Compact High Velocity Clouds
Robert Braun
and
braunr.tex
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\def\Lsun{\hbox{$L_\odot$}}
\def\Msun{\hbox{$M_\odot$}}
\def\HI{\hbox{H {\sc i}}}
\def\HII{\hbox{H {\sc ii}}}
\def\CO1_2{\hbox{CO$1\rightarrow 2$}}
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\begin{document}

\title{Compact High Velocity Clouds}
\author{Robert Braun}
\affil{Netherlands Foundation for Research in Astronomy, P.O.Box 2,
  7990 AA Dwingeloo, The Netherlands} 
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\begin{abstract}
  
  We summarize the observed properties of the CHVC population, which
  provide strong evidence for source distances in the range
  200--1000~kpc. At these distances, the population 
  corresponds to strongly dark-matter dominated sub-dwarf galaxies
  still accreting onto the more massive Local Group systems.  Recent
  searches for faint associated stellar populations have revealed
  red-giant candidates for which follow-up spectroscopy is scheduled. A
  sensitive \HI\ survey for CHVC counterparts in the NGC~628 galaxy
  group has allowed tentative detection of 40 candidates, for which
  confirming observations have been approved.  Many open issues should
  be resolved by observational programs within the coming years.

\end{abstract}

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\section{Introduction}

The \HI\  High Velocity Cloud (HVC) phenomenon has been studied for some
three decades, but it is only with the sensitive, all-sky imaging of
the LDS (Hartman \& Burton 1997) in the North and HIPASS
(Staveley-Smith et al 1999) in the South, that some important aspects
of the phenomenon are becoming apparent. Even a casual inspection of
these data reveal a striking dichotomy in the types of emission
features present. The vast majority of the emission flux is associated
with diffuse filamentary complexes extending over 10's of degrees, of
which the Magellanic Stream (Putman 2000) is a prime example. A much
smaller total flux is associated with a population of compact,
high-contrast features which are isolated from any other \HI\  emision
features both spatially and in velocity (the CHVCs). My attention was
first drawn to this second object class, while using the LDS data to
assess possible Galactic foreground confusion in the directions of
nearby galaxy groups in the fall of 1997. I was surprised to see high
contrast peaks of uncataloged high-velocity \HI\  which were
indistinguishable in the LDS data from the \HI\  signatures of nearby
dwarf galaxies. This was so intriguing to me that I set about making a
catalog of such objects based on the LDS data (covering
$\delta~=~-30$--90$^\circ$).  Together with Butler Burton, follow-up
observations of all candidate sources were obtained and a list of 65
confirmed objects were published (Braun \& Burton 1999).


\section{CHVC Properties}

In addition to having a distinctive, compact morphology (average FWHM
of 50$\pm$25 arcmin) the CHVCs also proved to have a very systematic
spatial and kinematic distribution on the sky. A global search over all
direction cosines for the reference system that minimized the velocity
dispersion of the population, returned the Local Group Standard of Rest
(LGSR) with high significance. In the LGSR, the CHVC population has a
velocity dispersion of only 70 \kms, in contrast to 95 \kms\  measured in
the Galactic Standard of Rest (GSR). But rather than being at rest in
the LGSR frame, the entire system is infalling by about 100 \kms\  toward
the Local Group barycenter. These distinctive kinematic properties of
the CHVC population were the first indication that they might reside at
substantial distances, and were not merely a local ISM or Galactic
phenomenon.

\subsection{Velocity Gradients and Multi-Core Systems}

Further indications for a substantial distance to these objects have
emerged from a program of high resolution \HI\ synthesis imaging with
the WSRT (Braun \& Burton 2000) and in total power with Arecibo
(Burton, Braun \& Chengalur 2000). The general picture which has
emerged is that of one or more compact cores (of 1--20~arcmin extent)
embedded in a common diffuse halo. On average about 40\% of the \HI\ 
line flux is due to the compact cores, although this varies enormously;
ranging from $<$1\% for the lowest flux objects (less than about
50~Jy-\kms) to about 50\% for brighter systems (100--300~Jy-\kms). Many
of the compact cores display velocity gradients (of 10--30 \kms\ 
amplitude) along the long dimension of an approximately elliptical
extent. For multi-core objects, each core has it's own distinct
kinematic axis, which is uncorrelated with that of other cores in the
same object (and can be perpendicular as often as parallel). It is
difficult to envision an external mechanism (such as tidal shear for
example) for imparting vastly different kinematic axes to the various
cores of a single object.  Resolved detection of the diffuse halos with
deep Arecibo imaging has shown that the halos do not participate in the
same velocity gradients of the cores, but are more nearly stationary at
the systemic velocity of the object and always have the 22+~\kms\ FWHM
linewidth of an 8000+~K gas.  This implies that either (1) the velocity
gradients of the cores have an internal (like self-gravity) rather than
external origin or (2) the objects are sufficiently long-lived that the
halos can become thermalized (and so erase their original kinematics).
In any case, the thermalization timescale for a 50~arcmin diffuse halo
is $\tau_t \sim D_{kpc}$~Myr, at a distance of $D_{kpc}$ in kpc.

The most extreme multi-core CHVC yet studied (CHVC115+13$-$275) has
some 10 major core components spanning about 30~arcmin on the sky with
centroid velocities distributed over no less than 70~\kms!  This object,
and others like it, either have an extremely short dynamical lifetime
($\tau_d < 0.1D_{kpc}$~Myr) or are bound by a large amount of dark matter.
From the very narrow \HI\ linewidths seen in the cores we know that
internal conditions are appropriate for maintaining \HI\ at about
100~K, which requires that the product, $n_H t > 1$ cm$^{-3}$Myr
(Draine 1978).

While self-gravity could account for all of these facts in a natural
way: (1) the cool \HI\ cores by the enhanced internal pressure of a
self-gravitating system, (2) the local velocity gradients as rotation
in dark-matter-dominated mini-halos, (3) the binding of multi-core objects
by a massive dark halo; it is not clear which alternative
scenario might work. The projected velocity fields of the best-resolved
cores can be well-modeled by a slowly rising rotation curve, leveling
off at 8~arcmin radius to a velocity of 15--20~\kms. The implied total
masses in these individual cores is about $D_{700}10^8$\Msun, while for
the high linewidth multi-core systems it is nearer $D_{700}10^9$\Msun,
in terms of an assumed distance $D_{700}$ normalized to 700~kpc. Even
at these rather substantial assumed distances, the dark-to-visible mass
ratios are quite high with individual cores ranging from,
$\Gamma$ = 10--40/$D_{700}$, while for the multi-core systems $\Gamma
\sim$ 50/$D_{700}$.

\subsection{Opaque \HI\ Clumps}

The objects with the narrowest \HI\ emission lines have also proven
particularly interesting. Compact clumps of opaque \HI\ (with 90~arcsec
FWHM) have been observed within the cores of at least one source to
date (CHVC125+41$-$207). Such clumps have \HI\ brightness temperatures
of 75~K, together with FWHM linewidths of less than about 2~\kms. These
values allow a reliable determination of the kinetic temperature (85~K)
and opacity ($\tau\sim$2) as well as an upper limit on turbulent
contributions to the internal linewidth ($<$1~\kms). Since we have
measured an angular size and excess column density for the clumps we can
estimate the distance from $D~=~dN_H/(n_H\theta)$, assuming crude
spherical symmetry, if we have an estimate of the \HI\ volume density,
$n_H$. 

We can perhaps demonstrate this method best by using M31 as an example. The
excess column density, $dN_H = 5\pm1\times10^{21}$cm$^{-2}$, and
angular size, $\theta = 60\pm20$~arcsec, of \HI\ clumps in the
North-East half of M31 can be estimated from Fig.~5 of Braun \&
Walterbos (1992). The \HI\ kinetic temperature, $T_k = 175\pm25$~K, and
estimated thermal pressure, $P/k = 1500\pm500$~cm$^{-3}$K, of the M31 mid-disk
are tabulated in Table~4 of the same reference. The implied volume
density, $n_H = 9\pm3$~cm$^{-3}$, leads to the distance estimate:
$D_{M31} = 670\pm220$~kpc. While rather crude, this approach gives a
plausible value for the distance to M31. For CHVC125+41$-$207, we have an
excess column density, $dN_H = 1.0\pm0.2\times10^{21}$cm$^{-2}$, and
angular size, $\theta = 90\pm15$~arcsec, of the \HI\ clumps for which
$T_k = 85\pm10$~K.  Although the thermal pressure, $P/k$, in the solar
neighborhood is about 2000~cm$^{-3}$K, it is expected to decline
rapidly with distance from the Galactic plane (eg. Wolfire et al. 1995)
such that beyond about 10~kpc we should encounter values, $P/k =
150\pm50$~cm$^{-3}$K, leading to an estimated volume density, $n_H =
2\pm1$~cm$^{-3}$. In fact, as described in Braun \& Burton (2000), an
\HI\ temperature equilibrium calculation was performed by Wolfire et
al. (2000) assuming a Local Group radiation field and a metallicity and
dust-to-gas ratio of 10\% Solar which allowed exactly these pressure
and density estimates to be made for this object. The resulting
distance estimate is, $D_{C125} = 600\pm300$~kpc.

\begin{figure}[t!]
\plottwo{braunr_fig1.tex}{braunr_fig2.tex}
\vspace*{-0.4cm}
\caption{Edge profiles of the indicated CHVCs. The logartithm of
  \HI\ column density is plotted against distance from the source
  centroid for both the Eastern and Western halves of the source. The
  dotted curve is the sky-plane projection of a spherical exponential
  with the parameters shown. 
}
\vspace*{-0.4cm}
\end{figure}


\subsection{Halo Edge Profiles}

Another result of the Arecibo imaging of CHVCs reported in Burton,
Braun \& Chengalur (2000) was the detection of approximately
exponential edge profiles of the diffuse halos between column densities
of about 10$^{19}$ down to the limiting sensitivity (1$\sigma$ over
70~\kms) of $2\times10^{17}$cm$^{-2}$. (BTW, these are probably some of
the deepest \HI\ emission measurements of resolved objects yet
obtained.)  The edge profiles are well-fit by the sky-plane
projection of a 3-D spherical exponential in \HI\ volume density,
$n_H(r) = n_o e^{-r/h}$, in terms of the radial distance, $r$, and
exponential scale length, $h$, yielding $ N_H(r) = 2 h n_o (r/ h) K_1 (
r/h) $, where $K_1$ is the modified Bessel function of order 1. Fitting
this form to the observed edge profiles allows accurate assessment of
both the central column density of the warm halo, $N_H(0)$, and the
scale length, $h$, in the plane of the sky. As before, with any
reasonable estimate of the thermal pressure, it becomes possible to
determine the source distance assuming crude spherical symmetry.
Assuming a pressure in the diffuse CHVC halos, $P/k \sim
100$~cm$^{-3}$K, results in distance estimates which vary between
150--1100~kpc for the ten CHVCs with measured edge profiles.

