Department of Astronomy
Nordita
Licentiate thesis
Effects of rotation and stratification
on magnetic flux concentrations
Supervisor:
Axel Brandenburg
Author:
Illa R. Losada
Second Supervisor:
Dan Kiselman
Mentor:
Juan Esteban Gonzalez
Alexis Brandeker
November 2014
“Le dije: Monta que te llevo al sol,
me dijo: Que tonterı́a, arderás!,
Le dije que no pensaba ir de dı́a y se reı́a,
ya verás le decı́a si te fı́as de este guı́a.
Dicen que cuando llegas hay un flash, y me
creı́a, me daba alas, parábamos a dar caladas
en coordenadas desordenadas,
sentados en el Meridiano de Greenwich,
dejábamos colgar las piernas,
sabiendo que la búsqueda era eterna,
y que hay muchas paradas a lo largo del
camino y que, lo importante no es llegar sino,
sino el camino en si, miramos atrás
y supimos que nadie volverı́a a vernos mas. ”
Kase O
NORDITA
STOCKHOLM UNIVERSITY
Abstract
Department of Astronomy
Effects of rotation and stratification on magnetic flux concentrations
by Illa R. Losada
The formation of magnetic flux concentrations in the Sun is still a matter of debate.
One observable manifestations of such concentrations is sunspots. A mechanism able
to spontaneously form magnetic flux concentrations in strongly stratified hydromagnetic
turbulence and in the presence of a weak magnetic field is the negative effective magnetic
pressure instability (NEMPI). This instability is caused by the local suppression of the
turbulence by the magnetic field. Due to the complexity of the system, and in order
to understand the fundamental physics behind the instability, the study started by considering simplified conditions. In this thesis we aim to move towards the complexity of
the Sun. Here we want to know whether the instability can develop under rotation and
in the case of a polytropic stratification instead of the simpler isothermal stratification.
We perform different kinds of simulations, namely direct numerical simulations (DNS)
and mean field simulations (MFS) of strongly stratified turbulence in the presence of
weak magnetic fields. We then study separately the effects of rotation and the change in
stratification.
It is found that slow rotation can suppress the instability. For Coriolis numbers larger
than 0.1 the MFS no longer result in growth, whereas the DNS start first with a decrease
of the growth rate of the instability and then, for Co > 0.06, an increase owing to the fact
that rotation leads to the onset of the dynamo instability, which couples with NEMPI in
a combined system. In fact, the suppression implies a constraint on the depth where the
instability can operate in the Sun. Since rotation is very weak in the uppermost layers
of the Sun, the formation of the flux concentration through this instability might be a
shallow phenomenon. The same constraint is found when we study the effects of polytropic stratification on NEMPI. In this case, the instability also develops, but it is much
more concentrated in the upper parts of the simulation domain than in the isothermal
case. In contrast to the isothermal case, where the density scale height is constant in the
computational domain, polytropic layers decrease their stratification deeper down, so it
becomes harder for NEMPI to operate.
With these studies we confirm that NEMPI can form magnetic flux concentrations even
in the presence of weak rotation and for polytropic stratification. When applied to the
Sun, the effects of rotation and the change of stratification constrain the depth where
NEMPI can develop to the uppermost layers, where the rotational influence is weak and
the stratification is strong enough.
List of Papers
The following papers are included in this licenciate thesis. They will be referred to by
their Roman numerals.
Paper I: Losada, I. R., Brandenburg, A., Kleeorin, N., Mitra, D., and Rogachevskii, I.
(2012). Rotational effects on the negative magnetic pressure instability (Paper I).
A&A, 548:A49
Paper II: Losada, I. R., Brandenburg, A., Kleeorin, N., and Rogachevskii, I. (2013).
Competition of rotation and stratification in flux concentrations (Paper II). A&A,
556:A83
Paper III: Losada, I. R., Brandenburg, A., Kleeorin, N., and Rogachevskii, I. (2014).
Magnetic flux concentrations in a polytropic atmosphere (Paper III). A&A, 564:A2
vii
Other Papers not included in this thesis
The following papers are not included in this licenciate thesis.
Warnecke, J., Losada, I. R., Brandenburg, A., Kleeorin, N., & Rogachevskii, I : 2013,
Bipolar magnetic structures driven by stratified turbulence with a coronal envelope,
ApJ, 777, L37.
Jabbari, S., Brandenburg, A., Losada, I. R., Kleeorin, N.,& Rogachevskii, I : 2014,
‘Magnetic flux concentrations from dynamo-generated fields, Astron. Astrophys.,
568, A112, arXiv: 1401.4102.
ix
Contents
Abstract
v
List of Papers
vii
Papers not included
ix
Abbreviations
xv
Symbols
xvii
Prologue
xix
1 Framework
1.1 Fundamental equations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Magnetohydrodynamics . . . . . . . . . . . . . . . . . . . . . . .
Some derivations from the momentum equation. . . . . . .
Some derivations from the induction equation. . . . . . . .
1.1.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2.1 Energy spectrum . . . . . . . . . . . . . . . . . . . . . .
1.1.2.2 Turbulent cascade and Kolmogorov turbulence . . . . .
1.1.2.3 Inverse cascade . . . . . . . . . . . . . . . . . . . . . . .
1.1.2.4 Driven turbulence . . . . . . . . . . . . . . . . . . . . .
1.1.3 Mean-Field equations . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3.1 Mean Field MHD equations . . . . . . . . . . . . . . . .
From E in the induction equation: dynamo instability. . . .
From F in the momentum equation: negative effective magnetic pressure instability (NEMPI). . . . . . . .
1.2 Energy transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
1
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2 MHD simulations
2.1 DNS and MFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
13
xi
10
11
xii
2.2
2.3
2.1.1 DNS . . . . . . . . . . . . . . . . . . .
2.1.2 MFS . . . . . . . . . . . . . . . . . . .
Pencil Code . . . . . . . . . . . . . . . . . . .
Simulation setup . . . . . . . . . . . . . . . .
2.3.1 Boundary conditions . . . . . . . . . .
Stress-free boundary conditions
Perfect conductor . . . . . . . .
Vertical field condition . . . . .
2.3.2 Non-dimensional numbers . . . . . . .
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3 Mechanisms
3.1 Parker instability: Flux-tube model . . . . . . . . . . .
3.1.1 Model . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Problems . . . . . . . . . . . . . . . . . . . . .
Initial field strength: . . . . . . . . . . .
Role of the overshoot layer: . . . . . . . .
Thickness of the tubes: . . . . . . . . . .
Helioseismology: . . . . . . . . . . . . . .
Dynamo mechanism: . . . . . . . . . . .
Horizontal-velocity maps: . . . . . . . . .
3.2 Turbu-thermomagnetic instability . . . . . . . . . . . .
3.3 Negative effective magnetic pressure instability . . . . .
3.3.1 Total pressure . . . . . . . . . . . . . . . . . . .
Global considerations: . . . . . . . . . . .
Mean-field considerations: . . . . . . . .
3.3.2 Computation of the effective magnetic pressure.
3.3.3 Parameterization . . . . . . . . . . . . . . . . .
4 Rotation and stratification on NEMPI
4.1 Effects of rotation . . . . . . . . . . . . . . . .
4.1.1 The Model . . . . . . . . . . . . . . . .
Turnover time τ : . . . . . . . .
Coriolis number Co
Co: . . . . . . .
Mean field parameters: . . . . .
4.1.2 Numerical results . . . . . . . . . . . .
4.1.2.1 Effective magnetic pressure .
4.1.2.2 Co dependence . . . . . . . .
4.1.2.3 θ dependence . . . . . . . . .
4.1.2.4 Spatial structure . . . . . . .
4.1.2.5 Dynamics . . . . . . . . . . .
4.1.2.6 Interaction with the dynamo
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xiii
4.2
Effects of stratification . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Brief notes about thermodynamics . . . . . . . . . . .
4.2.1.1 Ideal gas equation of state . . . . . . . . . . .
4.2.1.2 Gas laws . . . . . . . . . . . . . . . . . . . . .
Isothermal expansion: . . . . . . . . . . . . . . .
Adiabatic expansion: . . . . . . . . . . . . . . .
4.2.1.3 Stratification of the atmosphere . . . . . . . .
Isothermal atmosphere: . . . . . . . . . . . . . .
Adiabatic atmosphere (polytropic stratification):
4.2.2 The model of polytropic stratification . . . . . . . . . .
4.2.3 Numerical results . . . . . . . . . . . . . . . . . . . . .
4.2.3.1 Effective magnetic pressure . . . . . . . . . .
4.2.3.2 Structures . . . . . . . . . . . . . . . . . . . .
4.2.3.3 Dynamics . . . . . . . . . . . . . . . . . . . .
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39
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5 Conclusions
49
Bibliography
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Paper I
57
Paper II
67
Paper III
81
Abbreviations
DNS
Direct Numerical Simulations
ILES
Implicit Large Eddy Simulations
LES
Large Eddy Simulations
MFS
Mean Field Simulations
MHD
Magnetohydrodynamics
NEMPI
Negative Effective Magnetic Pressure Instability
NSSL
Near Surface Shear Layer
xv
Symbols
Symbol
Name
Unit
B
magnetic field
cv
specific heat at constant volume
cp
specific heat at constant pressure
Fν
viscous force
g
gravity
Hp
pressure scale height
Hρ
density scale height
J
current density
k
wavenumber
L
length
Ma
Mach number
p
pressure
Pr
Prandtl number
PrM
magnetic Prandtl number
Ra
Rayleigh number
Re
Reynolds number
ReM
magnetic Reynolds number
s
entropy
S
rate-of-strain tensor
T
temperature
U
velocity
xvii
xviii
p
hu2 i
urms
rms velocity
ν
kinematic viscosity
χ
thermal diffusivity
η
magnetic diffusivity
ρ
density
µ0
vacuum permeability
Ω
angular velocity
γ
polytropic index
τ
time
Π
momentum tensor
Prologue
“No book, however good, can survive a hostile
reading.”
Orson Scott Card, Ender’s Game
This work started in May 2012, when I first visited Nordita. It was a time when a new
theory for the formation of magnetic flux concentrations on the solar surface began to
take shape. This theory is based on the suppression of turbulent pressure by magnetic
fields and goes back to early work by Kleeorin, Rogachevskii, and Ruzmaikin in 1989 and
1990, but it became computational reality only with the thesis work of Koen Kemel in
October 2012. While the essence of this effect was already demonstrated in his thesis,
a number of important questions remained unanswered: can this theory really explain
active regions and even sunspots under more realistic conditions? Can it survive a change
in stratification or when there is rotation? These are questions that will be addressed in
the present thesis.
There were several other open questions at the time, such as the importance of spherical
geometry and the interaction with an underlying dynamo that is responsible for maintaining the overall magnetic field. Those are questions that are currently being addressed
in the thesis work of Sarah Jabbari, who started with me at the same time. Some of her
work on the dynamo involves the presence of rotation and therefore naturally connects
to my work discussed in the present thesis. This led to a joint publication that will be
addressed below, but it will not be included in the present thesis.
Eventually, of course, we need to ask about the broader implications of this new theory
for the formation of coronal mass ejections that can affect us here on Earth. One must
therefore include an outer corona, which was already done in the recent thesis of Jörn
Warnecke in 2013. The connection with magnetic flux concentrations led to another
xix
xx
CHAPTER 0. PROLOGUE
joint publication – this one with Jörn Warnecke – but it will also not be included in the
present thesis. Nevertheless, this work has been important in that it was the first example
showing the formation of bipolar spots, which are commonly also seen in the Sun.
At the heart of the new developments discussed in the present thesis is turbulence and
its interaction with magnetic fields. Therefore I begin by describing the essence of these
topics in Chapter 1 which describes the basic framework. The set of equations relevant
to the problem cannot be solved analytically, so we need to use simulations and some
approximations, which are briefly described in Chapter 2. Chapter 3 describes different
mechanisms to produce magnetic field concentrations, like the flux-tube model, and develops the central theory of this thesis, NEMPI. In Chapter 4, my current contributions
to this theory are explained. In particular I discuss how rotation and stratification influence the instability, and address these aspects in a solar context. Finally, Chapter 5
draws some conclusions and the upcoming work towards the end of my PhD.
1
Framework
“Big whirls have little whirls
That feed on their velocity,
And little whirls have littler whirls
And so on to viscosity”
L.F. Richardson
The framework of the present thesis comprises magnetic fields, mean field theory, and
turbulence. This chapter reviews some of the fundamental equations in solar physics and
introduces some new concepts that we develop in this work. The basic equations are
adapted from general books, like Schrijver et al. (2011) or Carroll and Ostlie (1996).
1.1
Fundamental equations
The Sun is a big ball of plasma. A plasma is a fluid state of charged particles. The
main difference with other fundamental states of matter is that plasmas are electrically
conducting and can therefore interact with electromagnetic fields. The aim of the present
work is then to describe the characteristics and evolution of plasma and its interaction
with electromagnetic fields.
We consider the continuum approximation and assume that we can describe the fluid by
its macroscopic properties. This approximation is valid when the mean distance between
particles is much smaller than the typical scales of the system, i.e. the macroscopic scale
of the system is much bigger than the microscopic one. In the solar interior, for example,
the typical mean inter-particle distance is 10−10 m, while the macroscopic scale of the
system is 108 m (Charbonneau, 2013). Even the mean-free path of photons is much
larger (10−4 m) than the inter-particle distance.
1.1.1
Magnetohydrodynamics
Magnetohydrodynamics (MHD) is the study of interactions between magnetic fields and
plasma flow. We consider here the case of non-relativistic, slowly varying plasmas (Choudhuri, 1998).
1
2
CHAPTER 1. FRAMEWORK
The MHD basic equations describe the evolution of the thermodynamic variables density ρ and specific entropy s, velocity U , and magnetic field B though the following
equations:
1. continuity equation (conservation of mass):
∂ρ
= −∇ · (ρU ),
∂t
(1.1)
2. momentum equation (conservation of momentum):
ρ
DU
= −∇p + J × B + ρg + F ν + ...,
Dt
(1.2)
∂B
= ∇ × (U × B − ηµ0 J ),
∂t
(1.3)
3. induction equation:
4. energy equation (conservation of energy):
ρT
Ds
= 2νρS + ηµ0 J 2 − ∇ · (F rad + F cond + ...) ,
Dt
(1.4)
where dots indicate the possibility of additional terms. In these equations, D/Dt =
∂/∂t + U · ∇ is the advective derivative1 with respect to the actual (turbulent) flow,2
B = B0 + ∇ × A is the magnetic field, B0 is an imposed uniform field, J = ∇ × B/µ0 is
the current density, µ0 is the vacuum permeability, η = 1/(µ0 σ) is the magnetic diffusivity,
σ is the electrical conductivity of the plasma, F ν = ∇ · (2νρS) is the viscous force, and
Sij = 21 (∂j Ui + ∂i Uj ) − 31 δij ∇ · U is the traceless rate-of-strain tensor of the flow. The
viscous force can also be written as
F ν = ∇ · (2νρS) = νρ(∇2 U + 31 ∇∇ · U + 2S · ∇ ln νρ).
(1.5)
In Equation (1.4), T is the temperature, which is related to ρ and s via s = cv ln T − (cp −
cv ) ln ρ + const, where cp and cv are the specific heats at constant pressure and constant
volume, respectively. The specific entropy is defined only up to an additive constant that
needs to be fixed a priori to the calculation. In the Pencil Code, which is used in this
thesis, this constant is chosen to be zero.
Often, we will not solve the energy equation, but we will assume an isothermal setup
(T = const) or an isentropic atmosphere (s = const). Also, we will drive turbulence “by
1
The term advection means the transport of some substance or quantity by the fluid due to its own
motion, i.e., moving of oil in a river or change in temperature due to wind motions. It is not the same
as convection, since convection implies the transport both by diffusion and advection. Mathematically,
the advection operator is u · ∇ and the advection equation for a vector quantity a in an incompressible
fluid (hence, ∇ · U = 0 and U is solenoidal), is: ∂a/∂t + (U · ∇)a = (a · ∇)U for a line element.
2
We are using a Lagrangian description of the fluid, i.e., we move with the fluid.
1.1. FUNDAMENTAL EQUATIONS
3
hand”, using an external source, modeled as a function f . In the numerical modeling,
this forcing function f is a sequence of random, white-in-time3 , Gaussian distributed,
plane, non-polarized waves with a certain average wavenumber kf , which represents the
inverse scale of the energy-carrying eddies in the system.
Some derivations from the momentum equation. The term J × B in the momentum equation is called the Lorentz force and it can be rewritten, using the definition
of current density:
2
B
J × B = (∇ × B) × B = (B · ∇)B − ∇
,
(1.6)
2µ0
where the first term on the right-hand side (rhs) comprises the magnetic curvature and
tension forces and the second term is the magnetic pressure gradient.
Using the definition of the advective derivative and Equation (1.6), we can write the
momentum equation as:
2
B
1
1
∂U
1
1
= −U
·{z
∇U} − ∇p + g + (B · ∇)B − ∇
+ ∇ · (2νρS) + f .
|
|{z}
∂t
ρ
ρ
ρ
2µ0
ρ
advection
| {z } |
{z
} forcing
{z
} |
environment
Lorentz force
diffusion
(1.7)
We can analyze further the meaning of the rhs terms in this equation. The first one,
U · ∇U , which is the advection term, is non-linear in the velocity U . The second and
third terms, ρ1 ∇p and g, respectively, are due to the environment or the state of the fluid.
Next, we have the Lorentz force, which is the only one that includes the magnetic field.
The diffusion term, F ν , includes second derivatives and tends to smooth gradients in the
velocity. Finally, we have the forcing. This term is needed in the cases where we drive
turbulence in the system, but we are not solving an energy equation, which could lead
to turbulent convection. This formulation allows us to have a well-defined and controlled
turbulent medium, which helps us to isolate the specific mechanism under study in the
system.
Since the advection term is non-linear in the velocity, it can introduce chaotic behaviour
and hence turbulence in the system. On the other hand, the diffusion term smoothes the
velocity gradients, so it will favour laminarity. So their comparison defines a dimensionless
quantity that is called the Reynolds number, which characterizes the flow pattern:
Re =
UL
k U · ∇U k
≈
,
−1
k ρ ∇ · (2νρS) k
ν
(1.8)
where U is the typical velocity of the plasma and L its typical length scale. At low
Reynolds number, the diffusion term dominates, so the flow is laminar; but for high
3
white-in-time means that the temporal frequency spectrum is flat
4
CHAPTER 1. FRAMEWORK
Reynolds number the advection term dominates, so the flow becomes turbulent. A standard Kolmogorov k −5/3 spectrum can only occur at wavenumbers k larger than the energy
injection wavenumber. Figure 1.1 shows examples of flows at different Reynolds numbers,
which are here only moderately large, because the flow speeds exceed ν/L by less than a
factor 400. As we shall see below, a small Reynolds number implies that the wavenumber interval between the injection wavenumber and the dissipation wavenumber is rather
short.
Figure 1.1: Effect of the Reynolds number on the flow pattern around a cylinder. (Extracted from http://forums.x-plane.org/index.php?showtopic=69180)
The Reynolds number allows us also to scale the system, since two different systems
with the same Reynolds number should have similar flow patterns. This allows us to
predict the behaviour of new ships or planes; or even in car designs, based on smaller
models in high speed flow channels or wind tunnels.
In the following sections we will be interested in the total pressure in the system. It
can be obtained by just grouping some terms and rewriting the equation as:
∂U
1
B2
1
= − ∇ pI + ρU U +
(1.9)
I − BB + g + ∇ · (2νρS) + f ,
∂t
ρ
2µ0
ρ
where I is the unit matrix while U U and BB denote dyadic products. The term in
parenthesis is the total momentum tensor:
Π = pI + ρU U +
B2
I − BB.
2µ0
(1.10)
It will play an important role in the following chapters.
Some derivations from the induction equation. Using Maxwell’s equations, we
can rewrite the induction equation as:
∂B
= ∇ × (U × B) + η∇2 B.
∂t
(1.11)
In this case we can also define a dimensionless number, called magnetic Reynolds number,
ReM , by comparing the relative strengths of both terms on the rhs of Equation (1.11):
ReM =
k∇×U ×B k
UL
≈
.
k ∇ × ηµ0 J k
η
(1.12)
1.1. FUNDAMENTAL EQUATIONS
5
Although the definition is similar to that of the Reynolds number, the magnetic Reynolds
number is not just a hydrodynamic effect, but takes into account the diffusive properties
of magnetic fields. For low values of ReM , the second term on the rhs of Equation (1.11),
a diffusion term, dominates; whereas for large enough values, ReM 1, the first term,
advection, does. In hydromagnetic turbulence we can define a critical magnetic Reynolds
number, Rm,crit , above which small-scale dynamo action is possible, for example.
Both numbers, Re and ReM , measure the importance of advection versus diffusion.
In the first case, from purely hydrodynamic contributions (momentum equation) and in
the second one, from the magnetic counterpart (induction equation). We can combine
both definitions and define the magnetic Prandtl number PrM , as the ratio between
hydrodynamic and magnetic diffusivity:
PrM =
ν
.
η
(1.13)
Usually, the exact values of Re and ReM and the estimates in Equations (1.8) and (1.12)
do not agree, because they depend on the definition of the length scale of the system L,
used in the approximation, as has been illustrated with examples shown by Chatterjee
et al. (2011).
The magnetic Prandtl number weighs the importance of the mechanisms responsible
for diffusion in the system. We can use the following approximation for Pr:
PrM =
T 5/2 ρ−1
T4
ν
∝
=
η
T −3/2
ρ
(1.14)
and compare a typical galaxy and the Sun. The temperature is roughly similar in both
cases (106 K), but the densities differs by around 24 orders of magnitude, so for the Sun
the magnetic Prandtl number is very small (roughly 10−4 ), whereas for galaxies it will
be orders of magnitude bigger (roughly 1011 ) (Brandenburg and Subramanian, 2005).
Therefore, the nature of the dynamo may be quite different in stars and in galaxies
(Schekochihin et al., 2002; Brandenburg and Subramanian, 2005).
1.1.2
Turbulence
The word turbulence is generally associated with random movements and instability.
Turbulent systems tend to have a large Reynolds number, Re 1. A key concept of
turbulence is the constancy of energy flux at each length scale or wavenumber. This
concept leads directly to the energy spectrum of turbulence.
6
1.1.2.1
CHAPTER 1. FRAMEWORK
Energy spectrum
The energy spectrum, E(k, t), represents the amount of energy at each wavenumber. The
wavenumber, k, defines the k-space of the velocity Fourier transformation:
Z L
1
û(k, t) =
eik·x u(x, t)d3 x.
(1.15)
(2π)3 0
The minimum wavenumber in our domain will then be kmin = 2π/L, where L is the
length scale of the system under consideration (i.e., size of the box for a simulation or the
depth of the convection zone for the Sun). Thus, the smaller the value of k, the bigger
the length scale. The kinetic energy spectrum is then:
1
EK (k, t) = ρ0
2
X
|û(k, t)|2 ,
(1.16)
k− <|k|6k+
where ρ0 is the averaged density, k± = k ± δk/2 defines the interval around the wavenumber k, and δk = 2π/L is the spectral resolution.
The actual form of the spectrum depends on the type of turbulence in the system, e.g,
if it is isotropic or anisotropic; homogeneous or inhomogeneous. It will peak at some
energy-carrying scale lf , with a wavenumber kf = 2π/lf . Sometimes, the energy spectrum
will be time-dependent, so the energy-carrying scale will change in time, leading to an
energy cascade (Brandenburg and Nordlund, 2011).
Turbulence is commonly associated with vorticity, ω = ∇ × u, so it is also useful to
define the kinetic helicity spectrum:
HK (k) =
1
2
X
(ω̂ ∗ · û + ω̂ · û∗ ),
(1.17)
k− <|k|6k+
This kinetic helicity spectrum always obeys the realizability condition (Brandenburg and
Nordlund, 2011):
|HK (k)| 6 2kEK (k) .
(1.18)
In a similar fashion, it is possible to define the magnetic energy spectrum EM (k) and
the corresponding magnetic helicity spectrum HM (k). Kinetic helicity is an important
quantity in the Sun, since it defines a threshold for the onset of an α-effect dynamo, see
Paper II.
1.1.2.2
Turbulent cascade and Kolmogorov turbulence
Kolmogorov theory (Frisch, 1995) describes isotropic homogeneous turbulence. This theory can be applied, for example, to a fluid in a statistically stationary state where we
inject energy at a given wavenumber to maintain turbulence. The energy spectra will
1.1. FUNDAMENTAL EQUATIONS
7
show a peak at the injection scale, so if the scale is large, the spectra will peak at a
correspondingly small wavenumber.
Nonlinearities in the hydrodynamic equations produce a cascade of energy from large
to small scales, with a slope k −5/3 . This slope changes to an exponential decrease at
the scale where the local (k-dependent) Reynolds number becomes about 1, Re(k) =
u(k)/kν ≈ 1, and this defines the dissipative scale kd , where the energy is dissipated into
heat. The range of wavenumbers where energy is transferred without dissipation from
the injection wavenumber, kf , to the dissipation wavenumber, kd , is called the inertial
range, see Figure 1.2.
Figure 1.2: Kolmogorov energy spectrum: it peaks at the injection scale, the energy
cascades towards small scales with a −5/3 slope and decreases exponentially at the dissipation scale. Figure extracted from Berselli et al. (2005).
The slope of the cascade can be obtained from dimensional analysis using the following
ansatz for the energy spectrum (e.g. Brandenburg and Nordlund, 2011):
E(k) = CK εa k b ,
(1.19)
where ε is the energy flux and CK is a constant, called the Kolmogorov constant.
We can obtain the exponents a and b using dimensional analysis:
[E] = L3 /τ 2 ,
[k] = 1/L,
[ε] = L2 /τ 2 .
(1.20)
8
CHAPTER 1. FRAMEWORK
Thus, for dimensional compatibility, we get the following equations:
)
(
a = 2/3
3 = 2a − b
⇒
b = −5/3
2 = 3a
(1.21)
So, the Kolmogorov spectrum is:
E(k) = CK ε2/3 k −5/3 .
1.1.2.3
(1.22)
Inverse cascade
The term inverse cascade is a process that refers to a stepwise transfer of energy from
one wavenumber to the next smaller one. This is just the other way around than in
Kolmogorov turbulence. Prominent examples include two-dimensional hydrodynamic
turbulence and three-dimensional hydrodynamic turbulence with helicity. An example is
the generation of large-scale magnetic fields from a small scale one. Figure 1.3 shows an
example of this type of energy transfer. In Figure 1.3a case, we drive the turbulence at a
high wavenumber (small scale, kf /kmin = 30) and the energy is transported towards larger
scales. The change in the spectrum is more evident in Figure 1.3b, where the temporal
evolution of the magnetic spectrum shows how the energy increases towards the big scales
in the simulation, keeping the same turbulent cascade towards the dissipation scale.
(a) This figure shows the energy and helicity spectra, both kinetic and magnetic.
Here we can see the energy peak at the
injection scale, the decay towards the dissipation range and the transfer of energy
(specially magnetic) towards big scales. Extracted from Paper II
(b) Evolution of the spectra of Bz at different times, ranging from tηt0 /Hρ2 ≈ 0.2 (blue
solid line), 0.5 (dotted line), 1 (dashed line),
and 2.7 (red dot-dashed line). We can see
how magnetic energy is transported towards
bigger scales in this MHD simulation. Extracted from Brandenburg et al. (2014).
.
Figure 1.3: Inverse cascade: in this case energy is injected at small scales and cascades
towards big ones. Normally, one can find this kind of cascade in the case of small-scale
helical turbulence that excites a large scale instability, like the dynamo instability.
1.1. FUNDAMENTAL EQUATIONS
1.1.2.4
9
Driven turbulence
In any given system, turbulence can be driven either by an instability or by explicit
stirring. For example, in the outer layers of the Sun, turbulence is driven by convection,
an instability of the entropy of the system. But in simulations it is convenient to emulate
this turbulence with explicit stirring. This allows us to control the type and properties
of the turbulence.
Numerically, solving turbulence is computational very demanding: we have to solve
at the same time many different scales of the system to have a full description of the
turbulence. As discussed above, in astrophysical systems the Reynolds number is usually
huge, up to Re ∼ 1014 in the solar interior. Since the length of the inertial range scales
with the Reynolds number as kd /kf ∼ Re3/4 , this length of scales is also huge. The hope
is often that the physics of interest happens at scales far from the dissipation range, so we
can assume that the physics is independent of it. Moreover, we assume that features at
intermediate scales depend on the Reynolds number in a known fashion, which allows us
to cut off the small scales that cannot be resolved. Thus, we are normally not interested
in the full inertial range, but as soon as our physics happens within the resolved scales,
we can solve just the scales of interest.
Chapter 2 describes in more detail how different kinds of simulations treat turbulence.
In particular, we consider numerical aspects and the application to the mean-field concept
and direct numerical simulations.
1.1.3
Mean-Field equations
The mean-field approach, also known as the Reynolds-averaged Navier-Stokes equations,
treats turbulent systems by writing all the quantities (such as F ) as averages (F ) and
fluctuations f , without making any assumption about their relative strengths:
F = F + f,
(1.23)
where F is a Reynolds average that must satisfy the Reynolds rules (Krause and Raedler,
1980):
f = 0,
(1.24)
F = F,
F + H = F + H,
(1.25)
(1.26)
F H = F H = F H,
(1.27)
F H 0 = 0.
(1.28)
10
1.1.3.1
CHAPTER 1. FRAMEWORK
Mean Field MHD equations
We now write the velocity and magnetic field in the MHD equations as sums of mean
values and fluctuations:
U = U + u,
B = B + b,
(1.29)
assuming that the mean values satisfy exactly or approximately the Reynolds rules. Now,
the MHD equations are averaged and written as:
the continuity equation:
Dρ
= −ρ∇ · U ,
Dt
(1.30)
DU
= −c2s ∇ ln ρ + g + F ,
Dt
(1.31)
∂B
= ∇ × (U × B + E − ηµ0 J ).
∂t
(1.32)
the momentum equation:
the induction equation:
Most of the computational approaches , e.g. the so-called implicit large eddy simulations
(ILES), ignore the terms F and E. We see however that these terms can lead to important
effects (see Chapter 2 for more on the computational approach).
From E in the induction equation: dynamo instability. The term E in the meanfield induction equation, Equation (1.32), is the mean electromotive force:
E = u × b,
(1.33)
which correlates the velocity and magnetic field fluctuations. The α effect refers to the
possibility that this correlation has a component parallel to the mean magnetic field, i.e.,
E = αB + . . ., where the dots refer other terms. This can lead to an amplification of the
mean magnetic field, e.g. Moffatt (1978).
From F in the momentum equation: negative effective magnetic pressure
instability (NEMPI). Just like in the induction equation, the nonlinear terms in the
momentum equation lead to small-scale correlations of the form F i = −∇j Πfij , where
Πfij = ui uj − bi bj + δij b2 is the stress tensor resulting from the fluctuating velocity and
magnetic fields. One of the contributions to F has to do with turbulent viscosity and
1.2. ENERGY TRANSPORT
11
depends just on the mean flow and is denoted by F K , while the other contribution
depends quadratically on the mean magnetic field and is denoted by F K . Further details
will be described in Chapter 3.
1.2
Energy transport
The basic mechanisms for transporting the energy generated at the Sun’s core to the
surface are radiation, convection and conduction (see, e.g Carroll and Ostlie, 1996). Radiation transports energy via photons, which are absorbed and re-emitted randomly,
thus its efficiency depends strongly on the opacity4 . Convection transports energy via
the motion of buoyant hot mass elements outward and cold elements inward. Conduction transports energy via collisions between particles such as electrons. Generally this
transport mechanism is not important, except in the corona.
The mechanism that will dominate the energy transport will depend on the conditions of
the gas. In the Sun the energy is transported via radiation in the interior out to 0.7R , via
convection from this point up to the surface, and via conduction in the corona, although
most of the energy is radiated away from the photosphere. Magnetic fields also transport
energy, and this is one of the important mechanisms of heating the corona.
4
Opacity is defined as the cross section for absorbing photons of wavelength λ per gram of stellar
material, i.e., the bigger it is, the more difficult it is for the photons to diffuse. Opacity is a function of
the composition, density and temperature of the gas.
2
MHD simulations
“1. A robot may not injure a human being, or,
through inaction, allow a human being to come
to harm.
2. A robot must obey the orders given it by
human beings except where such orders would
conflict with the First Law.
3. A robot must protect its own existence as
long as such protection does not conflict with
the First or Second Laws.”
Isaac Asimov
In the present work we are trying to explain certain aspects of solar physics developing a
new theory and parametrizations in the MHD equations. We use numerical simulations
to test this theory and check whether we get meaningful results. On the one hand,
numerical simulations have proven to be an essential tool in nowadays physics, since
analytic solutions often restrict the physics in unacceptable ways. But on the other hand,
we have to keep in mind the nature and limitations of our simulations. Therefore it is
crucial to develop numerical simulations that are able to test those analytic theories. This
chapter describes briefly the different kinds of simulations we use. Also the computational
code and some of the basic setup are discussed.
2.1
DNS and MFS
The finite machine power and its discrete nature forces the simulations to obey certain
constraints and limitations. There are numerous ways to solve the equations on machines
and normally each problem requires a deep knowledge to be translated into computers.
In MHD, we do this translation, generally through Direct Numerical Simulations (DNS),
Mean Field Simulations (MFS) and/or Large Eddy Simulations (LES). Here we will
describe just the first two kinds of simulations, DNS and MFS, since those are the ones
used in this thesis.
DNS provide a solution to the hydromagnetic equations as stated for describing the
Sun under certain conditions (we normally add or neglect terms depending on the specific
problem, like introducing radiative transfer just in atmospheric problems, not deep in the
13
14
CHAPTER 2. MHD SIMULATIONS
convection zone). DNS can only be used in parameter regime not applicable to the Sun
(too small values of Re and ReM , and too large PrM ). MFS, on the other hand, allow
us to extend the regime of applicability provided we can establish sufficient faith in its
accuracy. It is therefore important to develop both approaches and perform comparisons
wherever possible.
2.1.1
DNS
One of the major problems of solving the MHD equations in a high-Reynolds-number
regime is the range of different scales: from small-scale features to global scales. In the
case of the Sun, the spatial scale range from the size of the entire Sun (mean radius of
700 Mm) to the small granules at the surface (of 1 − 3 Mm). The time scale ranges
from the solar cycle (around 22 years) to the turnover time scale of the granules (around
5 minutes). The dissipative time scale is shorter still. Direct numerical simulations (DNS)
solve the full MHD equations on all scales – from the scale of the system down to the
viscous dissipation scale. Here one does not assume any model for turbulence, so its full
spatial and temporal range must be solved. We can estimate the spatial and temporal
resolution needed to perform such a simulation, and will find that the computational cost
is very high.
Solving problems with computers requires discretization in space, usually with a mesh,
and in time, with a finite time step. We will now estimate the computational resolution
of both scales.
The strength of turbulence is characterized by the Reynolds number (see Section 1.1.2)
and in DNS we are solving the full range of scales, down to the Kolmogorov dissipative scale. Therefore, the resolution needed will scale with the Reynolds number in the
following way: the Kolmogorov scale `K is:
`K = (ν 3 /)1/4 ,
(2.1)
where ν is the kinematic viscosity and is the rate of kinetic energy dissipation. To
resolve this scale, the increment ∆x of the mesh must be smaller than:
∆x ≤ `K .
(2.2)
The number N of points in the mesh must obey:
N ∆x > L,
(2.3)
where L is the integral scale (the biggest scale in the domain).
On the other hand, we can approximate the rate of kinetic energy dissipation as:
≈ u3rms /L,
(2.4)
2.1. DNS AND MFS
15
where urms is the root mean square (rms) of the velocity. Taking into account the definition of the Reynolds number, we find that the number of mesh points N 3 required scales
as:
N 3 ≥ Re9/4 = Re2.25 .
(2.5)
We can also make some estimates of the required temporal resolution. The time step
∆t must be chosen small enough not to lose track of the fluid particles. In fact, when
we solve partial differential equations using a finite differences method, we must satisfy
the Courant-Friedrich-Lewy condition (CFL condition, Courant et al., 1967) for a stable
scheme. This condition defines the Courant number:
C=
u∆t
≤ Cmax ,
∆x
(2.6)
where u is the velocity. Since there are also sound waves and Alfvén waves, the time step
is controlled by u = max(u2 + c2s + vA2 )1/2 . Cmax depends on the discretization method.
Cmax = 0.9 in the third order Runge-Kutta scheme used in the Pencil Code. The
turbulence time scale τ is:
L
,
(2.7)
τ=
urms
so the time step must typically be less than:
∆t =
τ
.
Re3/4
(2.8)
Combining both scales, it turns out that the number of operations scales as Re3 . So we
have computationally an upper limit on the Reynolds number, and it becomes impossible
to reach solar interior conditions, where the Reynolds number is of the order of Re ∼
1012 ...1013 . Due to intrinsic limitation on memory and CPU capacity, we cannot perform
DNS on the full range of scales, so we limit the resolution of our simulations, trying to
cover the physics of interest.
2.1.2
MFS
Mean field simulations (MFS) are an averaged version of the original equations. All linear
terms translate trivially into averaged terms, but for all nonlinear terms one has at least
one extra term that captures the correlations between fluctuations. A famous example
is the α effect in dynamo theory. Turbulent viscosity and turbulent magnetic diffusivity
are other such terms.
In principle there can be a large amount of extra terms, but most of the time they do
not change the character of the solution. In the case of turbulent viscosity and turbulent
magnetic diffusivity, turbulence just enhances the micro-physical values of viscosity and
magnetic diffusivity. In other cases, extra terms may be too small to affect the nature of
the system. The α effect is obviously an exception in that it produces a linear instability
16
CHAPTER 2. MHD SIMULATIONS
that leads to the growth of a large-scale magnetic field until this growth is limited by
other new nonlinear effects.
The subject of this thesis is another mean-field effect that also leads to an instability,
the negative effective magnetic pressure instability (NEMPI), but in this case the cause
it is not found in the mean-field induction equation, but in the mean-field momentum
equation. The nature of this instability is the concentration of magnetic flux and is
therefore potentially relevant to sunspot formation.
2.2
Pencil Code
All the simulations included in this thesis are performed with the Pencil Code. One
of the side projects I have been involved in is the development of the new web-page
of the code http://pencil-code.nordita.org/, a quick guide for beginners and some
additions and modifications to the code itself.
The Pencil Codeis an open source project that was initiated by Brandenburg and
Dobler (2002) during a one-month Summer School. In its core, it is a framework for
solving partial differential equations in 3D, 2D, 1D, and even in 0D, using either a laptop
as well as a supercomputer with up to tens of thousands of processors. The code is
currently hosted by Google Code under the URL Pencil-Code.GoogleCode.com. There
are now over 22,000 revisions of the code, which have been done by over 90 people during
various stages. The integrity of the code is monitored automatically by nightly tests
running some 60 samples of particular applications.
Basically, the code solves the equations using high-order explicit finite differences for
the first and second derivatives, i.e. the quantity is first discretized and its derivative is
computed using high-order finite differences. For a sixth order case, the first and second
derivatives need the value of the function in the six surrounding points:
fi0 = (−fi−3 + 9fi−2 − 45fi−1 + 45fi+1 − 9fi+2 + fi+3 )/(60∆x),
(2.9)
fi00 = (2fi−3 − 27fi−2 + 270fi−1 − 490fi + 270fi+1 − 27fi+2 + 2fi+3 )/(180∆x2 ), (2.10)
Thus we need to define ghost zones on the boundaries with the proper values of the
variables. Also, the code uses a pencil decomposition scheme to improve cache-efficiency:
the equations are solved along pencils in the yz-plane. This formulation minimizes the
required memory of auxiliary and derived variables, since they are defined just on one
pencil. The code is highly modular, which implies large flexibility. The magnetic field
is implemented using the magnetic vector potential A instead of the magnetic field B
itself. This way the divergence-free condition is always fulfilled.
Most of the applications are in, but not limited to, astrophysics. In fact, given the highly
modular structure of the code, it is ideally suited for adding new equations, new terms,
2.3. SIMULATION SETUP
17
etc, without affecting the working of the other users who want to stay clear of particular
developments that are useful only to a subgroup of people. One of these developments
includes the treatment of mean-field terms. With this in place, it is easy to do both DNS
and MFS of the same problem and compare the results of these two kind of simulations.
This will be of crucial importance for the rest of this thesis (Paper II; Paper III). Of
course, the success of MFS hinges on the correctness of the parameterizations used. But
even for that there is a tool in the code called the test-field method to compute mean-field
coefficients (used in Jabbari et al., 2014). This technique is well developed for the terms
in the induction equation, but it is not so well developed for parameterizations in the
momentum equation. Nevertheless, even in that case it is possible to compute mean-field
coefficients using more primitive methods that will be explained below in Section 3.3.
2.3
Simulation setup
All the simulations included in this thesis are Cartesian boxes in 2D or 3D. The specific
physical conditions, like density stratification or imposed magnetic field, depend on the
problem we want to study, but they share some basic initial setup.
The initial physical conditions of the simulations may have a big impact on the final
result and the solution to the actual problem, so they must be chosen carefully. Not all
those conditions have the same impact on the final result. Ideally, the problem should be
independent of the boundary conditions, but the initial rotation rate, if any, will change
the problem drastically.
2.3.1
Boundary conditions
Ideally, we would like to be able to solve the full physical system on the computer, but
generally this is impractical and not really useful. We are limited by the computer power
and our specific problem might be well localized and almost independent of the whole
system. If we are studying the convection zone in the Sun, we are not interested to resolve
the radiative atmosphere or the core. In this case, boundary conditions become a crucial
part of the problem. In the previous case, we can approximate the radiative interior
and surface by a radiative boundary layer, and solve the problem within it. Obviously,
boundary conditions are problem-dependent and must be meaningful.
Numerically, the need for boundary conditions comes from the computation of derivatives. Those computations require the value of the variables in the adjacent points, so we
need to fill these “ghost zones” with the appropriate values. In practice, in our simulations this requires also a way of filling the ghost zones for the density, even though there
is no boundary condition for density. One could do this using a one-side finite difference
formula (called 1s in the Pencil Code), but often a hydrostatic condition, hs, or an
extrapolating condition, a2, is numerically better behaved.
18
CHAPTER 2. MHD SIMULATIONS
MHD simulations will require boundary conditions for the velocity u, vector potential
A, and entropy s or temperature T . In our simulations, we are not solving the entropy
or temperature equations, so we need to set boundary conditions just for the velocity
and the magnetic field. We have chosen small domains near the top of the convective
layer, so we impose periodic boundary conditions in the horizontal directions (typically
x and y). The vertical boundary conditions are different for velocity and magnetic field.
We will use stress-free boundary conditions for the velocity and either perfect conductor
or vertical field conditions for the magnetic field in the top and bottom layers. We can
summarize these conditions as follows (Pétrélis et al., 2003):
Stress-free boundary conditions (for the velocity):
We assume that the flow is enclosed within the domain. Therefore, the top and bottom
layers act as a plane of reflection. In this case, the tangential components of the velocity
obey the stress-free boundary conditions:
∇z Ux = ∇z Uy = Uz = 0 .
(2.11)
Perfect conductor (for a horizontal magnetic field):
If we assume that the boundary is a perfect conductor, then the magnetic field is
frozen at this layer. In this case, ∇ · B = 0, which implies the continuity of the normal
component of the magnetic field at the interface:
Ax = Ay = ∇z Az = 0 .
(2.12)
This perfect conductor boundary condition means that there is no potential difference in
the boundary. In the Pencil Code we use the Weyl gauge for the vector potential:
dA
= −E ,
dt
(2.13)
where E = ηµ0 J − U × B is the electric field, so this condition implies:
Ex = Ey = Bz = 0 .
(2.14)
We use this boundary condition especially in the cases of an horizontally imposed initial
field.
Vertical field condition (for a vertical initial imposed magnetic field):
In the cases where we impose a vertical initial field, we set the tangential components
of the magnetic field on the boundaries to zero, i.e. Bx = By = 0. In this case, we apply
2.3. SIMULATION SETUP
19
a condition similar of that of the velocity:
∇z Ax = ∇z Ay = Az = 0 .
(2.15)
This condition approximates the conditions of a vacuum outside, although the correct
vacuum condition is more complicated and would involve solving a potential problem in
the outer space.
2.3.2
Non-dimensional numbers
The simulations are controlled by a set of non-dimensional numbers describing their
physical conditions, like the turbulence we have in the system, the energy injection scale,
etc. We try to use the same numbers in the different kinds of simulations for a better
comparison of the results. However, the different kinds of simulations (DNS vs MFS)
define different kinds of basic numbers.
Reynolds number: We perform DNS with a Reynolds number of Re = urms /νkf ≈ 36.
This number is much less than the actual Reynolds number in the Sun, but here we
are strongly limited by the simulation. However, we expect to capture the physics
of interest.
Magnetic Reynolds number: ReM = urms /ηkf ≈ 18.
Prandtl number: Pr = ν/η ≈ 0.5.
Energy injection scale: kf /k1 = 30. The injection scale defines also the bigger wavenumber we resolve in the system, the smallest scale.
Impose magnetic field strength: We adopt different values for the imposed magnetic field. B0 /Beq0 = 0.1, 0.05 in the case with rotation; and B0 /Beq0 = 0.1, 0.02, 0.05
for the polytropic stratification (see Chapter 4). In both cases, the magnetic
field is normalized by the equipartition field strength at some depth, generally
Beq0 = Beq (z = 0).
√
The equipartition magnetic field is defined as Beq = µ0 ρ urms , and it is a measure
of the kinetic energy available in a turbulent medium. In the Sun, the equipartition
field varies significantly with the depth, due to the strong density stratification and
the change in the convective motions velocity.
3
Mechanisms to produce flux concentrations
“ ’E’s not pinin’ ! ’E’s passed on! This parrot
is no more! He has ceased to be! ’E’s expired
and gone to meet ’is maker! ’E’s a stiff! Bereft
of life, ’e rests in peace! If you hadn’t nailed
’im to the perch ’e’d be pushing up the daisies!
’Is metabolic processes are now ’istory! ’E’s off
the twig! ’E’s kicked the bucket, ’e’s shuffled
off ’is mortal coil, run down the curtain and
joined the bleedin’ choir invisibile!! THIS IS
AN EX-PARROT!!”
Monty Python
The formation of magnetic flux concentrations in the Sun, like sunspots, is still an unresolved problem in solar physics. Different kinds of observations constrain the problem and
the theories that might explain them. Furthermore, any complete theory must involve
the solar dynamo, another problem still under debate. This chapter describes different mechanisms that attempt to produce magnetic flux concentrations and eventually
sunspots. We start with the most used mechanism: the flux-tube model, continue briefly
with another theoretical idea, the turbu-thermomagnetic instability, and finish with the
mechanism central to this thesis, the negative effective magnetic pressure instability.
3.1
Parker instability: Flux-tube model
The most popular theory to explain magnetic flux concentrations links these concentrations and the solar dynamo through flux tubes of magnetic fields that rise throughout
the convection zone due to the Parker instability and emerge at the surface. This section
briefly describes the basic model and the problems of the theory.
3.1.1
Model
The basic idea of the flux-tube model for the formation of sunspots and active regions is
that a tube of strong field concentration can rise through the convection zone and break
21
22
CHAPTER 3. MECHANISMS
into the photosphere, thus creating a strong bipolar magnetic structure. This idea was
first proposed by Parker in 1955 (Parker, 1955b), and a schematic picture is shown in
Figure 3.1. The initial position of such tubes changed from merely 2 × 104 km below the
surface in first paper of Parker (1955b) to the bottom of the overshoot layer in his later
paper (Parker, 1975). This idea was elaborated in many subsequent papers such as that
of Caligari et al. (1995).
The Sun’s poloidal field is sheared by differential rotation; turning it into a toroidal one,
which is stored at the bottom of the convection zone. When the field becomes strong
enough, magnetic buoyancy dominates and the flux tube rises. Basically, hydrostatic
equilibrium requires that the gas pressure po outside the tube must be balanced by the
magnetic pressure pm and gas pressure inside the tube pi : po = pm + pi , thus pi < po .
If the temperature inside the tube equals the one outside, then ρi < ρo , so the tube is
lighter than the surrounding and rises.
The model assumes that initial flux tubes are stored in mechanical equilibrium until
they reach the threshold for the buoyancy instability to kick in and rise. Thus, they need
to be initially stored in the deeper subadiabatically stratified layer, where the field can
be stronger and have net neutral buoyancy.
Figure 3.1: Polar diagram of a flux
tube emergence. The initial equilibrium flux tube is located at a latitude of 15° near the lower boundary of the overshoot region and the
initial field strength is 1.2 × 105 G.
(Caligari et al., 1995)
A lot of the initial work in this field has been done using the thin flux tube approximation (Spruit, 1981). Using this model, Moreno-Insertis (1986) showed that the rise time
of magnetic flux tubes can be as short as 36 days. This is short compared with the period
of the solar cycle. Subsequently, much attention has been paid to the relation between
the magnetic field strength of flux tubes and the tilt angle of the resulting bipolar regions.
This led to the estimate of some 100 − 200 k G to produce tilt angles compatible with the
observed ones (D’Silva and Choudhuri, 1993).
The fine characteristics of the model are still under development. Are the tubes monolithic or spaghetti-like? What is exactly the initial magnetic field needed for the rise?
What is the initial width of the tubes? All these questions require MHD simulations that
try to reproduce solar characteristics. These simulations normally impose a flux tube at
3.1. PARKER INSTABILITY: FLUX-TUBE MODEL
23
the bottom of the computational domain and analyze the evolution of such a tube in a
convective medium. Figure 3.2 is an example of such a simulation.
Figure 3.2: Evolution of a flux tube shown as a synthetic magnetogram in the photosphere
(left panel) and as a vertical cut (right panel). Figure from Rempel and Cheung (2014)
3.1.2
Problems
Although the flux-tube model is successful in forming magnetic flux concentrations, there
are some problems in its applicability to the Sun. This section summarizes some of these
problems.
Initial field strength: One might expect an initial field strength of the order of the
equipartition field1 in the overshoot layer, but it turns out that a field of the order of
104 G (Charbonneau and MacGregor, 1996) is not enough to make the buoyancy force
dominate over the Coriolis and convection forces. Moreover, simulations of Caligari et al.
(1995) show that tubes with initial equipartition field strength are unstable and that
the Coriolis force deflects such tubes, so that they emerge at high latitudes. Also the
emergence tilt of the pair of spots produced by a flux tube, is not in agreement with
Joy’s law 2 (Hale et al., 1919) and the flux tube is unable to maintain its identity against
1
Which is a measure of the kinetic energy of the turbulent convective flow available
Sunspots usually form in pairs or groups. The preceding, western, spot (usually larger and more
concentrated) is normally the first to form. Thus it is referred to as the leading spot. Joy’s law describes
the systematic tilt observed in the alignment of pairs of sunspots with the east-west direction. This tilt
is about 4o with respect to the solar equator with the leading spot nearer to the equator.
2
24
CHAPTER 3. MECHANISMS
dynamical effects of convective flows.
The minimum initial field strength necessary for the buoyancy force to dominate and
to lead to flux tubes that erupt roughly along radial paths is around 105 G, i.e., 10 times
bigger than the equipartition value in the overshoot region (D’Silva and Choudhuri, 1993).
This sets the threshold for the instability that makes the flux tubes erupt.
Getting and maintaining such a super-equipartition field strength is still a puzzle for
dynamo theorists. Simulations by Guerrero and Käpylä (2011) suggest that it is very
hard to get shear-generated magnetic flux tubes to reach the surface without losing too
much of their initial coherence and orientation.
Role of the overshoot layer: The role of the overshoot layer is unclear. Studies of
the magnetic field of fully convective stars, i.e. stars without a radiative interior and
therefore no overshoot region, also show the presence of magnetic fields (Mohanty and
Basri, 2003; Dobler et al., 2006; Johns-Krull, 2007). One is therefore tempted to suggest
that the overshoot layer is not an essential part of the dynamo.
Thickness of the tubes: The thickness of the flux tubes is also important. During
their rise they expand. A simulation that generates tube-like structures from just shear
was presented by Cline et al. (2003). This model would suggest that, on theoretical
grounds, the thickness of flux tubes would be comparable to the thickness of the shear
layer, i.e., the tachocline, which is about 13 Mm (Elliott and Gough, 1999).
Helioseismology: In the work by Zhao et al. (2010), sunspots appear to be shallow,
with converging inflows about a megameter below the surface. This would be compatible
with the picture that sunspots are produced by local surface effects leading to magnetic flux concentrations. However, the helioseismic technique used measures just purely
acoustic waves, not magnetosonic ones, which would be the relevant waves in magnetically dominated sunspots. Although helioseismology is currently the only technique that
allows us to dig into the solar interior, it fails in the areas of strong magnetic flux concentrations. So any conclusions derived from this technique must be examined carefully.
Dynamo mechanism: Dynamo solutions of convection with a lower shear layer have
been performed by Guerrero and Käpylä (2011), who find the production of magnetic
flux tubes, but they are only of equipartition strength. This is simply because the energy
needed to produce both shear and magnetic fields comes ultimately from the convection
itself, and is therefore limited.
Horizontal-velocity maps: Using a technique based on velocity maps and localcorrelation-tracking methods, Getling et al. (2014) computed the horizontal-velocity field
3.2. TURBU-THERMOMAGNETIC INSTABILITY
25
Figure 3.3:
Vertical cut along
the center of a sunspot, as obtained through local helioseismology observation showing the wavespeed perturbation, which extends
to about twice of the sunspot size
horizontally and to a depth of ∼ 4
Mm vertically. From Zhao et al.
(2010).
of a bipolar magnetic structure. These maps show some features hard to match with the
flux-tube model: the scale of the moving structures corresponds to mesogranules, not big
enough for the flux tube expectation, not small enough to fit into the convective scale;
the magnetic field lacks the typical imprint on the velocity map expected from flux tubes
and the vertical velocity shows a different direction inside regions of a given magnetic
polarity.
3.2
Turbu-thermomagnetic instability
For completeness, another potentially important mechanism should be mentioned here:
an instability resulting from the local suppression of turbulent heat flux by magnetic fields
(Kitchatinov and Mazur, 2000). The idea is that a local increase of the magnetic field
suppresses the turbulent heat flux, so the gas cools and the density increases to maintain
pressure equilibrium. This means that the gas contracts, so more magnetic field lines
will be drawn together and, as a result, the magnetic field increases further, leading to
even more heat suppression, etc. Not much work has been done on this since the original
paper by Kitchatinov and Mazur (2000), but preliminary investigations by Matthias
Rheinhardt (personal communication) suggest that this instability exists only because of
the assumption of a radiative boundary condition. Such a boundary condition sets the
turbulent diffusive flux at the top equal to the value of the radiative flux that would occur
if all the energy was removed by radiation at the surface. While such a condition captures
the essence of radiation, it is only an approximation to a more complete treatment that
would involve radiative transfer. So far, there are no successful simulations involving such
a more complete description.
3.3
Negative effective magnetic pressure instability
Another possible mechanisms for a local concentration of magnetic field is the negative
effective magnetic pressure instability (NEMPI), see Kleeorin et al. (1989, 1990); Kleeorin
26
CHAPTER 3. MECHANISMS
and Rogachevskii (1994); Kleeorin et al. (1996); Rogachevskii and Kleeorin (2007). This
mechanism would concentrate the otherwise turbulent distributed magnetic field at the
top of the convection zone. Similarly to the turbu-thermomagnetic instability, the field
can be concentrated by the suppression of turbulent pressure by a weak magnetic field.
In this case the source of free energy would be the small-scale turbulence instead of the
gravity field in the flux tubes theory; see Table 3.1.
The local reduction of turbulent pressure combined with strong stratification (corresponding to small density scale height, Hρ ) can lead to an instability that concentrates
the magnetic field. Basically, the effective magnetic pressure, i.e. combination of mean
magnetic pressure and turbulent pressure, can add a negative contribution to the total
pressure. Since the total pressure (gas + effective magnetic pressure) is assumed to be
constant in the system, the gas pressure must increase to balance the total pressure. This
inequilibrium in the different pressures changes the density and causes a flow movement.
Gas density is increasing, dragging and concentrating the otherwise disperse magnetic
field towards the point where the turbulence is suppressed.
Although NEMPI and the Parker instability are very different in nature, see Table 3.1,
it is also possible that both instabilities operate together somehow in the Sun. For
example, we can imagine a scenario of flux tube formation in the bulk of the convection
zone, where the flux tubes are concentrated locally by NEMPI near the surface.
Table 3.1: Comparison between different aspects of NEMPI and the Parker Instability
Turbulence
Scale
B stratification
Energy source
Initial field
Density variation
Instability criterion
NEMPI
turbulent
sufficiently many eddies
continuous stratified B
Parker Instability
non turbulent
small
non-uniform and initially
separated flux tubes
turbulent energy
gravitational field
−1
smooth: HB ≡ |∇ ln B| small structured: |∇ ln B| large
Hρ−1 ≡ |∇ ln ρ| large
Hρ−1 ≡ |∇ ln ρ| small
HB /Hρ 1
HB /Hρ 1
The following subsections describe the mathematical model of the negative effective
magnetic pressure instability, the mean-field parameterization, some results from previous
works, as well as some useful quantities used in the present thesis.
3.3.1
Total pressure
In order to study the mathematical nature of this pressure instability we have to study
the pressure in the system. The total pressure in a turbulent magnetic system is a
combination of the kinetic pressure of the gas, the turbulent pressure and the magnetic
3.3. NEGATIVE EFFECTIVE MAGNETIC PRESSURE INSTABILITY
27
pressure of the large-scale field.
Ptotal = PK,gas + Pt + PB .
(3.1)
The combination of magnetic pressure and turbulent pressure is the effective magnetic
pressure:
Peff = Pt + PB .
(3.2)
If this effective magnetic pressure becomes negative through the suppression of the turbulent pressure, the gas pressure must compensate this keep to maintain the total pressure
constant. This is the first condition to trigger the instability. We can now study further the different pressure terms either by global considerations or using the mean-field
approach.
Global considerations: We can compute the total stress tensor from the momentum
equation:
DU
= −c2s ∇ ln ρ + g + F M + F K .
(3.3)
Dt
The Lorentz force F M and the Reynolds stresses F K defines the total stress tensor:
1
F M + F K = − ∇ · Π.
ρ
(3.4)
In the case of isotropic turbulence, the isotropic part of this tensor, Π = δij Πij , is:
3
Π = δij ρUi Uj − Bi Bj + 12 δij B 2 ≈ ρU 2 − B 2 + B 2 = ρU 2 + B 2 − 12 B 2 .
2
(3.5)
The energy is approximately conserved in the system, so it is useful to rewrite this
expression as:
3
ρU 2 − B 2 + B 2 = ρU 2 + B 2 − 21 B 2 .
(3.6)
| {z }
2
const
Thus, any increase in the magnetic field will reduce the turbulent pressure in the system.
Mean-field considerations: This approach is useful for the study of NEMPI because
it allows us to split the problem into large-scale, mean quantities and fluctuations, or
a turbulent part. Therefore, we can use this approach to parametrize the system and
isolate the essential contributions that trigger the instability.
Using the mean momentum equation:
DU
= −c2s ∇ ln ρ + g + F M + F K ,
Dt
(3.7)
it is possible to compute the magnetic stress tensor from the Lorentz force, F M and the
28
CHAPTER 3. MECHANISMS
kinetic stress tensor form the Reynolds stresses, F K :
Magnetic stress tensor: it is derived from the Lorentz Force, F M . The total magnetic
stress tensor from the momentum equation takes the form:
(f)
FM i = (J × B)i = − 12 ∇i B 2 + (B · ∇)B = −∇j 21 B 2 δij − Bi Bj = ∇j Πij , (3.8)
where the subscript f means fluctuating field.
The mean equation counterpart is:
2
hb i
(f)
M (f)
F M = −∇j
δij − hbi bj i = ∇j Πij ,
2
(3.9)
where σijm is the magnetic stress tensor. In the presence of isotropic turbulence, the
magnetic stress tensor is reduced to:
hb2 i
hb2 i
1 hb2 i
hb2 i
WM
M (f)
δij + hbi bj i = −
δij +
δij = −
, (3.10)
Πij = −
δij = −
2
2
3
3
2
3
where Wm is the magnetic energy density.
Kinetic stress tensor: In the same fashion, we can compute the kinetic stress tensor from the Reynolds stresses in the momentum equation, and considering also
isotropic turbulence, we get:
2 hρv 2 i
2
hρv 2 i
δij =
δij = WK δij .
hρvi vj i =
3
3 2
3
(3.11)
Here, WK is the kinetic energy density.
The total turbulent pressure is then the sum of the kinetic and magnetic contributions:
2
1
pturb = WK + WM .
3
3
(3.12)
To understand the suppression of total pressure by a mean magnetic field, we note that
an increase in the mean magnetic field usually implies also an increase in the fluctuating
field, i.e., in WM . However, as WM increases, and since WK + WM is approximately
constant, we see that the turbulent pressure,
2
1
2
1
pturb = WK + WM = WK + WM − WM ,
3
3
3 | {z } 3
(3.13)
≈const
decreases with increasing values of WM :
1
δpt = − Wm .
3
(3.14)
3.3. NEGATIVE EFFECTIVE MAGNETIC PRESSURE INSTABILITY
29
This idea is at the heart of NEMPI.
Now, using this mean-field approach we can parametrize the system. We have seen
that the turbulent pressure decreases with increasing values of WM = 12 hb2 i. Here hb2 i
represents the magnetic fluctuations of the mean magnetic field, thus mathematically will
be related with this mean field through an, a priori, unknown function f (B). From now
on, instead, we will use a proportional function qp (B):
hb2 i = f (B)B 2 = qp 3 B 2
(3.15)
One of the goals of the present thesis is the characterization of this function qp , which is
a basic parameter in the definition of the effective magnetic pressure in the system:
Peff = 1 − qp (B)
3.3.2
B2
2µ0
(3.16)
Computation of the effective magnetic pressure.
Basically, the effective magnetic pressure measures the effects of the mean magnetic fields
on the turbulence which is some function of the mean magnetic field B, on the big scales
of the system. Thus, we need to quantify the effects of B on the system pressure. This
effective magnetic pressure is defined in mean-field theory through the function qp (B).
We can compute this function by running two simulations: one without imposed field
and one where the long-scale structures are not developed and another one with a fully
developed instability. Mathematically:
f
∆Πxx = ρ (u2x − u20x ) + 12 (b2 − b20 ) − (b2x − b20x ),
(3.17)
where the subscript 0 refers to the case with B0 = 0. We then calculate (Brandenburg
et al., 2012a)
f
qp = −2∆Πxx /B 2 .
(3.18)
Here, qp (β) is a function of β = B/Beq (z). This allows us then to calculate Peff =
1
(1 − qp )β 2 , the normalized effective magnetic pressure.
2
3.3.3
Parameterization
Following Kemel et al. (2012b), the function qp (β) is approximated in an ad-hoc fashion
by:
β2
qp (β) = 2 ? 2 ,
(3.19)
βp + β
where β? and βp are constants, β = B/Beq is the modulus of the normalized mean
magnetic field.
30
CHAPTER 3. MECHANISMS
According to Brandenburg et al. (2012a), the following approximate formulae apply:
βp ≈ 1.05 Re−1
M,
β? = 0.33 (for ReM < 30),
(3.20)
and
βp ≈ 0.035,
β? = 0.23 (for ReM > 60),
(3.21)
where ReM = urms /ηkf is the magnetic Reynolds number. Similar values for βp and
β? have also been confirmed in Paper II as well as various other subsequent papers
(Brandenburg et al., 2014; Jabbari et al., 2014). This will be explained in more detail in
Section 4.1.2.1.
4
Effects of rotation and variable stratification on
NEMPI
“I had nothing to do, so I started to figure out
the motion of the rotating plate.”
Richard P. Feynman
This chapter focuses on the papers included in this thesis. The first section highlights
the effects of rotation on NEMPI (Paper I; Paper II) while the second section describes
the effects of changing the type of stratification (Paper III).
4.1
Effects of rotation
We undertake the study of rotation on NEMPI by adding the effects of the Coriolis
force in the MHD equations. We perform both DNS and MFS. To put our results into
perspective, we consider relevant timescales that need to be compared with the rotational
timescale (Paper I; Paper II).
4.1.1
The Model
Since we are interested in quantifying the effects of rotation in the system, we consider
in this section the simplest case of an isothermal stratification. This allows for the
comparison with and the use of previous results (e.g. Brandenburg et al., 2012a; Kemel
et al., 2012b). In this setup we use an isothermal equation of state, so the sound speed cs
is constant and the gas pressure is given by p = ρc2s . We use the MHD equations described
in Chapter 1 and Section 3.3, but we include the Coriolis force in the momentum equation:
∂U
= ... − 2Ω × U
∂t
(in DNS, Paper II)
(4.1)
∂U
= ... − 2Ω × U
∂t
(in MFS, Paper I).
(4.2)
or
31
32
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
The angular velocity vector Ω is quantified by its scalar amplitude Ω and colatitude θ,
such that
Ω = Ω (− sin θ, 0, cos θ) .
(4.3)
In our Cartesian model, the z coordinate corresponds to radius, x to colatitude, and y to
azimuth.
We use the solar angular velocity measurements from helioseismology to see how the
effect of the Coriolis force on the turbulence varies throughout the solar convection zone.
Helioseismology provides the angular velocity versus depth, latitude and time, giving the
characteristic solar differential rotation shown in Figure 4.1 (time averaged). This implies
an angular velocity range in the Sun from around 2.8 × 10−6 s−1 at the equator at a depth
of 0.91R to around 2.3 × 10−6 s−1 at 60◦ latitude and near the surface.
Figure 4.1: Internal rotation of the Sun. Comparison of data from GONG
and MDI. In the right panel, black denotes GONG data, red denotes MDI
data. The rotation profile is the result of the inversion of helioseismological
data. Taken from R. Howe, National Solar Observatory, Tucson; more at
http://nsokp.nso.edu/ (image added 2003-09-12)
It is important to note the drop of angular velocity in the near-surface shear layer
(NSSL). The different angular velocities spanned within this layer have certain surface
manifestations. We measure different velocities using the Doppler effect and when tracking surface features. The Doppler technique measures the velocity at the slower surface
layer; whereas sunspots rotate faster, therefore they may be rooted at a faster-rotating
layer deeper down (Howe, 2009).
Instead of using the dimensional angular velocity, it can be useful to express the rota-
4.1. EFFECTS OF ROTATION
33
104
Figure 4.2: Turnover time τ versus depth
computed from the solar interior model of
Spruit (1974).
103
τ (h)
102
101
100
10-1
10-2103
102
101 100
z (Mm)
10-1 10-2
tional dependence in terms of the local turnover time as a position-dependent Coriolis
number, Co. To understand its definition and meaning, we describe first the turnover
time and its depth dependence.
Turnover time τ : The turnover time is a characteristic timescale of the system. Its
value depends on the system scale and the relevant velocities we are interested in.
In a convective medium, the convective turnover time τc is a dynamical timescale of
a flow parcel of the turbulent eddies moving over a correlation length. It represents
therefore a small-scale characteristic of the system, which depends on the typical velocity
and length scales of the convective eddies:
τc =
1
lc
≈
,
vc
urms kf
(4.4)
where we have not included a 2π factor in the relation between lc and kf . In the deeper
layers of the convection zone, the turnover time can range between a week and a month
(Schrijver and Zwaan, 2000).
Figure 4.2 shows the τ dependence with depth, computed from a solar convection model
of Spruit (1974). It uses mixing length theory and tries to match an empirical model for
the solar atmosphere with an interior model. In the Sun, τ cannot be measured directly,
it depends strongly on the solar convection model used. For example, Landin et al. (2010)
compares for different models the value of τ at a distance of one-half the mixing length
above the bottom of the convection zone, for different models and shows that it can vary
by up to 150% due to details in the convection model around 50% due to the inclusion
of rotation and another 70% due to the upper boundary atmosphere chosen (gray or
non-gray).
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
102
Figure 4.3: Coriolis number versus depth. τ is computed from
the mixing length model of Spruit
(1974) (also shown in the figure)
and Ω is computed from a simple
expansion of the form
5/2
where the C2
polynomial:
3/2
C2 (cos θ) = −
is the Gegenbauer
101
103
100
102
10-1
101
10-2
100
3
P31 (cos θ)
10-3 =
5 cos2 θ − 1 ,
sin θ
2
and ωn (r) are fits to the helioseismic observations.
104
τ
Co
5/2
Ω(r, θ) = ω0 (r) − ω2 (r)C2 (cos θ),
0◦
30 ◦
60 ◦
90 ◦
τ (h)
34
10-4
10-1
0.8
r/R ¯
0.9
10-2
In the solar convection zone, we can also define another timescale due to turbulent
resistive processes, which measures the typical time of decay of a magnetic field in the
domain:
1
.
(4.5)
τd =
ηt k12
This timescale is now associated a large scale characteristic time of the system.
We will see that yet another timescale arises in the study of the effects of rotation on
NEMPI:
1
τNEMPI =
,
(4.6)
λ∗0
where λ∗0 ≡ β? urms /Hρ represents the theoretical growth rate of structures in the presence
of rotation, and we remind that β? is a non-dimensional parameter of the order of unity
associated with NEMPI (Section 3.3.3). It turns out that NEMPI is suppressed when
2Ω > λ∗0 (Paper I). Since τc < λ−1
∗0 < τ , this is an intermediate time scale in the system.
Coriolis number Co
Co: Co is a non-dimensional parameter that measures the relative
importance of rotation and convection:
Co = 2Ωτc =
2Ω
.
urms kf
(4.7)
Using kf = urms /3ηt and the parameter CΩ = Ω/ηt k12 , which is often used in mean-field
dynamo theory, Co can also be expressed as
Co = 6ηt Ω/u2rms = 6 (ηt k1 /urms )2 CΩ .
(4.8)
4.1. EFFECTS OF ROTATION
35
In the Sun, Co has a strong radial dependence, varying from 10−4 at the surface to 10 at
the bottom of the convection zone.
A radial dependence of Co is shown in Figure 4.3. The values of the Coriolis number are
computed using the model of Figure 4.2 and a simple model for the angular velocity, where
the solar like profile arises from the superposition of contributions from the tachocline, a
small positive differential rotation throughout the convection zone and a sharp negative
contribution in the near surface layer. One should notice here that the angular velocity
throughout the solar interior varies by 30%, whereas the corresponding turnover time
varies by more than four orders of magnitude. This implies that Co will be much more
sensitive to the variation of the turnover time than to the Sun’s differential rotation. In
fact, Figure 4.3 shows that the change in the angular velocity between different latitudes
is unimportant for Co, but it shows a strong similarity with the turnover time profile,
specially if we show it in the same depth units, see the solid line in Figure 4.3.
Mean field parameters: As mean field parameters for Equation (3.19) we primarily
use qp0 = 20 and βp = 0.167, which corresponds to β? = 0.75.
We computed the actual best-fit values of these parameters in Paper II, and arrived at
the conclusion that they might be not accurate enough, see Sections 4.1.2.1 and 4.2.3.1,
but NEMPI develops even for this set of parameters and their use allows us a direct comparison with the results of Kemel et al. (2013b). Moreover the results seem independent
of the set of parameters chosen, see Figure 4.4.
4.1.2
Numerical results
4.1.2.1
Effective magnetic pressure
Using DNS, we can compute directly the effective magnetic pressure, Peff (β), and hence
qp (β) in the system (see Section 3.3.2.) We have checked that Peff (β) is indeed negative
and independent of Co in the range considered. We also computed the best fit parameters
for the MFS coefficients, which turn out to be β? = 0.44 and βp = 0.058, and therefore
qp0 = 57, see Figure 1 in Paper II.
However, in Paper I we use a different set of parameters: qp0 = 20 and βp = 0.167
(corresponding to β? = 0.75), hereafter MFS(i), based on a fit by Kemel et al. (2013b)
and compare with the set qp0 = 32 and βp = 0.058 (corresponding to β? = 0.33), hereafter
MFS(ii), based on the results by Brandenburg et al. (2012a). Despite these different sets of
parameters, the fact that an increase of β? deepens the minimum of Peff and increases the
growth rate of the resulting structure (Brandenburg et al., 2014), the effects of rotation
on the growth rate are the same in all the cases, see Figure 4.4. Therefore, we can
conclude that, qualitatively, the response of NEMPI to rotation is independent of the set
of parameters chosen as long as the instability develops.
36
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
Figure 4.4: Dependence of λ/λ∗0 on 2Ω/λ∗0 for DNS (red dashed line), compared with
MFS (i) where qp0 = 20 and βp = 0.167 (black solid line), and MFS (ii) where qp0 = 32
and βp = 0.058 (blue dash-dotted line). In this case no growth was found for Co ≥ 0.03.
In all cases we have B0 /Beq0 = 0.05 (Paper II).
4.1.2.2
Co dependence
Surprisingly, we find that, both in DNS and MFS, NEMPI gets strongly suppressed even
with slow rotation at values of Co around 0.014, see Figure 4.4. Applied to the Sun with
Ω ≈ 2 × 10−6 s−1 , we find for the corresponding correlation time τ = 2 h. This suggests
that NEMPI can explain the generation of structures only if they are confined to the
uppermost layers. Basically, Figures 4.3 and 4.4 constrain the depth where NEMPI can
develop. In the case of the Sun, this corresponds to the NSSL.
The suppression of NEMPI is similar in both types of simulations and for different
sets of MFS parameters until a Coriolis number of about 0.13, where we see a recovering
in the growth rate for the DNS. First of all, at this point it is important to note the
high degree of predictive power of the much less expensive MFS, provided we include the
physics relevant to the problem. Secondly, we show that testing the results with DNS
is important, since we can be missing some of the crucial aspects of the problem. In
this case, we link the recovery of the instability for large enough Co to the onset of the
dynamo, as we discuss further in Section 4.1.2.6.
We emphasize that the value of the turnover time and the NEMPI structures developed
in the simulations are very sensitive to the value of Co. Therefore, they have a strong
dependence on the size of the turbulent eddies, see Equation (4.4).
4.1. EFFECTS OF ROTATION
4.1.2.3
37
θ dependence
The study of the θ dependence was done in MFS. The colatitude is included in the
definition of the angular velocity vector, and since gravity and rotation are important,
the dot product g · Ω might change the growth rate of the instability according to the
value of θ:
)
Ω = Ω (− sin θ, 0, cos θ)
Ω · g = −gΩ cos θ.
(4.9)
g = (0, 0, −g) ,
However, g · Ω changes sign about the equator, but the growth rate is independent of the
hemisphere. Therefore, the growth rate depends only on (g · Ω)2 . A detailed calculation
presented in Paper I shows that the growth rate increases when (g · Ω)2 increases. Thus,
a larger growth rate is expected at the poles and NEMPI is strongly suppressed at the
equator, see Figure 4.5, where we perform MFS for different values of colatitude, θ.
We note a similar behaviour between 2D and 3D MFS simulations, although the growth
rate in the 2D case is about twice smaller than in the 3D counterpart. This is true even in
the absence of rotation. Thus, this difference in the growth rate represents a 3D feature
on the solution, as we can see in the next section.
Figure 4.5: Dependence of λ/λ∗0
on θ for two values of 2Ω/λ∗0 in
2-D (upper panel) and comparison of 2-D and 3-D cases (lower
panel) (MFS, paper I).
4.1.2.4
Spatial structure
Figures 4.6 and 4.7 show the spatial structure of the simulations in the MFS and DNS.
The MFS show a dependence on y (expanding to the azimuthal direction) that changes
with the colatitude. The structure shifts by 90◦ at the south pole, see Figure 4.6. By
contrast, this dependence is totally absent in the DNS, see Figure 4.7, right-most panel.
38
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
Figure 4.6: Visualization of By on the periphery of the computational domain during
the nonlinear stage of the instability for θ = 0◦ (corresponding to the north pole) and
Co = 0.03 (left figure) and Co = −0.03 (Paper I).
Figure 4.7: Visualization of By on the periphery of the computational domain for θ = 0◦
and Co = 0.03 in MFS (i) (qp0 = 20, βp = 0.167)(left figure), MFS(ii) (qp0 = 32,
βp = 0.058) (center) and DNS (right figure) (Paper II).
Also, the DNS structures are much more confined to the uppermost layers with increasing Coriolis number. These differences in the structures might be related to the neglect
of additional mean-field transport coefficients (qs , qg , qa ), although they were previously
shown to have a very small contribution (Brandenburg et al., 2012a; Käpylä et al., 2012).
In these simulations, we are just including qp , ηt , and νt in the mean-field equations.
However, the agreement between DNS and MFS is still remarkably good.
4.1.2.5
Dynamics
Dynamically, we find the typical “potato-sack” structure of previous papers (Brandenburg
et al., 2011, 2012a; Kemel et al., 2012b,a): the magnetic field gets concentrated and sinks,
since the effective magnetic pressure is negative so magnetic structures are negatively
buoyant and sink. However, this effect is less prominent in DNS as the Coriolis number
increases.
Besides, in MFS we found two structures in the computational domain that begin to
4.2. EFFECTS OF STRATIFICATION
39
Figure 4.8: Visualization of By on the periphery of the computational domain for four
times (normalized in terms of Tη ) during the nonlinear stage of the instability for θ = 90◦
(corresponding to the equator) and Co = 0.013, corresponding to 2Ω/λ∗0 ≈ 0.5 (Paper I).
oscillate in the saturated regime. At angles θ 6= 0, we note a slow migration of the
magnetic pattern to the left and for θ = 90◦ (equator) the magnetic pattern shows a
prograde motion, see Figure 4.8.
4.1.2.6
Interaction with the dynamo
Since we have rotation and stratification in the simulation, we expect to find kinetic
helicity and the onset of dynamo for high enough Coriolis number.
Actually, in these MFS a dynamo is not possible, since we have not included the
necessary ingredients, but in DNS we note the recovery of the growth rate at around
Co = 0.13 and we argue that this is a growth rate corresponding to the coupled system
consisting of NEMPI-dynamo instability (Jabbari et al., 2014).
Indeed, in our system the threshold of the dynamo instability is reached at the largest
Coriolis number, see Figure 4.9. However, it is important to note that the recovery of
the growth starts before a dynamo without NEMPI could be possible.
This idea is further studied in Jabbari et al. (2014), where we confirm the onset of a
dynamo with a Beltrami-like magnetic field and relax the constraints on the maximum
value of Co where NEMPI can still form till Co ≈ 0.1, which corresponds to τ = 5 h.
4.2
Effects of stratification
Despite the relative success of previous NEMPI studies in forming magnetic flux concentrations, in order to apply this theory to the Sun, we need to implement more realistic
setups. For this purpose, we study the effects of a polytropic stratification on NEMPI
(Paper III).
The density scale height, Hρ , is constant in an isothermal stratification, i.e., the density
variation is uniformly distributed over the entire domain depth. On the other hand, in
40
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
Figure 4.9: Relative kinetic helicity spectrum as a function of Gr Co for Gr = 0.03 with
Co = 0.03, 0.06, 0.13, 0.49, and 0.66 (red and blue symbols) compared with results from
earlier simulations of Brandenburg et al. (2012b) for Gr = 0.16 (small dots connected by
a dotted line). The solid line corresponds to f = 2Gr Co. The two horizontal dash-dotted
lines indicate the values of ∗f ≡ k1 /kf for which dynamo action is possible for kf /k1 = 5
and 30. Runs without an imposed field (blue filled symbols) demonstrate dynamo action
in two cases. The blue open symbol denotes a case where the dynamo is close to marginal
(Paper II).
a polytropic stratification, Hρ has a minimum in the upper layers, so the stratification is
very high in these layers and decreases sharply towards the bottom of the domain.
Stratification is essential in triggering NEMPI, since a fundamental requirement is
that the density scale height must be much smaller than the scale of the system, L
(Hρ L). Therefore, including a polytropic stratification might have dramatic impacts
on the instability development.
Previous MFS studies have already shown already the effects of an isentropic stratification, with an isothermal equation of state with constant sound speed cs (Brandenburg
et al., 2010). However, while their DNS studies showed signs of negative contributions to
the effective magnetic pressure, they could not find the onset of the instability, probably
because of insufficient scale separation. In turbulent convection, this is a parameter that
is very difficult to control with turbulent convection (Käpylä et al., 2012).
4.2. EFFECTS OF STRATIFICATION
4.2.1
41
Brief notes about thermodynamics
We would like to remind the reader of some basic thermodynamic1 equations relevant for
the further discussion in this chapter. The equations and definitions are adapted from
Chandrasekhar (1939) and Fitzpatrick (2006).
4.2.1.1
Ideal gas equation of state
An ideal gas is the simplest theoretical approximation to a real gas, governed by the
following equation of state:2
P V = nRT ,
(4.10)
where P is the pressure, V is the volume, n is the amount of substance (measured in
moles), R is the gas constant, and T is the temperature.
However, Equation (4.10) is not well defined in the case of the Sun. How can we define
the volume there? Volume of the entire Sun? Of the convection zone? So, in general,
instead of expressing the ideal gas equation of state in units of volume, we use density:
P =
R
ρT ,
µ
(4.11)
where µ is the molar mass.
4.2.1.2
Gas laws
We can consider the expansion of the ideal gas under constant temperature (isothermal
expansion) or without exchange of heat (adiabatic expansion).
Isothermal expansion: If the temperature of the gas is kept constant during the
expansion, from the ideal gas equation of state, we can derive the isothermal gas law:
P V = const .
(4.12)
Adiabatic expansion: If the system is insulated, i.e., there is no flow of energy in or
out of the system, the process takes place under constant heat conditions and we can
derive the adiabatic gas law:
P V γ = constant .
(4.13)
1
How heating and temperature affect physical processes.
An equation of state is a relation between thermodynamical variables, such as pressure, temperature,
volume or density; assuming that there are no independent quantities. In general: f (p, V, T ) = 0
2
42
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
Here, γ = cp /cv is the ratio of specifics heats at constant pressure, cp , and constant
volume, cv . It is also useful to write this expression in terms of pressure and temperature:
P 1−γ T γ = constant .
4.2.1.3
(4.14)
Stratification of the atmosphere
The equation of hydrostatic equilibrium for an atmosphere describes how pressure (or
density) changes with height in the absence of net movement of the gas:
dp
= −ρg .
dz
(4.15)
We can combine this equation with the ideal gas equation of state (Equation (4.10)), and
write this variation of pressure with height in the form:
µg
dp
=−
dz
p
RT
(4.16)
Isothermal atmosphere: In this case, we assume that the temperature is uniform,
then the solution of Equation (4.15) is simply:
z
p = p0 exp −
(4.17)
z0
is the isothermal scale height of the atmosphere. Thus the pressure varies
where z0 = RT
µg
exponentially with height. Since the density is proportional to the pressure ρ ∝ p/T , its
variation is also exponential with height:
z
ρ = ρ0 exp −
.
(4.18)
z0
Adiabatic atmosphere (polytropic stratification): Now, the specific heat is uniform throughout the atmosphere. Since P 1−γ T γ = const, we can use the hydrostatic
equilibrium equation (Equation (4.16)), to see that the temperature is proportional to
the height:
dP
γ
dT
γ − 1µg
=
→
=
.
(4.19)
P
γ−1
T
γ R
Therefore, the variation of temperature is proportional to the height, T ∝ z. Using the
adiabatic gas law (Equation (4.14)), we also see that the pressure and the density are
4.2. EFFECTS OF STRATIFICATION
43
proportional to the temperature:
P ∝ T n+1 ,
ρ ∝ T n.
(4.20)
(4.21)
Where n = 1/(γ −1). Now, the dependence of the density and pressure with height is very
different than in the isothermal case. Instead of the isothermal exponential dependence,
we have now a power law. So in the cases where z → 0, the temperature will drop to
zero, and thus the density and the pressure. This atmosphere presents a sharp boundary
for the thermodynamic variables, as can be seen in Figure 4.10.
In terms of the speed of the process, an isothermal change must be slow to keep the
temperature constant and an adiabatic process must be very rapid to avoid flows of
energy.
4.2.2
The model of polytropic stratification
We will now solve the MHD equations in the case of an isentropic atmosphere (the
entropy is held constant, so we do not need to solve the entropy equation) and the two
different stratifications described in the previous section. The solar convection zone is
nearly isentropic, mixing any entropy inhomogeneities, so for the purpose of studying the
effects of different stratification on NEMPI, we consider this a good approximation. Also,
this simplification was already used in the model described in Brandenburg et al. (2010),
where the DNS uses isothermal stratification and the MFS and adiabatic one.
In the previous section we showed that the isothermal and adiabatic atmospheres have
a very different change of density with height. In particular, there is a priori no obvious way of going from an isothermal atmosphere to an adiabatic one in a continuous
fashion. Therefore, instead of these usual stratification equations, we will use a generalized exponential function that allows us to show the variation in density of the different
atmospheres in a continuous way, see Figure 4.11.
Using the generalized “q-exponential”, the density stratification is now given by:
1/(γ−1) n
z
z
ρ
= 1 + (γ − 1) −
= 1−
,
ρ0
Hρ0
nHρ0
(4.22)
and the density scale height is:
Hρ (z) = Hρ0 − (γ − 1)z = Hρ0 − z/n ,
(4.23)
allowing the change between different stratification to be a continuous one. Here Hρ0
is the density scale height at some reference position, which we chose to be z = 0, so
Hρ0 = Hρ (z = 0). In an isentropic stratification, the density scale height is give by
Hρ = c2s /g.
44
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
Figure 4.10: Isothermal and polytropic relations for different values of γ using ρ ∝
Figure 4.11: ρ and Hρ from poly(z∞ − z)n with n = 1/(γ − 1).
tropes computed as q-exponentials
(Paper III).
Actually, with this model we are choosing an arbitrary z = 0, such that the scale
height is the same at this reference point, but the top of the polytropic layer shifts with
different polytropic index, i.e. z∞ = nHρ0 = Hρ0 /(γ − 1). Whereas in the usual model,
z∞ is chosen such that ρ = ρ0 and cs = cs0 at z = zref , which implies z∞ = zref in the
cs
in the polytropic one. Now, the total
isothermal case, while z∞ = zref + (m + 1) γ(−g
z)
density contrast is similar in the different cases chosen, but the vertical density gradient
increases in the upper layers with the increase of γ.
