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\begin{document}

\titlepage

\begin{flushright} RAL-93-071 \\ October 1993
\end{flushright}


\begin{center}
\vspace*{2cm}
{\large{\bf Determining the gluon distributions in the proton and photon  from
two-jet production at HERA}}
\end{center}

\vspace*{.75cm}
\begin{center}
J.R.\ Forshaw and R.G.\ Roberts \\
Rutherford Appleton Laboratory, \\ Chilton, Didcot OX11 0QX, England. \\
\end{center}

\vspace*{1.5cm}

\begin{abstract}
Two-jet production from the direct photon contribution at HERA is a
sensitive measure of the small-$x$ gluon in the proton. We propose
measurements of ratios of the jet cross-sections which will clearly
distinguish between gluons with or without singular behaviour at small $x$.
Furthermore, we show that analogous ratio measurements for the resolved
photon contribution provide a sensitive way of determining the gluon
distribution in the photon.
\end{abstract}


\newpage

{\large {\bf Introduction}}
\vspace*{0.5cm}

One of the aims of HERA is to study the structure of the proton and in
particular to learn about the distribution of gluons at small $x$ (i.e. $x$
\lapproxeq 10$^{-2}$). Here the gluon is expected to be dominant and we are in
an unexplored region of lepton-hadron scattering. The latest measurements of
the proton structure function $F_2^p(x,Q^2)$ from H1 \cite{h1f2} and ZEUS
\cite{zeusf2} show the distinct rise for $x \lapproxeq 10^{-2}$ which has
encouraged speculation that this may be a signal of so-called `Lipatov'
behaviour \cite{bfkl}. On the other hand it is possible to generate such a
rise using conventional leading log $Q^2$ evolution from a `valencelike' gluon
distribution at $Q_0^2=0.3$ GeV$^2$ \cite{grvprot}. Measuring $F_2^p$ however
is only an {\it indirect} probe of the gluon and this is the main reason why
the gluon is the least constrained of all the parton distributions to date.
There have been several methods proposed which aim to extract the small-$x$
gluon content of the proton at HERA rather more directly \cite{amcs,mns,bk}.

Here, we present an analysis of two-jet photoproduction which utilises the
separation of events into so-called `direct' and `resolved' components. Through
the construction of appropriate cross section ratios we show that HERA
should provide a sensitive and direct measurement of the small-$x$ gluon in
the proton in addition to revealing important information regarding the gluon
in the photon.

The first step we take is analogous to the procedure previously considered
for hadronic two-jet production \cite{mrs2j,cdf2j} where the configuration of
`same-side' jets allows very small $x$ values of the initial partons to be
examined. At HERA we propose isolating the contribution to jet photoproduction
from `direct' photon interactions (see fig.1(a)). We focus on the region where
both jets have equal rapidities and are travelling in the electron direction
(which we define to be that of positive rapidity). Such large and positive
rapidities mean that we are sensitive to the small-$x$ gluon within the proton.

The second step is to consider contributions like those of fig.1(b), where the
photon is resolved into its partonic components. We now study the region of
negative jet rapidities where, conversely to the first step, the cross
section is sensitive to the parton distributions in the photon for values of
$x_{\gamma}$ around $0.2 - 0.5$. With the proton gluon distribution
already constrained from step one, the resolved photon contribution to
two-jet production provides a sensitive measure of the parton distributions in
the photon. The possibility of using the two-jet data from HERA to provide
information on the parton content of the photon, especially on the gluon
distribution has been emphasised by several groups \cite{gs,dg,boo}. We wish
to emphasise that measurement of {\it ratios} of the two-jet cross sections is
a particularly clean and sensitive way of discriminating between different
parametrisations of the gluon distribution which tends to minimise the
experimental and theoretical uncertainties involved.

\vspace*{1.0cm}
{\large {\bf Step 1 $-$ the gluon in the proton}}
\vspace*{0.5cm}

To begin with, consider the direct photon contribution to two-jet production,
e.g. see fig.1(a). The two-jet cross section may be written to leading order
(LO) as

\begin{equation}
\frac{d^3\sigma^{dir}}{dy_1dy_2dp^2_T} \; = \;
zf_{\gamma /e}(z)\; xf_{j/p}(x,\mu)\; \frac{d \hat \sigma(\gamma j \rightarrow
k \l)} {d \hat t}  \label{d2sigdir}
\end{equation}

\noindent
where $f_{\gamma /e}(z)$ is the probability that the incoming electron will
emit an effectively real photon with a fraction $z$ of its momentum and
$f_{j/p}(x,\mu)$ is the momentum distribution of parton $j$ inside the proton
evaluated at scale $\mu$. The laboratory rapidities ($y_1$ and $y_2$) of the
final state partons (emitted with transverse momentum $p_T$) can be expressed
in terms of the momentum fractions $z$ and $x$:
\begin{eqnarray}
z = \frac{p_T}{\sqrt s}\; \sqrt {\frac{E_p}{E_e}}\; (e^{y_1} + e^{y_2})
\nonumber \\
x = \frac{p_T}{\sqrt s}\; \sqrt {\frac{E_e}{E_p}}\; (e^{-y_1} + e^{-y_2}).
\label{xzdefn}
\end{eqnarray}
The energies of the incoming electron and proton are $E_e$ and $E_p$
respectively and the centre-of-mass energy is $\sqrt s = 2\sqrt{E_e E_p}$.
In this analysis we shall study only the configuration where the two jets have
equal rapidities, i.e. $y_1 = y_2 = y$. At HERA energies, choosing $y \sim 1$
and $p_T = 5$ GeV, we find $x \simeq .003$.

There are two subprocesses in the direct photon contribution: (i) $\gamma \;
g \rightarrow q \; \bar q$ and (ii) $\gamma \; q (\bar q) \rightarrow
g \;q (\bar q)$ and the LO cross section of eqn.(\ref{d2sigdir}) takes the
simple form
\begin{equation}
\left . \frac{d^3\sigma^{dir}}{dy_1dy_2dp^2_T} \right |_{y_1=y_2=y} \;=\;
\;\frac{\pi \alpha \alpha_s}{4p_T^4}\;zf_{\gamma/e}(z)\;
\left [(\sum_{i} e_i^2)xg(x,\mu)\;+\;(10/3)F_2^p(x,\mu)\right ].
\label{xsecn}
\end{equation}
Since $xg(x,\mu)$ is much larger than $x\bar q(x,\mu)$ at small $x$ then (i)
dominates the cross section for $x \lapproxeq 10^{-2}$. Thus evaluating ratios
of the above cross section at different values of $y$ effectively measures the
ratio of the gluon distribution at different values of $x$. We suggest
measuring the ratio $\sigma_{dir}(y)/\sigma_{dir}(y=-0.5)$ (where we have
integrated over all $p_T \ge 5$ GeV in eqn.(\ref{xsecn}) to construct
$\sigma_{dir}(y)$). Fig.2 shows the expectations for this ratio from various
proposed gluons: $MRS D0'$, $MRS D-'$\cite{mrs} and $GRV$\cite{grvprot}. The
$D-'$ curve is generated from a singular gluon which, at $\mu ^2 = 4$ GeV$^2$
and small $x$, behaves as $ xg(x,\mu) \sim x^{-1/2}$ which is in contrast to
the $D0'$ curve which corresponds to $xg(x,\mu)\rightarrow$ constant as $x
\rightarrow 0$ at $\mu ^2 = 4$ GeV$^2$. The $GRV$ prediction leads to a
singular gluon distribution for $\mu^2 \gapproxeq 1$ GeV$^2$ due to the long
evolution time which results from starting evolution at low scales.
The curves of fig.2 were computed with $z$ in the range $0.2 \le z \le 0.7$.
These are typical HERA cuts and are intended to reduce background uncertainties
due to beam gas interactions ($z > 0.2$) and DIS interactions ($z < 0.7$), they
are also responsible for the cusps around $y = 0.1$.

