hep-ph0002073.tex
\documentstyle[12pt]{article}
\begin{document}
\begin{center}
{\large \bf Neutrino Tests of General and Special Relativity}\\
\vspace{1.0cm}
C. N. Leung\footnote{Talk presented at the Nufact'99 Workshop, 
Lyon, France, July 5-9, 1999.}\\
\bigskip
Department of Physics and Astronomy, University of Delaware\\ 
Newark, DE 19716, U.S.A.\\
\vspace{1.0cm}


{\bf Abstract}
\end{center}
We review the status of testing the principle of equivalence and 
Lorentz invariance from atmospheric and solar neutrino experiments.

\newpage
Let us begin by asking the question: do neutrinos obey the 
principle of equivalence?  The answer must of course come from 
experiments.  For ordinary matter, the most sensitive test of 
the equivalence principle comes from torsion balance experiments 
which measure the gravitational acceleration of macroscopic 
bodies.  The current best limit\cite{torex} is $10^{-12}$, i.e., 
all macroscopic bodies experience the same gravitational 
acceleration to an accuracy of one part in $10^{12}$.  Surely 
torsion balance experiments are not applicable to neutrinos.  
So the question is: what types of experiments are suitable for 
testing if neutrinos obey the principle of equivalence?

Suppose the neutrinos violate the principle of equivalence.  A 
consequence will be that different neutrino types (i.e., different
neutrino gravitational eigenstates) will couple to gravity with a 
slightly different strength.  Suppose the neutrino weak interaction 
eigenstates are not the same as their gravitational interaction 
eigenstates, but are linear superpositions of them.  Then, as a 
neutrino of definite flavour (e.g., $\nu_\mu$) travels through a 
gravitational field, the gravitational components of the flavour 
neutrino will develop different dynamical phases, which will result 
in neutrino flavour oscillations.  In other words, neutrino 
oscillation experiments provide a laboratory to test the 
equivalence principle for neutrinos\cite{Gasp,HL}. 

To parametrize the probabilities for neutrino oscillations arising 
from a violation of the equivalence principle (VEP), we follow the 
formalism in Ref.\cite{HLP} where the general equation governing 
neutrino flavour evolutions is found to be 

\begin{eqnarray}
i \frac{d}{dt} 
\left( \begin{array}{c} \nu_e \\ \nu_\mu \end{array} \right)
&=& 
\left\{
{\Delta m^2 \over 4E}
 \left[ \begin{array}{cc}
- \cos 2 \theta_M & \sin 2 \theta_M \\
\sin 2 \theta_M & \cos 2 \theta_M \end{array}
\right] \right. \nonumber \\
&+& \left.
E |\phi(r)| \Delta f
 \left[ \begin{array}{cc}
-\cos 2 \theta_G & e^{-i\beta} \sin 2 \theta_G \\
e^{i\beta} \sin 2 \theta_G & \cos 2 \theta_G \end{array}
\right] \right. \nonumber \\
&+& \left.
\frac{G_F N_e}{\sqrt{2}} 
\left[ \begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array} \right]
\right\}
\left( \begin{array}{c} \nu_e \\ \nu_\mu \end{array} \right)_.
\label{evol}
\end{eqnarray} 

We have assumed two neutrino flavours ($\nu_e$ and $\nu_\mu$) 
for simplicity.  The first and third line on the right-hand 
side of Eq.(\ref{evol}) are familiar from the usual studies of 
neutrino oscillations.  The first line describes flavour mixing 
arising from nondegenerate neutrino vacuum masses\cite{Ponte}.  
Here $E$ denotes the neutrino's energy, $\Delta m^2 \equiv m_2^2 
- m_1^2$ is the neutrino mass-squared difference, and $\theta_M$ 
is the mixing angle between the weak interaction eigenstates 
and the mass eigenstates of the neutrinos.  The third line 
describes the matter effects on neutrino flavour 
evolutions\cite{W}.  Here $G_F$ is the Fermi constant and 
$N_e$ is the electron density in matter.  To study neutrino 
oscillations in vacuum, simply set $N_e = 0$.  The second line 
on the right-hand side of Eq.(\ref{evol}) describes neutrino 
flavour mixing arising from VEP.  Here $\phi(r)$, which 
satisfies the boundary condition $\phi(r \rightarrow \infty) 
\rightarrow 0$, is the gravitational potential through which 
the neutrinos propagate, $\theta_G$ is the mixing angle between 
the weak interaction eigenstates and the gravitational 
interaction eigenstates of the neutrinos, $\beta$ is a phase 
factor which comes about because we have mixing among three 
generally distinct sets of neutrino eigenstates: weak, 
gravitational, and mass.  Finally, $\Delta f$ is a measure of 
VEP defined as $\Delta f \equiv f_2 - f_1$, where $f_{1,2}$ 
are parameters introduced in the linearized neutrino-gravity 
interaction Lagrangian density\cite{BD},
\begin{equation}
 {\cal L}_{{\rm int}} = \frac{i f_j}{4} \sqrt{8 \pi G_N} 
 h^{\alpha\beta} [\bar{\nu_j} \gamma_\alpha \partial_\beta \nu_j 
 - (\partial_\alpha \bar{\nu_j}) \gamma_\beta \nu_j], ~~~~j = 1,2                        
\end{equation}
to gauge the deviation from universal coupling to gravity.  
Here $\nu_{1,2}$ denote the neutrino gravitational eigenstates, 
$h^{\alpha\beta}$ is the background gravitational field, and   
$G_N$ is the Newton gravitational constant.  Einstein's theory 
of general relativity predicts $f_1 = f_2 = 1$.  VEP occurs 
when $f_1 \neq f_2$.  

It can be concluded from Eq.(\ref{evol}) that 
\begin{enumerate}
 \item VEP leads to neutrino flavour oscillations even if the 
	neutrinos are massless or degenerate (in this case the 
	phase factor $\beta$ can be eliminated by redefinition 
	of the neutrino fields);
 \item neutrino oscillation tests of the principle of equivalence 
	involve two parameters: $\Delta f$ and $\theta_G$; it is 
	also necessary to know the value of the local gravitational 
	potential;
 \item VEP oscillations have a different energy dependence from 
	oscillations due to nondegenerate neutrino masses.
\end{enumerate}

The dependence of VEP oscillations on $\phi(r)$ is a consequence 
of violating the principle of equivalence.  It is also a source 
of uncertainty.  Table 1 in Ref.\cite{HLP} shows that our local 
value of $|\phi|$ spans from $6 \times 10^{-10}$ for the Earth's 
gravitational potential to about $3 \times 10^{-5}$ for the 
gravitational potential due to our local supercluster\cite{Ken}.  
Its value may be even bigger if the contributions from more distant 
sources can be estimated.  Since $\phi$ appears to be dominated by  
distant sources, its value varies little over a typical neutrino 
path length for earthbound experiments and may thus be treated 
as a constant.  It is then convenient to treat $|\phi| \Delta f$ 
as a single parameter in phenomenological analyses.

In the constant $\phi$ approximation, the VEP flavour transition 
probability has the familiar form ($\Delta m^2$ is assumed to 
be zero here):
\begin{equation}
 P(\nu_e \rightarrow \nu_\mu) = \sin^2 (2\theta_G) \sin^2 \left(
 \frac{\pi L}{\lambda_G} \right)_, 
\label{VEPprob}
\end{equation}
where $L$ is the neutrino path length and $\lambda_G$ is the 
oscillation length given by 
\begin{equation}
 \lambda_G = \frac{\pi}{E |\phi| \Delta f} 
  = 6.2~{\rm km} \Bigl(\frac{10^{-19}}{|\phi| \Delta f}
 \Bigr) \Bigl(\frac{1~{\rm GeV}}{E}\Bigr)_. 
\label{VEPlength}
\end{equation}
If we compare this with the well-known vacuum oscillation 
probability due to a neutrino mass difference, we see that the 
two cases are related by the formal connection, 
\begin{equation}
 \frac{\Delta m^2}{4E} \rightarrow E |\phi| \Delta f ~~~~~~
 {\rm and} ~~~~~~ \theta_M \rightarrow \theta_G.
\label{VEPsub}
\end{equation}
This connection can also be gleaned from Eq.(\ref{evol}).  
In contrast to the case of flavour oscillations induced by a 
neutrino mass difference where the oscillation length increases 
with the neutrino's energy, VEP oscillations are characterized 
by an oscillation length that decreases with increasing neutrino 
energy.  The two mechanisms may therefore be distinguished 
by measuring the neutrino energy spectrum\cite{PHL,BKL,LK,MN}.  
Note also that VEP oscillations will be more prominent in 
experiments with a large $E \cdot L$, i.e., high energy 
neutrinos and/or long path lengths, which is ideal for 
the neutrino factory experiments discussed in this workshop.

In a certain class of string theories, VEP may arise through 
interactions with a massless dilaton field\cite{DP}.  This type 
of equivalence principle violation may also lead to neutrino 
oscillations, but with an energy dependence which is the same 
as in oscillations due to nondegenerate neutrino masses\cite
{HLstring}.  It is therefore difficult to distinguish this type 
of VEP oscillations from the mass mixing oscillations, although 
one can still use data from oscillation experiments to constrain 
the relevant neutrino-dilaton couplings\cite{HLstring}.  We 
shall not consider further VEP oscillations from string theory, 
but will focus on the VEP oscillations from Eq.(\ref{evol}), 
which share the same distinctive energy dependence\cite{GHKLP} 
with neutrino oscillations arising from a possible breakdown of 
Lorentz invariance\cite{CG}.

If Lorentz invariance is violated, different (massless) neutrino 
species may have different maximum attainable speeds which are 
close to but not necessarily equal to $c$.  Neutrino oscillations 
can occur if the neutrino flavour eigenstates are linear 
superpositions of their velocity eigenstates, defined to be the 
energy eigenstates at infinite momentum, with the probability 
(for two-neutrino mixing)\cite{CG}
\begin{equation}
 P(\nu_e \rightarrow \nu_\mu) = \sin^2 (2\theta_v) \sin^2 \left(
 \frac{\pi L}{\lambda_v} \right)_, 
\label{VLIprob}
\end{equation}
where $L$ is the neutrino path length, $\theta_v$ is the mixing 
angle between the weak interaction eigenstates and the velocity 
eigenstates of the neutrinos, and $\lambda_v$ is the oscillation 
length given by 
\begin{equation}
 \lambda_v = \frac{2 \pi}{E \Delta v} 
 = 1.24~{\rm km} \Bigl(\frac{10^{-18}}{\Delta v}
 \Bigr) \Bigl(\frac{1~{\rm GeV}}{E}\Bigr)_. 
\label{VLIlength}
\end{equation} 
Here $\Delta v = v_2 - v_1$ is the difference between the 
speeds of the two neutrino velocity eigenstates.  Comparing 
Eqs.(\ref{VLIprob}) and (\ref{VLIlength}) with Eqs.(\ref{VEPprob}) 
and (\ref{VEPlength}), the similarities between the VLI 
(violation of Lorentz invariance) oscillations and VEP 
oscillations (for constant $\phi$) are obvious.  