\subsection{Do LMC Distances Work?}

What about placing the CHVCs at the distance of the LMC/SMC? All
existing estimates of the thermal pressure at these distances lie at or
below about $P_{th}/k\sim 100$~cm$^{-3}$K. To this could be added the
ram pressure $P_{ram} \sim \rho v^2/2$ of passage through the hot halo
of the Galaxy. Assuming a typical relative velocity of 100~\kms, and a
Galactic halo temperature of 10$^6$K, gives $P_{ram} = 0.8 P_{th}$,
implying a significant, but not dominant contribution to the total
pressure.  In order to account for the \HI\ column densities and
angular sizes of both the opaque clumps seen in CHVC125+41$-$207 as
well as the diffuse halos of the ten CHVCs observed with Arecibo, we
would require some additional source of pressure to yield 3--20 times
higher values. It is not clear where this might come from. At a
distance of about 50~kpc, the thermalization timescale of the diffuse
CHVC halos is 50~Myr, while the dynamical lifetime of
multi-core CHVCs like CHVC115+13$-$275 is only 5 Myr. So, on the one
hand, the absence of velocity gradients in the diffuse halos demands a
long source lifetime, while on the other, the sources are too
short-lived for the halos to be thermalized. This scenario is very
difficult to reconcile with the observed CHVC properties.

\section{Current Work on CHVCs}

Although a large number of the CHVC attributes suggest Local Group
distances, the various distance determinations outlined above remain
indirect. Essentially, a self-consistent scenario has emerged, in which
many physical and kinematic properties of the CHVCs can be understood
if they are self-gravitating, dark-matter-dominated systems.  It is
very appealing to associate them with the low-mass ``building-blocks''
of galaxy formation (Blitz et al. 1999), which high resolution
numerical simulations suggest should still be found in large numbers in
the appropriate environments (Klypin et al. 1999, Moore et al.  1999).
If this connection can be demonstrated convincingly we would have the
opportunity to gain important insights into a wide range of fundamental
problems in astrophysics, through the study of these cosmological
fossils in our own ``backyard''.  However, demonstrating consistency
does not constitute a proof of the conjecture. We are pursuing several
different lines of research to clarify the nature of these objects.

\subsection{All-Sky CHVC Population}

Vincent de Heij (as part of his PhD work in Leiden) working together
with Mary Putman, has just completed cataloging the population of
Southern hemisphere CHVCs using the HIPASS data (Putman, De Heij et al.
2000). The Southern hemisphere data is particularly important in
constraining the kinematics of the population, since this is where it
extends to the highest positive velocities in the LSR reference frame.
It is also special in the sense that both the nearest external
galaxies, the Magellanic Clouds, as well as the nearest external galaxy
group, the Sculptor Group, are located there. Just as was seen
previously in the LDS data North of $\delta=-30^\circ$, there is a
clear distinction in the HIPASS data between the extended filamentary
complexes which make up the bulk of peculiar velocity \HI\ emission and
the compact, isolated CHVCs, which have the \HI\ appearance of nearby
dwarf galaxies. About 100 well-defined CHVCs were cataloged below
$\delta=0^\circ$ in the HIPASS data. A new analysis of the spatial and
kinematic properties of the all-sky CHVC population will be carried out
in the coming months. High resolution \HI\ imaging data has also been
acquired with the WSRT for eight additional objects. These targets were
chosen on the basis of high brightness temperatures in the LDS data, in
the hope of detecting more opaque clumps of the type seen in
CHVC125+41$-$207.

\subsection{Stars in CHVCs}

An unambiguous distance determination for the CHVCs would follow from
direct detection of an associated stellar population. A high surface
brightness stellar disk can already be ruled out for all of the CHVCs
outside of the Galactic plane Zone of Avoidance. The constraints on low
surface brightness populations are not yet very strong, especially
since they would be highly resolved into individual stars at distances
of 200--1000~kpc, which would be difficult to distinguish from the
dense Galactic foreground. If young, high mass stars were present, then
these should give rise to prominent \HII\ regions. Together with Ren\'e
Walterbos (NMSU), we have begun a program of narrow-band H$\alpha$
imaging of CHVCs with the APO 1-m; so far without detections in the
first three fields imaged. An older stellar population could be traced
by its most luminous and populous component, namely the red-giant
branch. Deep searches for associated red-gaints have been carried out
in the spring and summer of 2000 using the Mosaic cameras on the KPNO
4-m and CTIO 4-m together with Eva Grebel and Daniel Harbeck (MPIA) and
the LCO 2.5-m together with Carme Gallart (Yale/Chile) and Steve
Majewski (UVa). Besides several broad-band colors, the DDO51 filter,
centered on the MgH absorption feature at 5100 \AA, was used to allow
reliable discrimination of the many foreground white-dwarfs from faint
background objects. While still only partially analyzed, these data do
suggest a sparse population of candidate stars in several objects with
the colors of red-giants and luminosities consistent with a 700~kpc
distance. However, at these faint brightnesses, there is the
possibility of confusion by background galaxies at red-shifts of a few
tenths which resemble the sought for red-giant population when viewed
with typical ground-based angular resolutions of about 1~arcsec. Two
additional observing programs together with Eva Grebel and Kem Cook
(LLNL) have already been allocated for fall 2000 to clarify this issue;
namely high resolution imaging with the VLT, and multi-object
spectroscopy of candidate stars with Keck. Stay tuned \dots

\subsection{Exo-CHVCs}

Another way to circumvent the difficulties of distance determination of
the Local Group CHVCs is to detect CHVC counterparts in external groups
of galaxies. However, the low mass end (below M$_{HI}~\sim~10^8$
M$_\odot$) of the \HI\ mass function (HIMF) is still a topic of very
active current research. Only small numbers of low mass objects have
been detected to date in blind, large area surveys: eg. 4 out of 66 in
the AHISS (Zwaan et al. 1997), 4 out of 79 in the ``Arecibo
Slice'' (Spitzak \& Schneider 1998, ) 3 out of 263 in the HIPASS
(Kilborn et al. 1999) and 7 out of 265 in the ADBS (Rosenberg \&
Schneider 2000).  Consequently, there are substantial uncertainties in
the space densities at low HI mass due to small number statistics.

Targeted searches for uncataloged objects in specific environments are
beginning to supplement the blind surveys. Banks et al. (1999) detect
17 out of 27 objects with M$_{HI}~<~10^8$ M$_\odot$ in the Cen A group
of galaxies using HIPASS data. Verheijen et al. (2000)
detect comparable numbers of objects in the Ursa Major cluster in a
recent VLA survey.

Comparison of the HIMFs derived by the various authors is beginning to
show what might be substantial differences in the statistics of the low
mass populations seen in different environments. Within the Ursa Major
cluster, for example, the low mass HIMF is flat or even declining
towards lower masses. In the poorer, but still relatively rich,
environment of the Cen A group there appears to be a significant
increase to lower masses. The detected space density in the lowest
measured bin (11 objects centered at $2\times10^7$ M$_\odot$) is twice
that seen in the next lowest bin (6 objects centered at $6\times10^7$
M$_\odot$). A similar, but still low significance, upturn is apparent
in the population of ``field'' galaxies sampled by both the Southern
sky HIPASS data and the combined AHISS and Arecibo Slice data reported
by Schneider et al. (1998).

Detection of rather different HIMFs in different environments is not in
itself a surprising result. The interaction, merger and stripping rates
of low mass systems must depend sensitively on the richness of their
environment. Optical luminosity functions have not demonstrated a
strong dependence of shape with environment (eg. de Propris et al. 1995;
Loveday 1997; Marzke et al. 1998) but what they all seem to share is a
strong upturn in the space density of low luminosity systems below $M_B
\sim -$15. Given the much larger interaction cross-section of diffuse
gas over that of stars, we should expect dramatic differences in the
low mass end of the HIMF, even if the ``primordial'' HIMF were the same
everywhere.

The latest HI surveys have begun to reveal a rather interesting
population of sources at the very low mass end in poor environments.
The previously uncataloged \HI\ detections in the Cen~A group (Banks et
al. 1999) all have very low luminosity ($M_B \sim -$11), low surface
brightness $<\mu> \sim$ 26 mag arcsec$^{-2}$ optical counterparts. In
the case of the ADBS (Rosenberg \& Schneider 2000) fully 22 of 81
previously uncataloged objects have no clear optical counterpart down
to the limiting magnitude of the POSS (about 25 mag arcsec$^{-2}$). Of
these 22 objects, 11 have substantial extinction (A$_V >$ 2 mag) and
therefore do not provide strong limits, but 5 have negligible
extinction (A$_V <$ 0.3 mag) and are thus quite interesting. The most
extreme object in this category may be the possible Cen~A group member
HIPASS J1712$-$64 (Kilborn et al. 2000) for which an
upper limit of $\mu_B$ = 27 mag arcsec$^{-2}$ is associated with an HI
mass of $1.7\times10^7$ M$_\odot$.
Are we perhaps encountering the tip of an iceberg of very low mass
systems with only a faint (or even no) population of associated stars?

