26.12.2013 Views

1. In tr odu ct ion For many years, the superiority of partial-order ...

1. In tr odu ct ion For many years, the superiority of partial-order ...

1. In tr odu ct ion For many years, the superiority of partial-order ...

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

BDCFEHGJIK"LNMHOQPRMSGUTVOXWYGZM[E2./-,>FQ2&H!¡%'F%'-EK),!* 8=\ZZ%'&v8:%"E !ƒ&C4B8NOK&-N%'&<br />

"8-£+43./Ep&438N'-EA"84/<br />

!'!./:9%'&,%¦2 !¡./Ep'&a02K./%'-'6<br />

JK)9O9'qaSh}r./%'0-%K54I/#ƒT<br />

!¡%¡./EN%'&,0¨./E&%F%2 8ƒI†?K&,5:917),8¨%2&,%%'&-'…C'…!¡G‘]”),!¡%"%' 8G!'!¡)0+%*.D,!'d<br />

<br />

%'&K!¡)++=A!¡ 8¨F[Q>2.D-,>F¨1ƒ+,'%¡.354/67F8-+4BC.DE=I£./,!¡%F,>F#%'&K!¡)+=-¡./¡./%¡j1<br />

),8-¡4/.DË<br />

C">'&g!*%'"%'-E^C,8g!¡ F>'&a&-)¡.3!¡%¡.3>-!<br />

+,'%*.BX4D67"8-K+43./E?•"–—08-+,-,8o>F¡./%¡.3>-54L4/g)+,g%'&j!¡<br />

8ƒI -0+4/<br />

!N)j24/A!*F4D`'F43%'<br />

¢¡¢£¥¤§¦©¨¢©¡¢¤©¨¢©¦§¦©! "$#%$¨¢¤§&('*),+¢--.0/!''132'540'<br />

67£¥8¥9:§§;¢-.¥@¢A¥£¥8¥#&©;:+'>¢-7.<br />

mon¥prqoptsvuNws"n¥xHs<br />

y{z,|~}"~|o€Z}"‚©ƒy*„†… ‡~ˆ~‰H… |~‡"Š‡


!N1v%2&F.D0!¡ C">'&?!¡+,>F !-#8-0,!¡%'F%¡./EQ%'&,%p%'&G+,'%¡.354/67"8-N+43-¨&,!<br />

%'&02F4BC%¡./:!./{-<br />

>-),!*%'&a!./{-0<s<strong>tr</strong>ong>1.</s<strong>tr</strong>ong>/%"!N!¡ ">2&_!¡+,>Fj.3!¨54/OK5y!;4/ !'!N%'&,op Œ),54<br />

G17),80-%"54v8:A%FE¨F¡./2./-A%G%'&,l)¨%'%"54"8-<br />

8<br />

C">'&l.3!¨),!* 8ƒ#-!'-G+4D 8ƒIe9&.3!Z]F&-)¡.3!¡%¡.3>K8:%"E d<br />

OK&-0>F-'%"X.D¨%¡+,<br />

!9RA>F-F8%¡.ª«!¦ >-8%"54AFs,0+4/ !ŽFsy+435././EpOK&Z4D !¡%'6>F0^.D%20-A%ŽOv'qy!$I¦‰KO9-:- #<br />

),8-¡4L./<br />

>F,8@8:X%"EZ.B!;'F43%¡./:F4/g)./0+='%"%…>FG+,' 8<br />

./g)w2qy!¡O9*4B8rFsy+=-¡./0-%"!-#=%'&.3!K!¡<br />

8r17'¬%'&p' 8),>F%*.Dg./o!¡ ">2&g!¡+,>Fj!./{-I<br />

%'0%2&j8:X%"E(8-¡./:<br />

!¡)4/%"!GFs%'-,8k%'`+,'%¡.354/67"8-a+43-"!G./cE--"54I|†?<br />

Ž./,54L4/#KO9a4/qc%0&O©)a'<br />

!'>F¡./F),!./EHH%2&9.3!'!¡)Z1ü<br />

Œ)./'9%'&,C%54L4t!¡)FÄh),>F%2&.D-: 8jFÄ¡),>F%¡./:KE54#'<br />

5:…!¡)-X4z4/ 8o]F4L./ "dI<br />

%'&-F!-„&-,>F#+43-"!9%2&,%>-Q'F%¡./Á.B!Q8.L’¦-'-%Q%'&,i%'&g+,2%¡.354/67"8--Å %2%"54/6<br />

e9&.3!a:-"!h.DfC1j%'&Q4L./<br />

!¡%¡./EA%2 8g&-2IHe9&N17'0-p8.3!¡%¡./,>F%¡./`./0+,>F%"!Z+43-¨>F0+4/-%'- !'!-#<br />

"8-j8.3!¡%*.D,>F%*.D?./:<br />

!9%'&j%2%"54/67"8-$Å +,'%¡.354/67F8-…8.3!¡%¡./,>F%¡./@.3!K2%'&E,X4Ã%20%'&.3!.3!'!¡)aShZ')G0,8Q€<br />

OK&-'<br />

)'*.D#ŽT UÇU„}r./A%2Q-%…54I/#¦T5UUT YFI<br />

Æ<br />

+,'%*.BX4D67"8-…8.3!¡%¡./,>F%¡./?!¡&)438@543!¡0'&|!¡%"%2P>F'2 !¡+,,8!G%'k_!*%"%'@1j%'&<br />

1j08F4L./E,È`.D‹`O9¡438672&_!¡ C">'&?!¡%F%'H>F'' !¡+=,8!p%'ga+43¦IG†|&.z4/0%2%"54/6<br />

O9¡438o,8@./_a+4367F),!p!¡4/F4/oo%'&<br />

+,'%*.BX4D67"8-p+43-0S'ÐZy8F17'.38o€¬ˆpFG+4z.3>-%*.DEQ%2&j,54/y!h.B!$I<br />

%'%F54/67"8--Å<br />

†`…>2435./Ñ%2&,%%'&K4/!h.DE.z§u>-CA%K8.L’¦-'-,>F…-C),!¡(‘+,'%¡.354L4/¨"8-' 8G+43>-G'q6<br />

)<br />

Ÿ z,|~}"|¡ Ž¢:ˆ~ƒrŠz|~‡¡ ƒ£¥¤(ˆ¦~y¹yR~|~¥<br />

´¡¥0µ Öo×·HÕ¦ © <br />

8?!j!¡ F>'&?%2&')E&_@!¡+,>F0C1;+=A!'!./-l'&,C">F%'-¡./{-<br />

²L–—=—,® °!¡ C">'& !%'&2)E&¨!¡+,>FZ1¦%'%F54L4DG"8-' 8G+43,!-„, À –°Fº7±3–²«½¡¼°¡¿® ° À ²z–—,—,®5°Ž.B!w8F§, 8<br />

À<br />

Õ Õ Ö


!'!h.DEr.3!Z-E4L.DEC.DFG+,' 8Q%2Q%'&H!¡ C">'&o%¡./0N17Z+4BC<br />

%¡./00>F0+4/Fs./%ho1%2&.B!Z+=A!¡%'67+2y>F<br />

+ ‰w-,>F#O9…


«ó0¦He[«õuò/© ÷§¤¡ó¡ø «ö«øð<br />

^$ðH_`S*P¨acb¥IaTIUR¥MTS2NYJd;¤höJegfŠõ§¤ÿ£¤¡óhö"ø-ò¡ÿ/ú?Eý)]ò!¨ÿ£¤¡öhij§j§k2¤¦ö§¦¤©$ÿzò!Kõ7ö§¤¥©þ/ø"÷Q$/¦<br />

k0k 2¤uòø©2¤¡÷ò'ö7øF÷p £ö§¦¨¤ÿ¡ £ ÷ò2÷§ö§¦ò'öò õJe2ðpZ/þö§¦¤¡÷§¤Q «õQ5ø¦õ§ ó)¦h4o k)k ]'ö§¦¤¥<br />

ü$ðHl5mJIK!P¨R¥S*K4b¥IaTIUR¥MTS2NYJdn¤¡öQho<br />

£ò'ö§¤9ò!¨…÷§¤¥©ø"÷7öŽþ3ò¥ ÿ£5÷§¤Fðqnr2stvu0w3x*stvy*zO{'|}v}n~¥u0r`s)x*w€?|zTs€ ~‚8ƒ~z„0w8u)sÿ ~tv…w!€w0…J†¥s€4u0s‚3xn}£w!zTw!y2w¥~)~‡<br />

ö§¤h÷7ù&<br />

Z õ§¤¡÷7öh o k0kwõ7ø"ù5¤¥$#¦¨¤h÷§¤6*¤¡ö$¤¤¥Žh4k0j§ƒò<br />

ˆ5ðHl5K!‰QIK!MTNQŠ‹b¥IaTIUR¥MTS2NYŒd;¤¡öh4k0j§2¤…ö§¦¨¤9ÿzò2õ7ö8¤ÿ£¤¡ö§¤¡÷9ø'þe2ð<br />

ÿXö§¦¨¤¦÷§¤¡õ§-ÿ«ö £&©-ÿzò CLðqnr2stvu0wpx2st y2zT{|}v}~u)r/x*s~tvzTtvsÿ ~>‚&~¥zc„)wu)sy~¥tv…w!€?w)…n†¥s€u0s‚xn}£wzTw!y2w¥~0~0‡<br />

hij§j§k]”ó'ò*ÿ<br />

*¤ö§¦¨¤õ§¤¡ö¦ø'þJ©5÷§¤¡óhøƒ «ö«ø5õ £1C ö§¦Xò2ö¡ò2÷§¤ øFö¦ö7÷§¤Fð<br />

‘$ðH_`S*P¨a’QmJ‰QPR¥MTNQŠpY'd;¤¡öE<br />

>F%*.D_O98F§,Q%¡O9g!./0+4/Q+43./E_54/E¡./%'&a!-IQe9&0§,F!¡%H54/E¡./%'&g#!¡&OK<br />

Ï_%2&.B!¨!¡<br />

8‹'&g!*+,>Fp1¡%'&pÊ#–`+43./E\54/E¡./%'&g#,,8a%2&p+,!¡-),86>F8<br />

&-'Z.3!w%'0>'&,F>F%'-¡./{-p%'&j!¡<br />

!a%'&.3!¨@+'>F 8)'g%'&,C%H-)0-"C%' !<br />

./fŽ./E)'?T@>->F0+4L.3!¡&<br />

1%'&p+43,!Z'j-)0-"C%' 8a


8Q+43¦#J›¨#,8apE54u!¡-% #Q¤0#>F%"5././E0+' >F,8./%¡./,!9Ow&.B>2&Q'<br />

Ê#–o>->F-+%"!9G)§,.B!*&<br />

!!¡),>->F !'!17)4L4/%'&-^.D%'-%')',!p%'%"54L4/H"8-' 8<br />

>F)''-%¡4/0%%2')I£Ï71¦%'&p54/E¡./%'&¥%'-'¨./,%'<br />

8)'ÈZ+=-"%'j!*F4D >F%*.D<br />

!¡4/)%¡./`+4BC¦I.¥w%'N%'&,%p%'&-'02j%¡O9\>2&.3>F0+,C.D%"!w./?%'&.3!Z+'>F<br />

>F%¡./¦Ie;&H+2y>F 8)'a8A !‘%p- 8o%'g>F,!h.B8-¨54/%'-',%*.D:HEA54>'&.3>F !-I<br />

,8@"8-*.DEo!¡F4/<br />

!-#%'&w17),>F%¡./§¦p¨ª©[¨p«*¬­*®Q¯[°ª©¨>-Q‘17),>F%¡./Q%'&,%K!¡F4/ >F%"!<br />

v)K+)'+,!¡<br />

¨0-¨-!¡9%'&,C%¡¨!¡%'-+¨F%¡./k,8@+,-"C%'…!¡F4/ >F%¡./¦„£&O9-:- #<br />

Ê#–l./o%'&,%w./%p),!¡<br />

8)'G17jF8-¡./EP!¡F4/ >F%¡./l.3!j8.L’¦-'-% I@R%'-+l‡Q1 ½¾k./,!¡-'%F!p"8-*.DE!-#£F,8./%¡./o%'&,%.3!…8F4/-%' 8@2.354<br />

R./,>F¼½¾|"8-"!¨54L4…!¡%'-+,!¨Ow&.B>2&l./A%2-">F%<br />

>2&k+' >F,8./%¡./i./fè+4BCk.3!¨F./%'&-o—,®F•"®$¯"¯-–°F±3²L³¨%'')Q\—=®"•F®-¯F¯-–°"±¨²L³N1 X4B!*Ik†?<br />

+'+=-'%¡uÈa<br />

!¡),>2&g+43,!‘éA—=–í0ê-±LÂé¼é¯-I9e9&.3!K+'+,-'%¡0./F4B8!p^%¡./E&A%K>F2' !¡+,,8-,>FH-54L4<br />

F>'&c!¡+,>F !-I|R)++,!¡œ½¾Á.B!GE./:-i%'&Q),¨F,8./%¡./l%'&,%Z.3!N >F !'!'¡.L4/<br />

!'G!¡-%p19EA543!j!h.D,>F#£


ú?C3DFEý Ê/Ë<br />

«õ4¤¡ù5© ö]5÷§¤©øF÷7ö¡õ§5ó¡ó¤¡õ7õò!¨…÷§¤¡ö§5÷§põ7ø'ÿ£5ö «ø-©-ÿzò1=ð<br />

ïFðHGJIKL.MONQPR¥MTS2NVUWQIUXQYZBþ[E\<br />

«ó0¦He[«õuò/© ÷§¤¡ó¡ø «ö«øð<br />

^$ðH_`S*P¨acb¥IaTIUR¥MTS2NYJd;¤höJegfŠõ§¤ÿ£¤¡óhö"ø-ò¡ÿ/ú?Eý)]ò!¨ÿ£¤¡öhij§j§k2¤¦ö§¦¤©$ÿzò!Kõ7ö§¤¥©þ/ø"÷Q$/¦<br />

o k0k2¤uòø©2¤¡÷ò'ö7øF÷p £ö§¦¨¤ÿ¡ £ ÷ò2÷§ö§¦ò'öò õJe2ðpZ/þö§¦¤¡÷§¤Q «õQ5ø¦õ§ ó)¦h o k)k]'ö§¦¤¥<br />

ü$ðHl5mJIK!P¨R¥S*K4b¥IaTIUR¥MTS2NYJdn¤¡öQh<br />

£ò'ö§¤9ò!¨…÷§¤¥©ø"÷7öŽþ3ò¥ ÿ£5÷§¤Fðqnr2stvu0w3x*stvy*zO{'|}v}n~¥u0r`s)x*w€?|zTs€ ~‚8ƒ~z„0w8u)sÿ ~tv…w!€w0…J†¥s€4u0s‚3xn}£w!zTw!y2w¥~)~‡<br />

ö§¤h÷7ù&<br />

d;¤¡öŒh4k0j§3*¤Zö§¦¤wÿzò2õ7ö¨¤ÿ£¤hö§¤¡÷9ø2þÌe2ð B ÷§¨¤h÷5h o k)kpò¡þ/ö§¤¡÷h4k0j§¦ò‹2¤þDøF÷§¤9hij§j§k2ð<br />

ˆ5ðHl5K!‰QIK!MTNQŠ»b¥IaTIUR¥MTS2NY<br />

*¤ö§¦¨¤õ§¤¡ö¦ø'þJ©5÷§¤¡óhøƒ «ö«ø5õ £1C ö§¦Xò2ö¡ò2÷§¤¤¡ó¥¤hõ7õò2÷ ÿ£Zþ3ò¡ÿ«õ§¤Fð<br />