Eqs.(\ref{VEPlength}) and (\ref{VLIlength}) indicate the 
sensitivity we can expect for VEP and VLI tests from neutrino 
oscillation experiments.  Assuming maximal mixing, there will be 
appreciable flavour transitions if $\pi L/\lambda_{G,v} 
\sim O(1)$.  For atmospheric neutrinos, $E \sim (0.1 - 10^3)$ 
GeV and $L \sim (20 - 10^4)$ km, hence $|\phi| \Delta f$ (or 
$\Delta v/2$) in the range $(10^{-26} - 10^{-19})$ can be 
probed.  For solar neutrinos, $E \sim (0.1 - 10)$ MeV and, for 
vacuum oscillations, $L \sim 10^8$ km, hence $|\phi| \Delta f$ 
(or $\Delta v/2$) in the range $(10^{-25} - 10^{-23})$ can be 
probed.  For MSW solution to the solar neutrino problem, the 
solar gravitational potential, which is about $1.7 \times 
10^{-5}$ at the solar core and decreases to about $ 2 \times 
10^{-6}$ at the surface of the Sun, plays a significant role 
and the constant $\phi$ approximation is not as good here.  
Nevertheless we can obtain an order-of-magnitude estimate 
for the sensitivity limit : $|\phi| \Delta f$ (or $\Delta v/2$)
$\sim (10^{-23} - 10^{-22})$, by letting $L = 7 \times 
10^5$ km, the mean solar radius (see Fig. 2 in Ref.\cite{BKL} 
for a more accurate estimate).  For long-baseline experiments 
such as those envisaged for future neutrino factories, 
$E \sim (10 \, - \, 100)$ GeV and $L \sim ({\rm few} \times 10^2 
\, - \, {\rm few} \times 10^3)$ km, hence a sensitivity of 
$(10^{-25} \, - \, 10^{-23})$ for $|\phi| \Delta f$ (or 
$\Delta v/2$) can be reached.  These estimates demonstrate that 
neutrino oscillations can provide a very sensitive test for the 
fundamental principles of general and special relativity.

We now confront VEP and VLI with experiments.  Because of the 
limited time, we shall consider only atmospheric and solar 
neutrino experiments.  

Positive evidence for $\nu_\mu \rightarrow \nu_\tau$ 
transitions has been established by the Super-Kamiokande 
(SK) Collaboration\cite{SKatmos}.  An analysis\cite{FLY} of 
the 535 days of SK data on sub-GeV and multi-GeV events 
found that VEP and VLI oscillations were consistent with 
the data, although the $\chi^2$ fit was not as good as 
the fit for mass mixing oscillations.  However, later 
analyses\cite{LL,FLMS} that included more recent SK 
data\cite{SKupmu} on upward-going muon events, which 
corresponded to atmospheric neutrinos with higher energies: 
$E$ up to $\sim 10^3$ GeV, found that VEP and VLI oscillations 
were not compatible with the data.  In particular, Fogli 
{\it et al.}\cite{FLMS}, did a very thorough analysis of the 
VEP and VLI mechanisms with the SK data.  They allowed a 
power-law energy dependence for the oscillation length: 
$\lambda \propto E^{-n}$, and found that, at 90\% C.L., 
$n = - 0.9 \pm 0.4$, which identified the mass mixing mechanism 
as the mechanism for the observed $\nu_\mu \rightarrow \nu_\tau$ 
transitions.  VEP and VLI oscillations, which correspond to 
$n = 1$, are clearly incompatible with the data.  The possibility 
of both mass mixing and VEP (or VLI) mechanisms contributing to 
the flavour transitions, as described in Eq.(\ref{evol}), was 
also studied in Ref.\cite{FLMS}.  It was found that, for a wide 
range of parameter choices, including the VEP (or VLI) 
contributions did not improve the fit for the mass mixing 
mechanism, which allowed the authors to obtain the 90\% C.L. 
upper bounds for the $\nu_\mu$-$\nu_\tau$ sector:
\begin{equation}
 |\Delta f| < 10^{-19}, ~~~~~~~~
 |\Delta v| < 6 \times 10^{-24},
\end{equation}
independent of the values of the corresponding mixing angles.  
The limit on $\Delta f$ is obtained by assuming $|\phi| = 3 
\times 10^{-5}$, the contribution from the local supercluster.  
This limit on VEP is seven orders of magnitude more stringent 
than the best limit from torsion balance experiments\cite{torex}.  
The limit on $\Delta v$ is also the most stringent limit on VLI 
to-date.  Note finally that these bounds are consistent with the 
range of sensitivity discussed above and are within about an  
order of magnitude of the sensitivity limit for long-baseline 
experiments. 

As constraining as the SK atmospheric neutrino data are, they 
only tell us about VEP and VLI in the $\nu_\mu$-$\nu_\tau$ sector.  
To study flavour transitions involving $\nu_e$, we turn to solar 
neutrino experiments.  The observed solar neutrino deficit may be 
a result of long-wavelength neutrino vacuum oscillations or 
matter-enhanced flavour transitions (MSW effect)\cite{W,MS} in 
the Sun.  Based on the Standard Solar Model predictions in 
Ref.\cite{BP92}, it was found in Ref.\cite{PHL} that only 
matter-enhanced VEP oscillations were compatible with the 
available solar neutrino data then.  However, using the improved 
Standard Solar Model predictions\cite{BP98} and the latest solar 
neutrino data\cite{Home98,SAGE99,GALLEX99,SKsun99}, and treating 
the $^8$B neutrino flux as a free parameter, a recent 
study\cite{GNF} finds that long-wavelength VEP oscillations 
can also account for the solar neutrino deficit.  The authors 
of Ref.\cite{GNF} examined constraints from the observed solar 
neutrino rates and from the SK spectral data.  They found that, 
for $\nu_e \rightarrow \nu_\tau$ transitions, the allowed 
parameter space lay in the region 
\begin{equation}
 0.65 \leq \sin^2(2\theta_G) \leq 1.0 ~~{\rm and}~~ 
 3.3 \times 10^{-20} < |\Delta f| \leq 3.3 \times 10^{-18} 
\label{VEPvac}
\end{equation}
for VEP and 
\begin{equation}
 0.65 \leq \sin^2(2\theta_v) \leq 1.0 ~~{\rm and}~~ 
 2.0 \times 10^{-24} < |\Delta v| \leq 2.0 \times 10^{-22} 
\label{VLIvac}
\end{equation}
for VLI.  We have again used $|\phi| = 3 \times 10^{-5}$ to 
obtain the limits on $\Delta f$ in (\ref{VEPvac}).  For 
$\nu_e \rightarrow \nu_\mu$ transitions, constraints\cite{PKM} 
from the recent accelerator neutrino data from the CCFR 
Collaboration\cite{CCFR} reduce the allowed range for $|\Delta f|$ 
and $|\Delta v|$ to $3.3 \times 10^{-20} < |\Delta f| < 
6.7 \times 10^{-19}$ and $2.0 \times 10^{-24} < |\Delta v| < 
4.0 \times 10^{-23}$, for the same range of values for the 
corresponding mixing angle.  

The VEP and VLI mechanisms also admit a MSW solution to the 
solar neutrino problem.  One generally finds two disjointed 
allowed regions, one for small mixing angles and one for large 
mixings\cite{HLP,PHL,BKL,PKM,MK}.  Figure 1, which is due to 
P. I. Krastev, shows the 99\% confidence level allowed regions 
for $|\Delta f|$ and $\sin^2(2\theta_G)$ derived from comparing 
all available data on the solar neutrino rates, including the 
825 days of SK data\cite{SKsun99}, with the Standard Solar Model 
predictions in Ref.\cite{BP98}.  Figure 1 is obtained by using 
only the solar gravitational potential for $\phi(r)$ in 
Eq.(\ref{evol}) to determine the neutrino flavour evolution.  
For the $\nu_e \rightarrow \nu_\mu$ channel, the allowed regions  
in Figure 1 are completely ruled out by the constraints from the 
CCFR data\cite{PKM}.  For the $\nu_e \rightarrow \nu_\tau$ 
channel, only the large mixing angle region is incompatible 
with the CCFR data\footnote{The authors of Ref.\cite{PKM} claim 
that a three-neutrino mixing analysis rules out the MSW 
allowed regions completely, for both $\nu_e \rightarrow \nu_\mu$ 
and $\nu_e \rightarrow \nu_\tau$ transitions.}.  The remaining 
small mixing region may be constrained by the SK data on the 
recoil-electron energy spectrum, although an analysis\cite{MK} 
based on earlier (504 days) SK data did not find such a 
constraint.  

In conclusion, {\em in addition to} helping determine the 
masses and mixing angles of neutrinos, neutrino oscillation 
experiments constitute a very useful tool for testing the 
principle of equivalence and Lorentz invariance.  Current 
solar and atmospheric neutrino data already provide very 
stringent limits.  For the $\nu_\mu$-$\nu_\tau$ sector, 
atmospheric neutrino data imply that the principle of 
equivalence cannot be violated by more than one part in 
$10^{19}$ and Lorentz invariance cannot be violated by more 
than $6 \times 10^{-24}$.  Solar neutrino data provide limits 
for both the $\nu_e$-$\nu_\mu$ and $\nu_e$-$\nu_\tau$ sectors.  
The exact limits depend on the assumption of either MSW 
oscillations or long-wavelength vacuum oscillations, with the 
long-wavelength solution imposing the stronger bounds.  Future 
long-baseline experiments can help improve these limits with 
sufficiently long (thousands of kilometers) baselines and 
sufficiently high energy (hundreds of GeV) neutrinos.  A 
neutrino factory will be a big access for reaching these 
goals. \\

\begin{center}
{\bf Acknowledgement}\\
\end{center}
\smallskip
This work was supported in part by the U.S. Department of Energy 
under grant DE-FG02-84ER40163. \\
\bigskip


