%Paper: 
%From: dng@decu08.triumf.ca (Daniel Ng)
%Date: Wed, 17 Feb 93 15:57:34 -0800
%Date (revised): Thu, 4 Mar 93 16:52:21 -0800
%Date (revised): Wed, 30 Jun 93 09:28:27 -0700


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%\documentstyle[preprint,eqsecnum,revtex]{aps}
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%\def\baselinestretch{1.6}
\def\baselinestretch{1.43}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% some useful definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\331{\rm SU(3)_L \times U(1)_X}
\def\sm{\rm SU(2)_L \times U(1)_Y}
\def\Q{\rm U(1)_Q}
\def\noalignand{
             \noalign{\vbox{\vskip\abovedisplayskip \hbox{and}
              \vskip\belowdisplayskip}}}
\def\eff{{\it eff}}
%
% definitions for the loop section
%
\def\spp{\sin\alpha_{++}}
\def\cpp{\cos\alpha_{++}}
\def\tpp{\tan\alpha_{++}}
\def\sspp{\sin^2\alpha_{++}}
\def\ccpp{\cos^2\alpha_{++}}
\def\sp{\sin\alpha_+}
\def\cp{\cos\alpha_+}
\def\tp{\tan\alpha_+}
\def\ssp{\sin^2\alpha_+}
\def\ccp{\cos^2\alpha_+}
\def\Re{\,{\rm Re}\,}
\def\Im{\,{\rm Im}\,}
\def\Mp{M_{Y^+}}
\def\Mpp{M_{Y^{++}}}
\def\mpp{m_{H^{++}}}
\def\mp{m_{H^+}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% title page
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\draft
\preprint{IFP-460-UNC}
\preprint{TRI-PP-93-11}
\preprint
\preprint{February 1993}
\preprint{revised, June 1993}
\vspace{-0.5cm}
\begin{title}
\begin{center}
$Z$--$Z'$ mixing and oblique corrections \\
in an ${\rm SU(3) \times U(1)}$ model
\end{center}
\end{title}

\author{James T. Liu}
\begin{instit}
\begin{center}
Institute of Field Physics, Department of Physics and Astronomy,\\
University of North Carolina, Chapel Hill, NC  27599--3255, USA
\end{center}
\end{instit}
\author{Daniel Ng}
\begin{instit}
\begin{center}
TRIUMF, 4004 Wesbrook Mall\\
Vancouver, B.C., V6T 2A3, Canada
\end{center}
\end{instit}
%
%\maketitle
%
\begin{abstract}
{\baselineskip=20pt
We address the effects of the new physics predicted by the $\331$ model on
the precision electroweak measurements.  We consider
both $Z$--$Z'$ mixing and one-loop oblique corrections, using a combination
of neutral gauge boson mixing parameters and the parameters $S$ and $T$.
At tree level, we obtain strong limits on the $Z$--$Z'$ mixing angle,
$-0.0006<\theta<0.0042$ and find $M_{Z_2}>490 {\rm GeV}$ (both at 90\% C.L.).
The radiative corrections
lead to $T>0$ if the new Higgs are heavy, which bounds the Higgs masses to be
less than a few TeV.  $S$ can have either sign depending on the Higgs
mass spectrum.  Future experiments may soon place strong restrictions on this
model, thus making it eminently testable.

}
\end{abstract}
\newpage


\section{Introduction}
Recently a model based on the gauge group $\331$ has been proposed as a
possible explanation of the family replication question \cite{frampton}.
By matching the gauge coupling constants at the electroweak scale
\cite{ng}, the mass of the new
heavy neutral gauge boson, $Z'$, is bounded to be less than $2.2$ TeV and
the mass upper bound for the new charged gauge bosons, $Y^{\pm\pm}$ and
$Y^{\pm}$, is $435$ GeV \cite{massb}.  Since $Y^{++}$ and $Y^{+}$ carry two
units of
lepton number, they are called dileptons.  Unlike most extensions of the
standard model, in which the masses of the new gauge bosons are not bounded
from above, this model would be either realized or ruled out in the future
high energy colliders such as the superconducting supercollider and the next
linear collider.

The new $Z'$, by mixing with the standard model neutral gauge boson $Z$,
modifies the neutral current parameters as well as the $\rho$-parameter
\cite{langacker}.  The dileptons, $Y^{\pm\pm}$ and $Y^{\pm}$, and the
new charged Higgs, $H^{\pm\pm}$ and $H^{\pm}$, on the other hand, do not
participate directly in the precision LEP experiments \cite{lep} nor the
neutrino scattering experiments \cite{charm}.  Instead, they only enter
radiatively, mainly via their oblique corrections to the $W^{\pm}$ and $Z$
propagators \cite{peskin,altarelli,marciano,kennedy,holdom,golden}.
Nevertheless, such radiative corrections may be comparable to the tree level
corrections due to the $Z$--$Z'$ mixing.  Thus we treat both cases in the
following.

If the masses of the dileptons are degenerate, we may expect the oblique
corrections
to vanish.  However, the mass degeneracy is lifted when $\sm$ breaks
into $\Q$; thus the mass squared splitting would be on the order of
$M_W^2$.  As a result, the oblique corrections to the parameters $S$ and $T$
\cite{peskin}
are expected to be on the order of $(1/\pi)(M_W^2 / M_{Y^{++}}^2)$, where
$M_{Y^{++}}$ is the mass of $Y^{\pm\pm}$.  In addition, oblique
corrections due to the new heavy charged Higgs, $H^{\pm\pm}$ and $H^{\pm}$,
are induced by the small mixing between Higgs multiplets.  The contributions
have the general form
$(1/\pi)(M_W^2 / M_{Y^{++}}^2)(m_H^2/M_{Y^{++}}^2)$, where $m_H$ is the mass
of the new charged Higgs.  Hence, the heavy charged Higgs contributions
would be important even when the dilepton mass splitting is small.

Our analysis in this paper concentrates on both tree level and one-loop
oblique corrections to the standard model due to the new physics of the
$\331$ model.  For the dileptons and the new Higgs, which only
contribute radiatively, we use the $S$, $T$ and $U$ parameters.  However the
effects of the $Z'$, which enters at tree level, cannot be fully
incorporated into this formalism, and may instead be parametrized by a
$Z$--$Z'$ mixing angle as well as the mass of the heavy $Z_2$.  We thus use
five parameters to describe the new physics: the two $Z'$ parameters and the
three oblique ones.  Starting
with a discussion of tree level mixing, we perform a five
parameter fit to experimental data to put strong limits on the $Z$--$Z'$
mixing angle.  We then discuss the consequences of the fit on the other
particles by carrying out a complete
one-loop calculation of $S$ and $T$ for dilepton gauge bosons
and the new Higgs bosons.  The new quarks, which are SU(2) singlets,
do not contribute.


\section{Tree level mixing}
We first outline the model, following the notation given in
\cite{ng}. The fermions transform under $\rm SU(3)_c\times\331$
according to
%
\def\bold#1{{\bf #1}}
\begin{mathletters}
\begin{eqnarray}
\psi_{1,2,3} = \pmatrix {e\cr \nu_e\cr e^c\cr} \: , \pmatrix {\mu \cr
\nu_\mu
   \cr \mu^c \cr} \: , \pmatrix {\tau \cr \nu_\tau \cr \tau^c \cr}
     \qquad &\mathbin:& \qquad (\bold1, \: \bold3^\ast, \: 0) \ , \\
Q_{1,2} = \pmatrix {u\cr d\cr D\cr} \: , \pmatrix {c\cr s\cr S\cr}
     \qquad &\mathbin:&\qquad(\bold3,\: \bold3,\:
	-\textstyle\frac{1}{3})\ ,\\
Q_3 = \pmatrix {b\cr t\cr T\cr} \qquad &\mathbin:& \qquad
	(\bold3, \: \bold3^\ast,\: \textstyle\frac{2}{3} ) \ ,  \\
d^c, \: s^c, \: b^c \qquad &\mathbin:& \qquad (\bold3^\ast,\:\bold1,\:
	\textstyle\frac{1}{3}) \ ,  \\
u^c, \: c^c, \: t^c \qquad &\mathbin:& \qquad(\bold3^\ast,\:\bold1,\:
	-\textstyle\frac{2}{3}) \ , \\
D^c, \: S^c \qquad &\mathbin:&  \qquad (\bold3^\ast,\:\bold1,\:
	\textstyle\frac{4}{3}) \ ,  \\
T^c \qquad&\mathbin:&\qquad(\bold3^\ast,\:\bold1,\:\textstyle-\frac{5}{3})\ .
\end{eqnarray}
\end{mathletters}
%
where $D$, $S$ and $T$ are new quarks with charges $-4/3$, $-4/3$ and $5/3$
respectively.  The minimal Higgs multiplets required for the
symmetry breaking hierarchy and fermion masses are given by
%
\begin{mathletters}
\begin{eqnarray}
\label{eq:Hmult}
\Phi = \pmatrix{\phi^{++}\cr \phi^+\cr \phi^0\cr} \qquad \qquad
         &\mathbin:& \qquad (\bold1,\,\bold3,\,1) \ ,  \\
%
\Delta = \pmatrix{\Delta_1^+\cr \Delta^0\cr \Delta_2^-\cr} \qquad \qquad
         &\mathbin:& \qquad (\bold1,\,\bold3,\,0) \ , \\
%
\Delta ' = \pmatrix{\Delta '^0\cr \Delta '^-\cr \Delta '^{--}\cr} \qquad
       \quad &\mathbin:& \qquad (\bold1,\,\bold3,\,-1) \ ,  \\
%
\noalignand
\eta = \pmatrix {\eta_1^{++} & \eta_1^+/\sqrt{2} & \eta^0/\sqrt{2} \cr
                 \eta_1^+/\sqrt{2} & \eta_1 ^0 & \eta^-/\sqrt{2} \cr
                 \eta^0/\sqrt{2} & \eta^-/\sqrt{2} & \eta^{--} \cr}
      \qquad &\mathbin:& \qquad (\bold1,\,\bold6,\,0)
\ .
\end{eqnarray}
\end{mathletters}

The non-zero vacuum expectation value (VEV) of $\phi^0$, $u/\sqrt{2}$, breaks
$\331$ into $\sm$.  The SU(2) components of $\Delta$ and $\Delta'$ then
behave like the ordinary Higgs doublets of a two-Higgs standard model.
The sextet, $\eta$,
is required to obtain a realistic lepton mass spectrum.  For simplicity,
we will assume its VEVs are zero.  As $\331$ is
broken into $\sm$, the sextet will decompose into an SU(2) triplet, an
SU(2) doublet and a charged SU(2) singlet.  We will also assume that the mass
splitting of these scalars within their multiplets is small; hence their
contributions to $S$ and $T$ will be negligible.

As $\sm$ is broken by the VEVs of $\Delta^0$ and $\Delta'^0$,
$v/\sqrt{2}$ and $v'/\sqrt{2}$, they will provide masses for
the standard model gauge bosons, $W^\pm$ and $Z$.  The VEVs also induce
$Z$--$Z'$ mixing as well as
the mass splitting of $Y^{\pm\pm}$ and $Y^{\pm}$.  Hence we obtain the
masses for the charged gauge bosons,
%
\begin{mathletters}
\begin{eqnarray}
M^2_W &=& \textstyle\frac{1}{4} \: g^2 (v^2 + v'^2) \ , \\
%
M^2_{Y^+} &=& \textstyle\frac{1}{4} \: g^2(u^2 + v^2) \ ,
\\
%
\noalignand
M^2_{Y^{++}} &=& \textstyle\frac{1}{4} \: g^2 (u^2 + v'^2 ) \ ,\phantom{a}
\end{eqnarray}
\end{mathletters}
and the mass-squared matrix for $\{Z, \:  Z'\}$
%
\begin{eqnarray}
{\cal M}^2 = \pmatrix {M^2_Z & M^2_{ZZ'}\cr
M^2_{ZZ'} & M^2_{Z'}}\ ,
\end{eqnarray}
%
with
\begin{mathletters}
\begin{eqnarray}
M^2_Z &=& \frac{1}{4} \frac{g^2}{\cos^2\theta_W} \: (v^2+v'^2) \ ,  \\
M^2_{Z'} &=& \frac{1}{3} g^2 \left[
              \frac{\cos^2\theta_W}{1-4 \sin^2\theta_W} \: u^2
           \: + \:  \frac{1-4 \sin^2\theta_W}{4\cos^2\theta_W}\: v^2
  \hfill \right. \nonumber \\
          &&\qquad\left.
          \: +\: \frac{(1+2\sin^2\theta_W)^2}
                   {4 \cos^2\theta_W(1-4 \sin^2\theta_W)}\: v'^2
         \right] \ ,  \\
M^2_{ZZ'} &=& \frac{1}{4\sqrt{3}} \, g^2 \left[
         \frac{\sqrt{1-4 \sin^2\theta_W}}{\cos^2\theta_W}\: v^2 -
        \frac{1+2\sin^2\theta_W}
            {\cos^2\theta_W \sqrt{1-4\sin^2\theta_W}}\: v'^2 \right]  .
\end{eqnarray}
\end{mathletters}
%
The mass eigenstates are
%
\begin{mathletters}
\begin{eqnarray}
Z_1 &=& \cos\theta\ Z - \sin\theta\ Z' \ ,  \\
\noalignand
Z_2 &=& \sin\theta\ Z + \cos\theta\ Z' \ ,
\end{eqnarray}
\end{mathletters}
%
where the mixing angle is given by
%
\begin{equation}
\label{angle}
\tan^2\theta=\frac{M_Z^2-M_{Z_1}^2}{M_{Z_2}^2-M_Z^2} \ .
\end{equation}
%
with $M_{Z_1}$ and $M_{Z_2}$ being the masses for $Z_1$ and $Z_2$.
Here, $Z_1$ corresponds to the standard model neutral gauge boson and
$Z_2$ corresponds to the additional neutral gauge boson.
For small mixing, we find $\theta \approx {M^2_{ZZ'}}/{M^2_{Z_2}}\ll1$.

Since $M_{Z_1}$ has been precisely determined by the LEP experiments, the
new contributions are parametrized by the two $Z'$ parameters, $M_{Z_2}$ and
$\theta$.  The structure of the minimal Higgs sector gives additional
constraints on the allowed region of $(M_{Z_2},\theta)$ parameter space,
and forces $\theta\ll1$ for $M_{Z_2}\gg M_{Z_1}$.  However, we will not make
use of this constraint so as to allow for extended Higgs sectors.

While we have only been discussing tree level relations so far, it is
important to include both the standard model and new
radiative corrections as well.  We take the oblique
corrections into account by using the starred functions of Kennedy and Lynn
\cite{kennedy2}.  Following \cite{peskin}, the effect of new heavy particles
on the starred functions may be expressed in terms of $S$, $T$ and $U$.
The effects of the tree level $Z$--$Z'$ mixing and the presence of the
new $Z_2$ gauge boson can then be expressed as shifts of the starred
functions.  We ignore effects due to the combination of both
mixing and radiative corrections, as they are suppressed.

In order to perform a fit to experiment, we need to express the $\331$ model
predictions in terms of both tree level $Z'$ parameters, $(M_{Z_2},\theta)$,
and one-loop parameters, $(S,T,U)$.
This is most easily done by first calculating the
standard model observables with the addition of $S$, $T$ and $U$ and
then shifting the
results by the tree level parameters.  We consider both (i) $Z$-pole
experiments which are sensitive to the mixing only
and (ii) low energy experiments which are sensitive to both mixing and the
presence of the $Z_2$.  The experimental values that we use for the five
parameter fit, along with the standard model predictions
(for reference values of $m_t=150\rm GeV$ and $m_H=1000\rm GeV$
\cite{peskin}),
are given in table \ref{data}.  For the $Z$-pole data, $M_W/M_Z$ and
$Q_W(Cs)$, we use the values given in Ref.~\cite{langacker2}, while $g_L^2$
and $g_R^2$ are given in Ref.~\cite{pdb}.
We find it convenient to approximate the top quark and standard
model Higgs mass dependence through shifts in $S$, $T$ and $U$.

