Improvements to air mass calculations for ground

Improvements to air mass calculations for ground-based infrared measurements
Meier, Arndt; Goldman, A; Manning, PS; Stephen, TM; Rinsland, CP; Jones, NB; Wood, SW
Published in:
Journal of Quantitative Spectroscopy & Radiative Transfer
DOI:
10.1016/S0022-4073(02)00018-3
Published: 2004-01-01
Link to publication
Citation for published version (APA):
Meier, A., Goldman, A., Manning, P. S., Stephen, T. M., Rinsland, C. P., Jones, N. B., & Wood, S. W. (2004).
Improvements to air mass calculations for ground-based infrared measurements. Journal of Quantitative
Spectroscopy & Radiative Transfer, 83(1), 109-113. DOI: 10.1016/S0022-4073(02)00018-3
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Journal of Quantitative Spectroscopy &
Radiative Transfer 83 (2004) 109 – 113
www.elsevier.com/locate/jqsrt
Note
Improvements to air mass calculations for ground-based
infrared measurements
Arndt Meiera; ∗ , Aaron Goldmanb , Paul S. Manningb , Thomas M. Stephenb ,
Curtis P. Rinslandc , Nicholas B. Jonesd , Stephen W. Woodd
a
Department of Chemistry, University of Wollongong, NSW 2522, Australia
b
Department of Physics, University of Denver, Denver, CO 80208, USA
c
NASA Langley Research Center, Mail Stop 401A, Hampton, VA 23681-2199, USA
d
NIWA (National Institute of Water and Atmospheric Research Ltd.), Lauder, Private Bag 50061, Omakau,
Central Otago, New Zealand
Received 22 October 2001; received in revised form 8 January 2002; accepted 29 January 2002
Abstract
High-resolution ground-based infrared solar spectra are routinely recorded at the Network for the Detection
of Stratospheric Change (NDSC) stations. These data sets play a key role in providing a long-term record
of atmospheric composition and their links to climate change. The analysis of observed infrared spectra
involves comparison to a computer-modeled atmosphere where knowledge of the air mass distribution is an
essential component. This note summarises improvements made to an existing and widely used computer
code (FSCATM) to perform refractive ray-tracing and calculation of the air mass distribution. Changes were
made towards higher vertical resolution in the troposphere and increased numerical precision. The revised
FSCATM improves the analysis of infrared spectra mostly through the more accurate representation of the
temperature pro<le. Air mass di=erences with respect to earlier versions are documented and are typically
¡0:7%, exceptions being extreme cases of inversion layers. The current version provides ray tracing and air
mass calculations for any terrestrial observation site. The output <les are reported in a format compatible with
the SFIT and SFIT2 retrieval algorithms, which are widely used for NDSC infrared atmospheric studies. The
improved computer code, documentation, reference pro<les, and test cases are available electronically.
Published by Elsevier Ltd.
1. Introduction
The Air Mass Computer Program for Atmospheric Transmittance=Radiance Calculation FSCATM
[1] has been widely used for over a decade with a variety of atmospheric radiative transfer applications. Ray tracing and optical paths integrals based on this program have been applied extensively
∗
Corresponding author. Tel.: +61-2-9310-1800; fax: +61-2-9699-8615.
E-mail address: [email protected] (A. Meier).
0022-4073/04/$ - see front matter Published by Elsevier Ltd.
PII: S 0 0 2 2 - 4 0 7 3 ( 0 2 ) 0 0 0 1 8 - 3
110
A. Meier et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 83 (2004) 109 – 113
by the LOWTRAN codes [2]. Several improvements, including better accuracy with more e=ective
use of the atmospheric layers and preserving the hydrostatic equation, were developed for the widely
used Line-by-Line program known as LBLRTM and its FASTCODE predecessors [3]. In another
widely used Line-by-Line code, known as GENLN2 [4] independent calculations are applied for
this purpose, which are based on an algorithm similar to that of FSCATM [1], and allow to obtain
high-accuracy optical paths for the atmospheric trace gases.
The ray-tracing program FSCATM has been implemented in the SFIT (e.g. [5,6]) and in the
SFIT2 retrieval programs [7–10] to determine the slanted optical path of sunlight as seen from the
ground. These particular implementations of FSCATM have a set of SFIT-speci<c auxiliary programs
and are referred to as SFIT-FSCATM. These programs are widely used by the atmospheric infrared
remote sensing community, in particular within the NDSC [11,12].
SFIT retrieves total column amounts of atmospheric trace gases from ground-based solar infrared
spectra based on the observed absorption features, the observation geometry, and the model atmosphere provided by SFIT-FSCATM. The latter consists of total air masses, pressures, temperatures,
and volume mixing ratios (VMRs) for infrared active species in vertically-strati<ed layers. This
revision of FSCATM also improves the quality of satellite validation and long-term monitoring programs. The full report on which this Note is based is available from J. Quant. Spectrosc. Radiat.
Transfer as an electronic supplement [13].
2. Changes to FSCATM
The new version of FSCATM is backward compatible and incorporates the minimal number of
changes in the source code. All SFIT-FSCATM releases prior to version 2.01 (July 1999), had a
number of limitations which can lead to errors when the user atmosphere is de<ned with vertical
resolutions better than 2 km. The main limitations arise from the internal layering scheme of FSCATM which is used for needed interpolations. Consequently, the total number of internal model
layers has been increased, the numerical precision has been improved, the maximum number of
output layers has been raised, the number of standard molecules has been increased from 57 to
63, and the fundamental constants used were updated to be in agreement with the latest CODATA
recommendations [14]. The new molecules added include some important replacement CFCs which
are increasing rapidly in abundance.
SFIT uses its own auxiliary programs to have FSCATM perform the necessary ray tracing. Thus,
some changes were required in these programs to comply with the new FSCATM. Besides changes
in data formats the default boundary layer selections have been made self-consistent, the iterative
run for the determination of the apparent from the astronomical zenith angle has been automated and
can be achieved following either an internal or external iteration procedure, the number of pre-stored
observation sites was tripled (Table 1), the set of default a priori VMR pro<les was updated, the
user interface has been improved, and a new ab initio calculation of the atmospheric bending has
◦
been implemented resulting in an accuracy of better than 0:0012 for solar zenith angles of up to
◦
85 for any terrestrial site. The improvements made to the iterative determination of the atmospheric
bending result in faster convergence. The user is given the option to de<ne his own output altitude
scheme and to provide his own set of VMR pro<les to suit a particular retrieval code or site-speci<c
atmospheric conditions. In the case of pro<le retrieval codes such as SFIT2 the use of an output
A. Meier et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 83 (2004) 109 – 113
111
Table 1
List of observation sites supported by SFIT-FSCATM, most of which have NDSC status
Site
Eureka, Canada
L
Ny-Alesund,
Spitsbergen
Kiruna, Sweden
Poker Flat RR, Alaska
Harestua, Norway
Bremen, Germany
NPL Teddington, UK
Zugspitze, German Alps
Jungfraujoch, Swiss Alps
Moshiri, Japan
Rikubetsu, Japan
Mt Bancroft, CA
Denver, CO
Billings, Oklahoma
Tsukuba, Japan
Table Mountain, CA
JPL Pasadena, CA
Kitt Peak, AZ
Teneri=e, Canarian Islands
Mauna Loa, Hawaii
Wollongong, Australia
Lauder, New Zealand
Arrival Heights, Antarctica
South Pole, Antarctica
User speci<ed at run time
Latitude
◦
80:05 N
◦
78:92 N
◦
67:84 N
◦
65:119 N
◦
60:217 N
◦
53:107 N
◦
51:424 N
◦
47:422 N
◦
46:549 N
◦
44:367 N
◦
43:457 N
◦
37:584 N
◦
36:673 N
◦
36:605 N
◦
36:048 N
◦
34:382 N
◦
34:200 N
◦
31:90 N
◦
28:294 N
◦
19:539 N
◦
34:45 S
◦
45:045 S
◦
77:83 S
◦
89:83 S
any
Longitude
◦
86:42 W
◦
11:94 E
◦
20:41 E
◦
147:433 W
◦
10:753 E
◦
8:854 E
◦
0:343 W
◦
10:987 E
◦
7:986 E
◦
142:267 E
◦
143:766 E
◦
118:235 W
◦
104:963 W
◦
97:485 W
◦
140:116 E
◦
117:677 W
◦
118:172 W
◦
111:60 W
◦
16:490 W
◦
155:578 W
◦
150:88 E
◦
169:684 E
◦
166:67 E
any
Altitude (m)
610
20
419
505
596
27
30
2964
3580
280
370
3801
1643
317
31
2258
350
2090
2367
3398
30
370
200
2850
0 – 4000
altitude scheme of constant stepsize throughout the lower atmosphere is found to reduce unwanted
pro<le oscillations.
3. Impacts of the revision of FSCATM
Two case studies have been carried out for two locations each in order to evaluate the impacts
of the changes made. The <rst part of this study revealed that di=erences in air mass, pressure,
and temperature are small in the troposphere (¡0:42%) except for inversion layers. FSCATM data
products for altitudes above 12 km altitude agreed within the numerical precision.
The second part of the study investigated the impacts of the changes in SFIT-FSCATM on the
total column amounts (TCAs) retrieved from ground-based solar FTIR spectra recorded in Kiruna,
Sweden, under a wide range of meteorological conditions. The spectra were analysed using SFIT
1:09e [5,6]. The TCAs were retrieved from 125 di=erent absorption lines located in more than 100
atmospheric micro-windows.
112
A. Meier et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 83 (2004) 109 – 113
The detailed studies [13] reveal that in the absence of an inversion layer the e=ects of the changes
in SFIT-FSCATM on the TCAs retrieved with SFIT 1:09e are ¡0:7% for any species except water
vapor (2.5%) and ¡0:2% for any stratospheric species. Compared to other uncertainties in the
retrieval of TCAs, which typically add to several percent, a re-processing of spectra previously
analysed with SFIT-FSCATM 1995 is not necessary. However, the di=erences become signi<cant
for all tropospheric species if a strong inversion layer is present. This does not a=ect molecules with
a mostly stratospheric distribution. An exception is ClONO2 where a change in TCAs of several
percent is seen, which is caused by strong interference from an overlapping temperature-sensitive
CO2 line [13].