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\end{document}

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420 246 L
423 245 L
425 243 L
426 241 L
426 237 L
425 235 L
424 234 L
420 233 L
416 233 L
412 234 L
411 235 L
410 237 L
410 238 L
411 239 L
412 238 L
411 237 L
424 244 M 425 241 L
425 237 L
424 235 L
423 234 L
420 233 L
548 292 M 548 312 L
655 292 M 655 312 L
731 292 M 731 312 L
790 292 M 790 312 L
838 292 M 838 312 L
878 292 M 878 312 L
914 292 M 914 312 L
945 292 M 945 312 L
972 292 M 972 333 L
907 214 M 919 247 M 923 249 L
929 254 L
929 214 L
927 253 M 927 214 L
919 214 M 936 214 L
963 254 M 957 253 L
954 247 L
952 237 L
952 231 L
954 222 L
957 216 L
963 214 L
967 214 L
973 216 L
977 222 L
979 231 L
979 237 L
977 247 L
973 253 L
967 254 L
963 254 L
959 253 L
957 251 L
956 247 L
954 237 L
954 231 L
956 222 L
957 218 L
959 216 L
963 214 L
967 214 M 971 216 L
973 218 L
975 222 L
977 231 L
977 237 L
975 247 L
973 251 L
971 253 L
967 254 L
989 243 M 1010 243 L
1019 252 M 1020 251 L
1019 250 L
1018 251 L
1018 252 L
1019 254 L
1020 256 L
1024 257 L
1028 257 L
1032 256 L
1033 254 L
1034 252 L
1034 250 L
1033 248 L
1029 245 L
1024 243 L
1021 242 L
1019 239 L
1018 236 L
1018 233 L
1028 257 M 1031 256 L
1032 254 L
1033 252 L
1033 250 L
1032 248 L
1028 245 L
1024 243 L
1018 235 M 1019 236 L
1021 236 L
1027 234 L
1031 234 L
1033 235 L
1034 236 L
1021 236 M 1027 233 L
1032 233 L
1033 234 L
1034 236 L
1034 238 L
1155 292 M 1155 312 L
1262 292 M 1262 312 L
1338 292 M 1338 312 L
1397 292 M 1397 312 L
1445 292 M 1445 312 L
1486 292 M 1486 312 L
1521 292 M 1521 312 L
1552 292 M 1552 312 L
1580 292 M 1580 333 L
1515 214 M 1527 247 M 1531 249 L
1536 254 L
1536 214 L
1535 253 M 1535 214 L
1527 214 M 1544 214 L
1571 254 M 1565 253 L
1561 247 L
1560 237 L
1560 231 L
1561 222 L
1565 216 L
1571 214 L
1575 214 L
1581 216 L
1585 222 L
1586 231 L
1586 237 L
1585 247 L
1581 253 L
1575 254 L
1571 254 L
1567 253 L
1565 251 L
1563 247 L
1561 237 L
1561 231 L
1563 222 L
1565 218 L
1567 216 L
1571 214 L
1575 214 M 1579 216 L
1581 218 L
1583 222 L
1585 231 L
1585 237 L
1583 247 L
1581 251 L
1579 253 L
1575 254 L
1597 243 M 1618 243 L
1629 252 M 1631 253 L
1635 257 L
1635 233 L
1634 256 M 1634 233 L
1629 233 M 1640 233 L
1763 292 M 1763 312 L
1870 292 M 1870 312 L
1946 292 M 1946 312 L
2005 292 M 2005 312 L
2053 292 M 2053 312 L
2094 292 M 2094 312 L
2129 292 M 2129 312 L
2160 292 M 2160 312 L
2188 292 M 2188 333 L
2138 214 M 2150 247 M 2153 249 L
2159 254 L
2159 214 L
2157 253 M 2157 214 L
2150 214 M 2167 214 L
2194 254 M 2188 253 L
2184 247 L
2182 237 L
2182 231 L
2184 222 L
2188 216 L
2194 214 L
2198 214 L
2204 216 L
2207 222 L
2209 231 L
2209 237 L
2207 247 L
2204 253 L
2198 254 L
2194 254 L
2190 253 L
2188 251 L
2186 247 L
2184 237 L
2184 231 L
2186 222 L
2188 218 L
2190 216 L
2194 214 L
2198 214 M 2202 216 L
2204 218 L
2205 222 L
2207 231 L
2207 237 L
2205 247 L
2204 251 L
2202 253 L
2198 254 L
2225 257 M 2222 256 L
2220 252 L
2219 246 L
2219 243 L
2220 237 L
2222 234 L
2225 233 L
2228 233 L
2231 234 L
2234 237 L
2235 243 L
2235 246 L
2234 252 L
2231 256 L
2228 257 L
2225 257 L
2223 256 L
2222 254 L
2221 252 L
2220 246 L
2220 243 L
2221 237 L
2222 235 L
2223 234 L
2225 233 L
2228 233 M 2230 234 L
CS M
2231 235 L
2232 237 L
2234 243 L
2234 246 L
2232 252 L
2231 254 L
2230 256 L
2228 257 L
365 2188 M 2188 2188 L
365 2188 M 365 2147 L
548 2188 M 548 2168 L
655 2188 M 655 2168 L
731 2188 M 731 2168 L
790 2188 M 790 2168 L
838 2188 M 838 2168 L
878 2188 M 878 2168 L
914 2188 M 914 2168 L
945 2188 M 945 2168 L
972 2188 M 972 2147 L
1155 2188 M 1155 2168 L
1262 2188 M 1262 2168 L
1338 2188 M 1338 2168 L
1397 2188 M 1397 2168 L
1445 2188 M 1445 2168 L
1486 2188 M 1486 2168 L
1521 2188 M 1521 2168 L
1552 2188 M 1552 2168 L
1580 2188 M 1580 2147 L
1763 2188 M 1763 2168 L
1870 2188 M 1870 2168 L
1946 2188 M 1946 2168 L
2005 2188 M 2005 2168 L
2053 2188 M 2053 2168 L
2094 2188 M 2094 2168 L
2129 2188 M 2129 2168 L
2160 2188 M 2160 2168 L
2188 2188 M 2188 2147 L
365 292 M 365 2188 L
365 292 M 406 292 L
176 270 M 188 303 M 192 305 L
198 311 L
198 270 L
196 309 M 196 270 L
188 270 M 205 270 L
232 311 M 226 309 L
223 303 L
221 293 L
221 288 L
223 278 L
226 272 L
232 270 L
236 270 L
242 272 L
246 278 L
248 288 L
248 293 L
246 303 L
242 309 L
236 311 L
232 311 L
228 309 L
226 307 L
225 303 L
223 293 L
223 288 L
225 278 L
226 274 L
228 272 L
232 270 L
236 270 M 240 272 L
242 274 L
244 278 L
246 288 L
246 293 L
244 303 L
242 307 L
240 309 L
236 311 L
258 299 M 279 299 L
290 309 M 293 310 L
296 313 L
296 289 L
295 312 M 295 289 L
290 289 M 301 289 L
310 313 M 310 306 L
310 309 M 311 311 L
313 313 L
316 313 L
321 310 L
324 310 L
325 311 L
326 313 L
311 311 M 313 312 L
316 312 L
321 310 L
326 313 M 326 310 L
325 306 L
320 300 L
319 298 L
318 295 L
318 289 L
325 306 M 319 300 L
318 298 L
317 295 L
317 289 L
365 406 M 385 406 L
365 473 M 385 473 L
365 520 M 385 520 L
365 557 M 385 557 L
365 587 M 385 587 L
365 612 M 385 612 L
365 634 M 385 634 L
365 654 M 385 654 L
365 671 M 406 671 L
176 650 M 188 682 M 192 684 L
198 690 L
198 650 L
196 688 M 196 650 L
188 650 M 205 650 L
232 690 M 226 688 L
223 682 L
221 673 L
221 667 L
223 657 L
226 652 L
232 650 L
236 650 L
242 652 L
246 657 L
248 667 L
248 673 L
246 682 L
242 688 L
236 690 L
232 690 L
228 688 L
226 686 L
225 682 L
223 673 L
223 667 L
225 657 L
226 654 L
228 652 L
232 650 L
236 650 M 240 652 L
242 654 L
244 657 L
246 667 L
246 673 L
244 682 L
242 686 L
240 688 L
236 690 L
258 679 M 279 679 L
290 688 M 293 689 L
296 692 L
296 668 L
295 691 M 295 668 L
290 668 M 301 668 L
324 689 M 323 688 L
324 687 L
325 688 L
325 689 L
324 691 L
321 692 L
318 692 L
315 691 L
312 689 L
311 687 L
310 682 L
310 675 L
311 672 L
313 669 L
317 668 L
319 668 L
323 669 L
325 672 L
326 675 L
326 676 L
325 680 L
323 682 L
319 683 L
318 683 L
315 682 L
312 680 L
311 676 L
318 692 M 316 691 L
313 689 L
312 687 L
311 682 L
311 675 L
312 672 L
315 669 L
317 668 L
319 668 M 321 669 L
324 672 L
325 675 L
325 676 L
324 680 L
321 682 L
319 683 L
365 785 M 385 785 L
365 852 M 385 852 L
365 899 M 385 899 L
365 936 M 385 936 L
365 966 M 385 966 L
365 992 M 385 992 L
365 1014 M 385 1014 L
365 1033 M 385 1033 L
365 1050 M 406 1050 L
176 1029 M 188 1062 M 192 1064 L
198 1069 L
198 1029 L
196 1068 M 196 1029 L
188 1029 M 205 1029 L
232 1069 M 226 1068 L
223 1062 L
221 1052 L
221 1046 L
223 1037 L
226 1031 L
232 1029 L
236 1029 L
242 1031 L
246 1037 L
248 1046 L
248 1052 L
246 1062 L
242 1068 L
236 1069 L
232 1069 L
228 1068 L
226 1066 L
225 1062 L
223 1052 L
223 1046 L
225 1037 L
226 1033 L
228 1031 L
232 1029 L
236 1029 M 240 1031 L
242 1033 L
244 1037 L
246 1046 L
246 1052 L
244 1062 L
242 1066 L
240 1068 L
236 1069 L
258 1058 M 279 1058 L
290 1067 M 293 1068 L
296 1072 L
296 1047 L
295 1071 M 295 1047 L
290 1047 M 301 1047 L
312 1072 M 310 1060 L
312 1062 L
316 1064 L
319 1064 L
323 1062 L
325 1060 L
326 1057 L
326 1054 L
325 1051 L
323 1049 L
319 1047 L
316 1047 L
312 1049 L
311 1050 L
310 1052 L
310 1053 L
311 1054 L
312 1053 L
311 1052 L
319 1064 M 321 1062 L
324 1060 L
325 1057 L
325 1054 L
324 1051 L
321 1049 L
319 1047 L
312 1072 M 324 1072 L
312 1071 M 318 1071 L
324 1072 L
365 1164 M 385 1164 L
365 1231 M 385 1231 L
365 1279 M 385 1279 L
365 1315 M 385 1315 L
365 1345 M 385 1345 L
