HAL Id: inria-00070475
https://hal.inria.fr/inria-00070475
Submitted on 19 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Algebraic Immunities of functions over finite fields
Gwénolé Ars, Jean-Charles Faugère
To cite this version:
Gwénolé Ars, Jean-Charles Faugère. Algebraic Immunities of functions over finite fields. [Research Report] RR-5532, INRIA. 2005, pp.17. �inria-00070475�
ISRN INRIA/RR--5532--FR+ENG
a p p o r t
d e r e c h e r c h e
Thème SYM
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Algebraic Immunities of functions over finite fields
Gwénolé Ars — Jean-Charles Faugère
N° 5532
Mars 2005
-).0/213546/879;:=<?>@
ACBED 1FG0H D 9;4B :=I DCJK5L 9 BEMN
OPRQSUTWVEXZY\[]V_^a`cbdQeS0T;`f`d^EShgji2kmlonEpqTe`
rtsuiwvxTbu`fVay{zVay
|f}w~q~CisdbfaTsuTePqTesuPqT5 28[]Y8}su`f2[?W~R}T;`
=e"q yTRTs}wkS}wbdPqTeSU}wbdlo}kaTRqlmbdli is} pqRbdli sdi2S¢¡£¤¦¥w§x¨)bui¡£¤¦¥w§x©bdi
suTe`dlo`xbbdisd^_~ab}wR}km^Ebdlo}"bdbu}ªa`lo`aT«2Tki~CTe¬®bf2TqTesu}kml¯TZbuPqTaTjql°bulmi2)iwy&km2Tgqs}wloZ±SUSWpa²
Rl°bx^ isVEbusdT;}wS³´l~qPqTs{bdi}w_^RqlmbdThRTko}R}k`di=µ¶ki_ª³´l~qPqTese¬OPqlo`Z}km2Tgqs}wlolSUSWpqqlmbx^
isusdT;`c~Cij·bdi·TenEpR}"bulmi2R`h¸l°buP¹ki"¸ºkmT;}alq8buTsuS»}eisalq}¼SUiqi2S0lo}wk¶isaTesdlqR¬·½·T2lm«2T
~Rsdi2~jTescbulmT;`iwbuPql`0yfkTegqs}wloU±S0Shpqqlmbx^¾}wR¾}k`di8i2S0~RpabdTT¿a~qkll°bU}wR¾}2`c^_SU~abdibdlogCipqRR`¬
½·TT¿_buTRaT;ÀbuPqTaTRqlmbdliR`iy&km2Tgqs}wloZ±S0Shpqqlmbx^bdiU pRR*bulmi2R`¸lmbdP)SUTSUisu^gqpabbuPqT^aT²
~CTjWi2bdPRT´_pqShgjTesiCiR`dTepabdl«T´ipabu~qpabu`¸¶T´ki_iª}wbe¬½·T`cPRi"¸ÁbdPR}wb}kmkEbuPqTsdT;`cpqkmbu`igqbu}wlqT;
i2stSUTSUisu^_kmT;`d` pRR*bulmi2l«Tf`dlmSUlk}sdk^suTe`dpqk°b`iUSUTSUi2sd^W pqR*bulmi2R`tg_^0}PR}wq2Tiw5«"}wsul}gqkmT;`¬
y&R=bdPqTeÃÂq¸¶T{~qsui"«T&bdPR}wbeÂa i2s}WSUTSUi2sd^U pqj*bdli¸l°buPSUTSUi2sd^À`dlm¯eTkÃ}wRiqk^iRT{i2pabd~qpqbeÂ
lmtbuPqTsuThlo`Zqi=suTko}"bulmi28¸PqloPqibqT~CTR¼i8SUTeS0i2sd^ i2sZkiR`dTepabdl«Thipabu~qpabeÂ5buPR}w¼¸´T0}
iR`cbdsupRb}Z~Cik^ERiSUl}k_bdPR}wbTRTs}"bdT}wkkasuTko}"bdlij`¸lmbdPRipabtSUTSUi2sdlTe`e¬½·Tf}w~q~Rkm^buPqlo`bdPqTeisuTS
bui0bdPqT`dpqSUS}"bdliTeqTs}"buis}wjiSU~qpabuTT¿a~qkll°bukm^=bdPqTyfkTegqs}wlo{±SUShpqqlmbx^¬
ÄÆÅEÇ5ÈuÉWÊ "Ë y&km2Tgqs}wloy¶bcb}ªa`ÂRV_bdsuTe}wS¢³´lm~qPRTs`Âqµ¶ki_³´l~qPqTesu`eÂqyfkTegqsu}lZ±SUSWpRql°bx^
ÌtÍ_Î ÏCÐÑÒÓÔÕÏjÖ×ÔÕØ?ÙÚÛxܦݦÙÞ6ßtàÃÛxØ?Ø?ÛxÝtá
â
ÏjÜäãå¦Û±ÞæeÓÍaæeÓ
ç
Í_Î ÏCÐÔuÍqèàÃÎéÓ¾×êàæ?ÔÕÏCÖ×ÃÔuÎ êàÃÎéÓ
ë
æeì"íÜäÛcîïmããÞØ;ãÞ6Û
pqqTaTjql°bulmi2=S}"buPS}wbdlon2pRT{esu}kmT&qT{ko}se`dl`cbu}RTZpqqT{ iRbdli=RqlTZ`dpqs
¡£¤¦¥w§¨ q}R`¡£¤¦¥w§ © ko}fsu^_~abu}R}wk^a`cTt}kmgqsulon2pRTTe`cb«2Tki~q~¬tkkmT´s}wkl`dTk}&RRl°bulmi2
yfkgqs}wlo±SUSWpqRl°bx^{aT;`¶PRl5sdTeSUTEbu`#~R}ws Riwb buipabi2sd~R`tRql5Tb}wpj`d`dlj}pPql!CsuTSUTe2b¶~R}ws
gRkmia`e¬t³´TbcbuTlmSUSWpRql°bf}wkegqsdlonEpqTisusuTe`d~ji2RW}pa¿"enEpR}wbdliR`aT~qkpR`~CTbul°bbuTsuSUTqTb$#buTf`cTekmi2
