Testing graphs for colorability properties* Eldar

 !"#$!
%&' ( )& * +,-+&,'. -/ 0,*+123 45 67'&2' /-, ( 82 * ,*59-:8;&9 *<0-,8'1: =18>1? 08@&5 '1&
*)8<8'. '- :*A& BC&,8&2 =1&'1&, * 9&28,&9 +*8, -/ @&,'8>&2 -/ *5 85+C' 0,*+1 D =8'1 E @&,'8>&2
*,& *9F*>&5' -, 5-'? 982'850C821&2? =8'1 1801 +,-)*)8<8'.? )&'=&&5 '1& >*2& -/ D 2*'82/.850 ( *59
'1& >*2& '1*' 8' 1*2 '- )& :-98G&9 ). *99850 *59 ,&:-@850 :-,& '1*5 6HIJK &90&2 '- :*A& 8'
2*'82/. ( 3 L1& +,-+&,'. ( 82 >*<<&9 '&2'*)<&? 8/ /-, &@&,. 6 '1&,& &M82'2 *5 67'&2' /-, ( =1-2& '-'*<
5C:)&, -/ BC&,8&2 82 859&+&59&5' -/ '1& 28;& -/ '1& 85+C' 0,*+13 N-<9,&8>1? N-<9=*22&, *59 O-5
PQRS 21-=&9 '1*' >&,'*85 0,*+1 +,-+&,'8&2? <8A& T7>-<-,*)8<8'.? *9:8' *5 67'&2'3 U5 PRS * G,2' 2'&+
'-=*,92 * <-08>*< >1*,*>'&,8;*'8-5 -/ '1& '&2'*)<& 0,*+1 +,-+&,'8&2 =*2 :*9& ). +,-@850 '1*' *<<
G,2' -,9&, +,-+&,'8&2 -/ '.+& VWXY *,& '&2'*)<& =18<& '1&,& &M82' G,2' -,9&, 0,*+1 +,-+&,'8&2 -/
'.+& VXWY =18>1 *,& 5-' '&2'*)<&3 Z-, +,-@850 '1& +-28'8@& +*,'? 8' =*2 21-=5 '1*' *<< +,-+&,'8&2
9&2>,8)*)<& ). * @&,. 0&5&,*< '.+& -/ >-<-,850 +,-)<&: *,& '&2'*)<&3
[18<& '182 ,&2C<' 82 '801' /,-: '1& 2'*59+-85' -/ G,2' -,9&, &M+,&228-52? /C,'1&, 2'&+2 '-=*,92
'1& >1*,*>'&,8;*'8-5 -/ '1& '&2'*)<& 0,*+1 +,-+&,'8&2 >*5 )& '*A&5 ). >-5289&,850 '1& >-<-,850
+,-)<&: 852'&*93 U' 82 +,-@&5 1&,& '1*' -'1&, ><*22&2 -/ 0,*+1 +,-+&,'8&2? 9&2>,8)*)<& ). @*,8-C2
0&5&,*<8;*'8-52 -/ '1& >-<-,850 5-'8-5 C2&9 85 PRS ? *,& '&2'*)<&? 21-=850 '1*' '182 *++,-*>1 >*5
),-*9&5 '1& C59&,2'*59850 -/ '1& 5*'C,& -/ '1& '&2'*)<& 0,*+1 +,-+&,'8&23 L1& +,--/ >-:)85&2
2-:& 0&5&,*<8;*'8-52 -/ '1& :&'1-92 C2&9 85 PRS =8'1 *998'8-5*< :&'1-923
U' 82 *<2- -)2&,@&9 '1*' '1&2& '&2'*)8<8'. ,&2C<'2? *2 =&<< *2 ,&2C<'2 /,-: PRS *)-C' &M82'&5>& -/
5-57'&2'*)<& +,-+&,'8&2? >*5 )& &M'&59&9 '- >&,'*85 >-:)85*'-,8*< 2',C>'C,&2 ,&<*'&9 '- 0,*+12?
2C>1 *2 '-C,5*:&5'23
\]^ _`a_^b_b cdeafcga hi ajke lcl_f jce cll_cf_b k^ aj_ lfhg__bk^me hi aj_ nopq ]rstuv]s uwx] yozzn{|
}~€}}o
‚ƒcg„…a† hi rh‡l„a_f ugk_^g_| ˆ_gj^kh^ € vefc_… v^eaka„a_ hi ˆ_gj^h…hm†| ‰ckic| vefc_… Їck… cbbf_ee‹
_…bcfŒgea _gj^kh^cgk…

! " # $ " # # # %&' ( ) * " + # , - . /01 23 1 345 627861 98:; * #
-< ( = # - / H>? K ! " # - "+ / H>? K $ * , /07@67 #
* A B+ . "+ C B # # - . D ""+ ?E " # - #+ * # - " /F# #
#+ * G + * 7@672HI@ # # + ( / J K ( /F # *
" # B " "+ # # / ! # A # $
, " ( L " # B "+ %M' # + /F + # + A " # # B " ( " !B $ " "+ ( G # + # "+ N "# L %O' + "+ + # C G + # # " "D + # " "+ P P
N %Q' C RF"+ " G # RF"+ " # + + % S' ! %'$
N+ ) # LA T %QK' " ( # + %Q' L "D # + " "D + U # ( + %V' %V' %Q' # A # " C "+ # W XYZ[Y\ ]^] _`abc d II e 367 43f@3 g 34g @378@6 41 79g @ hij k 23@ 7@672HI@l m: 7n @ 47n@3 n2:fo 7n@3@
@p8676 2 e 367 43f@3 g 34g @379 41 79g @ hj i k qn8rn 86 :47 7@672HI@l
G # ( %Q' st+ Q
" # "+ ( " ( B ! $ s B+ D + G # F
A # " " # " "D %M' % ' %K' # # s %O' # # # G   # # !($ "+
A # + # RF"+
] d Z Z[ 41 2 ;32g n - q87n 2 @37@p 6@7 86 2 1 :r784: 1 345 74  l
8 @: 2 e :87@ 1 25 8I9 q87n 3@g @78784:6 41 ;32g n6o @2rn g 34 8f@f q87n 2 0r4I438:;o 2: Z Z[ 41 - 86 2 0r4I438:; 41 - 1 43 qn8rn :4 5 @5 H@3 41 2gg @236 26 2: 8:f r@f 6 H;32g n q87n 7n @
r4I436 2668;:@f 74 876 @378r@6 H@8:; 8f@:78r2I 74 7n46@ 2668;:@f H9 l - 86 r2II@f Z Z[ Y 81 87
2f5 876 2: 0r4I438:; l
Y Z G # ! + $ # # + ij %Q' " " B # N+ ) # LA T # " ( # " # G   # # # ( + F
" (" # ( " " # # # "+ # # " " C "+ #
A # "+ " # " " " "+ " # # %Q' ( # "+ ! $ " A F " L Q NF
+ ) # LA T # L M #
+ # L "+ # " # " "+ a 8 @: 2 e :87@ 1 25 8I9 41 0r4I43@f ;32g n6 2:f 2 6@ @:r@ ! ! $ 41
!
