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{\flushright CERN-TH.6913/93\\}
\vspace{1cm}
\begin{center}
{\Large \bf Non-perturbative unification\\
in the light of LEP results}\\
\vspace{4mm}
{Biswajoy Brahmachari, Utpal Sarkar}\\
\vspace{2mm}
{\em Theory Group, Physical Research Laboratory,\\
Ahmedabad 380 009, India}\\
\vspace{4mm}
{and }\\
\vspace{4mm}
{K. Sridhar$^{*}$}\\
\vspace{2mm}
{\em Theory Division, CERN, CH-1211, Geneva 23, Switzerland.}\\
\end{center}

\vspace{.5cm}
\begin{abstract}
We consider an alternative to conventional grand unified theories
originally proposed by Maiani, Parisi and Petronzio, where owing to
the existence of extra fermion generations at some intermediate
scale, the gauge couplings become large at high energies. We
first comment on how the non-supersymmetric version of this
scenario is ruled out; we then
consider the two-loop evolution of couplings in the supersymmetric
extension of this scenario, and check whether such a scenario is
feasible in the light of the precise values of couplings now
available from LEP.
\end{abstract}

\vspace{2cm}
\noindent
\vspace{1cm} $^{*)} $ sridhar@vxcern.cern.ch\\
CERN-TH.6913/93\\
June 1993\\

\vfill
\clearpage
\setcounter{page}{1}
\pagestyle{plain}
Grand unified theories (GUTs) offer the possibility of unifying the
SU(3), SU(2) and U(1) gauge groups of the standard model
into one large group at a high energy scale, $M_U$. This scale
is determined as the intersection point of the SU(3), SU(2)
and U(1) couplings. The particle content of the theory
completely determines the variation of the couplings with energy.
Given the particle content of the theory, therefore, one can
evolve the couplings determined at low energies to determine whether
there is unification.

The determination of the couplings at LEP has important consequences
for grand unified theories. The precise determination of the
Weinberg angle, $\theta_W$, and the strong coupling, $\alpha_s$,
at the $Z$-peak has helped in putting rather stringent constraints
on unified models \cite{amaldi,lepgut}. In particular, it has been
found \cite{amaldi} that in the standard model with three fermion
generations and one Higgs doublet, the couplings do not meet at a
single point at high energies. In contrast, in the minimal
supersymmetric extension of the standard model (with three
generations and two Higgs doublets), a single intersection point
obtains at about $10^{16}$~GeV.
The compatibility of this simple supersymmetric GUT with the
couplings determined from LEP is remarkable. Nonetheless, it is
important to study other models, which are alternatives to grand
unification, and see whether they are viable in the light of the
available experimental information on couplings.

An interesting alternative to GUTs was proposed by Maiani, Parisi
and Petronzio \cite{mpp} several years ago. In this scheme, the
couplings enter a non-perturbative phase at a high energy scale,
i.e. the theory is asymptotically divergent. Starting from the
renormalisation group equation for a coupling $\alpha$,
\begin{equation}
\label{e1}
{d\alpha \over dt} = \beta (\alpha ),
\end{equation}
where $\beta(\alpha)$ is the beta function and $t=\mbox{\rm ln}
(Q^2/\mu^2)$, $\mu$ being some reference scale, we obtain
\begin{equation}
\label{e2}
t = \int_{\alpha(\mu)}^{\alpha(Q^2)} {d\alpha \over \beta(\alpha)}.
\end{equation}
For $\beta(\alpha) > 0$ (asymptotically divergent theory) there is
a value of $t$, given by
\begin{equation}
\label{e3}
t = \int_{\alpha(\mu)}^{\infty} {d\alpha \over \beta(\alpha)}
< \infty ,
\end{equation}
for which $\alpha \rightarrow \infty$. If perturbation theory is to
be valid at all energy scales, we require $\alpha(\mu)=0$, so
that $t_c=\infty$, $\alpha(\mu)=0$ is the infra-red fixed
point. But if $\alpha(\mu)\ne 0$ but small, i.e. it is sufficiently
close to the infra-red fixed point, then there is a finite cut-off in
energy beyond which the theory is non-perturbative.

In Ref.~\cite{mpp}, it was assumed that the standard
SU(3)$\times$SU(2)$\times$U(1) theory, due to new fermion generations
that get switched on around the weak scale $\Lambda_F = 250$~GeV,
is asymptotically
divergent beyond $\Lambda_F$. The couplings $\alpha_{1,2,3}$ are
sufficiently close to zero at $\Lambda_F$ but not quite zero. As
a consequence, the theory is cut off at a scale $\Lambda$.
At this scale, the most interesting situation is that not just
one but all three couplings are large, i.e. of O(1). In fact, it
has been shown \cite{hung} that such a non-perturbative scenario
exhibits a "trapping" mechanism, whereby if one of the couplings
grows large, the other couplings will also increase. This effect,
by means of which all three couplings are large and of the
same order of magnitude at $\Lambda$, leads to what is called
non-perturbative unification. In Ref.~\cite{mpp} the cut-off
scale $\Lambda$ was assumed to be the Planck scale; however,
in subsequent studies \cite{cabfar,grunberg}, $\Lambda$ was
determined to be of the order of $10^{15}$~--$10^{17}$~GeV. Since
the low-energy couplings are close to the infra-red fixed point,
they are insensitive to the values of the couplings at the scale
$\Lambda$.

One natural extension of the above scenario is the inclusion of
supersymmetry. This was first considered in Ref.~\cite{cabfar},
and was later discussed in Refs.~\cite{grunberg,mp}. Other than
solving the hierarchy problem, the inclusion of supersymmetry is
attractive because it provides a framework for the existence
of new particles needed to make the theory asymptotically
divergent. In the case of the simplest $N=1$ supersymmetric
extension of the scenario, it suffices to consider $n_f=5$, where
$n_f$ is the number of fermion generations.

In this letter, we use the recent LEP values to check whether any
strong constraints on the non-perturbative unification scenario
can be obtained.
The values of $\mbox{\rm sin}^2\theta_W$ and $\alpha_s$ from LEP
are very
precise compared to that available from older experiments. One
strong constraint is on the number of extra chiral generations.
The present limit on the oblique parameters S, T and U allows only
three chiral fermion generations, while the vectorial
generations are not constrained. Thus in addition to the three
chiral fermion generations we are allowed to have only an even
number of generations.

We shall first specify the supersymmetric non-perturbative unification
scenario in detail. While discussing the results we shall also
comment on the results of the non-supersymmetric case. We
consider an SU(3)$\times$SU(2)$\times$U(1)
supersymmetric gauge theory with the assumption that an $N=1$
supersymmetry holds above the scale $\Lambda_s$. We assume $n_f=5$
supersymmetric generations and two Higgs supermultiplets. In the
discussion of the non-supersymmetric case we shall consider one
Higgs scalar and $n_f=8 \;\;\mbox{\rm and}\:\: 9$. From
the requirement that the Yukawa couplings do not become arbitrarily
large, a bound on the fermion masses can be obtained \cite{cmpp,bdm}.
This bound is that fermion masses are, in general, smaller than
200--250~GeV. We assume that the extra fermion generations, which are
required for the theory to be asymptotically divergent, are of the
order of 250 GeV in mass.