4.2.3
Numerical results
We will solve the MHD equations for different kinds of stratification (depending on the
parameter γ) in DNS and MFS. We will also use a horizontal and a vertical initially
imposed field B0 .
4.2.3.1
Effective magnetic pressure
Also in this case we use DNS to compute the value of the effective magnetic pressure and
MFS parameters. We study different values of the polytropic index and the two types of
imposed field. The results are plotted in Figures 4.12 and 4.13.
Similar to Paper II, the values of the mean-field parameters, qp ,βp and β? , depend also
on the stratification and on the initially imposed field. Peff becomes much more negative
for a vertical field and for γ = 5/3, where qp0 is smaller and βp larger. On the other hand,
the variation of β? is small in all cases, so we expect that the growth rate is similar in the
4.2. EFFECTS OF STRATIFICATION
Figure 4.12: Effective magnetic pressure obtained
from DNS in a polytropic layer with different γ
for horizontal (H, red curves) and vertical (V, blue
curves) mean magnetic fields (Paper III)
45
Figure 4.13: Parameters
qp0 , βp , and β? vs. γ for
horizontal (red line) and
vertical (blue line) fields
(Paper III)
different cases. To address this different range of parameters, we will solve the MFS for
two models, chosen such as to represent a strong (large β? ) and weak (small β? ) effect of
NEMPI:
• Model I (weak): β? = 0.33, qp = 32 and βp = 0.058,
• Model II (strong): β? = 0.63, qp = 9 and βp = 0.021.
As we will see, both models result in NEMPI and the overall results are similar, even
though qp and βp appear to be rather different.
4.2.3.2
Structures
The DNS and MFS show the growth of structures both for horizontal and vertical initially
imposed fields and for different polytropic indexes. While in the case of horizontal field
the structures sink after saturation (referred to as “potato-sack effect” owing to rapid
downward sinking of gas), in the case of vertical fields these structures no longer sink
and are therefore able to lead to a greater growth rate. As we see in Figure 4.14, nice
spot-like structures can be produced near the surface. The magnetic field lines tend to
concentrate at the surface and broaden out in deeper layers.
The stratification decreases with depth faster in the case of a polytropic atmosphere in
such a way that the instability cannot operate any further. This is because the stratification becomes so small that NEMPI cannot be excited. Therefore, in the case of polytropic
stratification, the structures are more confined to the upper layers of the simulations. We
46
CHAPTER 4. ROTATION AND STRATIFICATION ON NEMPI
Figure 4.14: Cuts of Bz /Beq (z) in (a) the xy plane at the top boundary (z/Hρ0 = 1.2)
and (b) the xz plane through the middle of the spot at y = 0 for γ = 5/3 and β0 = 0.05.
In the xz cut, we also show magnetic field lines and flow vectors obtained by numerically
averaging in azimuth around the spot axis (Paper III).
can see this by comparing the DNS results shown in Figure 3 of Brandenburg et al. (2013)
with Figure 4.14: in our case the depth of the structure is less than 3Hρ0 , whereas in the
former one it extends over more than 4Hρ0 .
4.2.3.3
Dynamics
Two-dimensional MFS have displayed tremendous surface dynamics of the generated
magnetic structures. Generally, and in the case of polytropic stratification, smaller structures tend to merge into bigger ones, as can be seen in Figure 4.15. The bigger the
structure, the stronger are the downflows generated in the center of the structure.
The instability is excited at some depth near the surface, and starts sucking material.
This triggers an overall movement of the flow towards the point of decreased magnetic
pressure. This flow drags the magnetic field lines with it and increase the gas pressure,
generating the final flux concentration. The movement can be clearly seen in Figure 4.15,
where the vector field traces velocities.
Although the different setups vary, the specific properties of the final flux concentration, such as horizontal extend, maximum value of the magnetic field and depth extension
remain similar in all cases. We confirm that the instability survive the change of stratification, imposed field direction and even the addition of rotation. It is clear that all the
simulation results shown here display strong field concentrations just at the surface of
the computational domain. In reality, the magnetic fields continue into the gas above the
photosphere, which is ignored in the present simulations. This has now been included
in subsequent simulations together with J. Warnecke and collaborators (Warnecke et al.,
2013), which is however beyond the scope of the present thesis.
4.2. EFFECTS OF STRATIFICATION
47
Figure 4.15: Merging of two smaller flux concentrations into a larger one, as shown by
Bz /Beq (z) in the xz plane for γ = 5/3 and β0 = 0.02. The arrows represent the velocity
field.
5
Past, present and future
“Th-th-th-that’s all folks!””
Porky Pig
The present thesis was focused on the effects of rotation and stratification on the
formation of magnetic flux concentrations. In the beginning of our work, we expected
that rotation might lead to a migration of magnetic fields, which turned out to be indeed
the case, but more important is actually a remarkably strong effect on the survival of
the instability altogether. Indeed, the present work has shown for the first time that the
negative effective magnetic pressure instability can only operate in the top-most layers
of the Sun, where the local turnover time is shorter than a day or perhaps just several
hours. This was a big surprise to us, but it now reinforces our idea that alternative
theories for the formation of active regions and perhaps sunspots might be connected
with the remarkable properties of strongly stratified hydromagnetic turbulence.
In the Sun, the surface layers are characterized by a remarkable drop in temperature.
Since the pressure and density scale heights are proportional to the temperature, this
means that the assumption of an isothermal stratification becomes poor. However, Paper III of this thesis now shows that much of our earlier understanding from isothermal
models carries over to the more complicated case of a polytropic stratification, provided
one applies these ideas locally. Eventually, however, the scale height becomes so short
that it is below the scale of the generated magnetic structures. This is when the local
approximation becomes questionable. However, the basic conclusion that the structures
are forced to become smaller near the surface is indeed borne out by the simulations
presented in Paper III.
In future work, I plan to focus on the effects of an outer corona, especially in the presence
of rotation. Some of this work is already in progress and shows that the presence of such a
layer is important in making the resulting magnetic flux concentrations more pronounced
and thus more easily detectable.
49
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Paper I
57
❆✫❆ ✺ ✁✂ ❆ ✾ ✭✷✄☎✷✆
❉✝✞✟ ☎✄✶☎✄✺☎✴✄✄✄ ✵✠✡✠☎✴✷✄☎✷✷✄✄☛✁
❝ ❊❙❖ ✌✍✎✌
☞
✏✑✒✓♦✔♦✕②
✖
✏✑✒✓♦✗✘②✑✙✚✑
❘✛✜✢✜✣✛✤✢✥ ❡❢❢❡✦✜✧ ✛✤ ✜❤❡ ✤❡♥✢✜✣★❡ ♠✢♥✤❡✜✣✦ ♣r❡✧✧✩r❡ ✣✤✧✜✢✐✣✥✣✜✪
■✬ ✮✬ ▲✯s✰✱✰✲✳✸ ✹ ✻✬ ❇✼✰✽✱✿✽❀✉✼❣❁✳❂ ✹ ◆✬ ❑❧✿✿✯✼❃✽❄✳❁ ✹ ❅✬ ▼❃❈✼✰❁ ✹ ✰✽✱ ■✬ ✮✯❣✰❋●✿✈s❍❃❃❄✳❁
❏ P◗❚❯❱t❲◗❳t ❨❩ ❬❭t❱❨❚❪❫❭❴❝❭❵ ❛❳❴❜◗❱❭❴❞❯❞ ❞◗ ❥❯ ❥❯❦q❳❯❵ ✇①✌✍③ ❥❯ ❥❯❦q❳❯ ④⑤◗❳◗❱❴❩◗⑥❵ ❙❚❯❴❳
◗⑦❲❯❴⑧⑨ ⑩❶❶❷❸❹⑩❺❻❹❼❸❶❼❽❷❾❷❿➀➁❷⑩❶❸➂❼➁
➃ ➄❳❭t❴tqt❨ ❞◗ ❬❭t❱❨❩í❭❴❝❯ ❞◗ ➅❯❳❯❱❴❯❭❵ ➅➆ ➇í❯ ❥á❝t◗❯❵ ❭➆❳❵ ❥❯ ❥❯❦q❳❯❵ ⑤◗❳◗❱❴❩◗❵ ❙❚❯❴❳
➈ ➉❨❱❞❴t❯❵ ➊❨❫❯⑧ ➄❳❭t❴tqt◗ ❨❩ ⑤◗❝❪❳❨⑧❨❦❫ ❯❳❞ ❙t❨❝➋❪❨⑧❲ ❛❳❴❜◗❱❭❴t❫❵ ➊❨❭⑧❯❦❭tq⑧⑧❭➌❯❝➋◗❳ ✌✇❵ ✎✍③➍✎ ❙t❨❝➋❪❨⑧❲❵ ❙➎◗❞◗❳
➏ P◗❚❯❱t❲◗❳t ❨❩ ❬❭t❱❨❳❨❲❫❵ ❬⑧➌❯➉❨❜❯ ❛❳❴❜◗❱❭❴t❫ ➅◗❳t◗❱❵ ❙t❨❝➋❪❨⑧❲ ❛❳❴❜◗❱❭❴t❫❵ ✎✍③➍✎ ❙t❨❝➋❪❨⑧❲❵ ❙➎◗❞◗❳
➐ P◗❚❯❱t❲◗❳t ❨❩ ➑◗❝❪❯❳❴❝❯⑧ ❊❳❦❴❳◗◗❱❴❳❦❵ ➒◗❳⑦➓q❱❴❨❳ ❛❳❴❜◗❱❭❴t❫ ❨❩ t❪◗ ➉◗❦◗❜❵ ➔❖➒ ③→✇❵ ①➣✎✍→ ➒◗◗❱⑦❙❪◗❜❯❵ ➄❭❱❯◗⑧
➊◗❝◗❴❜◗❞ ✌✇ ↔q⑧❫ ✌✍✎✌ ➆ ❬❝❝◗❚t◗❞ ✌✎ ❙◗❚t◗❲➌◗❱ ✌✍✎✌
↕➙➛➜➝↕➞➜
➟➠➡➢➤➥➢➦ ⑤❪◗ ❭q❱❩❯❝◗ ⑧❯❫◗❱❭ ❨❩ t❪◗ ❙q❳ ❯❱◗ ❭t❱❨❳❦⑧❫ ❭t❱❯t❴➧◗❞➨ ➄❳ t❪◗ ❚❱◗❭◗❳❝◗ ❨❩ tq❱➌q⑧◗❳❝◗ ➎❴t❪ ❯ ➎◗❯➋ ❲◗❯❳ ❲❯❦❳◗t❴❝ ➧◗⑧❞❵ ❯ ⑧❯❱❦◗⑦
❭❝❯⑧◗ ❴❳❭t❯➌❴⑧❴t❫ ❱◗❭q⑧t❴❳❦ ❴❳ t❪◗ ❩❨❱❲❯t❴❨❳ ❨❩ ❳❨❳q❳❴❩❨❱❲ ❲❯❦❳◗t❴❝ ❭t❱q❝tq❱◗❭❵ ❝❯❳ ➌◗ ◗➩❝❴t◗❞ ❨❳ t❪◗ ❭❝❯⑧◗ ❨❩ ❲❯❳❫ ④❲❨❱◗ t❪❯❳ t◗❳⑥
tq❱➌q⑧◗❳t ◗❞❞❴◗❭ ④❨❱ ❝❨❳❜◗❝t❴❨❳ ❝◗⑧⑧❭⑥➨ ⑤❪❴❭ ❴❳❭t❯➌❴⑧❴t❫ ❴❭ ❝❯q❭◗❞ ➌❫ ❯ ❳◗❦❯t❴❜◗ ❝❨❳t❱❴➌qt❴❨❳ ❨❩ tq❱➌q⑧◗❳❝◗ t❨ t❪◗ ◗➫◗❝t❴❜◗ ④❲◗❯❳⑦➧◗⑧❞⑥
❲❯❦❳◗t❴❝ ❚❱◗❭❭q❱◗ ❯❳❞ ❪❯❭ ❚❱◗❜❴❨q❭⑧❫ ➌◗◗❳ ❞❴❭❝q❭❭◗❞ ❴❳ ❝❨❳❳◗❝t❴❨❳ ➎❴t❪ t❪◗ ❩❨❱❲❯t❴❨❳ ❨❩ ❯❝t❴❜◗ ❱◗❦❴❨❳❭➨
➭➯➲➳➦ ➵◗ ➎❯❳t t❨ q❳❞◗❱❭t❯❳❞ t❪◗ ◗➫◗❝t❭ ❨❩ ❱❨t❯t❴❨❳ ❨❳ t❪❴❭ ❴❳❭t❯➌❴⑧❴t❫ ❴❳ ➌❨t❪ t➎❨ ❯❳❞ t❪❱◗◗ ❞❴❲◗❳❭❴❨❳❭➨
➸➤➢➺➠➻➳➦ ➵◗ q❭◗ ❲◗❯❳⑦➧◗⑧❞ ❲❯❦❳◗t❨❪❫❞❱❨❞❫❳❯❲❴❝❭ ❴❳ ❯ ❚❯❱❯❲◗t◗❱ ❱◗❦❴❲◗ ❴❳ ➎❪❴❝❪ t❪◗ ❚❱❨❚◗❱t❴◗❭ ❨❩ t❪◗ ❳◗❦❯t❴❜◗ ◗➫◗❝t❴❜◗ ❲❯❦❳◗t❴❝
❚❱◗❭❭q❱◗ ❴❳❭t❯➌❴⑧❴t❫ ❪❯❜◗ ❚❱◗❜❴❨q❭⑧❫ ➌◗◗❳ ❩❨q❳❞ t❨ ❯❦❱◗◗ ➎❴t❪ ❚❱❨❚◗❱t❴◗❭ ❨❩ ❞❴❱◗❝t ❳q❲◗❱❴❝❯⑧ ❭❴❲q⑧❯t❴❨❳❭➨
➼➤➳➽➾➢➳➦ ➵◗ ➧❳❞ t❪❯t t❪◗ ❴❳❭t❯➌❴⑧❴t❫ ❴❭ ❯⑧❱◗❯❞❫ ❭q❚❚❱◗❭❭◗❞ ❩❨❱ ❱◗⑧❯t❴❜◗⑧❫ ❭⑧❨➎ ❱❨t❯t❴❨❳ ➎❴t❪ ➅❨❱❴❨⑧❴❭ ❳q❲➌◗❱❭ ④❴➨◗➨ ❴❳❜◗❱❭◗ ➊❨❭❭➌❫
❳q❲➌◗❱❭⑥ ❯❱❨q❳❞ ✍➨✌➨ ⑤❪◗ ❭q❚❚❱◗❭❭❴❨❳ ❴❭ ❭t❱❨❳❦◗❭t ❯t t❪◗ ◗➚q❯t❨❱➨ ➄❳ t❪◗ ❳❨❳⑧❴❳◗❯❱ ❱◗❦❴❲◗❵ ➎◗ ➧❳❞ t❱❯❜◗⑧❴❳❦ ➎❯❜◗ ❭❨⑧qt❴❨❳❭ ➎❴t❪
❚❱❨❚❯❦❯t❴❨❳ ❴❳ t❪◗ ❚❱❨❦❱❯❞◗ ❞❴❱◗❝t❴❨❳ ❯t t❪◗ ◗➚q❯t❨❱ ➎❴t❪ ❯❞❞❴t❴❨❳❯⑧ ❚❨⑧◗➎❯❱❞ ❲❴❦❱❯t❴❨❳ ❯➎❯❫ ❩❱❨❲ t❪◗ ◗➚q❯t❨❱➨
➟➠➡➪➾➽➳➯➠➡➳➦ ➵◗ ❭❚◗❝q⑧❯t◗ t❪❯t t❪◗ ❚❱❨❦❱❯❞◗ ❱❨t❯t❴❨❳ ❨❩ t❪◗ ❲❯❦❳◗t❴❝ ❚❯tt◗❱❳ ❳◗❯❱ t❪◗ ◗➚q❯t❨❱ ❲❴❦❪t ➌◗ ❯ ❚❨❭❭❴➌⑧◗ ◗➩❚⑧❯❳❯t❴❨❳ ❩❨❱
t❪◗ ❩❯❭t◗❱ ❱❨t❯t❴❨❳ ❭❚◗◗❞ ❨❩ ❲❯❦❳◗t❴❝ t❱❯❝◗❱❭ ❱◗⑧❯t❴❜◗ t❨ t❪◗ ❚⑧❯❭❲❯ ❜◗⑧❨❝❴t❫ ❨❳ t❪◗ ❙q❳➨ ➄❳ t❪◗ ➌q⑧➋ ❨❩ t❪◗ ❞❨❲❯❴❳❵ ➋❴❳◗t❴❝ ❯❳❞ ❝q❱❱◗❳t
❪◗⑧❴❝❴t❴◗❭ ❯❱◗ ❳◗❦❯t❴❜◗ ❴❳ t❪◗ ❳❨❱t❪◗❱❳ ❪◗❲❴❭❚❪◗❱◗ ❯❳❞ ❚❨❭❴t❴❜◗ ❴❳ t❪◗ ❭❨qt❪◗❱❳➨
➶➹➘ ➴➷➬➮➱✃ ❲❯❦❳◗t❨❪❫❞❱❨❞❫❳❯❲❴❝❭ ④➑❐P⑥ ❒ ❪❫❞❱❨❞❫❳❯❲❴❝❭ ❒ tq❱➌q⑧◗❳❝◗ ❒ ❞❫❳❯❲❨
❮❰ ÏÐÑÒÓÔÕÖÑ×ÓÐ
✞Ø ÙÚÛ ÜÝÙÛÞ ßàÞÙâ Üã ÙÚÛ äÝØ✂ ÛØÛÞåæ çâ ÙÞàØâßÜÞÙÛè ÙÚÞÜÝåÚ ÙÝÞéÝ✵
êÛØÙ ëÜØìÛëÙçÜØ✶ îÚÛ ÙÚÛÞïÜèæØàïçë àâßÛëÙâ Üã ÙÚçâ ßÞÜëÛââ àÞÛ
ðÛêê ÝØèÛÞâÙÜÜè ÙÚÞÜÝåÚ ïçñçØå êÛØåÙÚ ÙÚÛÜÞæ ✭òçÙÛØâÛ ☎✾✺✡✆✶
❆êâÜ ÞÛàâÜØàéêæ ðÛêê ÝØèÛÞâÙÜÜè çâ ÙÚÛ ßàÞÙçàê ëÜØìÛÞâçÜØ Üã óç✵
ØÛÙçë ÛØÛÞåæ çØÙÜ ïàåØÛÙçë ÛØÛÞåæ ìçà èæØàïÜ àëÙçÜØ ✭ôàÞóÛÞ
☎✾☛✾õ öÛêèÜìçëÚ ÛÙ àê✶ ☎✾✁✡✆✶ ÷ÜâÙ ÞÛïàÞóàéêÛ çâ ÙÚÛ ßÜââçéçêçÙæ
Üã åÛØÛÞàÙçØå ïàåØÛÙçë øÛêèâ ÜØ ïÝëÚ êàÞåÛÞ âßàÙçàê àØè ÙÛï✵
ßÜÞàê âëàêÛâ ÙÚàØ ÙÚÛ ëÚàÞàëÙÛÞçâÙçë ÙÝÞéÝêÛØëÛ âëàêÛâ✶ îÚçâ Úàâ
ØÜð éÛÛØ âÛÛØ çØ ïàØæ ÙÚÞÛÛ✵èçïÛØâçÜØàê ÙÝÞéÝêÛØëÛ âçïÝêà✵
ÙçÜØâ ✭ùÞàØèÛØéÝÞå ✷✄✄☎õ ùÞàØèÛØéÝÞå ✫ äÝéÞàïàØçàØ ✷✄✄✺✆✂
éÝÙ ÙÚÛ ßÚæâçëâ Üã ÙÚçâ çâ éÛâÙ ÝØèÛÞâÙÜÜè çØ ÙÛÞïâ Üã ïÛàØ✵øÛêè
ÙÚÛÜÞæ✂ ðÚçëÚ ÛØëàßâÝêàÙÛâ ÙÚÛ ÛúÛëÙâ Üã ëÜïßêÛñ ïÜÙçÜØâ çØ
ÙÛÞïâ Üã ÛúÛëÙçìÛ ÛûÝàÙçÜØâ ãÜÞ ïÛàØ üÜð àØè ïÛàØ ïàåØÛÙçë
øÛêè ✭÷ÜúàÙÙ ☎✾☛✁õ ôàÞóÛÞ ☎✾☛✾õ ýÞàÝâÛ ✫ þÿèêÛÞ ☎✾✁✄✆✶
îÚÛ ÛúÛëÙâ Üã âÙÞàÙçøëàÙçÜØ àÞÛ ÝâÝàêêæ ÜØêæ çØëêÝèÛè ÙÜ êÛàè✵
çØå ÜÞèÛÞ àØè ÜãÙÛØ ÜØêæ çØ ëÜØØÛëÙçÜØ ðçÙÚ ÞÜÙàÙçÜØ✂ éÛëàÝâÛ ÙÚÛ
ÙðÜ ÙÜåÛÙÚÛÞ åçìÛ ÞçâÛ ÙÜ ÙÚÛ ãàïÜÝâ ✂ ÛúÛëÙ✂ ðÚçëÚ çâ àéêÛ ÙÜ
ÛñßêàçØ ÙÚÛ åÛØÛÞàÙçÜØ Üã êàÞåÛ✵âëàêÛ ïàåØÛÙçë øÛêèâ ✭ýÞàÝâÛ ✫
þÿèêÛÞ ☎✾✁✄✆✶ ✞Ø ÞÛëÛØÙ æÛàÞâ✂ ÚÜðÛìÛÞ✂ à ëÜïßêÛÙÛêæ èçúÛÞÛØÙ
ÛúÛëÙ àÞçâçØå ãÞÜï âÙÞÜØå âÙÞàÙçøëàÙçÜØ àêÜØÛ Úàâ ÞÛëÛçìÛè àÙÙÛØ✵
ÙçÜØ✟ ÙÚÛ âÝßßÞÛââçÜØ Üã ÙÝÞéÝêÛØÙ ßÞÛââÝÞÛ éæ à ðÛàó ïÛàØ ïàå✵
ØÛÙçë øÛêè✶ îÚçâ ÛúÛëÙ ïçïçëâ à ØÛåàÙçìÛ ÛúÛëÙçìÛ ✭ïÛàØ✵øÛêè✆
ïàåØÛÙçë ßÞÛââÝÞÛ ÜðçØå ÙÜ à ØÛåàÙçìÛ ëÜØÙÞçéÝÙçÜØ Üã ÙÝÞéÝ✵
êÛØëÛ ÙÜ ÙÚÛ ïÛàØ ïàåØÛÙçë ßÞÛââÝÞÛ✶ ❯ØèÛÞ âÝçÙàéêÛ ëÜØèçÙçÜØâ✂
ÙÚçâ êÛàèâ ÙÜ ÙÚÛ ØÛåàÙçìÛ ÛúÛëÙçìÛ ïàåØÛÙçë ßÞÛââÝÞÛ çØâÙàéçêçÙæ
✭◆❊÷ô✞✆✂ ðÚçëÚ ëàØ ëàÝâÛ ÙÚÛ ãÜÞïàÙçÜØ Üã ïàåØÛÙçë üÝñ ëÜØ✵
ëÛØÙÞàÙçÜØâ✶ ✞Ø ÙÝÞéÝêÛØëÛ âçïÝêàÙçÜØâ✂ ÙÚçâ çØâÙàéçêçÙæ Úàâ ÜØêæ
éÛÛØ âÛÛØ ÞÛëÛØÙêæ ✭ùÞàØèÛØéÝÞå ÛÙ àê✶ ✷✄☎☎✆✂ éÛëàÝâÛ âçåØçø✵
ëàØÙ âëàêÛ âÛßàÞàÙçÜØ çâ ØÛÛèÛè ÙÜ ÜìÛÞëÜïÛ ÙÚÛ ÛúÛëÙâ Üã ÙÝÞéÝ✵
êÛØÙ èçúÝâçÜØ ✭ùÞàØèÛØéÝÞå ÛÙ àê✶ ✷✄☎✷✆✶ ÷ÛàØ✵øÛêè ëÜØâçèÛÞà✵
ÙçÜØâ✂ ÚÜðÛìÛÞ✂ ÚàìÛ ßÞÛèçëÙÛè ÙÚÛ ÛñçâÙÛØëÛ Üã ◆❊÷ô✞ ãÜÞ à êÜØå
ÙçïÛ ✭ýêÛÛÜÞçØ ÛÙ àê✶ ☎✾✁✾✂ ☎✾✾✄✂ ☎✾✾✠õ ýêÛÛÜÞçØ ✫ þÜåàëÚÛìâóçç
☎✾✾ õ þÜåàëÚÛìâóçç ✫ ýêÛÛÜÞçØ ✷✄✄☛õ ùÞàØèÛØéÝÞå ÛÙ àê✶ ✷✄☎✄✆✶
✝ØÛ Üã ÙÚÛ ÞÛïàÞóàéêÛ çØâçåÚÙâ çâ ÙÚàÙ ◆❊÷ô✞ ëàØ ÜëëÝÞ àÙ
àØæ èÛßÙÚ✂ èÛßÛØèçØå ❥ÝâÙ ÜØ ÙÚÛ ìàêÝÛ Üã ÙÚÛ ïÛàØ ïàåØÛÙçë
øÛêè âÙÞÛØåÙÚ✶ ❍ÜðÛìÛÞ✂ ãÜÞ à èÜïàçØ Üã åçìÛØ èÛßÙÚ ÙÚÛ çØâÙà✵
éçêçÙæ ëàØ ÜØêæ ÜëëÝÞ çØ ÙÚÛ êÜëàÙçÜØ ðÚÛÞÛ ÙÚÛ èÛßÛØèÛØëÛ Üã Ûã✵
ãÛëÙçìÛ ÙÝÞéÝêÛØÙ ßÞÛââÝÞÛ ÜØ ÙÚÛ ÞàÙçÜ Üã øÛêè âÙÞÛØåÙÚ ÙÜ ÛûÝçßàÞ✵
ÙçÙçÜØ ìàêÝÛ Úàâ à ØÛåàÙçìÛ âêÜßÛ✶ ✝ØëÛ ÙÚçâ çâ ÜéÛæÛè✂ ÙÚÛ ÜØêæ
ÜÙÚÛÞ ØÛëÛââàÞæ ëÜØèçÙçÜØ ãÜÞ ◆❊÷ô✞ ÙÜ ÜëëÝÞ çâ ÙÚàÙ ÙÚÛ ÙÝÞéÝ✵
êÛØÙ èçúÝâçìçÙæ çâ êÜð ÛØÜÝåÚ✶ ✞Ø ßÞàëÙçëÛ ÙÚçâ ïÛàØâ ÙÚàÙ ÙÚÛÞÛ
àÞÛ ÛØÜÝåÚ ÙÝÞéÝêÛØÙ ÛèèçÛâ ðçÙÚçØ ÙÚÛ èÜïàçØ Üã çØìÛâÙçåàÙçÜØ
✭ùÞàØèÛØéÝÞå ÛÙ àê✶ ✷✄☎✷õ ýÛïÛê ÛÙ àê✶ ✷✄☎✷ë✆✶
❉ÛâßçÙÛ ÙÚÛ ßÜÙÛØÙçàê çïßÜÞÙàØëÛ Üã ◆❊÷ô✞✂ ïàØæ àèèçÙçÜØàê
ÛúÛëÙâ ÚàìÛ ØÜÙ æÛÙ éÛÛØ ÛñßêÜÞÛè✶ îÚÛ çèÛà çâ ÙÚàÙ ◆❊÷ô✞
ðÜÝêè çØÙÛÞàëÙ ðçÙÚ ÙÚÛ åêÜéàê èæØàïÜ ßÞÜèÝëçØå ÙÚÛ êàÞåÛ✵âëàêÛ
ïàåØÛÙçë øÛêè ãÜÞ ◆❊÷ô✞ ÙÜ àëÙ ÝßÜØ✶ îÚÝâ✂ ÙÚÛ øÛêè ØÛÛèâ ÙÜ éÛ
âÛêã✵ëÜØâçâÙÛØÙêæ åÛØÛÞàÙÛè✶ ✞èÛàêêæ✂ åêÜéàê åÛÜïÛÙÞæ çâ ØÛÛèÛè✂
àØè âÝëÚ ëàêëÝêàÙçÜØâ âÚÜÝêè éÛ ÙÚÞÛÛ✵èçïÛØâçÜØàê ✭✡❉✆✂ éÛ✵
ëàÝâÛ ÜØÛ ÛñßÛëÙâ üÝñ ëÜØëÛØÙÞàÙçÜØâ ØÜÙ ÙÜ éÛ ÙðÜ✵èçïÛØâçÜØàê
✭✷❉✆ ÜÞ àñçâæïïÛÙÞçë✶ ◆Ûð ïÛàØ✵øÛêè ëÜÛ✄ëçÛØÙâ ðçêê àßßÛàÞ
çØ âÝëÚ à ïÜÞÛ åÛØÛÞàê ëàâÛ✂ àØè ØÜÙ ïÝëÚ çâ óØÜðØ àéÜÝÙ ÙÚÛï✶
◆ÛìÛÞÙÚÛêÛââ✂ àêÙÚÜÝåÚ ÜÙÚÛÞ ÙÛÞïâ ïàæ àßßÛàÞ✂ çÙ ðçêê éÛ çØÙÛÞ✵
ÛâÙçØå ÙÜ çØìÛâÙçåàÙÛ ÙÚÛ ÛìÜêÝÙçÜØ Üã ◆❊÷ô✞ çØ ïÜÞÛ ÞÛàêçâÙçë
ëàâÛâ ðçÙÚ ❥ÝâÙ ÙÚÛ êÛàèçØå ÙÛÞï ÞÛâßÜØâçéêÛ ãÜÞ ÙÚÛ çØâÙàéçêçÙæ✶
❆ÞÙçëêÛ ßÝéêçâÚÛè éæ ❊❉ô äëçÛØëÛâ
❆ ✾✂ ßàåÛ ☎ Üã ✁
❆✫❆ ✺ ✁✂ ❆ ✾ ✭✷✄☎✷✆
❚✝✞ ❣✟✠✡ ✟❢ t✝✞ ♣☛✞☞✞❡t ♣✠♣✞☛ ✐☞ t✟ ✐❡✌✡✍✎✞ t✝✞ ✞✏✞✌t☞ ✟❢ ☛✟t✠♦
t✐✟❡ ✐❡ ◆❊✑✒✓ ✐❡ ✠ ✡✟✌✠✡ ❈✠☛t✞☞✐✠❡ ✎✟♠✠✐❡ ✠t ✠ ❣✐✈✞❡ ✡✠t✐t✍✎✞ ✐❡
t✝✞ ❙✍❡✉ ❚✟ t✝✐☞ ✞❡✎ ✇✞ ✎✞t✞☛♠✐❡✞ t✝✞ ✎✞♣✞❡✎✞❡✌✞ ✟❢ ❣☛✟✇t✝ ☛✠t✞
✠❡✎ ☞✠t✍☛✠t✐✟❡ ✡✞✈✞✡ ✟❢ ◆❊✑✒✓ ✟❡ ☛✟t✠t✐✟❡ ☛✠t✞ ✠❡✎ ✡✠t✐t✍✎✞✔ ✠❡✎
t✟ ✌✝✠☛✠✌t✞☛✐❝✞ ☛✟t✠t✐✟❡✠✡ ✞✏✞✌t☞ ✟❡ t✝✞ ☛✞☞✍✡t✐❡❣ ✤✍① ✌✟❡✌✞❡t☛✠♦
t✐✟❡☞✉ ❲✞ ☛✞☞t☛✐✌t ✟✍☛☞✞✡✈✞☞ t✟ ✠ ♠✞✠❡♦✕✞✡✎ t☛✞✠t♠✞❡t ✠❡✎ ✎✞❡✟t✞
✠✈✞☛✠❣✞✎ q✍✠❡t✐t✐✞☞ ❜② ✠❡ ✟✈✞☛❜✠☛✉ ❋✍☛t✝✞☛♠✟☛✞✔ ✇✞ ♠✠❛✞ t✝✞ ✠☞♦
☞✍♠♣t✐✟❡ ✟❢ ✠❡ ✐☞✟t✝✞☛♠✠✡ ✞q✍✠t✐✟❡ ✟❢ ☞t✠t✞✉ ❚✝✐☞ ✐☞ ✟❢ ✌✟✍☛☞✞
q✍✐t✞ ✍❡☛✞✠✡✐☞t✐✌✔ ✠☞ ❢✠☛ ✠☞ ✠♣♣✡✐✌✠t✐✟❡☞ t✟ t✝✞ ❙✍❡ ✠☛✞ ✌✟❡✌✞☛❡✞✎✉
❍✟✇✞✈✞☛✔ ✐t ✝✠☞ ❜✞✞❡ ❢✟✍❡✎ ✞✠☛✡✐✞☛ t✝✠t ◆❊✑✒✓ ✝✠☞ ☞✐♠✐✡✠☛ ♣☛✟♣♦
✞☛t✐✞☞ ❜✟t✝ ❢✟☛ ✠❡ ✐☞✟t✝✞☛♠✠✡ ✡✠②✞☛ ✇✐t✝ ✠❡ ✐☞✟t✝✞☛♠✠✡ ✞q✍✠t✐✟❡
✟❢ ☞t✠t✞ ✠❡✎ ✠ ❡✞✠☛✡② ✐☞✞❡t☛✟♣✐✌ ✟❡✞ ✇✐t✝ t✝✞ ♠✟☛✞ ❣✞❡✞☛✠✡ ♣✞☛♦
❢✞✌t ❣✠☞ ✡✠✇ ✖❑ä♣②✡ä ✞t ✠✡✉ ✗✘✙✗✮✉ ●✐✈✞❡ t✝✠t ✟✍☛ ❛❡✟✇✡✞✎❣✞ ✟❢
◆❊✑✒✓ ✐☞ ☞t✐✡✡ ☛✠t✝✞☛ ✡✐♠✐t✞✎✔ ✐t ✐☞ ✍☞✞❢✍✡ t✟ ✌✟❡☞✐✎✞☛ t✝✞ ❡✞✇ ✞❢♦
❢✞✌t☞ ✟❢ ☛✟t✠t✐✟❡ ✇✐t✝✐❡ t✝✞ ❢☛✠♠✞✇✟☛❛ ✟❢ t✝✞ ✌✟❡✌✞♣t✍✠✡✡② ☞✐♠♦
♣✡✞☛ ✌✠☞✞ ✟❢ ✠❡ ✐☞✟t✝✞☛♠✠✡ ✡✠②✞☛✉
❲✞ ❜✞❣✐❡ ✇✐t✝ t✝✞ ♠✟✎✞✡ ✞q✍✠t✐✟❡☞✔ ✎✐☞✌✍☞☞ t✝✞ ✡✐❡✞✠☛ t✝✞♦
✟☛② ✟❢ ◆❊✑✒✓ ✐❡ t✝✞ ♣☛✞☞✞❡✌✞ ✟❢ ☛✟t✠t✐✟❡✔ ✠❡✎ ✌✟❡☞✐✎✞☛ ✗✚
✠❡✎ ✸✚ ❡✍♠✞☛✐✌✠✡ ♠✟✎✞✡☞✉
✓❡ t✝✐☞ ✠☛☛✠❡❣✞♠✞❡t✔ ❸ ✌✟☛☛✞☞♣✟❡✎☞ t✟ ☛✠✎✐✍☞✔ ❹ t✟ ✌✟✡✠t✐t✍✎✞✔
✠❡✎ ❺ t✟ ✠❝✐♠✍t✝✉
❋✟✡✡✟✇✐❡❣ t✝✞ ☞✐♠♣✡✐❢②✐❡❣ ✠☞☞✍♠♣t✐✟❡ ✟❢ ☛✞✌✞❡t ✎✐☛✞✌t ❡✍♦
♠✞☛✐✌✠✡ ☞✐♠✍✡✠t✐✟❡☞ ✟❢ ◆❊✑✒✓ ✖❤☛✠❡✎✞❡❜✍☛❣ ✞t ✠✡✉ ✗✘✙✙✮✔ ✇✞
✠☞☞✍♠✞ t✝✠t t✝✞ ☛✟✟t♦♠✞✠❡♦☞q✍✠☛✞ t✍☛❜✍✡✞❡t ✈✞✡✟✌✐t②✔ ⑥⑦⑧s ✔ ✐☞ ✌✟❡♦
☞t✠❡t ✐❡ ☞♣✠✌✞ ✠❡✎ t✐♠✞✉ ❋✟☛ ✠❡ ✐☞✟t✝✞☛♠✠✡ ✎✞❡☞✐t② ☞t☛✠t✐✕✌✠t✐✟❡✔
✯ ❂ ✯❞ ✞①♣✖❾❸❁❻❼ ✮✼
✖❽✮
✇✝✞☛✞ ❻❼ ❂ ✪✰s ❁❃ ✐☞ t✝✞ ✎✞❡☞✐t② ☞✌✠✡✞ ✝✞✐❣✝t✔ ✇✞ t✝✞❡ ✝✠✈✞ r③④ ✖❸✮✉
❚✟ q✍✠❡t✐❢② t✝✞ ☞t☛✞❡❣t✝ ✟❢ t✝✞ ✐♠♣✟☞✞✎ ✕✞✡✎✔ ✇✞ ✠✡☞✟ ✎✞✕❡✞
r③④❞ ❂ r③④✖❸ ❂ ✘✮✉ ❚✝✞ ✈✠✡✍✞ ✟❢ ⑥⑦⑧s ✐☞ ✠✡☞✟ ☛✞✡✠t✞✎ t✟ t✝✞ ✈✠✡♦
✍✞☞ ✟❢ ✿❀ ✠❡✎ ❄❀ ✔ ✇✝✐✌✝ ✇✞ ✠☞☞✍♠✞ t✟ ❜✞ ✞q✍✠✡✔ ✇✐t✝ ✿❀ ❂ ❄❀ ❂
⑥⑦⑧s ❁✸❿➀ ✔ ✇✝✞☛✞ ❿➀ ✐☞ t✝✞ ✇✠✈✞❡✍♠❜✞☛ ✟❢ t✝✞ ✞❡✞☛❣②♦✌✠☛☛②✐❡❣ ✞✎♦
✎✐✞☞ ✟❢ t✝✞ ✍❡✎✞☛✡②✐❡❣ t✍☛❜✍✡✞❡✌✞✉ ❚✝✐☞ ❢✟☛♠✍✡✠ ✠☞☞✍♠✞☞ t✝✠t t✝✞
☛✞✡✞✈✠❡t ✌✟☛☛✞✡✠t✐✟❡ t✐♠✞ ✐☞ ✖⑥⑦⑧s ❿➀ ✮➁■ ✔ ✇✝✐✌✝ ✝✠☞ ❜✞✞❡ ☞✝✟✇❡ t✟
❜✞ ❢✠✐☛✡② ✠✌✌✍☛✠t✞ ✖❙✍☛ ✞t ✠✡✉ ✗✘✘❽✮✉
➂✜ ➃➄➅✥➆➇ ➈✣✥✧➇➉ ✧➊ ➋➌➍➎➏ ➐➄➈✣ ➇✧➈➆➈➄✧➅
✛✜ ✢✣✥ ✦✧★✥✩
❲✞ ✌✟❡☞✐✎✞☛ ✝✞☛✞ ✠❡ ✐☞✟t✝✞☛♠✠✡ ✞q✍✠t✐✟❡ ✟❢ ☞t✠t✞ ✇✐t✝ ✌✟❡☞t✠❡t
☞✟✍❡✎ ☞♣✞✞✎ ✪s ✔ ☞✟ t✝✞ ♠✞✠❡ ❣✠☞ ♣☛✞☞☞✍☛✞ ✐☞ ✬ ❂ ✯✪✰s ✉ ❚✝✞ ✞✈✟♦
✡✍t✐✟❡ ✞q✍✠t✐✟❡☞ ❢✟☛ ♠✞✠❡ ✈✞✡✟✌✐t② ❯✔ ♠✞✠❡ ✎✞❡☞✐t② ✯✔ ✠❡✎ ♠✞✠❡
✈✞✌t✟☛ ♣✟t✞❡t✐✠✡ ✱✔ ✠☛✞
✚❯
✚✲
✚✯
✚✲
✽✱
✽✲
❂ ❾✗✳ × ❯ ❾ ✪✰s ✴ ✡❡ ✯ ✵ ✶ ✵ ✹ ▼ ✵ ✹ ✻ ✼
✖✙✮
❂ ❾✯✴ ➲ ❯✼
✖✗✮
❂ ❯ × ❇ ❾ ✖✿❀ ✵ ✿✮❏✼
✖✸✮
✐☞ t✝✞ t✟t✠✡ ✖t✍☛❜✍✡✞❡t ♣✡✍☞ ♠✐✌☛✟☞✌✟♣✐✌✮ ✈✐☞✌✟✍☞ ❢✟☛✌✞ ✇✐t✝ ❄❀
❜✞✐❡❣ t✝✞ t✍☛❜✍✡✞❡t ✈✐☞✌✟☞✐t②✔ ✠❡✎ ❘❱ ❳ ❂ ✰■ ✖❨ ❱❩ ❳ ✵ ❨ ❳❩❱ ✮ ❾ ■▲ ❬❱ ❳ ✴ ➲ ❯
✐☞ t✝✞ t☛✠✌✞✡✞☞☞ ☛✠t✞ ✟❢ ☞t☛✠✐❡ t✞❡☞✟☛ ✟❢ t✝✞ ♠✞✠❡ ✤✟✇✉ ❚✝✞ ♠✞✠❡
❭✟☛✞❡t❝ ❢✟☛✌✞✔ ✹ ▼ ✔ ✐☞ ❣✐✈✞❡ ❜②
✖❴✮
✇✝✞☛✞ ❏ ❂ ✴ × ❇❁❵❞ t✝✞ ♠✞✠❡ ✌✍☛☛✞❡t ✎✞❡☞✐t②✔ ❵❞ ✐☞ t✝✞ ✈✠✌♦
✍✍♠ ♣✞☛♠✞✠❜✐✡✐t②✔ ✠❡✎ t✝✞ ✡✠☞t t✞☛♠✔ ✰■ ✴✖❪❫ ❇✰ ✮✔ ✟❡ t✝✞ ☛✐❣✝t✝✠❡✎
☞✐✎✞ ✟❢ ❊q✉ ✖❴✮ ✎✞t✞☛♠✐❡✞☞ t✝✞ t✍☛❜✍✡✞❡t ✌✟❡t☛✐❜✍t✐✟❡ t✟ t✝✞ ♠✞✠❡
❭✟☛✞❡t❝ ❢✟☛✌✞✉ ❋✟✡✡✟✇✐❡❣ ❤☛✠❡✎✞❡❜✍☛❣ ✞t ✠✡✉ ✖✗✘✙✗✮ ✠❡✎ ❑✞♠✞✡
✞t ✠✡✉ ✖✗✘✙✗✠✮✔ t✝✞ ❢✍❡✌t✐✟❡ ❪❫ ✖❥✮ ✐☞ ✠♣♣☛✟①✐♠✠t✞✎ ❜②❦
❥✰❧
✼
❪❫ ✖❥✮ ❂ ✰
❥❫ ✵ ❥✰
✖♥✮
✇✝✞☛✞ ❥❧ ✠❡✎ ❥❫ ✠☛✞ ✌✟❡☞t✠❡t☞✔ ❥ ❂ r❁r③④ ✐☞ t✝✞ ♠✟✎✍✡✍☞ ✟❢
⑤
t✝✞ ❡✟☛♠✠✡✐❝✞✎ ♠✞✠❡ ♠✠❣❡✞t✐✌ ✕✞✡✎✔ ✠❡✎ r③④ ❂ ❵❞ ✯ ⑥⑦⑧s t✝✞
✞q✍✐♣✠☛t✐t✐✟❡ ✕✞✡✎ ☞t☛✞❡❣t✝✉ ❚✝✞ ✠❡❣✍✡✠☛ ✈✞✡✟✌✐t② ✈✞✌t✟☛ ✳ ✐☞
q✍✠❡t✐✕✞✎ ❜② ✐t☞ ☞✌✠✡✠☛ ✠♠♣✡✐t✍✎✞ ⑨ ✠❡✎ ✌✟✡✠t✐t✍✎✞ ⑩✔ ☞✍✌✝ t✝✠t
✳ ❂ ⑨ ✖❾ ☞✐❡ ⑩✼ ✘✼ ✌✟☞ ⑩✮ ❶
❆ ✾✂ ➢➤➥➦ ✷ ➧➨ ✁
✞q✍✠t✐✟❡ ✟❢ ♠✟t✐✟❡✔ ✐❣❡✟☛✐❡❣ t✝✞ ❯ ➲ ✴❯ ❡✟❡✡✐❡✞✠☛✐t②✔
✽❯✖✲✼ ❹✼ ❸✮
✽✲
✇✝✞☛✞ ✚❁✚✲ ❂ ✽❁✽✲✵❯➲✴ ✐☞ t✝✞ ✠✎✈✞✌t✐✈✞ ✎✞☛✐✈✠t✐✈✞✔ ✿❀ ✠❡✎ ✿ ✠☛✞
t✍☛❜✍✡✞❡t ✠❡✎ ♠✐✌☛✟☞✌✟♣✐✌ ♠✠❣❡✞t✐✌ ✎✐✏✍☞✐✈✐t✐✞☞✔ ✶ ❂ ✖✘✼ ✘✼ ❾❃✮
✐☞ t✝✞ ✠✌✌✞✡✞☛✠t✐✟❡ ✎✍✞ t✟ t✝✞ ❣☛✠✈✐t② ✕✞✡✎✔
❅
P
✹ ✻ ❂ ✖❄❀ ✵ ❄✮ ❉✰ ❯ ✵ ■▲ ✴✴ ➲ ❯ ✵ ✗❖✴ ✡❡ ✯
✖◗✮
✯ ✹ ▼ ❂ ❏ × ❇ ✵ ✰■ ✴✖❪❫ ❇✰ ✮✼
✓❡ t✝✐☞ ☞✞✌t✐✟❡ ✇✞ ☞t✍✎② t✝✞ ✞✏✞✌t ✟❢ ☛✟t✠t✐✟❡ ✟❡ t✝✞ ❣☛✟✇t✝
☛✠t✞ ✟❢ ◆❊✑✒✓✉ ❋✟✡✡✟✇✐❡❣ ✞✠☛✡✐✞☛ ✇✟☛❛ ✖✞✉❣✉✔ t✝✞ ✠♣♣✞❡✎✐① ✟❢
❑✞♠✞✡ ✞t ✠✡✉ ✗✘✙✗✌✮✔ ✠❡✎ ❢✟☛ ☞✐♠♣✡✐✌✐t②✔ ✇✞ ❡✞❣✡✞✌t ✎✐☞☞✐♣✠t✐✟❡
♣☛✟✌✞☞☞✞☞✔ ✍☞✞ t✝✞ ✠❡✞✡✠☞t✐✌ ✠♣♣☛✟①✐♠✠t✐✟❡✔ ✴ ➲ ✯❯ ❂ ✘✔ ✠❡✎ ✠☞♦
☞✍♠✞ t✝✠t t✝✞ ✎✞❡☞✐t② ☞✌✠✡✞ ✝✞✐❣✝t ❻❼ ❂ ✌✟❡☞t✉ ❲✞ ✌✟❡☞✐✎✞☛ t✝✞
✖❷✮
❂ ❾✗✳ × ❯ ❾
✙
✯
✴✬❀➑❀ ✵ ✶✼
✖➒✮
✇✝✞☛✞ ✬❀➑❀ ❂ ✬ ✵ ✬③➓ ✐☞ t✝✞ t✟t✠✡ ♣☛✞☞☞✍☛✞ ✌✟❡☞✐☞t✐❡❣ ✟❢ t✝✞ ☞✍♠
✟❢ t✝✞ ♠✞✠❡ ❣✠☞ ♣☛✞☞☞✍☛✞ ✬✔ ✠❡✎ t✝✞ ✞✏✞✌t✐✈✞ ♠✠❣❡✞t✐✌ ♣☛✞☞♦
✰
☞✍☛✞✔ ✬③➓ ❂ ✖✙ ❾ ❪❫ ✮r ❁✗✔ ✇✝✞☛✞ r ❂ ➔❇➔✉ ❍✞☛✞ ✠❡✎ ✞✡☞✞✇✝✞☛✞
t✝✞ ✈✠✌✍✍♠ ♣✞☛♠✞✠❜✐✡✐t② ✐☞ ☞✞t t✟ ✍❡✐t②✉ ❲✞ ✠☞☞✍♠✞ ❢✟☛ ☞✐♠♣✡✐✌♦
✐t② t✝✠t ✽→ ❂ ✘✔ ✠❡✎ t✝✠t t✝✞ ♠✞✠❡ ♠✠❣❡✞t✐✌ ✕✞✡✎ ✟❡✡② ✝✠☞ ✠
❺♦✌✟♠♣✟❡✞❡t✔ ❇ ❂ ✖✘✼ r→ ✖❹✼ ❸✮✼ ✘✮✔ ☞✟ t✝✞ ♠✞✠❡ ♠✠❣❡✞t✐✌ t✞❡☞✐✟❡✔
❇ ➲ ✴❇ ✐❡ ❊q✉ ✖➒✮ ✈✠❡✐☞✝✞☞✉
❚✠❛✐❡❣ t✇✐✌✞ t✝✞ ✌✍☛✡ ✟❢ ❊q✉ ✖➒✮✔ ✠❡✎ ❡✟t✐❡❣ ❢✍☛t✝✞☛ t✝✠t ↔➣ ➲
✴ × ✴ × ❯ ❂ ❾↕❨ ➙ ✵ ❉➙ ✴ ➲ ❯✔ ✇✞ ✟❜t✠✐❡
➜
✽ ➛
↕❨ ➙ ✵ ❉➙ ✖❯ ➲ ✴ ✡❡ ✯✮ ❂ ❾✗✳ ➲ ✴✖✴ × ❯✮➙
✽✲
➞➟
➠
➟
➠
➡
✬❀➑❀ ❉ ➝ ✯
✬❀➑❀ ❉➙ ✯
✵❉ ➝ ❉➙
❾ ❉➝
✼
✯
✯
✯
✯
✖✙✘✮
✇✝✞☛✞ ✇✞ ✝✠✈✞ ✍☞✞✎ t✝✞ ✠❡✞✡✠☞t✐✌ ✠♣♣☛✟①✐♠✠t✐✟❡ ✐❡ t✝✞ ❢✟☛♠
✴ ➲ ❯ ❂ ❾❯ ➲ ✴ ✡❡ ✯ ✠❡✎ t✝✞ ❢✠✌t t✝✠t ✍❡✎✞☛ t✝✞ ✌✍☛✡ t✝✞ ❣☛✠✎✐✞❡t
✌✠❡ ❜✞ ♠✟✈✞✎ t✟ ✯✉ ❲✞ ✝✠✈✞ ✠✡☞✟ t✠❛✞❡ ✐❡t✟ ✠✌✌✟✍❡t t✝✠t ⑨→ ❂ ✘
✠❡✎ ✝✠✈✞ ✍☞✞✎ ❊q✉ ✖✸✘✮ ✟❢ ❑✞♠✞✡ ✞t ✠✡✉ ✖✗✘✙✗✌✮ t✟ ☛✞✡✠t✞ t✝✞ ✎✟✍♦
❜✡✞ ✌✍☛✡ ✟❢ ✖✴✬❀➑❀ ✮❁✯ t✟ t✝✞ ✡✠☞t t✞☛♠ ✐❡ ❊q✉ ✖✙✘✮✉ ❚✝✞ ✕☛☞t t✞☛♠ ✟❡
t✝✞ ☛✐❣✝t✝✠❡✎ ☞✐✎✞ ✟❢ ❊q✉ ✖✙✘✮ ❢✟☛ ❨ ➙ ✐☞ ♣☛✟♣✟☛t✐✟❡✠✡ t✟ ✖✴ × ❯✮➙ ✉
❚✠❛✐❡❣ t✝✞ ❸ ✌✟♠♣✟❡✞❡t ✟❢ t✝✞ ✌✍☛✡ ✟❢ ❊q✉ ✖➒✮ ✇✞ ✟❜t✠✐❡ t✝✞ ❢✟✡♦
✡✟✇✐❡❣ ✞q✍✠t✐✟❡ ❢✟☛ ✖✴ × ❯✮➙ ❦
➟
➠
✽
⑨➙
❨➙❶
✖✴ × ❯✮➙ ❂ ✗ ✳ ➲ ✴ ❾
✖✙✙✮
✽✲
❻❼
❚✝✞ ✐❡✎✍✌t✐✟❡ ✞q✍✠t✐✟❡ ❢✟☛ r→ ✖❹✼ ❸✮ ✐☞ ❣✐✈✞❡ ❜②
✚r→
❂ ❾r→ ✴ ➲ ❯✼
✚✲
✖✙✗✮
■ ❘
✇✝✞✟✞ ❉✴❉✠
❂
▲✁s✂❞✂ ❡t ✂❧ ✳ ◆❡❣✂t✄✈❡ ♠✂❣♥❡t✄☎ ♣r❡ss✆r❡ ✄♥st✂❜✄❧✄t✐
✡✴✡ ✰ ❯ ➲ ☛ ☞✌ ✍✝✞ ❛✎✏✞✑✍☞✏✞ ✎✞✟☞✏❛✍☞✏✞✒ ❋♦✟ ❛
✘✖❛✌✓❛ ✇✝✞✕ ✍✝✞ ✑✝❛✟❛✑✍✞✟☞✌✍☞✑ ✌✑❛✖✞ ♦✚ ✏❛✟☞❛✍☞♦✕✌ ☞✕ ✍✝✞ ♦✟☞✔☞✕❛✖
✓❛✔✕✞✍☞✑ ✣✞✖✎ ✇☞✍✝ ♦✕✖② ❛ ✗✲✑♦✓✘♦✕✞✕✍✱ ✙✉✍ ✡✴✡✗ ❂ ✵✱ ✍✝✞✟✞ ☞✌
✝♦✟☞✛♦✕✍❛✖ ✓❛✔✕✞✍☞✑ ✣✞✖✎ ☞✌ ✌✓❛✖✖✞✟ ✍✝❛✕ ✍✝✞ ✎✞✕✌☞✍② ✌✑❛✖✞ ✝✞☞✔✝✍✒
✕♦ ✌✍✟✞✍✑✝☞✕✔ ✍✞✟✓✱ ✌♦ ✍✝✞✟✞ ☞✌ ✕♦ ✍✞✟✓ ♦✚ ✍✝✞ ✚♦✟✓ ❇ ➲ ☛❯✒
➄✌ ✌✞✞✕ ✚✟♦✓ ❊q✒ ✭✜✵✮✱ ④ ☞✌ ✞☞✍✝✞✟ ✟✞❛✖ ♦✟ ✘✉✟✞✖② ☞✓❛✔☞✕❛✟②✱ ✌♦
❲✞ ✖☞✕✞❛✟☞✛✞ ❊q✌✒ ✭✶✵✮❾✭✶✜✮✱ ☞✕✎☞✑❛✍☞✕✔ ✌✓❛✖✖ ✑✝❛✕✔✞✌ ✙② ✢✒
❲✞ ✑♦✕✌☞✎✞✟ ❛✕ ✞q✉☞✖☞✙✟☞✉✓ ✇☞✍✝ ❛ ✑♦✕✌✍❛✕✍ ✓❛✔✕✞✍☞✑ ✣✞✖✎ ♦✚
✕♦ ✑♦✓✘✖✞⑧ ✞☞✔✞✕✏❛✖✉✞✌ ❛✟✞ ✘♦✌✌☞✙✖✞✱ ❛✌ ✇♦✉✖✎ ✙✞ ✟✞q✉☞✟✞✎ ✚♦✟
✔✟♦✇☞✕✔ ♦✌✑☞✖✖❛✍♦✟② ✌♦✖✉✍☞♦✕✌✒
❲☞✍✝♦✉✍ ✟♦✍❛✍☞♦✕ ✍✝✞ ✔✟♦✇✍✝ ✟❛✍✞ ♦✚ ❶❊❷❸❝ ☞✌ ✭❑✖✞✞♦✟☞✕ ✞✍ ❛✖✒
✍✝✞ ✚♦✟✓ ✭✵✤ ✥✦ ✤ ✵✮✱ ❛ ✛✞✟♦ ✓✞❛✕ ✏✞✖♦✑☞✍②✱ ❛✕✎ ✍✝✞ ✧✉☞✎ ✎✞✕✌☞✍②
❛✌ ✔☞✏✞✕ ✙② ❊q✒ ✭✽✮✒ ❲✞ ✍❛❦✞ ☞✕✍♦ ❛✑✑♦✉✕✍ ✍✝❛✍ ✍✝✞ ✚✉✕✑✍☞♦✕ ★✩ ❂
✶⑥⑥❈➈ ➉♦✔❛✑✝✞✏✌❦☞☞ ➊ ❑✖✞✞♦✟☞✕ ✜✵✵❭➈ ❑✞✓✞✖ ✞✍ ❛✖✒ ✜✵✶✜✎✮
★✩ ✭✪✮ ✎✞✘✞✕✎✌ ✙♦✍✝ ♦✕ ✥ ❛✕✎ ♦✕ ✫✱ ✇✝☞✑✝ ☞✓✘✖☞✞✌ ✍✝❛✍ ✭❑✞✓✞✖
✞✍ ❛✖✒ ✜✵✶✜✑✮
✬
❃
✹✾
✿ ✢✥
✎★ ✩
✢✫ ❄
❄
✿
❁
✿
❄
✿
❄
✶ ❾ ★✩ ❾
❾
✿✜
❄✤
❀
❅
✻
✫
✎✖✕ ✪
✥✦
✺
❂
✻
✫
✻
✼
❆
✭✶❈✮
❚✝✞ ✟♦✍❛✍☞♦✕ ✟✞✎✉✑✞✌ ✍✝✞ ✔✟♦✇✍✝ ✟❛✍✞ ♦✚ ❶❊❷❸❝✱ ✇✝☞✑✝ ✑❛✕ ✙✞
✘♦✌☞✍✞ ✑❛✌✞✱ ⑨ ① ✴⑨
✹
✯ ✷✸✷
✬
✺
❂
✻
✫
✻
✼
❆
✹
✬
✶ ❾ ★✩ ❾
✹
✡
✶
❖❾
✡✠
✎★ ✩
✶
✻
✎✖✕ ✪
❍❏
➲
❍❏
✢P ③ ❂ ✜
●③
❍❏
✎✪
✻
✥✦
✬
✡✠
✭✶▼✮
❳ ➲ ☛ ❾
✡✢✥❁
✢P ③
✇✝✞✟✞ ◗❙❱ ✭✪✮ ❂
✺
❩③
❍❏
❂ ❾ ✥✦
✻
❋♦✟ ❛✕ ❛✟✙☞✍✟❛✟② ✏✞✟✍☞✑❛✖ ☞✕✝♦✓♦✔✞✕✞☞✍② ♦✚ ✍✝✞ ✎✞✕✌☞✍②✱ ✇✞
☞⑨ ① ➌✮ ❛✕✎ ♦✙✍❛☞✕ ❛✕ ✞☞✔✞✕✏❛✖✉✞ ✘✟♦✙✖✞✓
➑
➍
❾ ✜❳ ➲ ☛✭☛ × ✢❯✮③ ✤ ✭✶❨✮
➎
➎ ✻
➎
➎
➏●③ ✰
✽❩ ① ❩③
④
✻
✻
✰ ▼❩
③
❪
✢P ③ ✤
✭✶❬✮
✻
④
✻
❂
✻
✻
❾ ④ ✭⑤✮ ✰ ▼❩
①
✦
✭✶❭✮
✤
④
✻
✻
✰ ▼❩
③
❍❏
❫
✶ ❾ ★✩ ✭✪✮
✻
✪
☞✌ ✍✝✞ ✞❴✞✑✍☞✏✞ ✓❛✔✕✞✍☞✑ ✘✟✞✌✲
❝✕✍✟♦✎✉✑☞✕✔ ❛ ✕✞✇ ✏❛✟☞❛✙✖✞ ❢③ ❂
❛✕✎
✍✝✞
④
☞✌
✍✝✞
❃
✾
✻
❄
✿
❩
❄
✿
③
✻
❄
✿
❄
❅ ❢③ ✰ ✿
❀✭✜❳ ➲ ☛✮ ❾
✻
✻
❍
▼❍
❏
❏
✫ ✢P ③ ☞✕ ❊q✌✒ ✭✶❨✮❾✭✶❭✮
✻
✎✪
➒
➒
➒
➒
➓ ❢ ✭⑤✮ ❂ ✵✤
❊q✉❛✍☞♦✕
↔↔
➣
✞q✉❛✍☞♦✕✱
✬
➙ ❢ ✭⑤✮ ✞⑧✘
✻
✼
➜✦
➙✭⑤✮ ❂
❄
❄
✻
✻
❄
❄
❅ ❢③ ❂ ④✦ ● ① ❢③ ✤
✻
✻
➝❽➞➟ ✪✩
✭✶✽✮
✭✜❈✮
✭✜❈✮
✑❛✕
✙✞
↕ ✭➙✮ ➣
❾ P
✟✞✎✉✑✞✎
❂
✵✱
✏☞❛
✍♦
✍✝✞
✹
▼❩ ① ❩③
☞
✻
✻
✰ ▼❩
③
⑨① ⑤
✭✜❨✮
✤
③➀➠➡
✞
✤
✭✜❬✮
❤
✇✝✞✟✞ ✼❆✦ ❂ ✥✦ ✴
✻
❏
✍②✘✞
➛
➣✭➙✮ ❂
❃
✇✝✞✟✞
❍
✻
▼❍
❏
✭✜▼✮
④
✶
✻
✼ ✭⑤✮ ✎◗
❙❱ ✭⑤✮
❆
✶
✻
❾
①
✤
✞☞✔✞✕✏❛✖✉✞✒
➔✑✝✟→✎☞✕✔✞✟
✍☞♦✕ ✚♦✟ ♦✕✞ ✏❛✟☞❛✙✖✞ ❢③ ❥
✻
④ ✭⑤✮ ❂ ❾✜
✦
⑨
✍✟❛✕✌✚♦✟✓❛✍☞♦✕
❛✕✎ ❛✚✍✞✟ ✌☞✓✘✖✞ ✍✟❛✕✌✚♦✟✓❛✍☞♦✕✌ ✇✞ ❛✟✟☞✏✞ ❛✍ ✍✝✞ ✚♦✖✖♦✇☞✕✔ ✞q✉❛✲
✿
✿
✿
✿
❀❖ ❾
✻
✇✝✞✟✞
➐
✻
✌✉✟✞ ✕♦✟✓❛✖☞✛✞✎ ✙② ✍✝✞ ✖♦✑❛✖ ✏❛✖✉✞ ♦✚ ✥
✒
❙❵
❤
✾
☞⑨ ① ●③ ❾ ➐
✹
✭☛ × ✢❯✮③ ❂ ✜
✡✠
✻
✵✒ ❝✕ ✍✝✞ ♦✘✲
➅
❺❻❼❙❽✷ ✴④✦ ✱ ✍✝✞ ✖❛✟✔✞✲✌✑❛✖✞ ☞✕✌✍❛✙☞✖☞✍② ☞✌ ✕♦✍
➅
✌✞✞❦ ❛ ✌♦✖✉✍☞♦✕ ✍♦ ❊q✒ ✭✶✽✮ ☞✕ ✍✝✞ ✚♦✟✓ ❢③ ✭✠✤ ➌✤ ⑤✮ ❂ ❢ ✭⑤✮ ✞⑧✘✭④✠ ✰
✻
✻
✼
✎◗❙❱ ● ① ✢✥❁
❆
✡
✡✠
✻
✍✝✞ ✞❴✞✑✍☞✏✞ ✕✞✔❛✍☞✏✞ ✓❛✔✕✞✍☞✑ ✘✟✞✌✌✉✟✞✒
❚✝✞ ✖☞✕✞❛✟☞✛✞✎ ✌②✌✍✞✓ ♦✚ ✞q✉❛✍☞♦✕✌ ✟✞❛✎✌ ❛✌