pR·Tsdbu}wl8i2suasuT0S0i2qiSUlo}wk6¬%fi2pR`aiRqiR`ZaT;`~qsdi2~qsul!b$e`ZaTTbcbuThlSUSWpqqlmb$À}kmgqsulon2pRTWTb
RipR`U}kpqkiR`0}wpR`u`dl¶aT;`0gji2sdqT;`0T¿a~qkll°buTe`0TbÀ}`d^_SU~abdibdlon2pRTe`e¬&%fipj`'bdTeRaij`hko}·RRl°bulmi2
(lSUSWpqqlmb$}wpq¿0 i2R*bulmi2R`¶}?«TefS)eSUilsdT{SU}l`´TkkT{e~jTeR=apqiShgqsuT&aT`ci2scbulmT;`#i2R`$epqbdl«Te`
sE}wsT;`¬*%fi2pR`SUiEbusdi2R`nEpqTbuipR`WkmT;`se`dpqk°b}"b`igabuT_pqT;`W`dpqsWkTe` i2R*bulmi2R`W`u}wj`S+SUilsuT
lRapRl`dTEb&aT;`s$;`cpRk°b}"bu``dlS0lko}wlsdT;`~R}ws&`dlS0~RkmTPR}qTeSUTEbkmle}lmsuTaTe`f«?}kmTepqs`)TbfS)¬,tqRÃÂ
RipR`´SUiEbdsuiR`´nEpqT{~CipRs´pqRT& i2R*bulmi2=}?«T;pqqTZS+SUilsdTZaTfb}wlkmkTZkCTb#buTkkmTnEpqT{S.-h2ÂE`dljRipR`
/}?«2iR`Z~R}2`ZqTsdTek}wbdli·qT~CTRR}wEb~R}`qT0ko}S+SUilsdTU~Cipqsk´`ci2scbulmT;`ZiR`$epabdl«T;`Â}wkis`
RipR`~CipR«ij`ij`xbusdpqlsuTZpRÆ~ji2km^_02S0TnEpqlTq2TRasuTZbdi2pabdT;`fkTe`suTko}"bulmi2R``d}R`S+SUilsuTaTk}
i2R*bulmi2=~CipqspR~qkpR`2su}Rqi2SWgqsuTZqT`disdbdlTe`e¬1%fipj`´pqbdlkmlo`ci2R`TbcbuTZ~Rsdi2~qsdl2b{~CipRse}wkopqkTs
T¿a~qkmlolmbdTeSUTEbdk3lSUSWpqRl°b}wkgRsdlonEpqTZqT54c`dpqSUS}"bdliTeqTs}"buis6
7 Ê ; È 8 ! }"bdbu}2n2pRT)}kmgqsulon2pRT´PRl5sdTeSUTEbÀ~R}ws+jiwbeÂPql!CsuTSUTe2b~R}sgqki_e`¶lS0Shpqqlmb$
}kmgqsulon2pRTÂ_gR}`dTaT"9Zs:gqqTes
Ch ,#
y&km2Tgqs}wlo}"bdbu}2ª_`&}wsuTW}wSUiRUbdPqThS0iE`xb{T ÀlTEb{}wbcbu}2ªa` is&~qpqgqklWªTe^sd^_~abui2`d^_`cbdTeS`ÂqgRkmiaª
lm~RPqTs`}wRU`cbdsuTe}S l~qPqTesu`e¬OPRT^busd^WbdisuTei"«2Ts}`cT;suTbªTe^g_^h`dik«_lmq}`d^_`cbdTeS i5}km2Tgqs}wlo
T;nEpR}"bulmi2R`¬0yfkTegqsu}l0}"bdbu}2ª_`Z¸¶TsuT0Rsu`cb}w~q~qklTebdiÆY8}"b`cpRS0ibdi²6±S}wlrtpRgqkmlo! T^·VaPqTSUTUl
"
e#g_^%$2}2nEpqT;`r}"bu}sdlìZyfkTgRsu}l}wbcb}ªa`¸¶TsuTW}wko`ci}w~q~qklTe)bui=gqkiaªlm~qPRTs`&l
"
#®ÂC¸PRTsuT
buPqTi2SU~qkmT¿al°bx^ i2sf}"bdbu}ª_lqUy ´V}wj)VaTsu~jTe2b¸}`Te«?}kmpj}"bdT;¬
&RisVEbdsuTe}S ³´l~qPqTeseÂjbdPRThS}wlsd^_~abuis}w~RPqlsdlmbdTesdlo}pR`dTeÆ is&gCi_ikTe}Æ pqRbdliPj}Æ~qsuT²
«_lipR`dk^ÆgjTeT¾}Pqlm2P·}km2Tgqs}wlo0aT2sdTeTWbui)ipqEbuTsµ¶TsukmTeª"}wSU~a²±Y8}`u`cTe^Æ}wkisulmbdPqS)¬W±
"'
#®ÂÃlmbl`
qTSUiR`cbds}"buTebdPR}wbki"¸ qTsuTT¶suTko}"bdlij`T¿al`cbe¬OPqTe`dT¶sdTek}wbdliR``dlmSU~qkl° ^WbdPqTy&km2Tgqs}wlo´}wbcb}ªa`¬
Vaih}W`dlqlmj}Eb¶`cbdT~l`´buiRRÀ pqRbdlisdT;`clo`xb}wEb´}2}wlR`cb#buPqTe`dT{}wbcbu}2ªa`¬±
"
;#®Â_bdPRT{qibdliÀi
y&km2Tgqs}wlo{±S0Shpqqlmbx^À i2sgji_ikTe}= pRR*bulmi2 suiS)(¶¨*=bdi!(
*
lo`lmEbusdiaapRTe¬
V_i2SUTÀsdTek}wbdliR`¸lmbdP¾ki"¸ aT2sdTeTU}k`di)T¿alo`xbWl µ¶kmiaª·³´l~qPqTeseÂ}wjbuii2R`cbdsupR*bbuPqT~ji2km^E²
RiSUl}k`d^a`xbuTS aTjqTegE^bdPRT0µ¶ki_ª8³´l~qPqTs;ÂC¸´ThpR`cTWbdPqlo`{TenEpR}"bulmi2ì&½·TU}w8}k`diÀT¿EbuTR8bdPqT
}km2Tgqs}wlof±SUShpqqlmbx^ÀbdiÀµ¶kiaª³´lm~qPRTs`¬
OPqTRs`xbhigavxT;*bdl«TiwbuPql`0~R}~jTesWlo`bui2TqTesu}kml¯TbuPqTqiwbulmi2¾iw{y&km2Tgqs}wlo±SUSWpqRl°bx^·bdi
pRR*bulmi2i"«Tst}_^RqlmbdTfRTkoq`+(-,}R0¸´T&l«Tbx¸¶iaTRRl°bulmi2R`tyfkTegqs}wlo±S0Shpqqlmbx^W i2s´VEbusdT;}wS
