1 3 5 аб9 ¤AAA 1. [5 points] The language consisting of the number

!"$#%&('*)))
+ ,.-0/1*2436587:9<;
*
=?>@ ACB 5D4E B D @ F 245*9G3C9<7H3I5D 2KJL7 >M@ 5$ENPO @RQ ST JU2 AIA 2KV @KW $O X B $5 X $5 ENPO @RQ 2YJ[Z @Q 2 @ 9
\<] S^S_$^S__8^SR_4__8^``R`4acb 3C9d245 @e@fMB Ng1 AI@ 2KJ BhQH@ D4E AiBYQjACB 5MD4E B D @ ,lm
k 36n @ 42 5 @oR@ fB Np1 AI@ 2KJ BhAiB 58q
D4E B D @ 7 >*B 7m3i9drs4t Qu@ DE ACBKQ \ E*9G3I5Dv7 >@jBYA 1 >*B O @ 7 ] _8^RSYacb ,
= >@QH@wBYQH@wA 27x9v2YJj7 >@ 9 @
?
ACB 5D4E B D @ 2YJ BYA6A 9<7 Q 3I5D97 >*B 7
E5 F 24Np1EM7 B O AI@ 58ENPO @Q V?2E
 \ 7 >M@Ž>&BYA 7H3I5DP1 Q 24O B O3 A 3I7GX b
,
= >@h@KB 9<3 @ 9<7 @fMB Np1 A6@ 3C9P1 Q 2O B O A X ] _YySzy{ |~} S^x8^x€$^```za \ 7 >@
, ?
BYQH@ 9<2N @ 5$EN‚O @Q 2YJ _ 9 T JU2 AIA 2KV @KW O$Xv7 >@ 9 B N @ 58ENPO @Q 2YJ S 9 b , ƒm5$X
ACWeBYA 9<2vV„2 Qu…T 9<E F†>eB 9?7 >@dAiB 5DE B D @ 2YJ BYA6A 7 >@ 1 QH@ˆ‡*f$@ 92KJ?‰ >*B 3I7H3I5‹ŠŒ9
 ,.-0/v123I5$7x9G;
‘’>*B 73i925 @jW8@ˆ‡ 5367u36245p2KJ“ \ 7 >@ D 2 ACW$@ 5 QxB 7H3I2 ub ”e• 24EpN B XvV Q 3I7 @m@ 367 >@RQB 9G3INp1 AI@@K– E B 7H3I25o7 >*B 7
FB 5gO @ 9<2 A n @KW JU2 Q “ T 2 Q V Q 3I7 @ 7 >@ n BKA E @ 2KJ“p3I5 ˆF A 29 @KW JU2 Q N \ 129u9G3IO A X‚365 FˆA E W 3I5D B 9 – E BYQH@
Q 2c27 b ,
“— ˜l“p˜ Sd}’_
S
“ }™S?š
“
Sšœ› /
“ }

“ }F 29mž*Ÿ
/‹ S
“ }¡Sš
S
S?š
S
S¢š
S
S?š
Sš’```
£‹,.-0/v123I5$7x9G;
¤ 2KVlN B 5$XdV B X9 BKQu@ 7 >M@Qu@ 7H2 QH@KBYQHQxB 5D @ 7 >@A6@ 7u7 @Q 9(3I5pkd¥d¥
¦¨§©m¥d‰„ª?««¥¨© ” § AI@KB 9 @ O @¨FBYQH@ JUE A
V >@ 5 F 24E5$7u365D AI@ 7u7 @RQ 9ˆ,
¬ 3 Q 9<7 A6@ 7ŠŒ9 F 2E5877 >@dAI@ 7H7 @Q 9ˆ­
S
®*@ 7u7 @Q
k
¦
¥
±
¯ E N°¥ FF E QuQH@ 5 Fˆ@ 9
S
S
S
§

©
ª
S
«
‰

S
= 27 BKA
RS €
¯ K2 V²V @„³ E*<9 7.E*9 @ 2E Q NPE A 7u3I5M24NP3 BYA JU2 Q NPE AiB
RS €8´
}¶ ± ^x·4¶ ± ^x·_4_
± ´µ$´µ$´
¸‹,.- S /v1*2436587:9<;
• 42 E¹9 B Vº365 FzACB 9H97 >*B 7‚7 >@p>*BKA 7H3I5D»1 Q 2O AI@ N¼3i9E5 W8@KF 3 WB O AI@ , = 2»1 Q 2Yn @ 7 > 3i9 T V @½W8@ˆ‡ 5 @KW 7 >M@
>*BYA 7u365DJUE5 F 7H3I25o7H2‚O @ ­
¾ ¤ ƒ ®= \ § b} X @ 9 T 3¿J(7 >@jÀcB n B 1 Q 24D QxB NLÁ >*BKA 7:9 T 2 Q 367 W 2 @ 9G5‹Š07 F 24Ng13 A6@
¾ ¤ ƒ ®= \ § b} 52 T 3ÂJ(7 >@jÀcB n B 1 Q 2D Q:B NLÁ F 24Ng13 A6@ 9 B 5 W½W 2 @ 9<5Ê07 >*BKA 7
¬ I3 5M3C9 > 7 >@ 1 Q 2c2KJPO8X FˆQu@KB 7u365D BÄF 245$7 QxBW 3 F 7u3I25 T V > 3 Fx> 1 Q 2Kn @ 9‚7 >*B 7½7 >@RQu@ 3C9p52l1 Q 24D QxB N
F 24Ng1E7 @Ť ƒ ® = ,
®*@ 7ŠŒ9?V Q 367 @jB 1 Q 24D QxB N
FRBYAIA6@KW ‰¥ ¯
¬Æ «$ªÄV > 3 F†> E*9 @ 9 ¤ ƒ ®=ÇB 9 B 9<EO Q 24E7H3I5 @ ­
ÈÉ4ÊMËÍÌMÎ$ÏÐ:ѐÒ(Ó
ÔKÕ ÐHÖ8×$Ø$ÙÐ:ÑÒ Ô8ÚÜÛ$ÛݐÞMÚàß$ß Òâá$ã Þä
å8æ$æ4ç Õ æè ÞéÞ è
Þ å ÚcÞ
è Þ á8ê$è ä?ë
‘’>*B 7 F 2E ACWe¤ ƒ ®= \ ‰¥ ¯
¬Æ «$ª b O @4”
‘ >@ 5pV .