Having specified the theory we can now address the question of the
evolution of the three couplings. The two-loop renormalisation group
equations for the couplings are given by the following coupled
differential equations:
\begin{equation}
\label{e4}
\mu{d\alpha_i(\mu) \over d\mu} = {1 \over 2\pi} \biggl \lbrack
a_i + {b_{ij} \over 4\pi}\alpha_j(\mu)+{b_{ik} \over
4\pi} \alpha_k(\mu) \biggr \rbrack \alpha_i^2(\mu) +
{2b_{ij} \over (4\pi)^2} \alpha_i^3(\mu) ,
\end{equation}
where $i,\ j,\ k = 1,\ 2,\ 3$ and $i \ne j \ne k$, and
$a_i$ and $b_{ij}$ are the one- and two-loop beta function coefficients.
In the range of energies between $M_Z$ and the supersymmetric threshold,
$M_s$, we use the non-supersymmetric beta functions to evolve the
couplings, whereas from $M_s$ onward the supersymmetric beta functions
are effective. We retrieve the result for the non-supersymmetric
scenario by taking $M_s = \Lambda_{MPP}$ and large $n_f$.

In the non-supersymmetric case the one-loop beta function
coefficients are \cite{jones}
\begin{eqnarray}
\label{e5}
b_j&=&\pmatrix{0 \cr -{22\over3} \cr -11\cr}+n_f\pmatrix{{20\over9} \cr
{4\over3} \cr {4\over3}\cr}+n_h\pmatrix{{1\over6} \cr
{1\over6} \cr {0}\cr}
\end{eqnarray}
while the two-loop beta functions are
\begin{eqnarray}
\label{e6}
a_{ij}&=&-\pmatrix{0&0&0 \cr0& {136\over3}&0 \cr0&0&
102\cr}+n_f\pmatrix{{95\over27}&1&{44\over9} \cr
{1\over3}&{49\over3}&4 \cr
{11\over18}&{3\over2}&{76\over3}\cr}+n_h\pmatrix{{1\over2}&{13\over6}&0
\cr  {1\over2}&{13\over6}&0 \cr 0&0&0\cr}
\end{eqnarray}
In the supersymmetric case the one-loop beta functions take the
form \cite{jones}
\begin{eqnarray}
\label{e7}
b_j&=&\pmatrix{0 \cr -6 \cr -9\cr}+n_f\pmatrix{{10\over3} \cr
2 \cr 2\cr}+n_h\pmatrix{{1\over2} \cr
{1\over2} \cr {0}\cr}
\end{eqnarray}
while the two-loop beta functions are
\begin{eqnarray}
\label{e8}
a_{ij}&=&-\pmatrix{0&0&0 \cr0& 24&0 \cr0&0&
54\cr}+n_f\pmatrix{{190\over27}&2&{88\over9} \cr
{2\over3}&14&8 \cr
{11\over9}&3&{68\over3}\cr}+n_h\pmatrix{{1\over2}&{3\over2}&0
\cr  {1\over2}&{7\over2}&0 \cr 0&0&0\cr}
\end{eqnarray}
In all these equations, $n_f$ and $n_h$ denote the number of
fermion generations and the number of Higgs doublets
respectively.

We integrate the coupled differential equations in Eq.~(\ref{e4})
numerically, with the initial values of the three couplings
$\alpha_{1,2,3}$ taken to be of O(1) at the unification scale
$\Lambda$. What we do in practice is to evolve downwards using
the renormalisation group equations for several values of $\Lambda$,
and check what the predicted values of the couplings at the scale
$M_Z$ are. The extra fermion generations are assumed to contribute
to the beta functions for all energies greater than 250~GeV.

We shall first comment on the non-supersymmetric scenario and
then present our main result, namely the supersymmetric
extension. In this case we find that for $n_f \leq 8$,
$\alpha_2(M_z)$ remains too small, and that $\alpha_{1,2}(M_z)$ falls
within the experimental bound for $n_f \geq 9$. But for $n_f
\geq 9$ the strong coupling constant evolves extremely fast and
$\alpha_3(M_z)$ becomes too
large. Thus the precision LEP data rule out the
non-supersymmetric scenario completely.

The results of the computation for the supersymmetric version
are shown in Fig.~1, where
$\alpha_{1,2,3}(M_Z)$ are shown as a function of $\Lambda$. The
solid, dashed and dotted curves are for $M_s=250$~GeV, 1.2~TeV and
5~TeV, respectively. The horizontal lines in the figures show the
upper and lower bounds on the couplings at $M_Z$ as determined
by the LEP experiment. These are as follows \cite{lep}:
\begin{eqnarray}
\label{e9}
\alpha_1 &=& 0.0101322 \pm 0.000024 \nonumber\\
\alpha_2 &=& 0.03322 \pm 0.00025 \nonumber\\
\alpha_3 &=& 0.120 \pm 0.006.
\end{eqnarray}
It is clear from the figure that the
non-perturbative unification scheme is certainly viable if we have
$M_s=1.2$~TeV and $\Lambda$ close to $0.78 \times 10^{17}$~GeV. We
have checked that the range of values allowed is $M_s = 1.2 \pm
0.2$~TeV and $\Lambda=$(0.7--0.8)$\times 10^{17}$~GeV. We have
also checked that the couplings at $M_Z$ are not sensitive to
the choice of the couplings at $\Lambda$. We have checked this
by varying these from 0.75 to 10.

Let us now summarise our results. We have studied the
non-perturbative unification scenario first proposed
by Maiani, Parisi and Petronzio. We point out that the
non-supersymmetric version of this scenario is ruled out by LEP
data. However, the supersymmetric extension of this scenario remains
a viable alternative to conventional grand unified theories and is
capable of predicting the precision values of couplings determined
from LEP. Our numerical results show that the non-perturbative
scale, $\Lambda$, at which all couplings are large, is around
0.7--0.8$\times 10^{17}$~GeV, with the supersymmetric threshold
$M_s$ around 1.0--1.4~TeV. If the scale $M_s$ gets either larger
or smaller it is then not possible to reproduce the values of the
couplings at $M_Z$. We should note that the agreement with the data
is obtained only for a constrained range of parameters of this
scenario. In principle, the effect of higher-order corrections
could be large and this may ruin the agreement. It is also likely
that more accurate measurements of the strong coupling $\alpha_3$
at low energies may be sufficient to either put strong constraints
or completely rule out this scenario. It is nevertheless interesting
that this scenario, at the two-loop level, is a possible alternative
to conventional grand unification.
\clearpage

\begin{thebibliography}{99}

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\bibitem{cmpp}N.~Cabibbo, L.~Maiani, G.~Parisi and R.~Petronzio,
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\bibitem{bdm}J.~Bagger, S.~Dimopoulos and E.~Masso,
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\bibitem{lep}For a recent review, see S.C.C.~Ting, preprint
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\end{thebibliography}

\newpage
\section*{Figure caption}
\renewcommand{\labelenumi}{Fig. \arabic{enumi}}
\begin{enumerate}
\item   %Fig.1
The couplings
$\alpha_{1,2,3} (M_Z)$ as a function of the non-perturbative unification
scale $\Lambda$. The solid, dashed and dotted curves are for
$M_s$=250~GeV, 1.2~TeV and 5~TeV, respectively. The horizontal lines
in the figures show the experimentally allowed upper and lower bounds
on the couplings at $M_Z$.
\end{enumerate}
\end{document}