The new contributions to the measurable quantities due to the presence
of the $Z_2$ and $Z$--$Z'$ mixing are given in the appendix.  For the
$(S,T,U)$ dependence of the observables, we use the results given in
Ref.~\cite{peskin}.  The result of the fit in the $(M_{Z_2},\theta)$ plane
(with $S$, $T$ and $U$ unrestricted) is presented in Fig.~\ref{fig1} and
indicates
that $Z$--$Z'$ mixing is highly restricted.  This is partially due to the
large couplings of the $Z'$ to quarks.  At 90\% C.L., we find
$-0.0006<\theta<0.0042$ and $M_{Z_2}>490\rm GeV$.  Note the latter
restriction is comparable to that obtained from tree level FCNC
considerations in the quark sector.

Although not used in the fit, the minimal Higgs sector leads to further
restrictions on the $Z_2$ mass and mixing.  The constraint on the $Z$--$Z'$
mixing is shown by the dotted line in Fig.~\ref{fig1}.  Due to the symmetry
breaking hierarchy, $u\gg v,v'$, the dilepton and $Z_2$ masses are related.
Using the limit $M_{Y^+}>300\rm GeV$ from polarized muon
decay \cite{carlson,beltrami},
we find $M_{Z_2}>1.4\rm TeV$, as indicated on the figure.  Because of the
upper bound on $\331$ unification,
%% (taken here as $\alpha_X<2\pi$ in the normalization of Ref.~\cite{ng}),
$M_{Z_2}$ must be below $2.2\rm TeV$, thus
giving a narrow window for the allowed $Z_2$ mass.

The presence of the $Z_2$ gauge boson affects the fit in the $S$--$T$
plane as shown in Fig.~\ref{fig2}.  We see that the tree level mixing may
appear as effective contributions to $S$ and $T$.  The dominant effect
is to give a positive contribution to $T$ due to the downshift in the
$Z_1$ mass.  The large region of negative $T$ corresponds to high $Z_2$
mass and small mixing.  Imposing an upper bound on $M_{Z_2}$ will affect the
fit in this region.  At 90\% C.L. we find
%
\begin{equation}
-1.34~\leq S~\leq~0.28\ , \qquad -3.07~\leq T~\leq~0.45\ ,
\label{STlimit}
\end{equation}
%
keeping in mind that the errors are nongaussian.
Although the definitions of $S$, $T$ and $U$ are model independent,
these numbers are
valid only for the $\331$ model due to the tree level effects.  We use these
results in the next section to constrain the new charged Higgs masses.

\section{Radiative corrections}
The radiative corrections arising from the dileptons and the new heavy
Higgs are process independent and may be parametrized by $S$, $T$ and $U$.
Following the notation of \cite{peskin}, we define
%$S$, $T$ and $U$ for radiative corrections by
%
\begin{mathletters}
\begin{eqnarray}
S&=&16\pi\left[\Pi_{33}'(0)-\Pi_{3Q}'(0)\right]\ ,\\
T&=&{4\pi\over \sin^2\theta_W M_W^2}\left[\Pi_{11}(0)-\Pi_{33}(0)\right]\ ,\\
U&=&16\pi\left[\Pi_{11}'(0)-\Pi_{33}'(0)\right]\ .
\end{eqnarray}
\end{mathletters}
%
In the above, the vacuum polarizations, $\Pi(q^2)$, and their derivatives
with respect to $q^2$, $\Pi'(q^2)$, include only new physics beyond the
standard model.  Implicit in this parametrization is the assumption that
the scale of new physics is much larger than $M_Z$.

%% In this letter,
%% we use the values for $S$ and $T$ obtained by the authors in Ref. \cite{roy}
%% %
%% \begin{equation}
%% \label{STlimit}
%% -1.92~\leq S~\leq~0.40\ , \qquad -1.50~\leq T~\leq~0.10\ ,
%% \end{equation}
%% %
%% at a $90\%$ confidence level.

The $\331$ model predicts three classes of new particles: the new quarks
$D$, $S$ and $T$, new gauge bosons, $Y^{\pm\pm}$, $Y^\pm$ and $Z'$ and new
Higgs scalars.  Since the new quarks are SU(2) singlets, they do not enter
into the oblique corrections which are only sensitive to SU(2) electroweak
physics.  Similarly, $Z'$ will not contribute except through $Z$--$Z'$
mixing which was addressed in the previous section.  Thus in the limit of
small mixing, only dileptons and new Higgs particles will contribute
radiatively to $S$ and $T$ (in addition to the deviations of the top
quark and standard model Higgs masses from their reference values).
Because of spontaneous symmetry
breaking, we must examine the new gauge and Higgs sector simultaneously.

In order to simplify the analysis of the Higgs sector, we assume that
the sextet $\eta$ does not acquire a VEV.  As a result it can be treated
separately from the dileptons, and we now focus on the three SU(3) triplet
Higgs, (\ref{eq:Hmult}--c).  These three Higgs contain a total of 18 states
of which 8 are ``eaten up'' by the Higgs mechanism to give masses to the
various gauge bosons.  Ignoring $Z$--$Z'$ mixing, the SU(2) doublets coming
from $\Delta$ and $\Delta'$ form a standard two-Higgs model with
$\tan\beta=v'/v$ and five physical Higgs particles, $h^\pm$, $a^0$ and
$h^0_{1,2}$ \cite{Hunt}.  The remaining 5 Higgs are given by
%
\begin{mathletters}
\begin{eqnarray}
\label{eq:higgs}
H^{\pm\pm}&=&\spp\phi^{\pm\pm}+\cpp\Delta^{\prime\pm\pm}\ ,\\
H^\pm&=&\sp\phi^++\cp\Delta_2^+\ ,\\
H^0&=&\sqrt{2}\Re\phi^0\ ,
\end{eqnarray}
\end{mathletters}
%
where we have defined the ratio of VEVs as $\tpp=v'/u$ and $\tp=v/u$.
These two VEV angles and $\tan\beta$ are not independent, but are related
by $\tan\beta=\tpp/\tp$.
Orthogonal to these states are the would be Goldstone bosons
%
\begin{mathletters}
\begin{eqnarray}
\pi^{\pm\pm}&=&\cpp\phi^{\pm\pm}-\spp\Delta^{\prime\pm\pm}\ ,\\
\pi^\pm&=&\cp\phi^+-\sp\Delta_2^+\ ,\\
\pi^0&=&\sqrt{2}\Im\phi^0\ ,
\end{eqnarray}
\end{mathletters}
%
corresponding to $Y^{\pm\pm}$, $Y^\pm$ and $Z'$ respectively.
Again we have assumed the $Z$--$Z'$ mixing is not important for one-loop
oblique corrections.

Since the two-Higgs model has already been considered in detail (see for
example Ref.~\cite{2higgs,2higgs2}), we will only
focus on the dileptons and additional Higgs.  Assuming the
symmetry breaking hierarchy $u\gg \{v,v'\}$, we see that $\{\tpp,\tp\}\ll 1$
so that $H^{\pm\pm}$ and $H^\pm$ are mostly SU(2) singlets, and the
would be Goldstone bosons giving masses to the dilepton doublet
($Y^{++}$, $Y^+$)
are mostly contained in the $\Phi$ doublet ($\phi^{++}$, $\phi^+$).
Although the mixings between the SU(2) singlet and doublet scalars are
small, the oblique corrections can be important as their contributions
are not protected by the custodial symmetry.
%The
%small mixing between the SU(2) singlet and doublet scalars prevents the
%dilepton and Higgs contributions from being separated and gives rise to
%non-trivial corrections to $S$ and $T$.

Let us first consider only the contributions from the dilepton gauge bosons
$(Y^{++},Y^+)$ which corresponds to the limit
$\{\tpp,\tp\}\to0$.  In this limit, the new Higgs, (\ref{eq:higgs}--c), are all
SU(2) singlets and only the dilepton doublet contributes to $S$, $T$ and $U$.
We find
%
\begin{mathletters}
\begin{eqnarray}
\label{eq:limSTU}
S&=&-{9\over4\pi}\ln{\Mp^2\over\Mpp^2}\ ,\\
T&=&{3\over16\pi\sin^2\theta_WM_W^2}F(\Mp^2,\Mpp^2)\ ,\\
U&=&-{1\over4\pi}\biggl[-{19\Mp^4-26\Mp^2\Mpp^2+19\Mpp^4
	\over3(\Mp^2-\Mpp^2)^2}	\nonumber\\
&&\qquad\qquad+{3\Mp^6-\Mp^4\Mpp^2-\Mp^2\Mpp^4+3\Mpp^6\over(\Mp^2-\Mpp^2)^3}
	\ln{\Mp^2\over\Mpp^2}\biggr]\ ,
\end{eqnarray}
\end{mathletters}
%
where $F$ is defined by
%
\begin{equation}
F(M_1^2,M_2^2)=M_1^2+M_2^2-2{M_1^2M_2^2\over M_1^2-M_2^2}
	\ln{M_1^2\over M_2^2}\ .
\end{equation}
%
Since $F(M_1^2,M_2^2)\ge0$ and vanishes only when the masses are
degenerate, we see that $T\ge0$ and parametrizes the size of custodial SU(2)
breaking.  $S$ vanishes when the dileptons are degenerate, but can pick up
either sign when the masses are split.  While $U$ does not play as
important a role in confronting experiment \cite{peskin}, we note that the
dilepton doublet gives $U\le0$.  This result is the opposite of that found
for a chiral fermion doublet where $U$ is non-negative.

A complete calculation of $S$ and $T$ must take into account the mixing
between the SU(2) singlet and doublet Higgs.  This is especially important in
light of the upper limit on the $\331$ breaking scale which puts a non-zero
lower bound on the mixing.  Because of the
mixing, the dileptons and physical Higgs combine in their contributions.
For $S$, we find the full result
%
\begin{eqnarray}
\label{eq:fullS}
S=-{1\over\pi}\biggl[&&{2\over3}\sspp-{1\over3}\ssp
	+{9\over4}\ln{\Mp^2\over\Mpp^2}\nonumber\\
&&+{1\over4}\sspp\ln{\mpp^2\over\Mpp^2}
	-{1\over4}\ssp\ln{\mp^2\over\Mp^2}\nonumber\\
&&-\sspp\ccpp G\biggl(\frac{\mpp^2}{\Mpp^2}\biggr)
       -\ssp\ccp G\biggl(\frac{\mp^2}{\Mp^2}\biggr)\biggr]\ .\qquad
\end{eqnarray}
%
The function $G$ is defined by
%
\begin{equation}
G(x)={7x^2-38x-29\over36(x-1)^2}
+{x^3-3x^2+21x+1\over12(x-1)^3}\ln{x}\ ,
\end{equation}
%
and vanishes when $x=1$.  $G$ is positive when the Higgs are heavier than the
dileptons and is usually negative when they are lighter.  We see that the
Higgs corrections always enter with a factor of either $\spp$ or $\sp$ and
arise because of the mixing of scalars with different hypercharges.  As a
result, $S$ reduces to Eqn.~(\ref{eq:limSTU}) in the limit when the Higgs do
not mix.

Turning to $T$, we find that it has the general form
%
\begin{eqnarray}
\label{eq:fullT}
T={3\over16\pi\sin^2\theta_WM_W^2}\biggl[
	&&F(\Mp^2,\Mpp^2)\nonumber\\
&&+\ssp\ccp F(\mp^2,\Mp^2)\nonumber\\
&&+\sspp\ccpp F(\mpp^2,\Mpp^2)\nonumber\\
&&-\ssp\ccpp[F(\mp^2,\Mpp^2)-F(\Mp^2,\Mpp^2)]\nonumber\\
&&-\ccp\sspp[F(\mpp^2,\Mp^2)-F(\Mpp^2,\Mp^2)]\nonumber\\
+&&{1\over3}\ssp\sspp[F(\mp^2,\mpp^2)-F(\Mp^2,\Mpp^2)]\nonumber\\
+&&{4\over3}\ssp(\ssp-\sspp)(\mp^2-\Mp^2)\nonumber\\
+&&{4\over3}\sspp(\sspp-\ssp)(\mpp^2-\Mpp^2)\biggr]\ .
\end{eqnarray}
%
In deriving this, we had to use the relation $\ccp\Mp^2=\ccpp\Mpp^2$ implied
by the definitions of $\tpp$ and $\tp$.  Again, the Higgs corrections
come in only through their small mixing into an SU(2) doublet.  We find that
$T$ is positive in most of parameter space and becomes large when the Higgs
or dilepton masses are split greatly, thus breaking custodial SU(2).
A similar calculation for $U$ is straightforward, but since experimental
constraints on $U$ are not as strong, we do not present it here.

The full expressions for $S$ and $T$ depend on four unknown parameters of
the new physics --- the two dilepton masses and the two new Higgs masses
(the VEV angles are determined completely from the dilepton masses).
In order to understand the general behavior of these radiative corrections,
we now turn to three interesting cases:
(a)~the dileptons are degenerate in mass, $\Mp=\Mpp$;
(b)~the dileptons are maximally split in mass, $\sspp=0$; and
(c)~the Higgs and dilepton masses are related by $\mp=\Mp$ and $\mpp=\Mpp$.

%{\parindent=0pt (a) $\Mp=\Mpp$}.
(a) $\Mp=\Mpp$.
In order to give identical masses to $Y^\pm$ and $Y^{\pm\pm}$, the VEVs, $v$
and $v'$ must be equal.  As a result, $\tan\beta=1$ and
$\sspp = \ssp = M^2_W / 2\Mpp^2 $.  From Eqn.~(\ref{eq:fullS}), we find
for $S$
%
\begin{equation}
\label{eq:Sdegen}
S={1\over2\pi}{M_W^2\over \Mpp^2}\left[
	-{1\over3}+{1\over4}\ln{\mp^2\over\mpp^2}
	+\ccpp\left(G\left({\mpp^2\over\Mpp^2}\right)
	+G\left({\mp^2\over\Mp^2}\right)\right)\right]\ .
\end{equation}
%
Note that even when {\it all} masses are degenerate, $S$ takes on a non-zero
result.  In this case, we see that the singlet--doublet mixing in the scalar
sector gives rise to a negative $S$ \cite{dugan,lavoura}.  For large Higgs mass
splittings, the second term in (\ref{eq:Sdegen}) dominates, and $S$ is
positive for $\mp\gg\mpp$ and negative for $\mp\ll\mpp$.  From the fit in
the previous section, (\ref{STlimit}), we see that $\mp\alt\mpp$ is favored.

For $T$, we find the simple result
%
\begin{equation}
T={1\over16\pi\sin^2\theta_WM_W^2}\sin^4\alpha_{++}F(\mp^2,\mpp^2)\ ,
\end{equation}
which gives the bounds
%
\begin{equation}
0\leq T \leq {1\over 64 \pi\sin^2\theta_W}{M_W^2\over \Mpp^2}
            {\max(\mpp^2,\mp^2)\over\Mpp^2}\ .
\end{equation}
%
The lower limit corresponds to Higgs mass degeneracy and the upper limit to
large mass splitting.
{}From Eqn.~(\ref{STlimit}), we obtain the upper bound for
the heavier Higgs, namely $\max(\mp,\mpp) \leq 7.0{\rm TeV}$, for $\Mpp
\leq 350 {\rm GeV}$.

%{\parindent=0pt (b) $\spp=0$}.
(b) $\sspp=0$.
Due to the VEV structure, the mass splitting of the dileptons is restricted
by the condition $|\Mp^2-\Mpp^2|\le M_W^2$.  The limiting case
$\Mp^2=\Mpp^2 + M_W^2$ can be realized by $v \gg v'$ or $\sspp\to0$.
In this case, the
doubly charged Higgs, which is $\Delta'^{\pm\pm}$, is a pure SU(2) singlet
and is not involved in the oblique corrections.

The parameter T is then given by
%
\begin{equation}
T=\cases{\displaystyle
{1\over16\pi\sin^2\theta_W}{M_W^2\over\Mpp^2}{\mp^2\over\Mpp^2}\ ,&
for $\displaystyle{\mp^2\over\Mpp^2} \gg 1$ ,\cr
\displaystyle-{3\over16\pi\sin^2\theta_W}{M_W^2\over\Mpp^2}\ ,&
for $\displaystyle {\mp^2\over\Mpp^2} \ll 1$ .\cr}
\end{equation}
%
We see that T can be negative if $\mp^2 \ll \Mpp^2$.
However, it is
negligible unless the dileptons are extremely light.  On the other hand, $T$
is always positive for heavy Higgs, $\mp^2 \gg \Mpp^2$.