The scale $\mu$ was taken to be $p_T/2$, as specified
by the prescription of Ellis, Kunszt and Soper \cite{eks} who have shown that
the scale $\mu$ for which the leading order calculation reproduces the less
scale dependent ${\cal O}(\alpha_s^3)$ result is given by:
\begin{equation}
\mu \approx \frac{{\rm cosh}(y_1-y_2)}{{\rm cosh}(0.7(y_1-y_2))} \frac{p_T}{2}
\quad \stackrel{y_1=y_2}{\longrightarrow} \quad \frac{p_T}{2}.
\label{mu}
\end{equation}
This (approximate) equality of the LO and NLO cross sections for the choice of
a common scale $\mu = {1\over 2}p_T$ when $y_1=y_2$ is also consistent with
the results of B\"odecker for two-jet direct photoproduction \cite{bod}.
Varying the value of $\mu$, e.g. to $p_T$, does not seriously alter the curves
in fig.2.

As the figure demonstrates, this is a sensitive measure since it effectively
measures the ratio of the magnitude of the gluon at small $x$ to that
around $x \sim 0.1$. The ratio differs by as much as 40\% between the
$MRS D0'$ and $MRS D-'$ predictions and experiment should easily be able to
distinguish between them. Note that we choose to evaluate the cross sections at
$y_1 = y_2$ since this maximises the sensitivity to the particular choice of
gluon distribution, otherwise contributions from larger $x$ values
tend to smear out the small-$x$ contribution.

Of course the predictions we have for the ratio in fig.2 does assume that
one can indeed separate the direct and resolved components of the photon on an
event by event basis. Recent preliminary results from HERA demonstrate that
making a suitable cut on $x_\gamma$ (see fig.1(b)), e.g $x_\gamma \ge 0.75$,
can provide the required clean separation \cite{marseille}. Furthermore, we
have checked, in LO, that the direct cross section is almost unaltered after
including the resolved component with $x_{\gamma} \ge 0.75$.

\vspace*{1.0cm}
{\large {\bf Step 2 $-$ the gluon in the photon}}
\vspace*{0.5cm}

We next turn to the resolved contribution, e.g. fig.1(b), where the two-jet
cross section, to leading order, is given by

\begin{equation}
\frac{d^3\sigma^{res}}{dy_1dy_2dp^2_T} \; = \;\int dz \, f_{\gamma /e}(z)\;
x_\gamma f_{i/\gamma}(x_\gamma,\mu) \; xf_{j/p}(x,\mu)\;
\frac{d \hat \sigma(i j  \rightarrow k \l)} {d \hat t}
\label{d2sigres}
\end{equation}
and the expression for $z$ in eqn.(\ref{xzdefn}) is now the expression for
the product $zx_\gamma$.

In the previous section, we saw that choosing $y_1$, $y_2$ large and positive
led to small $x$ for the proton, now we see that choosing $y_1$,
$y_2$ large and negative leads to small $zx_\gamma$. If we compute the
average  values of $x_\gamma$ we find that typically we are exploring the
range $0.18 < x_\gamma < 0.5$ for $-2 < y_1=y_2 < 0$.

Instead of having only two subprocesses, as in step one, we now have the
full set of leading order graphs which contribute to jet cross sections
in hadron-hadron scattering. We will assume that, from the analysis in step
one, the small-$x$ behaviour of the partons in the proton is now sufficiently
pinned down so that an analysis of the two-jet cross section can yield
direct information on the partons in the photon. Again we take the scale
$\mu={1\over 2}p_T$ in the LO expressions for hard cross sections.
To a large extent, the quark distributions in the photon are
already constrained from fits to $F_2^\gamma$ and this is reflected in various
popular parametrisations \cite{gs,dg,grv,lac} where the major differences
all reside in the assumed behaviour of the gluon.

To emphasise the role of the resolved contribution we therefore shift towards
more negative values of the rapidities $y_1$ and $y_2$. In fig.3 we show
predictions for the ratio of the resolved photon cross section (defined
as the component with $x_\gamma < 0.75$) for $-2 \le y \le 0$ to the direct
photon two-jet cross section at $y=0$. We choose to normalise to the direct
cross section at $y=0$ since this choice gives good sensitivity to the
normalisation (as well as the shape) of the parton distributions in the photon,
as well as ensuring that good statistics should be possible ($y=0$ is near the
peak of the direct cross section rapidity distribution). Again we integrate
over $p_T \ge 5$ GeV. It is clear from the figure that the large variations
imply that the ratio is indeed a sensitive measure of the gluon density in the
photon.

\vspace*{1.0cm}
{\large {\bf Conclusions}}
\vspace{0.5cm}

We have proposed that a measurement of the two-jet cross section ratio,
$\sigma_{dir}(y) /\sigma_{dir}(-1)$, for $y_1=y_2=y$ from
photoproduction at HERA will provide a sensitive test of the gluon
density in the proton. The relatively large values of $y$ which are accessible
enable the gluon content of the proton to be probed in the interesting
small-$x$ region. Since we expect many of the experimental uncertainties
involved in computing the ratio to cancel (and that any rapidity dependence of
the detector acceptance can be corrected for) we expect that the construction
of such a cross section ratio will be experimentally straightforward.

Already, events due to hard two-jet production at HERA have been seen clearly
for $p_T$ up to 20 GeV \cite{marseille} $-$ even a separation of these events
into `enriched direct $\gamma$' and `enriched resolved $\gamma$' samples
has been performed. These observations are extremely encouraging for the
method we suggest since, in step one, the small-$x$ gluon in the proton is
determined from the `clean' direct photon component. Having pinned down the
gluon in the proton one can then proceed to extract information on the gluon
density in the photon. This is step two of our recipe in which only the
resolved component of the photon contributes and where a measurement of the
ratio, $\sigma_{res}(y)/\sigma_{dir}(y=0)$, can go a long way in discriminating
between the various proposed gluon distributions of the photon.