: 5 H@36 627861 98:; K " # "  2:f $ #%
#  o q @ r2II 2 ;32g n - q87n . @378r@6 ! $ Z Z[ Y
Y Z M
81 - 2f5 876 2: 0r4I438:; q87n 7n@ 2ff8784:2I g 34g @379 7n27 1 43 @ @39 7n @ : 5 H@3 41 @378r@6 41 qn8rn 23@ r4I43@f q87n 86 8: # . # . l
G "+ # ! $F"+ !# + ( $ "+ #
(" "+ "+ , ( # + # - . B ? . ! + ( + + %Q' " " U A # + "$
L C F"+ ! $F"+ + "+ " + + " # " D # %Q'
! $F"+ A # F"+ " + # " # 5 67 " # L " "+ # + # " # " " " " L & + "F
G L "+ # " # d [ Z Z[ 41 2 ;32g n - q87n 2 @37@p 6@7 86 2 1 :r784: 1 345 % ' ? o 7n @ 6@7
41 2II :43f@3@f g2836 41 @378r@6 41 - o 74  l 8 @: 2 e :87@ 1 25 8I9 q87n 3@g @78784:6 41
0g 2830r4I43@f ;32g n6o 2: [ Z Z[ 41 - 86 2 0g2830r4I438:; 41 - 1 43 qn8rn :4 5 @5 H@3
41 2gg @236 26 2: 8:f r@f 6 H;32g n q87n 7n@ r4I436 2668;:@f 74 876 @37@p g2836 H@8:; 8f@:78r2I 74
7n46@ 2668;:@f H9 l - 86 r2II@f [ Z Z[ Y 81 87 2f5 876 2: 0g2830r4I438:; l
Y Z G + A # # F"+ " + +
(" # " !( $ F"+ (" # , ( F # H! ? K FF "+ # ( "U (
!"+ #" " # F $ " F ( F
, # L # B " L &
L S A # F
+ # + # " # "
L A # "+ F
# D C # (
L V # ( F" + # + j i + L O A # C + C # " # / # C # N+ ) G " " + C "+ # # + # " # " C # + + D ( # - !
$ " " # # - " G @f; @ f@:6879 # "+ !
$ + 03@; I23 # # + " # # #+
+ !
$ !
$ + # + # + " # Y\ \ a ^] 1 86 2 03@; I23 g 283 q87n f@:6879 o 2:f 2:f 627861 9 / 2:f / 1 43 645 @ / o 7n @: 86 2 ( Q /
2:f 27 5 467 ! l "
03@; I23
g283 q87n f@:6879 27 I@267
G # ( # ( # +
" # ( + # + " CU #
# # %Q'
Y\ \ a ^a $ 43 @ @39 K % 1 4II4q8:; g 34g @379l

2:f R 7n @3@ @p867 &
? &? !% R $ 2:f ? &? !% R $ q87n 7n @
gg 46@
7n27 86 2 ;32g n q87n @378r@6 o 2:f 7n27 86 2 R 07 g I@ 41 f86 48:7
@37@p 6@76 41 - 6 rn 7n27 1 43 @ @39  " " R 7n @ g 283 # # 86 03@; I23o q87n f@:6879 27 I@267
% 81 # # 86 2: @f; @ 41 o 2:f q87n f@:6879 27 5 467  % 81 # # 86 :47 2: @f; @ 41 l n @:o 27 I@267
#% # 41 7n@ R 07 g I@6 6g2: 8:f r@f r4g 8@6 41 qn@3@ @2rn # g I296 7n @
34I@ 41 # l
? &? !% R $ ? &? !% R $
+ " % F
R + # #
# # " # ( # # +
Y Z $ 43 2 g283 41 @37@p 6@76 q87n f@:6879 % o 2 @37@p 86 628f 74 / [YY q87n
7n@ g283 81 87 n26 H@7q @@: !% /$ 2:f !% ! /$ :@8;nH436 8: o 2:f 8: 2ff8784: 2II H 7 27
5 467 / 41 7n@ @378r@6 23@ 6 rn 7n27 7n@ : 5 H@3 41 5 7 2I :@8;nH436 41 2:f 8: 86 H@7q @@: !% ? /$ 2:f !% ? ! /$ l @ f@e :@ 8: 2: 2:2I4; 4 6 5 2::@3 7n@ 8:672:r@ qn@3@ 2
@37@p 86 628f 74 /02;3@@ q87n 7n@ g 283l
n@ g283 86 r2II@f / Z [Y [ 81 2II H 7 27 5 467 / 41 7n @ @378r@6 41 2:f 2II
H 7 27 5 467 / 41 7n@ @378r@6 41 f4 /02;3@@ q87n 7n @ g283l
%' # + B #
+
Y\ \ a ^ _`]bc $ 43 @ @39 / J K 7n@3@ @p8676 ? &E !/$ J K 6 rn 7n27 @ @39 0I4r2II903@; I23
g283 86 2I64 /03@; I23o 2:f @ @39 03@; I23 g283 86 2I64 /0I4r2II903@; I23l
G # + + + "+ " + A # # + # QM "+
" B ! % ' , ( , $
a^
$ 43 @ @39 / 7n@3@ @p8676 ? & !/$o 6 rn 7n27 1 43 @ @39 7n@3@ @p8676 ? & !/ $
627861 98:; 7n@ 1 4II4q8:; l 1 86 2 03@; I23 g283 q87n f@:6879 % o 7n @: 1 43 @ @39 J 2:f J o
27 I@267  41 7n@ g4668HI@ rn48r@6 41 2:f q87n 2:f 627861 9 7n27
86 2: /03@; I23 g283 qn46@ f@:6879 86 H@7q @@: % 2:f % ! l
Z[Z [ [Z Z Y X ? &E ! ? ? &E !/$$ # %
? ? &E !/$F +F + # " # " # " ? &E !/$F +F + " % % ! "
, #  " " R # ( # @ 8g2378784: # # # = "+  #  " " R ! # # "
A$ G # B " # !R " $ ,
3@e :@5 @:7 # B B # # #  " " R  " " # " # # # +  " " R  " " # " # # (
# + + - G " "+ ( # B N+ ) # LA T %QK'
Y\ \ a ^
_W XY
Y [ Y\ \ `a bc $ 43 @ @39 2:f / J K 7n@3@ @p8676 ? & ! /$
q87n 7n @ 1 4II4q8:; g 34g @379l
1 - 86 2 ;32g n q87n . @378r@6o 2:f 86 2: @ 8g2378784: 41 7n@ @37@p 6@7 41 - q87n 2:
43f@3 :47 @p r@@f8:; o 7n@: 7n@3@ @p8676 2 3@e :@5 @:7 41 q87n 43f@3 R o qn@3@ " R " o 1 43
qn8rn 2II g2836 41 6@76 H 7 27 5 467 / H? K 41 7n@5 23@ /03@; I23l
# " # # - # # ! # # $ (+
G # + + # + N+
) # # "+ " ) Q& G T G N + G ! %&' # # $ L %Q' # # a^ $ 43 @ @39 2:f 7n @3@ @p8676 @378r@6 7n@3@ @p867 f86 48:7 @37@p 6@76 ? & ! $ 6 rn 7n27 1 43 @ @39 ;32g n - q87n
Z[Z [ .