@ Q E5½‰¥ ¨
¯ ¬Æ $« ª T V @ V 3 AIA*@ 5 W E1p3I5g7 >@‡*Q 9G7?1 KB Q 72KJ(7 >@ 3¿J(9G7 B 7 @ N @ 5$7 T B 5 W
¾ X @ 9z­ ’
V„24E AiWA 2c241JU2 uQ @ n @RQ , =?> C3 9(N @KB 5&97 >*B 7 ¤ ƒ ®=ìQu@ 7HE Q 5 @íW 7 >M@ V Q 25 D B 5*9GV @Q ,‰ 2587 QxB4W 3 F H7 3I245Ã,
@ Q E5w‰¥ ¯
¬Æ $« ª T V @ V3 A6A@ 5 W E 1½3I5e7 M> @Ž@RA 9 @ 1 YB Q 7m2KJ7 >@ 3ÂJ9<7 B 7 @ N @ 587 T$B 5 W
¾ 52M­ ‘’>M@ 5eV d
V3 AIA>&BYA 7R, =?> C3 9N @KB 5*97 >*B 7 ¤ ƒ ® =’Qu@ 7HE Q 5 @íW 7 >@ V Q 42 5D B 5*<9 V @ Q ,?‰ 2587 QxBW 3 F 7HI3 25‹,
=?>@QH@ JU2 QH@ 7 >@QH@ 3i9?52v1 Q 24D Q:B Nî7u2 F 2Np1E7 @d¤ ƒ ®= ,
ï
ð,.- S_ 1*2436587:9<;
Æ 9<365Dv245 A X ¯ ƒ ¯ ¦²D B 7 @ 9 TW$QxB V B 5eñd¥¨© F 3 Q:F E367,‰ AI@KBKQuA X ACB O @RA Xc24E Q 3651E7:9 B 5 W 24E7H1E7,

7u2
NOTE: this is effectively an OR gate
x
y
x XOR y
this is effectively an AND gate
ò‹,.- S_ *
1 2436587:9<;
=?>@ JU2 A6A 2KV3I5DJ BF 7.V B 9?E&9 @KW 9 @ n @Q:BYA 7u3IN @ 93I5e7 >@ k Q 2E1*9 AI@KF 7uE QH@ ,
k.3In @ 5 B D Q 24E1 \<ó ^ˆôjbxT 9 > 2KV¹7 >*B 7JU2 Q„BYAIAõPö ó T 7 >@ JUE5 F 7u3I25p÷ \ø b } ø ôdõ 3C9àO*247 >wS q S
B 5 W 245$7u2,
ø ù ^ ø O @ 9GE Fx> 7 >*B ú
® @ 7 b } ÷ \ ø b:T 2 Q 3I5w27 >@Q V?2 QxW 9 T øù ôÅõâ}
7 ÷ \øù d
¾ SqS ­ *
—
—ù
õPö ó T V @d… 5M2YÇ
V 7 >&B 7.3I7 >*B 9 B 5o3658n R@ Q 9 @ \ õû b E5 W8@RQ
ô ,
ø ù ôÅõü}
Ã
ù
\øÃù ôdõbuôÅõ û }
ø ù ô \ õôdõ û ù b }
øù ôvS
}
øÃù }
ø d
ô õ ,o«3I5 Fˆ@
—
ø d
ô õ
—
ù
\ø ôdõbuôÅõ û
—
ø ô \ õôdõ û ù b
—
ø ôvS
—
ø
—
• 24E F 24E AiWeBYA 9G2v1 Q 2Kn @ 7 >*B 77 > 3i9JUE5 F 7H3I25p3C9 S q S?³ E*9G7O8XP527u3I5MDv7 *
> B ?