We believe that using {\it ratios} of the cross sections in this way reduces
both experimental and theoretical uncertainties and allows a relatively
simple and logical procedure to provide a sensitive determination of the gluon
densities in both the proton and photon.

\vspace*{1cm}
\noindent {\large {\bf Acknowledgements}}
\vspace*{0.5cm}

It is a pleasure to thank Jonathan Butterworth for many helpful discussions
and suggestions.


\newpage

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(1993) 391.
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\end{thebibliography}

\newpage

\vskip 1.0cm
\noindent{\large\bf Figure Captions}


\begin{itemize}
\item[Fig.\ 1] (a) A direct photon contribution to the hard two-jet
cross section. \newline \indent (b) A resolved photon contribution to the hard
two-jet cross section.

\item[Fig.\ 2] The ratio
$\left . \frac{d^2\sigma^{dir}}{dy_1dy_2} \right |_{y_1=y_2=y}
/\left . \frac{d^2\sigma^{dir}}{dy_1dy_2} \right |_{y_1=y_2=-0.5}$
for three choices of proton

\vspace*{0.2cm}
gluon density, i.e. $MRS D0'$, $MRS D-'$
\cite{mrs} and $GRV$\cite{grvprot}.

\item[Fig.\ 3] The ratio
$\left . \frac{d^2\sigma^{res}}{dy_1dy_2} \right |_{y_1=y_2=y}
/\left . \frac{d^2\sigma^{dir}}{dy_1dy_2} \right |_{y_1=y_2=0}$
  using (a) $MRS D-'$ and (b) $MRS D0'$ for the proton parton densities.
The labelled curves correspond to various choices of the photon parton
densities, LAC1, LAC3 \cite{lac}, GS2 \cite{gs}, GRV \cite{grv} and
DG \cite{dg}. Also shown are the corresponding predictions when the
gluon density in the photon is switched off.