‘$ðH_`S*P¨a’QmJ‰QPR¥MTNQŠpY'd;¤¡öE<br />

MONc•2SnUP¨RMOS*NY Ê#Ë ú?C D0E ýð<br />

“$ðH”5IU’QK!b¥MT•2I<br />

!9%¡O9054/%'-',%¡./: !$Ie9&<br />

Ž./E)'p‡,ÈZ‰KOÔ½¾?Fs%'-,8!Z¨+43¦È¹p88./E—9š!šZ%2H+43¼›ŠE--F%'<br />

!9%'&,%H—9š!šw./A%2-">F%"!9O;.D%2&P!¡%'-+¹NI<br />

FstC0+4/H!'!*)0<br />

Ÿ z,|~}"|¡ Ž¢:ˆ~ƒrŠz|~‡¡ ƒ£¥¤(ˆ¦~y¹yR~|~¥<br />

¤¥©*¤'ò2ö#-ö ÿ,ö§¦¨¤¡÷§¤ò'÷§¤5ø5 £-ö§¤¡÷ò'ó¡ö «ø õ¥Î<br />

Í<br />

¤ÿ£¤¡ó¡öòõ7ö§¤¥©1h4Ñ£iÒ=ö§¦Xò2ö £-ö§¤¡÷ò'ó¡ö7õ4$ «ö§¦1h o k)kFð<br />

Ï5Ð<br />

B ÷§¨¤h÷h4Ñ£iÒJ¤) «ö§¦¨¤h÷42¤þDøF÷§¤øF÷¡ò¡þ/ö§¤¡÷h o k0kFð<br />

Ï<br />

~tv…w!€w0…Q†¥s€u)s‚xn}£w!zTwy*w+~0~7ð<br />

qnr2stvu0w3x*stvy*zO{#„0sz£r`s€…w!€0tvyÓ~‚&~¥zJ„0w&u0sÿ<br />

dn¤¡ö#C<br />

2¤ö§¦¤÷§¤¡õ§-ÿ«ö £¨ ©$ÿzò!ð<br />

Ž.DE)'jÛÈe9&1½3¾?+43./Eg54/E¡./%'&<br />

Plan P<br />

A<br />

S O O F<br />

del<br />

need<br />

B<br />

+ O<br />

add<br />

A<br />

O add<br />

O<br />

add<br />

A<br />

S O del<br />

O F need<br />

B<br />

S O del<br />

O F need<br />

B<br />

Õ¢ Õ


!¡+, >F%<br />

54L4¡Fs.3!¡%¡./E\!*%'-+,!-I£†|&-œ½¾?88!KG!¡%'-+a%'N+43¦#./%K"8-"!%'&p-Oî!¡%2-+?¼—,²L³KO;.D%2&Q'<br />

%'r.D%'-">F%¡./Eè!*%'-+,!-I¼½¾f>F,!h.B8-F!054L4v+=A!'!./F¨F%¡./,!-„Ž&-,>F#ƒ17pA@+43o+'y8),>F<br />

!'!*67"8-' 8rK Œ).D:54/-A%5I<br />

.3!94/<br />

>F%*.D,!¨Fsy+4/./%0%2&.B!N%¡./E&%H>F'' !¡+=,8-,>Fg2&k!¡+,>FG1bN-_'&,C">F%'-¡./{- 8l!¨Q%'2-1K+43,!-I?e;&'%<br />

e9&Q!¡<br />

!¡+,,8!%'p%'&w%'+6¨4/-:F4,./:>-%¡./01ƒ%'&…54/E¡./%'&g#AC,8¨%'&K'-a5./.DE<br />

89./%'&w%''-…>F2'<br />

!Z >'&o>F'' !*+,,8r%'G' >F)"!./:N./A:y>-%*.Dg1%'&¨54/E¡./%'&@IH¥K%2j%'&,%;.DoE--F%¡./E<br />

8<br />

!-#¡C,8g >'&?8.L’¦-'-A%j!*-%…1<br />

a+43¦#ƒ%'&054/E*.D%2&!ZqN2&.3>F<br />

!…>F2' !¡+,,8!K%'00!h.DEC4DN2&Q%''-I<br />

>2&.3>F<br />

">2&?%''-G17jÊ#–iF<br />

Œ)-,>F#¦!¡),>2&?!`—0TVâÔ—N“ŽâÔ—NÛ#=%'&¨+4BC,!p'H8.3!¡%*.D,>F%N-),!*H%2&F.D<br />

+,'%*.B>F)43p+,-"%2(!*<br />

8o)…+43,!‘%'&.3!ZO;5Q%'aqj)p+'1!KG'<br />

!¡%'-+,!Z&,5:¨8.L’Ã-2-A%Z43F,>2.3!¡ILY<br />

Þnß .3!p%;4D !¡%j!43'E^!5ÛÜ2ÝݪàªáM#%'&,%w.3!-#<br />

†`H>-o!¡&Oî%'&,C%91b…QE./:-o+'2&0%''-w.3!jE' C%'-%'&,C%'&,C%1¦Ê#–IŽ./E)'pWp+2X:.38 !KpE).B8Z17<br />

%'&,%%'&p!./{-…1½¾ª«!!¡<br />

Ï%')./%¡./:F4/#O9H>-C?),!¡,ã‹%'g>F)%p+43,!Z./?%2&H%¡O9Q!¡ ">2&o%''- !-I<br />

%'&N174L4DO9./Eo8.B!2>F),!'!./¦Ï<br />

>2&?+43c>F)%' 8@./øÛÜ2ݨÝ2àná¡#£O90),!¡‹ãŠ%'o>F)A%¨Q67-G+%hl!¡-%j1K+43,!‘./ùÛ¥Ü2ÝÝ Þ;ß I<br />

j<br />

,!w%'&,%Z-:-'Q%¡./0NOv¨>F)%(G+43@.D¼Û¥Ü*Ý¨Ý àná #,O9H>F)A%p%w4D !¡%<br />

e9&N%'%"54L./%¡Q+'+=-'%¡Q0<br />

Þ;ß „%'&.3!./0+4L./ !Z%'&,%1ú¨Û¥Ü*ݨÝ2àná§ú,û üÚý4þ2ÿ¡ µ0µ àná ú¨ãwSÁpYúDIJ91>F)"!*#AO9p¨),!¡%<br />

p+43a./»ÛÜ2ݨÝ<br />

>2&g+43?>F)%' 8r.D¼Û¥Ü*Ý¨Ý Þ;ß .3!…>F)A%' 8@4/Q,>F„ƒ%2&.B!w.3!wE),"CA%'- 8r2&@./0+4L.D !N%'&,C% üùý¸þ*ÿ¡ µ)µ àná úpãKSÁpY ú¼û ú;ÛÜ2ÝݨÞ;ß úLIZe9&),!-#ƒ%'&<br />

%'&08.3!¨Ä¡./A%'<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

Õ¡¥‹Öâ ÖoÕ×n× ÖØ Öo× â%Ù ¦ã Ø Ö ÕÓ ©<br />

¥w%'a%'&,%0-:-2?+43k./³Û¥Ü2ÝÝ2àná|,8ÚÛÜ2Ý¨Ý Þ;ß<br />

.3!0).3Œ)#K!./,>Fg >2&c!¡%'-+`./fo+43l.3!¨EC.D:-<br />

TIHä¹xtn¥–Jå%wnæèçÿ“”x'éhp~“©næÈ‹to-:-'‹+43êÁ<br />

./ëÛÜ2Ý¨Ý àná #j%2&-'_Fs.3!¡%"!?i67-G+%h­!¡-%<br />

ì à +í¨îîî¥í Ã'ïñð(C1 +43,!;./ÛÜ2Ý¨Ý Þ;ß !*),>'&@%'&,%5ãKSÁ‘Y8ò<br />

ì à +¨íî¨îî¥í Ãï`ðAI<br />

“tIZœžw%•)ó¥x ws"n›sop˜•”•,çó“”x'éhp~“”næÈ4ãi+,!98.3!¡%¡./,>F%…+43,!v.D\ÛÜ2Ýݪàªá@%'08.3!¨Ä¡./A%Z!¡-%"!1+4BC,!./<br />

òöÁ ' #%'&-»ãwSÁ + Y/÷VãKSÁ ' Yò<br />

ì ðAI<br />

>FÄ¡),>F%¡./gC1 %'&p%¡O9¨+'+=-'%¡./ !9./0+4L./ !Z%'&,%,ú¨ÛÜ2Ýݪàªá§ú,û<br />

úªÛÜ2ÝÝ Þ;ß úLI<br />

†`^>-Cè8F§,aG1b),>F%¡./<br />

ãî%'&,C%…&,!Z%2& !¡0%¡O90+'+=-'%¡./ !j!w174L4/O…!-Ï æƒ-%VÁŠ


¨<br />

<br />

<br />

¨<br />

<br />

<br />

<br />

<br />

¨<br />

ã<br />

ã<br />

ã<br />

ã<br />

©<br />

¨<br />

<br />

<br />

<br />

¨<br />

©<br />

<br />

<br />

<br />

<br />

¨<br />

©<br />

<br />

¨<br />

<br />

<br />

<br />

<br />

!91¦%'&F./K' !*+, >F%¡./:¨!¡ ">2&%2'- !¢¤pÜ2ݧ¦Û'S)ÃpY ô ãwS¢¤pÜ2ݧ¦Û'SÁ‘Y'Y"I<br />

Á‹,8‹Ã‹'Z2&g!¡&,'j>F00Q8-¡./:X%*.D<br />

Ï%')./%¡./:F4/#ãc+,!9N+43§Á|./»Û¥Ü*ݨÝ<br />

!¡%2'IÔe9&.3!‘.3!p.L4L4/),!¡%'"C%' 8`./mŽ./E)'QW#£OK&-'G17j >2&?+43l./ÚÛÜ2Ýݪàªáig8!¡& 8è4L./a.B!<br />

,>F<br />

!*+,,8./EQ!¡-%K1¡+43,!;./Û¥Ü*ݨÝÞ;ßI<br />

8"5OKQ%'¨%'&¨>F''<br />

!%'&w%'%"54L./%¡H,8G8.B!bÄh./%' !'!M+'+,-2%¡./ !F%¡./0%'&<br />

†`;>-C!¡&Oc%'&,C%ãm!'C%¡.3!§,<br />

C">'&Q%2'- !-IZ-%"5.L4/ 8Q+'1!9'Z./g%'&jC++,-,8.LsÃI9eŽ0+':Z%'&Z§,"!¡%9+'+=-'%¡#<br />

8-+%'&Q1%'&j!¡<br />

8N./VÛ¥Ü*ݨÝ2àná£#54L44z./ *.D{ C%¡./,!91,%'&,C%+4BC'9>FA%F5./ 8<br />

O9K!¡&O_%'&,C%£1b£-:-'N+43>F%"5./<br />

>F,8a+'+=-'%¡#O9p%'p%'&,C%;CAa%¡OvN+43,!…C%;8.L’¦-'-%(8-+%2&,!./<br />

./Û¥Ü*ݨÝÞ;ßIe¦¨+':p%2&j!¡<br />

¡./{ %¡./,!$#¡,8r%'&-P!¡&O­F%¡./`%'&,%…Q%¡O9H+43,!<br />

ÛÜ2ݨÝ2ànáo&,5:H8.3!¨Ä¡./A%j!*-%"!914L./<br />

àná X4B!*0&,5:p%'&.3!K+2+,-'%¡I<br />

%K%2&j!'0j8-+%'&r./ÛÜ2ݨÝ<br />

It9 >'&a+43§Ái./»ÛÜ2Ýݪàªá@%'&-2(2 ú¨ãwSÁpYú8.3!¡%¡./,>F%Z+4BC,!./QÊ3–#OK&-'Vú¨ãKSÁ‘YŒúX.B!<br />

,!¡O9-<br />

¡./{ %¡./,!N1 ÁNIje9&¨Fst>F%…)¨F%¡4/\!¡a54L4D-<br />

ÛÜ2ݨÝÞ;ßg.3!9Ow&-g-:-'a+43a./Û¥Ü*ݨÝ<br />

Þ;ß ,8Q+=A!'!./2&Q%''-<br />

¨ ©<br />

<br />

<br />

Ž./E)2jWȉwXO²ã|+,!v1b'<br />

Û¥Ü2ÝÝ àná %',Û¥Ü*ݨÝÞ;ß<br />

+43@./P%2&j%''-IZe9&-Ã<br />

ô ãwSÁpY.L1v,8@4/a.z1ZS"±BY8Ë.3!p^4L.D C¡./{ %¡./?1 ÁŠ,8èS"±¨±/YF./%'&-<br />

‰wOŠ¨),>'&_!*54L4/-j.3!ñÛÜ2ÝÝ àªá<br />

%'&,C§ÛÜ2ÝݨÞ;ß¡îe9&G++./E?8 !'>F¡./


T —^S"TY —¨S"TCY<br />

“<br />

2&g%2'-¨Sh8.3!'>F),!'!¡ 8r./g%2&.B!p!* >F%¡./ƒYv,8r%'&H!./{-¨1%'&H!*)FA!¡%K+=-…+43@./g%'&¨!¡<br />

8g8)¡./Ea%'&H!* ">2&Q+'y>F !2!ZSh8.3!'>F),!'!¡ 8\./g%'&NFsy%…!* >F%¡./ƒY"I<br />

Fs+4D'<br />

>F%¡./lO9^!*&XO¥%'&,%pOK&.L4/½¾|>-o./,8- 8l%"q¨0'0%¡./0a+,-N+4BC¦#¡%2&Fs%'"<br />

Ï?%'&.3!¨!¡<br />

!¡%'-+,!M./Q%'&Z+43¦# .<br />

%¡./0w.3!9'F43%¡./:F4/Q!¡54L4¡,8GE'O…!4Da+,C4D¨.354L4/QO9./%'&a%'&p)H2&gO9j8-%'N¦£IÏo>F0+,¡./E0%2&j'F43%¡./:NF[\>2./-,>FQ18½¾_,8rÊ3–#O9Z§,"!¡%…>F,!h.B8-<br />

!p%'&,%Z >2&?54/E¡./%'&‚!¡%2-+o.3!ZFsy >F)%' 8è+,-j+43è.D`%'&0!¡ ">2&o%''-0,8<br />

%'&¨)H2&P!¡%'-+¦I<br />

O9p%'&-g>F,!.38-p%'&p%*.DGj>F0+4/FsA./%¡Q1<br />

8a./g%'&p+2 >F 8.DEg!* >F%¡./,!-#= >'&Q8p./o%'&j!¡ C">'&@%''-j>F2' !¡+,,8!K%'0G+43¦#<br />

¹p!9%2<br />

>'&Z./:>-%¡./jC1y%'&+43./Ep+'>F 8)'M1bŽ'& >2qg,8<br />

%'0Fs%'-,8@%'&,%w+4BC¦IKe9&A),!$#17K2&PFs >F)%' 8o,>F0+,-N+4BC¦Ï ¹…,54/{F./Eg%'&0)¨F >2&?1<br />

%¡./0<br />

!¡0!¡%2-+,!w.B!ZFs >F)%' 8oaAQ%*.DG !p%(Cg./%'-',548,8@%p%(X4z4vC%(^4/ 51*IN‰KO9-:- #<br />

%'&<br />

>F)%¡./,!1¦ >2&<br />

%'&…C,54/y!.3!M.3!9>F%'),54L4/Œ).D%2(!./0+4/j!./,>FZO9…>-Q0'%*.D{-w%'&K)HFj%2&,%ZR%'-+@?N.3!9Fs >F)%' 8r,>Fp179 >2&Q+4BC<br />