627861 98:; # . l
d II H? K g2836 23@ 03@; I23l
87n @3 2II g2836 23@ q87n f@:6878@6 27 I@267 ? o 43 2II g2836 23@ q87n f@:6878@6 I@66 7n2: ? l
S
F # # ) Q& # %Q' # " - Y\ \ a ^ _`abc $ 43 @ @39 8:7@; @3
2:f 1 :r784: K ! $  7n@3@ @p8676 7n@ 1 4II4q8:; g 34g @379l
1 - 86 2 ;32g n q87n . @378r@6o 7n@: 7n @3@ @p8676 2: @ 8g2378784: 2 3@e :@5 @:7 #  " " R  " " 41 7n27 627861 9 ? & ! $
# "
"
q87n
R 2:f
R H 7 R "
$ 43 2II  "
$ 43 2II
!R $03@; I23l
"
"
" l
R H 7 27 5 467 !K$ H? K 41 7n@5 7n@ g283
"
R o 1 43 2II
 " " # # 86 !K$03@; I23l
H 7 27 5 467 !R $ ? 41 7n@5 7n @ g 283
R H 7 27 5 467 !K$ H? K 41 7n @5 23@ 6 rn 7n27 1 43 2II
!K$ ? 41 7n @5 !# # $ !# # $ !K$ n4If6l
d II
"
# # 86
 " " H 7 27 5 467
+ # "+ L " ( L # +
a^ _`abc $ 43 @ @39 2:f K ! $  7n @3@ @p867 ? & ! $ 2:f ? & ! $
q87n 7n @ 1 4II4q8:; g 34g @379l
1 - 86 2 ;32g n q87n . @378r@6 7n @: 7n @3@ @p867 2: @ 8g2378784: #  " " R 41 2:f 2: 8:f r@f 6 H;32g n - 41 - o q87n 2: @ 8g2378784: #  " " R 41 7n@ @378r@6 41 - o
7n27 627861 9 Z[Z [ #
R l
#
1 43 2II  o 2:f # . l
: 7n@ @ 8g2378784: o g2836 23@ !R $03@; I23l
d II H 7 27 5 467 !K$ H? K 41 7n@ g 2836
"
V
"
R 23@ 6 rn 7n27 !# # $ ! # # $ !K$l
P # ( "+ + # ! $ "+ + + G
# + B # 2 ;32g n -< 2:f 2 g2378784: #  " " R 41 876 @378r@6o 2 ;32g n 86 2:
! $ Y !% /$ \ Z Y Z[ -< ZY[ 81 7n@3@ 86 2 g2378784: #  " " R  " " 41 876 @37@p 6@7 627861 98:; 7n@ 1 4II4q8:; l
Y Z 8 @:
" # " 1 43 2II
"
"
R 2:f
 " " l
1 J  o 7n@: 1 43 @ @39 e p @f  " " R o 2II g2836 # # 1 43  " " 23@ /03@; I23l
43@4 @3o 81 J  o 7n@: @87n@3 2II 7n @6@ g2836 n2 @ f@:6878@6 27 I@267 ? o 8: qn8rn r26@ 7n @
6 H;32g n 41 -< 6g2::@f H9 # 86 2 rI8 @o 43 2II 7n@6@ g2836 n2 @ f@:6878@6 I@66 7n2: ? o 8: qn8rn
r26@ 7n @ 6 H;32g n 41 -< 6g 2::@f H9 # 86 2: @f; @I@66 ;32g nl
R 2:f  " " o 7n@ g283 # # 86 2: /03@; I23 g 283l 43@4 @3o
1 43 @ @39 e p @f  " " R o 4:@ 41 7n@ 1 4II4q8:; 7n3@@ r26@6 4rr 36l 87n@3 7n@ f@:6878@6 41
2II 7n@ g2836 # # qn@3@ 2:f 239 4 @3  23@ H@7q @@: % 2:f  % 43 -<
r4:728:6 2II g 4668HI@ @f; @6 H@7q @@: # 2:f # o 2:f 7n @ f@:6878@6 41 2II 7n@6@ g2836 23@ 27 I@267
% 43 -< r4:728:6 :4 @f; @ H@7q @@: # 2:f # o 2:f 7n@ f@:6878@6 41 2II 7n@6@ g2836 23@ 27 5 467
 %l
$ 43 @ @39
"
"
%Q' + ( " # - -< ( - # - ) #
( - # #+ " -< - # + # + QV
E &
q87n g I2r@6o
-l
o 2:f K 
7n@3@ @p867 E & ! $ 2:f
! $o 6 rn 7n27 1 43 @ @39 ;32g n - 7n@3@ @p8676 2: @ 8g 2378784: #  " " R " R " o 2 ;32g n -< q87n 7n@ 625 @ @37@p 6@7 26 - qn8rn f8 @36 1 345 - 8: I@66 7n2: !K$ H>
?K
2:f 2: ! . . $0H26@f ! !K$ !R $$05 4f@I 1 43 -< 4 @3 qn8rn 86 2: 8:f r@f 6 H;32g n 41
Y\ \ ^] _ YY `abc $ 43 @ @39
O
! $ [Z Z + ! $ / !K$
? & ! ( S/ $
! $ 
/ ? & ! ! $$ ! $ ? & ! ! $$ ? & ! ( S/
$
+ + QV - #  " " R - #  " " R #+ ( S/ " R " ? & ! ( S/ $ # ? & ! ( S/ $. + + "+ + ! $
+ Q " # - "+ # " # # " !R $F # " ? # " ? # # !R $F =
# # # # "+ /
-< " " # - "+ # "
"
R !# # $ ! # # $ J / # # # " # ! # # $ ? " F G ? / H> !# . $ " / H  " " R ?K
?K
 " " R ! # # $ ? / " # #  " " R ! # # $ J  ? / F " # # " G E / H>? K "+ "
R # " # -< " (+ # - "
# J  # # # # ( # #
#
# # # ? # # " ? F # " G / H>? K " R S/ K
- + # -< # # " -< = # - / H>? K B "
s+ " )
%Q'$
QQ # + ! # # ^a _ YY `abc $ 43 @ @39 o o ! $ 2:f K ! $  7n@3@ @p867 E &? ! $o