365 1371 M 385 1371 L
365 1393 M 385 1393 L
365 1412 M 385 1412 L
365 1430 M 406 1430 L
176 1408 M 188 1441 M 192 1443 L
198 1449 L
198 1408 L
196 1447 M 196 1408 L
188 1408 M 205 1408 L
232 1449 M 226 1447 L
223 1441 L
CS M
221 1431 L
221 1425 L
223 1416 L
226 1410 L
232 1408 L
236 1408 L
242 1410 L
246 1416 L
248 1425 L
248 1431 L
246 1441 L
242 1447 L
236 1449 L
232 1449 L
228 1447 L
226 1445 L
225 1441 L
223 1431 L
223 1425 L
225 1416 L
226 1412 L
228 1410 L
232 1408 L
236 1408 M 240 1410 L
242 1412 L
244 1416 L
246 1425 L
246 1431 L
244 1441 L
242 1445 L
240 1447 L
236 1449 L
258 1437 M 279 1437 L
290 1446 M 293 1447 L
296 1451 L
296 1427 L
295 1450 M 295 1427 L
290 1427 M 301 1427 L
320 1449 M 320 1427 L
321 1451 M 321 1427 L
321 1451 M 309 1434 L
327 1434 L
317 1427 M 325 1427 L
365 1544 M 385 1544 L
365 1611 M 385 1611 L
365 1658 M 385 1658 L
365 1695 M 385 1695 L
365 1725 M 385 1725 L
365 1750 M 385 1750 L
365 1772 M 385 1772 L
365 1791 M 385 1791 L
365 1809 M 406 1809 L
176 1787 M 188 1820 M 192 1822 L
198 1828 L
198 1787 L
196 1826 M 196 1787 L
188 1787 M 205 1787 L
232 1828 M 226 1826 L
223 1820 L
221 1811 L
221 1805 L
223 1795 L
226 1789 L
232 1787 L
236 1787 L
242 1789 L
246 1795 L
248 1805 L
248 1811 L
246 1820 L
242 1826 L
236 1828 L
232 1828 L
228 1826 L
226 1824 L
225 1820 L
223 1811 L
223 1805 L
225 1795 L
226 1791 L
228 1789 L
232 1787 L
236 1787 M 240 1789 L
242 1791 L
244 1795 L
246 1805 L
246 1811 L
244 1820 L
242 1824 L
240 1826 L
236 1828 L
258 1816 M 279 1816 L
290 1826 M 293 1827 L
296 1830 L
296 1806 L
295 1829 M 295 1806 L
290 1806 M 301 1806 L
311 1826 M 312 1824 L
311 1823 L
310 1824 L
310 1826 L
311 1828 L
312 1829 L
316 1830 L
320 1830 L
324 1829 L
325 1827 L
325 1823 L
324 1821 L
320 1820 L
317 1820 L
320 1830 M 323 1829 L
324 1827 L
324 1823 L
323 1821 L
320 1820 L
323 1819 L
325 1816 L
326 1814 L
326 1811 L
325 1808 L
324 1807 L
320 1806 L
316 1806 L
312 1807 L
311 1808 L
310 1811 L
310 1812 L
311 1813 L
312 1812 L
311 1811 L
324 1817 M 325 1814 L
325 1811 L
324 1808 L
323 1807 L
320 1806 L
365 1923 M 385 1923 L
365 1990 M 385 1990 L
365 2037 M 385 2037 L
365 2074 M 385 2074 L
365 2104 M 385 2104 L
365 2129 M 385 2129 L
365 2151 M 385 2151 L
365 2171 M 385 2171 L
365 2188 M 406 2188 L
176 2167 M 188 2199 M 192 2201 L
198 2207 L
198 2167 L
196 2205 M 196 2167 L
188 2167 M 205 2167 L
232 2207 M 226 2205 L
223 2199 L
221 2190 L
221 2184 L
223 2174 L
226 2169 L
232 2167 L
236 2167 L
242 2169 L
246 2174 L
248 2184 L
248 2190 L
246 2199 L
242 2205 L
236 2207 L
232 2207 L
228 2205 L
226 2203 L
225 2199 L
223 2190 L
223 2184 L
225 2174 L
226 2171 L
228 2169 L
232 2167 L
236 2167 M 240 2169 L
242 2171 L
244 2174 L
246 2184 L
246 2190 L
244 2199 L
242 2203 L
240 2205 L
236 2207 L
258 2196 M 279 2196 L
290 2205 M 293 2206 L
296 2209 L
296 2185 L
295 2208 M 295 2185 L
290 2185 M 301 2185 L
311 2205 M 312 2204 L
311 2203 L
310 2204 L
310 2205 L
311 2207 L
312 2208 L
316 2209 L
320 2209 L
324 2208 L
325 2207 L
326 2205 L
326 2203 L
325 2200 L
321 2198 L
316 2196 L
313 2194 L
311 2192 L
310 2189 L
310 2185 L
320 2209 M 323 2208 L
324 2207 L
325 2205 L
325 2203 L
324 2200 L
320 2198 L
316 2196 L
310 2188 M 311 2189 L
313 2189 L
319 2186 L
323 2186 L
325 2188 L
326 2189 L
313 2189 M 319 2185 L
324 2185 L
325 2186 L
326 2189 L
326 2191 L
2188 292 M 2188 2188 L
2188 292 M 2147 292 L
2188 406 M 2168 406 L
2188 473 M 2168 473 L
2188 520 M 2168 520 L
2188 557 M 2168 557 L
2188 587 M 2168 587 L
2188 612 M 2168 612 L
2188 634 M 2168 634 L
2188 654 M 2168 654 L
2188 671 M 2147 671 L
2188 785 M 2168 785 L
2188 852 M 2168 852 L
2188 899 M 2168 899 L
2188 936 M 2168 936 L
2188 966 M 2168 966 L
2188 992 M 2168 992 L
2188 1014 M 2168 1014 L
2188 1033 M 2168 1033 L
2188 1050 M 2147 1050 L
2188 1164 M 2168 1164 L
2188 1231 M 2168 1231 L
2188 1279 M 2168 1279 L
2188 1315 M 2168 1315 L
2188 1345 M 2168 1345 L
2188 1371 M 2168 1371 L
2188 1393 M 2168 1393 L
2188 1412 M 2168 1412 L
2188 1430 M 2147 1430 L
2188 1544 M 2168 1544 L
2188 1611 M 2168 1611 L
2188 1658 M 2168 1658 L
2188 1695 M 2168 1695 L
2188 1725 M 2168 1725 L
2188 1750 M 2168 1750 L
2188 1772 M 2168 1772 L
2188 1791 M 2168 1791 L
2188 1809 M 2147 1809 L
2188 1923 M 2168 1923 L
2188 1990 M 2168 1990 L
2188 2037 M 2168 2037 L
2188 2074 M 2168 2074 L
2188 2104 M 2168 2104 L
2188 2129 M 2168 2129 L
2188 2151 M 2168 2151 L
2188 2171 M 2168 2171 L
2188 2188 M 2147 2188 L
CS [] 0 setdash M
CS [] 0 setdash M
1093 103 M 1126 134 M 1129 139 L
1129 129 L
1126 134 L
1124 137 L
1119 139 L
1108 139 L
1103 137 L
1101 134 L
1101 129 L
1103 126 L
1108 124 L
1121 119 L
1126 116 L
1129 113 L
1101 131 M 1103 129 L
1108 126 L
1121 121 L
1126 119 L
1129 116 L
1129 108 L
1126 106 L
1121 103 L
1111 103 L
1106 106 L
1103 108 L
1101 113 L
CS M
1101 103 L
1103 108 L
1150 157 M 1147 155 L
1150 152 L
1152 155 L
1150 157 L
1150 139 M 1150 103 L
1152 139 M 1152 103 L
1142 139 M 1152 139 L
1142 103 M 1160 103 L
1178 139 M 1178 103 L
1180 139 M 1180 103 L
1180 131 M 1185 137 L
1193 139 L
1198 139 L
1206 137 L
1209 131 L
1209 103 L
1198 139 M 1203 137 L
1206 131 L
1206 103 L
1170 139 M 1180 139 L
1170 103 M 1188 103 L
1198 103 M 1216 103 L
1228 154 M 1229 152 L
1228 151 L
1226 152 L
1226 154 L
1228 157 L
1229 159 L
1234 160 L
1240 160 L
1244 159 L
1246 157 L
1248 154 L
1248 151 L
1246 148 L
1241 145 L
1234 142 L
1231 140 L
1228 137 L
1226 132 L
1226 128 L
1240 160 M 1243 159 L
1244 157 L
1246 154 L
1246 151 L
1244 148 L
1240 145 L
1234 142 L
1226 131 M 1228 132 L
1231 132 L
1238 129 L
1243 129 L
1246 131 L
1248 132 L
1231 132 M 1238 128 L
1244 128 L
1246 129 L
1248 132 L
1248 136 L
1280 167 M 1275 162 L
1270 155 L
1265 144 L
1262 131 L
1262 121 L
1265 108 L
1270 98 L
1275 90 L
1280 85 L
1275 162 M 1270 152 L
1268 144 L
1265 131 L
1265 121 L
1268 108 L
1270 101 L
1275 90 L
1298 147 M 1301 144 L
1298 142 L
1296 144 L
1296 147 L
1298 152 L
1301 155 L
1309 157 L
1319 157 L
1327 155 L
1329 152 L
1332 147 L
1332 142 L
1329 137 L
1321 131 L
1309 126 L
1303 124 L
1298 119 L
1296 111 L
1296 103 L
1319 157 M 1324 155 L
1327 152 L
1329 147 L
1329 142 L
1327 137 L
1319 131 L
1309 126 L
1296 108 M 1298 111 L
1303 111 L
1316 106 L
1324 106 L
1329 108 L
1332 111 L
1303 111 M 1316 103 L
1327 103 L
1329 106 L
1332 111 L
1332 116 L
1368 157 M 1360 155 L
1355 147 L
1352 142 L
1350 134 L
1347 121 L
1347 111 L
1350 106 L
1355 103 L
1360 103 L
1368 106 L
1373 113 L
1375 119 L
1378 126 L
1380 139 L
1380 149 L
1378 155 L
1373 157 L
1368 157 L
1362 155 L
1357 147 L
1355 142 L
1352 134 L
1350 121 L
1350 111 L
1352 106 L
1355 103 L
1360 103 M 1365 106 L
1370 113 L
1373 119 L
1375 126 L
1378 139 L
1378 149 L
1375 155 L
1373 157 L
1352 131 M 1375 131 L
1414 106 M 1416 102 L
1416 111 L
1414 106 L
1411 109 L
1407 111 L
1404 111 L
1399 109 L
1396 106 L
1394 103 L
1393 99 L
1393 91 L
1394 86 L
1396 83 L
1399 80 L
1404 79 L
1407 79 L
1411 80 L
1414 83 L
1404 111 M 1400 109 L
1397 106 L
1396 103 L
1394 99 L
1394 91 L
1396 86 L
1397 83 L
1400 80 L
1404 79 L
1414 91 M 1414 79 L
1416 91 M 1416 79 L
1410 91 M 1420 91 L
1431 167 M 1436 162 L
1441 155 L
1447 144 L
1449 131 L
1449 121 L
1447 108 L
1441 98 L
1436 90 L
1431 85 L
1436 162 M 1441 152 L
1444 144 L
1447 131 L
1447 121 L
1444 108 L
1441 101 L
1436 90 L
CS [] 0 setdash M
CS [] 0 setdash M
130 1198 M 76 1223 M 130 1203 L
