 d 1518 2157 d 1517 2159 d 1515 2161 d 1506 2157 r 1507 2155 d
 1510 2154 d 1512 2153 d 1515 2153 d 1517 2154 d 1506 2170 r 1524 2164 d
 1506 2170 r 1524 2165 d 1510 2170 r 1514 2169 d 1516 2169 d 1518 2170 d
 1518 2172 d 1517 2174 d 1515 2175 d 1512 2177 d 1506 2179 r 1515 2176 d
 1517 2176 d 1518 2178 d 1517 2180 d 1515 2181 d 1506 2180 r 1515 2177 d
 1517 2177 d 1518 2178 d 1493 2187 r 1493 2212 d 1501 2187 r 1501 2212 d
 1486 2225 r 1484 2228 d 1480 2232 d 1510 2232 d 1482 2231 r 1510 2231 d
 1510 2225 r 1510 2238 d 1480 2257 r 1482 2253 d 1486 2250 d 1493 2249 d
 1497 2249 d 1504 2250 d 1508 2253 d 1510 2257 d 1510 2260 d 1508 2264 d
 1504 2267 d 1497 2268 d 1493 2268 d 1486 2267 d 1482 2264 d 1480 2260 d
 1480 2257 d 1482 2254 d 1483 2253 d 1486 2252 d 1493 2250 d 1497 2250 d
 1504 2252 d 1507 2253 d 1508 2254 d 1510 2257 d 1510 2260 r 1508 2263 d
 1507 2264 d 1504 2266 d 1497 2267 d 1493 2267 d 1486 2266 d 1483 2264 d
 1482 2263 d 1480 2260 d 1475 2275 r 1475 2290 d 1467 2296 r 1468 2297 d
 1469 2296 d 1468 2295 d 1467 2295 d 1465 2297 d 1465 2299 d 1465 2303 d
 1465 2305 d 1467 2306 d 1470 2306 d 1471 2305 d 1472 2303 d 1472 2300 d
 1465 2303 r 1465 2304 d 1467 2305 d 1470 2305 d 1471 2304 d 1472 2303 d
 1473 2304 d 1475 2306 d 1476 2307 d 1479 2307 d 1480 2306 d 1481 2305 d
 1482 2303 d 1482 2299 d 1481 2297 d 1480 2296 d 1479 2295 d 1478 2295 d
 1477 2296 d 1478 2297 d 1479 2296 d 1474 2305 r 1476 2306 d 1479 2306 d
 1480 2305 d 1481 2304 d 1482 2303 d 1475 2375 r 1477 2373 d 1482 2370 d
 1487 2367 d 1494 2366 d 1500 2366 d 1507 2367 d 1512 2370 d 1517 2373 d
 1519 2375 d 1477 2373 r 1483 2370 d 1487 2368 d 1494 2367 d 1500 2367 d
 1507 2368 d 1511 2370 d 1517 2373 d 1490 2385 r 1510 2394 d 1490 2387 r
 1507 2394 d 1490 2402 r 1510 2394 d 1490 2381 r 1490 2391 d 1490 2398 r
 1490 2406 d 1498 2413 r 1498 2430 d 1496 2430 d 1493 2429 d 1491 2427 d
 1490 2424 d 1490 2420 d 1491 2416 d 1494 2413 d 1498 2412 d 1501 2412 d
 1505 2413 d 1508 2416 d 1510 2420 d 1510 2423 d 1508 2427 d 1505 2430 d
 1498 2429 r 1494 2429 d 1491 2427 d 1490 2420 r 1491 2417 d 1494 2415 d
 1498 2413 d 1501 2413 d 1505 2415 d 1508 2417 d 1510 2420 d 1490 2441 r
 1510 2441 d 1490 2443 r 1510 2443 d 1498 2443 r 1494 2444 d 1491 2447 d
 1490 2450 d 1490 2454 d 1491 2455 d 1493 2455 d 1494 2454 d 1493 2452 d
 1491 2454 d 1490 2437 r 1490 2443 d 1510 2437 r 1510 2447 d 1480 2465 r
 1504 2465 d 1508 2466 d 1510 2469 d 1510 2472 d 1508 2475 d 1505 2476 d
 1480 2466 r 1504 2466 d 1508 2468 d 1510 2469 d 1490 2461 r 1490 2472 d
 1480 2486 r 1482 2485 d 1483 2486 d 1482 2487 d 1480 2486 d 1490 2486 r
 1510 2486 d 1490 2487 r 1510 2487 d 1490 2482 r 1490 2487 d 1510 2482 r
 1510 2492 d 1494 2515 r 1496 2514 d 1497 2515 d 1496 2517 d 1494 2517 d
 1491 2514 d 1490 2511 d 1490 2507 d 1491 2503 d 1494 2500 d 1498 2499 d
 1501 2499 d 1505 2500 d 1508 2503 d 1510 2507 d 1510 2510 d 1508 2514 d
 1505 2517 d 1490 2507 r 1491 2504 d 1494 2501 d 1498 2500 d 1501 2500 d
 1505 2501 d 1508 2504 d 1510 2507 d 1493 2528 r 1494 2528 d 1494 2527 d
 1493 2527 d 1491 2528 d 1490 2531 d 1490 2536 d 1491 2539 d 1493 2541 d
 1496 2542 d 1505 2542 d 1508 2543 d 1510 2545 d 1493 2541 r 1505 2541 d
 1508 2542 d 1510 2545 d 1510 2546 d 1496 2541 r 1497 2539 d 1498 2531 d
 1500 2527 d 1503 2525 d 1505 2525 d 1508 2527 d 1510 2531 d 1510 2535 d
 1508 2538 d 1505 2541 d 1498 2531 r 1500 2528 d 1503 2527 d 1505 2527 d
 1508 2528 d 1510 2531 d 1480 2556 r 1510 2556 d 1480 2557 r 1510 2557 d
 1480 2552 r 1480 2557 d 1510 2552 r 1510 2562 d 1490 2597 r 1505 2597 d
 1508 2598 d 1510 2602 d 1510 2605 d 1508 2609 d 1505 2612 d 1490 2598 r
 1505 2598 d 1508 2599 d 1510 2602 d 1490 2612 r 1510 2612 d 1490 2613 r
 1510 2613 d 1490 2592 r 1490 2598 d 1490 2608 r 1490 2613 d 1510 2612 r
 1510 2618 d 1490 2627 r 1510 2627 d 1490 2629 r 1510 2629 d 1494 2629 r
 1491 2632 d 1490 2636 d 1490 2639 d 1491 2643 d 1494 2644 d 1510 2644 d
 1490 2639 r 1491 2641 d 1494 2643 d 1510 2643 d 1490 2623 r 1490 2629 d
 1510 2623 r 1510 2633 d 1510 2639 r 1510 2648 d 1480 2658 r 1482 2657 d
 1483 2658 d 1482 2660 d 1480 2658 d 1490 2658 r 1510 2658 d 1490 2660 r
 1510 2660 d 1490 2654 r 1490 2660 d 1510 2654 r 1510 2664 d 1480 2674 r
 1504 2674 d 1508 2675 d 1510 2678 d 1510 2681 d 1508 2683 d 1505 2685 d
 1480 2675 r 1504 2675 d 1508 2676 d 1510 2678 d 1490 2669 r 1490 2681 d
 1491 2706 r 1490 2707 d 1494 2707 d 1491 2706 d 1490 2702 d 1490 2697 d
 1491 2693 d 1493 2692 d 1494 2692 d 1497 2693 d 1498 2696 d 1501 2703 d
 1503 2706 d 1504 2707 d 1494 2692 r 1496 2693 d 1497 2696 d 1500 2703 d
 1501 2706 d 1504 2707 d 1507 2707 d 1508 2706 d 1510 2702 d 1510 2697 d
 1508 2693 d 1505 2692 d 1510 2692 d 1508 2693 d 1490 2717 r 1491 2716 d
 1493 2717 d 1491 2718 d 1490 2717 d 1507 2717 r 1508 2716 d 1510 2717 d
 1508 2718 d 1507 2717 d 1484 2772 r 1487 2773 d 1480 2773 d 1484 2772 d
 1482 2769 d 1480 2765 d 1480 2762 d 1482 2758 d 1484 2755 d 1487 2753 d
 1491 2752 d 1498 2752 d 1503 2753 d 1505 2755 d 1508 2758 d 1510 2762 d
 1510 2765 d 1508 2769 d 1505 2772 d 1480 2762 r 1482 2759 d 1484 2756 d
 1487 2755 d 1491 2753 d 1498 2753 d 1503 2755 d 1505 2756 d 1508 2759 d
 1510 2762 d 1498 2772 r 1510 2772 d 1498 2773 r 1510 2773 d 1498 2767 r
 1498 2776 d 1498 2784 r 1498 2801 d 1496 2801 d 1493 2800 d 1491 2798 d
 1490 2795 d 1490 2791 d 1491 2787 d 1494 2784 d 1498 2783 d 1501 2783 d
 1505 2784 d 1508 2787 d 1510 2791 d 1510 2794 d 1508 2798 d 1505 2801 d
 1498 2800 r 1494 2800 d 1491 2798 d 1490 2791 r 1491 2788 d 1494 2786 d
 1498 2784 d 1501 2784 d 1505 2786 d 1508 2788 d 1510 2791 d 1480 2811 r
 1510 2821 d 1480 2812 r 1505 2821 d 1480 2830 r 1510 2821 d 1480 2807 r
 1480 2816 d 1480 2826 r 1480 2835 d 1475 2840 r 1477 2843 d 1482 2846 d
 1487 2849 d 1494 2850 d 1500 2850 d 1507 2849 d 1512 2846 d 1517 2843 d
 1519 2840 d 1477 2843 r 1483 2846 d 1487 2847 d 1494 2849 d 1500 2849 d
 1507 2847 d 1511 2846 d 1517 2843 d 2170 1737 r 2168 1739 d 2174 1739 d
 2170 1737 d 2168 1731 d 2168 1725 d 2170 1719 d 2172 1717 d 2174 1717 d
 2178 1719 d 2180 1723 d 2184 1733 d 2186 1737 d 2188 1739 d 2174 1717 r
 2176 1719 d 2178 1723 d 2182 1733 d 2184 1737 d 2188 1739 d 2192 1739 d
 2194 1737 d 2196 1731 d 2196 1725 d 2194 1719 d 2190 1717 d 2196 1717 d
 2194 1719 d 2154 1755 r 2156 1753 d 2158 1755 d 2156 1757 d 2154 1755 d
 2168 1755 r 2196 1755 d 2168 1757 r 2196 1757 d 2168 1749 r 2168 1757 d
 2196 1749 r 2196 1763 d 2168 1777 r 2196 1777 d 2168 1779 r 2196 1779 d
 2174 1779 r 2170 1783 d 2168 1789 d 2168 1793 d 2170 1799 d 2174 1801 d
 2196 1801 d 2168 1793 r 2170 1797 d 2174 1799 d 2196 1799 d 2168 1771 r
 2168 1779 d 2196 1771 r 2196 1785 d 2196 1793 r 2196 1807 d 2154 1873 r
 2156 1867 d 2160 1863 d 2168 1859 d 2174 1857 d 2182 1855 d 2194 1853 d
 2210 1851 d 2154 1873 r 2156 1869 d 2160 1865 d 2168 1861 d 2174 1859 d
 2182 1857 d 2194 1855 d 2210 1853 d 2154 1873 r 2154 1877 d 2156 1881 d
 2158 1883 d 2164 1883 d 2168 1881 d 2170 1879 d 2172 1873 d 2172 1867 d
 2154 1877 r 2158 1881 d 2164 1881 d 2168 1879 d 2170 1877 d 2172 1873 d
 2172 1867 r 2174 1873 d 2176 1877 d 2178 1879 d 2182 1881 d 2188 1881 d
 2192 1879 d 2194 1877 d 2196 1871 d 2196 1865 d 2194 1861 d 2192 1859 d
 2186 1857 d 2174 1873 r 2178 1877 d 2182 1879 d 2188 1879 d 2192 1877 d
 2194 1875 d 2196 1871 d 1430  236 r 1430  278 d 1428  236 r 1416  272 d
 1430  236 r 1416  278 d 1402  236 r 1416  278 d 1402  236 r 1402  278 d
 1400  236 r 1400  278 d 1436  236 r 1428  236 d 1402  236 r 1394  236 d
 1436  278 r 1424  278 d 1408  278 r 1394  278 d 1371  265 r 1386  290 d
 1370  265 r 1385  290 d 1385  265 r 1386  271 d 1386  265 d 1370  265 d
 1386  290 r 1370  290 d 1370  284 d 1371  290 d 1360  267 r 1361  266 d
 1360  265 d 1359  266 d 1359  268 d 1360  271 d 1361  272 d 1274  228 r
 1274  292 d 1272  228 r 1272  292 d 1274  228 r 1260  228 d 1274  292 r
 1260  292 d 1220  242 r 1218  246 d 1218  236 d 1220  242 d 1224  238 d
 1230  236 d 1234  236 d 1240  238 d 1244  242 d 1246  246 d 1248  252 d
 1248  262 d 1246  268 d 1244  272 d 1240  276 d 1234  278 d 1230  278 d
 1224  276 d 1220  272 d 1234  236 r 1238  238 d 1242  242 d 1244  246 d
 1246  252 d 1246  262 d 1244  268 d 1242  272 d 1238  276 d 1234  278 d
 1220  262 r 1220  278 d 1218  262 r 1218  278 d 1226  262 r 1214  262 d
 1202  262 r 1178  262 d 1178  258 d 1180  254 d 1182  252 d 1186  250 d
 1192  250 d 1198  252 d 1202  256 d 1204  262 d 1204  266 d 1202  272 d
 1198  276 d 1192  278 d 1188  278 d 1182  276 d 1178  272 d 1180  262 r
 1180  256 d 1182  252 d 1192  250 r 1196  252 d 1200  256 d 1202  262 d
 1202  266 d 1200  272 d 1196  276 d 1192  278 d 1164  236 r 1150  278 d
 1162  236 r 1150  272 d 1136  236 r 1150  278 d 1170  236 r 1156  236 d
 1142  236 r 1130  236 d 1120  258 r 1122  260 d 1120  262 d 1118  260 d
 1120  258 d 1090  228 r 1094  232 d 1098  238 d 1102  246 d 1104  256 d
 1104  264 d 1102  274 d 1098  282 d 1094  288 d 1090  292 d 1094  232 r
 1098  240 d 1100  246 d 1102  256 d 1102  264 d 1100  274 d 1098  280 d
 1094  288 d 1072  244 r 1068  242 d 1062  236 d 1062  278 d 1064  238 r
 1064  278 d 1072  278 r 1054  278 d 1026  236 r 1032  238 d 1036  244 d
 1038  254 d 1038  260 d 1036  270 d 1032  276 d 1026  278 d 1022  278 d
 1016  276 d 1012  270 d 1010  260 d 1010  254 d 1012  244 d 1016  238 d
 1022  236 d 1026  236 d 1030  238 d 1032  240 d 1034  244 d 1036  254 d
 1036  260 d 1034  270 d 1032  274 d 1030  276 d 1026  278 d 1022  278 r
 1018  276 d 1016  274 d 1014  270 d 1012  260 d 1012  254 d 1014  244 d
 1016  240 d 1018  238 d 1022  236 d  986  236 r  992  238 d  996  244 d
  998  254 d  998  260 d  996  270 d  992  276 d  986  278 d  982  278 d
  976  276 d  972  270 d  970  260 d  970  254 d  972  244 d  976  238 d
  982  236 d  986  236 d  990  238 d  992  240 d  994  244 d  996  254 d
  996  260 d  994  270 d  992  274 d  990  276 d  986  278 d  982  278 r
  978  276 d  976  274 d  974  270 d  972  260 d  972  254 d  974  244 d
  976  240 d  978  238 d  982  236 d  942  248 r  944  252 d  948  254 d
  952  254 d  954  250 d  954  246 d  952  242 d  948  238 d  940  236 d
  924  236 d  928  242 d  930  246 d  934  258 d  938  268 d  940  272 d
  944  276 d  950  278 d  956  278 d  960  276 d  960  272 d  958  270 d
  956  270 d  954  272 d  946  262 r  944  260 d  940  258 d  930  258 d
  926  256 d  924  252 d  928  264 d  924  284 r  920  283 d  916  282 d
  912  279 d  911  277 d  912  274 d  915  273 d  918  273 d  922  274 d
  924  278 d  926  282 d  926  285 d  924  288 d  923  289 d  921  290 d
  918  290 d  915  289 d  912  286 d  918  273 r  921  274 d  923  278 d
  924  282 d  924  286 d  923  289 d  900  273 r  908  298 d  899  273 r
  906  298 d  900  278 r  902  284 d  902  288 d  899  290 d  897  290 d