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1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d 3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 1 d cl s
339 1443 m -3 -1 d -3 -4 d -1 -5 d 0 -4 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d
2 3 d 1 6 d 0 4 d -1 5 d -2 4 d -4 1 d cl s 582 1437 m 3 2 d 3 3 d 0 -24 d s
582 1437 m 2 1 d 3 3 d 0 -23 d s 583 1438 m 2 1 d 4 4 d 0 -24 d s 604 1420 m
-1 -1 d 1 -1 d 1 1 d cl s 603 1420 m -1 -1 d 1 -1 d 1 1 d cl s 605 1421 m
-1 -1 d 1 -1 d 1 1 d cl s 614 1436 m 0 1 d 1 3 d 1 1 d 3 1 d 4 0 d 3 -1 d
1 -1 d 1 -3 d 0 -2 d -1 -2 d -3 -3 d -11 -12 d 16 0 d s 614 1436 m 0 1 d 1 2 d
1 1 d 2 1 d 5 0 d 2 -1 d 1 -1 d 1 -2 d 0 -2 d -1 -3 d -2 -3 d -12 -11 d 16 0 d
s 615 1437 m 0 1 d 1 2 d 1 2 d 2 1 d 5 0 d 2 -1 d 1 -2 d 2 -2 d 0 -2 d -2 -2 d
-2 -4 d -11 -11 d 16 0 d s 384 1779 m 6 -13 d 6 -11 d 6 -11 d 6 -11 d 7 -10 d
6 -9 d 6 -9 d 1 -2 d 6 -8 d 5 -7 d 7 -7 d 6 -7 d 7 -7 d 6 -6 d 7 -6 d 5 -4 d
5 -3 d 6 -4 d 9 -4 d 15 -7 d 4 -2 d 29 -16 d 15 -7 d s [12 6] 0 setdash
384 1892 m 6 -14 d 6 -11 d 6 -11 d 6 -11 d 7 -11 d 5 -10 d 6 -9 d 2 -2 d 5 -8 d
6 -7 d 5 -7 d 6 -7 d 8 -7 d 7 -7 d 7 -6 d 5 -4 d 6 -5 d 7 -4 d 15 -8 d 9 -4 d
2 -2 d 44 -26 d s [2 6] 0 setdash 384 2006 m 5 -13 d 6 -13 d 5 -11 d 5 -11 d
6 -10 d 5 -11 d 5 -8 d 6 -9 d 1 -1 d 4 -6 d 4 -6 d 6 -6 d 5 -6 d 8 -6 d
14 -13 d 3 -3 d 12 -11 d 12 -11 d 13 -10 d 7 -5 d 12 -10 d 12 -8 d 13 -8 d
7 -5 d s [] 0 setdash 340 1703 m 264 0 d 0 18 d -264 0 d cl s 831 1473 m
264 0 d 0 567 d -264 0 d cl s [2 6] 0 setdash 831 1473 m 0 0 d 53 0 d 0 0 d
53 0 d 0 0 d 52 0 d 0 0 d 53 0 d 0 0 d 53 0 d 0 0 d s [] 0 setdash 831 1473 m
0 567 d s 855 1473 m -24 0 d s 843 1513 m -12 0 d s 843 1554 m -12 0 d s
843 1594 m -12 0 d s 855 1635 m -24 0 d s 843 1675 m -12 0 d s 843 1716 m
-12 0 d s 843 1756 m -12 0 d s 855 1797 m -24 0 d s 843 1837 m -12 0 d s
843 1878 m -12 0 d s 843 1918 m -12 0 d s 855 1959 m -24 0 d s 855 1473 m
-24 0 d s 855 1959 m -24 0 d s 843 1999 m -12 0 d s 843 2040 m -12 0 d s
731 1485 m -4 -1 d -2 -4 d -1 -5 d 0 -4 d 1 -5 d 2 -4 d 4 -1 d 2 0 d 3 1 d
3 4 d 1 5 d 0 4 d -1 5 d -3 4 d -3 1 d cl s 730 1484 m -3 -1 d -3 -3 d -1 -6 d
0 -3 d 1 -6 d 3 -4 d 3 -1 d 2 0 d 4 1 d 2 4 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d
cl s 731 1486 m -3 -2 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 3 -1 d 3 0 d 3 1 d
2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -3 2 d cl s 749 1463 m -1 -1 d 1 -1 d 1 1 d cl
s 748 1463 m -1 -2 d 1 -1 d 1 1 d cl s 750 1464 m -2 -1 d 2 -1 d 1 1 d cl s
765 1485 m -4 -1 d -2 -4 d -1 -5 d 0 -4 d 1 -5 d 2 -4 d 4 -1 d 2 0 d 3 1 d
3 4 d 1 5 d 0 4 d -1 5 d -3 4 d -3 1 d cl s 764 1484 m -3 -1 d -3 -3 d -1 -6 d
0 -3 d 1 -6 d 3 -4 d 3 -1 d 2 0 d 4 1 d 2 4 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d
cl s 765 1486 m -3 -2 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 3 -1 d 3 0 d 3 1 d
2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -3 2 d cl s 783 1485 m 12 0 d -7 -9 d 4 0 d
2 -1 d 1 -1 d 1 -4 d 0 -2 d -1 -4 d -2 -2 d -3 -1 d -4 0 d -3 1 d -1 1 d -1 3 d
s 782 1484 m 13 0 d -7 -9 d 3 0 d 2 -1 d 2 -1 d 1 -4 d 0 -2 d -1 -3 d -3 -3 d
-3 -1 d -4 0 d -3 1 d -1 2 d -1 2 d s 784 1486 m 12 0 d -7 -9 d 4 0 d 2 -2 d
1 -1 d 1 -3 d 0 -2 d -1 -4 d -2 -2 d -4 -1 d -3 0 d -3 1 d -2 1 d -1 2 d s
708 1647 m -3 -1 d -3 -4 d -1 -5 d 0 -4 d 1 -5 d 3 -4 d 3 -1 d 2 0 d 4 1 d
2 4 d 1 5 d 0 4 d -1 5 d -2 4 d -4 1 d cl s 707 1646 m -3 -1 d -2 -3 d -2 -6 d
0 -4 d 2 -5 d 2 -4 d 3 -1 d 3 0 d 3 1 d 2 4 d 1 5 d 0 4 d -1 6 d -2 3 d -3 1 d
cl s 709 1648 m -4 -2 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 2 d cl s 726 1625 m -1 -1 d 1 -1 d 1 1 d cl
s 725 1625 m -1 -2 d 1 -1 d 2 1 d cl s 727 1626 m -1 -1 d 1 -1 d 1 1 d cl s
742 1647 m -3 -1 d -3 -4 d -1 -5 d 0 -4 d 1 -5 d 3 -4 d 3 -1 d 2 0 d 4 1 d
2 4 d 1 5 d 0 4 d -1 5 d -2 4 d -4 1 d cl s 741 1646 m -3 -1 d -2 -3 d -2 -6 d
0 -4 d 2 -5 d 2 -4 d 3 -1 d 3 0 d 3 1 d 2 4 d 1 5 d 0 4 d -1 6 d -2 3 d -3 1 d