The temperature sensitivity of a transition depends on its lower state energy E and the partition
function [15]. The full report [13] discusses the di=erences in retrieved TCAs as a function of
the lower state energies involved and the magnitude of the temperature misrepresentation, which
in our case is also a function of altitude and of the distribution of the molecule over altitude
[13]. A systematic error in the retrieved TCAs of 0:2% K −1 in temperature misrepresentation and
per 100 cm−1 above 300 cm−1 in the transition’s lower state energy E can be estimated for a
molecule entirely contained in the altitude range where the temperature error occurs. It is noted that,
this relation applies to ground-based FTIR observations irrespective of the source of a temperature
misrepresentation.
It is noted that, while it is common practice to select lines with minimal temperature sensitivity,
transitions with high-temperature sensitivity were also included in the studies for demonstrating the
behaviour of unavoidable interference lines.
4. Conclusions
The limited vertical resolution in the troposphere implemented in the 1995 version of SFITFSCATM can result in misrepresentations in pressure, temperature and air mass. The changes made
to SFIT-FSCATM substantially improve the representation of the tropospheric part of the model
atmosphere, which is particularly signi<cant if inversion layers are encountered. The di=erences
between the current version 2.03 (Oct 2001) and versions before 1999 are small if the temperature
and VMR pro<les provided are fairly smooth. High-altitude sites are generally less a=ected than
low-altitude observation sites.
Consistent with the conclusion that temperature errors are the main cause of problems with using
the previous SFIT-FSCATM version is the fact that di=erences in the TCAs retrieved show a clear
correlation with the lower state energies of the corresponding absorption lines [13].
In addition, the number of molecules has been expanded to include replacement-CFCs, which are
expected to reach detection limits in the near future. The corresponding default VMRs have been
updated according to recent measurements.
Acknowledgements
Research at the University of Denver was supported in part by NSF and in part by NASA.
Acknowledgement is made to the National Center for Atmospheric Research, which is supported
A. Meier et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 83 (2004) 109 – 113
113
by the National Science Foundation, for computer time used in this research. We wish to thank the
Australian Research Council and the New Zealand Foundation for Research, Science, and Technology
for funding; the Upper Atmosphere Research Program for funding NASA Langley; our colleagues at
the Swedish Institute of Space Physics and their collaboration partners for their support in recording
the solar spectra, the Atmospheric Watch Section of the Australian Bureau of Meteorology and the
Swedish Space Corporation at Esrange for use of their PTU sonde data, and all our colleagues from
the infrared working group of the NDSC for their encouraging support.
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“ † w “ …7w † r m t lq † p o † {7{7w m o Ž?u t pr ~7m qD{7…7p {tq o y&~7m “ ~† p oA¯† q o Ž;t l?† l?† w x t p m r ~76q m Am w † pAr t"r ~† rDt u
±7}„°&š=¹ ‰ º y7† lŽ/† w w t r tAt ¯7r † m l4~7m x ~"† “ “ …7p † “ s4t {7r m “ † wV{† r ~qu t p&r ~7oD† r Atq {7~7o p m “]r p † “ o]x† q o q |
°~7op † sŠ r p † “ m l7xA{7p t x p † ²±7}„°&š'~† q&¯o o l"m A{7w o Ao lr o Ž"m l"r ~7o ±S °¦¡ o | x|¹ ƒy‹ƒ7yˆ º ¢&† lŽ
m l4r ~7oD±S °&‚Dp o r p m o n † wV{7p t x p †  q¹ yŒ7yž7yV‰ – ºVr tŽo r o p Am l7o]r ~7o]q w † lr o ŽAt {7r m “ † wV{† r ~ t uq …7l7w m x ~r† q
q o o lu p t »r ~7ox p t …7lŽV|S°~7o q o{† p r m “ …7w † pm A{7w o Ao lr † r m t lqt u±7}„°&š ~† n o†]q o rSt uV±S °¿q {o “ m ³“
† …7‡m w m † p s/{7p t x p †  q&† lŽ/† p o]p o u o p p o Ž4r t † q±S °¿±7}„°&š;|°~7o q oD{7p t x p †  q&† p o]&m Žo w s/…q o Ž/¯s
r ~7o4† r Atq {7~7o p m “ m l7u p † p o Ž;p o At r o4q o lq m l7x;“ t A…7l7m r s ym l?{† p r m “ …7w † pA&m r ~7m lr ~7o4€zD7}i¹ ‰ ‰ y‰ ‚ º |
°~7m qp o nm q m t l4t uS±7}„°&š²m A{7p t n o qr ~7o]¼ …† w m r sAt uq † r o w w m r oDn † w m Ž7† r m t l/† lŽAw t l7x ¿ r o p  At l7m r t p m l7x
{7p t x p †  q |
±7}„°&š={o p u t p  q†4p † sŠ r p † “ m l7x"“ † w “ …7w † r m t lr t"Žo r o p Am l7o4r ~7o † m p † q qDŽm q r p m ¯7…7r m t l^† w t l7x
r ~7oDt {7r m “ † wS{† r ~"† lŽ/“ p o † r o q†At7Žo w† r Atq {7~7o p o† “ “ t p Žm l7x r t …q o p ¿q {o “ m ³7o Ž"{† p † Ao r o p q |°~7m q
At7Žo wD† r Atq {7~7o p o"“ t lq m q r q t u]r t r † w† m p4 † q q o q y{7p o q q …7p o q y&r o A{o p † r …7p o q y† lŽn t w …7Ao"Am ‡m l7x
p † r m tq¡ œ]š"™&q ¢u t pm l7u p † p o Ž † “ r m n o&q {o “ m o qm lAn o p r m “ † w w s¿q r p † r m ³7o ŽAw † s o p q |±S °;m l7u o p qr t r † w7“ t w …7Al
† At …7lr q&¡ °}„]q ¢St uS† r Atq {7~7o p m “r p † “ ox† q o qu p t  x p t …7lŽ¿ ¯† q o Ž4q t w † pm l7u p † p o Ž4q {o “ r p †¯† q o Ž t l
r ~7ot ¯q o p n o ŽA† ¯q t p {7r m t lAu o † r …7p o q y r ~7ot ¯q o p n † r m t l x o t Ao r p s† lŽAr ~7oAt7Žo wV† r Atq {7~7o p o&{7p t nm Žo Ž
¯s ±S °¿±7}„°&š;| rm ql7t r o Žr ~† r†]¯7p m o uSq …7A † p st uVr ~7m qp o {t p rm q{7…7¯7w m q ~7o Ž/† q†D€&t r o&m l4r ~7o
¹ ‰  º |