³´l~qPqTes}wRyfkTgRsu}l&lmSUSWpRql°bx^À isµ´kiaª³´lm~RPqTsaTeqiwbuTeÀsuTe`d~CTe*bulm«2Tk^!.0/21¤3§¶}R4./ 5{¤63§*¬
&lsu`cbe¸¶TÀ`cPqi"¸ buPR}"bbuPqTe`dTbx¸¶iÆqiwbulmi2R`}sdTklmRªTe·bui 9Zs:gqqTesgR}2`clo` is0}Æ`c~CTel°CisaTs
i2SUi2qiSUlo}wko`Â_buPqT87{|&zÁisaTs i2s9.0/ 5Z¤3§}RÀbuPqT tklmSUlR}"bulmi2ÆisaTs¶ i2s9.0/21¤3§¬t½·T~qsdi"«2T
buPR}"bhbdPqTaTjql°bulmi2¹i&}) pqRbdli¹i"«2Tsjql°buTÀRTekR`W2lm«2TÀlmSUSUTeql}wbdTk^¾} 9Zs:gqRTsWgj}`dl` ish}
kT¿aloi2s}w~qPqloi2suaTese¬;:&}?«_lq{} 9Zs:gqqTesgj}`dl`PqTekm~0pR`bdiZRRh~qsui~CTsdbdlTe`iWbdPqTloaTe}k_TRTs}"bdT;
g_^bdPqlo`gR}2`clo`¬ÀOPRTe`dT~qsdi2~jTescbulmT;`l«TUgCipqRR`i·bdPRTÀqiwbulmi2¼iy&km2Tgqs}wlo0±SUSWpqqlmbdlTe`e¬OPRl`
gCipRR)}wsuT&buPqT~ji"¸¶TsibuPqTRs`xbfi_T2lmTeEbfiwbuPqT ikki"¸lmq`dTsulmT;`¶¸PqlP)lo`qTE}"bulm«2T=<
./ 5 ¤63§
,?>
@BADCFEHG
@ACIKJ
>MLN
G
@ACOJ
>L=NPLRQ
.0/M1¤63§
,?>S=N
@ACTEUG
@ACIKJ
>
G
@BADCOJ
>MLVQ
¸l°buP%3}h pqR*bulmi2 sdi2S)(¨, buiW(¶©, ¬
&Rsdi2S buPqTe`dT`dTsulmT;`¸¶TÆl«TÆT¿a~qklolmb=gji2pqRq`=i y&km2Tgqs}wlo)±SUSWpqqlmbdlTe`e¬OPqT ¸¶T`dPqi"¸
}2`c^_SU~abuiwbdlogCipqRUi2!X is+./ 5{¤63§}wjZY\[]X¬½·TfsdTeS}wsuªbdPj}"btbuPqTflRpqTeRTfi5bdPqTjTko!(^,
i24.0/25{¤63§#}RWY)[_XaTe~jTeRq`¶iqk^UibuPqT8` ¥_ÂE¸PRTsuTe}`eÂ2bdPqTaT~CTjaTRT{lo`´i¥ is^.0/21¤3§
}RaY\[cb2¬
OPqT¼`cT;ij!~R}wsdbÀl`Àbdi T¿_bdTj bdPqT;`cT8Riwbdlij`U is pRR*bulmi2R`À¸lmbdP SUTeS0i2sdlTe`e¬ ½¼T8RiwbdloT
buPR}"by&km2Tgqs}wloW±SUShpqqlmbdlTe`e}wgCTT¿_buTRaT;8buibdPqT;`cT0 pqRbdliR`gqpabaT~CTj¼i2buPqTU_pqSWgCTs
iiR`dTepabdl«Ti2pabd~Rpabu`W¸´Tki_iª¼}wbe¬½¼T=`dPqi"¸bdPR}wbh}wkkbuPqTÀsuTe`dpqk°b`igqbu}wlqT; i2sSUTSUisu^_kmT;`d`
pRR*bulmi22lm«2TZ`dlS0lko}wsukm^suTe`dpqkmbu`iSUTSUisu^U pqRbdliR`g_^=}UPR}qTZiw«"}wsul}gqkmT;`¬y&RbdPqTeÃÂa¸´T
~Rsdi"«2TWbuPR}"b; i2sW}S0TeSUisu^Æ pqRbdlid3¹¸l°buP·SUTeS0i2sd^·`cl¯Te}wR·i2qkm^¼iqTi2pabd~RpabeÂl°¶bdPRTsuTl`
RihsuTko}"bulmi2À¸PqloP=qibaTe~jTeRi=SUTeS0i2sd^U i2s+eZij`cT;pabulm«2T{i2pabd~qpqbeÂ_bdPj}w=¸¶T}wi2R`xbusdpj*b¶}
~Cik^_qiSUlo}wkCbdPj}"bfTeqTs}"buTZ}kmksuTko}"bulmi2R`¶¸l°buPqipqbfS0TeSUisulmT;`¬½¼Te}w)}w~q~Rkm^buPqTbdPRTisuTS buiUbdPqT
`dpqSUS}"bulmi22TqTesu}wbdi2sf}wR)¸¶Ti2S0~RpabdTT¿a~qkmlolmbdk^f.0/21¤3§ is&`diSUT«"}wkpqTigXÂjl°bi2sdsuTe`d~ji2R
buiZX i2s-Xihkjq¬
V_T;*bulmi2·~RsdT;`cTe2b`buPqT0qTRqlmbdli¼iw#y&km2Tgqs}wlolSUSWpqqlmbdlTe`& isZSUTSUisu^_kmT;`d`f pqRbdliR`}wj
`diSUTh~qsdi2~jTescbulmT;`¬V_T;*bdli¼=aTe«iwbuTe)bui=buPqTUiSU~qpqbu}"bulmi28iw´T¿a~qkll°b}wR¼}`d^ESU~abuiwbulWgji2pqRq`
iy&km2Tgqs}wloZ±S0ShpqqlmbdlTe`e¬tyfR)`dTebdli 2TqTesu}kml¯T{bdPRTe`dTqiwbulmi2R`¶bdi0 pqRbdli)¸lmbdP)SUTSUisu^¬
')$ !¢ \
"!#!#$&%('*)+!# ,!-
zTb ( ,/.0214365 [_( ,7.8 @ 1:9;9:9:1<8
¨
1>=
@
1:9;9:9:1>=
© 5 gCT#}¶~Cik^ERiSUl}kwsulmq¸lmbdP«"}sdlo}wgqkTe` 8 @ 1;9:9:9;18
¨
1<=
@
1;9:9:9;1<=
©
i"«2Ts}hRqlmbdTRTekf( , ¸l°buPÆ}wsalR}wk¥_¬
&Ris{}ÀS0i2qiSUlo}wk 0@?A3B [ 8 ? Q
@DC:C;C 8E?