cl s 743 1648 m -4 -2 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 2 d cl s 760 1647 m 13 0 d -7 -9 d 3 0 d
2 -1 d 2 -2 d 1 -3 d 0 -2 d -1 -4 d -3 -2 d -3 -1 d -3 0 d -4 1 d -1 1 d -1 3 d
s 759 1646 m 13 0 d -7 -9 d 3 0 d 3 -1 d 1 -1 d 1 -4 d 0 -2 d -1 -3 d -2 -3 d
-4 -1 d -3 0 d -4 1 d -1 2 d -1 2 d s 761 1648 m 12 0 d -6 -10 d 3 0 d 2 -1 d
1 -1 d 1 -3 d 0 -2 d -1 -4 d -2 -2 d -3 -1 d -4 0 d -3 1 d -1 1 d -1 2 d s
782 1641 m 0 1 d 1 3 d 1 1 d 2 1 d 5 0 d 2 -1 d 1 -1 d 1 -3 d 0 -2 d -1 -2 d
-2 -4 d -11 -11 d 15 0 d s 781 1640 m 0 2 d 1 2 d 1 1 d 2 1 d 5 0 d 2 -1 d
1 -1 d 2 -2 d 0 -3 d -2 -2 d -2 -3 d -11 -12 d 16 0 d s 782 1642 m 0 1 d 2 2 d
1 1 d 2 2 d 4 0 d 3 -2 d 1 -1 d 1 -2 d 0 -2 d -1 -3 d -2 -3 d -12 -11 d 16 0 d
s 708 1809 m -3 -1 d -3 -4 d -1 -5 d 0 -4 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d
2 3 d 1 6 d 0 4 d -1 5 d -2 4 d -4 1 d cl s 707 1808 m -3 -1 d -2 -4 d -2 -5 d
0 -4 d 2 -5 d 2 -4 d 3 -1 d 3 0 d 3 1 d 2 4 d 1 5 d 0 4 d -1 5 d -2 4 d -3 1 d
cl s 709 1809 m -4 -1 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 1 d cl s 726 1787 m -1 -1 d 1 -1 d 1 1 d cl
s 725 1786 m -1 -1 d 1 -1 d 2 1 d cl s 727 1788 m -1 -1 d 1 -1 d 1 1 d cl s
742 1809 m -3 -1 d -3 -4 d -1 -5 d 0 -4 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d
2 3 d 1 6 d 0 4 d -1 5 d -2 4 d -4 1 d cl s 741 1808 m -3 -1 d -2 -4 d -2 -5 d
0 -4 d 2 -5 d 2 -4 d 3 -1 d 3 0 d 3 1 d 2 4 d 1 5 d 0 4 d -1 5 d -2 4 d -3 1 d
cl s 743 1809 m -4 -1 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 1 d cl s 760 1809 m 13 0 d -7 -9 d 3 0 d
2 -1 d 2 -2 d 1 -3 d 0 -2 d -1 -4 d -3 -2 d -3 -1 d -3 0 d -4 1 d -1 1 d -1 2 d
s 759 1808 m 13 0 d -7 -9 d 3 0 d 3 -1 d 1 -1 d 1 -4 d 0 -2 d -1 -3 d -2 -3 d
-4 -1 d -3 0 d -4 1 d -1 1 d -1 3 d s 761 1809 m 12 0 d -6 -9 d 3 0 d 2 -1 d
1 -1 d 1 -3 d 0 -3 d -1 -3 d -2 -2 d -3 -1 d -4 0 d -3 1 d -1 1 d -1 2 d s
792 1809 m -11 -16 d 17 0 d s 791 1808 m -11 -16 d 17 0 d s 793 1809 m
-12 -15 d 17 0 d s 792 1809 m 0 -24 d s 791 1808 m 0 -24 d s 793 1809 m 0 -23 d
s 708 1971 m -3 -2 d -3 -3 d -1 -6 d 0 -3 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d
2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 2 d cl s 707 1970 m -3 -1 d -2 -4 d -2 -5 d
0 -4 d 2 -5 d 2 -4 d 3 -1 d 3 0 d 3 1 d 2 4 d 1 5 d 0 4 d -1 5 d -2 4 d -3 1 d
cl s 709 1971 m -4 -1 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 1 d cl s 726 1949 m -1 -1 d 1 -1 d 1 1 d cl
s 725 1948 m -1 -1 d 1 -1 d 2 1 d cl s 727 1950 m -1 -1 d 1 -1 d 1 1 d cl s
742 1971 m -3 -2 d -3 -3 d -1 -6 d 0 -3 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d
2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 2 d cl s 741 1970 m -3 -1 d -2 -4 d -2 -5 d
0 -4 d 2 -5 d 2 -4 d 3 -1 d 3 0 d 3 1 d 2 4 d 1 5 d 0 4 d -1 5 d -2 4 d -3 1 d
cl s 743 1971 m -4 -1 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
3 3 d 1 6 d 0 3 d -1 6 d -3 3 d -3 1 d cl s 760 1971 m 13 0 d -7 -9 d 3 0 d
2 -2 d 2 -1 d 1 -3 d 0 -2 d -1 -4 d -3 -2 d -3 -1 d -3 0 d -4 1 d -1 1 d -1 2 d
s 759 1970 m 13 0 d -7 -9 d 3 0 d 3 -1 d 1 -1 d 1 -4 d 0 -2 d -1 -3 d -2 -3 d
-4 -1 d -3 0 d -4 1 d -1 1 d -1 3 d s 761 1971 m 12 0 d -6 -9 d 3 0 d 2 -1 d
1 -1 d 1 -3 d 0 -3 d -1 -3 d -2 -2 d -3 -1 d -4 0 d -3 1 d -1 1 d -1 2 d s
795 1967 m -1 2 d -3 2 d -3 0 d -3 -2 d -2 -3 d -1 -6 d 0 -5 d 1 -5 d 2 -2 d
3 -1 d 2 0 d 3 1 d 2 2 d 1 4 d 0 1 d -1 3 d -2 2 d -3 2 d -2 0 d -3 -2 d
-2 -2 d -1 -3 d s 795 1967 m -2 2 d -3 1 d -2 0 d -4 -1 d -2 -4 d -1 -5 d
0 -6 d 1 -4 d 2 -3 d 4 -1 d 1 0 d 3 1 d 3 3 d 1 3 d 0 1 d -1 3 d -3 3 d -3 1 d
-1 0 d -4 -1 d -2 -3 d -1 -3 d s 796 1968 m -1 2 d -4 1 d -2 0 d -3 -1 d
-2 -3 d -2 -6 d 0 -6 d 2 -4 d 2 -2 d 3 -1 d 1 0 d 4 1 d 2 2 d 1 3 d 0 1 d
-1 4 d -2 2 d -4 1 d -1 0 d -3 -1 d -2 -2 d -2 -4 d s 831 1473 m 264 0 d s
831 1497 m 0 -24 d s 884 1485 m 0 -12 d s 937 1485 m 0 -12 d s 989 1485 m
0 -12 d s 1042 1485 m 0 -12 d s 1095 1497 m 0 -24 d s 830 1442 m -4 -1 d
-2 -4 d -1 -5 d 0 -4 d 1 -5 d 2 -4 d 4 -1 d 2 0 d 3 1 d 3 4 d 1 5 d 0 4 d
-1 5 d -3 4 d -3 1 d cl s 829 1441 m -4 -1 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d