Although the Higgs
contributions are induced by the small mixing, namely $\ssp = M_W^2/\Mp^2$,
we obtain a stringent bound for the Higgs mass, $\mp \leq 3.5 {\rm TeV}$,
for $\Mpp \leq 350 {\rm GeV}$.
If we take the other limit $v' \gg v$, then $\ssp \to 0$.  By the same token,
we find $\mpp^2 \leq 3.5 {\rm TeV}$.  Combining this with the case for $v =
v'$ in part (a), we expect the new charged Higgs
to be lighter than a few TeV.  Using both limits and the restriction on
the Higgs mass, we also find $|S|\alt0.3$
provided all new particles are heaver than $M_W$.
%
%%% check this for S
%

%{\parindent=0pt (c) $\mp = \Mp$ and $\mpp = \Mpp$}.
(c) $\mp = \Mp$ and $\mpp = \Mpp$.
Both expressions for $S$ and $T$ simplify considerably when the Higgs masses
are equal to the dilepton doublet masses.
Since the symmetry breaking hierarchy ensures that the mass splittings for the
dileptons and the Higgs bosons are small, we find
%
\begin{mathletters}
\begin{eqnarray}
-{23\over12\pi}{M_W^2\over \Mpp^2}\le &S&\le
{19\over12\pi}{M_W^2\over\Mpp^2}\ ,\\
0 \leq &T& \leq {1\over 16\pi\sin^2\theta_W}{M_W^2\over \Mpp^2} \ .
\end{eqnarray}
\end{mathletters}
%
For $\Mpp \geq 250{\rm GeV}$, we obtain $-0.06\le S\le0.05$ and
$0 \leq T \leq 0.009$ as expected for a small mass splitting.


When the $\eta$ sextet is taken into account, it introduces 12 additional
physical Higgs fields.  In this case the mixing between scalars
in different SU(2) multiplets becomes more complicated.  Nevertheless,
our conclusions that $S$ can pick up corrections due to the mixing of scalars
with different hypercharge and that $T$ measures the mass splitting between
scalars still hold.  Without any fine tuning in the Higgs sector, we
expect all physical Higgs to be lighter than a few TeV.

\section{Conclusions}
To summarize, we have examined both tree level $Z$--$Z'$ mixing and
one-loop oblique effects induced by the new charged gauge bosons and Higgs
bosons in the $\331$ model.  The precision experiments constrain the mixing
angle to be in the range $-0.0006<\theta<0.0042$ and gives
$M_{Z_2}>490\rm GeV$.
Additional indirect lower bounds can be placed on the $Z_2$ mass from both
FCNC considerations and from the $Z'$--dilepton mass relation.  The latter
gives the strongest limit and, along with the upper bound on the $\331$
scale highly restricts the neutral gauge sector of the model, giving
$1.4<M_{Z_2}<2.2\rm TeV$.

Constraints on the new Higgs bosons are obtained from examination of
the one-loop radiative corrections using the parameters $S$ and $T$.
The parameter $T$ can be negative for very light charged Higgs and is
positive for heavy Higgs.  Hence we obtain an upper bound for the new
charged Higgs masses, namely $\mpp , \mp \leq \hbox{a few TeV}$.  The
Higgs sector places strong constraints on the mass splitting between
the singly and doubly charged members of the dilepton doublet.  Hence
no restrictions can be placed on the dilepton masses past that
coming from the Higgs structure.  Nevertheless, other experiments, in
particular polarized muon decay \cite{carlson}, strongly restrict the
dilepton spectrum.

We note that in this model, it is possible to obtain (small) negative
values of $S$ and $T$.  This result is quite general and occurs because of
scalar mixing.
In order to obtain a negative $T$, there has to be mixing between different
SU(2) multiplets (in this case singlets and doublets).  Mixing of states with
different hypercharge also allows negative $S$ for the case when all masses
are degenerate.  These observations have also been made in
Ref.~\cite{lavoura}.
%Tree level $Z$--$Z'$ mixing effects may also lead to
%apparant negative shifts in $S$ and $T$.

As the precision electroweak parameters are measured to higher accuracy, we
can start placing more stringent bounds on the new physics predicted by
this $\331$ model.  When the top quark mass is determined, it will
remove much uncertainty in the standard model contributions to $S$ and $T$;
the parameters then become much more sensitive to truly new physics.
Because the masses of the new particles are already tightly
constrained, both direct and indirect experiments at future colliders
may soon realize or rule out this model.

\bigskip
\centerline{{\bf Acknowledgements}}
J.T.L. would like to thank Paul Frampton and Plamen Krastev for useful
discussions.  This work was supported in part by the U.S. Department of
Energy under Grant No.~DE-FG05-85ER-40219 and by the Natural Science and
Engineering Research Council of Canada.

\begin{table}
%\centering
\caption{The experimentally measured values \cite{langacker2,pdb},
and standard model predictions \cite{peskin}
(for $m_t=150 {\rm GeV}$ and $m_H=1000 {\rm GeV}$)
used in the fit.}
\begin{tabular}{|c|c|c|} \hline
Quantity & experimental value & standard model \\ \hline
$M_Z$ (GeV) & $91.187 \pm 0.007$ & input   \\
$\Gamma _Z$ (GeV) & $2.491 \pm 0.007$ & $2.484$\\
$ R = \Gamma_{had}/ \Gamma_{l \bar{l}}$ & $20.87 \pm 0.07$ & $20.78$ \\
$\Gamma_{b \bar{b}}$ (MeV) & $373 \pm 9$ & $377.9$ \\
$A_{FB} (\mu)$ & $0.0152\pm 0.0027$ & $0.0126 $ \\
$A_{pol} (\tau)$ & $0.140\pm 0.018$ & $0.1297$ \\
$A_e(P_\tau)$ & $0.134\pm 0.030$ & $0.1297$ \\
$A_{FB} (b)$ & $0.093\pm 0.012$ & $0.0848$ \\
$A_{LR} $ & $0.100\pm 0.044$ & $0.1297$ \\
%%%$\Gamma_{l \bar{l}}$ (MeV) & $83.43 \pm 0.29$ & $83.5$ \\
\hline
$M_W/M_Z$ & $0.8789 \pm 0.0030$ & $0.8787$ \\
$Q_W (Cs)$ & $-71.04 \pm 1.81$ & $-73.31 $ \\
$g^2_L$ & $0.2990 \pm 0.0042$ & $0.3001$ \\
$g^2_R$ & $0.0321 \pm 0.0034$ & $0.0302$ \\
\end{tabular}
\label{data}
\end{table}

\appendix*{}
In the electroweak sector, we can choose three independent precisely
measured parameters, $\alpha$, $G_F$ and $M_{Z_1}$, from which in
principle we can predict all the outcome of experiments in the $\331$
theory. Due to the presence of an additional gauge boson, $Z'$, and the
corresponding $Z$--$Z'$ mixing, the results of the standard model
predictions, which are written in terms of the starred
functions \cite{kennedy2},
need to be modified.  If we neglect the effects due to
any combinations of both the
$Z'$ parameters and the standard model radiative corrections, the results
can be expressed as shifts with respect to the starred functions.

For convenience, we can define a parameter, $s^2_0$, which is given by
%
\begin{equation}
s^2_0~(1~-~s^2_0)~=~\frac{\pi\ \alpha(M_{Z_1})}{\sqrt2\ G_F\
M^2_{Z_1}}\ .
\end{equation}
%
{}From the present data, $s^2_0~=~0.23146\pm0.00034$ is precisely known.
Because of the $Z$--$Z'$ mixing,  the mass of the $Z_1$ is shifted by a factor
\begin{equation}
\label{dmz}
\frac{\delta M_{Z_1}}{M_{Z_1}} = -\frac{1}{2}
               \frac{M^2_{Z_2}}{M^2_{Z_1}}\theta^2 \ .
\end{equation}
%
Hence, we obtain
%
\begin{equation}
\frac{M_W/M_{Z_1}}{M_{W_\ast}/M_{Z_\ast}}~=~1+\frac{1}{2}
	\frac{1-s^2_0}{1-2s^2_0}
        \frac{M_{Z_2}^2}{M_{Z_1}^2}\theta^2\ .
\end{equation}

(i) $Z$--pole physics.  The gauge interaction of the light neutral gauge
boson, $Z_1$, is given by
%
\begin{equation}
\label{z1}
{\cal L}~=~\frac{e_\ast}{c_\ast s_\ast} \sqrt{Z_Z(f)}
  ~{Z_1}_{\mu} \left[ J^{\mu}_3(f)~-~Q(f)s^2_{\eff}(f)~J^{\mu}_V
        \right] \ , \\
\end{equation}
\begin{eqnarray}
\label{seff}
\delta s^2_{\eff}(f)~&=&~s^2_{\eff}(f)~-~s^2_\ast \nonumber \\
             &=&~\left[\frac{a^f+b^f}{Q(f)}-\frac{2b^f}{T_3(f)}\right]\theta
       \ ,\\
%
\noalignand
\frac{\delta Z_Z(f)}{Z_{Z_\ast}}~&=&~\frac{4b^f}{T_3(f)}\theta+
  \frac{M^2_{Z_2}}{M^2_{Z_1}}\theta^2 \ ,
\end{eqnarray}
%
where $a^f$ and $b^f$, given in Ref.~\cite{ng}, are the vector
and axial vector coupling coefficients for the $Z'$.
Therefore, the partial
width for the $Z$--boson relative to the standard model prediction is
given by
%
\begin{equation}
\label{width}
\frac{\Gamma(Z \rightarrow f \bar f)}{\Gamma(Z \rightarrow f \bar f)_\ast}~=~
 1~+~\frac{\delta Z_Z(f)}{Z_{Z_\ast}}
  -2Q(f) \frac{g_{V}(f)_\ast}{g^2_{V}(f)_\ast+g^2_{A}(f)_\ast}
  \delta s^2_{eff}(f)\ ,
\end{equation}
%
where ${g_V(f)}_\ast = \frac{1}{2} T_3(f)~-~Q(f){s^2}_\ast$ and
${g_A(f)}_\ast = -\frac{1}{2}T_3(f)$.
For $\Gamma(Z \rightarrow b \bar b )_\ast$, we also include the vertex
correction due to the top-quark.

By the same token, we can express the polarization asymmetry of
fermion $f$ as
%
\begin{eqnarray}
\frac{A_{pol}(f)}{{A_{pol}(f)}_*}~&=&~1~- \delta A(f)\ ,\\
\noalign{\vbox{\vskip\abovedisplayskip \hbox{with} \vskip\belowdisplayskip}}
\delta A(f)~&=&~~\frac{Q(f)}{g_{V}(f)_\ast}
   \frac{g^2_{A}(f)_\ast-g^2_{V}(f)_\ast}{g^2_{A}(f)_\ast+g^2_{V}(f)_\ast}
     \delta s^2_{eff}(f)\ .
\end{eqnarray}
%
Hence we obtain
\begin{eqnarray}
\frac{A_{pol}(\tau)}{A_{pol}(\tau)_\ast}~&=&~1-\delta A(\it l) \\
\frac{A_{FB}(\mu)}{A_{FB}(\mu)_\ast}~&=&~1-2 \delta A(\it l) \\
\frac{A_{FB}(b)}{A_{FB}(b)_\ast}~&=&~1-\delta A(b)-\delta A(\it l)\ .
\end{eqnarray}

(ii) low energy experiments.  The low energy interaction Hamiltonian is
given by \cite{ng}
%
\begin{equation}
\frac{4G_F}{\sqrt{2}} \left( 1+\frac{M_{Z_2}^2}{M_{Z_1}^2}\theta^2
\right) \left[ J_\mu J^\mu~-~2 \theta J'_\mu J^\mu +
\frac{M_{Z_1}^2}{M_{Z_2}^2} J'_\mu J'^\mu \right]\ .
\end{equation}
Therefore the effective left- and right-handed coupling coefficients for
neutrino scattering are modified to be
%
\begin{equation}
\label{R}
\epsilon_\lambda(q)~=~g^0_\lambda(q)_\ast
  (1+\frac{M_{Z_2}^2}{M_{Z_1}^2}\theta^2-4\theta a^\nu )
    -(\theta-4a^\nu \frac{M_{Z_1}^2}{M_{Z_2}^2})(a^q+\eta(\lambda)b^q)\ ,\\
\end{equation}
where $\eta(\lambda) = 1$ and $-1$ for $\lambda = R$ and $L$
respectively.
%
Hence we obtain
%
\begin{eqnarray}
\frac{g^2_\lambda}{{g^2_\lambda}_\ast}
    =&&\frac{\epsilon_\lambda(u)^2+\epsilon_\lambda(d)^2}
    {g^0_\lambda(u)^2_\ast+g^0_\lambda(d)^2_\ast} \nonumber \\
=&& 1+ 2(\frac{M_{Z_2}^2}{M_{Z_1}^2}\theta^2-4\theta a^\nu)\nonumber \\
 && -2\frac{g^0_\lambda(u)_\ast(a^u+\eta(\lambda) b^u)
        +g^0_\lambda(d)_\ast(a^d+\eta(\lambda) b^d)}
    {g^0_\lambda(u)^2_\ast+g^0_\lambda(d)^2_\ast}
   (\theta-4a^\nu \frac{M_{Z_1}^2}{M_{Z_2}^2})\ ,
\end{eqnarray}
%

For atomic parity violation, the weak charge is given by
%
\begin{eqnarray}
\frac{Q_W}{{Q_W}_\ast}&=&1 + \frac{M_{Z_2}^2}{M_{Z_1}^2}\theta^2
   + \frac{\delta C_1(u)(2Z+N)+  \delta C_1(d)(Z+2N)}
     {g^0_A(e)_\ast g^0_V(u)_\ast (2Z+N)+g^0_A(e)_\ast g^0_V(d)_\ast (Z+2N)}
\ ,\\
\noalign{\vbox{\vskip\abovedisplayskip \hbox{where}
\vskip\belowdisplayskip}}
\label{dC1}
\delta C_1(q)&=&- \theta (g^0_A(e)_\ast a^q+b^e g^0_V(q)_\ast)
   + \frac{M_{Z_1}^2}{M_{Z_2}^2}b^eb^q\ .
\end{eqnarray}
The quantities $g^0_{{R,L}_\ast}$ and $g^0_{{V,A}_\ast}$
in Eqs.~(\ref{R})--(\ref{dC1}) are evaluated at zero energy.