  894  289 d  892  286 d  890  282 d  887  273 r  891  286 d  891  289 d
  888  290 d  886  289 d  884  285 d  886  273 r  890  286 d  890  289 d
  888  290 d  875  228 r  871  232 d  867  238 d  863  246 d  861  256 d
  861  264 d  863  274 d  867  282 d  871  288 d  875  292 d  871  232 r
  867  240 d  865  246 d  863  256 d  863  264 d  865  274 d  867  280 d
  871  288 d  846  218 r  844  217 d  840  214 d  840  239 d  841  215 r
  841  239 d  846  239 r  835  239 d  805  209 r  827  247 d  798  218 r
  797  220 d  798  221 d  799  220 d  799  218 d  798  216 d  797  215 d
  793  214 d  788  214 d  785  215 d  784  216 d  782  218 d  782  221 d
  784  223 d  787  226 d  793  228 d  796  229 d  798  232 d  799  235 d
  799  239 d  788  214 r  786  215 d  785  216 d  784  218 d  784  221 d
  785  223 d  788  226 d  793  228 d  799  236 r  798  235 d  796  235 d
  790  238 d  786  238 d  784  236 d  782  235 d  796  235 r  790  239 d
  785  239 d  784  238 d  782  235 d  782  233 d  761  228 r  761  292 d
  759  228 r  759  292 d  773  228 r  759  228 d  773  292 r  759  292 d
   6 lw 1181  500 r 1335  513 d 1394  526 d 1437  539 d 1472  552 d 1501  565 d
 1527  578 d 1551  591 d 1574  604 d 1595  617 d 1617  630 d 1638  643 d
 1660  656 d 1683  669 d 1708  682 d 1734  695 d 1763  708 d 1795  721 d
 1832  734 d 1876  747 d 1936  760 d 2040  773 d 1926  786 d 1867  799 d
 1821  812 d 1781  825 d 1745  838 d 1712  851 d 1682  864 d 1653  877 d
 1626  890 d 1600  903 d 1576  916 d 1552  929 d 1528  942 d 1506  955 d
 1484  968 d 1463  981 d 1442  994 d 1422 1007 d 1402 1020 d 1383 1033 d
 1364 1046 d 1345 1059 d 1327 1072 d 1309 1085 d 1291 1098 d 1274 1111 d
 1257 1124 d 1240 1137 d 1224 1150 d 1208 1163 d 1192 1176 d 1176 1189 d
 1161 1202 d 1145 1215 d 1131 1228 d 1116 1241 d 1101 1254 d 1087 1267 d
 1073 1280 d 1059 1293 d 1045 1306 d 1032 1319 d 1018 1332 d 1005 1345 d
  992 1358 d  979 1371 d  967 1384 d  954 1397 d  942 1410 d  930 1423 d
  918 1436 d  906 1449 d  894 1462 d  883 1475 d  871 1488 d  860 1501 d
  849 1514 d  838 1527 d  828 1540 d  817 1553 d  807 1566 d  797 1579 d
  786 1592 d  777 1605 d  767 1618 d  757 1631 d  748 1644 d  738 1657 d
  729 1670 d  720 1683 d  711 1696 d  702 1709 d  694 1722 d  685 1735 d
  677 1748 d  668 1761 d  660 1774 d  652 1787 d  645 1800 d  637 1813 d
  629 1826 d  622 1839 d  615 1852 d  608 1865 d  601 1878 d  594 1891 d
  587 1904 d  580 1917 d  574 1930 d  568 1943 d  562 1956 d  556 1969 d
  550 1982 d  544 1995 d  538 2008 d  533 2021 d  528 2034 d  523 2047 d
  518 2060 d  513 2073 d  508 2086 d  504 2099 d  499 2112 d  495 2125 d
  491 2138 d  487 2151 d  483 2164 d  479 2177 d  476 2190 d  473 2203 d
  469 2216 d  466 2229 d  464 2242 d  461 2255 d  458 2268 d  456 2281 d
  454 2294 d  452 2307 d  450 2320 d  448 2333 d  447 2346 d  446 2359 d
  445 2372 d  444 2385 d  443 2398 d  442 2411 d  442 2424 d  442 2437 d
  442 2450 d  442 2463 d  443 2476 d  444 2489 d  445 2502 d  446 2515 d
  447 2528 d  449 2541 d  451 2554 d  453 2567 d  455 2580 d  458 2593 d
  461 2606 d  464 2619 d  467 2632 d  471 2645 d  475 2658 d  480 2671 d
  484 2684 d  489 2697 d  495 2710 d  501 2723 d  507 2736 d  513 2749 d
  520 2762 d  528 2775 d  535 2788 d  544 2801 d  553 2814 d  562 2827 d
  572 2840 d  583 2853 d  594 2866 d  606 2879 d  618 2892 d  632 2905 d
  646 2918 d  661 2931 d  678 2944 d  695 2957 d  714 2970 d  734 2983 d
  756 2996 d  781 3009 d  807 3022 d  837 3035 d  871 3048 d  910 3061 d
  958 3074 d 1022 3087 d 1181 3100 d   2 lw lt1 1181  500 r 1315  513 d
 1365  526 d 1401  539 d 1430  552 d 1456  565 d 1479  578 d 1501  591 d
 1523  604 d 1545  617 d 1567  630 d 1590  643 d 1614  656 d 1639  669 d
 1666  682 d 1696  695 d 1728  708 d 1764  721 d 1805  734 d 1855  747 d
 1921  760 d 2036  773 d 1910  786 d 1845  799 d 1794  812 d 1750  825 d
 1712  838 d 1676  851 d 1643  864 d 1613  877 d 1583  890 d 1556  903 d
 1529  916 d 1504  929 d 1479  942 d 1455  955 d 1432  968 d 1410  981 d
 1388  994 d 1367 1007 d 1346 1020 d 1326 1033 d 1306 1046 d 1287 1059 d
 1268 1072 d 1250 1085 d 1232 1098 d 1214 1111 d 1196 1124 d 1179 1137 d
 1163 1150 d 1146 1163 d 1130 1176 d 1114 1189 d 1098 1202 d 1083 1215 d
 1068 1228 d 1053 1241 d 1038 1254 d 1024 1267 d 1009 1280 d  995 1293 d
  982 1306 d  968 1319 d  955 1332 d  941 1345 d  928 1358 d  916 1371 d
  903 1384 d  891 1397 d  878 1410 d  866 1423 d  855 1436 d  843 1449 d
  831 1462 d  820 1475 d  809 1488 d  798 1501 d  787 1514 d  777 1527 d
  766 1540 d  756 1553 d  746 1566 d  736 1579 d  726 1592 d  716 1605 d
  707 1618 d  697 1631 d  688 1644 d  679 1657 d  670 1670 d  661 1683 d
  653 1696 d  644 1709 d  636 1722 d  628 1735 d  620 1748 d  612 1761 d
  604 1774 d  597 1787 d  589 1800 d  582 1813 d  575 1826 d  568 1839 d
  561 1852 d  554 1865 d  548 1878 d  541 1891 d  535 1904 d  529 1917 d
  523 1930 d  517 1943 d  512 1956 d  506 1969 d  501 1982 d  496 1995 d
  491 2008 d  486 2021 d  481 2034 d  476 2047 d  472 2060 d  468 2073 d
  464 2086 d  460 2099 d  456 2112 d  452 2125 d  449 2138 d  445 2151 d
  442 2164 d  439 2177 d  436 2190 d  433 2203 d  431 2216 d  429 2229 d
  426 2242 d  424 2255 d  423 2268 d  421 2281 d  419 2294 d  418 2307 d
  417 2320 d  416 2333 d  415 2346 d  415 2359 d  414 2372 d  414 2385 d
  414 2398 d  414 2411 d  415 2424 d  415 2437 d  416 2450 d  417 2463 d
  418 2476 d  420 2489 d  422 2502 d  424 2515 d  426 2528 d  428 2541 d
  431 2554 d  434 2567 d  437 2580 d  440 2593 d  444 2606 d  448 2619 d
  453 2632 d  457 2645 d  462 2658 d  467 2671 d  473 2684 d  479 2697 d
  485 2710 d  492 2723 d  499 2736 d  506 2749 d  514 2762 d  522 2775 d
  531 2788 d  541 2801 d  550 2814 d  561 2827 d  571 2840 d  583 2853 d
  595 2866 d  608 2879 d  621 2892 d  636 2905 d  651 2918 d  667 2931 d
  684 2944 d  703 2957 d  723 2970 d  744 2983 d  767 2996 d  792 3009 d
  819 3022 d  849 3035 d  883 3048 d  923 3061 d  970 3074 d 1033 3087 d
 1181 3100 d lt5 1026  500 r 1141  513 d 1191  526 d 1231  539 d 1267  552 d
 1300  565 d 1331  578 d 1362  591 d 1392  604 d 1423  617 d 1453  630 d
 1485  643 d 1517  656 d 1551  669 d 1586  682 d 1624  695 d 1664  708 d
 1709  721 d 1759  734 d 1819  747 d 1896  760 d 2030  773 d 1886  786 d
 1813  799 d 1756  812 d 1708  825 d 1665  838 d 1627  851 d 1592  864 d
 1560  877 d 1529  890 d 1500  903 d 1473  916 d 1447  929 d 1422  942 d
 1398  955 d 1375  968 d 1352  981 d 1331  994 d 1310 1007 d 1289 1020 d
 1270 1033 d 1250 1046 d 1232 1059 d 1213 1072 d 1196 1085 d 1178 1098 d
 1161 1111 d 1145 1124 d 1128 1137 d 1112 1150 d 1097 1163 d 1081 1176 d
 1066 1189 d 1052 1202 d 1037 1215 d 1023 1228 d 1009 1241 d  996 1254 d
  982 1267 d  969 1280 d  956 1293 d  943 1306 d  931 1319 d  918 1332 d
  906 1345 d  894 1358 d  883 1371 d  871 1384 d  860 1397 d  849 1410 d
  838 1423 d  827 1436 d  816 1449 d  806 1462 d  796 1475 d  786 1488 d
  776 1501 d  766 1514 d  756 1527 d  747 1540 d  738 1553 d  729 1566 d
  720 1579 d  711 1592 d  702 1605 d  694 1618 d  685 1631 d  677 1644 d
  669 1657 d  661 1670 d  653 1683 d  645 1696 d  638 1709 d  631 1722 d
  623 1735 d  616 1748 d  609 1761 d  602 1774 d  596 1787 d  589 1800 d
  583 1813 d  577 1826 d  570 1839 d  564 1852 d  558 1865 d  553 1878 d
  547 1891 d  542 1904 d  536 1917 d  531 1930 d  526 1943 d  521 1956 d
  516 1969 d  512 1982 d  507 1995 d  503 2008 d  498 2021 d  494 2034 d
  490 2047 d  486 2060 d  483 2073 d  479 2086 d  476 2099 d  472 2112 d
  469 2125 d  466 2138 d  463 2151 d  460 2164 d  458 2177 d  455 2190 d
  453 2203 d  451 2216 d  449 2229 d  447 2242 d  445 2255 d  443 2268 d
  442 2281 d  441 2294 d  440 2307 d  439 2320 d  438 2333 d  437 2346 d
  437 2359 d  436 2372 d  436 2385 d  436 2398 d  436 2411 d  436 2424 d
  437 2437 d  438 2450 d  438 2463 d  440 2476 d  441 2489 d  442 2502 d
  444 2515 d  446 2528 d  448 2541 d  450 2554 d  452 2567 d  455 2580 d
  458 2593 d  461 2606 d  464 2619 d  468 2632 d  471 2645 d  476 2658 d
  480 2671 d  484 2684 d  489 2697 d  494 2710 d  500 2723 d  505 2736 d
  511 2749 d  518 2762 d  524 2775 d  532 2788 d  539 2801 d  547 2814 d
  555 2827 d  564 2840 d  573 2853 d  582 2866 d  592 2879 d  603 2892 d
  614 2905 d  626 2918 d  639 2931 d  652 2944 d  666 2957 d  681 2970 d
  698 2983 d  715 2996 d  734 3009 d  754 3022 d  777 3035 d  803 3048 d
  832 3061 d  867 3074 d  913 3087 d 1026 3100 d   4 lw lt3 1792  500 r
 1840  513 d 1859  526 d 1873  539 d 1884  552 d 1893  565 d 1901  578 d
 1909  591 d 1916  604 d 1923  617 d 1929  630 d 1936  643 d 1943  656 d
 1951  669 d 1958  682 d 1967  695 d 1976  708 d 1986  721 d 1997  734 d
 2012  747 d 2030  760 d 2050  768 d 2050  778 r 2027  786 d 2008  799 d
 1994  812 d 1981  825 d 1970  838 d 1960  851 d 1950  864 d 1941  877 d
 1932  890 d 1924  903 d 1916  916 d 1909  929 d 1901  942 d 1894  955 d
 1887  968 d 1881  981 d 1874  994 d 1868 1007 d 1862 1020 d 1855 1033 d
 1849 1046 d 1843 1059 d 1838 1072 d 1832 1085 d 1827 1098 d 1821 1111 d
 1816 1124 d 1810 1137 d 1805 1150 d 1800 1163 d 1795 1176 d 1790 1189 d
 1785 1202 d 1780 1215 d 1776 1228 d 1771 1241 d 1766 1254 d 1762 1267 d
 1757 1280 d 1753 1293 d 1748 1306 d 1744 1319 d 1740 1332 d 1736 1345 d
 1732 1358 d 1728 1371 d 1724 1384 d 1720 1397 d 1716 1410 d 1712 1423 d
 1708 1436 d 1704 1449 d 1701 1462 d 1697 1475 d 1694 1488 d 1690 1501 d
 1687 1514 d 1683 1527 d 1680 1540 d 1677 1553 d 1673 1566 d 1670 1579 d
 1667 1592 d 1664 1605 d 1661 1618 d 1658 1631 d 1655 1644 d 1652 1657 d
 1649 1670 d 1646 1683 d 1643 1696 d 1640 1709 d 1637 1722 d 1635 1735 d
 1632 1748 d 1630 1761 d 1627 1774 d 1624 1787 d 1622 1800 d 1620 1813 d
 1617 1826 d 1615 1839 d 1613 1852 d 1610 1865 d 1608 1878 d 1606 1891 d
 1604 1904 d 1602 1917 d 1600 1930 d 1598 1943 d 1596 1956 d 1594 1969 d
 1592 1982 d 1590 1995 d 1588 2008 d 1587 2021 d 1585 2034 d 1583 2047 d
 1582 2060 d 1580 2073 d 1579 2086 d 1577 2099 d 1576 2112 d 1575 2125 d
 1573 2138 d 1572 2151 d 1571 2164 d 1570 2177 d 1569 2190 d 1568 2203 d
 1567 2216 d 1566 2229 d 1565 2242 d 1564 2255 d 1563 2268 d 1562 2281 d
 1562 2294 d 1561 2307 d 1561 2320 d 1560 2333 d 1560 2346 d 1559 2359 d
 1559 2372 d 1559 2385 d 1558 2398 d 1558 2411 d 1558 2424 d 1558 2437 d
 1558 2450 d 1558 2463 d 1558 2476 d 1558 2489 d 1559 2502 d 1559 2515 d
 1560 2528 d 1560 2541 d 1561 2554 d 1561 2567 d 1562 2580 d 1563 2593 d
 1564 2606 d 1565 2619 d 1566 2632 d 1567 2645 d 1568 2658 d 1570 2671 d
 1571 2684 d 1573 2697 d 1575 2710 d 1576 2723 d 1578 2736 d 1580 2749 d
 1583 2762 d 1585 2775 d 1588 2788 d 1590 2801 d 1593 2814 d 1596 2827 d
 1599 2840 d 1602 2853 d 1606 2866 d 1610 2879 d 1614 2892 d 1618 2905 d
 1622 2918 d 1627 2931 d 1632 2944 d 1638 2957 d 1644 2970 d 1650 2983 d