✻
❺❻❼❙❽✷ ✴④✦ ❛✕✎ ✎◗❙❱ ✴✎✪
➋
✞⑧✑☞✍✞✎✱ ✇✝☞✖✞ ✍✝✞ ✚✟✞q✉✞✕✑② ♦✚ ✍✝✞ ☞✕✞✟✍☞❛✖ ✇❛✏✞✌ ☞✌ ✟✞✎✉✑✞✎ ✙②
✬
✡
✭✜✜✮
✞⑧✑☞✍✞✎ ✇✝✞✕ ⑨ ① ✴⑨
✇✝☞✖✞
●③
➲
⑨
✬
✹
✯✷✸✷
✢
⑨①
④ ❂ ④✦
✫
☞✌ ✍✝✞ ➄✖✚✏➢✕ ✌✘✞✞✎ ✙❛✌✞✎ ♦✕ ✍✝✞ ❛✏✞✟❛✔✞✎
✦
↕ ✭➙✮ ☞✌
✎✞✕✌☞✍②✱ ✍✝✞ ✘♦✍✞✕✍☞❛✖ P
➲
✭✶⑥✮
❝✕ ✍✝✞ ❲❑⑦ ❛✘✘✟♦⑧☞✓❛✍☞♦✕✱ ✇✝☞✑✝ ☞✌ ✏❛✖☞✎ ✇✝✞✕ ⑨③ ❍❏ ⑩ ✶✱ ☞✒✞✒✱
✻
✻
❍
①
❏
➍
➎ ④✻
➎
➎
➎
➎
✻
✻ ➏
➙
➙✭④ ✰ ▼❩ ✮
③
⑨
↕ ✭➙✮ ❂
P
✬
④
④
✻
✻
✰ ▼❩
✻
✹
✻
✰ ▼❩
③
➝
✰
✹➑
✻
✻ ✬
➒
✪
★✩✦
➒
❽➞➟ ✩
➒
➒✤
✶❾
➒
✻
✻ ➓
❍
✭✶ ✰ ➙✮
❏
✭✜❭✮
✇✝✞✕ ✍✝✞ ✑✝❛✟❛✑✍✞✟☞✌✍☞✑ ✌✑❛✖✞ ♦✚ ✍✝✞ ✌✘❛✍☞❛✖ ✏❛✟☞❛✍☞♦✕ ♦✚ ✍✝✞ ✘✞✟✲
✍✉✟✙❛✍☞♦✕✌ ♦✚ ✍✝✞ ✓❛✔✕✞✍☞✑ ❛✕✎ ✏✞✖♦✑☞✍② ✣✞✖✎✌ ❛✟✞ ✓✉✑✝ ✌✓❛✖✖✞✟
✍✝❛✕ ✍✝✞ ✎✞✕✌☞✍② ✝✞☞✔✝✍ ✖✞✕✔✍✝✱ ❍❏ ✱ ✍✝✞ ✔✟♦✇✍✝ ✟❛✍✞ ♦✚ ✍✝✞ ✖❛✟✔✞✲
✌✑❛✖✞ ☞✕✌✍❛✙☞✖☞✍② ✭❶❊❷❸❝✮ ☞✌ ✔☞✏✞✕ ✙②
❛✕✎ ✇✞ ✝❛✏✞ ✉✌✞✎ ❊q✒ ✭❬✮ ✚♦✟ ★ ✩ ✇☞✍✝ ✪➤
❂ ✪✩
➛
★✩✦ ❛✕✎ ★✩✦
❂
↕ ✭➙✮✱ ☞✌ ✘♦✌✲
★ ✩ ✭✪ ❂ ✵✮✒ ➄✌ ✚♦✖✖♦✇✌ ✚✟♦✓ ❊q✒ ✭✜❭✮✱ ✍✝✞ ✘♦✍✞✕✍☞❛✖✱ P
☞✍☞✏✞ ✚♦✟ ➙ ➥ ✵ ❛✕✎ ➙ ➥ ➦✒ ❚✝✞✟✞✚♦✟✞✱ ✚♦✟ ✍✝✞ ✞⑧☞✌✍✞✕✑✞ ♦✚ ✍✝✞
❹
④ ❂
❿✺➀✻
✻
⑨
①
✻
④
✦
⑨
❾ ❺
✻
✻
❻❼❙❽✷
☞✕✌✍❛✙☞✖☞✍②✱ ✍✝✞ ✘♦✍✞✕✍☞❛✖ ✌✝♦✉✖✎ ✝❛✏✞ ❛ ✕✞✔❛✍☞✏✞ ✓☞✕☞✓✉✓✒ ❚✝☞✌
✭✜✵✮
✤
☞✌ ✘♦✌✌☞✙✖✞ ✇✝✞✕ ★ ✩✦
✇✝✞✟✞ ❺❻❼❙❽✷
❂
➁
✜❳ ➲ ➂ ☞✌ ✍✝✞ ✚✟✞q✉✞✕✑② ♦✚ ✍✝✞ ☞✕✞✟✍☞❛✖ ✇❛✏✞✌✒
➁
➃✞✟✞✱ ➂ ❂ ➂✴⑨ ☞✌ ✍✝✞ ✉✕☞✍ ✏✞✑✍♦✟ ♦✚ ➂✒ ➄ ✕✞✑✞✌✌❛✟② ✑♦✕✎☞✍☞♦✕ ✚♦✟
↕ ✭➙ ❂ ➙
✑❛✖✖✞✎ ✍✉✟✕☞✕✔ ✘♦☞✕✍✌✮ ☞✕ ✇✝☞✑✝ P
✺➧✻ ✮ ❂ ✵✒ ❋☞✔✉✟✞ ✶ ✌✝♦✇✌
↕ ✭➙✮ ✚♦✟ ✎☞❴✞✟✞✕✍ ✏❛✖✉✞✌ ♦✚ ❩✒ ❚✝☞✌ ✟✞✘✟✞✌✞✕✍❛✍☞♦✕ ❛✖✖♦✇✌
✍❛✕✝ P
↕ ✭➙✮✒
✉✌ ✍♦ ✎☞✌✍☞✕✔✉☞✌✝ ✍✝✞ ✙✞✝❛✏☞♦✟ ✚♦✟ ✖♦✇ ✏❛✖✉✞✌ ♦✚ P
✍✝✞ ☞✕✌✍❛✙☞✖☞✍② ☞✌
✎◗❙❱
✎✪
✻
✻
↕ ✭➙✮ ✝❛✌
➋ ✭✶ ✰ ➙✮ ✒ ❲✝✞✕ ✍✝✞ ✘♦✍✞✕✍☞❛✖ P
❛ ✕✞✔❛✍☞✏✞ ✓☞✕☞✓✉✓✱ ✍✝✞✟✞ ❛✟✞ ✍✇♦ ✘♦☞✕✍✌ ➙✺ ❛✕✎ ➙✻ ✭✍✝✞ ✌♦✲
↕ ✭➙ ❂ ➙
➨✌☞✕✔ ❊q✒ ✭✜❭✮ ❛✕✎ ✍✝✞ ✑♦✕✎☞✍☞♦✕ P
✺➧✻ ✮ ❂ ✵✱ ✇✞ ✞✌✍☞✲
✓❛✍✞ ✍✝✞ ✓❛⑧☞✓✉✓ ✔✟♦✇✍✝ ✟❛✍✞ ♦✚ ✍✝✞ ☞✕✌✍❛✙☞✖☞✍② ❛✌
✭✜✶✮
➅ ✵➆
❹
✶
❶❊❷❸❝ ✑❛✕ ✙✞ ✞⑧✑☞✍✞✎ ✞✏✞✕ ☞✕ ❛ ✉✕☞✚♦✟✓ ✓✞❛✕ ✓❛✔✕✞✍☞✑ ✣✞✖✎✱
④ ❂
④
➛
➫
✻
✻
❾ ▼❩ ✰
➩
➭
④
✻
✻
❾ ▼❩
➩
➯✻
✻ ✻
✰ ✽❩ ④
③ ➩
❿
➳✺➀✻ ✺➀✻
✤
✭✜✽✮
✜
❛✕✎ ✍✝✞ ✌♦✉✟✑✞ ♦✚ ✚✟✞✞ ✞✕✞✟✔② ♦✚ ✍✝✞ ☞✕✌✍❛✙☞✖☞✍② ☞✌ ✘✟♦✏☞✎✞✎ ✙② ✍✝✞
✌✓❛✖✖✲✌✑❛✖✞ ✍✉✟✙✉✖✞✕✑✞✒ ❝✕ ✑♦✕✍✟❛✌✍✱ ✍✝✞ ✚✟✞✞ ✞✕✞✟✔② ☞✕ ❸❛✟❦✞✟➇✌
✓❛✔✕✞✍☞✑
✙✉♦②❛✕✑②
☞✕✌✍❛✙☞✖☞✍②
✭❸❛✟❦✞✟
✶⑥❬❬✮ ♦✟
☞✕
✍✝✞
✇✝✞✟✞
☞✕✍✞✟✲
✑✝❛✕✔✞ ☞✕✌✍❛✙☞✖☞✍② ✭❚✌✞✟❦♦✏✕☞❦♦✏ ✶⑥❬✵➈ ❸✟☞✞✌✍ ✶⑥✽✜✮ ☞✌ ✎✟❛✇✕
✚✟♦✓ ✍✝✞ ✔✟❛✏☞✍❛✍☞♦✕❛✖ ✣✞✖✎✒ ⑦♦✍✝ ☞✕✌✍❛✙☞✖☞✍☞✞✌ ❛✟✞ ✞⑧✑☞✍✞✎ ☞✕ ❛
④➩ ❂
✪➤ ➝❽➞➟
✺➀✻
➵➙✺ ➙✻ ✭✜ ✰ ➙✺ ✰ ➙✻ ✮➸
❍❏
✭✶ ✰ ➙✺ ✮✭✶ ✰ ➙✻ ✮
➲
✭✜⑥✮
➺➻➼➽ ♣✂❣❡ ➾ ✁➚ ➪
❆✫❆ ✺ ✁✂ ❆ ✾ ✭✷✄☎✷✆
➌
❋✝✞✳ ✶✳ t✟♥❤ ❯✭❘✆
✮♦r ☛➌ ✡ ☛✠☛☞ ❂ ✄✌✄✷✂ ✍ ❂ ✄✂ ✟♥❛ ✎ ❂ ✄✌✄☎ ✭❛♦tt❡❛
❧✏♥❡✆✂ ✄✑☎ ✭❛✟s❤❡❛✲❛♦tt❡❛ ❧✏♥❡✆✂ ✟♥❛ ☎ ✭s♦❧✏❛ ❧✏♥❡✆✑
❋✝✞✳ ➟✳ ➠❡❞❡♥❛❡♥❝❡ ♦✮ ☛✠☛☞➡ ♦♥ ✷✎✠☛☞➡ ✮♦r t❤r❡❡ ✈✟❧✉❡s ♦✮ ✍ ✮♦r ✷➠ s✏➢✲
✉❧✟t✏♦♥s ✇✏t❤ ➤➡✠➤➥➦➡ ❂ ✄✌☎✑
➉✛ ✐②❨❃❅❈✿✛❈ ✛❃✛✙✐②✚✛❁✐❃✛✿❀ ❨✿❅✿②✚❈✚❅ ✐❁ ❈❳✚ ➄❃❅✐❃❀✐❁ ✛❭②❢
❜✚❅✱ ➄❃ ✤ ✵✥✧➧➨➩➍ ❻➫ ✯ ❴❁✐✛✜ ❻➫ ✤ ➧➨➩➍ ✧◗➭➯ ✱ ❄✚ ✽✿✛ ✚➇❨❅✚❁❁ ❈❳✐❁
✐✛ ❈✚❅②❁ ❃❩ ❈❳✚ ❨✿❅✿②✚❈✚❅ ➲➳ ✤ ✥✧➭➯ ❻▼✦ ✱ ❄❳✐✽❳ ✐❁ ❃❩❈✚✛ ❭❁✚✙ ✐✛
②✚✿✛❢✣✚❀✙ ✙✘✛✿②❃ ❈❳✚❃❅✘✯ ❵❳❭❁✱ ❄✚ ❳✿❬✚
➄❃ ✤ ➵➭➯ ✥✧➧✦➨➩➍ ✤ ➵ ✰➭➯ ❻▼ ✧➧➨➩➍ ✼✦➲➳ P
❋✝✞✳ ✒✳ ❚❤❡♦r❡t✏❝✟❧ ❛❡❞❡♥❛❡♥❝❡ ♦✮ ☛✠☛☞ ♦♥ ✍ ✮♦r ❛✏✓❡r❡♥t ✈✟❧✉❡s ♦✮ ✔
✉s✏♥❣ ❊q✑ ✭✸✄✆✑ ❚❤❡ ✏♥s❡t s❤♦✇s t❤❡ ❛❡❞❡♥❛❡♥❝❡ ♦✮ ☛✠☛☞ ♦♥ ✷✎✠☛☞ ❂
✔✕✴✖ ✮♦r ✍ ❂ ✄✗ ✭s♦❧✏❛✆✂ ✺✗ ✭❛♦tt❡❛✆✂ ✟♥❛ ✾✄✗ ✭❛✟s❤❡❛✆✑
❇✘ ✙✚✣✛✐✛✜ ✢ ✤ ✹✥✦ ✧★✦✩ ✱ ✪✬✯ ✰✵✻✼ ✽✿✛ ✿❀❁❃ ❜✚ ❄❅✐❈❈✚✛ ✿❁
❍
❏
▲▼◆✦ ❖▼◆✦
❉
P
★✧★✩ ✤ ● ❉ ❾ ✢ ■ ❉ ❾ ✵✢ ❁✐✛✦ ❑ ■ ✢✦
✰◗❙✼
✵
●
❱❃❅ ✢ ❲ ❉✱ ❄✚ ❃❜❈✿✐✛ ★✧★✩ ✤ ✽❃❁ ❑✧ ✵✱ ❄❳✐✽❳ ✐❁ ✐✛✙✚❨✚✛✙✚✛❈ ❃❩
❈❳✚ ❬✿❀❭✚ ❃❩ ✢✯ ❪✛ ❱✐✜✯ ✵ ❄✚ ❨❀❃❈ ❈❳✚ ✙✚❨✚✛✙✚✛✽✚ ❃❩ ★✧★✩ ❃✛ ❑ ❩❃❅
✙✐❫✚❅✚✛❈ ❬✿❀❭✚❁ ❃❩ ✢ ✿✛✙ ❃✛ ✵✥✧★✩ ✤ ✢▼◆✦ ❩❃❅ ✙✐❫✚❅✚✛❈ ❬✿❀❭✚❁
❃❩ ❑ ✰✐✛❁✚❈✼✯
❴✛❩❃❅❈❭✛✿❈✚❀✘✱ ❈❳✚ ✿❁✘②❨❈❃❈✐✽ ✿✛✿❀✘❁✐❁ ✙❃✚❁ ✛❃❈ ✿❀❀❃❄ ❩❭❀❀
✐✛❩❃❅②✿❈✐❃✛ ✿❜❃❭❈ ❈❳✚ ❁✘❁❈✚②✯ ❵❳✚❅✚❩❃❅✚ ❄✚ ❈❭❅✛ ✐✛ ❈❳✚ ❩❃❀❀❃❄❢
✐✛✜ ❈❃ ✛❭②✚❅✐✽✿❀ ❁✐②❭❀✿❈✐❃✛❁ ❃❩ ❈❳✚ ❩❭❀❀ ✵❥ ✿✛✙ ◗❥ ②✚✿✛❢✣✚❀✙
✚✬❭✿❈✐❃✛❁✯
❦♠ ♣①③④⑤⑥⑦⑧⑨ ⑤④⑩①⑨❶⑩
❪✛ ❈❳✐❁ ❁✚✽❈✐❃✛ ❄✚ ✙✐❁✽❭❁❁ ✛❭②✚❅✐✽✿❀ ②✚✿✛❢✣✚❀✙ ②❃✙✚❀✐✛✜✯ ❷✚
✽❃✛❁✐✙✚❅ ✽❃②❨❭❈✿❈✐❃✛✿❀ ✙❃②✿✐✛❁ ❃❩ ❁✐❸✚ ❹✦ ❃❅ ❹❺ ❄✐❈❳ ❨✚❅✐❃✙✐✽
❜❃❭✛✙✿❅✘ ✽❃✛✙✐❈✐❃✛❁ ✐✛ ❈❳✚ ❳❃❅✐❸❃✛❈✿❀ ✙✐❅✚✽❈✐❃✛✰❁✼ ✿✛✙ ❁❈❅✚❁❁❢❩❅✚✚
❨✚❅❩✚✽❈ ✽❃✛✙❭✽❈❃❅ ❜❃❭✛✙✿❅✘ ✽❃✛✙✐❈✐❃✛❁ ✐✛ ❈❳✚ ❬✚❅❈✐✽✿❀ ✙✐❅✚✽❈✐❃✛✯
❵❳✚ ❁②✿❀❀✚❁❈ ❄✿❬✚✛❭②❜✚❅ ❈❳✿❈ ✣❈❁ ❳❃❅✐❸❃✛❈✿❀❀✘ ✐✛❈❃ ❈❳✚ ✙❃②✿✐✛
❳✿❁ ❈❳✚ ❄✿❬✚✛❭②❜✚❅ ❻▼ ✤ ✵❼✧❹✯ ❵❳✚ ✛❭②✚❅✐✽✿❀ ❁✐②❭❀✿❈✐❃✛❁ ✿❅✚
❨✚❅❩❃❅②✚✙ ❄✐❈❳ ❈❳✚ ❽❿➀➁➂➃ ➄➅➆❿▼ ✱ ❄❳✐✽❳ ❭❁✚❁ ❁✐➇❈❳❢❃❅✙✚❅ ✚➇❢
❨❀✐✽✐❈ ✣✛✐❈✚ ✙✐❫✚❅✚✛✽✚❁ ✐✛ ❁❨✿✽✚ ✿✛✙ ✿ ❈❳✐❅✙❢❃❅✙✚❅ ✿✽✽❭❅✿❈✚ ❈✐②✚
❁❈✚❨❨✐✛✜ ②✚❈❳❃✙ ✰❇❅✿✛✙✚✛❜❭❅✜ ➈ ❥❃❜❀✚❅ ✵❙❙✵✼✯ ➉❁ ❭✛✐❈❁ ❃❩
➊▼
❀✚✛✜❈❳ ❄✚ ❭❁✚ ❻➊▼
▼ ✱ ✿✛✙ ❈✐②✚ ✐❁ ②✚✿❁❭❅✚✙ ✐✛ ❭✛✐❈❁ ❃❩ ✰➋➍ ❻▼ ✼ ✯
✕ ➎➏➏➐➑➒➒➐➓➔→➣↔↕→➙➛➓➜➝➙➙➝↔➓→➙➛➓➜→➙➞
❆ ✾✂ ❞✟❣❡
♦✮ ✁
✰◗❉✼
➸❃❈✐❬✿❈✚✙ ❜✘ ❈❳✚ ✿✛✿❀✘❈✐✽ ❅✚❁❭❀❈❁ ❃❩ ❈❳✚ ❨❅✚❬✐❃❭❁ ❁✚✽❈✐❃✛ ❄✚ ✛❃❅❢
②✿❀✐❸✚ ❈❳✚ ✜❅❃❄❈❳ ❅✿❈✚ ❃❩ ❈❳✚ ✐✛❁❈✿❜✐❀✐❈✘ ✿❀❈✚❅✛✿❈✐❬✚❀✘ ❜✘ ✿ ✬❭✿✛❢
❈✐❈✘ ★✩➺ ➻ ➼➽ ➧➨➩➍ ✧➾➚ ✯ ❪✛ ❈❳✚ ❩❃❀❀❃❄✐✛✜ ❄✚ ❈✿➪✚ ➧➨➩➍ ✧➋➍ ✤ ❙P❉✯
❱❭❅❈❳✚❅②❃❅✚✱ ❄✚ ❭❁✚ ➶➯ ✤ ➭➯ ✤ ❉❙➊❺ ➋➍ ✧❻➫ ✱ ❁❃ ❈❳✿❈ ❻➫ ➾➚ ➹ ◗◗
✿✛✙ ➭➯ ❻▼ ✧➧➨➩➍ ✤ ❉❙➊✦ ✯ ❵❳✐❁ ✿❀❁❃ ②✚✿✛❁ ❈❳✿❈ ❩❃❅ ✥ ✤ ❙P❙❉✱ ❩❃❅
✚➇✿②❨❀✚✱ ❄✚ ❳✿❬✚ ✵✥✧★✩➺ ✤ ❙P✵➘ ✿✛✙ ➄❃ ✤ ❙P❙❙➵✯
❱❃❅ ❈❳✚ ②❃✙✚❀❁ ❨❅✚❁✚✛❈✚✙ ❜✚❀❃❄✱ ❄✚ ❭❁✚ ➴➷➺ ✤ ✵❙ ✿✛✙
➼➷ ✤ ❙P❉➵➘✱ ❄❳✐✽❳ ✽❃❅❅✚❁❨❃✛✙❁ ❈❃ ➼➽ ✤ ❙P➘➬✱ ✿✛✙ ✐❁ ✿❨❨❅❃❨❅✐❢
✿❈✚ ❩❃❅ ❈❳✚ ❨✿❅✿②✚❈✚❅ ❅✚✜✐②✚ ✐✛ ❄❳✐✽❳ ➮➩ ➹ ❉✻ ✿✛✙ ❻➫ ✧❻▼ ✤ ◗❙
✰➱✚②✚❀ ✚❈ ✿❀✯ ✵❙❉✵✙✼✯ ❷✚ ❭❁✚ ✚✐❈❳✚❅ ✃➺ ✧✃❐❒➺ ✤ ❙P❉ ❃❅ ❙P❙➬✯ ❷✚
❅✚✽✿❀❀✱ ❳❃❄✚❬✚❅✱ ❈❳✿❈ ❈❳✚ ✜❅❃❄❈❳ ❅✿❈✚ ✙❃✚❁ ✛❃❈ ✙✚❨✚✛✙ ❃✛ ❈❳✐❁
✽❳❃✐✽✚✱ ❨❅❃❬✐✙✚✙ ❈❳✚ ❜❭❀➪ ❃❩ ❈❳✚ ✚✐✜✚✛❩❭✛✽❈✐❃✛ ✣❈❁ ✐✛❈❃ ❈❳✚ ✙❃❢
②✿✐✛✱ ❄❳✐✽❳ ✐❁ ❈❳✚ ✽✿❁✚ ❳✚❅✚ ❩❃❅ ❜❃❈❳ ❬✿❀❭✚❁ ❃❩ ✃➺✯ ❱❃❅ ❈❳✚ ❀❃❄✚❅
❬✿❀❭✚ ❃❩ ✃➺ ❈❳✚ ②✿➇✐②❭② ❃❩ ❈❳✚ ②✿✜✛✚❈✐✽ ❁❈❅❭✽❈❭❅✚❁ ✰✐✯✚✯✱ ❈❳✚
②✿➇✐②❭② ❃❩ ❈❳✚ ✚✐✜✚✛❩❭✛✽❈✐❃✛ ✐✛ ❮✼ ✐❁ ❁❀✐✜❳❈❀✘ ❳✐✜❳✚❅ ❭❨ ✐✛
❈❳✚ ✙❃②✿✐✛✱ ❜❭❈ ✐✛ ❜❃❈❳ ✽✿❁✚❁ ❈❳✚ ②✿➇✐②❭② ✐❁ ✽❃✛❈✿✐✛✚✙ ❄✐❈❳✐✛
❈❳✚ ✙❃②✿✐✛✯
❷✚ ✙✐❁✽❭❁❁ ✣❅❁❈ ❈❳✚ ✥ ✿✛✙ ❑ ✙✚❨✚✛✙✚✛✽✚ ❃❩ ✵❥ ✿✛✙ ◗❥ ❁❃❀❭❢
❈✐❃✛❁✯ ❴❁✐✛✜ ❑ ✤ ❙❰ ✱ ✹➬❰ ✱ ✿✛✙ Ï❙❰ ✱ ✽❃❅❅✚❁❨❃✛✙✐✛✜ ❈❃ Ï❙❰ ✱ ✹➬❰ ✱
✿✛✙ ❙❰ ❀✿❈✐❈❭✙✚✱ ❄✚ ✣✛✙ ❈❳✿❈ Ð✪➸❽❪ ✐❁ ❁❭❨❨❅✚❁❁✚✙ ❩❃❅ ❅❃❈✿❢
❈✐❃✛ ❅✿❈✚❁ ✿❅❃❭✛✙ ✥ ➹ ❙P❙❉➋➍ ❻▼ ✿✛✙ ❙P❙✵➬ ✐✛ ✵❥ ✿✛✙ ◗❥✱ ✿❁
✽✿✛ ❜✚ ❁✚✚✛ ✐✛ ❱✐✜❁✯ ◗ ✿✛✙ ✹✯ ❵❳✐❁ ✽❃❅❅✚❁❨❃✛✙❁ ❈❃ ➄❃ ✤ ❙P❙❙➵
✿✛✙ ❙P❙❉➬✱ ❄❳✐✽❳ ✿❅✚ ❅✚②✿❅➪✿❜❀✘ ❀❃❄ ❬✿❀❭✚❁✯ ❷✚ ✛❃❈✚ ✿ ❁✐②✐❀✿❅
❜✚❳✿❬✐❃❅ ✐✛ ✵❥ ✿✛✙ ◗❥Ñ Ð✪➸❽❪ ✐❁ ❁❭❨❨❅✚❁❁✚✙ ❩❃❅ ✚❬✚✛ ❀❃❄✚❅
❬✿❀❭✚❁ ❃❩ ✵✥✧★✩➺ ✿❁ ❑ ✐✛✽❅✚✿❁✚❁✯ ➸❃❅✚❃❬✚❅✱ ❈❳✚❅✚ ✐❁ ✬❭✿❀✐❈✿❈✐❬✚
✿✜❅✚✚②✚✛❈ ❜✚❈❄✚✚✛ ❈❳✚ ❅✚❁❭❀❈❁ ❃❩ ②✚✿✛❢✣✚❀✙ ❁✐②❭❀✿❈✐❃✛❁ ✿✛✙ ❈❳✚
❨❅✚✙✐✽❈✐❃✛❁ ❜✿❁✚✙ ❃✛ ✿❁✘②❨❈❃❈✐✽ ✿✛✿❀✘❁✐❁✱ ✚❬✚✛ ❈❳❃❭✜❳ ✐✛ ❈❳✚ ❩❃❅❢
②✚❅ ✽✿❁✚ ❄✚ ✛❃❅②✿❀✐❸✚✙ ❜✘ ★✩➺ ✱ ❄❳✐❀✚ ✐✛ ❈❳✚ ❀✿❈❈✚❅ ❄✚ ✛❃❅②✿❀✐❸✚✙
❜✘ ★✩ Ò ❁✚✚ ✪✬✯ ✰◗❙✼✯
Ð✚➇❈✱ ❄✚ ❬✿❅✘ ❑✯ ➉❁ ✚➇❨✚✽❈✚✙ ❩❅❃② ❈❳✚ ❅✚❁❭❀❈❁ ❃❩ Ó✚✽❈✯ ◗✱
✿✛✙ ✿❁ ✿❀❅✚✿✙✘ ❁✚✚✛ ✐✛ ❱✐✜❁✯ ◗ ✿✛✙ ✹✱ ❈❳✚ ❀✿❅✜✚❁❈ ✜❅❃❄❈❳ ❅✿❈✚❁
❃✽✽❭❅ ✿❈ ❈❳✚ ❨❃❀✚❁ ✰❑ ✤ ❙❰ ✼✱ ✿✛✙ Ð✪➸❽❪ ✐❁ ❈❳✚ ②❃❁❈ ❁❈❅❃✛✜❀✘
❁❭❨❨❅✚❁❁✚✙ ✿❈ ❈❳✚ ✚✬❭✿❈❃❅✯ ❵❳✚ ✜❅❃❄❈❳ ❅✿❈✚ ✿❁ ✿ ❩❭✛✽❈✐❃✛ ❃❩ ❑ ✐❁
✜✐❬✚✛ ✐✛ ❱✐✜✯ ➬ ❩❃❅ ❈❄❃ ❬✿❀❭✚❁ ❃❩ ✵✥✧★✩➺ ✱ ❁❳❃❄✐✛✜ ✿ ②✐✛✐②❭②
✿❈ ❑ ✤ Ï❙❰ ✰✐✯✚✯✱ ✿❈ ❈❳✚ ✚✬❭✿❈❃❅✼✯ ❪✛ ❈❳✚ ❭❨❨✚❅ ❨✿✛✚❀ ❃❩ ❱✐✜✯ ➬✱
■ ❘
▲✁s✂❞✂ ❡t ✂❧ ✳ ◆❡❣✂t✄✈❡ ♠✂❣♥❡t✄☎ ♣r❡ss✆r❡ ✄♥st✂❜✄❧✄t✐
❋✝✞✟ ✹✟ ❉❡♣❡♥❞❡♥☎❡ ✁❢ ☛✠☛ ✡✵ ✁♥ ✷☞✠☛ ✡✵ ❢✁r t❤r❡❡ ✈✂❧✆❡s ✁❢ ✌ ❢✁r ✸❉ s✄♠✍
✆❧✂t✄✁♥s ✇✄t❤ ❇✵✠ ❇✎✏✵ ❂ ✑✒✑✓
❋✝✞✟ ❹✟ ❺r❡❻✆❡♥☎✐ ✂♥❞ ✂♠♣❧✄t✆❞❡ ✂s ✂ ❢✆♥☎t✄✁♥ ✁❢ ☞ ❢✁r ✌
❂ ❼✑
❽
✂♥❞
❇✵ ✠❇✎✏✵ ❂ ✑✒❾ ✄♥ t❤❡ s✂t✆r✂t❡❞ r❡❣✄♠❡
❋✝✞✟ ✺✟ ❉❡♣❡♥❞❡♥☎❡ ✁❢ ☛✠☛ ✡✵ ✁♥ ✌ ❢✁r t✇✁ ✈✂❧✆❡s ✁❢ ✷☞ ✵ ✠☛ ✡✵ ✄♥ ✷❉ ✭✉✔✕
✔✖✗ ✔✘✙✖✚✮ ✂♥❞ ☎✁♠♣✂r✄s✁♥ ✁❢ ✷❉ ✂♥❞ ✸❉ ☎✂s❡s ✭✚♦✛✖✗ ✔✘✙✖✚✮
❋✝✞✟ ❿✟ ❺r❡❻✆❡♥☎✐ ✂♥❞ ✂♠♣❧✄t✆❞❡ ✌
✜✢ ✣❛✤✢ ✥✦✢✧ ★✩ ✪✢✦✥✫✬✦✯ ✰✱✢✱ ✜✢ ✪✢✦✬✪✰✲✬✢✧ ✴✥✪✦✢✫✤✢✦ ✬✴ ✦✴✫✥✬✰✴✶✦
✜✰✬✣ ✻✼✻✽
✾
❞❡♣❡♥❞❡♥☎❡
❢✁r ☞
❂
✑✒✑❾ ✂♥❞
❇✵ ✠❇✎✏✵ ❂ ✑✒❾
✿✯ ❛✦ ✜❛✦ ❛✫✦✴ ✧✴✶✢ ✰✶ ❙✢✲✬✱ ❀✱ ❁✴✜✢✤✢✪✯ ✬✣✰✦ ✰✦
✴✶✫② ❛✶ ❛❃❃✪✴❄✰❅❛✬✰✴✶ ✴❆ ✬✣✢ ❆✥✫✫② ❀✩ ✲❛✦✢✱ ❚✣✢ ✥✦✢❆✥✫✶✢✦✦ ✴❆
❶✶ ✦✥❅❅❛✪②✯ ✬✣✢ ✴✦✲✰✫✫❛✬✰✴✶ ❆✪✢q✥✢✶✲② ✧✢✲✪✢❛✦✢✦ ❖❛✶✧ ✬✣✢ ❃✢❴
✬✣✰✦ ✪✢✦✬✪✰✲✬✰✴✶ ✲❛✶ ❈✢ ❛✦✦✢✦✦✢✧ ❈② ✲✴❅❃❛✪✰✶❊ ★✩ ❛✶✧ ❀✩ ✪✢✦✥✫✬✦●
✪✰✴✧ ✰✶✲✪✢❛✦✢✦❳ ❆✴✪ ❆❛✦✬✢✪ ✪✴✬❛✬✰✴✶ ❛✦ ✬✣✢ ❊✪✴✜✬✣ ✪❛✬✢ ✧✰❅✰✶✰✦✣✢✦✱
✦✢✢ ✬✣✢ ✫✴✜✢✪ ❃❛✶✢✫ ✴❆ ❍✰❊✱ ❏✱ ❲✣✰✫✢ ✬✣✢ ❑ ✧✢❃✢✶✧✢✶✲✢ ✰✦ ✪✴✥❊✣✫②
❍✥✪✬✣✢✪❅✴✪✢✯ ✬✣✢ ✴✦✲✰✫✫❛✬✰✴✶ ❆✪✢q✥✢✶✲② ✰✦ ✦②✦✬✢❅❛✬✰✲❛✫✫② ✫✴✜✢✪ ❛✬
✦✰❅✰✫❛✪ ✰✶ ✬✣✢ ★✩ ❛✶✧ ❀✩ ✲❛✦✢✦✯ ✬✣✢ ❊✪✴✜✬✣ ✪❛✬✢✦ ❛✪✢ ❈② ❛✬ ✫✢❛✦✬ ❛
⑦
✫✴✜ ✫❛✬✰✬✥✧✢✦ ❖❈✢✫✴✜ ❸❏ ❳ ❛✶✧ ✣✰❊✣✢✪ ✲✫✴✦✢✪ ✬✴ ✬✣✢ ❃✴✫✢✦✱ ❲✢ ✪✢❴
❆❛✲✬✴✪ ✴❆ ✬✜✴ ✫✴✜✢✪ ✰✶ ✬✣✢ ★✩ ✲❛✦✢✱
❚✴
✧✢✬✢✪❅✰✶✢
✬✣✢
✴✦✲✰✫✫❛✬✴✪②
✲❛✫✫ ✬✣❛✬ ✬✣✢✦✢ ✴✦✲✰✫✫❛✬✰✴✶✦ ✴✲✲✥✪ ✴✶✫② ✰✶ ✬✣✢ ✶✴✶✫✰✶✢❛✪ ✪✢❊✰❅✢✯ ✦✴
❆✪✢q✥✢✶✲②✯
✜✢
✲✴✶✦✰✧✢✪
✬✣✢
✶✴ ❅✢❛✶✰✶❊❆✥✫ ✲✴❅❃❛✪✰✦✴✶ ✜✰✬✣ ✫✰✶✢❛✪ ✬✣✢✴✪② ✰✦ ❃✴✦✦✰❈✫✢✱
✤❛✫✥✢✦ ✴❆ ❯ ▼ ❖ ①P ◗ ❱ ❳ ❛✶✧ ❨▼ ❖ ①P ◗ ❱ ❳ ❛✬ ❛ ❩❄✢✧ ❃✴✰✶✬ ① P ✜✰✬✣✰✶ ✬✣✢
➀✰✤✢✶ ✬✣✢ ✲✴❅❈✰✶✢✧ ❃✪✢✦✢✶✲✢ ✴❆ ✪✴✬❛✬✰✴✶ ❛✶✧ ✦✬✪❛✬✰❩✲❛✬✰✴✶✯
✧✴❅❛✰✶✱ ❬✦ ✲❛✶ ❈✢ ✦✢✢✶ ✰✶ ❍✰❊✦✱ ❭ ❛✶✧ ❪✯ ✬✣✢✰✪ ❆✪✢q✥✢✶✲② ❛✶✧
✜✢ ✢❄❃✢✲✬ ✬✣✢ ✪✢✦✥✫✬✰✶❊ ✤✢✫✴✲✰✬② ❛✶✧ ❅❛❊✶✢✬✰✲ ❩✢✫✧✦ ✬✴ ❈✢ ✣✢✫✰❴
❛❅❃✫✰✬✥✧✢ ✧✢❃✢✶✧ ✴✶ ❈✴✬✣ ❫ ❛✶✧ ❑✱ ❚✣✢ ✴✦✲✰✫✫❛✬✰✴✶✦ ❛✪✢ ✶✴✬ ❛✫❴
✲❛✫✱ ❲✢ ❃✫✴✬ ✪✢✫❛✬✰✤✢ ❵✰✶✢✬✰✲✯ ✲✥✪✪✢✶✬✯ ❛✶✧ ✲✪✴✦✦ ✣✢✫✰✲✰✬✰✢✦ ✰✶ ✬✣✢
✜❛②✦ ✣❛✪❅✴✶✰✲ ✴✶✢✦✯ ❛✶✧ ✲❛✶ ❈✢ ✰✪✪✢❊✥✫❛✪ ✜✰✬✣ ✤❛✪✰❛❈✫✢ ❃✢✪✰✴✧✦✯
✥❃❃✢✪ ❃❛✶✢✫ ✴❆ ❍✰❊✱ ➁✱ ❚✣✢✦✢ ❛✪✢ ✣✢✪✢ ❛❈❈✪✢✤✰❛✬✢✧ ✰✶ ✬✢✪❅✦ ✴❆ ✬✣✢
❅❛❵✰✶❊ ✬✣✢ ❃✢✪✰✴✧ ✧✢✬✢✪❅✰✶❛✬✰✴✶ ❅✴✪✢ ✧✰❝✲✥✫✬✱ ❥✢✤✢✪✬✣✢✫✢✦✦✯
❆✥✶✲✬✰✴✶
✬✣✢ ❆✪✢q✥✢✶✲✰✢✦ ❆✴✪ ❯ ▼ ❛✶✧ ❨▼ ❛✪✢ ✦✰❅✰✫❛✪ ✴✤✢✪ ❈✪✴❛✧ ❃❛✪❛❅✢❴
⑦
✬✢✪ ✪❛✶❊✢✦✱ ❍✴✪ ❫❦ ✼③④❦ ⑤ ✿⑥★❏ ❛✬ ❑ ✾ ❭✿ ✯ ❥⑧⑨⑩❶ ✰✦ ✶✴ ✫✴✶❊✢✪
➂ ❖ ➃◗ ➄❳ ✾ ➅ ➃ ➲ ➄➆✼
➇
➈
➈
➅ ➃ ➆➅ ➄ ➆◗
❖❀★❳
✢❄✲✰✬✢✧✯ ❈✥✬ ✬✣✢✪✢ ❛✪✢ ✦✬✰✫✫ ✴✦✲✰✫✫❛✬✰✴✶✦ ✰✶ ❯ ▼ ❖ ①P ◗ ❱ ❳✯ ✜✣✰✲✣ ❅✥✦✬
➃ ❛✶✧ ➄ ❛✪✢ ✬✜✴ ❛✪❈✰✬✪❛✪② ✤✢✲✬✴✪✦✱ ❁✢✪✢✯ ➅➲➆ ✧✢✶✴✬✢✦ ➉✽
✬✣✢✶ ✣❛✤✢ ✦✴❅✢ ✴✬✣✢✪ ✲❛✥✦✢✱ ❲✢ ❩✶✧ ❛ ✦✥❈✦✬❛✶✬✰❛✫ ✤❛✪✰❛✬✰✴✶ ✰✶
✜✣✢✪✢
✬✣✢ ❛❅❃✫✰✬✥✧✢ ❆✴✪ ✬✣✢ ❅❛❄✰❅✥❅ ❊✪✴✜✬✣ ✪❛✬✢ ❆✴✪ ❫ ✾ ✿⑥✿❷ ❛✶✧
❛✤✢✪❛❊✰✶❊✱ ❚✣✢ ✪✢✫❛✬✰✤✢ ❵✰✶✢✬✰✲ ✣✢✫✰✲✰✬②✯ ➂ ❖➊◗ ➋❳✯ ✜✣✢✪✢ ➊
❫
✿⑥✿★✱ ❖❚✣✢ ✣✰❊✣ ❆✪✢q✥✢✶✲② ✰✶ ❯ ▼ ❛✶✧ ❨▼ ✰✶ ❍✰❊✱ ❭ ✲✴✪✪✢❴
➌ × ➋ ✰✦ ✬✣✢ ❅✢❛✶ ✤✴✪✬✰✲✰✬②✯ ✤❛✪✰✢✦ ❈✢✬✜✢✢✶ ✶✢❛✪✫② ➍❷ ✰✶ ✬✣✢
✦❃✴✶✧✦ ✬✴ ❛ ✪❛✶✧✴❅ ✦❅❛✫✫❴❛❅❃✫✰✬✥✧✢ ✲✣❛✶❊✢✱❳ ❚✣✢ ❆✪✢q✥✢✶✲② ✴❆
✫✴✜✢✪ ❃❛✪✬ ❛✶✧ ➎❷ ✰✶ ✬✣✢ ✥❃❃✢✪ ❃❛✪✬✱ ❚✣✰✦ ✲✣❛✶❊✢ ✴❆ ✦✰❊✶ ✰✦ ❆❛❅✰✫❴
✾
✾
✬✣✢ ✴✦✲✰✫✫❛✬✰✴✶✦ ✰✦ ✤✢✪② ✫✴✜ ❛✬ ✬✣✢ ❃✴✫✢✦✯ ❈✥✬ ✰✬ ✪✢❛✲✣✢✦ ❛ ❅❛❄✰❴
✰❛✪ ❆✪✴❅ ✫❛❅✰✶❛✪ ✲✴✶✤✢✲✬✰✴✶ ✜✣✢✪✢ ✥❃✜✢✫✫✰✶❊✦ ✢❄❃❛✶✧ ✬✴ ❃✪✴❴
❅✥❅ ❛✬ ❑ ✾ ❸❏ ❛✶✧ ✧✢✲✪✢❛✦✢✦ ❛❊❛✰✶ ✬✴✜❛✪✧ ✬✣✢ ✢q✥❛✬✴✪✱
✧✥✲✢ ✶✢❊❛✬✰✤✢ ✣✢✫✰✲✰✬② ✰✶ ✬✣✢ ✥❃❃✢✪ ❃❛✪✬✦✯ ❛✶✧ ✧✴✜✶✜✢✫✫✰✶❊✦ ❛✫✦✴
➏➐➑➒ ♣✂❣❡ ✓ ✁❢ ➓
❆✫❆ ✺ ✁✂ ❆ ✾ ✭✷✄☎✷✆
❋✝✞✳ ✽✳ ❉✟♣✟♥❞✟♥❝✟ ♦❢ ✈❛r✐♦✉s r✟❧❛t✐✈✟ ❤✟❧✐❝✐t✐✟s ❛♥❞ r✟❧❛t✐✈✟ ❛♠♣❧✐t✉❞✟s
♦♥ ③ ❢♦r t❤✟ ❝❛s✟ ✇✐t❤ ✡ ❂ ✄☛ ❛♥❞ ❈♦ ❂ ✄✠✄✵☞
❡①✌✍✎✏ ✍✑ ✒✓❡② ✓✔✒ ✒✓❡ ❜✕✒✒✕✖ ✕✗ ✒✓❡ ✏✕✖✍✔✎ ✘❡✙✚✙ ❇✛✍✎✏❡✎❜✜✛✚
❡✒ ✍✢✙ ✶✣✣✤✮✙ ❍✕✥❡✦❡✛✱ ✔✎ ✒✓❡ ✢✕✥❡✛ ✌✍✛✒ ✕✗ ✒✓❡ ✏✕✖✍✔✎ ❜✕✒✓ ❯
✍✎✏ ❲ ✍✛❡ ✛❡✢✍✒✔✦❡✢② ✑✖✍✢✢✱ ✍✑ ✧✍✎ ❜❡ ✑❡❡✎ ❜② ✧✕✎✑✔✏❡✛✔✎✚ ✒✓❡✔✛
✛❡✢✍✒✔✦❡ ✍✖✌✢✔✒✜✏❡✑✱ ★✘❯✮ ✍✎✏ ★✘❲✮✱ ✥✓❡✛❡
★✘ ✩✮ ✪ ✬ ✩✯ ✰✴✬✬ ✩✯ ✰✰✲
✘✸✸✮
✥✔✒✓ ✬✬✹✰✰ ❜❡✔✎✚ ✏❡✻✎❡✏ ✍✑ ✦✕✢✜✖❡ ✍✦❡✛✍✚❡✑✙
■✒ ✥✔✢✢ ❜❡ ✔✖✌✕✛✒✍✎✒ ✒✕ ✧✕✖✌✍✛❡ ✒✓❡ ✌✛❡✑❡✎✒ ✌✛❡✏✔✧✒✔✕✎✑ ✕✗
✢✍✛✚❡✼✑✧✍✢❡ ❦✔✎❡✒✔✧ ✍✎✏ ✖✍✚✎❡✒✔✧ ✓❡✢✔✧✔✒② ✌✛✕✏✜✧✒✔✕✎ ✥✔✒✓ ✛❡✑✜✢✒✑
✗✛✕✖ ✗✜✒✜✛❡ ✿◆❙✙ ❖✎❡ ✖✔✚✓✒ ❡①✌❡✧✒ ✏✔❀❡✛❡✎✧❡✑ ❜❡✒✥❡❡✎ ✒✓❡ ✒✥✕✱
❜❡✧✍✜✑❡ ✕✜✛ ✧✜✛✛❡✎✒ ✖❡✍✎✼✻❡✢✏ ✖✕✏❡✢✑ ✔✚✎✕✛❡ ✒✜✛❜✜✢❡✎✒ ✒✛✍✎✑✌✕✛✒
✧✕❡❁✧✔❡✎✒✑ ✒✓✍✒ ✍✛❡ ✍✑✑✕✧✔✍✒❡✏ ✥✔✒✓ ✓❡✢✔✧✔✒②❃ ✑❡❡ ✒✓❡ ✏✔✑✧✜✑✑✔✕✎
✍✒ ✒✓❡ ❡✎✏ ✕✗ ❑❡✖❡✢ ❡✒ ✍✢✙ ✘❄✤✶❄❜✮✙
❅❡ ✻✎✍✢✢② ✒✜✛✎ ✒✕ ✒✓❡ ✑✌✍✒✔✍✢ ✑✒✛✜✧✒✜✛❡ ✕✗ ◆❊●❏■✙ ■✎ ▲✔✚✙ ✣
✥❡ ✧✕✖✌✍✛❡ ▼P ✍✒ ✏✔❀❡✛❡✎✒ ✒✔✖❡✑ ✍✎✏ ✢✍✒✔✒✜✏❡✑ ✗✕✛ ✒✓❡ ❄✿ ✛✜✎✑✙
■✎ ✒✓❡ ❡①✌✕✎❡✎✒✔✍✢✢② ✚✛✕✥✔✎✚ ✌✓✍✑❡ ✕✗ ◆❊●❏■✱ ✒✓❡ ✑✒✛✜✧✒✜✛❡✑ ✏✕
✎✕✒ ✌✛✕✌✍✚✍✒❡ ✘✕✛ ✖✕✦❡ ✕✎✢② ✦❡✛② ✑✢✕✥✢②✮✙ ❚✛✍✦❡✢✔✎✚ ✥✍✦❡ ✑✕✢✜✼
✒✔✕✎✑ ✕✧✧✜✛ ✖✍✔✎✢② ✔✎ ✍ ✢✍✒❡✛ ✑✒✍✚❡ ✕✗ ◆❊●❏■✱ ✔✙❡✙✱ ✔✎ ✒✓❡ ✑✍✒✜✼
✛✍✒❡✏ ✛❡✚✔✖❡✙ ◆❡①✒✱ ✥❡ ✧✕✎✑✔✏❡✛ ✒✓❡ ✸✿ ✧✍✑❡✙ ■✎ ▲✔✚✙ ✶✤ ✥❡ ✑✓✕✥
✦✔✑✜✍✢✔◗✍✒✔✕✎✑ ✕✗ ✒✓❡ ✖✍✚✎❡✒✔✧ ✻❡✢✏ ✕✎ ✒✓❡ ✌❡✛✔✌✓❡✛② ✕✗ ✒✓❡ ✧✕✖✼
✌✜✒✍✒✔✕✎✍✢ ✏✕✖✍✔✎ ✗✕✛ ✗✕✜✛ ✏✔❀❡✛❡✎✒ ✒✔✖❡✑ ✗✕✛ ❘ ✪ ✤✙ ●✍✚✎❡✒✔✧
✑✒✛✜✧✒✜✛❡✑ ✍✛❡ ✔✎✧✢✔✎❡✏ ✔✎ ✒✓❡ ❱❳ ✌✢✍✎❡✙ ❚✓✔✑ ✔✑ ✍ ✏✔✛❡✧✒ ✛❡✑✜✢✒ ✕✗
✛✕✒✍✒✔✕✎✙ ❨✑ ❡①✌❡✧✒❡✏✱ ✒✓❡ ✔✎✧✢✔✎✍✒✔✕✎ ✔✑ ✕✌✌✕✑✔✒❡ ✗✕✛ ✎❡✚✍✒✔✦❡ ✦✍✢✼
✜❡✑ ✕✗ ❩❃ ✑❡❡ ▲✔✚✙ ✶✶✙ ❚✓❡ ✖✕✏✜✢✜✑ ✕✗ ✒✓❡ ✔✎✧✢✔✎✍✒✔✕✎ ✍✎✚✢❡ ✔✑
✍❜✕✜✒ ✸✤❬ ✱ ✧✕✛✛❡✑✌✕✎✏✔✎✚ ✒✕ ✤✙❭ ✛✍✏✔✍✎✑✱ ✥✓✔✧✓ ✔✑ ✎✕✒ ✧✕✖✌✍✒✼
✔❜✢❡ ✥✔✒✓ ✒✓❡ ✦✍✢✜❡ ✕✗ ❪✕ ❫ ✤❴✤✸✱ ❜✜✒ ✔✒ ✔✑ ✧✢✕✑❡✛ ✒✕ ✒✓❡ ✦✍✢✜❡
✕✗ ❩✴❵❣❥ ❫ ✤❴q❭✙ ❍✕✥❡✦❡✛✱ ✔✎ ✒✓✔✑ ✧✕✎✎❡✧✒✔✕✎ ✥❡ ✑✓✕✜✢✏ ✑✒✛❡✑✑
✒✓✍✒ ✥❡ ✓✍✦❡ ✔✖✌✕✑❡✏ ✌❡✛✔✕✏✔✧ ❜✕✜✎✏✍✛② ✧✕✎✏✔✒✔✕✎✑ ✔✎ ✒✓❡ ❳ ✏✔✼
✛❡✧✒✔✕✎✱ ✥✓✔✧✓ ✖❡✍✎✑ ✒✓✍✒ ✒✓❡ ✔✎✧✢✔✎✍✒✔✕✎ ✍✎✚✢❡✑ ✕✎✢② ✧✓✍✎✚❡ ✔✎
✏✔✑✧✛❡✒❡ ✑✒❡✌✑✙ ■✎ ✒✓❡ ❄✿ ✛✜✎✑✱ ✑✓✕✥✎ ✔✎ ▲✔✚✙ ✣✱ ✎✕ ✔✎✧✢✔✎✍✒✔✕✎ ✔✎
✒✓❡ ❱❳ ✌✢✍✎❡ ✔✑ ✌✕✑✑✔❜✢❡ ✍✒ ✍✢✢✙
④❡✒✜✛✎✔✎✚ ✒✕ ✒✓❡ ✧✍✑❡ ✕✗ ✌✕✑✔✒✔✦❡ ✦✍✢✜❡✑ ✕✗ ❩✱ ❜✜✒ ❘ ⑤ ✤✱ ✥❡
✎✕✒❡ ✍ ✑✢✕✥ ✖✔✚✛✍✒✔✕✎ ✕✗ ✒✓❡ ✖✍✚✎❡✒✔✧ ✌✍✒✒❡✛✎ ✒✕ ✒✓❡ ✢❡✗✒ ✘✓❡✛❡
✗✕✛ ❘ ✪ ⑥❭❬✮✱ ✧✕✛✛❡✑✌✕✎✏✔✎✚ ✒✕ ✌✕✢❡✥✍✛✏ ✖✔✚✛✍✒✔✕✎❃ ✑❡❡ ▲✔✚✙ ✶❄✙
❨✢✑✕ ✒✓❡ ✻❡✢✏ ✔✑ ✑✒✔✢✢ ✒✔✢✒❡✏ ✔✎ ✒✓❡ ❱❳ ✌✢✍✎❡✙ ▲✔✎✍✢✢②✱ ✗✕✛ ❘ ✪ ✣✤❬
✥❡ ✑❡❡ ✒✓✍✒ ✒✓❡ ✌✍✒✒❡✛✎ ✑✌❡❡✏ ✧✕✛✛❡✑✌✕✎✏✑ ✒✕ ✌✛✕✚✛✍✏❡ ✖✕✒✔✕✎❃
✑❡❡ ▲✔✚✙ ✶✸✙
❆ ✾✂ ♣❛❹✟ ❺ ♦❢ ✁
❋✝✞✳ ⑦✳ ⑧✈♦❧✉t✐♦♥ ♦❢ ⑨⑩ ✐♥ t❤✟ ❶③ ♣❧❛♥✟ ✐♥ ❛ ✷❉ s✐♠✉❧❛t✐♦♥ ❢♦r ❷❸ ❂ ✄✠✄☎
✭❝♦rr✟s♣♦♥❞✐♥❹ t♦ ❈♦ ❂ ✄✠✄✄❺✆ ❛♥❞ ⑨❸❻⑨❼❽❸ ❂ ✄✠☎ ❢♦r ✡ ❂ ✄☛ ✂ ✡ ❂ ✺☛ ✂
❛♥❞ ✡ ❂ ✾✄☛ ♥✟❛r t❤✟ t✐♠✟ ✇❤✟♥ t❤✟ ✐♥st❛❾✐❧✐t❿ s❛t✉r❛t✟s☞ ➀❤✟ ❞✐r✟❝t✐♦♥
♦❢ ➁ ✐s ✐♥❞✐❝❛t✟❞ ✐♥ t❤✟ ❧❛st r♦✇☞
➂➃ ➄➅➆➇➈➉➊➋➅➆➊
❨✢✒✓✕✜✚✓ ✒✓❡ ✌✓②✑✔✧✍✢ ✛❡✍✢✔✒② ✕✗ ◆❊●❏■ ✓✍✑ ✛❡✧❡✎✒✢② ❜❡❡✎ ✧✕✎✼
✻✛✖❡✏ ❜② ✏✔✛❡✧✒ ✎✜✖❡✛✔✧✍✢ ✑✔✖✜✢✍✒✔✕✎✑✱ ✔✒✑ ✌✕✒❡✎✒✔✍✢ ✛✕✢❡ ✔✎ ✌✛✕✼
✏✜✧✔✎✚ ✢✍✛✚❡✼✑✧✍✢❡ ✖✍✚✎❡✒✔✧ ✑✒✛✜✧✒✜✛❡✑ ✔✎ ✒✓❡ ❙✜✎ ✔✑ ✑✒✔✢✢ ✜✎✧✢❡✍✛✙
❚✓✔✑ ✌✍✌❡✛ ❜❡✚✔✎✑ ✒✓❡ ✒✍✑❦ ✕✗ ✔✎✦❡✑✒✔✚✍✒✔✎✚ ✔✒✑ ✌✛✕✌❡✛✒✔❡✑ ✜✎✏❡✛
✧✕✎✏✔✒✔✕✎✑ ✒✓✍✒ ✍✛❡ ✍✑✒✛✕✌✓②✑✔✧✍✢✢② ✔✖✌✕✛✒✍✎✒✙ ④✕✒✍✒✔✕✎ ✔✑ ✜❜✔➌✼
✜✔✒✕✜✑ ✍✎✏ ✧✢❡✍✛✢② ✔✖✌✕✛✒✍✎✒ ✔✎ ✒✓❡ ❙✜✎✙ ❚✓❡ ✌✛❡✑❡✎✒ ✥✕✛❦ ✓✍✑
✎✕✥ ✑✓✕✥✎ ✒✓✍✒ ✒✓❡ ✔✎✑✒✍❜✔✢✔✒② ✔✑ ✑✜✌✌✛❡✑✑❡✏ ✍✢✛❡✍✏② ✗✕✛ ✛✍✒✓❡✛
✑✢✕✥ ✛✕✒✍✒✔✕✎✙ ❚✓✔✑ ✔✑ ✛✍✒✓❡✛ ✑✜✛✌✛✔✑✔✎✚✱ ❜❡✧✍✜✑❡ ✛✕✒✍✒✔✕✎✍✢ ❡✗✼
✗❡✧✒✑ ✎✕✛✖✍✢✢② ❜❡✧✕✖❡ ✑✔✚✎✔✻✧✍✎✒ ✕✎✢② ✥✓❡✎ ❩ ✔✑ ✧✕✖✌✍✛✍❜✢❡
✒✕ ✒✓❡ ✔✎✦❡✛✑❡ ✒✜✛✎✕✦❡✛ ✒✔✖❡✱ ✥✓✔✧✓ ✔✑ ✏❡✻✎❡✏ ✓❡✛❡ ✍✑ ➍➎➏➐ ➑➒ ✙
❚✓❡ ✔✎✑✒✍❜✔✢✔✒② ✚✛✕✥✒✓ ✛✍✒❡ ✑✧✍✢❡ ✖✔✚✓✒ ❡①✌✢✍✔✎ ✒✓✔✑ ❜❡✓✍✦✔✕✜✛✱
✑✔✎✧❡ ✔✒ ✔✑ ✧✢✕✑❡✛ ✒✕ ✒✓❡ ✒✜✛❜✜✢❡✎✒ ✏✔❀✜✑✔✦❡ ✒✔✖❡ ✒✓✍✎ ✒✕ ✒✓❡ ✔✎✼
✦❡✛✑❡ ✒✜✛✎✕✦❡✛✱ ✥✓✔✧✓ ✔✑ ✗✍✑✒❡✛ ❜② ✒✓❡ ✑➌✜✍✛❡ ✕✗ ✒✓❡ ✑✧✍✢❡ ✑❡✌✍✼
✛✍✒✔✕✎ ✛✍✒✔✕ ✘❇✛✍✎✏❡✎❜✜✛✚ ❡✒ ✍✢✙ ❄✤✶✶✮✙ ❍✕✥❡✦❡✛✱ ✕✜✛ ✥✕✛❦ ✎✕✥
✑✜✚✚❡✑✒✑ ✒✓✍✒ ✒✓✔✑ ✔✑ ✎✕✒ ➌✜✔✒❡ ✛✔✚✓✒ ❡✔✒✓❡✛ ✍✎✏ ✒✓✍✒ ✒✓❡ ✧✕✛✛❡✧✒ ✍✎✼
✑✥❡✛ ✖✔✚✓✒ ❜❡ ✑✕✖❡✒✓✔✎✚ ✔✎ ❜❡✒✥❡❡✎✙ ■✎✏❡❡✏✱ ✥❡ ✻✎✏ ✓❡✛❡ ✒✓✍✒
✚✛✕✥✒✓ ✛✍✒❡ ✍✎✏ ✧✛✔✒✔✧✍✢ ✛✕✒✍✒✔✕✎ ✛✍✒❡ ✍✛❡ ✧✢✕✑❡ ✒✕ ✒✓❡ ✌✍✛✍✖❡✒❡✛
❵❣❥ ✪ ➓➔ ➍➎➏➐ ✴→➣ ✱ ✥✓✔✧✓ ✧✍✎ ❜❡ ✑✖✍✢✢❡✛ ✒✓✍✎ ✒✓❡ ✍✗✕✛❡✖❡✎✒✔✕✎❡✏
✒✜✛✎✕✦❡✛ ✒✔✖❡ ❜② ✍ ✗✍✧✒✕✛ ✕✗ ⑥✤✱ ✍✢✒✓✕✜✚✓ ✔✎ ✑✕✢✍✛ ✧✕✎✦❡✧✒✔✕✎✱
✥✓❡✛❡ ➑➒ →➣ ❫ ❄❴⑥ ✘❑❡✖❡✢ ❡✒ ✍✢✙ ❄✤✶❄✏✮ ✍✎✏ ➓➔ ❫ ✤❴❄✸ ✘❑❡✖❡✢
❡✒ ✍✢✙ ❄✤✶❄✧✮✱ ✔✒ ✔✑ ❡✑✒✔✖✍✒❡✏ ✒✕ ❜❡ ✕✎✢② ❫✶✤ ✒✔✖❡✑ ✑✖✍✢✢❡✛✙
❚✓❡ ✑✜✌✌✛❡✑✑✔✕✎ ✔✑ ✑✒✛✕✎✚❡✑✒ ✍✒ ✒✓❡ ❡➌✜✍✒✕✛✱ ✥✓❡✛❡ ↔ ✔✑ ✌❡✛✼
✌❡✎✏✔✧✜✢✍✛ ✒✕ ✒✓❡ ✏✔✛❡✧✒✔✕✎ ✕✗ ✒✓❡ ✚✛✍✦✔✒② ✻❡✢✏✱ ✔✙❡✙✱ ↔ ✹ ↕ ✪ ✤✱ ✍✎✏
✢❡✑✑ ✑✒✛✕✎✚ ✍✒ ✒✓❡ ✌✕✢❡✑ ✥✓❡✛❡ ↔ ✍✎✏ ↕ ✍✛❡ ❡✔✒✓❡✛ ✌✍✛✍✢✢❡✢ ✘✑✕✜✒✓
✌✕✢❡✮ ✕✛ ✍✎✒✔✌✍✛✍✢✢❡✢ ✘✎✕✛✒✓ ✌✕✢❡✮✙ ■✎ ✒✓❡ ✍❜✑❡✎✧❡ ✕✗ ✛✕✒✍✒✔✕✎✱ ✒✓❡
✖❡✍✎ ✖✍✚✎❡✒✔✧ ✻❡✢✏ ✕✎✢② ✦✍✛✔❡✑ ✔✎ ✍ ✌✢✍✎❡ ✒✓✍✒ ✔✑ ✎✕✛✖✍✢ ✒✕ ✒✓❡
✏✔✛❡✧✒✔✕✎ ✕✗ ✒✓❡ ✔✖✌✕✑❡✏ ✖❡✍✎ ✖✍✚✎❡✒✔✧ ✻❡✢✏✱ ✔✙❡✙✱ ➙ ✹ ➛❥ ✪ ✤✱
✥✓❡✛❡ ➙ ✑✒✍✎✏✑ ✗✕✛ ✒✓❡ ✥✍✦❡ ✦❡✧✒✕✛ ✕✗ ✒✓❡ ✛❡✑✜✢✒✔✎✚ ➜✕✥ ✍✎✏ ✖✍✚✼
✎❡✒✔✧ ✻❡✢✏✙ ❍✕✥❡✦❡✛✱ ✔✎ ✒✓❡ ✌✛❡✑❡✎✧❡ ✕✗ ✛✕✒✍✒✔✕✎ ✒✓❡ ✕✛✔❡✎✒✍✒✔✕✎
✕✗ ✒✓✔✑ ✌✢✍✎❡ ✧✓✍✎✚❡✑ ✑✜✧✓ ✒✓✍✒ ✎✕✥ ➙ ✹ ✘➛❥ ➝ ❵➞➟
❣❥ ↔ × ➛❥ ✮ ✪ ✤✙
■ ❘
▲✁s✂❞✂ ❡t ✂❧ ✳ ◆❡❣✂t✄✈❡ ♠✂❣♥❡t✄☎ ♣r❡ss✆r❡ ✄♥st✂❜✄❧✄t✐
❋✝✞✟ ✶✠✟ ❱✄s✆✂❧✄✡✂t✄✁♥ ✁❢ ❇② ✁♥ t❤❡ ♣❡r✄♣❤❡r✐ ✁❢ t❤❡ ☎✁♠♣✆t✂t✄✁♥✂❧ ❞✁♠✂✄♥ ❢✁r ✹ t✄♠❡s ✭♥✁r♠✂❧✄✡❡❞ ✄♥ t❡r♠s ✁❢ ❚ ☛ ✮ ❞✆r✄♥❣ t❤❡ ♥✁♥❧✄♥❡✂r st✂❣❡ ✁❢ t❤❡
✌
✚ ❾✛
✄♥st✂❜✄❧✄t✐ ❢✁r ☞ ❂ ✵ ✭☎✁rr❡s♣✁♥❞✄♥❣ t✁ t❤❡ ♥✁rt❤ ♣✁❧❡✮ ✂♥❞ ❈✁ ❂ ✵✍✵✎✏ ☎✁rr❡s♣✁♥❞✄♥❣ t✁ ✷✑✴✒✓✔ ✕ ✖✍✎ ✗✄♠❡ ✄s ❤❡r❡ ❣✄✈❡♥ ✄♥ ✆♥✄ts ✁❢ ❚ ☛ ❂ ✭✘✙ ❦ ✮
✛
❋✝✞✟ ✶✶✟ ❙✂♠❡ ✂s ✜✄❣ ✖✵✏ ❜✆t ❢✁r ✂ ♥❡❣✂t✄✈❡ ✈✂❧✆❡ ✁❢ ✑✏ ✄ ❡ ✏ ❈✁ ❂ ✢✵✍✵✎✏ ☎✁rr❡s♣✁♥❞✄♥❣ t✁ ✷✑✴✒✓✔ ✕ ✢✖✍✎
❋✝✞✟ ✶✣✟ ❱✄s✆✂❧✄✡✂t✄✁♥ ✁❢ ❇② ✁♥ t❤❡ ♣❡r✄♣❤❡r✐ ✁❢ t❤❡ ☎✁♠♣✆t✂t✄✁♥✂❧ ❞✁♠✂✄♥ ❢✁r ✹ t✄♠❡s ✭♥✁r♠✂❧✄✡❡❞ ✄♥ t❡r♠s ✁❢ ❚ ☛ ✮ ❞✆r✄♥❣ t❤❡ ♥✁♥❧✄♥❡✂r st✂❣❡ ✁❢ t❤❡
✌
✄♥st✂❜✄❧✄t✐ ❢✁r ☞ ❂ ✹✤ ✂♥❞ ❈✁ ❂ ✵✍✵✎✏ ☎✁rr❡s♣✁♥❞✄♥❣ t✁ ✷✑✴✒✓✔ ✕ ✖✍✎
❋✝✞✟ ✶✥✟ ❱✄s✆✂❧✄✡✂t✄✁♥ ✁❢ ❇② ✁♥ t❤❡ ♣❡r✄♣❤❡r✐ ✁❢ t❤❡ ☎✁♠♣✆t✂t✄✁♥✂❧ ❞✁♠✂✄♥ ❢✁r ✹ t✄♠❡s ✭♥✁r♠✂❧✄✡❡❞ ✄♥ t❡r♠s ✁❢ ❚ ☛ ✮ ❞✆r✄♥❣ t❤❡ ♥✁♥❧✄♥❡✂r st✂❣❡ ✁❢ t❤❡
✌
✄♥st✂❜✄❧✄t✐ ❢✁r ☞ ❂ ✾✵ ✭☎✁rr❡s♣✁♥❞✄♥❣ t✁ t❤❡ ❡q✆✂t✁r✮ ✂♥❞ ❈✁ ❂ ✵✍✵✖✎✏ ☎✁rr❡s♣✁♥❞✄♥❣ t✁ ✷✑✴✒✓✔ ✕ ✵✍✤
❆✦ ✧★✦✩✪✫✩✬✧✯✦✩ ✰✯✦✧✦✱✬✩✲✸ ✧✺✩✺✸ ✇✻✩★ ✦✻✩ ✯★✼✰✩ ✲✽✯★★✩✬ ✿❀ ❁
✯★✬ ❃ ✧✲ ✧★ ✦✻✩ ✪✯★✼✩ ♦❄ ❅
✽✯✦✦✩✪★
❉
✽✪♦✽✯✼✯✦✩✲ ✲✰♦✇✰❀
✦♦ ❊❅
✧★
❉
✦✻✩
❝♦✰✯✦✧✦✱✬✩✸ ✦✻✩ ✫✯✼★✩✦✧❝ ●✩✰✬
★✩✼✯✦✧❍✩
✇✻✩✪✩ ✫✯✼★✩✦✧❝ ✦✪✯❝✩✪✲ ✯✪✩ ✲✩✩★ ✦♦ ✪♦✦✯✦✩ ❄✯✲✦✩✪ ✦✻✯★ ✦✻✩ ✯✫✿✧✩★✦
❝♦✪✪✩❏
✽✰✯✲✫✯✸ ✧✺✩✺✸ ✧★ ✦✻✩ ✽✪♦✼✪✯✬✩ ✬✧✪✩❝✦✧♦★ ❨❩✧③♦★ ✩✦ ✯✰✺ ❬❅❅❭❪✺ ❫❍✩★
✲✽♦★✬✧★✼ ✦♦ ✽♦✰✩✇✯✪✬ ✫✧✼✪✯✦✧♦★✺ ❑✻✩ ✲✧✼★✧●❝✯★❝✩ ♦❄ ✦✻✧✲ ✪✩✲✱✰✦
✲✱★✲✽♦✦✲ ✪♦✦✯✦✩ ❄✯✲✦✩✪ ✦✻✯★ ✦✻✩ ✼✯✲ ✧✦✲✩✰❄ ❨❴✱✰❵❵✧★✩★ ❛ ❑✱♦✫✧★✩★
✧✲ ✱★❝✰✩✯✪✺ ▼✯✬ ✧✦ ✿✩✩★ ✩❖✱✯✦♦✪✇✯✪✬ ✫✧✼✪✯✦✧♦★✸ ♦★✩ ✫✧✼✻✦ ✻✯❍✩
❥❊❊✉❪✺
①
✬✧✪✩❝✦✧♦★✸
✦♦ ✽✪♦✼✪✯✬✩ ✪♦✦✯✦✧♦★✸ ✇✻✧❝✻ ✧✲ ✯ ❝✰✩✯✪ ✩❳✩❝✦ ✲✩✩★ ✧★ ✦✻✩ ❯✱★
✿✩✩★ ✦✩✫✽✦✩✬ ✦♦ ✯✲✲♦❝✧✯✦✩ ✦✻✧✲ ✇✧✦✻ ✦✻✩ ✩❖✱✯✦♦✪✇✯✪✬ ✫✧✼✪✯✦✧♦★ ♦❄
❲★✩ ♦❄ ♦✱✪ ✼♦✯✰✲ ❄♦✪ ❄✱✦✱✪✩ ✇♦✪❵ ✧✲ ✦♦ ❍✩✪✧❄❀ ✦✻✩ ✽✪✩✲✩★✦ ●★✬❏
✦✻✩ ✫✯✼★✩✦✧❝ P✱◗ ✿✩✰✦✲ ✧★ ✦✻✩ ❯✱★ ❄✪♦✫ ✇✻✧❝✻ ✲✱★✲✽♦✦✲ ✩✫✩✪✼✩✺
✧★✼✲ ✧★ ✬✧✪✩❝✦ ★✱✫✩✪✧❝✯✰ ✲✧✫✱✰✯✦✧♦★✲✺ ❯✱❝✻ ✲✧✫✱✰✯✦✧♦★✲ ✇♦✱✰✬
❲★ ✦✻✩ ♦✦✻✩✪ ✻✯★✬✸ ✯✦ ✦✻✩ ✩❖✱✯✦♦✪ ✦✻✧✲ ✫✧✼✪✯✦✧♦★ ❝♦✪✪✩✲✽♦★✬✲
✯✰✲♦ ✯✰✰♦✇ ✱✲ ✦♦ ✬✩✦✩✪✫✧★✩ ★✩✇ ✦✱✪✿✱✰✩★✦ ✦✪✯★✲✽♦✪✦ ❝♦✩④❝✧✩★✦✲✸
⑤✹✾✏ ♣✂❣❡ ⑥ ✁❢ ⑦
❆✫❆ ✺ ✁✂ ❆ ✾ ✭✷✄☎✷✆
s✝✞✝✐✟✠ t♦ t❤❡ q♣ ✡✟✠✟✞❡t❡✠ ✝♥✈♦☛❡☞ ✝♥ t❤❡ ✡✠❡s❡♥t st✉☞✌✳ ❙✉✍❤
✟☞☞✝t✝♦♥✟✐ ✡✟✠✟✞❡t❡✠s ✌✝❡✐☞ ♥❡✇ ❡✎❡✍ts✱ s♦✞❡ ♦✏ ✇❤✝✍❤ ✍♦✉✐☞ ❜❡
✝✞✡♦✠t✟♥t ✏♦✠ ✟✡✡✐✝✍✟t✝♦♥s t♦ t❤❡ ❙✉♥✳
❋✝♥✟✐✐✌✱ ✇❡ ❡♥☞ ✇✝t❤ ✟ ✍♦✞✞❡♥t ♦♥ t❤❡ ✝ss✉❡ ♦✏ s✍✟✐❡ s❡✡✟✠✟✑
t✝♦♥✳ ✒s ☞✝s✍✉ss❡☞ ✟❜♦✈❡✱ ✝♥ s♦✐✟✠ ✞✝①✝♥✓ ✐❡♥✓t❤ t❤❡♦✠✌✱ t❤❡ ✍♦✠✑
✠❡✐✟t✝♦♥ ✐❡♥✓t❤ ♦✏ t❤❡ t✉✠❜✉✐❡♥t ❡☞☞✝❡s ✝s ❡①✡❡✍t❡☞ t♦ s✍✟✐❡ ✇✝t❤
t❤❡ ✡✠❡ss✉✠❡ s✍✟✐❡ ❤❡✝✓❤t s✉✍❤ t❤✟t ❦❢ ❍✔ ✝s ✍♦♥st✟♥t ✟♥☞ ✟❜♦✉t ✕✳✖
✗❑❡✞❡✐ ❡t ✟✐✳ ✕✘✙✕☞✮✳ ❚❤❡♦✠❡t✝✍✟✐ ✍♦♥s✝☞❡✠✟t✝♦♥s ❤✟✈❡ s❤♦✇♥ ✏✉✠✑
t❤❡✠ t❤✟t t❤❡ ✓✠♦✇t❤ ✠✟t❡ ♦✏ ◆❊✚✛■ ✝s ✡✠♦✡♦✠t✝♦♥✟✐ t♦ ❦❢ ❍✔ ✳ ❙✝♥✍❡
✠♦t✟t✝♦♥ ✝s ☛♥♦✇♥ t♦ ☞❡✍✠❡✟s❡ t❤❡ s✝③❡ ♦✏ t❤❡ t✉✠❜✉✐❡♥t ❡☞☞✝❡s✱
✝✳❡✳✱ t♦ ✝♥✍✠❡✟s❡ t❤❡ ✈✟✐✉❡ ♦✏ ❦❢ ✱ ♦♥❡ ✞✝✓❤t ❜❡ t❡✞✡t❡☞ t♦ s✡❡✍✉✑
✐✟t❡ t❤✟t ✠♦t✟t✝♦♥ ✍♦✉✐☞ ❡✈❡♥ ❡♥❤✟♥✍❡ t❤❡ ✓✠♦✇t❤ ✠✟t❡ ♦✏ ◆❊✚✛■✳
✜♦✇❡✈❡✠✱ ✝♥ ✈✝❡✇ ♦✏ t❤❡ ✡✠❡s❡♥t ✠❡s✉✐ts✱ t❤✝s ♥♦✇ s❡❡✞s ✉♥✐✝☛❡✐✌✳
✢❝✣✤✥✦✧★✩✪★✬★✤✯✰✲ ❲✴ ✵✶✸✹✻ ✵✶✴ ✸✹❛✹②✼❛✽✿ r✴❀✴r✴✴ ❀❛r ✼✸✻❁✹❂ ✼✸✹② ✽✿✴❃
❀✽❄ ✿✽❂❂✴✿✵❁❛✹✿ ✵✶✸✵ ✶✸❅✴ ❁✼❇r❛❅✴❞ ✵✶✴ ❇r✴✿✴✹✵✸✵❁❛✹ ❛❀ ❛✽r r✴✿✽❄✵✿❈ ❉❄❄✸ ❘❈
▲❛✿✸❞✸ ●✸✿ ✿✽❇❇❛r✵✴❞ ❏② P✶▼ ❖r✸✹✵ ➇◗✴❯✸ ❞✴ ❉✹❅✴✿✵❁❂✸❯❁❱✹ ❳✸❨✸❳✸✹✸r❁✸✿
❇✸r✸ P❛✿✵❂r✸❞✽✸❩❞❛✿ ❬❭❪❪❫❈ ❴✶❁✿ ●❛r✻ ●✸✿ ✿✽❇❇❛r✵✴❞ ❁✹ ❇✸r✵ ❏② ✵✶✴ ❵✽r❛❇✴✸✹
❘✴✿✴✸r❯✶ ❳❛✽✹❯❁❄ ✽✹❞✴r ✵✶✴ ❣✿✵r❛▼②✹ ❘✴✿✴✸r❯✶ Pr❛❨✴❯✵ ❥❛❈ ❬❬❧♠④❬⑤ ❏② ✵✶✴
❥✸✵❁❛✹✸❄ ⑥❯❁✴✹❯✴ ⑦❛✽✹❞✸✵❁❛✹ ✽✹❞✴r ❖r✸✹✵ ❥❛❈ ❥⑥⑦ P⑧⑨❭④❃④❪❪⑩❶ ❷❣◗❸⑤ ❏②
❵❹ ❳❺⑥❴ ❣❯✵❁❛✹ ❻P❭❼❭⑩⑤ ❏② ✵✶✴ ❵✽r❛❇✴✸✹ ❘✴✿✴✸r❯✶ ❳❛✽✹❯❁❄ ✽✹❞✴r ✵✶✴
❣✵✼❛✿❇✶✴r❁❯ ❘✴✿✴✸r❯✶ Pr❛❨✴❯✵ ❥❛❈ ❬❬❧♠❪④⑤ ✸✹❞ ❏② ✸ ❂r✸✹✵ ❀r❛✼ ✵✶✴ ❖❛❅✴r✹✼✴✹✵
❛❀ ✵✶✴ ❘✽✿✿❁✸✹ ⑦✴❞✴r✸✵❁❛✹ ✽✹❞✴r ❯❛✹✵r✸❯✵ ❥❛❈ ❪❪❈❖❽❶❈❽❪❈❭❭❶❼ ❷❥❾⑤ ❉❘❸❈ ❲✴
✸❯✻✹❛●❄✴❞❂✴ ✵✶✴ ✸❄❄❛❯✸✵❁❛✹ ❛❀ ❯❛✼❇✽✵❁✹❂ r✴✿❛✽r❯✴✿ ❇r❛❅❁❞✴❞ ❏② ✵✶✴ ⑥●✴❞❁✿✶
❥✸✵❁❛✹✸❄ ❣❄❄❛❯✸✵❁❛✹✿ ❳❛✼✼❁✵✵✴✴ ✸✵ ✵✶✴ ❳✴✹✵✴r ❀❛r P✸r✸❄❄✴❄ ❳❛✼❇✽✵✴r✿ ✸✵ ✵✶✴
❘❛②✸❄ ❉✹✿✵❁✵✽✵✴ ❛❀ ❴✴❯✶✹❛❄❛❂② ❁✹ ⑥✵❛❯✻✶❛❄✼ ✸✹❞ ✵✶✴ ❥✸✵❁❛✹✸❄ ⑥✽❇✴r❯❛✼❇✽✵✴r
❳✴✹✵✴r✿ ❁✹ ▲❁✹✻❿❇❁✹❂❈
➀➁➂➁➃➁➄➅➁➆
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈ ❬❭❭❪⑤ ❣❇➈⑤ ④④❭⑤ ❼❬❶
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ➉ ▼❛❏❄✴r⑤ ❲❈ ❬❭❭❬⑤ ❳❛✼❇❈ P✶②✿❈ ❳❛✼✼❈⑤ ❪❶❧⑤ ❶❧❪
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ➉ ⑥✽❏r✸✼✸✹❁✸✹⑤ ❾❈ ❬❭❭④⑤ P✶②✿❈ ❘✴❇❈⑤ ❶❪❧⑤ ❪
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❥❛r❞❄✽✹❞⑤ ➴❈⑤ P✽❄✻✻❁✹✴✹⑤ P❈⑤ ⑥✵✴❁✹⑤ ❘❈ ⑦❈⑤ ➉ ❴✽❛✼❁✹✴✹⑤ ❉❈ ❪♠♠❭⑤
❣➉❣⑤ ❬❽❬⑤ ❬❧❧
❆ ✾✂ ➥➦➧➨ ✁ ➩➫ ✁
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❭⑤ ❣✿✵r❛✹❈ ❥✸❯✶r❈⑤ ❽❽❪⑤ ④
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾✴✼✴❄⑤ ❾❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ❻❁✵r✸⑤ ▼❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❪⑤
❣❇➈⑤ ❧❶❭⑤ ▲④❭
◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾✴✼✴❄⑤ ❾❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❬⑤ ❣❇➈⑤ ❧❶♠⑤
❪❧♠
❖❁➊❛✹⑤ ▲❈⑤ ▼✽❅✸❄❄ ➈r⑤ ❴❈ ▲❈⑤ ➉ ⑥❯✶❛✽⑤ ➈❈ ❬❭❭❽⑤ ❥✸✵✽r✴⑤ ❶❬❪⑤ ❶❽
❾➋❇②❄➋⑤ P❈ ➈❈⑤ ◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ❻✸✹✵✴r✴⑤ ❻❈ ➈❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈
❬❭❪❬⑤ ❻❥❘❣⑥⑤ ❶❬❬⑤ ❬❶⑩④
❾✴✼✴❄⑤ ❾❈⑤ ◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❬✸⑤ ❣✿✵r❛✹❈
❥✸❯✶r❈⑤ ❽❽❽⑤ ♠④
❾✴✼✴❄⑤ ❾❈⑤ ◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❬❏⑤ P✶②✿❈ ⑥❯r❈⑤
❁✹ ❇r✴✿✿ ➌➍➎➏➐➑➒➓➔→➣↔→↕➓➙➛
❾✴✼✴❄⑤ ❾❈⑤ ◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ❻❁✵r✸⑤ ▼❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❬❯⑤
⑥❛❄❈ P✶②✿❈⑤ ❬❼❭⑤ ❽❬❪
❾✴✼✴❄⑤ ❾❈⑤ ◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ❾❄✴✴❛r❁✹⑤ ❥❈⑤ ❻❁✵r✸⑤ ▼❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❬❭❪❬❞⑤
⑥❛❄❈ P✶②✿❈⑤ ▼❺❉➜❪❭❈❪❭❭❧➝✿❪❪❬❭❧❃❭❪❬❃❭❭❽❪❃❼
❾❄✴✴❛r❁✹⑤ ❥❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❪♠♠❶⑤ P✶②✿❈ ❘✴❅❈ ❵⑤ ④❭⑤ ❬❧❪⑩
❾❄✴✴❛r❁✹⑤ ❥❈ ❉❈⑤ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ➞❈⑤ ➉ ❘✽➊✼✸❁✻❁✹⑤ ❣❈ ❣❈ ❪♠❼♠⑤ ⑥❛❅❈ ❣✿✵r❛✹❈ ▲✴✵✵❈⑤
❪④⑤ ❬❧❶
❾❄✴✴❛r❁✹⑤ ❥❈ ❉❈⑤ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ➞❈⑤ ➉ ❘✽➊✼✸❁✻❁✹⑤ ❣❈ ❣❈ ❪♠♠❭⑤ ⑥❛❅❈ P✶②✿❈ ➈❵❴P⑤
❧❭⑤ ❼❧❼
❾❄✴✴❛r❁✹⑤ ❥❈⑤ ❻❛✹❞⑤ ❻❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❪♠♠❽⑤ P✶②✿❈ ⑦❄✽❁❞✿ ◗⑤ ④⑤ ❶❪❬❼
❾❄✴✴❛r❁✹⑤ ❥❈⑤ ❻❛✹❞⑤ ❻❈⑤ ➉ ❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈ ❪♠♠⑩⑤ ❣➉❣⑤ ❽❭❧⑤ ❬♠❽
❾r✸✽✿✴⑤ ⑦❈⑤ ➉ ❘➋❞❄✴r⑤ ❾❈❃⑧❈ ❪♠❼❭⑤ ❻✴✸✹❃➟✴❄❞ ✼✸❂✹✴✵❛✶②❞r❛❞②✹✸✼❁❯✿ ✸✹❞
❞②✹✸✼❛ ✵✶✴❛r② ❷❺➠❀❛r❞➜ P✴r❂✸✼❛✹ Pr✴✿✿❸
❻❛➡✸✵✵⑤ ⑧❈ ❾❈ ❪♠❧❼⑤ ❻✸❂✹✴✵❁❯ ➟✴❄❞ ❂✴✹✴r✸✵❁❛✹ ❁✹ ✴❄✴❯✵r❁❯✸❄❄② ❯❛✹❞✽❯✵❁✹❂ ➢✽❁❞✿
❷❳✸✼❏r❁❞❂✴➜ ❳✸✼❏r❁❞❂✴ ❹✹❁❅✴r✿❁✵② Pr✴✿✿❸
P✸r✻✴r⑤ ❵❈ ❥❈ ❪♠⑩⑩⑤ ❣❇➈⑤ ❪❶④⑤ ❼❪❪
P✸r✻✴r⑤ ❵❈❥❈ ❪♠❧♠⑤ ❳❛✿✼❁❯✸❄ ✼✸❂✹✴✵❁❯ ➟✴❄❞✿ ❷❥✴● ⑨❛r✻➜ ❺➠❀❛r❞ ❹✹❁❅✴r✿❁✵②
Pr✴✿✿❸
P✽❄✻✻❁✹✴✹⑤ P❈⑤ ➉ ❴✽❛✼❁✹✴✹⑤ ❉❈ ❪♠♠❼⑤ ❣➉❣⑤ ❽❽❬⑤ ❧❶❼
Pr❁✴✿✵⑤ ❵❈ ❘❈ ❪♠❼❬⑤ ⑥❛❄✸r ❻✸❂✹✴✵❛✶②❞r❛❞②✹✸✼❁❯✿ ❷▼❛r❞r✴❯✶✵➜ ▼❈ ❘✴❁❞✴❄ P✽❏❄❈
❳❛❈❸
❘❛❂✸❯✶✴❅✿✻❁❁⑤ ❉❈⑤ ➉ ❾❄✴✴❛r❁✹⑤ ❥❈ ❬❭❭❧⑤ P✶②✿❈ ❘✴❅❈ ❵⑤ ❧⑩⑤ ❭④⑩❽❭❧
⑥✽r⑤ ⑥❈⑤ ◗r✸✹❞✴✹❏✽r❂⑤ ❣❈⑤ ➉ ⑥✽❏r✸✼✸✹❁✸✹⑤ ❾❈ ❬❭❭❼⑤ ❻❥❘❣⑥⑤ ❽❼④⑤ ▲❪④
❴✿✴r✻❛❅✹❁✻❛❅⑤ ⑨❈ ❣❈ ❪♠⑩❭⑤ ⑥❛❅❈ P✶②✿❈ ▼❛✻❄❈⑤ ④⑤ ❼❧
➞❁✵✴✹✿✴⑤ ❵❈ ❪♠④❽⑤ ➤❈ ❣✿✵r❛❇✶②✿❈⑤ ❽❬⑤ ❪❽④
➤✴❄❞❛❅❁❯✶⑤ ⑨✸❈ ◗❈⑤ ❘✽➊✼✸❁✻❁✹⑤ ❣❈ ❣❈⑤ ➉ ⑥❛✻❛❄❛➡⑤ ▼❈ ▼❈ ❪♠❼❽⑤ ❻✸❂✹✴✵❁❯ ➟✴❄❞✿ ❁✹
✸✿✵r❛❇✶②✿❁❯✿ ❷❥✴● ⑨❛r✻➜ ❖❛r❞❛✹ ➉ ◗r✴✸❯✶❸
Paper II
67
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
❉✆✝✞ ✄✂✶✄✂✺✄✴✂✂✂✵✟ ✸ ✄✴✷✂✄✷✷✂✾✸✾
❝ ❊❙❖ ✡☛☞✌
✠
✍✎✏✑♦✒♦✓②
✔
✍✎✏✑♦✕✖②✎✗✘✎
❈✙✚✛✜✢✣✢✣✙✤ ✙❢ r✙✢✥✢✣✙✤ ✥✤♥ s✢r✥✢✣t✦✥✢✣✙✤ ✣✤ ß✧★ ✦✙✤✦✜✤✢r✥✢✣✙✤s
■✩ ❘✩ ▲✪✬✮✯✮✰✱✲ ✳ ✹✩ ❇✻✮✼✯✿✼❀✉✻❣✰✱✲ ✳ ◆✩ ❑❧✿✿✪✻❁✼❂✱✰✱❃ ✳ ✮✼✯ ■✩ ❘✪❣✮❄❅✿✈✬❋❁❁❂✱✰✱❃
●
①
⑦
❻
❍❏▼P◗❚❯❱ ❲❳❨ ❩❏❬❯❭ ❪❫❴❚◗❚❵❚❛ ❏❜ ❳❛❝❡❫❏❭❏❞❬ ❯❫P ❙❚❏❝❤❡❏❭✐ ❥❫◗❦❛▼❴◗❚❬❱ ❩❏❴❭❯❞❴❚❵❭❭❴♠❯❝❤❛❫ ✡✌❱ ☞☛♣q☞ ❙❚❏❝❤❡❏❭✐❱ ❙✇❛P❛❫
③❛④❯▼❚✐❛❫❚ ❏❜ ⑤❴❚▼❏❫❏✐❬❱ ⑤❭♠❯❍❏❦❯ ❥❫◗❦❛▼❴◗❚❬ ⑥❛❫❚❛▼❱ ❙❚❏❝❤❡❏❭✐ ❥❫◗❦❛▼❴◗❚❬❱ ☞☛♣q☞ ❙❚❏❝❤❡❏❭✐❱ ❙✇❛P❛❫
③❛④❯▼❚✐❛❫❚ ❏❜ ⑧❛❝❡❯❫◗❝❯❭ ❊❫❞◗❫❛❛▼◗❫❞❱ ⑨❛❫⑩❶❵▼◗❏❫ ❥❫◗❦❛▼❴◗❚❬ ❏❜ ❚❡❛ ❍❛❞❛❦❱ ❷❖⑨ ♣❸✌❱ ❹❺☞☛❸ ⑨❛❛▼⑩❙❡❛❦❯❱ ❪❴▼❯❛❭