E &? ! $ 2:f E &? ! $o 6 rn 7n27 1 43 @ @39 ;32g n - q87n . J @378r@6 7n@3@
@p8676 2: @ 8g2378784: #  " " R q87n " R " o 2:f 2 ;32g n -< q87n 7n@ 625 @ @37@p
6@7 26 - qn8rn f8 @36 1 345 - 8: I@66 7n2: !K$ H>? K g I2r@6o 6 rn 7n27 27 I@267 H> K 41 7n@ 8:f r@f
6 H;32g n6 41 - q87n @378r@6 23@ ! !R $ $0H26@f ! E !R $$05 4f@I6 1 43 -< 4 @3 l
Z[Z [ [Z Z Y X + ! $ -< " B ,+ ) M  ! ! $$ - " -< - #+ # + B #  " " R  " " # ! ! $ !  $ " # " " " R # J  # # -< # B " " # # # +  " " U # -<
# " # # +
+
"
"
"
R # -< " # # " # # # +  " " U # -< " # # " # # U # # " # # ( !R $F + " ? ! ( E
E
#+ B ( # C $
"
# + + # -< ) QQ #
" # - #+ " # # # + "
G " + # + # # "+ # "+ " " # - # -< " " " + # -< " # # # " " 
G # F 0r4I438:; # ! $F
# ( = " # # P !# -< # $ #  " " R  " " # # # " # + F # 05 4f@I8:; # % # # + (  " " R # " "+ # # R # + (  " " + # ( # B # "+ #
! $F"+ ^ $ 43 @ @39 o 2:f 1 :r784: ! $ 7n@3@ @p867 E &E ! $o E &E ! $ 2:f
E &E ! $o 6 rn 7n27 1 43 @ @39 ;32g n - q87n . J @378r@6 7n@3@ @p8676 2: @ 8g2378784:
#  " " R q87n R " o 627861 98:; 7n27 1 43 @ @39 o 27 I@267 !  !K$$ H> K 41 7n@ 8:f r@f
6 H;32g n6 - 41 - q87n @378r@6 627861 9 7n@ 1 4II4q8:; l
!
$ 43 @ @39 0r4I438:; 41 - 1 43 2:9 ! ! $ 627861 98:; # K 2:f $ #% #  o 7n@3@
@p8676 2: 8:f r@f 6 H;32g n - 41 - o qn8rn 86 2: ! $0H26@f ! !K$ !R $$05 4f@I 4 @3 1 43 2
;32g n -< qn8rn f8 @36 1 345 - 8: I@66 7n2: !K$ H>? K g I2r@6o 64 7n27 7n@ 3@6738r784: 41 7n @ ;8 @: r4I438:;
41 - 74 - 86 05 4f@I8:; 1 43 645 @ 627861 98:; " !K$l
Y\ \ [Z Z + ! $
! $ ? &
" !K$ / !K$ "+


 
? & ! ! $$ ! $ / OQ / 
!
Q
Q
? & !
" 
( S/
?
$
? & ! ! $$ ) QS - #  " " R #  " " R  " " #+ + + # U +
# # Q
(
Q 
? & ? &

! ! $$ ! $ /   / /
 Q Q Q ""+  ? / " - " E? E # # G "+ # # #
- " # "+ + Q # ""+
 / ! # B $
E?
" #
" R #  " " " ! ? & ! !R $$ !R $ / F
, "
E
"
"
H? K ? # # # R " ? / H? K ? / H? K # # ? / ? # !# # $ ! # # $ " ! ? ! ? $/ / "
 " " "
- " # # P F # - + # + + (
# % # # +  " " R " !"+ B$ ""+ E # " "+
F # #+ " / ! + /$
"+ # ( # # # ""+ E " # # # ! # !" # + (  " " R  " " ""+ # # " " # # # ! # " "+ ! $ + " # + ( ""+ # ? # # ""+
E ! ? & ! !R $$ !R $ / FU ""+ E " # + (  " " R ""+ #
# # " H? K # +
R " / H? K # #+ ! # # $ !# # $ / G
""+ E " " #  " " R #+ ! # # $ !# # $ / " #+ !# # $ ! # # $ /
, "
"
M
# " ? / ? # "  " " ""+ E ? / H? K  " " R / H? K U ( # # #
" ( # +  " " R + + Q
" "+ # # "+ # " # # " !R $F ? ? # # !R $F
G " - "+ # #  " " R  " " s+
-< + # # ) M  - " B " "
G # # !( $ ! $F"+
" F" !% /$F # ! $F" !% /$F # +  " "  ! + $ G " # # # " "+ # # " " "+
" ) MM " ( # !
#  7n@3@
! ! $ 627861 98:; K " # "  2:f $ #%
@p867 & !/ $o 6 rn 7n27 1 43 @ @39 % J K 2:f 1 25 8I9 41 0r4I43@f ;32g n6 q87n g 74 @378r@6
8: @2rn 5 @5 H@3o 7n@3@ @p8676 & !% $ 627861 98:; 7n@ 1 4II4q8:; l
1 2: 0H26@f !% $05 4f@I 1 43 -< 4 @3 #  " " R n26 2: 05 4f@I8:; 0r4I438:; 1 43
2:9 627861 98:; o 7n@: 7n@3@ @p8676 2: ! $0r4I432HI@ ;32g n - qn8rn f8 @36 1 345 -<
8: :4 5 43@ 7n2: / H>? K g I2r@6o qn@3@ . 86 7n@ : 5 H@3 41 @378r@6 41 -< l
Y\ \ ^] $ 43 @ @39 / J K 2:f
[Z Z # + FA #  
/ Q Q
? &? !% $ 
P -< #  " " R  " " F F # #+ " - #
 " " R ! $F # L # +  " " K J K ( # % # + # -< " # + + ( # # % # U # +  " " . # -< # # # + # #
# + # L " ? ! /
? /. G # #
+ (  " " F U
# - # # - F L +  " " (
# ) QQ ( #
q
"
q F # "
!