!¡%'-+Q:-9%'&p)¨F)%2 8<br />

+43¦#,!9!¡)G¡./{-<br />

!2!9.3!9'&<br />

8m.D²—¨S"TCY(%*.DG„917¨FstG+4D#K!'!¡)¨./E?%'&QEA543!0'Q!¡%'' 8`./fr4L.B!*% #9%'&<br />

->F0+4L.3!¡&<br />

Ioß>'&lFsy >F)%*.D_1<br />

¦p¨ª©[¨c«2¬­*®Q¯Q°n©a17),>F%¡./c>-k!./0+4/l'-%')'?%2&0§,"!*%HG-H


!2!0Fs+,-,!./:@170Ê#–Ò%'&,k17Ž½3¾I|R%'-+i‡_1pÊ#–|.3!a>->F0+4L.3!¡& 8<br />

R%2-+,!¨‡mC,8kW_2a4D<br />

F,!¡%"%9%¡./0#,!./,>FN >'&G./,!¡-'%¡./o>F,!¡%¡./%')%2 !9<br />

>F)%¡./Q19R%'-+Q‡0>-Q->F0+4L.3!¡&<br />

>F)%¡./g1%'&¨!¡%'-+¦IÏP>F%'"!*% #R%'-+@‡¨./œ½¾è.D:4/: !Z>-'2./E0)%;.D%'-">F%¡./P8-%' >F%*.D<br />

Fs<br />

8r./œ—^SÝY<br />

,8aF4L./¨./,%¡./@./Q"8-K%2H+2y8),>Fj¨-OÒ+4BC›IHIe9&.3!K!¡%'-+g>-Q->F0+4L.3!¡&<br />

8E !Ž./0%'&9EF+&¨' Œ)./' 8G%'Z'-+' !¡-%%'&K+,C'%¡.354L4/H"8-' 8<br />

%¡./0#OK&-'HÝ.3!%'&9)¨-!*#%'&-'p50F 8./E0M1b4L4/OK6<br />

e9&Z"8-¡./EN+'y>F<br />

8Q!9!¡),>2&¦I e;&K43F%*.D¦I(e;&.B!w' Œ)./' !p%K0!¡% —¨S¥ÝY%¡./0I9¹w17%'-<br />

%¡./o,8Q%'&-r1bC4z4/O…!w<br />

!'!‘.B!G>F0+4/-%'#4/k!¡%'-+,!N%'&,%02)F8-' 8lO9./%'&l' !¡+, >F%G%'œ—9š!ša'<br />

%'&G43F 8)2…F8-"!£ >2&j./%'-">F%*.DË !¡%'-+0O;.D%2&0' !¡+= >F%%'<br />

¹w17%'-%'&9+'-+'>F<br />

š!š # )+ƒ8%¡./Ep%'&£43F<br />

UUT-F0+4/FsA./%¡H,8GR%'-+N‡…C1'½¾&,!—^SÝY¦>F0+4/Fs6<br />

IMÊ3–o>->F0+4L.B!*& !9%'&.3!<br />

./%¡#AO9KO|>F,!.38-ZR%'-+\W‘1¦->F0+4L.3!¡&<br />

8)'H!9Ê#–#+2X:.38 8g—^SÝY%'+,C4DE.3>-54<br />

E"C+&¦I9S¹w4D%2-',%¡./:F4/#½¾_>-@),!¡p%'&H!20p+'>F<br />

¡./{-¨%'&j+43¦ILY<br />

!¡2%.3!;§,"!¡%…8p%'¨4L./<br />

,!w%'&,%H½¾o./,>F)"!<br />

eŽ0!¡)0C¡./{-j)…>F0+4/FsA./%¡g,54/!.3!-#,%2&p),!¡p1¨+,'%¡.354£"8-90<br />

C%'-K>FA!¡%1bK+,-F%'9"8-*.DErS'R%'-+Q‡Y,8G179)+u8%*.DEa%'&pE54¡!¡-%ZS'R%'-+gWY"IJK:-F54L4 #<br />

E'<br />

Œ)./' ! —^SÝY%¡./0p+=-K+43¦#OK&.L4/jÊ#–o4DQ2 Œ)./' !H—^S=¦ŽY%¡./0p+,-K+43¦IwR./,>FHN%'%F54L4D<br />

½¾o'<br />

8Q+43g2 Œ)./' !p¨2-+' !¡-%"%¡./@1M!h.D{-,—¨S=¦ŽY"#=,8g¨+,C'%¡.354L4/g"8-2 8QE"C+&Q' Œ)./' !<br />

"8-2<br />

!¡-%"%*.DQ1 !./{-.—^SÝYF#y8 !h.DE.DEa+'>F 8)' !wO9./%'&a4/XO9-K>FA!¡%F!O9)438r


F%¡./,!a&,5:?>F0+,C' 8kÊ#–ÔC,8³½¾­./|%'-'!G1¨'F43%¡./:?!¡ ">2&f!*+,>F?!./{-<br />

e9&o+'-:./),!Q!¡<br />

e9&¨Fs%'"a+'>F !'!./Eg%*.DGH2 Œ)./' 8`'&o8<br />

,8@'F43%¡./:G%¡./00>FA!¡%p+,-Ny8Ï<br />

Z%'FN.D%F!…!¡ C">'&o!¡+,>FN5\>F%"5./@Fsy+=-A%*.BX4z4/@17-Ov-Z8 !-I<br />

O9)438g++=<br />

!…>F%'),54L4/g:.B!h.D%2 8<br />

‰wXO9-:-5#%'>FG+4D-%2j)p,54/!.3!-#,O9NH),!*%…>F,!.38-p%'&NA)¨2&g54/E*.D%2&n),8-pNE./:-P!¡ C">'&g!*%'"%'-EI<br />

<<br />

8%'&6¨§,"!¡%Z!¡ ">2&¦#%'&j,54/!.3!.3!K!¡%'"X.DE&A%¡17'OKF8ƒI¦¹w1b%'-K>FG+4D-%*.DEa%'&p!¡ ">2&Q%'<br />

tF)4308-+%'&¦#ŽFA!¡%8—^SÝ:VY"„OK&-2 !-#Ê#–G./,>F)"!M%¡./0…>FA!¡%—¨S*¦VtY£WJú¨ãKSÁ‘YŒúL#<br />

%'&,%½¾QE--F%'<br />

ú.3!Z%'&¨)¨X:YŽS0ÛÜ2ݨÝ<br />

8@F''<br />

>2&@4/-:F4#¡!¡a%'&,%ZÊ#–l&,!ZFsy+4/2 8<br />

+43-"!N'0¯-³—,•]\A°¡¼—,±Bç”®F¿j517%'-ZFsy&,C),!¡%¡./:F4/oFsy+4/¡./EQ<br />

¡./{ %¡./,!1,%2&v+43,!£Fs+4/' 8¨F'2 !¡+,,8-,>F#£!¡),>2&è!w.D%2-"%¡./:08--+,-./E,#Q!./¨.L43¨,54/y!h.B!N>-<br />

!./¨.L43¡4/?+'<br />

8r)% I<br />

-'¡./<br />

!*(>24/ '6>F)%£178-+%'&6¨§,"!¡%!* ">2&¦#!./,>Fv%2&;>F'' !¡+=,8-,>F.B!<br />

e;&v>FA!¡%>F0+,C¡.3!¡N.3!£%<br />

8¨%2pF !'!'C¡.L4DGFsy+4/'Z54L44z./ *.D{ C%¡./,!1u%'&w+4BC,!Fs+4D' 8¨F6ã_8A !£%+' !¡-':9%'&K!¡)F'2<br />

.D ÛÜ2Ýݪàªá#Ž%'&0>F'' !*+,,8./E@4L.D C¡./{ %¡./,!N./§ãwSÁpYZ5gF''<br />

">2&¦I§¥K-:-2%'&F4/ !'!-#-:-l%'&)E&_%'&a%¡O9g+43-"!0C'%H!¡,>'&2./{- 8ƒ#O9<br />

8-+%'&6¨§,"!*%^!*<br />

>F%9%'&,%5#5:-FE#n½¾@O9.L4z4¦Fs+4/'w1b-O9-8 !-),!*…%'&Z!./{-…1#Û¥Ü*Ý¨Ý àná .3!£4/ !'!<br />

¨./E&%Fs+,<br />

Œ),X4¡%'¨%'&H!h.D{-N1Û¥Ü*Ý¨Ý Þ;ß I<br />

%'&,QK<br />

8o%'&,%,½¾f8 !N%'-,8?%2g)%'+=-¡17'‚Ê#–i),8-8-+%'&6¨§,F!¡%<br />

ßM0+./¡.3>-54L4/#O90&,5:a


IB#,%'&NA)¨F…>F8<br />

qK,8-%'-'^.D.3!¡%*.B>N>'&C.B>F<br />

Œ).D2 8Q%'02-+'y8),>FN%'& !¡pFs+,-¡./0-%"!Z>-g2&l%''-!./{-Q54/¨.3!N%H!*)[\>2./-A%N%'gFs+435./³½¾ª«!p8^.D,C,>F„£./<br />

.3!N0'N./A%2-'<br />

">2&0%''-.3!E' %'-%2&,0%'&,%£178½¾ª«!!¡ C">'&¨%'2-#%'&-0Ê#–@¨./E&%<br />

!¡4/)%¡./Q8-,!./%¡N1bÊ#–ª«!!*<br />

">2&o®§a ®5—gºb\A¼éXÂc\jÊ#–ª«!9!¡ C">'&a%''-w.3!K>F%'),X4z4/G43'E- I<br />

)%'+=-¡17'ê½¾o),8-…8-+%'&6¨§,"!*%…!¡<br />

8a,8a%'&,%<br />

Fs,0+4/#./%9¨./E&A%9FG+4D-%2F4DQ)"8-'<br />

5: !;1¸Û¥Ü2ÝÝ ànáed %2&9ë”–±¨²L®"¿ À ²L–—t¯ d C'p%'%"X4z4/a"8-' 8ƒIÏ@%'&.3!<br />

%'&p+43,!Z%K%'&N'-5././EG4D<br />

>2&Ž½¾g!¡4/)%¡./a+43Q>F'' !¡+=,8!%2j0Fs+,-%¡.354u)¨-!¡#<br />

>2&ù½¾l15.L4/ 8?+43k>F'' !*+,,8!‘%'gQ!./E4/Ê#–m1 5.L4/ 8`+4BC¦Ie9&>FA:-F!¡¨.3!j543!¡@+,A!2!./2&0%''-#%'&),!<br />

%'&p!¡4/)%¡./g8-,!./%¡01½¾ª«!!¡<br />

:¡./EŽ½¾?:-9Ê#–l),8-p8-+%'&6¨§,"!¡%p!¡ ">2&¦ItKFs,0+4/#,%2&-'j¨./E&%K2&<br />

+,'%*.B>F)435#%'&H8-,!h.D%¡g,8Q8.3!¡%2¡./2&j%''-.3!£%'&9+'+='%¡./¨1ƒy8 !£%2&,% C'K!¡4/)%¡./,!-IàÏ71ƒ%'&<br />

e;&;!*4/)%¡./08-,!./%h¨1up!*<br />

"8-2 8k!¡4/)%¡./c+43l./²½¾ª«!¨!¡ F>'&l%''-g,8kP4BC'EaA)¨


2&Q1%'& !¡Z15.L4D 8\½¾?+43,!wO9)438Q>F'' !¡+=,8Q%2^H4BC'Ep)HFj<br />

+43,!-#=%'&j!¡4/)%¡./o8-,!./%¡a1b9Ê#–`Ov)4B8rF,!.38-"'&gNOK5¨%'&,%O9)438aFs+435./g)9+,-*1b2,>F<br />

%''-<br />

!¡)4/%"!$I†?j!'5O|0%'-,8-,>Fa17HÛ¥Ü*ݨÝ2àná@%'¨&, :j¨&./E&-(!*4/)%¡./g8-,!./%¡Q%'&,»ÛÜ2Ý¨Ý Þ;ß I<br />

'<br />

:-"Ep!¡4/)%¡./o8-,!./%h - 17<br />

Fs,0+4/#179%'&aTTp+'F)43*4Dk!¡)'+*.B!h.DE<br />

Ê#–iFst>F-<br />

À °F±3¼°"±Ž' !¡o%'g!*)++,A!¡G%'&,%p%'&0!¡4/)%¡./l8-,!./%¡./ !jC1v%'&¨%¡O9+43-"!<br />

!./,>F0O90!¡-0?–<br />

%*4DI<br />

!¡&)438@8.z’¦-ZE'<br />

R./,>F0!¡4/)%¡./l8-,!./%hr.3!9./,!¡)[\>2./-%j%'aFs+4BX.DÚ½¾ª«!Z8¨./,,>F¨o)Z2qy!*Ov¡438gFs6<br />

">2&¦#9O9g- 8i%'`4DqkF43!¡-OK&-2o1bcFs+43,%¡./¦I<br />

+,-*.DG-A%"!aOw&-f),!h.DEc8-+%2&6¨§,"!¡%Q!¡<br />

!./{-%2&,%j%'&@¿±/¯-º7°F±bê$éAº7±¨¼—o1…!¡4/)%¡./,!N+':.38 !HC?Fsy+43,C%¡./¦Ig†`0%'a%'&,%<br />

†?a&A+,%'&<br />

8@+,-*1b >F%¡4/o).L1b'¨4/?S7.I IB#u%w-:-@.D%'-':543!FYK0Ea%'&<br />

.L1v%'&¨!¡4/)%¡./o+43,!p'¨8.3!¡%'¡./'&ko!./¨.L4BC)¨2&<br />

-oFs+435./_%'&N'q4/o17 Û¥Ü2ÝÝ àná %'&,@1b9ÛÜ2ÝݨÞnßI +¢= e;&H&+,%'& !h.B!<br />

Fs+,<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

UA Search Tree<br />

TO Search Tree<br />

* *<br />

* * * *<br />

*<br />

= Solut<strong>ion</strong> plan<br />

Ž./E)'¨VÈ£;K.L17'n!*4/)%¡./P8.3!¡%'*.D¦ò¥¤òõ7ùKò*ÿ ÿ>ƒ «õò!¨"ò!-öò¤"ð A ø9õ§¤¥¤£ö§¦ «õ¥]ÿ£¤¡ö# õŽõ§©©øFõ§¤ö§¦ò'ö#¤'ò2ó0¦wÿ£¤'ò¡þ,ø2þJø"ö§¦I"%$(&'&'6870òo"4$'&'& )§+<br />

lnm<br />

«õvòwõ7ø'ÿ£5ö «ø‹$ «ö§¦-¤Åò¡ÿ#©5÷7øò!ƒ ÿ¡ «ö?!Kð A ¦ò'ö4 «õ¥]p þF"%$(&'& 687 ¦ò'õ£p 6,7 ÿ£¤'ò¥¤¡õ¥]ø2þ3$/¦ «ó0¦rq 687 ò2÷§¤Kõ7ø'ÿ£5ö «ø5õ¥]<br />

Õ¢@


8o!¡--!w' !*,Fj./%w.3!K !*Q%'>F,!¡%2'),>F%K+'-a4/ 8a%'0Q-%¡./'j!¡)FG+,'Ž½¾‹,8`Ê#–i),!./E_Q"C,8¨./{- 8k!¡ ">2&<br />