’p m t pAr t;±S °•‰ | – ž7y† ˆ/w † s o pAm l7{7…7r At7Žo w† r Atq {7~7o p o4&† q“ t AAt l7w s;…q o Ž?&m r ~^±S °¿
±7}„°&𲡠! " # $% " ¢ y &~7m “ ~A&† qV~† lŽw o ŽA“ t p p o “ r w sD¯s±7}„°&š;| v^m r ~r ~7ol7o o Žu t pS¯o r r o p
r p t {tq {7~7o p m “&p o q t w …7r m t ly7r ~7o&l…7¯o pt uVw † s o p q{7p t nm Žo ŽAr t±7}„°&š²&† qm l“ p o † q o Ž u p t   ˆ]r tD‹‰
† lŽD¯o “ † Ao&r ~7o&q r † lŽ7† p Ž]u t pSr ~7o±S °‰ | – ž&Žm q r p m ¯7…7r m t l r ~7p t …7x ~Dm r q ! " & ³7w o |k&l7u t p r …7l† r o w s
m r&† q]t n o p w tt ¤ o Ž"r ~† rDr ~7o ³7l7o p4
‰ '(=q {† “ o Žr p t {tq {7~7o p m “ p o q t w …7r m t l;t ur ~7o ! " & n t w …7Ao
Am ‡m l7x"p † r m t/† lŽ"{7p o q q …7p oAr o A{o p † r …7p o{7p t ³7w o q]~† lŽo Žr t/±7}„°&š6o p ol7t rD † r “ ~7o Ž/¯s"r ~7o
q † Aon o p r m “ † wp o q t w …7r m t lA&m r ~7m l ±7}„°&š;| „&rr ~† rSr m Ao y ±7}„°&ši…q o ކ³7‡o Ž‹7 ¿ w † s o p y m lr o p l† w
At7Žo wS&m r ~
‚ '(·q {† “ m l7x4m l"r ~7oDr p t {tq {7~7o p oA† lŽ4w t o p]q r p † r tq {7~7o p o |&k&lŽo pD“ o p r † m l"“ t lŽm r m t lq
¡ q o o ¯o w t ]¢]r ~7o {7p o q q …7p o q yr o A{o p † r …7p o q† lŽœ]š"™&qD{7p t nm Žo Ž;† rr ~7o4† Ž7Žm r m t l† w&† w r m r …Žo qo p o
m x l7t p o Ž4¯s4±7}„°&š;|
±S °¿±7}„°&š'p o ¼ …7m p o qr tAm l7{7…7r]³7w o q |]°~7oD³7p q r yV“ † w w o Ž ) y7m q]† “ t lr p t w³7w oAq {o “ m u sm l7x
r ~7ox o t Ao r p sAt ur ~7ot ¯q o p n † r m t ly7r ~7o]† w r m r …Žo]w † s o p m l7x q “ ~7o Ao]u t pr ~7ot …7r {7…7r&† lŽ t r ~7o pp o ¼ …7m p o Ž
{† p † Ao r o p q q …“ ~»† qAr ~7ol…7¯o p4t uDr p † “ o"x† q o qAm lr ~7o"m l7{7…7r"† r Atq {7~7o p o | °~7oq o “ t lŽ^m l7{7…7r
³7w o yS“ † w w o Ž " yVŽo ³7l7o qDr ~7oAt7Žo w† r Atq {7~7o p or ~† rm q]…q o Ž"† qm l7{7…7rDr t/±7}„°&š;yVq {o “ m u sm l7x
{7p o q q …7p o yr o A{o p † r …7p oA† lŽ"n t w …7AoAm ‡m l7x"p † r m tqD¡ œ]š"™&q ¢u t pD† w wAt w o “ …7w o q† rD†4q o w u ¿“ t lq m q r o lr
q o r]t u† w r m r …Žo q |A°~7oA“ …7p p o lrDŽm q r p m ¯7…7r m t lt u&±S ° ‰ | – ž oŽo u † …7w r qr t4‹‰Dw † s o p qu t pr † {o ž4† lŽ"‚ ž
w † s o p qu t pr ~7ot …7r {7…7rt u±7}„°&š;y¯7…7rD† w w t q&r ~7o…q oAt u…7{"r t4‚ – ƒAm l7{7…7rDw † s o p q]† lŽ ‹ t …7r {7…7r
w† s o p q |
lr ~7o4³7w o q Žm q r p m ¯7…7r o Ž *4&m r ~^±S °•‰ | – ž o yr ~7o4{7p t x p †  m qA{7p t nm Žo Ž?r t“ p o † r o4r ~7o
) m l7{7…7r³7w oDu p t i…q o p&m l7{7…7r]† lŽ {7p o ¿q r t p o ŽAt p&…q o p ¿q {o “ m ³7o Ž"q m r oD† lŽ4w † s o p m l7xAm l7u t p  † r m t l|
°~7o]{7p t x p † ,
 + - m q{7p t nm Žo Ž r tA“ p o † r or ~7o " m l7{7…7r³7w o]¯s4“ t ¯7m l7m l7x †D³7w oD&m r ~ . …q rr ~7o
œ]š"™¦m l7u t p  † r m t l?¡ ¤l7t &l;† q]r ~7o ! ³7w o ¢]&m r ~;†4³7w o4“ t lr † m l7m l7x"{7p o q q …7p o † lŽr o A{† p † r …7p o
† rr ~7oq † AoD~7o m x ~r q&~7o p or ~7oDœ]š"™&q]† p oq {o “ m ³7o Ž /7|„¦r ~7m p Ž/{7p t x p † /y # yV“ † w “ …7w † r o q]r ~7o
{7p o q q …7p oAo m x ~r o Ž;† m pD † q q o qD† lŽ"p o u t p  † r qr ~7o ±7}„°&š6t …7r {7…7rDm lr t/r ~7oAr ~7p o o ³7w o qDr ~† rD† p o
p o ¼ …7m p o Ž;¯s?±S °i“ t lr † m l7m l7x;† m p † q qDu † “ r t p q¡ ! ¢ ySœ]š"™ {7p t ³7w o q ¡ ! - ¢]† lŽ;{7p o q q …7p o ¿
r o A{o p † r …7p o4{7p t ³7w o q ¡ ¢ |„²¯† r “ ~;t p q “ p m {7rA³7w o/m q{7p t nm Žo Ž;r tp …7l?r ~7o q o {7p t x p †  qDm lr ~7o
“ t p p o “ rq o ¼ …7o l“ o 0|S„w r ~7t …7x ~ r ~7o{7p t x p †  q y + - † lŽ # “ † l ¯o…q o ŽAr tD{7p o {† p o
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±7}„°&šim l7{7…7r† lŽp o u t p  † r±7}„°&šit …7r {7…7r y r ~7o m p…q om ql7t r † lŽ7† r t p s |Szo ln o pk&l7m n o p q m r s q
% # yVu t p&m lq r † l“ o yVm q&o † ¼ …† w w sq …7m r † ¯7w oA† lŽ4r ~7oDr o q r]“ † q o q&o“ t A{† p o Ž/† x† m lq r % # † p o
“ t lq m q r o lr&m r ~4† w wVp o q …7w r q{7p o q o lr o ŽA~7o p o |°~7oD±S °^q …7m r ot uV{7p t x p †  qŽto q~7t o n o pq o p n o† q† l
o ‡7† A{7w oDt uS~7t ^r t “ † p p s t …7r&r ~7o q o]t {o p † r m t lq |
r]m qm A{t p r † lrr t l7t r or ~† r&r ~7o p oA† p oDr ~7p o oAq o {o p † r oA† w r m r …ŽoAw † s o p m l7x/q “ ~7o Ao qm l"…q o |]°~7o
³7p q rm qr ~7oDt l7oD…q o Ž/u t pr ~7oDm l7{7…7rD† r Atq {7~7o p oq …7{7{7w m o Žr t ±7}„°&š'm l " |&°~7oAq o “ t lŽ/t l7o
m qq r t p o ŽAm l4¯7m l† p sAu t p  † rm lq m ŽoDr ~7oo ‡o “ …7r † ¯7w o]{7p t x p †  † lŽAp o  † m lql7t p  † w w s ~7m Ž7Žo l4u p t  r ~7o
…q o p† lŽ"&~7m “ ~op o u o pDr t/† qr ~7oAm lr o p l† ww † s o p m l7x"q “ ~7o AoAt u&±7}„°&š;|„lŽr ~7or ~7m p Ž"t l7oAm q
r ~7o]p o ¼ …7o q r o Ž4t …7r {7…7r&w † s o p m l7x4q “ ~7o Ao]u t p]±S °† q&q {o “ m ³7o Ž/m l/r ~7o]m l7m r m † w ) |
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¯o pt uw m Am r † r m t lq&~7m “ ~?“ † lw o † Žr t/o p p t p q]&~7o l;r ~7oA…q o pA† r Atq {7~7o p oAm qŽo ³7l7o ސ&m r ~;n o p r m “ † w
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‰ | – ž]t p&±S °&‚7|°~7o] † m l w m Am r † r m t lq&† p m q ou p t  r ~7om lr o p l† ww † s o p m l7x q “ ~7o Aot u±7}„°&š•&~7m “ ~
m q…q o ŽAu t pl7o o Žo Ž m lr o p {t w † r m t lq | r&“ t lq m q r o ŽAt u‹7]³7‡o ŽAw o n o w q† lŽA&† q“ t lq r p …“ r o ŽA…q m l7x ‚ '(
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† ls m lr o p l† wS¯t …7lŽ7† p s4w † s o pl7t o ‡7† “ r& † r “ ~4m qu t …7lŽV|°~…q y…q o p]Ž7† r †{7p t nm Žo Ž"† r–7y‰ y7yƒ7yS| |
'(it l7w s t …7w Ž4† w q tw o † Ž r tDp o † q t l† ¯7w o]{7p t ³7w o q&m r ~ r ~7o]t w Ž ±7}„°&š6‰ ž ž ƒ]n o p q m t ly¯o “ † …q oDr ~7o