#  o 7n@3@
W XYZ[Y\ ^a $ 43 @ @39 /o o 2:f ! ! $ 627861 98:; K " # "  2:f $ #%
@p867 !/ $ 2:f !/ $o 6 rn 7n27 1 43 @ @39 ;32g n - q87n . @378r@6 qn8rn 86 /01 23
1 345 H@8:; ! $0r4I432HI@o 2:f 1 43 @ @39 o 27 I@267 !  /$ H> K 41 7n@ 6@76 q87n @378r@6 41 6g 2: ;32g n6 qn8rn 23@ :47 ! $0r4I432HI@ 1 43 2:9 627861 98:; l
[Z Z ? & ! ? / $ "+ !K$ # +

/ Q
J K ! $ &
!
 !K$ $ + E &E ! $ " # ( " #
" # # - /F# # " ! $F" !  /$ H> K # " # !# + ( $ + # # ) MM # +
&
# ! $F" # #+ ! !K$ $F # -< = # - ? / H>? K F F
# Q s )  ( # - = # - / H>? K ! $F" "
Z[Z [ ^ $ 43 @ @39
e p @f
2:f o 7n@ g 34g @379 41 2 ;32g n H@8:; ! $0r4I432HI@ 86 7@672HI@l
[Z Z P / /F # + # ) ! E / $
" G Q ! E / $ " F # + - . ? H> # # # E K
F # #+ ! # . " # B$
G # , # + # # - # B G - # + # " # - "+ ! $F" # + #+ ! " C "+ ( #
" F # "$ # - ! $F" ( # "+ # ""+ ?E # - /F# #
" ! $F" G Q ""+ ?E D "
G " A # # # "+ # # # % ' ? # # " # Y Z d
1 :r784: * % ' ?
86 2: 43f@3@f g283 ! * $ r4:68678:; 41 2 6@7 41 Y[ Y  o qn8rn 86 r2II@f 7n@ [ Z 41
l
X [
2:f 2
+ " # QF FF + " # Q F G # " "+ " # ( # # " G g 3@85 2; @ ;32g n6 # F (

# " (+ # # #  " " 0f@:6879 # # ( # F +
# ( # # 03@; I23
# F # ( # # #
# # + # # + " C " # # # Y\ \ ^] 1 86 2 03@; I23 g 283 8: 2 rn237o 2:f 2:f 627861 9 / 2:f
/ 1 43 645 @ / o 7n@: 86 2 ( Q /
03@; I23
g283l
[Z Z # G F+ # F # "+
) Q  ( Q / F # # s ( Q / F "
^a _ X [ Y[ Z Z Y\ \ a ^ac $ 43 @ @39 % J K 2:f 7n@3@ @p867 &? !% $
2:f &? !% $ q87n 7n@ 1 4II4q8:; g 34g @379l
gg 46@ 7n27
2:f ! * $ 23@ rn2376o 2:f 7n27 23@ f86 48:7 @37@p
6@76 41 6 rn 7n27 1 43 @ @39  " " 7n@ g283 # # 86 03@; I23 2:f 876 * ! # # $0f@:6879 86
# 41 7n@ 07 g I@6 6g2: r4g 8@6 41 qn@3@
27 I@267 % l n @:o 27 I@267 #%
Y\ \ @2rn
#
g I296 7n@ 34I@ 41
# l
[Z Z ( # G " + " # U # + " # # # + # # #
* ! # # $
# ? &? ! % $ # # B
# ) QQ # ( # ? &? #%
U + F # # " ^ _ Y [ Y\ \ Z[ X [ c $ 43 @ @39 o 2:f / J K 7n@3@ @p8676 2 : 5 H@3
&E ! /$ q87n 7n@ 1 4II4q8:; g 34g @379l
86 2 0rn237 q87n . @378r@6o 2:f 86 2: @ 8g2378784: 41 7n@ @37@p 6@7 41 q87n 2:
1
43f@3 :47 @p r@@f8:; o 7n @: 7n@3@ @p8676 2 3@e :@5 @:7 41 41 43f@3 R o qn@3@ " R " o 1 43
Y\ \ qn8rn 2II g2836 41 6@76 H 7 27 5 467 / H? K 41 7n@5 23@ /03@; I23l
S
[Z Z Y X G # # N+ ) # ( # # ( # G # "+ # /F ( # # # # ( "+ ! /$ , ( # + " K  # # # C # +  " " ( # #
( # " # # ! + " K $ # #
# # "
s+ D G T G # N + G # # + Q ^
_ X [ Y[ Z Z Z[Z [ a^ c $ 43 @ @39 o 2:f 7n@3@ @p8676 2 2:7879
& ! $ 6 rn 7n27 1 43 @ @39 0rn237 q87n . @378r@6 7n@3@ @p867 f86 48:7 @37@p 6@76
627861 98:; Z[Z [ # . l
d II H? K g2836 23@ 03@; I23l
n @3@
@p8676 645 @
" "
6 rn 7n27 7n @ 0f@:6879 41 @ @39 g 283 86 27 I@267 l
[Z Z Y X " + F " # ! ( # B # N + G $
s+ # # N+ ) D G T G !