 1657 2996 d 1665 3009 d 1673 3022 d 1683 3035 d 1694 3048 d 1706 3061 d
 1721 3074 d 1741 3087 d 1792 3100 d   2 lw lt1 1792  500 r 1834  513 d
 1850  526 d 1861  539 d 1871  552 d 1879  565 d 1886  578 d 1893  591 d
 1900  604 d 1907  617 d 1914  630 d 1921  643 d 1929  656 d 1937  669 d
 1945  682 d 1954  695 d 1965  708 d 1976  721 d 1989  734 d 2005  747 d
 2025  760 d 2050  769 d 2050  777 r 2022  786 d 2002  799 d 1985  812 d
 1972  825 d 1959  838 d 1948  851 d 1938  864 d 1928  877 d 1919  890 d
 1910  903 d 1902  916 d 1894  929 d 1886  942 d 1878  955 d 1871  968 d
 1863  981 d 1857  994 d 1850 1007 d 1844 1020 d 1837 1033 d 1831 1046 d
 1825 1059 d 1819 1072 d 1813 1085 d 1807 1098 d 1802 1111 d 1796 1124 d
 1791 1137 d 1786 1150 d 1780 1163 d 1775 1176 d 1770 1189 d 1765 1202 d
 1760 1215 d 1756 1228 d 1751 1241 d 1746 1254 d 1742 1267 d 1737 1280 d
 1733 1293 d 1728 1306 d 1724 1319 d 1720 1332 d 1716 1345 d 1712 1358 d
 1708 1371 d 1703 1384 d 1699 1397 d 1696 1410 d 1692 1423 d 1688 1436 d
 1685 1449 d 1681 1462 d 1677 1475 d 1674 1488 d 1670 1501 d 1667 1514 d
 1664 1527 d 1660 1540 d 1657 1553 d 1654 1566 d 1651 1579 d 1647 1592 d
 1645 1605 d 1641 1618 d 1639 1631 d 1636 1644 d 1633 1657 d 1630 1670 d
 1627 1683 d 1624 1696 d 1622 1709 d 1619 1722 d 1617 1735 d 1614 1748 d
 1612 1761 d 1609 1774 d 1607 1787 d 1604 1800 d 1602 1813 d 1600 1826 d
 1598 1839 d 1595 1852 d 1593 1865 d 1591 1878 d 1589 1891 d 1587 1904 d
 1585 1917 d 1584 1930 d 1582 1943 d 1580 1956 d 1578 1969 d 1576 1982 d
 1575 1995 d 1573 2008 d 1572 2021 d 1570 2034 d 1569 2047 d 1567 2060 d
 1566 2073 d 1565 2086 d 1563 2099 d 1562 2112 d 1561 2125 d 1560 2138 d
 1559 2151 d 1558 2164 d 1557 2177 d 1556 2190 d 1555 2203 d 1554 2216 d
 1554 2229 d 1553 2242 d 1552 2255 d 1552 2268 d 1551 2281 d 1551 2294 d
 1550 2307 d 1550 2320 d 1550 2333 d 1549 2346 d 1549 2359 d 1549 2372 d
 1549 2385 d 1549 2398 d 1549 2411 d 1549 2424 d 1549 2437 d 1550 2450 d
 1550 2463 d 1550 2476 d 1551 2489 d 1551 2502 d 1552 2515 d 1553 2528 d
 1553 2541 d 1554 2554 d 1555 2567 d 1556 2580 d 1557 2593 d 1559 2606 d
 1560 2619 d 1561 2632 d 1563 2645 d 1564 2658 d 1566 2671 d 1568 2684 d
 1570 2697 d 1572 2710 d 1574 2723 d 1576 2736 d 1578 2749 d 1581 2762 d
 1583 2775 d 1586 2788 d 1589 2801 d 1592 2814 d 1595 2827 d 1599 2840 d
 1602 2853 d 1606 2866 d 1610 2879 d 1615 2892 d 1619 2905 d 1624 2918 d
 1629 2931 d 1635 2944 d 1640 2957 d 1647 2970 d 1653 2983 d 1661 2996 d
 1668 3009 d 1677 3022 d 1687 3035 d 1697 3048 d 1710 3061 d 1725 3074 d
 1745 3087 d 1792 3100 d lt5 1743  500 r 1779  513 d 1795  526 d 1808  539 d
 1819  552 d 1830  565 d 1839  578 d 1849  591 d 1859  604 d 1868  617 d
 1878  630 d 1888  643 d 1898  656 d 1909  669 d 1920  682 d 1932  695 d
 1945  708 d 1959  721 d 1975  734 d 1993  747 d 2018  760 d 2050  771 d
 2050  775 r 2015  786 d 1991  799 d 1973  812 d 1958  825 d 1945  838 d
 1932  851 d 1921  864 d 1911  877 d 1902  890 d 1892  903 d 1884  916 d
 1875  929 d 1868  942 d 1860  955 d 1853  968 d 1846  981 d 1839  994 d
 1832 1007 d 1826 1020 d 1819 1033 d 1813 1046 d 1807 1059 d 1802 1072 d
 1796 1085 d 1791 1098 d 1785 1111 d 1780 1124 d 1775 1137 d 1770 1150 d
 1765 1163 d 1760 1176 d 1755 1189 d 1751 1202 d 1746 1215 d 1742 1228 d
 1737 1241 d 1733 1254 d 1729 1267 d 1724 1280 d 1720 1293 d 1716 1306 d
 1712 1319 d 1708 1332 d 1704 1345 d 1701 1358 d 1697 1371 d 1694 1384 d
 1690 1397 d 1686 1410 d 1683 1423 d 1680 1436 d 1676 1449 d 1673 1462 d
 1670 1475 d 1667 1488 d 1663 1501 d 1660 1514 d 1657 1527 d 1654 1540 d
 1651 1553 d 1648 1566 d 1646 1579 d 1643 1592 d 1640 1605 d 1637 1618 d
 1635 1631 d 1632 1644 d 1630 1657 d 1627 1670 d 1625 1683 d 1622 1696 d
 1620 1709 d 1617 1722 d 1615 1735 d 1613 1748 d 1611 1761 d 1609 1774 d
 1606 1787 d 1604 1800 d 1602 1813 d 1600 1826 d 1598 1839 d 1596 1852 d
 1595 1865 d 1593 1878 d 1591 1891 d 1589 1904 d 1588 1917 d 1586 1930 d
 1584 1943 d 1583 1956 d 1581 1969 d 1580 1982 d 1578 1995 d 1577 2008 d
 1576 2021 d 1574 2034 d 1573 2047 d 1572 2060 d 1571 2073 d 1570 2086 d
 1568 2099 d 1567 2112 d 1566 2125 d 1565 2138 d 1565 2151 d 1564 2164 d
 1563 2177 d 1562 2190 d 1561 2203 d 1561 2216 d 1560 2229 d 1559 2242 d
 1559 2255 d 1558 2268 d 1558 2281 d 1557 2294 d 1557 2307 d 1557 2320 d
 1557 2333 d 1556 2346 d 1556 2359 d 1556 2372 d 1556 2385 d 1556 2398 d
 1556 2411 d 1556 2424 d 1556 2437 d 1557 2450 d 1557 2463 d 1557 2476 d
 1558 2489 d 1558 2502 d 1559 2515 d 1559 2528 d 1560 2541 d 1560 2554 d
 1561 2567 d 1562 2580 d 1563 2593 d 1564 2606 d 1565 2619 d 1566 2632 d
 1567 2645 d 1569 2658 d 1570 2671 d 1571 2684 d 1573 2697 d 1575 2710 d
 1576 2723 d 1578 2736 d 1580 2749 d 1582 2762 d 1584 2775 d 1586 2788 d
 1589 2801 d 1591 2814 d 1594 2827 d 1596 2840 d 1599 2853 d 1602 2866 d
 1606 2879 d 1609 2892 d 1613 2905 d 1616 2918 d 1620 2931 d 1625 2944 d
 1629 2957 d 1634 2970 d 1639 2983 d 1644 2996 d 1650 3009 d 1657 3022 d
 1664 3035 d 1672 3048 d 1681 3061 d 1693 3074 d 1707 3087 d 1743 3100 d
   6 lw lt0  391  656 r  391  890 d   1 lw  372 1003 r  417  994 d  372 1005 r
  417  992 d  383  997 r  385  991 d  388  987 d  393  986 d  397  986 d
  401  987 d  404  991 d  405  995 d  405 1000 d  404 1007 d  401 1010 d
  396 1011 d  391 1011 d  388 1010 d  385 1007 d  383 1002 d  383  997 d
  385  992 d  388  989 d  393  987 d  397  987 d  401  989 d  404  992 d
  405  995 d  405 1000 r  404 1005 d  401 1008 d  396 1010 d  391 1010 d
  388 1008 d  385 1005 d  383 1002 d  386 1021 r  386 1050 d  396 1021 r
  396 1050 d  372 1069 r  373 1064 d  378 1061 d  386 1059 d  391 1059 d
  399 1061 d  404 1064 d  405 1069 d  405 1072 d  404 1077 d  399 1080 d
  391 1082 d  386 1082 d  378 1080 d  373 1077 d  372 1072 d  372 1069 d
  373 1066 d  375 1064 d  378 1063 d  386 1061 d  391 1061 d  399 1063 d
  402 1064 d  404 1066 d  405 1069 d  405 1072 r  404 1075 d  402 1077 d
  399 1079 d  391 1080 d  386 1080 d  378 1079 d  375 1077 d  373 1075 d
  372 1072 d   4 lw lt3  451  656 r  451  890 d   1 lw lt0  432 1003 r
  477  994 d  432 1005 r  477  992 d  443  997 r  445  991 d  448  987 d
  453  986 d  457  986 d  461  987 d  464  991 d  465  995 d  465 1000 d
  464 1007 d  461 1010 d  456 1011 d  451 1011 d  448 1010 d  445 1007 d
  443 1002 d  443  997 d  445  992 d  448  989 d  453  987 d  457  987 d
  461  989 d  464  992 d  465  995 d  465 1000 r  464 1005 d  461 1008 d
  456 1010 d  451 1010 d  448 1008 d  445 1005 d  443 1002 d  446 1021 r
  446 1050 d  456 1021 r  456 1050 d  432 1069 r  433 1064 d  438 1061 d
  446 1059 d  451 1059 d  459 1061 d  464 1064 d  465 1069 d  465 1072 d
  464 1077 d  459 1080 d  451 1082 d  446 1082 d  438 1080 d  433 1077 d
  432 1072 d  432 1069 d  433 1066 d  435 1064 d  438 1063 d  446 1061 d
  451 1061 d  459 1063 d  462 1064 d  464 1066 d  465 1069 d  465 1072 r
  464 1075 d  462 1077 d  459 1079 d  451 1080 d  446 1080 d  438 1079 d
  435 1077 d  433 1075 d  432 1072 d   2 lw lt1  571  656 r  571  890 d
   1 lw lt0  563 1013 r  563  995 d  565  991 d  569  987 d  574  986 d
  579  986 d  582  987 d  584  989 d  585  992 d  585  995 d  584 1000 d
  579 1003 d  574 1005 d  569 1005 d  566 1003 d  565 1002 d  563  999 d
  563  995 r  565  992 d  569  989 d  574  987 d  581  987 d  584  989 d
  585  995 r  584  999 d  579 1002 d  574 1003 d  568 1003 d  565 1002 d
  565 1013 d  566 1021 r  566 1050 d  576 1021 r  576 1050 d  558 1064 r
  557 1067 d  552 1072 d  585 1072 d  553 1071 r  585 1071 d  585 1064 r
  585 1079 d   2 lw lt5  631  656 r  631  890 d   1 lw lt0  623 1013 r
  623  995 d  625  991 d  629  987 d  634  986 d  639  986 d  642  987 d
  644  989 d  645  992 d  645  995 d  644 1000 d  639 1003 d  634 1005 d
  629 1005 d  626 1003 d  625 1002 d  623  999 d  623  995 r  625  992 d
  629  989 d  634  987 d  641  987 d  644  989 d  645  995 r  644  999 d
  639 1002 d  634 1003 d  628 1003 d  625 1002 d  625 1013 d  626 1021 r
  626 1050 d  636 1021 r  636 1050 d  633 1090 r  636 1088 d  637 1085 d
  637 1082 d  636 1079 d  634 1077 d  628 1072 d  626 1071 d  625 1067 d
  625 1064 d  626 1061 d  629 1059 d  633 1059 d  636 1061 d  637 1064 d
  637 1067 d  636 1071 d  634 1072 d  628 1077 d  626 1079 d  625 1082 d
  625 1085 d  626 1088 d  629 1090 d  633 1090 d
e
%%Trailer
EndPSPlot



%!PS-Adobe-1.0
%%EndComments
save 50 dict begin /psplot exch def
/StartPSPlot
   {newpath 0 0 moveto 0 setlinewidth 0 setgray 1 setlinecap
    1 setlinejoin 72 300 div dup scale}def
/pending {false} def
/finish {pending {currentpoint stroke moveto /pending false def} if} def
/r {finish newpath moveto} def
/d {lineto /pending true def} def
/l {finish 4 2 roll moveto lineto currentpoint stroke moveto} def
/p {finish newpath moveto currentpoint lineto currentpoint stroke moveto} def
/e {finish gsave showpage grestore newpath 0 0 moveto} def
/lw {finish setlinewidth} def
/lt0 {finish [] 0 setdash} def
/lt1 {finish [3 5] 0 setdash} def
/lt2 {finish [20 10] 0 setdash} def
/lt3 {finish [60 10] 0 setdash} def
/lt4 {finish [3 10 20 10] 0 setdash} def
/lt5 {finish [3 10 60 10] 0 setdash} def
/lt6 {finish [20 10 60 10] 0 setdash} def
/EndPSPlot {clear psplot end restore}def
% end fixed prolog
StartPSPlot
%%EndProlog
%%Page: 1 1
   4 lw lt0 2050  500 r 2050 3100 d 2050  500 r 2018  500 d 2050  630 r
 2018  630 d 2050  760 r 1986  760 d 2050  890 r 2018  890 d 2050 1020 r
 2018 1020 d 2050 1150 r 2018 1150 d 2050 1280 r 1986 1280 d 2050 1410 r
 2018 1410 d 2050 1540 r 2018 1540 d 2050 1670 r 2018 1670 d 2050 1800 r
 1986 1800 d 2050 1930 r 2018 1930 d 2050 2060 r 2018 2060 d 2050 2190 r
 2018 2190 d 2050 2320 r 1986 2320 d 2050 2450 r 2018 2450 d 2050 2580 r
 2018 2580 d 2050 2710 r 2018 2710 d 2050 2840 r 1986 2840 d 2050 2970 r
 2018 2970 d 2050 3100 r 2018 3100 d 2114  714 r 2114  750 d 2128  764 r
 2130  762 d 2132  764 d 2130  766 d 2128  764 d 2090  788 r 2092  782 d
 2096  780 d 2102  780 d 2106  782 d 2108  788 d 2108  796 d 2106  802 d
 2102  804 d 2096  804 d 2092  802 d 2090  796 d 2090  788 d 2092  784 d
 2096  782 d 2102  782 d 2106  784 d 2108  788 d 2108  796 r 2106  800 d
 2102  802 d 2096  802 d 2092  800 d 2090  796 d 2108  788 r 2110  782 d
 2112  780 d 2116  778 d 2124  778 d 2128  780 d 2130  782 d 2132  788 d
 2132  796 d 2130  802 d 2128  804 d 2124  806 d 2116  806 d 2112  804 d
 2110  802 d 2108  796 d 2108  788 r 2110  784 d 2112  782 d 2116  780 d
 2124  780 d 2128  782 d 2130  784 d 2132  788 d 2132  796 r 2130  800 d
 2128  802 d 2124  804 d 2116  804 d 2112  802 d 2110  800 d 2108  796 d
 2114 1234 r 2114 1270 d 2128 1284 r 2130 1282 d 2132 1284 d 2130 1286 d
 2128 1284 d 2094 1316 r 2132 1316 d 2090 1318 r 2132 1318 d 2090 1318 r
 2120 1296 d 2120 1328 d 2132 1310 r 2132 1324 d 2090 1798 r 2092 1792 d