③❛④❯▼❚✐❛❫❚ ❏❜ ❩❯P◗❏ ❷❡❬❴◗❝❴❱ ❍❼ ❪❼ ❽❏♠❯❝❡❛❦❴❤❬ ❙❚❯❚❛ ❥❫◗❦❛▼❴◗❚❬ ❏❜ ❍◗❾❡❫❬ ❍❏❦❞❏▼❏P❱ ❩❵❴❴◗❯
❩❛❝❛◗❦❛P ☞❿ ③❛❝❛✐♠❛▼ ✡☛☞✡ ➀ ⑤❝❝❛④❚❛P ✡q ⑧❯❬ ✡☛☞✌
➁➂➃➄➅➁➆➄
➇➈➉➊➋➌➊➍ ❪❫ ❯ ❴❚▼❏❫❞❭❬ ❴❚▼❯❚◗Þ❛P ❚❵▼♠❵❭❛❫❚ ❭❯❬❛▼❱ ❯ ❵❫◗❜❏▼✐ ❡❏▼◗❾❏❫❚❯❭ ✐❯❞❫❛❚◗❝ Þ❛❭P ❝❯❫ ♠❛❝❏✐❛ ❵❫❴❚❯♠❭❛ ❯❫P ❴④❏❫❚❯❫❛❏❵❴❭❬ ❜❏▼✐ ❭❏❝❯❭
➎❵➏ ❝❏❫❝❛❫❚▼❯❚◗❏❫❴ P❵❛ ❚❏ ❯ ❫❛❞❯❚◗❦❛ ❝❏❫❚▼◗♠❵❚◗❏❫ ❏❜ ❚❵▼♠❵❭❛❫❝❛ ❚❏ ❚❡❛ ❭❯▼❞❛⑩❴❝❯❭❛ ➐✐❛❯❫⑩Þ❛❭P➑ ✐❯❞❫❛❚◗❝ ④▼❛❴❴❵▼❛❼ ❳❡◗❴ ✐❛❝❡❯❫◗❴✐❱
✇❡◗❝❡ ◗❴ ❝❯❭❭❛P ❫❛❞❯❚◗❦❛ ❛➒❛❝❚◗❦❛ ✐❯❞❫❛❚◗❝ ④▼❛❴❴❵▼❛ ◗❫❴❚❯♠◗❭◗❚❬ ➐❍❊⑧❷❪➑❱ ◗❴ ❏❜ ◗❫❚❛▼❛❴❚ ◗❫ ❝❏❫❫❛❝❚◗❏❫ ✇◗❚❡ P❬❫❯✐❏ ❴❝❛❫❯▼◗❏❴ ◗❫ ✇❡◗❝❡
✐❏❴❚ ❏❜ ❚❡❛ ✐❯❞❫❛❚◗❝ Þ❛❭P ▼❛❴◗P❛❴ ◗❫ ❚❡❛ ♠❵❭❤ ❏❜ ❚❡❛ ❝❏❫❦❛❝❚◗❏❫ ❾❏❫❛ ❯❫P ❫❏❚ ❯❚ ❚❡❛ ♠❏❚❚❏✐❱ ❯❴ ◗❴ ❏❜❚❛❫ ❯❴❴❵✐❛P❼ ❩❛❝❛❫❚ ✇❏▼❤ ❵❴◗❫❞
✐❛❯❫⑩Þ❛❭P ❡❬P▼❏✐❯❞❫❛❚◗❝ ❛➓❵❯❚◗❏❫❴ ❡❯❴ ❴❡❏✇❫ ❚❡❯❚ ❍❊⑧❷❪ ♠❛❝❏✐❛❴ ❴❵④④▼❛❴❴❛P ❯❚ ▼❯❚❡❛▼ ❭❏✇ ▼❏❚❯❚◗❏❫ ▼❯❚❛❴ ✇◗❚❡ ⑥❏▼◗❏❭◗❴ ❫❵✐♠❛▼❴
❯❴ ❭❏✇ ❯❴ ☛❼☞❼
➔→➣↔➍ ❨❛▼❛ ✇❛ ❛➏❚❛❫P ❚❡❛❴❛ ❛❯▼❭◗❛▼ ◗❫❦❛❴❚◗❞❯❚◗❏❫❴ ♠❬ ❴❚❵P❬◗❫❞ ❚❡❛ ❛➒❛❝❚❴ ❏❜ ▼❏❚❯❚◗❏❫ ♠❏❚❡ ❏❫ ❚❡❛ P❛❦❛❭❏④✐❛❫❚ ❏❜ ❍❊⑧❷❪ ❯❫P ❏❫ ❚❡❛
❛➒❛❝❚◗❦❛ ✐❯❞❫❛❚◗❝ ④▼❛❴❴❵▼❛❼ ↕❛ ❯❭❴❏ ➓❵❯❫❚◗❜❬ ❚❡❛ ❤◗❫❛❚◗❝ ❡❛❭◗❝◗❚❬ ▼❛❴❵❭❚◗❫❞ ❜▼❏✐ P◗▼❛❝❚ ❫❵✐❛▼◗❝❯❭ ❴◗✐❵❭❯❚◗❏❫❴ ➐③❍❙➑ ✇◗❚❡ ⑥❏▼◗❏❭◗❴
❫❵✐♠❛▼❴ ❯❫P ❴❚▼❛❫❞❚❡❴ ❏❜ ❴❚▼❯❚◗Þ❝❯❚◗❏❫ ❝❏✐④❯▼❯♠❭❛ ❚❏ ❦❯❭❵❛❴ ❫❛❯▼ ❚❡❛ ❴❏❭❯▼ ❴❵▼❜❯❝❛ ❯❫P ❝❏✐④❯▼❛ ◗❚ ✇◗❚❡ ❛❯▼❭◗❛▼ ✇❏▼❤ ❯❚ ❴✐❯❭❭❛▼ ❴❝❯❭❛
❴❛④❯▼❯❚◗❏❫ ▼❯❚◗❏❴❼ ➙❵▼❚❡❛▼❱ ✇❛ ❛❴❚◗✐❯❚❛ ❚❡❛ ❛➏④❛❝❚❛P ❏♠❴❛▼❦❯♠❭❛ ❴◗❞❫❯❭❴ ❏❜ ✐❯❞❫❛❚◗❝ ❡❛❭◗❝◗❚❬ ❯❚ ❚❡❛ ❴❏❭❯▼ ❴❵▼❜❯❝❛❼
➛➋➊➜➈➝↔➍ ❳❏ ❝❯❭❝❵❭❯❚❛ ❚❡❛ ▼❏❚❯❚◗❏❫❯❭ ❛➒❛❝❚ ❏❫ ❚❡❛ ❛➒❛❝❚◗❦❛ ✐❯❞❫❛❚◗❝ ④▼❛❴❴❵▼❛ ✇❛ ❝❏❫❴◗P❛▼ ♠❏❚❡ ③❍❙ ❯❫P ❯❫❯❭❬❚◗❝❯❭ ❴❚❵P◗❛❴ ❵❴◗❫❞
❚❡❛ ➞ ❯④④▼❏❯❝❡❼ ❳❏ ❴❚❵P❬ ❚❡❛ ❛➒❛❝❚❴ ❏❜ ▼❏❚❯❚◗❏❫ ❏❫ ❚❡❛ P❛❦❛❭❏④✐❛❫❚ ❏❜ ❍❊⑧❷❪ ✇❛ ❵❴❛ ♠❏❚❡ ③❍❙ ❯❫P ✐❛❯❫⑩Þ❛❭P ❝❯❭❝❵❭❯❚◗❏❫❴ ❏❜ ❚❡❛
❚❡▼❛❛⑩P◗✐❛❫❴◗❏❫❯❭ ❡❬P▼❏✐❯❞❫❛❚◗❝ ❛➓❵❯❚◗❏❫❴ ◗❫ ❯ ⑥❯▼❚❛❴◗❯❫ P❏✐❯◗❫❼
➟➋↔➠➡➊↔➍ ↕❛ Þ❫P ❚❡❯❚ ❚❡❛ ❞▼❏✇❚❡ ▼❯❚❛❴ ❏❜ ❍❊⑧❷❪ ❜▼❏✐ ❛❯▼❭◗❛▼ ✐❛❯❫⑩Þ❛❭P ❝❯❭❝❵❭❯❚◗❏❫❴ ❯▼❛ ✇❛❭❭ ▼❛④▼❏P❵❝❛P ✇◗❚❡ ③❍❙❱ ④▼❏❦◗P❛P
❚❡❛ ⑥❏▼◗❏❭◗❴ ❫❵✐♠❛▼ ◗❴ ♠❛❭❏✇ ☛❼☛♣❼ ❪❫ ❚❡❯❚ ❝❯❴❛❱ ❤◗❫❛❚◗❝ ❯❫P ✐❯❞❫❛❚◗❝ ❡❛❭◗❝◗❚◗❛❴ ❯▼❛ ❜❏❵❫P ❚❏ ♠❛ ✇❛❯❤ ❯❫P ❚❡❛ ▼❏❚❯❚◗❏❫❯❭ ❛➒❛❝❚ ❏❫
❚❡❛ ❛➒❛❝❚◗❦❛ ✐❯❞❫❛❚◗❝ ④▼❛❴❴❵▼❛ ◗❴ ❫❛❞❭◗❞◗♠❭❛ ❯❴ ❭❏❫❞ ❯❴ ❚❡❛ ④▼❏P❵❝❚◗❏❫ ❏❜ ➎❵➏ ❝❏❫❝❛❫❚▼❯❚◗❏❫❴ ◗❴ ❫❏❚ ◗❫❡◗♠◗❚❛P ♠❬ ▼❏❚❯❚◗❏❫❼ ➙❏▼ ❜❯❴❚❛▼
▼❏❚❯❚◗❏❫❱ P❬❫❯✐❏ ❯❝❚◗❏❫ ♠❛❝❏✐❛❴ ④❏❴❴◗♠❭❛❼ ❨❏✇❛❦❛▼❱ ❚❡❛▼❛ ◗❴ ❯❫ ◗❫❚❛▼✐❛P◗❯❚❛ ▼❯❫❞❛ ❏❜ ▼❏❚❯❚◗❏❫ ▼❯❚❛❴ ✇❡❛▼❛ P❬❫❯✐❏ ❯❝❚◗❏❫ ❏❫ ◗❚❴ ❏✇❫
◗❴ ❫❏❚ ❬❛❚ ④❏❴❴◗♠❭❛❱ ♠❵❚ ❚❡❛ ▼❏❚❯❚◗❏❫❯❭ ❴❵④④▼❛❴❴◗❏❫ ❏❜ ❍❊⑧❷❪ ◗❴ ♠❛◗❫❞ ❯❭❭❛❦◗❯❚❛P❼
➇➈➉➢➡➠↔→➈➉↔➍ ❷▼❏P❵❝❚◗❏❫ ❏❜ ✐❯❞❫❛❚◗❝ ➎❵➏ ❝❏❫❝❛❫❚▼❯❚◗❏❫❴ ❚❡▼❏❵❞❡ ❚❡❛ ❴❵④④▼❛❴❴◗❏❫ ❏❜ ❚❵▼♠❵❭❛❫❚ ④▼❛❴❴❵▼❛ ❯④④❛❯▼❴ ❚❏ ♠❛ ④❏❴❴◗♠❭❛ ❏❫❭❬ ◗❫
❚❡❛ ❵④④❛▼✐❏❴❚ ❭❯❬❛▼❴ ❏❜ ❚❡❛ ❙❵❫❱ ✇❡❛▼❛ ❚❡❛ ❝❏❫❦❛❝❚◗❦❛ ❚❵▼❫❏❦❛▼ ❚◗✐❛ ◗❴ ❭❛❴❴ ❚❡❯❫ ❚✇❏ ❡❏❵▼❴❼
➤➥➦ ➧➨➩➫➭➯ ✐❯❞❫❛❚❏❡❬P▼❏P❬❫❯✐◗❝❴ ➐⑧❨③➑ Ð ❡❬P▼❏P❬❫❯✐◗❝❴ Ð ❚❵▼♠❵❭❛❫❝❛ Ð ❙❵❫➲ P❬❫❯✐❏
➳➵ ➸➺➻➼➽➾➚➪➻➶➽➺
✝➹ ➘➴➷ ➬➮➹✁ ➱✃❐➹➷➘❒❮ ❰➷ÏÑÒ ✃Ó➷ ÔÓÕÑ➮❮➷Ñ Ö× ✃ Ï✃Ó❐➷✟Ò❮✃Ï➷ Ñ×✟
➹✃➱Õ ✭Ò➷➷✁ ➷✶❐✶✁ ØÕÙ✃➘➘ ✄✾Ú✽Û Ü✃ÓÝ➷Ó ✄✾Ú✾Û àÓ✃➮Ò➷ ✫ áâÑÏ➷Ó
✄✾✽✂Û ã➷ÏÑÕä❒❮➴ ➷➘ ✃Ï✶ ✄✾✽✸Û ✆ÒÒ➷➹ÑÓ❒åä➷Ó ✷✂✂✸Û æÓ✃➹Ñ➷➹Ö➮Ó❐
✫ ➬➮ÖÓ✃➱✃➹❒✃➹ ✷✂✂✺✃☎✶ ❆Ï➘➴Õ➮❐➴ ➱✃➹× Ñ➷➘✃❒ÏÒ Õç ➘➴❒Ò ÔÓÕ❮➷ÒÒ
Ó➷➱✃❒➹ Ò➮Öå➷❮➘ ➘Õ Ñ➷Ö✃➘➷✁ ❒➘ Ò➷➷➱Ò Ó➷Ï✃➘❒ä➷Ï× ❮Ï➷✃Ó ➘➴✃➘ ÓÕ➘✃➘❒Õ➹
➷➹➴✃➹❮➷Ò ➘➴➷ ➷è❮❒➷➹❮× Õç ➘➴➷ Ñ×➹✃➱Õ ❒ç ➘➴➷ éÕÓ❒ÕÏ❒Ò Ô✃Ó✃➱➷➘➷Ó
❒Ò ➹Õ➘ ä➷Ó× Ï✃Ó❐➷✶ ✝➹ ➘➴➷ ✃ÖÒ➷➹❮➷ Õç ÓÕ➘✃➘❒Õ➹ ✃➹Ñ Ò➴➷✃Ó✁ Õ➹Ï× Ò➱✃ÏÏ✟
Ò❮✃Ï➷ ➱✃❐➹➷➘❒❮ ❰➷ÏÑÒ ✃Ó➷ ❐➷➹➷Ó✃➘➷Ñ Ö× ê➴✃➘ ❒Ò Õç➘➷➹ Ó➷ç➷ÓÓ➷Ñ ➘Õ
✃Ò Ò➱✃ÏÏ✟Ò❮✃Ï➷ Ñ×➹✃➱Õ ✃❮➘❒Õ➹ ✭Ò➷➷✁ ➷✶❐✶✁ ã➷ÏÑÕä❒❮➴ ➷➘ ✃Ï✶ ✄✾✾✂Û
æÓ✃➹Ñ➷➹Ö➮Ó❐ ✫ ➬➮ÖÓ✃➱✃➹❒✃➹ ✷✂✂✺✃☎✶ áÕ➘✃➘❒Õ➹ Ï➷✃ÑÒ ➘Õ ✃➹ ë ➷ç✟
ç➷❮➘ ✭➬➘➷➷➹Ö➷❮Ý ➷➘ ✃Ï✶ ✄✾ ☎ ❒ç ➘➴➷Ó➷ ❒Ò ✃ÏÒÕ Ò➘Ó✃➘❒❰❮✃➘❒Õ➹ ❒➹ Ñ➷➹✟
Ò❒➘× ÕÓ ➘➮ÓÖ➮Ï➷➹➘ ❒➹➘➷➹Ò❒➘×✶ ì➴➷ ë ➷Ù➷❮➘ ❮✃➹ ÔÓÕÑ➮❮➷ ➱➷✃➹ ➱✃❐✟
➹➷➘❒❮ ❰➷ÏÑ ✃➹Ñ ➹➷➘ ➱✃❐➹➷➘❒❮ í➮î✶
➬➘Ó✃➘❒❰❮✃➘❒Õ➹ Ï➷✃ÑÒ ➘Õ ×➷➘ ✃➹Õ➘➴➷Ó ➷Ù➷❮➘ ➘➴✃➘ ÑÕ➷Ò ➹Õ➘ ÔÓÕÑ➮❮➷
➱✃❐➹➷➘❒❮ í➮î Ö➮➘ ➱➷Ó➷Ï× ❮Õ➹❮➷➹➘Ó✃➘➷Ò ❒➘ ÏÕ❮✃ÏÏ× Ö× ê➴✃➘ ❒Ò ➹Õê
Ó➷ç➷ÓÓ➷Ñ ➘Õ ✃Ò ➹➷❐✃➘❒ä➷ ➷Ù➷❮➘❒ä➷ ➱✃❐➹➷➘❒❮ ÔÓ➷ÒÒ➮Ó➷ ❒➹Ò➘✃Ö❒Ï❒➘×
✭ïðØÜ✝☎✶ ❉❒Ó➷❮➘ ➹➮➱➷Ó❒❮✃Ï Ò❒➱➮Ï✃➘❒Õ➹Ò ✭❉ï➬☎ Õç æÓ✃➹Ñ➷➹Ö➮Ó❐
➷➘ ✃Ï✶ ✭✷✂✄✄✃☎ ➴✃ä➷ Ò➴Õê➹ ❒➹ Ò➮ÓÔÓ❒Ò❒➹❐ Ñ➷➘✃❒Ï ➱✃➹× ✃ÒÔ➷❮➘Ò
Õç ïðØÜ✝ ➘➴✃➘ ê➷Ó➷ ÔÓ➷ä❒Õ➮ÒÏ× Ò➷➷➹ ❒➹ ➱➷✃➹✟❰➷ÏÑ Ò❒➱➮Ï✃➘❒Õ➹Ò
✭Øñ➬☎ Õç æÓ✃➹Ñ➷➹Ö➮Ó❐ ➷➘ ✃Ï✶ ✭✷✂✄✂☎ ✃➹Ñ ➘➴✃➘ ➴✃ä➷ Ö➷➷➹ ✃➹✟
➘❒❮❒Ô✃➘➷Ñ Ö✃Ò➷Ñ Õ➹ ✃➹✃Ï×➘❒❮✃Ï Ò➘➮Ñ❒➷Ò çÕÓ ÒÕ➱➷ ➘❒➱➷ ✭àÏ➷➷ÕÓ❒➹
➷➘ ✃Ï✶ ✄✾✽✾✁ ✄✾✾✂✁ ✄✾✾✸✁ ✄✾✾ Û àÏ➷➷ÕÓ❒➹ ✫ áÕ❐✃❮➴➷äÒÝ❒❒ ✄✾✾✵Û
áÕ❐✃❮➴➷äÒÝ❒❒ ✫ àÏ➷➷ÕÓ❒➹ ✷✂✂Ú☎✶
ì➴➷ ➱✃❒➹ Ô➴×Ò❒❮Ò Õç ➘➴❒Ò ➷Ù➷❮➘ ❒Ò ❮Õ➹➹➷❮➘➷Ñ ê❒➘➴ ➘➴➷ Ò➮Ô✟
ÔÓ➷ÒÒ❒Õ➹ Õç ➘➮ÓÖ➮Ï➷➹➘ ÔÓ➷ÒÒ➮Ó➷ Ö× ✃ ê➷✃Ý ➱➷✃➹ ➱✃❐➹➷➘❒❮ ❰➷ÏÑ
➘➴✃➘ ❒Ò Ï➷ÒÒ ➘➴✃➹ ➘➴➷ ➷ò➮❒Ô✃Ó➘❒➘❒Õ➹ ❰➷ÏÑ✶ ❆➘ Ï✃Ó❐➷ á➷×➹ÕÏÑÒ ➹➮➱✟
Ö➷ÓÒ✁ ➘➴➷ Ó➷Ò➮Ï➘❒➹❐ Ó➷Ñ➮❮➘❒Õ➹ Õç ➘➴➷ ➘➮ÓÖ➮Ï➷➹➘ ÔÓ➷ÒÒ➮Ó➷ ❒Ò Ï✃Ó❐➷Ó
➘➴✃➹ ➘➴➷ ✃ÑÑ➷Ñ ➱✃❐➹➷➘❒❮ ÔÓ➷ÒÒ➮Ó➷ çÓÕ➱ ➘➴➷ ➱➷✃➹ ➱✃❐➹➷➘❒❮ ❰➷ÏÑ
❒➘Ò➷Ïç✁ ÒÕ ➘➴✃➘ ➘➴➷ óôóõö÷øó ➱✃❐➹➷➘❒❮ ÔÓ➷ÒÒ➮Ó➷ ➘➴✃➘ ✃❮❮Õ➮➹➘Ò çÕÓ
➘➮ÓÖ➮Ï➷➹➘ ✃➹Ñ ➹Õ➹➘➮ÓÖ➮Ï➷➹➘ ❮Õ➹➘Ó❒Ö➮➘❒Õ➹Ò Ö➷❮Õ➱➷Ò ➹➷❐✃➘❒ä➷✶ ✝➹ ✃
Ò➘ÓÕ➹❐Ï× Ò➘Ó✃➘❒❰➷Ñ Ï✃×➷Ó✁ ❒✶➷✶✁ ✃ Ï✃×➷Ó ❒➹ ê➴❒❮➴ ➘➴➷ Ñ➷➹Ò❒➘× ä✃Ó❒➷Ò
➱➮❮➴ ➱ÕÓ➷ Ó✃Ô❒ÑÏ× ê❒➘➴ ➴➷❒❐➴➘ ➘➴✃➹ ➘➴➷ ➱✃❐➹➷➘❒❮ ❰➷ÏÑ ÑÕ➷Ò✁
➘➴❒Ò Ï➷✃ÑÒ ➘Õ ✃➹ ❒➹Ò➘✃Ö❒Ï❒➘× ➘➴✃➘ ❒Ò ✃➹✃ÏÕ❐Õ➮Ò ➘Õ Ü✃ÓÝ➷ÓùÒ ➱✃❐✟
➹➷➘❒❮ Ö➮Õ×✃➹❮× ❒➹Ò➘✃Ö❒Ï❒➘×✁ ➷î❮➷Ô➘ ➘➴✃➘ ➘➴➷Ó➷ ➘➴➷ ➱✃❐➹➷➘❒❮ ❰➷ÏÑ
ä✃Ó❒➷Ò ➱ÕÓ➷ Ó✃Ô❒ÑÏ× ê❒➘➴ ➴➷❒❐➴➘ ➘➴✃➹ ➘➴➷ Ñ➷➹Ò❒➘× ÑÕ➷Ò✶ æ➷❮✃➮Ò➷
➘➴➷ ➷Ù➷❮➘❒ä➷ ➱✃❐➹➷➘❒❮ ÔÓ➷ÒÒ➮Ó➷ ❒Ò ➹➷❐✃➘❒ä➷✁ ➱✃❐➹➷➘❒❮ Ò➘Ó➮❮➘➮Ó➷Ò
✃Ó➷ ➹➷❐✃➘❒ä➷Ï× Ö➮Õ×✃➹➘ ✃➹Ñ Ò❒➹Ý✁ ê➴❒❮➴ ➴✃Ò Ö➷➷➹ Ò➷➷➹ ❒➹ ➘➴➷ ❉ï➬
Õç æÓ✃➹Ñ➷➹Ö➮Ó❐ ➷➘ ✃Ï✶ ✭✷✂✄✄✃☎✶
✆➹➷ Õç ➘➴➷ ➱✃❒➹ Ò➮❮❮➷ÒÒ➷Ò Õç Ó➷❮➷➹➘ ❮Õ➱Ô✃Ó✃➘❒ä➷ êÕÓÝ Ö➷✟
➘ê➷➷➹ ❉ï➬ ✃➹Ñ Øñ➬ ❒Ò ➘➴➷ Ñ➷➱Õ➹Ò➘Ó✃➘❒Õ➹ Õç ✃ ➴❒❐➴ Ñ➷❐Ó➷➷ Õç
❆Ó➘❒❮Ï➷ Ô➮ÖÏ❒Ò➴➷Ñ Ö× ð❉Ü ➬❮❒➷➹❮➷Ò
❆✽✸✁ Ô✃❐➷ ✄ Õç ✄✷
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
♣✆✝✞✟❝t✟✈✝ ♣✠✇✝✆ ✠❢ ▼❋❙✳ ❚✡✝ ✝①☛☞♣✌✝s ✟♥❝✌✉✞✝ ✞✝t☛✟✌s ✆✝❣☛✆✞✍
✟♥❣ t✡✝ s✡☛♣✝ ☛♥✞ ✝✈✠✌✉t✟✠♥ ✠❢ st✆✉❝t✉✆✝s✱ t✡✝ ✞✝♣✝♥✞✝♥❝✝ ✠❢ t✡✝✟✆
✞✝♣t✡ ✠♥ t✡✝ ☞☛❣♥✝t✟❝ Þ✝✌✞ st✆✝♥❣t✡✱ ☛♥✞ t✡✝ ✞✝♣✝♥✞✝♥❝✝ ✠❢ t✡✝
❣✆✠✇t✡ ✆☛t✝ ✠♥ t✡✝ s❝☛✌✝ s✝♣☛✆☛t✟✠♥ ✆☛t✟✠✳ ❘✝❝✝♥t ▼❋❙ ✠❢ ▲✠s☛✞☛
✝t ☛✌✳ ✎✏✑✒✏❀ ✡✝✆✝☛❢t✝✆ ▲❇✓▼❘✔ ✡☛✈✝ s✡✠✇♥ t✡☛t ✟♥ t✡✝ ♣✆✝s✍
✝♥❝✝ ✠❢ ✝✈✝♥ ❥✉st ✇✝☛✕ ✆✠t☛t✟✠♥ t✡✝ ❣✆✠✇t✡ ✆☛t✝ ✠❢ ◆✖▼✗✘ ✟s
s✟❣♥✟Þ❝☛♥t✌② ✆✝✞✉❝✝✞✳ ✖①♣✆✝ss✝✞ ✟♥ t✝✆☞s ✠❢ t✡✝ ❈✠✆✟✠✌✟s ♥✉☞✍
❜✝✆✱ ❈✠ ❂ ✏✙✴✚r✛✜ ❦✢ ✱ ✇✡✝✆✝ ✙ ✟s t✡✝ ☛♥❣✉✌☛✆ ✈✝✌✠❝✟t②✱ ✚r✛✜ ✟s t✡✝
✆☞s ✈✝✌✠❝✟t② ✠❢ t✡✝ t✉✆❜✉✌✝♥❝✝✱ ☛♥✞ ❦✢ ✟s t✡✝ ✇☛✈✝♥✉☞❜✝✆ ✠❢ t✡✝
✝♥✝✆❣②✍❝☛✆✆②✟♥❣ ✝✞✞✟✝s✱ t✡✝ ❝✆✟t✟❝☛✌ ✈☛✌✉✝ ✠❢ ❈✠ ✇☛s ♣✆✝✞✟❝t✝✞ t✠
❜✝ ☛s ✌✠✇ ☛s ✑✳✑✣✳ ✤✌t✡✠✉❣✡ t✡✟s ✈☛✌✉✝ ✞✠✝s ♥✠t ♣✆✝❝✌✉✞✝ t✡✝ ✠♣✍
✝✆☛t✟✠♥ ✠❢ ◆✖▼✗✘ ✟♥ t✡✝ ✉♣♣✝✆ ♣☛✆ts ✠❢ t✡✝ ❙✉♥✱ ✇✡✝✆✝ ❈✠ ✟s ✟♥✍
✞✝✝✞ s☞☛✌✌ ✎☛❜✠✉t ✒✑❾✹ ☛t t✡✝ s✉✆❢☛❝✝✔✱ ✟t ✞✠✝s s✝✝☞ s✉✆♣✆✟s✟♥❣✌②
✌✠✇✱ ✇✡✟❝✡ ✆☛✟s✝s q✉✝st✟✠♥s ✆✝❣☛✆✞✟♥❣ t✡✝ ☛❝❝✉✆☛❝② ✠❢ ▼❋❙ ✟♥
t✡✟s ❝☛s✝✳ ❚✡✝ ♣✉✆♣✠s✝ ✠❢ t✡✝ ♣✆✝s✝♥t ♣☛♣✝✆ ✟s t✡✝✆✝❢✠✆✝ t✠ ❝✠☞✍
♣☛✆✝ ▼❋❙ ✠❢ ▲❇✓▼❘ ✇✟t✡ ❉◆❙ ✠❢ t✡✝ s☛☞✝ s✝t✉♣✳ ✘t t✉✆♥s ✠✉t
t✡☛t✱ ✇✡✟✌✝ ✇✝ ✞✠ ❝✠♥Þ✆☞ t✡✝ ❜☛s✟❝ ♣✆✝✞✟❝t✟✠♥ ✠❢ ▲❇✓▼❘✱ ✇✝
☛✌s✠ ✆✝s✠✌✈✝ ☛♥ ✝☛✆✌✟✝✆ ♥✠t✟❝✝✞ ✞✟s❝✆✝♣☛♥❝② ✟♥ t✡✝ ❣✆✠✇t✡ ✆☛t✝s
❜✝t✇✝✝♥ ❉◆❙ ☛♥✞ ▼❋❙ ✟♥ t✡✝ ☛❜s✝♥❝✝ ✠❢ ✆✠t☛t✟✠♥ ✎s✝✝ t✡✝ ☛♣✍
♣✝♥✞✟① ✠❢ ✓✝☞✝✌ ✝t ☛✌✳ ✏✑✒✏☛✔✳ ✘♥✞✝✝✞✱ ✟♥ t✡✝ ♣☛✆t✟❝✉✌☛✆ ❝☛s✝ ✠❢
☛ ☞☛❣♥✝t✟❝ ❘✝②♥✠✌✞s ♥✉☞❜✝✆ ✠❢ ✒✥ ☛♥✞ ☛ s❝☛✌✝ s✝♣☛✆☛t✟✠♥ ✆☛t✟✠
✠❢ ✣✑✱ t✡✝ ❢✠✆☞☛t✟✠♥ ✠❢ st✆✉❝t✉✆✝s ✟s ✉♥✉s✉☛✌✌② st✆✠♥❣ ☛♥✞ t✡✝ ☛✈✍
✝✆☛❣✝✞ st✆☛t✟Þ❝☛t✟✠♥ ❝✡☛♥❣✝s s✟❣♥✟Þ❝☛♥t✌② t✠ ☛✦✝❝t t✡✝ ✞✝t✝✆☞✟✍
♥☛t✟✠♥ ✠❢ t✡✝ ✝✦✝❝t✟✈✝ ☞☛❣♥✝t✟❝ ♣✆✝ss✉✆✝✳ ❍✠✇✝✈✝✆✱ ❜② ✆✝st✆✟❝t✍
✟♥❣ t✡✝ ☛♥☛✌②s✟s t✠ ✝☛✆✌② t✟☞✝s✱ ✇✝ ✠❜t☛✟♥ ❝✠✝✧❝✟✝♥ts t✡☛t ☛✆✝ ♥✠t
✠♥✌② ✟♥ ❜✝tt✝✆ ☛❣✆✝✝☞✝♥t ✇✟t✡ ☛♥ ✝☛✆✌✟✝✆ ❢✠✆☞✉✌☛ ✠❢ ❇✆☛♥✞✝♥❜✉✆❣
✝t ☛✌✳ ✎✏✑✒✏☛✔ ✇✟t✡ ☛ s☞☛✌✌✝✆ s❝☛✌✝ s✝♣☛✆☛t✟✠♥ ✆☛t✟✠ ❜✉t ☛✌s✠ ❣✟✈✝
▼❋❙ ✆✝s✉✌ts t✡☛t ☛❣✆✝✝ ❜✝tt✝✆ ✇✟t✡ ✠✉✆ ♥✝✇ ❉◆❙✳
❚✡✝ ❉◆❙ ☛✆✝ ✉s✝✞ ♣✆✟☞☛✆✟✌② t✠ ❝✠☞♣✉t✝ t✡✝ ❣✆✠✇t✡ ✆☛t✝s
☛♥✞ ☞☛❣♥✝t✟❝ Þ✝✌✞ st✆✉❝t✉✆✝s ✞✉✆✟♥❣ t✡✝ s☛t✉✆☛t✝✞ st☛t✝ ✇✟t✡✍
✠✉t ✟♥✈✠✕✟♥❣ t✡✝ ☞✝☛♥✍Þ✝✌✞ ❝✠♥❝✝♣t✳ ❇② ❝✠♥t✆☛st✱ t✡✝ ★ ☛♣✍
♣✆✠☛❝✡ ✎❖✆s③☛❣ ✒✶✩✑❀ ✗✠✉q✉✝t ✝t ☛✌✳ ✒✶✩✪❀ ✓✌✝✝✠✆✟♥ ✝t ☛✌✳ ✒✶✶✑❀
❘✠❣☛❝✡✝✈s✕✟✟ ✬ ✓✌✝✝✠✆✟♥ ✏✑✑✮✔ ✟s ✉s✝✞ t✠ ✞✝t✝✆☞✟♥✝ t✡✝ ✞✝♣✝♥✍
✞✝♥❝✝ ✠❢ ☞✝☛♥✍Þ✝✌✞ ❝✠✝✧❝✟✝♥ts ✠♥ t✡✝ ✆✠t☛t✟✠♥ ✆☛t✝✳ ❚✡✟s ❝☛♥
☛✌s✠ ❜✝ ✞✠♥✝ ✇✟t✡ ❉◆❙ ✎✓✝☞✝✌ ✝t ☛✌✳ ✏✑✒✏☛✔✳ ❍✝✆✝ ✇✝ ☛♣♣✌②
t✡✠s✝ ❝☛✌❝✉✌☛t✟✠♥s t✠ t✡✝ ❝☛s✝ ✇✟t✡ ✆✠t☛t✟✠♥✳
❲✝ ✆✝❝☛✌✌ t✡☛t ✇✝ ☛✞✠♣t ✡✝✆✝ ☛♥ ✟s✠t✡✝✆☞☛✌ st✆☛t✟Þ❝☛t✟✠♥
☛♥✞ ☛♥ ✟s✠t✡✝✆☞☛✌ ✝q✉☛t✟✠♥ ✠❢ st☛t✝✳ ❚✡✟s ✟s ✞✠♥✝ ❜✝❝☛✉s✝ t✡✝
✝✦✝❝t t✡☛t ✇✝ ☛✆✝ ✟♥t✝✆✝st✝✞ ✟♥ ✝①✟sts ✝✈✝♥ ✟♥ t✡✟s s✟☞♣✌✝st
❝☛s✝✱ ✇✡✝✆✝ t✝☞♣✝✆☛t✉✆✝ ☛♥✞ ♣✆✝ss✉✆✝ s❝☛✌✝ ✡✝✟❣✡t ☛✆✝ ❝✠♥st☛♥t✳
◆✠♥✟s✠t✡✝✆☞☛✌ s✝t✉♣s ✡☛✈✝ ❜✝✝♥ st✉✞✟✝✞ ☛t t✡✝ ☞✝☛♥✍Þ✝✌✞ ✌✝✈✝✌
❜✠t✡ ✇✟t✡ ✎✓✯♣②✌✯ ✝t ☛✌✳ ✏✑✒✏✱ ✏✑✒✣✔ ☛♥✞ ✇✟t✡✠✉t ✎❇✆☛♥✞✝♥❜✉✆❣
✝t ☛✌✳ ✏✑✒✑✔ ✝♥t✆✠♣② ✝✈✠✌✉t✟✠♥ ✟♥❝✌✉✞✝✞✳ ✘♥ ☛ st☛❜✌② st✆☛t✟Þ✝✞
✌☛②✝✆✱ ✝♥t✆✠♣② ✝✈✠✌✉t✟✠♥ ✌✝☛✞s t✠ ☛♥ ☛✞✞✟t✟✠♥☛✌ ✆✝st✠✆✟♥❣ ❢✠✆❝✝
☛♥✞ ✡✝♥❝✝ t✠ ✟♥t✝✆♥☛✌ ❣✆☛✈✟t② ✇☛✈✝s ✎❇✆✉♥t✍❱✯✟s✯✌✯ ✠s❝✟✌✌☛t✟✠♥s✔
t✡☛t st☛❜✟✌✟③✝ ◆✖▼✗✘ ✎✓✯♣②✌✯ ✝t ☛✌✳ ✏✑✒✏✔✳ ❚✡✉s✱ ❜② ✉s✟♥❣ ❜✠t✡
✟s✠t✡✝✆☞☛✌ st✆☛t✟Þ❝☛t✟✠♥ ☛♥✞ ☛♥ ✟s✠t✡✝✆☞☛✌ ✝q✉☛t✟✠♥ ✠❢ st☛t✝✱ ✇✝
✆✝❝✠✈✝✆ ☛ s✟t✉☛t✟✠♥ t✡☛t ✟s s✟☞✟✌☛✆ t✠ ☛♥ ☛✞✟☛❜☛t✟❝ ✌☛②✝✆✱ ✝①❝✝♣t
t✡☛t t✡✝ t✝☞♣✝✆☛t✉✆✝ ☛♥✞ ✡✝♥❝✝ t✡✝ ♣✆✝ss✉✆✝ s❝☛✌✝ ✡✝✟❣✡t ✞✝❝✆✝☛s✝
✇✟t✡ ✡✝✟❣✡t✳
❚✡✝ s②st✝☞ ✇✝ ☛✆✝ t✡✉s ✞✝☛✌✟♥❣ ✇✟t✡ ✟s ❣✠✈✝✆♥✝✞ ❜② t✡✝ ❝✠☞✍
❜✟♥✝✞ ☛❝t✟✠♥ ✠❢ ✆✠t☛t✟✠♥ ☛♥✞ st✆☛t✟Þ❝☛t✟✠♥✳ ✘♥ ♣✆✟♥❝✟♣✌✝✱ s✉❝✡ s②s✍
t✝☞s ✡☛✈✝ ❜✝✝♥ st✉✞✟✝✞ ☞☛♥② t✟☞✝s ❜✝❢✠✆✝✱ ❢✠✆ ✝①☛☞♣✌✝✱ t✠ ✞✝t✝✆✍
☞✟♥✝ t✡✝ ✰ ✝✦✝❝t ✟♥ ☞✝☛♥✍Þ✝✌✞ ✞②♥☛☞✠ t✡✝✠✆② ✎✓✆☛✉s✝ ✬ ❘✯✞✌✝✆
✒✶✥✑❀ ❇✆☛♥✞✝♥❜✉✆❣ ✬ ❙✉❜✆☛☞☛♥✟☛♥ ✏✑✑✲☛✔✳ ❚✡✝ ✞✟✦✝✆✝♥❝✝ t✠
✝☛✆✌✟✝✆ ✇✠✆✕ ✟s t✡✝ ❜✟❣ s❝☛✌✝ s✝♣☛✆☛t✟✠♥ ✆☛t✟✠✱ ✇✡✝✆✝ t✡✝ ✞✠☞☛✟♥
✟s ✉♣ t✠ ✣✑ t✟☞✝s ✌☛✆❣✝✆ t✡☛♥ t✡✝ s❝☛✌✝ ✠❢ t✡✝ ✝♥✝✆❣②✍❝☛✆✆②✟♥❣ ✝✞✍
✞✟✝s✳ ✤s ☞✝♥t✟✠♥✝✞✱ st✆☛t✟Þ❝☛t✟✠♥ ☛♥✞ ✆✠t☛t✟✠♥ ✌✝☛✞ t✠ ✕✟♥✝t✟❝ ✡✝✍
✌✟❝✟t② ☛♥✞ ☛♥ ✰ ✝✦✝❝t✳ ❲✝ t✡✝✆✝❢✠✆✝ ☛✌s✠ q✉☛♥t✟❢② ✡✝✆✝ t✡✝ ☛☞✠✉♥t
✠❢ ✕✟♥✝t✟❝ ✡✝✌✟❝✟t② ♣✆✠✞✉❝✝✞ ☛♥✞ ☛s❝✝✆t☛✟♥ ✇✡✝t✡✝✆ t✡✟s ✌✝☛✞s t✠
✠❜s✝✆✈☛❜✌✝ ✝✦✝❝ts ✟♥ t✡✝ ✆✝s✉✌t✟♥❣ ☞☛❣♥✝t✟❝ st✆✉❝t✉✆✝s✳ ❲✝ ✉s✝
✡✝✆✝ t✡✝ ✠♣♣✠✆t✉♥✟t② t✠ ✝①♣✌✠✆✝ t✡✝ ❢✝☛s✟❜✟✌✟t② ✠❢ ✞✝t✝✆☞✟♥✟♥❣ t✡✝
☞☛❣♥✝t✟❝ ✡✝✌✟❝✟t② s♣✝❝t✆✉☞ ❢✆✠☞ ☞✝☛s✉✆✝☞✝♥ts ✠❢ t✡✝ ☞☛❣♥✝t✟❝
❝✠✆✆✝✌☛t✟✠♥ t✝♥s✠✆ ☛✌✠♥❣ ☛ ✌✠♥❣✟t✉✞✟♥☛✌ st✆✟♣✳
❆✽✸✁ ➤➥➦➨ ✷ ➩➫ ✄✷
❲✝ ❜✝❣✟♥ ❜② ✞✟s❝✉ss✟♥❣ Þ✆st t✡✝ ❜☛s✟❝ ✝q✉☛t✟✠♥s t✠ ✞✝t✝✆☞✟♥✝
t✡✝ ✝✦✝❝t✟✈✝ ☞☛❣♥✝t✟❝ ♣✆✝ss✉✆✝ ❢✆✠☞ ❉◆❙ ☛♥✞ t✡✝ ★ ☛♣♣✆✠☛❝✡
✎❙✝❝t✳ ✏✔✱ ❝✠☞♣☛✆✝ ❣✆✠✇t✡ ✆☛t✝s ❢✠✆ ▼❋❙ ☛♥✞ ❉◆❙ ✎❙✝❝t✳ ✮✔✱
☛♥✞ t✉✆♥ t✡✝♥ t✠ t✡✝ ☞✝☛s✉✆✝☞✝♥t ✠❢ ✕✟♥✝t✟❝ ☛♥✞ ☞☛❣♥✝t✟❝ ✡✝✍
✌✟❝✟t② ❢✆✠☞ s✉✆❢☛❝✝ ☞✝☛s✉✆✝☞✝♥ts ✎❙✝❝t✳ ✲✔ ❜✝❢✠✆✝ ❝✠♥❝✌✉✞✟♥❣ ✟♥
❙✝❝t✳ ✪✳
✵✻ ✼✾✿ ♠❁❃✿❄
❲✝ ❝✠♥s✟✞✝✆ ❉◆❙ ✠❢ ☛♥ ✟s✠t✡✝✆☞☛✌✌② st✆☛t✟Þ✝✞ ✌☛②✝✆
✎❇✆☛♥✞✝♥❜✉✆❣ ✝t ☛✌✳ ✏✑✒✒☛❀ ✓✝☞✝✌ ✝t ☛✌✳ ✏✑✒✏☛✔ ☛♥✞ s✠✌✈✝
t✡✝ ✝q✉☛t✟✠♥s ❢✠✆ t✡✝ ✈✝✌✠❝✟t② ❯✱ t✡✝ ☞☛❣♥✝t✟❝ ✈✝❝t✠✆ ♣✠t✝♥✍
t✟☛✌ ❅✱ ☛♥✞ t✡✝ ✞✝♥s✟t② ❊ ✟♥ t✡✝ ♣✆✝s✝♥❝✝ ✠❢ ✆✠t☛t✟✠♥ ✙✱
❉❯
✒
❂ ■✏❏ × ❯ ■ ❑P✜ ◗ ✌♥ ❊ ❳ ❨ × ❩ ❳ ❬ ❳ ❭ ❳ ❪❫ ❴
❉●
❊
❵❅
❵●
❵❊
❵●
✎✒✔
❂ ❯ × ❩ ❳ ❛❞P ❅❴
✎✏✔
❂ ■◗ ➲ ❊❯❴
✎✣✔
✇✡✝✆✝ ❉✴❉● ❂ ❵✴❵● ❳ ❯ ➲ ◗ ✟s t✡✝ ☛✞✈✝❝t✟✈✝ ✞✝✆✟✈☛t✟✈✝✱ ❡ ✟s t✡✝
✕✟♥✝☞☛t✟❝ ✈✟s❝✠s✟t②✱ ❛ ✟s t✡✝ ☞☛❣♥✝t✟❝ ✞✟✦✉s✟✈✟t② ✞✉✝ t✠ ❙♣✟t③✝✆
❝✠♥✞✉❝t✟✈✟t② ✠❢ t✡✝ ♣✌☛s☞☛✱ ❩ ❂ ❩❤ ❳ ◗× ❅ ✟s t✡✝ ☞☛❣♥✝t✟❝ Þ✝✌✞✱
❩❤ ❂ ✎✑❴ ✐❤❴ ✑✔ ✟s t✡✝ ✟☞♣✠s✝✞ ✉♥✟❢✠✆☞ Þ✝✌✞✱ ❨ ❂ ◗ × ❩✴❧❤ ✟s t✡✝
❝✉✆✆✝♥t ✞✝♥s✟t②✱ ❧❤ ✟s t✡✝ ✈☛❝✉✉☞ ♣✝✆☞✝☛❜✟✌✟t②✱ ❪❫ ❂ ◗ ➲ ✎✏❡❊♦✔
✟s t✡✝ ✈✟s❝✠✉s ❢✠✆❝✝✱ ④⑤ ⑥ ❂ ⑦P ✎❵ ⑥ ⑧ ⑤ ❳ ❵⑤ ⑧ ⑥ ✔ ■ ⑦⑨ ⑩⑤ ⑥ ◗ ➲ ❯ ✟s t✡✝
t✆☛❝✝✌✝ss ✆☛t✝✍✠❢✍st✆☛✟♥ t✝♥s✠✆✳ ❚✡✝ ☛♥❣✉✌☛✆ ✈✝✌✠❝✟t② ✈✝❝t✠✆ ❏ ✟s
q✉☛♥t✟Þ✝✞ ❜② ✟ts s❝☛✌☛✆ ☛☞♣✌✟t✉✞✝ ✙ ☛♥✞ ❝✠✌☛t✟t✉✞✝ ❶✱ s✉❝✡ t✡☛t
❏ ❂ ✙ ✎■ s✟♥ ❶❴ ✑❴ ❝✠s ❶✔✳ ✤s ✟♥ ▲❇✓▼❘✱ ❷ ❝✠✆✆✝s♣✠♥✞s t✠ ✆☛✞✟✉s✱
❸ t✠ ❝✠✌☛t✟t✉✞✝✱ ☛♥✞ ❹ t✠ ☛③✟☞✉t✡✳ ❚✡✝ ❢✠✆❝✟♥❣ ❢✉♥❝t✟✠♥ ❬ ❝✠♥✍
s✟sts ✠❢ ✆☛♥✞✠☞✱ ✇✡✟t✝✍✟♥✍t✟☞✝✱ ♣✌☛♥✝✱ ♥✠♥♣✠✌☛✆✟③✝✞ ✇☛✈✝s ✇✟t✡
☛ ❝✝✆t☛✟♥ ☛✈✝✆☛❣✝ ✇☛✈✝♥✉☞❜✝✆ ❦✢ ✳ ❚✡✝ t✉✆❜✉✌✝♥t ✆☞s ✈✝✌✠❝✟t② ✟s
☛♣♣✆✠①✟☞☛t✝✌② ✟♥✞✝♣✝♥✞✝♥t ✠❢ ❷ ✇✟t✡ ✚r✛✜ ❂ ❺❻P ❼⑦❽P ❿ ✑➀✒ ❑✜ ✳
❚✡✝ ❣✆☛✈✟t☛t✟✠♥☛✌ ☛❝❝✝✌✝✆☛t✟✠♥ ❭ ❂ ✎✑❴ ✑❴ ■➁✔ ✟s ❝✡✠s✝♥ s✉❝✡ t✡☛t
❦⑦ ➂➃ ❂ ✒✱ s✠ t✡✝ ✞✝♥s✟t② ❝✠♥t✆☛st ❜✝t✇✝✝♥ ❜✠tt✠☞ ☛♥✞ t✠♣ ✟s
✝①♣✎✏➄✔ ❿ ✲✣✲ ✟♥ ☛ ✞✠☞☛✟♥ ■➄ ➅ ❦⑦ ❷ ➅ ➄✳ ❍✝✆✝✱ ➂➃ ❂ ❑P✜ ✴➁ ✟s t✡✝
✞✝♥s✟t② s❝☛✌✝ ✡✝✟❣✡t ☛♥✞ ❦⑦ ❂ ✏➄✴➆ ✟s t✡✝ s☞☛✌✌✝st ✇☛✈✝♥✉☞❜✝✆
t✡☛t Þts ✟♥t✠ t✡✝ ❝✉❜✟❝ ✞✠☞☛✟♥ ✠❢ s✟③✝ ➆⑨ ✳ ✘♥ ☞✠st ✠❢ ✠✉✆ ❝☛✌✍
❝✉✌☛t✟✠♥s✱ st✆✉❝t✉✆✝s ✞✝✈✝✌✠♣ ✇✡✠s✝ ✡✠✆✟③✠♥t☛✌ ✇☛✈✝♥✉☞❜✝✆ ❦ ➇
✟s ❝✌✠s✝ t✠ ❦⑦ ✳ ❲✝ ☛✞✠♣t ❈☛✆t✝s✟☛♥ ❝✠✠✆✞✟♥☛t✝s ✎❸❴ ❹❴ ❷✔✱ ✇✟t✡
♣✝✆✟✠✞✟❝ ❜✠✉♥✞☛✆② ❝✠♥✞✟t✟✠♥s ✟♥ t✡✝ ❸✍ ☛♥✞ ❹✍✞✟✆✝❝t✟✠♥s ☛♥✞
st✆✝ss✍❢✆✝✝✱ ♣✝✆❢✝❝t✌② ❝✠♥✞✉❝t✟♥❣ ❜✠✉♥✞☛✆✟✝s ☛t t✡✝ t✠♣ ☛♥✞ ❜✠t✍
t✠☞ ✎❷ ❂ ➧➆➈ ✴✏✔✳ ✘♥ ☛✌✌ ❝☛s✝s✱ ✇✝ ✉s✝ ☛ s❝☛✌✝ s✝♣☛✆☛t✟✠♥ ✆☛✍
t✟✠ ❦✢ ✴❦⑦ ✠❢ ✣✑✱ ☛ ß✉✟✞ ❘✝②♥✠✌✞s ♥✉☞❜✝✆ ❘✝ ➉ ✚r✛✜ ✴❡❦✢ ✠❢ ✣✪✱
☛♥✞ ☛ ☞☛❣♥✝t✟❝ ✗✆☛♥✞t✌ ♥✉☞❜✝✆ ✗✆ ➊ ❂ ❡✴❛ ✠❢ ✑✳✲✳ ❚✡✝ ☞☛❣✍
♥✝t✟❝ ❘✝②♥✠✌✞s ♥✉☞❜✝✆ ✟s t✡✝✆✝❢✠✆✝ ❘✝ ➊ ❂ ✗✆ ➊ ❘✝ ❂ ✒✥✳ ❚✡✝
✈☛✌✉✝ ✠❢ ✐❤ ✟s s♣✝❝✟Þ✝✞ ✟♥ ✉♥✟ts ✠❢ t✡✝ ✈✠✌✉☞✝✍☛✈✝✆☛❣✝✞ ✈☛✌✉✝
➍
✐➋➌❤ ❂ ❧❤ ❊❤ ✚r✛✜ ✱ ✇✡✝✆✝ ❊❤ ❂ ❺❊❼ ✟s t✡✝ ✈✠✌✉☞✝✍☛✈✝✆☛❣✝✞ ✞✝♥✍
s✟t②✱ ✇✡✟❝✡ ✟s ❝✠♥st☛♥t ✟♥ t✟☞✝✳ ✤s ✟♥ ✝☛✆✌✟✝✆ ✇✠✆✕✱ ✇✝ ☛✌s✠ ✞✝Þ♥✝
➍
t✡✝ ✌✠❝☛✌ ✝q✉✟♣☛✆t✟t✟✠♥ Þ✝✌✞ st✆✝♥❣t✡ ✐➋➌ ✎❷✔ ❂ ❧❤ ❊ ✚r✛✜ ✳ ✘♥ ✠✉✆
✉♥✟ts✱ ❦⑦ ❂ ❑✜ ❂ ❧❤ ❂ ❊❤ ❂ ✒✳ ✘♥ ☛✞✞✟t✟✠♥ t✠ ✈✟s✉☛✌✟③☛t✟✠♥s ✠❢ t✡✝
☛❝t✉☛✌ ☞☛❣♥✝t✟❝ Þ✝✌✞✱ ✇✝ ☛✌s✠ ☞✠♥✟t✠✆ ✐➎ ✱ ✇✡✟❝✡ ✟s ☛♥ ☛✈✝✆☛❣✝
✠✈✝✆ ❹ ☛♥✞ ☛ ❝✝✆t☛✟♥ t✟☞✝ ✟♥t✝✆✈☛✌ ➏●✳ ❚✟☞✝ ✟s s✠☞✝t✟☞✝s s♣✝❝✟Þ✝✞
✟♥ t✝✆☞s ✠❢ t✉✆❜✉✌✝♥t✍✞✟✦✉s✟✈✝ t✟☞✝s ● ❛➐❤ ❦⑦P ✱ ✇✡✝✆✝ ❛➐❤ ❂ ✚r✛✜ ✴✣❦✢
✟s t✡✝ ✝st✟☞☛t✝✞ t✉✆❜✉✌✝♥t ✞✟✦✉s✟✈✟t②✳
❚✡✝ s✟☞✉✌☛t✟✠♥s ☛✆✝ ♣✝✆❢✠✆☞✝✞ ✇✟t✡ t✡✝ ✗✝♥❝✟✌ ❈✠✞✝⑦ ✱ ✇✡✟❝✡
✉s✝s s✟①t✡✍✠✆✞✝✆ ✝①♣✌✟❝✟t Þ♥✟t✝ ✞✟✦✝✆✝♥❝✝s ✟♥ s♣☛❝✝ ☛♥✞ ☛ t✡✟✆✞✍
✠✆✞✝✆ ☛❝❝✉✆☛t✝ t✟☞✝✍st✝♣♣✟♥❣ ☞✝t✡✠✞✳ ❲✝ ✉s✝ ☛ ♥✉☞✝✆✟❝☛✌ ✆✝s✠✍
✌✉t✟✠♥ ✠❢ ✏✲✪⑨ ☞✝s✡ ♣✠✟♥ts✳
➑ ➒➓➓➔→➣➣➔↔↕➙➛➜➝➙➞➟↔➠➡➞➞➡➜↔➙➞➟↔➠➙➞➢
■
❘ ▲♦s✁✂✁ ❡✄ ✁❛ ✿ ❈♦☎✆❡✄✐♥❣ ❡✝❡✞✄s ✐♥ ✞♦♥✞❡♥✄r✁✄✐♥❣ ☎✁❣♥❡✄✐✞ ß✉①
❲✟ ❝✠✡☛☞✌✟ ✇✍✎✏ ☞✑✒ ✟✓✎✟✑✒ ✟☞✌✔✍✟✌ ▼❋✕ ✠✖ ✗✘❑▼✙✱ ✇✏✟✌✟
✇✟ ✚✠✔❧✟ ✎✏✟ ✟❧✠✔✛✎✍✠✑ ✟q✛☞✎✍✠✑✚ ✖✠✌ ✡✟☞✑ ❧✟✔✠❝✍✎✜ ❯✱ ✡✟☞✑ ✒✟✑❞
✚✍✎✜ ✢✱ ☞✑✒ ✡✟☞✑ ❧✟❝✎✠✌ ☛✠✎✟✑✎✍☞✔ ❆✱ ✍✑ ✎✏✟ ✖✠✌✡
✣❯
✣t
✧
❂ ❾❯ ➲ ✤❯ ❾ ✷✥ × ❯ ❾ ✦ ✤ ✔✑ ✢ ✰ ✩ ✰ ✪ ✫✬ ✭
★
✮✯✲
❂ ❯ × ❇ ❾ ✮✳✴ ✰ ✳✲ ❏ ✭
✮✵✲
✣❆
✣t
✣✢
❂ ❾❯ ➲ ✤✢ ❾ ✢✤ ➲ ❯✭
✮✶✲
✣t
✇✏✟✌✟ ✪ ✫✬ ❂ ✪ ✫ ✰ ✪ ✬ ✱ ✇✍✎✏
✸
✢✪✫ ❂ ❾ ✤
✧
✹
✮✺ ❾ ✻♣ ✲ ❇
✧
✼
✮✽✲
➼➽➾➚ ➪➚ ➶♦r☎✁❛✐➹❡✂ ❡✝❡✞✄✐➘❡ ☎✁❣♥❡✄✐✞ ✆r❡ss✉r❡➴ ➷➬➮ ➱✃❐➴ ❒♦r ✄❮r❡❡ ➘✁❛✉❡s
❜✟✍✑✾ ✎✏✟ ✡✟☞✑❞♠✟✔✒ ✡☞✾✑✟✎✍❝ ☛✌✟✚✚✛✌✟ ✖✠✌❝✟✱ ☞✑✒
❁
✪ ✬ ❂ ✮❀✴ ✰ ❀✲
✍✚
✎✏✟
❊● ◆
✧
❃ ❯ ✰
✸
❄
♦❒ ❈♦➴ ✞♦☎✆✁r❡✂ ❰✐✄❮ ÏÐ
❅
➱Ñ❐ ❒♦r ✂✐✝❡r❡♥✄ ✞♦☎Ò✐♥✁✄✐♦♥s ♦❒ ✃Ó ✁♥✂ ✃Ô ➴
✁s ✂✐s✞✉ss❡✂ ✐♥ ✄❮❡ ✄❡①✄
✮❉✲
✤✤ ➲ ❯ ✰ ✷❙✤ ✔✑ ✢
✎✠✎☞✔ ✮✎✛✌❜✛✔✟✑✎ ☛✔✛✚ ✡✍❝✌✠✚❝✠☛✍❝✲ ❧✍✚❝✠✛✚ ✖✠✌❝✟❢ ❍✟✌✟✱
❂
✸
✧
✸
✮❖ ●P ◆ ✰ ❖ ◆P● ✲ ❾
◗ ✤ ➲ ❯ ✍✚ ✎✏✟ ✎✌☞❝✟✔✟✚✚ ✌☞✎✟❞✠✖❞✚✎✌☞✍✑
❄ ●◆
✎✟✑✚✠✌ ✠✖ ✎✏✟ ✡✟☞✑ ❚✠✇ ☞✑✒ ✻ ♣ ✍✚ ☞☛☛✌✠✓✍✡☞✎✟✒ ❜✜ ✮❑✟✡✟✔ ✟✎ ☞✔❢
✷❱✺✷❜✲
✡☞✾✑✟✎✍❝ ❚✛❝✎✛☞✎✍✠✑✚ ➵➁ ❢ ④✏✟ ✟↔✟❝✎✍❧✟ ✡☞✾✑✟✎✍❝ ☛✌✟✚✚✛✌✟ ✍✚ ✎✏✟✑
✸
✧
✒✟✎✟✌✡✍✑✟✒ ✛✚✍✑✾ ✎✏✟ ✟q✛☞✎✍✠✑ ➩❴➫ ✮❳✲ ❂
Õ✺ ❾ ✻♣ ✮❳✲Ö❳ ❢ ④✏✟ ✌✟❞
✧
✚✛✔✎ ✍✚ ☛✔✠✎✎✟✒ ✍✑ ❋✍✾❢ ✺ ✖✠✌ ✎✏✌✟✟ ❧☞✔✛✟✚ ✠✖ ❹✠ ✒✛✌✍✑✾ ☞✑ ✟☞✌✔✜ ✎✍✡✟
✧
❳
❨
✻♣ ✮❳✲ ❂
✚✡☞✔✔❞✚❝☞✔✟ ✒✜✑☞✡✠ ☞❝✎✍✠✑✱ ✇✏✍❝✏ ❝☞✑ ☛✌✠✒✛❝✟ ♠✑✍✎✟ ❜☞❝✈✾✌✠✛✑✒
✧
✧
❳♣ ✰ ❳
✭
✮❩✲
✍✑✎✟✌❧☞✔ ✇✏✟✑ ✚✎✌✛❝✎✛✌✟ ✖✠✌✡☞✎✍✠✑ ✍✚ ✚✎✍✔✔ ✇✟☞✈✱ ☞✑✒ ✎✏✟ ❜☞❝✈❞
✾✌✠✛✑✒ ✚✎✌☞✎✍♠❝☞✎✍✠✑ ✌✟✡☞✍✑✚ ✛✑❝✏☞✑✾✟✒✱ ✚✠ ✎✏☞✎ ✎✏✟ ✌✟✚✛✔✎ ✍✚ ✑✠✎
✜✟✎ ☞↔✟❝✎✟✒❢ ❲✟ ✑✠✎✟ ✎✏☞✎ ✟❧✟✑ ✍✑ ✎✏✟ ❹✠ ❂ ❱Ø✺Ù ❝☞✚✟✱ ✍✑ ✇✏✍❝✏
✇✏✍❝✏ ✍✚ ✠✑✔✜ ☞ ✖✛✑❝✎✍✠✑ ✠✖ ✎✏✟ ✌☞✎✍✠ ❳
❬
❭ ❇❭❪❫❴❵ ✮③✲❢ ❍✟✌✟✱ ❳❨
✎✏✟ ✍✑✚✎☞❜✍✔✍✎✜ ✍✚ ✑✠ ✔✠✑✾✟✌ ✚✠ ☛✌✠✡✍✑✟✑✎✱ ✇✟ ✏☞❧✟ ✎✠ ✌✟✚✎✌✍❝✎ ✠✛✌❞
☞✑✒ ❳♣ ☞✌✟ ❝✠✟❤❝✍✟✑✎✚ ✎✏☞✎ ✏☞❧✟ ❜✟✟✑ ✒✟✎✟✌✡✍✑✟✒ ✖✌✠✡ ☛✌✟❧✍✠✛✚
✚✟✔❧✟✚ ✎✠ ✟☞✌✔✜ ✎✍✡✟✚✱ ✚✍✑❝✟ ✎✏✟ ✑✟✾☞✎✍❧✟ ✟↔✟❝✎✍❧✟ ✡☞✾✑✟✎✍❝ ☛✌✟✚❞
✑✛✡✟✌✍❝☞✔ ✚✍✡✛✔☞✎✍✠✑✚ ✍✑ ✎✏✟ ☞❜✚✟✑❝✟ ✠✖ ✌✠✎☞✎✍✠✑ ✮✘✌☞✑✒✟✑❜✛✌✾
✟✎ ☞✔❢ ✷❱✺✷☞✲❢ ❥✑ ❦q❢ ✮✽✲ ✇✟ ✏☞❧✟ ✎☞✈✟✑ ✍✑✎✠ ☞❝❝✠✛✑✎ ✎✏☞✎ ✎✏✟ ✡✟☞✑
✡☞✾✑✟✎✍❝ ♠✟✔✒ ✍✚ ✍✑✒✟☛✟✑✒✟✑✎ ✠✖ ②✱ ✚✠ ✎✏✟ ✡✟☞✑ ✡☞✾✑✟✎✍❝ ✎✟✑✚✍✠✑
❧☞✑✍✚✏✟✚❢
✎✏✟
✑✠✑✒✍✡✟✑✚✍✠✑☞✔ ☛☞✌☞✡✟✎✟✌ ⑥✌
✮✘✌☞✑✒✟✑❜✛✌✾
✚✍✠✑☞✔
✎✛☞✔✔✜ ✎✏✟ ✚☞✡✟ ✖✠✌ ☞✔✔ ✎✏✌✟✟ ❧☞✔✛✟✚ ✠✖ ❹✠❢ ❲✟ ☞✔✚✠ ❝✠✡☛☞✌✟ ✎✏✟
✌✟✚✛✔✎✍✑✾ ☛✌✠♠✔✟✚ ✇✍✎✏ ✎✏✠✚✟ ✖✌✠✡ ❦q❢ ✮❩✲ ✖✠✌ ✒✍↔✟✌✟✑✎ ❝✠✡❜✍✑☞❞
④✏✟ ✚✎✌✟✑✾✎✏ ✠✖ ✾✌☞❧✍✎☞✎✍✠✑☞✔ ✚✎✌☞✎✍♠❝☞✎✍✠✑ ✍✚ ❝✏☞✌☞❝✎✟✌✍⑤✟✒
❜✜
✚✛✌✟ ☞↔✟❝✎✚ ✎✏✟ ❜☞❝✈✾✌✠✛✑✒ ✚✎✌☞✎✍♠❝☞✎✍✠✑ ☞✑✒ ✏✟✑❝✟ ✎✏✟ ☛✌✟✚✚✛✌✟
❝✏☞✑✾✟✚ ☞✎ ✔☞✎✟✌ ✎✍✡✟✚❢ ④✏✟ ✌✟✚✛✔✎✍✑✾ ☛✌✠♠✔✟✚ ✠✖ ➩❴➫ ✮❳✲ ☞✌✟ ❧✍✌❞
✟✎
☛☞✌☞✡✟✎✟✌
☞✔❢
✍✚
✷❱✺✷❜✲❢
✎✏✟
❸✑✠✎✏✟✌
❹✠✌✍✠✔✍✚
❂
✧
⑦❪✦ ⑧⑨
★
❬
✍✡☛✠✌✎☞✑✎
✑✛✡❜✟✌✱
❹✠
✮⑩❶ ⑧⑨ ✲
❷✸
✎✍✠✑✚ ✠✖ ❳❨ ☞✑✒ ❳♣ ❢ ❥✎ ✎✛✌✑✚ ✠✛✎ ✎✏☞✎ ✎✏✟ ❝✛✌❧✟✚ ✖✠✌ ✒✍↔✟✌✟✑✎ ❧☞✔✛✟✚
✠✖ ❹✠ ☞✌✟ ❜✟✚✎ ✌✟☛✌✠✒✛❝✟✒ ✖✠✌ ❳❨ ❂ ❱Ø✯✯ ☞✑✒ ❳♣ ❂ ❱Ø❱✵❉❢
✑✠✑✒✍✡✟✑❞
❂
✷❺❪❻❼❽★ ⑧⑨ ❢
❸✔✎✟✌✑☞✎✍❧✟✔✜✱ ✇✟ ✑✠✌✡☞✔✍⑤✟ ✎✏✟ ✾✌✠✇✎✏ ✌☞✎✟ ✠✖ ✎✏✟ ✍✑✚✎☞❜✍✔✍✎✜ ❜✜
➙➛Ú➛ ÛÜ➠Ý➡➠➨➢➤➥➦ Þ➡➠à➢➤➨➢Ýá➧
☞ q✛☞✑✎✍✎✜
❲✟
❿➀➁ ❬ ❳❨ ❻❼❽★ ❪⑩❶ ✭
✮✺❱✲
✑✠✇
❝✠✡☛☞✌✟
✎✏✟
❧☞✔✛✟✚
✇✍✎✏
✎✏✟✠✌✟✎✍❝☞✔
☛✌✟✒✍❝✎✍✠✑✚
✖✠✌ ✻ ♣ ✮❳✲❢ ❲✟ ✎☞✈✟ ✍✑✎✠ ☞❝❝✠✛✑✎ ✎✏✟ ✖✟✟✒❜☞❝✈ ✠✖ ✎✏✟ ✡☞✾✑✟✎✍❝
♠✟✔✒ ✠✑ ✎✏✟ ✎✛✌❜✛✔✟✑✎ ❚✛✍✒ ❚✠✇❢ ❲✟ ✛✚✟ ☞ ✡✟☞✑❞♠✟✔✒ ☞☛☛✌✠☞❝✏✱
✇✏✍❝✏ ✍✚ ✡✠✎✍❧☞✎✟✒ ❜✜ ✎✏✟ ☞✑☞✔✜✎✍❝ ✌✟✚✛✔✎✚ ✠✖ ✗✘❑▼✙ ☞✑✒ ✎✏✟
♠✑✒✍✑✾ ✎✏☞✎ ➂❦▼➃❥ ✍✚ ✚✛☛☛✌✟✚✚✟✒ ✇✏✟✑ ✷❺ ➄
➅ ❿➀➁ ❢
✇✏✟✌✟❜✜ ❧✟✔✠❝✍✎✜✱ ☛✌✟✚✚✛✌✟✱ ☞✑✒ ✡☞✾✑✟✎✍❝ ♠✟✔✒ ☞✌✟ ✚✟☛☞✌☞✎✟✒ ✍✑✎✠
✡✟☞✑ ☞✑✒
❚✛❝✎✛☞✎✍✑✾
☛☞✌✎✚❢ ❲✟
☞✔✚✠
☞✚✚✛✡✟ ❧☞✑✍✚✏✍✑✾
✡✟☞✑
✡✠✎✍✠✑❢ ④✏✟ ✚✎✌☞✎✟✾✜ ✠✖ ✠✛✌ ☞✑☞✔✜✎✍❝ ✒✟✌✍❧☞✎✍✠✑ ✍✚ ✎✠ ✒✟✎✟✌✡✍✑✟
✎✏✟ ❺
➆➇ ➈➉➉➊➋➌➍➎➊ ➏➐➑➒➊➌➍➋ ➓➔➊→→➣➔➊
✒✟☛✟✑✒✟✑❝✍✟✚ ✠✖
✎✏✟
✚✟❝✠✑✒
✡✠✡✟✑✎✚ ✖✠✌
✎✏✟
❧✟✔✠❝✍✎✜
❻● ✮t✭ â✲ ❻ ◆ ✮t✭ â✲✱ ✎✏✟ ✡☞✾✑✟✎✍❝ ♠✟✔✒ ➸● ✮t✭ â✲ ➸ ◆ ✮t✭ â✲✱ ☞✑✒ ✎✏✟ ❝✌✠✚✚❞
❥✑
✎✏✍✚
✚✟❝✎✍✠✑
✇✟
✚✎✛✒✜
✎✏✟
✟↔✟❝✎
✠✖
✌✠✎☞✎✍✠✑
✠✑
✎✏✟
✖✛✑❝❞
✎✍✠✑ ✻♣ ✮❳✲❢ ❲✟ ❝✠✑✚✍✒✟✌ ♠✌✚✎ ✎✏✟ ✌✟✚✛✔✎✚ ✠✖ ↕➂✕ ☞✑✒ ✎✛✌✑ ✎✏✟✑
✎✠ ☞✑ ☞✑☞✔✜✎✍❝☞✔ ✎✌✟☞✎✡✟✑✎❢
✏✟✔✍❝✍✎✜ ✎✟✑✚✠✌ ➸● ✮t✭ â✲ ❻ ◆ ✮t✭ â✲✱ ✇✏✟✌✟ ➵ ☞✌✟ ❚✛❝✎✛☞✎✍✠✑✚ ✠✖ ✡☞✾❞
✑✟✎✍❝ ♠✟✔✒ ☛✌✠✒✛❝✟✒ ❜✜ ✎☞✑✾✔✍✑✾ ✠✖ ✎✏✟ ✔☞✌✾✟❞✚❝☞✔✟ ♠✟✔✒❢ ④✠ ✎✏✍✚
✟✑✒ ✇✟ ✛✚✟ ✎✏✟ ✟q✛☞✎✍✠✑✚ ✖✠✌ ❚✛❝✎✛☞✎✍✠✑✚ ✠✖ ❧✟✔✠❝✍✎✜ ☞✑✒ ✡☞✾❞
✑✟✎✍❝ ♠✟✔✒ ✍✑ ✌✠✎☞✎✍✑✾ ✎✛✌❜✛✔✟✑❝✟✱ ✇✏✍❝✏ ☞✌✟ ✠❜✎☞✍✑✟✒ ❜✜ ✚✛❜✎✌☞❝✎❞
✍✑✾ ✟q✛☞✎✍✠✑✚ ✖✠✌ ✎✏✟ ✡✟☞✑ ♠✟✔✒✚ ✖✌✠✡ ✎✏✟ ❝✠✌✌✟✚☛✠✑✒✍✑✾ ✟q✛☞❞
➙➛➜➛ ➝➞➟➠➡➢➤➥➦ ➡➠➧➞➦➨➧
✎✍✠✑✚ ✖✠✌ ✎✏✟ ☞❝✎✛☞✔ ✮✡✟☞✑ ☛✔✛✚ ❚✛❝✎✛☞✎✍✑✾✲ ♠✟✔✒✚❢
❥✑ ✎✏✟ ▼❋✕ ✠✖ ✗✘❑▼✙✱ ✇✟ ☞✚✚✛✡✟✒ ✎✏☞✎ ➩❴➫ ✮❳✲ ✒✠✟✚ ✑✠✎ ❝✏☞✑✾✟
✚✍✾✑✍♠❝☞✑✎✔✜ ✇✍✎✏ ❹✠ ✍✑ ✎✏✟ ✌☞✑✾✟ ❝✠✑✚✍✒✟✌✟✒❢ ❲✍✎✏ ↕➂✕ ✇✟
❝☞✑ ❝✠✡☛✛✎✟ ➩❴➫ ✮❳✲ ❜✜ ❝☞✔❝✛✔☞✎✍✑✾ ✎✏✟ ❝✠✡❜✍✑✟✒ ✙✟✜✑✠✔✒✚ ☞✑✒
ãäåäæä çèéêëìíìî êïðñòíèìó
▼☞✓✇✟✔✔ ✚✎✌✟✚✚ ✖✠✌ ☞ ✌✛✑ ✇✍✎✏ ☞✑✒ ☞ ✌✛✑ ✇✍✎✏✠✛✎ ☞✑ ✍✡☛✠✚✟✒ ✡☞✾❞
✑✟✎✍❝ ♠✟✔✒❢ ④✏✍✚ ☞✔✔✠✇✚ ✛✚ ✎✠ ❝✠✡☛✛✎✟ ✻♣ ✮❳✲ ✛✚✍✑✾ ❦q❢ ✮✺✽✲ ✠✖
➯
✻♣ ❂ ❾✷
✢ ✮❻
④✏✟ ✟q✛☞✎✍✠✑✚ ✖✠✌ ✎✏✟ ❚✛❝✎✛☞✎✍✠✑✚ ✠✖ ❧✟✔✠❝✍✎✜ ☞✑✒ ✡☞✾✑✟✎✍❝ ♠✟✔✒✚
☞✌✟ ✾✍❧✟✑ ❜✜
✘✌☞✑✒✟✑❜✛✌✾ ✟✎ ☞✔❢ ✮✷❱✺✷☞✲➭
➺➻
✸
✧
✧
✧
✧
❾ ❻
✲ ✰
➵ ❾ ➸
➳
➳
➁➳
✧
✧
❇ ✭
✮✺✺✲
❂
✣t
✇✏✟✌✟ ✎✏✟ ✚✛❜✚❝✌✍☛✎✚ ❱ ✍✑✒✍❝☞✎✟ ❧☞✔✛✟✚ ✠❜✎☞✍✑✟✒ ✖✌✠✡ ☞ ✌✟✖✟✌✟✑❝✟
✌✛✑ ✇✍✎✏ ❫➁
❂
❱❢ ④✏✍✚ ✟✓☛✌✟✚✚✍✠✑ ✒✠✟✚ ✑✠✎ ✎☞✈✟ ✍✑✎✠ ☞❝❝✠✛✑✎
✺
✣ô✮ â✭ t✲
✣ ➵✮ â✭ t✲
❁
❅
❇ ➲ ✤ ➵ ✰ ➵ ➲ ✤❇ ❾ ✤ õ
ö ø
✰ ✷ô × ✥ ✰ ÷ ✭
✮✺✷✲
✢
ö ù
❂ ❇ ➲ ✤ô ❾ ô ➲ ✤❇ ✰ ÷ ✭
✮✺Ù✲
✣t
úûü➴ ✆✁❣❡ ü ♦❒ ýþ
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
✇✆❡✝❡ ❊q✳ ✞✶✟✮ ✐s ✇✝✐✠✠❡✡ ✐✡ ❛ ✝❡❢❡✝❡✡❝❡ ❢✝❛♠❡ ✝♦✠❛✠✐✡❣ ✇✐✠✆ ❝♦✡✲
s✠❛✡✠ ❛✡❣♥☛❛✝ ✈❡☛♦❝✐✠② ☞✱ ♣ ❂ ♣✌ ✰ ✞❇ ➲ ❜✮ ❛✝❡ ✠✆❡ ß♥❝✠♥❛✠✐♦✡s ♦❢
✠♦✠❛☛ ✍✝❡ss♥✝❡✱ ♣✌ ❛✝❡ ✠✆❡ ß♥❝✠♥❛✠✐♦✡s ♦❢ ß♥✐❞ ✍✝❡ss♥✝❡✱ ❇ ✐s ✠✆❡
♠❡❛✡ ♠❛❣✡❡✠✐❝ Þ❡☛❞✱ ❛✡❞ ✎ ✐s ✠✆❡ ♠❡❛✡ ß♥✐❞ ❞❡✡s✐✠②✳ ❋♦✝ s✐♠✍☛✐❝✲
ö ✉ ❛✡❞ ◆
ö ✒✱
✐✠② ✇❡ ✡❡❣☛❡❝✠ ❡✏❡❝✠s ♦❢ ❝♦♠✍✝❡ss✐✑✐☛✐✠②✳ ❚✆❡ ✠❡✝♠s ◆
✇✆✐❝✆ ✐✡❝☛♥❞❡ ✡♦✡☛✐✡❡❛✝ ❛✡❞ ♠♦☛❡❝♥☛❛✝ ✈✐s❝♦♥s ❛✡❞ ❞✐ss✐✍❛✠✐✈❡
✠❡✝♠s✱ ❛✝❡ ❣✐✈❡✡ ✑②
✖
✶✕
ö ✉ ❂ ✓ ➲ ✔✓ ❾ ✓ ➲ ✔✓ ✰
◆
✞✶✚✮
❥ × ❜ ❾ ❥ × ❜ ✰ ✗✘ ✞✓✮✙
✎
✖
✕
ö ✒ ❂ ✔ × ✓ × ❜ ❾ ✓ × ❜ ❾ ✛✔ × ❜ ✙
◆
✞✶✜✮
✇✆❡✝❡ ✎ ✗✘ ✞✓✮ ✐s ✠✆❡ ♠♦☛❡❝♥☛❛✝ ✈✐s❝♦♥s ❢♦✝❝❡ ❛✡❞ ❥ ❂ ✔ × ❜✴✢✵
✐s ✠✆❡ ß♥❝✠♥❛✠✐✡❣ ❝♥✝✝❡✡✠ ❞❡✡s✐✠②✳ ❚♦ ❡☛✐♠✐✡❛✠❡ ✠✆❡ ✍✝❡ss♥✝❡ ✠❡✝♠
❢✝♦♠ ✠✆❡ ❡q♥❛✠✐♦✡ ♦❢ ♠♦✠✐♦✡ ✞✶✟✮✱ ✇❡ ❝❛☛❝♥☛❛✠❡ ✔×✞✔ × ✓✮✳ ❚✆❡✡
✇❡ ✝❡✇✝✐✠❡ ✠✆❡ ♦✑✠❛✐✡❡❞ ❡q♥❛✠✐♦✡ ❛✡❞ ❊q✳ ✞✶✣✮ ✐✡ ❋♦♥✝✐❡✝ s✍❛❝❡✳
✤✥✦✥✦✥ ✧★✩✪✬✯✹❧✻ ✹✼✼✾✩✹✯❤
❲❡ ❛✍✍☛② ✠✆❡ ✠✇♦✲s❝❛☛❡ ❛✍✍✝♦❛❝✆ ❛✡❞ ❡①✍✝❡ss ✠✇♦✲✍♦✐✡✠ ❝♦✝✝❡☛❛✲
✠✐♦✡ ❢♥✡❝✠✐♦✡s ✐✡ ✠✆❡ ❢♦☛☛♦✇✐✡❣ ❢♦✝♠✿
❈
❀❁ ✞❃✮❀ ❄✞❅✮ ❂
❈
❂
❈
❂
❞❦❉ ❞❦● ❀❁ ✞❦❉ ✮❀ ❄ ✞❦● ✮ ❡①✍④✐✞❦❉ ➲ ❃ ✰ ❦● ➲ ❅✮⑥
✤✥✦✥➤✥ ✧❤✻ ➥✪✹✼✼✾✩✹✯❤
❞❦ ❞❑ ❍❁ ❄ ✞❦✙ ■✮ ❡①✍✞✐❦ ➲ r ✰ ✐❑ ➲ ❘✮
❞❦ ❍❁ ❄ ✞❦✙ ❏✮ ❡①✍✞✐❦ ➲ r✮
✞✶▲✮
✞s❡❡✱ ❡✳❣✳✱ ▼♦✑❡✝✠s ❖ ❙♦✇❛✝❞ ✶P◗✜✮✳ ❯❡✝❡ ❛✡❞ ❡☛s❡✇✆❡✝❡✱ ✇❡ ❞✝♦✍
✠✆❡ ❝♦♠♠♦✡ ❛✝❣♥♠❡✡✠ t ✐✡ ✠✆❡ ❝♦✝✝❡☛❛✠✐♦✡ ❢♥✡❝✠✐♦✡s✱ ❍❁ ❄ ✞❦✙ ❏✮ ❂
ö ❁ ❳ ❀ ❄ ✮✱ ✇✆❡✝❡
❱✞❀
❈
ö
❩✮ ❂
❨✞❦ ✰ ❑✴✟✮❩✞❾❦ ✰ ❑✴✟✮ ❡①✍ ✞✐❑ ➲ ❘✮ ❞❑✙
❱✞❨❳
✇✐✠✆ ✠✆❡ ✡❡✇ ✈❛✝✐❛✑☛❡s ❘ ❂ ✞❃ ✰ ❅✮✴✟✙ r ❂ ❃ ❾ ❅✱ ❑ ❂ ❦❉ ✰ ❦● ✱
❦ ❂ ✞❦❉ ❾ ❦● ✮✴✟✳ ❚✆❡ ✈❛✝✐❛✑☛❡s ❘ ❛✡❞ ❑ ❝♦✝✝❡s✍♦✡❞ ✠♦ ✠✆❡ ☛❛✝❣❡
s❝❛☛❡s✱ ✇✆✐☛❡ r ❛✡❞ ❦ ❝♦✝✝❡s✍♦✡❞ ✠♦ ✠✆❡ s♠❛☛☛ s❝❛☛❡s✳ ❚✆✐s ✐♠✍☛✐❡s
✠✆❛✠ ✇❡ ✆❛✈❡ ❛ss♥♠❡❞ ✠✆❛✠ ✠✆❡✝❡ ❡①✐s✠s ❛ s❡✍❛✝❛✠✐♦✡ ♦❢ s❝❛☛❡s✱
✠✆❛✠ ✐s✱ ✠✆❡ ✠♥✝✑♥☛❡✡✠ ❢♦✝❝✐✡❣ s❝❛☛❡ ❬❭ ✐s ♠♥❝✆ s♠❛☛☛❡✝ ✠✆❛✡ ✠✆❡
❝✆❛✝❛❝✠❡✝✐s✠✐❝ s❝❛☛❡ ❱❪ ♦❢ ✐✡✆♦♠♦❣❡✡❡✐✠② ♦❢ ✠✆❡ ♠❡❛✡ ♠❛❣✡❡✠✐❝
Þ❡☛❞✳
✤✥✦✥✤✥ ❫❴❵✹③⑤✩⑦✬ ⑧✩✾ ③❤✻ ✬✻✯✩⑦⑨ ⑩✩⑩✻⑦③✬
❲❡ ❞❡✝✐✈❡ ❡q♥❛✠✐♦✡s ❢♦✝ ✠✆❡ ❢♦☛☛♦✇✐✡❣ ❝♦✝✝❡☛❛✠✐♦✡ ❢♥✡❝✠✐♦✡s✿
ö ❁ ❳ ❸ ❄ ✮✱ ❛✡❞ ❹❁ ❄ ✞❦✙ ❏✮ ❂
ö ❁ ❳ ❀ ❄ ✮✱ ❶❁ ❄ ✞❦✙ ❏✮ ❂ ✎❷❉ ❱✞❸
❍❁ ❄ ✞❦✙ ❏✮ ❂ ❱✞❀
ö ❁ ❳ ❀ ❄ ✮✳ ❚✆❡ ❡q♥❛✠✐♦✡s ❢♦✝ ✠✆❡s❡ ❝♦✝✝❡☛❛✠✐♦✡ ❢♥✡❝✠✐♦✡s ❛✝❡ ❣✐✈❡✡
❱✞❸
✑②
❺ ❍❁ ❄ ✞❦✮
❺t
❺❶❁ ❄ ✞❦✮
❺t
❺❹❁ ❄ ✞❦✮
❺t
❯❡✝❡❛❢✠❡✝ ✇❡ ✆❛✈❡ ♦♠✐✠✠❡❞ ✠✆❡ ❘✲❛✝❣♥♠❡✡✠ ✐✡ ✠✆❡ ❝♦✝✝❡☛❛✠✐♦✡
❢♥✡❝✠✐♦✡s ❛✡❞ ✡❡❣☛❡❝✠❡❞ ✠❡✝♠s ➒➓✞➔●→ ✮✱ ❛✡❞ ➍❁ ❄➀ ✐s ✠✆❡ ❢♥☛☛② ❛✡✠✐✲
ö ➂✱
s②♠♠❡✠✝✐❝ ➣❡✈✐✲↔✐✈✐✠❛ ✠❡✡s♦✝✳ ↕✡ ❊qs✳ ✞✶◗✮➙✞✶P✮✱ ✠✆❡ ✠❡✝♠s ◆
➄
➌
ö ✱ ❛✡❞ ◆
ö ❛✝❡ ❞❡✠❡✝♠✐✡❡❞ ✑② ✠✆❡ ✠✆✐✝❞ ♠♦♠❡✡✠s ❛✍✍❡❛✝✐✡❣ ❞♥❡
◆
➂
➌
✠♦ ✠✆❡ ✡♦✡☛✐✡❡❛✝ ✠❡✝♠s❳ ✠✆❡ s♦♥✝❝❡ ✠❡✝♠s ➁❁ ❄ ✱ ➁❁➄❄ ✱ ❛✡❞ ➁❁ ❄ ✱ ✇✆✐❝✆
❝♦✡✠❛✐✡ ✠✆❡ ☛❛✝❣❡✲s❝❛☛❡ s✍❛✠✐❛☛ ❞❡✝✐✈❛✠✐✈❡s ♦❢ ✠✆❡ ♠❡❛✡ ♠❛❣✡❡✠✐❝
❛✡❞ ✈❡☛♦❝✐✠② Þ❡☛❞s✱ ❛✝❡ ❣✐✈❡✡ ✑② ❊qs✳ ✞➛✣✮➙✞➛▲✮ ✐✡ ▼♦❣❛❝✆❡✈s➜✐✐
❖ ➝☛❡❡♦✝✐✡ ✞✟➞➞✚✮✳ ❚✆❡s❡ ✠❡✝♠s ❞❡✠❡✝♠✐✡❡ ✠♥✝✑♥☛❡✡✠ ♠❛❣✡❡✠✐❝
❞✐✏♥s✐♦✡ ❛✡❞ ❡✏❡❝✠s ♦❢ ✡♦✡♥✡✐❢♦✝♠ ♠❡❛✡ ✈❡☛♦❝✐✠② ♦✡ ✠✆❡ ♠❡❛✡
❡☛❡❝✠✝♦♠♦✠✐✈❡ ❢♦✝❝❡✳
❋♦✝ ✠✆❡ ❞❡✝✐✈❛✠✐♦✡ ♦❢ ❊qs✳ ✞✶◗✮➙✞✶P✮ ✇❡ ♥s❡ ❛✡ ❛✍✍✝♦❛❝✆ ✠✆❛✠
✐s s✐♠✐☛❛✝ ✠♦ ✠✆❛✠ ❛✍✍☛✐❡❞ ✐✡ ▼♦❣❛❝✆❡✈s➜✐✐ ❖ ➝☛❡❡♦✝✐✡ ✞✟➞➞✚✮✳ ❲❡
✠❛➜❡ ✐✡✠♦ ❛❝❝♦♥✡✠ ✠✆❛✠ ✐✡ ❊q✳ ✞✶P✮ ✠✆❡ ✠❡✝♠s ✇✐✠✆ ✠❡✡s♦✝s ✠✆❛✠ ❛✝❡
s②♠♠❡✠✝✐❝ ✐✡ ❻ ❛✡❞ ➟ ❞♦ ✡♦✠ ❝♦✡✠✝✐✑♥✠❡ ✠♦ ✠✆❡ ♠❡❛✡ ❡☛❡❝✠✝♦♠♦✠✐✈❡
❢♦✝❝❡ ✑❡❝❛♥s❡ ➠❿ ❂ ➍❿ ❄❁ ❹❁ ❄ ✳ ❲❡ s✍☛✐✠ ❛☛☛ ✠❡✡s♦✝s ✐✡✠♦ ✡♦✡✆❡☛✐❝❛☛✱
➇➡➉
❶❁ ❄ ✙ ❛✡❞ ✆❡☛✐❝❛☛✱ ❶❁ ❄ ✙ ✍❛✝✠s✳ ❚✆❡ ✆❡☛✐❝❛☛ ✍❛✝✠ ♦❢ ✠✆❡ ✠❡✡s♦✝ ♦❢ ♠❛❣✲
➇➡➉
✡❡✠✐❝ ß♥❝✠♥❛✠✐♦✡s ❶❁ ❄ ❞❡✍❡✡❞s ♦✡ ✠✆❡ ♠❛❣✡❡✠✐❝ ✆❡☛✐❝✐✠②✱ ❛✡❞ ✠✆❡
➇➡➉
❡q♥❛✠✐♦✡ ❢♦✝ ❶❁ ❄ ❢♦☛☛♦✇s ❢✝♦♠ ♠❛❣✡❡✠✐❝ ✆❡☛✐❝✐✠② ❝♦✡s❡✝✈❛✠✐♦✡ ❛✝✲
❣♥♠❡✡✠s ✞s❡❡✱ ❡✳❣✳✱ ➝☛❡❡♦✝✐✡ ❖ ▼♦❣❛❝✆❡✈s➜✐✐ ✶PPP❳ ➢✝❛✡❞❡✡✑♥✝❣
❖ ❙♥✑✝❛♠❛✡✐❛✡ ✟➞➞✜❛✱ ❛✡❞ ✝❡❢❡✝❡✡❝❡s ✠✆❡✝❡✐✡✮✳
➂
ö ➂
❂ ❻✞❦ ➲ ❇✮❼❁ ❄ ✰ ❱❽
❁ ❄❿➀ ❍❿➀ ✰ ➁❁ ❄ ✰ ➃❁ ❄ ✙
✞✶◗✮
ö ➄✙
❂ ❾❻✞❦ ➲ ❇✮❼❁ ❄ ✰ ➁❁➄❄ ✰ ➃
❁❄
✞✶➅✮
➇➈➉
❂ ❻✞❦ ➲ ❇✮➆ ❍❁ ❄ ✞❦✮ ❾ ❶❁ ❄ ✞❦✮ ❾ ❶❁ ❄ ➊
➌
ö ➌✙
✰ ➋❽❄❿ ✞❦● ✮❹❁❿ ✞❦✮ ✰ ➁❁ ❄ ✰ ➃
❁❄
✞✶P✮
✇✆❡✝❡
❼❁ ❄ ✞❦✮ ❂ ✎❷❉ ➆❹❁ ❄✞❦✮ ❾ ❹ ❄❁ ✞❾❦✮➊✙
➋❽
❁ ❄ ✞❦✮ ❂ ✟➍❁ ❄❿ ➎➀ ➏❿➀ ✙
❽
❽
❱❽
❁ ❄❿➀ ❂ ➋❁❿ ✞❦❉ ✮ ➐ ❄➀ ✰ ➋ ❄➀ ✞❦● ✮ ➐❁❿ ➑
❆✽✸✁ ➻➼➽➾ ➚ ➪➶ ✄✷
❚✆❡ s❡❝♦✡❞✲♠♦♠❡✡✠ ❊qs✳ ✞✶◗✮➙✞✶P✮ ✐✡❝☛♥❞❡ ✠✆❡ Þ✝s✠✲♦✝❞❡✝
s✍❛✠✐❛☛ ❞✐✏❡✝❡✡✠✐❛☛ ♦✍❡✝❛✠♦✝s ❛✍✍☛✐❡❞ ✠♦ ✠✆❡ ✠✆✐✝❞✲♦✝❞❡✝ ♠♦✲
♠❡✡✠s ➦ ➇➧➧➧➉ ✳ ❚♦ ❝☛♦s❡ ✠✆❡ s②s✠❡♠✱ ✇❡ ❡①✍✝❡ss ✠✆❡ s❡✠ ♦❢ ✠✆❡ ✠✆✐✝❞✲
ö➨ ➩ ◆
ö ➦ ➇➧➧➧➉ ✠✆✝♦♥❣✆ ✠✆❡ ☛♦✇❡✝ ♠♦♠❡✡✠s ➦ ➇➧➧➉ ✳
♦✝❞❡✝ ✠❡✝♠s ◆
❲❡ ♥s❡ ✠✆❡ s✍❡❝✠✝❛☛ ➥ ❛✍✍✝♦①✐♠❛✠✐♦✡✱ ✇✆✐❝✆ ✍♦s✠♥☛❛✠❡s ✠✆❛✠ ✠✆❡
ö ➦ ➇➧➧➧➉ ✞❦✮✱ ❢✝♦♠ ✠✆❡ ❝♦✡✲