m lr o p {t w † r m t lp t …7r m l7oAt …7w Ž"¯oA“ † w w o ŽV| ›&t o n o p ym lr ~7oA{7p † “ r m “ † w“ † q ot u†A…q o pD{7p t nm Žo Ž"m l7{7…7r
† r Atq {7~7o p o Žo ³7l7o ކ rDr ~7o4† w r m r …Žo qDt u–7y‰ y‚7y7yS‹yƒ7y | | ‰ ƒ7y ‰ ˆ7y ‰ Œ7yV‚ –7y | | y‰ – – '('m l7u t p  † r m t l;m q
u t …7lŽ4¯t r ~"† ro † “ ~/m lr o p l† wS¯t …7lŽ7† p s4w † s o p]† lŽ/† rm l7¿ ¯o r o o l† w r m r …Žo q |] m l“ oA±7}„°&š ‰ ž ž ƒ
³7lŽ7q& † r “ ~7m l7x{7p o q q …7p o y7r o A{o p † r …7p o y† lŽ œ]š"™Ž7† r †† ro † “ ~4t uSm r qm lr o p l† wV¯t …7lŽ7† p s4w † s o p q–7y
‚7y‹ySˆ7ySŒ7y‰ –7y‰ ‚7y‰ ‹yS† lŽ?‰ ˆ '('r ~7oAm lr o p {t w † r m t l;p t …7r m l7oAm qDl7t r]o ‡o “ …7r o Ž;† lŽ;Ž7† r † {7p t nm Žo Ž
¯s"r ~7o …q o pA† rDr ~7o † Ž7Žm r m t l† w&† w r m r …Žo qt u]‰ y7ySƒ7yyž7y‰ ‰ y‰ /† lމ ƒ '(6† p o l7t r“ t lq m Žo p o ŽV|
}t lq o ¼ …7o lr w s ySr ~7oA{7~s7q m “ † w&Ž7† r † {7p t nm Žo ޝs"r ~7oA…q o pA† r]t7Ž7Žn † w …7o qDt u&† w r m r …Žo qD¯o w t ²‰ ˆ '(
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&† q&† Ž7Žo Ž/r t4“ t n o pr ~7oDl7o o Ž7qt uAtq r]† {7{7w m “ † r m t lq |]°~7oAtq rq m x l7m ³“ † lr“ ~† l7x o q&m A{7w o Ao lr o Ž
q m l“ oDœo p q m t l"‚7| –7‰]† p o ,
‰ ¢·°~7or t r † wl…7¯o pt um lr o p l† wAt7Žo w7w † s o p qS&† qm l“ p o † q o Žu p t ¦‹7r tDƒ Œ7|S°~7ol7o ?¯t …7lŽ7† p s
w † s o p q† p oDw t7“ † r o Ž/† r]–7yV–7| ƒ7y‰ y‰ | ƒ7y‚7yV‚7| ƒ7y7y‹yVƒ7yˆ7yyVŒ7yVž7y‰ –7yS‰ ‰ y‰ ‚7yS‰ 7y‰ ‹y‰ ƒ † lމ ˆ
'(i† w r m r …Žo y7&~7m w oD† ¯t n o&r ~7o s † p o† qm l o † p w m o p&n o p q m t lqt u±7}„°&š;|¡ m l4r ~7o&w † r o q rn o p q m t l
r ~7o]l…7¯o p&† qm l“ p o † q o Ž4r t ‚ – ž7y7q o o]¯o w t D| ¢
‚¢·°~7o&l…7¯o pt uAt7Žo w7w † s o p q y m lr o p l† w† lŽDo ‡r o p l† w y† qSo w wV† qSr ~7ol…7¯o pt uAt w o “ …7w o q y7† p o
l7tAw t l7x o pŽo ³7l7o Ž4m l/…7w r m {7w ow t7“ † r m t lq&r ~7p t …7x ~7t …7rr ~7oDq t …7p “ oD“ t7Žo |°~7o q oD† p o]l7t q {o “ m Š
³7o ŽDt l“ o&m r ~†±”™S°&™„]€’„]™„]š"¾°&¾™;q r † r o Ao lr y ~7o l“ o&† w q tr ~7ol† Ao’† p † Ao r o p m o Ž
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„m p]š"† q q}t A{7…7r o p’p t x p † iu t p&„&r Atq {7~7o p m “D°p † lq Am r r † l“ o ¸ ™&† Žm † l“ o }† w “ …7w † r m t l;¡ {† Š
p † Ao r o p m q o Ž4±7}„°&š¢ |
¢·°~7o] † ‡m …7il…7¯o pt uSt …7r {7…7r&w † s o p q~† q¯o o l/m l“ p o † q o Ž4r t4 ‹|
‹7¢·°~7ol…7¯o pSt u7q r † lŽ7† p ŽAt w o “ …7w o q~† qV¯o o lm l“ p o † q o Ž]u p t »ƒr tˆ 7|°~7oq m ‡]l7o At w o “ …7w o q
† Ž7Žo Ž?† p o/ƒ Œ •”]}w ”Dyƒ ž ²±‰  ‹ „ySˆ –•} › yˆ7‰²±‰ ‹‚ £yˆ ‚•}±}‰ ‰ 7yS† lŽ?ˆ 
i±‰ ‹‰ £|°~7oAAt w o “ …7w † pAo m x ~r qD† q q m x l7o Žr t// r ~7o q oAAt w o “ …7w o qA† p o ˆ| ‹ˆ7ySŒ 7| –  7yV‹ ‹| – žy
‰ – –7| ‹ˆ7y‰ Œ|  ƒ ž7y† lŽ"‰ ‰ ˆ7| ž ƒ yp o q {o “ r m n o w s |
ƒ¢·°~7o]At w o “ …7w † p]o m x ~r&t uS› * A~† q&¯o o l"“ t p p o “ r o Ž u p t ²–7| – –Dr tA ‹| –
ˆ¢·°~7oo p p t p~† lŽw m l7x/~† q&¯o o lm A{7p t n o ŽV|]¾p p t pAo q q † x o q&l7t »m l“ w …Žo ³7w o l† Ao q ySq ~7t »r ~7o
l† Ao]t uSr ~7oD“ † w w m l7x4p t …7r m l7o† lŽ x m n oq {o “ m ³“D~7m lr qr t &† p Ž7qr ~7o]{tq q m ¯7w oA“ † …q o q |
}~† l7x o q&† {7{7w m o Ž/r tAn o p q m t l/‚7| – ‚q m l“ oDr ~7oDp o w o † q oDt un o p q m t l"‚7| –7‰m l“ w …Žo ,
 ¢·°~7o† “ “ …7p † “ sm l r ~7o&³7l† wt …7r {7…7r~† q¯o o l m l“ p o † q o ŽV|„w wV‹Dp o {t p r o ŽAŽm x m r q† p oo ‡7† “ r y &~7m w o
{7p o nm t …q w s r ~7o‹ ]Žm x m r&† qq …7¯ . o “ rr tDq m x l7m ³“ † lr&l…7Ao p m “ † wVp t …7lŽŠ t ´4o p p t p q |¡ °o “ ~7l7m “ † w w s
r ~7o]m lr o p Ao Žm † r o]p o q …7w r qt uSr ~7o]t {7r m “ † wV{† r ~4w o l7x r ~y7r ~7o]r t r † wl…7¯o p&t uS† m p&At w o “ …7w o q]† lŽ
r ~7ol…7¯o p&t uo † “ ~ t ur ~7om lŽm nm Ž…† wAt w o “ …7w o q† p o]q r t p o ސ&m r ~/ˆDp † r ~7o pr ~† l ‹Aq m x l7m ³“ † lr
Žm x m r q&u t po † “ ~/w † s o p]¡ t …7r {7…7r&m l/³7w o ) ¢ ¢ |
Œ¢·°~7oDu …7lŽ7† Ao lr † w“ t lq r † lr q…q o Ž4o p o]…7{VŽ7† r o Ž/† lŽ/† p o]l7t m l"† x p o o Ao lr&&m r ~4r ~7oDw † r o q r
}&”z&„°„ip o “ t AAo lŽ7† r m t lq ¹ ‰ ‹ º |4›&t o n o p yS† w wn † w …7o qA† ´Vo “ r o Ž“ ~† l7x o ޝs;q …7¯q r † lr m † w w s
w o q q&r ~† l/–7| ‰Dµ |
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ž¢·°~7o&r t r † w7l…7¯o pt uVm lr o p l† wAt7Žo ww † s o p q&† qm l“ p o † q o ŽAr t‚ – žm A{7w o Ao lr m l7x4–7| ‚ ¤ q r o {q
u p t '–/r t" – ¤'† w r m r …Žo y–7| ƒ ¤'q r o {qDu p t ' –4r t/‹– ¤/y‰ | – ¤'q r o {qDu p t ·‹–/r t"ˆ – ¤/y
‚7| – ¤·q r o {qDu p t 'ˆ –4r t"Œ – ¤/ySƒ7| – ¤'q r o {qDu p t ·Œ –/r t;‰  – ¤/yS† lކ/³7l† w¯t …7lŽ7† p s;† r
ž ž ž ž ž7| – ¤† qm l{7p o nm t …qSn o p q m t lq |S°~7o…q o pS † s]{7p t nm Žom l7{7…7rŽ7† r †&† rS…7{Dr t]‚ – ƒ&† w r m r …Žo q |
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°~7m qq o “ r m t lŽo q “ p m ¯o qr ~7o“ ~† l7x o q † Žor t&r ~7o† …7‡m w m † p s{7p t x p †  qQ+ - $ † lŽ # y
&~7m “ ~"† p oq {o “ m ³“Dr t4±S °»† {7{7w m “ † r m t lq | l7t »† w w t q&u t p&r ~7oDt {7r m t l† wp o † Žm l7x t u†A…q o p
Žo ³7l7o Ž"o ‡r o p l† w¯t …7lŽ7† p s/w † s o p]Žo ³7l7m r m t l³7w o |°~7m ql7o »u o † r …7p oDt n o p p m Žo q&r ~7o¯7…7m w r Š m l;Žo u † …7w r q
† rDp …7lr m Ao ym u]Žo q m p o ŽV|°~7m qA† w w t o Ž…qr t/p o t p x† l7m q o r ~7o4Žo u † …7w rA¯t …7lŽ7† p sw † s o pAq “ ~7o Ao m l†
q o w u Š “ t lq m q r o lrD † l7l7o p y&~7m w oAx m nm l7x"r ~7o…q o p]Ao † lqr t/“ t lr m l…7oAr t4…q or ~7ot w Ž"¯t …7lŽ7† p s"w † s o p