76 1223 M 130 1244 L
84 1223 M 130 1241 L
127 1205 M 127 1241 L
130 1203 M 130 1244 L
78 1275 M 81 1272 L
84 1275 L
81 1277 L
78 1277 L
76 1275 L
76 1269 L
78 1264 L
84 1262 L
130 1262 L
76 1269 M 78 1267 L
84 1264 L
130 1264 L
94 1254 M 94 1275 L
130 1254 M 130 1272 L
CS [] 0 setdash M
 0 255 255 C
847 1600 M 936 1600 L
779 1603 M 961 1603 L
746 1606 M 977 1606 L
727 1609 M 982 1609 L
714 1612 M 986 1612 L
711 1615 M 982 1615 L
708 1618 M 977 1618 L
709 1621 M 968 1621 L
710 1624 M 958 1624 L
711 1627 M 948 1627 L
715 1630 M 937 1630 L
720 1633 M 923 1633 L
726 1637 M 909 1637 L
731 1640 M 892 1640 L
741 1643 M 873 1643 L
751 1646 M 856 1646 L
763 1649 M 832 1649 L
2162 509 M 2163 509 L
2160 512 M 2164 512 L
2157 515 M 2165 515 L
2155 518 M 2167 518 L
2153 521 M 2168 521 L
2150 525 M 2169 525 L
2148 528 M 2171 528 L
2146 531 M 2172 531 L
2144 534 M 2173 534 L
2142 537 M 2173 537 L
2139 540 M 2174 540 L
2137 543 M 2175 543 L
2135 546 M 2176 546 L
2133 549 M 2177 549 L
2132 552 M 2178 552 L
2130 555 M 2178 555 L
2128 558 M 2179 558 L
2126 561 M 2179 561 L
2125 564 M 2179 564 L
2123 567 M 2180 567 L
2121 571 M 2180 571 L
2120 574 M 2180 574 L
2118 577 M 2181 577 L
2116 580 M 2181 580 L
2114 583 M 2182 583 L
2112 586 M 2182 586 L
2110 589 M 2182 589 L
2108 592 M 2183 592 L
2106 595 M 2183 595 L
2104 598 M 2183 598 L
2102 601 M 2184 601 L
2100 604 M 2184 604 L
2099 607 M 2184 607 L
2097 610 M 2184 610 L
2095 613 M 2184 613 L
2094 616 M 2184 616 L
2092 620 M 2184 620 L
2091 623 M 2184 623 L
2089 626 M 2184 626 L
2087 629 M 2184 629 L
2086 632 M 2184 632 L
2084 635 M 2184 635 L
2083 638 M 2184 638 L
2081 641 M 2184 641 L
2080 644 M 2184 644 L
2079 647 M 2184 647 L
2078 650 M 2184 650 L
2077 653 M 2184 653 L
2076 656 M 2184 656 L
2076 659 M 2184 659 L
2075 662 M 2184 662 L
2075 665 M 2184 665 L
2075 669 M 2184 669 L
2075 672 M 2184 672 L
2075 675 M 2184 675 L
2076 678 M 2184 678 L
2076 681 M 2185 681 L
2077 684 M 2185 684 L
2077 687 M 2185 687 L
2077 690 M 2185 690 L
2078 693 M 2185 693 L
2078 696 M 2185 696 L
2079 699 M 2185 699 L
2079 702 M 2185 702 L
2079 705 M 2185 705 L
2080 708 M 2185 708 L
2080 711 M 2185 711 L
2081 714 M 2185 714 L
2081 718 M 2185 718 L
CS M
2082 721 M 2185 721 L
2083 724 M 2185 724 L
2083 727 M 2185 727 L
2084 730 M 2185 730 L
2084 733 M 2185 733 L
2085 736 M 2185 736 L
2085 739 M 2185 739 L
2085 742 M 2185 742 L
2086 745 M 2185 745 L
2086 748 M 2185 748 L
2086 751 M 2185 751 L
2087 754 M 2185 754 L
2087 757 M 2185 757 L
2087 760 M 2185 760 L
2087 764 M 2185 764 L
2088 767 M 2185 767 L
2088 770 M 2185 770 L
2088 773 M 2185 773 L
2088 776 M 2185 776 L
2088 779 M 2185 779 L
2088 782 M 2185 782 L
2088 785 M 2185 785 L
2087 788 M 2185 788 L
2087 791 M 2185 791 L
2087 794 M 2185 794 L
2087 797 M 2185 797 L
2087 800 M 2185 800 L
2087 803 M 2184 803 L
2087 806 M 2184 806 L
2087 809 M 2184 809 L
2086 813 M 2184 813 L
2086 816 M 2184 816 L
2086 819 M 2184 819 L
2086 822 M 2185 822 L
2085 825 M 2185 825 L
2085 828 M 2185 828 L
2085 831 M 2185 831 L
2085 834 M 2185 834 L
2084 837 M 2185 837 L
2084 840 M 2185 840 L
2083 843 M 2185 843 L
2083 846 M 2185 846 L
2082 849 M 2185 849 L
2082 852 M 2185 852 L
2081 855 M 2185 855 L
2081 858 M 2185 858 L
2080 862 M 2185 862 L
2080 865 M 2185 865 L
2079 868 M 2185 868 L
2079 871 M 2185 871 L
2078 874 M 2185 874 L
2077 877 M 2186 877 L
2077 880 M 2186 880 L
2076 883 M 2186 883 L
2076 886 M 2186 886 L
2075 889 M 2186 889 L
2074 892 M 2186 892 L
2074 895 M 2186 895 L
2073 898 M 2186 898 L
2072 901 M 2186 901 L
2072 904 M 2186 904 L
2071 907 M 2186 907 L
2070 911 M 2186 911 L
2069 914 M 2186 914 L
2068 917 M 2186 917 L
2068 920 M 2186 920 L
2067 923 M 2186 923 L
2066 926 M 2186 926 L
2066 929 M 2186 929 L
2065 932 M 2186 932 L
2064 935 M 2186 935 L
2064 938 M 2186 938 L
2063 941 M 2186 941 L
2062 944 M 2186 944 L
2062 947 M 2186 947 L
2061 950 M 2186 950 L
2060 953 M 2186 953 L
2059 956 M 2186 956 L
2058 960 M 2186 960 L
2057 963 M 2186 963 L
2057 966 M 2186 966 L
2056 969 M 2186 969 L
2055 972 M 2186 972 L
2054 975 M 2186 975 L
2054 978 M 2186 978 L
2053 981 M 2186 981 L
2053 984 M 2186 984 L
2052 987 M 2186 987 L
2052 990 M 2186 990 L
2051 993 M 2186 993 L
2051 996 M 2186 996 L
2051 999 M 2186 999 L
2051 1002 M 2186 1002 L
2051 1006 M 2186 1006 L
2051 1009 M 2186 1009 L
2052 1012 M 2186 1012 L
2052 1015 M 2186 1015 L
2052 1018 M 2186 1018 L
2053 1021 M 2186 1021 L
2053 1024 M 2186 1024 L
2054 1027 M 2186 1027 L
2055 1030 M 2186 1030 L
2055 1033 M 2185 1033 L
2056 1036 M 2185 1036 L
2057 1039 M 2185 1039 L
2059 1042 M 2185 1042 L
2061 1045 M 2185 1045 L
2063 1048 M 2185 1048 L
2064 1051 M 2185 1051 L
2066 1055 M 2185 1055 L
2068 1058 M 2185 1058 L
2069 1061 M 2185 1061 L
2071 1064 M 2185 1064 L
2073 1067 M 2185 1067 L
2076 1070 M 2185 1070 L
2080 1073 M 2185 1073 L
2083 1076 M 2185 1076 L
2086 1079 M 2185 1079 L
2089 1082 M 2185 1082 L
2092 1085 M 2185 1085 L
2095 1088 M 2185 1088 L
2098 1091 M 2185 1091 L
2100 1094 M 2185 1094 L
2103 1097 M 2185 1097 L
2106 1100 M 2185 1100 L
2109 1104 M 2185 1104 L
2112 1107 M 2185 1107 L
2116 1110 M 2185 1110 L
2119 1113 M 2185 1113 L
2122 1116 M 2185 1116 L
2125 1119 M 2185 1119 L
2128 1122 M 2184 1122 L
2132 1125 M 2184 1125 L
2135 1128 M 2184 1128 L
2137 1131 M 2184 1131 L
2140 1134 M 2184 1134 L
2143 1137 M 2184 1137 L
2145 1140 M 2184 1140 L
2148 1143 M 2184 1143 L
2150 1146 M 2183 1146 L
2152 1149 M 2183 1149 L
2154 1153 M 2183 1153 L
2156 1156 M 2183 1156 L
2158 1159 M 2183 1159 L
2160 1162 M 2182 1162 L
2162 1165 M 2182 1165 L
2164 1168 M 2182 1168 L
2165 1171 M 2182 1171 L
2166 1174 M 2182 1174 L
2168 1177 M 2181 1177 L
2169 1180 M 2181 1180 L
2170 1183 M 2180 1183 L
2172 1186 M 2178 1186 L
2173 1189 M 2176 1189 L
 255 0 255 C
802 1606 M 932 1606 L
777 1609 M 942 1609 L
765 1612 M 946 1612 L
760 1615 M 944 1615 L
759 1618 M 938 1618 L
762 1621 M 931 1621 L
768 1624 M 917 1624 L
779 1627 M 899 1627 L
793 1630 M 875 1630 L
814 1633 M 839 1633 L
2142 672 M 2144 672 L
2137 675 M 2149 675 L
2133 678 M 2153 678 L
2131 681 M 2154 681 L
2130 684 M 2155 684 L
2129 687 M 2156 687 L
2127 690 M 2157 690 L
2127 693 M 2157 693 L
2126 696 M 2158 696 L
2126 699 M 2159 699 L
2126 702 M 2160 702 L
2125 705 M 2161 705 L
2125 708 M 2161 708 L
2125 711 M 2162 711 L
2124 714 M 2162 714 L
2124 718 M 2163 718 L
2124 721 M 2163 721 L
2124 724 M 2163 724 L
2124 727 M 2164 727 L
2124 730 M 2164 730 L
2124 733 M 2165 733 L
2124 736 M 2165 736 L
2124 739 M 2166 739 L
2124 742 M 2166 742 L
2124 745 M 2166 745 L
2124 748 M 2166 748 L
2124 751 M 2166 751 L
2124 754 M 2167 754 L
2124 757 M 2167 757 L
2124 760 M 2167 760 L
2124 764 M 2167 764 L
2123 767 M 2167 767 L
2123 770 M 2167 770 L
2123 773 M 2168 773 L
2123 776 M 2168 776 L
2123 779 M 2168 779 L
2123 782 M 2168 782 L
2123 785 M 2168 785 L
2123 788 M 2168 788 L
2123 791 M 2168 791 L
2123 794 M 2168 794 L
2123 797 M 2168 797 L
2122 800 M 2168 800 L
2122 803 M 2168 803 L
2121 806 M 2168 806 L
2121 809 M 2169 809 L
2120 813 M 2169 813 L
2120 816 M 2169 816 L
2120 819 M 2169 819 L
2119 822 M 2169 822 L
2119 825 M 2169 825 L
2118 828 M 2169 828 L
2118 831 M 2169 831 L
2117 834 M 2169 834 L
2117 837 M 2169 837 L
2116 840 M 2169 840 L
2116 843 M 2169 843 L
2115 846 M 2169 846 L
2115 849 M 2169 849 L
2114 852 M 2169 852 L
2113 855 M 2169 855 L
2113 858 M 2169 858 L