>
¨ = B Q
@FC:C;C
=GB
N
©
ÂH°¤JI 1<K §:HML[ON
¨PRQ
@ I PTS
N ©
U Q @ K U
lo`&e}wkkmT;
buPqT
WV YX=
i&buPql`USUi2qiSUlo}wk6Â#aTRiwbdT;[Z\:]5¤0@?M3B §h}RHI^HL[_N
¨PRQ
@ I PS
N ©U Q @ K U l`
e}wkkmT;ÀbuPqT+` 6X KB ibuPql`fS0i2qiSUlo}wk6ÂqaTRiwbdT;@Z\:]5¤
0@?M3B*1<0
§¬±bdPqT i2kmki"¸lmRRÂEbdPqT`dTb
i}wkkjSUi2qiSUlo}wko`#lÀ«"}wsul}gqkTe` 8 @ 1;9:9;9:18
¨
1<=
@
1;9:9;9:1<=
©
l`¶aTeqiwbuTeg_^ba ¤0c13 §*Âais`dlmSU~qk^UgE^ba ¬
±buPqTZbdPqTeisu^Àiw 9Zs$:2gqqTes¶gj}`dTe`eÂa¸´TqTeTebdii2R`dlaTesf} dV EV6V<X Vbe*x¬
"f
#hg*¬
O¸´i&iwq`cpjPisaTsulmRl`ÃbdPqT X KB^ji 2 >kVK=K `ml BEV<X e7{|fzg}RZbdPRT 6nV
V <X=2 aTRRTe)}`¶ i2kmki"¸f`2<
oÅqprs säÊErutTvJw xV ¤JI 1<K §+[ ¤nI
@
1:9;9:9;1I ¨ 1K
@
1:9;9:9:1<K
© § EX ¤JIxy1<K yé§{z}|¨/~é@ 2
0 ? 3 B *T 0 ?G3 B
Hm¤nI 1K §;H*H°¤JI y1<K y§:H
V
H°¤JI 1<K §:H [DHm¤nI y1K y§:H EX%
l
Z l
JV
EV >V42n6V l
i B2WV
¤nI 1K § E
¤JIxy1K y§^zf¨/~©
DR6i
*T Xn+DX!l +--(V<X Vi=2 .0214365
0@?M36B - 0@? 3B 0}? *T 0@? V 0@? [ *T 0@? EX 36B *T 3B
-
X=J >XW
l
+¡^ 6nVV<X Vi=2 .05W1;.¢365
OPqTesdT}sdTS}w_^ÀibdPqTesS0i2qiSUlo}wki2suaTesdlqE`¬
y qi2q¯Tesdih~ji2km^_qi2S0lo}wkA£lm¤ .05 lo`´¸sulmbcbdTe}2`,£[ N
?¥BY¦
?¥B
0@?A3B Â ¦
?¥Bc§
[¨q¬½·TZpj`cT{bdPqT
i2kmki"¸lqhRiwbu}wbdliR`M<
©W¤h£a§ [ª
¦
?¥B
0@?M36B H¦
?«¥B §
[u¨¬ <bdPqT`dTb´i
2
iT£U}R®a ¤h£a§ [ 0@?E36B H ¦
?«¥B §
[(¨¬<bdPqT
`dTbi
VMV¢
iwx£
½·TqTqibdTÀbuPqT
XV 2
ÂbuPqT
BGXV VMJ¯k22n
}wR¾bdPqT
BGXV
¸l°buP¹suTe`d~jT;*bh}
i2suqTs°Âag_^@±³²¹¤£q§*±´Z¤h£a§}R}±«µ¤£q§¶sdT;`c~CTebdl«Tk^¬
e
&qisT;}P)aTjql°bulmi2ÃÂR`dTT
"f
#®¬g
OPqTloaT;}wklf(-, .0c135 TeqTs}"buTeÀg_^=}`dpqgR`dTbf£l`qTqibdTeg_^c¶¦£¸·*¬
¹&RaTsfbdPqT}gji"«2T{qibu}wbdliÃÂq}»º <¼=2D2 B l`aTRqT;}2`¶ ikkmi"¸f`e¬
oÅqprs säÊErutTvt P a Bl # 2V 0 VMVTV (^,
.0c135½
l "xkVXV>X=2Rq^¾
nj2 ¡ [¿ª:£
@
1;9:9;9:1£ © ¬ V8 nXBÀ 8B Xa º >¼=2D2 78
¶J±«µ¤£
@ § 1:9;9:9;1±«µ¤£
©
§·F[¿¶n±«µ¤À §· 9
&Ris}2lm«2T loaT;}wk À Â#lmbu` 9Zs:gRqTs0gR}`dlo`Wlo`UqiwbUpqqlonEpqT¬ µ´pqb0buPqT KXnBX º >¼=2D2fB Â
¸PRlPl`&aTRRTe)}`¶ i2kmki"¸f`Â_lo`pqqlonEpqTk^=aTbdTesdSUlqTe¬
oÅqprs
säÊErutTv º
<¼ 4B7B
¡\[ ª 3 @
1;9:9;9 3 © ¬
V W dnX=B mÀ 4BX%>X nB>X
º
>¼=2D2
B7B jV%
#±´Z¤63
P
§W[ b
EX n dV EV #V
3 P
MVX iM2i2 n 2 !2nV
±x² ¤ä¡ª 3 P
¬?§
Ê#Ê s säÊEr(tTvJw
P
/
B anX MV
( ,/.8 @ 1:9:9;9:1<8
¨ 5 MX
¤@z ªb 1;9:9;9j1X6¬
++Z
¡ º
<¼=:
ZBV
/
jVZ
l
¡ D nV [V>X=2
.8 @
1:9;9:9:1<8 5 .8
~ @ 1:9;9:9j1<8
¨
5
V
l
>k>V=K
`ml B
V <X=2G
l ¡a(-, .8
~ @ 1:9:9;9j18
¨ 5
8
º
<¼=2D2 BV
/4(-, .8
~ @ 1;9:9;9:18
¨ 5
V_i0lm¸´TZ¸}wEb#buiWRj}W~ji2km^_qi2S0lo}wk5aTe~jTeRalqUi=`dT«2Ts}wko`t«"}wsul}gqkTe` 8
~ @ 1:9;9:9;18
¨
Âa¸¶Ttvxpj`xb
RTTe=bdiÀiSU~qpabuT} 9Zs$:2gqqTsgR}2`clo`¸lmbdP)iqTibuPqTe`dTisaTs`¬
J ' "!#!# '³
zTbfi2R`dlaTesf}h pqR*bulmi2 32L$#
(¨
,&%
(©
,
0('% 3
ÂjaTqibdT;}2`
= @ [ 3 @ ¤0 § 1;9:9;9;1>=
© [ 3 © ¤0 §*¬
)
pqsi2gavxTebdl«T)lo`Ubdi `cbdpRq^ }wkTegqs}wlo=T;n2pj}"bdlij`UlmRqpRT; g_^¾buPqT82su}~qP¹i 3 ¸PqloP lo`Ubdi
`dikpabulmi2R`fi28bdPRTRTeki(^,W}wR8qiwbi (-,?ÂCbuPqT0}km2Tgqs}wlokmiE`cpqsuTi+(^,w¬ZOi=suTe`cbdsulo*b&buPqTU`xbupRa^
iTenEpR}"bulmi2bdi4(-,?ÂC¸´T}2qRTek)T;n2pj}"bdlij`
8 ,P E 8 P
Â5aTRiwbdT;Æ}`buPqTW`dTb
0 , E 0
}wjÆij`cloaTs
TekmTeSUTEbu`ibuPqTlqTe}wk
À [ ¶= @ E 3 @ ¤0 § 1;9:9:91<=
© E 3 © ¤0 § 1<0
, E 0 · 9
± `d^_S0SUTbdsul)su^_~abdi2s}w~qP_^2ÂbdPqTesdTÆlo`Ubx¸¶iÁlmSU~Cisdbu}wEb=}~q~qkle}"bdlij`2<VEbusdT;}wS ³´l~qPqTes=}wj
µ¶kiaª³´lm~qPRTs;¬
* +
, -.0/2121213/0-4
5
.6/121216/
57
* +
8 9:9;9
9:9;9
5
.6/21211/
57
-.6/21211/0-4 1121
<>=@?A:BDC EGFHIJA:? KMLNPOQRESFHIAT?