q “ ~7o AoA¡ m uŽm ´Vo p o lr ¢† lŽ r tAAo o r&r ~7o]o Ao p x m l7x l7o o Ž7q&t uS{7p t ³7w m l7x r tt w q¡ q o o]¯o w t ]¢ |
°~7o† …7‡m w m † p s/{7p t x p †  ql7t »q …7{7{t p r…q o p Š {7p t nm Žo Ž"™&¾±š”z¦† lŽ4 † r “ ~7m l7x {7p o q q …7p o ¿ r o AŠ
{o p † r …7p o³7w o q&m r ~† ls/l…7¯o p]t u¯t …7lŽ7† p s/w † s o p q¯o r o o l – † lŽ/‚ – ƒ4¡ {7p o nm t …q w s"³7‡o Ž/r t ‹‰
w † s o p q ¢ |S„l4† Ž7Žm r m t l† w† …7‡m w m † p s {7p t x p † /y ! ym q{7p t nm Žo Ž r ~† r† w w t qr tD † {4† lAo ‡m q r m l7x q o r
t u ?† lŽA“ t p p o q {t lŽm l7x{7p o q q …7p o ¿ r o A{o p † r …7p o&³7w o&t lr tD† lsDl7o ¯t …7lŽ7† p sw † s o pq “ ~7o Ao |
rD{o p u t p  q†4w t x† p m r ~7Am “Am lr o p {t w † r m t l?t l{7p o q q …7p o q† lŽ"œ]š"™&q† lކ/w m l7o † pm lr o p {t w † r m t l?t l
r o A{o p † r …7p o]n † w …7o q | °~7m qp o nm q m t l?t ur ~7o {7p t x p †  qD† q q t7“ m † r o ސ&m r ~±7}„°&š=m l“ t p {t p † r o qDr ~7p o o4At p oAu o † r …7p o q
r t m A{7p t n or ~7o{7p t x p †  q&“ t lq m q r o l“ s† lŽ"“ t A{7…7r m l7x/q {o o ŽV|D„w r m r …Žo q]m l " † p oDl7t ¦&p m r Š
r o l;&m r ~^‰ Ao r o pp o q t w …7r m t l¡ {7p o nm t …q w s^‰ – – – (/¢Šr ~7m qDp o ¼ …7m p o Ž;l7t“ ~† l7x o qDm l?±7}„°&š;|S°~7o
¯t …7lŽ7† p sw † s o pq o w o “ r m t lq&m r ~7m l ~† n o¯o o l  † Žo&q o w u Š “ t lq m q r o lr¡ q o o&q o “ r m t lA‹| ‰ ¢† lŽA† l
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m A{7p t n o Ž † w x t p m r ~7 &† qm A{7w o Ao lr o Ž4m lr t r tAŽo r o p Am l7o]r ~7o³7p q rx …7o q qu t pr ~7ot ¯q o p n o Ž
o l7m r ~;† l7x w o4¡ q o oAq o “ r m t l‹| ‚¢ |]°~7ow † r r o p]p o ¼ …7m p o q]r ~† r+ - m qo ‡o “ …7r o Ž"¯o u t p o Vm | o |
r ~7o m p&t p Žo pm qp o n o p q o Ž4† q“ t A{† p o Ž r tr ~7o‰ ž ž ƒDo Žm r m t l| p o † Ž7qr ~7o]t …7r {7…7ru p t  + r t“ † w “ …7w † r o"r ~7o/† m pAl…7¯o p4Žo lq m r s† rr ~7o4t ¯q o p n † r m t l^† w r m r …Žo"† lŽ;m r4“ t …7lr qDr ~7o/l…7¯o pAt u
At w o “ …7w o q]q r t p o Ž m l " y&~7m “ ~"† w w t qr ~7o]…q oDt u†7o ‡m ¯7w ol…7¯o p&t uSAt w o “ …7w o q]† rp …7lr m Ao |
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Žm ´Vo p o lr&t …7r {7…7r&w † s o p m l7x4q “ ~7o Ao q y7&~7m “ ~"“ † …q o Ž/q t AoD“ t l7u …q m t l/m l/r ~7o]{† q r |
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¯t …7lŽ7† p s4w † s o pq “ ~7o Ao q ,
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n7‚7| – ‡† w w t ir ~7o4Žo r † m w&m l?r ~7o m l7{7…7r {7p t ³7w o qr t/¯o/“ † p p m o Ž;r ~7p t …7x ~?“ t p p o “ r w s;m l?r ~7o4“ † w “ …7w † r m t l
¡ “ t A{† p oD±Sm x …7p o q&ŒA† lŽ4ž¢ |
°~7o p oo p oDl7t4Žm ´Vo p o l“ o q]¯o r o o l"r ~7o† m p] † q q o q“ † w “ …7w † r o Ž"&m r ~;±S °¿±7}„°&š'n o p q m t lq
n7‚7| –7‰† lމ ž ž ƒu t pS† w r m r …Žo q† ¯t n o&‰ @‚ '(»u t po m r ~7o pq m r om lA† x p o o Ao lr&m r ~Dt …7p…7lŽo p q r † lŽm l7x]r ~† r
r ~7o p o&† q&l7t4“ t l47m “ rD¯o r o o l"r ~7om l7{7…7rD† lŽ/r ~7om lr o p l† wSw † s o p m l7x/q “ ~7o AoA† ¯t n or ~7m q~7o m x ~r yVm l
o m r ~7o pr ~7o&t w ŽDt pl7o ^“ † w “ …7w † r m t lq |›&t o n o p y r ~7ow † r o q r&±S °¿±7}„°&š n o p q m t l q ~7t qŽm ´Vo p o l“ o q
t u…7{/r t ‚Am l"r ~7oDw † q rt um r q&‹4q m x l7m ³“ † lrDŽm x m r q&r ~7p t …7x ~7t …7r]† w w† w r m r …Žo q y&~7m “ ~"m qr ~7oDp o q …7w rt u
p o Ž…“ o Ž4p t …7lŽ¿ t ´"o p p t p q† q&Žo q “ p m ¯o Ž/m l"q o “ r m t l/‹|
”&lAr ~7o&&~7t w o y7Žm ´Vo p o l“ o qo ‡7“ o o Žm l7x –7| ƒ]µ¦† p ot l7w sAq o o l m lAr ~7oam p …7l†D“ † q o† lŽA† p op o q r p m “ r o Ž
r t † w r m r …Žo q&¯o w t 
‹ '(•† lŽ4t7“ “ …7p&t l7w s4m l/r o A{o p † r …7p oD† lŽ4m l/r ~7o]r t r † wVl…7¯o p&t uSAt w o “ …7w o q |
v^~7o lr ~7o4p o q …7w r qAŽo q “ p m ¯o Ž^† ¯t n o/† lŽ;m lr ~7o4u t w w t &m l7x;q o “ r m t l^ƒ7| ‚/o p o4{7p o q o lr o Ž?† rAr ~7o
l7u p † p o Ž;vt p ¤m l7x?Àp t …7{?š/o o r m l7xt u&r ~7o/€zD7}¦m l^£t p Žo † …7‡m l o {‚ – –7‰ ySr ~7o/±° ™i“ t A…7Š
l7m r s"o ‡{7p o q q o Ž"m lr o p o q rDm lr ~7oAo ´Vo “ r qr ~7o “ ~† l7x o q] † s/~† n ot lœ]š"™»{7p t ³7w o p o r p m o n † w ySl7t r . …q r
°}„]q y7† lŽ4&~† rm l47…7o l“ or ~7oD“ ~7t m “ oDt u† w r m r …Žoq “ ~7o Ao] † s ~† n o |š/t p o t n o p yŽm q “ …q q m t l† r&r ~7o
€zD7}¦‚ – –7‰  sA{tq m …7'&m r ~t l7o t ur ~7o t p m x m l† w† …7r ~7t p qt u&±7}„°&š ¡ | „|S}w t …7x ~V¢p o n o † w o Ž
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l7t l7Š r ~7o p  † wVo ¼ …7m w m ¯7p m …7•o ´Vo “ r q&† lŽ † “ ~7p t  † r m “&¯o ~† nm t …7p&r ~† rm Žo † w w s4t …7w Ž p o ¼ …7m p oDm lŽm nm Ž…† w
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‰ 7| – – | ƒ7‰ ‚ ž ¾ ‚ ‹ | ƒ7‰ ‚ ž ¾ ‚ ‹ –7| – – –
‰ ‚7| – – | ˆ – – ‚ ¾ ‚ ‹ | ˆ – – ‚ ¾ ‚ ‹ –7| – – –
‰ ‰ | – – | ˆ ž ˆ ‹¾ ‚ ‹ | ˆ ž ˆ ‹¾ ‚ ‹ –7| – – –
‰ –7| – – | Œ –7‰ Œ ¾ ‚ ‹ | Œ –7‰ Œ ¾ ‚ ‹ –7| – – –
ž7| – – | ž7‰   ¾ ‚ ‹ | ž7‰ ‹‚ ¾ ‚ ‹ –7| – ž ž
Œ7| – – | ‰ –  – ¾ ‚ ƒ | ‰ – 7‰ ¾ ‚ ƒ –7| – ž
| – – | ‰ ‰ ƒ Œ ¾ ‚ ƒ | ‰ ‰ ƒ ž ¾ ‚ ƒ –7| – Œ ˆ
ˆ7| – – | ‰ ‚ ž ¾ ‚ ƒ | ‰ ‚ ž Œ ¾ ‚ ƒ –7| – 
ƒ7| – – | ‰ ‹ ‹ž ¾ ‚ ƒ | ‰ ‹ƒ – ¾ ‚ ƒ –7| – ˆ ž
‹| – – | ‰ ˆ7‰ ‹¾ ‚ ƒ | ‰ ˆ7‰ ˆ ¾ ‚ ƒ –7| ‰ ‚ ‹
7| ‹ˆ | ž ‹7 ˆ ¾ ‚ ‹ | ž ‹Œ – ¾ ‚ ‹ –7| – ‹‚
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‰ ‚7| – – | ‰ – ‹7 ¾ ‚ ƒ | ‰ – ‹7 ¾ ‚ ƒ
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‰ –7| – – | ‰ ‹ˆ ƒ ¾ ‚ ƒ | ‰ ‹ˆ ƒ ¾ ‚ ƒ
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ž7| – – | ž ‚   ¾ ‚ ‹ | ž ‚  ‹¾ ‚ ‹