\end{itemize}


\end{document}

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  452 1777 d  454 1778 d  437 1778 r  445 1774 d  451 1774 d  452 1775 d
  454 1778 d  454 1782 d 1339 1788 r 1367 1788 d 1382 1801 r 1385 1802 d
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 2311 1807 r 2307 1805 d 2303 1801 d 2302 1793 d 2302 1788 d 2303 1780 d
 2307 1775 d 2311 1774 d 2314 1774 d 2319 1775 d 2322 1780 d 2324 1788 d
 2324 1793 d 2322 1801 d 2319 1805 d 2314 1807 d 2311 1807 d 2308 1805 d
 2307 1804 d 2305 1801 d 2303 1793 d 2303 1788 d 2305 1780 d 2307 1777 d
 2308 1775 d 2311 1774 d 2314 1774 r 2318 1775 d 2319 1777 d 2321 1780 d
 2322 1788 d 2322 1793 d 2321 1801 d 2319 1804 d 2318 1805 d 2314 1807 d
  424 3013 r 2313 3013 d  424 3013 r  424 2962 d  613 3013 r  613 2988 d
  802 3013 r  802 2988 d  991 3013 r  991 2988 d 1180 3013 r 1180 2988 d
 1369 3013 r 1369 2962 d 1558 3013 r 1558 2988 d 1746 3013 r 1746 2988 d
 1935 3013 r 1935 2988 d 2124 3013 r 2124 2988 d 2313 3013 r 2313 2962 d
  424 1838 r  424 3013 d  424 1838 r  475 1838 d  424 1897 r  449 1897 d
  424 1956 r  449 1956 d  424 2015 r  449 2015 d  424 2073 r  449 2073 d
  424 2132 r  475 2132 d  424 2191 r  449 2191 d  424 2250 r  449 2250 d
  424 2308 r  449 2308 d  424 2367 r  449 2367 d  424 2426 r  475 2426 d
  424 2485 r  449 2485 d  424 2543 r  449 2543 d  424 2602 r  449 2602 d
  424 2661 r  449 2661 d  424 2719 r  475 2719 d  424 2778 r  449 2778 d
  424 2837 r  449 2837 d  424 2896 r  449 2896 d  424 2954 r  449 2954 d
  424 3013 r  475 3013 d  381 1857 r  377 1855 d  373 1851 d  372 1843 d
  372 1838 d  373 1830 d  377 1825 d  381 1824 d  384 1824 d  389 1825 d
  392 1830 d  394 1838 d  394 1843 d  392 1851 d  389 1855 d  384 1857 d
  381 1857 d  378 1855 d  377 1854 d  375 1851 d  373 1843 d  373 1838 d
  375 1830 d  377 1827 d  378 1825 d  381 1824 d  384 1824 r  388 1825 d
  389 1827 d  391 1830 d  392 1838 d  392 1843 d  391 1851 d  389 1854 d
  388 1855 d  384 1857 d  377 2145 r  380 2146 d  384 2151 d  384 2118 d
  383 2149 r  383 2118 d  377 2118 r  391 2118 d  373 2439 r  375 2437 d
  373 2436 d  372 2437 d  372 2439 d  373 2442 d  375 2443 d  380 2445 d
  386 2445 d  391 2443 d  392 2442 d  394 2439 d  394 2436 d  392 2432 d
  388 2429 d  380 2426 d  377 2424 d  373 2421 d  372 2416 d  372 2412 d
  386 2445 r  389 2443 d  391 2442 d  392 2439 d  392 2436 d  391 2432 d
  386 2429 d  380 2426 d  372 2415 r  373 2416 d  377 2416 d  384 2413 d
  389 2413 d  392 2415 d  394 2416 d  377 2416 r  384 2412 d  391 2412 d
  392 2413 d  394 2416 d  394 2420 d  373 2733 r  375 2732 d  373 2730 d
  372 2732 d  372 2733 d  375 2736 d  380 2738 d  386 2738 d  391 2736 d
  392 2733 d  392 2729 d  391 2725 d  386 2724 d  381 2724 d  386 2738 r
  389 2736 d  391 2733 d  391 2729 d  389 2725 d  386 2724 d  389 2722 d
  392 2719 d  394 2716 d  394 2711 d  392 2708 d  391 2706 d  386 2705 d
  380 2705 d  375 2706 d  373 2708 d  372 2711 d  372 2713 d  373 2714 d
  375 2713 d  373 2711 d  391 2721 r  392 2716 d  392 2711 d  391 2708 d
  389 2706 d  386 2705 d  386 3029 r  386 2999 d  388 3032 r  388 2999 d
  388 3032 r  370 3008 d  396 3008 d  381 2999 r  392 2999 d 2313 1838 r
 2313 3013 d 2313 1838 r 2262 1838 d 2313 1897 r 2288 1897 d 2313 1956 r
 2288 1956 d 2313 2015 r 2288 2015 d 2313 2073 r 2288 2073 d 2313 2132 r
 2262 2132 d 2313 2191 r 2288 2191 d 2313 2250 r 2288 2250 d 2313 2308 r
 2288 2308 d 2313 2367 r 2288 2367 d 2313 2426 r 2262 2426 d 2313 2485 r
 2288 2485 d 2313 2543 r 2288 2543 d 2313 2602 r 2288 2602 d 2313 2661 r
 2288 2661 d 2313 2719 r 2262 2719 d 2313 2778 r 2288 2778 d 2313 2837 r
 2288 2837 d 2313 2896 r 2288 2896 d 2313 2954 r 2288 2954 d 2313 3013 r
 2262 3013 d 1359 1745 r 1369 1723 d 1361 1745 r 1369 1726 d 1378 1745 r
 1369 1723 d 1366 1716 d 1363 1713 d 1359 1712 d 1358 1712 d 1356 1713 d
 1358 1715 d 1359 1713 d 1355 1745 r 1366 1745 d 1374 1745 r 1383 1745 d
  226 2281 r  226 2263 d  228 2259 d  232 2255 d  237 2254 d  242 2254 d
  245 2255 d  247 2257 d  248 2260 d  248 2263 d  247 2268 d  242 2271 d
  237 2273 d  232 2273 d  229 2271 d  228 2270 d  226 2266 d  226 2263 r
  228 2260 d  232 2257 d  237 2255 d  244 2255 d  247 2257 d  248 2263 r
  247 2266 d  242 2270 d  237 2271 d  231 2271 d  228 2270 d  228 2281 d
  204 2289 r  217 2289 d  204 2290 r  217 2290 d  210 2290 r  207 2291 d
  205 2292 d  204 2294 d  204 2297 d  205 2298 d  206 2298 d  207 2297 d
  206 2296 d  205 2297 d  204 2286 r  204 2290 d  217 2286 r  217 2292 d
  210 2304 r  210 2315 d  208 2315 d  206 2314 d  205 2313 d  204 2312 d
  204 2309 d  205 2306 d  207 2304 d  210 2303 d  211 2303 d  214 2304 d
  216 2306 d  217 2309 d  217 2311 d  216 2313 d  214 2315 d  210 2314 r
  207 2314 d  205 2313 d  204 2309 r  205 2307 d  207 2305 d  210 2304 d
  211 2304 d  214 2305 d  216 2307 d  217 2309 d  205 2331 r  204 2332 d
  207 2332 d  205 2331 d  204 2328 d  204 2325 d  205 2322 d  206 2321 d
  207 2321 d  209 2322 d  210 2324 d  211 2329 d  212 2331 d  213 2332 d
  207 2321 r  208 2322 d  209 2324 d  211 2329 d  211 2331 d  213 2332 d
  215 2332 d  216 2331 d  217 2328 d  217 2325 d  216 2322 d  214 2321 d
  217 2321 d  216 2322 d  209 2352 r  212 2349 d  217 2346 d  223 2342 d
  231 2341 d  237 2341 d  245 2342 d  251 2346 d  256 2349 d  259 2352 d