2112 862 M 2169 862 L
2112 865 M 2169 865 L
2111 868 M 2169 868 L
2111 871 M 2169 871 L
2110 874 M 2170 874 L
2110 877 M 2170 877 L
2109 880 M 2170 880 L
2109 883 M 2170 883 L
2108 886 M 2170 886 L
2107 889 M 2170 889 L
2107 892 M 2170 892 L
2106 895 M 2170 895 L
2105 898 M 2170 898 L
2104 901 M 2170 901 L
2103 904 M 2170 904 L
2102 907 M 2170 907 L
2102 911 M 2170 911 L
2101 914 M 2170 914 L
2100 917 M 2170 917 L
2099 920 M 2170 920 L
2098 923 M 2170 923 L
2098 926 M 2170 926 L
2097 929 M 2170 929 L
2096 932 M 2170 932 L
2095 935 M 2170 935 L
2094 938 M 2170 938 L
2094 941 M 2170 941 L
2093 944 M 2170 944 L
2092 947 M 2170 947 L
2091 950 M 2171 950 L
2091 953 M 2171 953 L
2090 956 M 2171 956 L
2089 960 M 2171 960 L
2089 963 M 2171 963 L
2088 966 M 2171 966 L
2088 969 M 2171 969 L
2087 972 M 2171 972 L
2087 975 M 2171 975 L
2086 978 M 2171 978 L
2086 981 M 2171 981 L
2085 984 M 2171 984 L
2085 987 M 2171 987 L
2084 990 M 2171 990 L
2084 993 M 2171 993 L
2084 996 M 2171 996 L
2085 999 M 2171 999 L
2085 1002 M 2171 1002 L
2086 1006 M 2170 1006 L
2086 1009 M 2170 1009 L
2087 1012 M 2170 1012 L
2087 1015 M 2169 1015 L
2087 1018 M 2169 1018 L
2088 1021 M 2169 1021 L
2089 1024 M 2168 1024 L
2091 1027 M 2168 1027 L
2092 1030 M 2168 1030 L
2094 1033 M 2167 1033 L
2095 1036 M 2167 1036 L
2096 1039 M 2167 1039 L
2099 1042 M 2166 1042 L
2102 1045 M 2166 1045 L
2104 1048 M 2165 1048 L
2107 1051 M 2165 1051 L
2110 1055 M 2164 1055 L
2114 1058 M 2164 1058 L
2117 1061 M 2163 1061 L
2121 1064 M 2162 1064 L
2124 1067 M 2159 1067 L
2129 1070 M 2157 1070 L
2137 1073 M 2154 1073 L
 0 0 0 C
CS [] 0 setdash M
CS M 3 100 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
774 1626 M 778 1627 L
790 1630 L
802 1631 L
814 1632 L
CS M
827 1633 L
839 1633 L
851 1632 L
863 1631 L
875 1630 L
887 1629 L
900 1627 L
903 1626 L
757 1619 M 766 1623 L
774 1626 M 766 1623 L
903 1626 M 912 1625 L
924 1622 L
936 1619 L
938 1619 L
757 1619 M 761 1611 L
938 1619 M 948 1613 L
952 1611 L
761 1611 M 766 1610 L
778 1608 L
790 1606 L
802 1604 L
808 1604 L
927 1604 M 936 1606 L
948 1610 L
952 1611 M 948 1610 L
808 1604 M 814 1603 L
827 1603 L
839 1602 L
851 1602 L
863 1602 L
875 1602 L
887 1602 L
900 1602 L
912 1603 L
924 1603 L
927 1604 M 924 1603 L
2145 1073 M 2152 1073 L
2153 1073 L
2126 1065 M 2127 1066 L
2139 1072 L
2145 1073 M 2139 1072 L
2153 1073 M 2161 1065 L
2126 1065 M 2115 1057 L
2161 1065 M 2164 1061 L
2165 1057 L
2108 1050 M 2115 1057 L
2115 1057 L
2165 1057 M 2166 1050 L
2101 1042 M 2103 1045 L
2108 1050 M 2103 1045 L
2166 1050 M 2167 1042 L
2101 1042 M 2095 1035 L
2167 1042 M 2168 1035 L
2091 1027 M 2091 1028 L
2095 1035 M 2091 1028 L
2168 1035 M 2169 1027 L
2091 1027 M 2088 1020 L
2169 1027 M 2169 1020 L
2088 1020 M 2086 1012 L
2169 1020 M 2170 1012 L
2086 1012 M 2084 1004 L
2170 1012 M 2170 1004 L
2084 1004 M 2084 997 L
2170 1004 M 2171 997 L
2084 997 M 2084 989 L
2171 997 M 2171 989 L
2084 989 M 2085 982 L
2171 989 M 2171 982 L
2085 982 M 2086 974 L
2171 982 M 2171 974 L
2086 974 M 2087 966 L
2171 974 M 2171 966 L
2087 966 M 2089 959 L
2171 966 M 2171 959 L
2089 959 M 2091 951 L
2171 959 M 2171 951 L
2091 951 M 2091 950 L
2093 944 L
2171 951 M 2171 944 L
2093 944 M 2095 936 L
2171 944 M 2171 936 L
2095 936 M 2097 928 L
2171 936 M 2171 928 L
2097 928 M 2099 921 L
2171 928 M 2171 921 L
2099 921 M 2101 913 L
2171 921 M 2171 913 L
2101 913 M 2102 906 L
2171 913 M 2171 906 L
2102 906 M 2103 903 L
2104 898 L
2171 906 M 2170 898 L
2104 898 M 2106 891 L
2170 898 M 2170 891 L
2106 891 M 2108 883 L
2170 891 M 2170 883 L
2108 883 M 2110 875 L
2170 883 M 2170 875 L
2110 875 M 2111 868 L
2170 875 M 2170 868 L
2111 868 M 2113 860 L
2170 868 M 2170 860 L
2113 860 M 2114 853 L
2170 860 M 2170 853 L
2114 853 M 2115 845 L
2170 853 M 2170 845 L
2115 845 M 2115 843 L
2116 837 L
2170 845 M 2169 837 L
2116 837 M 2118 830 L
2169 837 M 2169 830 L
2118 830 M 2119 822 L
2169 830 M 2169 822 L
2119 822 M 2120 815 L
2169 822 M 2169 815 L
2120 815 M 2121 807 L
2169 815 M 2169 807 L
2121 807 M 2121 800 L
2169 807 M 2169 800 L
2121 800 M 2122 792 L
2169 800 M 2168 792 L
2122 792 M 2123 784 L
2168 792 M 2168 784 L
2123 784 M 2123 777 L
2168 784 M 2168 777 L
2123 777 M 2124 769 L
2168 777 M 2168 769 L
2124 769 M 2124 762 L
2168 769 M 2167 762 L
2124 762 M 2124 754 L
2167 762 M 2167 754 L
2124 754 M 2124 746 L
2167 754 M 2167 746 L
2124 746 M 2124 739 L
2167 746 M 2166 739 L
2124 739 M 2124 731 L
2166 739 M 2166 731 L
2124 731 M 2124 724 L
2166 731 M 2165 724 L
2124 724 M 2124 716 L
2165 724 M 2164 716 L
2124 716 M 2125 709 L
2164 709 M 2164 710 L
2164 716 M 2164 710 L
2125 709 M 2125 701 L
2164 709 M 2161 701 L
2125 701 M 2126 693 L
2161 701 M 2159 693 L
2126 693 M 2127 686 L
2127 686 L
2159 693 M 2157 686 L
2127 686 M 2132 678 L
2157 686 M 2154 678 L
2132 678 M 2138 671 L
2144 671 M 2152 673 L
2154 678 M 2152 673 L
2138 671 M 2139 669 L
2144 671 M 2139 669 L
CS [] 0 setdash M
769 1649 M 778 1650 L
790 1651 L
802 1650 L
814 1650 L
823 1649 L
738 1642 M 741 1643 L
754 1646 L
766 1649 L
769 1649 M 766 1649 L
823 1649 M 827 1649 L
839 1648 L
851 1646 L
863 1644 L
875 1642 L
879 1642 L
721 1634 M 729 1638 L
738 1642 M 729 1638 L
879 1642 M 887 1640 L
900 1638 L
912 1636 L
920 1634 L
711 1626 M 717 1631 L
721 1634 M 717 1631 L
920 1634 M 924 1633 L
936 1630 L
948 1628 L
953 1626 L
711 1626 M 705 1619 L
953 1626 M 960 1624 L
972 1620 L
977 1619 L
705 1619 M 714 1611 L
977 1619 M 985 1614 L
988 1611 L
714 1611 M 717 1611 L
729 1608 L
741 1606 L
751 1604 L
974 1604 M 985 1609 L
988 1611 M 985 1609 L
751 1604 M 754 1603 L
766 1602 L
778 1602 L
790 1601 L
802 1600 L
814 1599 L
827 1599 L
839 1598 L
851 1598 L
863 1598 L
875 1598 L
887 1598 L
900 1598 L
912 1598 L
924 1599 L
936 1600 L
948 1601 L
960 1602 L
972 1603 L
974 1604 M 972 1603 L
2176 1194 M 2176 1194 L
2176 1194 L
2174 1186 L
2176 1194 M 2180 1186 L
2174 1186 M 2171 1179 L
2180 1186 M 2182 1179 L
2171 1179 M 2167 1171 L
2182 1179 M 2183 1171 L
2163 1164 M 2164 1166 L
2167 1171 M 2164 1166 L
2183 1171 M 2184 1164 L
2163 1164 M 2158 1156 L
2184 1164 M 2184 1156 L
2158 1156 M 2153 1148 L
2184 1156 M 2185 1148 L
2147 1141 M 2152 1147 L
2153 1148 M 2152 1147 L
2185 1148 M 2185 1141 L
2147 1141 M 2140 1133 L
2185 1141 M 2185 1133 L
2134 1126 M 2139 1132 L
2140 1133 M 2139 1132 L
2185 1133 M 2185 1126 L
2126 1118 M 2127 1120 L
2134 1126 M 2127 1120 L
2185 1126 M 2186 1118 L
2126 1118 M 2119 1111 L
2186 1118 M 2186 1111 L
2111 1103 M 2115 1107 L
2119 1111 M 2115 1107 L
2186 1111 M 2186 1103 L
2103 1095 M 2103 1096 L
2111 1103 M 2103 1096 L
2186 1103 M 2186 1095 L
2103 1095 M 2095 1088 L
2186 1095 M 2186 1088 L
2088 1080 M 2091 1084 L
2095 1088 M 2091 1084 L
2186 1088 M 2186 1080 L
2088 1080 M 2080 1073 L
2186 1080 M 2186 1073 L
2074 1065 M 2079 1071 L
2080 1073 M 2079 1071 L
2186 1073 M 2186 1065 L
2074 1065 M 2068 1057 L
2186 1065 M 2186 1057 L
2063 1050 M 2067 1056 L
2068 1057 M 2067 1056 L
2186 1057 M 2186 1050 L
2063 1050 M 2059 1042 L
2186 1050 M 2186 1042 L
2059 1042 M 2055 1035 L
2186 1042 M 2186 1035 L
2053 1027 M 2054 1032 L
2055 1035 M 2054 1032 L
2186 1035 M 2186 1027 L
2053 1027 M 2051 1020 L
2186 1027 M 2186 1020 L
2051 1020 M 2050 1012 L
2186 1020 M 2186 1012 L
2050 1012 M 2050 1004 L
2186 1012 M 2186 1004 L
2050 1004 M 2051 997 L
2186 1004 M 2186 997 L
2051 997 M 2051 989 L