2 -3 d 4 -1 d 2 0 d 4 1 d 2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d cl s
830 1443 m -3 -1 d -2 -4 d -1 -5 d 0 -4 d 1 -6 d 2 -3 d 3 -1 d 3 0 d 3 1 d
2 3 d 1 6 d 0 4 d -1 5 d -2 4 d -3 1 d cl s 1074 1437 m 2 2 d 3 3 d 0 -24 d s
1073 1437 m 2 1 d 4 3 d 0 -23 d s 1074 1438 m 3 1 d 3 4 d 0 -24 d s 1095 1420 m
-1 -1 d 1 -1 d 1 1 d cl s 1095 1420 m -2 -1 d 2 -1 d 1 1 d cl s 1096 1421 m
-1 -1 d 1 -1 d 1 1 d cl s 1105 1436 m 0 1 d 2 3 d 1 1 d 2 1 d 5 0 d 2 -1 d
1 -1 d 1 -3 d 0 -2 d -1 -2 d -2 -3 d -12 -12 d 16 0 d s 1105 1436 m 0 1 d 1 2 d
1 1 d 2 1 d 5 0 d 2 -1 d 1 -1 d 1 -2 d 0 -2 d -1 -3 d -2 -3 d -11 -11 d 15 0 d
s 1106 1437 m 0 1 d 1 2 d 1 2 d 3 1 d 4 0 d 2 -1 d 2 -2 d 1 -2 d 0 -2 d -1 -2 d
-3 -4 d -11 -11 d 16 0 d s 875 1652 m 5 -7 d 5 -7 d 5 -7 d 5 -5 d 5 -6 d 5 -5 d
5 -5 d 5 -5 d 4 -3 d 4 -4 d 4 -3 d 5 -3 d 5 -3 d 7 -3 d 19 -9 d 6 -2 d 6 -3 d
13 -4 d 8 -3 d 6 -2 d 5 -3 d 9 -4 d 9 -5 d 9 -5 d 8 -6 d 9 -6 d s [12 6]
 0 setdash 875 1842 m 5 -8 d 5 -8 d 5 -8 d 5 -6 d 5 -7 d 5 -6 d 5 -6 d 5 -5 d
4 -4 d 4 -4 d 4 -3 d 5 -4 d 5 -3 d 6 -4 d 20 -10 d 6 -3 d 8 -3 d 18 -7 d 6 -3 d
6 -3 d 9 -5 d 9 -6 d 9 -6 d 8 -6 d 9 -7 d s [2 6] 0 setdash 876 2040 m 3 -7 d
4 -9 d 4 -9 d 5 -8 d 4 -8 d 4 -7 d 4 -6 d 4 -7 d 4 -5 d 5 -5 d 2 -3 d 3 -3 d
3 -3 d 4 -3 d 4 -2 d 4 -2 d 6 -3 d 12 -4 d 5 -2 d 3 -1 d 14 -8 d 14 -7 d 8 -5 d
8 -5 d 9 -6 d 9 -7 d 10 -8 d 8 -7 d 8 -7 d s [] 0 setdash 831 1713 m 264 0 d
0 41 d -264 0 d cl s 1322 1473 m 264 0 d 0 567 d -264 0 d cl s [2 6] 0 setdash
1322 1473 m 0 0 d 53 0 d 0 0 d 53 0 d 0 0 d 53 0 d 0 0 d 53 0 d 0 0 d 52 0 d
0 0 d s [] 0 setdash 1322 1473 m 0 567 d s 1346 1544 m -24 0 d s 1334 1579 m
-12 0 d s 1334 1615 m -12 0 d s 1334 1650 m -12 0 d s 1346 1685 m -24 0 d s
1334 1721 m -12 0 d s 1334 1756 m -12 0 d s 1334 1792 m -12 0 d s 1346 1827 m
-24 0 d s 1334 1863 m -12 0 d s 1334 1898 m -12 0 d s 1334 1933 m -12 0 d s
1346 1969 m -24 0 d s 1346 1544 m -24 0 d s 1334 1508 m -12 0 d s 1346 1969 m
-24 0 d s 1334 2004 m -12 0 d s 1334 2040 m -12 0 d s 1245 1556 m -4 -1 d
-2 -4 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d 2 3 d 2 6 d 0 3 d
-2 6 d -2 4 d -3 1 d cl s 1244 1555 m -4 -1 d -2 -4 d -1 -5 d 0 -4 d 1 -5 d
2 -4 d 4 -1 d 2 0 d 3 1 d 3 4 d 1 5 d 0 4 d -1 5 d -3 4 d -3 1 d cl s
1245 1556 m -3 -1 d -2 -3 d -2 -6 d 0 -3 d 2 -6 d 2 -3 d 3 -1 d 2 0 d 4 1 d
2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d cl s 1263 1534 m -1 -1 d 1 -1 d 1 1 d cl
s 1262 1533 m -1 -1 d 1 -1 d 1 1 d cl s 1263 1535 m -1 -1 d 1 -1 d 1 1 d cl s
1275 1551 m 2 1 d 4 4 d 0 -24 d s 1274 1550 m 3 2 d 3 3 d 0 -24 d s 1276 1552 m
2 1 d 3 3 d 0 -23 d s 1222 1697 m -4 -1 d -2 -3 d -1 -6 d 0 -3 d 1 -6 d 2 -3 d
4 -1 d 2 0 d 4 1 d 2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d cl s 1221 1697 m
-3 -1 d -3 -4 d -1 -6 d 0 -3 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d 2 3 d 1 6 d
0 3 d -1 6 d -2 4 d -4 1 d cl s 1223 1698 m -4 -1 d -2 -3 d -1 -6 d 0 -4 d
1 -5 d 2 -4 d 4 -1 d 2 0 d 3 1 d 2 4 d 2 5 d 0 4 d -2 6 d -2 3 d -3 1 d cl s
1240 1676 m -1 -1 d 1 -1 d 1 1 d cl s 1239 1675 m -1 -1 d 1 -1 d 1 1 d cl s
1241 1677 m -1 -2 d 1 -1 d 1 1 d cl s 1252 1693 m 3 1 d 3 3 d 0 -23 d s
1252 1692 m 2 1 d 3 4 d 0 -24 d s 1253 1694 m 2 1 d 4 3 d 0 -24 d s 1273 1692 m
0 1 d 1 2 d 1 1 d 2 1 d 5 0 d 2 -1 d 1 -1 d 1 -2 d 0 -2 d -1 -3 d -2 -3 d
-11 -11 d 16 0 d s 1272 1691 m 0 1 d 1 2 d 1 2 d 3 1 d 4 0 d 2 -1 d 2 -2 d
1 -2 d 0 -2 d -1 -2 d -3 -4 d -11 -11 d 16 0 d s 1274 1692 m 0 2 d 1 2 d 1 1 d
2 1 d 5 0 d 2 -1 d 1 -1 d 1 -2 d 0 -3 d -1 -2 d -2 -3 d -12 -12 d 16 0 d s
1222 1839 m -4 -1 d -2 -3 d -1 -6 d 0 -4 d 1 -5 d 2 -4 d 4 -1 d 2 0 d 4 1 d
2 4 d 1 5 d 0 4 d -1 6 d -2 3 d -4 1 d cl s 1221 1838 m -3 -1 d -3 -3 d -1 -6 d
0 -3 d 1 -6 d 3 -3 d 3 -1 d 2 0 d 4 1 d 2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d
cl s 1223 1840 m -4 -1 d -2 -4 d -1 -5 d 0 -4 d 1 -5 d 2 -4 d 4 -1 d 2 0 d
3 1 d 2 4 d 2 5 d 0 4 d -2 5 d -2 4 d -3 1 d cl s 1240 1818 m -1 -2 d 1 -1 d