  212 2349 r  218 2346 d  223 2344 d  231 2342 d  237 2342 d  245 2344 d
  250 2346 d  256 2349 d  226 2363 r  248 2373 d  226 2365 r  245 2373 d
  226 2382 r  248 2373 d  255 2369 d  258 2366 d  259 2363 d  259 2361 d
  258 2360 d  256 2361 d  258 2363 d  226 2358 r  226 2369 d  226 2377 r
  226 2387 d  209 2393 r  212 2396 d  217 2399 d  223 2403 d  231 2404 d
  237 2404 d  245 2403 d  251 2399 d  256 2396 d  259 2393 d  212 2396 r
  218 2399 d  223 2401 d  231 2403 d  237 2403 d  245 2401 d  250 2399 d
  256 2396 d  209 2442 r  259 2414 d  226 2477 r  226 2460 d  228 2455 d
  232 2452 d  237 2450 d  242 2450 d  245 2452 d  247 2453 d  248 2457 d
  248 2460 d  247 2465 d  242 2468 d  237 2469 d  232 2469 d  229 2468 d
  228 2466 d  226 2463 d  226 2460 r  228 2457 d  232 2453 d  237 2452 d
  244 2452 d  247 2453 d  248 2460 r  247 2463 d  242 2466 d  237 2468 d
  231 2468 d  228 2466 d  228 2477 d  197 2495 r  217 2495 d  197 2496 r
  217 2496 d  207 2495 r  205 2493 d  204 2491 d  204 2489 d  205 2486 d
  207 2484 d  210 2483 d  211 2483 d  214 2484 d  216 2486 d  217 2489 d
  217 2491 d  216 2493 d  214 2495 d  204 2489 r  205 2487 d  207 2485 d
  210 2484 d  211 2484 d  214 2485 d  216 2487 d  217 2489 d  197 2492 r
  197 2496 d  217 2495 r  217 2499 d  197 2505 r  198 2504 d  199 2505 d
  198 2506 d  197 2505 d  204 2505 r  217 2505 d  204 2506 r  217 2506 d
  204 2502 r  204 2506 d  217 2502 r  217 2509 d  204 2516 r  217 2516 d
  204 2517 r  217 2517 d  210 2517 r  207 2518 d  205 2519 d  204 2521 d
  204 2524 d  205 2525 d  206 2525 d  207 2524 d  206 2523 d  205 2524 d
  204 2513 r  204 2517 d  217 2513 r  217 2519 d  209 2545 r  212 2541 d
  217 2538 d  223 2535 d  231 2533 d  237 2533 d  245 2535 d  251 2538 d
  256 2541 d  259 2545 d  212 2541 r  218 2538 d  223 2537 d  231 2535 d
  237 2535 d  245 2537 d  250 2538 d  256 2541 d  215 2564 r  217 2559 d
  221 2556 d  229 2554 d  234 2554 d  242 2556 d  247 2559 d  248 2564 d
  248 2567 d  247 2572 d  242 2575 d  234 2576 d  229 2576 d  221 2575 d
  217 2572 d  215 2567 d  215 2564 d  217 2560 d  218 2559 d  221 2557 d
  229 2556 d  234 2556 d  242 2557 d  245 2559 d  247 2560 d  248 2564 d
  248 2567 r  247 2570 d  245 2572 d  242 2573 d  234 2575 d  229 2575 d
  221 2573 d  218 2572 d  217 2570 d  215 2567 d  209 2586 r  212 2589 d
  217 2592 d  223 2595 d  231 2597 d  237 2597 d  245 2595 d  251 2592 d
  256 2589 d  259 2586 d  212 2589 r  218 2592 d  223 2594 d  231 2595 d
  237 2595 d  245 2594 d  250 2592 d  256 2589 d  424 2096 r  519 2091 d
  613 2085 d  707 2080 d  802 2074 d  896 2068 d  991 2062 d 1085 2055 d
 1180 2048 d 1274 2041 d 1369 2034 d 1463 2027 d 1558 2019 d 1652 2011 d
 1746 2002 d 1841 1992 d 1935 1982 d 2030 1970 d 2124 1956 d 2219 1942 d
 2313 1929 d lt1  424 2739 r  519 2650 d  613 2563 d  707 2482 d  802 2405 d
  896 2334 d  991 2268 d 1085 2210 d 1180 2157 d 1274 2111 d 1369 2072 d
 1463 2039 d 1558 2012 d 1652 1989 d 1746 1971 d 1841 1957 d 1935 1944 d
 2030 1933 d 2124 1923 d 2219 1912 d 2313 1903 d lt3  424 2163 r  519 2164 d
  613 2164 d  707 2162 d  802 2160 d  896 2156 d  991 2152 d 1085 2145 d
 1180 2138 d 1274 2129 d 1369 2119 d 1463 2108 d 1558 2096 d 1652 2083 d
 1746 2068 d 1841 2051 d 1935 2034 d 2030 2015 d 2124 1994 d 2219 1974 d
 2313 1954 d lt4  424 2139 r  519 2131 d  613 2122 d  707 2113 d  802 2104 d
  896 2095 d  991 2084 d 1085 2074 d 1180 2063 d 1274 2052 d 1369 2040 d
 1463 2029 d 1558 2017 d 1652 2005 d 1746 1993 d 1841 1980 d 1935 1968 d
 2030 1955 d 2124 1941 d 2219 1927 d 2313 1914 d lt5  424 2300 r  519 2303 d
  613 2307 d  707 2311 d  802 2315 d  896 2320 d  991 2326 d 1085 2333 d
 1180 2340 d 1274 2350 d 1369 2361 d 1463 2374 d 1558 2389 d 1652 2404 d
 1746 2419 d 1841 2431 d 1935 2437 d 2030 2431 d 2124 2403 d 2219 2363 d
 2313 2321 d lt0  424 1868 r  519 1870 d  613 1871 d  707 1873 d  802 1875 d
  896 1877 d  991 1879 d 1085 1882 d 1180 1884 d 1274 1886 d 1369 1889 d
 1463 1891 d 1558 1893 d 1652 1895 d 1746 1897 d 1841 1897 d 1935 1897 d
 2030 1896 d 2124 1893 d 2219 1888 d 2313 1884 d lt1  424 1878 r  519 1879 d
  613 1880 d  707 1882 d  802 1884 d  896 1885 d  991 1887 d 1085 1889 d
 1180 1892 d 1274 1894 d 1369 1897 d 1463 1899 d 1558 1901 d 1652 1904 d
 1746 1906 d 1841 1907 d 1935 1907 d 2030 1905 d 2124 1902 d 2219 1897 d
 2313 1892 d lt3  424 1872 r  519 1874 d  613 1876 d  707 1878 d  802 1880 d
  896 1883 d  991 1885 d 1085 1887 d 1180 1889 d 1274 1892 d 1369 1894 d
 1463 1896 d 1558 1898 d 1652 1900 d 1746 1901 d 1841 1902 d 1935 1901 d
 2030 1900 d 2124 1896 d 2219 1891 d 2313 1886 d lt4  424 1881 r  519 1883 d
  613 1886 d  707 1888 d  802 1891 d  896 1893 d  991 1896 d 1085 1898 d
 1180 1901 d 1274 1903 d 1369 1905 d 1463 1907 d 1558 1908 d 1652 1909 d
 1746 1909 d 1841 1909 d 1935 1907 d 2030 1905 d 2124 1900 d 2219 1894 d
 2313 1889 d lt5  424 1879 r  519 1880 d  613 1882 d  707 1884 d  802 1886 d
  896 1888 d  991 1890 d 1085 1892 d 1180 1894 d 1274 1895 d 1369 1897 d
 1463 1899 d 1558 1900 d 1652 1902 d 1746 1903 d 1841 1903 d 1935 1903 d
 2030 1901 d 2124 1897 d 2219 1893 d 2313 1888 d lt0  904 2900 r  904 2867 d
  906 2900 r  906 2867 d  899 2900 r  918 2900 d  923 2898 d  925 2897 d
  926 2894 d  926 2891 d  925 2887 d  923 2886 d  918 2884 d  906 2884 d
  918 2900 r  921 2898 d  923 2897 d  925 2894 d  925 2891 d  923 2887 d