❞❡✈✐❛✠✐♦✡s ♦❢ ✠✆❡ ✠✆✐✝❞✲♠♦♠❡✡✠ ✠❡✝♠s✱ ◆
✠✝✐✑♥✠✐♦✡s ✠♦ ✠✆❡s❡ ✠❡✝♠s ❛✏♦✝❞❡❞ ✑② ✠✆❡ ✑❛❝➜❣✝♦♥✡❞ ✠♥✝✑♥✲
ö ➦ ➇➧➧➧➫✵➉ ✞❦✮✱ ❛✝❡ ❡①✍✝❡ss❡❞ ✠✆✝♦♥❣✆ s✐♠✐☛❛✝ ❞❡✈✐❛✠✐♦✡s ♦❢
☛❡✡❝❡✱ ◆
✠✆❡ s❡❝♦✡❞ ♠♦♠❡✡✠s✿
ö ➦ ➇➧➧➧➉ ✞❦✮ ❾ ◆
ö ➦ ➇➧➧➧➫✵➉ ✞❦✮ ❂ ❾ ➦
◆
➇➧➧➉ ✞❦✮ ❾ ➦ ➇➧➧➫✵➉ ✞❦✮
➥✞➏✮
✞✟➞✮
✞➭✝s➯❛❣ ✶P◗➞❳ ➳♦♥q♥❡✠ ❡✠ ❛☛✳ ✶P◗▲❳ ➝☛❡❡♦✝✐✡ ❡✠ ❛☛✳ ✶PP➞❳
▼♦❣❛❝✆❡✈s➜✐✐ ❖ ➝☛❡❡♦✝✐✡ ✟➞➞✚✮✱ ✇✆❡✝❡ ➥✞➏✮ ✐s ✠✆❡ s❝❛☛❡✲
❞❡✍❡✡❞❡✡✠ ✝❡☛❛①❛✠✐♦✡ ✠✐♠❡✱ ✇✆✐❝✆ ❝❛✡ ✑❡ ✐❞❡✡✠✐Þ❡❞ ✇✐✠✆ ✠✆❡ ❝♦✝✲
✝❡☛❛✠✐♦✡ ✠✐♠❡ ♦❢ ✠✆❡ ✠♥✝✑♥☛❡✡✠ ✈❡☛♦❝✐✠② Þ❡☛❞ ❢♦✝ ☛❛✝❣❡ ▼❡②✡♦☛❞s
✡♥♠✑❡✝s✳ ❚✆❡ q♥❛✡✠✐✠✐❡s ✇✐✠✆ ✠✆❡ s♥✍❡✝s❝✝✐✍✠ ✞➞✮ ❝♦✝✝❡s✍♦✡❞ ✠♦
✠✆❡ ✑❛❝➜❣✝♦♥✡❞ ✠♥✝✑♥☛❡✡❝❡ ✞s❡❡ ✑❡☛♦✇✮✳ ❲❡ ❛✍✍☛② ✠✆❡ s✍❡❝✠✝❛☛ ➥
❛✍✍✝♦①✐♠❛✠✐♦✡ ♦✡☛② ❢♦✝ ✠✆❡ ✡♦✡✆❡☛✐❝❛☛ ✍❛✝✠ ❶❁ ❄ ♦❢ ✠✆❡ ✠❡✡s♦✝ ♦❢
♠❛❣✡❡✠✐❝ ß♥❝✠♥❛✠✐♦✡s✳ ➛ ➵♥s✠✐Þ❝❛✠✐♦✡ ❢♦✝ ✠✆❡ ➥ ❛✍✍✝♦①✐♠❛✠✐♦✡ ✐✡
❞✐✏❡✝❡✡✠ s✐✠♥❛✠✐♦✡s ✆❛s ✑❡❡✡ ♦✏❡✝❡❞ ✠✆✝♦♥❣✆ ✡♥♠❡✝✐❝❛☛ s✐♠♥☛❛✲
✠✐♦✡s ❛✡❞ ❛✡❛☛②✠✐❝❛☛ s✠♥❞✐❡s ✞s❡❡✱ ❡✳❣✳✱ ➢✝❛✡❞❡✡✑♥✝❣ ❡✠ ❛☛✳ ✟➞➞✚❳
➢✝❛✡❞❡✡✑♥✝❣ ❖ ❙♥✑✝❛♠❛✡✐❛✡ ✟➞➞✜✑✱ ✟➞➞◗❳ ▼♦❣❛❝✆❡✈s➜✐✐ ❡✠ ❛☛✳
✟➞✶✶✮✳
✤✥✦✥➸✥ ➺✩❧❵③⑤✩⑦ ✩⑧ ✻❴❵✹③⑤✩⑦✬ ⑧✩✾ ③❤✻ ✬✻✯✩⑦⑨ ⑩✩⑩✻⑦③✬
➂
➌
❲❡ s♦☛✈❡ ❊qs✳ ✞✶◗✮➙✞✶P✮ ✡❡❣☛❡❝✠✐✡❣ ✠✆❡ s♦♥✝❝❡s ➁❁ ❄ ✙ ➁❁➄❄ ✙ ➁❁ ❄ ✇✐✠✆
✠✆❡ ☛❛✝❣❡✲s❝❛☛❡ s✍❛✠✐❛☛ ❞❡✝✐✈❛✠✐✈❡s✳ ❚✆❡ ✠❡✝♠s ✇✐✠✆ ✠✆❡ ☛❛✝❣❡✲s❝❛☛❡
s✍❛✠✐❛☛ ❞❡✝✐✈❛✠✐✈❡s✱ ✇✆✐❝✆ ❞❡✠❡✝♠✐✡❡ ✠✆❡ ✠♥✝✑♥☛❡✡✠ ♠❛❣✡❡✠✐❝ ❞✐❢✲
❢♥s✐♦✡✱ ❝❛✡ ✑❡ ✠❛➜❡✡ ✐✡✠♦ ❛❝❝♦♥✡✠ ✑② ✍❡✝✠♥✝✑❛✠✐♦✡s✳ ❲❡ s♥✑✠✝❛❝✠
❢✝♦♠ ❊qs✳ ✞✶◗✮➙✞✶P✮ ✠✆❡ ❝♦✝✝❡s✍♦✡❞✐✡❣ ❡q♥❛✠✐♦✡s ✇✝✐✠✠❡✡ ❢♦✝ ✠✆❡
✑❛❝➜❣✝♦♥✡❞ ✠♥✝✑♥☛❡✡❝❡ ♥s✐✡❣ ✠✆❡ s✍❡❝✠✝❛☛ ➥ ❛✍✍✝♦①✐♠❛✠✐♦✡✳ ❲❡
❛ss♥♠❡ ✠✆❛✠ ✠✆❡ ❝✆❛✝❛❝✠❡✝✐s✠✐❝ ✠✐♠❡ ♦❢ ✈❛✝✐❛✠✐♦✡ ♦❢ ✠✆❡ s❡❝♦✡❞
♠♦♠❡✡✠s ✐s s♥✑s✠❛✡✠✐❛☛☛② ☛❛✝❣❡✝ ✠✆❛✡ ✠✆❡ ❝♦✝✝❡☛❛✠✐♦✡ ✠✐♠❡ ➥✞➏✮
❢♦✝ ❛☛☛ ✠♥✝✑♥☛❡✡❝❡ s❝❛☛❡s✳ ❚✆✐s ❛☛☛♦✇s ♥s ✠♦ ❣❡✠ ❛ s✠❛✠✐♦✡❛✝② s♦✲
☛♥✠✐♦✡ ❢♦✝ ✠✆❡ ❡q♥❛✠✐♦✡s ❢♦✝ ✠✆❡ s❡❝♦✡❞✲♦✝❞❡✝ ♠♦♠❡✡✠s✱ ➦ ➇➧➧➉ ✳
■
❚✟✠✡✱
✇☛
☞✌✌✍✈☛
☞✎
✎✟☛
❘ ▲♦s✁✂✁ ❡✄ ✁❛ ✿ ❈♦☎✆❡✄✐♥❣ ❡✝❡✞✄s ✐♥ ✞♦♥✞❡♥✄r✁✄✐♥❣ ☎✁❣♥❡✄✐✞ ß✉①
❢✏✑✑✏✇✍✒✓
✡✎☛☞✔✕✖✡✎☞✎☛
✡✏✑✠✎✍✏✒
✏❢
❊✗✡✳ ✭✶✘✮✙✭✶✚✮✛
❾✥
✜✢ ✣ ✭ ❦✮ ❂ ✤
✢ ✣♠✦
✧
✜
✲
★✩✪
✭ ❦✮ ✰ ✫✬✭ ❦ ➲ ❇✮✯♠✦ ✭ ❦✮ ✴
♠✦
✭✵✶✮
❤✢ ✣ ✭ ❦✮ ❂ ✷✫✬✭ ❦ ➲ ❇✮✯✢ ✣ ✭ ❦✮✴
✸✢ ✣ ✭ ❦✮ ❂ ✫✬✭ ❦ ➲ ❇✮❉
❾✥
✢♠
✭✵✵✮
✧
✲
✜♠ ✣ ✭ ❦✮ ✷ ❤♠ ✣ ✭ ❦✮
✹
✭✵✺✮
❲☛ ✟☞✈☛ ☞✡✡✠✻☛✔ ✎✟☞✎ ✎✟☛✌☛ ✍✡ ✒✏ ✡✻☞✑✑✖✡❝☞✑☛ ✔✕✒☞✻✏ ✍✒ ✎✟☛
❜☞❝✼✓✌✏✠✒✔ ✎✠✌❜✠✑☛✒❝☛✳ ❍☛✌☛✱ ✎✟☛ ✏✽☛✌☞✎✏✌ ❉
❾✥
✢✣
✍✡ ✎✟☛ ✍✒✈☛✌✡☛ ✏❢
❀
❾✥
✎✟☛ ✏✽☛✌☞✎✏✌ ✾✢ ✣ ✷ ✬❉
✭❁❃✔✑☛✌ ☛✎ ☞✑✳ ✵❄❄✺✮ ☞✒✔ ✎✟☛ ✏✽☛✌☞✎✏✌ ✤
✢✣
✢ ✣♠✦
❀
✍✡ ✎✟☛ ✍✒✈☛✌✡☛ ✏❢ ✎✟☛ ✏✽☛✌☞✎✏✌ ✾✢♠ ✾ ✣✦ ✷ ✬ ✤
✭❊✑✽☛✌✍✒ ☛✎ ☞✑✳ ✵❄❄❅✮✳
✢ ✣♠✦
❚✟☛✡☛ ✏✽☛✌☞✎✏✌✡ ☞✌☛ ✓✍✈☛✒ ❜✕
❉
❾✥
❑
ö
❂ ❆✭❋✮ ✭✾✢ ✣ ✰ ❋ ●✢ ✣♠ ❏♠ ✰ ❋ ❏✢ ✣ ✮
✢✣
➊➋➌➍ ➎➍ ➏❡✆❡♥✂❡♥✞❡ ♦➐ ➑➒➑➓➔ ♦♥ →➣➒➑➓➔ ➐♦r ➏↔↕ ➙r❡✂ ✂✁s➛❡✂ ❛✐♥❡➜➝ ✞♦☎➞
▼
❑
ö
❂ ✾✢ ✣ ✰ ❋ ●✢ ✣♠ ❏
♠ ✷ ❋ P✢ ✣ ✰ ❖✭❋ ✮✴
✭✵◆✮
✆✁r❡✂ ➟✐✄➛ ➠➡↕ ➙✐➜ ➟➛❡r❡ ➢➤➔ ➥ →➦ ✁♥✂ ➧➤ ➥ ➦➨➩➫➯ ➙➳❛✁✞➵ s♦❛✐✂ ❛✐♥❡➜➝
✁♥✂ ➠➡↕ ➙✐✐➜ ➟➛❡r❡ ➢➤➔ ➥ ➸→ ✁♥✂ ➧ ➤ ➥ ➦➨➦➺➻ ➙➳❛✉❡ ✂✁s➛➞✂♦✄✄❡✂ ❛✐♥❡➜
❾✥
✥
❬❙✥ ✾✢♠ ✾ ✣✦ ✰ ❙❑ ❏✢ ✣♠✦ ✰ ❙▼ ✭●✢♠ ♣ ✾ ✣✦
✤
✭◗✮ ❂
✢ ✣♠✦
❑
■♥ ✄➛✐s ✞✁s❡ ♥♦ ❣r♦➟✄➛ ➟✁s ➐♦✉♥✂ ➐♦r ❈♦ ➼ ➦➨➦➸
✰ ❙❱ ●✢ ♣♠ ● ✣❥✦ ❏ ♣❥ ✰ ❙❳ ✭●✢♠ ♣ ❏ ✣ ♣✦ ✰ ● ✣✦ ♣ ❏✢ ♣♠ ✮❨
❚✟☛ ❝✏✒✎✌✍❜✠✎✍✏✒ ✏❢ ✎✠✌❜✠✑☛✒❝☛ ✎✏ ✎✟☛ ✻☛☞✒✖Þ☛✑✔ ✻☞✓✒☛✎✍❝
➹
➘
❑
t✥ ✭➆✮ ✷ t❑ ✭➆✮ ❩➆ ✛
✽✌☛✡✡✠✌☛ ✍✡ ✓✍✈☛✒ ❜✕ ✎✟☛ ❢✠✒❝✎✍✏✒ t➶ ✭➆✮ ❂
❑
ö
❂ ✾✢♠ ✾ ✣✦ ✰ ❋ ✭●✢♠ ♣ ✾ ✣✦ ✰ ● ✣✦ ♣ ✾✢♠ ✮❏
♣ ✷ ❋ ✭✾✢♠ P ✣✦
▼
✰ ✾ ✣✦ P✢♠ ✷ ✵●✢♠ ♣ ● ✣❥✦ ❏ ♣❥ ✮ ✰ ❖✭❋ ✮✴
✭✵❅✮
ö ❂ ❏ ❩❏✱ ❆✭❋✮ ❂ ✶❩✭✶ ✰ ❋❑ ✮✱ ❋ ❂ ✵✬✭❏✮ ✭ ❦ ➲ ◗✮❩❏✱
✇✟☛✌☛ ❏
✢
✢
✧
✶
t➶ ✭➆✮ ❂
❙✥ ❂
✶✵➆
❑
➴
✰ ◆❄⑤
✾✢ ✣ ✍✡ ✎✟☛ ❭✌✏✒☛❝✼☛✌ ✎☛✒✡✏✌✳
✠✡☛
✍✡✏✎✌✏✽✍❝
✎✟☛
❢✏✑✑✏✇✍✒✓
❢✏✌
✻✏✔☛✑
★✩✪
❜☞❝✼✓✌✏✠✒✔ ✎✠✌❜✠✑☛✒❝☛✛
✎✟☛
✟✏✻✏✓☛✒☛✏✠✡
☞✒✔
❑
★✩✪
✥
✷ ✵✭➷✬✩ ✮
✶ ✰ ❆✭✵❋✮✴ ❙❑ ❂ ❙✥ ✰ ✵ ✷ ◆❆✭❋✮✴ ❙▼ ❂ ✵❋ ❆✭✵❋✮✴ ❙❯ ❂ ✵❆✭❋✮ ✷ ❙✥ ✴
❑
❙ ❱ ❂ ✵ ✷ ❙✥ ☞✒✔ ❙❳ ❂ ✵❋ ❬❆✭❋✮ ✷ ❆✭✵❋✮❨✱ P✢ ✣ ✭❏✮ ❂ ✾✢ ✣ ✷ ❏✢ ❏ ✣ ❩❏ ✱
❲☛
■♥ ✁❛❛ ✞✁s❡s ➟❡ ➛✁➽❡
➾➔ ➒➾➚➪➔ ➥ ➦➨➦➺
ö
✰ ● ✣✦ ♣ ✾✢♠ ✮❏ ♣ ✰ ❙❯ ✭✾✢♠ ❏ ✣✦ ✰ ✾ ✣✦ ❏✢♠ ✮
✇✟☛✌☛
✎✟☛
★❑✪
✥
✭❄✮ ✷ ➴
❑
➬
➴
★❑✪
✥
★✩✪
✥
✭❄✮ ✷ ◆⑤
✧
✚
✭◆➆✮ ✰
✵q
❢✠✒❝✎✍✏✒✡
✭◆➆✮ ✷ ➴
➴
★ ✣✪
✢
★❑✪
✥
★✩✪
❑
✭◆➆✮
✭❄✮ ✷ ✶❄➴
★❑✪
✥
✭◆➆✮
✲ ➮✲
ø ✭✶❼➆❑ ✮ ✷ ◆⑤
ø ✭✶❼➆❑ ✮
➴
✥
✥
✭ ➱✮✱
⑤
★ ✣✪
✢
ø ✭✃✮✱
➴
✢
✭ ➱✮✱
✴
ø ✭✃✮✱
⑤
✢
✭✵✚✮
☞✒✔
✎✟☛✍✌
❪❫ ❴ P✢ ✣ ✭❏✮ ❵ ✭❏✮✱
☞✡✕✻✽✎✏✎✍❝✡ ☞✌☛ ✓✍✈☛✒ ✍✒ ➅✽✽☛✒✔✍④ ➅✳ ❸✏✑✑✏✇✍✒✓ ☛☞✌✑✍☛✌ ✇✏✌✼
❑
✇✟☛✌☛ ❵ ✭❏✮ ❂ ❞✭❏✮❩❧q❏ ✱ ✎✟☛ ☛✒☛✌✓✕ ✡✽☛❝✎✌✠✻ ✍✡ ❞✭❏✮ ❂ ✭t ✷
✭❐✌☞✒✔☛✒❜✠✌✓ ☛✎ ☞✑✳ ✵❄✶✵☞✮✱ ✇☛ ✒✏✇ ✔☛Þ✒☛ ☞ ✻☞✓✒☛✎✍❝ ❁☛✕✒✏✑✔✡
❾✥
❾❥
✱ ❏✩ ❂ ✶❩②③ ✱ ☞✒✔ ✎✟☛ ✑☛✒✓✎✟ ②③ ✍✡ ✎✟☛ ✻☞④✍✻✠✻ ✡❝☞✑☛
✶✮❏
✭❏❩❏✩ ✮
✩
✒✠✻❜☛✌ ❜☞✡☛✔ ✏✒ ✎✟☛ ✡❝☞✑☛ ②③
✜
✢✣
✭ ❦✮
❂
✏❢ ✎✠✌❜✠✑☛✒✎ ✻✏✎✍✏✒✡✳ ❚✟☛ ✎✠✌❜✠✑☛✒✎ ❝✏✌✌☛✑☞✎✍✏✒ ✎✍✻☛ ✍✡ ✬✭❏✮
❂
❾➭
✱ ✇✟☛✌☛ ✎✟☛ ❝✏☛⑥❝✍☛✒✎ ⑤ ❂ ✭t ✷ ✶ ✰ ⑦✮❩✭t ✷ ✶✮✳ ❚✟✍✡
⑤ ✬✩ ✭❏❩❏✩ ✮
❂ ✵q❩❏③ ✱ ✇✟✍❝✟ ✍✡ ✌☛✑☞✎☛✔ ✎✏ ✎✟☛
✥❰❯
❁☛ ❒ ✔☛Þ✒☛✔ ☛☞✌✑✍☛✌ ✈✍☞ ❁✻ ❂ ✵q❁☛ ❒ ✳ ❸✏✌ ❙ ❮ ❙➇➈ ❩◆❁✻
✱ ✎✟☛
❢✠✒❝✎✍✏✒ t➶ ✭➆✮ ✍✡ ✓✍✈☛✒ ❜✕
✈☞✑✠☛ ✏❢ ✎✟☛ ❝✏☛⑥❝✍☛✒✎ ⑤ ❝✏✌✌☛✡✽✏✒✔✡ ✎✏ ✎✟☛ ✡✎☞✒✔☞✌✔ ❢✏✌✻ ✏❢
✎✟☛ ✎✠✌❜✠✑☛✒✎ ✔✍⑧✠✡✍✏✒ ❝✏☛⑥❝✍☛✒✎ ✍✒ ✎✟☛ ✍✡✏✎✌✏✽✍❝ ❝☞✡☛✱ ✍✳☛✳✱ ⑨
❂
❷ ⑩
❶
❑
❑
❑
❪❫ ❴
❪❫ ❴
✬✭❏✮ ❞✭❏✮ ✔❏ ❂ ✬✩ ❪❫ ❴❩✺✳ ❍☛✌☛ ✎✟☛ ✎✍✻☛ ✬✩ ❂ ②③ ❩
❷
❑
☞✒✔
❪❫ ❴ ✍✡ ✎✟☛ ❝✟☞✌☞❝✎☛✌✍✡✎✍❝ ✎✠✌❜✠✑☛✒✎ ✈☛✑✏❝✍✎✕ ✍✒ ✎✟☛ ✡❝☞✑☛ ②③ ✳
✒☛✒✎ ⑦ ❂ ❄ ☞✒✔ ✎✟☛ ❝✏☛⑥❝✍☛✒✎ ⑤ ❂ ✶✳ ❻✏✎✍✏✒✡ ✍✒ ✎✟☛ ❜☞❝✼✓✌✏✠✒✔
✭✺❄✮
✺❅
➬
✶❼
t ♣ ✭➆✮ ❂
☛④✽✏✒☛✒✎ ⑦ ❂ t ✷ ✶ ☞✒✔ ✎✟☛ ❝✏☛⑥❝✍☛✒✎ ⑤ ❂ ✵✳ ❺✒ ✎✟☛ ❝☞✡☛ ✏❢ ☞
✎✠✌❜✠✑☛✒❝☛ ✇✍✎✟ ☞ ✡❝☞✑☛✖✍✒✔☛✽☛✒✔☛✒✎ ❝✏✌✌☛✑☞✎✍✏✒ ✎✍✻☛✱ ✎✟☛ ☛④✽✏✖
❑
Ï✏ ✴
✑✒ ❁✻ ✷
❅
✥❰❯
☞✒✔ ❢✏✌ ❙➇➈ ❩◆❁✻
❮ ❙ ❮ ❙➇➈ ❩◆ ✎✟☛ ❢✠✒❝✎✍✏✒ t➶ ✭➆✮ ✍✡ ✓✍✈☛✒ ❜✕
❸✏✌ ✎✟☛ ❭✏✑✻✏✓✏✌✏✈Õ✡ ✎✕✽☛ ❜☞❝✼✓✌✏✠✒✔ ✎✠✌❜✠✑☛✒❝☛ ✭✍✳☛✳✱ ❢✏✌ ☞
✎✠✌❜✠✑☛✒❝☛ ✇✍✎✟ ☞ ❝✏✒✡✎☞✒✎ ☛✒☛✌✓✕ ❹✠④ ✏✈☛✌ ✎✟☛ ✡✽☛❝✎✌✠✻✮✱ ✎✟☛
❧
◆
t➶ ✭➆✮ ❂
✶ ✰ ❅Ð ✑✒✭◆➆✮Ð ✰ ✺✵ ➆
❑
➮
❧
✷
✵❅
❑
Ï✏ ✴
✭✺✶✮
✺❅
✇✟☛✌☛ Ï✏ ❂ ✵➷✬✩ ✳ ❚✟✍✡ ✡✟✏✇✡ ✎✟☞✎ ❢✏✌ ✎✟☛ ✈☞✑✠☛✡ ✏❢ Ï✏ ✏❢ ✍✒✎☛✌✖
❾▼
☛✡✎ ✭Ï✏ Ñ ❄✹❄❼✮✱ ✎✟☛ ❝✏✌✌☛❝✎✍✏✒ ✎✏ t➶ ✍✡ ✒☛✓✑✍✓✍❜✑☛ ✭❜☛✑✏✇ ✶❄
✮✱
✇✟✍❝✟ ✍✡ ✍✒ ☞✓✌☛☛✻☛✒✎ ✇✍✎✟ ✎✟☛ ✒✠✻☛✌✍❝☞✑ Þ✒✔✍✒✓✡ ✍✒ ❸✍✓✳ ✶✳
✎✠✌❜✠✑☛✒❝☛ ☞✌☛ ☞✡✡✠✻☛✔ ✎✏ ❜☛ ✒✏✒✟☛✑✍❝☞✑✳
❊✗✠☞✎✍✏✒✡ ✭✵✶✮✙✭✵❅✮ ✕✍☛✑✔
ÒÓ ÔÖ×ØÖÙØÚ ÛÜÜÛÝàÚ ÖÜ áâãäå Øæ çáè éæê ãëè
★✩✪
✜✢ ✣ ✭ ❦✮ ❂ ✜
✭ ❦✮ ✷ ❤✢ ✣ ✭ ❦✮✴
✢✣
❿
❽
❤✢ ✣ ✭ ❦✮ ❂
✇✟☛✌☛ ❽
✶ ✷ ❋
✶ ✰ ✵❽
✭✵❼✮
➀
✵ ✰ ❽
❑
✵✭✶ ✰ ✵❽✮
❑
❑
❂ ✵✬ ✭ ❦ ➲ ➁➂ ✮ ✱ ➁ ➂
❾✥
☞❝❝✏✠✒✎ ✎✟☞✎ ✤
P♠✦ ✭ ❦✮
✢ ✣♠✦
❂
✭✵✘✮
❇➃
➄✱ ☞✒✔ ✇☛ ✟☞✈☛ ✎☞✼☛✒ ✍✒✎✏
P✢ ✣ ✭ ❦✮✳ ➅❢✎☛✌ ✎✟☛ ✍✒✎☛✓✌☞✎✍✏✒ ✍✒
❦
❉✁✂
✌❀
ñ
❢✏✌ ✔✍⑧☛✌☛✒✎ ✈☞✑✠☛✡ ✏❢ Ï✏ ☞✒✔ ❝☞✑❝✠✖
✡☛☛ ❸✍✓✳ ✵✳ ❺✎ ✎✠✌✒✡ ✏✠✎ ✎✟☞✎
✌
✡✟✏✇✡ ☞
✔☛❝✑✍✒☛ ✇✍✎✟ ✍✒❝✌☛☞✡✍✒✓ ✈☞✑✠☛✡ ✏❢ Ï✏ ✎✟☞✎ ✍✡ ✡✍✻✍✑☞✌ ✎✏ ✎✟☛ ✏✒☛
✡☛☛✒ ✍✒ ✎✟☛ ❻❸
✂
✏❢
▲
☞
✭❝✏✌✌☛✡✽✏✒✔✍✒✓ ✎✏ ➆
✡✽☞❝☛✱ ✇☛ ✏❜✎☞✍✒ ✎✟☛ ✻☞✓✒☛✎✍❝ ✎☛✒✡✏✌ ❤✢ ✣ ✍✒ ✽✟✕✡✍❝☞✑ ✡✽☞❝☛✛
❤✢ ✣ ✭➆✮ ❂ t✥ ✭➆✮✾✢ ✣ ✰ t❑ ✭➆✮➆✢ ✣ ✴
❲☛ ✟☞✈☛ ✽☛✌❢✏✌✻☛✔
✑☞✎☛✔ ✎✟☛ ✓✌✏✇✎✟ ✌☞✎☛
❷
❂
✇▼
ìíîí ïðñ òóô õ÷ùúòûüý÷ó þüÿ
★✩✪
✜
✭ ❦✮✴
✢✣
❐❭❻❁✱ ✇✟✏ ✠✡☛✔ t➶✩ ❂ ✵❄ ☞✒✔ ➆➶ ❂ ❄✹✶❼✘
❂ ❄✹✘❅✮✳ ❲✟✍✑☛ ✡✏✻☛ ✓✌✏✇✎✟ ✍✡ ✡✎✍✑✑ ✽✏✡✡✍✖
❜✑☛ ❢✏✌ Ï✏ ❂ ❄✹✶✺ ☞✒✔ ❄✳❼❼✱ ✎✟☛ Þ☛✑✔ ❜☛✓✍✒✡ ✎✏ ☞✎✎☞✍✒ ✡✕✡✎☛✻☞✎✍❝
✭✵❧✮
✈☞✌✍☞✎✍✏✒✡ ✍✒ ✎✟☛
③
✔✍✌☛❝✎✍✏✒ ✎✟☞✎ ☞✌☛ ✻✏✌☛ ✡✍✻✍✑☞✌ ✎✏ ✎✟✏✡☛ ✍✒ ☞
✔✕✒☞✻✏✳ ❺✒ ✎✟☞✎ ❝☞✡☛✱ ✇☛ ✇✏✠✑✔ ✟☞✈☛ ✎✏ ✔☛☞✑ ✇✍✎✟ ☞ ❝✏✠✽✑☛✔ ✡✕✡✖
✇✟☛✌☛ ➆
❂
❙❩❙➇➈ ✱ ☞✒✔ ✎✟☛ ❢✠✒❝✎✍✏✒✡ t✥ ✭➆✮ ☞✒✔ t❑ ✭➆✮ ☞✌☛ ✓✍✈☛✒
✍✒ ➅✽✽☛✒✔✍④ ➅✳ ❲☛ ❝✏✒✡✍✔☛✌ ✎✟☛ ❝☞✡☛ ✍✒ ✇✟✍❝✟ ☞✒✓✠✑☞✌ ✈☛✑✏❝✍✎✕
✍✡ ✽☛✌✽☛✒✔✍❝✠✑☞✌ ✎✏ ✎✟☛ ✻☛☞✒ ✻☞✓✒☛✎✍❝ Þ☛✑✔✳ ❚✟☛ ✌☛✡✠✑✎✡ ❝☞✒ ☛☞✡✖
✎☛✻✱ ☞✒✔ ☞ ✔✍✌☛❝✎ ❝✏✻✽☞✌✍✡✏✒ ✇✍✎✟ ✎✟☛
✁
❊❻
❊
❺ ✓✌✏✇✎✟ ✌☞✎☛ ✇✏✠✑✔
✒✏✎ ❜☛ ✽✏✡✡✍❜✑☛✳ ❲☛ ✌☛✎✠✌✒ ✎✏ ✎✟✍✡ ✍✡✡✠☛ ✑☞✎☛✌ ✍✒
❺✒
❸✍✓✳
✍✑✕ ❜☛ ✓☛✒☛✌☞✑✍➉☛✔ ✎✏ ✎✟☛ ❝☞✡☛ ✏❢ ✎✟☛ ☞✌❜✍✎✌☞✌✕ ☞✒✓✑☛ ❜☛✎✇☛☛✒ ✎✟☛
▲
☞✒✓✠✑☞✌ ✈☛✑✏❝✍✎✕ ☞✒✔ ✎✟☛ ✻☛☞✒ ✻☞✓✒☛✎✍❝ Þ☛✑✔✳
✍✒✓ ✎✏ ➆
✵
✇☛
❝✏✻✽☞✌☛ ✎✟☛
❐❭❻❁✱ ✇✟✏ ✠✡☛✔ t➶✩
☞
❂
❂
✓✌✏✇✎✟ ✌☞✎☛
✵❄ ☞✒✔ ➆➶
❂
✂
☛❝✎✳ ❅✳✶✳
✇✍✎✟
✎✟☛
❻❸
✂
✏❢
❄✹✶❼✘ ✭❝✏✌✌☛✡✽✏✒✔✖
❄✹✘❅✮✳ ❚✟✍✡ ✡☛✎ ✏❢ ✽☞✌☞✻☛✎☛✌✡ ✍✡ ❜☞✡☛✔ ✏✒ ☞ Þ✎ ❜✕
❆
➻➸➝ ✆✁❣❡ ➺ ♦➐ ➩→
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
❋✆✝✳ ✞✳ ②t✲✟✈❡r✟✠❡❞ ❇✡ ❢☛r ❈☛ ❂ ✂☞✂✂ ✭❧✌✍t☎✁ ✂✵✂✸ ✭♠✐✎✎❧✌☎✁ ✟❛❞ ✂✵✂ ✭✏✐❣✑t☎ ✟✒ ❞✓✔❡r❡❛✒ ✒✓✕❡✖✵
❑✗✘✗✙ ✗✚ ✛✙✜ ✢✣✤✥✣✛✮ ✦♦✧ ❦★ ✴❦✶ ✩ ✪✤ ✛✬✯ ❘✗ ▼ ✩ ✥✰✜ ❲✗ ✬♦✚✗ ✚❤✛✚
✚❤✗ ✱✧♦✇✚❤ ✧✛✚✗✹ ✦♦✧ ✚❤✗ ✻✼❙ ✛✧✗ ✛✾♦✿✚ ✚❤✧✗✗ ✚❀✘✗✹ ✙✛✧✱✗✧ ✚❤✛✬
✚❤♦✹✗ ♦✦ ✚❤✗ ❉◆❙✜ ❁✹ ✗①❃✙✛❀✬✗✯ ❀✬ ✚❤✗ ❀✬✚✧♦✯✿❄✚❀♦✬❅ ✚❤❀✹ ✘❀✱❤✚ ✾✗
❄✛✿✹✗✯ ✾❊ ✛✬ ❀✬✛❄❄✿✧✛✚✗ ✗✹✚❀✘✛✚✗ ♦✦ ✚❤✗ ✘✗✛✬●❍✗✙✯ ❄♦✗■❄❀✗✬✚✹
✦♦✧ ✚❤✗✹✗ ❃✛✧✚❀❄✿✙✛✧ ❏✛✙✿✗✹ ♦✦ ❦★ ✴❦✶ ✛✬✯ ❘✗ ▼ ✜ ▲✬✯✗✗✯❅ ✛❄❄♦✧✯❀✬✱
✚♦ ❖P✜ ✢✣✣✮ ♦✦ ◗✧✛✬✯✗✬✾✿✧✱ ✗✚ ✛✙✜ ✢✣✤✥✣✛✮❅ ✇❤♦ ✿✹✗✯ ❦★ ✴❦✶ ✩ ❚❅
✚❤✗✹✗ ❃✛✧✛✘✗✚✗✧✹ ✹❤♦✿✙✯ ✾✗ q♣❯ ✩ ✪✣ ✛✬✯ ❱♣ ✩ ✤❳✤❚✰ ✢❄♦✧✧✗●
✹❃♦✬✯❀✬✱ ✚♦ ❱❨ ✩ ✤❳✪✪✮ ✦♦✧ ❘✗ ▼ ✩ ✥✰✜ ❩❤❀✹ ✛✹✹✿✘✗✹ ✚❤✛✚ ✚❤✗✹✗
❃✛✧✛✘✗✚✗✧✹ ✛✧✗ ❀✬✯✗❃✗✬✯✗✬✚ ♦✦ ✚❤✗ ❏✛✙✿✗ ♦✦ ❦★ ❅ ✇❤❀❄❤ ❀✹ ✬♦✚ ✚✧✿✗
✗❀✚❤✗✧❬ ✹✗✗ ❑✗✘✗✙ ✗✚ ✛✙✜ ✢✣✤✥✣✛✮✜ ❩♦ ❄✙✛✧❀✦❊ ✚❤❀✹ P✿✗✹✚❀♦✬❅ ✇✗ ✬♦✇
❃✗✧✦♦✧✘ ✪❉ ✻✼❙ ✇❀✚❤ ✚❤❀✹ ✬✗✇ ✹✗✚ ♦✦ ❃✛✧✛✘✗✚✗✧✹✜ ❩❤♦✹✗ ✧✗✹✿✙✚✹
✛✧✗ ✛✙✹♦ ✹❤♦✇✬ ❀✬ ✼❀✱✜ ✣✜ ▲✚ ✚✿✧✬✹ ♦✿✚ ✚❤✛✚ ✇❀✚❤ ✚❤✗✹✗ ❃✛✧✛✘✗✚✗✧✹
✚❤✗ ✧✗✹✿✙✚❀✬✱ ✱✧♦✇✚❤ ✧✛✚✗✹ ✛✧✗ ❀✬✯✗✗✯ ✘✿❄❤ ❄✙♦✹✗✧ ✚♦ ✚❤♦✹✗ ♦✦ ✚❤✗
❉◆❙❅ ✹✿✱✱✗✹✚❀✬✱ ✚❤✛✚ ✚❤✗ ✦♦✧✘✗✧ ✹✗✚ ♦✦ ✘✗✛✬●❍✗✙✯ ❄♦✗■❄❀✗✬✚✹
✘❀✱❤✚ ❀✬✯✗✗✯ ❤✛❏✗ ✾✗✗✬ ❀✬✛❄❄✿✧✛✚✗✜ ❁✹ ✛✙✙✿✯✗✯ ✚♦ ❀✬ ✚❤✗ ❀✬✚✧♦✯✿❄●
✚❀♦✬❅ ✚❤❀✹ ❄♦✿✙✯ ✾✗ ✾✗❄✛✿✹✗ ◆❖✻❭▲ ❀✹ ❏✗✧❊ ✹✚✧♦✬✱ ✦♦✧ ❦★ ✴❦✶ ✩ ✪✤
✛✬✯ ✙✗✛✯✹ ✚♦ ❀✬❤♦✘♦✱✗✬✗♦✿✹ ✘✛✱✬✗✚❀❄ ❍✗✙✯✹✜ ✼♦✧ ✚❤✗✹✗ ❍✗✙✯✹❅
✚❤✗ ✿✹✿✛✙ ✯✗✚✗✧✘❀✬✛✚❀♦✬ ♦✦ ✘✗✛✬●❍✗✙✯ ❄♦✗■❄❀✗✬✚✹❅ ✛✹ ✿✹✗✯ ✾❊
◗✧✛✬✯✗✬✾✿✧✱ ✗✚ ✛✙✜ ✢✣✤✥✣✛✮❅ ❀✹ ✬♦ ✙♦✬✱✗✧ ❏✛✙❀✯ ✾✗❄✛✿✹✗ ✦♦✧ ❀✬●
❤♦✘♦✱✗✬✗♦✿✹ ✘✛✱✬✗✚❀❄ ❍✗✙✯✹ ✚❤✗✧✗ ✇♦✿✙✯ ✾✗ ✛✯✯❀✚❀♦✬✛✙ ✚✗✧✘✹
❀✬ ✚❤✗ ❃✛✧✛✘✗✚✧❀③✛✚❀♦✬ ✦♦✧ ✚❤✗ ✘✗✛✬ ❘✗❊✬♦✙✯✹●✻✛①✇✗✙✙ ✹✚✧✗✹✹
✢❄✦✜ ❑✗✘✗✙ ✗✚ ✛✙✜ ✣✤✥✣❄✮✜ ❲✗ ✬♦✚✗ ✚❤✛✚ ✦♦✧ ✚❤❀✹ ❄♦✘❃✛✧❀✹♦✬ ✇✗
❤✛❏✗ ❪✗❃✚ ✚❤✗ ❏✛✙✿✗ ♦✦ ❫❴❯ ❀✬ ✚❤✗ ✬♦✧✘✛✙❀③✛✚❀♦✬ ♦✦ ✾♦✚❤ ✛①✗✹ ✿✬●
❄❤✛✬✱✗✯✜ ❵♦✇✗❏✗✧❅ ❀✦ ✇✗ ✛❄❄✗❃✚ ✚❤✛✚ ✚❤✗ ❄♦✧✧✗❄✚ ❏✛✙✿✗ ♦✦ ❱❨ ❀✹ ✬♦✚
✤✜❜❚❅ ✾✿✚ ✤✜✪✪❅ ✚❤✗ ✱✧✛❃❤✹ ✦♦✧ ❉◆❙ ✛✬✯ ✻✼❙ ✢❀❀✮ ✇♦✿✙✯ ✛✙✘♦✹✚
❄♦❀✬❄❀✯✗ ✇❀✚❤ ✚❤✛✚ ✦♦✧ ❉◆❙ ✢❀✮✜
▲✬ ✼❀✱✜ ✪ ✇✗ ✹❤♦✇ ✚❤✗ ❝❥●✛❏✗✧✛✱✗✯ ♥s ✦♦✧ ✉♦ ✩ ✤❳✤✤④❅ ✤✜✤✪❅
✛✬✯ ✤✜✤④ ✛✚ ✯❀⑤✗✧✗✬✚ ✚❀✘✗✹✜ ❲❤✗✬ ❄♦✘❃✛✧❀✬✱ ✧✗✹✿✙✚✹ ✦♦✧ ✯❀⑤✗✧✗✬✚
✧♦✚✛✚❀♦✬ ✧✛✚✗✹❅ ♦✬✗ ✹❤♦✿✙✯ ✚✛❪✗ ❀✬✚♦ ✛❄❄♦✿✬✚ ✚❤✛✚ ✚❤✗ ✱✧♦✇✚❤ ✧✛✚✗✹
❆✽✸✁ ❿✟✠❡
☛❢ ✄✷
❋✆✝✳ ⑥✳ ⑦✈☛⑧⑨✒✓☛❛ ☛❢ ❇⑩ ❶❇❷❸ ❢☛r r⑨❛✖ ☛❢ ❹❺✓❻❺ ✒❺r❡❡ ✟r❡ ✖❺☛❹❛ ✓❛
❼✓✠✵ ✸✵ ❽❺❡ ✒❺r❡❡ ❺☛r✓❾☛❛✒✟⑧ ⑧✓❛❡✖ ❻☛rr❡✖❿☛❛❞ ✒☛ ✒❺❡ ✟❿❿r☛➀✓✕✟✒❡ ✈✟⑧⑨❡✖
☛❢ ❇⑩❶❇❷❸ ✓❛ ✒❺❡ ✒❺r❡❡ r☛❹✖ ☛❢ ❼✓✠✵ ✸✵
✾✗❄♦✘✗ ✹✚✧♦✬✱✙❊ ✧✗✯✿❄✗✯✜ ▲✬✯✗✗✯❅ ❀✬ ✚❤✗ ✙✛✹✚ ✧♦✇ ♦✦ ✼❀✱✜ ✪ ✇✗
❄❤♦✹✗ ✚❤✗ ✚❀✘✗✹ ✹✿❄❤ ✚❤✛✚ ✚❤✗ ✛✘❃✙❀✚✿✯✗ ♦✦ ◆❖✻❭▲ ❀✹ ❄♦✘❃✛✧✛●
✾✙✗ ✦♦✧ ✉♦ ✩ ✤❳✤✤④ ✛✬✯ ✤✜✤✪✜ ❵♦✇✗❏✗✧❅ ✦♦✧ ✉♦ ✩ ✤❳✤④ ✇✗ ✧✛✬
✘✿❄❤ ✙♦✬✱✗✧ ✛✬✯ ✚❤✗ ✛✘❃✙❀✚✿✯✗ ♦✦ ◆❖✻❭▲ ❀✹ ❤✗✧✗ ✗❏✗✬ ✙✛✧✱✗✧❬
✹✗✗ ✼❀✱✜ ➁❅ ✇❤✗✧✗ ✇✗ ✹❤♦✇ ♥✶ ✴♥➂➃ ❅ ✇❤❀❄❤ ❀✹ ✚❤✗ ✬♦✧✘✛✙❀③✗✯
✘✛✱✬✗✚❀❄ ❍✗✙✯ ✹✚✧✗✬✱✚❤ ✦♦✧ ✚❤✗ ❤♦✧❀③♦✬✚✛✙ ✇✛❏✗✬✿✘✾✗✧ ❦ ✩ ❦✶
❀✬ ✚❤✗ ✚♦❃ ✙✛❊✗✧✹ ✇❀✚❤ ✣ ➄ ❦✶ ➅ ➄ ✪✜ ▲✚ ❀✹ ❄✙✗✛✧ ✚❤✛✚ ✚❤✗ ✦♦✧✘✛●
✚❀♦✬ ♦✦ ✹✚✧✿❄✚✿✧✗✹ ✚❤✧♦✿✱❤ ◆❖✻❭▲ ✧✗✘✛❀✬✹ ✘♦✧✗ ✹✚✧♦✬✱✙❊ ❄♦✬●
❍✬✗✯ ✚♦ ✚❤✗ ✿❃❃✗✧✘♦✹✚ ✙✛❊✗✧✹ ✛✹ ✇✗ ❀✬❄✧✗✛✹✗ ✚❤✗ ❏✛✙✿✗ ♦✦ ✉♦✜
■
❘ ▲♦s✁✂✁ ❡✄ ✁❛ ✿ ❈♦☎✆❡✄✐♥❣ ❡✝❡✞✄s ✐♥ ✞♦♥✞❡♥✄r✁✄✐♥❣ ☎✁❣♥❡✄✐✞ ß✉①
❋✟✠✳ ✺✳ ❇② ✁✄ ✄❤❡ ✆❡r✐✆❤❡r✡ ♦☛ ✄❤❡ ✞♦☎✆✉✄✁✄✐♦♥✁❛ ✂♦☎✁✐♥ ☛♦r ❈♦ ❂ ✵☞✵✵✌ ✭❧✍❢✎✮✱ ✵ ✵✏ ✭♠✑❞❞❧✍✮✱ ✁♥✂ ✵ ✵✌ ✭✒✑✓✔✎✮ ✁✄ ✄❤❡ s✁☎❡ ✄✐☎❡s ✁s ✐♥ ✕✐❣
❚❤❡ ✖✗ ✘✗ ③ ✞♦♦r✂✐♥✁✄❡s ✁r❡ ✐♥✂✐✞✁✄❡✂ ✐♥ ✄❤❡ ☎✐✂✂❛❡ ☛r✁☎❡
✏
❲❡ ♥♦✄❡ ✄❤❡ s✄r♦♥❣ s✉r☛✁✞❡ ❡✝❡✞✄ ☛♦r ❈♦ ❂ ✵☞✵✏ ✐♥ ✄❤❡ ❛✁s✄ ✄✐☎❡ ☛r✁☎❡
❊✙✚✛ ✜✢✣ ✤✢ ✥ ✦✧✶✸★ t✩✚✣✚ ✪✫ ✫t✪✬✬ ✛✢t✪✯✚✰✲✬✚ ✴✣✢✇t✩ ✢✜ ✫t✣✷✯t✷✣✚✫★
✇✩✪✯✩ ✪✫ ✹✪✻✚✣✚✛t ✜✣✢✼ ✇✩✰t ✪✫ ✫✚✚✛ ✪✛ ▼✽✾❀ ✫✚✚ ✽✪✴❁ ❃❁
❄✩✚✫✚ Þ✴✷✣✚✫ ✫✩✢✇ t✩✚ ✴✚✛✚✣✰t✪✢✛ ✢✜ ✫t✣✷✯t✷✣✚✫ t✩✰t ✲✚✴✪✛
t✢ ✫✪✛❅ ✫✷✲✫✚❆✷✚✛t✬❉❁ ❍✢✇✚✙✚✣★ ✜✢✣ ✤✢
✥
✦✧✦✸ ✰✛✹ ✬✰✣✴✚✣★ t✩✪✫
✫✪✛❅✪✛✴ ✪✫ ✼✷✯✩ ✬✚✫✫ ♣✣✢✼✪✛✚✛t❁ ●✛✫t✚✰✹★ t✩✚ ✫t✣✷✯t✷✣✚✫ ✣✚✼✰✪✛
✯✢✛Þ✛✚✹ t✢ t✩✚ ✫✷✣✜✰✯✚ ✬✰❉✚✣✫★ ✇✩✪✯✩ ✪✫ ✫✚✚✛ ✼✢✣✚ ✯✬✚✰✣✬❉ ✪✛ ✙✪✈
✫✷✰✬✪❏✰t✪✢✛✫ ✢✜ ❑◆ ✰t t✩✚ ♣✚✣✪♣✩✚✣❉ ✢✜ t✩✚ ✯✢✼♣✷t✰t✪✢✛✰✬ ✹✢✼✰✪✛
✜✢✣ ✤✢ ✥ ✦✧✦✸❀ ✫✚✚ ✽✪✴❁ ❖★ ✇✩✪✯✩ ✪✫ ✜✢✣ ✰♣♣✣✢P✪✼✰t✚✬❉ t✩✚ ✫✰✼✚
t✪✼✚✫ ✰✫ ✽✪✴❁ ✸❁
❄✢ ✢✷✣ ✫✷✣♣✣✪✫✚★ t✩✚ ✬✰✣✴✚✈✫✯✰✬✚ ✫t✣✷✯t✷✣✚✫ ✫t✪✬✬ ✣✚✼✰✪✛ ✪✛✹✚✈
♣✚✛✹✚✛t ✢✜ t✩✚ ◗✈✹✪✣✚✯t✪✢✛★ ✇✩✪✯✩ ✪✫ ✯✬✚✰✣✬❉ ✰t ✙✰✣✪✰✛✯✚ ✇✪t✩ ✣✚✈
❋✟✠✳ ➂✳ ❘❡s✉❛✄s ♦☛ ➃✕➄ ♦☛ ▲➅➆➃❘ s❤♦➇✐♥❣ ❇② ✁✄ ✄❤❡ ✆❡r✐✆❤❡r✡ ♦☛ ✄❤❡
✞♦☎✆✉✄✁✄✐♦♥✁❛ ✂♦☎✁✐♥ ☛♦r ❈♦ ❂ ➈✵☞✵✏ ✐♥ ✄❤❡ ▲➅➆➃❘ ✞✁s❡ ✭❧✍❢✎✮ ✁♥✂
✫✷✬t✫ ✢✜ t✩✚ ✯✢✣✣✚✫♣✢✛✹✪✛✴ ▼✽✾❁ ●✛ ✽✪✴❁ ❙ ✇✚ ✣✚♣✣✢✹✷✯✚ ✰ ✣✚✫✷✬t
➇✐✄❤ ✄❤❡ ♥❡➇ s❡✄ ♦☛ ✆✁r✁☎❡✄❡rs ✭✒✑✓✔✎✮ ✁✄ ✄❤❡ s✁☎❡ ✄✐☎❡
✫✪✼✪✬✰✣ t✢ t✩✰t ✢✜ ❯❱❳▼❨ ✜✢✣ ✤✢ ✥ ➧✦✧✦✸❁ ❊✙✚✛ ✰t ✢t✩✚✣ ✰✛✴✬✚✫
✐♥ ❇② ➉❇➊ s❤♦➇♥ ❤❡r❡ ✐s ❛✁r❣❡r ✄❤✁♥ ✄❤✁✄ s❤♦➇♥ ✐♥ ▲➅➆➃❘ ✮
✫✷✯✩ ✰✫ ❩ ✥ ❬❖
❭
❭
✰✛✹ ❪✦ ★ ✛✢ ✙✰✣✪✰t✪✢✛ ✪✛ t✩✚ ◗✈✹✪✣✚✯t✪✢✛ ✪✫ ✫✚✚✛❀
✭❚❤❡ r✁♥❣❡
✫✚✚ ✽✪✴❁ ❫❁ ❄✩✚ ✣✚✰✫✢✛ ✜✢✣ t✩✪✫ ✹✪✫✯✣✚♣✰✛✯❉ ✲✚t✇✚✚✛ ❴❵✾ ✰✛✹
t✩✚ ✯✢✣✣✚✫♣✢✛✹✪✛✴ ▼✽✾ ✪✫ ✛✢t ❉✚t ✷✛✹✚✣✫t✢✢✹❁ ✽✷✣t✩✚✣✼✢✣✚★ t✩✚
✯✢✛Þ✛✚✼✚✛t ✢✜ ✫t✣✷✯t✷✣✚✫ t✢ t✩✚ ✫✷✣✜✰✯✚ ✬✰❉✚✣✫★ ✇✩✪✯✩ ✪✫ ✫✚✚✛ ✫✢
✯✬✚✰✣✬❉ ✪✛ ❴❵✾★ ✫✚✚✼✫ t✢ ✲✚ ✰✲✫✚✛t ✪✛ t✩✚ ✯✢✣✣✚✫♣✢✛✹✪✛✴ ▼✽✾❁
Þ✚✬✹ ✪✫ ✚✫✫✚✛t✪✰✬✬❉ t✇✢✈✹✪✼✚✛✫✪✢✛✰✬❁ ●✛ t✩✚ ✬✢✇✚✣ ♣✰✛✚✬ ✢✜ ✽✪✴❁ ❖
✢✜ ❯❱❳▼❨★ ✰ ✯✢✼♣✰✣✪✫✢✛ ✲✚t✇✚✚✛ ❃❴ ✰✛✹ ✸❴ ▼✽✾ ✇✰✫ ✫✩✢✇✛
✜✢✣ ✤✢
❜❝❥❝ ❦q④⑤⑥⑦⑧⑨q⑩ q❶ ❷❸❹ ❥❺ ⑥⑩❻ ❼❺ ❻⑥❷⑥ q❶ ❽❾❿➀➁
➋
✦✧✦✶ ✰✫ ✰ ✜✷✛✯t✪✢✛ ✢✜ ✬✰t✪t✷✹✚❁ ➌t t✩✚ ♣✢✬✚★ t✩✚ ✛✢✣✈
✼✰✬✪❏✚✹ ✴✣✢✇t✩ ✣✰t✚✫ ✇✚✣✚ ➍➎➍➏➐
➋
✦✧✦❫ ✰✛✹ ✦❁✶❬ ✜✢✣ ❃❴ ✰✛✹
✸❴ ▼✽✾★ ✣✚✫♣✚✯t✪✙✚✬❉❁ ❄✩✪✫ ✹✪✻✚✣✚✛✯✚ ✪✫ ✫✼✰✬✬✚✣ ✜✢✣ ✫✼✰✬✬✚✣ ✙✰✬✈
❄✩✚ ✰♣♣✰✣✚✛t ✬✰✯❅ ✢✜ ◗ ✹✚♣✚✛✹✚✛✯✚ ✢✜ t✩✚ ✬✰✣✴✚✈✫✯✰✬✚ ✼✰✴✛✚t✪✯
✷✚✫ ✢✜ ✤✢★ ✲✷t ✪t ✪✛✯✣✚✰✫✚✫ ✇✪t✩ ✪✛✯✣✚✰✫✪✛✴ ✙✰✬✷✚✫ ✢✜ ✤✢❀ ✫✚✚
Þ✚✬✹ ✪✛ t✩✚ ❴❵✾ ✫✩✢✇✫ t✩✰t t✩✪✫ ✯✢✛t✣✪✲✷t✪✢✛ t✢ t✩✚ ✼✰✴✛✚t✪✯
✽✪✴❁ ➑❁ ➒✚ ✛✢t✚ t✩✰t t✩✚ ❃❴ ✣✚✫✷✬t ✪✛ t✩✪✫ Þ✴✷✣✚ ✫✷♣✚✣✫✚✹✚✫ t✩✰t
➓➔✏✱ ✆✁❣❡ → ♦☛ ➣↔
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
❋✆✝✳ ✼✳ ❇② ❛✞ ✞❤❡ ♣❡✟✐♣❤❡✟✠ ♦✡ ✞❤❡ ❝♦☛♣☞✞❛✞✐♦✌❛✍ ❞♦☛❛✐✌ ✡♦✟ ❈♦ ❂ ✂✎✂✂ ❛✌❞ ✏ ❂ ✹✺✑ ✭✉✒✒✓✔ ✔✕✖☎ ❛✌❞ ✾✂✑ ✭❧✕✖✓✔ ✔✕✖☎✁ ❛✞ ✞❤✟❡❡ ❞✐✗❡✟❡✌✞ ✞✐☛❡t ✭✡✟♦☛
❧✓❢✘ ✘✕ ✔r✙✚✘☎✮ ❚❤❡ ①✱ ✛✱ ③ ❝♦♦✟❞✐✌❛✞❡t ❛✟❡ ✐✌❞✐❝❛✞❡❞ ✐✌ ✞❤❡ ☛✐❞❞✍❡ ✡✟❛☛❡✮
❹❺ ❻❼❽❾❿❼➀ ➁❽➂ ➃➁➄❽❾❿❼➀ ➅❾➆❼➀❼❿➇
✯❩ ❀❁❁✩❅❣ ✻✦❃❀❃✩✦❅ ❃✦ ✦❖✻ s❃✻✦❅❣●❩ s❃✻❀❃✩❍✶❁ s✩❄❖●❀❃✩✦❅s✲ ✇✶ ❀❖■
❃✦❄❀❃✩❏❀●●❩ ❀●s✦ ❊✻✦❁❖❏✶ ⑧✩❅✶❃✩❏ ✴✶●✩❏✩❃❩✪ ❳❅ ❃✴✩s s✶❏❃✩✦❅ ✇✶ ➈❖❀❅■
❃✩✧❩ ❃✴✩s✲ ❏✦❄❊❀✻✶ ❃✴✶ ✴✶●✩❏✩❃❩ ✇✩❃✴ ✶❀✻●✩✶✻ ✇✦✻⑧✲ ❀❅❁ ❀❁❁✻✶ss ❃✴✶
➈❖✶s❃✩✦❅ ✇✴✶❃✴✶✻ ❃✴✩s ❄✩❣✴❃ ●✶❀❁ ❃✦ ✦❙s✶✻✈❀❙●✶ ✶❨✶❏❃s✪ ➉●● ✻✶■
s❖●❃s ❊✻✶s✶❅❃✶❁ ✩❅ ❃✴✩s s✶❏❃✩✦❅ ❀✻✶ ❙❀s✶❁ ✦❅ ❃✩❄✶ s✶✻✩✶s✲ ✇✩❃✴ ✶✻✻✦✻
❙❀✻s ❙✶✩❅❣ ✶s❃✩❄❀❃✶❁ ❀s ❃✴✶ ●❀✻❣✶s❃ ❁✶❊❀✻❃❖✻✶ ✧✻✦❄ ❀❅❩ ✦❅✶■❃✴✩✻❁
✦✧ ❃✴✶ ✧❖●● ❃✩❄✶ s✶✻✩✶s✪
➊➋➌➋ ➍➎➏➐➑➐➒➓ ➔→➣↔↕➑➒➐➣➙
❋✆✝✳ ✜✳ ❉❡♣❡✌❞❡✌❝❡ ♦✡ ✢✣✢✤✵ ♦✌ ✷✥✣✢✤✵ ✐✌ ✞❤❡ ✸❉ ❛✌❞ ✷❉ ❝❛t❡t ✡♦✟ ✏ ❂
✂✑ ✭❝♦✟✟❡t♣♦✌❞✐✌♥ ✞♦ ✞❤❡ ♣♦✍❡☎✮
✦✧ ★✩❣✪ ✬ ✦✧ ▲✯❑▼✰✲ ✴✶✻✶ ✿ ✇❀s ❁✶❃✶✻❄✩❅✶❁ ✧✻✦❄ ❃✴✶ ❀❄❊●✩❍■
❏❀❃✩✦❅ ✦✧ ❃✴✶ ❃✦❃❀● ❄❀❣❅✶❃✩❏ ❍✶●❁ ◆✇✴✩❏✴ ✩❅❏●❖❁✶s ❃✴✶ ✩❄❊✦s✶❁
❍✶●❁P ✻❀❃✴✶✻ ❃✴❀❅ ✧✻✦❄ ❃✴✶ ❁✶✈✩❀❃✩✦❅s ✦✧ ❃✴✶ ❄❀❣❅✶❃✩❏ ❍✶●❁ ✧✻✦❄
❃✴✶ ✩❄❊✦s✶❁ ✦❅✶✪ ◗✴✩s ✻✶s❖●❃✶❁ ✩❅ ❀ ✧✦❖✻ ❃✩❄✶s s❄❀●●✶✻ ✶s❃✩❄❀❃✶
✦✧ ✿✪ ★❖✻❃✴✶✻❄✦✻✶✲ ❃✴✶ ❏✻✩❃✩❏❀● ✈❀●❖✶ ✦✧ ❘✦✲ ❀❙✦✈✶ ✇✴✩❏✴ ❯❱▼❲❳
s✴❖❃s ✦❨✲ ✩s ❅✦✇ ❁✶●❀❩✶❁ ❙❩ ❀ ✧❀❏❃✦✻ ✦✧ ❀❙✦❖❃ ❬❭✬✪
◗✴✶ ❊●✦❃ ✩❅ ★✩❣✪ ❪ ✴❀s ❙✶✶❅ ❁✦❅✶ ✧✦✻ ❃✴✶ ❄✦✻✶ ✦❊❃✩❄✩s❃✩❏ s✶❃
✦✧ ❄✶❀❅■❍✶●❁ ❊❀✻❀❄✶❃✶✻s ◆q❫❴ ❵ ❬❜ ❀❅❁ ❥❫ ❵ ❜❦♠④⑤P✲ ❙❖❃ ❃✴✶
✶ss✶❅❃✩❀● ❏✦❅❏●❖s✩✦❅s ❃✴❀❃ ❃✴✶ ❣✻✦✇❃✴ ✻❀❃✶s ✩❅ ❬⑥ ❀❅❁ ✬⑥ ❀✻✶
s✩❄✩●❀✻ s✴✦❖●❁ ❅✦❃ ❁✶❊✶❅❁ ✦❅ ❃✴✩s✪ ◗✴✶ ✻✶❄❀✩❅✩❅❣ ❁✩❨✶✻✶❅❏✶s ❙✶■
❃✇✶✶❅ ⑥❯⑦ ❀❅❁ ▼★⑦ ✻✶❣❀✻❁✩❅❣ ❃✴✶ ●❀❏⑧ ✦✧ ⑨ ❁✶❊✶❅❁✶❅❏✶ ✦✧ ❃✴✶
❄✶❀❅ ❍✶●❁ ❀❅❁ ❃✴✶ ❏✦❅❍❅✶❄✶❅❃ ✦✧ s❃✻❖❏❃❖✻✶s ❃✦ ❃✴✶ s❖✻✧❀❏✶ ●❀❩■
✶✻s ❄✩❣✴❃ ❙✶ ✻✶●❀❃✶❁ ❃✦ ❃✴✶ ❀❙s✶❅❏✶ ✦✧ ❄✶❀❅■❍✶●❁ ❃✻❀❅s❊✦✻❃ ❏✦■
✶⑩❏✩✶❅❃s ✦❃✴✶✻ ❃✴❀❅ q❫ ✲ ❶❷ ✲ ❀❅❁ ❸❷ ✪ ✯❩ ❀❅❁ ●❀✻❣✶✲ ✴✦✇✶✈✶✻✲ ❃✴✶
❀❣✻✶✶❄✶❅❃ ❙✶❃✇✶✶❅ ⑥❯⑦ ❀❅❁ ▼★⑦ ✩s ✻✶❄❀✻⑧❀❙●❩ ❣✦✦❁ ✩❅ ❃✴❀❃
❃✴✶ ❊✻✶❁✩❏❃✶❁ ❁✶❏●✩❅✶ ✦✧ ❯❱▼❲❳ ❀❃ ✻❀❃✴✶✻ ❄✦❁✶s❃ ✻✦❃❀❃✩✦❅ ✻❀❃✶s
✩s ✧❖●●❩ ❏✦❅❍✻❄✶❁ ❙❩ ⑥❯⑦✪
❆✽✸✁ ♣❛♥❡ ✽ ♦✡ ✄✷
❳❅ ❃❖✻❙❖●✶❅❏✶✲ ❃✴✶ ❊✻✶s✶❅❏✶ ✦✧ ✻✦❃❀❃✩✦❅ ❀❅❁ s❃✻❀❃✩❍❏❀❃✩✦❅ ❣✩✈✶s
✻✩s✶ ❃✦ ⑧✩❅✶❃✩❏ ✴✶●✩❏✩❃❩ ❀❅❁ ❀❅ ➛ ✶❨✶❏❃ ◆❑✻❀❖s✶ ➜ ✰➝❁●✶✻ ♠➞❪❜➟
✯✻❀❅❁✶❅❙❖✻❣ ✶❃ ❀●✪ ❬❜♠✬P✪ ➉s ❀ ❄✶❀s❖✻✶ ✦✧ ⑧✩❅✶❃✩❏ ✴✶●✩❏✩❃❩✲ ✇✶
❁✶❃✶✻❄✩❅✶ ❃✴✶ ❅✦✻❄❀●✩➠✶❁ ✴✶●✩❏✩❃❩ ❀s
➡➢ ❵ ➤ ➲ ➥➦➧➢ ➨➩➫➭➯ ❦
◆✬❬P
❳❅ ★✩❣✪ ➞ ✇✶ ❏✦❄❊❀✻✶ ✦❖✻ ❊✻✶s✶❅❃ ✻❖❅s ❀❃ ➧➢ ➦➧➳ ❵ ✬❜ ✇✩❃✴ ❃✴✦s✶
✦✧ ✯✻❀❅❁✶❅❙❖✻❣ ✶❃ ❀●✪ ◆❬❜♠❬❙P ❀❃ ➧➢ ➦➧➳ ❵ ➵ s✴✦✇✩❅❣ ➡➢ ✈✶✻s❖s
➸✻ ❘✦✪ ★✦✻ ✦❖✻ ❊✻✶s✶❅❃ ✻❖❅s ◆✻✶❁ ❍●●✶❁ s❩❄❙✦●sP✲ ⑧✩❅✶❃✩❏ ✴✶●✩❏■
✩❃❩ ✩s ❏●✶❀✻●❩ ✈✶✻❩ s❄❀●●✲ ✇✴✩❏✴ ✩s ❀ ❏✦❅s✶➈❖✶❅❏✶ ✦✧ ❃✴✶ s❄❀●●
✈❀●❖✶ ✦✧ ❘✦✪ ❘✦❄❊❀✻✶❁ ✇✩❃✴ ✶❀✻●✩✶✻ ✻❖❅s ❀❃ ➧➢ ➦➧➳ ❵ ➵✲ ✇✴✩❏✴
❣❀✈✶ ➡➢ ➺ ❬ ➸✻ ❘✦✲ ❃✴✶ ❊✻✶s✶❅❃ ✦❅✶s s✴✦✇ ❀❙✦❖❃ ❃✇✩❏✶ ❀s ❄❖❏✴
✴✶●✩❏✩❃❩✪ ❳❅❃✶✻✶s❃✩❅❣●❩✲ ✧✦✻ ✻❀❊✩❁ ✻✦❃❀❃✩✦❅ ❃✴✶ ✻✶●❀❃✩✈✶ ⑧✩❅✶❃✩❏ ✴✶■
●✩❏✩❃❩ ❁✶❏●✩❅✶s ✇✴✶❅ ❃✴✶ ❊✻✦❁❖❏❃ ➸✻ ❘✦ ✩s ●❀✻❣✶✻ ❃✴❀❅ ❀❙✦❖❃ ❜✪➵✪
◗✴✶ ❄❀➻✩❄❖❄ ✈❀●❖✶ ✦✧ ➡➢ ❃✴❀❃ ❏❀❅ ❙✶ ✻✶❀❏✴✶❁ ✩s ❀❙✦❖❃ ❜✪✬✪ ❳❅ ❀
✧❖●●❩ ❊✶✻✩✦❁✩❏ ❁✦❄❀✩❅✲ ❁❩❅❀❄✦ ❀❏❃✩✦❅ ✇✦❖●❁ ❙✶ ❊✦ss✩❙●✶ ✇✴✶❅
➡➢ ➼ ◆➧➢ ➦➧➳ P➽➳ ✲ ✇✴✩❏✴ ✩s ❜❦❬ ✩❅ ❃✴✩s ❏❀s✶✪ ➾✦✇✶✈✶✻✲ ❙✶❏❀❖s✶ ✦✧
s❃✻❀❃✩❍❏❀❃✩✦❅ ❀❅❁ ❙✦❖❅❁❀✻✩✶s✲ ❃✴✶ ✦❅s✶❃ ✩s ❁✶●❀❩✶❁ ❀❅❁ ❅✦ ❁❩❅❀❄✦
❀❏❃✩✦❅ ✴❀s ❙✶✶❅ ✧✦❖❅❁ ✩❅ ❃✴✶ s✩❄❖●❀❃✩✦❅s ✦✧ ✯✻❀❅❁✶❅❙❖✻❣ ✶❃ ❀●✪
◆❬❜♠❬❙P✪ ➾✦✇✶✈✶✻✲ ✩❅ ❃✴✶ ❊✻✶s✶❅❃ ❏❀s✶✲ ❁❩❅❀❄✦ ❀❏❃✩✦❅ ✩s ❊✦ss✩❙●✶
✧✦✻ ➡➢ ➼ ♠➦✬❜✲ ✇✴✩❏✴ ●✶❀❁s ❃✦ ❀ ✯✶●❃✻❀❄✩■●✩⑧✶ ❄❀❣❅✶❃✩❏ ❍✶●❁ ✇✩❃✴
✈❀✻✩❀❃✩✦❅ ✩❅ ❃✴✶ ➚ ❁✩✻✶❏❃✩✦❅✪ ⑥❩❅❀❄✦ ❀❏❃✩✦❅ ✩s ❁✶❄✦❅s❃✻❀❃✶❁ ✩❅
■
❘ ▲♦s✁✂✁ ❡✄ ✁❛ ✿ ❈♦☎✆❡✄✐♥❣ ❡✝❡✞✄s ✐♥ ✞♦♥✞❡♥✄r✁✄✐♥❣ ☎✁❣♥❡✄✐✞ ß✉①
❋✟✠✳ ✗✗✳ ❈♦☎✆✁r✐s♦♥ ♦❢ ❾❿✎✁✈❡r✁❣❡✂ ✙② ❢♦r ❈♦ ❂ ✵☛✶✸ ✁♥✂ ✵ ✸✶
t✧ ✤✢ ✮✣✲❧✢✲ t✜✣✦ t✜✣t ✧★ ⑤❸❹❺◗ ✣✮✧✦✢❆ ❷✤✻✩✧✼✥✮✰✱ ✪✧✲✢ ✯✧✲❽ ✩✦
t✜✣t ✫✩✲✢❝t✩✧✦ ✩✥ ✦✢❝✢✥✥✣✲✰❆
➀➁➂➁ ➃➄➅➆➇➈➉ ➊➋➇➌➍➎➏➐➋➈➏
❋✟✠✳ ✾✳ ❘❡❛✁✄✐✈❡ ❦✐♥❡✄✐✞ ❤❡❛✐✞✐✄✡ s✆❡✞✄r✉☎ ✁s ✁ ❢✉♥✞✄✐♦♥ ♦❢ ●r ❈♦ ❢♦r
●r ❂ ✵☛✵✸ ✇✐✄❤ ❈♦ ❂ ✵☛✵✸☞ ✵ ✵✌☞ ✵ ✶✸☞ ✵ ✹✍☞ ✁♥✂ ✵ ✌✌ ✭r❡✂ ✁♥✂ ❜❛✉❡ s✡☎✎
❜♦❛s✏ ✞♦☎✆✁r❡✂ ✇✐✄❤ r❡s✉❛✄s ❢r♦☎ ❡✁r❛✐❡r s✐☎✉❛✁✄✐♦♥s ♦❢ ❇r✁♥✂❡♥❜✉r❣
❡✄ ✁❛
✭✷✵✶✷❜✏ ❢♦r ●r ❂ ✵☛✶✌ ✭s☎✁❛❛ ✂♦✄s ✞♦♥♥❡✞✄❡✂ ❜✡ ✁ ✂♦✄✄❡✂ ❛✐♥❡✏
❚❤❡ s♦❛✐✂ ❛✐♥❡ ✞♦rr❡s✆♦♥✂s ✄♦ ✒✑
❂ ✷●r ❈♦ ❚❤❡ ✄✇♦ ❤♦r✐③♦♥✄✁❛ ✂✁s❤✎
✓
✂♦✄✄❡✂ ❛✐♥❡s ✐♥✂✐✞✁✄❡ ✄❤❡ ✈✁❛✉❡s ♦❢ ✒
✔ ✕✖ ✴✕✑ ❢♦r ✇❤✐✞❤ ✂✡♥✁☎♦ ✁✞✄✐♦♥
✑
✐s ✆♦ss✐❜❛❡ ❢♦r ✕✑ ✴✕✖ ❂ ✺ ✁♥✂ ✸✵
❘✉♥s ✇✐✄❤♦✉✄ ✁♥ ✐☎✆♦s❡✂ Þ❡❛✂ ✭❜❛✉❡
❥✥ ✣ ❝✧✦✥✢➑✼✢✦❝✢ ✧★ t✜✢ ♣✲✧✫✼❝t✩✧✦ ✧★ ❽✩✦✢t✩❝ ✜✢✮✩❝✩t✰✱ t✜✢ ✪✣❧P
✦✢t✩❝ ✬✢✮✫ ✥✜✧✼✮✫ ✣✮✥✧ ✤✢ ✜✢✮✩❝✣✮❆ ➒✧✯✢✻✢✲✱ ✥✩✦❝✢ ✪✣❧✦✢t✩❝ ✜✢P
✮✩❝✩t✰ ✩✥ ❝✧✦✥✢✲✻✢✫✱ ✣✦✫ ✯✣✥ ❯✢✲✧ ✩✦✩t✩✣✮✮✰✱ ✩t ✥✜✧✼✮✫ ✲✢✪✣✩✦ ❯✢✲✧✱
✣t ✮✢✣✥t ✧✦ ✣ ✫✰✦✣✪✩❝✣✮ t✩✪✢ ✥❝✣✮✢ ❄❵✢✲❧✢✲ ❙❉➓q❊❆ ❍✜✩✥ ❝✧✦✫✩t✩✧✦
❝✣✦ ✤✢ ✧✤✢✰✢✫ ✩★ t✜✢ ✪✣❧✦✢t✩❝ ✬✢✮✫ ✩✥ ✤✩P✜✢✮✩❝✣✮✱ ✩❆✢❆✱ ✯✩t✜ ✧♣♣✧P
✥✩t✢ ✥✩❧✦✥ ✧★ ✪✣❧✦✢t✩❝ ✜✢✮✩❝✩t✰ ✣t ✮✣✲❧✢ ✣✦✫ ✥✪✣✮✮ ✯✣✻✢✦✼✪✤✢✲✥
Þ❛❛❡✂ s✡☎❜♦❛s✏ ✂❡☎♦♥s✄r✁✄❡ ✂✡♥✁☎♦ ✁✞✄✐♦♥ ✐♥ ✄✇♦ ✞✁s❡s ❚❤❡ ❜❛✉❡ ♦✆❡♥
❄♠✢✢✜✣★✢✲ ❙❉❉➔→ ❻✩ ❙❉❉❉❊❆ ❭✢ ✦✧✯ ✣✥❽ ✯✜✢t✜✢✲ ✥✩❧✦✣t✼✲✢✥ ✧★ t✜✩✥
s✡☎❜♦❛ ✂❡♥♦✄❡s ✁ ✞✁s❡ ✇❤❡r❡ ✄❤❡ ✂✡♥✁☎♦ ✐s ✞❛♦s❡ ✄♦ ☎✁r❣✐♥✁❛
❝✧✼✮✫ ✩✦ ♣✲✩✦❝✩♣✮✢ ✤✢ ✫✢t✢❝t✢✫ ✣t t✜✢ ✥✧✮✣✲ ✥✼✲★✣❝✢❆ ❍✧ ✣✫✫✲✢✥✥ t✜✩✥
➑✼✢✥t✩✧✦✱ ✯✢ ✼✥✢ ✧✼✲ ✥✩✪✼✮✣t✩✧✦ ✣t ✩✦t✢✲✪✢✫✩✣t✢ ✲✧t✣t✩✧✦ ✥♣✢✢✫
✯✩t✜ ❃✧
❏
❑▼❑◆✱ ✯✜✢✲✢ ✪✣❧✦✢t✩❝ ➣✼❖ ❝✧✦❝✢✦t✲✣t✩✧✦✥ ✣✲✢ ✯✢✮✮
✫✢✻✢✮✧♣✢✫ ✣t t✜✢ ✥✼✲★✣❝✢ ✧★ t✜✢ ✫✧✪✣✩✦✱ ✣✦✫ ❝✧✪♣✣✲✢ t✜✢ ✜✢✮✩❝✩t✰
✯✩t✜ ✣ ✮✣✲❧✢✲ ✻✣✮✼✢ ✧★ ❑❆❙◆❆
❹✢✣✥✼✲✩✦❧ ✪✣❧✦✢t✩❝ ✜✢✮✩❝✩t✰ ✩✥ ✦✧t✧✲✩✧✼✥✮✰ ✫✩↔❝✼✮t ✤✢❝✣✼✥✢
✩t ✩✦✻✧✮✻✢✥ t✜✢ ✪✣❧✦✢t✩❝ ✻✢❝t✧✲ ♣✧t✢✦t✩✣✮✱ ✯✜✩❝✜ ✩✥ ❧✣✼❧✢ ✫✢P
♣✢✦✫✢✦t❆ ➒✧✯✢✻✢✲✱ ✼✦✫✢✲ t✜✢ ✣✥✥✼✪♣t✩✧✦ ✧★ ✜✧✪✧❧✢✦✢✩t✰ ✣✦✫
✩✥✧t✲✧♣✰✱ t✜✢ ❅✧✼✲✩✢✲ t✲✣✦✥★✧✲✪ ✧★ t✜✢ ✪✣❧✦✢t✩❝ ❝✧✲✲✢✮✣t✩✧✦ t✢✦P
✥✧✲ ✩✥
ö ö
↕➙ ➛ ❄ ➜❊ ❏ ❄➝➙ ➛ ➞ ➟➙ ➟ ➛ ❊
➭➠ ➡ ➢ ❄➟❊
❋✟✠✳ ✗✘✳ ❱✐s✉✁❛✐③✁✄✐♦♥ ♦❢ ✙ ✚ ✁♥✂ ✙② ❢♦r ✄❤❡ r✉♥ ✇✐✄❤ ❈♦ ❂ ✵☛✺ s❤♦✇✐♥❣
✂✡♥✁☎♦ ✁✞✄✐♦♥ ❲❡ ♥♦✄❡ ✄❤❡ ✞❛❡✁r s✐❣♥✁✄✉r❡ ♦❢ ✁ ❇❡❛✄r✁☎✐ Þ❡❛✂ s❤♦✇✐♥❣
✈✁r✐✁✄✐♦♥ ✐♥ ✄❤❡ ✛ ✂✐r❡✞✄✐♦♥
ö
✯✜✢✲✢ ➜
❏
q➤➟
❴
➞ ✽➙ ➛➥
✩➟➥ ➦➢ ❄➟❊
➓➤➟
❴
➧
❄◆◆❊
➜➨➟ ✩✥ t✜✢ ✼✦✩t ✻✢❝t✧✲ ✧★ ➜ ✣✦✫ ➡ ➢ ❄➟❊ ✣✦✫ ➦➢ ❄➟❊
✣✲✢ ✪✣❧✦✢t✩❝ ✢✦✢✲❧✰ ✣✦✫ ✪✣❧✦✢t✩❝ ✜✢✮✩❝✩t✰ ✥♣✢❝t✲✣✱ ✯✜✩❝✜ ✧✤✢✰
t✜✢ ✲✢✣✮✩❯✣✤✩✮✩t✰ ❝✧✦✫✩t✩✧✦ ❞➭➠ ➡ ➢ ❄➟❊ ⑥ ➟➩➦➢ ❄➟❊➩❆ ➒✢✲✢✱ t✜✢ ★✣❝P
t✜✢ ✣✤✥✢✦❝✢ ✧★ ✣✦ ✩✪♣✧✥✢✫ ✬✢✮✫✱ ✯✜✩❝✜ ✮✢✣✫✥ t✧ ✥✮✩❧✜t✮✰ ✥✪✣✮✮✢✲
✻✣✮✼✢✥ ✧★ ✽❀ ★✧✲ t✜✢ ✥✣✪✢ ✻✣✮✼✢ ✧★ ❁✲ ❃✧ ❄✥✢✢ ✤✮✼✢ ✥✰✪✤✧✮✥ ✩✦
❅✩❧❆ ❉❊❆ ❍✜✢ ❝✣✥✢ ❃✧ ❏ ❑▼◆◆ ✩✥ ❝✮✧✥✢ t✧ ✪✣✲❧✩✦✣✮ ✣✦✫ t✜✢ ✬✢✮✫ ✩✥
✥✮✧✯✮✰ ✫✢❝✣✰✩✦❧✱ ✯✜✩❝✜ ✩✥ ✩✦ ✣❧✲✢✢✪✢✦t ✯✩t✜ t✜✢ ✢❖♣✢❝t✢✫ ♣✧✥✩P
t✩✧✦ ✧★ t✜✢ ✪✣✲❧✩✦✣✮ ✮✩✦✢❆
◗✦ ❅✩❧❆ ❙❑ ✯✢ ✥✜✧✯ ✻✩✥✼✣✮✩❯✣t✩✧✦✥ ✧★ ❳ ❨ ✣✦✫ ❳❩ ★✧✲ ✣ ✲✼✦
✯✩t✜ ❃✧
❏
❑▼❬ ✥✜✧✯✩✦❧ ✫✰✦✣✪✧ ✣❝t✩✧✦❆ ❭✢ ✦✧t✢ t✜✢ ✣♣♣✲✧❖✩P
✪✣t✢ ♣✜✣✥✢ ✥✜✩★t ✧★ ❉❑
❪
✤✢t✯✢✢✦ ❳ ❨ ✣✦✫ ❳❩ ✱ ✯✜✩❝✜ ✜✣✥ ✤✢✢✦ ✥✢✢✦
❴
✩✦ ✢✣✲✮✩✢✲ ✥✩✪✼✮✣t✩✧✦✥ ✧★ ❫ Pt✰♣✢ ✫✰✦✣✪✧ ✣❝t✩✧✦ ★✲✧✪ ★✧✲❝✢✫ t✼✲P
✤✼✮✢✦❝✢ ❄❵✲✣✦✫✢✦✤✼✲❧ ❞❑❑❙❊❆ ❥✥ ✣✮✮✼✫✢✫ t✧ ✩✦ ♠✢❝t❆ q❆❙✱ t✜✢ ♣✧✥P
✥✩✤✩✮✩t✰ ✧★ ✫✰✦✣✪✧ ✣❝t✩✧✦ ✪✩❧✜t ✤✢ ✲✢✥♣✧✦✥✩✤✮✢ ★✧✲ t✜✢ ❝✧✦t✩✦P
✼✢✫ ❧✲✧✯t✜ ★✧✼✦✫ ✩✦ ④⑤♠ ★✧✲ ❃✧ ⑥ ❑▼❙◆❆ ⑦✩✥✼✣✮✩❯✣t✩✧✦✥ ✧★ t✜✢
t✧✲ ❞ ✩✦ ★✲✧✦t ✧★ ➡ ➢ ❄➟❊ ✩✥ ➫✼✥t ✣ ❝✧✦✥✢➑✼✢✦❝✢ ✧★ t✜✢ ★✣❝t✧✲ ❙➯❞ ✩✦
t✜✢ ✫✢✬✦✩t✩✧✦ ✧★ ✢✦✢✲❧✰❆ ❹✣tt✜✣✢✼✥ ✢t ✣✮❆ ❄❙❉➓❞❊ ✼✥✢✫ t✜✢ ✥✧✮✣✲
✯✩✦✫ ✫✣t✣ ★✲✧✪ ⑦✧✰✣❧✢✲ ◗◗ t✧ ✫✢t✢✲✪✩✦✢ ➦➢ ❄➟❊ ★✲✧✪ t✜✢ ✩✦ ✥✩t✼
✪✢✣✥✼✲✢✪✢✦t✥ ✧★ ➲✱ ✯✜✩✮✢ ❵✲✣✦✫✢✦✤✼✲❧ ✢t ✣✮❆ ❄❞❑❙❙✤❊ ✣♣♣✮✩✢✫
t✜✢ t✢❝✜✦✩➑✼✢ t✧ ✪✢✣✥✼✲✩✦❧ ➦➢ ❄➟❊ ✣t ✜✩❧✜ ✜✢✮✩✧❧✲✣♣✜✩❝ ✮✣t✩t✼✫✢✥✱
✯✜✢✲✢ ➦➢ ❄➟❊ ✩✥ ✬✦✩t✢ ✣✦✫ t✼✲✦✢✫ ✧✼t t✧ ✤✢ ✤✩P✜✢✮✩❝✣✮❆ ❭✢ ✦✧✯
✣✫✧♣t t✜✢ ✥✣✪✢ ✪✢t✜✧✫ ✼✥✩✦❧ ❅✧✼✲✩✢✲ t✲✣✦✥★✧✲✪✥ ✩✦ t✜✢ ⑧ ✫✩✲✢❝P
t✩✧✦❆ ◗✦ t✜✢ ♠✼✦✱ t✜✩✥ ❝✧✲✲✢✥♣✧✦✫✥ t✧ ✪✢✣✥✼✲✩✦❧ ➲ ✣✮✧✦❧ ✣ ❞➤ ✲✩✦❧
✣t ✣ ✬❖✢✫ ♣✧✮✣✲ ✮✣t✩t✼✫✢✱ ✯✜✢✲✢ ✧✦✢ ✪✩❧✜t ✜✣✻✢ ✣ ❝✜✣✦❝✢ t✧ ✧✤P
✥✢✲✻✢ t✜✢ ★✼✮✮ ❝✩✲❝✼✪★✢✲✢✦❝✢ ✣t t✜✢ ✥✣✪✢ t✩✪✢❆ ◗✦ ❅✩❧❆ ❙❞ ✯✢ ✥✜✧✯
t✜✢ ✲✢✥✼✮t ★✧✲ t✜✲✢✢ ✻✣✮✼✢✥ ✧★ ❃✧❆
◗t t✼✲✦✥ ✧✼t t✜✣t ➦➢ ❄➟❊ ✩✥ ❝✧✪♣✣t✩✤✮✢ ✯✩t✜ ❯✢✲✧ ★✧✲ ✧✼✲ ✩✦t✢✲P
✪✢✫✩✣t✢ ✻✣✮✼✢ ✧★ ❃✧❆ ❅✧✲ ★✣✥t✢✲ ✲✧t✣t✩✧✦ ❄❃✧
❏
❑▼❙◆❊✱ ➦➢ ❄➟❊
⑧⑨P✣✻✢✲✣❧✢✫ ❳❩ ★✧✲ ❃✧ ❏ ❑▼❙◆ ✣✦✫ ❑❆◆❙ ✥✜✧✯ t✜✣t ✥t✲✼❝t✼✲✢✥ ✯✩t✜
✩✥ ✦✢❧✣t✩✻✢ ✣t ✮✣✲❧✢ ✯✣✻✢✦✼✪✤✢✲✥ ❄➟
✻✣✲✩✣t✩✧✦ ✩✦ t✜✢ ⑩ ✫✩✲✢❝t✩✧✦ ✥t✩✮✮ ✢✪✢✲❧✢ ✩✦ ★✲✧✦t ✧★ ✣ ✦✢✯ ❝✧✪P
✥t✩✮✮
♣✧✦✢✦t t✜✣t ✻✣✲✩✢✥ ✥t✲✧✦❧✮✰ ✩✦ t✜✢ ❶ ✫✩✲✢❝t✩✧✦ ✣✦✫ t✜✣t ✤✢❝✧✪✢✥
✯✣✻✢✦✼✪✤✢✲✥ ❄❑▼❙❬ ➵ ➟➨➟❀ ➵ ❑▼➔❊❆ ❅✧✲ ➟➨➟❀ ➵ ❑▼❙❬✱ t✜✢ ✪✣❧✦✢t✩❝
✥t✲✧✦❧✢✲ ✣✥ t✜✢ ✻✣✮✼✢ ✧★ ❃✧ ✩✥ ✩✦❝✲✢✣✥✢✫❆
✜✢✮✩❝✩t✰ ✩✥ ✣❧✣✩✦ ✦✢❧✣t✩✻✢❆ ➒✧✯✢✻✢✲✱ t✜✢ ✢✲✲✧✲ ✤✣✲✥ ✣✲✢ ✮✣✲❧✢ ✣✦✫
❷✼✲ ✲✢✥✼✮t✥ ★✧✲ ❃✧
❏
❑▼❙◆ ✣✦✫ ❑❆◆❙ ✪✩❧✜t ✤✢ ✢❖✣✪♣✮✢✥ ✧★
❝✧✪♣✣t✩✤✮✢
✯✩t✜
❯✢✲✧
✯✩t✜✩✦
➳
✢✲✲✧✲
➟❀ ❊ ✣✦✫ ♣✧✥✩t✩✻✢ ❄✤✼t
✤✣✲✥❊
✣t
✩✦t✢✲✪✢✫✩✣t✢
✲✧t✣t✩✧✦ ✩✥ ✣✮✲✢✣✫✰ ✥✧ ★✣✥t t✜✣t ✥t✲✼❝t✼✲✢ ★✧✲✪✣t✩✧✦ ✻✩✣ ⑤❸❹❺◗ ✩✥
✣ ✫✰✦✣✪✧ ❝✧✼♣✮✢✫ t✧ ⑤❸❹❺◗❆ ♠✼❝✜ ❝✧✼♣✮✢✫ ✥✰✥t✢✪✥ ✣✲✢ ✢❖P
✩✪♣✧✥✥✩✤✮✢❆ ◗t ✩✥ t✜✢✲✢★✧✲✢ ✼✦❝✮✢✣✲ ✯✜✢t✜✢✲ ✪✢✣✦✩✦❧★✼✮ ❝✧✦❝✮✼P
♣✢❝t✢✫ t✧ ✜✣✻✢ ✣✦ ✧✻✢✲✣✮✮ ✢✦✜✣✦❝✢✪✢✦t ✧★ ❧✲✧✯t✜❆ ❍✜✩✥ ♣✧✥✥✩P
✥✩✧✦✥ ❝✣✦ ✤✢ ✫✲✣✯✦ ★✲✧✪ ✧✼✲ ✲✢✥✼✮t✥❆
✤✩✮✩t✰✱ ✯✜✩❝✜ ✩✥ ✦✧t ✩✦❝✮✼✫✢✫ ✩✦ t✜✢ ♣✲✢✥✢✦t ✪✢✣✦P✬✢✮✫ ✪✧✫✢✮✱
◗✦ t✜✢ ✦✧✲t✜✢✲✦ ✜✢✪✩✥♣✜✢✲✢ ✧★ t✜✢ ♠✼✦✱ ✣ ✤✩P✜✢✮✩❝✣✮ ✥♣✢❝t✲✼✪
✜✣✥ ✲✢❝✢✦t✮✰ ✤✢✢✦ ✫✢✪✧✦✥t✲✣t✢✫ ✩✦ ✥♣✜✢✲✩❝✣✮ ❧✢✧✪✢t✲✰ ❄❻✣✤✤✣✲✩
✩✥ ✢❖♣✢❝t✢✫ ✯✜✢✲✢ ✪✣❧✦✢t✩❝ ✜✢✮✩❝✩t✰ ✩✥ ✦✢❧✣t✩✻✢ ✧✦ ✣✮✮ ✥❝✣✮✢✥ ✢❖P
❴
✢t ✣✮❆ ❞❑❙◆❊ ✤✰ ❝✧✼♣✮✩✦❧ ✣✦ ❫
✫✰✦✣✪✧ t✧ ⑤❸❹❺◗❆ ❼✧✧❽✩✦❧ ✣t
❝✢♣t t✜✢ ✮✣✲❧✢✥t ✧✦✢✥✱ ✯✜✢✲✢ t✜✢ ❫ ✢➸✢❝t ✧♣✢✲✣t✢✥❆ ❍✜✩✥ ✥✢✦✥✢
❅✩❧❆ ❞✱ ✯✢ ❝✧✦❝✮✼✫✢ t✜✣t ★✧✲ ❃✧ ⑥ ❑▼❙◆ t✜✢ ❝✧✼♣✮✢✫ ✥✰✥t✢✪ ✯✩t✜
✩✥ ✲✢✻✢✲✥✢✫ ✩✦ t✜✢ ✥✧✮✣✲ ✯✩✦✫ ★✣✲ ★✲✧✪ t✜✢ ♠✼✦ ❄❵✲✣✦✫✢✦✤✼✲❧
⑤❸❹❺◗ ✣✦✫ ✫✰✦✣✪✧ ✩✦✥t✣✤✩✮✩t✰ ✩✥ ✢❖❝✩t✢✫ ✩✦ ✣ ❝✣✥✢ ✯✜✢✲✢ t✜✢ ✫✰P
✢t ✣✮❆ ❞❑❙❙✤❊❆ ❍✜✩✥ ✜✣✥ ✣✮✥✧ ✤✢✢✦ ✥✢✢✦ ✩✦ ✥✩✪✼✮✣t✩✧✦✥ ✧★ ✪✣❧P
✦✣✪✧ ✣✮✧✦✢ ✯✧✼✮✫ ✦✧t ✤✢ ✢❖❝✩t✢✫ ✣✦✫ t✜✣t t✜✢ ❧✲✧✯t✜ ✲✣t✢ ✤✢❧✩✦✥
✦✢t✩❝ ✢➫✢❝t✣ ★✲✧✪ ✣ ✫✰✦✣✪✧P✣❝t✩✻✢ ✥♣✜✢✲✢ ❄❭✣✲✦✢❝❽✢ ✢t ✣✮❆ ❞❑❙❙❊✱
➺➻✸☞ ✆✁❣❡ ✍ ♦❢ ✶✷
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
♠✦❝✗ ✪✗✚ ❛❜✧♣✢✦✪✚ ★❛✢✦✚✧ ♣❙ ✪✗✚✧✚ ✧✜✚❝✪✬❛ ❛✬✚ ❜✚✢♣✖ ✪✗✚✘✬ ♠❛✛✮
✘♠✦♠ ✜♣✧✧✘❜✢✚ ★❛✢✦✚✧ ✩✘★✚✣ ❜✙ ✪✗✚ ❝♣✬✬✚✧✜♣✣✤✘✣✩ ✬✚❛✢✘❩❛❜✘✢✘✪✙
❝♣✣✤✘✪✘♣✣✧❘ ⑤❪❫ ⑤❬❭✴ ❴ ❵❫ ❛✣✤ ⑤❪❥ ⑤❭✴❬ ❴ ❵ ❥ ❘ ✬✚✧✜✚❝✪✘★✚✢✙✲
❚✗✚ ✧✜✚❝✪✬❛ ✧✗♣✖ ✪✗❛✪❘ ✖✗✘✢✚ ✪✗✚ ★✚✢♣❝✘✪✙ ❛✣✤ ♠❛✩✣✚✪✘❝ ♦✚✢✤✧
✗❛★✚ ✧✘✩✣✘♦❝❛✣✪ ✗✚✢✘❝✘✪✙ ♣✣✢✙ ❛✪ ✪✗✚ ✢❛✬✩✚✧✪ ✧❝❛✢✚❘ ✪✗✚✙ ✬✚♠❛✘✣