JKaOK5P%2g%'<br />

!0F,8¨4/c>2&A!¡-|+,%'&,!N./|%'&o!¡ ">2&c%'2-g)%¡.L4‘l!¡4/)%¡./x.B!<br />

!'G+4z./Ec!¡%2"%'-ElFs+4D'<br />

>F%' 8r2&A!./E0",8^4D<br />

17),8ƒI¹­+,%'&a.3!K!¡F4/<br />

!'!¨'-%2)',!N%'o%'&Q'%0,8k!¡F4/ >F%"!0%'&-¨+,%'&¦I_e;&g!'0a+,%'&k5?'&¦#Ã.D%2-"%¡./:0!'G+4z./E@.3!p'F43%*.D:F4D@./,!¡-,!./%¡./:Q%2Q%'&08.B!*6<br />

Ï_>F%'"!*%…%'g8-+%2&6¨§,"!¡%j!¡<br />

Z.L1)Z&A6<br />

%'¡./F2' >F% I£Ïa)Fs+,-*.DG-A%"!$#AO9…8.38^§,,80%2&,%OK&-‹½¾P,8GÊ#–@'&l%'-'¨./,%2 !-„.L1…% #%'&Q!¡ ">2&<br />

!'G+4z./E,#Fp),8-K8-+%'&6¨§,F!¡%K!¡ ">2&¦#A!¡)EE !¡%"!M%'&,%v!*4/)%¡./,!9'<br />

),+ ¦Xò2õtp )§+ ÿ£¤'ò¥¤¡õ¥]yø2þ#$#¦ «ó)¦rq ),+ ò2÷§¤9õ7ø'ÿ£5ö «ø5õ¥]uö§¦¨¤¥0K,fuq:687v*p£687‹fwq )8+ v*p )§+ ð5Z1¤¨¤¡÷ò¡ÿT]<br />

ò!¨#"%$'&(&<br />

ö£ø'þFp² ø¨¤¡õò'÷§¤õ7ø'ÿ£5ö «ø5õ¥]yö§¦¨¤8¤*1©2¤¡óhö§¤¥95ù82¤¡÷ø'þ ø¤¡õ£ö§¦Xò2ö¡ù& õ7ö42¤ö§¤¡õ7ö§¤¥pö7ø5(*¨Hò9õ7ø2ÿ£ ö «ø<br />

þxqZø<br />

A ¦ «õÌ«õõ«ù©$ÿ£¨ö§¦¤H¤*1©2¤¡óhö§¤¥<br />

«õ.y¡‘ip3vzq9$#¦¨¤#q1fxï;ò0ò©©5÷7ø”ò2ó0¦¨¤hõ.p3vzqpò'õ3q¨ú3òrppý¡ò©©5÷7ø”ò2ó0¦¨¤¡õ|{\ðpú<br />

ù&*¤¡÷ø'þ¦õò2ù©$ÿ£¤¡õþ/ø"÷ò6 £5ø"ù& zò*ÿ «õ7ö7÷ £¨ ö «øð ý A ¦¨¤h÷§¤þ/øF÷§¤]õ £ ó¥¤0q )8+D} q:6,7]ö§¦¤5¤*1©2¤hó¡ö§¤¥, ù&*¤¡÷ø'þ<br />

<br />

lcm «õ"÷§¤'ò2ö§¤h÷£ö§¦XòjøF÷4¤Åò¡ÿ,ö7øZö§¦¤&¤*1©*¤¡ó¡ö§¤¥15ù82¤¡÷ø'þ=ÿ£¤*ò+¤¡õ¤*1©-ÿ«øF÷§¤¥.9Ç;ÈQ]*jò2ö<br />

ÿ£¤'ò¥¤¡õ&¤=1©$ÿ«ø"÷§¤¥-<br />

ù9ø"õ7ö¡òMþ3ò2óhö7øF÷¦ø2þ'^-ð<br />

A ¦¤4 «ö§¤¡÷ò2ö £¤õò2ù5©-ÿ¡ £¨…õ7ö7÷ò2ö§¤¥H$¦ò2õ¤¥© ö§¦ƒ/ÿ¡ «ù&«ö§¤- £`¤*1 ò'ó¡ö¨ÿ£Kö§¦¨¤õò'ù5¤4$Ãò+Kö§¦Xò2öƒø5÷#¤¥© ö§¦ƒT(X÷7õ7öŽõ7ö7÷ò'ö§¤¥<br />

ïFïFð<br />

øFö§¤]¦ ø!$¤¥¤h÷¥]ö§¦Xò2ö¦ö§¦¨¤©2¤¡÷¨þ/ø"÷7ùKò ó¥¤ø2þc «ö§¤¡÷ò2ö £¤õò'ù5©$ÿ¡ £6 «õ¡÷§¤ÿzò2ö £¤ÿ£` £ õ§¤¥5õ «ö £¤9ö7ø9ö§¦¤ò2ó¡ö§Xò*ÿ<br />

$¦ò'õ¡ð--¤<br />

¤¥© ö§¦ƒ/ÿ¡ «ù& «ö85õ§¤ð<br />

Õ:9*£


8a67).L1b'¨4/\8.3!¡%2¡./F !'!'¡.L4/<br />

./,8-<br />

C">'&g!*%'"%'-E0%'&,%9.3!9-G+4D 8rq !w08"C%¡.3>p8.z’¦-'-,>FI<br />

!¡)+=-¡./…%20Ê#–„%'&j!¡<br />

>F%2)'0%'&,%Z)p' !*)4D%F!p'<br />

¹w4/%'&)E&o)p'q!¡O9¡438?85./o5g-54#ƒO90>FÄh<br />

>2.L§u>-54L4/A#Ã1bK8.3!¡%'*.DQ!¡%'"C%'-E#¦%2&-'\C'002!¡+&.3!¡%¡.3>-%2<br />

>F 8./E\!¡ >F%*.D,!-#Ovp&,5:p!¡&OKa%'&,%KN+,'%¡.354/67F8-K+43-…>-Q-),!¡r./%"!¨!¡ ">2&_%2'-0.3!0!*54L4/- I?†i./%'&k!¡0Q!¡ ">2&k!¡%'"%2-E./ !-#!¡),>'&c!j2.3!./,!-#Z"%'&-8.L’¦-'-A%9'E)G-A% I££./,!¡%F,>F#<br />

'qQ¹<br />

!w%'&¨2qy!*Ov¡438ƒª«!0]5R),!'!¡aP54/ydtI(~o8F4B5./EQ%'&08<br />

Æ #ƒ#–3¾‚o>--:-A%'),X4z4/g8-%' >F%w%'&,%K¨>FÓ.3>F%KO9.L4L4 >->F)<br />

g~xF%¡./¦#ƒO90!¡&O­%'&,%Z%'&.3!j'E)0-A%p>-oF%N&, :\r+,%'-%¡.354…8:A%FE0:-NÊ3–<br />

%¡O9g+43-"!-I@†?Q8-0,!¡%2"%'0%2&,%V½¾f8<br />

!Z1v&-)*.B!*%¡.3>-!jG'j2 8.L4D`%'&,oÊ#–Ï e9&.3!j8:%"E‘.B!<br />

./?%'&,%Z./%j>-`Fsy+4/./%H>F-2%"5./?%¡A+=<br />

F>'&Q!¡+,>FI†|&-%'&-99%9%'&.3!K8:X%"E<br />

./,8-+,-,8-%p1¡%'&w1>F%9%'&,%½3¾P&,!K¨!¡54L4/-…!¡<br />

!¡%*.D¦#,1>F)"!*I†?j543!¡8 !2>F¡./F%*.B>F‘.3!…%'&-KŒ)<br />

>F%K1 G>F004/67),!¡ 8Q&-)*.B!*%¡.3>jQ)K2q!¡O9¡438Q+''&A!¡<br />

#¦%2&,%j!¡0G"8-¡./EA!¨!¡&)438`'&¦IQe9&.3!(.B!<br />

&O9-:-<br />

8`2&k>F0+,' !9½3¾f,8oÊ#–i?Q+,C'%¡.3>F)43¨+'F,8./%¡./^¢@1— + #ŽR%'-+o‡Q1½¾lO9.L4z4"8-1— O9./%'&o' !*+, >F%p%'<br />

./A%2'y8),>F<br />

' #A!./,>FK%'& !*;!*%'-+,!Ž./A%'-F>F% I‰KO9-:- #$./%q !£G'v!*-,!¡K%'Z"8-8— ' F,8./%¡./w•N1— IKe9&.3!9.L4L4/),!¡%'"%2 !p0!./0+4/0+43./EQ&-)¡.3!¡%¡.3>N%'&,%KO9N'F1b-Z%'<br />

>2&./-:<br />

–²¾¯9&-)¡.3!¡%¡.3>Èj]F+'F17-K%'&N"8-¡./EA!w%'&,%9.DF438o%2&Z1b-O9 !¡%91543!¡N+' >F,8./%¡./,!'dI<br />

!9%2&í¨±3—t½b¼<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

!¡ F>'&¦#g>-kFsy+= >F%0%'&,%V½¾ÒO9.L4z4Z%'-,8l%'o)%'+=-¡1b'<br />

Ê3–I_t08.3!¡%'¡./'&c!¡%2"%'-E./ !-#!¡),>'&c!N./%'-"%¡./:QF%¡./PÇtI«“I<br />

~¥0á × âTS ¦ä â<br />

ž€ â {ÕÓ”Ô×~Ó<br />

ŽF4<br />

Õ:9cÉ


8Q%'G+'y8),>F¨%'&N+%¡./54!¡ ">2&gZ%'&N+%¡./54¡+43¦#ƒ‘.3!Z%KE),C"%'-<br />

8ƒI‘Ï%Z.3!p%'&¨FÓ.3>F%"!2dg>F¡./%¡.3>¨%'&,C%jRA>F-F8%¡.-0+4/X 8<br />

.3!p>F004Do),!¡<br />

#Ž%'&,%¨Ê#–‹>-%NFsy+4/./%a%'&.3!N&-)¡.3!¡%¡.3>g!‘F’¦ >F%¡./:F4/m!,½¾|-),!¡a./%<br />

¥w%¡.3>F#&O9-:-<br />

+ O9./%'&?2 !¡+, >F%N%'— ' I0Z)¨%'Q%'&.3!Z./,F%Z1¡%'&.3!Z8<br />

8G%'p-0„.I I/# .z1o–<br />

+43,!0,8`%'%F54L4DoF8-'<br />

!j+43k0'&./E&4/l%'&,k%'&-5#@+4BC-0%'&,%¨Fs+4D' !¨%'&a0'a&./E&4/_F%' 8<br />

"%2<br />

+43G§,"!¡%9O9.L4L4Ã+=-¡17'Ô…!2%¡.3!§, !%'&.3!<br />

1ƒ./%"!£4L./<br />

>-),!¡‘.L1̽¾@.3!9Fs+,,8./E+43§Á­,8GÊ3–è.3!9Fs+,,8./E<br />

½3¾P&,!vCg8:X%"E…:-Ê3–è2&.L438gC1ŒÁŠ%94/ !*%(!;&.DE&è!9%'&jGA!¡%K&./E&4/<br />

>F'2<br />

8P>2&.L438?15ÃjI0e9&.3!Z.3!‘%'')0!./,>F-:-'P>2&.L4B8`15í.B!Na4L./ ¡./{ %¡./l1K!¡00>2&.z438`1 ÁN#<br />

"%2<br />

80&./E&-Z%'&,g¨>2&.z438@1ÁNI)2%'&-'02#A%2&-'p5<br />

,8a%'&-2F1b2p^>2&.L438gC1Ãî>-Q


F%¡./0!¡&Ov 8Z%2&,%½¾a&,!£K+=%'-%¡.354y8:A%FE:-ŽÊ3–a-),!¡./% >-CjF%"!Z<s<strong>tr</strong>ong>1.</s<strong>tr</strong>ong>/,>F'+="%*.DE<br />

Fs+4DC.D%¨>F-'%"5./?"8-¡./EQ&-)¡.3!¡%¡.3>-!-IG†?¨XOŠFs,¨./0%2&H+F>F%¡.3>-54F’¦<br />

j!¡),>2&g&-)*.B!*%¡.3>p./%'Ž½¾l,8aÊ#–I<br />

#ƒO90%'¨%'&,%p"8-¡./Eg&-)¡.3!¡%*.B>-!^4/Paq0!¡-,!¡¨17j!¡0!¡ F>'&?!¡%'F%'-E./ !-Ï Ï<br />

Ž./"!*%<br />

8%'&6¨§,F!¡%!¡ ">2&¦#&-)¡.3!¡%¡.3>-!80—,¼º./0+':K%2&vF[Q>2.D-,>F¨1ƒ%'&K!¡ ">2&N./<br />

+,'%*.B>F)435#172&<br />

0<br />

8d#A!8F§, 80 *4z./- #!./,>F…"8-¡./Ep&-)¡.3!¡%¡.3>-!<br />

!¡%'F%'-EZ./0OK&.3>2&0Ê#–g,8g½¾g'j]-!¡,>2&'./{-<br />

>F%ƒ%'&'F43%*.D:+,-*1b2,>F1J½¾,8ZÊ#–G),8- !*),>'&¨!¡%'"%2-E./ !-I¦e9&),!-#<br />

8K%£!./E.L§u>-A%*4D¨5’¦<br />

F>'&_!*%'"%'-EP%2&,%p.3!¨%¨!¡,>'&'.D{- 8ƒÈQ8-+%'&6¨§,F!¡%<br />

O9'&¦I !¡<br />

!¡%*.DE%¡./¦#!./,>FK./%M.B!<br />

†`K),!¡K%'&w¨./67EA543!&-)¡.3!¡%¡.3>Z!%'&wF0G4/j-0+4/<br />

>F%¡./¦IvŽ./E)2T ݨ!¡&O…!9%2&Z.DG+,>F%…C1 ¨./67E543!KQ%2&pZF%¡./¦#ƒ!./,>FjF-A%FEItpFs,0+4/#£),8-^8-+%2&6¨§,"!¡%H!* ">2&?<br />

+43-"!¨'N./0+':<br />

8gÇÇŠ¡¬,8QÊ#–`./0+': 8@ÇVn¡I9e9&),!-#<br />

%'&N+'F%¡./¦IwJKg%'&N%'&-K&,,8ƒ#=%'&.3!Z8A !w%…>F%'"8.B>F%w)<br />

17'©)Z,54/y!h.B!;./o%'&p+'-:.D),!p!¡<br />

,!Z%'&,%p%2&H+=%'-%¡.354&-)¡.3!¡%¡.3>a8:XCA%"CEjOK!Z%p!./E.L§u>-%¨-)E&<br />

%'&-2#=.D%¨!./0+4/o0<br />

!¡%./%"!¡F4L1¡0'…!./E.L§u>-%¡4/I¹w17%'-<br />

%'¨!¡&Oc)+¦I£ÏQ%2&-v8X.D,!$#%'&p8:XCA%"CEK¨./E&%C.z17<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

5000<br />

Nodes Explored<br />

4000<br />

3000<br />

2000<br />

TO<br />

UA<br />

TO-MG<br />

UA-MG<br />

TO without MinGoals<br />

UA without MinGoals<br />

TO with MinGoals<br />

UA with MinGoals<br />

TO<br />

UA<br />

TO-MG<br />

1000<br />

UA-MG<br />

0<br />

3 4 5 6<br />

Depth <strong>of</strong> Problem<br />

Ž.DE)'0T ÝÈZ-+%'&r§,"!¡%…!¡ C">'&QO;.D%2&g,8aO9./%'&)%Z¨./67EA543!<br />

ŽFbš<br />

’ååŸH•¥n©“”–~n©wqopœ›žéhp~“›w¡Dp"stn¥–JåtŸ p~•›Ÿ#å,n©•<br />

54L4#w.D%a.3!Q>F-'%F5./4Di+,A!2!./


!-IQJK)N' !¡)4/%"!¨!./0+4/@.L4z4/),!¡%2"%'a%'&,%Z./l)p2qy!*Ov¡438<br />

)pFs,0+4/G.DkŽ./E)'0Ua.L4L4/),!¡%'"C%'<br />

>2.B!h.D,!0+'8),>F !0@-E4L./E./F%…8)N%'0!¡ ">2&g!¡+,>F¨>F0+' !2!./oSh8.3!'>F),!'!¡ 8@+'-:./),!4/=Y"I +'<br />