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$\sin^2\theta_W<1/4$, giving $M_{Z_2}<3.2\rm TeV$ with corresponding
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\figure{90\% C.L.\ allowed region in $(M_{Z_2},\theta)$ parameter space.
The dotted lines indicate the constraints from the minimal Higgs structure.
Also included are the FCNC bound of Ref.~\cite{ng}, the lower bound from
the $Z'$--dilepton mass relation, and the upper bound on $\331$ unification.
\label{fig1}}

\figure{Best fit point (cross) and 90\% C.L.\ contour in the $S$--$T$ plane for
the $\331$ model (solid line).
%% The cross represents the mininium chi-squared fit.
For comparison, the model independent
(oblique parameters only) fit to the same data is also shown (dotted
line).  $S=T=0$ corresponds to the reference point $m_t=150 {\rm GeV}$
and $m_H=1000 {\rm GeV}$.  $U$ is always taken as a free parameter.
\label{fig2}}

\end{document}

%-----------  figure 1  -------


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635 237 L
851 197 M 862 230 M 866 232 L
872 237 L
872 197 L
870 235 M 870 197 L
862 197 M 879 197 L
906 237 M 901 235 L
897 230 L
895 220 L
895 214 L
897 205 L
901 199 L
906 197 L
910 197 L
916 199 L
920 205 L
922 214 L
922 220 L
920 230 L
916 235 L
910 237 L
906 237 L
902 235 L
901 233 L
899 230 L
897 220 L
897 214 L
899 205 L
901 201 L
902 199 L
906 197 L
910 197 M 914 199 L
916 201 L
918 205 L
920 214 L
920 220 L
918 230 L
916 233 L
914 235 L
910 237 L
945 237 M 939 235 L
935 230 L
933 220 L
933 214 L
935 205 L
939 199 L
945 197 L
949 197 L
954 199 L
958 205 L
960 214 L
960 220 L
958 230 L
954 235 L
949 237 L
945 237 L
941 235 L
939 233 L
937 230 L
935 220 L
935 214 L
937 205 L
939 201 L
941 199 L
945 197 L
949 197 M 953 199 L
954 201 L
956 205 L
958 214 L
958 220 L
956 230 L
954 233 L
953 235 L
949 237 L
983 237 M 978 235 L
974 230 L
972 220 L
972 214 L
974 205 L
978 199 L
983 197 L
987 197 L
993 199 L
997 205 L
999 214 L
999 220 L
997 230 L
993 235 L
987 237 L
983 237 L
979 235 L
978 233 L
976 230 L
974 220 L
974 214 L
976 205 L
978 201 L
979 199 L
983 197 L
987 197 M 991 199 L
993 201 L
995 205 L
997 214 L
997 220 L
995 230 L
993 233 L
991 235 L
987 237 L
1184 197 M 1195 230 M 1199 232 L
1205 237 L
1205 197 L
1203 235 M 1203 197 L
1195 197 M 1213 197 L
1232 237 M 1228 218 L
1232 222 L
1238 224 L
1243 224 L
1249 222 L
1253 218 L
1255 212 L
1255 208 L
1253 203 L
1249 199 L
1243 197 L
1238 197 L
1232 199 L
1230 201 L
1228 205 L
1228 206 L
1230 208 L
1232 206 L
1230 205 L
1243 224 M 1247 222 L
1251 218 L
1253 212 L
1253 208 L
1251 203 L
1247 199 L
1243 197 L
1232 237 M 1251 237 L
1232 235 M 1242 235 L
1251 237 L
1278 237 M 1272 235 L
1268 230 L
1267 220 L
1267 214 L
1268 205 L
1272 199 L
1278 197 L
1282 197 L
1288 199 L
1292 205 L
1293 214 L
1293 220 L
1292 230 L
1288 235 L
1282 237 L
1278 237 L
1274 235 L
1272 233 L
1270 230 L
1268 220 L
1268 214 L
1270 205 L
1272 201 L
1274 199 L
1278 197 L
1282 197 M 1286 199 L
1288 201 L
1290 205 L
1292 214 L
1292 220 L
1290 230 L
CS M
1288 233 L
1286 235 L
1282 237 L
1317 237 M 1311 235 L
1307 230 L
1305 220 L
1305 214 L
1307 205 L
1311 199 L
1317 197 L
1320 197 L
1326 199 L
1330 205 L
1332 214 L
1332 220 L
1330 230 L
1326 235 L
1320 237 L
1317 237 L
1313 235 L
1311 233 L
1309 230 L
1307 220 L
1307 214 L
1309 205 L
1311 201 L
1313 199 L
1317 197 L
1320 197 M 1324 199 L
1326 201 L
1328 205 L
1330 214 L
1330 220 L
1328 230 L
1326 233 L
1324 235 L
1320 237 L
1517 197 M 1525 230 M 1527 228 L
1525 226 L
1523 228 L
1523 230 L
1525 233 L
1527 235 L
1532 237 L
1540 237 L
1546 235 L
1548 233 L
1550 230 L
1550 226 L
1548 222 L
1542 218 L
1532 214 L
1529 212 L
1525 208 L
1523 203 L
1523 197 L
1540 237 M 1544 235 L
1546 233 L
1548 230 L
1548 226 L
1546 222 L
1540 218 L
1532 214 L
1523 201 M 1525 203 L
1529 203 L
1538 199 L
1544 199 L
1548 201 L
1550 203 L
1529 203 M 1538 197 L
1546 197 L
1548 199 L
1550 203 L
1550 206 L
1573 237 M 1567 235 L
1563 230 L
1561 220 L
1561 214 L
1563 205 L
1567 199 L
1573 197 L
1577 197 L
1582 199 L
1586 205 L
1588 214 L
1588 220 L
1586 230 L
1582 235 L
1577 237 L
1573 237 L
1569 235 L
1567 233 L
1565 230 L
1563 220 L
1563 214 L
1565 205 L
1567 201 L
1569 199 L
1573 197 L
1577 197 M 1581 199 L
1582 201 L
1584 205 L
1586 214 L
1586 220 L
1584 230 L
1582 233 L
1581 235 L
1577 237 L
1611 237 M 1606 235 L
1602 230 L
1600 220 L
1600 214 L
1602 205 L
1606 199 L
1611 197 L
1615 197 L
1621 199 L
1625 205 L
1627 214 L
1627 220 L
1625 230 L
1621 235 L
1615 237 L
1611 237 L
1607 235 L
1606 233 L
1604 230 L
1602 220 L
1602 214 L
1604 205 L
1606 201 L
1607 199 L
1611 197 L
1615 197 M 1619 199 L
1621 201 L
1623 205 L
1625 214 L
1625 220 L
1623 230 L
1621 233 L
1619 235 L
1615 237 L
1650 237 M 1644 235 L
1640 230 L
1638 220 L
1638 214 L
1640 205 L
1644 199 L
1650 197 L
1654 197 L
1659 199 L
1663 205 L
1665 214 L
1665 220 L
1663 230 L
1659 235 L
1654 237 L
1650 237 L
1646 235 L
1644 233 L
1642 230 L
1640 220 L
1640 214 L
1642 205 L
1644 201 L
1646 199 L
1650 197 L
1654 197 M 1658 199 L
1659 201 L
1661 205 L
1663 214 L
1663 220 L
1661 230 L
1659 233 L
1658 235 L
1654 237 L
1850 197 M 1858 230 M 1860 228 L
1858 226 L
1856 228 L
1856 230 L
1858 233 L
1860 235 L
1866 237 L
1873 237 L
1879 235 L
1881 233 L
1883 230 L
1883 226 L
1881 222 L
1875 218 L
1866 214 L
1862 212 L
1858 208 L
1856 203 L
1856 197 L
1873 237 M 1877 235 L
1879 233 L
1881 230 L
1881 226 L
1879 222 L
1873 218 L
1866 214 L
1856 201 M 1858 203 L
1862 203 L
1871 199 L
1877 199 L
1881 201 L
1883 203 L
1862 203 M 1871 197 L
1879 197 L
1881 199 L
1883 203 L
1883 206 L
1898 237 M 1895 218 L
1898 222 L
1904 224 L
1910 224 L
1916 222 L
1920 218 L
1921 212 L
1921 208 L
1920 203 L
1916 199 L
1910 197 L
1904 197 L
1898 199 L
1896 201 L
1895 205 L
1895 206 L
1896 208 L
1898 206 L
1896 205 L
1910 224 M 1914 222 L
1918 218 L
1920 212 L
1920 208 L
1918 203 L
1914 199 L
1910 197 L
1898 237 M 1918 237 L
1898 235 M 1908 235 L
1918 237 L
1945 237 M 1939 235 L
1935 230 L
1933 220 L
1933 214 L
1935 205 L
1939 199 L
1945 197 L
1948 197 L
1954 199 L
1958 205 L
1960 214 L
1960 220 L
1958 230 L
1954 235 L
1948 237 L
1945 237 L
1941 235 L
1939 233 L
1937 230 L
1935 220 L
1935 214 L
1937 205 L
1939 201 L
1941 199 L
1945 197 L
1948 197 M 1952 199 L
1954 201 L
1956 205 L
1958 214 L
1958 220 L
1956 230 L
1954 233 L
1952 235 L
1948 237 L
1983 237 M 1977 235 L
1973 230 L
1972 220 L
1972 214 L
1973 205 L
1977 199 L
1983 197 L
1987 197 L
1993 199 L
1997 205 L
1998 214 L
1998 220 L
1997 230 L
1993 235 L
1987 237 L
1983 237 L
1979 235 L
1977 233 L
1975 230 L
1973 220 L
1973 214 L
1975 205 L
1977 201 L
1979 199 L
CS M
1983 197 L
1987 197 M 1991 199 L
1993 201 L
1995 205 L
1997 214 L
1997 220 L
1995 230 L
1993 233 L
1991 235 L
1987 237 L
2183 197 M 2191 230 M 2193 228 L
2191 226 L
2189 228 L
2189 230 L
2191 233 L
2193 235 L
2199 237 L
2207 237 L
2212 235 L
2214 232 L
2214 226 L
2212 222 L
2207 220 L
2201 220 L
2207 237 M 2210 235 L
2212 232 L
2212 226 L
2210 222 L
2207 220 L
2210 218 L
2214 214 L
2216 210 L
2216 205 L
2214 201 L
2212 199 L
2207 197 L
2199 197 L
2193 199 L
2191 201 L
2189 205 L
2189 206 L
2191 208 L
2193 206 L
2191 205 L
2212 216 M 2214 210 L
2214 205 L
2212 201 L
2210 199 L
2207 197 L
2239 237 M 2233 235 L
2230 230 L
2228 220 L
2228 214 L
2230 205 L
2233 199 L
2239 197 L
2243 197 L
2249 199 L
2253 205 L
2255 214 L
2255 220 L
2253 230 L
2249 235 L
2243 237 L
2239 237 L
2235 235 L
2233 233 L
2232 230 L
2230 220 L
2230 214 L
2232 205 L
2233 201 L
2235 199 L
2239 197 L
2243 197 M 2247 199 L
2249 201 L
2251 205 L
2253 214 L
2253 220 L
2251 230 L
2249 233 L
2247 235 L
2243 237 L
2278 237 M 2272 235 L
2268 230 L
2266 220 L
2266 214 L
2268 205 L
2272 199 L
2278 197 L
2282 197 L
2287 199 L
2291 205 L
2293 214 L
2293 220 L
2291 230 L
2287 235 L
2282 237 L
2278 237 L
2274 235 L
2272 233 L
2270 230 L
2268 220 L
2268 214 L
2270 205 L
2272 201 L
2274 199 L
2278 197 L
2282 197 M 2285 199 L
2287 201 L
2289 205 L
2291 214 L
2291 220 L
2289 230 L
2287 233 L
2285 235 L
2282 237 L
2316 237 M 2311 235 L
2307 230 L
2305 220 L
2305 214 L
2307 205 L
2311 199 L
2316 197 L
2320 197 L
2326 199 L
2330 205 L
2332 214 L
2332 220 L
2330 230 L
2326 235 L
2320 237 L
2316 237 L
2312 235 L
2311 233 L
2309 230 L
2307 220 L
2307 214 L
2309 205 L
2311 201 L
2312 199 L
2316 197 L
2320 197 M 2324 199 L
2326 201 L
2328 205 L
2330 214 L
2330 220 L
2328 230 L
2326 233 L
2324 235 L
2320 237 L
328 2261 M 2261 2261 L
328 2261 M 328 2240 L
394 2261 M 394 2240 L
461 2261 M 461 2240 L
528 2261 M 528 2240 L
594 2261 M 594 2219 L
661 2261 M 661 2240 L
728 2261 M 728 2240 L
794 2261 M 794 2240 L
861 2261 M 861 2240 L
928 2261 M 928 2219 L
994 2261 M 994 2240 L
1061 2261 M 1061 2240 L
1128 2261 M 1128 2240 L
1194 2261 M 1194 2240 L
1261 2261 M 1261 2219 L
1327 2261 M 1327 2240 L
1394 2261 M 1394 2240 L
1461 2261 M 1461 2240 L
1527 2261 M 1527 2240 L
1594 2261 M 1594 2219 L
1661 2261 M 1661 2240 L
1727 2261 M 1727 2240 L
1794 2261 M 1794 2240 L
1861 2261 M 1861 2240 L
1927 2261 M 1927 2219 L
1994 2261 M 1994 2240 L
2061 2261 M 2061 2240 L
2127 2261 M 2127 2240 L
2194 2261 M 2194 2240 L
2261 2261 M 2261 2219 L
328 255 M 328 2261 L
328 255 M 348 255 L
328 355 M 348 355 L
328 455 M 369 455 L
328 556 M 348 556 L
328 656 M 348 656 L
328 756 M 348 756 L
328 857 M 369 857 L
328 957 M 348 957 L
328 1057 M 348 1057 L
328 1157 M 348 1157 L
328 1258 M 369 1258 L
328 1358 M 348 1358 L
328 1458 M 348 1458 L
328 1559 M 348 1559 L
328 1659 M 369 1659 L
328 1759 M 348 1759 L
328 1859 M 348 1859 L
328 1960 M 348 1960 L
328 2060 M 369 2060 L
328 2160 M 348 2160 L
328 2261 M 348 2261 L
125 435 M 133 452 M 168 452 L
193 476 M 187 474 L
183 468 L
181 458 L
181 452 L
183 443 L
187 437 L
193 435 L
197 435 L
202 437 L
206 443 L
208 452 L
208 458 L
206 468 L
202 474 L
197 476 L
193 476 L
189 474 L
187 472 L
185 468 L
183 458 L
183 452 L
185 443 L
187 439 L
189 437 L
193 435 L
197 435 M 200 437 L
202 439 L
204 443 L
206 452 L
206 458 L
204 468 L
202 472 L
200 474 L
197 476 L
224 439 M 222 437 L
224 435 L
225 437 L
224 439 L
250 476 M 245 474 L
241 468 L
239 458 L
239 452 L
241 443 L
245 437 L
250 435 L
254 435 L
260 437 L
264 443 L
266 452 L
266 458 L
264 468 L
260 474 L
254 476 L
250 476 L
247 474 L
245 472 L
243 468 L
241 458 L
241 452 L
243 443 L
245 439 L
247 437 L
250 435 L
254 435 M 258 437 L
260 439 L
262 443 L
264 452 L
264 458 L
262 468 L
260 472 L
258 474 L
254 476 L
295 472 M 295 435 L
297 476 M 297 435 L
297 476 M 275 447 L
306 447 L
289 435 M 302 435 L
125 836 M 133 854 M 168 854 L
193 877 M 187 875 L
183 869 L
181 859 L
181 854 L
183 844 L
187 838 L
193 836 L
197 836 L
202 838 L
206 844 L
208 854 L
208 859 L
206 869 L
202 875 L
197 877 L
193 877 L
189 875 L
CS M
187 873 L
185 869 L
183 859 L
183 854 L
185 844 L
187 840 L
189 838 L
193 836 L
197 836 M 200 838 L
202 840 L
204 844 L
206 854 L
206 859 L
204 869 L
202 873 L
200 875 L
197 877 L
224 840 M 222 838 L
224 836 L
225 838 L
224 840 L
250 877 M 245 875 L
241 869 L
239 859 L
239 854 L
241 844 L
245 838 L
250 836 L
254 836 L
260 838 L
264 844 L
266 854 L
266 859 L
264 869 L
260 875 L
254 877 L
250 877 L
247 875 L
245 873 L
243 869 L
241 859 L
241 854 L
243 844 L
245 840 L
247 838 L
250 836 L
254 836 M 258 838 L
260 840 L
262 844 L
264 854 L
264 859 L
262 869 L
260 873 L
258 875 L
254 877 L
279 869 M 281 867 L
279 865 L
277 867 L
277 869 L
279 873 L
281 875 L
287 877 L
295 877 L
301 875 L
302 873 L
304 869 L
304 865 L
302 861 L
297 857 L
287 854 L
283 852 L
279 848 L
277 842 L
277 836 L
295 877 M 299 875 L
301 873 L
302 869 L
302 865 L
301 861 L
295 857 L
287 854 L
277 840 M 279 842 L
283 842 L
293 838 L
299 838 L
302 840 L
304 842 L
283 842 M 293 836 L
301 836 L
302 838 L
304 842 L
304 846 L
145 1237 M 193 1278 M 187 1276 L
183 1270 L
181 1261 L
181 1255 L
183 1245 L
187 1239 L
193 1237 L
197 1237 L
202 1239 L
206 1245 L
208 1255 L
208 1261 L
206 1270 L
202 1276 L
197 1278 L
193 1278 L