Together with Butler Burton, we have undertaken an attempt to probe the
extreme low mass end of the HIMF in a poor environment by carrying out
a deep survey of the NGC~628 galaxy group. Nineteen sparse pointings,
distributed over a region of about 1~Mpc (or 5 degrees) in diameter,
were each observed with a 12 hour integration using the recently
upgraded Westerbork array. The 5$\sigma$ HI mass sensitivity at each
field center was $2\times10^6$ M$_\odot$ over the minimum expected
linewidth of 32~km~s$^{-1}$ FWHM (although the velocity resolution was
5~km~s$^{-1}$). Since the pointings were sparsely distributed, they
only overlap at the 5\% level of the circular Gaussian primary beam
with 2100 arcsec FWHM. At these ``cracks'' in the hexagonal pointing
pattern, the 5$\sigma$ mass sensitivity is degraded to $4\times10^7$
M$_\odot$ over 32~km~s$^{-1}$.  Applying a significance criterion of
0.5 random noise detections per data cube (varying between 5.5 and 5.0
times $\sigma$ depending on the degree of velocity smoothing, and hence
the number of independent pixels) resulted in a list of 48 tentative
detections in the complete survey. Of these, only 7 correspond to
previously cataloged galaxies. One of the remaining 41 candidates has
an obvious optical counterpart in the POSS data, while three more have
faint wisps in the POSS that may be low surface brightness optical
counterparts (with peak $\mu_R \sim$ 25 mag arcsec$^{-2}$). The
remaining 37 candidates have no optical counterparts down to this
surface brightness limit. Given the noise statistics we expect about
10 of our candidates to be random noise peaks, which is also the number
of ``negative sources'' found with the same criteria in the survey data.
Confirming observations of our low mass candidates with the Arecibo
telescope have been approved for fall 2000. 

\section{Conclusions}

These are very interesting times for high velocity \HI\ cloud
research. Substantial progress has been made in determining the
physical properties of these objects. The weight of current evidence
seems to favor a large mean distance for the compact isolated objects,
the CHVCs. More insights and perhaps definitive evidence should follow
within the next year or two from  a number of ongoing programs.

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% For examples on including figures, see the file vla2000_sample.ps
% at http://www.nrao.edu/vla2000/proceedings/. 
% For examples of figures, equations or tables, please see the file
% vla2000_man.ps at the same site. Also available as
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% comment this out if you want to include acknowledgements

\acknowledgements

It is a pleasure to acknowledge the valuable input and collaboration of
many individuals in the work described here: Butler Burton, Jayaram
Chengalur, Vincent de Heij and Mary Putman for \HI\ aspects and Kem
Cook, Carme Gallart, Eva Grebel, Daniel Harbeck, Steve Majewski and
Ren\'e Walterbos for the optical program. This work could not have been
done without the generous allotment of telescope time by the ESO, Keck,
LCO, NAIC, NOAO, and NFRA time allocation committees.


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\reference 
Schneider, S.E., Spitzak, J.G. \& Rosenberg, J.L. 1998, ApJ 507, L9

\reference 
Spitzak, J.G. \& Schneider, S.E. 1998, ApJS 119, 159

\reference 
Staveley-Smith, L., Koribalski, B.S., Stewart, I. et al. 1999, 
in ``Imaging at Radio through Submillimeter
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\reference 
Verheijen, M. et al. 2000, these proceedings

\reference
Wolfire, M.G., McKee, C.F., Hollenbach, D. \& Tielens, A.G.G.M. 1995,

\reference
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}
\end{references}