# %Q' # " + Q $ ( " . # + # F
! * $ # * * ! $F+
# # + R R "+ " # q
# ! # # +$ " # # +  " " "
# " ! + QV " " # "$
V
Y\ \ ^
$ 43 @ @39 o R 2:f 7n @3@ @p8676 & ! R $ 6 rn 7n27 1 43 @ @39 0rn237 q87n
@378r@6o 2:f @ @39 @ 8g2378784: #  " " R 41 876 @378r@6o 7n@3@ @p867 # #
. J
6 rn 7n27 # . 1 43 @ @39
"
"
R 2:f # # 86 03@; I23 1 43 @ @39
"
"
Rl
) &M ? ! &E ! R ? H? K $$ +
#  " " R  " " # " ? H? K H ? K # " F + + # +  " # " #  " " R + ""+ ? # # F ( # # # " B "
[Z Z # FF"+ " G " # # # " " "+ #
"+ " + MQ " ( # ^] $ 43 @ @39 R 2:f 1 25 8I9
41 0g2830r4I43@f ;32g n6 7n@3@ @p867 & !R $ 2:f
& !R $o 6 rn 7n27 81 2 !  . $0H26@f ! /$05 4f@I ;32g n 1 43 2 ;32g n -< 4 @3 2 g2378784:
E
#  " " R 86 0g 2830r4I432HI@o 7n@: 7n@3@ @p8676 2 ;32g n - qn8rn 5 29 f8 @3 1 345 -< 4:I9
4: 7n@ g2836 #%
%# ' ? 2:f 86 0g2830r4I432HI@l
Y\ \ [Z Z ) 
( " # 
" #


& Q R & Q &? ! $
&? ! $ O
O
O
O
! & Q R  O



& Q &? ! O $
&? ! O $ & Q &? ! O $
$
, #  " " R # # -< !
# + # # # # $ , FF # - FF
# - Q F ) && # # #
#  " " R ! & !Q &? ! ! $$ &? ! ! $ F # Q F
G # + + & " #  " " R  " " " &? ! ! $F - # -< # O
+ ( # + # ? ! J ! # #  " " "+ R # - "
%# ' ? ( + # F ? ! J ! # #  " " "+
R # # - %# ' ? - " F " # # # + # # # ! $ " E ?E + # + # # # " ? G ( R # # R # # " # # + # " R # # + # F " R # # ! ! + # # # # ( # Q F " R # # R # # #+ + # R # # + # F R # # ?! " # # $ , # " # - " # # " R # # " ( ! + # # # E + # # # ? $ # " R # # " (
G # - # # # # # "+ R # # +
"+ R # # # # - "+ R # # # # - ! # -< # - + # R # # R # # " $
# " # - " # - " # #  " " ) &Q ( # # " # "+
FF # G FF # - "
W XYZ[Y\ ^a $ 43 @ @39 / J K 2:f @ @39 1 25 8I9 41 g 2830r4I43@f ;32g n6 7n@3@ @p867 !/ $ 2:f
!/ $o 6 rn 7n27 1 43 @ @39 ;32g n - q87n . @378r@6 qn8rn 86 /01 23 1 345 H@8:; 0g2830r4I432HI@o
27 I@267 H> K 41 7n@ 6@76 41 @378r@6 41 - 6g 2: 8:f r@f 6 H;32g n6 qn8rn 23@ :47 0g 2830r4I432HI@l
[Z Z "+ !K$
! $ & ! $ ? / ! $
& ! $ # J K U #
E &? !M/
QK

$
"+
E &? !M/

$
P - . /F# # " FF" ) MQ
-< = # - ? / H>? K B #  " " R M/ " R " E &? !M/  $ H> K # " # - # -< # # L - /F# # " FF" " R M/ ( -
= # -< + #%
%# ' ? FF" ! = #
- / H>? K $ )  " " FF" "
Z[Z [ ^ $ 43 2:9 e p @f 1 25 8I9
41 0g2830r4I43@f 6 H;32g n6o 7n @ g 34g @379 41 2 ;32g n H@8:;
0g 2830r4I432HI@ 86 7@672HI@l
[Z Z ) !/ $ !/ $ " G Q B
" # # + # # - !  $ " E # + # " # - "+ FF" FF" + /F# # " FF" D ""+ ?E "
+ # # + /07@67 # + * A "+ C
B " # # . "F
"+ ?E " # #+ * " / H>? K C #+ * U + * 7@672HI@ # # + / ( /F C " # B
, + + "+ ( "
B+ D + ! $
" ( B , + # + i &&& j &&& ! $ ( ij # #
p B
Q
# C # # "+ # # + ij L # # # # #
# # , * 8:f8678:; 86n2HI@ # #
+ / ( + " # #+ # " /F# # #+ ! %Q' # # # # $
# * " * " # + # F ! # ( $ + 0r4I432HI@ # ( F # " # - !$ " ( "+ # G # "+ # # + ij # # "+ # F"+ ^] @39 e 367 43f@3 74 3:25 @:7 g 34g @379 41 79g @ hij k 86 8:f8678:; 86n2HI@ 1 345 7n@ g 34g 0
@379 41 H@8:; 0r4I432HI@ 1 43 645 @ l
Y\ \ [Z Z Y X P + i j ! $ #F
! $ ! ( + #+ * # ! $ !K K$ ! $  " "
Q !p $  " "
Q # # Q !p $ " # Q " D + # ( # # U # ("
"+ #" " G !K K$ # - ! + "
!  $
 " " Q !p $  " " Q # ! $ ! $ " ! $ ! $
+ # J K # " )
QQ
# G ! # " $ #  " " " ! # " D # ( $ G " # "+ #
+ # # # # "+ ! # $ #  " " # + # ! $ # G # + " # + F
# U %Q' # # # "
C # " " + + D ( # + 03@; I23
# # ( # " G # + + #
( # ^a _WZ [ \ Y Y[ Z Z Y\ \ a^ac $ 43 @ @39 K %  2:f R 7n@3@ @p867
&? !% R $ 2:f &? !% R $ q87n 7n@ 1 4II4q8:; g 34g @379l
gg 46@ 7n27 86 2 74 3:25 @:7 q87n @378r@6 o 2:f 7n27 86 2 R 07 g I@ 41
f86 48:7 @37@p 6@76 41 6 rn 7n27 1 43 @ @39  " " R 7n@ g283 # # 86 03@; I23o q87n 7n @
f@:6879 41 7n @ @f; @6 g48:78:; 1 345 # 74 # H@8:; 27 I@267 % 81 # g48:76 74 # 8: o 2:f H@8:; 27