189 1276 L
187 1274 L
185 1270 L
183 1261 L
183 1255 L
185 1245 L
187 1241 L
189 1239 L
193 1237 L
197 1237 M 200 1239 L
202 1241 L
204 1245 L
206 1255 L
206 1261 L
204 1270 L
202 1274 L
200 1276 L
197 1278 L
224 1241 M 222 1239 L
224 1237 L
225 1239 L
224 1241 L
250 1278 M 245 1276 L
241 1270 L
239 1261 L
239 1255 L
241 1245 L
245 1239 L
250 1237 L
254 1237 L
260 1239 L
264 1245 L
266 1255 L
266 1261 L
264 1270 L
260 1276 L
254 1278 L
250 1278 L
247 1276 L
245 1274 L
243 1270 L
241 1261 L
241 1255 L
243 1245 L
245 1241 L
247 1239 L
250 1237 L
254 1237 M 258 1239 L
260 1241 L
262 1245 L
264 1255 L
264 1261 L
262 1270 L
260 1274 L
258 1276 L
254 1278 L
289 1278 M 283 1276 L
279 1270 L
277 1261 L
277 1255 L
279 1245 L
283 1239 L
289 1237 L
293 1237 L
299 1239 L
302 1245 L
304 1255 L
304 1261 L
302 1270 L
299 1276 L
293 1278 L
289 1278 L
285 1276 L
283 1274 L
281 1270 L
279 1261 L
279 1255 L
281 1245 L
283 1241 L
285 1239 L
289 1237 L
293 1237 M 297 1239 L
299 1241 L
301 1245 L
302 1255 L
302 1261 L
301 1270 L
299 1274 L
297 1276 L
293 1278 L
145 1639 M 193 1679 M 187 1677 L
183 1671 L
181 1662 L
181 1656 L
183 1646 L
187 1640 L
193 1639 L
197 1639 L
202 1640 L
206 1646 L
208 1656 L
208 1662 L
206 1671 L
202 1677 L
197 1679 L
193 1679 L
189 1677 L
187 1675 L
185 1671 L
183 1662 L
183 1656 L
185 1646 L
187 1642 L
189 1640 L
193 1639 L
197 1639 M 200 1640 L
202 1642 L
204 1646 L
206 1656 L
206 1662 L
204 1671 L
202 1675 L
200 1677 L
197 1679 L
224 1642 M 222 1640 L
224 1639 L
225 1640 L
224 1642 L
250 1679 M 245 1677 L
241 1671 L
239 1662 L
239 1656 L
241 1646 L
245 1640 L
250 1639 L
254 1639 L
260 1640 L
264 1646 L
266 1656 L
266 1662 L
264 1671 L
260 1677 L
254 1679 L
250 1679 L
247 1677 L
245 1675 L
243 1671 L
241 1662 L
241 1656 L
243 1646 L
245 1642 L
247 1640 L
250 1639 L
254 1639 M 258 1640 L
260 1642 L
262 1646 L
264 1656 L
264 1662 L
262 1671 L
260 1675 L
258 1677 L
254 1679 L
279 1671 M 281 1669 L
279 1667 L
277 1669 L
277 1671 L
279 1675 L
281 1677 L
287 1679 L
295 1679 L
301 1677 L
302 1675 L
304 1671 L
304 1667 L
302 1664 L
297 1660 L
287 1656 L
283 1654 L
279 1650 L
277 1644 L
277 1639 L
295 1679 M 299 1677 L
301 1675 L
302 1671 L
302 1667 L
301 1664 L
295 1660 L
287 1656 L
277 1642 M 279 1644 L
283 1644 L
293 1640 L
299 1640 L
CS M
302 1642 L
304 1644 L
283 1644 M 293 1639 L
301 1639 L
302 1640 L
304 1644 L
304 1648 L
145 2040 M 193 2080 M 187 2078 L
183 2072 L
181 2063 L
181 2057 L
183 2047 L
187 2042 L
193 2040 L
197 2040 L
202 2042 L
206 2047 L
208 2057 L
208 2063 L
206 2072 L
202 2078 L
197 2080 L
193 2080 L
189 2078 L
187 2076 L
185 2072 L
183 2063 L
183 2057 L
185 2047 L
187 2043 L
189 2042 L
193 2040 L
197 2040 M 200 2042 L
202 2043 L
204 2047 L
206 2057 L
206 2063 L
204 2072 L
202 2076 L
200 2078 L
197 2080 L
224 2043 M 222 2042 L
224 2040 L
225 2042 L
224 2043 L
250 2080 M 245 2078 L
241 2072 L
239 2063 L
239 2057 L
241 2047 L
245 2042 L
250 2040 L
254 2040 L
260 2042 L
264 2047 L
266 2057 L
266 2063 L
264 2072 L
260 2078 L
254 2080 L
250 2080 L
247 2078 L
245 2076 L
243 2072 L
241 2063 L
241 2057 L
243 2047 L
245 2043 L
247 2042 L
250 2040 L
254 2040 M 258 2042 L
260 2043 L
262 2047 L
264 2057 L
264 2063 L
262 2072 L
260 2076 L
258 2078 L
254 2080 L
295 2076 M 295 2040 L
297 2080 M 297 2040 L
297 2080 M 275 2051 L
306 2051 L
289 2040 M 302 2040 L
2261 255 M 2261 2261 L
2261 255 M 2240 255 L
2261 355 M 2240 355 L
2261 455 M 2219 455 L
2261 556 M 2240 556 L
2261 656 M 2240 656 L
2261 756 M 2240 756 L
2261 857 M 2219 857 L
2261 957 M 2240 957 L
2261 1057 M 2240 1057 L
2261 1157 M 2240 1157 L
2261 1258 M 2219 1258 L
2261 1358 M 2240 1358 L
2261 1458 M 2240 1458 L
2261 1559 M 2240 1559 L
2261 1659 M 2219 1659 L
2261 1759 M 2240 1759 L
2261 1859 M 2240 1859 L
2261 1960 M 2240 1960 L
2261 2060 M 2219 2060 L
2261 2160 M 2240 2160 L
2261 2261 M 2240 2261 L
CS [] 0 setdash M
CS [6 12] 0 setdash M
796 255 M 808 307 L
821 361 L
834 411 L
848 456 L
861 498 L
874 536 L
888 571 L
901 603 L
914 633 L
928 661 L
941 687 L
954 712 L
968 734 L
981 755 L
994 775 L
1007 794 L
1021 812 L
1034 828 L
1047 844 L
1061 859 L
1074 873 L
1088 886 L
1101 898 L
1114 910 L
1127 922 L
1141 932 L
1154 943 L
1167 952 L
1181 962 L
1194 970 L
1207 979 L
1221 987 L
1234 995 L
1247 1002 L
1261 1009 L
1274 1016 L
1287 1023 L
1301 1029 L
1314 1035 L
1327 1041 L
1341 1046 L
1354 1051 L
1367 1057 L
1381 1061 L
1394 1066 L
1407 1071 L
1421 1075 L
1434 1079 L
1447 1084 L
1461 1088 L
1474 1091 L
1487 1095 L
1501 1099 L
1514 1102 L
1527 1106 L
1541 1109 L
1554 1112 L
1567 1115 L
1581 1118 L
1594 1121 L
1607 1123 L
1621 1126 L
1634 1129 L
1647 1131 L
1661 1134 L
1674 1136 L
1687 1138 L
1701 1141 L
1714 1143 L
1727 1145 L
1741 1147 L
1754 1149 L
1767 1151 L
1781 1153 L
1794 1155 L
1807 1156 L
1821 1158 L
1834 1160 L
1847 1162 L
1861 1163 L
1874 1165 L
1887 1166 L
1901 1168 L
1914 1169 L
1927 1171 L
1941 1172 L
1954 1173 L
1967 1175 L
1981 1176 L
1994 1177 L
2007 1179 L
2021 1180 L
2034 1181 L
2047 1182 L
2061 1183 L
2074 1184 L
2087 1186 L
2101 1187 L
2114 1188 L
2127 1189 L
2141 1190 L
2154 1191 L
2167 1192 L
2181 1192 L
2194 1193 L
2207 1194 L
2221 1195 L
2234 1196 L
2247 1197 L
2260 1198 L
384 2261 M 394 2065 L
408 1895 L
421 1775 L
434 1687 L
448 1621 L
461 1569 L
474 1528 L
488 1495 L
501 1467 L
514 1445 L
528 1425 L
541 1409 L
554 1395 L
568 1383 L
581 1372 L
594 1363 L
608 1355 L
621 1347 L
634 1341 L
648 1335 L
661 1330 L
674 1325 L
688 1321 L
701 1317 L
714 1314 L
728 1310 L
741 1307 L
754 1305 L
768 1302 L
781 1300 L
794 1298 L
808 1296 L
821 1294 L
834 1292 L
848 1291 L
861 1289 L
874 1288 L
888 1287 L
901 1285 L
914 1284 L
928 1283 L
941 1282 L
954 1281 L
968 1280 L
981 1280 L
994 1279 L
1007 1278 L
1021 1277 L
1034 1277 L
1047 1276 L
1061 1275 L
1074 1275 L
1088 1274 L
1101 1274 L
1114 1273 L
1127 1273 L
1141 1272 L
1154 1272 L
1167 1271 L
1181 1271 L
1194 1271 L
1207 1270 L
1221 1270 L
1234 1270 L
1247 1269 L
1261 1269 L
1274 1269 L
1287 1268 L
1301 1268 L
1314 1268 L
1327 1268 L
1341 1267 L
1354 1267 L
1367 1267 L
1381 1267 L
1394 1266 L
1407 1266 L
1421 1266 L
1434 1266 L
1447 1266 L
1461 1265 L
1474 1265 L
1487 1265 L
1501 1265 L
CS M
1514 1265 L
1527 1265 L
1541 1265 L
1554 1264 L
1567 1264 L
1581 1264 L
1594 1264 L
1607 1264 L
1621 1264 L
1634 1264 L
1647 1263 L
1661 1263 L
1674 1263 L
1687 1263 L
1701 1263 L
1714 1263 L
1727 1263 L
1741 1263 L
1754 1263 L
1767 1263 L
1781 1263 L
1794 1262 L
1807 1262 L
1821 1262 L
1834 1262 L
1847 1262 L
1861 1262 L
1874 1262 L
1887 1262 L
1901 1262 L
1914 1262 L
1927 1262 L
1941 1262 L
1954 1262 L
1967 1262 L
1981 1261 L
1994 1261 L
2007 1261 L
2021 1261 L
2034 1261 L
2047 1261 L
2061 1261 L
2074 1261 L
2087 1261 L
2101 1261 L
2114 1261 L
2127 1261 L
2141 1261 L
2154 1261 L
2167 1261 L
2181 1261 L
2194 1261 L
2207 1261 L
2221 1261 L
2234 1261 L
2247 1261 L
2260 1260 L
CS [] 0 setdash M
CS [] 0 setdash M
1062 131 M 1092 172 M 1059 131 L
1094 172 M 1061 131 L
1069 172 M 1065 160 L
1067 172 L
1094 172 L
1059 131 M 1086 131 L
1088 143 L
1084 131 L
1105 132 M 1106 131 L
1105 130 L
1104 131 L
1104 132 L
1105 135 L
1106 136 L
1110 137 L
1114 137 L
1118 136 L
1119 135 L
1120 132 L
1120 130 L
1119 128 L
1116 125 L
1110 123 L
1108 122 L
1105 120 L
1104 116 L
1104 113 L
1114 137 M 1117 136 L
1118 135 L
1119 132 L
1119 130 L
1118 128 L
1114 125 L
1110 123 L
1104 115 M 1105 116 L
1108 116 L
1113 114 L
1117 114 L
1119 115 L
1120 116 L
1108 116 M 1113 113 L
1118 113 L
1119 114 L
1120 116 L
1120 118 L
1164 158 M 1164 131 L
1166 158 M 1166 131 L
1166 152 M 1170 156 L
1176 158 L
1179 158 L
1185 156 L
1187 152 L
1187 131 L
1179 158 M 1183 156 L
1185 152 L
1185 131 L
1187 152 M 1191 156 L
1197 158 L
1201 158 L
1206 156 L
1208 152 L
1208 131 L
1201 158 M 1204 156 L
1206 152 L
1206 131 L
1158 158 M 1166 158 L
1158 131 M 1172 131 L
1179 131 M 1193 131 L
1201 131 M 1214 131 L
1228 154 M 1228 152 L
1226 152 L
1226 154 L
1228 156 L
1231 158 L
1239 158 L
1243 156 L
1245 154 L
1247 150 L
1247 137 L
1249 133 L
1251 131 L
1245 154 M 1245 137 L
1247 133 L
1251 131 L
1253 131 L
1245 150 M 1243 149 L
1231 147 L
1226 145 L
1224 141 L
1224 137 L
1226 133 L
1231 131 L
1237 131 L
1241 133 L
1245 137 L
1231 147 M 1228 145 L
1226 141 L
1226 137 L
1228 133 L
1231 131 L
1282 154 M 1283 158 L
1283 150 L
1282 154 L
1280 156 L
1276 158 L
1268 158 L
1264 156 L
1262 154 L
1262 150 L
1264 149 L
1268 147 L
1278 143 L
1282 141 L
1283 139 L
1262 152 M 1264 150 L
1268 149 L
1278 145 L
1282 143 L
1283 141 L
1283 135 L
1282 133 L
1278 131 L
1270 131 L
1266 133 L
1264 135 L
1262 139 L
1262 131 L
1264 135 L
1314 154 M 1316 158 L
1316 150 L
1314 154 L
1312 156 L
1308 158 L
1301 158 L
1297 156 L
1295 154 L
1295 150 L
1297 149 L
1301 147 L
1310 143 L
1314 141 L
1316 139 L
1295 152 M 1297 150 L
1301 149 L
1310 145 L
1314 143 L
1316 141 L
1316 135 L
1314 133 L
1310 131 L
1303 131 L
1299 133 L
1297 135 L
1295 139 L
1295 131 L
1297 135 L
1374 179 M 1370 175 L
1366 170 L
1362 162 L
1360 152 L
1360 145 L
1362 135 L
1366 127 L
1370 122 L
1374 118 L
1370 175 M 1366 168 L
1364 162 L
1362 152 L
1362 145 L
1364 135 L
1366 129 L
1370 122 L
1412 166 M 1414 160 L
1414 172 L
1412 166 L
1408 170 L
1403 172 L
1399 172 L
1393 170 L
1389 166 L
1387 162 L
1385 156 L
1385 147 L
1387 141 L
1389 137 L
1393 133 L
1399 131 L
1403 131 L
1408 133 L
1412 137 L
1399 172 M 1395 170 L
1391 166 L
1389 162 L
1387 156 L
1387 147 L
1389 141 L
1391 137 L
1395 133 L
1399 131 L
1412 147 M 1412 131 L
1414 147 M 1414 131 L
1406 147 M 1420 147 L
1431 147 M 1455 147 L
1455 150 L
1453 154 L
1451 156 L
1447 158 L
1441 158 L
1435 156 L
1431 152 L
1430 147 L
1430 143 L
1431 137 L
1435 133 L
1441 131 L
1445 131 L
1451 133 L
1455 137 L
1453 147 M 1453 152 L
1451 156 L
1441 158 M 1437 156 L
1433 152 L
1431 147 L
1431 143 L
1433 137 L
1437 133 L
1441 131 L
1466 172 M 1480 131 L
1468 172 M 1480 137 L
1493 172 M 1480 131 L
1462 172 M 1474 172 L
1485 172 M 1497 172 L
1505 179 M 1508 175 L
1512 170 L
1516 162 L
1518 152 L
1518 145 L
1516 135 L
1512 127 L
1508 122 L
1505 118 L
1508 175 M 1512 168 L
1514 162 L
CS M
1516 152 L
1516 145 L
1514 135 L
1512 129 L
1508 122 L
CS [] 0 setdash M
CS [] 0 setdash M
85 755 M 45 785 M 85 752 L
45 787 M 85 754 L
45 762 M 56 758 L
45 760 L
45 787 L
85 752 M 85 779 L
74 781 L
85 777 L
68 801 M 68 836 L
45 874 M 85 841 L
45 876 M 85 843 L
45 851 M 56 846 L
45 849 L
45 876 L
85 841 M 85 868 L
74 870 L
85 866 L
49 892 M 47 890 L
45 892 L
47 894 L
50 894 L
54 892 L
56 890 L
58 942 M 85 942 L
58 944 M 85 944 L
64 944 M 60 948 L
58 953 L
58 957 L
60 963 L
64 965 L
85 965 L
58 957 M 60 961 L
64 963 L
85 963 L
64 965 M 60 969 L
58 975 L
58 978 L
60 984 L
64 986 L
85 986 L
58 978 M 60 982 L
64 984 L
85 984 L
58 936 M 58 944 L
85 936 M 85 950 L
85 957 M 85 971 L
85 978 M 85 992 L
45 1005 M 47 1003 L
49 1005 L
47 1007 L
45 1005 L
58 1005 M 85 1005 L
58 1007 M 85 1007 L
58 1000 M 58 1007 L
85 1000 M 85 1013 L
58 1025 M 85 1046 L
58 1027 M 85 1048 L
58 1048 M 85 1025 L
58 1021 M 58 1032 L
58 1040 M 58 1052 L
85 1021 M 85 1032 L
85 1040 M 85 1052 L
45 1065 M 47 1063 L
49 1065 L
47 1067 L
45 1065 L
58 1065 M 85 1065 L
58 1067 M 85 1067 L
58 1059 M 58 1067 L
85 1059 M 85 1073 L
58 1086 M 85 1086 L
58 1088 M 85 1088 L
64 1088 M 60 1092 L
58 1098 L
58 1102 L
60 1107 L
64 1109 L
85 1109 L
58 1102 M 60 1105 L
64 1107 L
85 1107 L
58 1080 M 58 1088 L
85 1080 M 85 1094 L
85 1102 M 85 1115 L
58 1134 M 60 1130 L
62 1128 L
66 1127 L
70 1127 L
74 1128 L
75 1130 L
77 1134 L
77 1138 L
75 1142 L
74 1144 L
70 1146 L
66 1146 L
62 1144 L
60 1142 L
58 1138 L
58 1134 L
60 1130 M 64 1128 L
72 1128 L
75 1130 L
75 1142 M 72 1144 L
64 1144 L
60 1142 L
62 1144 M 60 1146 L
58 1150 L
60 1150 L
60 1146 L
74 1128 M 75 1127 L
79 1125 L
81 1125 L
85 1127 L
87 1132 L
87 1142 L
89 1148 L
91 1150 L
81 1125 M 83 1127 L
85 1132 L
85 1142 L
87 1148 L
91 1150 L
93 1150 L
97 1148 L
99 1142 L
99 1130 L
97 1125 L
93 1123 L
91 1123 L
87 1125 L
85 1130 L