2186 997 M 2186 989 L
2051 989 M 2053 982 L
2186 989 M 2186 982 L
2053 982 M 2054 974 L
2186 982 M 2186 974 L
2054 974 M 2054 973 L
2056 966 L
2186 974 M 2186 966 L
2056 966 M 2058 959 L
2186 966 M 2186 959 L
2058 959 M 2060 951 L
2186 959 M 2186 951 L
2060 951 M 2062 944 L
2186 951 M 2186 944 L
2062 944 M 2064 936 L
2186 944 M 2186 936 L
2064 936 M 2066 928 L
CS M
2186 936 M 2186 928 L
2066 928 M 2067 925 L
2068 921 L
2186 928 M 2186 921 L
2068 921 M 2070 913 L
2186 921 M 2186 913 L
2070 913 M 2071 906 L
2186 913 M 2186 906 L
2071 906 M 2073 898 L
2186 906 M 2186 898 L
2073 898 M 2075 891 L
2186 898 M 2186 891 L
2075 891 M 2076 883 L
2186 891 M 2186 883 L
2076 883 M 2078 875 L
2186 883 M 2186 875 L
2078 875 M 2079 871 L
2079 868 L
2186 875 M 2186 868 L
2079 868 M 2081 860 L
2186 868 M 2186 860 L
2081 860 M 2082 853 L
2186 860 M 2186 853 L
2082 853 M 2083 845 L
2186 853 M 2186 845 L
2083 845 M 2084 837 L
2186 845 M 2186 837 L
2084 837 M 2085 830 L
2186 837 M 2186 830 L
2085 830 M 2086 822 L
2186 830 M 2186 822 L
2086 822 M 2087 815 L
2186 822 M 2186 815 L
2087 815 M 2087 807 L
2186 815 M 2186 807 L
2087 807 M 2088 800 L
2186 807 M 2186 800 L
2088 800 M 2088 792 L
2186 800 M 2186 792 L
2088 792 M 2088 784 L
2186 792 M 2186 784 L
2088 784 M 2088 777 L
2186 784 M 2186 777 L
2088 777 M 2088 769 L
2186 777 M 2186 769 L
2088 769 M 2088 762 L
2186 769 M 2186 762 L
2088 762 M 2087 754 L
2186 762 M 2186 754 L
2087 754 M 2087 746 L
2186 754 M 2186 746 L
2087 746 M 2086 739 L
2186 746 M 2186 739 L
2086 739 M 2084 731 L
2186 739 M 2186 731 L
2084 731 M 2083 724 L
2186 731 M 2186 724 L
2083 724 M 2081 716 L
2186 724 M 2186 716 L
2081 716 M 2079 709 L
2186 716 M 2186 709 L
2077 701 M 2079 707 L
2079 709 M 2079 707 L
2186 709 M 2186 701 L
2077 701 M 2076 693 L
2186 701 M 2186 693 L
2076 693 M 2075 686 L
2186 693 M 2186 686 L
2075 686 M 2074 678 L
2186 686 M 2186 678 L
2074 678 M 2074 671 L
2186 678 M 2186 671 L
2074 671 M 2074 663 L
2186 671 M 2186 663 L
2074 663 M 2076 655 L
2186 663 M 2185 655 L
2076 655 M 2078 648 L
2185 655 M 2185 648 L
2078 648 M 2079 644 L
2080 640 L
2185 648 M 2185 640 L
2080 640 M 2083 633 L
2185 640 M 2185 633 L
2083 633 M 2087 625 L
2185 633 M 2185 625 L
2087 625 M 2091 617 L
2185 625 M 2184 617 L
2091 617 M 2091 617 L
2095 610 L
2184 617 M 2184 610 L
2095 610 M 2100 602 L
2184 610 M 2184 602 L
2100 602 M 2103 597 L
2104 595 L
2184 602 M 2184 595 L
2104 595 M 2109 587 L
2184 595 M 2183 587 L
2109 587 M 2114 580 L
2183 587 M 2183 580 L
2114 580 M 2115 577 L
2119 572 L
2183 580 M 2182 572 L
2119 572 M 2123 564 L
2182 572 M 2181 564 L
2123 564 M 2127 558 L
2128 557 L
2181 564 M 2180 557 L
2128 557 M 2133 549 L
2180 557 M 2178 549 L
2133 549 M 2137 542 L
2178 549 M 2176 542 L
2137 542 M 2139 537 L
2142 534 L
2173 534 M 2176 542 L
2176 542 L
2142 534 M 2147 526 L
2173 534 M 2170 526 L
2147 526 M 2151 519 L
2170 526 M 2167 519 L
2151 519 M 2152 518 L
2161 511 L
2167 519 M 2164 511 L
2161 511 M 2164 510 L
2164 511 M 2164 510 L
608 747 M CS [] 0 setdash M
617 787 M 617 747 L
619 787 M 619 747 L
642 787 M 642 747 L
644 787 M 644 747 L
612 787 M 625 787 L
637 787 M 650 787 L
619 768 M 642 768 L
612 747 M 625 747 L
637 747 M 650 747 L
671 774 M 665 772 L
662 768 L
660 762 L
660 758 L
662 753 L
665 749 L
671 747 L
675 747 L
681 749 L
685 753 L
687 758 L
687 762 L
685 768 L
681 772 L
675 774 L
671 774 L
667 772 L
664 768 L
662 762 L
662 758 L
664 753 L
667 749 L
671 747 L
675 747 M 679 749 L
683 753 L
685 758 L
685 762 L
683 768 L
679 772 L
675 774 L
702 774 M 702 747 L
704 774 M 704 747 L
704 768 M 708 772 L
714 774 L
717 774 L
723 772 L
725 768 L
725 747 L
717 774 M 721 772 L
723 768 L
723 747 L
725 768 M 729 772 L
735 774 L
739 774 L
744 772 L
746 768 L
746 747 L
739 774 M 742 772 L
744 768 L
744 747 L
696 774 M 704 774 L
696 747 M 710 747 L
717 747 M 731 747 L
739 747 M 752 747 L
764 762 M 787 762 L
787 766 L
785 770 L
783 772 L
779 774 L
773 774 L
768 772 L
764 768 L
762 762 L
762 758 L
764 753 L
768 749 L
773 747 L
777 747 L
783 749 L
787 753 L
785 762 M 785 768 L
783 772 L
773 774 M 769 772 L
766 768 L
764 762 L
764 758 L
766 753 L
769 749 L
773 747 L
818 770 M 819 774 L
819 766 L
818 770 L
816 772 L
812 774 L
804 774 L
800 772 L
798 770 L
798 766 L
800 764 L
804 762 L
814 758 L
818 756 L
819 754 L
798 768 M 800 766 L
804 764 L
814 760 L
818 758 L
819 756 L
819 751 L
818 749 L
814 747 L
806 747 L
802 749 L
800 751 L
798 754 L
798 747 L
800 751 L
835 787 M 835 754 L
837 749 L
841 747 L
844 747 L
848 749 L
850 753 L
837 787 M 837 754 L
839 749 L
841 747 L
829 774 M 844 774 L
864 770 M 864 768 L
862 768 L
862 770 L
864 772 L
868 774 L
875 774 L
879 772 L
881 770 L
883 766 L
883 753 L
885 749 L
887 747 L
881 770 M 881 753 L
883 749 L
887 747 L
889 747 L
881 766 M 879 764 L
868 762 L
862 760 L
860 756 L
860 753 L
862 749 L
868 747 L
873 747 L
877 749 L
881 753 L
868 762 M 864 760 L
862 756 L
862 753 L
864 749 L
868 747 L
902 787 M 902 747 L
904 787 M 904 747 L
923 774 M 904 754 L
914 762 M 925 747 L
912 762 M 923 747 L
896 787 M 904 787 L
918 774 M 929 774 L
896 747 M 910 747 L
918 747 M 929 747 L
941 762 M 964 762 L
964 766 L
962 770 L
960 772 L
956 774 L
950 774 L
945 772 L
941 768 L
939 762 L
939 758 L
CS M
941 753 L
945 749 L
950 747 L
954 747 L
960 749 L
964 753 L
962 762 M 962 768 L
960 772 L
950 774 M 946 772 L
943 768 L
941 762 L
941 758 L
943 753 L
946 749 L
950 747 L
1025 781 M 1025 747 L
1008 764 M 1043 764 L
1114 781 M 1116 776 L
1116 787 L
1114 781 L
1110 785 L
1104 787 L
1100 787 L
1095 785 L
1091 781 L
1089 778 L
1087 772 L
1087 762 L
1089 756 L
1091 753 L
1095 749 L
1100 747 L
1104 747 L
1110 749 L
1114 753 L
1100 787 M 1097 785 L
1093 781 L
1091 778 L
1089 772 L
1089 762 L
1091 756 L
1093 753 L
1097 749 L
1100 747 L
1114 762 M 1114 747 L
1116 762 M 1116 747 L
1108 762 M 1122 762 L
1145 787 M 1131 747 L
1145 787 M 1158 747 L
1145 781 M 1156 747 L
1135 758 M 1152 758 L
1127 747 M 1139 747 L
1150 747 M 1162 747 L
1174 787 M 1174 747 L
1175 787 M 1175 747 L
1168 787 M 1181 787 L
1168 747 M 1197 747 L
1197 758 L
1195 747 L
1208 787 M 1208 747 L
1210 787 M 1210 747 L
1202 787 M 1216 787 L
1202 747 M 1231 747 L
1231 758 L
1229 747 L
1243 787 M 1243 747 L
1245 787 M 1245 747 L
1256 776 M 1256 760 L
1237 787 M 1268 787 L
1268 776 L
1266 787 L
1245 768 M 1256 768 L
1237 747 M 1268 747 L
1268 758 L
1266 747 L
1279 787 M 1304 747 L
1281 787 M 1306 747 L
1306 787 M 1279 747 L
1276 787 M 1287 787 L
1299 787 M 1310 787 L
1276 747 M 1287 747 L
1299 747 M 1310 747 L
1368 781 M 1368 747 L
1351 764 M 1385 764 L
1455 781 M 1456 787 L
1456 776 L
1455 781 L
1451 785 L
1445 787 L
1439 787 L
1433 785 L
1429 781 L
1429 778 L
1431 774 L
1433 772 L
1437 770 L
1449 766 L
1453 764 L
1456 760 L
1429 778 M 1433 774 L
1437 772 L
1449 768 L
1453 766 L
1455 764 L
1456 760 L
1456 753 L
1453 749 L
1447 747 L
1441 747 L
1435 749 L
1431 753 L
1429 758 L
1429 747 L
1431 753 L
1481 787 M 1468 747 L
1481 787 M 1495 747 L
1481 781 M 1493 747 L
1472 758 M 1489 758 L
1464 747 M 1476 747 L
1487 747 M 1499 747 L
1533 781 M 1535 776 L
1535 787 L
1533 781 L
1530 785 L
1524 787 L
1520 787 L
1514 785 L
1510 781 L
1508 778 L
1507 772 L
1507 762 L
1508 756 L
1510 753 L
1514 749 L
1520 747 L
1524 747 L
1530 749 L
1533 753 L
1520 787 M 1516 785 L
1512 781 L
1510 778 L
1508 772 L
1508 762 L
1510 756 L
1512 753 L