  921 2886 d  918 2884 d  899 2867 r  910 2867 d  915 2884 r  921 2870 d
  925 2867 d  928 2867 d  929 2870 d  915 2884 r  918 2881 d  925 2867 d
  937 2879 r  956 2879 d  956 2883 d  955 2886 d  953 2887 d  950 2889 d
  945 2889 d  940 2887 d  937 2884 d  936 2879 d  936 2876 d  937 2871 d
  940 2868 d  945 2867 d  948 2867 d  953 2868 d  956 2871 d  955 2879 r
  955 2884 d  953 2887 d  945 2889 r  942 2887 d  939 2884 d  937 2879 d
  937 2876 d  939 2871 d  942 2868 d  945 2867 d  982 2887 r  983 2889 d
  983 2884 d  982 2887 d  977 2889 d  972 2889 d  967 2887 d  966 2886 d
  966 2884 d  967 2881 d  971 2879 d  979 2876 d  982 2875 d  983 2873 d
  966 2884 r  967 2883 d  971 2881 d  979 2878 d  982 2876 d  983 2873 d
  983 2870 d  982 2868 d  977 2867 d  972 2867 d  967 2868 d  966 2871 d
  966 2867 d  967 2868 d 1002 2889 r  998 2887 d  994 2884 d  993 2879 d
  993 2876 d  994 2871 d  998 2868 d 1002 2867 d 1006 2867 d 1010 2868 d
 1013 2871 d 1015 2876 d 1015 2879 d 1013 2884 d 1010 2887 d 1006 2889 d
 1002 2889 d  999 2887 d  996 2884 d  994 2879 d  994 2876 d  996 2871 d
  999 2868 d 1002 2867 d 1006 2867 r 1009 2868 d 1012 2871 d 1013 2876 d
 1013 2879 d 1012 2884 d 1009 2887 d 1006 2889 d 1028 2900 r 1028 2867 d
 1029 2900 r 1029 2867 d 1023 2900 r 1029 2900 d 1023 2867 r 1034 2867 d
 1044 2889 r 1053 2867 d 1045 2889 r 1053 2870 d 1063 2889 r 1053 2867 d
 1039 2889 r 1050 2889 d 1058 2889 r 1067 2889 d 1075 2879 r 1094 2879 d
 1094 2883 d 1093 2886 d 1091 2887 d 1088 2889 d 1083 2889 d 1079 2887 d
 1075 2884 d 1074 2879 d 1074 2876 d 1075 2871 d 1079 2868 d 1083 2867 d
 1086 2867 d 1091 2868 d 1094 2871 d 1093 2879 r 1093 2884 d 1091 2887 d
 1083 2889 r 1080 2887 d 1077 2884 d 1075 2879 d 1075 2876 d 1077 2871 d
 1080 2868 d 1083 2867 d 1123 2900 r 1123 2867 d 1125 2900 r 1125 2867 d
 1123 2884 r 1120 2887 d 1117 2889 d 1113 2889 d 1109 2887 d 1106 2884 d
 1104 2879 d 1104 2876 d 1106 2871 d 1109 2868 d 1113 2867 d 1117 2867 d
 1120 2868 d 1123 2871 d 1113 2889 r 1110 2887 d 1107 2884 d 1106 2879 d
 1106 2876 d 1107 2871 d 1110 2868 d 1113 2867 d 1118 2900 r 1125 2900 d
 1123 2867 r 1129 2867 d 1169 2900 r 1169 2867 d 1171 2900 r 1171 2867 d
 1164 2900 r 1183 2900 d 1188 2898 d 1190 2897 d 1191 2894 d 1191 2889 d
 1190 2886 d 1188 2884 d 1183 2883 d 1171 2883 d 1183 2900 r 1187 2898 d
 1188 2897 d 1190 2894 d 1190 2889 d 1188 2886 d 1187 2884 d 1183 2883 d
 1164 2867 r 1175 2867 d 1204 2900 r 1204 2867 d 1206 2900 r 1206 2867 d
 1206 2884 r 1209 2887 d 1213 2889 d 1217 2889 d 1221 2887 d 1223 2884 d
 1223 2867 d 1217 2889 r 1220 2887 d 1221 2884 d 1221 2867 d 1199 2900 r
 1206 2900 d 1199 2867 r 1210 2867 d 1217 2867 r 1228 2867 d 1245 2889 r
 1240 2887 d 1237 2884 d 1236 2879 d 1236 2876 d 1237 2871 d 1240 2868 d
 1245 2867 d 1248 2867 d 1253 2868 d 1256 2871 d 1258 2876 d 1258 2879 d
 1256 2884 d 1253 2887 d 1248 2889 d 1245 2889 d 1242 2887 d 1239 2884 d
 1237 2879 d 1237 2876 d 1239 2871 d 1242 2868 d 1245 2867 d 1248 2867 r
 1252 2868 d 1255 2871 d 1256 2876 d 1256 2879 d 1255 2884 d 1252 2887 d
 1248 2889 d 1271 2900 r 1271 2873 d 1272 2868 d 1275 2867 d 1279 2867 d
 1282 2868 d 1283 2871 d 1272 2900 r 1272 2873 d 1274 2868 d 1275 2867 d
 1266 2889 r 1279 2889 d 1301 2889 r 1296 2887 d 1293 2884 d 1291 2879 d
 1291 2876 d 1293 2871 d 1296 2868 d 1301 2867 d 1304 2867 d 1309 2868 d
 1312 2871 d 1313 2876 d 1313 2879 d 1312 2884 d 1309 2887 d 1304 2889 d
 1301 2889 d 1298 2887 d 1294 2884 d 1293 2879 d 1293 2876 d 1294 2871 d
 1298 2868 d 1301 2867 d 1304 2867 r 1307 2868 d 1310 2871 d 1312 2876 d
 1312 2879 d 1310 2884 d 1307 2887 d 1304 2889 d 1326 2889 r 1326 2867 d
 1328 2889 r 1328 2867 d 1328 2884 r 1331 2887 d 1336 2889 d 1339 2889 d
 1344 2887 d 1345 2884 d 1345 2867 d 1339 2889 r 1342 2887 d 1344 2884 d
 1344 2867 d 1321 2889 r 1328 2889 d 1321 2867 r 1333 2867 d 1339 2867 r
 1350 2867 d 1409 2895 r 1410 2892 d 1410 2900 d 1409 2895 d 1406 2898 d
 1401 2900 d 1398 2900 d 1393 2898 d 1390 2895 d 1388 2892 d 1387 2887 d
 1387 2879 d 1388 2875 d 1390 2871 d 1393 2868 d 1398 2867 d 1401 2867 d
 1406 2868 d 1409 2871 d 1410 2875 d 1398 2900 r 1394 2898 d 1391 2895 d
 1390 2892 d 1388 2887 d 1388 2879 d 1390 2875 d 1391 2871 d 1394 2868 d
 1398 2867 d 1429 2889 r 1425 2887 d 1421 2884 d 1420 2879 d 1420 2876 d
 1421 2871 d 1425 2868 d 1429 2867 d 1433 2867 d 1437 2868 d 1440 2871 d
 1442 2876 d 1442 2879 d 1440 2884 d 1437 2887 d 1433 2889 d 1429 2889 d
 1426 2887 d 1423 2884 d 1421 2879 d 1421 2876 d 1423 2871 d 1426 2868 d
 1429 2867 d 1433 2867 r 1436 2868 d 1439 2871 d 1440 2876 d 1440 2879 d
 1439 2884 d 1436 2887 d 1433 2889 d 1455 2889 r 1455 2867 d 1456 2889 r
 1456 2867 d 1456 2884 r 1460 2887 d 1464 2889 d 1467 2889 d 1472 2887 d
 1474 2884 d 1474 2867 d 1467 2889 r 1471 2887 d 1472 2884 d 1472 2867 d
 1450 2889 r 1456 2889 d 1450 2867 r 1461 2867 d 1467 2867 r 1479 2867 d
 1490 2900 r 1490 2873 d 1491 2868 d 1494 2867 d 1498 2867 d 1501 2868 d
 1502 2871 d 1491 2900 r 1491 2873 d 1493 2868 d 1494 2867 d 1485 2889 r
 1498 2889 d 1514 2889 r 1514 2867 d 1515 2889 r 1515 2867 d 1515 2879 r
 1517 2884 d 1520 2887 d 1523 2889 d 1528 2889 d 1529 2887 d 1529 2886 d
 1528 2884 d 1526 2886 d 1528 2887 d 1509 2889 r 1515 2889 d 1509 2867 r
 1520 2867 d 1540 2900 r 1539 2898 d 1540 2897 d 1542 2898 d 1540 2900 d