❝✢✚❛✬✢✙ ❜✚✢♣✖ ✪✗✚✘✬ ♠❛✛✘♠✦♠ ✜♣✧✧✘❜✢✚ ★❛✢✦✚✧✲ q✪ ✢❛✬✩✚ ✧❝❛✢✚✧
✯✧♠❛✢✢ ❬✻❘ ❜♣✪✗ ✗✚✢✘❝✘✪✘✚✧ ❛✬✚ ✣✚✩❛✪✘★✚ ✯✘✣✤✘❝❛✪✚✤ ❜✙ ♣✜✚✣ ✧✙♠✮
❜♣✢✧✻❘ ❜✦✪ ✪✗✚ ♠❛✩✣✚✪✘❝ ✗✚✢✘❝✘✪✙ ✘✧ ✜✬✚✤♣♠✘✣❛✣✪✢✙ ✜♣✧✘✪✘★✚ ❛✪
✖❛★✚✣✦♠❜✚✬✧ ✧✢✘✩✗✪✢✙ ❜✚✢♣✖ ❬② ✲ ❚✗✘✧ ✘✧ ❝♣✣✧✘✧✪✚✣✪ ✖✘✪✗ ❨✘✩✲ ✹✴❘
✖✗✘❝✗ ❛✢✧♣ ✧✗♣✖✧ ✜♣✧✘✪✘★✚ ★❛✢✦✚✧❘ ❛✢✪✗♣✦✩✗ ♣✣✢✙ ✘✣ ✪✗✚ ❝❛✧✚ ♣❙
❙❛✧✪✚✬ ✬♣✪❛✪✘♣✣ ✯③♣ ④ ✵⑥✹❯✻✲ ⑦✚✢♣✖ ✪✗✚ ❙♣✬❝✘✣✩ ✧❝❛✢✚❘ ❜♣✪✗ ✚✣✮
✚✬✩✙ ✧✜✚❝✪✬❛ ✧✗♣✖ ❛ ❬⑧⑨⑩ ✧✜✚❝✪✬✦♠❘ ✖✗✘❝✗ ✘✧ ✧✗❛✢✢♣✖✚✬ ✪✗❛✣ ✪✗✚
✖✗✘✪✚ ✣♣✘✧✚ ✧✜✚❝✪✬✦♠ ✯❬⑩ ✻ ❛✣✤ ✧✘♠✘✢❛✬ ✪♣ ✖✗❛✪ ✗❛✧ ❜✚✚✣ ✧✚✚✣ ✘✣
✗✚✢✘❝❛✢✢✙ ✤✬✘★✚✣ ✤✙✣❛♠♣✧ ✯⑦✬❛✣✤✚✣❜✦✬✩ ✴✵✵✹✻✲ ✰✚ ❛✢✧♣ ✣♣✪✚ ✪✗✚
✦✜✬✘✧✚ ♣❙ ♠❛✩✣✚✪✘❝ ❛✣✤ ✱✘✣✚✪✘❝ ✜♣✖✚✬ ❛✪ ✪✗✚ ✧♠❛✢✢✚✧✪ ✖❛★✚✣✦♠✮
❜✚✬ ✯❬ ④ ❬❶ ✻❘ ✖✗✘❝✗ ✘✧ ❛✩❛✘✣ ✧✘♠✘✢❛✬ ✪♣ ✗✚✢✘❝❛✢✢✙ ✤✬✘★✚✣ ✤✙✣❛♠♣✧✲
❷♣✖✚★✚✬❘ ✘✪ ✘✧ ✗✚✬✚ ✣♣✪ ❛✧ ✧✪✬♣✣✩ ❛✧ ✘✣ ✪✗✚ ✤✙✣❛♠♣ ❝❛✧✚✲
❸❹ ❺❻❼❽❿➀➁➂❻❼➁ ➃❼➄ ➄➂➁❽➀➁➁➂❻❼
❋✐❣✳ ✶✆✳ ◆✝r✞✟❧✠✡❡❞ ✞✟☛♥❡t✠☞ ❤❡❧✠☞✠t✌ s✍❡☞tr✟ ❢✝r ❞✠✎❡r❡♥t ✈✟❧✉❡s ✝❢
t❤❡ ❈✝r✠✝❧✠s ♥✉✞✏❡r✁ ❈✝✑ ■♥ ✟❧❧ ✍✟♥❡❧s✁ t❤❡ s✟✞❡ r✟♥☛❡ ✠s s❤✝✇♥✁
✏✉t ❢✝r ❈✝ ❂ ✂✒ t❤❡ ♥✝r✞✟❧✠✡❡❞ ❤❡❧✠☞✠t✌ ❡①☞❡❡❞s t❤✠s r✟♥☛❡ ✟♥❞
r❡✟☞❤❡s ❾✂✒✂✺✑
❋✐❣✳ ✶✓✳ ❑✠♥❡t✠☞ ✟♥❞ ✞✟☛♥❡t✠☞ ❡♥❡r☛✌ ✟♥❞ ❤❡❧✠☞✠t✌ s✍❡☞tr✟ ☞✝✞✍✉t❡❞
❢r✝✞ t❤❡ ❢✉❧❧ ✸✔ ❞✟t✟ s❡t ❢✝r ❈✝ ❂ ✂✒✂✸✑ P✝s✠t✠✈❡ ✭♥❡☛✟t✠✈❡☎ ✈✟❧✉❡s
✝❢ s✍❡☞tr✟❧ ❤❡❧✠☞✠t✌ ✟r❡ ✠♥❞✠☞✟t❡❞ ✇✠t❤ Þ❧❧❡❞ ✭✝✍❡♥☎ s✌✞✏✝❧s✑ ❲❡ ♥✝t❡
t❤❡ ❡♥❤✟♥☞❡✞❡♥t ✝❢ s✍❡☞tr✟❧ ✍✝✇❡r ✟t t❤❡ s✞✟❧❧❡st ✇✟✈❡♥✉✞✏❡r ✝❢ t❤❡
❞✝✞✟✠♥✁ ❦✕ ✑
✖✗✘❝✗ ♠❛✙ ❜✚ ✚✛✜✢❛✘✣✚✤ ❜✙ ❛ ✤✘✥✦✧✘★✚ ♠❛✩✣✚✪✘❝ ✗✚✢✘❝✘✪✙ ✪✬❛✣✧✮
✜♣✬✪ ✯✰❛✬✣✚❝✱✚ ✚✪ ❛✢✲ ✴✵✹✴✻✲
✼✾✿✾ ❊❀❁❃❄❅ ❇❀❉ ●❁❍❏▲❏▼❅ ❖◗❁▲▼❃❇
❚♣ ✜✦✪ ✪✗✚ ❛❜♣★✚ ❝♣✣✧✘✤✚✬❛✪✘♣✣✧ ✘✣ ✬✚✢❛✪✘♣✣ ✪♣ ✪✗✚ ❛❝✪✦❛✢ ✗✚✢✘❝✘✪✙
❝♣✣✪✚✣✪❘ ✖✚ ✣♣✖ ❝♣♠✜❛✬✚ ✖✘✪✗ ✪✗✚ ♠❛✩✣✚✪✘❝ ❛✣✤ ✱✘✣✚✪✘❝ ✚✣✚✬✩✙
❛✣✤ ✗✚✢✘❝✘✪✙ ✧✜✚❝✪✬❛ ❝♣♠✜✦✪✚✤ ❙✬♣♠ ✪✗✚ ❙✦✢✢✙ ❯❱ ✤❛✪❛ ✧✚✪❳ ✧✚✚
❨✘✩✲ ✹❯✲ ❚✗✚ ♠❛✩✣✚✪✘❝ ❛✣✤ ✱✘✣✚✪✘❝ ✗✚✢✘❝✘✪✙ ✧✜✚❝✪✬❛ ❛✬✚ ✣♣✬♠❛✢✮
✘❩✚✤ ❜✙ ❬❭✴ ❛✣✤ ✹❭✴❬❘ ✬✚✧✜✚❝✪✘★✚✢✙❘ ✧♣ ✪✗❛✪ ♣✣✚ ❝❛✣ ✚✧✪✘♠❛✪✚ ✗♣✖
❆✽✸✁ ✍✟☛❡ ✄✂ ✝❢ ✄✷
❚✗✚ ✜✬✚✧✚✣✪ ✖♣✬✱ ✗❛✧ ❝♣✣♦✬♠✚✤ ✪✗✚ ✬❛✪✗✚✬ ✧✪✬✘✣✩✚✣✪ ✬✚✧✪✬✘❝✪✘♣✣✧
♣❙ ➅⑦➆➇➈❘ ✧✗♣✖✘✣✩ ✪✗❛✪ ➉➊➇➋➌ ✘✧ ❛✢✬✚❛✤✙ ✧✦✜✜✬✚✧✧✚✤ ❙♣✬
✬❛✪✗✚✬ ✖✚❛✱ ✬♣✪❛✪✘♣✣ ✯③♣ ➍
➎ ✵⑥✵❯✻✲ ❚✗✘✧ ✤✚♠♣✣✧✪✬❛✪✚✧ ✪✗✚ ✜✬✚✮
✤✘❝✪✘★✚ ✜♣✖✚✬ ♣❙ ✪✗♣✧✚ ✚❛✬✢✘✚✬ ➇❨➏✲ ➐✣ ✪✗✚ ♣✪✗✚✬ ✗❛✣✤❘ ✘✪ ❛✢✧♣
✧✗♣✖✧ ✪✗❛✪ ✪✗✚ ❝♣✣✧✘✤✚✬❛✪✘♣✣ ♣❙ ✪✗✚ ♠✚✬✚ ✚✛✘✧✪✚✣❝✚ ♣❙ ❛ ✣✚✩❛✪✘★✚
✚✥✚❝✪✘★✚ ♠❛✩✣✚✪✘❝ ✜✬✚✧✧✦✬✚ ✘✧ ✣♣✪ ✧✦➑❝✘✚✣✪✲ ✰✚ ✱✣✚✖ ❛✢✬✚❛✤✙
✪✗❛✪ ✧✦➑❝✘✚✣✪✢✙ ✧✪✬♣✣✩ ✧✪✬❛✪✘♦❝❛✪✘♣✣ ❛✣✤ ✧❝❛✢✚ ✧✚✜❛✬❛✪✘♣✣ ❛✬✚ ✪✖♣
✘♠✜♣✬✪❛✣✪ ✣✚❝✚✧✧❛✬✙ ❝♣✣✤✘✪✘♣✣✧✲ ➌✣ ✪✗✘✧ ✧✚✣✧✚❘ ✪✗✚ ✚✛✘✧✪✚✣❝✚ ♣❙
➉➊➇➋➌ ♠✘✩✗✪ ❜✚ ❛ ♠♣✬✚ ❙✬❛✩✘✢✚ ✜✗✚✣♣♠✚✣♣✣ ✪✗❛✪ ✪✗✚ ✚✛✘✧✪✚✣❝✚
♣❙ ❛ ✣✚✩❛✪✘★✚ ♠❛✩✣✚✪✘❝ ✜✬✚✧✧✦✬✚❘ ✖✗✘❝✗ ✘✧ ❙❛✘✬✢✙ ✬♣❜✦✧✪ ❛✣✤ ❝❛✣
❜✚ ★✚✬✘♦✚✤ ✚★✚✣ ✘✣ ❛❜✧✚✣❝✚ ♣❙ ✧✪✬❛✪✘♦❝❛✪✘♣✣ ✯⑦✬❛✣✤✚✣❜✦✬✩ ✚✪ ❛✢✲
✴✵✹✵✻✲ ❨♣✬ ✪✗✚ ✬❛✪✗✚✬ ✧♠❛✢✢ ③♣✬✘♣✢✘✧ ✣✦♠❜✚✬✧ ❝♣✣✧✘✤✚✬✚✤ ✗✚✬✚❘ ✣♣
♠✚❛✧✦✬❛❜✢✚ ❝✗❛✣✩✚ ♣❙ ➒➓ ✖❛✧ ✧✚✚✣ ✘✣ ✪✗✚ ✧✘♠✦✢❛✪✘♣✣✧❘ ✖✗✘❝✗ ✘✧
✘✣ ❛✩✬✚✚♠✚✣✪ ✖✘✪✗ ♣✦✬ ✪✗✚♣✬✙ ✜✬✚✤✘❝✪✘✣✩ ✪✗❛✪ ✪✗✚ ❝✗❛✣✩✚ ✘✧ ♣❙ ✪✗✚
♣✬✤✚✬ ③♣⑩ ✲
q✜✜✢✘✚✤ ✪♣ ✪✗✚ ➏✦✣ ✖✘✪✗ ➔ ④ ✴ × ✹✵→➣ ✧→❶ ❘ ✪✗✚ ✧✪✬♣✣✩ ✧✚✣✧✘✮
✪✘★✘✪✙ ♣❙ ✪✗✚ ✘✣✧✪❛❜✘✢✘✪✙ ✪♣ ✖✚❛✱ ✬♣✪❛✪✘♣✣ ✘♠✜✢✘✚✧ ✪✗❛✪ ➉➊➇➋➌ ❝❛✣
♣✣✢✙ ✜✢❛✙ ❛ ✬♣✢✚ ✘✣ ✪✗✚ ✦✜✜✚✬♠♣✧✪ ✢❛✙✚✬✧❘ ✖✗✚✬✚ ✪✗✚ ❝♣✬✬✚✢❛✪✘♣✣
✪✘♠✚ ✘✧ ✧✗♣✬✪✚✬ ✪✗❛✣ ③♣❭✴➔ ↔ ✴ ✗♣✦✬✧✲ q✢✪✗♣✦✩✗ ✪✗✘✧ ★❛✢✦✚ ♠✘✩✗✪
❝✗❛✣✩✚ ✖✘✪✗ ❛ ❝✗❛✣✩✘✣✩ ✤✚✩✬✚✚ ♣❙ ✧✪✬❛✪✘♦❝❛✪✘♣✣❘ ✪✗✘✧ ✖♣✦✢✤ ❜✚
✧✦✬✜✬✘✧✘✣✩ ❛✧ ✘✪ ✖♣✦✢✤ ✚✛❝✢✦✤✚ ✚★✚✣ ✪✗✚ ✢♣✖✚✬ ✜❛✬✪✧ ♣❙ ✪✗✚ ✧✦✜✚✬✮
✩✬❛✣✦✢❛✪✘♣✣ ✢❛✙✚✬❘ ✖✗✚✬✚ ↕ ✘✧ ♣❙ ✪✗✚ ♣✬✤✚✬ ♣❙ ♣✣✚ ✤❛✙✲ ➐✣ ✪✗✚ ♣✪✗✚✬
✗❛✣✤❘ ✖✚ ✗❛★✚ ✪♣ ✱✚✚✜ ✘✣ ♠✘✣✤ ✪✗❛✪ ♣✦✬ ❝♣✣❝✢✦✧✘♣✣✧❘ ✖✗✘❝✗ ❛✬✚
❜❛✧✚✤ ♣✣ ✘✧♣✪✗✚✬♠❛✢ ♠♣✤✚✢✧❘ ✧✗♣✦✢✤ ❜✚ ✪❛✱✚✣ ✖✘✪✗ ❝❛✬✚✲ ➌✪ ✖♣✦✢✤
✪✗✚✬✚❙♣✬✚ ❜✚ ✦✧✚❙✦✢ ✪♣ ✚✛✪✚✣✤ ✪✗✚ ✜✬✚✧✚✣✪ ✧✪✦✤✘✚✧ ✪♣ ✜♣✢✙✪✬♣✜✘❝
✢❛✙✚✬✧ ✖✗✚✬✚ ✪✗✚ ✧❝❛✢✚ ✗✚✘✩✗✪ ★❛✬✘✚✧ ✖✘✪✗ ✤✚✜✪✗✲ ✰✚ ❛✢✧♣ ✣♣✪✚ ✪✗❛✪
✖✚❛✱ ✬♣✪❛✪✘♣✣ ✯③♣ ④ ✵⑥✵❯✻ ✚✣✗❛✣❝✚✧ ✪✗✚ ✧✦✬❙❛❝✚ ❛✜✜✚❛✬❛✣❝✚✲ q✪
✪✗✚ ✧❛♠✚ ✪✘♠✚❘ ❛✧ ✖✚ ❛✬✩✦✚✤ ✘✣ ➏✚❝✪✲ ➙✲✹❘ ✪✗✚ ✧✘✣✱✘✣✩ ♣❙ ✧✪✬✦❝✪✦✬✚✧
❜✚❝♣♠✚✧ ✢✚✧✧ ✜✬♣♠✘✣✚✣✪❘ ✖✗✘❝✗ ✧✦✩✩✚✧✪✧ ✪✗❛✪ ✪✗✚✙ ♠✘✩✗✪ ✬✚♠❛✘✣
❝♣✣♦✣✚✤ ✪♣ ✪✗✚ ✧✦✬❙❛❝✚ ✢❛✙✚✬✧✲ ❷♣✖✚★✚✬❘ ✜✬✚✢✘♠✘✣❛✬✙ ➇❨➏ ✤♣ ✣♣✪
✘✣✤✘❝❛✪✚ ❛ ✧✘✩✣✘♦❝❛✣✪ ✤✚✜✚✣✤✚✣❝✚ ♣❙ ✪✗✚ ✚✘✩✚✣❙✦✣❝✪✘♣✣ ♣✣ ③♣ ❙♣✬
★❛✢✦✚✧ ❜✚✢♣✖ ✵✲✹✲ ➐✦✬ ✘✣✪✚✬✜✬✚✪❛✪✘♣✣❘ ✘❙ ❝♣✬✬✚❝✪❘ ✖♣✦✢✤ ✪✗✚✬✚❙♣✬✚
✣✚✚✤ ✪♣ ❜✚ ❛ ✬✚✧✦✢✪ ♣❙ ✣♣✣✢✘✣✚❛✬✘✪✙✲
➌❙ ✖✚ ✖✚✬✚ ✪♣ ❛✜✜✢✙ ➉➊➇➋➌ ✪♣ ✪✗✚ ❙♣✬♠❛✪✘♣✣ ♣❙ ❛❝✪✘★✚ ✬✚✩✘♣✣✧
✘✣ ✪✗✚ ➏✦✣❘ ✖✚ ✧✗♣✦✢✤ ✱✚✚✜ ✘✣ ♠✘✣✤ ✪✗❛✪ ✪✗✚ ✧❝❛✢✚ ♣❙ ✧✪✬✦❝✪✦✬✚✧
✖♣✦✢✤ ❜✚ ➛➜➝ ✜✬✚✧✧✦✬✚ ✧❝❛✢✚ ✗✚✘✩✗✪✧ ✯➆✚♠✚✢ ✚✪ ❛✢✲ ✴✵✹✴❛✻✲ q✪
✪✗✚ ✤✚✜✪✗ ✖✗✚✬✚ ✪✗✚ ✪✦✬✣♣★✚✬ ✪✘♠✚ ✘✧ ❛❜♣✦✪ ✪✖♣ ✗♣✦✬✧❘ ✖✚ ✚✧✪✘✮
♠❛✪✚ ✪✗✚ ✬♠✧ ★✚✢♣❝✘✪✙ ✪♣ ❜✚ ❛❜♣✦✪ ➞✵✵ ♠➟✧❘ ✧♣ ✪✗✚ ✧❝❛✢✚ ✗✚✘✩✗✪
✖♣✦✢✤ ❜✚ ❛❜♣✦✪ ❯ ➇♠❘ ❝♣✬✬✚✧✜♣✣✤✘✣✩ ✪♣ ❛ ➉➊➇➋➌ ✧❝❛✢✚ ♣❙ ❛✪
✢✚❛✧✪ ✴✵ ➇♠✲ ❚✗✘✧ ♠✘✩✗✪ ✧✪✘✢✢ ❜✚ ♣❙ ✘✣✪✚✬✚✧✪ ❙♣✬ ✚✛✜✢❛✘✣✘✣✩ ✜✢❛✩✚
✬✚✩✘♣✣✧ ✘✣ ✪✗✚ ➏✦✣✲ ③✢✚❛✬✢✙❘ ♠♣✬✚ ✖♣✬✱ ✦✧✘✣✩ ✬✚❛✢✘✧✪✘❝ ♠♣✤✚✢✧
✖♣✦✢✤ ❜✚ ✬✚➠✦✘✬✚✤ ❙♣✬ ♠❛✱✘✣✩ ♠♣✬✚ ❝♣✣❝✢✦✧✘★✚ ✧✪❛✪✚♠✚✣✪✧✲
➈✚✩❛✬✤✘✣✩ ✪✗✚ ✜✬♣✤✦❝✪✘♣✣ ♣❙ ✱✘✣✚✪✘❝ ✗✚✢✘❝✘✪✙ ❛✣✤ ✪✗✚ ✜♣✧✧✘❜✢✚
✤✚✪✚❝✪✘♣✣ ♣❙ ❛ ♠❛✩✣✚✪✘❝ ✗✚✢✘❝✘✪✙ ✧✜✚❝✪✬✦♠❘ ♣✦✬ ✬✚✧✦✢✪✧ ✧✦✩✩✚✧✪
■
t❤✟t
t❤✠
✡✠☛✟t☞✈✠
♠✟✌✍✠t☞❝
❤✠☛☞❝☞t②
❘ ▲♦s✁✂✁ ❡✄ ✁❛ ✿ ❈♦☎✆❡✄✐♥❣ ❡✝❡✞✄s ✐♥ ✞♦♥✞❡♥✄r✁✄✐♥❣ ☎✁❣♥❡✄✐✞ ß✉①
❝✟✍✍✎t
❜✠
✠✏✑✠❝t✠✒
t✎
❜✠
ö ❂ Ú ✯Ú✢ Ú
ö ö
✇❤✠✡✠ Ú ❂ ê✯êëì ✢ Ú
Ï
Ï
Ï Ñ ❂ ÚÏ Ú Ñ ✢ ✟✍✒
♠✎✡✠ t❤✟✍ ✟❜✎✓t ✵✔✵✕✔ ❚❤☞✖ ☞✖ ✟ ❝✎✍✖✠✗✓✠✍❝✠ ✎❢ ❝✎✡✡✠✖✑✎✍✒☞✍✌☛②
☛✎✇ ✈✟☛✓✠✖ ✎❢ ❦☞✍✠t☞❝ ❤✠☛☞❝☞t②✔ ❲✠ Þ✍✒ t❤✟t t❤✠ ✍✎✡♠✟☛☞❧✠✒ ❦☞✲
✍✠t☞❝ ❤✠☛☞❝☞t② ☞✖ ✌☞✈✠✍ ❜② ✘✙
✚ ✷✛✡ ✜✎✔ ❋✎✡ t❤✠ ❙✓✍✢ ✇✠ ✠✏✲
❾✶
✑✠❝t ✛✡ ❂ ✭✣✙ ❍✤ ✮
✚ ✵✳✕✻✢ ✇❤☞❝❤ ✟✌✡✠✠✖ ✇☞t❤ ✇❤✟t ☞✖ ✓✖✠✒
☞✍ ✎✓✡ ✖☞♠✓☛✟t☞✎✍✖❀ t❤✓✖ t❤✠✡✠ ☞✖ ✍✎t ♠✓❝❤ ✡✎✎♠ ❢✎✡ ♠✎✡✠ ✎✑✲
t☞♠☞✖t☞❝
✠✖t☞♠✟t✠✖✔
✥✍ t❤☞✖ ❝✎✍✍✠❝t☞✎✍ ✇✠
✖❤✎✓☛✒
✍✎t✠
t❤✟t
☞✍
ø
Ø
✶ ❂
✷✬
t❤✠ ♠☞✏☞✍✌ ☛✠✍✌t❤ ✇☞t❤ ✪✧★✩
✚
❂ ✪✧★✩ ❍♣ ❢✎✡
✕✳✻ ❜✠☞✍✌ ✟✍ ✠♠✑☞✡☞❝✟☛ ✑✟✡✟♠✲
✠t✠✡✔ ❋✎✡ ☞✖✠✍t✡✎✑☞❝ ✖t✡✟t☞Þ❝✟t☞✎✍✢ t❤✠ ✑✡✠✖✖✓✡✠ ✖❝✟☛✠ ❤✠☞✌❤t ❍♣
☞✖ ✡✠☛✟t✠✒ t✎ ❍✤ ✈☞✟ ✫❍♣
✚
❍✤ ✔ ❲☞t❤ ✣✙
❂
✷✬✯✦✧★✩ ✇✠ ✎❜t✟☞✍
❾✶
✚ ✵✳✕✻✔ ❲✠ ✍✎t✠ ❤✠✡✠
✣✙ ❍✤ ❂ ✷✬ ✫✯✪✧★✩ ✚ ✷✬✢ ✖✎ ✛✡ ❂ ✭✣✙ ❍✤ ✮
ï
Õ✮
ã ✕ Û
î
Õ
ø
Ø
Ö ❂ ã
ø
á
✶ ❂
✟✡❝t✟✍✭
✭Õ Ô ✕✮
Õ
✷✬
î
í
✟✡❝t✟✍✭
✭Õ Ô ✼✮
✷Õ
ã ✼ Û
Õ
î
í
✬
ï
Õ✮
î
Õ
❾✶
❑✠♠✠☛ ✠t ✟☛✔ ✭✷✵✕✷✟✮ t❤✠ ✈✟☛✓✠ ✎❢ ✣✙ ❍✤ ✭❂ ✛✡
✮ ✇✟✖ ✠✖t☞♠✟t✠✒
❜✟✖✠✒ ✎✍ ✖t✠☛☛✟✡ ♠☞✏☞✍✌ ☛✠✍✌t❤ t❤✠✎✡②✢ ✓✖☞✍✌ ✦✧★✩
î
í
✭Õ Ô ✕✮
Ö
✟✡❝t✟✍✭
Ö
Õ✮
ï
ðÕ
ã
î
ã ✕ Û
✼
Õ
ø
ø
ø
ø
á
Ö ❂ ØÖ ã ❒ Ø✶ Ô ✼ðá ✶ Û
ø
ø
ø
á
â ❂ Ø✶ ã ðá ✶ ✳
✭Ü✔❐✮
t❤✟t✢ ✎✇☞✍✌ t✎ ✟ ♠☞✖t✟❦✠✢ ✇✠ ✓✍✒✠✡✠✖t☞♠✟t✠✒ t❤✠ ✈✟☛✓✠ ✎❢ ✣✙ ❍✤
❜② ✟ ❢✟❝t✎✡ ✎❢ ✷✔✻✔ ❚❤☞✖ ❢✟❝t✎✡ ✟☛✖✎ ❤✟✖ ✟✍ ✠✍❤✟✍❝☞✍✌ ✠✰✠❝t ✎✍ t❤✠
✥✍ t❤✠ ❝✟✖✠ ✎❢ Õ ñ ✕ t❤✠✖✠ ❢✓✍❝t☞✎✍✖ ✟✡✠ ✌☞✈✠✍ ❜②
✌✡✎✇t❤ ✡✟t✠ ✎❢ ◆❊▼✱✥✔ ❚❤✠ ❝✎✡✡✠❝t ✈✟☛✓✠ ✖❤✎✓☛✒ t❤✠✍ ❜✠ ☛✟✡✌✠✡
✟✍✒ ✇✎✓☛✒ ✍✎✇ ❜✠ ❝☛✠✟✡☛② ❢✟✖t✠✡ t❤✟✍ t❤✠ t✓✡❜✓☛✠✍tÐ✒☞✰✓✖☞✈✠ ✡✟t✠✔
ø ✭Õ✮ ò
Ø
✶
❜✠✌☞✍✖ t✎ ❜✠ ✖✓✑✑✡✠✖✖✠✒ ❜② ✡✎t✟t☞✎✍✢ ✠✰✠❝t✖ ✡✠☛✟t✠✒ t✎ ✒②✍✟♠✎
ø ✭Õ✮ ò
á
✶
ç
✕
✕ ã
ð
❐✬
ä
ÕÛ
✕ð
ç
✕
✕ ã
ó✬
ø ✭Õ✮ ò ã
Ø
Ö
Õ Û
✼
❋✓✡t❤✠✡♠✎✡✠✢ ✟✖ ✇✠ ❤✟✈✠ ✖❤✎✇✍ ❤✠✡✠✢ ✟t t❤✠ ✑✎☞✍t ✇❤✠✡✠ ◆❊▼✱✥
✟❝t☞✎✍ ✡✠☞✍❢✎✡❝✠ t❤✠ ❝✎✍❝✠✍t✡✟t☞✎✍ ✎❢ ✴✓✏✢ ✠✈✠✍ t❤✎✓✌❤ t❤✠ ✒②✲
ä
❐✬
Õ ô
❒
✕ð
✍✟♠✎ ✟☛✎✍✠ ✇✎✓☛✒ ✍✎t ②✠t ❜✠ ✠✏❝☞t✠✒✔ ✥✍ t❤☞✖ ✖✠✍✖✠✢ t❤✠ ✖t✡☞✍✌✠✍t
✡✠✖t✡☞❝t☞✎✍✖ ✎❢ ✸✹❑▼✺ ❢✡✎♠ ▼❋❙ ✟✑✑✠✟✡ ✍✎✇ ☛✠✖✖ ✖t✡☞✍✌✠✍t ☞✍
✥✍ t❤✠ ❝✟✖✠ ✎❢ Õ õ ✕ t❤✠✖✠ ❢✓✍❝t☞✎✍✖ ✟✡✠ ✌☞✈✠✍ ❜②
❉◆❙✔ ✥t ♠☞✌❤t ❜✠ ❤✎✑✠✒ t❤✟t t❤☞✖ ✍✠✇ ❢✠✟t✓✡✠ ❝✟✍ ✠✈✠✍t✓✟☛☛② ❜✠
✡✠✑✡✎✒✓❝✠✒ ❜② ▼❋❙✢ ✖✓❝❤ ✟✖ t❤✎✖✠ ✎❢ ❏✟❜❜✟✡☞ ✠t ✟☛✔ ✭✷✵✕✼✮ t❤✟t
t✟❦✠ t❤✠ ✪ ✠✰✠❝t ☞✍t✎ ✟❝❝✎✓✍t✔
❆✽✾❁❃❄❅❇●❖❇P❇❁◗❯❱
✬
ø ✭Õ✮ ò
Ø
✶
Ö
Û
Õ
Õ
❳❨ ❩❬❭❪❫ ❴❵❨❪ ❴❨❞❨❥ q❵③ ❬❨❥④q⑤❥ ⑥❵❞❞❨❪❩⑦ ⑥❵❪⑥❨③❪⑧
✬
ø ✭Õ✮ ò
á
✶
Ö
ó✬
Ô
Û
Õ
Õ
❐✬
ã
î
❐
Ö
✬
ø ✭Õ✮ ò ã
Ø
î
Ö
❐✬
ã
î
ô
✼Õ
Õ
⑨❪⑩ ❩❬❨ ⑨❪❶⑤❨❪⑥❨ ❵q ❞❭⑩❪❨❩⑨⑥ ⑦❩③⑤⑥❩⑤③❨ q❵③❞❭❩⑨❵❪ ❵❪ ❩❬❨ ❞❨❭⑦⑤③❨❞❨❪❩ ❵q ❷❸❹
❭❪❺ ❻❸ ⑨❪ ❼❽❿ ❭❪❺ ❭❪ ❭❪❵❪➀❞❵⑤⑦ ③❨q❨③❨❨ q❵③ ⑤⑦❨q⑤❥ ⑦⑤⑩⑩❨⑦❩⑨❵❪⑦ ❩❬❭❩ ❬❭➁❨
❥❨❺ ❩❵ ⑨❞④③❵➁❨❞❨❪❩⑦ ⑨❪ ❩❬❨ ④③❨⑦❨❪❩❭❩⑨❵❪ ❭❪❺ ❭ ❞❵③❨ ❩❬❵③❵⑤⑩❬ ❭❪❭❥➀⑦⑨⑦➂ ➃❬⑨⑦
÷Ýù
ú ✟✡✠ ✌☞✈✠✍ ❜②
❚❤✠ ❢✓✍❝t☞✎✍✖ Øà ✭Ú✮
➄❵③❫ ➄❭⑦ ⑦⑤④④❵③❩❨❺ ⑨❪ ④❭③❩ ➅➀ ❩❬❨ ➆⑤③❵④❨❭❪ ➇❨⑦❨❭③⑥❬ ➈❵⑤❪⑥⑨❥ ⑤❪❺❨③ ❩❬❨
➉⑦❩③❵❼➀❪ ➇❨⑦❨❭③⑥❬ ➊③❵➋❨⑥❩ ❽❵➂ ➌➌➍➎➏➌➐ ➅➀ ❩❬❨ ❿➄❨❺⑨⑦❬ ➇❨⑦❨❭③⑥❬ ➈❵⑤❪⑥⑨❥ ⑤❪⑧
❺❨③ ❩❬❨ ④③❵➋❨⑥❩ ⑩③❭❪❩⑦ ➑➌➒⑧➌➓➒➒⑧➏➓➍➑ ❭❪❺ ➌➓➒➌⑧➏➍➎➍ ➔→➇➣➐ ➉↔↕➐ ➅➀ ➆➙ ➈➛❿➃
÷ûù ú
Ø
✭Ú✮ ❂
à
➉⑥❩⑨❵❪ ➜➊➓➝➓➑➐ ➅➀ ❩❬❨ ➆⑤③❵④❨❭❪ ➇❨⑦❨❭③⑥❬ ➈❵⑤❪⑥⑨❥ ⑤❪❺❨③ ❩❬❨ ➉❩❞❵⑦④❬❨③⑨⑥
✬
➇❨⑦❨❭③⑥❬ ➊③❵➋❨⑥❩ ❽❵➂ ➌➌➍➎➒➏➐ ❭❪❺ ➅➀ ❭ ⑩③❭❪❩ q③❵❞ ❩❬❨ ➞❵➁❨③❪❞❨❪❩ ❵q ❩❬❨
➇⑤⑦⑦⑨❭❪ ➟❨❺❨③❭❩⑨❵❪ ⑤❪❺❨③ ⑥❵❪❩③❭⑥❩ ❽❵➂ ➒➒➂➞➠➡➂➠➒➂➓➓➡➝ ➔❽❴➐ →➇↕➂ ❳❨ ❭⑥❫❪❵➄❥⑧
❨❺⑩❨ ❩❬❨ ❭❥❥❵⑥❭❩⑨❵❪ ❵q ⑥❵❞④⑤❩⑨❪⑩ ③❨⑦❵⑤③⑥❨⑦ ④③❵➁⑨❺❨❺ ➅➀ ❩❬❨ ❿➄❨❺⑨⑦❬ ❽❭❩⑨❵❪❭❥
➉❥❥❵⑥❭❩⑨❵❪⑦
➈❵❞❞⑨❩❩❨❨
❭❩ ❩❬❨ ➈❨❪❩❨③ q❵③ ➊❭③❭❥❥❨❥
➈❵❞④⑤❩❨③⑦
Ø
÷Öù ú
✭Ú✮ ❂
à
❭❩ ❩❬❨ ➇❵➀❭❥
→❪⑦❩⑨❩⑤❩❨ ❵q ➃❨⑥❬❪❵❥❵⑩➀ ⑨❪ ❿❩❵⑥❫❬❵❥❞ ❭❪❺ ❩❬❨ ❽❭❩⑨❵❪❭❥ ❿⑤④❨③⑥❵❞④⑤❩❨③ ➈❨❪❩❨③⑦
Ò
❳â
ÿ✴✹
ü
ýþ✧
Ò
✻
ú
✼Ú
✬
❳✼
✷✬
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✼
û
✖☞♠☞☛✟✡☛②
❳
Ö
❚✎ ☞✍t✠✌✡✟t✠ ✎✈✠✡ t❤✠ ✟✍✌☛✠✖ ☞✍ ➱✲✖✑✟❝✠ ☞✍ ❙✠❝t✔ ✼✔✷✢ ✇✠ ✓✖✠✒ t❤✠
Ø
÷ûù
✶
ú
✭Ú✮
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✕
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✟✡❝t✟✍ Ú
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úâ
Ú
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Ö
✕ Ô Õ ❝✎✖ Ó
ø
❰
Ï ÑÝà ❂
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✕ Ô Õ ❝✎✖ Ó
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✭Ü✔✕✮
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✒Ó ✒× ❂ á
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ú Ö ☛✍ ✺♠
ã Ú
✭Ü✔ó✮
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✭✭ Ô ðÚ
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✭Ü✔✭✮
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✭✕ Ô Õ ❝✎✖ Ó✮
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✟✡❝t✟✍ Ú
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Ö Ï ÑÝà Ô á â ✭ÙÏ Ñ ÚÝà Ô ÙÏÝ Ú Ñà Ô ÙÏà Ú ÑÝ
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✶ Ï Ñ Ô Ø Ö ÚÏ Ñ Û
✒ ❳Û
ú Ö ✭✣✯✣ ✮Ö â ❂ Ú
ú Ö ✯✂
ø ❂ Õ✔ ❚❤✠ ✠✏✑☛☞❝☞t ❢✎✡♠
❂ Ú
û
ð
❢✎☛☛✎✇☞✍✌ ☞✒✠✍t☞t☞✠✖ ✭✺✎✌✟❝❤✠✈✖❦☞☞ ✃ ❑☛✠✠✎✡☞✍ ✷✵✵❐✢ ✷✵✵❒✮❮
✣Ï Ñ ✖☞✍ Ó
✭Ü✔ð✮
÷Ýù
÷Ýù
ú ✟✍✒ á
ú ❢✎✡
✎❢ t❤✠ ❢✓✍❝t☞✎✍✖ Øà ✭Ú✮
✭Ú✮
à
➶➹➘ ➸➵➨ ➭➩➸➨➴➘➷➸➭➹➩ ➭➩ ➬ ➮➺➧➷➽➨
ø
❰
ÏÑ ❂
✒ ❳Û
÷Ýù ú
✭Ú✮Û
à
÷Ýù
ú
áà
✭Ú✮✢
❢✎✡
ó ê✯êëì ✢ ✟✍✒
➦➧➧➨➩➫➭➯ ➦➲ ➳➵➨ ➭➫➨➩➸➭➸➭➨➺ ➻➺➨➫ ➭➩ ➼➨➽➸➾ ➚➾➪
ø ✭❳ Ö ✮
Ø
à
ü
ý
Ý
ø ✭Õ✭✂
ø ✮✮✂
ø
✒✂
ø ❂
Ø
à
✟✍✒
î
ø ✭❳ Ö ✮
Ø
à
ü
ý
✶
⑨❪ ➣⑨❪❫➢④⑨❪⑩➐ ❩❬❨ ➤⑨⑩❬ ➊❨③q❵③❞❭❪⑥❨ ➈❵❞④⑤❩⑨❪⑩ ➈❨❪❩❨③ ❽❵③❩❬ ⑨❪ ➙❞❨➥➐ ❭❪❺ ❩❬❨
❽❵③❺⑨⑥ ➤⑨⑩❬ ➊❨③q❵③❞❭❪⑥❨ ➈❵❞④⑤❩⑨❪⑩ ➈❨❪❩❨③ ⑨❪ ➇❨➀❫➋❭➁⑨❫➂
ÿ✴✹
ü
ýþ✧
Ò
úÖ
✼Ú
ï
ú
▼ ✭Ú✮
Û
✭Ü✔✕✕✮
❒
❆✽✄☎
✆✁❣❡
✶✶
♦♦
✶✆
❆✫❆ ✺✺ ✁ ❆✽✸ ✭✷✂✄✸☎
÷ ❂ ✶ ❾ ✟☛÷ ✠ ✰ ✟☛÷ ✹ ❧✡✞✶ ✰ ☛÷ ☞✠ ✮✌ ❍❡✝❡ ✇❡ ✆❤✈❡ t❤❦❡✡ ✐✡t♦
✇✆❡✝❡ ▼✞☛✮
❤❛❛♦✍✡t t✆❤t ❘♠ ✏ ✶✌ ❋♦✝ ❇ ✎ ❇✑✒✴✓ ❘♠✔✕✹ ✱ t✆❡✖❡ ❢✍✡❛t✐♦✡✖ ❤✝❡
❣✐✈❡✡ ❜②
✶
✘✙✚ ÷
✗✔ ✞☛✮
✛ ✟ ❾ ☛÷ ✠ ❧✡ ❘♠✢
✜
✣
✤
✟ ✠
✟
✘✙✚ ÷
✗✠ ✞☛✮ ✛ ❾ ☛÷ ❧✡ ❘♠ ✰
✢
✶✜
✜
✦
★
✟
✟
✥ ✠
✘✠✚ ÷
✘✠✚ ÷
✗✔ ✞☛✮
✛
✶❾
☛÷ ✢ ✗✠ ✞☛✮
✛ ❾ ☛÷ ✠ ✢
✶✧
✥
✜
✦
★
✟
✥ ✠
✘✠✚ ÷
❈✔ ✞☛✮ ✛
✶❾
☛÷ ➲
✶✜
✶✓
❋♦✝ ❇✑✒✴✓❘♠✔✕✹ ✎ ❇ ✎ ❇✑✒✴✓✱ t✆❡✖❡ ❢✍✡❛t✐♦✡✖ ❤✝❡ ❣✐✈❡✡ ❜②
✣
✤
✟
✶✩ ✓ ✠
✘✙✚ ÷
✗✔ ✞☛✮
✛ ✟ ✰ ☛÷ ✠ ✟ ❧✡ ☛÷ ❾
✰ ☛÷ ✢
✶✜ ✼
✜
✣
✤
✟ ✠
✟
✘✙✚ ÷
✗✠ ✞☛✮ ✛ ☛÷ ✓ ❧✡ ☛÷ ❾
❾ ✥☛÷ ✠ ➲
✶✜
✜
❖t✆❡✝ ❢✍✡❛t✐♦✡✖ ✐✡ t✆✐✖ ❛❤✖❡ ✆❤✈❡ t✆❡ ✖❤♠❡ ❤✖②♠✪t♦t✐❛✖ ❤✖ ✐✡ t✆❡
❛❤✖❡ ♦❢ ❇ ✎ ❇✑✒✴✓❘♠✔✕✹ ✌ ❋♦✝ ❇ ✏ ❇✑✒✴✓✱ t✆❡✖❡ ❢✍✡❛t✐♦✡✖ ❤✝❡
❣✐✈❡✡ ❜②
✥
✬
✩
✬
✘✙✚ ÷
✘✙✚ ÷
✢ ✗✠ ✞☛✮
✛❾ ✰
✢
✗✔ ✞☛✮
✛ ❾
☛÷
☛÷ ✠
☛÷
☛÷ ✠
✥✬
✥
✥✬
✥
✘✠✚ ÷
✘✠✚ ÷
✗✔ ✞☛✮
✛
❾
✢ ✗✠ ✞☛✮
✛❾
✰
✢
✼☛÷
✟☛÷ ✠
✼☛÷
☛÷ ✠
✶
✥✬
✘✠✚ ÷
❈✔ ✞☛✮
✛
❾
➲
÷
✟✯☛ ✟☛÷ ✠
❚✆❡ ❢✍✡❛t✐♦✡✖ q✔ ✞☛✮ ❤✡❞ q✠ ✞☛✮ ❤✝❡ ❣✐✈❡✡ ❜②
✶ ✲ ✘✙✚
✘✙✚
✘✙✚
✗ ✞✧✮ ❾ ✗✔ ✞✓☛✮ ❾ ✔✠ ✗✠ ✞✓☛✮
✶✟ ✔
✻ ✘✠✚
✘✠✚
✘✠✚
❾ ✞✳✵✙ ✮✠ ✗✔ ✞✧✮ ❾ ✟❈✔ ✞✧✮ ❾ ✶✧✗✔ ✞✓☛✮
✿ ❀✿
✾ ✲
✘✠✚
✰ ✟✧❈✔ ✞✓☛✮ ✰
✗ø ✔ ✞✶✩☛✠ ✮ ❾ ✟❈ø ✔ ✞✶✩☛✠ ✮ ✢
✟✬
✻
✶ ✲ ✔ ✘✙✚
✘✠✚
✘✠✚
q✠ ✞☛✮ ❂
✗✠ ✞✓☛✮ ✰ ✞✳✵✙ ✮✠ ✗✔ ✞✧✮ ❾ ✩❈✔ ✞✧✮
✠
✶✟
q✔ ✞☛✮ ❂
✾ ❃
✘✠✚
✘✠✚
❾ ✶✧✗✔ ✞✓☛✮ ✰ ✩✧❈✔ ✞✓☛✮ ✰
✗ø ✔ ✞✶✩☛✠ ✮
✟✬
❄❀✿
❾ ✩❈ø ✔ ✞✶✩☛✠ ✮ ❅
❉❊●❊r❊■❏❊❑
▲◆P◗◆P❙ ❯❱ ❲❳❨❩❙ ❬◆❭❪❫❴❵❱ ❝❵❥P❭❪❫❴❵❱ ♥♣s✉① ③❴④❱❙ ⑤⑥❙ ⑦❳
▲P⑧④①◆④⑨sP◗❙ ❝❱ ⑩⑥⑥❲❙ ❝❪❶❙ ❷❷⑥❙ ❨⑩❩
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❸ ❹s⑨P⑧❺⑧④✉⑧④❙ ❻❱ ⑩⑥⑥❷⑧❙ ❼❫❴❵❱ ❽◆❪❱❙ ❩❲⑦❙ ❲
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❸ ❹s⑨P⑧❺⑧④✉⑧④❙ ❻❱ ⑩⑥⑥❷⑨❙ ❝❸❝❙ ❩⑤❳❙ ❨⑤❷
❆✽✸✁ ➾➚➪➶ ✄✷ ➹➘ ✄✷
✞❁✌✶✟✮
✞❁✌✶✥✮
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❸ ❹s⑨P⑧❺⑧④✉⑧④❙ ❻❱ ⑩⑥⑥⑦❙ ❝❵❥P❭④❱ ❿⑧➀❫P❱❙ ⑤⑩❨❙ ❷⑥⑦
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻➁❪❴♣➁❙ ❼❱❙ ❸ ❯❭❫⑧❺❺◆①❙ ❝❱ ⑩⑥⑥❩❙ ❼❫❴❵❱ ♥♣s✉①❵❙ ❲➂❙ ❲⑥⑩⑥
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑥❙ ❝❵❥P❭④❱ ❿⑧➀❫P❱❙ ⑤⑤❲❙ ❷
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻◆❺◆♣❙ ❻❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❯✉❥P⑧❙ ③❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲❲⑧❙
❝❪❶❙ ⑦❩⑥❙ ➆❷⑥
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❹s⑨P⑧❺⑧④✉⑧④❙ ❻❱❙ ▲⑧♣❭◗❫❙ ❝❱❙ ❸ ❬❭♣①❵❥◆✉④❙ ❯❱ ➆❱ ⑩⑥❲❲⑨❙ ❝❪❶❙
⑦⑤❩❙ ❳
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻◆❺◆♣❙ ❻❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑩⑧❙ ❝❪❶❙ ⑦❩❳❙
❲⑦❳
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❽➁①♣◆P❙ ❻❱➇➈❱❙ ❸ ❻◆❺◆♣❙ ❻❱ ⑩⑥❲⑩⑨❙ ❝❸❝❙ ❷⑤❳❙ ❝⑤❷
▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❬P◆❵❵◆♣❙ ➉❱❙ ❻➁❪❴♣➁❙ ❼❱ ❶❱❙ ◆❥ ⑧♣❱ ⑩⑥❲⑤❙ ❝❪❶❙ ⑦➂⑩❙ ❲⑩⑦
➊♣❪◆P✉④❙ ➋❱❙ ❬❭♣s⑨◆➃ ➅❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥⑥❷❙ ❼❫❴❵❱ ❽◆➃❱ ➊❙ ⑦❲❙
⑥⑤➂⑤⑥⑩
❶⑧⑨⑨⑧P✉❙ ❹❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❯✉❥P⑧❙ ③❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑤❙
❝❸❝❙ ✉④ ❪P◆❵❵ ➌➍➎➏➐➑➒➓➔→➣↔↕➙➛➓➜
❶✉❙ ➈❱ ❲❳❳❳❙ ❼❫❴❵❱ ❽◆➃❱ ➆◆❥❥❱❙ ❨⑤❙ ⑤❲❳❨
❻➁❪❴♣➁❙ ❼❱ ❶❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❯⑧④❥◆P◆❙ ❯❱ ❶❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱
⑩⑥❲⑩❙ ❯❿❽❝❹❙ ❩⑩⑩❙ ⑩❩➂❷
❻➁❪❴♣➁❙ ❼❱ ❶❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❯⑧④❥◆P◆❙ ❯❱ ❶❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙
➅❱ ⑩⑥❲⑤❙ ❹❭♣⑧P ⑧④① ❝❵❥P❭❪❫❴❵✉➀⑧♣ ③❴④⑧❺❭❵ ⑧④① ❯⑧◗④◆❥✉➀ ❝➀❥✉➃✉❥❴❙ ◆①❵❱ ❝❱ ❬❱
❻❭❵❭➃✉➀❫◆➃❙ ➊❱ ❯❱ ①◆ ❬❭s➃◆✉⑧ ③⑧♣ ❼✉④❭❙ ❸ ➝❱ ➝⑧④❙ ❼P❭➀❱ ➅❝➞ ❹❴❺❪❱❙ ⑩❳❩
➌➍➎➏➐➑➒➓➣➓➓↔➣➟➠➣➜
❻◆❺◆♣❙ ❻❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❯✉❥P⑧❙ ③❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑩⑧❙
❹❭♣⑧P ❼❫❴❵❱❙ ③➉➅➡❲⑥❱❲⑥⑥⑦➢❵❲❲⑩⑥⑦➇⑥❲⑩➇⑥⑥⑤❲➇❨
❻◆❺◆♣❙ ❻❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑩⑨❙ ❝❵❥P❭④❱
❿⑧➀❫P❱❙ ⑤⑤⑤❙ ❳❷
❻◆❺◆♣❙ ❻❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑩➀❙ ❼❫❴❵❱
❹➀P✉❪❥⑧ ➌➍➎➏➐➑➒➓➣→➙↔→↕➓➤➜
❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ❲❳❳❩❙ ❼❫❴❵❱ ❽◆➃❱ ➊❙ ❷⑥❙ ⑩⑦❲➂
❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ❲❳❳❳❙ ❼❫❴❵❱ ❽◆➃❱ ➊❙ ❷❳❙ ➂⑦⑩❩
❻♣◆◆❭P✉④❙ ❿❱❙ ❯❭④①❙ ❯❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ❲❳❳⑤❙ ❼❫❴❵❱ ♥♣s✉①❵ ▲❙ ❷❙ ❩❲⑩❨
❻♣◆◆❭P✉④❙ ❿❱❙ ❯❭④①❙ ❯❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ❲❳❳➂❙ ❝❸❝❙ ⑤⑥⑦❙ ⑩❳⑤
❻♣◆◆❭P✉④❙ ❿❱ ➅❱❙ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ➥❱❙ ❸ ❽s➦❺⑧✉➄✉④❙ ❝❱ ❝❱ ❲❳❨❳❙ ❹❭➃❱ ❝❵❥P❭④❱ ➆◆❥❥❱❙
❲❷❙ ⑩⑦❩
❻♣◆◆❭P✉④❙ ❿❱ ➅❱❙ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ➥❱❙ ❸ ❽s➦❺⑧✉➄✉④❙ ❝❱ ❝❱ ❲❳❳⑥❙ ❹❭➃❱ ❼❫❴❵❱ ❶➊➋❼❙
⑦⑥❙ ❨⑦❨
❻P⑧s❵◆❙ ♥❱❙ ❸ ❽➁①♣◆P❙ ❻❱➇➈❱ ❲❳❨⑥❙ ❯◆⑧④➇➧◆♣① ❺⑧◗④◆❥❭❫❴①P❭①❴④⑧❺✉➀❵ ⑧④① ①❴➇
④⑧❺❭ ❥❫◆❭P❴ ➨➉➩➫❭P①➡ ❼◆P◗⑧❺❭④ ❼P◆❵❵➭
➆❭❵⑧①⑧❙ ➅❱ ❽❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❯✉❥P⑧❙ ③❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥❲⑩❙
❝❸❝❙ ❷❩❨❙ ❝❩❳ ➨➆▲❻❯❽➭
❯⑧❥❥❫⑧◆s❵❙ ➯❱ ➈❱❙ ❬❭♣①❵❥◆✉④❙ ❯❱ ➆❱❙ ❸ ❹❺✉❥❫❙ ➳❱ ❲❳❨⑩❙ ❼❫❴❵❱ ❽◆➃❱ ➆◆❥❥❱❙ ❩❨❙ ❲⑩❷➂
❯❭➵⑧❥❥❙ ➈❱ ❻❱ ❲❳⑦❨❙ ❯⑧◗④◆❥✉➀ ➧◆♣① ◗◆④◆P⑧❥✉❭④ ✉④ ◆♣◆➀❥P✉➀⑧♣♣❴ ➀❭④①s➀❥✉④◗ ßs✉①❵
➨➳⑧❺⑨P✉①◗◆➡ ➳⑧❺⑨P✉①◗◆ ➞④✉➃◆P❵✉❥❴ ❼P◆❵❵➭
➉P❵➦⑧◗❙ ❹❱ ❝❱ ❲❳⑦⑥❙ ❶❱ ♥♣s✉① ❯◆➀❫❱❙ ❩❲❙ ⑤➂⑤
➉❵❵◆④①P✉➸➃◆P❙ ❯❱ ⑩⑥⑥⑤❙ ❝❸❝ ❽◆➃❱❙ ❲❲❙ ⑩❨⑦
❼⑧P➄◆P❙ ➊❱ ❿❱ ❲❳⑦❳❙ ➳❭❵❺✉➀⑧♣ ❺⑧◗④◆❥✉➀ ➧◆♣①❵ ➨❿◆➺ ➝❭P➄➡ ➉➩➫❭P① ➞④✉➃◆P❵✉❥❴
❼P◆❵❵➭
❼❭s➻s◆❥❙ ❝❱❙ ♥P✉❵➀❫❙ ➞❱❙ ❸ ➆➼❭P⑧❥❙ ❶❱ ❲❳⑦➂❙ ❶❱ ♥♣s✉① ❯◆➀❫❱❙ ⑦⑦❙ ⑤⑩❲
❽➁①♣◆P❙ ❻❱➇➈❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❸ ❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱ ⑩⑥⑥⑤❙ ❬◆❭❪❫❴❵❱ ❝❵❥P❭❪❫❴❵❱ ♥♣s✉①
③❴④❱❙ ❳⑦❙ ⑩❩❳
❽❭⑨◆P❥❵❙ ❼❱ ➈❱❙ ❸ ❹❭➺⑧P①❙ ❝❱ ❯❱ ❲❳⑦❷❙ ❝❵❥P❭④❱ ❿⑧➀❫P❱❙ ⑩❳➂❙ ❩❳
❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱❙ ❸ ❻♣◆◆❭P✉④❙ ❿❱ ⑩⑥⑥❩❙ ❼❫❴❵❱ ❽◆➃❱ ➊❙ ⑦⑥❙ ⑥❩➂⑤❲⑥
❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱❙ ❸ ❻♣◆◆❭P✉④❙ ❿❱ ⑩⑥⑥⑦❙ ❼❫❴❵❱ ❽◆➃❱ ➊❙ ⑦➂❙ ⑥❷➂⑤⑥⑦
❽❭◗⑧➀❫◆➃❵➄✉✉❙ ➅❱❙ ❻♣◆◆❭P✉④❙ ❿❱❙ ❻➁❪❴♣➁❙ ❼❱ ❶❱❙ ❸ ▲P⑧④①◆④⑨sP◗❙ ❝❱ ⑩⑥❲❲❙ ❼❫❴❵❱ ❽◆➃❱
➊❙ ❨❩❙ ⑥❷➂⑤❲❩
❹◆◆❫⑧➫◆P❙ ❿❱ ❲❳❳➂❙ ❼❫❴❵❱ ❽◆➃❱ ➊❙ ❷⑤❙ ❲⑩❨⑤
❹❥◆◆④⑨◆➀➄❙ ❯❱❙ ❻P⑧s❵◆❙ ♥❱❙ ❸ ❽➁①♣◆P❙ ❻❱➇➈❱ ❲❳➂➂❙ ➽❱ ❿⑧❥sP➫❭P❵➀❫❱❙ ⑩❲⑧❙ ⑤➂❳
➯⑧P④◆➀➄◆❙ ❶❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❸ ❯✉❥P⑧❙ ③❱ ⑩⑥❲❲❙ ❝❸❝❙ ❷⑤❩❙ ❝❲❲
➯⑧P④◆➀➄◆❙ ❶❱❙ ▲P⑧④①◆④⑨sP◗❙ ❝❱❙ ❸ ❯✉❥P⑧❙ ③❱ ⑩⑥❲⑩❙ ❶❱ ❹❪⑧❱ ➯◆⑧❥❫◆P ❹❪⑧❱ ➳♣✉❺❱❙ ⑩❙
❝❲❲
➽◆♣①❭➃✉➀❫❙ ➝⑧❱ ▲❱❙ ❽s➦❺⑧✉➄✉④❙ ❝❱ ❝❱❙ ❸ ❹❭➄❭♣❭➵❙ ③❱ ③❱ ❲❳❨⑤❙ ❯⑧◗④◆❥✉➀ ➧◆♣①❵ ✉④
⑧❵❥P❭❪❫❴❵✉➀❵ ➨❿◆➺ ➝❭P➄➡ ❬❭P①❭④ ❸ ▲P◆⑧➀❫➭
➽◆♣①❭➃✉➀❫❙ ➝⑧❱ ▲❱❙ ❽s➦❺⑧✉➄✉④❙ ❝❱ ❝❱❙ ❸ ❹❭➄❭♣❭➵❙ ③❱ ③❱ ❲❳❳⑥❙ ➋❫◆ ❝♣❺✉◗❫❥❴
➳❫⑧④➀◆ ➨❹✉④◗⑧❪❭P◆➡ ➯❭P① ❹➀✉◆④❥✉➧➀ ❼s⑨♣➭
Paper III
81
❆✫❆ ✺ ✁✂ ❆✷ ✭✷✄☎✁✆
❉✝✞✟ ☎✄✶☎✄✺☎✴✄✄✄✁✵ ✠ ☎✴✷✄☎✠✷✷✠☎✺
❝ ❊❙❖ ☛☞✌✍
✡
✎✏✑✒♦✓♦✔②
✕
✎✏✑✒♦✖✗②✏✘✙✏
▼❛❣✚✛✜✢✣ ß✤✥ ✣✦✚✣✛✚✜✧❛✜✢✦✚★ ✢✚ ❛ ♣✦✩✪✜✧✦♣✢✣ ❛✜t✦★♣✬✛✧✛
■✮ ❘✮ ▲✯s✰✱✰✲✳✸ ✹ ✻✮ ❇r✰✼✱✽✼✾✉r✿✲✳✸ ✹ ◆✮ ❑❧✽✽✯r❀✼❁✳✲✳❂ ✹ ✰✼✱ ■✮ ❘✯✿✰❃❄✽✈s❅❀❀❁✳✲✳❂
❈ ❋●❍❏P◗❚❯ ❱❲❳ ❨●❩❚❬ ❭♥❪◗P◗❫◗❴ ●❵ ❲❴❝❡♥●❬●❜❩ ❚♥❏ ❙◗●❝❞❡●❬❢ ❤♥P✐❴❍❪P◗❩❯ ❨●❪❬❚❜❪◗❫❬❬❪❥❚❝❞❴♥ ☛❦❯ ✌☞♠q✌ ❙◗●❝❞❡●❬❢❯ ❙✇❴❏❴♥
❴①❢❚P❬③ ④⑤⑤⑥⑦⑧④⑨⑩⑧❶⑦⑤❶❷⑥❸⑥❹❺❻⑥④⑤⑦❼❶❻
❽ ❾❴❿❚❍◗❢❴♥◗ ●❵ ➀❪◗❍●♥●❢❩❯ ➀❬❥❚❋●✐❚ ❤♥P✐❴❍❪P◗❩ ➁❴♥◗❴❍❯ ❙◗●❝❞❡●❬❢ ❤♥P✐❴❍❪P◗❩❯ ✌☞♠q✌ ❙◗●❝❞❡●❬❢❯ ❙✇❴❏❴♥
➂ ❾❴❿❚❍◗❢❴♥◗ ●❵ ➃❴❝❡❚♥P❝❚❬ ❊♥❜P♥❴❴❍P♥❜❯ ➄❴♥①➅❫❍P●♥ ❤♥P✐❴❍❪P◗❩ ●❵ ◗❡❴ ❋❴❜❴✐❯ ➆❖➄ ♠➇❦❯ ➈✍✌☞➇ ➄❴❴❍①❙❡❴✐❚❯ ❭❪❍❚❴❬
➉ ❾❴❿❚❍◗❢❴♥◗ ●❵ ❨❚❏P● ➆❡❩❪P❝❪❯ ❋➊ ❭➊ ➋●❥❚❝❡❴✐❪❞❩ ❙◗❚◗❴ ❤♥P✐❴❍❪P◗❩ ●❵ ❋P➌❡♥❩ ❋●✐❜●❍●❏❯ ♠☞❦q➇☞ ❋P➌❡♥ ❋●✐❜●❍●❏❯ ❨❫❪❪P❚
❨❴❝❴P✐❴❏ ✌➈ ➍❫❬❩ ☛☞✌❦ ➎ ➀❝❝❴❿◗❴❏ ☛❦ ➍❚♥❫❚❍❩ ☛☞✌✍
➏➐➑➒➓➏➔➒
→➣↔↕➙➛↕➜ ❙◗❍●♥❜❬❩ ❪◗❍❚◗P➝❴❏ ❡❩❏❍●❢❚❜♥❴◗P❝ ◗❫❍❥❫❬❴♥❝❴ ❡❚❪ ❍❴❝❴♥◗❬❩ ❥❴❴♥ P❏❴♥◗P➝❴❏ ❚❪ ❚ ❝❚♥❏P❏❚◗❴ ❵●❍ ❴➞❿❬❚P♥P♥❜ ◗❡❴ ❪❿●♥◗❚♥❴●❫❪
❵●❍❢❚◗P●♥ ●❵ ❢❚❜♥❴◗P❝ ➟❫➞ ❝●♥❝❴♥◗❍❚◗P●♥❪ ❥❩ ◗❡❴ ♥❴❜❚◗P✐❴ ❴➠❴❝◗P✐❴ ❢❚❜♥❴◗P❝ ❿❍❴❪❪❫❍❴ P♥❪◗❚❥P❬P◗❩ ➡❋❊➃➆❭➢➊ ➃❫❝❡ ●❵ ◗❡P❪ ✇●❍❞ ❡❚❪
❥❴❴♥ ❏●♥❴ ❵●❍ P❪●◗❡❴❍❢❚❬ ❬❚❩❴❍❪❯ P♥ ✇❡P❝❡ ◗❡❴ ❏❴♥❪P◗❩ ❪❝❚❬❴ ❡❴P❜❡◗ P❪ ❝●♥❪◗❚♥◗ ◗❡❍●❫❜❡●❫◗➊
➤➥➦➧➜ ➨❴ ♥●✇ ✇❚♥◗ ◗● ❞♥●✇ ✇❡❴◗❡❴❍ ❴❚❍❬P❴❍ ❝●♥❝❬❫❪P●♥❪ ❍❴❜❚❍❏P♥❜ ◗❡❴ ❪P➌❴ ●❵ ❢❚❜♥❴◗P❝ ❪◗❍❫❝◗❫❍❴❪ ❚♥❏ ◗❡❴P❍ ❜❍●✇◗❡ ❍❚◗❴❪ ❝❚❍❍❩ ●✐❴❍
◗● ◗❡❴ ❝❚❪❴ ●❵ ❿●❬❩◗❍●❿P❝ ❬❚❩❴❍❪❯ P♥ ✇❡P❝❡ ◗❡❴ ❪❝❚❬❴ ❡❴P❜❡◗ ❏❴❝❍❴❚❪❴❪ ❪❡❚❍❿❬❩ ❚❪ ●♥❴ ❚❿❿❍●❚❝❡❴❪ ◗❡❴ ❪❫❍❵❚❝❴➊
➩➙↕➫➣➭➧➜ ❲● ❚❬❬●✇ ❵●❍ ❚ ❝●♥◗P♥❫●❫❪ ◗❍❚♥❪P◗P●♥ ❵❍●❢ P❪●◗❡❴❍❢❚❬ ◗● ❿●❬❩◗❍●❿P❝ ❬❚❩❴❍❪❯ ✇❴ ❴❢❿❬●❩ ❚ ❜❴♥❴❍❚❬P➌❚◗P●♥ ●❵ ◗❡❴ ❴➞❿●♥❴♥◗P❚❬
❵❫♥❝◗P●♥ ❞♥●✇♥ ❚❪ ◗❡❴ ➯①❴➞❿●♥❴♥◗P❚❬➊ ❲❡P❪ P❢❿❬P❴❪ ◗❡❚◗ ◗❡❴ ◗●❿ ●❵ ◗❡❴ ❿●❬❩◗❍●❿P❝ ❬❚❩❴❍ ❪❡P❵◗❪ ✇P◗❡ ❝❡❚♥❜P♥❜ ❿●❬❩◗❍●❿P❝ P♥❏❴➞ ❪❫❝❡
◗❡❚◗ ◗❡❴ ❪❝❚❬❴ ❡❴P❜❡◗ P❪ ❚❬✇❚❩❪ ◗❡❴ ❪❚❢❴ ❚◗ ❪●❢❴ ❍❴❵❴❍❴♥❝❴ ❡❴P❜❡◗➊ ➨❴ ❫❪❴❏ ❥●◗❡ ❢❴❚♥①➝❴❬❏ ❪P❢❫❬❚◗P●♥❪ ➡➃➲❙➢ ❚♥❏ ❏P❍❴❝◗ ♥❫❢❴❍P❝❚❬
❪P❢❫❬❚◗P●♥❪ ➡❾❋❙➢ ●❵ ❵●❍❝❴❏ ❪◗❍❚◗P➝❴❏ ◗❫❍❥❫❬❴♥❝❴ ◗● ❏❴◗❴❍❢P♥❴ ◗❡❴ ❍❴❪❫❬◗P♥❜ ➟❫➞ ❝●♥❝❴♥◗❍❚◗P●♥❪ P♥ ❿●❬❩◗❍●❿P❝ ❬❚❩❴❍❪➊ ➁❚❪❴❪ ●❵ ❥●◗❡
❡●❍P➌●♥◗❚❬ ❚♥❏ ✐❴❍◗P❝❚❬ ❚❿❿❬P❴❏ ❢❚❜♥❴◗P❝ ➝❴❬❏❪ ✇❴❍❴ ❝●♥❪P❏❴❍❴❏➊
➳➙➧➵➸↕➧➜ ➃❚❜♥❴◗P❝ ❪◗❍❫❝◗❫❍❴❪ ❥❴❜P♥ ◗● ❵●❍❢ ❚◗ ❚ ❏❴❿◗❡ ✇❡❴❍❴ ◗❡❴ ❢❚❜♥❴◗P❝ ➝❴❬❏ ❪◗❍❴♥❜◗❡ P❪ ❚ ❪❢❚❬❬ ❵❍❚❝◗P●♥ ●❵ ◗❡❴ ❬●❝❚❬ ❴➺❫P❿❚❍◗P◗P●♥
➝❴❬❏ ❪◗❍❴♥❜◗❡ ✇P◗❡ ❍❴❪❿❴❝◗ ◗● ◗❡❴ ◗❫❍❥❫❬❴♥◗ ❞P♥❴◗P❝ ❴♥❴❍❜❩➊ ❤♥❬P❞❴ ◗❡❴ P❪●◗❡❴❍❢❚❬ ❝❚❪❴ ✇❡❴❍❴ ❪◗❍●♥❜❴❍ ➝❴❬❏❪ ❝❚♥ ❜P✐❴ ❍P❪❴ ◗● ❢❚❜♥❴◗P❝
➟❫➞ ❝●♥❝❴♥◗❍❚◗P●♥❪ ❚◗ ❬❚❍❜❴❍ ❏❴❿◗❡❪❯ P♥ ◗❡❴ ❿●❬❩◗❍●❿P❝ ❝❚❪❴ ◗❡❴ ❜❍●✇◗❡ ❍❚◗❴ ●❵ ❋❊➃➆❭ ❏❴❝❍❴❚❪❴❪ ❵●❍ ❪◗❍❫❝◗❫❍❴❪ ❏❴❴❿❴❍ ❏●✇♥➊ ➃●❍❴●✐❴❍❯
◗❡❴ ❪◗❍❫❝◗❫❍❴❪ ◗❡❚◗ ❵●❍❢ ❡P❜❡❴❍ ❫❿ ❡❚✐❴ ❚ ❪❢❚❬❬❴❍ ❡●❍P➌●♥◗❚❬ ❪❝❚❬❴ ●❵ ❚❥●❫◗ ❵●❫❍ ◗P❢❴❪ ◗❡❴P❍ ❬●❝❚❬ ❏❴❿◗❡➊ ➲●❍ ✐❴❍◗P❝❚❬ ➝❴❬❏❪❯ ❢❚❜♥❴◗P❝
❪◗❍❫❝◗❫❍❴❪ ●❵ ❪❫❿❴❍①❴➺❫P❿❚❍◗P◗P●♥ ❪◗❍❴♥❜◗❡❪ ❚❍❴ ❵●❍❢❴❏❯ ❥❴❝❚❫❪❴ ❪❫❝❡ ➝❴❬❏❪ ❪❫❍✐P✐❴ ❏●✇♥✇❚❍❏ ❚❏✐❴❝◗P●♥ ◗❡❚◗ ❝❚❫❪❴❪ ❋❊➃➆❭ ✇P◗❡ ❡●❍P①
➌●♥◗❚❬ ❢❚❜♥❴◗P❝ ➝❴❬❏❪ ◗● ❍❴❚❝❡ ❿❍❴❢❚◗❫❍❴ ♥●♥❬P♥❴❚❍ ❪❚◗❫❍❚◗P●♥ ❥❩ ✇❡❚◗ P❪ ❝❚❬❬❴❏ ◗❡❴ ➻❿●◗❚◗●①❪❚❝❞➼ ❴➠❴❝◗➊ ❲❡❴ ❡●❍P➌●♥◗❚❬ ❝❍●❪❪①❪❴❝◗P●♥
●❵ ❪❫❝❡ ❪◗❍❫❝◗❫❍❴❪ ❵●❫♥❏ P♥ ❾❋❙ P❪ ❚❿❿❍●➞P❢❚◗❴❬❩ ❝P❍❝❫❬❚❍❯ ✇❡P❝❡ P❪ ❍❴❿❍●❏❫❝❴❏ ✇P◗❡ ➃➲❙ ●❵ ❋❊➃➆❭ ❫❪P♥❜ ❚ ✐❴❍◗P❝❚❬ ❢❚❜♥❴◗P❝ ➝❴❬❏➊
→➣↔➽➸➵➧➥➣↔➧➜ ❨❴❪❫❬◗❪ ❥❚❪❴❏ ●♥ P❪●◗❡❴❍❢❚❬ ❢●❏❴❬❪ ❝❚♥ ❥❴ ❚❿❿❬P❴❏ ❬●❝❚❬❬❩ ◗● ❿●❬❩◗❍●❿P❝ ❬❚❩❴❍❪➊ ➲●❍ ✐❴❍◗P❝❚❬ ➝❴❬❏❪❯ ❢❚❜♥❴◗P❝ ➟❫➞ ❝●♥①
❝❴♥◗❍❚◗P●♥❪ ●❵ ❪❫❿❴❍①❴➺❫P❿❚❍◗P◗P●♥ ❪◗❍❴♥❜◗❡❪ ❵●❍❢❯ ✇❡P❝❡ ❪❫❿❿●❍◗❪ ❪❫❜❜❴❪◗P●♥❪ ◗❡❚◗ ❪❫♥❪❿●◗ ❵●❍❢❚◗P●♥ ❢P❜❡◗ ❥❴ ❚ ❪❡❚❬❬●✇ ❿❡❴♥●❢❴♥●♥➊
➾➚➪ ➶➹➘➴➷➬ ❢❚❜♥❴◗●❡❩❏❍●❏❩♥❚❢P❝❪ ➡➃❳❾➢ ➮ ❡❩❏❍●❏❩♥❚❢P❝❪ ➮ ◗❫❍❥❫❬❴♥❝❴ ➮ ❙❫♥③ ❏❩♥❚❢●
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❆ØÖÞãÚÛ á×ÙÚÞâàÛÝ Ùå ÷❉ö ýãÞÛÔãÛâ
❆✷✂ áÕèÛ ☎ äé ☎☎
❆✫❆ ✺ ✁✂ ❆✷ ✭✷✄☎✁✆
s✝❝✞ s✟✠♣❧✟✡❝☛☞✟✌♥s ✝s✟♥❣ ✠✌r❡ r❡☛❧✟s☞✟❝ ✠✌❞❡❧s✍ ■♥ ☞✞✟s ♣☛♣❡r✱
✇❡ ☞✞❡r❡✎✌r❡ ♥✌✇ ❝✌♥s✟❞❡r ☛ ♣✌❧②☞r✌♣✟❝ s☞r☛☞✟✡❝☛☞✟✌♥✱ ✎✌r ✇✞✟❝✞
☞✞❡ ❞❡♥s✟☞② s❝☛❧❡ ✞❡✟❣✞☞ ✟s s✠☛❧❧❡s☞ ✟♥ ☞✞❡ ✝♣♣❡r ❧☛②❡rs✱ ☛♥❞ ☞✞❡
❞❡♥s✟☞② ✈☛r✟☛☞✟✌♥ ☞✞❡r❡✎✌r❡ ❣r❡☛☞❡s☞✍
◆✏✑✒■ ✟s ☛ ❧☛r❣❡✓s❝☛❧❡ ✟♥s☞☛t✟❧✟☞② ☞✞☛☞ ❝☛♥ t❡ ❡①❝✟☞❡❞ ✟♥ s☞r☛☞✓
✟✡❡❞ s✠☛❧❧✓s❝☛❧❡ ☞✝rt✝❧❡♥❝❡✍ ❚✞✟s r❡q✝✟r❡s ✔✟✐ s✝✕❝✟❡♥☞ s❝☛❧❡ s❡♣✓
☛r☛☞✟✌♥ ✟♥ ☞✞❡ s❡♥s❡ ☞✞☛☞ ☞✞❡ ✠☛①✟✠✝✠ s❝☛❧❡ ✌✎ ☞✝rt✝❧❡♥☞ ✠✌✓
☞✟✌♥s✱ ✖✱ ✠✝s☞ t❡ ✠✝❝✞ s✠☛❧❧❡r ☞✞☛♥ ☞✞❡ s❝☛❧❡ ✌✎ ☞✞❡ s②s☞❡✠✱ ▲❀
☛♥❞ ✔✟✟✐ s☞r✌♥❣ ❞❡♥s✟☞② s☞r☛☞✟✡❝☛☞✟✌♥ s✝❝✞ ☞✞☛☞ ☞✞❡ ❞❡♥s✟☞② s❝☛❧❡
✞❡✟❣✞☞ ❍✗ ✟s ✠✝❝✞ s✠☛❧❧❡r ☞✞☛♥ ▲❀ ✟✍❡✍✱
✖ ✘ ❍✗ ✘ ▲✳
✔✙✐
✚✌✇❡✈❡r✱ t✌☞✞ ☞✞❡ s✟③❡ ✌✎ ☞✝rt✝❧❡♥☞ ✠✌☞✟✌♥s ☛♥❞ ☞✞❡ ☞②♣✟❝☛❧ s✟③❡
✌✎ ♣❡r☞✝rt☛☞✟✌♥s ❞✝❡ ☞✌ ◆✏✑✒■ ❝☛♥ t❡ r❡❧☛☞❡❞ ☞✌ ☞✞❡ ❞❡♥s✟☞②
s❝☛❧❡ ✞❡✟❣✞☞✍ ❋✝r☞✞❡r✠✌r❡✱ ❡☛r❧✟❡r ✇✌r♦ ✌✎ ❑❡✠❡❧ ❡☞ ☛❧✍ ✔✛✜✙✢✐
✝s✟♥❣ ✟s✌☞✞❡r✠☛❧ ❧☛②❡rs s✞✌✇s ☞✞☛☞ ☞✞❡ s❝☛❧❡ ✌✎ ♣❡r☞✝rt☛☞✟✌♥s ❞✝❡
☞✌ ◆✏✑✒■ ❡①❝❡❡❞s ☞✞❡ ☞②♣✟❝☛❧ ❞❡♥s✟☞② s❝☛❧❡ ✞❡✟❣✞☞✍ ❯♥❧✟♦❡ ☞✞❡
✟s✌☞✞❡r✠☛❧ ❝☛s❡✱ ✟♥ ✇✞✟❝✞ ☞✞❡ s❝☛❧❡ ✞❡✟❣✞☞ ✟s ❝✌♥s☞☛♥☞✱ ✟☞ ❞❡✓
❝r❡☛s❡s r☛♣✟❞❧② ✇✟☞✞ ✞❡✟❣✞☞ ✟♥ ☛ ♣✌❧②☞r✌♣✟❝ ❧☛②❡r✍ ■☞ ✟s ☞✞❡♥ ✝♥✓
❝❧❡☛r ✞✌✇ s✝❝✞ s☞r✝❝☞✝r❡s ❝✌✝❧❞ ✡☞ ✟♥☞✌ ☞✞❡ ♥☛rr✌✇ s♣☛❝❡ ❧❡✎☞ t②
☞✞❡ s☞r☛☞✟✡❝☛☞✟✌♥ ☛♥❞ ✇✞❡☞✞❡r ☞✞❡ s❝☛❧✟♥❣s ❞❡r✟✈❡❞ ✎✌r ☞✞❡ ✟s✌☞✞❡r✓
✠☛❧ ❝☛s❡ ❝☛♥ s☞✟❧❧ t❡ ☛♣♣❧✟❡❞ ❧✌❝☛❧❧② ☞✌ ♣✌❧②☞r✌♣✟❝ ❧☛②❡rs✍
◆✏✑✒■ ✞☛s ☛❧r❡☛❞② t❡❡♥ s☞✝❞✟❡❞ ♣r❡✈✟✌✝s❧② ✎✌r ♣✌❧②☞r✌♣✟❝
❧☛②❡rs ✟♥ ✠❡☛♥✓✡❡❧❞ s✟✠✝❧☛☞✟✌♥s ✔✑❋✣❀ ❇r☛♥❞❡♥t✝r❣ ❡☞ ☛❧✍ ✛✜✙✜❀
❑ ♣②❧ ❡☞ ☛❧✍ ✛✜✙✛❀ ❏☛tt☛r✟ ❡☞ ☛❧✍ ✛✜✙✢✐✱ t✝☞ ♥✌ s②s☞❡✠☛☞✟❝ ❝✌✠✓
♣☛r✟s✌♥ ✞☛s t❡❡♥ ✠☛❞❡ ✇✟☞✞ ◆✏✑✒■ ✟♥ ✟s✌☞✞❡r✠☛❧ ✌r ✟♥ ♣✌❧②✓
☞r✌♣✟❝ ❧☛②❡rs ✇✟☞✞ ❞✟✤❡r❡♥☞ ✈☛❧✝❡s ✌✎ ☞✞❡ ♣✌❧②☞r✌♣✟❝ ✟♥❞❡①✍ ❚✞✟s
✇✟❧❧ t❡ ❞✌♥❡ ✟♥ ☞✞❡ ♣r❡s❡♥☞ ♣☛♣❡r✱ t✌☞✞ ✟♥ ✑❋✣ ☛♥❞ ❉◆✣✍
❚✞✌s❡ ☞✇✌ ❝✌✠♣❧❡✠❡♥☞☛r② ☞②♣❡s ✌✎ s✟✠✝❧☛☞✟✌♥s ✞☛✈❡ ♣r✌✈❡❞
☞✌ t❡ ☛ ❣✌✌❞ ☞✌✌❧ ✎✌r ✝♥❞❡rs☞☛♥❞✟♥❣ ☞✞❡ ✝♥❞❡r❧②✟♥❣ ♣✞②s✟❝s ✌✎
◆✏✑✒■✍ ✥♥ ❡①☛✠♣❧❡ ☛r❡ ☞✞❡ s☞✝❞✟❡s ✌✎ ☞✞❡ ❡✤❡❝☞s ✌✎ r✌☞☛☞✟✌♥
✌♥ ◆✏✑✒■ ✔✦✌s☛❞☛ ❡☞ ☛❧✍ ✛✜✙✛✱ ✛✜✙✢✐✱ ✇✞❡r❡ ✑❋✣ ✞☛✈❡ t❡❡♥
☛t❧❡ ☞✌ ❣✟✈❡ q✝☛♥☞✟☞☛☞✟✈❡❧② ✝s❡✎✝❧ ♣r❡❞✟❝☞✟✌♥s t❡✎✌r❡ ❝✌rr❡s♣✌♥❞✓
✟♥❣ ❉◆✣ ✇❡r❡ ☛t❧❡ ☞✌ ❝✌♥✡r✠ ☞✞❡ r❡s✝❧☞✟♥❣ ❞❡♣❡♥❞❡♥❝❡✍
✧★ P✩✪✬✮✯✩✰✲✴ ✵✮✯✶✮✲✸✴✶✮✲✩✹
❲❡ ❞✟s❝✝ss ✞❡r❡ ☞✞❡ ❡q✝☛☞✟✌♥ ✎✌r ☞✞❡ ✈❡r☞✟❝☛❧ ♣r✌✡❧❡ ✌✎ ☞✞❡ ✻✝✟❞
❞❡♥s✟☞② ✟♥ ☛ ♣✌❧②☞r✌♣✟❝ ❧☛②❡r✍ ■♥ ☛ ❈☛r☞❡s✟☛♥ ♣❧☛♥❡✓♣☛r☛❧❧❡❧ ❧☛②❡r