5 467  % 47n@3q86@ 64 81 # g48:76 74 # 8: 7n@: 7n@ f@:6879 41 @f; @6 g48:78:; 1 345 # 74 #
# 41 7n@ R 07 g I@6 6g 2: r4g 8@6 41 8: 86 27 I@267 % l n @:o 27 I@267 #%
qn@3@ @2rn # g I296 7n @ 34I@ 41 # l "
Y\ \ , @ 8g2378784: #  " " R # # ( # " # , 3@e :@5 @:7 # B # # " # " # + , # N+ C "+ %S'
QM
^ _WZ [ \ Y Y[ Z Z XY Y [ Y\ \ ` bc $ 43 @ @39 2:f / J K
7n@3@ @p8676 &E ! /$ q87n 7n@ 1 4II4q8:; g 34g @379l
1 86 2 74 3:25 @:7 q87n . @378r@6o 2:f 86 2: @ 8g 2378784: 41 7n@ @37@p 6@7 41 q87n
2: 43f@3 :47 @p r@@f8:; o 7n@: 7n@3@ @p8676 2 3@e :@5 @:7 41 41 43f@3 R o qn @3@ " R " o 1 43
qn8rn 2II g2836 41 6@76 H 7 27 5 467 / H? K 41 7n@5 23@ /03@; I23l
Y\ \ # ! $ " # #
# "+ s+ " + # # ) QS %Q' # ( # (
B ^
_WZ [ \ Y Y[ Z Z Y\ \ a^ c $ 43 @ @39 2:f @ @39 K ! $  7n@3@
@p8676 & ! $ q87n 7n@ 1 4II4q8:; g 34g @379l
1 86 2 74 3:25 @:7 q87n . @378r@6o 7n @: 7n@3@ @p8676 2: @ 8g2378784: #  " " R 2:f 2 3@e : @5 @:7 #  " " R  " " 41 7n27 627861 9 Y\ \ R H 7 R "
$ 43 2II  "
$ 43 2II
"
" l
R H 7 27 5 467 !K$ H? K 41 7n@5 7n@ g283
"
R o 1 43 2II
!R $03@; I23l
"
 " " # # 86 !K$03@; I23l
H 7 27 5 467 !R $ ? 41 7n@5 7n @ g 283
R H 7 27 5 467 !K$ H? K 41 7n @5 23@ 6 rn 7n27 1 43 2II
!K$ ? 41 7n @5 !# # $ !# # $ !K$ n4If6l
d II
"
# # 86
 " " H 7 27 5 467
"
G " # G # # # _ Z Y Z [ \ Y c 8 @: 2 74 3:25 @:7 < 2:f 2 g2378784: #  " " R 41 876 @378r@6o 2: ! $ Y !% /$ \ Z Y Z[ ZY[ 86 2 74 3:25 @:7 q87n 2 g2378784:
#  " " R  " " 41 876 @37@p 6@7o 627861 98:; 7n@ 1 4II4q8:; l
Y Z " # " 1 43 2II
"
"
R 2:f
1 J  o 7n@: 1 43 @ @39 e p @f  "
43@4 @3o 81 J  o 7n @: 1 43 @ @39
 " " l
1 43  " " 23@ /03@; I23l
 " " 7n @ f@:6879 41 7n@ @f; @6 g48:78:; 1 345 # 74 # 86 27 I@267 ? o 2:f 7n@ 6 H74 3:25 @:7 41 6g2::@f H9 # 86 732:6878 @l
"
R o 2II g2836
Q
# # $ 43 @ @39
"
"
R 2:f
 " " o 7n@ g283 # # 86 2: /03@; I23 g 283l 43@4 @3o
1 43 @ @39 e p @f  " " R o 4:@ 41 7n@ 1 4II4q8:; 7n3@@ r26@6 4rr 36l 87n@3 2II 7n @ g2836
# # qn@3@ 2:f 239 4 @3  627861 9 % " ! # # $ "  % 43 2II
@f; @6 41 < H@7q @@: # 2:f # g48:7 1 345 # 74 # o 2:f % " ! # # $ 1 43 2II 43 2II
@f; @6 41 < H@7q @@: # 2:f # g48:7 1 345 # 74 # o 2:f % " ! # # $ 1 43 2II l
) S ! + # + QV # F
# + Q $ # # +
MQ " ( # + # < = #
/ H>? K G F"+ ! #
+ ij $ " " " "+ " # < " F" + # < F" , # + # %Q' " "+ # #
+ ij # G # # ( # F" +
# + j i U %Q' " "+ + # " # # + # B ! (
# %Q' # # # # " + #+ # # $
P ! $  # ( # # # 1 43q 23f g283 # ! $ ! $
! "# $ ! $ ! $ , 1 43q 23f 738g I@ #
# # G ( + ( # # + "
# " # "+ + " # B +
d 74 3:25 @:7 86 628f 74 627861 9 + 81 876 @37@p 6@7 86 7n@ f86 48:7 :84:
41 7n3@@ 6@76 627861 98:; 7n @ 1 4II4q8:; l
Y Z Q&
2:f 6g2:6 2 r4g 9 41 8: l
o 2:f 7n@ 6 H74 3:25 @:76 8:f r@f H9
r4g 9 41 l
$ 43 @ @39  " "
2:f
23@ 8645 43g n8r 2:f r4:728: :4
 o @ @39 @37@p 41 # g48:76 74 @ @39 @37@p 41 # l
G ? . /02g237 # =
# / H>? K ? # # F"+ #
" + # + " # %Q' s # + # # + C [Z Z Z ^]
& ! $ 2:f
n@3@
@p8676 2 r4:672:7 / & 6 rn 7n27 1 43 @ @39 7n@3@ @p867 7q 4 74 3:25 @:76
! $o H47n q87n & ! $ @378r@6o 627861 98:; 7n@ 1 4II4q8:; l
&
2:f
f4 :47 r4:728: 2: 8:f r@f r4g 9 41 l
2:f
23@ / & 02g237l
2:f n2 @ 7n @ g 34g @379 7n27 @ @39 @37@p n26 8:0f@;3@@ 2:f 4 70f@;3@@ 27 I@267 2:f
1 43 @ @39 6@7 41 @378r@6 q87n 68 @ H@7q @@: 2:f ? 7n@3@ 23@ 27 I@267 ? ? 8:r45 8:; @f; @6
2:f ? ? 4 7; 48:; @f; @6l
@39 74 3:25 @:7 q87n
@378r@6
2gg @236 7n @ 625 @ : 5 H@3 41 785 @6 8:
2:f
l
[Z Z Y X + ( ? # +  " " !  " " Q ( # # U Q G Q Q ( " # + # " ( " # # # !# $ #+ # # # " " " ! % '
, ( , $
G Q ? " + ? Q #+ # + # #+ # " / " H ?? K Q ? ! / ? $ ? Q ? # Q