 1540 2889 r 1540 2867 d 1542 2889 r 1542 2867 d 1536 2889 r 1542 2889 d
 1536 2867 r 1547 2867 d 1558 2900 r 1558 2867 d 1560 2900 r 1560 2867 d
 1560 2884 r 1563 2887 d 1566 2889 d 1569 2889 d 1574 2887 d 1577 2884 d
 1579 2879 d 1579 2876 d 1577 2871 d 1574 2868 d 1569 2867 d 1566 2867 d
 1563 2868 d 1560 2871 d 1569 2889 r 1572 2887 d 1575 2884 d 1577 2879 d
 1577 2876 d 1575 2871 d 1572 2868 d 1569 2867 d 1553 2900 r 1560 2900 d
 1591 2889 r 1591 2871 d 1593 2868 d 1598 2867 d 1601 2867 d 1606 2868 d
 1609 2871 d 1593 2889 r 1593 2871 d 1594 2868 d 1598 2867 d 1609 2889 r
 1609 2867 d 1610 2889 r 1610 2867 d 1587 2889 r 1593 2889 d 1604 2889 r
 1610 2889 d 1609 2867 r 1615 2867 d 1626 2900 r 1626 2873 d 1628 2868 d
 1631 2867 d 1634 2867 d 1637 2868 d 1639 2871 d 1628 2900 r 1628 2873 d
 1629 2868 d 1631 2867 d 1621 2889 r 1634 2889 d 1650 2900 r 1648 2898 d
 1650 2897 d 1652 2898 d 1650 2900 d 1650 2889 r 1650 2867 d 1652 2889 r
 1652 2867 d 1645 2889 r 1652 2889 d 1645 2867 r 1656 2867 d 1674 2889 r
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 1674 2867 d 1677 2867 d 1682 2868 d 1685 2871 d 1687 2876 d 1687 2879 d
 1685 2884 d 1682 2887 d 1677 2889 d 1674 2889 d 1671 2887 d 1667 2884 d
 1666 2879 d 1666 2876 d 1667 2871 d 1671 2868 d 1674 2867 d 1677 2867 r
 1680 2868 d 1683 2871 d 1685 2876 d 1685 2879 d 1683 2884 d 1680 2887 d
 1677 2889 d 1699 2889 r 1699 2867 d 1701 2889 r 1701 2867 d 1701 2884 r
 1704 2887 d 1709 2889 d 1712 2889 d 1717 2887 d 1718 2884 d 1718 2867 d
 1712 2889 r 1715 2887 d 1717 2884 d 1717 2867 d 1694 2889 r 1701 2889 d
 1694 2867 r 1706 2867 d 1712 2867 r 1723 2867 d 1858 2818 r 1855 2815 d
 1852 2810 d 1849 2804 d 1847 2796 d 1847 2790 d 1849 2782 d 1852 2776 d
 1855 2771 d 1858 2768 d 1855 2815 r 1852 2809 d 1851 2804 d 1849 2796 d
 1849 2790 d 1851 2782 d 1852 2777 d 1855 2771 d 1871 2798 r 1871 2796 d
 1870 2796 d 1870 2798 d 1871 2799 d 1874 2801 d 1881 2801 d 1884 2799 d
 1885 2798 d 1887 2795 d 1887 2783 d 1889 2780 d 1890 2779 d 1885 2798 r
 1885 2783 d 1887 2780 d 1890 2779 d 1892 2779 d 1885 2795 r 1884 2793 d
 1874 2791 d 1870 2790 d 1868 2787 d 1868 2783 d 1870 2780 d 1874 2779 d
 1879 2779 d 1882 2780 d 1885 2783 d 1874 2791 r 1871 2790 d 1870 2787 d
 1870 2783 d 1871 2780 d 1874 2779 d 1900 2818 r 1903 2815 d 1906 2810 d
 1909 2804 d 1911 2796 d 1911 2790 d 1909 2782 d 1906 2776 d 1903 2771 d
 1900 2768 d 1903 2815 r 1906 2809 d 1908 2804 d 1909 2796 d 1909 2790 d
 1908 2782 d 1906 2777 d 1903 2771 d 1954 2812 r 1954 2779 d 1955 2812 r
 1965 2783 d 1954 2812 r 1965 2779 d 1976 2812 r 1965 2779 d 1976 2812 r
 1976 2779 d 1978 2812 r 1978 2779 d 1949 2812 r 1955 2812 d 1976 2812 r
 1982 2812 d 1949 2779 r 1958 2779 d 1971 2779 r 1982 2779 d 1993 2812 r
 1993 2779 d 1995 2812 r 1995 2779 d 1989 2812 r 2008 2812 d 2012 2810 d
 2014 2809 d 2016 2806 d 2016 2803 d 2014 2799 d 2012 2798 d 2008 2796 d
 1995 2796 d 2008 2812 r 2011 2810 d 2012 2809 d 2014 2806 d 2014 2803 d
 2012 2799 d 2011 2798 d 2008 2796 d 1989 2779 r 2000 2779 d 2005 2796 r
 2011 2782 d 2014 2779 d 2017 2779 d 2019 2782 d 2005 2796 r 2008 2793 d
 2014 2779 d 2046 2809 r 2047 2812 d 2047 2806 d 2046 2809 d 2044 2810 d
 2039 2812 d 2033 2812 d 2028 2810 d 2025 2807 d 2025 2804 d 2027 2801 d
 2028 2799 d 2031 2798 d 2041 2795 d 2044 2793 d 2047 2790 d 2025 2804 r
 2028 2801 d 2031 2799 d 2041 2796 d 2044 2795 d 2046 2793 d 2047 2790 d
 2047 2783 d 2044 2780 d 2039 2779 d 2033 2779 d 2028 2780 d 2027 2782 d
 2025 2785 d 2025 2779 d 2027 2782 d 2089 2812 r 2089 2779 d 2090 2812 r
 2090 2779 d 2084 2812 r 2100 2812 d 2105 2810 d 2108 2807 d 2109 2804 d
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 2162 2804 d 2160 2803 d  665 2559 r  646 2559 d  646 2592 d  675 2559 r
  675 2587 d  680 2592 d  689 2592 d  694 2587 d  694 2559 d  694 2573 r
  675 2573 d  723 2563 r  718 2559 d  708 2559 d  703 2563 d  703 2587 d
  708 2592 d  718 2592 d  723 2587 d  746 2559 r  737 2559 d  742 2559 r
  742 2592 d  737 2587 d  665 2324 r  646 2324 d  646 2357 d  675 2324 r
  675 2352 d  680 2357 d  689 2357 d  694 2352 d  694 2324 d  694 2338 r
  675 2338 d  723 2328 r  718 2324 d  708 2324 d  703 2328 d  703 2352 d
  708 2357 d  718 2357 d  723 2352 d  732 2352 r  737 2357 d  746 2357 d
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  675 2199 d  680 2204 d  689 2204 d  694 2199 d  703 2195 r  703 2199 d
  708 2204 d  718 2204 d  723 2199 d  723 2195 d  703 2175 d  703 2171 d
  723 2171 d  948 2131 r  948 2107 d  944 2103 d  929 2103 d  929 2136 d
  944 2136 d  948 2131 d  972 2117 r  977 2117 d  977 2107 d  972 2103 d
  963 2103 d  958 2107 d  958 2131 d  963 2136 d  972 2136 d  977 2131 d
  977 2127 d  567 2044 r  571 2044 d  571 2034 d  567 2030 d  557 2030 d
  552 2034 d  552 2058 d  557 2063 d  567 2063 d  571 2058 d  571 2054 d
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  581 2049 d  590 2049 r  600 2030 d  609 2063 r  619 2030 d  629 2063 d
  571 1911 r  571 1940 d  571 1935 r  567 1940 d  557 1940 d  552 1935 d
  552 1925 d  557 1921 d  567 1921 d  571 1925 d  581 1940 r  581 1925 d
  586 1921 d  595 1921 d  600 1925 d  600 1921 r  600 1940 d  629 1925 r
  624 1921 d  614 1921 d  609 1925 d  609 1935 d  614 1940 d  624 1940 d
  629 1935 d  629 1921 d  638 1921 r  638 1940 d  638 1935 r  643 1940 d