 2098 1788 d 2108 1786 d 2114 1786 d 2124 1788 d 2130 1792 d 2132 1798 d
 2132 1802 d 2130 1808 d 2124 1812 d 2114 1814 d 2108 1814 d 2098 1812 d
 2092 1808 d 2090 1802 d 2090 1798 d 2092 1794 d 2094 1792 d 2098 1790 d
 2108 1788 d 2114 1788 d 2124 1790 d 2128 1792 d 2130 1794 d 2132 1798 d
 2132 1802 r 2130 1806 d 2128 1808 d 2124 1810 d 2114 1812 d 2108 1812 d
 2098 1810 d 2094 1808 d 2092 1806 d 2090 1802 d 2128 2300 r 2130 2298 d
 2132 2300 d 2130 2302 d 2128 2300 d 2094 2332 r 2132 2332 d 2090 2334 r
 2132 2334 d 2090 2334 r 2120 2312 d 2120 2344 d 2132 2326 r 2132 2340 d
 2128 2820 r 2130 2818 d 2132 2820 d 2130 2822 d 2128 2820 d 2090 2844 r
 2092 2838 d 2096 2836 d 2102 2836 d 2106 2838 d 2108 2844 d 2108 2852 d
 2106 2858 d 2102 2860 d 2096 2860 d 2092 2858 d 2090 2852 d 2090 2844 d
 2092 2840 d 2096 2838 d 2102 2838 d 2106 2840 d 2108 2844 d 2108 2852 r
 2106 2856 d 2102 2858 d 2096 2858 d 2092 2856 d 2090 2852 d 2108 2844 r
 2110 2838 d 2112 2836 d 2116 2834 d 2124 2834 d 2128 2836 d 2130 2838 d
 2132 2844 d 2132 2852 d 2130 2858 d 2128 2860 d 2124 2862 d 2116 2862 d
 2112 2860 d 2110 2858 d 2108 2852 d 2108 2844 r 2110 2840 d 2112 2838 d
 2116 2836 d 2124 2836 d 2128 2838 d 2130 2840 d 2132 2844 d 2132 2852 r
 2130 2856 d 2128 2858 d 2124 2860 d 2116 2860 d 2112 2858 d 2110 2856 d
 2108 2852 d  150  500 r  150 3100 d  150  500 r  182  500 d  150  630 r
  182  630 d  150  760 r  214  760 d  150  890 r  182  890 d  150 1020 r
  182 1020 d  150 1150 r  182 1150 d  150 1280 r  214 1280 d  150 1410 r
  182 1410 d  150 1540 r  182 1540 d  150 1670 r  182 1670 d  150 1800 r
  214 1800 d  150 1930 r  182 1930 d  150 2060 r  182 2060 d  150 2190 r
  182 2190 d  150 2320 r  214 2320 d  150 2450 r  182 2450 d  150 2580 r
  182 2580 d  150 2710 r  182 2710 d  150 2840 r  214 2840 d  150 2970 r
  182 2970 d  150 3100 r  182 3100 d 2050  500 r  150  500 d 1964  500 r
 1964  532 d 1868  500 r 1868  564 d 1772  500 r 1772  532 d 1676  500 r
 1676  564 d 1580  500 r 1580  532 d 1484  500 r 1484  564 d 1388  500 r
 1388  532 d 1292  500 r 1292  564 d 1196  500 r 1196  532 d 1100  500 r
 1100  564 d 1004  500 r 1004  532 d  908  500 r  908  564 d  812  500 r
  812  532 d  716  500 r  716  564 d  620  500 r  620  532 d  524  500 r
  524  564 d  428  500 r  428  532 d  332  500 r  332  564 d  236  500 r
  236  532 d 1868  290 r 1868  326 d 1882  340 r 1884  338 d 1886  340 d
 1884  342 d 1882  340 d 1844  366 r 1846  360 d 1852  356 d 1862  354 d
 1868  354 d 1878  356 d 1884  360 d 1886  366 d 1886  370 d 1884  376 d
 1878  380 d 1868  382 d 1862  382 d 1852  380 d 1846  376 d 1844  370 d
 1844  366 d 1846  362 d 1848  360 d 1852  358 d 1862  356 d 1868  356 d
 1878  358 d 1882  360 d 1884  362 d 1886  366 d 1886  370 r 1884  374 d
 1882  376 d 1878  378 d 1868  380 d 1862  380 d 1852  378 d 1848  376 d
 1846  374 d 1844  370 d 1844  406 r 1846  400 d 1852  396 d 1862  394 d
 1868  394 d 1878  396 d 1884  400 d 1886  406 d 1886  410 d 1884  416 d
 1878  420 d 1868  422 d 1862  422 d 1852  420 d 1846  416 d 1844  410 d
 1844  406 d 1846  402 d 1848  400 d 1852  398 d 1862  396 d 1868  396 d
 1878  398 d 1882  400 d 1884  402 d 1886  406 d 1886  410 r 1884  414 d
 1882  416 d 1878  418 d 1868  420 d 1862  420 d 1852  418 d 1848  416 d
 1846  414 d 1844  410 d 1844  444 r 1846  438 d 1850  436 d 1856  436 d
 1860  438 d 1862  444 d 1862  452 d 1860  458 d 1856  460 d 1850  460 d
 1846  458 d 1844  452 d 1844  444 d 1846  440 d 1850  438 d 1856  438 d
 1860  440 d 1862  444 d 1862  452 r 1860  456 d 1856  458 d 1850  458 d
 1846  456 d 1844  452 d 1862  444 r 1864  438 d 1866  436 d 1870  434 d
 1878  434 d 1882  436 d 1884  438 d 1886  444 d 1886  452 d 1884  458 d
 1882  460 d 1878  462 d 1870  462 d 1866  460 d 1864  458 d 1862  452 d
 1862  444 r 1864  440 d 1866  438 d 1870  436 d 1878  436 d 1882  438 d
 1884  440 d 1886  444 d 1886  452 r 1884  456 d 1882  458 d 1878  460 d
 1870  460 d 1866  458 d 1864  456 d 1862  452 d 1676  290 r 1676  326 d
 1690  340 r 1692  338 d 1694  340 d 1692  342 d 1690  340 d 1652  366 r
 1654  360 d 1660  356 d 1670  354 d 1676  354 d 1686  356 d 1692  360 d
 1694  366 d 1694  370 d 1692  376 d 1686  380 d 1676  382 d 1670  382 d
 1660  380 d 1654  376 d 1652  370 d 1652  366 d 1654  362 d 1656  360 d
 1660  358 d 1670  356 d 1676  356 d 1686  358 d 1690  360 d 1692  362 d
 1694  366 d 1694  370 r 1692  374 d 1690  376 d 1686  378 d 1676  380 d
 1670  380 d 1660  378 d 1656  376 d 1654  374 d 1652  370 d 1652  406 r
 1654  400 d 1660  396 d 1670  394 d 1676  394 d 1686  396 d 1692  400 d
 1694  406 d 1694  410 d 1692  416 d 1686  420 d 1676  422 d 1670  422 d
 1660  420 d 1654  416 d 1652  410 d 1652  406 d 1654  402 d 1656  400 d
 1660  398 d 1670  396 d 1676  396 d 1686  398 d 1690  400 d 1692  402 d
 1694  406 d 1694  410 r 1692  414 d 1690  416 d 1686  418 d 1676  420 d
 1670  420 d 1660  418 d 1656  416 d 1654  414 d 1652  410 d 1658  458 r
 1660  456 d 1662  458 d 1660  460 d 1658  460 d 1654  458 d 1652  454 d
 1652  448 d 1654  442 d 1658  438 d 1662  436 d 1670  434 d 1682  434 d
 1688  436 d 1692  440 d 1694  446 d 1694  450 d 1692  456 d 1688  460 d
 1682  462 d 1680  462 d 1674  460 d 1670  456 d 1668  450 d 1668  448 d
 1670  442 d 1674  438 d 1680  436 d 1652  448 r 1654  444 d 1658  440 d
 1662  438 d 1670  436 d 1682  436 d 1688  438 d 1692  442 d 1694  446 d
 1694  450 r 1692  454 d 1688  458 d 1682  460 d 1680  460 d 1674  458 d
 1670  454 d 1668  450 d 1484  290 r 1484  326 d 1498  340 r 1500  338 d
 1502  340 d 1500  342 d 1498  340 d 1460  366 r 1462  360 d 1468  356 d
 1478  354 d 1484  354 d 1494  356 d 1500  360 d 1502  366 d 1502  370 d
 1500  376 d 1494  380 d 1484  382 d 1478  382 d 1468  380 d 1462  376 d
 1460  370 d 1460  366 d 1462  362 d 1464  360 d 1468  358 d 1478  356 d
 1484  356 d 1494  358 d 1498  360 d 1500  362 d 1502  366 d 1502  370 r
 1500  374 d 1498  376 d 1494  378 d 1484  380 d 1478  380 d 1468  378 d
 1464  376 d 1462  374 d 1460  370 d 1460  406 r 1462  400 d 1468  396 d
 1478  394 d 1484  394 d 1494  396 d 1500  400 d 1502  406 d 1502  410 d
 1500  416 d 1494  420 d 1484  422 d 1478  422 d 1468  420 d 1462  416 d
 1460  410 d 1460  406 d 1462  402 d 1464  400 d 1468  398 d 1478  396 d
 1484  396 d 1494  398 d 1498  400 d 1500  402 d 1502  406 d 1502  410 r
 1500  414 d 1498  416 d 1494  418 d 1484  420 d 1478  420 d 1468  418 d
 1464  416 d 1462  414 d 1460  410 d 1464  452 r 1502  452 d 1460  454 r
 1502  454 d 1460  454 r 1490  432 d 1490  464 d 1502  446 r 1502  460 d
 1292  290 r 1292  326 d 1306  340 r 1308  338 d 1310  340 d 1308  342 d
 1306  340 d 1268  366 r 1270  360 d 1276  356 d 1286  354 d 1292  354 d
 1302  356 d 1308  360 d 1310  366 d 1310  370 d 1308  376 d 1302  380 d
 1292  382 d 1286  382 d 1276  380 d 1270  376 d 1268  370 d 1268  366 d
 1270  362 d 1272  360 d 1276  358 d 1286  356 d 1292  356 d 1302  358 d
 1306  360 d 1308  362 d 1310  366 d 1310  370 r 1308  374 d 1306  376 d
 1302  378 d 1292  380 d 1286  380 d 1276  378 d 1272  376 d 1270  374 d
 1268  370 d 1268  406 r 1270  400 d 1276  396 d 1286  394 d 1292  394 d
 1302  396 d 1308  400 d 1310  406 d 1310  410 d 1308  416 d 1302  420 d
 1292  422 d 1286  422 d 1276  420 d 1270  416 d 1268  410 d 1268  406 d
 1270  402 d 1272  400 d 1276  398 d 1286  396 d 1292  396 d 1302  398 d
 1306  400 d 1308  402 d 1310  406 d 1310  410 r 1308  414 d 1306  416 d
 1302  418 d 1292  420 d 1286  420 d 1276  418 d 1272  416 d 1270  414 d
 1268  410 d 1276  436 r 1278  438 d 1280  436 d 1278  434 d 1276  434 d
 1272  436 d 1270  438 d 1268  444 d 1268  452 d 1270  458 d 1272  460 d
 1276  462 d 1280  462 d 1284  460 d 1288  454 d 1292  444 d 1294  440 d
 1298  436 d 1304  434 d 1310  434 d 1268  452 r 1270  456 d 1272  458 d
 1276  460 d 1280  460 d 1284  458 d 1288  452 d 1292  444 d 1306  434 r
 1304  436 d 1304  440 d 1308  450 d 1308  456 d 1306  460 d 1304  462 d
 1304  440 r 1310  450 d 1310  458 d 1308  460 d 1304  462 d 1300  462 d
 1076  446 r 1078  440 d 1084  436 d 1094  434 d 1100  434 d 1110  436 d
 1116  440 d 1118  446 d 1118  450 d 1116  456 d 1110  460 d 1100  462 d
 1094  462 d 1084  460 d 1078  456 d 1076  450 d 1076  446 d 1078  442 d
 1080  440 d 1084  438 d 1094  436 d 1100  436 d 1110  438 d 1114  440 d
 1116  442 d 1118  446 d 1118  450 r 1116  454 d 1114  456 d 1110  458 d
 1100  460 d 1094  460 d 1084  458 d 1080  456 d 1078  454 d 1076  450 d
  922  340 r  924  338 d  926  340 d  924  342 d  922  340 d  884  366 r
  886  360 d  892  356 d  902  354 d  908  354 d  918  356 d  924  360 d
  926  366 d  926  370 d  924  376 d  918  380 d  908  382 d  902  382 d
  892  380 d  886  376 d  884  370 d  884  366 d  886  362 d  888  360 d
  892  358 d  902  356 d  908  356 d  918  358 d  922  360 d  924  362 d
  926  366 d  926  370 r  924  374 d  922  376 d  918  378 d  908  380 d
  902  380 d  892  378 d  888  376 d  886  374 d  884  370 d  884  406 r
  886  400 d  892  396 d  902  394 d  908  394 d  918  396 d  924  400 d
  926  406 d  926  410 d  924  416 d  918  420 d  908  422 d  902  422 d
  892  420 d  886  416 d  884  410 d  884  406 d  886  402 d  888  400 d
  892  398 d  902  396 d  908  396 d  918  398 d  922  400 d  924  402 d
  926  406 d  926  410 r  924  414 d  922  416 d  918  418 d  908  420 d
  902  420 d  892  418 d  888  416 d  886  414 d  884  410 d  892  436 r
  894  438 d  896  436 d  894  434 d  892  434 d  888  436 d  886  438 d
  884  444 d  884  452 d  886  458 d  888  460 d  892  462 d  896  462 d
  900  460 d  904  454 d  908  444 d  910  440 d  914  436 d  920  434 d
  926  434 d  884  452 r  886  456 d  888  458 d  892  460 d  896  460 d
  900  458 d  904  452 d  908  444 d  922  434 r  920  436 d  920  440 d
  924  450 d  924  456 d  922  460 d  920  462 d  920  440 r  926  450 d
  926  458 d  924  460 d  920  462 d  916  462 d  730  340 r  732  338 d
  734  340 d  732  342 d  730  340 d  692  366 r  694  360 d  700  356 d
  710  354 d  716  354 d  726  356 d  732  360 d  734  366 d  734  370 d
  732  376 d  726  380 d  716  382 d  710  382 d  700  380 d  694  376 d
  692  370 d  692  366 d  694  362 d  696  360 d  700  358 d  710  356 d
  716  356 d  726  358 d  730  360 d  732  362 d  734  366 d  734  370 r
  732  374 d  730  376 d  726  378 d  716  380 d  710  380 d  700  378 d
  696  376 d  694  374 d  692  370 d  692  406 r  694  400 d  700  396 d
  710  394 d  716  394 d  726  396 d  732  400 d  734  406 d  734  410 d
  732  416 d  726  420 d  716  422 d  710  422 d  700  420 d  694  416 d
  692  410 d  692  406 d  694  402 d  696  400 d  700  398 d  710  396 d
  716  396 d  726  398 d  730  400 d  732  402 d  734  406 d  734  410 r
  732  414 d  730  416 d  726  418 d  716  420 d  710  420 d  700  418 d