1 1 d cl s 1239 1817 m -1 -1 d 1 -1 d 1 1 d cl s 1241 1818 m -1 -1 d 1 -1 d
1 1 d cl s 1252 1835 m 3 1 d 3 3 d 0 -24 d s 1252 1834 m 2 1 d 3 3 d 0 -23 d s
1253 1835 m 2 1 d 4 4 d 0 -24 d s 1283 1839 m -11 -16 d 17 0 d s 1282 1838 m
-11 -16 d 17 0 d s 1284 1840 m -12 -16 d 17 0 d s 1283 1839 m 0 -24 d s
1282 1838 m 0 -23 d s 1284 1840 m 0 -24 d s 1222 1981 m -4 -1 d -2 -4 d -1 -5 d
0 -4 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 4 1 d 2 3 d 1 6 d 0 4 d -1 5 d -2 4 d -4 1 d
cl s 1221 1980 m -3 -1 d -3 -3 d -1 -6 d 0 -4 d 1 -5 d 3 -4 d 3 -1 d 2 0 d
4 1 d 2 4 d 1 5 d 0 4 d -1 6 d -2 3 d -4 1 d cl s 1223 1981 m -4 -1 d -2 -3 d
-1 -6 d 0 -3 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d 2 3 d 2 6 d 0 3 d -2 6 d -2 3 d
-3 1 d cl s 1240 1959 m -1 -1 d 1 -1 d 1 1 d cl s 1239 1958 m -1 -1 d 1 -1 d
1 1 d cl s 1241 1960 m -1 -1 d 1 -1 d 1 1 d cl s 1252 1976 m 3 1 d 3 4 d
0 -24 d s 1252 1976 m 2 1 d 3 3 d 0 -24 d s 1253 1977 m 2 1 d 4 3 d 0 -23 d s
1286 1977 m -1 3 d -3 1 d -2 0 d -4 -1 d -2 -4 d -1 -5 d 0 -6 d 1 -5 d 2 -2 d
4 -1 d 1 0 d 3 1 d 2 2 d 2 4 d 0 1 d -2 3 d -2 3 d -3 1 d -1 0 d -4 -1 d
-2 -3 d -1 -3 d s 1286 1977 m -1 2 d -4 1 d -2 0 d -3 -1 d -3 -3 d -1 -6 d
0 -6 d 1 -4 d 3 -3 d 3 -1 d 1 0 d 3 1 d 3 3 d 1 3 d 0 1 d -1 4 d -3 2 d -3 1 d
-1 0 d -3 -1 d -3 -2 d -1 -4 d s 1287 1978 m -1 2 d -3 1 d -3 0 d -3 -1 d
-2 -3 d -1 -6 d 0 -5 d 1 -5 d 2 -2 d 3 -1 d 1 0 d 4 1 d 2 2 d 1 3 d 0 2 d
-1 3 d -2 2 d -4 1 d -1 0 d -3 -1 d -2 -2 d -1 -3 d s 1322 1473 m 264 0 d s
1322 1497 m 0 -24 d s 1375 1485 m 0 -12 d s 1428 1485 m 0 -12 d s 1481 1485 m
0 -12 d s 1534 1485 m 0 -12 d s 1586 1497 m 0 -24 d s 1321 1442 m -4 -1 d
-2 -4 d -1 -5 d 0 -4 d 1 -5 d 2 -4 d 4 -1 d 2 0 d 3 1 d 3 4 d 1 5 d 0 4 d
-1 5 d -3 4 d -3 1 d cl s 1320 1441 m -3 -1 d -3 -3 d -1 -6 d 0 -3 d 1 -6 d
3 -3 d 3 -1 d 2 0 d 4 1 d 2 3 d 1 6 d 0 3 d -1 6 d -2 3 d -4 1 d cl s
1322 1443 m -4 -1 d -2 -4 d -1 -5 d 0 -4 d 1 -6 d 2 -3 d 4 -1 d 2 0 d 3 1 d
2 3 d 2 6 d 0 4 d -2 5 d -2 4 d -3 1 d cl s 1565 1437 m 2 2 d 4 3 d 0 -24 d s
1564 1437 m 2 1 d 4 3 d 0 -23 d s 1566 1438 m 2 1 d 3 4 d 0 -24 d s 1586 1420 m
-1 -1 d 1 -1 d 2 1 d cl s 1586 1420 m -1 -1 d 1 -1 d 1 1 d cl s 1587 1421 m
-1 -1 d 1 -1 d 1 1 d cl s 1597 1436 m 0 1 d 1 3 d 1 1 d 2 1 d 5 0 d 2 -1 d
1 -1 d 1 -3 d 0 -2 d -1 -2 d -2 -3 d -12 -12 d 16 0 d s 1596 1436 m 0 1 d 1 2 d
1 1 d 2 1 d 5 0 d 2 -1 d 1 -1 d 2 -2 d 0 -2 d -2 -3 d -2 -3 d -11 -11 d 16 0 d
s 1597 1437 m 0 1 d 1 2 d 2 2 d 2 1 d 4 0 d 3 -1 d 1 -2 d 1 -2 d 0 -2 d -1 -2 d
-2 -4 d -12 -11 d 16 0 d s 1366 1539 m 4 -1 d 3 -2 d 4 -1 d 4 -2 d 4 -1 d
4 -1 d 4 -1 d 3 -1 d 4 -1 d 4 -1 d 4 -1 d 2 0 d 3 -1 d 2 0 d 3 0 d 4 -1 d 4 0 d
4 0 d 8 -1 d 6 0 d 4 0 d 3 0 d 3 -1 d 4 0 d 5 -1 d 5 -1 d 16 -2 d 5 -1 d 3 0 d
4 -1 d 2 0 d 6 0 d 6 -1 d 5 0 d 5 0 d 6 0 d 5 0 d 5 0 d 6 0 d s [12 6]
 0 setdash 1366 1732 m 4 -2 d 4 -3 d 4 -2 d 3 -2 d 5 -2 d 4 -2 d 3 -2 d 4 -1 d
5 -2 d 3 -1 d 4 -2 d 1 0 d 3 -1 d 3 -1 d 3 0 d 3 -1 d 4 0 d 5 -1 d 7 0 d 7 -1 d
4 -1 d 4 0 d 1 0 d 44 -10 d 6 0 d 6 -1 d 5 0 d 6 -1 d 5 0 d 6 0 d 6 0 d 4 0 d s
[2 6] 0 setdash 1366 2033 m 8 -4 d 8 -4 d 9 -4 d 8 -4 d 8 -5 d 3 -1 d 4 -3 d
5 -3 d 6 -4 d 13 -8 d 5 -4 d 4 -2 d 3 -2 d 3 -1 d 1 -1 d 4 -2 d 5 -1 d 4 -2 d
5 -1 d 5 -1 d 6 -2 d 7 -1 d 8 -1 d 7 -1 d 6 -1 d 6 0 d 6 0 d 6 0 d 6 0 d 6 0 d
1 0 d s [] 0 setdash 1322 1643 m 264 0 d 0 85 d -264 0 d cl s 932 1249 m
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930 1247 m 22 -59 d s 933 1250 m 23 -59 d s 385 2100 m -4 -2 d -4 -4 d -2 -3 d
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0 -40 d s 489 2113 m 15 -39 d s 488 2112 m 15 -39 d s 490 2115 m 15 -40 d s
519 2113 m -15 -39 d s 518 2112 m -15 -39 d s 520 2115 m -15 -40 d s 519 2113 m
0 -39 d s 518 2112 m 0 -39 d s 520 2115 m 0 -40 d s 543 2084 m -14 -20 d s
541 2082 m -13 -19 d s 544 2085 m -13 -20 d s 529 2084 m 14 0 d s 528 2082 m
13 0 d s 531 2085 m 13 0 d s 529 2064 m 14 0 d s 528 2063 m 13 0 d s 531 2065 m
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873 2101 m -3 -2 d -4 -3 d -2 -4 d -2 -6 d 0 -5 d 2 -4 d 4 -2 d 4 0 d 3 2 d