\end{document}

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1284 1325 L
1291 1323 L
1297 1321 L
1304 1318 L
1310 1315 L
1317 1311 L
1324 1306 L
1330 1301 L
1337 1294 L
1343 1287 L
1350 1279 L
1357 1270 L
1363 1261 L
1370 1251 L
1376 1242 L
1383 1233 L
1390 1225 L
1396 1217 L
1403 1209 L
1409 1202 L
1416 1196 L
1423 1189 L
1429 1183 L
1436 1177 L
1442 1172 L
1449 1167 L
1455 1163 L
1462 1159 L
1469 1158 L
1475 1157 L
1482 1158 L
1488 1159 L
1495 1161 L
1502 1163 L
1508 1165 L
1515 1167 L
1521 1168 L
1528 1168 L
1535 1167 L
1541 1165 L
1548 1162 L
1554 1157 L
1561 1151 L
1567 1144 L
1574 1135 L
1581 1125 L
1587 1114 L
1594 1103 L
1600 1091 L
1607 1081 L
1614 1072 L
1620 1065 L
1627 1061 L
1633 1060 L
1640 1060 L
1647 1063 L
1653 1067 L
1660 1072 L
1666 1077 L
1673 1080 L
1680 1083 L
1686 1085 L
1693 1085 L
1699 1085 L
1706 1084 L
1713 1082 L
1719 1080 L
1726 1079 L
1732 1076 L
1739 1074 L
1746 1071 L
1752 1068 L
1759 1064 L
1765 1059 L
1772 1053 L
1779 1045 L
1785 1037 L
1792 1027 L
1798 1015 L
1805 1002 L
1811 989 L
1818 974 L
1825 959 L
1831 945 L
1838 933 L
1844 921 L
1851 910 L
1858 901 L
1864 892 L
1871 883 L
1877 875 L
1884 867 L
1891 859 L
1897 852 L
1904 846 L
1910 843 L
1917 845 L
1924 853 L
1930 867 L
1937 885 L
1943 906 L
1950 929 L
1957 952 L
1963 975 L
1970 996 L
1976 1015 L
1983 1030 L
CS [] 0 setdash M
1031 191 M 1041 235 M 1041 191 L
1043 235 M 1043 191 L
1035 235 M 1060 235 L
1066 233 L
1068 231 L
1071 227 L
1071 223 L
1068 218 L
1066 216 L
1060 214 L
1043 214 L
1060 235 M 1064 233 L
1066 231 L
1068 227 L
1068 223 L
1066 218 L
1064 216 L
1060 214 L
1035 191 M 1050 191 L
1054 214 M 1058 212 L
1060 210 L
1066 195 L
1068 193 L
1071 193 L
1073 195 L
1058 212 M 1060 208 L
1064 193 L
1066 191 L
1071 191 L
1073 195 L
1073 197 L
1087 216 M 1087 214 L
1085 214 L
1085 216 L
1087 218 L
1092 220 L
1100 220 L
1104 218 L
1106 216 L
1108 212 L
1108 197 L
1111 193 L
CS M
1113 191 L
1106 216 M 1106 197 L
1108 193 L
1113 191 L
1115 191 L
1106 212 M 1104 210 L
1092 208 L
1085 206 L
1083 202 L
1083 197 L
1085 193 L
1092 191 L
1098 191 L
1102 193 L
1106 197 L
1092 208 M 1087 206 L
1085 202 L
1085 197 L
1087 193 L
1092 191 L
1150 235 M 1150 191 L
1153 235 M 1153 191 L
1150 214 M 1146 218 L
1142 220 L
1138 220 L
1131 218 L
1127 214 L
1125 208 L
1125 204 L
1127 197 L
1131 193 L
1138 191 L
1142 191 L
1146 193 L
1150 197 L
1138 220 M 1134 218 L
1129 214 L
1127 208 L
1127 204 L
1129 197 L
1134 193 L
1138 191 L
1144 235 M 1153 235 L
1150 191 M 1159 191 L
1174 235 M 1171 233 L
1174 231 L
1176 233 L
1174 235 L
1174 220 M 1174 191 L
1176 220 M 1176 191 L
1167 220 M 1176 220 L
1167 191 M 1182 191 L
1197 220 M 1197 197 L
1199 193 L
1205 191 L
1209 191 L
1216 193 L
1220 197 L
1199 220 M 1199 197 L
1201 193 L
1205 191 L
1220 220 M 1220 191 L
1222 220 M 1222 191 L
1190 220 M 1199 220 L
1213 220 M 1222 220 L
1220 191 M 1228 191 L
1260 216 M 1262 220 L
1262 212 L
1260 216 L
1258 218 L
1253 220 L
1245 220 L
1241 218 L
1239 216 L
1239 212 L
1241 210 L
1245 208 L
1256 204 L
1260 202 L
1262 199 L
1239 214 M 1241 212 L
1245 210 L
1256 206 L
1260 204 L
1262 202 L
1262 195 L
1260 193 L
1256 191 L
1247 191 L
1243 193 L
1241 195 L
1239 199 L
1239 191 L
1241 195 L
1325 244 M 1321 239 L
1316 233 L
1312 225 L
1310 214 L
1310 206 L
1312 195 L
1316 187 L
1321 181 L
1325 176 L
1321 239 M 1316 231 L
1314 225 L
1312 214 L
1312 206 L
1314 195 L
1316 189 L
1321 181 L
1342 216 M 1342 214 L
1339 214 L
1339 216 L
1342 218 L
1346 220 L
1354 220 L
1358 218 L
1361 216 L
1363 212 L
1363 197 L
1365 193 L
1367 191 L
1361 216 M 1361 197 L
1363 193 L
1367 191 L
1369 191 L
1361 212 M 1358 210 L
1346 208 L
1339 206 L
1337 202 L
1337 197 L
1339 193 L
1346 191 L
1352 191 L
1356 193 L
1361 197 L
1346 208 M 1342 206 L
1339 202 L
1339 197 L
1342 193 L
1346 191 L
1384 220 M 1384 191 L
1386 220 M 1386 191 L
1386 208 M 1388 214 L
1392 218 L
1396 220 L
1403 220 L
1405 218 L
1405 216 L
1403 214 L
1400 216 L
1403 218 L
1377 220 M 1386 220 L
1377 191 M 1392 191 L
1440 214 M 1438 212 L
1440 210 L
1442 212 L
1442 214 L
1438 218 L
1434 220 L
1428 220 L
1421 218 L
1417 214 L
1415 208 L
1415 204 L
1417 197 L
1421 193 L
1428 191 L
1432 191 L
1438 193 L
1442 197 L
1428 220 M 1423 218 L
1419 214 L
1417 208 L
1417 204 L
1419 197 L
1423 193 L
1428 191 L
1476 216 M 1478 220 L
1478 212 L
1476 216 L
1474 218 L
1470 220 L
1461 220 L
1457 218 L
1455 216 L
1455 212 L
1457 210 L
1461 208 L
1472 204 L
1476 202 L
1478 199 L
1455 214 M 1457 212 L
1461 210 L
1472 206 L
1476 204 L
1478 202 L
1478 195 L
1476 193 L
1472 191 L
1463 191 L
1459 193 L
1457 195 L
1455 199 L
1455 191 L
1457 195 L
1493 208 M 1518 208 L
1518 212 L
1516 216 L
1514 218 L
1510 220 L
1503 220 L
1497 218 L
1493 214 L
1491 208 L
1491 204 L
1493 197 L
1497 193 L
1503 191 L
1507 191 L
1514 193 L
1518 197 L
1516 208 M 1516 214 L
1514 218 L
1503 220 M 1499 218 L
1495 214 L
1493 208 L
1493 204 L
1495 197 L
1499 193 L
1503 191 L
1556 214 M 1554 212 L
1556 210 L
1558 212 L
1558 214 L
1554 218 L
1549 220 L
1543 220 L
1537 218 L
1533 214 L
1531 208 L
1531 204 L
1533 197 L
1537 193 L
1543 191 L
1547 191 L
1554 193 L
1558 197 L
1543 220 M 1539 218 L
1535 214 L
1533 208 L
1533 204 L
1535 197 L
1539 193 L
1543 191 L
1570 244 M 1575 239 L
1579 233 L
1583 225 L
1585 214 L
1585 206 L
1583 195 L
1579 187 L
1575 181 L
1570 176 L
1575 239 M 1579 231 L
1581 225 L
1583 214 L
1583 206 L
1581 195 L
1579 189 L
1575 181 L
CS [32 24] 0 setdash M
CS [] 0 setdash M
184 1028 M 139 1038 M 184 1038 L
139 1040 M 184 1040 L
139 1032 M 139 1040 L
184 1032 M 184 1047 L
154 1070 M 156 1063 L
160 1059 L
167 1057 L
171 1057 L
177 1059 L
181 1063 L
184 1070 L
184 1074 L
181 1080 L
177 1084 L
171 1086 L
167 1086 L
160 1084 L
156 1080 L
154 1074 L
154 1070 L
156 1065 L
160 1061 L
167 1059 L
171 1059 L
177 1061 L
181 1065 L
184 1070 L
184 1074 M 181 1078 L
177 1082 L
CS M
171 1084 L
167 1084 L
160 1082 L
156 1078 L
154 1074 L
154 1110 M 156 1105 L
158 1103 L
163 1101 L
167 1101 L
171 1103 L
173 1105 L
175 1110 L
175 1114 L
173 1118 L
171 1120 L
167 1122 L
163 1122 L
158 1120 L
156 1118 L
154 1114 L
154 1110 L
156 1105 M 160 1103 L
169 1103 L
173 1105 L
173 1118 M 169 1120 L
160 1120 L
156 1118 L
158 1120 M 156 1122 L
154 1126 L
156 1126 L
156 1122 L
171 1103 M 173 1101 L
177 1099 L
179 1099 L
184 1101 L
186 1107 L
186 1118 L
188 1124 L
190 1126 L
179 1099 M 181 1101 L
184 1107 L
184 1118 L
186 1124 L
190 1126 L
192 1126 L
196 1124 L
198 1118 L
198 1105 L
196 1099 L
192 1097 L
190 1097 L
186 1099 L
184 1105 L
131 1189 M 135 1185 L
142 1181 L
150 1177 L
160 1175 L
169 1175 L
179 1177 L
188 1181 L
194 1185 L
198 1189 L
135 1185 M 144 1181 L
150 1179 L
160 1177 L
169 1177 L
179 1179 L
186 1181 L
194 1185 L
139 1206 M 184 1206 L
139 1208 M 179 1233 L
144 1208 M 184 1233 L
139 1233 M 184 1233 L
139 1200 M 139 1208 L
139 1227 M 139 1240 L
184 1200 M 184 1212 L
177 1250 M 204 1250 L
177 1251 M 204 1251 L
177 1267 M 204 1267 L
177 1268 M 204 1268 L
177 1246 M 177 1255 L
177 1263 M 177 1272 L
190 1251 M 190 1267 L
204 1246 M 204 1255 L
204 1263 M 204 1272 L
131 1280 M 135 1285 L
142 1289 L
150 1293 L
160 1295 L
169 1295 L
179 1293 L
188 1289 L
194 1285 L
198 1280 L
135 1285 M 144 1289 L
150 1291 L
160 1293 L
169 1293 L
179 1291 L
186 1289 L
194 1285 L
131 1360 M 135 1356 L
142 1352 L
150 1348 L
160 1346 L
169 1346 L
179 1348 L
188 1352 L
194 1356 L
198 1360 L
135 1356 M 144 1352 L
150 1350 L
160 1348 L
169 1348 L
179 1350 L
186 1352 L
194 1356 L
160 1398 M 163 1396 L
165 1398 L
163 1400 L
160 1400 L
156 1396 L
154 1392 L
154 1386 L
156 1379 L
160 1375 L
167 1373 L
171 1373 L
177 1375 L
181 1379 L
184 1386 L
184 1390 L
181 1396 L
177 1400 L