  696  416 d  694  414 d  692  410 d  696  452 r  734  452 d  692  454 r
  734  454 d  692  454 r  722  432 d  722  464 d  734  446 r  734  460 d
  538  340 r  540  338 d  542  340 d  540  342 d  538  340 d  500  366 r
  502  360 d  508  356 d  518  354 d  524  354 d  534  356 d  540  360 d
  542  366 d  542  370 d  540  376 d  534  380 d  524  382 d  518  382 d
  508  380 d  502  376 d  500  370 d  500  366 d  502  362 d  504  360 d
  508  358 d  518  356 d  524  356 d  534  358 d  538  360 d  540  362 d
  542  366 d  542  370 r  540  374 d  538  376 d  534  378 d  524  380 d
  518  380 d  508  378 d  504  376 d  502  374 d  500  370 d  500  406 r
  502  400 d  508  396 d  518  394 d  524  394 d  534  396 d  540  400 d
  542  406 d  542  410 d  540  416 d  534  420 d  524  422 d  518  422 d
  508  420 d  502  416 d  500  410 d  500  406 d  502  402 d  504  400 d
  508  398 d  518  396 d  524  396 d  534  398 d  538  400 d  540  402 d
  542  406 d  542  410 r  540  414 d  538  416 d  534  418 d  524  420 d
  518  420 d  508  418 d  504  416 d  502  414 d  500  410 d  506  458 r
  508  456 d  510  458 d  508  460 d  506  460 d  502  458 d  500  454 d
  500  448 d  502  442 d  506  438 d  510  436 d  518  434 d  530  434 d
  536  436 d  540  440 d  542  446 d  542  450 d  540  456 d  536  460 d
  530  462 d  528  462 d  522  460 d  518  456 d  516  450 d  516  448 d
  518  442 d  522  438 d  528  436 d  500  448 r  502  444 d  506  440 d
  510  438 d  518  436 d  530  436 d  536  438 d  540  442 d  542  446 d
  542  450 r  540  454 d  536  458 d  530  460 d  528  460 d  522  458 d
  518  454 d  516  450 d  346  340 r  348  338 d  350  340 d  348  342 d
  346  340 d  308  366 r  310  360 d  316  356 d  326  354 d  332  354 d
  342  356 d  348  360 d  350  366 d  350  370 d  348  376 d  342  380 d
  332  382 d  326  382 d  316  380 d  310  376 d  308  370 d  308  366 d
  310  362 d  312  360 d  316  358 d  326  356 d  332  356 d  342  358 d
  346  360 d  348  362 d  350  366 d  350  370 r  348  374 d  346  376 d
  342  378 d  332  380 d  326  380 d  316  378 d  312  376 d  310  374 d
  308  370 d  308  406 r  310  400 d  316  396 d  326  394 d  332  394 d
  342  396 d  348  400 d  350  406 d  350  410 d  348  416 d  342  420 d
  332  422 d  326  422 d  316  420 d  310  416 d  308  410 d  308  406 d
  310  402 d  312  400 d  316  398 d  326  396 d  332  396 d  342  398 d
  346  400 d  348  402 d  350  406 d  350  410 r  348  414 d  346  416 d
  342  418 d  332  420 d  326  420 d  316  418 d  312  416 d  310  414 d
  308  410 d  308  444 r  310  438 d  314  436 d  320  436 d  324  438 d
  326  444 d  326  452 d  324  458 d  320  460 d  314  460 d  310  458 d
  308  452 d  308  444 d  310  440 d  314  438 d  320  438 d  324  440 d
  326  444 d  326  452 r  324  456 d  320  458 d  314  458 d  310  456 d
  308  452 d  326  444 r  328  438 d  330  436 d  334  434 d  342  434 d
  346  436 d  348  438 d  350  444 d  350  452 d  348  458 d  346  460 d
  342  462 d  334  462 d  330  460 d  328  458 d  326  452 d  326  444 r
  328  440 d  330  438 d  334  436 d  342  436 d  346  438 d  348  440 d
  350  444 d  350  452 r  348  456 d  346  458 d  342  460 d  334  460 d
  330  458 d  328  456 d  326  452 d 2050 3100 r  150 3100 d 1964 3100 r
 1964 3068 d 1868 3100 r 1868 3036 d 1772 3100 r 1772 3068 d 1676 3100 r
 1676 3036 d 1580 3100 r 1580 3068 d 1484 3100 r 1484 3036 d 1388 3100 r
 1388 3068 d 1292 3100 r 1292 3036 d 1196 3100 r 1196 3068 d 1100 3100 r
 1100 3036 d 1004 3100 r 1004 3068 d  908 3100 r  908 3036 d  812 3100 r
  812 3068 d  716 3100 r  716 3036 d  620 3100 r  620 3068 d  524 3100 r
  524 3036 d  428 3100 r  428 3068 d  332 3100 r  332 3036 d  236 3100 r
  236 3068 d   1 lw 2228  640 r 2270  640 d 2228  642 r 2270  642 d 2240  654 r
 2256  654 d 2228  634 r 2228  666 d 2238  666 d 2228  664 d 2248  642 r
 2248  654 d 2270  634 r 2270  648 d 2228  680 r 2230  678 d 2232  680 d
 2230  682 d 2228  680 d 2242  680 r 2270  680 d 2242  682 r 2270  682 d
 2242  674 r 2242  682 d 2270  674 r 2270  688 d 2242  710 r 2244  706 d
 2246  704 d 2250  702 d 2254  702 d 2258  704 d 2260  706 d 2262  710 d
 2262  714 d 2260  718 d 2258  720 d 2254  722 d 2250  722 d 2246  720 d
 2244  718 d 2242  714 d 2242  710 d 2244  706 r 2248  704 d 2256  704 d
 2260  706 d 2260  718 r 2256  720 d 2248  720 d 2244  718 d 2246  720 r
 2244  722 d 2242  726 d 2244  726 d 2244  722 d 2258  704 r 2260  702 d
 2264  700 d 2266  700 d 2270  702 d 2272  708 d 2272  718 d 2274  724 d
 2276  726 d 2266  700 r 2268  702 d 2270  708 d 2270  718 d 2272  724 d
 2276  726 d 2278  726 d 2282  724 d 2284  718 d 2284  706 d 2282  700 d
 2278  698 d 2276  698 d 2272  700 d 2270  706 d 2266  740 r 2268  738 d
 2270  740 d 2268  742 d 2266  740 d 2236  792 r 2238  794 d 2240  792 d
 2238  790 d 2236  790 d 2232  792 d 2230  794 d 2228  800 d 2228  808 d
 2230  814 d 2232  816 d 2236  818 d 2240  818 d 2244  816 d 2248  810 d
 2252  800 d 2254  796 d 2258  792 d 2264  790 d 2270  790 d 2228  808 r
 2230  812 d 2232  814 d 2236  816 d 2240  816 d 2244  814 d 2248  808 d
 2252  800 d 2266  790 r 2264  792 d 2264  796 d 2268  806 d 2268  812 d
 2266  816 d 2264  818 d 2264  796 r 2270  806 d 2270  814 d 2268  816 d
 2264  818 d 2260  818 d 1294  970 r 1296  969 d 1298  966 d 1298  963 d
 1295  962 d 1292  962 d 1289  963 d 1287  966 d 1285  972 d 1285  983 d
 1289  980 d 1292  979 d 1301  976 d 1308  973 d 1310  972 d 1313  969 d
 1315  965 d 1315  961 d 1313  958 d 1310  958 d 1309  959 d 1309  961 d
 1310  962 d 1303  968 r 1302  969 d 1301  972 d 1301  979 d 1299  982 d
 1296  983 d 1305  980 d 1319  983 r 1318  986 d 1317  989 d 1315  991 d
 1314  992 d 1312  991 d 1311  989 d 1311  987 d 1312  984 d 1315  983 d
 1317  982 d 1320  982 d 1321  983 d 1322  984 d 1323  985 d 1323  987 d
 1322  989 d 1320  991 d 1311  987 r 1312  985 d 1315  984 d 1317  983 d
 1320  983 d 1322  984 d 1311 1000 r 1329  994 d 1311 1000 r 1329  995 d
 1315 1000 r 1319  999 d 1321  999 d 1323 1000 d 1323 1002 d 1322 1004 d
 1320 1005 d 1317 1007 d 1311 1009 r 1320 1006 d 1322 1006 d 1323 1008 d
 1322 1010 d 1320 1011 d 1311 1010 r 1320 1007 d 1322 1007 d 1323 1008 d
 1298 1017 r 1298 1042 d 1306 1017 r 1306 1042 d 1291 1055 r 1289 1058 d
 1285 1062 d 1315 1062 d 1287 1061 r 1315 1061 d 1315 1055 r 1315 1068 d
 1285 1087 r 1287 1083 d 1291 1080 d 1298 1079 d 1302 1079 d 1309 1080 d
 1313 1083 d 1315 1087 d 1315 1090 d 1313 1094 d 1309 1097 d 1302 1098 d
 1298 1098 d 1291 1097 d 1287 1094 d 1285 1090 d 1285 1087 d 1287 1084 d
 1288 1083 d 1291 1082 d 1298 1080 d 1302 1080 d 1309 1082 d 1312 1083 d
 1313 1084 d 1315 1087 d 1315 1090 r 1313 1093 d 1312 1094 d 1309 1096 d
 1302 1097 d 1298 1097 d 1291 1096 d 1288 1094 d 1287 1093 d 1285 1090 d
 1280 1105 r 1280 1120 d 1273 1126 r 1274 1127 d 1275 1126 d 1274 1125 d
 1273 1125 d 1271 1126 d 1270 1127 d 1270 1129 d 1270 1133 d 1270 1135 d
 1271 1136 d 1273 1137 d 1275 1137 d 1276 1136 d 1278 1134 d 1280 1129 d
 1280 1128 d 1282 1126 d 1285 1125 d 1287 1125 d 1270 1133 r 1270 1134 d
 1271 1135 d 1273 1136 d 1275 1136 d 1276 1135 d 1278 1133 d 1280 1129 d
 1285 1125 r 1285 1126 d 1285 1128 d 1286 1132 d 1286 1134 d 1285 1136 d
 1285 1137 d 1285 1128 r 1287 1132 d 1287 1135 d 1286 1136 d 1285 1137 d
 1283 1137 d 1428 2010 r 1430 2009 d 1432 2006 d 1432 2003 d 1429 2002 d
 1426 2002 d 1423 2003 d 1421 2006 d 1419 2012 d 1419 2023 d 1423 2020 d
 1426 2019 d 1435 2016 d 1442 2013 d 1444 2012 d 1447 2009 d 1449 2005 d
 1449 2001 d 1447 1998 d 1444 1998 d 1443 1999 d 1443 2001 d 1444 2002 d
 1437 2008 r 1436 2009 d 1435 2012 d 1435 2019 d 1433 2022 d 1430 2023 d
 1439 2020 d 1453 2023 r 1452 2026 d 1451 2029 d 1449 2031 d 1448 2032 d
 1446 2031 d 1445 2029 d 1445 2027 d 1446 2024 d 1449 2023 d 1451 2022 d
 1454 2022 d 1455 2023 d 1456 2024 d 1457 2025 d 1457 2027 d 1456 2029 d
 1454 2031 d 1445 2027 r 1446 2025 d 1449 2024 d 1451 2023 d 1454 2023 d
 1456 2024 d 1445 2040 r 1463 2034 d 1445 2040 r 1463 2035 d 1449 2040 r
 1453 2039 d 1455 2039 d 1457 2040 d 1457 2042 d 1456 2044 d 1454 2045 d
 1451 2047 d 1445 2049 r 1454 2046 d 1456 2046 d 1457 2048 d 1456 2050 d
 1454 2051 d 1445 2050 r 1454 2047 d 1456 2047 d 1457 2048 d 1432 2057 r
 1432 2082 d 1440 2057 r 1440 2082 d 1425 2095 r 1423 2098 d 1419 2102 d
 1449 2102 d 1421 2101 r 1449 2101 d 1449 2095 r 1449 2108 d 1419 2127 r
 1421 2123 d 1425 2120 d 1432 2119 d 1436 2119 d 1443 2120 d 1447 2123 d
 1449 2127 d 1449 2130 d 1447 2134 d 1443 2137 d 1436 2138 d 1432 2138 d
 1425 2137 d 1421 2134 d 1419 2130 d 1419 2127 d 1421 2124 d 1422 2123 d
 1425 2122 d 1432 2120 d 1436 2120 d 1443 2122 d 1446 2123 d 1447 2124 d
 1449 2127 d 1449 2130 r 1447 2133 d 1446 2134 d 1443 2136 d 1436 2137 d
 1432 2137 d 1425 2136 d 1422 2134 d 1421 2133 d 1419 2130 d 1414 2145 r
 1414 2160 d 1406 2166 r 1407 2167 d 1408 2166 d 1407 2165 d 1406 2165 d
 1404 2167 d 1404 2169 d 1404 2173 d 1404 2175 d 1406 2176 d 1409 2176 d
 1410 2175 d 1411 2173 d 1411 2170 d 1404 2173 r 1404 2174 d 1406 2175 d
 1409 2175 d 1410 2174 d 1411 2173 d 1412 2174 d 1414 2176 d 1415 2177 d
 1418 2177 d 1419 2176 d 1420 2175 d 1421 2173 d 1421 2169 d 1420 2167 d
 1419 2166 d 1418 2165 d 1417 2165 d 1416 2166 d 1417 2167 d 1418 2166 d
 1413 2175 r 1415 2176 d 1418 2176 d 1419 2175 d 1420 2174 d 1421 2173 d
  948  749 r  950  748 d  952  745 d  952  742 d  949  741 d  946  741 d
  943  742 d  941  745 d  939  751 d  939  762 d  943  759 d  946  758 d
  955  755 d  962  752 d  964  751 d  967  748 d  969  744 d  969  740 d
  967  737 d  964  737 d  963  738 d  963  740 d  964  741 d  957  747 r
  956  748 d  955  751 d  955  758 d  953  761 d  950  762 d  959  759 d
  973  762 r  972  765 d  971  768 d  969  770 d  968  771 d  966  770 d
  965  768 d  965  766 d  966  763 d  969  762 d  971  761 d  974  761 d
  975  762 d  976  763 d  977  764 d  977  766 d  976  768 d  974  770 d
  965  766 r  966  764 d  969  763 d  971  762 d  974  762 d  976  763 d
  965  779 r  983  773 d  965  779 r  983  774 d  969  779 r  973  778 d
  975  778 d  977  779 d  977  781 d  976  783 d  974  784 d  971  786 d
  965  788 r  974  785 d  976  785 d  977  787 d  976  789 d  974  790 d
  965  789 r  974  786 d  976  786 d  977  787 d  952  796 r  952  821 d
  960  796 r  960  821 d  945  834 r  943  837 d  939  841 d  969  841 d
  941  840 r  969  840 d  969  834 r  969  847 d  939  866 r  941  862 d
  945  859 d  952  858 d  956  858 d  963  859 d  967  862 d  969  866 d
  969  869 d  967  873 d  963  876 d  956  877 d  952  877 d  945  876 d
  941  873 d  939  869 d  939  866 d  941  863 d  942  862 d  945  861 d
  952  859 d  956  859 d  963  861 d  966  862 d  967  863 d  969  866 d