62 1196 M 64 1196 L
64 1194 L
62 1194 L
60 1196 L
58 1200 L
58 1207 L
60 1211 L
62 1213 L
66 1215 L
79 1215 L
83 1217 L
85 1219 L
62 1213 M 79 1213 L
83 1215 L
85 1219 L
85 1221 L
66 1213 M 68 1211 L
70 1200 L
72 1194 L
75 1192 L
79 1192 L
83 1194 L
85 1200 L
85 1205 L
83 1209 L
79 1213 L
70 1200 M 72 1196 L
75 1194 L
79 1194 L
83 1196 L
85 1200 L
58 1234 M 85 1234 L
58 1236 M 85 1236 L
64 1236 M 60 1240 L
58 1246 L
58 1250 L
60 1255 L
64 1257 L
85 1257 L
58 1250 M 60 1254 L
64 1255 L
85 1255 L
58 1228 M 58 1236 L
85 1228 M 85 1242 L
85 1250 M 85 1263 L
58 1282 M 60 1279 L
62 1277 L
66 1275 L
70 1275 L
74 1277 L
75 1279 L
77 1282 L
77 1286 L
75 1290 L
74 1292 L
70 1294 L
66 1294 L
62 1292 L
60 1290 L
58 1286 L
58 1282 L
60 1279 M 64 1277 L
72 1277 L
75 1279 L
75 1290 M 72 1292 L
64 1292 L
60 1290 L
62 1292 M 60 1294 L
58 1298 L
60 1298 L
60 1294 L
74 1277 M 75 1275 L
79 1273 L
81 1273 L
85 1275 L
87 1280 L
87 1290 L
89 1296 L
91 1298 L
81 1273 M 83 1275 L
85 1280 L
85 1290 L
87 1296 L
91 1298 L
93 1298 L
97 1296 L
99 1290 L
99 1279 L
97 1273 L
93 1271 L
91 1271 L
87 1273 L
85 1279 L
45 1313 M 85 1313 L
45 1315 M 85 1315 L
45 1307 M 45 1315 L
85 1307 M 85 1321 L
70 1332 M 70 1355 L
66 1355 L
62 1354 L
60 1352 L
58 1348 L
58 1342 L
60 1336 L
64 1332 L
70 1330 L
74 1330 L
79 1332 L
83 1336 L
85 1342 L
85 1346 L
83 1352 L
79 1355 L
70 1354 M 64 1354 L
60 1352 L
58 1342 M 60 1338 L
64 1334 L
70 1332 L
74 1332 L
79 1334 L
83 1338 L
85 1342 L
45 1413 M 47 1407 L
52 1404 L
56 1402 L
62 1400 L
72 1398 L
79 1398 L
83 1400 L
85 1404 L
85 1407 L
83 1413 L
77 1417 L
74 1419 L
68 1421 L
58 1423 L
50 1423 L
47 1421 L
45 1417 L
45 1413 L
47 1409 L
52 1405 L
56 1404 L
62 1402 L
72 1400 L
79 1400 L
83 1402 L
85 1404 L
85 1407 M 83 1411 L
77 1415 L
74 1417 L
68 1419 L
58 1421 L
50 1421 L
47 1419 L
45 1417 L
64 1402 M 64 1419 L
37 1480 M 41 1477 L
47 1473 L
54 1469 L
64 1467 L
72 1467 L
81 1469 L
CS M
89 1473 L
95 1477 L
99 1480 L
41 1477 M 49 1473 L
54 1471 L
64 1469 L
72 1469 L
81 1471 L
87 1473 L
95 1477 L
58 1496 M 85 1496 L
58 1498 M 85 1498 L
70 1498 M 64 1500 L
60 1504 L
58 1507 L
58 1513 L
60 1515 L
62 1515 L
64 1513 L
62 1511 L
60 1513 L
58 1490 M 58 1498 L
85 1490 M 85 1504 L
62 1529 M 64 1529 L
64 1527 L
62 1527 L
60 1529 L
58 1532 L
58 1540 L
60 1544 L
62 1546 L
66 1548 L
79 1548 L
83 1550 L
85 1552 L
62 1546 M 79 1546 L
83 1548 L
85 1552 L
85 1554 L
66 1546 M 68 1544 L
70 1532 L
72 1527 L
75 1525 L
79 1525 L
83 1527 L
85 1532 L
85 1538 L
83 1542 L
79 1546 L
70 1532 M 72 1529 L
75 1527 L
79 1527 L
83 1529 L
85 1532 L
45 1586 M 85 1586 L
45 1588 M 85 1588 L
64 1586 M 60 1582 L
58 1579 L
58 1575 L
60 1569 L
64 1565 L
70 1563 L
74 1563 L
79 1565 L
83 1569 L
85 1575 L
85 1579 L
83 1582 L
79 1586 L
58 1575 M 60 1571 L
64 1567 L
70 1565 L
74 1565 L
79 1567 L
83 1571 L
85 1575 L
45 1580 M 45 1588 L
85 1586 M 85 1594 L
45 1607 M 47 1606 L
49 1607 L
47 1609 L
45 1607 L
58 1607 M 85 1607 L
58 1609 M 85 1609 L
58 1602 M 58 1609 L
85 1602 M 85 1615 L
62 1629 M 64 1629 L
64 1627 L
62 1627 L
60 1629 L
58 1632 L
58 1640 L
60 1644 L
62 1646 L
66 1648 L
79 1648 L
83 1650 L
85 1652 L
62 1646 M 79 1646 L
83 1648 L
85 1652 L
85 1654 L
66 1646 M 68 1644 L
70 1632 L
72 1627 L
75 1625 L
79 1625 L
83 1627 L
85 1632 L
85 1638 L
83 1642 L
79 1646 L
70 1632 M 72 1629 L
75 1627 L
79 1627 L
83 1629 L
85 1632 L
58 1667 M 85 1667 L
58 1669 M 85 1669 L
64 1669 M 60 1673 L
58 1679 L
58 1683 L
60 1688 L
64 1690 L
85 1690 L
58 1683 M 60 1686 L
64 1688 L
85 1688 L
58 1661 M 58 1669 L
85 1661 M 85 1675 L
85 1683 M 85 1696 L
62 1725 M 58 1727 L
66 1727 L
62 1725 L
60 1723 L
58 1719 L
58 1711 L
60 1707 L
62 1706 L
66 1706 L
68 1707 L
70 1711 L
74 1721 L
75 1725 L
77 1727 L
64 1706 M 66 1707 L
68 1711 L
72 1721 L
74 1725 L
75 1727 L
81 1727 L
83 1725 L
85 1721 L
85 1713 L
83 1709 L
81 1707 L
77 1706 L
85 1706 L
81 1707 L
37 1738 M 41 1742 L
47 1746 L
54 1750 L
64 1752 L
72 1752 L
81 1750 L
89 1746 L
95 1742 L
99 1738 L
41 1742 M 49 1746 L
54 1748 L
64 1750 L
72 1750 L
81 1748 L
87 1746 L
95 1742 L
CS [] 0 setdash M
CS [32 24] 0 setdash M
559 1258 M 560 908 L
563 557 L
568 255 L
559 1258 M 560 1608 L
563 1958 L
568 2261 L
CS [] 0 setdash M
568 2060 M 794 2060 L
730 2073 L
784 2060 L
730 2047 L
794 2060 L
601 1960 M CS [] 0 setdash M
611 2000 M 611 1960 L
612 2000 M 612 1960 L
624 1989 M 624 1973 L
605 2000 M 636 2000 L
636 1989 L
634 2000 L
612 1981 M 624 1981 L
605 1960 M 618 1960 L
672 1994 M 674 1989 L
674 2000 L
672 1994 L
668 1998 L
662 2000 L
659 2000 L
653 1998 L
649 1994 L
647 1990 L
645 1985 L
645 1975 L
647 1969 L
649 1965 L
653 1962 L
659 1960 L
662 1960 L
668 1962 L
672 1965 L
674 1969 L
659 2000 M 655 1998 L
651 1994 L
649 1990 L
647 1985 L
647 1975 L
649 1969 L
651 1965 L
655 1962 L
659 1960 L
689 2000 M 689 1960 L
691 2000 M 715 1963 L
691 1996 M 715 1960 L
715 2000 M 715 1960 L
684 2000 M 691 2000 L
709 2000 M 720 2000 L
684 1960 M 695 1960 L
757 1994 M 759 1989 L
759 2000 L
757 1994 L
753 1998 L
747 2000 L
743 2000 L
738 1998 L
734 1994 L
732 1990 L
730 1985 L
730 1975 L
732 1969 L
734 1965 L
738 1962 L
743 1960 L
747 1960 L
753 1962 L
757 1965 L
759 1969 L
743 2000 M 740 1998 L
736 1994 L
734 1990 L
732 1985 L
732 1975 L
734 1969 L
736 1965 L
740 1962 L
743 1960 L
805 2000 M 805 1960 L
807 2000 M 807 1960 L
799 2000 M 807 2000 L
799 1960 M 813 1960 L
826 2000 M 824 1998 L
826 1996 L
828 1998 L
826 2000 L
826 1987 M 826 1960 L
828 1987 M 828 1960 L
820 1987 M 828 1987 L
820 1960 M 834 1960 L
847 1987 M 847 1960 L
849 1987 M 849 1960 L
849 1981 M 853 1985 L
859 1987 L
863 1987 L
868 1985 L
870 1981 L
870 1960 L
863 1987 M 867 1985 L
868 1981 L
868 1960 L
870 1981 M 874 1985 L
880 1987 L
884 1987 L
890 1985 L
892 1981 L
892 1960 L
884 1987 M 888 1985 L
890 1981 L
890 1960 L
841 1987 M 849 1987 L
841 1960 M 855 1960 L
863 1960 M 876 1960 L
884 1960 M 897 1960 L
911 2000 M 909 1998 L
911 1996 L
913 1998 L
911 2000 L
911 1987 M 911 1960 L
913 1987 M 913 1960 L
905 1987 M 913 1987 L
CS M
905 1960 M 918 1960 L
932 2000 M 932 1967 L
934 1962 L
938 1960 L
942 1960 L
945 1962 L
947 1965 L
934 2000 M 934 1967 L
936 1962 L
938 1960 L
926 1987 M 942 1987 L
CS [] 0 setdash M
CS [32 24] 0 setdash M
1727 255 M 1727 2261 L
CS [] 0 setdash M
1727 656 M 1527 656 L
1592 643 L
1537 656 L
1592 669 L
1527 656 L
1447 556 M CS [] 0 setdash M
1467 582 M 1461 581 L
1457 577 L
1455 573 L
1453 567 L
1453 561 L
1455 557 L
1461 556 L
1465 556 L
1469 557 L
1474 563 L
1478 569 L
1482 577 L
1484 582 L
1467 582 M 1463 581 L
1459 577 L
1457 573 L
1455 567 L
1455 561 L
1457 557 L
1461 556 L
1467 582 M 1470 582 L
1474 581 L
1476 577 L
1480 561 L
1482 557 L
1484 556 L
1470 582 M 1472 581 L
1474 577 L
1478 561 L
1480 557 L
1484 556 L
1486 556 L
1495 561 M 1510 537 L
1496 561 M 1511 537 L
1511 561 M 1495 537 L
1493 561 M 1500 561 L
1507 561 M 1514 561 L
1493 537 M 1500 537 L
1507 537 M 1514 537 L
1584 590 M 1553 573 L
1584 556 L
1630 588 M 1632 586 L
1630 584 L
1628 586 L
1628 588 L
1630 592 L
1632 594 L
1638 596 L
1645 596 L
1651 594 L
1653 592 L
1655 588 L
1655 584 L
1653 581 L
1647 577 L
1638 573 L
1634 571 L
1630 567 L
1628 561 L
1628 556 L
1645 596 M 1649 594 L
1651 592 L
1653 588 L
1653 584 L
1651 581 L
1645 577 L
1638 573 L
1628 559 M 1630 561 L
1634 561 L
1644 557 L
1649 557 L
1653 559 L
1655 561 L
1634 561 M 1644 556 L
1651 556 L
1653 557 L
1655 561 L
1655 565 L
1678 581 M 1671 556 L
1678 581 M 1672 556 L
1690 581 M 1690 556 L
1690 581 M 1692 556 L
1665 577 M 1669 581 L
1674 582 L
1699 582 L
1665 577 M 1669 579 L
1674 581 L
1699 581 L
CS [] 0 setdash M
CS [32 24] 0 setdash M
1194 556 M 1194 1960 L
CS [] 0 setdash M
1194 1759 M 1394 1759 L
1330 1772 L
1384 1759 L
1330 1746 L
1394 1759 L
1227 1659 M CS [] 0 setdash M
1236 1699 M 1228 1659 L
1238 1699 M 1243 1665 L
1236 1699 M 1242 1659 L
1263 1699 M 1242 1659 L
1263 1699 M 1255 1659 L
1265 1699 M 1257 1659 L
1231 1699 M 1238 1699 L
1263 1699 M 1271 1699 L
1222 1659 M 1234 1659 L
1249 1659 M 1263 1659 L
1279 1665 M 1284 1652 L
1282 1640 L
1280 1665 M 1285 1652 L
1283 1640 L
1296 1665 M 1285 1652 L
1276 1665 M 1283 1665 L
1291 1665 M 1298 1665 L
1278 1640 M 1286 1640 L
1338 1693 M 1369 1676 L
1338 1659 L
1415 1691 M 1417 1690 L
1415 1688 L
1413 1690 L
1413 1691 L
1415 1695 L
1417 1697 L
1423 1699 L
1431 1699 L
1436 1697 L
1438 1693 L
1438 1688 L
1436 1684 L
1431 1682 L
1425 1682 L
1431 1699 M 1434 1697 L
1436 1693 L
1436 1688 L
1434 1684 L
1431 1682 L
1434 1680 L
1438 1676 L
1440 1672 L
1440 1666 L
1438 1663 L
1436 1661 L
1431 1659 L
1423 1659 L
1417 1661 L
1415 1663 L
1413 1666 L
1413 1668 L
1415 1670 L
1417 1668 L
1415 1666 L
1436 1678 M 1438 1672 L
1438 1666 L
1436 1663 L
1434 1661 L
1431 1659 L
1463 1699 M 1458 1697 L
1454 1691 L
1452 1682 L
1452 1676 L
1454 1666 L
1458 1661 L
1463 1659 L
1467 1659 L
1473 1661 L
1477 1666 L
1479 1676 L
1479 1682 L
1477 1691 L
1473 1697 L
1467 1699 L
1463 1699 L
1459 1697 L
1458 1695 L
1456 1691 L
1454 1682 L
1454 1676 L
1456 1666 L
1458 1663 L
1459 1661 L
1463 1659 L
1467 1659 M 1471 1661 L
1473 1663 L
1475 1666 L
1477 1676 L
1477 1682 L
1475 1691 L
1473 1695 L
1471 1697 L
1467 1699 L
1502 1699 M 1496 1697 L
1492 1691 L
1490 1682 L
1490 1676 L
1492 1666 L
1496 1661 L
1502 1659 L
1506 1659 L
1511 1661 L
1515 1666 L
1517 1676 L
1517 1682 L
1515 1691 L
1511 1697 L
1506 1699 L
1502 1699 L
1498 1697 L
1496 1695 L
1494 1691 L
1492 1682 L
1492 1676 L
1494 1666 L
1496 1663 L
1498 1661 L
1502 1659 L
1506 1659 M 1510 1661 L
1511 1663 L
1513 1666 L
1515 1676 L
1515 1682 L
1513 1691 L
1511 1695 L
1510 1697 L
1506 1699 L
1587 1693 M 1589 1688 L
1589 1699 L
1587 1693 L
1583 1697 L
1577 1699 L
1573 1699 L
1567 1697 L
1563 1693 L
1562 1690 L
1560 1684 L
1560 1674 L
1562 1668 L
1563 1665 L
1567 1661 L
1573 1659 L
1577 1659 L
1583 1661 L
1587 1665 L
1573 1699 M 1569 1697 L
1565 1693 L
1563 1690 L
1562 1684 L
1562 1674 L
1563 1668 L
1565 1665 L
1569 1661 L
1573 1659 L
1587 1674 M 1587 1659 L
1589 1674 M 1589 1659 L
1581 1674 M 1594 1674 L
1606 1674 M 1629 1674 L
1629 1678 L
1627 1682 L
1625 1684 L
1621 1686 L
1615 1686 L
1610 1684 L
1606 1680 L
1604 1674 L
1604 1670 L
1606 1665 L
1610 1661 L
1615 1659 L
1619 1659 L
1625 1661 L
1629 1665 L
1627 1674 M 1627 1680 L
1625 1684 L
1615 1686 M 1612 1684 L
1608 1680 L
1606 1674 L
1606 1670 L
1608 1665 L
1612 1661 L
1615 1659 L
1640 1699 M 1654 1659 L
1642 1699 M 1654 1665 L
1667 1699 M 1654 1659 L
1637 1699 M 1648 1699 L
1660 1699 M 1671 1699 L
CS [] 0 setdash M
2159 1229 M 2182 1229 L
2221 1229 L
CS M
2260 1229 L
844 1237 M 880 1236 L
919 1235 L
959 1235 L
998 1234 L
1038 1234 L
1077 1233 L
1117 1233 L
1156 1232 L
1195 1232 L
1235 1232 L
1274 1232 L
1314 1231 L
1353 1231 L
1393 1231 L
1432 1231 L
1472 1231 L
1511 1231 L
1551 1230 L
1590 1230 L
1629 1230 L
1669 1230 L
1708 1230 L
1748 1230 L
1787 1230 L
1827 1230 L
1866 1230 L
1905 1230 L
1945 1229 L
1984 1229 L
2024 1229 L
2063 1229 L
2103 1229 L
2142 1229 L
2159 1229 M 2142 1229 L
692 1245 M 722 1243 L
762 1241 L
801 1239 L
840 1237 L
844 1237 M 840 1237 L
629 1254 M 643 1251 L
683 1246 L
692 1245 M 683 1246 L
593 1262 M 604 1259 L
629 1254 M 604 1259 L
593 1262 M 569 1270 L
555 1278 M 564 1272 L
569 1270 M 564 1272 L
555 1278 M 546 1286 L
539 1294 L
536 1303 L
535 1311 L
539 1319 L
546 1327 L
559 1335 L
564 1338 L
587 1344 L
1935 1344 M 1945 1343 L
1984 1342 L
2024 1342 L
2063 1341 L
2103 1340 L
2142 1339 L
2182 1338 L
2221 1337 L
2260 1337 L
587 1344 M 604 1347 L
643 1351 L
657 1352 L
1504 1352 M 1511 1352 L
1551 1351 L
1590 1350 L
1629 1349 L
1669 1349 L
1708 1348 L
1748 1347 L
1787 1346 L
1827 1346 L
1866 1345 L
1905 1344 L
1935 1344 M 1905 1344 L
657 1352 M 683 1353 L
722 1354 L
762 1355 L
801 1356 L
840 1356 L
880 1356 L
919 1357 L
959 1357 L
998 1356 L
1038 1356 L
1077 1356 L
1117 1356 L
1156 1356 L
1195 1355 L
1235 1355 L
1274 1355 L
1314 1354 L
1353 1354 L
1393 1353 L
1432 1353 L
1472 1352 L
1504 1352 M 1472 1352 L
stroke
grestore
showpage
end