B F 42 5*9 @K– E @ 5 Fˆ@ 2YJ
7 3I7Rе9 v
7 >@jFB 5 Fz@AIAiB 7u36245p7 >@ 2 Qu@ Nw,
ù
¾ 2587H2­ ¬ 2 Q.B 5$Xeý ö ó T ÷ \ ý ôdõû b } ý*, § Q 2c2KJH­
ù
ù
ù
÷ \ ý ôdõ û b} \ ý ôdõ û bHôdõü} ý ô \ õ û ôÅõ&b} ý ôúSÅ} ý
ù
«c365 Fˆ@ V @d… 52KVÇ7 >*B 7
ý ôdõû ö ó T ÷h3C9?2587H2,
€
þ ,.- S /v1*2436587:9<;
¤m@QH@ 3C9?7 >@dQu@KF E QuQu@ 5 Fˆ@
QH@ACB 7u3I25pJU2 Q 7 >M@ŽQ E55365DP7u3IN @
= \ 5 b 2KJ 9G24N @ JUE5 F 7H3I245í
ÿ \ |‹b}ǀÿ \ | / bàšS
ÿ \ SKb } S
«c2 A n @ 7 >M@
Qu@KF E QuQH@ 5 Fˆ@.Qu@AiB 7H3I245 B 5 W @Rf 1 QH@ 9u9 = \ 5 b E&9<3I5MD¢q527 B 7H3I25‹, • 2EoN B X B 9H9<EN @ 7 >*B 7 | 3C9
B 1*2KV @RQ 2YJ„/$,
ƒ
9u9GEN @ 7 >*B 7 | } / T JU2 Q 9G24N
@f 1 B 5&9<3I25p2YJÃ7 >@¨Qu@KF E QuQu@ 5 Fˆ@ , =?>@
O Q:B 5 Fx>@ 9
7 >MQu@@ 7u36N @ 9ˆ, =?>@v‡*Q 9<7
B 5 Wh@KB4Fx> 2KJ 7 >@ 9 @ O QxB 5 F†>@ 9¢7 >Qu@@
Q EM553I5MDp7u36N @ , =?>@AiB 9<7 AI@ n @A 2YJ„7
7 >M@ 9GENw­
@ I3 5$7 @ D @Q _ , ‘»@PFB 5 F 25*9<7 Q E F 7 B 7 Qu@R@Qu@ 1 Qu@ 9 @ 5$7u3I5MD‚7 >@
7u21 AI@ n @RAF 2587 Q 36OE7 @ 9 S J Q 2N 7 >@.@K– E B 7H3I245 €4ÿ \ | / b$š»S4TMB 5 W
A6@ n @A \ O @A 2YV%7 >@PQ 2c27 bÅF 245$7 Q 3IOE7 @ 9 € \ 245 @ J Q 2N @KBF†> 5M2 W8@4b
7u36N @ 9ˆ, =?> E*9¢7 >@
7 >hA6@ n @A 2YJ„7 >@ 7 QH@@jF 245$7 Q 3IOE7 @ 9 € 7H2‚7 >@
>M@ 7 QH@@ 3i9¢7 >
@ 7 >hA6@ n @ATB 5 W 7 > E*9m7 >M@ 7u27 BKAàQ E55365Dp7u36N @ 3i9
S¢š €mšl€ — š4š € =?> 3C9.9<EMN
@ n BYA E B 7 @ 9?7u2M­
ù
€ ˜ S
€ ˜ S
S
S
ù
€ ˜


«c3I5 Fˆ@ V @jBYQH@ŽA 2c2 … 3I5DP245 A X‚JU2 Q 7 >@jB 9<X$Np17H247H3 FmQ E55365D‚7H3IN @ \ 365e247 >M@Q ?
V 2 QxW 9V @„³ E*9G7mV B 5$7
¥q5M247 B 7u36245 T 527 B 5 @RfBF 7 B 5*9GV @QzbxTàA6@ 7dE*9Ž36D452 Qu@ 7 >@ NPE A 7H3I1 A 3 FB 7H3In @úB 5 W 4B WW 367u36n @pF 25*9<7 B 5$7x9 T
AI@íB n$3I5MDE*9V3I7 > \ € b ,?«c365 Fˆ@p}’A 2D |(T 24E Q.Q EM553I5MD‚7H3IN @ 3C9 \ €Kycb V > 3 F†> FB 5½O @ JUE Q 7 >@RQ
ù ! "# b ,
9<36Np1 A 3 ‡*@KW 7u2 \ |bxT V > 3 Fx> 3C9 B O2E7 \ |
$‹,.- S /v1*2436587:9<; %# #"
\ Ng2 W&'&4b ,p« > 2KV"Xc2E Q V?2 Qu…»B 5 W @Rf 1 AiB 365hO Q 3 @)( X > 2KV"Xc2E F 24Np1ME7 @KW Xc24E Q
‰ 24Np1ME7 @eS /Y± 
B 5*9GV @Q ,
¬ 3 Q 9<7 T V @h… 52KV 7 >*B 7oV @wFB 5 Qu@KW E Fˆ@ 7 >M@ O B 9 @ O @ JU2 Qu@w@Rf 1*245
\ Np2 W,&'&4b:T‚S /Y±  ##%" *  ##" \ Np2 W,&'&b , ‘»@ìBKA 9G2’9 B VL365 AI@KF 7HE
@f 1*245 @ 5$7
O$Xe7 BY… 3I5MDp3I7
Ng2 W 7 >M@ 7u247H3 @ 5$7JUE5 F 7H3I245 \ BY…B ªE AI@Q е91 >
1 Q 2 W E F 7