  969  869 r  967  872 d  966  873 d  963  875 d  956  876 d  952  876 d
  945  875 d  942  873 d  941  872 d  939  869 d  934  884 r  934  899 d
  927  905 r  928  906 d  929  905 d  928  904 d  927  904 d  925  905 d
  924  906 d  924  908 d  924  912 d  924  914 d  925  915 d  927  916 d
  929  916 d  930  915 d  932  913 d  934  908 d  934  907 d  936  905 d
  939  904 d  941  904 d  924  912 r  924  913 d  925  914 d  927  915 d
  929  915 d  930  914 d  932  912 d  934  908 d  939  904 r  939  905 d
  939  907 d  940  911 d  940  913 d  939  915 d  939  916 d  939  907 r
  941  911 d  941  914 d  940  915 d  939  916 d  937  916 d  516 1009 r
  518 1008 d  520 1005 d  520 1002 d  517 1001 d  514 1001 d  511 1002 d
  509 1005 d  507 1011 d  507 1022 d  511 1019 d  514 1018 d  523 1015 d
  530 1012 d  532 1011 d  535 1008 d  537 1004 d  537 1000 d  535  997 d
  532  997 d  531  998 d  531 1000 d  532 1001 d  525 1007 r  524 1008 d
  523 1011 d  523 1018 d  521 1021 d  518 1022 d  527 1019 d  541 1022 r
  540 1025 d  539 1028 d  537 1030 d  536 1031 d  534 1030 d  533 1028 d
  533 1026 d  534 1023 d  537 1022 d  539 1021 d  542 1021 d  543 1022 d
  544 1023 d  545 1024 d  545 1026 d  544 1028 d  542 1030 d  533 1026 r
  534 1024 d  537 1023 d  539 1022 d  542 1022 d  544 1023 d  533 1039 r
  551 1033 d  533 1039 r  551 1034 d  537 1039 r  541 1038 d  543 1038 d
  545 1039 d  545 1041 d  544 1043 d  542 1044 d  539 1046 d  533 1048 r
  542 1045 d  544 1045 d  545 1047 d  544 1049 d  542 1050 d  533 1049 r
  542 1046 d  544 1046 d  545 1047 d  520 1056 r  520 1081 d  528 1056 r
  528 1081 d  513 1094 r  511 1097 d  507 1101 d  537 1101 d  509 1100 r
  537 1100 d  537 1094 r  537 1107 d  507 1126 r  509 1122 d  513 1119 d
  520 1118 d  524 1118 d  531 1119 d  535 1122 d  537 1126 d  537 1129 d
  535 1133 d  531 1136 d  524 1137 d  520 1137 d  513 1136 d  509 1133 d
  507 1129 d  507 1126 d  509 1123 d  510 1122 d  513 1121 d  520 1119 d
  524 1119 d  531 1121 d  534 1122 d  535 1123 d  537 1126 d  537 1129 r
  535 1132 d  534 1133 d  531 1135 d  524 1136 d  520 1136 d  513 1135 d
  510 1133 d  509 1132 d  507 1129 d  502 1144 r  502 1159 d  494 1165 r
  495 1166 d  496 1165 d  495 1164 d  494 1164 d  492 1166 d  492 1168 d
  492 1172 d  492 1174 d  494 1175 d  497 1175 d  498 1174 d  499 1172 d
  499 1169 d  492 1172 r  492 1173 d  494 1174 d  497 1174 d  498 1173 d
  499 1172 d  500 1173 d  502 1175 d  503 1176 d  506 1176 d  507 1175 d
  508 1174 d  509 1172 d  509 1168 d  508 1166 d  507 1165 d  506 1164 d
  505 1164 d  504 1165 d  505 1166 d  506 1165 d  501 1174 r  503 1175 d
  506 1175 d  507 1174 d  508 1173 d  509 1172 d  276 1848 r  278 1847 d
  280 1844 d  280 1841 d  277 1840 d  274 1840 d  271 1841 d  269 1844 d
  267 1850 d  267 1861 d  271 1858 d  274 1857 d  283 1854 d  290 1851 d
  292 1850 d  295 1847 d  297 1843 d  297 1839 d  295 1836 d  292 1836 d
  291 1837 d  291 1839 d  292 1840 d  285 1846 r  284 1847 d  283 1850 d
  283 1857 d  281 1860 d  278 1861 d  287 1858 d  301 1861 r  300 1864 d
  299 1867 d  297 1869 d  296 1870 d  294 1869 d  293 1867 d  293 1865 d
  294 1862 d  297 1861 d  299 1860 d  302 1860 d  303 1861 d  304 1862 d
  305 1863 d  305 1865 d  304 1867 d  302 1869 d  293 1865 r  294 1863 d
  297 1862 d  299 1861 d  302 1861 d  304 1862 d  293 1878 r  311 1872 d
  293 1878 r  311 1873 d  297 1878 r  301 1877 d  303 1877 d  305 1878 d
  305 1880 d  304 1882 d  302 1883 d  299 1885 d  293 1887 r  302 1884 d
  304 1884 d  305 1886 d  304 1888 d  302 1889 d  293 1888 r  302 1885 d
  304 1885 d  305 1886 d  280 1895 r  280 1920 d  288 1895 r  288 1920 d
  273 1933 r  271 1936 d  267 1940 d  297 1940 d  269 1939 r  297 1939 d
  297 1933 r  297 1946 d  267 1965 r  269 1961 d  273 1958 d  280 1957 d
  284 1957 d  291 1958 d  295 1961 d  297 1965 d  297 1968 d  295 1972 d
  291 1975 d  284 1976 d  280 1976 d  273 1975 d  269 1972 d  267 1968 d
  267 1965 d  269 1962 d  270 1961 d  273 1960 d  280 1958 d  284 1958 d
  291 1960 d  294 1961 d  295 1962 d  297 1965 d  297 1968 r  295 1971 d
  294 1972 d  291 1974 d  284 1975 d  280 1975 d  273 1974 d  270 1972 d
  269 1971 d  267 1968 d  262 1983 r  262 1998 d  253 2011 r  269 2011 d
  252 2012 r  269 2012 d  252 2012 r  264 2002 d  264 2016 d  269 2008 r
  269 2014 d 1940  839 r 1944  833 d 1948  839 d 1934  845 r 1944  835 d
 1954  845 d 1944  835 r 1944  869 d 1920  909 r 1962  883 d 1920  911 r
 1962  885 d 1920  885 r 1930  883 d 1920  883 d 1920  911 d 1962  883 r
 1962  911 d 1952  911 d 1962  909 d 1962  919 r 1958  922 d 1957  924 d
 1958  927 d 1961  927 d 1966  925 d 1974  923 d 1957  924 r 1958  925 d
 1961  925 d 1966  924 d 1974  922 d 1966  925 r 1961  928 d 1958  930 d
 1957  933 d 1957  935 d 1958  937 d 1960  939 d 1963  939 d 1969  937 d
 1982  934 d 1957  935 r 1960  937 d 1963  937 d 1969  936 d 1982  933 d
 1920 1800 r 1962 1774 d 1920 1802 r 1962 1776 d 1920 1776 r 1930 1774 d
 1920 1774 d 1920 1802 d 1962 1774 r 1962 1802 d 1952 1802 d 1962 1800 d
 1957 1810 r 1957 1813 d 1958 1815 d 1960 1816 d 1980 1825 d 1982 1827 d
 1957 1813 r 1960 1815 d 1980 1824 d 1981 1825 d 1982 1827 d 1982 1830 d
 1957 1831 r 1960 1830 d 1964 1826 d 1975 1814 d 1980 1810 d 1982 1809 d
 1920 3002 r 1962 2976 d 1920 3004 r 1962 2978 d 1920 2978 r 1930 2976 d
 1920 2976 d 1920 3004 d 1962 2976 r 1962 3004 d 1952 3004 d 1962 3002 d
 1949 3029 r 1982 3022 d 1949 3030 r 1982 3021 d 1962 3012 r 1958 3015 d
 1957 3017 d 1958 3020 d 1961 3020 d 1967 3018 d 1969 3018 d 1972 3020 d
 1973 3022 d 1973 3026 d 1972 3028 d 1969 3032 d 1957 3017 r 1958 3018 d
 1961 3018 d 1967 3017 d 1969 3017 d 1972 3018 d 1973 3020 d 1974 3022 d
 1974 3024 d 1973 3028 d 1969 3032 d 1966 3034 d 1961 3036 d 1957 3038 d
 1940 3078 r 1944 3084 d 1948 3078 d 1934 3072 r 1944 3082 d 1954 3072 d
 1944 3048 r 1944 3082 d 1940  527 r 1944  521 d 1948  527 d 1934  533 r
 1944  523 d 1954  533 d 1944  523 r 1944  557 d 1920  597 r 1962  571 d
 1920  599 r 1962  573 d 1920  573 r 1930  571 d 1920  571 d 1920  599 d
 1962  571 r 1962  599 d 1952  599 d 1962  597 d 1949  624 r 1982  617 d
 1949  625 r 1982  616 d 1962  607 r 1958  610 d 1957  612 d 1958  615 d
 1961  615 d 1967  613 d 1969  613 d 1972  615 d 1973  617 d 1973  621 d
 1972  623 d 1969  627 d 1957  612 r 1958  613 d 1961  613 d 1967  612 d
 1969  612 d 1972  613 d 1973  615 d 1974  617 d 1974  619 d 1973  623 d
 1969  627 d 1966  629 d 1961  631 d 1957  633 d 2170 1737 r 2168 1739 d
 2174 1739 d 2170 1737 d 2168 1731 d 2168 1725 d 2170 1719 d 2172 1717 d
 2174 1717 d 2178 1719 d 2180 1723 d 2184 1733 d 2186 1737 d 2188 1739 d
 2174 1717 r 2176 1719 d 2178 1723 d 2182 1733 d 2184 1737 d 2188 1739 d
 2192 1739 d 2194 1737 d 2196 1731 d 2196 1725 d 2194 1719 d 2190 1717 d
 2196 1717 d 2194 1719 d 2154 1755 r 2156 1753 d 2158 1755 d 2156 1757 d
 2154 1755 d 2168 1755 r 2196 1755 d 2168 1757 r 2196 1757 d 2168 1749 r
 2168 1757 d 2196 1749 r 2196 1763 d 2168 1777 r 2196 1777 d 2168 1779 r
 2196 1779 d 2174 1779 r 2170 1783 d 2168 1789 d 2168 1793 d 2170 1799 d
 2174 1801 d 2196 1801 d 2168 1793 r 2170 1797 d 2174 1799 d 2196 1799 d
 2168 1771 r 2168 1779 d 2196 1771 r 2196 1785 d 2196 1793 r 2196 1807 d
 2154 1873 r 2156 1867 d 2160 1863 d 2168 1859 d 2174 1857 d 2182 1855 d
 2194 1853 d 2210 1851 d 2154 1873 r 2156 1869 d 2160 1865 d 2168 1861 d
 2174 1859 d 2182 1857 d 2194 1855 d 2210 1853 d 2154 1873 r 2154 1877 d
 2156 1881 d 2158 1883 d 2164 1883 d 2168 1881 d 2170 1879 d 2172 1873 d
 2172 1867 d 2154 1877 r 2158 1881 d 2164 1881 d 2168 1879 d 2170 1877 d
 2172 1873 d 2172 1867 r 2174 1873 d 2176 1877 d 2178 1879 d 2182 1881 d
 2188 1881 d 2192 1879 d 2194 1877 d 2196 1871 d 2196 1865 d 2194 1861 d
 2192 1859 d 2186 1857 d 2174 1873 r 2178 1877 d 2182 1879 d 2188 1879 d
 2192 1877 d 2194 1875 d 2196 1871 d 1094  236 r 1106  292 d 1092  236 r
 1108  292 d 1102  250 r 1110  252 d 1114  256 d 1116  262 d 1116  268 d
 1114  272 d 1110  276 d 1104  278 d 1098  278 d 1090  276 d 1086  272 d
 1084  266 d 1084  260 d 1086  256 d 1090  252 d 1096  250 d 1102  250 d
 1108  252 d 1112  256 d 1114  262 d 1114  268 d 1112  272 d 1108  276 d
 1104  278 d 1098  278 r 1092  276 d 1088  272 d 1086  266 d 1086  260 d
 1088  256 d 1092  252 d 1096  250 d   6 lw 1580 2320 r 1580 2515 d   1 lw
 1561 2614 r 1594 2614 d 1561 2616 r 1590 2625 d 1561 2614 r 1594 2625 d
 1561 2636 r 1594 2625 d 1561 2636 r 1594 2636 d 1561 2638 r 1594 2638 d
 1561 2609 r 1561 2616 d 1561 2636 r 1561 2643 d 1594 2609 r 1594 2619 d
 1594 2632 r 1594 2643 d 1584 2661 r 1604 2649 d 1584 2662 r 1604 2650 d
 1584 2650 r 1589 2649 d 1584 2649 d 1584 2662 d 1604 2649 r 1604 2662 d
 1599 2662 d 1604 2661 d 1586 2670 r 1585 2669 d 1584 2670 d 1585 2671 d
 1587 2671 d 1589 2670 d 1590 2669 d 1575 2680 r 1575 2708 d 1585 2680 r
 1585 2708 d 1582 2748 r 1585 2747 d 1586 2744 d 1586 2740 d 1585 2737 d
 1583 2736 d 1577 2731 d 1575 2729 d 1574 2726 d 1574 2723 d 1575 2720 d
 1578 2718 d 1582 2718 d 1585 2720 d 1586 2723 d 1586 2726 d 1585 2729 d
 1583 2731 d 1577 2736 d 1575 2737 d 1574 2740 d 1574 2744 d 1575 2747 d
 1578 2748 d 1582 2748 d   4 lw lt3 1657 2320 r 1657 2515 d   1 lw lt0
 1638 2614 r 1671 2614 d 1638 2616 r 1667 2625 d 1638 2614 r 1671 2625 d
 1638 2636 r 1671 2625 d 1638 2636 r 1671 2636 d 1638 2638 r 1671 2638 d
 1638 2609 r 1638 2616 d 1638 2636 r 1638 2643 d 1671 2609 r 1671 2619 d
 1671 2632 r 1671 2643 d 1661 2661 r 1681 2649 d 1661 2662 r 1681 2650 d
 1661 2650 r 1666 2649 d 1661 2649 d 1661 2662 d 1681 2649 r 1681 2662 d
 1676 2662 d 1681 2661 d 1663 2670 r 1662 2669 d 1661 2670 d 1662 2671 d
 1664 2671 d 1666 2670 d 1667 2669 d 1652 2680 r 1652 2708 d 1662 2680 r
 1662 2708 d 1659 2748 r 1662 2747 d 1663 2744 d 1663 2740 d 1662 2737 d
 1660 2736 d 1654 2731 d 1652 2729 d 1651 2726 d 1651 2723 d 1652 2720 d
 1655 2718 d 1659 2718 d 1662 2720 d 1663 2723 d 1663 2726 d 1662 2729 d
 1660 2731 d 1654 2736 d 1652 2737 d 1651 2740 d 1651 2744 d 1652 2747 d
 1655 2748 d 1659 2748 d   2 lw lt1 1791 2320 r 1791 2515 d   1 lw lt0
 1783 2638 r 1783 2620 d 1785 2616 d 1789 2612 d 1794 2611 d 1799 2611 d
 1802 2612 d 1804 2614 d 1805 2617 d 1805 2620 d 1804 2625 d 1799 2628 d
 1794 2630 d 1789 2630 d 1786 2628 d 1785 2627 d 1783 2624 d 1783 2620 r
 1785 2617 d 1789 2614 d 1794 2612 d 1801 2612 d 1804 2614 d 1805 2620 r
 1804 2624 d 1799 2627 d 1794 2628 d 1788 2628 d 1785 2627 d 1785 2638 d
 1786 2646 r 1786 2675 d 1796 2646 r 1796 2675 d 1778 2689 r 1777 2692 d
 1772 2697 d 1805 2697 d 1773 2696 r 1805 2696 d 1805 2689 r 1805 2704 d
   2 lw lt5 1868 2320 r 1868 2515 d   1 lw lt0 1860 2638 r 1860 2620 d
 1862 2616 d 1866 2612 d 1871 2611 d 1876 2611 d 1879 2612 d 1881 2614 d
 1882 2617 d 1882 2620 d 1881 2625 d 1876 2628 d 1871 2630 d 1866 2630 d