154 1386 M 156 1381 L
160 1377 L
167 1375 L
171 1375 L
177 1377 L
181 1381 L
184 1386 L
154 1417 M 184 1417 L
154 1419 M 184 1419 L
160 1419 M 156 1423 L
154 1430 L
154 1434 L
156 1440 L
160 1442 L
184 1442 L
154 1434 M 156 1438 L
160 1440 L
184 1440 L
160 1442 M 156 1446 L
154 1453 L
154 1457 L
156 1463 L
160 1465 L
184 1465 L
154 1457 M 156 1461 L
160 1463 L
184 1463 L
154 1411 M 154 1419 L
184 1411 M 184 1425 L
184 1434 M 184 1449 L
184 1457 M 184 1472 L
152 1481 M 152 1504 L
142 1514 M 143 1515 L
144 1514 L
143 1512 L
142 1512 L
139 1514 L
138 1515 L
137 1519 L
137 1524 L
138 1528 L
139 1529 L
142 1530 L
144 1530 L
147 1529 L
150 1525 L
152 1519 L
153 1516 L
156 1514 L
160 1512 L
163 1512 L
137 1524 M 138 1526 L
139 1528 L
142 1529 L
144 1529 L
147 1528 L
150 1524 L
152 1519 L
161 1512 M 160 1514 L
160 1516 L
162 1522 L
162 1526 L
161 1529 L
160 1530 L
160 1516 M 163 1522 L
163 1528 L
162 1529 L
160 1530 L
157 1530 L
131 1540 M 135 1544 L
142 1548 L
150 1553 L
160 1555 L
169 1555 L
179 1553 L
188 1548 L
194 1544 L
198 1540 L
135 1544 M 144 1548 L
150 1551 L
160 1553 L
169 1553 L
179 1551 L
186 1548 L
194 1544 L
CS [32 24] 0 setdash M
CS [6 12] 0 setdash M
483 1734 M 511 1729 L
540 1720 L
568 1707 L
596 1693 L
625 1677 L
653 1660 L
682 1643 L
710 1624 L
739 1605 L
767 1585 L
796 1564 L
824 1544 L
852 1522 L
881 1501 L
909 1479 L
938 1457 L
966 1435 L
995 1412 L
1023 1390 L
1052 1367 L
1080 1344 L
1109 1320 L
1137 1297 L
1165 1273 L
1194 1250 L
1222 1226 L
1251 1202 L
1279 1178 L
1308 1154 L
1336 1129 L
1365 1105 L
1393 1081 L
1421 1056 L
1450 1032 L
1478 1007 L
1507 982 L
1535 958 L
1564 933 L
1592 908 L
1621 883 L
1649 858 L
1677 833 L
1706 808 L
1734 783 L
1763 758 L
1791 732 L
1820 707 L
1848 682 L
1877 656 L
1905 631 L
1933 606 L
1962 580 L
1990 555 L
2019 529 L
2047 503 L
2076 478 L
2104 452 L
2133 427 L
2161 401 L
CS [6 12] 0 setdash M
554 649 M 687 649 L
CS [] 0 setdash M
554 743 M 687 743 L
CS [32 24] 0 setdash M
554 838 M 687 838 L
724 649 M CS [] 0 setdash M
724 637 M 735 681 M 735 637 L
737 681 M 762 641 L
737 677 M 762 637 L
762 681 M 762 637 L
729 681 M 737 681 L
756 681 M 769 681 L
729 637 M 741 637 L
784 643 M 780 642 L
778 638 L
776 631 L
776 628 L
778 621 L
780 618 L
784 616 L
787 616 L
790 618 L
793 621 L
794 628 L
794 631 L
CS M
793 638 L
790 642 L
787 643 L
784 643 L
782 642 L
780 640 L
779 638 L
778 631 L
778 628 L
779 621 L
780 619 L
782 618 L
784 616 L
787 616 M 789 618 L
790 619 L
792 621 L
793 628 L
793 631 L
792 638 L
790 640 L
789 642 L
787 643 L
808 637 M 806 639 L
808 641 L
810 639 L
810 634 L
808 630 L
806 628 L
863 681 M 863 637 L
865 681 M 865 637 L
865 660 M 869 664 L
876 666 L
880 666 L
886 664 L
888 660 L
888 637 L
880 666 M 884 664 L
886 660 L
886 637 L
857 681 M 865 681 L
857 637 M 871 637 L
880 637 M 895 637 L
941 662 M 979 662 L
941 649 M 979 649 L
1033 672 M 1037 674 L
1044 681 L
1044 637 L
1042 679 M 1042 637 L
1033 637 M 1052 637 L
1096 666 M 1094 660 L
1090 655 L
1084 653 L
1082 653 L
1075 655 L
1071 660 L
1069 666 L
1069 668 L
1071 674 L
1075 679 L
1082 681 L
1086 681 L
1092 679 L
1096 674 L
1098 668 L
1098 655 L
1096 647 L
1094 643 L
1090 639 L
1084 637 L
1077 637 L
1073 639 L
1071 643 L
1071 645 L
1073 647 L
1075 645 L
1073 643 L
1082 653 M 1077 655 L
1073 660 L
1071 666 L
1071 668 L
1073 674 L
1077 679 L
1082 681 L
1086 681 M 1090 679 L
1094 674 L
1096 668 L
1096 655 L
1094 647 L
1092 643 L
1088 639 L
1084 637 L
1115 641 M 1113 639 L
1115 637 L
1117 639 L
1115 641 L
1157 674 M 1155 672 L
1157 670 L
1159 672 L
1159 674 L
1157 679 L
1153 681 L
1147 681 L
1140 679 L
1136 674 L
1134 670 L
1132 662 L
1132 649 L
1134 643 L
1138 639 L
1145 637 L
1149 637 L
1155 639 L
1159 643 L
1161 649 L
1161 651 L
1159 658 L
1155 662 L
1149 664 L
1147 664 L
1140 662 L
1136 658 L
1134 651 L
1147 681 M 1142 679 L
1138 674 L
1136 670 L
1134 662 L
1134 649 L
1136 643 L
1140 639 L
1145 637 L
1149 637 M 1153 639 L
1157 643 L
1159 649 L
1159 651 L
1157 658 L
1153 662 L
1149 664 L
1178 637 M 1176 639 L
1178 641 L
1180 639 L
1180 634 L
1178 630 L
1176 628 L
1233 681 M 1229 660 L
1233 664 L
1239 666 L
1245 666 L
1252 664 L
1256 660 L
1258 653 L
1258 649 L
1256 643 L
1252 639 L
1245 637 L
1239 637 L
1233 639 L
1231 641 L
1229 645 L
1229 647 L
1231 649 L
1233 647 L
1231 645 L
1245 666 M 1250 664 L
1254 660 L
1256 653 L
1256 649 L
1254 643 L
1250 639 L
1245 637 L
1233 681 M 1254 681 L
1233 679 M 1243 679 L
1254 681 L
1283 681 M 1277 679 L
1273 672 L
1271 662 L
1271 655 L
1273 645 L
1277 639 L
1283 637 L
1287 637 L
1294 639 L
1298 645 L
1300 655 L
1300 662 L
1298 672 L
1294 679 L
1287 681 L
1283 681 L
1279 679 L
1277 677 L
1275 672 L
1273 662 L
1273 655 L
1275 645 L
1277 641 L
1279 639 L
1283 637 L
1287 637 M 1292 639 L
1294 641 L
1296 645 L
1298 655 L
1298 662 L
1296 672 L
1294 677 L
1292 679 L
1287 681 L
1325 681 M 1319 679 L
1315 672 L
1313 662 L
1313 655 L
1315 645 L
1319 639 L
1325 637 L
1329 637 L
1336 639 L
1340 645 L
1342 655 L
1342 662 L
1340 672 L
1336 679 L
1329 681 L
1325 681 L
1321 679 L
1319 677 L
1317 672 L
1315 662 L
1315 655 L
1317 645 L
1319 641 L
1321 639 L
1325 637 L
1329 637 M 1334 639 L
1336 641 L
1338 645 L
1340 655 L
1340 662 L
1338 672 L
1336 677 L
1334 679 L
1329 681 L
1349 637 M CS [32 24] 0 setdash M
724 743 M CS [] 0 setdash M
724 721 M 735 765 M 735 721 L
737 765 M 737 721 L
750 753 M 750 736 L
729 765 M 762 765 L
762 753 L
760 765 L
737 744 M 750 744 L
729 721 M 762 721 L
762 734 L
760 721 L
779 747 M 779 744 L
777 744 L
777 747 L
779 749 L
783 751 L
792 751 L
796 749 L
798 747 L
800 742 L
800 728 L
802 723 L
804 721 L
798 747 M 798 728 L
800 723 L
804 721 L
806 721 L
798 742 M 796 740 L
783 738 L
777 736 L
775 732 L
775 728 L
777 723 L
783 721 L
790 721 L
794 723 L
798 728 L
783 738 M 779 736 L
777 732 L
777 728 L
779 723 L
783 721 L
838 747 M 840 751 L
840 742 L
838 747 L
836 749 L
832 751 L
823 751 L
819 749 L
817 747 L
817 742 L
819 740 L
823 738 L
834 734 L
838 732 L
840 730 L
817 744 M 819 742 L
823 740 L
834 736 L
838 734 L
840 732 L
CS M
840 726 L
838 723 L
834 721 L
825 721 L
821 723 L
819 726 L
817 730 L
817 721 L
819 726 L
857 765 M 857 730 L
859 723 L
863 721 L
867 721 L
871 723 L
874 728 L
859 765 M 859 730 L
861 723 L
863 721 L
850 751 M 867 751 L
878 721 M CS [32 24] 0 setdash M
724 838 M CS [] 0 setdash M
724 816 M 733 860 M 741 816 L
735 860 M 741 827 L
750 860 M 741 816 L
750 860 M 758 816 L
752 860 M 758 827 L
766 860 M 758 816 L
726 860 M 741 860 L
760 860 M 773 860 L
783 833 M 808 833 L
808 837 L
806 841 L
804 843 L
800 846 L
794 846 L
787 843 L
783 839 L
781 833 L
781 829 L
783 822 L
787 818 L
794 816 L
798 816 L
804 818 L
808 822 L
806 833 M 806 839 L
804 843 L
794 846 M 789 843 L
785 839 L
783 833 L
783 829 L
785 822 L
789 818 L
794 816 L
842 841 M 844 846 L
844 837 L
842 841 L
840 843 L
836 846 L
827 846 L
823 843 L
821 841 L
821 837 L
823 835 L
827 833 L
838 829 L
842 827 L
844 825 L
821 839 M 823 837 L
827 835 L
838 831 L
842 829 L
844 827 L
844 820 L
842 818 L
838 816 L
829 816 L
825 818 L
823 820 L
821 825 L
821 816 L
823 820 L
861 860 M 861 825 L
863 818 L
867 816 L
871 816 L
876 818 L
878 822 L
863 860 M 863 825 L
865 818 L
867 816 L
855 846 M 871 846 L
882 816 M CS [32 24] 0 setdash M
1312 2071 M CS [] 0 setdash M
999 2049 M 1035 2087 M 1037 2080 L
1037 2093 L
1035 2087 L
1031 2091 L
1024 2093 L
1020 2093 L
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CS M
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1602 2049 L
1606 2049 M 1610 2051 L
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1615 2070 L
1610 2074 L
1606 2076 L
1626 2049 M CS [32 24] 0 setdash M
stroke
grestore
showpage
end