2KJ„7<V„2‚1 Q 3IN @ 9 T 7 >@Qu@ JU2 Qu@T/- \ &'&b} \ SS ˜ SYb \ & ˜ SYb}™¶4_
 ##" *Ç " } S¶ \ Np2 W,&'&b ,
@ 85 7H3 B 7u3I5MD,"«c365 Fˆ@ìS /Y± +* 
Qu@ 7 >*B 7½V @ FB 5 Qu@íW E Fˆ@ 7 >@
3àJUEM5 F 7u36245 b.- \ &&4b , &'& 3C9m7 >@
,«c3I5 Fz@v€4¶¶ ± * ± \ Ng2 Wo¶_Íb:T
0‹,.- S /v1*2436587:9<;
‰ 245*9G3 W8@RQ 7 >@ D Q 42 E12145 3 T V > 3 †F > i3 9m7 > @ 9 @ 7 ] S4^x€$^ / ^6&4a E5 W$@Q NPE A 7H3I1 A 3 FzB 7u36245eNp2 Ww· , ‘’>&B 7 BYQH@
BYA6A 2YJ3I7x99GEOD Q 24EM*
1 9 ” \ ¯ 2v1 Q 2cY2 J HQ @K– ME 3 Qu@íW , b
¬ 3 Q <9 7
2KJ KB AIAT V P
@ … 5 2KV¡J Q 2N ®B D QxB M5 D @ ŠŒ9Ž7 M> @ 2 QH@ N 7 >*B 7dV @ 2 5 A X >&B n @ 7u2 A 2c2 …»B j
7 9<EMOD Q 24E1*9
\
\
2YJ9<36Z @ 42 5 @ ³ &
E 9<7?7 >@ 3 8W @ 587H3I7GX b:Tc8TMB 5 W ± 7 >@ V > 2 AI@ D Q 2 E1 b , ¬ 2 Q 7 >@ 9GEOD Q 24E1&9¢2KJ G9 3IZ @¨8T 9G3I5 Fˆ@
±
7 M> @ 3 $W @ 85 7H3I7GXPN‚E*9G7O @ I3 5 B $5 X½9<EOD Q 2E1 T V @jFB 5 ³ *
E 9<7.7 Q o
X 2E7 KB AIA 7 >M@ 1*2c9H9<3IOM3 A 367u3 @ 9JU2 Q 7 >@ 27 >@RQ
@A6@ N @ 5$7 \ B 5 W 9 @@ 7 >*B 7m7 >@ X BYA6A V?2 QH…b ­ ] YS a ] S^x€Ía ] S ^ / a ] S ^)&4a ] S ^x€8^ / ^)&4a
+ 7,.- S /v1*243I5$7x9G;
= >@ D Q:B 1 > O @RA 2KV’3C9 ˆF @RQ 7 B I3 5 A v
?
X 5247 B 1 AiB 5 @ D xQ B 1 >‹T O @íFB E*9 @ 7 >@QH@dBYQH@jFˆQ 29u9<365D A 365 @ 9z,§ Q 2Kn @ 367?3C9
5247 B 1 ACB 5 BYQ D QxB 1 > E*G9 3I5D B 7 >@ 2 Qu@ NÜXc24E 9 B V²63 5 FˆACB 9u9ˆ,
=?>@ ME 11 @ Q?‡ n @ 9?n @Q 7u3 Fˆ@ 9 BKQu@ ³ E*9<798 *
T B 5 W,: E Q:B 7H2YV.9 … 3е9 =?>@ 2 Qu@ Nº7 @A6A 9?E*97 >&B 7 B 5$XpD Q:B 1 >
V > 3 F†>½F 285 7 B 3I&
5 9 B‚F 218XP2YJ;8 C3 9?527m1 ACB 5 YB Q ,
+ +,.- S /v1*243I5$7x9G;
*
‘’>*B 7j3C9d7 >@P@f 1 í@ F 7 @KW $5 ENPO @ Q 2YJ.7 Q 361 IA @ 9
2KJ S ŠŒ9Ž365 BeQxB 5 W 24N
ª f 1 AiB 365 > 2YV Xc24E F BYAiF E AiB 7 @íW Xc42 E Q.B 5*9<V @ Q ,
| qO3I7ú9<7 Q 3I5MD TB 9u9GENp3I5MD |=<܀͔
\ ¬ 2 Q.@fMB Np1 AI@cT 7 >@ 9<7 Q 3I5MD _$S4S4SR_8SS4S4SS‚>*B 9¢±v7 Q 361 AI@ 9z, b
®*@ 74>LO @ 7 >@¨QxB 5 W 24N n BYQ 3 B O AI@ JU2 Q 7 >@ 5$ENPO @RQ 2KJ 7 Q 3I1 A6@ 9365e7 >@ 9<7 Q 365D, ®*@ 7Rе9 F 25*9<3 W8@Q 7 >@
QxB 5 W 2Nºn BYQ 3 B O A6@ 9?> \ JU2 QdS @=
A@Ç| ˜ cb V > 3 Fx>pBKQu@PS 3ÂJÃ7 >@ 5 @Rf 7 7 >MQu@@ OM3I7x9„9<7 BYQ 7H3I5D B 7 BYQH@PS
B 5 Ww_ 247 >@Q V3i9 @ , ¯ 2KV V @>&B n @ 7 >*B 79> } > ù š > š > š=cš > yYû , =?>M@v@f 1 @KF 7 @KW n BYA E @
—
—
JU2 Q B 5$B
X > 3C9 ³ E*9<7„7 >@ 1 Q 24O B O3 A 3I7GXv7 >*B 7„3I7 3C9 S4T V > 3 Fx> 3i97 >M@ 1 Q 24O B O3 A 3I7GXv7 >&B 77 >MQu@@ 9<1 @KF 3 ‡F O3I7:9