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ˆ7| – – | ‰  ‚ ƒ ¾ ‚ ƒ | ‰  ‚ ƒ ¾ ‚ ƒ
–7| – – –
ƒ7| – – | ‰ ‹ž ‚ ¾ ‚ ƒ | ‰ ‹ž Œ ¾ ‚ ƒ
–7| ‹– ‚
‹| – – | ‰ ˆ Œ ¾ ‚ ƒ | ‰ ˆ Œ ƒ ¾ ‚ ƒ
–7| ‹‰ 
7| – – | ‰ Œ ‚ ¾ ‚ ƒ | ‰ Œ  ¾ ‚ ƒ
–7| – ƒ 
‚7| – – | ‚ –  ¾ ‚ ƒ | ‚ –  ¾ ‚ ƒ
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‰ | – – | ‚  Œ ˆ ¾ ‚ ƒ | ‚ 7‰ ‹¾ ‚ ƒ Š 7| –7‰ Œ
| ‹‚ | ‰ ƒ ž ƒ ¾ ‚ ƒ | ‰ ƒ ‚ Œ ¾ ‚ ƒ Š ‹| ‚ –7‰
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† m p& † q q³7w o q&u t po † “ ~ At w o “ …7w o | lŽm nm Ž…† w† m p& † q q³7w o q&u t po † “ ~4At w o “ …7w oDt …7w Ž p o ¼ …7m p o†Du …7l7Š
Ž7† Ao lr † w7p o Žo q m x l4t ur ~7o]“ t7Žo]† lސt …7w ŽA † ¤ o&~7t …q o ¤ o o {7m l7x…“ ~ At p o“ t A{7w m “ † r o ŽV|›&t o n o p y
r ~7om A{7p t n o Ao lr† “ ~7m o n † ¯7w o]m qm lŽo o Ž4n o p sAq  † w wV† lŽAm r&† q“ t l“ w …Žo Ž4r ~† rq m A{7w sA…q m l7x †Dq  † w w
o l7t …7x ~"† w r m r …ŽoAq r o {q m o ¡ ‚ – – 4¢t …7w Ž4p o Ž…“ oA† ls4m lr o p {t w † r m t l"o p p t p qr tA&m r ~7m l"r ~7oDl…7Ao p m “ † w
{7p o “ m q m t ly~7o l“ oA† n t m Žm l7xAr ~7oDl7o o Ž4u t p&†u …7lŽ7† Ao lr † wp o Žo q m x l|
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{7p o “ m q m t lo lnm q † x o Ž¡ ‹ q m x l7m ³“ † lrDŽm x m r q ¢&&† qm A{7w o Ao lr o Ž"m l±7}„°&š'œo p q m t l‚7| – ¯s4p † m q m l7x
r ~7o4l…7¯o p t um lr o p l† w&w † s o p qu p t =ƒ ž/r t;‚ – ž7y† qAŽo q “ p m ¯o Žm lr ~7o/{7p o nm t …q q o “ r m t l|?„x† m lo
“ ~7tq o/p o † w ¿ t p w Ž?Ž7† r †7yr ~7m qAr m Ao/u p t 6r ~7o4vt w w t l7x t l7x?q m r o yw t7“ † r o Ž –"=† ¯t n o"q o †"w o n o wt l
r ~7oD„…q r p † w m † l’† “ m ³““ t† q r]¡  ‹| ‹ˆ yS‰ ƒ –7| Œ Œ ¾¢ |°~7oq r …Žs/t uSr ~7m q]Ž7† r †m qu …7p r ~7o p]Žo o {o l7o Ž"m l
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m ln o p q m t l/w † s o p q&† p oDl7t p  † w w s/† ¯q o lr† lŽ w t7“ † w’°&k»q t lŽo q† p oD† n † m w † ¯7w oAŽ7† m w s/u p t  r ~7oA s7Žl7o s
am l7xq u t p Ž¿7 Am r ~"† m p {t p r |
°~7o t ¯q o p n † r m t l?Ž7† s“ ~7tq o l;m qDr ~7o4ž > ”“ r y&‰ ž ž ž7|4°~7oAw t7“ † w&’°&k q t lŽo p o † “ ~7o Ž;†"“ o m w m l7x
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{7p o q q …7p o]† lŽAr o A{o p † r …7p o&{7p t ³7w o qr t±7}„°&š;| °~7o]’°&kq t lŽor o A{o p † r …7p o&{7p t ³7w om q&q ~7t &lAm l
±Sm x …7p o †7|
v^m r ~r ~7m qDm l7{7…7rAŽ7† r † o “ p o † r o Ž"‹/q o r q]t uAt7Žo w† r Atq {7~7o p o q]u t p]w † r o pD…q oAm l;r ~7o † l† w s7q m q
t uq t w † p&±° ™»q {o “ r p †&m r ~"±S °&‚ ¡ q o “ r m t l"ƒ7| ¢ | o r Š ‰ y7p o u o p p o Ž r tA† q‹‰ ¸ ƒ ž¸ y {7p t nm Žo qŽ7† r †Dr t
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 o r Š 7yp o u o p p o ŽAr t† q‚ – ƒ¸ ‚ – ž¸ y {7p t nm Žo q&Ž7† r †]r t±7}„°&š•œ]‚7| – ]† r&‚ – ƒD† w r m r …Žo q † r “ ~7m l7xr ~7o
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t lr t r ~7oA‹‰q r † lŽ7† p Ž"† w r m r …Žo q¡ °‹‰ ¢l7t p  † w w s"~† lŽo Ž"r t4±7}„°&š;|°~7o q oo p p t p q]† p op o Ž…“ o Ž
q m x l7m ³“ † lr w s"m ur ~7oAŽ7† r †Am q]q † A{7w o ކ r]†A…“ ~"~7m x ~7o pDu p o ¼ …7o l“ s¡ °&‚ – ƒ¢† q~† q&¯o “ t AoA{tq q m ¯7w o
&m r ~/r ~7o]w † r o q r&n o p q m t l4t u±7}„°&š6¡ p m x ~r{† l7o w ¢ |
°~7o Žm ´Vo p o l“ o q“ † …q o ޝs/{7…q ~7m l7x"r ~7oAl…7¯o pDt um lr o p l† ww † s o p qu p t ·ƒ ž r t"‚ – ž4† w t l7oA~† q
t 7l w s"† n o p s/ † p x m l† wSo ´Vo “ rt l"r ~7ot …7r {7…7r |}t A{† p m l7x4r ~7ot …7r {7…7ru p t ' o r Š ‰† lށ o r Š ‚4q ~7t q
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›&t o n o p ym lr o p {t w † r m t lo p p t p q yVm l{† p r m “ …7w † p]m lr ~7or o A{o p † r …7p o{7p t ³7w o yS† p oAq m x l7m ³“ † lr w sp o Š
Ž…“ o Žm ur ~7o&’°&kq t lŽom qq † A{7w o ސ&m r ~…“ ~~7m x ~7o pp o q t w …7r m t l ¡  o r Š ¢ |S°~7o&m lr o p {t w † r m t lo p p t p q
m l"r ~7om l7{7…7r]r o A{o p † r …7p o q&m lr p t7Ž…“ o Ž"¯s4r ~7oq m A{7w o ’°&k¦q t lŽoAŽ7† r †A“ t ln o p q m t l"{7p t x p † i…q o Ž
¡ u p t ²¹ ¹ ‰ ƒ º º ¢† p o&m w w …q r p † r o ŽAm l/±Sm x …7p o] ¯|°~7o q o&o p p t p q† p o&r ~7op o q {t lq m ¯7m w m r s t uVr ~7o…q o p y
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r o x p † r o&r ~7oDq t …7lŽm l7x Ž7† r †7|›&o l“ o y7u p t i†D{7p † “ r m “ † wV{t m lr&t unm o Dy7r ~7o~7m x ~7o p&l…7¯o p&t um lr o p l† w
At7Žo ww † s o p qm l"±7}„°&š·t ´Vo p&† l/† Žn † lr † x o]&~7o p o]~7m x ~"p o q t w …7r m t l/m l7{7…7r]Ž7† r †Dm q† n † m w † ¯7w o¿A¯s
q ~7m u r m l7xr ~7o&{7p t ¯7w o  t uV{7p t {o pm lr o x p † r m t lAt uVx o t {7~s7q m “ † w{† p † Ao r o p qSu p t  r ~7o&…q o pr t±7}„°&š;|
›&t o n o p y r ~7o&œ]š"™{7p t ³7w o qm lŽm “ † r oDr ~† rr ~7o p oAm x ~r¯oAt p o&Ao p m rm l r ~7ou t …7pr m Ao q~7m x ~7o p
l…7¯o pt um lr o p l† wAt7Žo wSw † s o p q |°~7oDœ]š"™^{7p t ³7w oDt uSl7m r p t x o l4~† lŽo Ž/r tA±7}„°&š·m q† q q …7Ao Ž
“ t lq r † lr† r†D“ t l“ o lr p † r m t lAt uS Œ7| ‰ µ |›&o l“ o y7oo ‡{o “ rr ~7ot …7r {7…7rœ]š"™{7p t ³7w or t]¯or ~7oq † Ao |
°~7m qm qr p …7o&r tDr ~7ow † q r&Žm x m r&m uS‚ – ž]At7Žo wVw † s o p q† p o…q o ŽVy¯7…7r&Žo nm † r m t lqt uV…7{ r t ‰ | – ‹7µ¦† p oq o o l
m u±7}„°&š²œ]‚7| – ‚]&m r ~4t l7w s ƒ žDw † s o p qm q…q o ŽV|°~7o{7p m “ o]m l"}’k^r m Ao]u t pp …7l7l7m l7xAr ~7oD‚ – ž]w † s o p
n o p q m t l4m qq  † w w† lŽ4† lŽ At p o]r ~† l4t …7r o m x ~r o ŽA¯s r ~7o]~7m x ~7o p{7p o “ m q m t l"† “ ~7m o n o Ž4m l/r ~7o]œ]š"™&q |