>F%'"!*%v%2H%2&H!./E.L§u>-%…F’¦<br />

%'Q&F4/+³½¾i0'G%'&,?Ê#–#¦%'&a' !¡)4/%"!N'<br />

†|&.L4/%2&¨./67E543!p&-)¡.3!¡%¡.3>Q8.38l%j!¡--<br />

!2!./A%'-2 !¡%¡./E,#,!./,>Fp%'&Z&-)¡.3!¡%¡.3>‘&,8N:-2!./E.L§u>-%KF’¦ >F%v%'&Z+,-*1b2,>F<br />

-:-'%2&F4D<br />

1ê'¼ºb\g+43-"!-#K!¡o¨),>2&c!¡?%'&,%¨Ê#–£¢±3ºb\o¨./67EA543!¨)%'+,-¡17'a!V½¾¤¢±¨ºb\A¼éºK¨./67E543!-I<br />

>F%¡./:- !'!£1ƒ¨./67EA543!Ž.3!85./08-+,-,8-% #Ov§,,8N./%£./%'-' !¡%¡./EN%'&,%Ž.DG%'& !¡<br />

†|&.L4Dw%'&KF’¦<br />

!ƒ0'v8.L’¦-'-,>F9%'&,N%'&),!¡91,+,C'%¡.354AF8-"!-I¦¹w17%'-<br />

Fs+,-¡./0-%"!-#%'&),!¡1,¨./67EAX4B!£aq<br />

8k0%*.D:%'0%2&\8-:F4/+G-A%¨1K+,'%*.BX4D67"8-j+43./E<br />

54L4#%'&0'q!¡O9¡438`¡./E./,54L4/_&F4/+=<br />

Œ)-%0+43./Ec!¡y!*%'-!¨&,5:Q-0+4/ 8l+,2%¡.354…"8-F!-Il†f&.L4/o%08--+4/<br />

,8l0!¡%!¡)N+43./EQ&-)¡.3!¡%¡.3>-!Z!¡),>'&o!9¨./67E543!-I<br />

+,5.38Q%2!¡+,<br />

F>'&?!¡+,>Fa>F0+' !'!h.Do./kR >F%¡./iVA#ƒO9^8 !2>F¡./-X4z4/ 8r./%'-"%*.D:j!'0+4L./E\C,8Q!¡&Ov 8G%'&,%w),8-9./%'-"%¡./:j!206<br />

./,!¡-,!./%¡./:<br />

C">'&¦IwÏ71O9H>FH'&i0'a+,O9-¡17)4(!¡%'"C%'-E#2&|Ê3–­,8ø½¾­!¡%¡.L4L4(+=-¡1b' F<br />

Œ),54L4DI9…!./0+4L.3>2.D%¡#ƒ);.DG+4D-G-A%"C%¡./g1£./%'-"%*.D:j!'0+4L./EQ),!¡ !9¨./67E543!…!9¨+2)6<br />

<br />

>2&_>2&.3>F+=./A%5#ƒ./%¨Fsy+4/' !‘4/o%'&A!¡0+43lFs%'-,!./,!pO;.D%2&_%'&^1b-O9 !¡%<br />

./Eg&-)¡.3!¡%*.B>„9%p<br />

e;&.B!9!¡%2"%'-E‘.3!+,O9-¡17)4#yX4D%2&)E&¨./,>F0+4/-%'I + ~ >-),!¡Z1ƒ%'&.3!./,>FG+4D-%2- !'!-#O9<br />

EAX4B!$I<br />

8(1b2‹)!'C0+4/;!*-%¡-),!¡./%'-"%¡./:K!'C0+4L.DENO9./%'&<br />

%'%'&-'9OK!Ž+'


%./a¨./,8ƒ#Ovw%')'0%'N%'&<br />

¨./67EAX4B!O9)438G-:-%'-2¨./,%'KG%'&.3!+2FK),8-98-+%'&6¨§,"!¡%K!¡<br />

!$ILY0JK)9' !¡)4/%"!9>24/ ¡4/G.z4L4/),!¡%'F%'p%'&K)%*.z4L./%¡C1¡%'&K+43./EaF 8a-X4D<br />

¨./67EAX4B!(./?)p2q!¡O9¡438o85./¦#¡!h.D,>FGo‡AÛa1v)p‡‡+2F,!h.B8-<br />

e;&(8"C%¡.3>Z!¡),>->F<br />

">2&_!¡%'"C%'-E#Ž./%'-"%¡./:aFH-C%' 8¨!¡ ">2&0!¡%'"%2-EK././%¡.354L4/2.L§, 8?8-+%'&@2&,8ƒ#%2&A),!-#FG !./,>F' !./E4/\!¡-,!h.D%*.D:<br />

./0./%"!<br />

>F%17'­)£./%'-"%¡./:K!'C0+4L.DENFsy+=-¡./0-%"!-#O9./%'&<br />

%'p!¡4/)%¡./8.3!¡%2¡./FQ%'&-_8<br />

!NOvG&, :¨.38-A%¡.L§, 8`./l%'&.3!j+,C+,-0>-<br />

Fs+,-¡./0-%"!¨8@.z4L4/),!¡%'F%'a&XO¥%'&0:¡./),!N+'+=-'%¡./<br />

:./EQ !¡%"2&o%''-05@F,8./%¡./,!-Io†i./%'&kgG'0Fs+' !'!./:Q+43./Eo43E),E#O9.L4L4K%'&a%¡./0\>F!¡%<br />

>F,8./%¡./,54Z+'<br />

C%'-K179½¾k%'&,r1b…Ê#–McJK0¨./E&%Z%'&./qè!*,#u!h.D,>FG%'&¨Ov'q<br />

+,-p80-CA%¡4/oE'<br />

Œ)./' 8?%20.38-%¡.L1bo./%'-">F%*.DEo!¡%'-+,!p>-è.D,>F2 !¡0O9./%'&`%'&0Fs+' !'!./:- !'!‘1v%2&0+,-F%'<br />

'<br />

8rShZ €­~y88#ƒT UÇÇ„‰K-2%'{-


:./EA!9%'&,C% ½¾l-Äh!K8)¨%'¨./%"!w' 8),>F 8o!¡ ">2&g!¡+,>FNO9.L4z4<br />

./A%2-">F%¡./r.B!w&./E&o-)E&¦#=%'&H!2<br />

8a-!¡¨17j!./0+4/aF!¡%<br />

1<br />

!'!w%'&,Q%2&j+'8),>F%…C1 %'&j>F!¡%K+,-Z8p17KÊ#–_C,8Q%'&p)¨F)438x.D,>F)QiFsy+=-A%*.BX4‘>FA!*%0+,-ay8?,8i!¡%¡.L4L4<br />

%'&,%a>F''<br />

!-I9e9&.3!Z>-g&,++=-¦#17KFs,0+4/#=.L1%'&pFs+,-%¡.354A)¨-!¡<br />

¡./{ %¡./,!w1 ,½¾o+,'%*.BX4u"8-.3!9E2 %'-%2&,%2&pFsy+=-A%*.BX4Ž>F!¡%9+,-K8Z1b½¾I£Ï<br />

4L./<br />

#£&O9-:- #ƒO9¨O9)438@4L.Dq%'g5:C.B8è%'&>-!¡¨OK&-2Ž½¾c+,5!p?Fs+,-%¡.354K>FA!¡%p+,-<br />

E--"X4<br />

8ƒ#ƒ>F,!.38-jg++2A>2&g%'&,%Z>-gE),C"%'-p%'&,%K%2&j>FA!¡%Z+,-Zy8‘1b`½¾<br />

8H,8ƒ#t./,!¡%'<br />

'-X.D,!w+,C4D¨.354Sh!4/E!9%'&j>FA!¡%w+,-Zy8‘1b9Ê#–l543!¡0'-X.D,!w+,C4D¨.3547Y"I<br />

80FA!¡%+,-9y8w17½¾r.3!8¨./,%2<br />

>F%¡./EP%2&H"8-¡./EA!NS'R%'-+o‡YFI!;K+ƒ8%¡./Eg%2&HEA54 !¡-%p2-5./,!p+=4/A^.BX4v!<br />

%'&0>FA!¡%pC1v!¡F4/<br />

>'&o+' >F,8.D%*.Do./_o),¨F,8./%¡./<br />

—,®F•F®-¯F¯”–°F±¨²z³Ž%'')9—=®"•F®-¯F¯-–°"±¨²L³Ž1<br />

./%"!9%'2)%'&:54/)p./PC\2F%'<br />

!9QQ]->F,!¡-':%¡./: dN"8-*.DE0!¡%2"%'-EN./QOK&.3>2&Q+,-"C%'"!'Z"8-' 8^.L1 %'&-<br />

+'+=-'%¡0'F4L./<br />

À ¼¯F¯”±7ê-²L³;.D%'-">F% I<br />

-:-<br />

¹p!ZQ.L4L4/),!¡%'"%*.DPC1%'&.3!…++2A>2&¦#u>F,!h.B8-jG!./0+4/0+'+=A!./%¡./,54£43E),ENO9./%'&?>F6<br />

>F%F!-#¦!¡),>2&_!0]2.L1 À ,8±°5#¦%'&-?88k°¡dI0‰w-,>F#¡`+,-"C%'p>-_88lS(8F4/-%'Y<br />

8./%¡./,549F’Ã<br />

8ƒI‘†?¨'F1b-Z%'Q>F,8./%¡./,!j!*),>'&o!<br />

+'+=A!./%¡./,!p8-+=-,8.DEo@%'&0!¡%"%2Z.D`OK&.3>'&@./%Z.3!p++4L.D<br />

À dG./?)pFstG+4Da!¨¿® À ® —=¿® —=• ³a•"¼—=¿±¨º7±3¼—t¯”I^S¥K%'j%'&,C% #=4L.Dq0+' >F,8./%¡./,!-#8-+=-,8-,>F<br />

]<br />

Æ &,+CcS"T5UÇVY…!¡&O9 8o%'&,C%jO9./%'&l%'&.3!p%¡+,a194BC6<br />

>F,8./%¡./,!0C'!./0+4/Q+'+=A!./%¡./,!-IDY<br />

>2.38QOK&-%'&-Hr+' >F,8./%¡./l.3!N%'')¨./kQ+,2%¡.354L4D`"8-' 8`+43¦I<br />

E),E¨./%p.3!,¥…¸M67&,"8o%'o8<br />

8Q)%Z2.354>-!¡N1;é—,–í^ê$±zÂéA¼é¯K+43,!-#t%'&.3!…8 >2.3!./<br />

‰wXO9-:-5#y!9O9p+,./%'<br />

8r./g+=4/A¨.354 %*.DGI<br />

>-Q->FG+4z.3!¡&<br />

>2.L§, 8Q!Ž1bC4z4/O…!-I£¹Z¨+,-"C%'8—0#!£F,8./%¡./,!-#t+'S—¨YF#Z4L.3!¡%K1£S),>F,8./%¡./,547Yv88!$#y88!FS—¨YF#Z4L.3!¡%K1£S),>F,8./%¡./,547Yv8F4/-%'<br />

Ï_88.D%*.D¦#¦./%N&,!pG4L.B!*%HC1;>F,8./%¡./,54K88!-#£>-88!FS—^Y"#¦,8?G4L.3!¡%jC1;>F,8./%¡./,54<br />

8F43!FS—^Y"Ï<br />

!-#9>-8F43!FS—¨YF„F%"5././E?+,5./"!³²µǵµ í Ý8F#¡Ow&-'®ǵµp.3!0@>FÄ¡),>F%¡./:g!¡-%¨1…8-+,-6<br />

8F4/-%'<br />

>F%GSF./%'&-0_88 8`jg8F4/-%' 8l>F,8./%¡./ƒY"I<br />

8-,>F_>F,8./%¡./,!¨,8ÚÝ^.B!‘%'&Q>F,8./%¡./,54vF’¦<br />

>F,8./%¡./¦#ƒ-:-'Q>F,8./%¡./,54<br />

¹Z,54/E),!wO9./%'&g%2&j>F,!¡%'"X.D%Z%'&,%K-:-2\8F4/-%'¨¨),!¡%K


8Ž½3¾F‰'‹¡#OK&.3>'&^.B!++'+*.BC%'917%'&.3!<br />

Ž./E)2(T5“p!¡&O…!Z:-"!./G1u%'&`½¾g54/E¡./%'&@#A>-54L4/<br />

e;&v+*.Da'08.L’Ã-2-,>FKF%¨%'og!¡-%N1…8-+,-,8-,>Fc>F,8./%¡./,!-I<br />

ÛgC,8?‡F,8.D%*.D,54KF’Ã >F%F!Z8<br />

´@„ƒ./%j'-%2)',!ja-O¬!¡%'-+§—<br />

>F%"!%2&,%v2…!¡F4/ >F%' 8G17%'&.3!9%2",!17'C%¡./0'KFs,>F%¡4/a%'&A!¡KOw&A!¡<br />

),>F,8./%¡./,54IKe9&ZF’¦<br />

>2.354L./{F./E_a+43m!*%'-+@.B!‘%'&<br />

8-+,-,8-,>Fk>F,8./%¡./,!N'0Q!¡)2.354L./{- 8ƒ#½¾F‰'‹<br />

>F%91<br />

>F%"!-IJ91>F)"!¡#N!¡%'-+Q>-F%2 8ƒI<br />

!¡+=<br />

>2.3!¡F4/#%'&08F§,./%¡./l1Œ— H ò !*+, >2.354L./{-S— í ´QYF#OK&-'Ž—Ñ.B!NQ!¡%'-+¦#F´ .B!NQ>F6<br />

}@2j+'<br />

#5.3!!Ž174L4/XOZ!-I<br />

Ä¡),>F%¡./:…!¡-%1¦8-+,-,8-,>F>F,8.D%*.D,!./Ž—G#,8³¸9.3!£%'&…!*-%8.z’¦-'-,>Fw+,-"C%'<br />

8è1b.½¾F‰'‹l!Z174L4/O…!-I0†`!'5g%'&,C%p%hO9<br />

e;&8F§,./%¡./_C1w!*%'-+o./A%2-">F%¡./o.3!NE--"X4z./{-<br />

°¡–• ºÃ.L1%'&-P2p)"8-' 8@O9./%'&@' !¡+, >F%p%20 >2&g%'&-p,8r%'&p174L4/XO;.DE<br />

!¡%'-+,!;./?0+43l±3—=º7®<br />

H!¡%2-+g&,!Z0+2 >F,8./%¡./k¼°¨¿® À ® —,¿® —,•5³0•F¼—,¿±¨º7±¨¼—0%'&,C%K.3!Z88 8@…8F4/-%' 8oF¨¨17% Ï e9&.3!p08.L§, 8_8F§,./%¡./c54L4/O…!Z),!p%2g8-%' >F%p./%'-">F%¡./E@+,-"C%'"!<br />

>-%'<br />

!¡%5#u!Z8.38@)…¡./E./,54v8F§,./%¡./¦IjKFstC0+4/#ƒ%hO9!*%'-+,!Z%'&,%<br />

O9./%'&?a!./0+4/j./Fs+,-,!./:a%'<br />

8è./A%'-F>F%N.z1Z\!*%'-+_>F,8./%¡./,54L4/c88!a°p,8`%'&%'&-j&,!‘+' >F,8./%¡./‹°FI<br />