BYQH@PS , =?>@Qu@ JU2 Qu
@ C D- > ; } Sí· ,FE?X A 365 @KBYQ 3I7GXv2YJ @f 1 @KF 7 B 7H3I25‹­
yKû —
yKû — S
| ˜ 
}
C -D>½; } G C - > ; } G
·
·
IH ù
I H ù
/
+ ,.- S /v1*243I5$7x9G;
®*@ 7BJ O @eB 5ìEM5 W 3 QH@KF 7 @KW D QxB
B 5 W½B 9H9<EN @ 7 >*B 77 >@ n @Q 7H3 Fˆ@
J T V > 3 F†> N @KB 5*97 >*B 7„3I7?3i9 B 5
W L 36,
n @Q 7H3 Fˆ@ 9 B 5 B
5 J TB 5 W K
1 > V 3I7 > | n @RQ 7u3 Fˆ@ 9z,eƒ
9u9GEN @ J >*B 95M2 A 2c21*92 Q 1
Y
B
H
Q
@
® @ 4
9
5$ENPO @Qu@KW J Q 24N S 7u2 | , *
7 K¡O @ 7 >@jB4W³xBFˆ@ 5
| O8X | N B 7 Q 3 f 9<E Fx> 7 >*B 74K \ u^MLb} S 3ÂJÃ7 >@RQu@ 3i9 B 5
\ uM^ Lb(}Ç_ 27 >@RQ V3C9 @ ,
BYQ:BYA6AI@A„@KW D @ 9 T
F XgN B 7 Q 3 f UJ 2 Q
@KW D @ O @ 7<V @@ 5
¯ K2 V F 25*9<3 W8@Q 7 >@ 9<E FFz@ 9u9G3In @ 1*2YV @ Q 9 2YJ7 > 3i9¢N B 7 Q 3 f N
­ K T K — T K K T‹``` , Æ 9 @ 3I5 W E F H7 3I245e7H2p1 Q 2Kn @
7 >*B 79K \ u^MLb 3i9?7 >@ 5$EN‚O @Q 2KJ1 B 7 > 9 2YJ AI@ 5D47 >o@RfBF 7 A X O @ 7GV @@ 5pn @Q 7 @ fO
B 5 W n @ Q 7 @f L 365PJ,
> S O @ 7GV @@ 5
E B 9 @.FB 9 @ ­ } S , =?>@ 2 Q 36D43I5 BYA N B 7 Q 3 f KlD43In @ 9E*97 >@ 5$ENPO @RQ 2YJ1 B 7 > 92YJ AI@ 5D47 e
B 5$Xpn @Q 7u3 Fˆ@ 9 B 5 WQL O @íFB E*9 @ K \ u^RL&b} S 3TS 7 >@QH@ 3C9 B 5 @KW D @ O @ 7GV @@ 5p7 >@ Nw,
U 5 W E F 7H3I25 > X$1*247 >M@ 9<3i9ˆ­Ž«E11*2c9 @ 7 >*B 7K9 û ù \ u^MLb.F 2 QuQu@íF 7 A Xo7 @AIA 9¢E&9m7 >@ 5$ENPO @Q Y2 J 1 B 7 > 9
2YJ
AI@ 5D47 >o@RfBF 7 A X O @ 7GV @@ 5on @RQ 7 @RfQ
B 5 W n @RQ 7 @RfVL 3I5PJj,
U 5 W E F 7H3I25e9<7 @ 1‹­ ®*@ 7E*9 FRBYACF E ACB 7 @ K9.O8XPN‚E A 7u361 A X$3¿5D K9 û ù O8XOK,WE?X W8@ˆ‡ 5367u36245 T 9
K \ u^MLb 3i9ˆ­
K \ u^RL&b } G
¯ 42 7 @ 7 >*B 7?JU2 Q.@ n @Q X õ*T V > 3 F†>pQH@ 1
2YJ(1 B 7 > 9?2YJ AI@ 5D7 >P@fMB4F 7 A X ˜ S J Q 2N
K \ õM^ Lb 3i9¢7 >@ 58EMN‚O @Q 2YJ„1 B 7 > 9m2KJ A6@
7 >M@ 5$ENPO @Q 2YJ AI@ 5D7 > q 1 B 7 > 9?J Q 24N
õ D3In @ 9 E*9¢7 >@ 7u27 BYA 5$ENPO @Q 2KJ 1 B 7 >
y
XH ù
ù
K û \ u^xõbY K \ õ^MLb
ù
QH@ 9 @ 5$7x9 B 5½3I5$7 @Q N @KW 3 B 7 @ n @RQ 7 @RfT K9 û \ u^:õ&b 3C9?7 >M@ 5$ENPO @Q
n @Q 7 @fZ
7u2jn @Q 7 @fPõ \ O$Xv7 >@ 365 W E F 7u3I25 > X$127 >@ 9<3C9 bxTMB 5 W
5D7 >ìS J Q 2N õ 7u2 L ,9[hE A 7u361 A X$3I5Dv7 >@ 9 @ 7u2D @ 7 >@Q D436n @ 9¢E&9
7H2 L 7 >*B 7D2‚7 >Q 2ED > õTMB 5 W 9<ENpNg3I5Dd7 >M@ 9 @ EM1o2Kn @Q.BKAIA
> J Q 2N°n @RQ 7 @RfQ
7H2‚n @RQ 7 @Rf L ,
92YJ AI@ 5D7 \
+$£,.- S /v1*243I5$7x9G;
U 5o7 > 3C9?1 Q 24O AI@ NÜXc24EeV3 A6A*Qu@KW E Fˆ@ 7 >@ «EO*9 @ 7