1516 749 L
1520 747 L
1533 762 M 1533 747 L
1535 762 M 1535 747 L
1528 762 M 1541 762 L
1555 787 M 1555 747 L
1557 787 M 1557 747 L
1568 776 M 1568 760 L
1549 787 M 1580 787 L
1580 776 L
1578 787 L
1557 768 M 1568 768 L
1549 747 M 1580 747 L
1580 758 L
1578 747 L
1641 781 M 1641 747 L
1624 764 M 1659 764 L
1667 747 M CS [] 0 setdash M
608 633 M CS [] 0 setdash M
639 668 M 640 673 L
640 662 L
639 668 L
635 672 L
629 673 L
623 673 L
617 672 L
614 668 L
614 664 L
615 660 L
617 658 L
621 656 L
633 652 L
637 650 L
640 646 L
614 664 M 617 660 L
621 658 L
633 654 L
637 652 L
639 650 L
640 646 L
640 639 L
637 635 L
631 633 L
625 633 L
619 635 L
615 639 L
614 645 L
614 633 L
615 639 L
656 660 M 656 639 L
658 635 L
664 633 L
667 633 L
673 635 L
677 639 L
658 660 M 658 639 L
660 635 L
664 633 L
677 660 M 677 633 L
679 660 M 679 633 L
650 660 M 658 660 L
671 660 M 679 660 L
677 633 M 685 633 L
698 660 M 698 620 L
700 660 M 700 620 L
700 654 M 704 658 L
708 660 L
712 660 L
717 658 L
721 654 L
723 648 L
723 645 L
721 639 L
717 635 L
712 633 L
708 633 L
704 635 L
700 639 L
712 660 M 716 658 L
719 654 L
721 648 L
721 645 L
719 639 L
716 635 L
712 633 L
692 660 M 700 660 L
692 620 M 706 620 L
737 648 M 760 648 L
760 652 L
758 656 L
756 658 L
752 660 L
746 660 L
741 658 L
737 654 L
735 648 L
735 645 L
737 639 L
741 635 L
746 633 L
750 633 L
756 635 L
760 639 L
758 648 M 758 654 L
756 658 L
746 660 M 742 658 L
739 654 L
737 648 L
737 645 L
739 639 L
742 635 L
746 633 L
775 660 M 775 633 L
777 660 M 777 633 L
777 648 M 779 654 L
783 658 L
787 660 L
792 660 L
794 658 L
794 656 L
792 654 L
791 656 L
792 658 L
769 660 M 777 660 L
769 633 M 783 633 L
808 673 M 808 633 L
810 673 M 810 633 L
835 673 M 810 648 L
819 656 M 835 633 L
817 656 M 833 633 L
802 673 M 816 673 L
827 673 M 839 673 L
802 633 M 816 633 L
827 633 M 839 633 L
850 656 M 850 654 L
848 654 L
848 656 L
850 658 L
854 660 L
862 660 L
866 658 L
867 656 L
869 652 L
869 639 L
871 635 L
873 633 L
867 656 M 867 639 L
869 635 L
873 633 L
875 633 L
867 652 M 866 650 L
854 648 L
848 646 L
846 643 L
846 639 L
848 635 L
854 633 L
CS M
860 633 L
864 635 L
867 639 L
854 648 M 850 646 L
848 643 L
848 639 L
850 635 L
854 633 L
889 660 M 889 633 L
891 660 M 891 633 L
891 654 M 894 658 L
900 660 L
904 660 L
910 658 L
912 654 L
912 633 L
904 660 M 908 658 L
910 654 L
910 633 L
912 654 M 916 658 L
921 660 L
925 660 L
931 658 L
933 654 L
933 633 L
925 660 M 929 658 L
931 654 L
931 633 L
883 660 M 891 660 L
883 633 M 896 633 L
904 633 M 918 633 L
925 633 M 939 633 L
952 673 M 950 672 L
952 670 L
954 672 L
952 673 L
952 660 M 952 633 L
954 660 M 954 633 L
946 660 M 954 660 L
946 633 M 960 633 L
981 660 M 975 658 L
971 654 L
969 648 L
969 645 L
971 639 L
975 635 L
981 633 L
985 633 L
991 635 L
994 639 L
996 645 L
996 648 L
994 654 L
991 658 L
985 660 L
981 660 L
977 658 L
973 654 L
971 648 L
971 645 L
973 639 L
977 635 L
981 633 L
985 633 M 989 635 L
993 639 L
994 645 L
994 648 L
993 654 L
989 658 L
985 660 L
1012 673 M 1012 633 L
1014 673 M 1014 633 L
1033 660 M 1014 641 L
1023 648 M 1035 633 L
1021 648 M 1033 633 L
1006 673 M 1014 673 L
1027 660 M 1039 660 L
1006 633 M 1020 633 L
1027 633 M 1039 633 L
1052 656 M 1052 654 L
1050 654 L
1050 656 L
1052 658 L
1056 660 L
1064 660 L
1068 658 L
1070 656 L
1072 652 L
1072 639 L
1073 635 L
1075 633 L
1070 656 M 1070 639 L
1072 635 L
1075 633 L
1077 633 L
1070 652 M 1068 650 L
1056 648 L
1050 646 L
1048 643 L
1048 639 L
1050 635 L
1056 633 L
1062 633 L
1066 635 L
1070 639 L
1056 648 M 1052 646 L
1050 643 L
1050 639 L
1052 635 L
1056 633 L
1091 660 M 1091 633 L
1093 660 M 1093 633 L
1093 654 M 1097 658 L
1102 660 L
1106 660 L
1112 658 L
1114 654 L
1114 633 L
1106 660 M 1110 658 L
1112 654 L
1112 633 L
1085 660 M 1093 660 L
1085 633 M 1098 633 L
1106 633 M 1120 633 L
1152 673 M 1152 633 L
1154 673 M 1154 633 L
1152 654 M 1148 658 L
1145 660 L
1141 660 L
1135 658 L
1131 654 L
1129 648 L
1129 645 L
1131 639 L
1135 635 L
1141 633 L
1145 633 L
1148 635 L
1152 639 L
1141 660 M 1137 658 L
1133 654 L
1131 648 L
1131 645 L
1133 639 L
1137 635 L
1141 633 L
1146 673 M 1154 673 L
1152 633 M 1160 633 L
1172 648 M 1195 648 L
1195 652 L
1193 656 L
1191 658 L
1187 660 L
1181 660 L
1175 658 L
1172 654 L
1170 648 L
1170 645 L
1172 639 L
1175 635 L
1181 633 L
1185 633 L
1191 635 L
1195 639 L
1193 648 M 1193 654 L
1191 658 L
1181 660 M 1177 658 L
1173 654 L
1172 648 L
1172 645 L
1173 639 L
1177 635 L
1181 633 L
1201 633 M CS [] 0 setdash M
608 443 M CS [] 0 setdash M
639 478 M 640 484 L
640 472 L
639 478 L
635 482 L
629 484 L
623 484 L
617 482 L
614 478 L
614 474 L
615 470 L
617 468 L
621 466 L
633 463 L
637 461 L
640 457 L
614 474 M 617 470 L
621 468 L
633 465 L
637 463 L
639 461 L
640 457 L
640 449 L
637 445 L
631 443 L
625 443 L
619 445 L
615 449 L
614 455 L
614 443 L
615 449 L
677 478 M 679 484 L
679 472 L
677 478 L
673 482 L
667 484 L
662 484 L
656 482 L
652 478 L
652 474 L
654 470 L
656 468 L
660 466 L
671 463 L
675 461 L
679 457 L
652 474 M 656 470 L
660 468 L
671 465 L
675 463 L
677 461 L
679 457 L
679 449 L
675 445 L
669 443 L
664 443 L
658 445 L
654 449 L
652 455 L
652 443 L
654 449 L
694 484 M 694 443 L
696 484 M 708 449 L
694 484 M 708 443 L
721 484 M 708 443 L
721 484 M 721 443 L
723 484 M 723 443 L
689 484 M 696 484 L
721 484 M 729 484 L
689 443 M 700 443 L
716 443 M 729 443 L
743 470 M 741 468 L
743 466 L
744 468 L
743 470 L
743 447 M 741 445 L
743 443 L
744 445 L
743 447 L
793 484 M 793 443 L
795 484 M 795 443 L
787 484 M 810 484 L
816 482 L
818 480 L
820 476 L
820 472 L
818 468 L
816 466 L
810 465 L
810 484 M 814 482 L
816 480 L
818 476 L
818 472 L
816 468 L
814 466 L
810 465 L
795 465 M 810 465 L
816 463 L
818 461 L
820 457 L
820 451 L
818 447 L
816 445 L
810 443 L
787 443 L
810 465 M 814 463 L
816 461 L
818 457 L
818 451 L
816 447 L
814 445 L
810 443 L
835 484 M 835 443 L
837 484 M 837 443 L
829 484 M 852 484 L
858 482 L
860 480 L
862 476 L
862 470 L
860 466 L
858 465 L
852 463 L
837 463 L
852 484 M 856 482 L
858 480 L
860 476 L
860 470 L
858 466 L
CS M
856 465 L
852 463 L
829 443 M 843 443 L
877 480 M 875 482 L
877 484 L
879 482 L
879 478 L
877 474 L
875 472 L
918 470 M 916 465 L
912 461 L
906 459 L
904 459 L
898 461 L
894 465 L
893 470 L
893 472 L
894 478 L
898 482 L
904 484 L
908 484 L
914 482 L
918 478 L
920 472 L
920 461 L
918 453 L
916 449 L
912 445 L
906 443 L
900 443 L
896 445 L
894 449 L
894 451 L
896 453 L
898 451 L
896 449 L
904 459 M 900 461 L
896 465 L
894 470 L
894 472 L
896 478 L
900 482 L
904 484 L
908 484 M 912 482 L
916 478 L
918 472 L
918 461 L
916 453 L
914 449 L
910 445 L
906 443 L
941 484 M 935 482 L
933 478 L
933 472 L
935 468 L
941 466 L
948 466 L
954 468 L
956 472 L
956 478 L
954 482 L
948 484 L
941 484 L
937 482 L
935 478 L
935 472 L
937 468 L
941 466 L
948 466 M 952 468 L
954 472 L
954 478 L
952 482 L
948 484 L
941 466 M 935 465 L
933 463 L
931 459 L
931 451 L
933 447 L
935 445 L
941 443 L
948 443 L
954 445 L
956 447 L
958 451 L
958 459 L
956 463 L
954 465 L
948 466 L
941 466 M 937 465 L
935 463 L
933 459 L
933 451 L
935 447 L
937 445 L
941 443 L
948 443 M 952 445 L
954 447 L
956 451 L
956 459 L
954 463 L
952 465 L
948 466 L
964 443 M CS [] 0 setdash M
stroke
grestore
showpage
end






hep-ph0002073.extracted_bib
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\end{thebibliography}