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u p t ²~7m x ~7w s{7p o q q …7p o Š ¯7p t† Žo l7o Ž"&† r o pn † {t …7p]w m l7o q | lr ~7o{7p o nm t …qDq o “ r m t l"m rD&† qq ~7t &l/r ~† r
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¹ ž ºA}t l7l7t pD£ 7&y t l7o q]€£yVvtt7ށ v¦y*ao s7q ÀyV™m lq w † lŽ?}’Syš/…7p “ p † s/± 7|D™o r p m o n † wt u›]}w
† lŽ^›€]”{7p t ³7w o q u p t =x p t …7lŽŠ ¯† q o ޱ° ™•Ž7† r †…q m l7x^±S °&‚7| l^™&z'£t . ¤ t n?† lŽ^À
œm q “ t lr m yo Žm r t p q y !@ y{† x o q‹Œ ƒ ¿ ‹Œ Œ7y ˜ „]¼ …7m w †7y r † w s y‰ ž ž Œ7|
’† p “ t “ m o lr m ³“ t4o°o “ ~7l7t w t x m “ t4Ž „¯7p … m t|
¹ ‰ – º’St …7x† r “ ~7o n;€]y}t l7l7t p £ 7y™m lq w † lŽ}’S|; l7u p † p o Ž?Ao † q …7p o Ao lr qDt ur ~7o4t t l7o4n o p r m “ † w
Žm q r p m ¯7…7r m t l† ¯t n oam r r’o † ¤V| X ! y‰ ž ž ƒ ‰ – – , ‰ ˆ ˆ Œ ž ¿7‰ ˆ ˆ ž|
¹ ‰ ‰ ºa…7p sw t
š 7|¦€&o r t p ¤?u t p r ~7ozo r o “ r m t l^t u r p † r tq {7~7o p m “"}~† l7x o | E ! , yV‰ ž ž7‰ ‰ ‹ž7‰ , ‰ ˆ ž ¿‰  ‹|S o o† w q tA~r r &{ , ¸ ¸ &&D| lŽ7q “ | q ¸|
¹ ‰ ‚ ºa…7p sw t"
š 7yS¥V† lŽo pD™]|°~7oA€zD7}¿4m r q]q r † r …q]† u r o p‰ –As o † p qt ut {o p † r m t l|] l l ,›&t ¤¤ † m Žt4k&l7m nVyV‚ – – –7| {|‰ ˆ ¿‰ ˆ Œ7|
X !@ yV† {7{t p ty † {† &
¹ ‰  ºš/o m o p4„y&Àt w Ž † l^„yš"† l7l7m l7x’y& r o {7~7o l»°&š;y™m lq w † lŽ»}’Sy t l7o q4€£yvtt7Ž^ v¦|
A{7p t n o Ao lr qr t]„m pš"† q q}† w “ …7w † r m t lqu t pÀp t …7lŽŠ £† q o Ž l7u p † p o Žš/o † q …7p o Ao lr q | X y r ~7m q&m q q …7o y‚ – – ‚7|
¹ ‰ ‹ ºš/t ~7p +’ 7y°S† sw t pA£€D|^}&”z&„°„²p o “ t AAo lŽo Ž?n † w …7o q t u&r ~7o4u …7lŽ7† Ao lr † w&{7~s7q m “ † w“ t l7Š
q r † lr q ,=‰ ž ž Œ7| y‚ – – –  ‚ ,  ƒ7‰ ¿ ‹ž ƒ| „w q ti† n † m w † ¯7w o¦t l7w m l7o u p t  €& ° ,
~r r &{ , ¸ ¸ {7~s7q m “ q | l7m q r | x t n¸ “ …7…V¸ }t lq r † lr q ¸ m lŽo ‡V| ~r Aw |
¹ ‰ ƒ ºš/o m o pD„|A°~7o4±S °Š °tt w q]Š&†/“ t A{7p o ~7o lq m n o q o rDt u† …7‡m w m † p s{7p t x p †  q&u t p]p …7l7l7m l7x;±S °
‰ | – ž o]† lŽ"±S °&‚7yV‰ ž ž ‹ ¿‚ – –7‰ |S¾w o “ r p t l7m “D† “ “ o q q ,
~r r &{ , ¸ ¸ &&D| …7t D| o Ž…| † …V¸ † p lŽr ¸ q u r tt w q | ~r /|
¹ ‰ ˆ ºAÀt w Ž † l?„|™o {t p rAt u&r ~7o/±° ™ p o r p m o n † wm lr o p “ t A{† p m q t l?t u&r ~7o/€zD7}i‰ ž ž ˆ7|"„l7l…† w
š/o o r m l7x"t u&r ~7oAm l7u p † p o Ž;t p ¤m l7x/x p t …7{;t ur ~7o4€zD7}y/k&l7m n o p q m r st uzo ln o p yzo ln o pA}&”Dy
„{7p m w‰ ž ž ˆ7|
¹ ‰  ºš/o m o pA„y°tt l^ÀD}yS™m lq w † lŽ}’SyÀt w Ž † l?„|; {o “ r p tq “ t {7m “4„&r w † qDt u&„&r Atq {7~7o p m “4š/m Š
“ p t &m lŽt qm l/r ~7oš/m Ž7Žw o l7u p † ¿™o ŽV|°o “ ~7l7m “ † w™o {t p r ™&±?p o {t p r€&t/‰ ‚ 7y o Žm q ~" lq r m Š
r …7r o]t u {† “ o’~s7q m “ q yBam p …7l†7yS‰ ž ž|
¹ ‰ Œ º™t r ~7 † l ˜ ySo r† w |/°~7o4›& °&™„]€iš/t w o “ …7w † p  {o “ r p tq “ t {7m “4z]† r † ¯† q oA† lŽ;›&„v aD¡ ›& Š
°&™„]€^„&r Atq {7~7o p m “vt p ¤7q r † r m t lV¢‰ ž ž ˆo Žm r m t l| % @ $ y€&t n"‰ ž ž Œ ˆ –¡ ƒ¢ , ˆ ˆ ƒ ¿‰ –|
¹ ‰ ž º°tt l ÀD}|’q o …Žt Š w m l7o w m q r q yw m l7o&{† p † Ao r o p q³7r r o ŽDr tw † ¯t p † r t p sD“ p tq q Š q o “ r m t lDAo † q …7p o Ao lr q |
{7p m n † r o“ t A/| y7‚ – –7‰ | ˜ m l7o w m q r q]† lŽ/Žo q “ p m {7r m t lq† p oD† n † m w † ¯7w oo w o “ r p t l7m “ † w w s"u p t 
u r &{ , ¸ ¸  † p ¤‹q …7l| . {7w | l† q †7| x t n¸ {7…7¯V¸ {q o …Žt w m l7o q |
¹ ‚ – ºDœ† p † l† q mS’S|„¯q t p {7r m t l/q {o “ r p †At u›]}±}¿‚ ‚† p t …7lŽ/Œ ‚ ž“  $D† r† r Atq {7~7o p m “D“ t lŽm r m t lq |
Q X X y‰ ž ž ‚ ‹7 ¡ ‹7¢ , ‚ ƒ7‰ ¿‚ ƒ ƒ7|
¹ ‚7‰ ºDœ† p † l† q m’Sy ˜ mD¥Sy€&o r “ ~7m l7t n?œy}~7o p …7¤…7p m„|» {o “ r p † w† ¯q t p {7r m t l^“ to “ m o lr/Ž7† r †"t l
›]}±}¿‚ ‚/† lށ± - u t pp o At r o Š q o lq m l7x;† {7{7w m “ † r m t lq | X y
‰ ž ž ‹ ƒ ‚¡ ¸ ‹7¢ ,  ‚  ¿  ‚|
¹ ‚ ‚ ºDœ† p † l† q m’Sy€&o r “ ~7m l7t n/œ|]°~7o p  † wm l7u p † p o Ž"† ¯q t p {7r m t l“ to “ m o lr q]t u}±}¿‰ ‚A† rD† r At Š
q {7~7o p m ““ t lŽm r m t lq | X y‰ ž ž ‹ ƒ7‰ ¡ ƒ¢ , ˆ  ž ¿ ˆ Œ|
¹ ‚  º™o m q m l7x o p„]™]&y t l7o qD€£yš"† r r ~7o q&v"„yV™m lq w † lŽ?}’S|A t …7r ~7o p l"~7o Am q {7~7o p o Am Žw † r m r …Žo
x p t …7lŽ¿ ¯† q o Ž]Ao † q …7p o Ao lr qt u}w ”€]” * ,Sš/o r ~7t7Ž]t u† l† w s7q m q y q o † q t l† w“ s7“ w o y† lŽ]w t l7x ¿ r o p 
r p o lŽV| ! y‰ ž ž ƒ ‰ – – , ‚ 7‰ Œ  ¿ ‚ 7‰ ž 7|
¹ ‚ ‹ º’So l7l7o p47| ! |4„]Ž7Žm q t l7Š vo q w o s y
™o † Žm l7x4š/„y‰ ž ƒ ž7| ˜ }&}&}^ƒ ž ¿7 ƒ ‹ˆ7|
4b
¹ ‚ ƒ º™t r ~7 † l ˜ ySo r† w |}…7p p o lrD…7{VŽ7† r o qDr t/r ~7o4›& °&™„]€ At w o “ …7w † p q {o “ r p tq “ t {7m “4Ž7† r † ¯† q o y
‚ – –7‰ |¾w o “ r p t l7m “D† “ “ o q q† r ,S~r r {&, ¸ ¸ &&D| ~7m r p † l| “ t /|
¹ ‚ ˆ º°t r ~/™„|„m p І lŽ4€ * Š ¯7p t† Žo l7m l7x {† p † Ao r o p qt uS&† r o pn † {t p ,ˆ – ‹r t ‚ ‚‰]“  $ | y7‚ – – – ‚ –7‰ , ‚7‰ Œ ¿‚ ‹7|
¹ ‚ º£m p ¤Dš;| }p tq q Š q o “ r m t lqVt u}w ”€]”‚&…7lŽo p†n † p m o r st u7† r Atq {7~7o p m ““ t lŽm r m t lq |z ˜ ™;zo …7r q “ ~7o
±St p q “ ~…7l7xq І lŽ4œo p q …“ ~q † lq r † w ru …7p ˜ …7u r Š…7lŽ"™&† …7Au † ~7p r r o “ ~7l7m ¤Vy”&¯o p {7u † ´Vo l7~7t u o lyÀo p Š
 † ls y?{7p m n † r o"“ t A/| y‚ – –7‰ | ˜ m l7o w m q r q/† lŽ?Žo q “ p m {7r m t lq † p o/† n † m w † ¯7w o"o w o “ r p t l7m “ † w w su p t 
u r {| Žu ŽV| Žw p | Žo ¸ {7…7¯V¸ q {o “ r p tq “ t {7m “ Ž7† r † ¯† q o ¸ }w ”€]”‚¸A¡ “ p tq q Š q o “ r m t lq ¢† lŽ
u r {| Žu ŽV| Žw p | Žo ¸ {7…7¯V¸ q {o “ r p tq “ t {7m “ Ž7† r † ¯† q o ¸ t u { p o {t p r x o p  † lV¸A¡ Ž7† r †Žo q “ p m {7r m t lV¢ |