«cEN
1 Q 2O AI@ Nw,
9 @KBYQ:F†> 1 Q 24O A6@ N
7H2v7 >@ «cEMO*9 @ 7
«EN
W8@KF 3C9<36245
T B 5 W
¾ c« EO&9 @ 7«EN^]_a`cbdfeQghbHsci)jk_6l­.D43In @ 5 B 9 @ 7 ó } ] ø ù ^```z^ ø y a 2KJ | 5 B 7uE QxBYA $5 ENPO R@ Q 9 B 5M247 >M@Q 5 B 7uE QxBYA 5$EN‚O @QWmzT8‡ 5 WeB 9<EO&9 @ 72KJ ó V > 29 @j@AI@ N @ 587:9 B4MW W E 1½7u2 @Mf B4F 7 A X m ,
ó ]øù ^R```^ ø a K2 J | 5 B 7HE QxBKA 5$EN‚O @Q 9 T(B 5 W
¾ c« EO&9 @ 7P«cEN on _adpT]qpCscr,ghbusci6jk_6l­dD43In @ 5 B 9 @ 7 ¡
y
B 5M247 >M@Q 5 B 7uE Q:YB A 5$ENPO @RQAmzT8W 2 @ 97 >@Qu@¨@f i3 9<7 B G9 EO*9 @ 7?2KJ ó <9 E Fx> 7 *
> B 7„I3 7x9 @AI@ N @ 5$7x9 B4WW EM1
7u2 @fMB4F 7 A X mx”
> B4WlB 5ì2 Q:B4FˆA6@ V > 3 Fx> F 24E AiW <9 2 A n @ 7 >@ 8W @KF i3 9<3I25ì1 Q 24O A6@ N \ 365 F 245&9<7 B 587
§ Q K2 n @ 7 >*B v
7 3¿J7 >*B v
7 Xc2E *
7u36N 4@ bxT 7 >@ e
5 Xc24E F 2 E ACW E*9 @ 7 > 3C9?2 QxBFˆAI@ 7u2g<9 2 A n @ 7 >@ 9 @KKB QxFx> 1 Q 2O AI@ N I3 5e1*2 A X$52Np3 BKA 7u36N @ ,
U J‹7 >M@Qu@ 3C952ú9<EO*9 @ 7 T V @¨FB 5 ‡ 5 W 7 >*B ?
7 3I5 F 25*9<7 B 5$7?7u36N @ O$X ³ E*9G7 RF BYAIA 3I5Dd7 >@
W$@KF C3 9G3I25‚2 QxB4FzAI@ ,
®*@ 7
««Í¦ @KF
Qu@ 1 Qu@ 9 @ 5877 >@ «cEO*9 @ 7 «cEN ¦ @KF 3i9<3I25e2 QxBFˆAI@ , ‘â@jFB 5o&
E 9 @ 7 >@ JU2 AIA 2KV365D YB A D42 Q 3I7 > Nw­
¾ ¬ 2 Q4
} S 7 > Q 2 ED > |
r 3¿J \ ««$¦ @íF \<ó\sm]ø $a TtmxbubxT$Qu@ Ng2Yn @ ø J Q 2N ó
¶
¾ HQ @ u7 E Q 5 ó ,
‰ 2 QHQu@KF 7H5 @ 9H9ˆ­ ó BKA V B XM9 >&B 9 B 9<EO&9 @ 7jV > 3 Fx>ìBWW 9dE1ì7u2 m 9<365 Fˆ@ V @ 245 A X Qu@ Ng2Yn @ ø 3¿J7 >@
W8@KF C3 9<36245½2 QxBFˆAI@ 9<7H3 AIA 9 B XM9BuuX @ 9vv7u2p7 >@vQu@ N B 3I5M3I5DP9 @ 7m2KJ @AI@ N @ 587:9ˆ, ¬ E Q 7 >@QTÃB 7.7 >@v@ 5 W 2YJ„7 >@
BYA D42 Q 3I7 > N @ n @RQ X @AI@ N @ 587 ø V > 3 F†> 3C99G7u3 AIA 365 ó 3C93I5 FˆA E W$@KW 3I5w_6x_6b)yp9GEO*9 @ 7V > 3 Fx>½B4WW 9¢E1½7u2 m
\ 27 >@RQ V3C9 @cT ø V„24E AiW >&B n @ O @@ 5 QH@ Np2Kn @KW J Q 24N ó b , =?>M@Qu@ JU2 Qu@ 7 >@
@A6@ N @ 5$7x9‹2YJ ó¹\ B 77 >@
@ 5 W 2YJ
7 >M@BKA D2 Q 367 > N b B4WMW E1e7u2 m ,
©¢EM553I5MD = 3IN @ ­ ‘»@
A 2c21e7 >Q 24ED > 7 >M@
@AI@ N @ 5$7x9‹2YJ ó @RfBF 7 A X‚25 Fˆ@cT E*9<365D F 25*9<7 B 5$77u36N @ 25
@KBF†> 3I7 @QxB 7u36245‹,?¥.E Q 7H3IN @ 3C9 FˆA6@KBYQHA XP1*2 A X$52Np3 BKA ,
+$¸,.- S /v1*243I5$7x9G;
¬ 3IDE Qu@ 2E7vV >*B 7P7 > C3 9v¦ ¬ ƒ W 2 @ 9ˆ, =?>M@ 5 T D43In @ 5 B 1 BYQ 7u3 F E ACBKQvQxB 5 W 24N 9G7 Q 365Dw2YJ _ 9 B 5 W S ü
9 2KJ