%

%-----------  figure 2 ---------------
%
%!PS-Adobe-2.0 EPSF-2.0
%%Creator: SM
%%BoundingBox: 18 144 593 718
%%DocumentFonts: Helvetica
%%EndComments
 20 dict begin
72 300 div dup scale
1 setlinejoin 0 setlinecap
/Helvetica findfont 55 scalefont setfont
/B { stroke newpath } def /F { moveto 0 setlinecap} def
/C { CS M 1 1 3 { pop 3 1 roll 255 div } for SET_COLOUR } def
/CS { currentpoint stroke } def
/CF { currentpoint fill } def
/L { lineto } def /M { moveto } def
/P { moveto 0 1 rlineto stroke } def
/T { 1 setlinecap show } def
errordict /nocurrentpoint { pop 0 0 M currentpoint } put
/SET_COLOUR { pop pop pop } def
 80 600 translate
gsave
CS [] 0 setdash M
CS M 2 setlinewidth
/P { moveto 0 2.05 rlineto stroke } def
 0 0 0 C
CS [] 0 setdash M
255 255 M 2261 255 L
255 255 M 255 275 L
305 255 M 305 275 L
355 255 M 355 275 L
405 255 M 405 275 L
455 255 M 455 275 L
506 255 M 506 296 L
556 255 M 556 275 L
606 255 M 606 275 L
656 255 M 656 275 L
706 255 M 706 275 L
756 255 M 756 275 L
806 255 M 806 275 L
857 255 M 857 275 L
907 255 M 907 275 L
957 255 M 957 275 L
1007 255 M 1007 296 L
1057 255 M 1057 275 L
1107 255 M 1107 275 L
1157 255 M 1157 275 L
1208 255 M 1208 275 L
1258 255 M 1258 275 L
1308 255 M 1308 275 L
1358 255 M 1358 275 L
1408 255 M 1408 275 L
1458 255 M 1458 275 L
1508 255 M 1508 296 L
1559 255 M 1559 275 L
1609 255 M 1609 275 L
1659 255 M 1659 275 L
1709 255 M 1709 275 L
1759 255 M 1759 275 L
1809 255 M 1809 275 L
1859 255 M 1859 275 L
1910 255 M 1910 275 L
1960 255 M 1960 275 L
2010 255 M 2010 296 L
2060 255 M 2060 275 L
2110 255 M 2110 275 L
2160 255 M 2160 275 L
2210 255 M 2210 275 L
2261 255 M 2261 275 L
461 197 M 469 214 M 503 214 L
519 230 M 521 228 L
519 226 L
517 228 L
517 230 L
519 233 L
521 235 L
527 237 L
534 237 L
540 235 L
542 233 L
544 230 L
544 226 L
542 222 L
536 218 L
527 214 L
523 212 L
519 208 L
517 203 L
517 197 L
534 237 M 538 235 L
540 233 L
542 230 L
542 226 L
540 222 L
534 218 L
527 214 L
517 201 M 519 203 L
523 203 L
532 199 L
538 199 L
542 201 L
544 203 L
523 203 M 532 197 L
540 197 L
542 199 L
544 203 L
544 206 L
963 197 M 970 214 M 1005 214 L
1024 230 M 1028 232 L
1034 237 L
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1024 197 M 1042 197 L
1489 197 M 1506 237 M 1501 235 L
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1506 197 L
1510 197 L
1516 199 L
1520 205 L
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1522 220 L
1520 230 L
1516 235 L
1510 237 L
1506 237 L
1503 235 L
1501 233 L
1499 230 L
1497 220 L
1497 214 L
1499 205 L
1501 201 L
1503 199 L
1506 197 L
1510 197 M 1514 199 L
1516 201 L
1518 205 L
1520 214 L
1520 220 L
1518 230 L
1516 233 L
1514 235 L
1510 237 L
1991 197 M 2002 230 M 2006 232 L
2012 237 L
2012 197 L
2010 235 M 2010 197 L
2002 197 M 2019 197 L
255 2261 M 2261 2261 L
255 2261 M 255 2240 L
305 2261 M 305 2240 L
355 2261 M 355 2240 L
405 2261 M 405 2240 L
455 2261 M 455 2240 L
506 2261 M 506 2219 L
556 2261 M 556 2240 L
606 2261 M 606 2240 L
656 2261 M 656 2240 L
706 2261 M 706 2240 L
756 2261 M 756 2240 L
806 2261 M 806 2240 L
857 2261 M 857 2240 L
907 2261 M 907 2240 L
957 2261 M 957 2240 L
1007 2261 M 1007 2219 L
1057 2261 M 1057 2240 L
1107 2261 M 1107 2240 L
1157 2261 M 1157 2240 L
1208 2261 M 1208 2240 L
1258 2261 M 1258 2240 L
1308 2261 M 1308 2240 L
1358 2261 M 1358 2240 L
1408 2261 M 1408 2240 L
1458 2261 M 1458 2240 L
1508 2261 M 1508 2219 L
1559 2261 M 1559 2240 L
1609 2261 M 1609 2240 L
1659 2261 M 1659 2240 L
1709 2261 M 1709 2240 L
1759 2261 M 1759 2240 L
1809 2261 M 1809 2240 L
1859 2261 M 1859 2240 L
1910 2261 M 1910 2240 L
1960 2261 M 1960 2240 L
2010 2261 M 2010 2219 L
2060 2261 M 2060 2240 L
2110 2261 M 2110 2240 L
2160 2261 M 2160 2240 L
2210 2261 M 2210 2240 L
2261 2261 M 2261 2240 L
255 255 M 255 2261 L
255 288 M 275 288 L
255 355 M 275 355 L
255 422 M 296 422 L
255 489 M 275 489 L
255 556 M 275 556 L
255 623 M 275 623 L
255 689 M 275 689 L
255 756 M 296 756 L
255 823 M 275 823 L
255 890 M 275 890 L
255 957 M 275 957 L
255 1024 M 275 1024 L
255 1090 M 296 1090 L
255 1157 M 275 1157 L
255 1224 M 275 1224 L
255 1291 M 275 1291 L
255 1358 M 275 1358 L
255 1425 M 296 1425 L
255 1492 M 275 1492 L
255 1559 M 275 1559 L
255 1625 M 275 1625 L
255 1692 M 275 1692 L
255 1759 M 296 1759 L
255 1826 M 275 1826 L
255 1893 M 275 1893 L
255 1960 M 275 1960 L
255 2027 M 275 2027 L
255 2093 M 296 2093 L
255 2160 M 275 2160 L
255 2227 M 275 2227 L
149 402 M 156 419 M 191 419 L
222 438 M 222 402 L
224 442 M 224 402 L
224 442 M 203 413 L
233 413 L
216 402 M 230 402 L
149 736 M 156 753 M 191 753 L
206 769 M 208 767 L
206 765 L
205 767 L
205 769 L
206 773 L
208 775 L
214 776 L
222 776 L
228 775 L
230 771 L
230 765 L
228 761 L
222 759 L
216 759 L
222 776 M 226 775 L
228 771 L
228 765 L
226 761 L
222 759 L
226 757 L
230 753 L
231 749 L
231 744 L
230 740 L
228 738 L
222 736 L
214 736 L
208 738 L
206 740 L
205 744 L
205 746 L
206 748 L
208 746 L
206 744 L
228 755 M 230 749 L
230 744 L
228 740 L
226 738 L
222 736 L
149 1070 M 156 1088 M 191 1088 L
206 1103 M 208 1101 L
206 1099 L
205 1101 L
205 1103 L
206 1107 L
208 1109 L
214 1111 L
222 1111 L
228 1109 L
230 1107 L
231 1103 L
231 1099 L
230 1095 L
224 1091 L
214 1088 L
210 1086 L
206 1082 L
205 1076 L
205 1070 L
222 1111 M 226 1109 L
228 1107 L
230 1103 L
230 1099 L
228 1095 L
222 1091 L
214 1088 L
205 1074 M 206 1076 L
210 1076 L
220 1072 L
226 1072 L
230 1074 L
231 1076 L
210 1076 M 220 1070 L
228 1070 L
230 1072 L
231 1076 L
231 1080 L
149 1405 M 156 1422 M 191 1422 L
210 1437 M 214 1439 L
220 1445 L
220 1405 L
218 1443 M 218 1405 L
210 1405 M 228 1405 L
199 1739 M 216 1779 M 210 1777 L
206 1772 L
205 1762 L
205 1756 L
206 1746 L
210 1741 L
216 1739 L
220 1739 L
226 1741 L
230 1746 L
232 1756 L
232 1762 L
CS M
230 1772 L
226 1777 L
220 1779 L
216 1779 L
212 1777 L
210 1775 L
208 1772 L
206 1762 L
206 1756 L
208 1746 L
210 1743 L
212 1741 L
216 1739 L
220 1739 M 224 1741 L
226 1743 L
228 1746 L
230 1756 L
230 1762 L
228 1772 L
226 1775 L
224 1777 L
220 1779 L
199 2073 M 210 2106 M 214 2108 L
220 2114 L
220 2073 L
218 2112 M 218 2073 L
210 2073 M 228 2073 L
2261 255 M 2261 2261 L
2261 288 M 2240 288 L
2261 355 M 2240 355 L
2261 422 M 2219 422 L
2261 489 M 2240 489 L
2261 556 M 2240 556 L
2261 623 M 2240 623 L
2261 689 M 2240 689 L
2261 756 M 2219 756 L
2261 823 M 2240 823 L
2261 890 M 2240 890 L
2261 957 M 2240 957 L
2261 1024 M 2240 1024 L
2261 1090 M 2219 1090 L
2261 1157 M 2240 1157 L
2261 1224 M 2240 1224 L
2261 1291 M 2240 1291 L
2261 1358 M 2240 1358 L
2261 1425 M 2219 1425 L
2261 1492 M 2240 1492 L
2261 1559 M 2240 1559 L
2261 1625 M 2240 1625 L
2261 1692 M 2240 1692 L
2261 1759 M 2219 1759 L
2261 1826 M 2240 1826 L
2261 1893 M 2240 1893 L
2261 1960 M 2240 1960 L
2261 2027 M 2240 2027 L
2261 2093 M 2219 2093 L
2261 2160 M 2240 2160 L
2261 2227 M 2240 2227 L
CS [] 0 setdash M
600 422 M 612 419 L
626 422 L
600 422 M 598 440 L
626 422 M 627 422 L
642 430 L
657 439 L
659 440 L
598 440 M 599 459 L
659 440 M 673 450 L
686 459 L
599 459 M 605 478 L
686 459 M 688 460 L
703 472 L
710 478 L
605 478 M 610 496 L
710 478 M 718 485 L
733 496 L
610 496 M 612 500 L
618 515 L
733 496 M 733 497 L
749 510 L
754 515 L
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754 515 M 764 523 L
775 533 L
625 533 M 627 537 L
633 552 L
775 533 M 779 537 L
794 550 L
796 552 L
633 552 M 642 570 L
796 552 M 809 564 L
816 570 L
642 570 M 642 572 L
650 589 L
816 570 M 825 579 L
836 589 L
650 589 M 657 606 L
658 608 L
836 589 M 840 593 L
855 607 L
855 608 L
658 608 M 667 626 L
855 608 M 870 622 L
875 626 L
667 626 M 673 639 L
675 645 L
875 626 M 885 637 L
893 645 L
675 645 M 684 663 L
893 645 M 901 652 L
912 663 L
684 663 M 688 672 L
692 682 L
912 663 M 916 667 L
931 682 L
931 682 L
692 682 M 701 700 L
931 682 M 946 697 L
949 700 L
701 700 M 703 706 L
709 719 L
949 700 M 961 713 L
967 719 L
709 719 M 717 738 L
967 719 M 976 728 L
985 738 L
717 738 M 718 740 L
726 756 L
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1003 756 L
726 756 M 733 774 L
734 775 L
1003 756 M 1007 760 L
1021 775 L
734 775 M 742 793 L
1021 775 M 1022 776 L
1037 792 L
1039 793 L
742 793 M 749 810 L
750 812 L
1039 793 M 1052 808 L
1056 812 L
750 812 M 757 830 L
1056 812 M 1068 824 L
1073 830 L
757 830 M 764 846 L
765 849 L
1073 830 M 1083 841 L
1090 849 L
765 849 M 772 868 L
1090 849 M 1098 857 L
1107 868 L
772 868 M 779 885 L
780 886 L
1107 868 M 1113 874 L
1124 886 L
780 886 M 787 905 L
1124 886 M 1128 891 L
1141 905 L
787 905 M 794 923 L
1141 905 M 1144 908 L
1158 923 L
794 923 M 794 925 L
800 942 L
1158 923 M 1159 925 L
1174 942 L
1174 942 L
800 942 M 807 960 L
1174 942 M 1189 959 L
1190 960 L
807 960 M 809 968 L
813 979 L
1190 960 M 1204 977 L
1206 979 L