braunr_fig2.tex
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%%EndComments
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72 300 div dup scale
1 setlinejoin 0 setlinecap
/Helvetica findfont 55 scalefont setfont 
/B {currentpoint stroke newpath moveto} 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 eofill} def
/L {lineto} def /M {moveto} def
/P {moveto 0 1 rlineto stroke} def
/T {currentlinecap exch 1 setlinecap show setlinecap} def
errordict /nocurrentpoint {pop 0 0 M currentpoint} put
/SET_COLOUR systemdict /processcolors known
  { processcolors 1 gt } { false } ifelse
    { (setrgbcolor) } { (pop pop pop) } ifelse cvx def
 80 600 translate
gsave
CS [32 24] 0 setdash M
CS M 2 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add dup -2 div 0 exch /rmoveto cvx /rlineto cvx /stroke cvx ] cvx def
 0 0 0 C
CS M 2 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add dup -2 div 0 exch /rmoveto cvx /rlineto cvx /stroke cvx ] cvx def
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CS [] 0 setdash M
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403 284 L
409 282 L
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1756 315 L
CS M
1756 318 L
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311 1415 L
305 1412 L
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CS M
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2261 1945 M 2216 1945 L
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CS [] 0 setdash M
CS [6 12] 0 setdash M
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791 364 M 791 364 L
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364 1734 M 364 1734 L
364 1839 M 364 1839 L
364 1945 M 2261 1945 L
364 2050 M 364 2050 L
364 2155 M 364 2155 L
364 2261 M 364 2261 L
CS [] 0 setdash M
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1361 1092 L
1356 1089 L
1350 1087 L
1344 1087 L
1339 1089 L
1333 1093 L
1328 1099 L
1322 1105 L
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1203 1165 L
1198 1178 L
1192 1191 L
1187 1202 L
1181 1213 L
1175 1221 L
1170 1229 L
1164 1237 L
1158 1244 L
1153 1253 L
1147 1262 L
1141 1272 L
1136 1282 L
1130 1292 L
1125 1301 L
1119 1309 L
1113 1317 L
1108 1324 L
1102 1330 L
1096 1335 L
1091 1339 L
1085 1342 L
1079 1344 L
1074 1345 L
1068 1345 L
1063 1344 L
1057 1344 L
1051 1344 L
1046 1345 L
1040 1346 L
1034 1349 L
1029 1352 L
1023 1355 L
1017 1360 L
1012 1364 L
1006 1370 L
1001 1376 L
995 1384 L
989 1392 L
984 1400 L
978 1410 L
972 1419 L
967 1429 L
961 1439 L
955 1448 L
950 1457 L
944 1466 L
938 1473 L
933 1480 L
927 1485 L
922 1490 L
916 1495 L
910 1498 L
905 1501 L
899 1504 L
893 1506 L
888 1508 L
882 1510 L
876 1512 L
871 1515 L
865 1518 L
860 1521 L
854 1524 L
848 1529 L
843 1533 L
837 1538 L
831 1543 L
826 1548 L
820 1553 L
814 1558 L
809 1563 L
803 1567 L
798 1571 L
792 1574 L
786 1578 L
781 1581 L
775 1584 L
769 1587 L
764 1590 L
758 1593 L
753 1597 L
747 1601 L
741 1604 L
736 1609 L
730 1613 L
724 1618 L
719 1623 L
713 1628 L
707 1634 L
702 1640 L
696 1646 L
690 1653 L
685 1661 L
679 1670 L
674 1679 L
668 1690 L
662 1701 L
657 1713 L
651 1726 L
645 1739 L
640 1752 L
634 1766 L
628 1780 L
623 1793 L
617 1806 L
612 1819 L
606 1831 L
600 1843 L
595 1855 L
589 1865 L
583 1875 L
578 1884 L
572 1893 L
566 1901 L
561 1909 L
555 1916 L
550 1922 L
544 1928 L
538 1934 L
533 1939 L
527 1945 L
521 1950 L
516 1955 L
510 1960 L
504 1966 L
499 1971 L
493 1977 L
488 1983 L
482 1988 L
CS M
476 1994 L
471 1999 L
465 2004 L
459 2009 L
454 2013 L
448 2017 L
442 2021 L
437 2024 L
431 2027 L
426 2029 L
420 2031 L
414 2032 L
CS [32 24] 0 setdash M
415 2032 M 420 2032 L
426 2032 L
431 2031 L
437 2029 L
443 2028 L
448 2025 L
454 2023 L
460 2020 L
465 2016 L
471 2013 L
477 2009 L
482 2004 L
488 2000 L
493 1996 L
499 1991 L
505 1986 L
510 1982 L
516 1977 L
522 1973 L
527 1969 L
533 1965 L
539 1961 L
544 1957 L
550 1954 L
555 1951 L
561 1949 L
567 1946 L
572 1944 L
578 1942 L
584 1941 L
589 1940 L
595 1939 L
601 1938 L
606 1937 L
612 1936 L
617 1935 L
623 1934 L
629 1934 L
634 1933 L
640 1932 L
646 1930 L
651 1929 L
657 1928 L
663 1926 L
668 1924 L
674 1923 L
679 1921 L
685 1919 L
691 1918 L
696 1917 L
702 1915 L
708 1915 L
713 1914 L
719 1913 L
725 1913 L
730 1913 L
736 1913 L
741 1913 L
747 1913 L
753 1913 L
758 1913 L
764 1913 L
770 1913 L
775 1913 L
781 1913 L
787 1912 L
792 1911 L
798 1910 L
804 1909 L
809 1908 L
815 1906 L
820 1904 L
826 1902 L
832 1899 L
837 1897 L
843 1894 L
849 1890 L
854 1887 L
860 1883 L
866 1879 L
871 1874 L
877 1869 L
882 1863 L
888 1857 L
894 1851 L
899 1844 L
905 1836 L
911 1828 L
916 1819 L
922 1810 L
928 1800 L
933 1790 L
939 1780 L
944 1770 L
950 1760 L
956 1750 L
961 1740 L
967 1731 L
973 1723 L
978 1715 L
984 1708 L
990 1702 L
995 1698 L
1001 1694 L
1006 1691 L
1012 1689 L
1018 1687 L
1023 1686 L
1029 1685 L
1035 1685 L
1040 1684 L
1046 1683 L
1052 1682 L
1057 1681 L
1063 1679 L
1069 1677 L
1074 1674 L
1080 1672 L
1085 1669 L
1091 1666 L
1097 1662 L
1102 1658 L
1108 1654 L
1114 1650 L
1119 1646 L
1125 1640 L
1131 1635 L
1136 1629 L
1142 1623 L
1147 1616 L
1153 1609 L
1159 1602 L
1164 1595 L
1170 1588 L
1176 1581 L
1181 1574 L
1187 1567 L
1193 1560 L
1198 1553 L
1204 1545 L
1209 1537 L
1215 1529 L
1221 1520 L
1226 1510 L
1232 1499 L
1238 1487 L
1243 1474 L
1249 1460 L
1255 1446 L
1260 1431 L
1266 1416 L
1271 1401 L
1277 1386 L
1283 1371 L
1288 1356 L
1294 1341 L
1300 1326 L
1305 1311 L
1311 1295 L
1317 1280 L
1322 1265 L
1328 1251 L
1333 1237 L
1339 1224 L
1345 1211 L
1350 1199 L
1356 1187 L
1362 1175 L
1367 1163 L
1373 1150 L
1379 1137 L
1384 1124 L
1390 1111 L
1396 1098 L
1401 1086 L
1407 1073 L
1412 1060 L
1418 1046 L
1424 1029 L
1429 1010 L
1435 986 L
1441 957 L
1446 922 L
CS [] 0 setdash M
1031 191 M 1041 235 M 1041 191 L
1043 235 M 1043 191 L
1035 235 M 1060 235 L
1066 233 L
1068 231 L
1071 227 L
1071 223 L
1068 218 L
1066 216 L
1060 214 L
1043 214 L
1060 235 M 1064 233 L
1066 231 L
1068 227 L
1068 223 L
1066 218 L
1064 216 L
1060 214 L
1035 191 M 1050 191 L
1054 214 M 1058 212 L
1060 210 L
1066 195 L
1068 193 L
1071 193 L
1073 195 L
1058 212 M 1060 208 L
1064 193 L
1066 191 L
1071 191 L
1073 195 L
1073 197 L
1087 216 M 1087 214 L
1085 214 L
1085 216 L
1087 218 L
1092 220 L
1100 220 L
1104 218 L
1106 216 L
1108 212 L
1108 197 L
1111 193 L
1113 191 L
1106 216 M 1106 197 L
1108 193 L
1113 191 L
1115 191 L
1106 212 M 1104 210 L
1092 208 L
1085 206 L
1083 202 L
1083 197 L
1085 193 L
1092 191 L
1098 191 L
1102 193 L
1106 197 L
1092 208 M 1087 206 L
1085 202 L
1085 197 L
1087 193 L
1092 191 L
1150 235 M 1150 191 L
1153 235 M 1153 191 L
1150 214 M 1146 218 L
1142 220 L
1138 220 L
1131 218 L
1127 214 L
1125 208 L
1125 204 L
1127 197 L
1131 193 L
1138 191 L
1142 191 L
1146 193 L
1150 197 L
1138 220 M 1134 218 L
1129 214 L
1127 208 L
1127 204 L
1129 197 L
1134 193 L
1138 191 L
1144 235 M 1153 235 L
1150 191 M 1159 191 L
1174 235 M 1171 233 L
1174 231 L
1176 233 L
1174 235 L
1174 220 M 1174 191 L
1176 220 M 1176 191 L
1167 220 M 1176 220 L
1167 191 M 1182 191 L
1197 220 M 1197 197 L
1199 193 L
1205 191 L
1209 191 L
1216 193 L
1220 197 L
1199 220 M 1199 197 L
1201 193 L
1205 191 L
1220 220 M 1220 191 L
1222 220 M 1222 191 L
CS M
1190 220 M 1199 220 L
1213 220 M 1222 220 L
1220 191 M 1228 191 L
1260 216 M 1262 220 L
1262 212 L
1260 216 L
1258 218 L
1253 220 L
1245 220 L
1241 218 L
1239 216 L
1239 212 L
1241 210 L
1245 208 L
1256 204 L
1260 202 L
1262 199 L
1239 214 M 1241 212 L
1245 210 L
1256 206 L
1260 204 L
1262 202 L
1262 195 L
1260 193 L
1256 191 L
1247 191 L