✇✟☞✞ ♣✌❧②☞r✌♣✟❝ s☞r☛☞✟✡❝☛☞✟✌♥✱ ☞✞❡ ☞❡✠♣❡r☛☞✝r❡ ❣r☛❞✟❡♥☞ ✟s ❝✌♥✓
s☞☛♥☞✱ s✌ ☞✞❡ ☞❡✠♣❡r☛☞✝r❡ ❣✌❡s ❧✟♥❡☛r❧② ☞✌ ③❡r✌ ☛☞ ✼✽ ✍ ❚✞❡ ☞❡✠✓
♣❡r☛☞✝r❡✱ ✾ ✱ ✟s ♣r✌♣✌r☞✟✌♥☛❧ ☞✌ ☞✞❡ sq✝☛r❡ ✌✎ ☞✞❡ s✌✝♥❞ s♣❡❡❞✱ ✿❁❂ ✱
☛♥❞ ☞✞✝s ☛❧s✌ ☞✌ ☞✞❡ ❞❡♥s✟☞② s❝☛❧❡ ✞❡✟❣✞☞ ❍✗ ✔✼✐✱ ✇✞✟❝✞ ✟s ❣✟✈❡♥
t② ❍✗ ❃ ✿❁❂ ❄❅ ✎✌r ☛♥ ✟s❡♥☞r✌♣✟❝ s☞r☛☞✟✡❝☛☞✟✌♥✱ ✇✞❡r❡ ❊ ✟s ☞✞❡ ☛❝✓
❝❡❧❡r☛☞✟✌♥ ❞✝❡ ☞✌ ☞✞❡ ❣r☛✈✟☞②✍ ❋✌r ☛ ♣❡r✎❡❝☞ ❣☛s✱ ☞✞❡ ❞❡♥s✟☞② ● ✟s
♣r✌♣✌r☞✟✌♥☛❧ ☞✌ ✾ ▼ ✱ ☛♥❞ ☞✞❡ ♣r❡ss✝r❡ ❖ ✟s ♣r✌♣✌r☞✟✌♥☛❧ ☞✌ ✾ ▼◗❘ ✱
s✝❝✞ ☞✞☛☞ ❖❄● ✟s ♣r✌♣✌r☞✟✌♥☛❧ ☞✌ ✾ ✱ ✇✞❡r❡ ❙ ✟s ☞✞❡ ♣✌❧②☞r✌♣✟❝ ✟♥✓
❞❡①✍ ❋✝r☞✞❡r✠✌r❡✱ ✇❡ ✞☛✈❡ ❖✔✼✐ ❱ ●✔✼✐❳ ✱ ✇✞❡r❡ ❨ ❃ ✔❙ ❩ ✙✐❄❙ ✟s
☛♥✌☞✞❡r ✝s❡✎✝❧ ❝✌❡✕❝✟❡♥☞✍
❋✌r ☛ ♣❡r✎❡❝☞ ❣☛s✱ ☞✞❡ s♣❡❝✟✡❝ ❡♥☞r✌♣② ❝☛♥ t❡ ❞❡✡♥❡❞ ✔✝♣ ☞✌
☛♥ ☛❞❞✟☞✟✈❡ ❝✌♥s☞☛♥☞✐ ☛s ❬ ❃ ✿❭ ❧♥✔❖❄●❪ ✐✱ ✇✞❡r❡ ❫ ❃ ✿ ❴ ❄✿❭ ✟s ☞✞❡
r☛☞✟✌ ✌✎ s♣❡❝✟✡❝ ✞❡☛☞s ☛☞ ❝✌♥s☞☛♥☞ ♣r❡ss✝r❡ ☛♥❞ ❝✌♥s☞☛♥☞ ❞❡♥s✟☞②✱
r❡s♣❡❝☞✟✈❡❧②✍ ❋✌r ☛ ♣✌❧②☞r✌♣✟❝ s☞r☛☞✟✡❝☛☞✟✌♥✱ ✇❡ ✞☛✈❡
❡①♣✔❬❄✿❭ ✐ ❃ ❖❄●❪ ❱ ●❳❾❪ ❵
✔✛✐
s✌ ❬ ✟s ❝✌♥s☞☛♥☞ ✇✞❡♥ ❨ ❃ ❫✱ ✇✞✟❝✞ ✟s ☞✞❡ ❝☛s❡ ✎✌r ☛♥ ✟s❡♥✓
☞r✌♣✟❝ s☞r☛☞✟✡❝☛☞✟✌♥✍ ■♥ ☞✞❡ ✎✌❧❧✌✇✟♥❣✱ ✇❡ ✠☛♦❡ ☞✞✟s ☛ss✝✠♣☞✟✌♥
☛♥❞ s♣❡❝✟✎② ✎r✌✠ ♥✌✇ ✌♥❧② ☞✞❡ ✈☛❧✝❡ ✌✎ ❫✍ ❋✌r ☛ ✠✌♥☛☞✌✠✟❝ ❣☛s✱
✇❡ ✞☛✈❡ ❫ ❃ ❛❄✢✱ ✇✞✟❝✞ ✟s r❡❧❡✈☛♥☞ ✎✌r ☞✞❡ ✣✝♥✱ ✇✞✟❧❡ ✎✌r ☛ ❞✟✓
☛☞✌✠✟❝ ✠✌❧❡❝✝❧☛r ❣☛s✱ ✇❡ ✞☛✈❡ ❫ ❃ ❜❄❛✱ ✇✞✟❝✞ ✟s r❡❧❡✈☛♥☞ ✎✌r ☛✟r✍
■♥ ☞✞✌s❡ ❝☛s❡s✱ ☛ s☞r☛☞✟✡❝☛☞✟✌♥ ✇✟☞✞ ❨ ❃ ❫ ❝☛♥ t❡ ✠✌☞✟✈☛☞❡❞ t②
☛ss✝✠✟♥❣ ♣❡r✎❡❝☞ ✠✟①✟♥❣ ☛❝r✌ss ☞✞❡ ❧☛②❡r✍ ❚✞❡ ✟s✌☞✞❡r✠☛❧ ❝☛s❡
✇✟☞✞ ❫ ❃ ✙ ❝☛♥ t❡ ✠✌☞✟✈☛☞❡❞ t② ☛ss✝✠✟♥❣ r☛♣✟❞ ✞❡☛☞✟♥❣❢❝✌✌❧✟♥❣
☞✌ ☛ ❝✌♥s☞☛♥☞ ☞❡✠♣❡r☛☞✝r❡✍
❆✷✂ ❻❷➆⑨ ✷ ⑥➀ ☎☎
❤❥❦♠ ✉♠ ④⑤⑥⑦⑧⑨⑩❶❷❸ ❷❹❺ ❻⑥❸❼⑦⑩⑥❻❽❿ ⑩⑨❸❷⑦❽⑥❹⑤ ➀⑥⑩ ❺❽➁⑨⑩⑨❹⑦ ➂❷❸➃⑨⑤ ⑥➀ ➄
➅⑧⑨❹ ❿❷❸❿➃❸❷⑦⑨❺ ➃⑤❽❹➆ ⑦⑧⑨ ❿⑥❹➂⑨❹⑦❽⑥❹❷❸ ➀⑥⑩❶➃❸❷ ➇ ➈ ✭➉➊ ➋ ➉✆➌ ➅❽⑦⑧
➍ ➎ ☎➏✭➄ ➋ ☎✆➐
➑✝r ☛✟✠ ✟s ☞✌ s☞✝❞② ☞✞❡ ❝✞☛♥❣❡ ✟♥ ☞✞❡ ♣r✌♣❡r☞✟❡s ✌✎ ◆✏✑✒■
✟♥ ☛ ❝✌♥☞✟♥✝✌✝s ✎☛s✞✟✌♥ ☛s ✇❡ ❣✌ ✎r✌✠ ☛♥ ✟s✌☞✞❡r✠☛❧❧② s☞r☛☞✟✓
✡❡❞ ❧☛②❡r ☞✌ ☛ ♣✌❧②☞r✌♣✟❝ ✌♥❡✍ ■♥ ☞✞❡ ❧☛☞☞❡r ❝☛s❡✱ ☞✞❡ ✻✝✟❞ ❞❡♥s✟☞②
✈☛r✟❡s ✟♥ ☛ ♣✌✇❡r ❧☛✇ ✎☛s✞✟✌♥✱ ● ❱ ✔✼✽ ➒ ✼✐▼ ✱ ✇✞✟❧❡ ✟♥ ☞✞❡ ✎✌r✠❡r✱
✟☞ ✈☛r✟❡s ❡①♣✌♥❡♥☞✟☛❧❧②✱ ● ❱ ❡①♣✔✼✽ ➒ ✼✐✍ ❚✞✟s ✟s s✞✌✇♥ ✟♥ ❋✟❣✍ ✙
✇✞❡r❡ ✇❡ ❝✌✠♣☛r❡ ☞✞❡ ❡①♣✌♥❡♥☞✟☛❧ ✟s✌☞✞❡r✠☛❧ ☛☞✠✌s♣✞❡r❡ ✇✟☞✞
☛ ✎☛✠✟❧② ✌✎ ♣✌❧②☞r✌♣✟❝ ☛☞✠✌s♣✞❡r❡s ✇✟☞✞ ❫ ❃ ✙✳✛✱ ✙✍➓✱ ☛♥❞ ❛❢✢✍
❈❧❡☛r❧②✱ ☞✞❡r❡ ✟s ♥✌ ❝✌♥☞✟♥✝✌✝s ❝✌♥♥❡❝☞✟✌♥ t❡☞✇❡❡♥ ☞✞❡ ✟s✌☞✞❡r✓
✠☛❧ ❝☛s❡ ☛♥❞ ☞✞❡ ♣✌❧②☞r✌♣✟❝ ✌♥❡ ✟♥ ☞✞❡ ❧✟✠✟☞ ❫ ➔ ✙✍ ❚✞✟s ❝☛♥♥✌☞
t❡ ✡①❡❞ t② r❡s❝☛❧✟♥❣ ☞✞❡ ✟s✌☞✞❡r✠☛❧ ❞❡♥s✟☞② s☞r☛☞✟✡❝☛☞✟✌♥✱ t❡✓
❝☛✝s❡ ✟♥ ❋✟❣✍ ✙ ✟☞s ✈☛❧✝❡s ✇✌✝❧❞ s☞✟❧❧ ❧✟❡ ❝❧✌s❡r ☞✌ ❛❢✢ ☞✞☛♥ ☞✌ ✙✍➓
✌r ✙✍✛✍ ✥♥✌☞✞❡r ♣r✌t❧❡✠ ✇✟☞✞ ☞✞✟s ❞❡s❝r✟♣☞✟✌♥ ✟s ☞✞☛☞ ✎✌r ♣✌❧②✓
☞r✌♣✟❝ s✌❧✝☞✟✌♥s ☞✞❡ ❞❡♥s✟☞② ✟s ☛❧✇☛②s ③❡r✌ ☛☞ ✼ ❃ ✼✽ ✱ t✝☞ ✡♥✟☞❡ ✟♥
☞✞❡ ✟s✌☞✞❡r✠☛❧ ❝☛s❡✍ ❚✞❡s❡ ❞✟✤❡r❡♥☞ t❡✞☛✈✟✌rs t❡☞✇❡❡♥ ✟s✌☞✞❡r✓
✠☛❧ ☛♥❞ ♣✌❧②☞r✌♣✟❝ ☛☞✠✌s♣✞❡r❡s ❝☛♥ t❡ ✝♥✟✡❡❞ t② ✝s✟♥❣ ☞✞❡ ❣❡♥✓
❡r☛❧✟③❡❞ ❡①♣✌♥❡♥☞✟☛❧ ✎✝♥❝☞✟✌♥ ♦♥✌✇♥ ☛s ☞✞❡ →➣✓❡①♣✌♥❡♥☞✟☛❧↔ ✔s❡❡✱
❡✍❣✍✱ ↕☛✠☛♥✌ ✛✜✜✛✐✱ ✇✞✟❝✞ ✟s ❞❡✡♥❡❞ ☛s
➝
➞❘➟➠❘❾➛➡
❵
➙➛ ✔➜✐ ❃ ✙ ❩ ✔✙ ➒ ➣✐➜
✔✢✐
✇✞❡r❡ ☞✞❡ ♣☛r☛✠❡☞❡r ➣ ✟s r❡❧☛☞❡❞ ☞✌ ❫ ✈✟☛ ➣ ❃ ✛ ➒ ❫✍ ❚✞✟s
❣❡♥❡r☛❧✟③☛☞✟✌♥ ✌✎ ☞✞❡ ✝s✝☛❧ ❡①♣✌♥❡♥☞✟☛❧ ✎✝♥❝☞✟✌♥ ✇☛s ✌r✟❣✟♥☛❧❧②
✟♥☞r✌❞✝❝❡❞ t② ❚s☛❧❧✟s ✔✙➢➤➤✐ ✟♥ ❝✌♥♥❡❝☞✟✌♥ ✇✟☞✞ ☛ ♣✌ss✟t❧❡ ❣❡♥❡r✓
☛❧✟③☛☞✟✌♥ ✌✎ ☞✞❡ ❇✌❧☞③✠☛♥♥✓➥✟tts s☞☛☞✟s☞✟❝s✍ ■☞s ✝s❡✎✝❧♥❡ss ✟♥ ❝✌♥✓
♥❡❝☞✟✌♥ ✇✟☞✞ s☞❡❧❧☛r ♣✌❧②☞r✌♣❡s ✞☛s t❡❡♥ ❡✠♣❧✌②❡❞ t② ✒❧☛s☞✟♥✌ ➦
✒❧☛s☞✟♥✌ ✔✙➢➢✢✐✍ ❚✞✝s✱ ☞✞❡ ❞❡♥s✟☞② s☞r☛☞✟✡❝☛☞✟✌♥ ✟s ❣✟✈❡♥ t②
●
●➧
➨
➩
❃ ✙ ❩ ✔❫ ➒ ✙✐ ➒
✼
❍✗➧
➫➭❘➟➠❪ ❾ ❘➡
➩
❃ ✙➒
✼
❙❍✗➧
➫▼
❵
✔➓✐
✇✞✟❝✞ r❡❞✝❝❡s ☞✌ ●❄●➧ ❃ ❡①♣✔➒✼❄❍✗➧ ✐ ✎✌r ✟s✌☞✞❡r✠☛❧ s☞r☛☞✟✡❝☛✓
☞✟✌♥ ✇✟☞✞ ❫ ➔ ✙ ☛♥❞ ❙ ➔ ➯✍ ❚✞❡ ❞❡♥s✟☞② s❝☛❧❡ ✞❡✟❣✞☞ ✟s ☞✞❡♥
❣✟✈❡♥ t②
❍✗ ✔✼✐ ❃ ❍✗➧ ➒ ✔❫ ➒ ✙✐✼ ❃ ❍✗➧ ➒ ✼❄❙✳
✔❛✐
■♥ ☞✞❡ ✎✌❧❧✌✇✟♥❣✱ ✇❡ ✠❡☛s✝r❡ ❧❡♥❣☞✞s ✟♥ ✝♥✟☞s ✌✎ ❍✗➧ ❃ ❍✗ ✔✜✐✍
■♥ ❋✟❣✍ ✛ ✇❡ s✞✌✇ ☞✞❡ ❞❡♣❡♥❞❡♥❝✟❡s ✌✎ ●✔✼✐ ☛♥❞ ❍✗ ❣✟✈❡♥ t②
✏qs✍ ✔➓✐ ☛♥❞ ✔❛✐ ✎✌r ❞✟✤❡r❡♥☞ ✈☛❧✝❡s ✌✎ ❫✍ ❈✌✠♣☛r❡❞ ✇✟☞✞ ❋✟❣✍ ✙✱
✇✞❡r❡ ✼✽ ✟s ✞❡❧❞ ✡①❡❞✱ ✟♥ ❋✟❣✍ ✛ ✟☞ ✟s ❡q✝☛❧ ☞✌ ✼✽ ❃ ❙❍✗➧ ❃
❍✗➧ ❄✔❫ ➒ ✙✐✍ ❚✞❡ ☞✌☞☛❧ ❞❡♥s✟☞② ❝✌♥☞r☛s☞ ✟s r✌✝❣✞❧② ☞✞❡ s☛✠❡ ✟♥
☛❧❧ ✎✌✝r ❝☛s❡s ✎✌r ❞✟✤❡r❡♥☞ ❫✱ t✝☞ ✎✌r ✟♥❝r❡☛s✟♥❣ ✈☛❧✝❡s ✌✎ ❫✱ ☞✞❡
✈❡r☞✟❝☛❧ ❞❡♥s✟☞② ❣r☛❞✟❡♥☞ t❡❝✌✠❡s ♣r✌❣r❡ss✟✈❡❧② s☞r✌♥❣❡r ✟♥ ☞✞❡
✝♣♣❡r ❧☛②❡rs✍
✥ss✝✠✟♥❣ ☞✞☛☞ ☞✞❡ r☛❞✟✝s ➲ ✌✎ ☞✞❡ r❡s✝❧☞✟♥❣ s☞r✝❝☞✝r❡s ✟s ♣r✌✓
♣✌r☞✟✌♥☛❧ ☞✌ ❍✗ ✱ ✇❡ s♦❡☞❝✞ ✟♥ ❋✟❣✍ ✢ ☛ s✟☞✝☛☞✟✌♥ ✟♥ ✇✞✟❝✞ ➲ ✟s
■✳ ❘✳ ▲♦s ✁ ❡✂ ❛✳✿ ▼ ✄☎❡✂✐❝ ✤✉① ❝♦☎❝❡☎✂r ✂✐♦☎s ✐☎
ρ/ρ0
➃➄➅➄ ➆➇➈ ➉➊➋➈➌
γ =1
10
❲✕ ★❁❧✈✕ t❤✕ ✕➍✽✓t✘❁✧★ ✔❁❆ t❤✕ ❉✓❣✧✕t✘✪ ✈✕✪t❁❆ ✖❁t✕✧t✘✓❧ ➎✦ t❤✕
✈✕❧❁✪✘t✩ ➏✦ ✓✧❞ t❤✕ ❞✕✧★✘t✩ ✙✦ ✘✧ t❤✕ ✔❁❆❉
γ =5/3
➐➎
1
➐➑
➀➏
➀➑
0.1
➀✙
Hρ /Hρ0
➀➑
γ =5/3
3.0
γ =1
−3
−2
✯ ➏ × ➒ ✣ ➓➔→ ➣ ↔
✯
❖
✙
➣ × ➒ ➙ ➛ ✣ ➜➝ ✣ ➞✫↔
✯ ✣✙➞ ➲ ➏↔
✛↕✥
✛➟✥
✛➠✥
❃❤✕❆✕ ➀✰➀➑ ✯ ➐✰➐➑➙➏➲➞ ✘★ t❤✕ ✓❞✈✕✪t✘✈✕ ❞✕❆✘✈✓t✘✈✕ ❃✘t❤ ❆✕★✖✕✪t
t❁ t❤✕ ✓✪t✽✓❧ ✛t✽❆❈✽❧✕✧t✥ ➡❁❃✦ ➒ ✯ ➒→ ➙ ➞ × ➎ ✘★ t❤✕ ❉✓❣✧✕t✘✪
⑧✕❧❞✦ ➒→ t❤✕ ✘❉✖❁★✕❞ ✽✧✘✔❁❆❉ ⑧✕❧❞✦ ➣ ✯ ➞ × ➒✰➔→ t❤✕ ✪✽❆❆✕✧t
❞✕✧★✘t✩✦ ➔→ t❤✕ ✈✓✪✽✽❉ ✖✕❆❉✕✓❈✘❧✘t✩✦ ✫ ✯ ➢ ➙ ➤ t❤✕ ❆✕❞✽✪✕❞
✕✧t❤✓❧✖✩✦ ➢ ✯ ➥ ➦ ➧ t❤✕ ✕✧t❤✓❧✖✩✦ ➤ ✘★ t❤✕ ❣❆✓✈✘t✓t✘❁✧✓❧ ✖❁t✕✧t✘✓❧✦
1.5
0.0
−4
♣♦❛②✂r♦♣✐❝ ✂♠♦s♣✆❡r❡
−1
z/Hρ0
0
1
❋✝✞✟ ✷✟ P♦❛②✂r♦♣❡s ✭❊✠✳ ✭✹✮✮ ✇✐✂✆ ✡ ❂ ✶ ✭s♦❛✐✁ ❛✐☎❡✮✱ ✶✳☛ ✭✁ s✆✲✁♦✂✂❡✁✮✱ ✶✳✹
✭✁♦✂✂❡✁✮✱ ☎✁ ✺✴✸ ✭✁ s✆❡✁✮ ☎✁ ✁❡☎s✐✂② s❝ ❛❡ ✆❡✐✄✆✂ ✭❊✠✳ ✭✺✮✮ ❢♦r ❾✹ ☞
❾③✌❍✍✵ ☞ ✶✎☛✳ ❚✆❡ ✂♦✂ ❛ ✁❡☎s✐✂② ❝♦☎✂r s✂ ✐s s✐♠✐❛ r ❢♦r ✡ ❂ ✶ ☎✁ ✺✴✸✳
➩
❴
✣➝ ✯ ➨ ➏ ➙ ➫ ➞➞ ➲ ➏ ➙ ❅➭➞ ❧✧ ✙
✛➯✥
✘★ ✓ t✕❆❉ ✓✖✖✕✓❆✘✧❣ ✘✧ t❤✕ ✈✘★✪❁✽★ ✔❁❆✪✕ ✣➜➝✦ ➭ ✘★ t❤✕ t❆✓✪✕❧✕★★
❆✓t✕❯❁✔❯★t❆✓✘✧ t✕✧★❁❆ ❃✘t❤ ✪❁❉✖❁✧✕✧t★
➳➵ ➸ ✯ ❴➩ ✛➨ ➸ ➺ ➵ ➙ ➨➵ ➺ ➸ ✥ ✣ ❴➫ ➻➵ ➸ ➞ ➲ ➏↔
✛❖❏✥
➜ ✘★ t❤✕ ⑨✘✧✕❉✓t✘✪ ✈✘★✪❁★✘t✩✦ ✓✧❞ ➓ ✘★ t❤✕ ❉✓❣✧✕t✘✪ ❞✘➼✽★✘❁✧ ✪❁❯
✕➽✪✘✕✧t ✪✓✽★✕❞ ❈✩ ✕❧✕✪t❆✘✪✓❧ ✪❁✧❞✽✪t✘✈✘t✩ ❁✔ t❤✕ ➡✽✘❞✗ ➾★ ✘✧
➚❁★✓❞✓ ✕t ✓❧✗ ✛❅❏❖❅✥✦ ✜ ✪❁❆❆✕★✖❁✧❞★ t❁ ❆✓❞✘✽★✦ ➪ t❁ ✪❁❧✓t✘t✽❞✕✦
✓✧❞ ➶ t❁ ✓❇✘❉✽t❤✗ ✼❤✕ ✔❁❆✪✘✧❣ ✔✽✧✪t✘❁✧ ➛ ✪❁✧★✘★t★ ❁✔ ❆✓✧❞❁❉✦
❃❤✘t✕❯✘✧❯t✘❉✕✦ ✖❧✓✧✕✦ ✧❁✧✖❁❧✓❆✘❇✕❞ ❃✓✈✕★ ❃✘t❤ ✓ ✪✕❆t✓✘✧ ✓✈✕❆✓❣✕
❃✓✈✕✧✽❉❈✕❆ ❱➹ ✗
➃➄➘➄ ➴➊➷➬➋➮➱✃ ❐➊➬➋❒❮❒➊➬❰ ➮➬➋ Ï➮➱➮➉➈❮➈➱❰
❋✝✞✟ ✏✟ ❙❦❡✂❝✆ s✆♦✇✐☎✄ ✂✆❡ ❡①♣❡❝✂❡✁ s✐✑❡ ✁✐s✂r✐❜✉✂✐♦☎ ♦❢ ✂✆❡ ☎❡ r❛② ❝✐r✲
❝✉❛ r ◆❊▼P■ ❡✐✄❡☎❢✉☎❝✂✐♦☎ s✂r✉❝✂✉r❡s ✂ ✁✐✒❡r❡☎✂ ✆❡✐✄✆✂s✳
❤✓❧✔ t❤✕ ❞✕✖t❤✗ ❲✘t❤ ✙ ✚ ✛✜✢ ✣ ✜✥♥ ✦ t❤✕ ❞✕✧★✘t✩ ★✪✓❧✕ ❤✕✘❣❤t ✘★
✫✬ ✛✜✥ ✯ ✛✜✢ ✣ ✜✥✰✻✗ ✼❤✽★✦ ✾✘❣✗ ❀ ✓✖✖❧✘✕★ t❁ ✓ ✪✓★✕ ✘✧ ❃❤✘✪❤
❄ ✯ ✛✜✢ ✣✜✥✰❅ ✯ ✛✻✰❅✥ ✫✬ ✛✜✥✗ ✼❤✕ ★❁❧✓❆ ✪❁✧✈✕✪t✘❁✧ ❇❁✧✕ ✘★ ✧✕✓❆❧✩
✘★✕✧t❆❁✖✘✪ ✓✧❞ ❃✕❧❧ ❞✕★✪❆✘❈✕❞ ❈✩ ✻ ✯ ❀✰❅✗ ✼❤✘★ ❉✕✓✧★ t❤✓t t❤✕
★t❆✽✪t✽❆✕★ ❁✔ ✾✘❣✗ ❀ ❤✓✈✕ ❄ ✯ ✛❀✰●✥ ✫✬ ✛✜✥✗ ✼❤✕ ❆✕★✽❧t★ ❁✔ ❑✕❉✕❧
✕t ✓❧✗ ✛❅❏❖❀✥ ✓✧❞ ◗❆✓✧❞✕✧❈✽❆❣ ✕t ✓❧✗ ✛❅❏❖●✥ ★✽❣❣✕★t t❤✓t t❤✕ ❤❁❆✘❯
❇❁✧t✓❧ ❃✓✈✕✧✽❉❈✕❆ ❁✔ ★t❆✽✪t✽❆✕★✦ ❱❳ ✦ ✔❁❆❉✕❞ ❈✩ ❨❩❬❭❪✦ ✘★ ❧✕★★
t❤✓✧ ❁❆ ✓❈❁✽t ✫✬❫❴ ✦ ★❁ t❤✕✘❆ ❤❁❆✘❇❁✧t✓❧ ❃✓✈✕❧✕✧❣t❤ ✘★ ❵
❥❅q✫✬ ✗ ④✧✕
❃✓✈✕❧✕✧❣t❤ ✪❁❆❆✕★✖❁✧❞★ t❁ t❤✕ ❞✘★t✓✧✪✕ ❈✕t❃✕✕✧ t❃❁ ✧❁❞✕★✦ ✘✗✕✗✦
t❤✕ ❞✘★t✓✧✪✕ ❈✕t❃✕✕✧ t❃❁ ★✖❤✕❆✕★✦ ❃❤✘✪❤ ✘★ ● ❄✗ ✼❤✽★✦ ✘✧ t❤✕
✘★❁t❤✕❆❉✓❧ ✪✓★✕ ❃✕ ❤✓✈✕ ❄✰✫✬ ✯ ❅q✰● ⑤ ❖⑥⑦✦ ❃❤✘✪❤ ✘❉✖❧✘✕★
t❤✓t ★✽✪❤ ✓ ★t❆✽✪t✽❆✕ ❃❁✽❧❞ ✧❁t ⑧t ✘✧t❁ t❤✕ ✘★✕✧t❆❁✖✘✪ ✓t❉❁★✖❤✕❆✕
❞✕★✪❆✘❈✕❞ ✓❈❁✈✕✗ ✼❤✘★ ✖❆❁✈✘❞✕★ ✓✧ ✓❞❞✘t✘❁✧✓❧ ❉❁t✘✈✓t✘❁✧ ✔❁❆ ❁✽❆
✖❆✕★✕✧t ❃❁❆⑨✗
❪✧ t❤✕ ➀❨➁ ❃✕ ✽★✕ ★t❆✕★★❯✔❆✕✕ ❈❁✽✧❞✓❆✩ ✪❁✧❞✘t✘❁✧★ ✔❁❆ t❤✕ ✈✕❯
❧❁✪✘t✩ ✓t t❤✕ t❁✖ ✓✧❞ ❈❁tt❁❉Ð ✘✗✕✗✦ ➨Ñ ➺ Ò ✯ ➨Ñ ➺ Ó ✯ ➺Ñ ✯ ❏✗
✾❁❆ t❤✕ ❉✓❣✧✕t✘✪ ⑧✕❧❞ ❃✕ ✽★✕ ✕✘t❤✕❆ ✖✕❆✔✕✪t ✪❁✧❞✽✪t❁❆ ❈❁✽✧❞✓❆✩
✪❁✧❞✘t✘❁✧★✦ Ô Ò ✯ ÔÓ ✯ ➨Ñ ÔÑ ✯ ❏✦ ❁❆ ✈✕❆t✘✪✓❧ ⑧✕❧❞ ✪❁✧❞✘t✘❁✧★✦
➨Ñ Ô Ò ✯ ➨Ñ ÔÓ ✯ ÔÑ ✯ ❏✦ ✓❣✓✘✧ ✓t ❈❁t❤ t❤✕ t❁✖ ✓✧❞ ❈❁tt❁❉✗ ➾❧❧
✈✓❆✘✓❈❧✕★ ✓❆✕ ✓★★✽❉✕❞ ✖✕❆✘❁❞✘✪ ✘✧ t❤✕ ➪ ✓✧❞ ➶ ❞✘❆✕✪t✘❁✧★✗
✼❤✕ t✽❆❈✽❧✕✧t ❆❉★ ✈✕❧❁✪✘t✩ ✘★ ✓✖✖❆❁Õ✘❉✓t✕❧✩ ✘✧❞✕✖✕✧❞✕✧t ❁✔ ✜
❃✘t❤ ÖØÙÚ ✯ ÛÜ➩ Ý❴Þ➩ ⑤ ❏⑥❖ ➥Ú ✗ ✼❤✕ ❣❆✓✈✘t✓t✘❁✧✓❧ ✓✪✪✕❧✕❆✓t✘❁✧
ß ✯ ✛❏↔ ❏↔ ✣à✥ ✘★ ✪❤❁★✕✧ ★✽✪❤ t❤✓t ❱❴ ✫✬→ ✯ ❖✦ ❃❤✕❆✕ ❱❴ ✯ ❅q✰á
✓✧❞ á ✘★ t❤✕ ★✘❇✕ ❁✔ t❤✕ ❞❁❉✓✘✧✗ ❲✘t❤ ❁✧✕ ✕Õ✪✕✖t✘❁✧ ✛➁✕✪t✗ ❀✗⑦✥✦
❃✕ ✓❧❃✓✩★ ✽★✕ t❤✕ ✈✓❧✽✕ ❱➹ ✰❱❴ ✯ ❀❏ ✔❁❆ t❤✕ ★✪✓❧✕ ★✕✖✓❆✓t✘❁✧ ❆✓t✘❁✗
✾❁❆ ➒→ ❃✕ ✪❤❁❁★✕ ✕✘t❤✕❆ ✓ ❤❁❆✘❇❁✧t✓❧ ⑧✕❧❞ ✖❁✘✧t✘✧❣ ✘✧ t❤✕ ➶ ❞✘❆✕✪❯
t✘❁✧ ❁❆ ✓ ✈✕❆t✘✪✓❧ ❁✧✕ ✖❁✘✧t✘✧❣ ✘✧ t❤✕ ✜ ❞✘❆✕✪t✘❁✧✗ ✼❤✕ ❧✓tt✕❆ ✪✓★✕✦
➒→ ✯ ✛❏↔ ❏↔ â→✥✦ ✘★ ✽★✽✓❧❧✩ ✪❁❉❈✘✧✕❞ ❃✘t❤ t❤✕ ✽★✕ ❁✔ t❤✕ ✈✕❆t✘✪✓❧
⑧✕❧❞ ❈❁✽✧❞✓❆✩ ✪❁✧❞✘t✘❁✧✦ ❃❤✘❧✕ t❤✕ ✔❁❆❉✕❆ ❁✧✕✦ ➒→ ✯ ✛❏↔ â→ ↔ ❏✥✦
✘★ ✪❁❉❈✘✧✕❞ ❃✘t❤ ✽★✘✧❣ ✖✕❆✔✕✪t ✪❁✧❞✽✪t❁❆ ❈❁✽✧❞✓❆✩ ✪❁✧❞✘t✘❁✧★✗
✼❤✕ ★t❆✕✧❣t❤ ❁✔ t❤✕ ✘❉✖❁★✕❞ ⑧✕❧❞ ✘★ ✕Õ✖❆✕★★✕❞ ✘✧ t✕❆❉★ ❁✔ âãä→ ✯
âãä ✛✜ ✯ ❏✥✦ ❃❤✘✪❤ ✘★ t❤✕ ✕➍✽✘✖✓❆t✘t✘❁✧ ⑧✕❧❞ ★t❆✕✧❣t❤ ✓t ✜ ✯ ❏✗
❴Þ➩
å✕❆✕✦ t❤✕ ✕➍✽✘✖✓❆t✘t✘❁✧ ⑧✕❧❞ âãä ✛✜✥ ✯ ✛➔→ ✙✛✜✥✥
ÖØÙÚ ✗ ✼❤✕ ✘❉❯
✖❁★✕❞ ⑧✕❧❞ ✘★ ✧❁❆❉✓❧✘❇✕❞ ❈✩ âãä→ ✓✧❞ ❞✕✧❁t✕❞ ✓★ æ→ ✯ â→ ✰âãä→ ✦
❃❤✘❧✕ æ ✯ ç➒ç✰âãä ✘★ t❤✕ ❉❁❞✽❧✽★ ❁✔ t❤✕ ✧❁❆❉✓❧✘❇✕❞ ❉✕✓✧ ❉✓❣❯
✧✕t✘✪ ⑧✕❧❞✗ ✼✘❉✕ ✘★ ✕Õ✖❆✕★★✕❞ ✘✧ t✕❆❉★ ❁✔ t❤✕ t✽❆❈✽❧✕✧t❯❞✘➼✽★✘✈✕
➩ ✰➓ ✦ ❃❤✕❆✕ ➓ ✯ Ö ✰❀❱ ✛➁✽❆ ✕t ✓❧✗ ❅❏❏➠✥ ✘★ ✓✧
t✘❉✕✦ èéê ✯ ✫✬→
é→
é→
ØÙÚ
➹
✕★t✘❉✓t✕ ✔❁❆ t❤✕ t✽❆❈✽❧✕✧t ❉✓❣✧✕t✘✪ ❞✘➼✽★✘✈✘t✩ ✽★✕❞ ✘✧ t❤✕ ➀❨➁✗
④✽❆ ✈✓❧✽✕★ ❁✔ ➜ ✓✧❞ ➓ ✓❆✕ ✪❤✓❆✓✪t✕❆✘❇✕❞ ❈✩ ★✖✕✪✘✔✩✘✧❣ t❤✕
⑨✘✧✕t✘✪ ✓✧❞ ❉✓❣✧✕t✘✪ ë✕✩✧❁❧❞★ ✧✽❉❈✕❆★✦
⑩❶ ❷❸❹ ❺❻❼❽❿
ë✕ ✯ ÖØÙÚ ✰➜❱➹ ↔
❪✧ t❤✘★ ★✕✪t✘❁✧ ❃✕ ★t✽❞✩ ❨❩❬❭❪ ✘✧ ➀❨➁ ✔❁❆ t❤✕ ✖❁❧✩t❆❁✖✘✪ ❧✓✩✕❆✗
➂❁❆❆✕★✖❁✧❞✘✧❣ ❬✾➁ ✓❆✕ ✖❆✕★✕✧t✕❞ ✘✧ ➁✕✪t✗ ●✗
❪✧ ❉❁★t ❁✔ t❤✘★ ✖✓✖✕❆ ✛✕Õ✪✕✖t ✘✧ ➁✕✪t✗ ❀✗⑦✥ ❃✕ ✽★✕ ë✕ ✯ ❀↕ ✓✧❞
❄Ù ✯ ❖➠✦ ❃❤✘✪❤ ✓❆✕ ✓❧★❁ t❤✕ ✈✓❧✽✕★ ✽★✕❞ ❈✩ ❑✕❉✕❧ ✕t ✓❧✗ ✛❅❏❖❀✥✗
❄Ù ✯ ÖØÙÚ ✰➓❱➹ ⑥
✛❖❖✥
ì☛✱ ♣ ✄❡ ✸ ♦❢ ✶✶
❆✫❆ ✺ ✁✂ ❆✷ ✭✷✄☎✁✆
❋✝✞✳ ✹✳ ❙♥❛✟✠✡☛☞✠ ☛❢ ❇② ❢✌☛♠ ❉✍❙ ❢☛✌ ✎ ❂ ✺✴✸ ❛♥❞ ✏✵ ❂ ✄✑✄✷ ✭✉✒✒✓✔ ✔♦✕✆✂ ✄✑✄✺ ✭✖✐✗✗✘✓ ✔♦✕✆✂ ❛♥❞ ✄✑☎ ✭✘♦✕✓✔ ✔♦✕✆ ❛☞ ❞✙✚❡✌❡♥☞ ☞✙♠❡✠ ✭✙♥❞✙❝❛☞❡❞ ✙♥
☞t✌rt❧❡♥☞✛❞✙✚t✠✙✈❡ ☞✙♠❡✠✂ ✙♥❝✌❡❛✠✙♥✜ ❢✌☛♠ ❧❡❢☞ ☞☛ ✌✙✜✡☞✆ ✙♥ ☞✡❡ ✟✌❡✠❡♥❝❡ ☛❢ ❛ ✡☛✌✙❤☛♥☞❛❧ ✣❡❧❞ t✠✙♥✜ ☞✡❡ ✟❡✌❢❡❝☞ ❝☛♥❞t❝☞☛✌ r☛t♥❞❛✌❜ ❝☛♥❞✙☞✙☛♥✢
❚✤✥ ✦✧★ ✩✪✥ ♣✥✪✬✮✪✯✥✰ ✇✱✲✤ ✲✤✥ P✶✻✼✽✾ ❈✿❀✶❁ ❃❄❄❅❊●●
❅❍■❏❑▲▼❏◆❖❍◗❘◆◆❘▲❍❏◆❖❍◗❏◆❯❁ ✇✤✱❱✤ ❲❳✥❳ ❳✱①✲✤❨✮✪✰✥✪ ✥①❨
♣❩✱❱✱✲ ❬❭✱✲✥ ✰✱❪✥✪✥❭❱✥❳ ✱❭ ❳♣✩❱✥ ✩❭✰ ✩ ✲✤✱✪✰❨✮✪✰✥✪ ✩❱❱❲✪✩✲✥ ✲✱✯✥
❳✲✥♣♣✱❭❫ ✯✥✲✤✮✰❴ ❵✥ ❲❳✥ ✩ ❭❲✯✥✪✱❱✩❩ ✪✥❳✮❩❲✲✱✮❭ ✮✬ ❣❥❦q ✯✥❳✤
♣✮✱❭✲❳❴
s③s③ ④⑤⑥⑦⑧⑤⑨⑩❶❷ Þ❸❷❹❺
❵✥ ✬✮❱❲❳ ✮❭ ✲✤✥ ❱✩❳✥ ❻ ❼ ❥❽❾ ✩❭✰ ❳✤✮✇ ✱❭ ❿✱❫❴ ➀ ➁✱❳❲✩❩✱➂✩❨
✲✱✮❭❳ ✮✬ ➃➄ ✩✲ ✰✱❪✥✪✥❭✲ ✱❭❳✲✩❭✲❳ ✬✮✪ ✲✤✪✥✥ ➁✩❩❲✥❳ ✮✬ ✲✤✥ ✱✯♣✮❳✥✰
✤✮✪✱➂✮❭✲✩❩ ✯✩❫❭✥✲✱❱ ❬✥❩✰ ❳✲✪✥❭❫✲✤❴ ❿✮✪ ➅➆ ❼ ➇➈➇❣❁ ✩ ✯✩❫❭✥✲✱❱
❳✲✪❲❱✲❲✪✥ ✱❳ ❱❩✥✩✪❩➉ ➁✱❳✱➊❩✥ ✩✲ ➋❽➌➍➎ ❼ ➏➈➀❾❁ ✇✤✱❩✥ ✬✮✪ ➅➆ ❼ ➇➈➇❥
❳✲✪❲❱✲❲✪✥❳ ✩✪✥ ✩❩✪✥✩✰➉ ✬❲❩❩➉ ✰✥➁✥❩✮♣✥✰ ✩✲ ➋❽➌➍➎ ❼ ➇➈➀❣❴ ➐❭ ✲✤✩✲ ❱✩❳✥
➑➅➆ ❼ ➇➈➇❥➒❁ ✩✲ ✥✩✪❩➉ ✲✱✯✥❳ ➑➋❽➌➍➎ ❼ ➇➈➀❣➒❁ ✲✤✥✪✥ ✩✪✥ ✲✇✮ ❳✲✪❲❱❨
✲❲✪✥❳❁ ✇✤✱❱✤ ✲✤✥❭ ➊✥❫✱❭ ✲✮ ✯✥✪❫✥ ✩✲ ➋❽➌➍➎ ❼ ➏➈❾➓❴ ❚✤✥ ❫✪✮✇✲✤
↕ ✬✮✪ ✲✤✥
✪✩✲✥ ✮✬ ✲✤✥ ✯✩❫❭✥✲✱❱ ❳✲✪❲❱✲❲✪✥ ✱❳ ✬✮❲❭✰ ✲✮ ➊✥ ➔ → ❣➣➍➆ ❽↔➙➆
↕
✪❲❭❳ ❳✤✮✇❭ ✱❭ ❿✱❫❴ ➀❴ ❚✤✱❳ ✱❳ ❩✥❳❳ ✲✤✩❭ ✲✤✥ ➁✩❩❲✥ ✮✬ ➔ → ❥➣➍➆ ❽↔➙➆
✬✮❲❭✰ ✥✩✪❩✱✥✪ ✬✮✪ ✲✤✥ ✱❳✮✲✤✥✪✯✩❩ ❱✩❳✥ ➑➛✥✯✥❩ ✥✲ ✩❩❴ ❣➇➏❣➊➒❴
❿✮✪ ❻ ❼ ❥❽❾ ✩❭✰ ➅➆ ➜ ➇➈➇❣❁ ✲✤✥ ✯✩❫❭✥✲✱❱ ❳✲✪❲❱✲❲✪✥❳ ➊✥❨
❱✮✯✥ ❳✯✩❩❩✥✪ ➑➝➞ ↔➙➆ ❼ ❣➒ ❭✥✩✪ ✲✤✥ ❳❲✪✬✩❱✥❴ ➐❭ ✲✤✥ ❭✮❭❩✱❭✥✩✪
✪✥❫✱✯✥❁ ✱❴✥❴❁ ✩✲ ❩✩✲✥ ✲✱✯✥❳❁ ✲✤✥ ❳✲✪❲❱✲❲✪✥❳ ✯✮➁✥ ✰✮✇❭✇✩✪✰ ✰❲✥
✲✮ ✲✤✥ ❳✮❨❱✩❩❩✥✰ ➟♣✮✲✩✲✮❨❳✩❱➠➡ ✥❪✥❱✲❁ ✇✤✱❱✤ ✇✩❳ ❬✪❳✲ ❳✥✥❭ ✱❭
➢❿★ ➑➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ❣➇➏➇➒ ✩❭✰ ❩✩✲✥✪ ❱✮❭❬✪✯✥✰ ✱❭ ✦✧★
➑➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ❣➇➏➏➒❴ ❚✤✥ ✯✩❫❭✥✲✱❱ ❳✲✪❲❱✲❲✪✥❳ ❳✱❭➠ ✱❭ ✲✤✥
❭✮❭❩✱❭✥✩✪ ❳✲✩❫✥ ✮✬ ✧➥➢P➐❁ ➊✥❱✩❲❳✥ ✩❭ ✱❭❱✪✥✩❳✥ ✱❭ ✲✤✥ ✯✥✩❭
✯✩❫❭✥✲✱❱ ❬✥❩✰ ✱❭❳✱✰✥ ✲✤✥ ✤✮✪✱➂✮❭✲✩❩ ✯✩❫❭✥✲✱❱ ➦❲① ✲❲➊✥ ✱❭❱✪✥✩❳✥❳
✲✤✥ ✩➊❳✮❩❲✲✥ ➁✩❩❲✥ ✮✬ ✲✤✥ ✥❪✥❱✲✱➁✥ ✯✩❫❭✥✲✱❱ ♣✪✥❳❳❲✪✥❴ ➧❭ ✲✤✥
✮✲✤✥✪ ✤✩❭✰❁ ✩ ✰✥❱✪✥✩❳✥ ✱❭ ✲✤✥ ❭✥❫✩✲✱➁✥ ✥❪✥❱✲✱➁✥ ✯✩❫❭✥✲✱❱ ♣✪✥❳❨
❳❲✪✥ ✱❳ ➊✩❩✩❭❱✥✰ ✮❲✲ ➊➉ ✱❭❱✪✥✩❳✥✰ ❫✩❳ ♣✪✥❳❳❲✪✥❁ ✇✤✱❱✤ ✱❭ ✲❲✪❭
❩✥✩✰❳ ✲✮ ✤✱❫✤✥✪ ✰✥❭❳✱✲➉❁ ❳✮ ✲✤✥ ✯✩❫❭✥✲✱❱ ❳✲✪❲❱✲❲✪✥❳ ➊✥❱✮✯✥ ✤✥✩➁❨
✱✥✪ ✲✤✩❭ ✲✤✥ ❳❲✪✪✮❲❭✰✱❭❫❳ ✩❭✰ ❳✱❭➠❴ ❚✤✱❳ ♣✮✲✩✲✮❨❳✩❱➠ ✥❪✥❱✲ ✤✩❳
➊✥✥❭ ❱❩✥✩✪❩➉ ✮➊❳✥✪➁✥✰ ✱❭ ✲✤✥ ♣✪✥❳✥❭✲ ✦✧★ ✇✱✲✤ ✲✤✥ ♣✮❩➉✲✪✮♣✱❱
❩✩➉✥✪ ➑❳✥✥ ✲✤✥ ✪✱❫✤✲ ❱✮❩❲✯❭ ✱❭ ❿✱❫❴ ➀➒❴
s③➨③ ➩❸⑥⑩⑦➫❶❷ Þ❸❷❹❺
➭✥❱✥❭✲ ✦✧★ ❲❳✱❭❫ ✱❳✮✲✤✥✪✯✩❩ ❩✩➉✥✪❳ ✤✩➁✥ ❳✤✮✇❭ ✲✤✩✲ ❳✲✪✮❭❫ ❱✱✪❨
❱❲❩✩✪ ➦❲① ❱✮❭❱✥❭✲✪✩✲✱✮❭❳ ❱✩❭ ➊✥ ♣✪✮✰❲❱✥✰ ✱❭ ✲✤✥ ❱✩❳✥ ✮✬ ✩ ➁✥✪✲✱❨
❱✩❩ ✯✩❫❭✥✲✱❱ ❬✥❩✰ ➑➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ❣➇➏❾❁ ❣➇➏➀➒❴ ❚✤✱❳ ✱❳ ✩❩❳✮
❆✷✂ ✟❛✜❡ ✁ ☛❢ ☎☎
✮➊❳✥✪➁✥✰ ✱❭ ✲✤✥ ♣✪✥❳✥❭✲ ❳✲❲✰➉ ✮✬ ✩ ♣✮❩➉✲✪✮♣✱❱ ❩✩➉✥✪➯ ❳✥✥ ❿✱❫❴ ❥❁
✇✤✥✪✥ ✇✥ ❳✤✮✇ ✲✤✥ ✥➁✮❩❲✲✱✮❭ ✮✬ ➃➲ ✮❭ ✲✤✥ ♣✥✪✱♣✤✥✪➉ ✮✬ ✲✤✥ ❱✮✯❨
♣❲✲✩✲✱✮❭✩❩ ✰✮✯✩✱❭ ✬✮✪ ❻ ❼ ❥❽❾ ✩❭✰ ➅➆ ❼ ➇➈➇❥ ✩✲ ✰✱❪✥✪✥❭✲ ✲✱✯✥❳❴ ➳
✰✱❪✥✪✥❭❱✥ ✲✮ ✲✤✥ ✦✧★ ✬✮✪ ❻ ❼ ➏ ➑➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ❣➇➏❾➒ ❳✥✥✯❳
✲✮ ➊✥ ✲✤✩✲ ✬✮✪ ❻ ❼ ❥❽❾ ✲✤✥ ✯✩❫❭✥✲✱❱ ❳✲✪❲❱✲❲✪✥❳ ✩✪✥ ❳✤✩❩❩✮✇✥✪ ✲✤✩❭
✬✮✪ ❻ ❼ ➏➯ ❳✥✥ ❿✱❫❴ ❦❁ ✇✤✥✪✥ ✇✥ ❳✤✮✇ ➵➸ ✩❭✰ ➵➺ ❳❩✱❱✥❳ ✮✬ ➃➲
✲✤✪✮❲❫✤ ✲✤✥ ❳♣✮✲❴ ➧✇✱❭❫ ✲✮ ♣✥✪✱✮✰✱❱✱✲➉ ✱❭ ✲✤✥ ➵➸ ♣❩✩❭✥❁ ✇✥ ✤✩➁✥
❳✤✱✬✲✥✰ ✲✤✥ ❩✮❱✩✲✱✮❭ ✮✬ ✲✤✥ ❳♣✮✲ ✲✮ ➵ ❼ ➸ ❼ ➇❴ ❵✥ ❭✮✲✥ ✩❩❳✮ ✲✤✩✲ ✲✤✥
❬✥❩✰ ❩✱❭✥❳ ✮✬ ✲✤✥ ✩➁✥✪✩❫✥✰ ✯✩❫❭✥✲✱❱ ❬✥❩✰ ❳✤✮✇ ✩ ❳✲✪❲❱✲❲✪✥ ✪✩✲✤✥✪
❳✱✯✱❩✩✪ ✲✮ ✲✤✥ ✮❭✥ ✬✮❲❭✰ ✱❭ ➢❿★ ✮✬ ➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ➑❣➇➏➀➒❴
❚✤✥ ✮✪✱❫✱❭ ✮✬ ❱✱✪❱❲❩✩✪ ❳✲✪❲❱✲❲✪✥❳ ✱❳ ✩❳❳✮❱✱✩✲✥✰ ✇✱✲✤ ✩ ❱➉❩✱❭✰✪✱❱✩❩
❳➉✯✯✥✲✪➉ ✬✮✪ ✲✤✥ ➁✥✪✲✱❱✩❩ ✯✩❫❭✥✲✱❱ ❬✥❩✰❴ ❚✤✥ ❫✪✮✇✲✤ ✪✩✲✥ ✮✬ ✲✤✥
↕ ❁ ✇✤✱❱✤
✯✩❫❭✥✲✱❱ ❬✥❩✰ ✱❭ ✲✤✥ ❳♣✮✲ ✱❳ ✬✮❲❭✰ ✲✮ ➊✥ ➔ → ➇➈➻➣➍➆ ❽↔➙➆
✱❳ ❳✱✯✱❩✩✪ ✲✮ ✲✤✥ ➁✩❩❲✥ ✮✬ ➏❴❾ ✬✮❲❭✰ ✥✩✪❩✱✥✪ ✬✮✪ ✲✤✥ ✱❳✮✲✤✥✪✯✩❩ ❱✩❳✥
➑➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ❣➇➏❾➒❴
s③➼③ ➽➾➾❸➫⑩⑦➚❸ ➪❶➶⑨❸⑩⑦➫ ➹⑥❸❺❺➘⑥❸
➳❳ ♣✮✱❭✲✥✰ ✮❲✲ ✱❭ ★✥❱✲❴ ➏❁ ✲✤✥ ✯✩✱❭ ✪✥✩❳✮❭ ✬✮✪ ✲✤✥ ✬✮✪✯✩✲✱✮❭
✮✬ ❳✲✪✮❭❫❩➉ ✱❭✤✮✯✮❫✥❭✥✮❲❳ ❩✩✪❫✥❨❳❱✩❩✥ ✯✩❫❭✥✲✱❱ ❳✲✪❲❱✲❲✪✥❳ ✱❳
✲✤✥ ❭✥❫✩✲✱➁✥ ❱✮❭✲✪✱➊❲✲✱✮❭ ✮✬ ✲❲✪➊❲❩✥❭❱✥ ✲✮ ✲✤✥ ❩✩✪❫✥❨❳❱✩❩✥ ✯✩❫❨
❭✥✲✱❱ ♣✪✥❳❳❲✪✥❁ ❳✮ ✲✤✩✲ ✲✤✥ ✥❪✥❱✲✱➁✥ ✯✩❫❭✥✲✱❱ ♣✪✥❳❳❲✪✥ ➑✲✤✥ ❳❲✯
✮✬ ✲❲✪➊❲❩✥❭✲ ✩❭✰ ❭✮❭✲❲✪➊❲❩✥❭✲ ❱✮❭✲✪✱➊❲✲✱✮❭❳➒ ❱✩❭ ➊✥ ❭✥❫✩✲✱➁✥ ✩✲
✤✱❫✤ ✯✩❫❭✥✲✱❱ ➭✥➉❭✮❩✰❳ ❭❲✯➊✥✪❳❴ ❚✤✥ ✥❪✥❱✲✱➁✥ ✯✩❫❭✥✲✱❱ ♣✪✥❳❨
❳❲✪✥ ✤✩❳ ➊✥✥❭ ✰✥✲✥✪✯✱❭✥✰ ✬✪✮✯ ✦✧★ ✬✮✪ ✱❳✮✲✤✥✪✯✩❩❩➉ ❳✲✪✩✲✱❬✥✰
✬✮✪❱✥✰ ✲❲✪➊❲❩✥❭❱✥ ➑➤✪✩❭✰✥❭➊❲✪❫ ✥✲ ✩❩❴ ❣➇➏➇❁ ❣➇➏❣➒ ✩❭✰ ✬✮✪ ✲❲✪➊❲❨
❩✥❭✲ ❱✮❭➁✥❱✲✱✮❭ ➑➛ ♣➉❩ ✥✲ ✩❩❴ ❣➇➏❣➒❴ ❚✮ ❳✥✥ ✇✤✥✲✤✥✪ ✲✤✥ ❭✩✲❲✪✥ ✮✬
♣✮❩➉✲✪✮♣✱❱ ❳✲✪✩✲✱❬❱✩✲✱✮❭ ✤✩❳ ✩❭➉ ✱❭➦❲✥❭❱✥ ✮❭ ✲✤✥ ✥❪✥❱✲✱➁✥ ✯✩❫❨
❭✥✲✱❱ ♣✪✥❳❳❲✪✥❁ ✇✥ ❲❳✥ ✦✧★❴
❵✥ ❬✪❳✲ ✥①♣❩✩✱❭ ✲✤✥ ✥❳❳✥❭❱✥ ✮✬ ✲✤✥ ✥❪✥❱✲ ✮✬ ✲❲✪➊❲❩✥❭❱✥ ✮❭ ✲✤✥
✥❪✥❱✲✱➁✥ ✯✩❫❭✥✲✱❱ ♣✪✥❳❳❲✪✥❴ ❵✥ ❱✮❭❳✱✰✥✪ ✲✤✥ ✯✮✯✥❭✲❲✯ ✥➴❲✩❨
✲✱✮❭ ✱❭ ✲✤✥ ✬✮✪✯
➷
➷➋
➬ ➮➱ ❼ ✃
➷
➷➵ ❐
❒➱ ❐ ❮ ➬ ❰ ➱ Ï
➑➏❣➒
✇✤✥✪✥
Ñ
Õ
❒➱ ❐ ❼ ➬ ➮ ➱ ➮ ❐ ❮ Ð➱ ❐ Ò ❮ Ó↕❽❣Ô➆ ✃ ➃➱ ➃ ❐❽Ô➆ ✃ ❣Ö➬ ×➱ ❐
✱❳ ✲✤✥ ✯✮✯✥❭✲❲✯ ❳✲✪✥❳❳ ✲✥❭❳✮✪ ✩❭✰ Ð➱ ❐ ✲✤✥ ➛✪✮❭✥❱➠✥✪ ✲✥❭❳✮✪❴
➑➏❾➒
■✳ ❘✳ ▲♦s ✁ ❡✂ ❛✳✿ ▼ ✄☎❡✂✐❝ ✤✉① ❝♦☎❝❡☎✂r ✂✐♦☎s ✐☎
♣♦❛②✂r♦♣✐❝ ✂♠♦s♣✆❡r❡
❋✝✞✟ ✺✟ ❙☎ ♣s✆♦✂s ❢r♦♠ ❉◆❙ s✆♦✇✐☎✄ ❇③ ♦☎ ✂✆❡ ♣❡r✐♣✆❡r② ♦❢ ✂✆❡ ❝♦♠♣✉✂ ✂✐♦☎ ❛ ✁♦♠ ✐☎ ❢♦r ✠ ❂ ✡✴✸ ☎✁ ☛✵ ❂ ☞✌☞✡ ✂ ✁✐✍❡r❡☎✂ ✂✐♠❡s ❢♦r ✂✆❡ ❝ s❡ ♦❢
✈❡r✂✐❝ ❛ ✣❡❛✁ ✉s✐☎✄ ✂✆❡ ✈❡r✂✐❝ ❛ ✣❡❛✁ ❜♦✉☎✁ r② ❝♦☎✁✐✂✐♦☎✳
❋✝✞✟ ✻✟ ❈✉✂s ♦❢ ❇③ ✴❇✎✏ ✭✑✮ ✐☎ ✭ ✮ ✂✆❡ ✒✓ ♣❛ ☎❡ ✂ ✂✆❡ ✂♦♣ ❜♦✉☎✁ r② ✭✑✴❍✔✵ ❂ ✶✌✷✮ ☎✁ ✭❜✮ ✂✆❡ ✒✑ ♣❛ ☎❡ ✂✆r♦✉✄✆ ✂✆❡ ♠✐✁✁❛❡ ♦❢ ✂✆❡ s♣♦✂ ✂ ✓ ❂ ☞ ❢♦r
✠ ❂ ✡✴✸ ☎✁ ☛✵ ❂ ☞✌☞✡✳ ■☎ ✂✆❡ ✒✑ ❝✉✂✱ ✇❡ ❛s♦ s✆♦✇ ♠ ✄☎❡✂✐❝ ✣❡❛✁ ❛✐☎❡s ☎✁ ✤♦✇ ✈❡❝✂♦rs ♦❜✂ ✐☎❡✁ ❜② ☎✉♠❡r✐❝ ❛❛② ✈❡r ✄✐☎✄ ✐☎ ✕✐♠✉✂✆ r♦✉☎✁ ✂✆❡
s♣♦✂ ①✐s✳
✖✗✘✙✚✛✘✗ ✜✙✚✚✢✥✦t✛✙✘✧ ★✢t✩✢✢✘ ✪✢✥✙✜✛t✫ ✦✘✬ ✬✢✘✧✛t✫ ✯✰✜t✰✦✲
t✛✙✘✧ ✹✙✚ ✥✙✩✲✼✦✜✽ ✘✰♥★✢✚ t✰✚★✰✥✢✘✜✢✾ t✽✢ ✦✪✢✚✦✗✢✬ ♥✙♥✢✘t✰♥
✢❀✰✦t✛✙✘ ✛✧
❁
❁
✦✚✢ ✬✢t✢✚♥✛✘✢✬ ★✫ t✽✢ ✧✰♥ ✙✹ t✽✢ ❺✢✫✘✙✥✬✧ ✦✘✬ ✼✦❻✩✢✥✥ ✧t✚✢✧✧
t✢✘✧✙✚✧❼
❨
●❅ ❥ ❆ ❄ ❽❅ ❽ ❥ ❏ ❣❅ ❥ ❹q④⑤➭⑥ ❾ ❿❅ ❿ ❥ ④➭⑥ ❶
P◗➀❱
❳
❨
✩✽✢✚✢ ✦✘ ✙✪✢✚★✦✚ ♥✢✦✘✧ ❊❲ ✦✪✢✚✦✗✛✘✗✾ ●❅ ❥ ❆ ●❅ ❥ ❏●❅ ❥ ✛✧ t✽✢ ♥✢✦✘
♥✙♥✢✘t✰♥ ✧t✚✢✧✧ t✢✘✧✙✚✾ ✧❩✥✛t ✛✘t✙ ✜✙✘t✚✛★✰t✛✙✘✧ ✚✢✧✰✥t✛✘✗ ✹✚✙♥
t✽✢ ♥✢✦✘ ❬✢✥✬ P✛✘✬✛✜✦t✢✬ ★✫ ✧✰❩✢✚✧✜✚✛❩t ♥❱ ✦✘✬ t✽✢ ✯✰✜t✰✦t✛✘✗
❳
❬✢✥✬ P✛✘✬✛✜✦t✢✬ ★✫ ✧✰❩✢✚✧✜✚✛❩t ✹❱❭ ❪✽✢ t✢✘✧✙✚ ●❅ ❥ ✽✦✧ t✽✢ ✧✦♥✢
✹✙✚♥ ✦✧ ❫❀❭ P◗❴❱✾ ★✰t ✦✥✥ ❀✰✦✘t✛t✛✢✧ ✽✦✪✢ ✘✙✩ ✦tt✦✛✘✢✬ ✦✘ ✙✪✢✚★✦✚❵
✛❭✢❭✾
❪✽✛✧ ✜✙✘t✚✛★✰t✛✙✘✾ t✙✗✢t✽✢✚ ✩✛t✽ t✽✢ ✜✙✘t✚✛★✰t✛✙✘ ✹✚✙♥ t✽✢ ♥✢✦✘
❳
❬✢✥✬✾ ●❅ ❥ ✾ ✜✙♥❩✚✛✧✢✧ t✽✢ t✙t✦✥ ♥✢✦✘ ♥✙♥✢✘t✰♥ t✢✘✧✙✚❭ ❪✽✢ ✜✙✘✲
t✚✛★✰t✛✙✘ ✹✚✙♥ t✽✢ ✯✰✜t✰✦t✛✘✗ ❬✢✥✬✧ ✛✧ ✧❩✥✛t ✛✘t✙ ✦ ✜✙✘t✚✛★✰t✛✙✘
❨➁⑥
t✽✦t ✛✧ ✛✘✬✢❩✢✘✬✢✘t ✙✹ t✽✢ ♥✢✦✘ ♥✦✗✘✢t✛✜ ❬✢✥✬ ●❅ ❥ P✩✽✛✜✽ ✬✢t✢✚✲
♥✛✘✢✧ t✽✢ t✰✚★✰✥✢✘t ✪✛✧✜✙✧✛t✫ ✦✘✬ ★✦✜➂✗✚✙✰✘✬ t✰✚★✰✥✢✘t ❩✚✢✧✧✰✚✢❱
❨➁➃
✦✘✬ ✦ ✜✙✘t✚✛★✰t✛✙✘ t✽✦t ✬✢❩✢✘✬✧ ✙✘ t✽✢ ♥✢✦✘ ♥✦✗✘✢t✛✜ ❬✢✥✬ ●❅ ❥ ❭
❨
❨➁➃
❨➁⑥
❪✽✢ ✬✛➄✢✚✢✘✜✢ ★✢t✩✢✢✘ t✽✢ t✩✙✾ ➅●❅ ❥ ❆ ●❅ ❥ ❾ ●❅ ❥ ✾ ✛✧ ✜✦✰✧✢✬ ★✫
t✽✢ ♥✢✦✘ ♥✦✗✘✢t✛✜ ❬✢✥✬ ✦✘✬ ✛✧ ❩✦✚✦♥✢t✢✚✛➆✢✬ ✛✘ t✽✢ ✹✙✚♥
❤
⑦
❳
q
●❅ ❥ ❆ ❄ ❞ ❅ ❞ ❥ ❏ ❣❅ ❥ ❦ ❏ ❧ ④⑤➭⑥ ❾ ⑧❅ ⑧ ❥ ④➭⑥ ❾ ⑤⑨❄ ⑩❅ ❥ ❶
❤
⑦
❨
q
q
➇➈
➍❅ ❑
➍ ❥❧ ❖
➅●❅ ❥ ❆ ➭⑥ ➉➊ ⑧❅ ⑧ ❥ ❾ ➉➋ ❣❅ ❥ ❧ ④⑤ ❾ ➉➌ ❑
❁❃
❄ ❯❅ ❆ ❾
❁❊ ❥
●❅ ❥ ❏ ❄ ❑ ❅ ❖
P◗❚❱
P◗❷❱
❨
❪✽✢ ✜✙✘t✚✛★✰t✛✙✘✧✾ ●❅ ❥ ✾ ✩✽✛✜✽ ✚✢✧✰✥t ✹✚✙♥ t✽✢ ✯✰✜t✰✦t✛✙✘✧ ❸ ❆
❯❾❯ ✦✘✬ ❹ ❆ ❧❾ ❧ ✙✹ ✪✢✥✙✜✛t✫ ✦✘✬ ♥✦✗✘✢t✛✜ ❬✢✥✬✧✾ ✚✢✧❩✢✜t✛✪✢✥✫✾
P◗➎❱
✩✽✢✚✢ t✽✢ ✜✙✢➏✜✛✢✘t ➉➋ ✚✢❩✚✢✧✢✘t✧ t✽✢ ✛✧✙t✚✙❩✛✜ t✰✚★✰✥✢✘✜✢ ✜✙✘✲
t✚✛★✰t✛✙✘ t✙ t✽✢ ♥✢✦✘ ♥✦✗✘✢t✛✜ ❩✚✢✧✧✰✚✢✾ t✽✢ ✜✙✢➏✜✛✢✘t ➉➊ ✚✢❩✚✢✲
✧✢✘t✧ t✽✢ t✰✚★✰✥✢✘✜✢ ✜✙✘t✚✛★✰t✛✙✘ t✙ t✽✢ ♥✢✦✘ ♥✦✗✘✢t✛✜ t✢✘✧✛✙✘✾
➐✷✱ ♣ ✄❡ ✡ ♦❢ ✶✶
❆✫❆ ✺ ✁✂ ❆✷ ✭✷✄☎✁✆
❋✝✞✳ ✼✳ ❊✟❡✠✡✐✈❡ ♠❛☛☞❡✡✐✠ ♣✌❡✍✍✎✌❡ ♦✏✡❛✐☞❡♥ ❢✌♦♠ ❉◆❙ ✐☞ ❛ ♣♦✑②✡✌♦♣✐✠
✑❛②❡✌ ✇✐✡✒ ♥✐✟❡✌❡☞✡ ✓ ❢♦✌ ✒♦✌✐③♦☞✡❛✑ ✭✔✂ ✌❡♥ ✠✎✌✈❡✍✆ ❛☞♥ ✈❡✌✡✐✠❛✑ ✭✕✂ ✏✑✎❡
✠✎✌✈❡✍✆ ♠❡❛☞ ♠❛☛☞❡✡✐✠ ✣❡✑♥✍s
✖✗✘✙✚ t✗✚ ❝✛✚✜❝✘✚✢t q❣ ✘✤ t✗✚ ✥✢✘✤✛tr✛✦✘❝ t✉r✧✉✙✚✢❝✚ ❝✛✢tr✘✧✉✲
t✘✛✢ t✛ t✗✚ ★✚✥✢ ★✥✩✢✚t✘❝ ✦r✚✤✤✉r✚✪ ✥✢✬ ✘t ❝✗✥r✥❝t✚r✘✮✚✤ t✗✚ ✚✯✲
✯✚❝t ✛✯ ✰✚rt✘❝✥✙ ✰✥r✘✥t✘✛✢✤ ✛✯ t✗✚ ★✥✩✢✚t✘❝ ✱✚✙✬ ❝✥✉✤✚✬ ✧✴ t✗✚
✰✚rt✘❝✥✙ ★✥✩✢✚t✘❝ ✦r✚✤✤✉r✚ ✩r✥✬✘✚✢t✵ ❍✚r✚✪ ✶❼ ✸ ✘✤ t✗✚ ✉✢✘t ✰✚❝t✛r
✘✢ t✗✚ ✬✘r✚❝t✘✛✢ ✛✯ t✗✚ ✩r✥✰✘t✴ ✱✚✙✬ ✹✘✢ t✗✚ ✰✚rt✘❝✥✙ ✬✘r✚❝t✘✛✢✻✵
❲✚ ❝✛✢✤✘✬✚r ❝✥✤✚✤ ✖✘t✗ ✗✛r✘✮✛✢t✥✙ ✥✢✬ ✰✚rt✘❝✥✙ ★✚✥✢ ★✥✩✢✚t✘❝
✱✚✙✬✤ ✤✚✦✥r✥t✚✙✴✵ ✽✢✥✙✴t✘❝✥✙✙✴✪ t✗✚ ❝✛✚✜❝✘✚✢t✤ q✾ ✪ q❣ ✿ ✥✢✬ q❀ ✗✥✰✚
✧✚✚✢ ✛✧t✥✘✢✚✬ ✉✤✘✢✩ ✧✛t✗ t✗✚ ✤✦✚❝tr✥✙ ❁ ✥✦✦r✛✥❝✗ ✹❘✛✩✥❝✗✚✰✤❦✘✘
❂ ❑✙✚✚✛r✘✢ ❃❄❄❅✻ ✥✢✬ t✗✚ r✚✢✛r★✥✙✘✮✥t✘✛✢ ✥✦✦r✛✥❝✗ ✹❑✙✚✚✛r✘✢
❂ ❘✛✩✥❝✗✚✰✤❦✘✘ ❇❈❈●✻✵ ❚✗✚ ✯✛r★ ✛✯ ■❏✵ ✹❇❅✻ ✘✤ ✥✙✤✛ ✛✧t✥✘✢✚✬
✉✤✘✢✩ ✤✘★✦✙✚ ✤✴★★✚tr✴ ✥r✩✉★✚✢t✤▲ ✚✵✩✵✪ ✯✛r ✥ ✗✛r✘✮✛✢t✥✙ ✱✚✙✬✪
t✗✚ ✙✘✢✚✥r ❝✛★✧✘✢✥t✘✛✢ ✛✯ t✗r✚✚ ✘✢✬✚✦✚✢✬✚✢t tr✉✚ t✚✢✤✛r✤✪ ▼✸ ❖✿ ✶❼ ✸ ✶❼ ❖
✥✢✬ P✸ P ❖ ✪ ✴✘✚✙✬✤ ■❏✵ ✹❇❅✻✪ ✖✗✘✙✚ ✯✛r t✗✚ ✰✚rt✘❝✥✙ ✱✚✙✬✪ t✗✚ ✙✘✢✚✥r
❝✛★✧✘✢✥t✘✛✢ ✛✯ ✛✢✙✴ t✖✛ ✘✢✬✚✦✚✢✬✚✢t tr✉✚ t✚✢✤✛r✤✪ ▼✸ ❖ ✥✢✬ P✸ P ❖ ✵
◗r✚✰✘✛✉✤ ❯❱❳ ✤t✉✬✘✚✤ ✹❨r✥✢✬✚✢✧✉r✩ ✚t ✥✙✵ ❃❄❇❃✻ ✗✥✰✚ ✤✗✛✖✢
t✗✥t q❀ ✥✢✬ q❣ ✥r✚ ✢✚✩✙✘✩✘✧✙✚ ✯✛r ✯✛r❝✚✬ t✉r✧✉✙✚✢❝✚✵ ❚✛ ✥✰✛✘✬
t✗✚ ✯✛r★✥t✘✛✢ ✛✯ ★✥✩✢✚t✘❝ ✤tr✉❝t✉r✚✤ ✘✢ t✗✚ ✢✛✢✙✘✢✚✥r ✤t✥✩✚ ✛✯
❱■❩◗❬✪ ✖✗✘❝✗ ✖✛✉✙✬ ★✛✬✘✯✴ ✛✉r r✚✤✉✙t✤✪ ✖✚ ✉✤✚ ✗✚r✚ ✥ ✙✛✖✚r
✤❝✥✙✚ ✤✚✦✥r✥t✘✛✢ r✥t✘✛✪ ❭❪ ❫❭❴ ❵ ❜✪ ❦✚✚✦✘✢✩ ❭❴ ❞❤ ❵ ❇✪ ✥✢✬ ✉✤✲
✘✢✩ ❘✚ ❵ ❇●❄ ✥✢✬ ❥❧ ❵ ❅❄✪ ✥✤ ✘✢ ❨r✥✢✬✚✢✧✉r✩ ✚t ✥✙✵ ✹❃❄❇❃✻✵
❚✛ ✬✚t✚r★✘✢✚ q✾ ✹①✻✪ ✘t ✘✤ ✤✉✜❝✘✚✢t t✛ ★✚✥✤✉r✚ t✗✚ t✗r✚✚ ✬✘✥✩✛✢✥✙
❪
❝✛★✦✛✢✚✢t✤ ✛✯ ④✸ ❖ ✧✛t✗ ✖✘t✗ ✥✢✬ ✖✘t✗✛✉t ✥✢ ✘★✦✛✤✚✬ ★✥✩✢✚t✘❝
❪
⑨
✱✚✙✬ ✉✤✘✢✩ q✾ ❵ ❾❃➭⑤ ⑥④ ⑦⑦ ❫⑧ ✵
❬✢ ⑩✘✩✵ ❅ ✖✚ ✦r✚✤✚✢t t✗✚ r✚✤✉✙t✤ ✯✛r ✯✛r❝✚✬ t✉r✧✉✙✚✢❝✚ ✘✢ t✗✚
✦✛✙✴tr✛✦✘❝ ✙✥✴✚r ✖✘t✗ ✬✘❶✚r✚✢t ❷ ✯✛r ✗✛r✘✮✛✢t✥✙ ✥✢✬ ✰✚rt✘❝✥✙ ★✚✥✢
★✥✩✢✚t✘❝ ✱✚✙✬✤✵ ❬t t✉r✢✤ ✛✉t t✗✥t t✗✚ ✢✛r★✥✙✘✮✚✬ ✚❶✚❝t✘✰✚ ★✥✩✲
✢✚t✘❝ ✦r✚✤✤✉r✚✪
❸❹❺ ❵
❇
❃
✹❇ ❾ q✾ ✻①⑨ ✿
✹❇❻✻
✗✥✤ ✥ ★✘✢✘★✉★ ✰✥✙✉✚ ❸❧❽❿ ✥t ①❧❽❿ ✵ ⑩✛✙✙✛✖✘✢✩ ❑✚★✚✙ ✚t ✥✙✵
✹❃❄❇❃✥✻✪ t✗✚ ✯✉✢❝t✘✛✢ q✾ ✹①✻ ✘✤ ✥✦✦r✛➀✘★✥t✚✬ ✧✴➁
q✾ ✹①✻ ❵
q✾⑤
①⑨➃
✿
❵ ⑨
⑨
⑨
①✾ ➂ ①⑨
❇ ➂ ① ❫①✾
✹❇❈✻
❴➄⑨
✖✗✚r✚ q✾⑤ ✪ ①✾ ✪ ✥✢✬ ①➃ ❵ ①✾ q✾⑤ ✥r✚ ❝✛✢✤t✥✢t✤✵ ❚✗✘✤ ✚❏✉✥t✘✛✢ ❝✥✢
✧✚ ✉✢✬✚r✤t✛✛✬ ✥✤ ✥ ❏✉✚✢❝✗✘✢✩ ✯✛r★✉✙✥ ✯✛r t✗✚ ✚❶✚❝t✘✰✚ ★✥✩✢✚t✘❝
✦r✚✤✤✉r✚▲ ✤✚✚ ➅✥✧✧✥r✘ ✚t ✥✙✵ ✹❃❄❇➆✻✵ ❚✗✚ ❝✛✚✜❝✘✚✢t✤ ①✾ ✥✢✬ ①➃ ✥r✚
r✚✙✥t✚✬ t✛ ❸❧❽❿ ✥t ①❧❽❿ ✰✘✥ ✹❑✚★✚✙ ✚t ✥✙✵ ❃❄❇❃✥✻
➇➈
➈
⑨
①✾ ❵ ①❧❽❿
✹❃❄✻
❾❃❸❧❽❿ ✿ ①➃ ❵ ①✾ ➂ ❾❃❸❧❽❿ ➉
❆✷✂ ♣❛☛❡
♦❢ ☎☎
❋✝✞✳ ➊✳ ➋❛✌❛♠❡✡❡✌✍ ➌➍➎ ✂ ➏➍ ✂ ❛☞♥ ➏➐ ❢♦✌ ✡✒❡ ❢✎☞✠✡✐♦☞ ➌➍ ✭➏✆ ✭✍❡❡ ❊➑s ✭☎➒✆✆
✈❡✌✍✎✍ ✓ ❢♦✌ ✒♦✌✐③♦☞✡❛✑ ✭✌❡♥ ✑✐☞❡✆ ❛☞♥ ✈❡✌✡✐✠❛✑ ✭✏✑✎❡ ✑✐☞❡✆ ♠❡❛☞ ♠❛☛☞❡✡✐✠
✣❡✑♥✍s
❬✢ ⑩✘✩✵ ❻ ✖✚ ✤✗✛✖ t✗✚✤✚ ✱tt✘✢✩ ✦✥r✥★✚t✚r✤ ✯✛r t✗✚ ✯✉✢❝t✘✛✢ q✾ ✹①✻
✯✛r ✦✛✙✴tr✛✦✘❝ ✙✥✴✚r ✖✘t✗ ✬✘❶✚r✚✢t ❷ ✯✛r ✗✛r✘✮✛✢t✥✙ ✥✢✬ ✰✚rt✘❝✥✙
★✚✥✢ ★✥✩✢✚t✘❝ ✱✚✙✬✤✵ ❚✗✚ ✚❶✚❝t✤ ✛✯ ✢✚✩✥t✘✰✚ ✚❶✚❝t✘✰✚ ★✥✩✢✚t✘❝
✦r✚✤✤✉r✚ ✥r✚ ✩✚✢✚r✥✙✙✴ ✤tr✛✢✩✚r ✯✛r ✰✚rt✘❝✥✙ ★✥✩✢✚t✘❝ ✱✚✙✬✤ ✹q✾⑤
✘✤ ✙✥r✩✚r ✥✢✬ ①✾ ✤★✥✙✙✚r✻ t✗✥✢ ✯✛r ✗✛r✘✮✛✢t✥✙ ✛✢✚✤ ✹q✾⑤ ✘✤ ✤★✥✙✙✚r
❴➄⑨
✥✢✬ ①✾ ✙✥r✩✚r✻✪ ✧✉t t✗✚ ✰✥✙✉✚✤ ①➃ ❵ ①✾ q✾⑤ ✥r✚ ✤✘★✘✙✥r ✘✢ ✧✛t✗
❝✥✤✚✤✪ ✥✢✬ ✘✢❝r✚✥✤✘✢✩ ✯r✛★ ❄✵➆❜ ✹✯✛r ❷ ❵ ❇✻ t✛ ❄✵➓ ✹✯✛r ❷ ❵ ❜❫➆✻▲
✤✚✚ ⑩✘✩✵ ❻✵
➔→ ➣↔↕➙➛➜↔➝➞ ➟➠➡➞➢
❲✚ ✢✛✖ ❝✛✢✤✘✬✚r t✖✛ ✤✚t✤ ✛✯ ✦✥r✥★✚t✚r✤ t✗✥t ✖✚ r✚✯✚r t✛ ✥✤
❩✛✬✚✙ ❬ ✹✖✘t✗ q✾⑤ ❵ ➆❃ ✥✢✬ ①✾ ❵ ❄➉❄❜❻ ❝✛rr✚✤✦✛✢✬✘✢✩ t✛
①➃ ❵ ❄➉➆➆✻ ✥✢✬ ❩✛✬✚✙ ❬❬ ✹q✾⑤ ❵ ❈ ✥✢✬ ①✾ ❵ ❄➉❃❇ ❝✛rr✚✤✦✛✢✬✲
✘✢✩ t✛ ①➃ ❵ ❄➉➓➆✻✵ ❚✗✚✤✚ ❝✥✤✚✤ ✥r✚ r✚✦r✚✤✚✢t✥t✘✰✚ ✛✯ t✗✚ ✤tr✛✢✩
✹✙✥r✩✚ ①➃ ✻ ✥✢✬ ✖✚✥❦ ✹✤★✥✙✙ ①➃ ✻ ✚❶✚❝t✤ ✛✯ ❱■❩◗❬✵ ⑩✛✙✙✛✖✘✢✩ ✚✥r✲
✙✘✚r ✤t✉✬✘✚✤ ✹❨r✥✢✬✚✢✧✉r✩ ✚t ✥✙✵ ❃❄❇❃✻✪ ✖✚ ✱✢✬ q❀ t✛ ✧✚ ❝✛★✦✥t✘✲
✧✙✚ ✖✘t✗ ✮✚r✛✵ ❲✚ t✗✉✤ ✢✚✩✙✚❝t t✗✘✤ ❝✛✚✜❝✘✚✢t ✘✢ t✗✚ ✯✛✙✙✛✖✘✢✩✵
➤➥➦➥ ➧➨➩➫➯➲➳➲➵ ➸➺➯➺➻➫➼➫➯➽ ➺➲➾ ➫➽➼➳➻➺➼➫➽
❚✗✚ ✦✉r✦✛✤✚ ✛✯ t✗✘✤ ✤✚❝t✘✛✢ ✘✤ t✛ ✤✉★★✥r✘✮✚ t✗✚ ✱✢✬✘✢✩✤ ✯✛r t✗✚
✘✤✛t✗✚r★✥✙ ❝✥✤✚ ✘✢ ❩⑩❳✵ ➚✢✚ ✛✯ t✗✚ ❦✚✴ r✚✤✉✙t✤ ✘✤ t✗✚ ✦r✚✬✘❝t✘✛✢
✛✯ t✗✚ ✩r✛✖t✗ r✥t✚ ✛✯ ❱■❩◗❬✵ ❚✗✚ ✖✛r❦ ✛✯ ❑✚★✚✙ ✚t ✥✙✵ ✹❃❄❇➆✻
✤✗✛✖✚✬ t✗✥t ✘✢ t✗✚ ✘✬✚✥✙ ❝✥✤✚ ✹✢✛ t✉r✧✉✙✚✢t ✬✘❶✉✤✘✛✢✻✪ t✗✚ ✩r✛✖t✗
r✥t✚ ➪ ✘✤ ✥✦✦r✛➀✘★✥t✚✬ ✖✚✙✙ ✧✴
➪ ➶ ①➃ ➹➘❧❀ ❫❞❤
✹✢✛ t✉r✧✉✙✚✢t ✬✘❶✉✤✘✛✢✻➉
✹❃❇✻
■✳ ❘✳ ▲♦s ✁ ❡✂ ❛✳✿ ▼ ✄☎❡✂✐❝ ✤✉① ❝♦☎❝❡☎✂r ✂✐♦☎s ✐☎
❍✝✇✞✈✞✟✱ t✠✟✡✠☛✞☞t ✌✍✎☞✞t✏✑ ❞✏✒✠✓✏✝☞✱ ✔✕ ✱ ✑✍☞ ✑☛✞✍✟☛✖ ☞✝t ✡✞ ☞✞♥
✎☛✞✑t✞❞ ✍☞❞ ✏✓ ✑❤✏✞✗✖ ✟✞✓✘✝☞✓✏✡☛✞ ❢✝✟ ✓❤✠tt✏☞✎ ✝✒ ◆✙✚✛✜ ✏❢ t❤✞
t✠✟✡✠☛✞☞t ✞❞❞✏✞✓ ✍✟✞ t✝✝ ✡✏✎ ✍☞❞ ✔✕ t✝✝ ☛✍✟✎✞❣ ❚❤✏✓ ✇✍✓ ❞✞✌✝☞♥
✓t✟✍t✞❞ ✏☞ ✢✏✎❣ ✣✼ ✝❢ ❇✟✍☞❞✞☞✡✠✟✎ ✞t ✍☛❣ ✭✷✥✣✷✮❣ ❆ ❤✞✠✟✏✓t✏✑
✍☞✓✍t✦✱ ✇❤✏✑❤ ✏✓ ✌✝t✏✈✍t✞❞ ✡✖ ✓✏✌✏☛✍✟ ✑✏✟✑✠✌✓t✍☞✑✞✓ ✏☞ ✌✞✍☞♥
✧✞☛❞ ❞✖☞✍✌✝ t❤✞✝✟✖ ✭❑✟✍✠✓✞ ✫ ★ ❞☛✞✟ ✣✶✩✥✮✱ ✏✓ t✝ ✍❞❞ ✍
t✞✟✌ ❾✔✕ ❦✪ t✝ t❤✞ ✟✏✎❤t❤✍☞❞ ✓✏❞✞ ✝❢ ✙❊❣ ✭✷✣✮✱ ✇❤✞✟✞ ❦ ✏✓ t❤✞
✇✍✈✞☞✠✌✡✞✟ ✝❢ ◆✙✚✛✜❣
❚✝ ✓✘✞✑✏❢✖ t❤✞ ✞✬✘✟✞✓✓✏✝☞ ❢✝✟ ✯✱ ✇✞ ☞✝✟✌✍☛✏✦✞ t❤✞ ✇✍✈✞☞✠✌♥
✡✞✟ ✝❢ t❤✞ ✘✞✟t✠✟✡✍t✏✝☞✓ ✡✖ t❤✞ ✏☞✈✞✟✓✞ ❞✞☞✓✏t✖ ✓✑✍☛✞ ❤✞✏✎❤t ✍☞❞
❞✞☞✝t✞ t❤✏✓ ✡✖ ✰ ✲ ❦✴✵ ❣ ❚❤✞ ✇✍✈✞☞✠✌✡✞✟ ✝❢ t❤✞ ✞☞✞✟✎✖♥✑✍✟✟✖✏☞✎
t✠✟✡✠☛✞☞t ✞❞❞✏✞✓ ❦✸ ✏✓ ✏☞ ☞✝☞❞✏✌✞☞✓✏✝☞✍☛ ❢✝✟✌ ✰✸ ✲ ❦✸ ✴✵ ✱ ✍☞❞
t❤✞ ☞✝✟✌✍☛✏✦✞❞ ❤✝✟✏✦✝☞t✍☛ ✇✍✈✞☞✠✌✡✞✟ ✝❢ t❤✞ ✟✞✓✠☛t✏☞✎ ✌✍✎♥
☞✞t✏✑ ✓t✟✠✑t✠✟✞✓ ✏✓ ✟✞❢✞✟✟✞❞ t✝ ✍✓ ✰✹ ❂ ❦✹ ✴✵ ❣ ✢✝✟ ◆✙✚✛✜✱
t❤✞✓✞ ✈✍☛✠✞✓ ❤✍✈✞ ✡✞✞☞ ✞✓t✏✌✍t✞❞ t✝ ✡✞ ✰✹ ❂ ✥✺✩✽✣❣✥✱ ✍☞❞ ✑✍☞
✞✈✞☞ ✡✞ ✓✌✍☛☛✞✟ ❢✝✟ ✈✞✟t✏✑✍☛ ✌✍✎☞✞t✏✑ ✧✞☛❞✓ ✭❇✟✍☞❞✞☞✡✠✟✎ ✞t ✍☛❣
✷✥✣✻✮❣ ❯✓✏☞✎ ✍☞ ✍✘✘✟✝✬✏✌✍t✞ ✍✓✘✞✑t ✟✍t✏✝ ✝❢ ✠☞✏t✖ ❢✝✟ ✌✍✎☞✞t✏✑
✾
✓t✟✠✑t✠✟✞✓✱ ✇✞ ❤✍✈✞ ✰ ❂
✷✰✹ ❀ ✣✺✣✽✣❣✻❣ ✜☞ ✓t✞☛☛✍✟ ✌✏✬✏☞✎
☛✞☞✎t❤ t❤✞✝✟✖ ✭❱✏t✞☞✓✞ ✣✶❁❃✮✱ t❤✞ ✌✏✬✏☞✎ ☛✞☞✎t❤ ✏✓ ❄✸ ❂ ❅❈❉❋ ✴✵ ✱
✇❤✞✟✞ ❅❈❉❋ ❀ ✣✺● ✏✓ ✍ ☞✝☞❞✏✌✞☞✓✏✝☞✍☛ ✌✏✬✏☞✎ ☛✞☞✎t❤ ✘✍✟✍✌♥
✞t✞✟❣ ❙✏☞✑✞ ❦✸ ❂ ✷❏❖❄✸ ✱ ✇✞ ✍✟✟✏✈✞ ✍t t❤✞ ❢✝☛☛✝✇✏☞✎ ✞✓t✏✌✍t✞P
✰✸ ❂ ✷❏◗❖❅❈❉❋ ❀ ●✺❁❣ ❬❲✇✏☞✎ t✝ ✍ ✑✝☞❢✠✓✏✝☞ ✡✞t✇✞✞☞ ✘✟✞✓✓✠✟✞
✍☞❞ ❞✞☞✓✏t✖ ✓✑✍☛✞ ❤✞✏✎❤t✓✱ t❤✏✓ ✈✍☛✠✞ ✇✍✓ ✠☞❞✞✟✞✓t✏✌✍t✞❞ ✡✖
❑✞✌✞☛ ✞t ✍☛❣ ✭✷✥✣❃✮ t✝ ✡✞ ✷✺✻✱ ✍☛t❤✝✠✎❤ ✍☞ ✏☞❞✞✘✞☞❞✞☞t ✑✍☛✑✠♥
☛✍t✏✝☞ ✝❢ t❤✏✓ ✈✍☛✠✞ ❢✟✝✌ t✠✟✡✠☛✞☞t ✑✝☞✈✞✑t✏✝☞ ✓✏✌✠☛✍t✏✝☞✓ ✇✝✠☛❞
✓t✏☛☛ ✡✞ ✠✓✞❢✠☛❣❳ ❯✓✏☞✎ ✔✕ ❀ ❨❩❈❭ ❖❃❦✸ ✱ t❤✞ t✠✟✡✠☛✞☞t ✌✍✎☞✞t✏✑ ❞✏❢♥
❢✠✓✏✈✞ ✟✍t✞ ❢✝✟ ✍☞ ✏✓✝t❤✞✟✌✍☛ ✍t✌✝✓✘❤✞✟✞ ✏✓ ✎✏✈✞☞ ✡✖
❨❩❈❭ ✰✪
✪
❪
✔✕ ❦ ❂
❃✴✵ ✰✸
✭✷✷✮
✍☞❞ t❤✞ ✎✟✝✇t❤ ✟✍t✞ ✝❢ ◆✙✚✛✜ ✏☞ t❤✍t ☞✝✟✌✍☛✏✦✍t✏✝☞ ✏✓
✯
✔✕ ❦✪
❂ ❃❫❴
✰✸
❾ ✣✺
✰✪
✭✷❃✮
❯✓✏☞✎ ❫❴ ❂ ✥✺✷❃✱ ✇❤✏✑❤ ✏✓ t❤✞ ✟✞☛✞✈✍☞t ✈✍☛✠✞ ❢✝✟ ❤✏✎❤ ✌✍✎♥
☞✞t✏✑ ★✞✖☞✝☛❞✓ ☞✠✌✡✞✟✓ ✭❇✟✍☞❞✞☞✡✠✟✎ ✞t ✍☛❣ ✷✥✣✷✮✱ ✇✞ ✧☞❞
✯❖✔✕ ❦✪ ❀ ✷✺✼❾✣✺❃ ❢✝✟ ✰ ❀ ✣✺✣❾✣✺✻❣ ❍✝✇✞✈✞✟✱ ✓✏☞✑✞ ✢✏✎❣ ✩ ✓❤✝✇✓