 1863 2628 d 1862 2627 d 1860 2624 d 1860 2620 r 1862 2617 d 1866 2614 d
 1871 2612 d 1878 2612 d 1881 2614 d 1882 2620 r 1881 2624 d 1876 2627 d
 1871 2628 d 1865 2628 d 1862 2627 d 1862 2638 d 1863 2646 r 1863 2675 d
 1873 2646 r 1873 2675 d 1870 2715 r 1873 2713 d 1874 2710 d 1874 2707 d
 1873 2704 d 1871 2702 d 1865 2697 d 1863 2696 d 1862 2692 d 1862 2689 d
 1863 2686 d 1866 2684 d 1870 2684 d 1873 2686 d 1874 2689 d 1874 2692 d
 1873 2696 d 1871 2697 d 1865 2702 d 1863 2704 d 1862 2707 d 1862 2710 d
 1863 2713 d 1866 2715 d 1870 2715 d   6 lw 1045  500 r 1032  513 d 1024  526 d
 1016  539 d 1008  552 d  999  565 d  990  578 d  979  591 d  967  604 d
  953  617 d  937  630 d  918  643 d  894  656 d  865  669 d  827  682 d
  777  695 d  707  708 d  601  721 d  425  734 d  150  744 d  150  802 r
  408  812 d  573  825 d  673  838 d  740  851 d  788  864 d  824  877 d
  853  890 d  875  903 d  894  916 d  910  929 d  923  942 d  934  955 d
  944  968 d  953  981 d  960  994 d  967 1007 d  973 1020 d  979 1033 d
  983 1046 d  988 1059 d  992 1072 d  996 1085 d  999 1098 d 1003 1111 d
 1006 1124 d 1008 1137 d 1011 1150 d 1013 1163 d 1016 1176 d 1018 1189 d
 1020 1202 d 1022 1215 d 1024 1228 d 1025 1241 d 1027 1254 d 1028 1267 d
 1030 1280 d 1031 1293 d 1032 1306 d 1034 1319 d 1035 1332 d 1036 1345 d
 1037 1358 d 1038 1371 d 1039 1384 d 1040 1397 d 1041 1410 d 1042 1423 d
 1043 1436 d 1043 1449 d 1044 1462 d 1045 1475 d 1046 1488 d 1046 1501 d
 1047 1514 d 1048 1527 d 1048 1540 d 1049 1553 d 1050 1566 d 1050 1579 d
 1051 1592 d 1051 1605 d 1052 1618 d 1052 1631 d 1053 1644 d 1053 1657 d
 1054 1670 d 1054 1683 d 1054 1696 d 1055 1709 d 1055 1722 d 1056 1735 d
 1056 1748 d 1056 1761 d 1057 1774 d 1057 1787 d 1057 1800 d 1058 1813 d
 1058 1826 d 1058 1839 d 1059 1852 d 1059 1865 d 1059 1878 d 1060 1891 d
 1060 1904 d 1060 1917 d 1060 1930 d 1061 1943 d 1061 1956 d 1061 1969 d
 1061 1982 d 1061 1995 d 1062 2008 d 1062 2021 d 1062 2034 d 1062 2047 d
 1062 2060 d 1063 2073 d 1063 2086 d 1063 2099 d 1063 2112 d 1063 2125 d
 1063 2138 d 1064 2151 d 1064 2164 d 1064 2177 d 1064 2190 d 1064 2203 d
 1064 2216 d 1064 2229 d 1065 2242 d 1065 2255 d 1065 2268 d 1065 2281 d
 1065 2294 d 1065 2307 d 1065 2320 d 1065 2333 d 1065 2346 d 1066 2359 d
 1066 2372 d 1066 2385 d 1066 2398 d 1066 2411 d 1066 2424 d 1066 2437 d
 1066 2450 d 1066 2463 d 1066 2476 d 1066 2489 d 1066 2502 d 1066 2515 d
 1066 2528 d 1066 2541 d 1066 2554 d 1066 2567 d 1066 2580 d 1066 2593 d
 1066 2606 d 1066 2619 d 1066 2632 d 1066 2645 d 1066 2658 d 1066 2671 d
 1066 2684 d 1066 2697 d 1066 2710 d 1066 2723 d 1066 2736 d 1066 2749 d
 1066 2762 d 1066 2775 d 1066 2788 d 1065 2801 d 1065 2814 d 1065 2827 d
 1065 2840 d 1065 2853 d 1065 2866 d 1064 2879 d 1064 2892 d 1064 2905 d
 1064 2918 d 1063 2931 d 1063 2944 d 1063 2957 d 1062 2970 d 1062 2983 d
 1061 2996 d 1061 3009 d 1060 3022 d 1059 3035 d 1058 3048 d 1057 3061 d
 1055 3074 d 1053 3087 d 1045 3100 d 1155  500 r 1168  513 d 1176  526 d
 1184  539 d 1192  552 d 1201  565 d 1210  578 d 1221  591 d 1233  604 d
 1247  617 d 1263  630 d 1283  643 d 1307  656 d 1336  669 d 1374  682 d
 1425  695 d 1496  708 d 1603  721 d 1782  734 d 2050  744 d 2050  802 r
 1800  812 d 1632  825 d 1530  838 d 1462  851 d 1414  864 d 1377  877 d
 1348  890 d 1326  903 d 1307  916 d 1291  929 d 1278  942 d 1266  955 d
 1257  968 d 1248  981 d 1240  994 d 1233 1007 d 1227 1020 d 1222 1033 d
 1217 1046 d 1212 1059 d 1208 1072 d 1204 1085 d 1201 1098 d 1197 1111 d
 1195 1124 d 1192 1137 d 1189 1150 d 1187 1163 d 1184 1176 d 1182 1189 d
 1180 1202 d 1178 1215 d 1177 1228 d 1175 1241 d 1173 1254 d 1172 1267 d
 1170 1280 d 1169 1293 d 1168 1306 d 1166 1319 d 1165 1332 d 1164 1345 d
 1163 1358 d 1162 1371 d 1161 1384 d 1160 1397 d 1159 1410 d 1158 1423 d
 1157 1436 d 1157 1449 d 1156 1462 d 1155 1475 d 1154 1488 d 1154 1501 d
 1153 1514 d 1152 1527 d 1152 1540 d 1151 1553 d 1150 1566 d 1150 1579 d
 1149 1592 d 1149 1605 d 1148 1618 d 1148 1631 d 1147 1644 d 1147 1657 d
 1146 1670 d 1146 1683 d 1146 1696 d 1145 1709 d 1145 1722 d 1144 1735 d
 1144 1748 d 1144 1761 d 1143 1774 d 1143 1787 d 1143 1800 d 1142 1813 d
 1142 1826 d 1142 1839 d 1141 1852 d 1141 1865 d 1141 1878 d 1140 1891 d
 1140 1904 d 1140 1917 d 1140 1930 d 1140 1943 d 1139 1956 d 1139 1969 d
 1139 1982 d 1139 1995 d 1138 2008 d 1138 2021 d 1138 2034 d 1138 2047 d
 1138 2060 d 1137 2073 d 1137 2086 d 1137 2099 d 1137 2112 d 1137 2125 d
 1137 2138 d 1136 2151 d 1136 2164 d 1136 2177 d 1136 2190 d 1136 2203 d
 1136 2216 d 1136 2229 d 1135 2242 d 1135 2255 d 1135 2268 d 1135 2281 d
 1135 2294 d 1135 2307 d 1135 2320 d 1135 2333 d 1135 2346 d 1134 2359 d
 1134 2372 d 1134 2385 d 1134 2398 d 1134 2411 d 1134 2424 d 1134 2437 d
 1134 2450 d 1134 2463 d 1134 2476 d 1134 2489 d 1134 2502 d 1134 2515 d
 1134 2528 d 1134 2541 d 1134 2554 d 1134 2567 d 1134 2580 d 1134 2593 d
 1134 2606 d 1134 2619 d 1134 2632 d 1134 2645 d 1134 2658 d 1134 2671 d
 1134 2684 d 1134 2697 d 1134 2710 d 1134 2723 d 1134 2736 d 1134 2749 d
 1134 2762 d 1134 2775 d 1134 2788 d 1135 2801 d 1135 2814 d 1135 2827 d
 1135 2840 d 1135 2853 d 1135 2866 d 1136 2879 d 1136 2892 d 1136 2905 d
 1136 2918 d 1137 2931 d 1137 2944 d 1137 2957 d 1138 2970 d 1138 2983 d
 1139 2996 d 1139 3009 d 1140 3022 d 1141 3035 d 1142 3048 d 1143 3061 d
 1144 3074 d 1147 3087 d 1155 3100 d   4 lw lt3  551  500 r  422  513 d
  343  526 d  266  539 d  187  552 d  150  558 d  150 1118 r  163 1124 d
  190 1137 d  216 1150 d  240 1163 d  262 1176 d  283 1189 d  303 1202 d
  322 1215 d  340 1228 d  356 1241 d  372 1254 d  387 1267 d  401 1280 d
  415 1293 d  428 1306 d  440 1319 d  452 1332 d  463 1345 d  473 1358 d
  484 1371 d  493 1384 d  503 1397 d  512 1410 d  520 1423 d  529 1436 d
  537 1449 d  544 1462 d  552 1475 d  559 1488 d  566 1501 d  573 1514 d
  579 1527 d  585 1540 d  591 1553 d  597 1566 d  602 1579 d  608 1592 d
  613 1605 d  618 1618 d  623 1631 d  628 1644 d  632 1657 d  637 1670 d
  641 1683 d  645 1696 d  649 1709 d  653 1722 d  657 1735 d  661 1748 d
  665 1761 d  668 1774 d  672 1787 d  675 1800 d  678 1813 d  681 1826 d
  684 1839 d  687 1852 d  690 1865 d  693 1878 d  696 1891 d  698 1904 d
  701 1917 d  703 1930 d  706 1943 d  708 1956 d  710 1969 d  713 1982 d
  715 1995 d  717 2008 d  719 2021 d  721 2034 d  723 2047 d  725 2060 d
  727 2073 d  729 2086 d  730 2099 d  732 2112 d  734 2125 d  735 2138 d
  737 2151 d  738 2164 d  740 2177 d  741 2190 d  743 2203 d  744 2216 d
  745 2229 d  746 2242 d  748 2255 d  749 2268 d  750 2281 d  751 2294 d
  752 2307 d  753 2320 d  754 2333 d  755 2346 d  756 2359 d  756 2372 d
  757 2385 d  758 2398 d  758 2411 d  759 2424 d  760 2437 d  760 2450 d
  761 2463 d  761 2476 d  762 2489 d  762 2502 d  762 2515 d  763 2528 d
  763 2541 d  763 2554 d  763 2567 d  763 2580 d  763 2593 d  763 2606 d
  763 2619 d  763 2632 d  763 2645 d  763 2658 d  762 2671 d  762 2684 d
  761 2697 d  761 2710 d  760 2723 d  759 2736 d  759 2749 d  758 2762 d
  757 2775 d  756 2788 d  755 2801 d  753 2814 d  752 2827 d  750 2840 d
  749 2853 d  747 2866 d  745 2879 d  743 2892 d  740 2905 d  737 2918 d
  734 2931 d  731 2944 d  728 2957 d  723 2970 d  719 2983 d  714 2996 d
  708 3009 d  701 3022 d  693 3035 d  683 3048 d  671 3061 d  654 3074 d
  630 3087 d  548 3100 d 1652  500 r 1784  513 d 1865  526 d 1943  539 d
 2025  552 d 2050  556 d 2050 1125 r 2023 1137 d 1997 1150 d 1972 1163 d
 1949 1176 d 1927 1189 d 1907 1202 d 1888 1215 d 1869 1228 d 1852 1241 d
 1836 1254 d 1821 1267 d 1806 1280 d 1792 1293 d 1779 1306 d 1767 1319 d
 1755 1332 d 1743 1345 d 1732 1358 d 1722 1371 d 1712 1384 d 1702 1397 d
 1693 1410 d 1684 1423 d 1676 1436 d 1668 1449 d 1660 1462 d 1652 1475 d
 1645 1488 d 1638 1501 d 1631 1514 d 1625 1527 d 1618 1540 d 1612 1553 d
 1607 1566 d 1601 1579 d 1595 1592 d 1590 1605 d 1585 1618 d 1580 1631 d
 1575 1644 d 1570 1657 d 1566 1670 d 1561 1683 d 1557 1696 d 1553 1709 d
 1549 1722 d 1545 1735 d 1541 1748 d 1538 1761 d 1534 1774 d 1531 1787 d
 1527 1800 d 1524 1813 d 1521 1826 d 1518 1839 d 1515 1852 d 1512 1865 d
 1509 1878 d 1506 1891 d 1503 1904 d 1501 1917 d 1498 1930 d 1496 1943 d
 1493 1956 d 1491 1969 d 1489 1982 d 1486 1995 d 1484 2008 d 1482 2021 d
 1480 2034 d 1478 2047 d 1476 2060 d 1474 2073 d 1473 2086 d 1471 2099 d
 1469 2112 d 1467 2125 d 1466 2138 d 1464 2151 d 1463 2164 d 1461 2177 d
 1460 2190 d 1458 2203 d 1457 2216 d 1456 2229 d 1454 2242 d 1453 2255 d
 1452 2268 d 1451 2281 d 1450 2294 d 1449 2307 d 1448 2320 d 1447 2333 d
 1446 2346 d 1445 2359 d 1444 2372 d 1444 2385 d 1443 2398 d 1442 2411 d
 1441 2424 d 1441 2437 d 1440 2450 d 1440 2463 d 1439 2476 d 1439 2489 d
 1438 2502 d 1438 2515 d 1438 2528 d 1438 2541 d 1437 2554 d 1437 2567 d
 1437 2580 d 1437 2593 d 1437 2606 d 1437 2619 d 1437 2632 d 1437 2645 d
 1438 2658 d 1438 2671 d 1438 2684 d 1439 2697 d 1439 2710 d 1440 2723 d
 1440 2736 d 1441 2749 d 1442 2762 d 1443 2775 d 1444 2788 d 1445 2801 d
 1446 2814 d 1448 2827 d 1449 2840 d 1451 2853 d 1453 2866 d 1455 2879 d
 1457 2892 d 1459 2905 d 1462 2918 d 1465 2931 d 1468 2944 d 1472 2957 d
 1476 2970 d 1480 2983 d 1485 2996 d 1491 3009 d 1498 3022 d 1506 3035 d
 1516 3048 d 1528 3061 d 1544 3074 d 1568 3087 d 1649 3100 d   2 lw lt1
 1100  500 r 1096  513 d 1093  526 d 1090  539 d 1088  552 d 1085  565 d
 1083  578 d 1080  591 d 1077  604 d 1073  617 d 1069  630 d 1065  643 d
 1060  656 d 1053  669 d 1045  682 d 1034  695 d 1018  708 d  995  721 d
  955  734 d  880  747 d  639  760 d  150  761 d  150  785 r  677  786 d
  880  799 d  950  812 d  986  825 d 1007  838 d 1022  851 d 1032  864 d
 1040  877 d 1046  890 d 1051  903 d 1055  916 d 1059  929 d 1062  942 d
 1064  955 d 1066  968 d 1068  981 d 1070  994 d 1071 1007 d 1073 1020 d
 1074 1033 d 1075 1046 d 1076 1059 d 1077 1072 d 1078 1085 d 1079 1098 d
 1079 1111 d 1080 1124 d 1081 1137 d 1081 1150 d 1082 1163 d 1082 1176 d
 1083 1189 d 1083 1202 d 1084 1215 d 1084 1228 d 1084 1241 d 1085 1254 d
 1085 1267 d 1085 1280 d 1086 1293 d 1086 1306 d 1086 1319 d 1087 1332 d
 1087 1345 d 1087 1358 d 1087 1371 d 1088 1384 d 1088 1397 d 1088 1410 d
 1088 1423 d 1088 1436 d 1088 1449 d 1089 1462 d 1089 1475 d 1089 1488 d
 1089 1501 d 1089 1514 d 1090 1527 d 1090 1540 d 1090 1553 d 1090 1566 d
 1090 1579 d 1090 1592 d 1090 1605 d 1090 1618 d 1090 1631 d 1091 1644 d
 1091 1657 d 1091 1670 d 1091 1683 d 1091 1696 d 1091 1709 d 1091 1722 d
 1091 1735 d 1091 1748 d 1092 1761 d 1092 1774 d 1092 1787 d 1092 1800 d
 1092 1813 d 1092 1826 d 1092 1839 d 1092 1852 d 1092 1865 d 1092 1878 d
 1092 1891 d 1092 1904 d 1092 1917 d 1093 1930 d 1093 1943 d 1093 1956 d
 1093 1969 d 1093 1982 d 1093 1995 d 1093 2008 d 1093 2021 d 1093 2034 d
 1093 2047 d 1093 2060 d 1093 2073 d 1093 2086 d 1093 2099 d 1093 2112 d