1243 193 L
1241 195 L
1239 199 L
1239 191 L
1241 195 L
1325 244 M 1321 239 L
1316 233 L
1312 225 L
1310 214 L
1310 206 L
1312 195 L
1316 187 L
1321 181 L
1325 176 L
1321 239 M 1316 231 L
1314 225 L
1312 214 L
1312 206 L
1314 195 L
1316 189 L
1321 181 L
1342 216 M 1342 214 L
1339 214 L
1339 216 L
1342 218 L
1346 220 L
1354 220 L
1358 218 L
1361 216 L
1363 212 L
1363 197 L
1365 193 L
1367 191 L
1361 216 M 1361 197 L
1363 193 L
1367 191 L
1369 191 L
1361 212 M 1358 210 L
1346 208 L
1339 206 L
1337 202 L
1337 197 L
1339 193 L
1346 191 L
1352 191 L
1356 193 L
1361 197 L
1346 208 M 1342 206 L
1339 202 L
1339 197 L
1342 193 L
1346 191 L
1384 220 M 1384 191 L
1386 220 M 1386 191 L
1386 208 M 1388 214 L
1392 218 L
1396 220 L
1403 220 L
1405 218 L
1405 216 L
1403 214 L
1400 216 L
1403 218 L
1377 220 M 1386 220 L
1377 191 M 1392 191 L
1440 214 M 1438 212 L
1440 210 L
1442 212 L
1442 214 L
1438 218 L
1434 220 L
1428 220 L
1421 218 L
1417 214 L
1415 208 L
1415 204 L
1417 197 L
1421 193 L
1428 191 L
1432 191 L
1438 193 L
1442 197 L
1428 220 M 1423 218 L
1419 214 L
1417 208 L
1417 204 L
1419 197 L
1423 193 L
1428 191 L
1476 216 M 1478 220 L
1478 212 L
1476 216 L
1474 218 L
1470 220 L
1461 220 L
1457 218 L
1455 216 L
1455 212 L
1457 210 L
1461 208 L
1472 204 L
1476 202 L
1478 199 L
1455 214 M 1457 212 L
1461 210 L
1472 206 L
1476 204 L
1478 202 L
1478 195 L
1476 193 L
1472 191 L
1463 191 L
1459 193 L
1457 195 L
1455 199 L
1455 191 L
1457 195 L
1493 208 M 1518 208 L
1518 212 L
1516 216 L
1514 218 L
1510 220 L
1503 220 L
1497 218 L
1493 214 L
1491 208 L
1491 204 L
1493 197 L
1497 193 L
1503 191 L
1507 191 L
1514 193 L
1518 197 L
1516 208 M 1516 214 L
1514 218 L
1503 220 M 1499 218 L
1495 214 L
1493 208 L
1493 204 L
1495 197 L
1499 193 L
1503 191 L
1556 214 M 1554 212 L
1556 210 L
1558 212 L
1558 214 L
1554 218 L
1549 220 L
1543 220 L
1537 218 L
1533 214 L
1531 208 L
1531 204 L
1533 197 L
1537 193 L
1543 191 L
1547 191 L
1554 193 L
1558 197 L
1543 220 M 1539 218 L
1535 214 L
1533 208 L
1533 204 L
1535 197 L
1539 193 L
1543 191 L
1570 244 M 1575 239 L
1579 233 L
1583 225 L
1585 214 L
1585 206 L
1583 195 L
1579 187 L
1575 181 L
1570 176 L
1575 239 M 1579 231 L
1581 225 L
1583 214 L
1583 206 L
1581 195 L
1579 189 L
1575 181 L
CS [32 24] 0 setdash M
CS [] 0 setdash M
184 1028 M 139 1038 M 184 1038 L
139 1040 M 184 1040 L
139 1032 M 139 1040 L
184 1032 M 184 1047 L
154 1070 M 156 1063 L
160 1059 L
167 1057 L
171 1057 L
177 1059 L
181 1063 L
184 1070 L
184 1074 L
181 1080 L
177 1084 L
171 1086 L
167 1086 L
160 1084 L
156 1080 L
154 1074 L
154 1070 L
156 1065 L
160 1061 L
167 1059 L
171 1059 L
177 1061 L
181 1065 L
184 1070 L
184 1074 M 181 1078 L
177 1082 L
171 1084 L
167 1084 L
160 1082 L
156 1078 L
154 1074 L
154 1110 M 156 1105 L
158 1103 L
163 1101 L
167 1101 L
171 1103 L
173 1105 L
175 1110 L
175 1114 L
173 1118 L
171 1120 L
167 1122 L
163 1122 L
158 1120 L
156 1118 L
154 1114 L
154 1110 L
156 1105 M 160 1103 L
169 1103 L
173 1105 L
173 1118 M 169 1120 L
160 1120 L
156 1118 L
158 1120 M 156 1122 L
154 1126 L
156 1126 L
156 1122 L
171 1103 M 173 1101 L
177 1099 L
179 1099 L
184 1101 L
186 1107 L
186 1118 L
188 1124 L
190 1126 L
179 1099 M 181 1101 L
184 1107 L
184 1118 L
186 1124 L
190 1126 L
192 1126 L
196 1124 L
198 1118 L
198 1105 L
196 1099 L
192 1097 L
190 1097 L
186 1099 L
184 1105 L
131 1189 M 135 1185 L
142 1181 L
150 1177 L
160 1175 L
169 1175 L
179 1177 L
188 1181 L
194 1185 L
198 1189 L
135 1185 M 144 1181 L
CS M
150 1179 L
160 1177 L
169 1177 L
179 1179 L
186 1181 L
194 1185 L
139 1206 M 184 1206 L
139 1208 M 179 1233 L
144 1208 M 184 1233 L
139 1233 M 184 1233 L
139 1200 M 139 1208 L
139 1227 M 139 1240 L
184 1200 M 184 1212 L
177 1250 M 204 1250 L
177 1251 M 204 1251 L
177 1267 M 204 1267 L
177 1268 M 204 1268 L
177 1246 M 177 1255 L
177 1263 M 177 1272 L
190 1251 M 190 1267 L
204 1246 M 204 1255 L
204 1263 M 204 1272 L
131 1280 M 135 1285 L
142 1289 L
150 1293 L
160 1295 L
169 1295 L
179 1293 L
188 1289 L
194 1285 L
198 1280 L
135 1285 M 144 1289 L
150 1291 L
160 1293 L
169 1293 L
179 1291 L
186 1289 L
194 1285 L
131 1360 M 135 1356 L
142 1352 L
150 1348 L
160 1346 L
169 1346 L
179 1348 L
188 1352 L
194 1356 L
198 1360 L
135 1356 M 144 1352 L
150 1350 L
160 1348 L
169 1348 L
179 1350 L
186 1352 L
194 1356 L
160 1398 M 163 1396 L
165 1398 L
163 1400 L
160 1400 L
156 1396 L
154 1392 L
154 1386 L
156 1379 L
160 1375 L
167 1373 L
171 1373 L
177 1375 L
181 1379 L
184 1386 L
184 1390 L
181 1396 L
177 1400 L
154 1386 M 156 1381 L
160 1377 L
167 1375 L
171 1375 L
177 1377 L
181 1381 L
184 1386 L
154 1417 M 184 1417 L
154 1419 M 184 1419 L
160 1419 M 156 1423 L
154 1430 L
154 1434 L
156 1440 L
160 1442 L
184 1442 L
154 1434 M 156 1438 L
160 1440 L
184 1440 L
160 1442 M 156 1446 L
154 1453 L
154 1457 L
156 1463 L
160 1465 L
184 1465 L
154 1457 M 156 1461 L
160 1463 L
184 1463 L
154 1411 M 154 1419 L
184 1411 M 184 1425 L
184 1434 M 184 1449 L
184 1457 M 184 1472 L
152 1481 M 152 1504 L
142 1514 M 143 1515 L
144 1514 L
143 1512 L
142 1512 L
139 1514 L
138 1515 L
137 1519 L
137 1524 L
138 1528 L
139 1529 L
142 1530 L
144 1530 L
147 1529 L
150 1525 L
152 1519 L
153 1516 L
156 1514 L
160 1512 L
163 1512 L
137 1524 M 138 1526 L
139 1528 L
142 1529 L
144 1529 L
147 1528 L
150 1524 L
152 1519 L
161 1512 M 160 1514 L
160 1516 L
162 1522 L
162 1526 L
161 1529 L
160 1530 L
160 1516 M 163 1522 L
163 1528 L
162 1529 L
160 1530 L
157 1530 L
131 1540 M 135 1544 L
142 1548 L
150 1553 L
160 1555 L
169 1555 L
179 1553 L
188 1548 L
194 1544 L
198 1540 L
135 1544 M 144 1548 L
150 1551 L
160 1553 L
169 1553 L
179 1551 L
186 1548 L
194 1544 L
CS [32 24] 0 setdash M
CS [6 12] 0 setdash M
483 1944 M 511 1938 L
540 1925 L
568 1908 L
596 1888 L
625 1867 L
653 1844 L
682 1820 L
710 1796 L
739 1770 L
767 1744 L
796 1717 L
824 1690 L
852 1662 L
881 1634 L
909 1606 L
938 1577 L
966 1548 L
995 1519 L
1023 1490 L
1052 1460 L
1080 1431 L
1109 1401 L
1137 1370 L
1165 1340 L
1194 1310 L
1222 1279 L
1251 1249 L
1279 1218 L
1308 1187 L
1336 1156 L
1365 1125 L
1393 1094 L
1421 1062 L
1450 1031 L
1478 1000 L
1507 968 L
1535 937 L
1564 905 L
1592 873 L
1621 842 L
1649 810 L
1677 778 L
1706 746 L
1734 714 L
1763 682 L
1791 650 L
1820 618 L
1848 586 L
1877 554 L
1905 522 L
1933 489 L
1962 457 L
1990 425 L
2019 392 L
2043 364 L
CS [6 12] 0 setdash M
554 649 M 687 649 L
CS [] 0 setdash M
554 743 M 687 743 L
CS [32 24] 0 setdash M
554 838 M 687 838 L
724 649 M CS [] 0 setdash M
724 637 M 735 681 M 735 637 L
737 681 M 762 641 L
737 677 M 762 637 L
762 681 M 762 637 L
729 681 M 737 681 L
756 681 M 769 681 L
729 637 M 741 637 L
784 643 M 780 642 L
778 638 L
776 631 L
776 628 L
778 621 L
780 618 L
784 616 L
787 616 L
790 618 L
793 621 L
794 628 L
794 631 L
793 638 L
790 642 L
787 643 L
784 643 L
782 642 L
780 640 L
779 638 L
778 631 L
778 628 L
779 621 L
780 619 L
782 618 L
784 616 L
787 616 M 789 618 L
790 619 L
792 621 L
793 628 L
793 631 L
792 638 L
790 640 L
789 642 L
787 643 L
808 637 M 806 639 L
808 641 L
810 639 L
810 634 L
808 630 L
806 628 L
863 681 M 863 637 L
865 681 M 865 637 L
865 660 M 869 664 L
876 666 L
880 666 L
886 664 L
888 660 L
888 637 L
880 666 M 884 664 L
886 660 L
886 637 L
857 681 M 865 681 L
857 637 M 871 637 L
880 637 M 895 637 L
941 662 M 979 662 L
941 649 M 979 649 L
1029 672 M 1031 670 L
1029 668 L
1027 670 L
1027 672 L
1029 677 L
1031 679 L
1037 681 L
1046 681 L
1052 679 L
1054 677 L
1056 672 L
1056 668 L
1054 664 L
1048 660 L
1037 655 L
1033 653 L
1029 649 L
1027 643 L
1027 637 L
1046 681 M 1050 679 L