IA @ 5MD47 > |z / T V367 > h
_ B 5 WœS O @ 3I5D @K– E BYA6A X A 3 …c@A X T V >*B 7j3C9
7 >@ 1 Q 24O B O3 A 3I7GXw7 >*B 77 >@ 9G7 Q 3I5e
D 3C9
B4FFz@ 17 @íW O$XP7 > 3i9m¦ ¬ ƒ ¨
” ¯ 247 @ 7 >*B 7.7 >M@ 25 A X B4FFˆ@ 17u365Dv9G7 B 7 @ 3i9?7 >@ ux9GNp3 A6@ X{vŽ9G7 B 7 @ ,
1
1
1
1
0
0
1
1
0
start
0
0
0
0,1
=?>@v@KB 9<3 @ 9<7
V B Xe7H2 @f 1 Qu@ 9H9mV >*B 7
7 > 3i9
¦ ¬ ƒ W 2 @ 9
3C9.7 >*B 7
3I7 B4FFz@ 17x9 B 9<7 Q 3I5MDp3ÂJ„3I7 F 2587 B 3I5&9
@fMB4F 7 A X €w_ 9 T 5245 @ 2KJdV > 3 F†>lBKQu@½B4WR³xB4Fˆ@ 5$7, ¯ 2YV AI@ 7е9 F 24EM587v7 >@ 58ENPO @Q 2YJÅ9<E Fx> 9<7 Q 3I5MDc9v2YJ
AI@ 5D47 >ì| , ®*@ 7ŠŒ9ÅN BY…c@ 7 >MQu@@ 3I5 W 3In$3C9<36O AI@ú_8S E53I7:9Ž7H2|uH1 Q 27 @KF 7}vo7 >@ 245 @ 9
J Q 2N @KBF†> 247 >@QRT V @
7 >M@ 5 >*B n @ 7 >Qu@@ 2KJ7 >@ 9 @ E5367x9 B 5 Ww| ˜ ¶ 247 >@QvS 9
7u2p1 AiB4Fˆ@ , ‘»@PFB 5 ³ E&9<7
13 F†… 7 >@ 9<1*247:9ÅJU2 Q
7 >M@_$S 1 B 3 Q 9 B 5 W‚‡*AIA 7 >@PS 93I5 @ n @Q X8V >M@Qu@.@A 9 @ ­9~ yKûc ,
¤ 2KV @ n @RQT 7 > 3C9 W 2 @ 9?5247 F 2E5$79<7 Q 365Dc9?V > 3 F†>g@ 5 €
W  365 _ , ®*@ 7Rе9 ‡*f 7 >M@
ACB 9<7O367?7u2vO @ Z @Q 2 B 5 W
N BK…c@ 7GV?2v365 W 36n83i9<3IO AI@ E53I7:9¢2KJ _$S ,«c3INg3 ACBKQuA X T 7 >M@Qu@jBYQH@ ~ yKûc 9G7 Q 3I5D9¢N BW8@ 365o7 > 3C9?V B Xc,

=?>@QH@ JU2 QH@ 7 >@QH@dBYQH@ ~ yKcû š ~ yYû | qOM3I7.9<7 Q 365Dc9 BFFˆ@ 1— 7 @KW O$Xp7 > 3C9¦ ¬ ƒj,«c365 Fˆ@ 7 >@Qu@ÅBYQu@jKy
9<7 Q 365Dc9 BYA6A 7u2D @ 7 >@QRT 7 >@ 1 Q 24O  B O3 A 3I7G— Xp 3C9z­
~ yYûc š ~ yYû

— 
 y
&
+ð,.- S /v1*243I5$7x9G;
U J U?Fx> 2c2c9 @e@AI@ N @ 85 7:9 \ V3I7 >hQH@ 1 ACBFˆ@ N @ 587 b 2E7.2YJ ] S4^`R``u|‹av@ n @Q Xp7u36N @ V3I7 > B 5 @K– E BKA(F†>*B 5 Fˆ@
> B 2YJ Fx> 2c2c9G3I5D @íB4Fx> 25 c@ T V &
7 3C97 >@ 1 Q 24O B O 3 A 3I7GXv7 >*B 7?7 >@ 9 @í– E @ 5 ˆF @U D @ 7„3C9„9<7 Q 3 F 7 A Xj3I5 FˆQH@KB 9G3I5D ”
¬ 3 Q 9<7 T> 2KV N B 5$X½9 @K– E @ 5 Fz@ 9 F 24E AiWPU D @ 7 ”¹=?>@Qu@PBKQu@P|ìFx> 23 Fˆ@ 9 @KBF†> 7H3IN @cT 9<2e7 >M@Qu@úBYQu@g| @K– E BYA6A X A 3 …c@A X‚2E7 F 24N @ 9z, ¯ 2KV¡V @ 5 @@KW 7H2 F 2E5$7
7 >@ 58EMN‚O @Q 2KJ„9 @K– E @ 5 Fˆ@ 9V > 3 Fx>wBKQu@ 9G7 Q 3 F 7 A X
3I5 FˆQu@KB 9<365D, =?>@ 36Np1*2 Q 7 B 5$7.3I5*9G3ID > 7
3i9m7 >*B 7
7 >M@Qu@ 3i9 BwS q SPF 2 QHQu@ 9G1*245 W8@ 5 Fˆ@ O @ 7GV @@ 5w9<EMO*9 @ 7:9
2YJ
] S4^R```x|‹aPB 5 W 9G7 Q 3 F 7 A Xp365 FˆQu@íB 9<365DP9 @í– E @ 5 Fˆ@ 9z, ¬ 2 Q
B 58X½9<EMO*9 @ 7.2YJ @A6@ N @ 5$7x97 >@Qu@ 3C9 @fMB4F 7 A Xp25 @
V B Xj7u2