  652 1940 d  657 1935 d  667 1954 r  667 1921 d  667 1930 r  686 1940 d
  676 1935 r  686 1921 d  714 1935 r  709 1940 d  700 1940 d  695 1935 d
  700 1930 d  709 1930 d  714 1925 d  709 1921 d  700 1921 d  695 1925 d
  752 1935 r  757 1940 d  767 1940 d  771 1935 d  771 1925 d  767 1921 d
  757 1921 d  752 1925 d  752 1935 d  781 1921 r  781 1940 d  781 1935 r
  786 1940 d  795 1940 d  800 1935 d  800 1921 d  814 1954 r  819 1954 d
  819 1921 d  814 1921 r  824 1921 d  838 1940 r  838 1925 d  843 1921 d
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  451  427 d  452  426 d  454  423 d  454  420 d  452  416 d  448  413 d
  440  410 d  437  408 d  433  405 d  432  400 d  432  396 d  446  429 r
  449  427 d  451  426 d  452  423 d  452  420 d  451  416 d  446  413 d
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  452  399 d  454  400 d  437  400 r  445  396 d  451  396 d  452  397 d
  454  400 d  454  404 d 1339  410 r 1367  410 d 1382  423 r 1385  424 d
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 2307  426 d 2305  423 d 2303  415 d 2303  410 d 2305  402 d 2307  399 d
 2308  397 d 2311  396 d 2314  396 r 2318  397 d 2319  399 d 2321  402 d
 2322  410 d 2322  415 d 2321  423 d 2319  426 d 2318  427 d 2314  429 d
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  207  943 r  208  944 d  209  946 d  211  951 d  211  953 d  213  954 d
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 1841  722 d 1935  695 d 2030  667 d 2124  638 d 2219  610 d 2313  584 d
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 1274 1178 d 1369 1184 d 1463 1190 d 1558 1196 d 1652 1202 d 1746 1206 d
 1841 1203 d 1935 1191 d 2030 1164 d 2124 1113 d 2219 1050 d 2313  987 d
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 1841  546 d 1935  544 d 2030  540 d 2124  534 d 2219  526 d 2313  519 d
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 1558  541 d 1652  541 d 1746  541 d 1841  540 d 1935  537 d 2030  533 d
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 1841  548 d 1935  544 d 2030  539 d 2124  531 d 2219  523 d 2313  515 d
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 1558  544 d 1652  544 d 1746  543 d 1841  542 d 1935  539 d 2030  535 d
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 1851 1404 d 1852 1399 d 1855 1393 d 1871 1434 r 1871 1401 d 1873 1434 r
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 1890 1418 d 1892 1413 d 1892 1410 d 1890 1405 d 1887 1402 d 1882 1401 d
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 1890 1413 d 1890 1410 d 1889 1405 d 1885 1402 d 1882 1401 d 1866 1434 r
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 1912 1412 d 1911 1404 d 1908 1398 d 1904 1393 d 1901 1390 d 1904 1437 r
 1908 1431 d 1909 1426 d 1911 1418 d 1911 1412 d 1909 1404 d 1908 1399 d
 1904 1393 d 1955 1434 r 1955 1401 d 1957 1434 r 1966 1405 d 1955 1434 r
 1966 1401 d 1978 1434 r 1966 1401 d 1978 1434 r 1978 1401 d 1979 1434 r
 1979 1401 d 1951 1434 r 1957 1434 d 1978 1434 r 1984 1434 d 1951 1401 r
 1960 1401 d 1973 1401 r 1984 1401 d 1995 1434 r 1995 1401 d 1997 1434 r
 1997 1401 d 1990 1434 r 2009 1434 d 2014 1432 d 2016 1431 d 2017 1428 d
 2017 1425 d 2016 1421 d 2014 1420 d 2009 1418 d 1997 1418 d 2009 1434 r
 2012 1432 d 2014 1431 d 2016 1428 d 2016 1425 d 2014 1421 d 2012 1420 d
 2009 1418 d 1990 1401 r 2001 1401 d 2006 1418 r 2012 1404 d 2016 1401 d
 2019 1401 d 2020 1404 d 2006 1418 r 2009 1415 d 2016 1401 d 2047 1431 r
 2049 1434 d 2049 1428 d 2047 1431 d 2046 1432 d 2041 1434 d 2035 1434 d
 2030 1432 d 2027 1429 d 2027 1426 d 2028 1423 d 2030 1421 d 2033 1420 d
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  838  568 d  843  564 d  852  564 d  857  568 d  857  583 r  857  559 d
  852  554 d  843  554 d  838  559 d 1949  348 r 1949  289 d 1952  348 r
 1952  289 d 1969  331 r 1969  308 d 1941  348 r 1985  348 d 1985  334 d
 1983  348 d 1952  320 r 1969  320 d 1941  289 r 1960  289 d 2005  348 r
 2002  345 d 2005  342 d 2008  345 d 2005  348 d 2005  328 r 2005  289 d
 2008  328 r 2008  289 d 1997  328 r 2008  328 d 1997  289 r 2016  289 d
 2047  328 r 2041  325 d 2039  322 d 2036  317 d 2036  311 d 2039  306 d
 2041  303 d 2047  300 d 2053  300 d 2058  303 d 2061  306 d 2064  311 d
 2064  317 d 2061  322 d 2058  325 d 2053  328 d 2047  328 d 2041  325 r
 2039  320 d 2039  308 d 2041  303 d 2058  303 r 2061  308 d 2061  320 d
 2058  325 d 2061  322 r 2064  325 d 2069  328 d 2069  325 d 2064  325 d
 2039  306 r 2036  303 d 2033  297 d 2033  294 d 2036  289 d 2044  286 d
 2058  286 d 2067  283 d 2069  280 d 2033  294 r 2036  292 d 2044  289 d
 2058  289 d 2067  286 d 2069  280 d 2069  278 d 2067  272 d 2058  269 d
 2041  269 d 2033  272 d 2030  278 d 2030  280 d 2033  286 d 2041  289 d
 2089  294 r 2086  292 d 2089  289 d 2092  292 d 2089  294 d 2162  339 r
 2165  336 d 2162  334 d 2159  336 d 2159  339 d 2165  345 d 2173  348 d
 2184  348 d 2193  345 d 2195  339 d 2195  331 d 2193  325 d 2184  322 d
 2176  322 d 2184  348 r 2190  345 d 2193  339 d 2193  331 d 2190  325 d
 2184  322 d 2190  320 d 2195  314 d 2198  308 d 2198  300 d 2195  294 d
 2193  292 d 2184  289 d 2173  289 d 2165  292 d 2162  294 d 2159  300 d
 2159  303 d 2162  306 d 2165  303 d 2162  300 d 2193  317 r 2195  308 d
 2195  300 d 2193  294 d 2190  292 d 2184  289 d
e
%%Trailer
EndPSPlot