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2 1 d 3 0 d 2 -1 d 1 -1 d 1 -2 d 0 -2 d -1 -2 d -2 -3 d -9 -9 d 13 0 d s
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-4 -4 d -3 -5 d -4 -8 d -2 -9 d 0 -8 d 2 -9 d 4 -8 d 3 -6 d 4 -3 d s 976 2113 m
0 -39 d s 975 2112 m 0 -39 d s 977 2115 m 0 -40 d s 976 2113 m 15 -39 d s
975 2112 m 15 -39 d s 977 2115 m 16 -40 d s 1006 2113 m -15 -39 d s 1005 2112 m
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1031 2085 m -13 -20 d s 1017 2084 m 13 0 d s 1016 2082 m 13 0 d s 1018 2085 m
13 0 d s 1017 2064 m 13 0 d s 1016 2063 m 13 0 d s 1018 2065 m 13 0 d s
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5 5 d 4 6 d 4 8 d 2 5 d s 1377 2100 m 3 0 d 2 -2 d 2 -4 d 4 -15 d 2 -3 d 2 -2 d
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10 0 d -5 -8 d 3 0 d 2 -1 d 0 -1 d 1 -3 d 0 -2 d -1 -2 d -1 -2 d -3 -1 d -3 0 d
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0 -2 d -1 -3 d -2 -1 d -2 -1 d -3 0 d -3 1 d -1 0 d -1 2 d s 1405 2085 m 11 0 d
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4 -7 d 4 -6 d 3 -4 d s 1466 2120 m -4 -4 d -3 -6 d -4 -7 d -2 -10 d 0 -7 d
2 -10 d 4 -7 d 3 -6 d 4 -4 d s 1469 2122 m -4 -4 d -4 -5 d -4 -8 d -2 -9 d
0 -8 d 2 -9 d 4 -8 d 4 -6 d 4 -3 d s 1481 2113 m 0 -39 d s 1479 2112 m 0 -39 d
s 1482 2115 m 0 -40 d s 1481 2113 m 15 -39 d s 1479 2112 m 16 -39 d s
1482 2115 m 15 -40 d s 1511 2113 m -15 -39 d s 1510 2112 m -15 -39 d s
1512 2115 m -15 -40 d s 1511 2113 m 0 -39 d s 1510 2112 m 0 -39 d s 1512 2115 m
0 -40 d s 1534 2084 m -13 -20 d s 1533 2082 m -13 -19 d s 1536 2085 m -14 -20 d
s 1521 2084 m 13 0 d s 1520 2082 m 13 0 d s 1522 2085 m 14 0 d s 1521 2064 m
13 0 d s 1520 2063 m 13 0 d s 1522 2065 m 14 0 d s 1543 2121 m 4 -4 d 4 -6 d
3 -7 d 2 -10 d 0 -7 d -2 -10 d -3 -7 d -4 -6 d -4 -4 d s 1542 2120 m 4 -4 d
3 -6 d 4 -7 d 2 -10 d 0 -7 d -2 -10 d -4 -7 d -3 -6 d -4 -4 d s 1544 2122 m
4 -4 d 4 -5 d 3 -8 d 2 -9 d 0 -8 d -2 -9 d -3 -8 d -4 -6 d -4 -3 d s 403 1406 m
0 -10 d s 402 1405 m 0 -9 d s 403 1406 m 0 -9 d s 399 1403 m 8 -5 d s
398 1403 m 8 -5 d s 399 1404 m 8 -5 d s 407 1403 m -8 -5 d s 406 1403 m -8 -5 d
s 407 1404 m -8 -5 d s 414 1407 m 2 1 d 2 3 d 0 -17 d s 414 1407 m 1 1 d 3 2 d
0 -17 d s 415 1408 m 1 1 d 3 2 d 0 -17 d s 433 1411 m -3 -1 d -1 -3 d -1 -4 d
0 -2 d 1 -4 d 1 -3 d 3 0 d 1 0 d 3 0 d 1 3 d 1 4 d 0 2 d -1 4 d -1 3 d -3 1 d
cl s 432 1410 m -2 -1 d -2 -2 d -1 -4 d 0 -3 d 1 -4 d 2 -2 d 2 -1 d 2 0 d 2 1 d
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cl s 448 1406 m 0 -10 d s 448 1405 m 0 -9 d s 449 1406 m 0 -9 d s 444 1403 m
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452 1403 m -9 -5 d s 453 1404 m -9 -5 d s 461 1406 m 0 -10 d s 460 1405 m
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472 1407 m 2 1 d 2 3 d 0 -17 d s 472 1407 m 1 1 d 3 2 d 0 -17 d s 473 1408 m
1 1 d 3 2 d 0 -17 d s 497 1411 m -8 -17 d s 497 1410 m -8 -17 d s 498 1411 m
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523 1407 m -1 1 d -2 2 d -2 1 d -3 0 d -1 -1 d -2 -2 d -1 -1 d -1 -3 d 0 -4 d
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2 -1 d 3 0 d 2 1 d 1 2 d 1 1 d 0 3 d s 523 1407 m -1 2 d -1 1 d -2 1 d -3 0 d
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1 2 d 1 1 d 0 3 d s 518 1400 m 5 0 d s 518 1400 m 4 0 d s 519 1401 m 4 0 d s
527 1400 m 10 0 d 0 2 d -1 1 d -1 1 d -1 1 d -3 0 d -1 -1 d -2 -1 d -1 -3 d
0 -2 d 1 -2 d 2 -2 d 1 0 d 3 0 d 1 0 d 2 2 d s 527 1400 m 10 0 d 0 1 d -1 2 d
-1 1 d -2 0 d -2 0 d -2 0 d -1 -2 d -1 -2 d 0 -2 d 1 -2 d 1 -2 d 2 -1 d 2 0 d
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7 -17 d s 540 1410 m 6 -17 d s 541 1411 m 6 -17 d s 553 1411 m -6 -17 d s
553 1410 m -7 -17 d s 554 1411 m -7 -17 d s 890 1406 m 0 -10 d s 890 1405 m
0 -9 d s 891 1406 m 0 -9 d s 886 1403 m 8 -5 d s 886 1403 m 8 -5 d s 887 1404 m
8 -5 d s 894 1403 m -8 -5 d s 894 1403 m -8 -5 d s 895 1404 m -8 -5 d s
901 1407 m 2 1 d 3 3 d 0 -17 d s 901 1407 m 2 1 d 2 2 d 0 -17 d s 902 1408 m