) ÁVEbdsuTe}S³´lm~qPRTs;ÂC¸¶T0pR`cTh pqRbdliR`{bui=RkmbdTesTkTSUTEbu`U¤8 @ 1:9:9;9:1<8
¨
§*¬0V_i¸PRT¸¶Thqi}
}wbcb}ªUi=bdPqlo``xbusdpj*bdpRsdT2ÂE¸¶T`cpq~R~jiE`cT;=ª_qi"¸ÀTekmTeSUTEbu`¤= @ 1:9;9:9j1>=
©
§¶}wRÀbdsu^UbdihRRsdTek}wbdliR`
i2·¤8 @ 1:9;9:9:1<8
¨
§¬t½ PqTsuTe}2`Â_lƵ´kiaª³´l~qPqTs;Âaqi2a²6klqTe}s´ pRR*bulmi2R`f}wsuTpR`dTelmj`cloaTZbdPqT~RsdiaT;`d`
buisdT;}"bdTWbdPqTUiaaT;8SUTe`u`u}wT2¬Zy~Ci2`u`clgqkTW¸}?^=bui¸sul°buTh}km2Tgqs}wloTenEpR}wbdliR`{lo`&bui=lEbdsui_qpRT;
lEbdTesdSUTeql}wbdT«"}wsul}gqkmT;`}` %¬5³´ipqsdbdi2l`¶PR}?«2TqiqTl
"
M#®¬
%&i"¸ ¸¶T¸lmkk~qsuTe`dTEbf}0qTRqlmbdli)iy&km2Tgqs}wlo&±SUShpqqlmbdlTe` i2sgjibdPÆ}2`cT;`¬
=2K
oÅqprs
säÊErutTv
P !VmBnX ®B 6nV
3 L(¶¨,
%
(©, EX@À
[ ¶= @ E 3 @ ¤0 § 1;9:9:9;1<=
© E
3 © ¤0 § 1>0
, E 0 · 9
Xn+D
RM2K n6bV 9RV g`l
.0/ 5 ¤63§ [ Y X6ªZ«\;]j¤§ 1 z À ¬ 9
RM2K n6bV DKB g`l
.0/M1¤63§ [ Y X6ªZ«\;]R¤ 1>0 § 1 z À ¬ 9
y{`¶}=loaTe}kj¸lmbdPRTek=TenEpR}"bulmi2R`tlo`¶su}2alo}wk6Â2bdPqTesdTZl`¶}wTenEpql«"}wkTRT&gCTbx¸¶TT
À
}RbuPqTZ`dTb
i`ci2kmpqbdliiw
À
¸PqlP=l`tbdPqTZs}w~qPUiP3¬Vai .0/C¤3§tl`¶}2TqTesu}kml¯e}wbdli0iwyfkTegqs}wlo±SUSWpqqlmbx^
qTRqT;lmÆ}wsdbdlokT
"
?#}wj=jsu`cblmEbdsuiaapRTelmÆ}wsdbdlokT
"'
#6¬
'«'³ ' "!#!# '³
OPRl`fqTRqlmbdli8qiET;`c/bf2lm«2TZpj`f}U¸¶}?^ÀbdiPR}?«2Ty&km2Tgqs}wloZ±SUSWpqqlmbdlTe`eÂR¸¶T}RRbdPRTS¸lmbdP
9Zs:gRqTsgR}2`clo`}ei2sualq`ci2SUT¶i2suqTs`i2US0i2qiSUlo}wko`¬½¼TfOPRl`lo`suTe`dpqSUTlm0bdPRTqT¿_bbdPRTisuTS)¬
Å_Ê Å t*vnw P ^VnX #BD2nV 3cL=(¨,
%
(©,
KXnBX
º
<¼ !B V"À jV!d--V <X=2
.0214365
>V n m DB BdV
`
V7
EV ¢
V Àn
l l
./ 5{¤63§ [(Z«\;]C¤§
c>X nB>X
º
<¼=2D2B-V xÀcjV 2D nV V <X=2-V .05W1;.¢365
V DB B
V
`
VEV
V Àn
l l
.0/M1¤63§ [uZ\:]5¤ 1<0 §
ÊÃÊT&ls`xb¶¸´TfPj}?«TfqibdloT;UbdPR}wb# i2s¶}W7{|fz¼isaTes
.0c135
}wRÀ}_^h~Cik^_qiSUlo}wk£5ÂZ«\:]5¤£q§ [
Z\:]j¤"a ¤h£a§d§}wR{ i2s}w tklmSUlR}"bulmi2isaTs .0214365 }wR}E^&~ji2km^_qi2S0lo}wkÃÂZ«\:]5¤ 1<0 § [uZ\:]5¤"a ¤j§ 1<0 §*¬
YÆi2sdTei"«Tes#bui0suTeqpRTi}0~ji2km^_qi2SUl}kM£ÀgE^}wqibdPqTesiqTÂq¸´TqTeTebdPj}"b©h¤£q§ ©W¤j§¬
y{`}kmk{~ji2km^_qi2S0lo}wk{iw À }sdTÆsuTeapjTe bui ¯Tesdi¹gE^!} 9Zs:gqRTsÀgR}2`clo`eÂbdPqT;`cT8gCiwbuP suTS}wsuªa`
~Rsdi"«2T´buPqTbuPqTi2sdTeS¬®! lo`t}~Cik^_qiSUlo}wkai À `dpRP0bdPj}"b"Z«\;]C¤§ [_./ 5Z¤3§*Â2sdT;`c~¬Z«\;]C¤ 1<0 §+[
./21¤3§Â"bdPqTe" l`suTeapjTehg_^bdPqT 9Zs:gqRTsgR}`dlo`¡ is} 7{|fzi2suaTeseÂ"suTe`d~CTe*b;¬ÃbuPqT tkmlSUlmj}"bdli
i2suqTs;Â2`dibdPRTsuT&lo`,£bzÆ¡UÂa`dpRPbdPj}"b#©W¤h£a§"°$,©W¤§¬ &qsuiS bdPqT&Rs`xbsdTeS}wsuªCÂ2¸´T{~qsui"«TbuPR}"b¡
iEbu}lmj`¶}0klmRTe}ws2TqTesu}wbdT;Àä}S0lk^=`d}wbdlo`x ^_lq0bdPqTiRql°bulmi2ibuPqTbdPqTeisuTS)¬
OPqTeÀbuPqTZqTRqlmbdliiwsuTeqpRT;9Zs:gqqTes#gR}2`clo`´lmSU~qk^UbdPR}wb´buPqTZkmlqTe}s´2TqTesu}wbdT;Uä}wSUlkm^lo`´}
klqTe}sdk^lmjaT~CTRqTEbfä}wSUlkm^2¬ %