✍☞ ✏☞✑✟✞✍✓✞ ✝❢ ❫❴ ✇✏t❤ ✏☞✑✟✞✍✓✏☞✎ ✘✝☛✖t✟✝✘✏✑ ✏☞❞✞✬✱ ✝☞✞ ✌✏✎❤t
✞✬✘✞✑t ✍ ✑✝✟✟✞✓✘✝☞❞✏☞✎ ✏☞✑✟✞✍✓✞ ✏☞ t❤✞ ✎✟✝✇t❤ ✟✍t✞ ✝❢ ◆✙✚✛✜
❢✝✟ ✍ ✘✝☛✖t✟✝✘✏✑ ☛✍✖✞✟✱ ✏☞ ✇❤✏✑❤ ✴✵ ✈✍✟✏✞✓ ✓t✟✝☞✎☛✖ ✇✏t❤ ❤✞✏✎❤t ③❣
✜☞❞✞✞❞✱ ✏☞ ✍ ✘✝☛✖t✟✝✘✏✑ ✍t✌✝✓✘❤✞✟✞✱ ✴✵ ✏✓ ✘✟✝✘✝✟t✏✝☞✍☛ t✝ ❞✞✘t❤❣
❚❤✠✓✱ ✍t ✍☞✖ ✎✏✈✞☞ ❞✞✘t❤ t❤✞✟✞ ✏✓ ✍ ☛✍✖✞✟ ✡✞☞✞✍t❤✱ ✇❤✞✟✞ t❤✞ ✓t✟✍t♥
✏✧✑✍t✏✝☞ ✏✓ ☛✞✓✓ ✓t✟✝☞✎ ✍☞❞ t❤✞ ✎✟✝✇t❤ ✟✍t✞ ✝❢ ◆✙✚✛✜ ✏✓ ☛✝✇✞✟❣ ✜☞
✍❞❞✏t✏✝☞✱ t❤✞✟✞ ✏✓ ✍ t❤✏☞☞✞✟✱ ✌✝✟✞ ✓t✟✝☞✎☛✖ ✓t✟✍t✏✧✞❞ ☛✍✖✞✟ ✍✡✝✈✞✱
✇❤✞✟✞ ◆✙✚✛✜ ✌✏✎❤t ✎✟✝✇ ❢✍✓t✞✟ ✏❢ ✝☞☛✖ t❤✞ ✓t✟✠✑t✠✟✞✓ ✎✞☞✞✟✍t✞❞
✡✖ ◆✙✚✛✜ ❤✍✈✞ ✞☞✝✠✎❤ ✟✝✝✌ t✝ ❞✞✈✞☛✝✘ ✡✞❢✝✟✞ t❤✞✖ t✝✠✑❤ t❤✞
t✝✘ ✝❢ t❤✞ ✍t✌✝✓✘❤✞✟✞ ✍t ③❵ ✱ ✇❤✞✟✞ t❤✞ t✞✌✘✞✟✍t✠✟✞ ✈✍☞✏✓❤✞✓❣
❜❥❧❥ q④⑤⑥⑦Þ④⑧⑨ ④⑩❶⑤❷❸❹⑥❺
✜☞ t❤✞ ❢✝☛☛✝✇✏☞✎✱ ✇✞ ✑✝☞✓✏❞✞✟ ✚✢❙ ✍☞❞ ✑✝✌✘✍✟✞ ✏t ✇✏t❤
❻◆❙❣ ❼✞ ✍☛✓✝ ✑✝✌✘✍✟✞ ✝✠✟ ✚✢❙ ✟✞✓✠☛t✓ ✇✏t❤ t❤✝✓✞ ✝❢ ❻◆❙
✭❇✟✍☞❞✞☞✡✠✟✎ ✞t ✍☛❣ ✷✥✣✣❽ ❑✞✌✞☛ ✞t ✍☛❣ ✷✥✣❃✮ ✠✓✏☞✎ ✍ ✓✏✌✏☛✍✟
✘✝☛✖t✟✝✘✏✑ ✓✞t✠✘❣
❚❤✞ ✎✝✈✞✟☞✏☞✎ ✞❊✠✍t✏✝☞✓ ❢✝✟ t❤✞ ✌✞✍☞ ❊✠✍☞t✏t✏✞✓ ✭❞✞☞✝t✞❞ ✡✖
✍☞ ✝✈✞✟✡✍✟✮ ✍✟✞ ❢✍✏✟☛✖ ✓✏✌✏☛✍✟ t✝ t❤✝✓✞ ❢✝✟ t❤✞ ✝✟✏✎✏☞✍☛ ✞❊✠✍t✏✝☞✓✱
✞✬✑✞✘t t❤✍t ✏☞ t❤✞ ✚✢❙ ✈✏✓✑✝✓✏t✖ ✍☞❞ ✌✍✎☞✞t✏✑ ❞✏✒✠✓✏✈✏t✖ ✍✟✞
✟✞✘☛✍✑✞❞ ✡✖ t❤✞✏✟ t✠✟✡✠☛✞☞t ✑✝✠☞t✞✟✘✍✟t✓✱ ✍☞❞ t❤✞ ✌✞✍☞ ❿✝✟✞☞t✦
❢✝✟✑✞ ✏✓ ✓✠✘✘☛✞✌✞☞t✞❞ ✡✖ ✍ ✘✍✟✍✌✞t✞✟✏✦✍t✏✝☞ ✝❢ t❤✞ t✠✟✡✠☛✞☞t ✑✝☞♥
t✟✏✡✠t✏✝☞ t✝ t❤✞ ✞✒✞✑t✏✈✞ ✌✍✎☞✞t✏✑ ✘✟✞✓✓✠✟✞❣
♣♦❛②✂r♦♣✐❝ ✂♠♦s♣✆❡r❡
❚❤✞ ✞✈✝☛✠t✏✝☞ ✞❊✠✍t✏✝☞✓ ❢✝✟ ✌✞✍☞ ✈✞✑t✝✟ ✘✝t✞☞t✏✍☛ ➀✱ ✌✞✍☞
✈✞☛✝✑✏t✖ ➁✱ ✍☞❞ ✌✞✍☞ ❞✞☞✓✏t✖ ➂✱ ✍✟✞
➃➀
➃➄
❂ ➁ × ➅ ❾ ✔➆ ➭➇ ➈❪
❻➁
❻➄
❻➂
❻➄
❂
✣➉
➂
➎
✪
➈ × ➅ ➊ ➋✭➌➍ ➅ ❖✷➭➇ ✮ ❾ ➏➆ ➐ ❾ ➋✴❪
❂ ❾➂➋ ➲ ➁❪
✭✷✻✮
✭✷❁✮
✭✷●✮
✇❤✞✟✞ ❻❖❻➄ ❂ ➃❖➃➄ ➊ ➁ ➲ ➋ ✏✓ t❤✞ ✍❞✈✞✑t✏✈✞ ❞✞✟✏✈✍t✏✈✞ ✇✏t❤ ✟✞♥
✓✘✞✑t t✝ t❤✞ ✌✞✍☞ ✗✝✇✱ ➂ t❤✞ ✌✞✍☞ ❞✞☞✓✏t✖✱ ✴ ❂ ➑ ➊ ➒ t❤✞ ✌✞✍☞
↔↕➙
t❤✞
✟✞❞✠✑✞❞ ✞☞t❤✍☛✘✖✱ ➑ ❂ ➓ ➔ → t❤✞ ✌✞✍☞ ✞☞t❤✍☛✘✖✱ → ➣ ➂
✌✞✍☞ t✞✌✘✞✟✍t✠✟✞✱ ➒ t❤✞ ✎✟✍✈✏t✍t✏✝☞✍☛ ✘✝t✞☞t✏✍☛✱ ✔➆ ❂ ✔✕ ➊ ✔✱ ✍☞❞
➏➆ ❂ ➏✕ ➊ ➏ ✍✟✞ t❤✞ ✓✠✌✓ ✝❢ t✠✟✡✠☛✞☞t ✍☞❞ ✌✏✑✟✝✘❤✖✓✏✑✍☛ ✈✍☛✠✞✓
✝❢ ✌✍✎☞✞t✏✑ ❞✏✒✠✓✏✈✏t✖ ✍☞❞ ➛✏☞✞✌✍t✏✑ ✈✏✓✑✝✓✏t✏✞✓✱ ✟✞✓✘✞✑t✏✈✞☛✖❣
❆☛✓✝✱ ➈ ❂ ➋ × ➅❖➭➇ ✏✓ t❤✞ ✌✞✍☞ ✑✠✟✟✞☞t ❞✞☞✓✏t✖✱ ➭➇ ✏✓ t❤✞ ✈✍✑♥
✠✠✌ ✘✞✟✌✞✍✡✏☛✏t✖✱
✪
❾➐ ❂ ➜ ➁ ➊ ➙➝ ➋➋ ➲ ➁ ➊ ✷➞➋ ☛☞ ➂
✭✷✼✮
✏✓ ✍ t✞✟✌ ✍✘✘✞✍✟✏☞✎ ✏☞ t❤✞ ✌✞✍☞ ✈✏✓✑✝✠✓ ❢✝✟✑✞ ❾➏➆ ➐✱ ✇❤✞✟✞ ➞ ✏✓
t❤✞ t✟✍✑✞☛✞✓✓ ✟✍t✞♥✝❢♥✓t✟✍✏☞ t✞☞✓✝✟ ✝❢ t❤✞ ✌✞✍☞ ✗✝✇ ✇✏t❤ ✑✝✌✘✝♥
☞✞☞t✓ ➟➠ ➡ ❂ ➙✪ ✭➜ ➡ ➢ ➠ ➊ ➜➠ ➢ ➡ ✮ ❾ ➝➙ ➤➠ ➡ ➋ ➲ ➁✱ ✍☞❞ ✧☞✍☛☛✖ t❤✞ t✞✟✌
➋✭➌➍ ➅✪ ❖✷➭➇ ✮ ✝☞ t❤✞ ✟✏✎❤t❤✍☞❞ ✓✏❞✞ ✝❢ ✙❊❣ ✭✷❁✮ ❞✞t✞✟✌✏☞✞✓ t❤✞
t✠✟✡✠☛✞☞t ✑✝☞t✟✏✡✠t✏✝☞ t✝ t❤✞ ✞✒✞✑t✏✈✞ ✌✍✎☞✞t✏✑ ✘✟✞✓✓✠✟✞❣ ❍✞✟✞✱
➌➍ ❞✞✘✞☞❞✓ ✝☞ t❤✞ ☛✝✑✍☛ ✧✞☛❞ ✓t✟✞☞✎t❤❽ ✓✞✞ ✙❊❣ ✭✣✶✮❣ ❚❤✏✓ t✞✟✌
✞☞t✞✟✓ ✇✏t❤ ✍ ✘☛✠✓ ✓✏✎☞✱ ✓✝ ✘✝✓✏t✏✈✞ ✈✍☛✠✞✓ ✝❢ ➌➍ ✑✝✟✟✞✓✘✝☞❞
t✝ ✍ ✓✠✘✘✟✞✓✓✏✝☞ ✝❢ t❤✞ t✝t✍☛ t✠✟✡✠☛✞☞t ✘✟✞✓✓✠✟✞❣ ❚❤✞ ☞✞t ✞✒✞✑t
✝❢ t❤✞ ✌✞✍☞ ✌✍✎☞✞t✏✑ ✧✞☛❞ ☛✞✍❞✓ t✝ ✍☞ ✞✒✞✑t✏✈✞ ✌✞✍☞ ✌✍✎♥
☞✞t✏✑ ✘✟✞✓✓✠✟✞ t❤✍t ✡✞✑✝✌✞✓ ☞✞✎✍t✏✈✞ ❢✝✟ ➌➍ ➥ ✣❣ ❚❤✏✓ ✑✍☞ ✏☞♥
❞✞✞❞ ✡✞ t❤✞ ✑✍✓✞ ❢✝✟ ✌✍✎☞✞t✏✑ ★✞✖☞✝☛❞✓ ☞✠✌✡✞✟✓ ✇✞☛☛ ✍✡✝✈✞
✠☞✏t✖ ✭❇✟✍☞❞✞☞✡✠✟✎ ✞t ✍☛❣ ✷✥✣✷✮❽ ✓✞✞ ✍☛✓✝ ✢✏✎❣ ✼ ❢✝✟ ✍ ✘✝☛✖t✟✝✘✏✑
✍t✌✝✓✘❤✞✟✞❣
❚❤✞ ✡✝✠☞❞✍✟✖ ✑✝☞❞✏t✏✝☞✓ ❢✝✟ ✚✢❙ ✍✟✞ t❤✞ ✓✍✌✞ ✍✓ ❢✝✟ ❻◆❙✱
✏❣✞❣✱ ✓t✟✞✓✓♥❢✟✞✞ ❢✝✟ t❤✞ ✌✞✍☞ ✈✞☛✝✑✏t✖ ✍t t❤✞ t✝✘ ✍☞❞ ✡✝tt✝✌❣ ✢✝✟
t❤✞ ✌✞✍☞ ✌✍✎☞✞t✏✑ ✧✞☛❞✱ ✇✞ ✠✓✞ ✞✏t❤✞✟ ✘✞✟❢✞✑t ✑✝☞❞✠✑t✝✟ ✡✝✠☞❞♥
✍✟✖ ✑✝☞❞✏t✏✝☞✓ ✭❢✝✟ ❤✝✟✏✦✝☞t✍☛✱ ✏✌✘✝✓✞❞ ✌✍✎☞✞t✏✑ ✧✞☛❞✓✮ ✝✟ ✈✞✟♥
t✏✑✍☛ ✧✞☛❞ ✑✝☞❞✏t✏✝☞✓ ✭❢✝✟ ✈✞✟t✏✑✍☛✱ ✏✌✘✝✓✞❞ ✧✞☛❞✓✮ ✍t t❤✞ t✝✘ ✍☞❞
✡✝tt✝✌❣ ❆☛☛ ✌✞✍☞♥✧✞☛❞ ✈✍✟✏✍✡☛✞✓ ✍✟✞ ✍✓✓✠✌✞❞ t✝ ✡✞ ✘✞✟✏✝❞✏✑ ✏☞
t❤✞ ➦ ✍☞❞ ➧ ❞✏✟✞✑t✏✝☞✓❣ ❚❤✞ ✚✢❙ ✍✟✞ ✘✞✟❢✝✟✌✞❞ ✍✎✍✏☞ ✇✏t❤ t❤✞
✛➨➩➫➯➳ ➵➸➺➨✱ ✇❤✏✑❤ ✏✓ ✞❊✠✏✘✘✞❞ ✇✏t❤ ✍ ✌✞✍☞♥✧✞☛❞ ✌✝❞✠☛✞ ❢✝✟
✓✝☛✈✏☞✎ t❤✞ ✑✝✟✟✞✓✘✝☞❞✏☞✎ ✞❊✠✍t✏✝☞✓❣
❜❥➻❥ ➼➽➾④➚❷④⑨ ➪④➶❷❸➚⑤⑧ ⑨④➾④⑥⑨④⑥➚④ ❹➹ ➘➼q➴➷
❚✝ ✎✞t ✍☞ ✏❞✞✍ ✍✡✝✠t t❤✞ ✈✞✟t✏✑✍☛ ❞✞✘✞☞❞✞☞✑✞ ✝❢ ◆✙✚✛✜✱ ✇✞
☞✝✇ ✑✝☞✓✏❞✞✟ t❤✞ ✟✞✓✠☛t✏☞✎ ❞✞✘✞☞❞✞☞✑✏✞✓ ✝❢ ➬➮➱ ✭③✮❽ ✓✞✞ t❤✞ ☛✞❢t♥
❤✍☞❞ ✘✍☞✞☛✓ ✝❢ ✢✏✎❣ ✶❣ ❼✞ ☞✝t✞ t❤✍t ➬➮➱ ✏✓ ✃✠✓t ✍ ❢✠☞✑t✏✝☞ ✝❢ ❫
✭✙❊✓❣ ✭✣✩✮ ✍☞❞ ✭✣✶✮✮✱ ✇❤✏✑❤ ✍☛☛✝✇✓ ✠✓ t✝ ✍✘✘✟✝✬✏✌✍t✞ t❤✞ ☛✝✑✍☛
✎✟✝✇t❤ ✟✍t✞✓ ✍✓ ✭★✝✎✍✑❤✞✈✓➛✏✏ ✫ ❑☛✞✞✝✟✏☞ ✷✥✥✼❽ ❑✞✌✞☛ ✞t ✍☛❣
✷✥✣❃✮
✯➇ ❂
❐❒
✴✵➇
❮
❾✷
❰➙
❞➬➮➱ ✪
❪
❞❫✪
✭✷✩✮
✇❤✏✑❤ ✍✟✞ ✘☛✝tt✞❞ ✏☞ t❤✞ ✟✏✎❤t❤✍☞❞ ✘✍☞✞☛✓ ✝❢ ✢✏✎❣ ✶ ❢✝✟ ✚✝❞✞☛ ✜❣
❜❥❜❥ Ï❹➶❸Ð❹⑥❷⑤⑧ Þ④⑧⑨❺
❚✝ ✍☞✍☛✖✦✞ t❤✞ ➛✏☞✞✌✍t✏✑ ✓t✍✎✞ ✝❢ ✚✢❙✱ ✇✞ ✌✞✍✓✠✟✞ t❤✞ ✈✍☛✠✞ ✝❢
t❤✞ ✌✍✬✏✌✠✌ ❞✝✇☞✗✝✇ ✓✘✞✞❞✱ Ñ➢ÑÒÓÔÕ
❈Ö❋ ✍t ✞✍✑❤ ❤✞✏✎❤t❣ ❼✞ t❤✞☞
ØÙÚ ♣ ✄❡ Û ♦Ü ÝÝ
❆✫❆ ✺ ✁✂ ❆✷ ✭✷✄☎✁✆
❋✝✞✳ ✶✶✳ ❙✠♠❛ ✠s ✎✐❣✘ ☎✄ ✭✑♦✡✐✢♦☛✏✠♣ ✣❛♣❞✆✂ ❷✉✏ ☞♦✡ ▼♦❞❛♣ ✜✜✘
❋✝✞✳ ✾✳ ❈♦♠✟✠✡✐s♦☛ ♦☞ P❡✌ ✭③✆ ✠☛❞ ✍✵ ✭③✆ ✐☛ ▼✎❙ ☞♦✡ ✟♦♣②✏✡♦✟✐❝ ♣✠②❛✡s
✇✐✏✑ ☞♦✉✡ ✈✠♣✉❛s ♦☞ ✒ ✭t✓✔ t✓ ❜✓tt✓✕✆ ✠☛❞ ✏✑✡❛❛ ✈✠♣✉❛s ♦☞ ✖ ✭❞✐✗❛✡❛☛✏
♣✐☛❛ ✏②✟❛s✆✘
❋✝✞✳ ✶❸✳ ❙☛✠✟s✑♦✏s ♦☞ ❹❺ ☞✡♦♠ ▼✎❙ ❞✉✡✐☛❣ ✏✑❛ ❻✐☛❛♠✠✏✐❝ ❣✡♦✇✏✑ ✟✑✠s❛
☞♦✡ ❞✐✗❛✡❛☛✏ ✈✠♣✉❛s ♦☞ ✒ ✠☛❞ ❹✵❼❹❡❽✵ ☞♦✡ ✒ ❾ ☎ ✭t✓✔✆ ✠☛❞ ✺❼❿ ✭❜✓tt✓✕✆
✇✐✏✑ ✖✵ ❾ ✄➀✄✷ ✭➁➂➃t✆ ✠☛❞ ✄✘☎ ✭➄➅➆➇t✆ ✐☛ ✏✑❛ ✟✡❛s❛☛❝❛ ♦☞ ✠ ✑♦✡✐✢♦☛✏✠♣ ✣❛♣❞
☞♦✡ ▼♦❞❛♣ ✜✘
❋✝✞✳ ✶✙✳ ❉❛✟❛☛❞❛☛❝❛ ♦☞ ❣✡♦✇✏✑ ✡✠✏❛ ✠☛❞ ✑❛✐❣✑✏ ✇✑❛✡❛ ✏✑❛ ❛✐❣❛☛☞✉☛❝✚
✏✐♦☛ ✠✏✏✠✐☛s ✐✏s ♠✠①✐♠✉♠ ✈✠♣✉❛ ✭✏✑❛ ♦✟✏✐♠✠♣ ❞❛✟✏✑ ♦☞ ◆❊▼✛✜✆ ♦☛ ✣❛♣❞
s✏✡❛☛❣✏✑ ☞✡♦♠ ▼✎❙ ☞♦✡ ❞✐✗❛✡❛☛✏ ✈✠♣✉❛s ♦☞ ✒ ✐☛ ✏✑❛ ✟✡❛s❛☛❝❛ ♦☞ ✠ ✑♦✡✐✚
✢♦☛✏✠♣ ✣❛♣❞ ☞♦✡ ▼♦❞❛♣ ✜✘
✤✥✦✥r✧★♥✥ ✦❤✥ ✦★✧✥ ★♥✦✥r✩✪❧ ✤✬r★♥✮ ✯❤★✰❤ ✦❤✥ ✧✪✱★✧✬✧ ✤✲✯♥✴
✸✲✯ ✹✻✥✥✤ ★♥✰r✥✪✹✥✹ ✥✱✻✲♥✥♥✦★✪❧❧✼ ✪♥✤ ✯❤✥♥ ✦❤✥ ❤✥★✮❤✦ ✲✽ ✦❤✥
✻✥✪✿ ★✹ ✰✲♥✹✦✪♥✦ ✪♥✤ ✥q✬✪❧ ✦✲ ❀❇ ❁ ❚❤★✹ ✼★✥❧✤✹ ✦❤✥ ✮r✲✯✦❤ r✪✦✥ ✲✽
✦❤✥ ★♥✹✦✪❂★❧★✦✼ ✪✹ ❃ ❄ ✤ ❧♥ ⑤❯⑤❅●❍■
❏❑▲ ❖✤◗❁
❘♥ ❱★✮✹❁ ❲❳ ✪♥✤ ❲❲ ✯✥ ✻❧✲✦❨ r✥✹✻✥✰✦★✩✥❧✼ ✽✲r ❩✲✤✥❧✹ ❘ ✪♥✤ ❘❘❨
❴ ❥ ✪♥✤ ❀ ✩✥r✹✬✹ ❤✲r★❦✲♥✦✪❧ ★✧✻✲✹✥✤ ✧✪✮♥✥✦★✰
❃ ❬★♥ ✬♥★✦✹ ✲✽ ❭❪ ❖❫❵❢
❇
④✥❧✤ ✹✦r✥♥✮✦❤❨ ⑥❢ ❖⑥⑦⑧ ❁ ❚❤✥ ✧✪✱★✧✬✧ ✮r✲✯✦❤ r✪✦✥✹ ✽✲r ⑨ ❄ ⑩❖❶
❆✷✂ ✟✠❣❛ ➣ ♦☞ ☎☎
❴ ✽✲r ❩✲✤✥❧ ❘
✪♥✤ ⑨ ❄ ❲ ✪r✥ ✹★✧★❧✪r ✽✲r ❂✲✦❤ ✧✲✤✥❧✹ ❬➈➉⑩ ❭❪ ❖❫❵❢
❴
✪♥✤ ❲➊➉➋❳ ❭❪ ❖❫❵❢ ✽✲r ❩✲✤✥❧ ❘❘❥❁ ❘✦ ✦✬r♥✹ ✲✬✦ ✦❤✪✦ ✽✲r ⑨ ❄ ⑩❖❶❨
✦❤✥ ✮r✲✯✦❤ r✪✦✥ ❃ ✪✦✦✪★♥✹ ✪ ✧✪✱★✧✬✧ ✪✦ ✹✲✧✥ ✩✪❧✬✥ ⑥❢ ❄ ⑥❏❑▲ ❨
✪♥✤ ✦❤✥♥ ★✦ ✤✥✰r✥✪✹✥✹ ✯★✦❤ ★♥✰r✥✪✹★♥✮ ⑥❢ ❨ ✯❤★❧✥ ★♥ ✪♥ ★✹✲✦❤✥r✧✪❧
r✬♥ ❃ ★✹ ♥✥✪r❧✼ ✰✲♥✹✦✪♥✦ ✽✲r ✮r✥✪✦✥r ④✥❧✤ ✹✦r✥♥✮✦❤❨ ✥✱✰✥✻✦ ♥✥✪r
✦❤✥ ✹✬r✽✪✰✥ ✯❤✥r✥ ✦❤✥ ✻r✲✱★✧★✦✼ ✦✲ ✦❤✥ ❂✲✬♥✤✪r✼ ★✹ ✦✲✲ ✹✧✪❧❧❁
❚❤★✹ ✰❧✲✹✥ ✻r✲✱★✧★✦✼ r✥✤✬✰✥✹ ✦❤✥ ✮r✲✯✦❤ r✪✦✥❁ ❱✲r ❩✲✤✥❧ ❘ ✯★✦❤
⑨ ❄ ❲❨ ✦❤✥ ✤✥✰❧★♥✥ ✲✽ ❃ ❬✦✲✯✪r✤ ✯✥✪✿✥r ④✥❧✤✹ ✲♥ ✦❤✥ ❧✥✽✦❤✪♥✤
✹★✤✥ ✲✽ ✦❤✥ ✻❧✲✦❥ ❂✥✮★♥✹ ✯❤✥♥ ✦❤✥ ✤★✹✦✪♥✰✥ ✦✲ ✦❤✥ ✦✲✻ ❂✲✬♥✤✪r✼
❬❀❪●➌ ➍ ❀ ❇ ➎ ❲➏➋ ❫❵❢ ✽✲r ➐❢ ❄ ❳➏❳➋❥ ★✹ ❧✥✹✹ ✦❤✪♥ ✦❤✥ r✪✤★✬✹ ✲✽
✧✪✮♥✥✦★✰ ✹✦r✬✰✦✬r✥✹ ❬➑ ➎ ➋➒❖➓➔ ➎ ❲➏⑩ ❫❵❢ ✬✹★♥✮ ➓➔ ❫❵❢ ❄ ❲❥❁ ❘♥
❩✲✤✥❧ ❘❘ ✯★✦❤ ⑨ ❄ ❲❨ ✦❤✥ ✤✥✰❧★♥✥ ✲✽ ❃ ✲✰✰✬r✹ ✽✲r ✹✦r✲♥✮✥r ④✥❧✤✹❨
❂✬✦ ✦❤✥ ✤★✹✦✪♥✰✥ ✦✲ ✦❤✥ ✦✲✻ ❂✲✬♥✤✪r✼ ❬➎❲➏❳ ❫❵❢ ❥ ★✹ ✹✦★❧❧ ♥✥✪r❧✼ ✦❤✥
✹✪✧✥ ✪✹ ✽✲r ❩✲✤✥❧ ❘❁
❘♥ ✪♥ ★✹✲✦❤✥r✧✪❧ ❧✪✼✥r❨ ✦❤✥ ❤✥★✮❤✦ ✯❤✥r✥ ✦❤✥ ✥★✮✥♥✽✬♥✰✦★✲♥
✻✥✪✿✹ ★✹ ✿♥✲✯♥ ✦✲ ✤✥✰r✥✪✹✥ ✯★✦❤ ★♥✰r✥✪✹★♥✮ ④✥❧✤ ✹✦r✥♥✮✦❤→ ✹✥✥
■✳ ❘✳ ▲♦s ✁ ❡✂ ❛✳✿ ▼ ✄☎❡✂✐❝ ✤✉① ❝♦☎❝❡☎✂r ✂✐♦☎s ✐☎
❋✝❣✞ ✶✟✞ ❉❡♣❡☎✁❡☎❝❡ ♦❢ ✄r♦✇✂✆ r ✂❡ ☎✁ ♦♣✂✐♠ ❛ ✁❡♣✂✆ ♦❢ ◆❊▼P■ ♦☎
✣❡❛✁ s✂r❡☎✄✂✆ ❢r♦♠ ▼✠✡ ❢♦r ✁✐☛❡r❡☎✂ ✈ ❛✉❡s ♦❢ ☞ ✐☎ ✂✆❡ ♣r❡s❡☎❝❡ ♦❢
✈❡r✂✐❝ ❛ ✣❡❛✁ ❢♦r ▼♦✁❡❛ ■✳
✌✍✎✏ ✻ ✑✒ ❑✓✔✓❧ ✓t ✕❧✏ ✭✷✖✗✷✕✮✏ ❖♥✓ ✔✍✎✘t ✘✕✙✓ ✓✚✛✓✜t✓✢ t✘✍✥ ✢✓❞
✜✦✓✕✥✓ t✑ ❜✓ ❧✓✥✥ ✥t✓✓✛ ✍♥ t✘✓ ✛✑❧✧t✦✑✛✍✜ ✜✕✥✓★ ❜✓✜✕✩✥✓ t✘✓ ✑✛t✍✔✕❧
✢✓✛t✘ ✪✘✓✦✓ ✫✬✯✰✱ ✑✜✜✩✦✥ ✜✕♥♥✑t ✓✕✥✍❧✧ ❜✓ ✢✓✜✦✓✕✥✓✢ ✪✍t✘✑✩t
✥✩✲✓✦✍♥✎ ✕ ✢✦✕✔✕t✍✜ ✢✓✜✦✓✕✥✓ ✑✒ t✘✓ ✎✦✑✪t✘ ✦✕t✓✏ ❚✘✍✥ ✍✥ ✘✑✪✓✙✓✦
♥✑t t✘✓ ✜✕✥✓★ ✕♥✢ ✪✓ ✴♥✢ t✘✕t t✘✓ ✑✛t✍✔✕❧ ✢✓✛t✘ ✑✒ ✫✬✯✰✱ ✍✥
♥✑✪ ✒✕❧❧✍♥✎ ✑✲ ✔✑✦✓ q✩✍✜✵❧✧ ✍♥ ✯✑✢✓❧ ✱★ ❜✩t ✍✥ ✔✑✦✓ ✥✍✔✍❧✕✦ ✒✑✦
✯✑✢✓❧ ✱✱✸ ✥✓✓ t✘✓ ✥✓✜✑♥✢ ✛✕♥✓❧✥ ✑✒ ✌✍✎✥✏ ✗✖ ✕♥✢ ✗✗✏ ❚✘✍✥ ✔✓✕♥✥
t✘✕t ✍♥ ✕ ✛✑❧✧t✦✑✛✍✜ ❧✕✧✓✦★ ✫✬✯✰✱ ✪✑✦✵✥ ✔✑✦✓ ✓✲✓✜t✍✙✓❧✧★ ✕♥✢ ✍t✥
✎✦✑✪t✘ ✦✕t✓ ✍✥ ✒✕✥t✓✥t ✪✘✓♥ t✘✓ ✔✕✎♥✓t✍✜ ✴✓❧✢ ✍✥ ♥✑t t✑✑ ✥t✦✑♥✎✏
❆t t✘✓ ✥✕✔✓ t✍✔✓★ t✘✓ ✑✛t✍✔✕❧ ✢✓✛t✘ ✑✒ ✫✬✯✰✱ ✍♥✜✦✓✕✥✓✥★ ✍✏✓✏★
t✘✓ ✦✓✥✩❧t✍♥✎ ✙✕❧✩✓ ✑✒ ③❇ ✍♥✜✦✓✕✥✓✥ ✕✥ ✹✺ ✢✓✜✦✓✕✥✓✥✏
❚✘✓ ✦✓✥✩❧t✍♥✎ ✎✦✑✪t✘ ✦✕t✓✥ ✕✦✓ ✥✑✔✓✪✘✕t ❧✓✥✥ ✒✑✦ ✯✑✢✓❧ ✱
✕♥✢ ✥✑✔✓✪✘✕t ✘✍✎✘✓✦ ✒✑✦ ✯✑✢✓❧ ✱✱ t✘✕♥ t✘✑✥✓ ✑✒ ✓✕✦❧✍✓✦ ✔✓✕♥❞
✴✓❧✢ ✜✕❧✜✩❧✕t✍✑♥✥ ✑✒ ❑✓✔✓❧ ✓t ✕❧✏ ✭✷✖✗✷✕★ t✘✓✍✦ ✌✍✎✏ ✻✮★ ✪✘✑ ✒✑✩♥✢
✽ ❀❁ ❃ ❄❅❈ ✍♥ ✕ ✔✑✢✓❧ ✪✍t✘ ● ◗ ✖❅❙✷ ✕♥✢ ● ◗ ✖❅✖❯✏ ❚✘✓✥✓
✼❍✾✺
❂
❏
✾
✢✍✲✓✦✓♥✜✓✥ ✍♥ t✘✓ ✎✦✑✪t✘ ✦✕t✓✥ ✕✦✓ ✛❧✕✩✥✍❜❧✧ ✓✚✛❧✕✍♥✓✢ ❜✧ ✢✍✲✓✦❞
✓♥✜✓✥ ✍♥ t✘✓ ✔✓✕♥❞✴✓❧✢ ✛✕✦✕✔✓t✓✦✥✏
❱✍✥✩✕❧✍❲✕t✍✑♥✥ ✑✒ t✘✓ ✦✓✥✩❧t✍♥✎ ✘✑✦✍❲✑♥t✕❧ ✴✓❧✢ ✥t✦✩✜t✩✦✓✥ ✕✦✓
✥✘✑✪♥ ✍♥ ✌✍✎✏ ✗✷ ✒✑✦ t✪✑ ✙✕❧✩✓✥ ✑✒ ❳ ✕♥✢ ✹✺ ✏ ✱♥✜✦✓✕✥✓ ✍♥ t✘✓
✛✕✦✕✔✓t✓✦ ❳ ✦✓✥✩❧t✥ ✍♥ ✕ ✥t✦✑♥✎✓✦ ❧✑✜✕❧✍❲✕t✍✑♥ ✑✒ t✘✓ ✍♥✥t✕❜✍❧✍t✧ ✕t
t✘✓ ✥✩✦✒✕✜✓ ❧✕✧✓✦★ ✪✘✓✦✓ t✘✓ ✢✓♥✥✍t✧ ✥✜✕❧✓ ✘✓✍✎✘t ✍✥ ✔✍♥✍✔✩✔ ✕♥✢
t✘✓ ✎✦✑✪t✘ ✑✒ ✫✬✯✰✱ ✍✥ ✥t✦✑♥✎✓✥t✏
❨❩❬❩ ❭❪❫❴❵❤❥❦ Þ❪❦④⑤
✱♥ t✘✓ ✛✦✓✥✓♥✜✓ ✑✒ ✕ ✙✓✦t✍✜✕❧ ✴✓❧✢★ t✘✓ ✓✕✦❧✧ ✓✙✑❧✩t✍✑♥ ✑✒ t✘✓ ✍♥❞
✥t✕❜✍❧✍t✧ ✍✥ ✥✍✔✍❧✕✦ t✑ t✘✕t ✒✑✦ ✕ ✘✑✦✍❲✑♥t✕❧ ✴✓❧✢✏ ✱♥ ❜✑t✘ ✜✕✥✓✥★
t✘✓ ✔✕✚✍✔✩✔ ✴✓❧✢ ✥t✦✓♥✎t✘ ✑✜✜✩✦✥ ✕t ✕ ✥✑✔✓✪✘✕t ❧✕✦✎✓✦ ✢✓✛t✘
✪✘✓♥ ✥✕t✩✦✕t✍✑♥ ✍✥ ✦✓✕✜✘✓✢★ ✓✚✜✓✛t t✘✕t ✥✘✑✦t❧✧ ❜✓✒✑✦✓ ✥✕t✩✦✕❞
t✍✑♥ t✘✓✦✓ ✍✥ ✕ ❜✦✍✓✒ ✍♥t✓✦✙✕❧ ✢✩✦✍♥✎ ✪✘✍✜✘ t✘✓ ❧✑✜✕t✍✑♥ ✑✒ ✔✕✚❞
✍✔✩✔ ✴✓❧✢ ✥t✦✓♥✎t✘ ✦✍✥✓✥ ✥❧✍✎✘t❧✧ ✩✛✪✕✦✢✥ ✍♥ t✘✓ ✙✓✦t✍✜✕❧ ✴✓❧✢
✜✕✥✓✏ ✱♥ t✘✓ ✥✕t✩✦✕t✓✢ ✜✕✥✓★ ✘✑✪✓✙✓✦★ t✘✓ ⑥✩✚ ✜✑♥✜✓♥t✦✕t✍✑♥✥ ✒✦✑✔
✫✬✯✰✱ ✕✦✓ ✔✩✜✘ ✥t✦✑♥✎✓✦ ✜✑✔✛✕✦✓✢ t✑ t✘✓ ✜✕✥✓ ✑✒ ✕ ✘✑✦✍❲✑♥❞
t✕❧ ✴✓❧✢ ✕♥✢ ✍t ❧✓✕✢✥ t✑ t✘✓ ✒✑✦✔✕t✍✑♥ ✑✒ ✔✕✎♥✓t✍✜ ⑥✩✚ ✜✑♥❞
✜✓♥t✦✕t✍✑♥✥ ✑✒ ✓q✩✍✛✕✦t✍t✍✑♥ ✴✓❧✢ ✥t✦✓♥✎t✘ ✭⑦✦✕♥✢✓♥❜✩✦✎ ✓t ✕❧✏
✷✖✗❙★ ✷✖✗⑧✮✏ ❚✘✍✥ ✍✥ ✛✑✥✥✍❜❧✓ ❜✓✜✕✩✥✓ t✘✓ ✦✓✥✩❧t✍♥✎ ✙✓✦t✍✜✕❧ ⑥✩✚
t✩❜✓ ✍✥ ♥✑t ✕✢✙✓✜t✓✢ ✢✑✪♥✪✕✦✢ ✪✍t✘ t✘✓ ⑥✑✪ t✘✕t ✢✓✙✓❧✑✛✥ ✕✥ ✕
♣♦❛②✂r♦♣✐❝ ✂♠♦s♣✆❡r❡
❋✝❣✞ ✶⑨✞ ✡ ♠❡ s ✠✐✄✳ ⑩❶ ❷✈❡r✂✐❝ ❛ ✣❡❛✁❸❹ ❺✉✂ ❢♦r ▼♦✁❡❛ ■■✳
❋✝❣✞ ✶❻✞ ❼♦♠♣ r✐s♦☎ ♦❢ ❽ ❾❿➀ ❢r♦♠ ▼✠✡ ❢♦r ▼♦✁❡❛s ■ ❷s♦❛✐✁ ❛✐☎❡❸ ☎✁ ■■
❷✁ s✆❡✁ ❛✐☎❡❸❹ s✆♦✇✐☎✄ ❡①♣♦☎❡☎✂✐ ❛ ✄r♦✇✂✆ ❢♦❛❛♦✇❡✁ ❺② ☎♦☎❛✐☎❡ r s ✂✉➁
r ✂✐♦☎✳ ■☎ ❺♦✂✆ ❝ s❡s ✇❡ ✆ ✈❡ ☞ ➂ ➃➄❶ ☎✁ ☎ ✐♠♣♦s❡✁ ✈❡r✂✐❝ ❛ ♠ ✄☎❡✂✐❝
✣❡❛✁ ✇✐✂✆ ➅➆ ➂ ➇➈➇➃✳
✜✑♥✥✓q✩✓♥✜✓ ✑✒ ✫✬✯✰✱✏ ❚✘✓ ❧✕tt✓✦ ✓✲✓✜t ✍✥ t✘✓ ✕✒✑✦✓✔✓♥t✍✑♥✓✢
➉✛✑t✕t✑❞✥✕✜✵➊ ✓✲✓✜t★ ✪✘✍✜✘ ✕✜t✥ ✕✥ ✕ ♥✑♥❧✍♥✓✕✦ ✥✕t✩✦✕t✍✑♥ ✔✓✜✘❞
✕♥✍✥✔ ✑✒ ✫✬✯✰✱ ✪✍t✘ ✕ ✘✑✦✍❲✑♥t✕❧ ✴✓❧✢✏
✱♥ ✌✍✎✥✏ ✗❙ ✕♥✢ ✗⑧ ✪✓ ✛❧✑t t✘✓ ✎✦✑✪t✘ ✦✕t✓✥ ✼ ✕♥✢ t✘✓ ✘✓✍✎✘t✥
✪✘✓✦✓ t✘✓ ✓✍✎✓♥✒✩♥✜t✍✑♥ ✕tt✕✍♥✥ ✍t✥ ✔✕✚✍✔✩✔ ✙✕❧✩✓✥ ✒✑✦ ✢✍✲✓✦✓♥t
●✺ ◗ ✹✺ ❀✹➋➌✺ ✒✑✦ ✯✑✢✓❧✥ ✱ ✕♥✢ ✱✱★ ✦✓✥✛✓✜t✍✙✓❧✧✏ ✌✑✦ ❳ ◗ ❯❀❙★ t✘✓
✔✕✚✍✔✩✔ ✎✦✑✪t✘ ✦✕t✓ ✍✥ ✘✍✎✘✓✦ ❧✕✦✎✓✦ t✘✕♥ ✒✑✦ ❳ ◗ ✗✏ ❚✘✍✥ ✍✥
✽ ✒✑✦ ❳ ◗ ❯❀❙
t✦✩✓ ✒✑✦ ✯✑✢✓❧✥ ✱ ✕♥✢ ✱✱★ ✪✘✓✦✓ t✘✓✧ ✕✦✓ ➍➎✗✖ ❁❂ ❀❍➏✺
✽
✕♥✢ ❯➎❈ ❁❂ ❀❍➏✺ ✒✑✦ ❳ ◗ ✗✏ ❚✘✓ ♥✑♥✔✑♥✑t✑♥✑✩✥ ❜✓✘✕✙✍✑✦ ✥✓✓♥ ✍♥
t✘✓ ✢✓✛✓♥✢✓♥✜✓ ✑✒ ✼ ✑♥ ✹✺ ✍✥ ✥✩✎✎✓✥t✍✙✓ ✑✒ t✘✓ ✛✦✓✥✓♥✜✓ ✑✒ ✢✍✲✓✦❞
✓♥t ✔✑✢✓ ✥t✦✩✜t✩✦✓✥★ ✕❧t✘✑✩✎✘ ✕ ✢✍✦✓✜t ✍♥✥✛✓✜t✍✑♥ ✑✒ t✘✓ ✦✓✥✩❧t✍♥✎
✔✕✎♥✓t✍✜ ✴✓❧✢ ✢✍✢ ♥✑t ✥✘✑✪ ✕♥✧ ✑❜✙✍✑✩✥ ✢✍✲✓✦✓♥✜✓✥✏ ➐✑✪✓✙✓✦★
t✘✍✥ ✍✦✦✓✎✩❧✕✦ ❜✓✘✕✙✍✑✦ ✔✕✧ ❜✓ ✦✓❧✕t✓✢ t✑ ✕✦t✍✒✕✜t✥ ✦✓✥✩❧t✍♥✎ ✒✦✑✔
✕ ✴♥✍t✓ ✢✑✔✕✍♥ ✥✍❲✓ ✕♥✢ ✪✓✦✓ ♥✑t ✦✓✎✕✦✢✓✢ ✍✔✛✑✦t✕♥t ✓♥✑✩✎✘ t✑
➑✩✥t✍✒✧ ✒✩✦t✘✓✦ ✍♥✙✓✥t✍✎✕t✍✑♥✏
✫✓✚t ✪✓ ✒✑✜✩✥ ✑♥ ✕ ✜✑✔✛✕✦✍✥✑♥ ✑✒ t✘✓ ✎✦✑✪t✘ ✦✕t✓✥ ✑❜❞
t✕✍♥✓✢ ✒✦✑✔ ✯✌➒ ✒✑✦ ✘✑✦✍❲✑♥t✕❧ ✕♥✢ ✙✓✦t✍✜✕❧ ✴✓❧✢✥✏ ❚✘✓ ✙✕❧✩✓✥
✑✒ ●✺ ★ ③❇ ★ ✕♥✢ ●✭③❇ ✮ ◗ ✹✺ ❀✹➋➌✭③❇ ✮ ✒✑✦ ✘✑✦✍❲✑♥t✕❧ ✕♥✢ ✙✓✦t✍✜✕❧
✴✓❧✢✥ ✕✦✓ ✜✑✔✛✕✦✓✢ ✍♥ ❚✕❜❧✓ ✗ ✒✑✦ ❜✑t✘ ✔✑✢✓❧✥✏ ➓✓ ✥✓✓ t✘✕t
✫✬✯✰✱ ✍✥ ✔✑✥t ✓✲✓✜t✍✙✓ ✍♥ ✦✓✎✍✑♥✥ ✪✘✓✦✓ t✘✓ ✔✓✕♥ ✔✕✎♥✓t✍✜
✴✓❧✢ ✍✥ ✕ ✥✔✕❧❧ ✒✦✕✜t✍✑♥ ✑✒ t✘✓ ❧✑✜✕❧ ✓q✩✍✛✕✦t✍t✍✑♥ ✴✓❧✢ ✕♥✢ t✧✛❞
✍✜✕❧❧✧ ✥❧✍✎✘t❧✧ ❧✓✥✥ ✒✑✦ ❳ ◗ ❯❀❙ t✘✕♥ ✒✑✦ ❳ ◗ ✗✏ ✱♥✢✓✓✢★ ✒✑✦
➔→❹ ♣ ✄❡ ➣ ♦❢ ⑩⑩
❆✫❆ ✺ ✁✂ ❆✷ ✭✷✄☎✁✆
❋✐❣✳ ✶✝✳ ❙✞❛♣s❤♦ts ❢✟♦♠ ▼✠❙ s❤♦✇✡✞☛ ❇③ ♦✞ t❤❡ ♣❡✟✡♣❤❡✟② ♦❢ t❤❡ ❝♦♠♣☞t❛t✡♦✞❛✌ ❞♦♠❛✡✞ ❢♦✟ ✍ ❂ ✺✴✸ ❛✞❞ ✎✵ ❂ ✄✏✄✺ ❛t ❞✡✑❡✟❡✞t t✡♠❡s ❢♦✟ ▼♦❞❡✌ ■
❢♦✟ t❤❡ ❝❛s❡ ♦❢ ❛ ✈❡✟t✡❝❛✌ ✣❡✌❞✒
❋✐❣✳ ✶✓✳ ❙✡♠✡✌❛✟ t♦ ✠✡☛✒ ☎ ♦❢ ▼✠❙✂ ❜☞t ❢♦✟ ▼♦❞❡✌ ■■ ❛t t✡♠❡s s✡♠✡✌❛✟ t♦ t❤♦s❡ ✡✞ t❤❡ ❉◆❙ ♦❢ ✠✡☛✒ ✺✒ ❚❤❡✟❡ ❛✟❡ ✞♦✇ ♠♦✟❡ st✟☞❝t☞✟❡s t❤❛✞ ✡✞ t❤❡ ❡❛✟✌✡❡✟
▼✠❙ ♦❢ ✠✡☛✒ ☎ ✂ ❛✞❞ t❤❡② ❞❡✈❡✌♦♣ ♠♦✟❡ ✟❛♣✡❞✌②✒
✔✕✖❧✗ ✶✳ ❈♦♠♣❛✟✡s♦✞ ♦❢ t❤❡ ♦♣t✡♠❛✌ ❞❡♣t❤ ✘✙ ❛✞❞ t❤❡ ❝♦✟✟❡s♣♦✞❞✡✞☛
✞♦✟♠❛✌✡✚❡❞ ♠❛☛✞❡t✡❝ ✣❡✌❞ st✟❡✞☛t❤ ✎✭✘✙ ✆ ❢♦✟ t❤✟❡❡ ✈❛✌☞❡s ♦❢ ✍ ❢♦✟ ✡♠✛
♣♦s❡❞ ❤♦✟✡✚♦✞t❛✌ ❛✞❞ ✈❡✟t✡❝❛✌ ♠❛☛✞❡t✡❝ ✣❡✌❞s ♦❢ ✞♦✟♠❛✌✡✚❡❞ st✟❡✞☛t❤s
✎✵ ❂ ❇✵✴❇✜✢✵ ✂ ❢♦✟ ▼♦❞❡✌ ■✒
▼♦❞
■
■
■
■■
■■
✍
☎
☎✒✁
✺✧✸
☎
✺✧✸
❍♦✟✡✚♦✞t❛✌ ✣❡✌❞
✎✵
✘✙ ✴✤✥✵ ✎✭✘✙ ✆
✄✒✄✺ ❾✄✏✼
✄✒✄✸✁
✄✒✄✸
✄✏✸✁ ✄✒✄✸✺
✄✒✄✷
✄✏✦✺ ✄✒✄✷★
✄✒✷✄ ❾✄✏✷★ ✄✒☎✼
✄✒✄✦
✄✏★✁ ✄✒☎✷
❱❡✟t✡❝❛✌ ✣❡✌❞
✎✵ ✘✙ ✴✤✥✵ ✎✭✘✙ ✆
✄✒✄✁
✄✏✼
✄✒✄✺✦
✄✒✄✸
✄✏✼✺ ✄✒✄✁✸
✄✒✄✷ ☎✒✄
✄✒✄✸☎
✄✒☎✷ ☎✒✷
✄✒✷✷
✄✒✄✺ ☎✒✄
✄✒✄✦
✩✪✬✮✯ ✰✱ ✲✹✻✽ ✾ ✿❀ ❁❃❄❅ ❊✪● ❏✪●✿❑✪▲❖P✯ ◗✮✯✬❀ P▲✬ ❁❃❘❅ ❊✪● ❯✮●❲
❖✿❳P✯ ◗✮✯✬❀✱ ❨❏✿✯✮ ❊✪● ✩✪✬✮✯ ✰✰✱ ✲✹✻✽ ✾ ✿❀ ❩❬❃❩❭❅ ❊✪● ❏✪●✿❑✪▲❲
❖P✯ ◗✮✯✬❀ P▲✬ ❪❃❬❬❅ ❊✪● ❯✮●❖✿❳P✯ ◗✮✯✬❀❫ ❴✮●✮✱ ❨✮ ❏P❯✮ ✉❀✮✬
✲✹✻✽✾ ❵ ✲❥ ❦♥qr ✹✻✽ ①❬④⑤❥ ✾✱ ❨❏✮●✮ ❦⑥ ✹⑦✾ ✿❀ ❖❏✮ ⑧❲✮⑨⑩✪▲✮▲❖✿P✯ ❊✉▲❳❲
❖✿✪▲ ✬✮◗▲✮✬ ❶❷ ❸❹❫ ✹❁✾❫
❺✮ ✮⑨⑩✮❳❖ ❖❏P❖ ❏✿❻❏✮● ❯P✯✉✮❀ ✪❊ ✲❼ ❨✿✯✯ ✯✮P✬ ❖✪ ❻●✮P❖✮● ❻●✪❨❖❏
●P❖✮❀❫ ❽✪ ❯✮●✿❊❷ ❖❏✿❀✱ ❨✮ ❳✪❿⑩P●✮ ✿▲ ➀✿❻❫ ❩➁ ❖❏✮ ❖✿❿✮ ✮❯✪✯✉❖✿✪▲❀
✪❊ ➂ ➃➄➅ ❊✪● ✩✪✬✮✯❀ ✰ ✹❨✿❖❏ ✲❼ ❵ ➆➇❁❁✾ P▲✬ ✩✪✬✮✯ ✰✰ ✹❨✿❖❏
✲❼ ❵ ➆➇❘❁✾❫ ❽❏✮ ❻●✪❨❖❏ ●P❖✮ ❏P❀ ▲✪❨ ✿▲❳●✮P❀✮✬ ❶❷ P ❊P❳❖✪● ✪❊ ❬❫❄
♥ ①➉ ❵ ❁➇➋ ❖✪ ➋❫➁✾✱ ❨❏✿❳❏ ✿❀ ❀✯✿❻❏❖✯❷ ❿✪●✮ ❖❏P▲ ❨❏P❖ ✿❀
✹❊●✪❿ ➈④⑤❥
➊
✮⑨⑩✮❳❖✮✬ ❊●✪❿ ✲❼ ✱ ❨❏✿❳❏ ❏P❀ ✿▲❳●✮P❀✮✬ ❶❷ P ❊P❳❖✪● ✪❊ ❩❫➋❫ ❽❏✿❀
❳❏P▲❻✮ ✿▲ ❖❏✮ ❻●✪❨❖❏ ●P❖✮ ❳P▲ P✯❀✪ ❶✮ ❀✮✮▲ ✿▲ ➀✿❻❫ ❩❩ P▲✬ ➀✿❻❫ ❩❄
❊✪● ✩✪✬✮✯ ✰✰ ✹✿▲ ❳✪❿⑩P●✿❀✪▲ ❨✿❖❏ ➀✿❻❀❫ ❩➆ P▲✬ ❩❁ ❊✪● ✩✪✬✮✯ ✰✾❫
❽❏✮ ✬✮⑩✮▲✬✮▲❳✮ ✪❊ ❖❏✮ ❻●✪❨❖❏ ●P❖✮ ✪▲ ❖❏✮ ❿P❻▲✮❖✿❳ ◗✮✯✬ ❀❖●✮▲❻❖❏
✿❀ ❹✉P✯✿❖P❖✿❯✮✯❷ ❀✿❿✿✯P● ❊✪● ✩✪✬✮✯❀ ✰ P▲✬ ✰✰❫ ✰▲ ⑩P●❖✿❳✉✯P●✱ ✿❖ ❶✮❲
❳✪❿✮❀ ❳✪▲❀❖P▲❖ ❊✪● ➌ ❵ ❩✱ ❶✉❖ ✬✮❳✯✿▲✮❀ ❊✪● ➌ ❵ ➁①❁ P❀ ❖❏✮ ◗✮✯✬
✿▲❳●✮P❀✮❀❫ ❽❏✮ ✿▲❳●✮P❀✮ ✪❊ ✻✽ ❨✿❖❏ ➍❥ ✿❀✱ ❏✪❨✮❯✮●✱ ✯✮❀❀ ❀❖●✪▲❻ ❊✪●
✩✪✬✮✯ ✰✰❫
➎▲P⑩❀❏✪❖❀ ✪❊ ➍➏ ❊●✪❿ ✩➀➎ ❊✪● ➌ ❵ ➁①❁ P▲✬ ✲❥ ❵ ➆➇➆➁ P❖
✬✿➐✮●✮▲❖ ❖✿❿✮❀ ❊✪● ✩✪✬✮✯ ✰ P●✮ ❀❏✪❨▲ ✿▲ ➀✿❻❫ ❩❘❫ ➑✪❿⑩P●✿❀✪▲
❨✿❖❏ ❖❏✮ ●✮❀✉✯❖❀ ✪❊ ✩➀➎ ❊✪● ✩✪✬✮✯ ✰✰ ✹❀✮✮ ➀✿❻❫ ❩❭✾ ❀❏✪❨❀ ❖❏P❖
❆✷✂ ♣❛☛❡ ☎✄ ♦❢ ☎☎
✩✪✬✮✯ ✰✰ ◗❖❀ ❖❏✮ ➒➓➎ ❶✮❖❖✮●❫ ❽❏✿❀ ✿❀ P✯❀✪ ❀✮✮▲ ❶❷ ❳✪❿⑩P●✿▲❻
➀✿❻❫ ❩❭ ❨✿❖❏ ➀✿❻❫ ➁❫ ❴✪❨✮❯✮●✱ ✪✉● ❶P❀✿❳ ❳✪▲❳✯✉❀✿✪▲❀ ❊✪●❿✉✯P❖✮✬
✿▲ ❖❏✿❀ ⑩P⑩✮● P●✮ ▲✪❖ P➐✮❳❖✮✬❫
➔→ ➣↔↕➙➛➜➝➞↔↕➝
❽❏✮ ⑩●✮❀✮▲❖ ❨✪●➟ ❏P❀ ✬✮❿✪▲❀❖●P❖✮✬ ❖❏P❖ ✿▲ P ⑩✪✯❷❖●✪⑩✿❳ ✯P❷✮●✱
❶✪❖❏ ✿▲ ✩➀➎ P▲✬ ➒➓➎✱ ➓❸✩➠✰ ✬✮❯✮✯✪⑩❀ ⑩●✿❿P●✿✯❷ ✿▲ ❖❏✮ ✉⑩⑩✮●❲
❿✪❀❖ ✯P❷✮●❀✱ ⑩●✪❯✿✬✮✬ ❖❏✮ ❿✮P▲ ❿P❻▲✮❖✿❳ ◗✮✯✬ ✿❀ ▲✪❖ ❖✪✪ ❀❖●✪▲❻❫
✰❊ ❖❏✮ ◗✮✯✬ ❻✮❖❀ ❀❖●✪▲❻✮●✱ ➓❸✩➠✰ ❳P▲ ❀❖✿✯✯ ✬✮❯✮✯✪⑩✱ ❶✉❖ ❖❏✮ ❿P❻❲
▲✮❖✿❳ ❀❖●✉❳❖✉●✮❀ ▲✪❨ ✪❳❳✉● P❖ ❻●✮P❖✮● ✬✮⑩❖❏❀ P▲✬ ❖❏✮ ❻●✪❨❖❏ ●P❖✮
✪❊ ➓❸✩➠✰ ✿❀ ✯✪❨✮●❫ ❴✪❨✮❯✮●✱ P❖ ❀✪❿✮ ⑩✪✿▲❖ ❨❏✮▲ ❖❏✮ ❿P❻❲
▲✮❖✿❳ ◗✮✯✬ ❻✮❖❀ ❖✪✪ ❀❖●✪▲❻✱ ➓❸✩➠✰ ✿❀ ❀✉⑩⑩●✮❀❀✮✬ ✿▲ ❖❏✮ ❳P❀✮ ✪❊
P ⑩✪✯❷❖●✪⑩✿❳ ✯P❷✮●✱ ❨❏✿✯✮ ✿❖ ❨✪✉✯✬ ❀❖✿✯✯ ✪⑩✮●P❖✮ ✿▲ ❖❏✮ ✿❀✪❖❏✮●❿P✯
❳P❀✮✱ ⑩●✪❯✿✬✮✬ ❖❏✮ ✬✪❿P✿▲ ✿❀ ✬✮✮⑩ ✮▲✪✉❻❏❫ ❽❏✮ ❀✯✪❨ ✬✪❨▲ ✪❊
➓❸✩➠✰ ✿❀ ▲✪❖ ✬✿●✮❳❖✯❷ P ❳✪▲❀✮❹✉✮▲❳✮ ✪❊ P ✯✪▲❻✮● ❖✉●▲✪❯✮● ❖✿❿✮
P❖ ❻●✮P❖✮● ✬✮⑩❖❏❀✱ ❶✉❖ ✿❖ ✿❀ ●✮✯P❖✮✬ ❖✪ ❀❖●P❖✿◗❳P❖✿✪▲ ❶✮✿▲❻ ❖✪✪ ❨✮P➟
❊✪● ➓❸✩➠✰ ❖✪ ❶✮ ✮⑨❳✿❖✮✬❫
➡❷ P▲✬ ✯P●❻✮✱ ❖❏✮ ❀❳P✯✿▲❻ ●✮✯P❖✿✪▲❀ ✬✮❖✮●❿✿▲✮✬ ⑩●✮❯✿✪✉❀✯❷ ❊✪●
✿❀✪❖❏✮●❿P✯ ✯P❷✮●❀ ❨✿❖❏ ❳✪▲❀❖P▲❖ ❀❳P✯✮ ❏✮✿❻❏❖ ❀❖✿✯✯ ❀✮✮❿ ❖✪ P⑩⑩✯❷
✯✪❳P✯✯❷ ❖✪ ⑩✪✯❷❖●✪⑩✿❳ ✯P❷✮●❀ ❨✿❖❏ ❯P●✿P❶✯✮ ❀❳P✯✮ ❏✮✿❻❏❖❀❫ ✰▲ ⑩P●❲
❖✿❳✉✯P●✱ ❖❏✮ ❏✪●✿❑✪▲❖P✯ ❀❳P✯✮ ✪❊ ❀❖●✉❳❖✉●✮❀ ❨P❀ ⑩●✮❯✿✪✉❀✯❷ ✬✮❖✮●❲
❿✿▲✮✬ ❖✪ ❶✮ P❶✪✉❖ ❘❃❪ ④⑤ ✹➢✮❿✮✯ ✮❖ P✯❫ ❬➆❩❁➤ ➡●P▲✬✮▲❶✉●❻ ✮❖ P✯❫
❬➆❩❄✾❫ ➥✪✪➟✿▲❻ ▲✪❨ P❖ ➀✿❻❫ ❄✱ ❨✮ ❀✮✮ ❖❏P❖ ❊✪● ✲❥ ❵ ➆➇➆❬ P▲✬
➌ ❵ ➁①❁✱ ❖❏✮ ❀❖●✉❳❖✉●✮❀ ❏P❯✮ P ❨P❯✮✯✮▲❻❖❏ ✪❊ ➦❁ ④⑤❥ ✱ ❶✉❖ ❖❏✿❀ ✿❀
P❖ P ✬✮⑩❖❏ ❨❏✮●✮ ④⑤ ➦ ➆➇❁ ④⑤❥ ❫ ❽❏✉❀✱ ✯✪❳P✯✯❷ ❨✮ ❏P❯✮ P ❨P❯✮❲
✯✮▲❻❖❏ ✪❊ ➦❩➆ ④⑤ ❫ ❽❏✮ ❀✿❖✉P❖✿✪▲ ✿❀ ❀✿❿✿✯P● ✿▲ ❖❏✮ ▲✮⑨❖ ⑩P▲✮✯ ✪❊
➀✿❻❫ ❄ ❨❏✮●✮ ❖❏✮ ❨P❯✮✯✮▲❻❖❏ ✿❀ ➦❘ ④⑤❥ ✱ P▲✬ ❖❏✮ ❀❖●✉❳❖✉●✮❀ P●✮ P❖
P ✬✮⑩❖❏ ❨❏✮●✮ ④⑤ ➦ ❩➇➁ ④⑤❥✱ ❀✪ ✯✪❳P✯✯❷ ❨✮ ❏P❯✮ P ❨P❯✮✯✮▲❻❖❏
✪❊ ➦➋ ④⑤ ❫ ❺✮ ❳P▲ ❖❏✮●✮❊✪●✮ ❳✪▲❳✯✉✬✮ ❖❏P❖ ✪✉● ✮P●✯✿✮● ●✮❀✉✯❖❀ ❊✪●
✿❀✪❖❏✮●❿P✯ ✯P❷✮●❀ ❳P▲ ❀❖✿✯✯ ❶✮ P⑩⑩✯✿✮✬ ✯✪❳P✯✯❷ ❖✪ ⑩✪✯❷❖●✪⑩✿❳ ✯P❷✮●❀❫
➧ ▲✮❨ P❀⑩✮❳❖✱ ❏✪❨✮❯✮●✱ ❖❏P❖ ❨P❀ ▲✪❖ ❷✮❖ P▲❖✿❳✿⑩P❖✮✬ P❖ ❖❏✮
❖✿❿✮✱ ❳✪▲❳✮●▲❀ ❖❏✮ ✿❿⑩✪●❖P▲❳✮ ✪❊ ➓❸✩➠✰ ❊✪● ❯✮●❖✿❳P✯ ◗✮✯✬❀❫
❺❏✿✯✮ ➓❸✩➠✰ ❨✿❖❏ ❏✪●✿❑✪▲❖P✯ ❿P❻▲✮❖✿❳ ◗✮✯✬ ❀❖✿✯✯ ✯✮P✬❀ ❖✪ ✬✪❨▲❲
➨✪❨❀ ✿▲ ❖❏✮ ▲✪▲✯✿▲✮P● ●✮❻✿❿✮ ✹❖❏✮ ➩⑩✪❖P❖✪❲❀P❳➟➫ ✮➐✮❳❖✾✱ ✪✉●
⑩●✮❀✮▲❖ ❨✪●➟ ▲✪❨ ❳✪▲◗●❿❀ ❖❏P❖ ❀❖●✉❳❖✉●✮❀ ❳✪▲❀✿❀❖✿▲❻ ✪❊ ❯✮●❖✿❳P✯
■✳ ❘✳ ▲♦s ✁ ❡✂ ❛✳✿ ▼ ✄☎❡✂✐❝ ✤✉① ❝♦☎❝❡☎✂r ✂✐♦☎s ✐☎
✣✝✞✟✠ ✟✡ ♥✡☛ ✠☞♥✌✍ ❜✎☛ ✏✝✑✒✓ ✑ ✠☛✏✝♥t☛✓ ✒✡✔✕✑✏✑❜✞✝ ☛✡ ✡✏ ☞♥ ✝✖✒✝✠✠
✡❢ ☛✓✝ ✝q✎☞✕✑✏☛☞☛☞✡♥ ✈✑✞✎✝ ✭❇✏✑♥✟✝♥❜✎✏t ✝☛ ✑✞✗ ✷✘✙✚✍ ✷✘✙✛✮✗ ❚✓☞✠
✔✑✌✝✠ ◆❊✜✢✥ ✑ ✈☞✑❜✞✝ ✔✝✒✓✑♥☞✠✔ ❢✡✏ ✠✕✡♥☛✑♥✝✡✎✠✞✦ ✕✏✡✟✎✒✧
☞♥t ✔✑t♥✝☛☞✒ ✠✕✡☛✠ ☞♥ ☛✓✝ ✠✎✏❢✑✒✝ ✞✑✦✝✏✠✗ ❖✎✏ ✕✏✝✠✝♥☛ ✠☛✎✟✦
☛✓✝✏✝❢✡✏✝ ✠✎✕✕✡✏☛✠ ☞✟✝✑✠ ✑❜✡✎☛ ✑ ✠✓✑✞✞✡✇ ✡✏☞t☞♥ ❢✡✏ ✑✒☛☞✈✝ ✏✝✧
t☞✡♥✠ ✑♥✟ ✠✎♥✠✕✡☛✠ ✭❇✏✑♥✟✝♥❜✎✏t ✷✘✘★❀ ❇✏✑♥✟✝♥❜✎✏t ✝☛ ✑✞✗ ✷✘✙✘❀
❑☞☛☞✑✠✓✈☞✞☞ ✝☛ ✑✞✗ ✷✘✙✘❀ ❙☛✝☞♥ ✫ ◆✡✏✟✞✎♥✟ ✷✘✙✷✮✍ ✒✡♥☛✏✑✏✦ ☛✡ ✒✡✔✧
✔✡♥ ☛✓☞♥✌☞♥t ☛✓✑☛ ✠✎♥✠✕✡☛✠ ❢✡✏✔ ♥✝✑✏ ☛✓✝ ❜✡☛☛✡✔ ✡❢ ☛✓✝ ✒✡♥✧
✈✝✒☛☞✈✝ ③✡♥✝ ✭✢✑✏✌✝✏ ✙✶✩★❀ ❙✕☞✝t✝✞ ✫ ❲✝☞✠✠ ✙✶✪✘❀ ❉✬❙☞✞✈✑ ✫
❈✓✡✎✟✓✎✏☞ ✙✶✶✚✮✗ ✜✡✏✝ ✠✕✝✒☞✣✒✑✞✞✦✍ ☛✓✝ ✠☛✎✟☞✝✠ ✡❢ ✯✡✠✑✟✑ ✝☛ ✑✞✗
✭✷✘✙✚✮ ✕✡☞♥☛ ☛✡✇✑✏✟ ☛✓✝ ✕✡✠✠☞❜☞✞☞☛✦ ☛✓✑☛ ✔✑t♥✝☛☞✒ ✰✎✖ ✒✡♥✒✝♥☛✏✑✧
☛☞✡♥✠ ❢✡✏✔ ☞♥ ☛✓✝ ☛✡✕ ✻ ✜✔✍ ☞✗✝✗✍ ☞♥ ☛✓✝ ✎✕✕✝✏ ✕✑✏☛ ✡❢ ☛✓✝ ✠✎✕✝✏✧
t✏✑♥✎✞✑☛☞✡♥ ✞✑✦✝✏✗
❚✓✝✏✝ ✑✏✝ ✡❜✈☞✡✎✠✞✦ ✔✑♥✦ ✡☛✓✝✏ ☞✠✠✎✝✠ ✡❢ ◆❊✜✢✥ ☛✓✑☛ ♥✝✝✟
☛✡ ❜✝ ✎♥✟✝✏✠☛✡✡✟ ❜✝❢✡✏✝ ☞☛ ✒✑♥ ❜✝ ✑✕✕✞☞✝✟ ☞♥ ✑ ✔✝✑♥☞♥t❢✎✞ ✇✑✦
☛✡ ☛✓✝ ❢✡✏✔✑☛☞✡♥ ✡❢ ✑✒☛☞✈✝ ✏✝t☞✡♥✠ ✑♥✟ ✠✎♥✠✕✡☛✠✗ ❖♥✝ q✎✝✠☛☞✡♥ ☞✠
✇✓✝☛✓✝✏ ☛✓✝ ✓✦✟✏✡t✝♥ ☞✡♥☞③✑☛☞✡♥ ✞✑✦✝✏ ✑♥✟ ☛✓✝ ✏✝✠✎✞☛☞♥t ❍❾ ✡✕✑✒✧
☞☛✦ ☞♥ ☛✓✝ ✎✕✕✝✏ ✞✑✦✝✏✠ ✡❢ ☛✓✝ ❙✎♥ ✑✏✝ ☞✔✕✡✏☛✑♥☛ ☞♥ ✕✏✡✈☞✟✧
☞♥t ✑ ✠✓✑✏✕ ☛✝✔✕✝✏✑☛✎✏✝ ✟✏✡✕ ✑♥✟ ✇✓✝☛✓✝✏ ☛✓☞✠ ✇✡✎✞✟ ✝♥✓✑♥✒✝
☛✓✝ t✏✡✇☛✓ ✏✑☛✝ ✡❢ ◆❊✜✢✥✍ ❥✎✠☛ ✞☞✌✝ ✠☛✏✡♥t ✟✝♥✠☞☛✦ ✠☛✏✑☛☞✣✒✑✧
☛☞✡♥ ✟✡✝✠✗ ❆♥✡☛✓✝✏ ☞✔✕✡✏☛✑♥☛ q✎✝✠☛☞✡♥ ✒✡♥✒✝✏♥✠ ☛✓✝ ✏✝✞✝✈✑♥✒✝
✡❢ ✑ ✏✑✟☞✑☛☞♥t ✠✎✏❢✑✒✝✍ ✇✓☞✒✓ ✑✞✠✡ ✝♥✓✑♥✒✝✠ ☛✓✝ ✟✝♥✠☞☛✦ ✒✡♥☛✏✑✠☛✗
❋☞♥✑✞✞✦✍ ✡❢ ✒✡✎✏✠✝✍ ✡♥✝ ♥✝✝✟✠ ☛✡ ✈✝✏☞❢✦ ☛✓✑☛ ☛✓✝ ✑✠✠✎✔✕☛☞✡♥ ✡❢
❢✡✏✒✝✟ ☛✎✏❜✎✞✝♥✒✝ ☞✠ ✎✠✝❢✎✞ ☞♥ ✏✝✕✏✝✠✝♥☛☞♥t ✠☛✝✞✞✑✏ ✒✡♥✈✝✒☛☞✡♥✗
✜✑♥✦ t✏✡✎✕✠ ✓✑✈✝ ✒✡♥✠☞✟✝✏✝✟ ✔✑t♥✝☛☞✒ ✰✎✖ ✒✡♥✒✝♥☛✏✑☛☞✡♥✠ ✎✠✧
☞♥t ✏✝✑✞☞✠☛☞✒ ☛✎✏❜✎✞✝♥☛ ✒✡♥✈✝✒☛☞✡♥ ✭❑☞☛☞✑✠✓✈☞✞☞ ✝☛ ✑✞✗ ✷✘✙✘❀ ✱✝✔✕✝✞
✷✘✙✙❀ ❙☛✝☞♥ ✫ ◆✡✏✟✞✎♥✟ ✷✘✙✷✮✗ ❍✡✇✝✈✝✏✍ ✡♥✞✦ ✑☛ ✠✎✲✒☞✝♥☛✞✦
✞✑✏t✝ ✏✝✠✡✞✎☛☞✡♥ ✒✑♥ ✡♥✝ ✝✖✕✝✒☛ ✠☛✏✡♥t ✝♥✡✎t✓ ✠✒✑✞✝ ✠✝✕✑✏✑☛☞✡♥
❜✝☛✇✝✝♥ ☛✓✝ ✠✒✑✞✝ ✡❢ ☛✓✝ ✠✔✑✞✞✝✠☛ ✝✟✟☞✝✠ ✑♥✟ ☛✓✝ ✠☞③✝ ✡❢ ✔✑t✧
♥✝☛☞✒ ✠☛✏✎✒☛✎✏✝✠✗ ❚✓✑☛ ☞✠ ✇✓✦ ❢✡✏✒✝✟ ☛✎✏❜✎✞✝♥✒✝ ✓✑✠ ✑♥ ✑✟✈✑♥☛✑t✝
✡✈✝✏ ✒✡♥✈✝✒☛☞✡♥✗ ❯✞☛☞✔✑☛✝✞✦✍ ✓✡✇✝✈✝✏✍ ✠✎✒✓ ✑✠✠✎✔✕☛☞✡♥✠ ✠✓✡✎✞✟
♥✡ ✞✡♥t✝✏ ❜✝ ♥✝✒✝✠✠✑✏✦✗ ❖♥ ☛✓✝ ✡☛✓✝✏ ✓✑♥✟✍ ☞❢ ✠✒✑✞✝ ✠✝✕✑✏✑☛☞✡♥
☞✠ ✕✡✡✏✍ ✡✎✏ ✕✏✝✠✝♥☛ ✕✑✏✑✔✝☛✝✏☞③✑☛☞✡♥ ✔☞t✓☛ ♥✡ ✞✡♥t✝✏ ❜✝ ✑✒✒✎✧
✏✑☛✝ ✝♥✡✎t✓✍ ✑♥✟ ✡♥✝ ✇✡✎✞✟ ♥✝✝✟ ☛✡ ✏✝✕✞✑✒✝ ☛✓✝ ✔✎✞☛☞✕✞☞✒✑☛☞✡♥
❜✝☛✇✝✝♥ ✴✵ ✑♥✟ ✸✹ ☞♥ ❊q✗ ✭✷★✮ ❜✦ ✑ ✒✡♥✈✡✞✎☛☞✡♥✗ ❚✓☞✠ ✕✡✠✠☞✧
❜☞✞☞☛✦ ☞✠ ❢✑☞✏✞✦ ✠✕✝✒✎✞✑☛☞✈✝ ✑♥✟ ✏✝q✎☞✏✝✠ ✑ ✠✝✕✑✏✑☛✝ ☞♥✈✝✠☛☞t✑☛☞✡♥✗
◆✝✈✝✏☛✓✝✞✝✠✠✍ ☞♥ ✠✕☞☛✝ ✡❢ ☛✓✝✠✝ ☞✠✠✎✝✠✍ ☞☛ ☞✠ ☞✔✕✡✏☛✑♥☛ ☛✡ ✝✔✕✓✑✧
✠☞③✝ ☛✓✑☛ ☛✓✝ q✎✑✞☞☛✑☛☞✈✝ ✑t✏✝✝✔✝♥☛ ❜✝☛✇✝✝♥ ❉◆❙ ✑♥✟ ✜❋❙ ☞✠
✑✞✏✝✑✟✦ ✠✎✏✕✏☞✠☞♥t✞✦ t✡✡✟✗
✺✼❦✽✾❁❂❃❄❅❃●❃✽❏P◗ ❱❤❳❨ ❩❬❭❪ ❩❫❨ ❨❴❵❵❬❭❞❣❧ ❳④ ❵❫❭❞ ⑤⑥ ❞❤❣ ⑦❴❭❬❵❣❫④ ⑧❣❨❣❫❭⑨❤
⑩❬❴④⑨❳❶ ❴④❧❣❭ ❞❤❣ ❷❨❞❭❬❸⑥④ ⑧❣❨❣❫❭⑨❤ ❹❭❬❺❣⑨❞ ❻❬❼ ❽❽❿➀➁❽➂ ⑤⑥ ❞❤❣ ➃❩❣❧❳❨❤
⑧❣❨❣❫❭⑨❤ ⑩❬❴④⑨❳❶ ❴④❧❣❭ ❞❤❣ ❵❭❬❺❣⑨❞ ➄❭❫④❞❨ ➅❽➆➇❽➈➆➆➇➁➈❿➅ ❫④❧ ❽➈➆❽➇➁❿➀❿
➉➊❼⑧❼➋❼➂ ❷❼➌❼➍➂ ⑤⑥ ⑦➎ ⑩➏➃❱ ❷⑨❞❳❬④ ➐❹➈➑➈➅➂ ⑤⑥ ❞❤❣ ⑦❴❭❬❵❣❫④ ⑧❣❨❣❫❭⑨❤ ⑩❬❴④⑨❳❶
❴④❧❣❭ ❞❤❣ ❷❞➒❬❨❵❤❣❭❳⑨ ⑧❣❨❣❫❭⑨❤ ❹❭❬❺❣⑨❞ ❻❬❼ ❽❽❿➀➆➁➂ ❫④❧ ⑤⑥ ❫ ➄❭❫④❞ ➓❭❬➒ ❞❤❣
➔❬→❣❭④➒❣④❞ ❬➓ ❞❤❣ ⑧❴❨❨❳❫④ ➣❣❧❣❭❫❞❳❬④ ❴④❧❣❭ ⑨❬④❞❭❫⑨❞ ❻❬❼ ➆➆❼➔↔↕❼↔➆❼➈➈↕➑
➉❻❼➙❼➂ ➊❼⑧❼➍❼ ➛❣ ❫⑨❪④❬❩❶❣❧➄❣ ❞❤❣ ❫❶❶❬⑨❫❞❳❬④ ❬➓ ⑨❬➒❵❴❞❳④➄ ❭❣❨❬❴❭⑨❣❨ ❵❭❬→❳❧❣❧
⑤⑥ ❞❤❣ ➃❩❣❧❳❨❤ ❻❫❞❳❬④❫❶ ❷❶❶❬⑨❫❞❳❬④❨ ⑩❬➒➒❳❞❞❣❣ ❫❞ ❞❤❣ ⑩❣④❞❣❭ ➓❬❭ ❹❫❭❫❶❶❣❶
⑩❬➒❵❴❞❣❭❨ ❫❞ ❞❤❣ ⑧❬⑥❫❶ ➊④❨❞❳❞❴❞❣ ❬➓ ❱❣⑨❤④❬❶❬➄⑥ ❳④ ➃❞❬⑨❪❤❬❶➒ ❫④❧ ❞❤❣ ❻❫❞❳❬④❫❶
♣♦❛②✂r♦♣✐❝ ✂♠♦s♣✆❡r❡
➃❴❵❣❭⑨❬➒❵❴❞❣❭ ⑩❣④❞❣❭❨ ❳④ ➋❳④❪ ❵❳④➄➂ ❞❤❣ ➜❳➄❤ ❹❣❭➓❬❭➒❫④⑨❣ ⑩❬➒❵❴❞❳④➄ ⑩❣④❞❣❭
❻❬❭❞❤ ❳④ ➎➒❣ ➂ ❫④❧ ❞❤❣ ❻❬❭❧❳⑨ ➜❳➄❤ ❹❣❭➓❬❭➒❫④⑨❣ ⑩❬➒❵❴❞❳④➄ ⑩❣④❞❣❭ ❳④
⑧❣⑥❪❺❫→❳❪❼
➝➞➟➞➠➞➡➢➞➤
➌❭❫④❧❣④⑤❴❭➄➂ ❷❼ ❽➈➈➁➂ ❷❵➥➂ ➅❽➁➂ ➁↔➀
➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆➈➂ ❷❨❞❭❬④❼ ❻❫⑨❤❭❼➂ ↔↔➆➂ ➁
➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❣➒❣❶➂ ➙❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❳❞❭❫➂ ❸❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆➆➂
❷❵➥➂ ❿↕➈➂ ➋➁➈
➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❣➒❣❶➂ ➙❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆❽➂ ❷❵➥➂ ❿↕➀➂
➆❿➀
➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆↔➂ ❷❵➥➂ ❿❿➅➂ ➋❽↔
➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➔❭❣❨❨❣❶➂ ➏❼➂ ➥❫⑤⑤❫❭❳➂ ➃❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆↕➂
❷➦❷➂ ➁➅❽➂ ❷➁↔
❸➧➃❳❶→❫➂ ➃❼➂ ➦ ⑩❤❬❴❧❤❴❭❳➂ ❷❼ ⑧❼ ➆➀➀↔➂ ❷➦❷➂ ❽❿❽➂ ➅❽➆
➥❫⑤⑤❫❭❳➂ ➃❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❳❞❭❫➂ ❸❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆↔➂
❷➦❷➂ ➁➁➅➂ ❷➆➈➅
➙ ❵⑥❶ ➂ ❹❼ ➥❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❫④❞❣❭❣➂ ➐❼ ➥❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼
❽➈➆❽➂ ➐❻⑧❷➃➂ ↕❽❽➂ ❽↕➅➁
➙❣➒❣❶➂ ➙❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆❽❫➂ ❷❨❞❭❬④❼
❻❫⑨❤❭❼➂ ↔↔↔➂ ➀➁
➙❣➒❣❶➂ ➙❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❳❞❭❫➂ ❸❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆❽⑤➂
➃❬❶❼ ❹❤⑥❨❼➂ ❽➑➈➂ ↔❽➆
➙❣➒❣❶➂ ➙❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❳❞❭❫➂ ❸❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆↔➂
➃❬❶❼ ❹❤⑥❨❼➂ ❽➑❿➂ ❽➀↔
➙❳❞❳❫❨❤→❳❶❳➂ ➊❼ ❻❼➂ ➙❬❨❬→❳⑨❤❣→➂ ❷❼ ➔❼➂ ➛❭❫⑥➂ ❷❼ ❷❼➂ ➦ ➐❫④❨❬❴❭➂ ❻❼ ❻❼ ❽➈➆➈➂ ❷❵➥➂
❿➆➀➂ ↔➈❿
➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ➆➀➀↕➂ ❹❤⑥❨❼ ⑧❣→❼ ⑦➂ ➁➈➂ ❽❿➆➅
➙❶❣❣❬❭❳④➂ ❻❼ ➊❼➂ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ➨❼➂ ➦ ⑧❴➩➒❫❳❪❳④➂ ❷❼ ❷❼ ➆➀➑➀➂ ➃❬→❼ ❷❨❞❭❬④❼ ➋❣❞❞❼➂
➆➁➂ ❽❿↕
➙❶❣❣❬❭❳④➂ ❻❼ ➊❼➂ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ➨❼➂ ➦ ⑧❴➩➒❫❳❪❳④➂ ❷❼ ❷❼ ➆➀➀➈➂ ➃❬→❼ ❹❤⑥❨❼ ➥⑦❱❹➂
❿➈➂ ➑❿➑
➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❬④❧➂ ➐❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ➆➀➀↔➂ ❹❤⑥❨❼ ➣❶❴❳❧❨ ➌➂ ➁➂ ↕➆❽➑
➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❬④❧➂ ➐❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ➆➀➀➅➂ ❷➦❷➂ ↔➈❿➂ ❽➀↔
➙❭❫❴❨❣➂ ➣❼➂ ➦ ⑧ ❧❶❣❭➂ ➙❼➇➜❼ ➆➀➑➈➂ ➐❣❫④➇➫❣❶❧ ➐❫➄④❣❞❬❤⑥❧❭❬❧⑥④❫➒❳⑨❨ ❫④❧
❸⑥④❫➒❬ ❱❤❣❬❭⑥ ➉➏➭➓❬❭❧➯ ❹❣❭➄❫➒❬④ ❹❭❣❨❨➍
➋❬❨❫❧❫➂ ➊❼ ⑧❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➐❳❞❭❫➂ ❸❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆❽➂
❷➦❷➂ ➁↕➑➂ ❷↕➀
➋❬❨❫❧❫➂ ➊❼ ⑧❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼ ❽➈➆↔➂ ❷➦❷➂
➁➁➅➂ ❷➑↔
❻❣❩⑨❬➒⑤➂ ➛❼ ❷❼ ➆➀➅➆➂ ❹❤⑥❨❼ ➣❶❴❳❧❨➂ ↕➂ ↔➀➆
❹❫❭❪❣❭➂ ⑦❼ ❻❼ ➆➀➁➁➂ ❷❵➥➂ ➆❽➆➂ ↕➀➆
❹❫❭❪❣❭➂ ⑦❼ ❻❼ ➆➀➅➅➂ ❷❵➥➂ ➆↕➁➂ ➑➆➆
❹❫❭❪❣❭➂ ⑦❼ ❻❼ ➆➀❿➁➂ ❷❵➥➂ ➆➀➑➂ ❽➈➁
❹❶❫❨❞❳④❬➂ ❷❼ ⑧❼➂ ➦ ❹❶❫❨❞❳④❬➂ ❷❼ ➆➀➀↔➂ ❹❤⑥❨❼ ➋❣❞❞❼ ❷➂ ➆❿↕➂ ↔➑↕
⑧❣➒❵❣❶➂ ➐❼ ❽➈➆➆➂ ❷❵➥➂ ❿↕➈➂ ➆➁
⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼➂ ➦ ➙❶❣❣❬❭❳④➂ ❻❼ ❽➈➈❿➂ ❹❤⑥❨❼ ⑧❣→❼ ⑦➂ ❿➅➂ ➈➁➅↔➈❿
➃❵❳❣➄❣❶➂ ⑦❼ ❷❼➂ ➦ ➛❣❳❨❨➂ ❻❼ ➏❼ ➆➀➑➈➂ ❻❫❞❴❭❣➂ ❽➑❿➂ ➅➆➅
➃❵❭❴❳❞➂ ➜❼ ⑩❼ ➆➀➑➆➂ ❷➦❷➂ ➀➑➂ ➆➁➁
➃⑨❤ ❨❨❶❣❭➂ ➐❼➂ ⑩❫❶❳➄❫❭❳➂ ❹❼➂ ➣❣❭❭❳➩➇➐❫❨➂ ❷❼➂ ➦ ➐❬❭❣④❬➇➊④❨❣❭❞❳❨➂ ➣❼ ➆➀➀↕➂ ❷➦❷➂
❽➑➆➂ ➋➅➀
➃❞❣❳④➂ ⑧❼ ➣❼➂ ➦ ❻❬❭❧❶❴④❧➂ ❼ ❽➈➆❽➂ ❷❵➥➂ ❿➁↔➂ ➋➆↔
➃❴❭➂ ➃❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➦ ➃❴⑤❭❫➒❫④❳❫④➂ ➙❼ ❽➈➈➑➂ ➐❻⑧❷➃➂ ↔➑➁➂ ➋➆➁
❱❨❫❶❶❳❨➂ ⑩❼ ➆➀➑➑➂ ➥❼ ➃❞❫❞❼ ❹❤⑥❨❼➂ ➁❽➂ ↕❿➀
➨❳❞❣④❨❣➂ ⑦❼ ➆➀➁↔➂ ➲❼ ❷❨❞❭❬❵❤⑥❨❼➂ ↔❽➂ ➆↔➁
➳❫➒❫④❬➂ ❱❼ ❽➈➈❽➂ ➃❞❫❞❼ ➐❣⑨❤❼ ❷❵❵❶❼➂ ↔➈➁➂ ↕➑➅
➛❫❭④❣⑨❪❣➂ ➥❼➂ ➋❬❨❫❧❫➂ ➊❼ ⑧❼➂ ➌❭❫④❧❣④⑤❴❭➄➂ ❷❼➂ ➙❶❣❣❬❭❳④➂ ❻❼➂ ➦ ⑧❬➄❫⑨❤❣→❨❪❳❳➂ ➊❼
❽➈➆↔➂ ❷❵➥➂ ❿❿❿➂ ➋↔❿
➵➸➺ ♣ ✄❡ ➻➻ ♦➼ ➻➻