'G)"8-'<br />

8Q%(>F%2),54L4Dg88?°./o%'&j+43¦#ƒ!¡0F8-¡./EQ%'&p%¡OvG+,-"C%'"!<br />

¥w%'p%'&,%Z%'&Z§,"!*%(!¡%2-+g-<br />

>F !'!'2IÏ_E--"54#£)j8F§,./%¡./k19./A%'-F>F%¡./o.3!¨Q!¡)[\>2./-%^>F*.D%2-¡./?17<br />

¨./E&%jF¡./%'-¡./¦I<br />

E),FA%2-F.DEG%'&,%K%'&p2<br />

½¾F‰'‹`Fsy%2-,8!ja+43¦Ie;&0+'-6<br />

Ž./E)2\T5ÛQ!¡&O…!pQ!'>2&-%¡.3>¨Fs,0+4/¨.L4L4/),!¡%'"%*.DEo&O<br />

>2&g+,-"%2(C'0!¡&OKog%'&N4/F17%p1v >2&o+,-F%' #ƒ,8@%'&¨),>F,8./%¡./,54<br />

>F,8./%¡./,!‘1v<br />

I‘S†?¨4/g!¡&O­%'&¨+' >F,8./%¡./,!jC,8QF’¦ >F%"!w >F !'!''@%'¨.L4L4/),!¡%'"%20%'&<br />

88!wo%'&j*.DE&A%<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

¿ +'S— H Yò‚+2S—¨Y>¹º´@I<br />

¿ 88!FS— H Y»ò 88!FS—^Y>¹ ì Ý1ú¥²µ´Vµ í Ý8 ô >-88!FS¥—¨Y#»¼´Vµž½C´ ðAI<br />

¿ 8F4B!$S— H Y»ò 8F43!$S—¨Y>¹ ì Ý.úŠ²µǵµ í Ý8 ô >-8F4B!5S¥—¨Y#»¾´Vµ.½¿´»ðAI<br />

¿ >-88!FS— H Yò ì ²µ´ µ í Ý8ŒúŠ²E´Vµ í Ý8 ô >-88!FS—^Yr»¾´Vµ õ ½C´À» ´ µ<br />

òÁ´Vµz¸8´»ðAI<br />

¿ >-8F4B!$S— H Yò ì ²µ´ µ í Ý8ŒúŠ²E´Vµ í Ý8 ô >-8F43!-S—^Yr»¾´Vµ õ ½C´À»¾´ µ<br />

ò´Vµz¸,´ ðAI<br />

8.3!¨Ä¡),>F%¡./o&438!-È<br />

¿ j!¡%'-+g88!w0>F,8./%¡./o%'&,%.3!…8F4/-%' 8@


%È ú?CDFEý Ê/Ë<br />

GJIKL.MONQPR¥MTS2NVUWQIUXQYZBþ[E\ «õ4¤¡ù5© ö]5÷§¤©øF÷7ö¡õ§5ó¡ó¤¡õ7õò!¨…÷§¤¡ö§5÷§põ7ø'ÿ£5ö «ø-©-ÿzò1=ð<br />

ï<br />

^<br />

ü<br />

£92¤¡ö?$¤¥¤¥ hÔÓzÕ?jò9h Îo k0kFð<br />

¤ÿ£¤¡ö§¤h÷£ø2þ[e/<br />

k> «ö§¦¤¡÷¡ùKò2÷7ô!ÌÍ Î Dne*Ï)] ø"÷Ž÷§¤©$ÿzò'ó¥¤5h Îo k0k$3 «ö§¦…õ§©2¤¡ó) zò¡ÿ¡ £¢¥¤ú?h Î?o k0k D×Í Î ýð<br />

Ï<br />

y2zT{xØ3sz r s)xczOt sÿ ~‚&~¥zJ„0w&u0sÿ ~tv…w!€w0…Q†¥s€u)s‚xn}£w!zTwy*w+~0~0‡<br />

qnr2stvu0wx2st<br />

_`S*P¨a’QmJ‰QPR¥MTNQŠpY'd;¤¡öE *¤ö§¦¨¤õ§¤¡ö¦ø'þJ©5÷§¤¡óhøƒ «ö«ø5õ £1C ö§¦Xò2ö¡ò2÷§¤¤¡ó¥¤hõ7õò2÷ ÿ£Zþ3ò¡ÿ«õ§¤Fð<br />

‘<br />

%2&k >'&l+=-"%'5IPtN.D,!*%",>F#%'&G§,"!¡%¨+=-"%'p./k%'&Q+43c%N%'&%2+_C1…%'&<br />

),8-'<br />

>F,8./%¡./ À Ie;&.B!‘+,-F%'j88!Ò°j,8?>F,8.D%*.D,54L4Dk88!Gé0.L1jºŽ.3!j%2')I0e9&<br />

+,EG&,!Z+'<br />

!%¡O9p1¡%'&w+4BC,!+2y8),>F 8Q!p' !*)4D%91¡88./E‘-O‹>F,8./%¡./,54¦+,-F%'<br />

§,E)'w.L4L4D),!*%'"%'<br />

>F%F!rÙ§ÚÜÛÞÝ]ßv,8¿Ù¡Û«ÛÞÚ¥ßv2\!¡F4/ >F%' 8è./k%'&<br />

%'@%'&+43¦IrÏk0+43¦#M%'&\>F,8.D%*.D,54KF’Ã<br />

>2.BX4z./{ %*.D?+'>F !'!-#,,8G./@%'&j%2&-v+43@%'&-g'p% I<br />

!¡+=<br />

Œ).D2 !94/+=4/A¨.354¡%¡./0p+=-K+43QE--"%2 8ƒ#yC,8a%'&p%¡./0<br />

e;&…-Oî!*%'-+¦#=R%'-+Q‡F2'<br />

R%'-+o‡'&0!¡+,>F ! d ÛÜ2Ý¨Ý àná .B!M-:-432E-<br />

%'&…!209'F43%¡./,!¡&./+a&438!F%*.Dg.3!N!¡)[Q>2.D-%H>F*.D%2-¡./o17…E),"%'-F./EQ%'&,%Z%'&<br />

+,C.D%'<br />

!¡)4/%¡./Ek+43,!Q2g),¨F%2 8a:.30¨!./0+4/p./Fs+,-,!./:0!¡%">F%¡.3><br />

>F,!¡-2:X%¡./:jC++'A>2&\X4z4/O…!./%'-">F%*.D,!9%'¨FA!*%+,-891b8½¾F‰'‹N4/OkF%¡./EN%'&K!¡ ">2&0!¡+,>F<br />

%'<br />

./%H>F,!h.B8-F!-#!j!¡&OK@./kŽ.DE)'gT-‡,I‹½¾F‰'‹l4/?>F,!.38-"!N),¨-?ZKö§¦¨¤¦þ/øF÷7ù¤¡÷ƒó'ò'õ§¤] £5õ§¤¡÷7ö¦õ7ö§¤¥© h4o k0k ò!¨H £<br />

¤0<br />

£ õ§¤¡÷7öõ7ö§¤¥©jõ§©2¤¡ó0 zò*ÿ¡ £¢¥¤ú?h o k)kDµÍ Î ýð4Z/þ,ö§¦¨¤¡÷§¤ «õ øwõ§ ó0¦,h o k)k]Xö§¦¨¤¥jö§¤¡÷7ù& £Xò2ö§¤;òp÷§¤¥©øF÷7ö<br />

ö§¦¤ÿzò2ö7ö§¤¡÷¡ó'ò2õ§¤]2<br />

ÿ£ ÷§¤Fð5qnr2st u)wx*stvy2zT{|}v}ÑÐQ|:¦~¸tvyoÐnr2tvu0rHe5u)|y9„0w8|……w)…5‚8~¥zJ„)w8u0sÿ ~¥t …w€?w)…J†¥s€u)s‚xn}£w!zOw!y2w¥~0~¥‡<br />

þBò+<br />

«ö«øò¡ÿ/ýMÿzò'õ7ö&¤ÿ£¤¡ö§¤h÷ø'þ#e2ð B ÷§¤¡÷h o k0kwò¡þ/ö§¤¡÷8hk)j§,ò<br />

ˆ-ò¼l5K!‰QIK!MTNQŠgbIaOIURMOS*NY8d;¤¡ö¸h4k0j§2¤9ö§¦¤ZúT5óhøƒ<br />

*¤þ/øF÷§¤8hij§j§kFð<br />

¤¥©*¤'ò2ö#-ö ÿ,ö§¦¨¤¡÷§¤ò'÷§¤5ø5 £-ö§¤¡÷ò'ó¡ö «ø õ¥Î<br />

Í<br />

¤ÿ£¤¡ó¡öòõ7ö§¤¥©1h4Ñ£iÒ=ö§¦Xò2ö £-ö§¤¡÷ò'ó¡ö7õ4$ «ö§¦1h o k)kFð<br />

Ï5Ð<br />

B ÷§¨¤h÷h4Ñ£iÒJ¤) «ö§¦¨¤h÷42¤þDøF÷§¤øF÷¡ò¡þ/ö§¤¡÷h o k0kFð<br />

Ï<br />

y2zT{/„0sz£r`s€…w!€0tvyÓ~‚&~z„0w&u0sÿ ~tv…w!€w0…Q†¥s€u0s‚3xn}£w!zTw!y2w¥~)~7ð<br />

qnr2stvu0wx2st<br />

dn¤¡ö#C<br />

2¤ö§¦¤÷§¤¡õ§-ÿ«ö £¨ ©$ÿzò!ð<br />

ÿ£¤Zö§¦¤¡÷§¤8¤*1 «õ7ö7õ9ò9õ7ö§¤¥©1hÎo k0k $ «ö§¦1¨ ùKò2÷7ô¤¥¨ó¡ø¨ «ö«øXò*ÿŽòÒÌÍ3Î¥D*e*Ï<br />

ˆ³l5mJIK!P¨R¥S*K9KS*aOI1b¥IaTIUR¥MTS2NY-‹¦<br />

«ö§¦1©5÷§¤¡óhøƒ«ö«ø»e]Aõ§5ó0¦¨ö§¦Xò2ö8hÓÖÕ?j«õ9ò¡þ/ö§¤¡÷8h Î?o k0kwò!¨jö§¦¤¡÷§¤5 «õ5ø¨úT5óhøƒ«ö«øò¡ÿ/ý<br />

ò!¨HòZõ7ö§¤¥©.hÔÓzÕ?j&$<br />

“ ”5IU’QK!b¥MT•2I MONc•2SnUP¨RMOS*NY Ê#Ë %È£ú?C D0E ýð<br />

Ž.DE)'0T “Èe9&,½¾¦6 Æ<br />

+43./EQ54/E¡./%'&<br />

E--"C%' 8¨:.B‘./%"!p]->F,!*-':X%*.D: dp"8-*.DE0!¡%2"%'-EI4½¾F‰'‹G.3!9!¡%¡.L4L4Ž‘+,'%¡.354/67F8-v+43-5#,,8<br />

Ð ö§¤¥©ŽˆV2¤H «ù5©$ÿ£¤hù5¤¥-ö§¤¥gõ7øNö§¦Xò2övö§¦¨¤pö«ù5¤…ó¡øFõ7ö8«õ`hú&'ý)]'5õ £¨ö§¦¤9F÷ò©¦aö7÷ò¥¤¡÷7õò*ÿ¡ö§¤¡ó0¦¨ £Å¤¡õ<br />

ï!‘$ðJZ?^þBò2ó¡ö¥]<br />

£2¤6 £ Ð ¤¡ó¡ö «ø`“-ð Ë õ,ò£÷§¤hõ§$ÿ«ö,ö§¦¨¤#ÇnÈnÃ4ÄÌ «ù©$ÿ£¤¡ù¤¥-öò2ö«øjò9ö§¦¨¤¦ó¡ø"÷7÷§¤¡õ§©ø¨ £¨ lnm Ã%Ä «ù©$ÿ£¤¡ù¤¥-öò2ö«ø<br />

¤¡õ7ó¡÷<br />

«ù5¤ó¡øFõ7ö#©2¤¡÷# ø¨¤þ/ø"÷Žö§¦ «õ4¤¥$QÿzòXò¤Kò2õ¦ö§¦¤¥` £Zþ/øF÷¦ö§¦¤øF÷ £! £ò¡ÿ=ÿzò!¨ò!¤]chú&'ý¦ò<br />

¦Xò¥¤ö§¦¨¤õò'ù5¤ö<br />

£¤ÿ£Fð<br />

húàý)]÷§¤hõ§©2¤¡ó¡ö<br />

Õ:9XÖ


!K%K>F,!h.B8-jX4z4£+,'%¡.354L4/Q"8-' 8r+43,!KK-:-g54L4¡),¨F0+4/-%'#,-CH&,5::X*.BCF,8./%¡./,!9,8¨F’¦ >F%"!-I£ÏG%'&KE--"X4u>-!¡#17‘E./:-Ž½¾Q+43Q,80p>F2' !¡+,,8.DE<br />

%'&F./+2<br />

8oF,!.38-'<br />

8aO;.D%2&2-?8-:.3!¡aP]24/>-543dQ>F¡./%'-¡./o179./%'-">F%*.D<br />

88./%¡./,54v>F!¡%K.3!w./lR%'-+o‡,IZÏoE--"X4<br />

!*)4D%*.DEQ+43@.3!ZE),FA%2- 8Q%'a-X4Bdt#¦O900 lQ>F¡./%'-¡./l%'&,%p4/<br />

!¡%'-+l>-?->F0+4L.3!¡&<br />

IB#./%K¨),!¡%K%KFs,¨./p%'&N' !¡%91%'&<br />

>F,!.38-"!w+=-"%'9+,5./"!w%'08-%'-'^.D‘./A%'-F>F%¡./,!-„.I<br />

+43¦I<br />

!N%'&,%V½¾|&,!^X:-HÊ#–‹>-CkF2 !¡8-+=-,8!p@%'&0!¡+, >2.L§u>N43E),CE#<br />

!./{-¨1Œ½3¾ª«!K!¡<br />

%''-Z.3!w-:-943'E-K%'&,QÊ#–ª«!-I<br />

!2!¡l&-'a.3!¨%'&,%N%'&\>F!¡%¨1…+43kFs%'-,!./l.3!N%0!¡4/F4/m8-+=-,8-A%a<br />

e;&E--F5494D<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

p q<br />

O<br />

[ t u ]<br />

q<br />

r O<br />

s<br />

O<br />

Add Operator:<br />

r<br />

O<br />

[ u s]<br />

p q<br />

O<br />

[ t u]<br />

r<br />

O<br />

[ u s]<br />

q<br />

r O<br />

s<br />

p q<br />

O<br />

t u<br />

u<br />

O<br />

r<br />

s<br />

q<br />

r O<br />

s<br />

O<br />

O<br />

Ž.DE)'0T ÛȹZQFs,0+4/p.L4L4/),!¡%'"%*.DEQ%2&1½¾F‰'‹o54/E¡./%'&<br />

Ê#–l+43¦#¦R%2-+,!jT#¾“#,,8@Û¨1%'&1½¾k54/E*.D%2&<br />

>FA!*%K%'&H!20H!9%'&H>F'' !¡+=,8./Eg!¡%'-+,!91<br />

8X.D¦#,8`+'-`E),"%'-0%2&,%.½¾ª«!p!¡ ">2&<br />

%'&ZFsy+2 !'!./:- !'!9C1Ã%2&…+=-"%'43E),E#./%…X4B!*^8-+=-,8!9a%'&Z,%')'Z1¦%'&Z+4BC,!9%'&,%<br />