OPqlo`#bdPqTeisuTS l«Tfpj`´}¸}?^hbdihiSU~qpabuTfbuPqT{y&km2Tgqs}wlo±SUSWpqRl°bulmT;`¬ &lRÀ}'9Zs:gRqTs´gR}`dl`
ibdPqlo`ZlqTe}wk À PR}?«TW}=gR}8bdPqTeisuTbule}wkiSU~qkT¿almbx^)gqpabl`Z«Tesd^T ÀlmTe2bl~qs}bdloT¬OPqTesdThl`
ibdPqTesSUTbdPRi_R`bdi0RRf./
1
¤3§¶~qsuTe`dTEbdT;=l "2 ' ÂÃ?#6¬
YÆi2sdTei"«TeseÂE¸´TPR}?«2T`cTe«Ts}wkC~qsui~CTsdbdlTe`}2`¶bdPqTiSU~R}wsulo`ci2=gCTbx¸¶TTbdPRl`gCiwbuP)qiwbulmi2R`¬
Ê#Ê
s
säÊEr(tTvt
P -VmBnX
3cL=(¨, '% £©
,
l 2
.0/21¤3§ hk.0/ 5Z¤3§
ÊÃÊ zÃTb&iR`dloaTs# }h~Cik^_qiSUlo}wki À `ci0buPR}"b#Z«\;]C¤§ [_./ 5Z¤3§*¬
½·TPR}?«TZ«\;]j¤ 1<0 §9h[Z«\;]C¤§*¬tOP_pR`9./21¤3§^h Z«\:]5¤ 1>0 §^h Z«\:]5¤§ [ .0/25{¤63§*¬ %
± bdPqT¾}wsdbdlokT
"
#®Â&¸¶T·¸¶}2bbdi RR }wkTgRsu}lsdTek}wbdli(£!i bdPqT·s}w~qP iw3`u}"bul`c ^_lmR
Z\:]j¤h£ 1>0 §+[_.0/ 1 ¤63§`cibuPR}"bT£Z}wgCTt¸sul°bdbdT}2`M£5¤02143 §+[ £ @ ¤0 § S £ * ¤0c13 §¸lmbdP¸Z«\;]j¤£
@
1<0 §+[
Z\:]j¤h£
@
§-Z\:]5¤£
*
1>0
§¬&±Æä}2*beÂC¸¶Th}Æl«T¸lmbdP8bdPqlo`fbx¸¶i=y&km2Tgqs}wlo±SUSWpqRl°bulmT;`{}ÀiRql°bulmi2
iT¿_lo`cbdTjTiwbdPqT;`cTsuTko}"bulmi2R`e¬
Ê#Ê s säÊEr(tTv
P -VmBnX
3cL=(¨, '%
£©
,
l
2K!>kBJ
£}z
À 26hBR
Z«\;]j¤£ 1<0 § [ ./21¤3§
jV4
l
£
B
½
62
£¤02143 § [
£ @ ¤0 § S £ * ¤0c13 § ½
lbZ«\;]j¤h£
@
1<0 §+[Z«\:]C¤£
@
§[Z«\;]C¤h£
*
1<0 §
n
.0/21¤3§F[ .0/25{¤63§
V>V/i 28
3cL=(
¨* '% £ * l 2 l
>V EX nV i ! Bj24MXdj¯] 2n-VEX nV E
ÊÃÊ®g./21¤3§+[ .0/ 5{¤3§ÂqkmTb£}0~ji2km^_qi2SUl}kÃ`ci0bdPj}"b#Z«\;]C¤h£a§ [ .0/ 5Z¤3§Â«£=})gjT¸sul°bdbdTe
}2`+£
@ ¤0 § S £ * ¤02143 §`ci)buPR}"b£
*
PR}?«2TUqiÆSUiqi2S0lo}wk¸PRlP¾aTe~jTeRq`i2qkm^¼iw 0 ¬=OPRl`SUT;}wR`
buPR}"b#Z\:]j¤h£
*
§^ Z«\:]5¤£
*
1<0 §*¬
½·T¾PR}?«TZ«\;]j¤£q§ [ Y 8 ¤JZ«\:]5¤£
@ § 1 Z\:]5¤£
*
§d§ [ Z«\;]C¤h£ 1>0 §=bdPRT¿Z«\:]C¤£
@ § [ Z«\;]C¤h£ 1>0 §
Z\:]j¤h£
*
§{ Z«\;]j¤£
*
1<0 §*¬
OP_pR`^£=`u}"bul`cRT;`¶bdPqTi2Ralmbdli)iwbdPqT~Rsdi2~jiE`clmbdliì
&RisbuPqT)}`dTÀi93 Lg(¨*
'% £ *
Ât}Æ~ji2km^_qi2SUl}k£ z À `u}"bdlo`c ^ElqcZ\:]j¤h£
1>0
§Z[).0/
1
¤3§W}
gCT¸sul°bdbdT¾}2`+£5¤
021<=
@ § [ £ @ ¤0 § S = @ £ * ¤0
§¬=y&`¸Z\:]5¤£
*
1>0
§ Z«\;]C¤h£
@
§ÂxZ«\;]C¤h£a§[Z«\;]j¤h£
@
§h
Z\:]j¤h£
1>0
§¬ %
y{`f¸¶TPR}?«T i2pqRÆal!CTesdTeEbf~qsdi2~jTescbulmT;`iwbuPqTe`dT}wkTegqsu}lZlSUSWpqqlmbdlTe`eÂR¸¶TWe}w)l«TgCipqj
ibuPqTlsf«"}wkpqT¬
W, %Z ¢W 5»
±buPql``dTebdliÃÂR¸´Tl«TZgCipqRR`ibdPqT;`cTy&km2Tgqs}wlo{±S0ShpqqlmbdlTe`e¬
'«'³®#' <$Y'*
zTb{iR`dloaTs3¼}U pqj*bdliÆi (¶¨
,
i2 (¶©
,
¬½¼TW¸¶}2bbuiRR8~ji2km^_qi2S0lo}wko`¸lmbdPaTesuTT8./ 5{¤63§*Â
suTe`d~CTe*b ./21¤3§}eisalq 0 ÂlhbdPqTloaTe}k À TRTs}"bdT;g_^ = @ E 3 @ ¤0 § 1;9:9;9:1<=
© E 3 © ¤0 § 1<0 , E 0
}RTe`d~jT;lo}wkkm^2Âa¸´Ti2R`dlaTesbdPqT8(-, . @ 1;9:9:9;1
¨
1
@
1;9:9:9:1
©
5 À ÂRqTqibdTeg_^¬
y{` À lo`{}À¯TsuiÀalSUTR`dlmi2R}wklqTe}wk6ÂR¸¶Tª_qi"¸ bdPj}"bfbuPqTWsulmRºl`{}klmqT;}ws{«Tebdi2s&`c~j}T¸lmbdP