813 979 M 819 998 L
1206 979 M 1220 994 L
1222 998 L
819 998 M 825 1015 L
825 1016 L
1222 998 M 1235 1012 L
1238 1016 L
825 1016 M 831 1035 L
1238 1016 M 1250 1030 L
1254 1035 L
831 1035 M 836 1053 L
1254 1035 M 1265 1048 L
1270 1053 L
836 1053 M 840 1068 L
841 1072 L
1270 1053 M 1280 1066 L
1285 1072 L
841 1072 M 846 1090 L
1285 1072 M 1296 1085 L
1300 1090 L
846 1090 M 850 1109 L
1300 1090 M 1311 1103 L
1316 1109 L
850 1109 M 854 1128 L
1316 1109 M 1326 1122 L
1331 1128 L
854 1128 M 855 1131 L
858 1146 L
1331 1128 M 1341 1141 L
1345 1146 L
858 1146 M 862 1165 L
1345 1146 M 1356 1160 L
1360 1165 L
862 1165 M 865 1183 L
1360 1165 M 1372 1179 L
1375 1183 L
865 1183 M 868 1202 L
1375 1183 M 1387 1199 L
1389 1202 L
868 1202 M 870 1220 L
1389 1202 M 1402 1219 L
1403 1220 L
870 1220 M 870 1222 L
872 1239 L
1403 1220 M 1417 1238 L
1418 1239 L
872 1239 M 874 1258 L
1418 1239 M 1432 1258 L
874 1258 M 875 1276 L
1432 1258 M 1432 1259 L
1445 1276 L
875 1276 M 876 1295 L
1445 1276 M 1448 1279 L
1459 1295 L
876 1295 M 876 1313 L
1459 1295 M 1463 1300 L
1472 1313 L
876 1313 M 876 1332 L
1472 1313 M 1478 1321 L
1485 1332 L
876 1332 M 875 1351 L
1485 1332 M 1493 1343 L
1499 1351 L
875 1351 M 874 1369 L
1499 1351 M 1508 1365 L
1511 1369 L
874 1369 M 873 1388 L
1511 1369 M 1524 1387 L
1524 1388 L
873 1388 M 871 1406 L
1524 1388 M 1537 1406 L
869 1425 M 870 1414 L
871 1406 M 870 1414 L
1537 1406 M 1539 1409 L
1549 1425 L
869 1425 M 867 1443 L
1549 1425 M 1554 1432 L
1561 1443 L
867 1443 M 865 1462 L
1561 1443 M 1569 1456 L
1573 1462 L
865 1462 M 864 1480 L
1573 1462 M 1584 1480 L
1585 1480 L
864 1480 M 865 1499 L
1585 1480 M 1596 1499 L
865 1499 M 868 1518 L
1596 1499 M 1600 1505 L
1607 1518 L
868 1518 M 870 1524 L
874 1536 L
1607 1518 M 1615 1530 L
1618 1536 L
874 1536 M 881 1555 L
1618 1536 M 1629 1555 L
881 1555 M 885 1564 L
890 1573 L
1629 1555 M 1630 1556 L
1639 1573 L
890 1573 M 900 1592 L
1639 1573 M 1645 1584 L
1650 1592 L
900 1592 M 901 1592 L
913 1610 L
1650 1592 M 1660 1610 L
913 1610 M 916 1614 L
927 1629 L
1660 1610 M 1660 1612 L
1669 1629 L
927 1629 M 931 1634 L
943 1648 L
1669 1629 M 1676 1641 L
1679 1648 L
943 1648 M 946 1651 L
960 1666 L
1679 1648 M 1688 1666 L
960 1666 M 961 1668 L
976 1683 L
979 1685 L
1688 1666 M 1691 1673 L
1696 1685 L
979 1685 M 992 1696 L
999 1703 L
1696 1685 M 1705 1703 L
999 1703 M 1007 1710 L
1021 1722 L
1705 1703 M 1706 1706 L
CS M
1713 1722 L
1021 1722 M 1022 1722 L
1037 1734 L
1046 1741 L
1713 1722 M 1721 1741 L
1046 1741 M 1052 1745 L
1068 1756 L
1072 1759 L
1721 1741 M 1721 1742 L
1728 1759 L
1072 1759 M 1083 1766 L
1098 1777 L
1100 1778 L
1728 1759 M 1735 1778 L
1100 1778 M 1113 1786 L
1128 1796 L
1129 1796 L
1735 1778 M 1736 1783 L
1741 1796 L
1129 1796 M 1144 1805 L
1159 1814 L
1160 1815 L
1741 1796 M 1746 1815 L
1160 1815 M 1174 1822 L
1189 1831 L
1193 1833 L
1746 1815 M 1751 1833 L
1193 1833 M 1204 1839 L
1220 1847 L
1228 1852 L
1751 1833 M 1751 1835 L
1755 1852 L
1228 1852 M 1235 1855 L
1250 1863 L
1265 1870 L
1266 1870 L
1755 1852 M 1757 1870 L
1266 1870 M 1280 1877 L
1296 1884 L
1306 1889 L
1757 1870 M 1758 1889 L
1306 1889 M 1311 1891 L
1326 1898 L
1341 1904 L
1349 1908 L
1758 1889 M 1755 1908 L
1349 1908 M 1356 1911 L
1372 1917 L
1387 1922 L
1396 1926 L
1749 1926 M 1751 1920 L
1755 1908 M 1751 1920 L
1396 1926 M 1402 1928 L
1417 1933 L
1432 1939 L
1448 1944 L
1450 1945 L
1736 1945 M 1736 1944 L
1749 1926 M 1736 1944 L
1450 1945 M 1463 1949 L
1478 1953 L
1493 1957 L
1508 1962 L
1516 1963 L
1709 1963 M 1721 1956 L
1736 1945 M 1721 1956 L
1516 1963 M 1524 1965 L
1539 1968 L
1554 1971 L
1569 1974 L
1584 1976 L
1600 1977 L
1615 1978 L
1630 1978 L
1645 1978 L
1660 1976 L
1676 1974 L
1691 1970 L
1706 1965 L
1709 1963 M 1706 1965 L
CS [6 12] 0 setdash M
CS [] 0 setdash M
CS M 4 setlinewidth
/P { moveto 0 4.05 rlineto stroke } def
1328 1610 M 1289 1650 L
1328 1650 M 1289 1610 L
1289 1650 M CS M 2 setlinewidth
/P { moveto 0 2.05 rlineto stroke } def
CS [] 0 setdash M
1238 139 M 1269 174 M 1271 179 L
1271 168 L
1269 174 L
1265 177 L
1260 179 L
1254 179 L
1248 177 L
1244 174 L
1244 170 L
1246 166 L
1248 164 L
1252 162 L
1263 158 L
1267 156 L
1271 152 L
1244 170 M 1248 166 L
1252 164 L
1263 160 L
1267 158 L
1269 156 L
1271 152 L
1271 145 L
1267 141 L
1261 139 L
1256 139 L
1250 141 L
1246 145 L
1244 150 L
1244 139 L
1246 145 L
CS [] 0 setdash M
CS [] 0 setdash M
131 1239 M 91 1257 M 131 1257 L
91 1259 M 131 1259 L
91 1245 M 102 1243 L
91 1243 L
91 1272 L
102 1272 L
91 1270 L
131 1251 M 131 1264 L
CS [] 0 setdash M
CS [6 12] 0 setdash M
901 1511 M 911 1510 L
928 1510 L
946 1510 L
964 1511 L
964 1511 L
868 1521 M 875 1517 L
893 1512 L
901 1511 M 893 1512 L
964 1511 M 982 1513 L
999 1516 L
1017 1519 L
1023 1521 L
854 1530 M 857 1527 L
868 1521 M 857 1527 L
1023 1521 M 1035 1523 L
1052 1527 L
1064 1530 L
854 1530 M 847 1539 L
1064 1530 M 1070 1531 L
1088 1536 L
1098 1539 L
847 1539 M 844 1548 L
1098 1539 M 1106 1541 L
1123 1546 L
1129 1548 L
844 1548 M 843 1558 L
1129 1548 M 1141 1552 L
1157 1558 L
843 1558 M 844 1567 L
1157 1558 M 1159 1558 L
1177 1564 L
1183 1567 L
844 1567 M 846 1576 L
1183 1567 M 1194 1571 L
1208 1576 L
846 1576 M 850 1585 L
1208 1576 M 1212 1577 L
1230 1584 L
1232 1585 L
850 1585 M 854 1594 L
1232 1585 M 1248 1591 L
1255 1594 L
854 1594 M 857 1601 L
859 1604 L
1255 1594 M 1265 1599 L
1277 1604 L
859 1604 M 865 1613 L
1277 1604 M 1283 1606 L
1298 1613 L
865 1613 M 872 1622 L
1298 1613 M 1301 1614 L
1318 1622 L
1319 1622 L
872 1622 M 875 1626 L
879 1631 L
1319 1622 M 1336 1630 L
1339 1631 L
879 1631 M 887 1641 L
1339 1631 M 1354 1639 L
1358 1641 L
887 1641 M 893 1647 L
896 1650 L
1358 1641 M 1372 1647 L
1377 1650 L
896 1650 M 905 1659 L
1377 1650 M 1389 1656 L
1395 1659 L
905 1659 M 911 1665 L
914 1668 L
1395 1659 M 1407 1665 L
1413 1668 L
914 1668 M 924 1678 L
1413 1668 M 1425 1675 L
1430 1678 L
924 1678 M 928 1682 L
934 1687 L
1430 1678 M 1442 1684 L
1447 1687 L
934 1687 M 945 1696 L
1447 1687 M 1460 1694 L
1464 1696 L
945 1696 M 946 1697 L
956 1705 L
1464 1696 M 1478 1704 L
1480 1705 L
956 1705 M 964 1711 L
968 1715 L
1480 1705 M 1496 1715 L
1496 1715 L
968 1715 M 979 1724 L
1496 1715 M 1511 1724 L
979 1724 M 982 1725 L
992 1733 L
1511 1724 M 1513 1725 L
1526 1733 L
992 1733 M 999 1739 L
1004 1742 L
1526 1733 M 1531 1736 L
1541 1742 L
1004 1742 M 1017 1751 L
1017 1752 L
1541 1742 M 1549 1748 L
1555 1752 L
1017 1752 M 1031 1761 L
1555 1752 M 1567 1759 L
1569 1761 L
1031 1761 M 1035 1764 L
1044 1770 L
1569 1761 M 1583 1770 L
1044 1770 M 1052 1775 L
1058 1779 L
1583 1770 M 1584 1771 L
1596 1779 L
1058 1779 M 1070 1787 L
1073 1788 L
1596 1779 M 1602 1784 L
1609 1788 L
1073 1788 M 1087 1798 L
1609 1788 M 1620 1797 L
1621 1798 L
1087 1798 M 1088 1798 L
1102 1807 L
1621 1798 M 1633 1807 L
1102 1807 M 1106 1809 L
1118 1816 L
1633 1807 M 1638 1810 L
1645 1816 L
1118 1816 M 1123 1819 L
1134 1825 L
1645 1816 M 1655 1824 L
1657 1825 L
1134 1825 M 1141 1830 L
1150 1835 L
1657 1825 M 1668 1835 L
1150 1835 M 1159 1840 L
1167 1844 L
1668 1835 M 1673 1839 L
1678 1844 L
1167 1844 M 1177 1849 L
1184 1853 L
1678 1844 M 1689 1853 L
1184 1853 M 1194 1859 L
1201 1862 L
1689 1853 M 1691 1855 L
1698 1862 L
1201 1862 M 1212 1868 L
1219 1872 L
1698 1862 M 1708 1872 L
1219 1872 M 1230 1877 L
1237 1881 L
1708 1872 M 1708 1872 L
1717 1881 L
1237 1881 M 1248 1886 L
1256 1890 L
1717 1881 M 1725 1890 L
1256 1890 M 1265 1894 L
1276 1899 L
1725 1890 M 1726 1891 L
1733 1899 L
1276 1899 M 1283 1903 L
1296 1909 L
1733 1899 M 1740 1909 L
1296 1909 M 1301 1911 L
1316 1918 L
1740 1909 M 1744 1914 L
1747 1918 L
1316 1918 M 1318 1919 L
1336 1926 L
1337 1927 L
1747 1918 M 1753 1927 L
1337 1927 M 1354 1934 L
1360 1936 L
1753 1927 M 1758 1936 L
1360 1936 M 1372 1941 L
1383 1946 L
1758 1936 M 1762 1944 L
1762 1946 L
1383 1946 M 1389 1948 L
1406 1955 L
1762 1946 M 1766 1955 L
CS M
1406 1955 M 1407 1955 L
1425 1962 L
1432 1964 L
1766 1955 M 1768 1964 L
1432 1964 M 1442 1968 L
1458 1973 L
1768 1964 M 1768 1973 L
1458 1973 M 1460 1974 L
1478 1980 L
1487 1983 L
1768 1973 M 1767 1983 L
1487 1983 M 1496 1985 L
1513 1991 L
1518 1992 L
1767 1983 M 1763 1992 L
1518 1992 M 1531 1995 L
1549 2000 L
1553 2001 L
1756 2001 M 1762 1994 L
1763 1992 M 1762 1994 L
1553 2001 M 1567 2004 L
1584 2008 L
1595 2010 L
1741 2010 M 1744 2009 L
1756 2001 M 1744 2009 L
1595 2010 M 1602 2012 L
1620 2015 L
1638 2017 L
1655 2019 L
1668 2019 L
1695 2019 M 1708 2018 L
1726 2015 L
1741 2010 M 1726 2015 L
1668 2019 M 1673 2020 L
1691 2020 L
1695 2019 M 1691 2020 L
CS [] 0 setdash M
CS [6 12] 0 setdash M
CS [] 0 setdash M
CS M 4 setlinewidth
/P { moveto 0 4.05 rlineto stroke } def
CS M 2 setlinewidth
/P { moveto 0 2.05 rlineto stroke } def
stroke
grestore
showpage
end