 1093 2125 d 1093 2138 d 1093 2151 d 1093 2164 d 1094 2177 d 1094 2190 d
 1094 2203 d 1094 2216 d 1094 2229 d 1094 2242 d 1094 2255 d 1094 2268 d
 1094 2281 d 1094 2294 d 1094 2307 d 1094 2320 d 1094 2333 d 1094 2346 d
 1094 2359 d 1094 2372 d 1094 2385 d 1094 2398 d 1094 2411 d 1094 2424 d
 1094 2437 d 1094 2450 d 1094 2463 d 1094 2476 d 1094 2489 d 1094 2502 d
 1094 2515 d 1095 2528 d 1095 2541 d 1095 2554 d 1095 2567 d 1095 2580 d
 1095 2593 d 1095 2606 d 1095 2619 d 1095 2632 d 1095 2645 d 1095 2658 d
 1095 2671 d 1095 2684 d 1095 2697 d 1095 2710 d 1095 2723 d 1095 2736 d
 1095 2749 d 1095 2762 d 1095 2775 d 1095 2788 d 1095 2801 d 1095 2814 d
 1095 2827 d 1095 2840 d 1095 2853 d 1095 2866 d 1095 2879 d 1095 2892 d
 1095 2905 d 1095 2918 d 1095 2931 d 1096 2944 d 1096 2957 d 1096 2970 d
 1096 2983 d 1096 2996 d 1096 3009 d 1096 3022 d 1096 3035 d 1096 3048 d
 1097 3061 d 1097 3074 d 1098 3087 d 1100 3100 d lt5 1079  500 r 1071  513 d
 1066  526 d 1062  539 d 1058  552 d 1054  565 d 1049  578 d 1044  591 d
 1038  604 d 1032  617 d 1025  630 d 1017  643 d 1006  656 d  993  669 d
  977  682 d  955  695 d  925  708 d  879  721 d  803  734 d  648  747 d
  166  760 d  150  760 d  150  786 r  263  786 d  669  799 d  809  812 d
  881  825 d  924  838 d  953  851 d  974  864 d  989  877 d 1002  890 d
 1011  903 d 1019  916 d 1026  929 d 1032  942 d 1037  955 d 1041  968 d
 1045  981 d 1048  994 d 1051 1007 d 1054 1020 d 1056 1033 d 1058 1046 d
 1060 1059 d 1062 1072 d 1064 1085 d 1065 1098 d 1067 1111 d 1068 1124 d
 1069 1137 d 1070 1150 d 1071 1163 d 1073 1176 d 1074 1189 d 1074 1202 d
 1075 1215 d 1076 1228 d 1077 1241 d 1077 1254 d 1078 1267 d 1079 1280 d
 1079 1293 d 1080 1306 d 1081 1319 d 1081 1332 d 1082 1345 d 1082 1358 d
 1083 1371 d 1083 1384 d 1083 1397 d 1084 1410 d 1084 1423 d 1085 1436 d
 1085 1449 d 1085 1462 d 1086 1475 d 1086 1488 d 1086 1501 d 1087 1514 d
 1087 1527 d 1087 1540 d 1088 1553 d 1088 1566 d 1088 1579 d 1088 1592 d
 1089 1605 d 1089 1618 d 1089 1631 d 1089 1644 d 1090 1657 d 1090 1670 d
 1090 1683 d 1090 1696 d 1090 1709 d 1091 1722 d 1091 1735 d 1091 1748 d
 1091 1761 d 1091 1774 d 1092 1787 d 1092 1800 d 1092 1813 d 1092 1826 d
 1092 1839 d 1093 1852 d 1093 1865 d 1093 1878 d 1093 1891 d 1093 1904 d
 1093 1917 d 1093 1930 d 1094 1943 d 1094 1956 d 1094 1969 d 1094 1982 d
 1094 1995 d 1094 2008 d 1094 2021 d 1095 2034 d 1095 2047 d 1095 2060 d
 1095 2073 d 1095 2086 d 1095 2099 d 1095 2112 d 1095 2125 d 1096 2138 d
 1096 2151 d 1096 2164 d 1096 2177 d 1096 2190 d 1096 2203 d 1096 2216 d
 1096 2229 d 1097 2242 d 1097 2255 d 1097 2268 d 1097 2281 d 1097 2294 d
 1097 2307 d 1097 2320 d 1097 2333 d 1098 2346 d 1098 2359 d 1098 2372 d
 1098 2385 d 1098 2398 d 1098 2411 d 1098 2424 d 1098 2437 d 1098 2450 d
 1099 2463 d 1099 2476 d 1099 2489 d 1099 2502 d 1099 2515 d 1099 2528 d
 1099 2541 d 1100 2554 d 1100 2567 d 1100 2580 d 1100 2593 d 1100 2606 d
 1100 2619 d 1100 2632 d 1101 2645 d 1101 2658 d 1101 2671 d 1101 2684 d
 1101 2697 d 1101 2710 d 1102 2723 d 1102 2736 d 1102 2749 d 1102 2762 d
 1102 2775 d 1102 2788 d 1103 2801 d 1103 2814 d 1103 2827 d 1103 2840 d
 1104 2853 d 1104 2866 d 1104 2879 d 1105 2892 d 1105 2905 d 1105 2918 d
 1106 2931 d 1106 2944 d 1106 2957 d 1107 2970 d 1107 2983 d 1108 2996 d
 1108 3009 d 1109 3022 d 1110 3035 d 1111 3048 d 1112 3061 d 1113 3074 d
 1115 3087 d 1121 3100 d lt1 1100  500 r 1056  513 d 1028  526 d 1001  539 d
  978  552 d  952  565 d  926  578 d  897  591 d  856  604 d  821  617 d
  793  630 d  748  643 d  694  656 d  628  669 d  544  682 d  398  695 d
  281  708 d  150  715 d  150  836 r  176  838 d  321  851 d  425  864 d
  503  877 d  565  890 d  613  903 d  654  916 d  688  929 d  717  942 d
  742  955 d  763  968 d  782  981 d  799  994 d  814 1007 d  827 1020 d
  839 1033 d  850 1046 d  860 1059 d  870 1072 d  878 1085 d  883 1098 d
  893 1111 d  900 1124 d  906 1137 d  912 1150 d  917 1163 d  922 1176 d
  927 1189 d  932 1202 d  936 1215 d  940 1228 d  942 1241 d  946 1254 d
  951 1267 d  954 1280 d  957 1293 d  960 1306 d  963 1319 d  966 1332 d
  968 1345 d  971 1358 d  973 1371 d  974 1384 d  976 1397 d  979 1410 d
  981 1423 d  983 1436 d  985 1449 d  987 1462 d  989 1475 d  991 1488 d
  992 1501 d  994 1514 d  995 1527 d  997 1540 d  998 1553 d  999 1566 d
 1001 1579 d 1001 1592 d 1003 1605 d 1004 1618 d 1006 1631 d 1007 1644 d
 1008 1657 d 1009 1670 d 1010 1683 d 1011 1696 d 1012 1709 d 1013 1722 d
 1014 1735 d 1015 1748 d 1016 1761 d 1016 1774 d 1017 1787 d 1018 1800 d
 1019 1813 d 1020 1826 d 1020 1839 d 1021 1852 d 1022 1865 d 1023 1878 d
 1023 1891 d 1024 1904 d 1025 1917 d 1025 1930 d 1026 1943 d 1026 1956 d
 1027 1969 d 1028 1982 d 1028 1995 d 1029 2008 d 1029 2021 d 1030 2034 d
 1031 2047 d 1031 2060 d 1032 2073 d 1032 2086 d 1033 2099 d 1033 2112 d
 1033 2125 d 1034 2138 d 1034 2151 d 1035 2164 d 1035 2177 d 1036 2190 d
 1036 2203 d 1037 2216 d 1037 2229 d 1037 2242 d 1038 2255 d 1038 2268 d
 1039 2281 d 1039 2294 d 1039 2307 d 1040 2320 d 1040 2333 d 1040 2346 d
 1041 2359 d 1041 2372 d 1041 2385 d 1042 2398 d 1042 2411 d 1042 2424 d
 1043 2437 d 1043 2450 d 1043 2463 d 1044 2476 d 1044 2489 d 1044 2502 d
 1045 2515 d 1045 2528 d 1045 2541 d 1045 2554 d 1046 2567 d 1046 2580 d
 1046 2593 d 1047 2606 d 1047 2619 d 1047 2632 d 1048 2645 d 1048 2658 d
 1048 2671 d 1048 2684 d 1049 2697 d 1049 2710 d 1049 2723 d 1050 2736 d
 1050 2749 d 1050 2762 d 1050 2775 d 1051 2788 d 1051 2801 d 1051 2814 d
 1052 2827 d 1052 2840 d 1052 2853 d 1053 2866 d 1053 2879 d 1054 2892 d
 1054 2905 d 1054 2918 d 1055 2931 d 1056 2944 d 1056 2957 d 1057 2970 d
 1058 2983 d 1059 2996 d 1060 3009 d 1061 3022 d 1062 3035 d 1064 3048 d
 1067 3061 d 1071 3074 d 1076 3087 d 1100 3100 d lt5  887  500 r  805  513 d
  760  526 d  719  539 d  678  552 d  635  565 d  583  578 d  540  591 d
  485  604 d  411  617 d  349  630 d  263  643 d  159  656 d  150  657 d
  150  894 r  216  903 d  296  916 d  363  929 d  420  942 d  469  955 d
  512  968 d  550  981 d  576  994 d  612 1007 d  639 1020 d  663 1033 d
  684 1046 d  699 1059 d  722 1072 d  739 1085 d  754 1098 d  768 1111 d
  781 1124 d  794 1137 d  805 1150 d  813 1163 d  823 1176 d  835 1189 d
  844 1202 d  850 1215 d  860 1228 d  868 1241 d  875 1254 d  882 1267 d
  888 1280 d  894 1293 d  900 1306 d  906 1319 d  911 1332 d  915 1345 d
  920 1358 d  926 1371 d  930 1384 d  933 1397 d  938 1410 d  943 1423 d
  946 1436 d  950 1449 d  954 1462 d  957 1475 d  961 1488 d  964 1501 d
  967 1514 d  970 1527 d  973 1540 d  976 1553 d  979 1566 d  981 1579 d
  984 1592 d  987 1605 d  989 1618 d  991 1631 d  994 1644 d  996 1657 d
  998 1670 d 1000 1683 d 1003 1696 d 1005 1709 d 1007 1722 d 1009 1735 d
 1011 1748 d 1013 1761 d 1014 1774 d 1016 1787 d 1018 1800 d 1020 1813 d
 1022 1826 d 1023 1839 d 1025 1852 d 1026 1865 d 1028 1878 d 1030 1891 d
 1031 1904 d 1033 1917 d 1034 1930 d 1036 1943 d 1037 1956 d 1039 1969 d
 1040 1982 d 1042 1995 d 1043 2008 d 1044 2021 d 1046 2034 d 1047 2047 d
 1048 2060 d 1050 2073 d 1051 2086 d 1052 2099 d 1053 2112 d 1055 2125 d
 1056 2138 d 1057 2151 d 1058 2164 d 1060 2177 d 1061 2190 d 1062 2203 d
 1063 2216 d 1065 2229 d 1066 2242 d 1067 2255 d 1068 2268 d 1069 2281 d
 1071 2294 d 1072 2307 d 1073 2320 d 1074 2333 d 1075 2346 d 1077 2359 d
 1078 2372 d 1079 2385 d 1080 2398 d 1081 2411 d 1083 2424 d 1084 2437 d
 1085 2450 d 1086 2463 d 1088 2476 d 1089 2489 d 1090 2502 d 1091 2515 d
 1093 2528 d 1094 2541 d 1095 2554 d 1097 2567 d 1098 2580 d 1100 2593 d
 1101 2606 d 1103 2619 d 1104 2632 d 1106 2645 d 1107 2658 d 1109 2671 d
 1110 2684 d 1112 2697 d 1114 2710 d 1115 2723 d 1117 2736 d 1119 2749 d
 1121 2762 d 1123 2775 d 1125 2788 d 1127 2801 d 1130 2814 d 1132 2827 d
 1134 2840 d 1137 2853 d 1140 2866 d 1142 2879 d 1145 2892 d 1148 2905 d
 1152 2918 d 1155 2931 d 1159 2944 d 1163 2957 d 1168 2970 d 1173 2983 d
 1178 2996 d 1184 3009 d 1191 3022 d 1198 3035 d 1207 3048 d 1219 3061 d
 1232 3074 d 1253 3087 d 1313 3100 d lt1 1100  500 r  566  513 d  375  526 d
  150  532 d  150 1620 r  160 1631 d  171 1644 d  182 1657 d  196 1670 d
  201 1683 d  213 1696 d  223 1709 d  232 1722 d  241 1735 d  248 1748 d
  259 1761 d  268 1774 d  276 1787 d  284 1800 d  292 1813 d  300 1826 d
  307 1839 d  315 1852 d  322 1865 d  329 1878 d  336 1891 d  344 1904 d
  350 1917 d  356 1930 d  362 1943 d  368 1956 d  374 1969 d  380 1982 d
  386 1995 d  392 2008 d  397 2021 d  403 2034 d  408 2047 d  413 2060 d
  418 2073 d  423 2086 d  428 2099 d  433 2112 d  438 2125 d  442 2138 d
  447 2151 d  452 2164 d  456 2177 d  460 2190 d  464 2203 d  468 2216 d
  473 2229 d  477 2242 d  480 2255 d  484 2268 d  488 2281 d  492 2294 d
  496 2307 d  500 2320 d  503 2333 d  506 2346 d  510 2359 d  513 2372 d
  517 2385 d  520 2398 d  523 2411 d  527 2424 d  530 2437 d  533 2450 d
  536 2463 d  539 2476 d  542 2489 d  545 2502 d  548 2515 d  551 2528 d
  554 2541 d  557 2554 d  560 2567 d  563 2580 d  566 2593 d  568 2606 d
  571 2619 d  574 2632 d  577 2645 d  580 2658 d  583 2671 d  585 2684 d
  588 2697 d  591 2710 d  593 2723 d  596 2736 d  599 2749 d  603 2762 d
  606 2775 d  609 2788 d  612 2801 d  615 2814 d  619 2827 d  622 2840 d
  626 2853 d  629 2866 d  633 2879 d  638 2892 d  642 2905 d  647 2918 d
  652 2931 d  658 2944 d  664 2957 d  671 2970 d  679 2983 d  688 2996 d
  698 3009 d  711 3022 d  726 3035 d  745 3048 d  770 3061 d  806 3074 d
  847 3087 d 1100 3100 d lt5  150 1708 r  152 1709 d  172 1722 d  192 1735 d
  211 1748 d  230 1761 d  248 1774 d  266 1787 d  284 1800 d  302 1813 d
  319 1826 d  335 1839 d  352 1852 d  368 1865 d  384 1878 d  400 1891 d
  415 1904 d  430 1917 d  445 1930 d  460 1943 d  475 1956 d  489 1969 d
  503 1982 d  517 1995 d  526 2008 d  544 2021 d  560 2034 d  572 2047 d
  585 2060 d  598 2073 d  611 2086 d  623 2099 d  636 2112 d  649 2125 d
  661 2138 d  673 2151 d  686 2164 d  698 2177 d  710 2190 d  722 2203 d
  735 2216 d  747 2229 d  759 2242 d  770 2255 d  782 2268 d  793 2281 d
  805 2294 d  818 2307 d  830 2320 d  842 2333 d  854 2346 d  865 2359 d
  876 2372 d  886 2385 d  897 2398 d  908 2411 d  920 2424 d  939 2437 d
  951 2450 d  958 2463 d  976 2476 d  989 2489 d 1002 2502 d 1015 2515 d
 1028 2528 d 1041 2541 d 1055 2554 d 1069 2567 d 1083 2580 d 1097 2593 d
 1111 2606 d 1126 2619 d 1140 2632 d 1156 2645 d 1171 2658 d 1187 2671 d
 1204 2684 d 1220 2697 d 1243 2710 d 1255 2723 d 1273 2736 d 1292 2749 d
 1311 2762 d 1331 2775 d 1352 2788 d 1374 2801 d 1396 2814 d 1420 2827 d
 1444 2840 d 1470 2853 d 1497 2866 d 1525 2879 d 1555 2892 d 1586 2905 d
 1620 2918 d 1663 2931 d 1704 2944 d 1737 2957 d 1782 2970 d 1832 2983 d
 1886 2996 d 1951 3009 d 2016 3022 d 2050 3028 d   4 lw lt0 1100  500 r
 1100 3100 d
e
%%Trailer
EndPSPlot