Õ:9*@


8a+43,!v.B!`¥Z¸67&,"8G17<br />

%'&p+43-p>F,!.38-"!-I;R,#,54/%'&)E&Q%'&pFsy%2-,!./Q1+,'%¡.354L4/Q"8-'<br />

!O9./%'&>F,8.D%*.D,54uF’¦ >F%"!-#C.L1Ã%2&…!¡+,>FKC1u+43,!£.3!M' !¡%'¡.3>F%' 8rSI E=I/# 4D¨),¨F-'%"5./>F0+)%"%¡./,X4t8:%"E !<br />

†?9&,5:v!*&XOwj%'&,%½¾#w+,'%*.BX4D67"8-+43-<br />

:-0@%'%"54/67F8-H+43-5#Ê#–#!./,>FQ./%"!0CF0¨./%'0-%"!0X4z4/O…!‘170gG'<br />

">2&f!*+,>FP,8x+,%2-A%¡.354L4/cG'Q./%'F4L4L.DE-A%QF8-¡./Em>2&.3>F !-Iî‰wO9-:- #%'&-'<br />

>F0+,>F%!¡<br />

!K%'&,C%pOvN¨./E&%j>F,!.38- #¡!w.z4L4/),!¡%'F%' 8@./_Ž./E)'QT WtI(eŽ%"X4D67"8-<br />

1v>FG¨./%'0-%j!¡%'"%2-E./<br />

!%Ž9-,8jC1y%'&K!¡+= >F%'')gI£¹K%Ž%'&9%'&-£Fsy%'2-0.3!£%'&9!¡%'"%2-E…C1,5./A%F5./.DE<br />

+43./Ep4L./<br />

°¡®"¿¨!¡-%Z1v!¡%'-+,!p8)*.DEg!* ">2&g)%¡.L4%'&-'jFs.3!¡%"!p^4L.D C¡./{ %¡./?1%2&^!*%'-+,!<br />

@º7¼º7–²¨²z³Qé—,¼°h¿®<br />

%'&,%.3!Z0!¡4/)%¡./@+4BC¦I<br />

0+,' 8a%2CAaO9F4z4/67qOKo+4BC-"!-#½¾`.3!…>F,!*-':X%*.D:^!h.D,>FN./%Z' Œ)./' !Z >'&@+4BC<br />

Æ<br />

Œ)./' 8@


A ú?C3D Eý ầ<br />

«õ4¤¡ù5© ö]5÷§¤©øF÷7ö¡õ§5ó¡ó¤¡õ7õò!¨…õ7ö7ø©ð<br />

ïFðHGJIKL.MONQPR¥MTS2NVUWQIUXQYZBþ[E\<br />

«ó0¦He[«õuò/© ÷§¤¡ó¡ø «ö«øð<br />

^$ðH_`S*P¨acb¥IaTIUR¥MTS2NYJd;¤höJegfŠõ§¤ÿ£¤¡óhö"ø-ò¡ÿ/ú?Eý)]ò!¨ÿ£¤¡öhij§j§k2¤¦ö§¦¤©$ÿzò!Kõ7ö§¤¥©þ/ø"÷Q$/¦<br />

k0k *¤/¤0 «ö§¦¨¤¡÷uò4©-ÿzòKõ7ö§¤¥©5©ø"õ7õ £$ÿ£H2¤þ/øF÷§¤h ij§j§k ö§¦Xò2öuò5õ'e=ø"÷ƒò!9ø©2¤h÷ò2ö7øF÷<br />

ü$ðHl5mJIK!P¨R¥S*K&b¥IaTIUR¥MTS2NY'dn¤¡öJh4o<br />

ó)¦(òõ7ö§¤¥©n:ó0¦5ø-ø"õ§¤ø¨¤ø2þyö§¦¨¤£þ/ø'ÿ ÿ«ø!$3 £9$¦ò¥-õ¦ö7ø9ùKò'ô¤8eŽö7÷§¤£þ/ø"÷4hij§j§k<br />

dn¤¡öh4k0j§p2¤õ§<br />

B ÷§¨¤h÷h k0j§ ò¡þ/ö§¤¡÷h ij§j§k ð<br />

Ï<br />

*¤ö§¦¨¤õ§¤¡ö¦ø'þJ©5÷§¤¡óhøƒ «ö«ø5õ £1C ö§¦Xò2ö¡ò2÷§¤ øFö#¤¡ó¥¤¡õ7õò'÷ ÿ£Nö7÷§¤Fð<br />

‘$ðH_`S*P¨a’QmJ‰QPR¥MTNQŠpY'd;¤¡öE<br />

MONc•2SnUP¨RMOS*NY ầ A ú?C D0E ýð<br />

“$ðH”5IU’QK!b¥MT•2I<br />

qaS Æ &,C+¦#ƒT UÇVY"#17Fs,0+4/I9‰KO|8H%2& !¡Z4/ !'!¡6>F0^.D%2%' 8a+43-"!K>FG+,'<br />

Ke9O9<br />

>F%¨G4/ !'!¡6>F0^.D%2%' 8o+43-j%2Q&, :H%2&!'008:%"E !<br />

%'½¾cC,8gÊ#–M‹JK0¨./E&%jFs+,<br />

#£%'&.3!N.3!¨%H >F !2!'¡.L4/_%2')I?¹p!¨_Fs,0+4/#M./<br />

:-V½¾|%'&,%,½¾|&,!NX:-HÊ#–I?‰KO9-:-<br />

>F%¡./oO9N./A%'2y8),>F0Qe9O9 q6¨4L.DqH+43-5#¡>-54L4/ 8uèwÊ #ƒ,8o!¡&O­%'&,%w.D%F!p!¡ ">2&?!¡+,>F<br />

%'&.3!p!¡<br />

!-I +54<br />

.3!9432E-K%'&,Q-:-QÊ3–ª«!./o!¡0j>2./">F)!*%",>F<br />

!¡-%"!£%'&.èwÊ0+'>F 8)'I£èwʨ.3!Z+'+,!./%¡./,54+4BC-FI£Ï%£.3!!¡%'F5./E&A%*1b2O;C"8K%2(!¡-9%'&,C%Ëèwʨ.3!Ž4/ !'!>F0¨./%'%2 8j%2&,.½¾I¡e9&K54/E*.D%2&!<br />

!¡<br />

„=&Ov-:- #.D`R%'-+g‡=#AOw&-' !H½¾`"8-"!954L4¦./%'-">F%¡./EQ!¡%'-+,!-#¥èKÊo8A !w% I<br />

'jŒ)./%'j!./¨.L43<br />

!£%ƒ./00 8.3%'F4/¨"8-54L4./A%'-F>F%¡./E…+,-"%2"!-#$./%5…&,5:%'(88H88.D%*.D,54<br />

R./,>F0èwÊ8A<br />

8a+,-F%'"! 43%'-./Q%'&K+43./E+2y>F !'!%'N+'8),>F<br />

"8-*.DE!'&l%''-G.3!¨@4BC'E-0%'&,C_Ê#–ª«!¨!¡ ">2&_%2'-2 !¡%' 8`k%'&a%hO9<br />

e;&+'1…%2&,%V½¾ª«!¨!¡<br />

!w18ã|F4BC-C),!¡Q./%Q>-kE--"%2Q+4BC,!0%'&,C%!¡&,'g>F00l4L./ ¡./{ %¡./,!$#94/ 8./Ek%'?>F,!.38-"FG+,¡.3!¡¦#=2&è!*&,'j%2&p4L./<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

£ ÷ò2÷§pö§¦Xò2ö¡ò5õ¸e2ðQZ/þö§¦¤¡÷§¤Ì «õ# ø9õ§ ó)¦1ho k)k ]Xö§¦¨¤¥…ö§¤¡÷7ù& £Xò2ö§¤vòp÷§¤¥©ø"÷7öÃþBò+ ÿ£ ÷§¤Fð<br />

£…ö§¦¨¤ÿ¡<br />

~tv…w!€w0…Q†¥s€u)s‚xn}£w!zTwy*w+~0~0‡<br />

qªr2stvu)wx*stvy*zO{#|}v}n~¨u0r`s)x*w!€|zTs€§~‚&~¥zJ„0w&u0sÿ<br />

B ÷§¨¤¡÷8ho k0k 2¤þDøF÷§¤ h ij§j§k ð Í ¤¥©*¤'ò2ö8¨-ö ÿ¡ö§¦¤¡÷§¤…ò2÷§¤5 øpõ7ö§¤¥© õ&©XøFõ7õ £-ÿ£g*¤¡ö$¤¤¥<br />

ˆ5ðHl5K!‰QIK!MTNQŠ‹b¥IaTIUR¥MTS2NY<br />

o k0kò!¨ h4ij§j§k$#¦ƒ «ó0¦9¤ÿ£¤¡ö§¤eÎ<br />

h<br />

Ȧ5ø-ø"õ§¤9òõ7ö§¤©9hÔãiѧäEå!Ò£úT©øFõ7õ £-ÿ£1h o k)k'ýƒö§¦ò'ö¡ò5õ¸eŽö§¦Xò2ö/ «õ#©ø"õ7õ £$ÿ£12¤¡ö?$¤¥¤¥ h4k0j§ò1h4ij§j§k:<br />

Ï<br />

«ö¡ò*þDö§¤¡÷h4k0j§ò`2¤þDøF÷§¤h4ij§j§kFð<br />

øF÷§¤¡÷/<br />

qnr2stvu0w3x*stvy2zT{#„0sz r |}£zOw!€0y2|zTtçæ!w¥~‚8ƒ~zJ„)w8u)sy~¥tv…w!€?w)…J†¥s€4u0s‚xn}£wzTw!y2w¥~0~¥‡<br />

dn¤¡ö#C<br />

2¤ö§¦¤÷§¤¡õ§-ÿ«ö £¨ ©$ÿzò!ð<br />

Ž./E)'0T§?tȹ ¸M'+=A!./%¡./,54 ¸ 43-…F%'-¡./{- !Ke9O9 qƒª«!<br />

8),8,>F^.Da%'&K!¡ F>'&0%2'-Ie9&9§,E)'Z!¡&O…!£%'&'-…!*%'-+,!-#c— + #c— ' #AC,8V— #OK&-'K >'&Ž— P<br />

'<br />

>F,8.D%*.D€¢ P ,8¨88 80>F,8./%¡./,!ëê P #ì¢ + #ì¢ ' #A,8I¢ Ie9&§,,54u!¡%2-+H&,!£+' >F,8./%¡./,!<br />

&,!£+'<br />

A $¤'ò'ô£þ/øF÷ö§¦ «õƒó¡ø"ù5©ò'÷«õ7øH2¤¡ó*ò õ§¤]-ÿ¡ «ô¤4ÇnÈ…ò lnm ]«öQ«õuòŽþ/øF÷7ùKò¡ÿóhø õ7ö7÷§5ó¡ö,÷ò2ö§¦¤¡÷,ö§¦ò!Kò£÷§¤'ò¡ÿ¡ «õ7ö«ó<br />

ï!“$ð-1¤#5õ§¤<br />

ÿ£jòXò*ÿ£¢¤¥ð<br />

©-ÿzò¨¤h÷¥]ò!¨…ö§¦¨¤¡÷§¤þ/øF÷§¤ù9øF÷§¤¤*ò2õ<br />

Õ§GnÉ


âë— ' âë— + ,>FI0Ïo1 >F% #ƒ./%p.3!N!./0+4/Q%'g!¡&OŠ%'&,% #ƒ),8-<br />

½¾k4/?E--"%'¨%'&0+43ø—<br />

8%2&6¨§,"!¡%v!* ">2&¦#èwÊQFs+4D' !HG'K+43,!%'&,GÊ3–@a%'&.3!Fs,0+4/¨ShC,80543!¡jG'<br />

F),!'!¡ 8xF¹w4L4/ !¡%'-€»Þ9!¡-AF<br />

J91>F)"!*#,j>-CP543!¡Q>F,!¡%'2),>F%KFstC0+4/<br />

!p%'&,%p54/%'&)E&P0+43-j5QF0¨./%'%' 8r%'&,o%'&- #y.D%F!…!¡ C">'&g!*+,>Fp.3!w%H—=®"•F®-¯F¯-–°"±¨²L³p¯-í¨–²3²L®5°"I9e9&H>F0¨./%'0-%<br />

4/<br />

8kF%'¨%'&,%¨./Ó,)-,>F !rX:-"54L4K+,-¡17'C,>FIcÏ<br />

!¡%'F%'-E?),!*<br />

>F%¨1K' 8),8,>Fl./c@+,'%¡.354/67"8-¨+43->-CkX:-'OK&F4/ %'&-0>F6<br />

+,'%*.B>F)435#%'&QF’¦<br />

!.38-"%*.D,!-IKÏè>F0+,¡./Ea%hO90+43-F!-#ƒj¨),!¡%Z>-'F17)4z4/?>F,!.38-p%'&N++./EQ2./+4/ !p),8-¡4/.DEQ%2& !¡Z.3!'!¡) !-I<br />

Õ§G Õ


UUtTY(,8k~92'-%'%0,8k†`F4B8iSFT UU‡Yj8 !'>F*.D2&¦I e;&-0'F§,jẐ¡1ª«!£O9'q¨!¡-*.BX4z./{ 2./-,>2.D<br />

8ƒ#ŽOv‘1b>F),!Zo%'&¨),8-¡4/.DEo+'+,-'%¡./ !Z19%'&<br />

1vg+,C'%¡.3>F)43j85./_!*%''),>F%')'IZÏ,!¡%'<br />

F>'&0!¡+,>FK,8N&Ol%'&K!¡ ">2&0!¡%'"%2-E(X’Ã >F%F!¦%'&9F[\>2./-,>F0C1,)+43-"!-I8¥w-:-'%2&F4D !2!-#<br />

!¡<br />

!¡%*.DEQ2F4BC%¡./,!¡&./+,!Z'&G+,-"C%'8— P þcõ +zö 'zö÷÷÷ö + A'ø<br />

'&k%2'-gO9.L4L4pE--"54L4/c'&?!¡a54L4D-N%'&,oÊ#–ª¾!p!¡<br />

*4D`F),!'!*<br />

!¡%K%2&F.DwF’Ã >F%wQ%'&j!¡ F>'&¦Ie;&.B!w!¡)F% #&O9-:- #.3!w%K!K!./0+4/¨!<br />

!¡-¡.354L./{F./-54K>F0+,*.B!*?19%'&¨:X¡./),!‘+43./EèX4DE¡./%'&!Z?a+,2%¡.3>F)6<br />

543!¡g>-2¡./<br />

#ƒT UU‡AY"#!¡&O9./Ë &XO|%'&j8.L’¦-'-,>F !;./g>F0¨./%'0-%K!¡%'"C%'-E./ !<br />

43K+'


#X ÿ C,8@X µ #ƒ%'&p17'0-Z' !¡)4/%¡./Er1b'n%'&0>FG¨./%'0-%(!¡%2"%'-Ea17<br />

1%'&¨F 8¨OK&-0+43,!'G'<br />

543!¡j8<br />

8PC,8o%'%"X4z4/@"8-' 8@+43,!Z./f]"4D C'./Eg+43-"!'dtIHe9&-?!¡&O9 8Q%2&,%p%'&<br />

+,'%*.BX4z4/o"8-2<br />

8@+43,!-#ƒ"C%'&-K%'&,@%'%"X4z4/@"8-' 8r+4BC,!-#ƒ' !¡)4/%w.Dc]-!*%'"Ej>F06<br />

'-),!¡¨1+,'%*.BX4z4/@"8-'<br />

>-),!¡9%'&-p>-N'-+' !¡-%¡43'EA)¨'&g!¡+,>FI<br />

8:A%FE<br />

#OvZ&,5:<br />

~¨17y>F),!./E0);C,54/y!.3!9\¨!./E4/p.3!'!*)#,0F4/#+=-"%'"8-*.DEa>F0¨./%'0-%<br />