jql°buTalS0TeR`dlmi2ìtOPqlo``cpqgj`cT;*bdlil«TZbuPql`&almSUTeR`cli¬
¡l`} 9Zs:gqRTsgR}`dlo`´i À isf}0kT¿aloi2su}~qPqlofi2suaTes = @
C:C;C
= © 8 @
C:C;C
8 ¨ 5 iw À ¬
OP_pR` lo`}0kmlqTe}s«T;*bdi2s`c~R}2T¸lmbdP 0 ? H«I¾zf( ¨,
¬}`}0klmRTe}wsgj}`dl`e¬
OPqTelo`}U«T;*buis`c~j}TialSUTR`dlmi2Æ¥"¨5¬
=2K
½·TZqTeapRT&buPR}"b¶bdPRT&lSU}T{iw¥"¨
S
b&SUiRiSUl}k`´l lo`}klmqT;}wsukm^UaTe~jTeRaTEb¶ä}wSUlkm^2Â2buPqT
buPqTsuTl`&}hklqTe}ssdTek}wbdli=lbdPqlo`ä}S0lk^=}wRbuPql`fsdTek}wbdliisusdT;`c~Cijq`´bdi}0~ji2km^_qi2S0lo}wki
À ¬
OP_pR`ij`cloaTsulq·bdPqT¥
¨ S
b)Rs`xb=SUi2qiSUlo}wko`0 isbuPqT 7Z|fz i2suaTesU is4./ 5Z¤3§}R bdPqT
#kmlSUlmR}wbdliÀi2suqTst i2s ./ 1 ¤3§tl`¶}W`dpÀlTEbijal°bulmi2bdihPR}?«T{}sdTek}wbdli=}RURjUbdPqTaTesuTT¬
y{`{bdPqTU}wkTegqsu}l±SUShpqqlmbx^8isusuTe`d~ji2Rbdi)}=aTesuTT2Âj¸¶ThRTTe8bdiipR2bZbdPRThSUiRiSUl}k`fbdPqTesdT
lo`hlmk( ,/.0c135 ¶0 , E 0c13
, E 3 · ishbdPqT)aTesuTT ¬¾zÃTbaTeqiwbuT}a
bdPqT_pqSWgCTs0iw{S0i2qiw²
SUlo}wklm ( ,7. @ 1:9:9;9:1
5 ¶ , P E P
¸lmbdPaTesuTT ¬&OPqTe)bdPqThEpRSWgCTs&iS0i2qiSUlo}wk YZ`u}"bul`c ^_lmR
£5¤Y§ [ l_( ,7.02135 ¶0 , E 0213
, E 3 ·Àl`@a
¨/~é
}wR buPqT8_pqSWgCTsiwSUiqi2SUl}k9Y}y
`u}"bul`c ^_lmR £5¤Y}y
1<0 §F[ l%(^, .0c135 ¶0 , E 0c13
, E 3 ·¶lo`¥"©a
¨ ¬
½·T0e}wÆbusu}2apRTebdPRl`i2Ralmbdli}2`&}`cTesdlTe`eÂC}=gji2pqRÆibdPqTUyfkTegqs}wlo±SUSWpqqlmbx^)¸lmkkgjT
buPqTRs`xbfaTesuTTZiwbdPqT`dTsulTe`¶¸l°buP8}0qTE}"bdl«TZis¯eTsui0i_T ÀlTEbe¬tOPRTe`dT`dTsulTe`}wsuT<
./ 5 ¤63§
,?>
@BADCFEHG
@ACIKJ
>MLN
G
@ACOJ
>L=NPLRQ
.0/M1¤63§
,?>S=N
@AC E G
@ACIKJ
>
G
@BADCOJ
>MLVQ
½·TqiwbulT&buPR}"b¶bdPqTal!5TsuTRT{gCTbx¸¶TTeÀbdPRT{gCiwbuPy&km2Tgqs}wlof±SUSWpRql°bulmT;`¶l`¶iRkm^UbuPqTZPj}wq2T
i«"}wsulo}wgqkTZ<
./ 5{¤63§ .0/21¤63§
X % X E Y
X S Y % X
J #<T MD!-!#$-
±8bdPqlo``cT;*bdliÂC¸¶TW2lm«2TT¿a~qklolmb{gCipqRR`{i2ÆbdPRT0y&km2Tgqs}wlo±SUSWpqRl°bulmT;`&¸PqloPlo`{iqk^)gji2pqRq`
i2bdPqTjsu`cb{aTesuTTiwbdPRTW`cTesdlTe`f¸l°buP8}UqTE}"bdl«Ti2sf¯TesdiiET2ÀlTEbe¬OPqTƸ¶TWiSU~R}wsuTZbdPqT;`cT
gCipRRbdibuPqThiSU~qpabuTeÆaTesuTTibuPqTh`dTsulTe` i2sfl«TeÆ«?}kmpRTiw X 1 Y+}wRÆ¥_¬y Rsu`cb&gCipqj)l`
2lm«2TgE^SUlmqi2sdlqY g_^ b=<
Ê#Ê s säÊEr *vJw P -VmBnX 3cL=(¨
, % (©
,
l 7i
.0/ 5 ¤3§ h #
G
¨G~
@J G, A @ J
* ¥
¨/~
@
*
¥ [
.0/21¤63§ h"# ¨ G, A @ J
*
¥
¨* ¥ [
ÊÃÊ ½·TZe}wÀ~qsui"«T&l°b is^.0/ 5 ¤63§*ÂEbdPqTPR}qT&iw«"}wsulo}wgqkT&¸lkmk52lm«2T{}w=TenEpql«?}kmTeEb¶gCipqjbdi
./ 1 ¤3§¬
y{`xa
¨/~©
aTRiwbdT;`5bdPRTEpRSWgCTsiESUi2qiSUlo}wko`5¸l°buPaT2sdTeT ¬½·TtPR}?«2T¥"¨/~é [ N G, A @?J
G
¨G~é
J
PQ
a P
¨/~é
¬
Y8isuTi"«Tes^a
¨/~é
[a
G, A @JG
¨/~é
JA
¨/~é
¬
OP_pR` i2s-Y\[ b2Âq¥ ¨/~
@
h,N
I
SRQ
>MLVQ!
" # PQ
a P
¨G~
@ ¬
y{`#a
¨/~é
a
¨/~
@
ÂabuPqT N
I
SRQ
>MLVQ!
" # PQ
a P
¨G~é
@*
¥"¨/~
@ ¬
®¥aÂ_bdPRT N I SRQ!