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2 0 d 2 0 d 2 0 d 2 3 d 1 4 d 0 2 d -1 4 d -2 3 d -2 1 d cl s 920 1410 m
-3 -1 d -1 -2 d -1 -4 d 0 -3 d 1 -4 d 1 -2 d 3 -1 d 1 0 d 3 1 d 1 2 d 1 4 d
0 3 d -1 4 d -1 2 d -3 1 d cl s 921 1411 m -3 -1 d -1 -2 d -1 -4 d 0 -3 d
1 -4 d 1 -2 d 3 -1 d 1 0 d 3 1 d 1 2 d 1 4 d 0 3 d -1 4 d -1 2 d -3 1 d cl s
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949 1406 m 0 -9 d s 944 1403 m 8 -5 d s 944 1403 m 8 -5 d s 945 1404 m 8 -5 d s
952 1403 m -8 -5 d s 952 1403 m -8 -5 d s 953 1404 m -8 -5 d s 960 1407 m 1 1 d
3 3 d 0 -17 d s 959 1407 m 2 1 d 2 2 d 0 -17 d s 960 1408 m 2 1 d 2 2 d 0 -17 d
s 985 1411 m -8 -17 d s 984 1410 m -8 -17 d s 985 1411 m -8 -17 d s 974 1411 m
11 0 d s 973 1410 m 11 0 d s 974 1411 m 11 0 d s 1010 1407 m -1 1 d -1 2 d
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3 0 d 2 0 d 1 2 d 1 2 d 0 2 d s 1009 1406 m 0 2 d -2 1 d -2 1 d -3 0 d -1 -1 d
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0 1 d 0 3 d s 1010 1407 m 0 2 d -2 1 d -2 1 d -3 0 d -1 -1 d -2 -1 d -1 -2 d
-1 -2 d 0 -4 d 1 -3 d 1 -1 d 2 -2 d 1 -1 d 3 0 d 2 1 d 2 2 d 0 1 d 0 3 d s
1006 1400 m 4 0 d s 1005 1400 m 4 0 d s 1006 1401 m 4 0 d s 1015 1400 m 10 0 d
0 2 d -1 1 d -1 1 d -2 1 d -2 0 d -2 -1 d -1 -1 d -1 -3 d 0 -2 d 1 -2 d 1 -2 d
2 0 d 2 0 d 2 0 d 2 2 d s 1014 1400 m 10 0 d 0 1 d -1 2 d -1 1 d -1 0 d -3 0 d
-1 0 d -2 -2 d -1 -2 d 0 -2 d 1 -2 d 2 -2 d 1 -1 d 3 0 d 1 1 d 2 2 d s
1015 1401 m 10 0 d 0 1 d -1 2 d -1 1 d -1 0 d -3 0 d -1 0 d -2 -2 d -1 -2 d
0 -2 d 1 -2 d 2 -2 d 1 -1 d 3 0 d 1 1 d 2 2 d s 1028 1411 m 6 -17 d s
1027 1410 m 7 -17 d s 1028 1411 m 7 -17 d s 1041 1411 m -7 -17 d s 1040 1410 m
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1389 1406 m 0 -9 d s 1385 1403 m 8 -5 d s 1384 1403 m 8 -5 d s 1385 1404 m
8 -5 d s 1393 1403 m -8 -5 d s 1392 1403 m -8 -5 d s 1393 1404 m -8 -5 d s
1400 1407 m 2 1 d 2 3 d 0 -17 d s 1400 1407 m 1 1 d 3 2 d 0 -17 d s 1401 1408 m
1 1 d 3 2 d 0 -17 d s 1419 1411 m -3 -1 d -1 -3 d -1 -4 d 0 -2 d 1 -4 d 1 -3 d
3 0 d 1 0 d 3 0 d 1 3 d 1 4 d 0 2 d -1 4 d -1 3 d -3 1 d cl s 1418 1410 m
-2 -1 d -2 -2 d -1 -4 d 0 -3 d 1 -4 d 2 -2 d 2 -1 d 2 0 d 2 1 d 2 2 d 1 4 d
0 3 d -1 4 d -2 2 d -2 1 d cl s 1419 1411 m -2 -1 d -2 -2 d -1 -4 d 0 -3 d
1 -4 d 2 -2 d 2 -1 d 2 0 d 2 1 d 2 2 d 1 4 d 0 3 d -1 4 d -2 2 d -2 1 d cl s
1434 1406 m 0 -10 d s 1434 1405 m 0 -9 d s 1435 1406 m 0 -9 d s 1430 1403 m
8 -5 d s 1430 1403 m 8 -5 d s 1431 1404 m 8 -5 d s 1438 1403 m -8 -5 d s
1438 1403 m -8 -5 d s 1439 1404 m -8 -5 d s 1447 1406 m 0 -10 d s 1447 1405 m
0 -9 d s 1448 1406 m 0 -9 d s 1443 1403 m 8 -5 d s 1443 1403 m 8 -5 d s
1444 1404 m 8 -5 d s 1451 1403 m -8 -5 d s 1451 1403 m -8 -5 d s 1452 1404 m
-8 -5 d s 1459 1407 m 1 1 d 3 3 d 0 -17 d s 1458 1407 m 2 1 d 2 2 d 0 -17 d s
1459 1408 m 2 1 d 2 2 d 0 -17 d s 1484 1411 m -8 -17 d s 1483 1410 m -8 -17 d s
1484 1411 m -8 -17 d s 1472 1411 m 12 0 d s 1472 1410 m 11 0 d s 1473 1411 m
11 0 d s 1509 1407 m -1 1 d -2 2 d -1 1 d -4 0 d -1 -1 d -2 -2 d -1 -1 d 0 -3 d
0 -4 d 0 -2 d 1 -2 d 2 -2 d 1 0 d 4 0 d 1 0 d 2 2 d 1 2 d 0 2 d s 1508 1406 m
-1 2 d -1 1 d -2 1 d -3 0 d -2 -1 d -1 -1 d -1 -2 d -1 -2 d 0 -4 d 1 -3 d
1 -1 d 1 -2 d 2 -1 d 3 0 d 2 1 d 1 2 d 1 1 d 0 3 d s 1509 1407 m -1 2 d -1 1 d
-2 1 d -3 0 d -2 -1 d -1 -1 d -1 -2 d -1 -2 d 0 -4 d 1 -3 d 1 -1 d 1 -2 d
2 -1 d 3 0 d 2 1 d 1 2 d 1 1 d 0 3 d s 1505 1400 m 4 0 d s 1504 1400 m 4 0 d s
1505 1401 m 4 0 d s 1514 1400 m 9 0 d 0 2 d -1 1 d 0 1 d -2 1 d -2 0 d -2 -1 d
-2 -1 d 0 -3 d 0 -2 d 0 -2 d 2 -2 d 2 0 d 2 0 d 2 0 d 1 2 d s 1513 1400 m
10 0 d 0 1 d -1 2 d -1 1 d -1 0 d -3 0 d -2 0 d -1 -2 d -1 -2 d 0 -2 d 1 -2 d
1 -2 d 2 -1 d 3 0 d 1 1 d 2 2 d s 1514 1401 m 10 0 d 0 1 d -1 2 d -1 1 d -1 0 d
-3 0 d -2 0 d -1 -2 d -1 -2 d 0 -2 d 1 -2 d 1 -2 d 2 -1 d 3 0 d 1 1 d 2 2 d s
1527 1411 m 6 -17 d s 1526 1410 m 6 -17 d s 1527 1411 m 6 -17 d s 1539 1411 m
-6 -17 d s 1539 1410 m -7 -17 d s 1540 1411 m -7 -17 d s
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