1052 677 L
1054 672 L
1054 668 L
CS M
1052 664 L
1046 660 L
1037 655 L
1027 641 M 1029 643 L
1033 643 L
1044 639 L
1050 639 L
1054 641 L
1056 643 L
1033 643 M 1044 637 L
1052 637 L
1054 639 L
1056 643 L
1056 647 L
1082 681 M 1075 679 L
1071 672 L
1069 662 L
1069 655 L
1071 645 L
1075 639 L
1082 637 L
1086 637 L
1092 639 L
1096 645 L
1098 655 L
1098 662 L
1096 672 L
1092 679 L
1086 681 L
1082 681 L
1077 679 L
1075 677 L
1073 672 L
1071 662 L
1071 655 L
1073 645 L
1075 641 L
1077 639 L
1082 637 L
1086 637 M 1090 639 L
1092 641 L
1094 645 L
1096 655 L
1096 662 L
1094 672 L
1092 677 L
1090 679 L
1086 681 L
1115 641 M 1113 639 L
1115 637 L
1117 639 L
1115 641 L
1145 681 M 1138 679 L
1134 672 L
1132 662 L
1132 655 L
1134 645 L
1138 639 L
1145 637 L
1149 637 L
1155 639 L
1159 645 L
1161 655 L
1161 662 L
1159 672 L
1155 679 L
1149 681 L
1145 681 L
1140 679 L
1138 677 L
1136 672 L
1134 662 L
1134 655 L
1136 645 L
1138 641 L
1140 639 L
1145 637 L
1149 637 M 1153 639 L
1155 641 L
1157 645 L
1159 655 L
1159 662 L
1157 672 L
1155 677 L
1153 679 L
1149 681 L
1178 637 M 1176 639 L
1178 641 L
1180 639 L
1180 634 L
1178 630 L
1176 628 L
1247 677 M 1247 637 L
1250 681 M 1250 637 L
1250 681 M 1226 649 L
1260 649 L
1241 637 M 1256 637 L
1283 681 M 1277 679 L
1273 672 L
1271 662 L
1271 655 L
1273 645 L
1277 639 L
1283 637 L
1287 637 L
1294 639 L
1298 645 L
1300 655 L
1300 662 L
1298 672 L
1294 679 L
1287 681 L
1283 681 L
1279 679 L
1277 677 L
1275 672 L
1273 662 L
1273 655 L
1275 645 L
1277 641 L
1279 639 L
1283 637 L
1287 637 M 1292 639 L
1294 641 L
1296 645 L
1298 655 L
1298 662 L
1296 672 L
1294 677 L
1292 679 L
1287 681 L
1325 681 M 1319 679 L
1315 672 L
1313 662 L
1313 655 L
1315 645 L
1319 639 L
1325 637 L
1329 637 L
1336 639 L
1340 645 L
1342 655 L
1342 662 L
1340 672 L
1336 679 L
1329 681 L
1325 681 L
1321 679 L
1319 677 L
1317 672 L
1315 662 L
1315 655 L
1317 645 L
1319 641 L
1321 639 L
1325 637 L
1329 637 M 1334 639 L
1336 641 L
1338 645 L
1340 655 L
1340 662 L
1338 672 L
1336 677 L
1334 679 L
1329 681 L
1349 637 M CS [32 24] 0 setdash M
724 743 M CS [] 0 setdash M
724 721 M 735 765 M 735 721 L
737 765 M 737 721 L
750 753 M 750 736 L
729 765 M 762 765 L
762 753 L
760 765 L
737 744 M 750 744 L
729 721 M 762 721 L
762 734 L
760 721 L
779 747 M 779 744 L
777 744 L
777 747 L
779 749 L
783 751 L
792 751 L
796 749 L
798 747 L
800 742 L
800 728 L
802 723 L
804 721 L
798 747 M 798 728 L
800 723 L
804 721 L
806 721 L
798 742 M 796 740 L
783 738 L
777 736 L
775 732 L
775 728 L
777 723 L
783 721 L
790 721 L
794 723 L
798 728 L
783 738 M 779 736 L
777 732 L
777 728 L
779 723 L
783 721 L
838 747 M 840 751 L
840 742 L
838 747 L
836 749 L
832 751 L
823 751 L
819 749 L
817 747 L
817 742 L
819 740 L
823 738 L
834 734 L
838 732 L
840 730 L
817 744 M 819 742 L
823 740 L
834 736 L
838 734 L
840 732 L
840 726 L
838 723 L
834 721 L
825 721 L
821 723 L
819 726 L
817 730 L
817 721 L
819 726 L
857 765 M 857 730 L
859 723 L
863 721 L
867 721 L
871 723 L
874 728 L
859 765 M 859 730 L
861 723 L
863 721 L
850 751 M 867 751 L
878 721 M CS [32 24] 0 setdash M
724 838 M CS [] 0 setdash M
724 816 M 733 860 M 741 816 L
735 860 M 741 827 L
750 860 M 741 816 L
750 860 M 758 816 L
752 860 M 758 827 L
766 860 M 758 816 L
726 860 M 741 860 L
760 860 M 773 860 L
783 833 M 808 833 L
808 837 L
806 841 L
804 843 L
800 846 L
794 846 L
787 843 L
783 839 L
781 833 L
781 829 L
783 822 L
787 818 L
794 816 L
798 816 L
804 818 L
808 822 L
806 833 M 806 839 L
804 843 L
794 846 M 789 843 L
785 839 L
783 833 L
783 829 L
785 822 L
789 818 L
794 816 L
842 841 M 844 846 L
844 837 L
842 841 L
840 843 L
836 846 L
827 846 L
823 843 L
821 841 L
821 837 L
823 835 L
827 833 L
838 829 L
842 827 L
844 825 L
821 839 M 823 837 L
827 835 L
838 831 L
842 829 L
844 827 L
844 820 L
842 818 L
838 816 L
829 816 L
CS M
825 818 L
823 820 L
821 825 L
821 816 L
823 820 L
861 860 M 861 825 L
863 818 L
867 816 L
871 816 L
876 818 L
878 822 L
863 860 M 863 825 L
865 818 L
867 816 L
855 846 M 871 846 L
882 816 M CS [32 24] 0 setdash M
1312 2071 M CS [] 0 setdash M
999 2049 M 1035 2087 M 1037 2080 L
1037 2093 L
1035 2087 L
1031 2091 L
1024 2093 L
1020 2093 L
1014 2091 L
1010 2087 L
1008 2082 L
1005 2076 L
1005 2066 L
1008 2059 L
1010 2055 L
1014 2051 L
1020 2049 L
1024 2049 L
1031 2051 L
1035 2055 L
1037 2059 L
1020 2093 M 1016 2091 L
1012 2087 L
1010 2082 L
1008 2076 L
1008 2066 L
1010 2059 L
1012 2055 L
1016 2051 L
1020 2049 L
1054 2093 M 1054 2049 L
1056 2093 M 1056 2049 L
1081 2093 M 1081 2049 L
1083 2093 M 1083 2049 L
1047 2093 M 1062 2093 L
1075 2093 M 1090 2093 L
1056 2072 M 1081 2072 L
1047 2049 M 1062 2049 L
1075 2049 M 1090 2049 L
1100 2093 M 1115 2049 L
1102 2093 M 1115 2055 L
1129 2093 M 1115 2049 L
1096 2093 M 1108 2093 L
1121 2093 M 1134 2093 L
1171 2087 M 1173 2080 L
1173 2093 L
1171 2087 L
1167 2091 L
1161 2093 L
1157 2093 L
1150 2091 L
1146 2087 L
1144 2082 L
1142 2076 L
1142 2066 L
1144 2059 L
1146 2055 L
1150 2051 L
1157 2049 L
1161 2049 L
1167 2051 L
1171 2055 L
1173 2059 L
1157 2093 M 1152 2091 L
1148 2087 L
1146 2082 L
1144 2076 L
1144 2066 L
1146 2059 L
1148 2055 L
1152 2051 L
1157 2049 L
1192 2084 M 1197 2087 L
1203 2093 L
1203 2049 L
1201 2091 M 1201 2049 L
1192 2049 M 1211 2049 L
1239 2093 M 1232 2091 L
1230 2087 L
1230 2080 L
1232 2076 L
1239 2074 L
1247 2074 L
1253 2076 L
1255 2080 L
1255 2087 L
1253 2091 L
1247 2093 L
1239 2093 L
1234 2091 L
1232 2087 L
1232 2080 L
1234 2076 L
1239 2074 L
1247 2074 M 1251 2076 L
1253 2080 L
1253 2087 L
1251 2091 L
1247 2093 L
1239 2074 M 1232 2072 L
1230 2070 L
1228 2066 L
1228 2057 L
1230 2053 L
1232 2051 L
1239 2049 L
1247 2049 L
1253 2051 L
1255 2053 L
1258 2057 L
1258 2066 L
1255 2070 L
1253 2072 L
1247 2074 L
1239 2074 M 1234 2072 L
1232 2070 L
1230 2066 L
1230 2057 L
1232 2053 L
1234 2051 L
1239 2049 L
1247 2049 M 1251 2051 L
1253 2053 L
1255 2057 L
1255 2066 L
1253 2070 L
1251 2072 L
1247 2074 L
1295 2087 M 1293 2084 L
1295 2082 L
1297 2084 L
1297 2087 L
1295 2091 L
1291 2093 L
1285 2093 L
1279 2091 L
1274 2087 L
1272 2082 L
1270 2074 L
1270 2061 L
1272 2055 L
1276 2051 L
1283 2049 L
1287 2049 L
1293 2051 L
1297 2055 L
1300 2061 L
1300 2063 L
1297 2070 L
1293 2074 L
1287 2076 L
1285 2076 L
1279 2074 L
1274 2070 L
1272 2063 L
1285 2093 M 1281 2091 L
1276 2087 L
1274 2082 L
1272 2074 L
1272 2061 L
1274 2055 L
1279 2051 L
1283 2049 L
1287 2049 M 1291 2051 L
1295 2055 L
1297 2061 L
1297 2063 L
1295 2070 L
1291 2074 L
1287 2076 L
1333 2087 M 1333 2049 L
1314 2068 M 1352 2068 L
1373 2084 M 1377 2087 L
1384 2093 L
1384 2049 L
1382 2091 M 1382 2049 L
1373 2049 M 1392 2049 L
1436 2078 M 1434 2072 L
1430 2068 L
1424 2066 L
1421 2066 L
1415 2068 L
1411 2072 L
1409 2078 L
1409 2080 L
1411 2087 L
1415 2091 L
1421 2093 L
1426 2093 L
1432 2091 L
1436 2087 L
1438 2080 L
1438 2068 L
1436 2059 L
1434 2055 L
1430 2051 L
1424 2049 L
1417 2049 L
1413 2051 L
1411 2055 L
1411 2057 L
1413 2059 L
1415 2057 L
1413 2055 L
1421 2066 M 1417 2068 L
1413 2072 L
1411 2078 L
1411 2080 L
1413 2087 L
1417 2091 L
1421 2093 L
1426 2093 M 1430 2091 L
1434 2087 L
1436 2080 L
1436 2068 L
1434 2059 L
1432 2055 L
1428 2051 L
1424 2049 L
1453 2068 M 1491 2068 L
1512 2084 M 1516 2087 L
1522 2093 L
1522 2049 L
1520 2091 M 1520 2049 L
1512 2049 M 1531 2049 L
1554 2084 M 1558 2087 L
1564 2093 L
1564 2049 L
1562 2091 M 1562 2049 L
1554 2049 M 1573 2049 L
1608 2089 M 1608 2049 L
1610 2093 M 1610 2049 L
1610 2093 M 1587 2061 L
1621 2061 L
1602 2049 M 1617 2049 L
1626 2049 M CS [32 24] 0 setdash M
stroke
grestore
showpage
end