>MLVQ
" # PQ
a P
¨/~©
¥"¨5¬
OP_pR`bdPRTsuTZlo`}U~Cik^ERiSUl}k5lm À ¸l°buPÆaT2sdTeTZki"¸¶TsisTenEpR}k5bdi
G, A @ JG
¨/~
@?J
* ¬
®¥ [aÂa¸¶TqiqiwbPR}?«2T}U`cbdsulblmqT;nEpR}wkl°bx^}` ¨G~
@ [ "N
>MLVQ
" # PQ
a P
¨G~
@
is-X
S
biaq¬
µ¶pabf¸´T}sdT`dpqsdTZbuPR}"b
N
>MLVQ
"
PRQ a P
¨/~
@ w¨G~
@ ¬
OPqT%./ 5{¤63§ h
¨/~
@
* ¬ %
&RisbdPRT}`dTiw¥ [ aÂ_buPqTgji2pqRi%./21¤63§¶l`bdPqTgCipqj2lm«2TlmbdPRT}wsdbdlokTe`
"'  #®¬
OPqlo`~qsui~Ci2`dl°bulmi2ai_Te`RiwbZbu}wª2ThlEbdi)}eipR2bZbdPRT0_pqShgjTesiw´i2pabd~Rpabu`i 3¬W®blo`{i2~abdlS}wk
i2siRkm^¼iqTi2pabd~qpqb is3¬µ¶pabWl µ´kiaªÁ³´l~qPqTese¸´TÀpj`cTl¾TeqTs}wkl_«Ts`dlmgqkT0 pqRbdliÃÂ`di
Y [ X¬´½·TqTeTebuil«TiwbuPqTs&gji2pqRq`&iqk^À i2s0.0/ 5Z¤3§¬¶OPRTqT¿_b&gCipRRq`fe}wÆgCTT¿_bdTeRaT;
bui!.0/21¤3§¶g_^buPqTPR}qTZiw«"}wsul}gqkmT2lm«2T=lbdPqT~RsdTe«Elipj`¶`dTebdliì
Ê#Ê s säÊEr *vt P -VmBnX 3cL=(¨
, % (©
,
l 2
n©^~èG~
, A @
, A @
!¥"¨E
.0/
5
¤63§ h
¤OX
S
YƧ
*
S
¤d¤OX
S
Y)§¥ ¨ § "
>MLN
E
q¤Y
S
X§
S b E
¤OX S Y S
b?§
MX!
©{~¨/~
, A @
, A @ ¥"¨M l 2
.0/ 5{¤3§^h
¤X
S Y E
b;§
*
E
¤OX S Y S
b?§
S
¤
* S Y S
X§
E
¤OX S Y S
b;§
S
q¤ b E
§
½ l K
[ ¤ E ¥ S
¨G~é
A @
* § S
¤u¤OX
S Y E
b?§§ Q
>L=N
¥ >
>MLN
§
MX
][
@ "
>L=N
¤X
S
YƧ
"
>MLN
ÊÃÊ OPql`~Rsdi_iwl`¶buTePqRle}wkÃ}wjnEpqlmbdTkiqjÂa¸´Ti2qkm^=T¿a~qko}wllbdPqlo`f}wsdbdlokTPqi"¸ buiURRl°b
}RsdT Tsbdi
" #Ã i2sfi2S0~RkmTbdT~qsuiEix¬
&lsu`cb¸´Tki"¸´Tes´gCipqjÀbuPqT_pqSWgCTsiwSUiqi2S0lo}wko`¶¸l°buPqTsuTTZki"¸´Tes´buPR}w g_^
¨/~é^~
¨/~é
E
¤X
S
YƧ
¨/~é^~ A ,
¨/~é
¬ty&R)¸¶T{jRbx¸´i}2`cT2 ¥_ÂqbdPqlo`SUTe}R`
©^~èG~
, A @
, A @
!¥"¨5ÂR}R ¥_¬
½ lmbdP8gCipRRq`{i)bdPRl`&gqlmRiSUl}k`eÂR¸¶TWe}w) ipRRÆ}ki"¸´Tesfgji2pqR8}2`f}~Cik^_qiSUlo}wkÃl ¸lmbdP
qTsuTTX
S
Y¼¬y `cp lmTeEbiRql°bulmi2=buiWRjÀbuPqTaT2sdTeT lo`¶bdiUPR}?«2TfbdPRl`ki"¸´Tesgji2pqRPqlm2PqTs
buPR}w)¥"¨¬
¹{`clqbdPqTZ: :2kaTes{lqT;n2pj}wkl°bx^2ÂC2lm«2TpR`{bdPj}"b}=nEpR}qsu}wbdlo~ji2km^_qi2SUl}kl SWpj`xbZgjT0~jiE`clmbdl«T
}R=bdPqTebuPqTsuTe`dpqk°bibuPqT~qsui~Ci2`dl°bulmi2ì %
OPqlo`gCipqj)l`RiwbfpR`dT pqklmbdPRl`f isuS¬tµ¶pab{l°b&e}w)l«TpR`f}Æ}`d^ESU~abuiwbulZTe`cbdlS}"bulmi2lfX
i;./ 5 ¤63§*Âa i2s-Y\[_X¬
Ê Ê 88äa
Ç ³vnw
P ^>V nX=2
3cL=(¨,
%
(¶¨,
b
X
./ 5 ¤3§ h
S
¨¸~
¤ b?§
¥h
*
,
E
@K@
S
¨¸~
¤ b?§ ¥
y{`&¸¶TW}8`cTeTÂRbdPqlo`&gCipRRÆlo`fgR}2) isfki"¸¶Tsf«"}wkpqTi#¥_Âjlmb{lo`f¸¶isdbdP)buPR}w)buPqTWgCipRRÆl«Te
g_^À~Rsdi2~jiE`clmbdli)q¬¬OPqTe¸¶Tl«T}0gjTbcbdTesfgCipqR i2sf¥[a¬
½·T¾}w i2S0~j}wsuT8bdPRTe`dT¼T¿_~RkmlolmbÆgji2pqRq` isÆy&km2Tgqs}wlo8±SUSWpRql°bx^! i2sƵ´kiaÁ³´l~qPqTeseÂ& is
T¿aTSU~qkT¬0&RisfR¿_T;)«"}wkpqTe`&iw#¥_ÂDX }wRfY·Âj¸¶ThqTbdTesdSUlR}"buTW}gCipqj8alsdT;*bdTekm^ suiSbdPqT0`cTesdlT¬
½·TZPR}?«TZiSU~R}sdTfbdPqlo`¶gji2pqR¸l°buPEgCipRRq`¶iwÃ~qsui~Ci2`dlmbdliR`¶q¬}R=R¬m& is¥[ bh}wR!X [_Y¼¬
&lpRsdTU=<´³´i2SU~R}wsul`diiwgji2pqRq`f}2isalmRWbuPqT_gi«"}wsulo}wgqkTe`
&lpqsuTÀl«Tpj`bdPRTWal!CTesdTeRTW}2isalmRhbuPqT«"}wkpqTi XÂR¸lmbdP%Y [ X¬¶½·TW`dTTbuPqTWklmRTe}ws
gCTPj}?«ElisgqpqbbdPqT}2`c^_SU~abdibdloij`xb}wEb
@
¨
.0/ 5 ¤3§´ i2pqRl`fqiwbi_ia¬
OPqT;`cTgCipqjq`aT~CTRi2ÀbdPRTZ«"}kmpqTi¥_ÂaR2pqsdT0`cPqi"¸ bdPR}wb´buPqTgji2pqRiw~Rsdi2~jiE`clmbdliq¬
lo`gR}2= i2sf`cS}kmk5RTekì
%&i"¸Âa¸´T2lm«2TZ}0gCTbcbuTsfgCipRRi%(
* ¬
Ê#Ê s säÊEr *v P -VmBnX 3cL=(¨*
'%
(©*
.0/25{¤63§ h b E ` b E
¤OX
S
Y)§
9