2 QxW8@Q 7 >@ N%3I5P9G7 Q 3 F 7 A Xd3I5 FˆQH@KB 9G3I5D.2 Q:W8@Q , ƒm58Xj9G7 Q 3 F 7 A X
3I5 FˆQu@KB 9<365Dd9 @í– E @ 5 Fˆ@ 2KJ @A6@ N @ 5$7x9
F 2 QuQu@ 9<1*245 W 97u2 ,
B q @A6@ N @ 5$7
9GEO*9 @ 7 \ ux9G7 Q 3 F 7 A X{v 36Np1 A 3 @ 97 >*B 7d52h7GV?2 @AI@ N @ 5c7x9 BYQH@ 7 >@ 9 B N @4b ,
«c365 Fˆ@ 7 >@Qu@jBKQu@ ~ y 9GEO*9 @ 7x9 T 7 >@ 1 Q 2O B OM3 A 367GX‚2KJ D @ 7H7u365D B 9G7 Q 3 F 7 A XP3I5 FˆQH@KB 9G3I5DP9 @K– E @ 5 Fˆ@ 3C9ˆ­

~y

| +$ò,.- S /v1*243I5$7x9G;
U N B D3I5 @ 7 >&B 7 U?>*B n @ 9 @AI@KF 7 @KW / FBKQxW 9
2E7
2YJ B 9G7 B
D B N @ 2YJ _‚– E @ 9G7u36245*9z, • 2E FB 5 B 9 … N @ E1e7u2 4_ X
– E @ 9<7H3I245gV3 AIA O @ uHX @ 9 vd2 Q uu5M2,ƒv»ƒ77 >@
@ 5 W 2YJ(7 >@
” U J(9<2 T D436n @.BvF 24Np1 AI@ 7 @ 9<7 QxB 7 @ DX‚JU2 Q
/ FBKQxW 9 U(> 2 AiW\
>7 *B 7m7 >@QH@ 3C952P9<7 QxB 7 @ DXoV > 3 Fx>eBYA6A 2KV.9¢Xc2Ee7u2 BYA V
5 W BYQ:W / eFBYQ:WwW8@KFx…eB 5 W»B 9 … Xc2Eh7u2e1 AiB X B
@ f9 ‚5M2 – E @ 9<7u36245*9z,W[hXv245 A X Qu@ 9<1*245*9 @ 7u2 @KBF†>
D B N @cT$FB 5pXc24E BKA V B XM9 ‡ D4E QH@
@fMB4F 7 A XvV > 3 F†>
7 >@d– E @ 9G7u36245*9Xc24EgV?24E ACWpB 9 … , U J(5M247 T 1 Q 2Kn @
B XM9 ‡ D4E QH@ 2E7m7 >@jFBYQ:Wp>*B 5 W ,
®*@ 7ŠŒ9 F 25*9<3 W8@Q¨BYAIA 7 >M@ 1*2c9H9<3IO AI@vQu@ 9<1*245*9 @ 9mV > 3 F†> Xc24E F 2E ACW D @ 7.7u2gXc24E Qd_p– E @ 9<7H3I25*9ˆ, • 2E
V?2E ACWPA 3 …c@ 7u2 >*B n @
B JUE5 F 7H3I245PJ Q 24N 7 >@.Qu@ 9G125*9 @ 9dscr8ts7 >@ 9 @ 7?2KJ ‡ n @¨FBYQ:W 1*2 …c@RQ?>*B 5 W 9ˆ, =?>&B 7
3C9 T JU2 Q.@ n @Q Xe9 @Q 3 @ 9?2KJ Qu@ 9<1*245*9 @ 9mXc2EoV„24E AiWoA 3 …c@ 7H2‚O @vB O AI@ 7u2PE53 – E @RA XP3 W8@ 5$7u3¿JUX‚V > 3 Fx>hFRBYQxW 9 U
B N > 2 ACW 365DP3I5eN‚X >*B 5 W ,m«c365 Fˆ@U?F 24E AiW O @> 2 ACW 365D B 5$X½/ FRBYQxW 9 T Xc24Ee5 @@KW 7 > 3i9JUE5 F 7H3I25h7u2PO @
245$7u2M,
¯ 2KV A6@ 7ŠŒ9 W 2 BhA 367u7 A6@pF 24E5$7u365D, UdFB 5 QH@ 9<1*245 W X @ 9Ž2 Q 5M2 @KB4Fx> 7u36N @cT 9<2»7 >M@Qu@eBKQu@e —M„ }
S4^:_ ± ·$^ / &í¶ V B XM9 UdF 24E AiWìQu@ 9G125 W 7u2wXc2E QP– E @ 9<7H3I245&9ˆ, ¤ 2KV @ n @RQT 7 >@QH@eBYQH@ ~ — }î8^ /… ·8^ … ¶4_
> UF 24E AiW O @d> 2 ACW 365D ´ «c365 Fˆ@ 7 >@
AiB 7u7 @Q 9 @ 73C9 AiBYQ D  @QRT 7 >@QH@ 3C9?5M2
1*2c9H9<3IO AI@d>*B 5 W 9¢2KJ / FRBYQxW 9?V > 3 Fx\
V B Xw7 >*B 7d7 >M@ JUE5 F 7u36245 F 24E AiW O @ 245$7u2 TB 5 W 7 >@RQu@ JU2 Qu@ 52½V B Xw7 >*B 7dXc24E F 24E AiW DE BYQ:B 5$7 @@ 7 >*B 7
Xc24E FB 5 BKA V B XM9?3 W8@ 587H3ÂJUXv7 >M@F 24Np1 A6@ 7 @¨FBKQxWp>*B 5 W ,
·