¹ ‚ Œ ºAÀp m Ar ~z&v°]y t l7o q]€£yš"† r r ~7o q&v"„| lr o p ~7o Am q {7~7o p m “Ap † r m t4† lŽ"† l7l…† w“ s7“ w oAt u“ † p Š
¯t lswq …7w ³Žo4¡ ”]}&7¢&r t r † w“ t w …7Alq]u p t ²x p t …7lŽ¿ ¯† q o Ž"±° ™¦q {o “ r p †7| ! y‰ ž ž Œ ‰ –  , Œ ‹ ‹7 ¿Œ ‹ƒ ‹|
¹ ‚ ž º™m lq w † lŽ^}’Syš/o m o p„yÀp m Ar ~?z&v°]yS}~7m t … ˜ |/Àp t …7lŽŠ ¯† q o ŽAo † q …7p o Ao lr q]t ur p t {t Š
q {7~7o p m “}&”DyV}‚ ›ˆ7y7† lŽ4›]}€u p t i† …q r p † w m †A† r ‹  Ž…7p m l7x"‰ ž ž Š ‰ ž ž Œ7| ! y‚ – –7‰ ‰ – ˆ , ‚ – ž7‰  ¿ ‚ – ž ‚ ‹|
¹  – º’So r o p q t l/z]£yš"† p x m r † l š;y7o Žm r t p q | X ! ! ! , ! + |€&„D „y7v;† q ~7m l7x r t l/zD}y‰ ž ž ƒ7|
¹ 7‰ º™&† lŽo wv 7yv…;±yV™…q q o w w š;yS¥V† t7Žl
s š;yV€† q ~ 7| % , E E 0, + ! |;„]À]k²š/t l7t x p † {7~
‰ ‚ 7|„Ao p m “ † lÀo t {7~s7q m “ † w&k&l7m t ly‚ – – –7|"¾w o “ r p t l7m “/† “ “ o q qr t"›&„ ˜ ”¾ t ¯q o p n † r m t lqA† lŽ
l…7Ao p t …qp o u o p o l“ o q† p oD† n † m w † ¯7w oA† r~r r &{ , ¸ ¸ ~† w to Ž7† r †7| w † p “ | l† q †7| x t n¸|
¹  ‚ º£p t &l¦° ˜ yDÀ…7lq t l¦š"™]yD}~† l7x^„ |'„°&š”] ˜ o n o w ‚œo p q m t l ‚^zo q “ p m {7r m t l|6°o “ ~7Š
l7m “ † w™o {t p r/° ˜ £Š ž ƒ Š –7‰ y€&„D „y&š"† s‰ ž ž ƒ7|¦±7…7p r ~7o p4m l7u t p  † r m t l^m q/† n † m w † ¯7w o;t l7w m l7o;† r
~r r &{ , ¸ ¸ m q m q | Žw p | Žo ¸ u r {V¸ † r Atq ¸ † r Atq ¸ n o p q m t l‚¸|
¹   ºA¥t ¯o “ ¤Aš/œ| X + ! |S}† ¯7p m Žx ok&l7m n o p q m r s ’p o q qkay
}† ¯7p m Žx o y‚ lŽ o Žm r m t lyS‰ ž ž –7|
¹  ‹ ºš/o m o p]„| ! ! &, ! , % E + ! , + E ) , yn t w …7Ao"‚  ˆ
t u X |„w u p o Ž¿ vo x o l7o p ¿ lq r m r …7r o y£p o Ao p ~† n o lyS‰ ž ž| 7€ –7‰  ˆ Š
ƒ – ‚|
¹  ƒ º°tt l"ÀD}+| ’ ˜ ’† q † Žo l†7y7{7p m n † r o“ t A…7l7m “ † r m t ly7„…7x4‚ – –7‰ |Sq o o† w q t
~r r &{ , ¸ ¸  † p ¤‹q …7l| . {7w | l† q †7| x t n¸ ‹ Š ¯† w w tt l| ~r Aw |
¹  ˆ ºA}w m  † r o&š/t l7m r t p m l7x]† lŽzm † x l7tq r m “ q ˜ † ¯t p † r t p sD …7A † p sD™o {t p r€&t]‚ ‹‰ ž ž ˆ Š ‰ ž ž| }š"z ˜
™o {t p r]‚ ‹y7k] zo {7r&t u}t AAo p “ o y€]”„„y† lŽ4¾ln4™o q ˜ † ¯y£t …7w Žo pD}&”Dyzo “A‰ ž ž Œ7|
¹  º°tt lÀD}y £w † nm o p Š ±y  o l£y zp t …7m l£ 7| „&r Atq {7~7o p m “}&”]}w * Ao † q …7p o Ž]¯s]q t w † pt7“ “ …7w r † r m t l
q {o “ r p t Ao r p s | X y7‚ – –7‰ ‚ Œ , ‚ Œ  ƒ ¿‚ Œ  Œ7|
¹  Œ ºš"† ~7m o …¾&yzo At …7w m l’Syzo w ¯t …7m w w o ˜ yV™t w † lŽ"Ày™m lq w † lŽ;}’SyV¥V† lŽo p]™]|œo p r m “ † w“ t w …7Al
† ¯7…7lŽ7† l“ o qDt u&›]}€ Žo Ž…“ o Ž;u p t •x p t …7lŽŠ ¯† q o Žm l7u p † p o Žq t w † pq {o “ r p † , ˜ t l7x Š r o p ·r p o lŽ
† lŽ n † p m † ¯7m w m r s | ! ! y‰ ž ž ƒ , ‚ – , ‚ ž ž ¿7‰ –|
¹  ž º€&t w r Àyo r&† w | r p † r tq {7~7o p m “›£p“ t l“ o lr p † r m t l {7p t ³7w o]t ¯7r † m l7o Ž u p t  u † p Š m l7u p † p o Ž o Am q q m t l
q {o “ r p tq “ t {s | X yV‰ ž ž ‚ ‹ , ‚ Œ7‰ ¿ ‚ Œ ‹|
¹ ‹– ºa]† s o 7yVzt …7x w † q&„]™]y † “ ¤ † l}›DyV r t w † p q ¤mS™yS¥V† lŽo p]™]yV™t w † lŽÀ|&°t Š zm Ao lq m t l† w
š/t7Žo w}† w “ …7w † r m t lAt u±Sw …7t p m l7o ¿7}t lr † m l7m l7x™o q o p n t m p {o “ m o qm lr ~7o r p † r tq {7~7o p o | ! yV‰ ž ž7‰ ž ˆ , ‰ ‚ Œ ˆ ƒ ¿7‰ ‚ Œ Œ7‰ |
¹ ‹‰ ºD„lŽp o † o°v¦y&}…7r r o p/À„y›&…q q † m l»€Dy™&† Žu t p ŽŠ al7to p s 7y„lŽp † oš”D| ›&s7Žp t x o l …7w Š
³Žo/† lŽ;™&† Žt l?m l† lŽt n o pDr ~7o vo q r o p l?€&t p r ~;„&r w † lr m “ | ! y
‰ ž ž7‰ ž ˆ , ‰ Œ ƒ  ¿‰ Œ ˆ –7|
7
8
¹ ‹‚ ºa]† l† ¤m Žt …/š;y m l7x ~/›£y7œ† w o lr m l a]š;y}p …7r o l/’+7|„¦°t Š zm Ao lq m t l† wS r …Žs t uS¾r ~† l7o
† lŽ4’p t {† l7oD”&‡m Ž7† r m t l/m l4r ~7oD°p t {tq {7~7o p o | @ ! yV‰ ž ž7‰ ž ˆ, ‰ ƒ  ž ƒ ¿
‰ ƒ ‹‰ 7|
¹ ‹ ºat …7p r m Žm qayS£t p “ ~7o p q]™]y±† ¯7m † l’S|zm q r p m ¯7…7r m t l;t uš/o r ~sw£p t Am Žom lr ~7o4 r p † r tq {7~7o p o |
X yV‰ ž ž Œ ‚ ƒ , ƒ – ƒ ¿ƒ – Œ7|
¹ ‹ ‹ ºA}t ‡™„y£w tq qDv 7y t l7o q™ ˜ y™t &w o s;z]š;|"”& ”²† lŽr ~7o „r Atq {7~7o p m “4}s7“ w o4t u t7Žm l7o |
X yV‰ ž ž ž ‚ ˆ , ‰ Œ ƒ ¿7‰ Œ ˆ –7|
¹ ‹ƒ º™m lq w † lŽ}’Sy£t …7x ~7l7o p4™&¾&y ˜ † p q o l }y r t ¤ o q À]š;y£p † …7w r v¦|zm …7p l† w&œ]† p m † r m t lqt u
„r Atq {7~7o p m “€&m r p m “ ”&‡m Žo ,Àp t …7lŽŠ ¯† q o Ž/ l7u p † p o ށ {o “ r p tq “ t {7m “Aš/o † q …7p o Ao lr q† lŽ/r ~7o m p
lr o p {7p o † r m t lA&m r ~4°m Ao Š Žo {o lŽo lr’~7t r t7“ ~7o Am “ † wVš/t7Žo w}† w “ …7w † r m t lq | ! y‰ ž Œ ‹ Œ ž , ž ˆ7‰  ¿ž ˆ ‚ ‚7|
8 1 "%&%-4
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€&o r t p ¤Au t p&r ~7oDzo r o “ r m t l4t u r p † r tq {7~7o p m “D}~† l7x o y
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~r r {&, ¸ ¸ &&D| lŽ7q “ | l“ o {| l7t† †7| x t n¸
€&t l7w m l7o † pAw o † q rq ¼ …† p o qD³7r r m l7x/{7p t x p † ·u t pDx p t …7lŽŠ ¯† q o Ž;q t w † p±° ™ q {o “ r p †7yS¯s
}| ’S|S™m lq w † lŽVy ˜ „]™&}|¡ „w w t qq “ † w m l7x;t u†/x m n o l?q o rAt u&† Š {7p m t p mœ]š"™ {7p t ³7w o q y¯7…7rl7t r
{7p t ³7w oDp o r p m o n † w | ¢
m q]¯o m l7x . t m lr w s;Žo n o w t {7{o ޝs"r ~7o4±S °i‰A“ p o † r t p q]† lŽ€& v"„ ˜ † …Žo p | °~7o “ t l“ o {7r
x to qD…“ ~?u …7p r ~7o pr ~7t …7x ~y† qm rm q{7p m  † p m w s†"{7p t ³7w o4p o r p m o n † w&{7p t x p † /|"›&t o n o p yr ~7o
At7Žo wV† r Atq {7~7o p o&…q o ŽAm l4r ~7o]±S °&‚Dp o r p m o n † wm q{7p t nm Žo ŽAr ~7p t …7x ~4±S °¿±7}„°&š²m l4r ~7o
q † Ao]&† s † qu t p±S ° ‰ |
§  t w † p]¥o l7m r ~/„l7x w o yr s{7m “ † w w s4x m n o l/m l"Žo x p o o q |
§ °t r † wS}t w …7Al/„At …7lr¡ m l ! ( $* ¢
+œt w …7Aoš/m ‡m l7x4™&† r m t
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