!" $ ( /F G # / & ! # $ # ! $ ( # ? #+ "
"
Z[Z [ ^a
34g @379 86 :47 7@672HI@l
[Z Z ( /F # / / & ?? , ( + ! # %M' " ( $ B " # # + " # A #
( # " , & ! $ ! # # V  $ # # + # & ! $ !D $ + # " # D + # & ! $ # + # & ! $ +
# " # + # & ! $ " ""+ # # !" #
" # A $ G /F#
# #+ "
[Z Z Z ^ n@3@ @p8676 2 g 34g @379 41 74 3:25 @:76 41 79g @ hj i k qn8rn 86 8:f8678:; 86n2HI@
1 345 o 2:f 7n 6 86 :47 7@672HI@l
[Z Z + D # # + ( + # + #
"+ + # # (
+ # ( (+ ( + # ! j i # $ L + #
+ + # ( (+ ( + # + (
#
? + # + ? ? ? ? # + # ? QS
L . #+ " "+ (
# + # "+ # "+ # ! # # # $ G " # # # # " # " " " # "+ " "+ s+ # ? !. $ < + # # L #+ # ( " " # + "+ " "+ < " # "+ # ! $ # + # + + # < "+ # + " + # L ( + # # s+ # G ! # # $ # # # # #  K  s+ " # # + # " " # < "+ # # # # "+ # " # # "# # # ! + " # #
( D # $ "
# N+ ) "+ # " # " ( "+ # # + ij " ( # ( # F # (
J  # %Q' L S ! " ( ( # F" # + j i # + # QV
%Q'$ G"+ # A # " # L L G # ! $ " U ( # # 2 0rn237 < 2:f 2 g2378784: #  " " R 41 876 @378r@6o 2 rn237 86 2:
! $ Y !% /$ \ Z Y Z[ < ZY[ 81 7n@3@ 86 2 g2378784: #  " " R  " " 41 876 @37@p 6@7 627861 98:; 7n@ 1 4II4q8:; l
8 @:
Y Z " # " 1 43 2II
"
"
R 2:f
 " " l
1 J  o 7n@: 1 43 @ @39 e p @f  " " R o 2II g2836 # # 1 43  " " 23@ /03@; I23l
43@4 @3o 81 J  o 7n@: 7n@3@ @p8676  " " 6 rn 7n27 7n@ 0f@:6878@6 41 7n@6@ g 2836 23@ 27
I@267 o 2:f 7n @ 3@6738r784: 41 7n@ g283 1 :r784: 41 < 74 %# ' ? 86 7n@ r4:672:7 1 :r784: l
R 2:f  " " o 7n@ g283 # # 86 2: /03@; I23 g 283l 43@4 @3o
1 43 @ @39 e p @f  " " R 2:f  " " o 81 1 43 2:9 # 2:f # 7n@ g283 1 :r784:
41 < n26 2I @ 4: o 7n @: 7n@ 0f@:6878@6 41 2II 7n@ g2836 # # qn@3@ 2:f 239
4 @3  23@ 27 I@267 % l
$ 43 @ @39
"
"
" "+ # # + ij #
( U " B # " G # # ( # + + # N+ ) C G
+ # L "+ # # ( C "+ # " ! $F" # + ! ! $ #+ # C B " B J K "+ " ! # $ " # %Q' # # + ij "+ # "+ " " " QO
+ # - . H>? K
!# ( $ " " # (+ " # # "+ # " " + "
F %Q' "+ FF"+ #
!( $ ! $F"+ " F # ! $FF + # F"+ %Q' " " " # ( # "+ # ! $FF"+ + " " # ! ( # $ " + L # %Q' " " # " # B
/F C # # / # # "+ # F"+ + # " # A # " + # - . H>E K !# ( $ " " # " # " (" "+
# F ! F$F"+ " # "+ # + # # G F" + F" + F
" %Q' " ( # " +
L + + - . # D #
+ %Q' " F" # ! .$ B " B+ " # + # ! .$ # %M' " # " ! %Q' $ " A # # # #
( + B C # "+ B # F ( MK
+ " F" " " " (
# ( # + "+ !+ " "+ L )$ "
# + +
% '
%Q'
%M'
% '
, N , C )# N N G # N+ ) 4 3:2I 41 d I; 4387n56  ! OO $ VK KO
, # # LA+ # 45 H80
:27438r2 QK !QKKK$ &  S , # # LA+ N " " # B d 4 3:2I 4: 45g 78:; MK !QKK  $ V Q V Q
, L n@ 34H2H8I8678r @7n4f + ! OOQ$
%&' s s" T p 73@5 2I 32g n n @439 , C ! OSV$
% ' , A D L ," " + 34r@@f8:;6 41 7n@ M $ m !QKKQ$ %S' , A+ L D C N BFN + " C d 4 3:2I 4: 86r3@7@ 27n@5 278r6 Q ! OOO$ V M
%V' G # # , + n@ II@78: 41 7n @
34g @2: d 664r82784: 1 43 n@43@78r2I 45g 7@3 r8@:r@ S& !QKK  $ OSF Q %O' G #
!QKK  $ QV QO&
( 34r@@f8:;6 41 7n@ MM d m %K' F " + " 34r@@f8:;6 41 7n@  S !QKKQ$ SM SO
%' , # A N G N+ ) ( # " 34r@@f8:;6 41 7n@ MS d :: 2I $ m ! OO $ Q QK M
%Q'
%M'
P L P N + ( 4 3:2I 41 7n@ d & ! OOV$ &M S&K !, + # MS L OO $
P ) G G 34r@@f8:;6
41 7n@ Q> $ m K O
% ' G P ) " # + # LA T 2:f $ :r784:2I d :2I9686 S ! OOS$ MQQ MMS
#
+ )
@45 @738r
%&' T # L LA T N+ ) 86 8;n79 ! # C + 45 H8:27438r6o 2 I 3f 46
T G L T G LA + $
T s+ # L s ! OO $ QO& M&Q
% ' G # # " 34r@@f8:;6 41 7n @
 $ m !QKKK$ Q&  Q&V
% S'
%V'
N N C " # " 2:f 45 H8:27438r6  ! OV&$ O  O 32g n6
+ ! $ 2:fH44 41 2:f45 8 @f 45g 78:; !L ND C # N# N
$ !QKK  $
N %O' N N"# # L N" A # + F
d 4 3:2I 41 45g 78:; Q& ! OO $ Q&Q QS  34rl 4II4 @ :7@3l Q K
%QK' LA T N # ! s # ) L $ OSV MOO K  %Q ' , "" # (+ 34r@@f8:;6 41
7n @ V $ m ! OSS$ QQQ QQS
MQ