:!¡&OK<br />

F0+,C"%¡./:Q,54/!.3!jC1…%¡OvQ+43-F!-Io†?a&,<br />

C">'&a!¡+,>FZ1¡Z+,'%¡.354/67"8-9+43- #Q½¾#.3!w—,®§a5® °Ž43'E-%'&,0%2&(!¡ C">'&a!¡+,>FK1<br />

%'&,%%'&…!¡<br />

#ŽÊ#–IZÏ,8- 8P1bp>F-'%"X.Do+''&?!¡+,>FN.3!ZFs+,-%¡.354L4/<br />

G%'%"54/67F8-…+43-<br />

!¡X4z4/-¨%'&,`Ê3–ª«!-IrR./,>F˜½¾i+,5y!‘4/_Q!¡54L49+,4/¨.354K%¡./0G.D,>F2-0-A%N+,-¨8:-<br />

Ê#–#y.D%;.B!wE--"X4z4/Q0'pF[\>2./-A%5I<br />

8o%'&,%,½¾ª«!N!¡ ">2&k!¡+,>FQ8:X%"E5o%N >F !'!'¡.L4/k%'"C,!43%'¨./%'<br />

†`%'&-k!¡&O9<br />

C">'&g!*%'"%'-E\,8r&-)¡.3!¡%¡.3>-!Z%'&,%Z'<br />

@F[\>2./-,>FgEA5./¦#ƒ8-+,-,8./EQ./?!¡)'&g!K8-+%'&6¨§,"!¡%p!¡ F>'&¦#,>-Cg'&‹!¡+,>F !-#p!./,>F<br />

!¡&O9<br />

!'!¡6>F0^.D%2%' 8d0!¡%'F%'-E./ !95>F2 %'p' 8),8,>2./ !w./g%2&j!¡ ">2&g!¡+,>FIÏQ+,2%¡.3>F)6<br />

!¡G]24/<br />

#ƒO908-0,!¡%2"%' 8@%'&,%jae9O9 q6¨4L.Dq0+43- #üèKÊ#¦>-o&,5:0G43'E-j!* ">2&è!*+,>F¨%'&,<br />

43<br />

)K%2%"54/67"8-9+43-pg!*0p+'2.L§u><br />

‰wOîE--"54'j%2&<br />

8l!¡0^.DG+,'%FA%p%2"8-’¡!Z%'&,%¨'¨1KE--"X4v'F4/-:XC,>FIge9&<br />

+43-"!-#£O90&,5:0Fs,¨./<br />

¡4/N.z4L4/),!¡%'F%' !£&O_%2&v+43./E‘4BCE),E#%'&9!¡ ">2&0!¡%'"C%'-E# ,8N%'&&-)¡.3!¡%¡.3>-!<br />

,54/!.3!>24/<br />

8g>-gX’Ã >F%w%'&p'F43%¡./:¨8:X%"E !91¡%'&N%¡OvN+43./Eg!¡%¡4/ !-I<br />

%'&,%K2p),!¡<br />

!¡)4/%"!Ž./0%'&.3!£+,+,-!*&)438¨F,!.38-' 80!‘./A: !*%¡./EA%¡./0C1,%'&9+,A!'!h.D2&A!¡Z%¡O9H'2&.3>Fg1p+,-F%'aS”]F !*%"24/A!¡F4/Q'F43%2 8Q%'0%2&Z.B!2!¡) !9./: !¡%¡./EAC%' 8G./g%'&.3!w+,+,- I<br />

"8-2<br />

Æ &-SFT UUÛY&,5:9>F0+,' 8‘%'&2F4BC%¡./:9)%¡.L4z./%¡jC1¡°h®5é¯-±¨—AÂ<br />

ÏH88./%¡./¦#ˆp¨'&g!¡%2"%'-E./ !9%2&,%K'j8.3!¡%'¡./


!¡-%"%¡./Q,8Q!¡ C">'&g!*%'"%'6<br />

JK)w2&o+43_!¡%'-+r.3!-#¦F%¡./?WIKe9&),!-#a%¡O90+43,!Z&,5:p%'&H!20<br />

+=-"%';.D,!*%",>F#¦!9%'<br />

¹ À ²L–—^.3!…G+,5./€²£¢ í âI"#OK&-'¤¢N.3!…a!¡-%K1!¡%'-+,!$#,,8§âÁ.3!K%'&Q]FF%' 8ƒI<br />

Ñ Ø8ØKâ=© ª<br />

Ñ ¥ QÕ3ž5Ó<br />

ÿ 4<br />

!¡-%p1K!¡%'-+,!-IN¹w4D%2&)E&?%'&.3!(1b254L.3!¡<br />

!./0+4L.L§, !N)j,54/!.3!-#Ž./%p' Œ)./' !‘),!p%'g8F§,G+4BC<br />

Œ).D:54/-,>F0Fs+4z.3>2./%¡4/I<br />

!¡ ">2&Q%''-pE--F%' 8aF !KC1¡%'&H!20Z+,-"C%' #,8<br />

<br />

1bK54L4¸— H í — HH ô ¢ + #J— H â%— HH .L1v,8a4Da.L1tYŽS— H Y8âCYŽS— HH Y"I<br />

<br />

¿ ¹î+43¼›­.3!K¨Ê#–M½h®º7® —t¯”±¨¼—aS`½¾½h®Xº7®5—¯-±3¼—tY¦.L1F./%'&- È<br />

›Ò.B!w%'&Z././%¡.354+43¦#<br />

½¾¦67Fs%'-,!./ƒY"#9%'&-‹!¡0g+43|%'&,%^.B!a Œ)./:X54/-%g%'Ú›».3!Q`0-¨


ÐK./:-ùÁ ô ÛÜ2ÝÝ àªá ,8\à ô Û¥Ü2ÝÝÞ;ß#Jà ô ãwSÁpY.L1;,8r4/Q.L1v+43¼ÃÒ.B!p^4L./ ¡./{ %¡./<br />

¿<br />

!w1 %2&F.Dw' !¡+, >F%*.D:H!¡ F>'&Q%'2- !-#<br />

1¡+43ùÁ­,8aF./%'&-ZF,8./%¡./§±#,>FHÊ#–l!¡F4/ >F%"!`±j!9%2&jEAX4 #tÊ3–lO;.z4L4>F,!.38-j54L4¡+=-"%'"!9%'&,%Z>'&./-:V±#<br />

+'<br />

>2&Q+=-"%'wÊ3–`>F,!.38-"!p54L4¡+=A!./%¡./,!wF 8|ÿ'›.ln¥p"sH•©wxHs­*p"¡¢¡£–¦È<br />

+ ò ²§¢ +2í â + "#!¡),>2&k%'&,%¤¢ + ò ¢ = ¹ ì —9š!šðo,8³â = ½ â + Ilæƒ-%Ž¤ F,8./%¡./,!ZC1¡%'&H!*%'-+,!./ùÁ = I e;&-ùÁ + .3!ZQT-6!¡%2-+½¾¦67Fs%'-,!./gC1Á = .L1'È<br />

¿ ±%ò ¦c¨n©[¨c«2¬J­2®Q¯Q°n©S¥¤¨Y"#OK&-21±w.B!w%'&p+' >F,8.D%*.DPC1M!¡0j!¡%'-+—`´2µ0µ0š(./ùÁ = #=,8<br />

¿ — š!š 88!H±#,8<br />

¿ â + .B!ZN¨././54!¡-%K1>F,!.3!¡%'-%KF8-¡./EA!…!*),>'&Q%'&,C%<br />

â = â + #,,8 <br />

S— šš í — ´*µ0µ)š Y ô â + #,C,8<br />

<br />

S—9š!µ0· í —9š!š-Y ô â + #tOK&-'1—9š!µ)·ƒ.3!9%'&‘43!¡%…8F4/-%'-Z18±w.DÚÁ + #,,8<br />

!¡%'-+a./ùÁ + ./A%'-F>F%"!9O9./%'&—9š!š<br />

Õ§G§Q


m[štp!n§” ¨e9&.3!Z4/-0\1bC4z4/O…!w17'»%'&a8F§,.D%*.D_1H½¾IaÐw.D:-?+43³Á = #ŽO9./%'&o1543!¡<br />

çó“”xox“<br />

>F,8./%¡./‹±#n½¾g>F,!.38-"!54L4,+=-"%'"!¦%2&,% >'&./-:H±#,8‘17¡ >'&0!¡),>2&¨+,-"C%'½¾Q%'&-<br />

+'<br />

./,!¡-'%"!w./%Z./?%'&¨+43_!*),>'&o%'&,%w./%Z.3!ZF,!.38-"!<br />

54L4>F,!.3!¡%'-%j>F¨FŽâ3V = ò³â3V + ÷¤¢ = ¢ =$ â ÿ + ÷%¢ =& ¢ = ò â ÿ = #./%91bC4z4/O…!9%2&,%5à =<br />

OK&-'Vâ<br />

*.D{ C%¡./o1ŒÁ = I<br />

.3!…H4z./<br />

sy%2-,!./?4/-0a#O9>-_!*&XO¥%'&,%-à + .B!NlT-6!¡%'-+?Ê#–Ž67Fsy%2-,!./_C1ŒÃ = I<br />

;Z!./Eo%'&eZJK6ß<br />

#[Ã = .3!ZN4L./ ¡./{ %¡./o1HÁ = #,!*0%'&j%¡O9¨+43,!K&,5:p%2&H!'Gj!¡-%K1EA543!-Ie9&-'F17'#.L1<br />

Ž./"!¡%<br />

>F%"!p!*0¨EA54±p./?Fs+,,8./EùÁ = #,Ê#–i!¡F4/ >F%"!1±(.D`Fsy%'-,8./E\Ã = Ï R >F,8ƒ#Ã./%pH),!*%…F%¡./?&+,%'& !h.B!$#Ã =<br />

4L./<br />

%'&,%.3!-#t.L1ŒÁ +2í Á '`ô Û¥Ü2ÝÝ àná ,8§Á +-õ<br />

+ í à ' ô ãwSÁpYF#A%2&-»Ã + ,8‹Ã ' 'j%9%'&p!'0p%2'-(8-+%2&<br />

çó“”xox“v~a%'&j8F§,./%¡./o1ãZ#.L1¸Ã<br />

.D\ÛÜ2ÝÝ Þ;ß „t1b)2%'&-'02#'ÁÒ.3!Z543!¡%…8-+%2& 0 .D\ÛÜ2ÝݪàªáMI‰K-,>F#t./%(!*)[\>F !K%20+':p%'&,%.L1<br />

0<br />

+43,!-Á + ,8¼Á ' 'j%…8-+%2& 0 ./Û¥Ü2ÝÝ àná ,8¼Á +-õ<br />

Èe9&¨!¡%"%'-G-A%9:X>F)),!4/Q&438!917…8-+%2&gÝI<br />

+K–¯-®H•F–¯-®<br />

À Èr;K,8-G%'&&+,%'& !h.B!^%'&,%j%2&\!¡%F%'-0-%j&438!N17N+4BC,!0%H8-+%2&<br />

,"—=¿éA•5º7±3¼—l¯”º7®<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

OK&.3>2&Q./%K./%'-">F%F!-I¥K0%'&-K"8-*.DE!K'j88 8r%'0%'&p+43¦I<br />

ÿ !<br />

çÿ“”x x¥“ x¥“emopr–"“8” ’m#éH–”ùp±áóx “›“”p~•éhxHsH¤lp"sF”›p»ã<br />

= ò ²§¢ = í â V =


+ ò ²§¢ + í â + H,8¡Á ' ò ²§¢ ' í â ' F#v%a8-+%'&é¦1-ŠTa./<br />

%'&-'@FsA.3!¡%a%¡O9è8.3!¡%*.D,>F%Q+43,!$#9Á<br />

ô ãKSÁ + Yc÷`ãKSÁ ' Y"I£e9&-@SF,8‹>-!¡#<br />

&-,>F#9ãwSÁ<br />

+ ò9¢ ' „&-,>F#ƒ2&o%'&,%Z./?G+4BCù— P ´ ÿ<br />

â<br />

8o2&g>FA%2"8.3>F%"!%2&(!¡)++=A!./%¡./¦I9e9&-'F17'#%'&p!¡%"%2-0-A%&438!M1b9+43,!9%K8-+%'&>¦-?TI<br />

s)(|s)* s '<br />

áÿxH¡§éåprn¥ptsop˜•”•Vçó“”xox“I“xo“Žä<br />

8%'&¨§,"!*%!¡ ">2&0>FA%2'4u!¡%'F%'-EI£e¦j8j!¡=#./%<br />

†?KOk+':9%'&,C%Ê3–\.3!>F0+4/-%'w),8-;ZF0+,>F%Z!¡4/)%¡./¦I9~F17'j8C.DEa!¡,#O9p+':Z%'&p174L4/O9./E04/-0tI<br />

8j+43gà = 2&Q%'&,%5à + .3!K0!¡) ,8‹Ã + .3!KaT-6!¡%2-+Ê#–Ž67Fsy%'-,!h.D<br />

e9&-Q%'&-2pFsA.3!¡%"!wj+43»Ã<br />

= I 1Ã<br />

= .3!0?!¡%2¡.3>F%^!*) C,8ÚÃ > .B!GP>F0+,>F%!¡C4D)%*.D¦#%'&g!*-%HC1…1543!¡<br />

çó“”xox“?R./,>F\Ã<br />

>F,8./%¡./,!‘./Úà = #¤G#¦¨),!¡%p%p'&./-: !H±I Æ ,!.38-K%'&<br />

!¡%'-+G./Ã<br />

8@+43¼Ã + ò ²§¢ = ¹ ì —9šš¨ð í â + "#=OK&-'»â + ½ â?>5I Æ 4/ ¡4/#à + .3!pa!¡) Ï )'%'&-20'#=Fp./%9.3!9"8-2 8aF,8.D%*.D,!K1<br />

8F4/-%'-Z1̱w./\Ã<br />

sy%2-,!./Pæƒ-G0&C4B8ƒI ' s;(.s;*!s<br />

%'&jeZJK6ß<br />

.3!…^Ê3–Ž67Fs%'-,!./¦I<br />

çó“”xox“Kæƒ-%0¦@2&l&,!Z4/-E%'&kÝ#Ã.B!N<br />

+K–¯-®Q•"–¯-®<br />

!¡)F%¡./?&A+=%'&<br />

+ %'&,%.3!9F0+,>F%j!¡C4D)%*.D¦#¦%'&-¼Ã"><br />

BG-fTI ' s)(|s)*!s<br />

Õ§G Ö


áÿxH¡§éåprn¥ptsop˜•”•Vçó“”xox“I“xo“>ÿ<br />

8%2&6¨§,"!¡%K!¡ ">2&Q!¡%'"%2-EI¡e9&Z' !¡)4/%9174L4/O…!<br />

†?ZOf+2X:K%'&,%H½¾@.3!9>F0+4/-%'p),8-…NF%N%'&,%pÊ#–x.3!j>F0+4/-%'IaÏ<br />

17'»%'&!*<br />

+,'%*.B>F)435#O9(!¡&O|Z!¡),>2&Q%'&,%HÃ">.3!ZN4L./<br />

!N%'o!¡&OŠ%'&,%‘.z1`Ã + .B!¨rÊ3–Ž67Fs%'-,!./¦#£%'&-l%'&-'<br />

çó“”xox“QR./,>FQÊ#–x.B!¨>FG+4D-%2#¦./%0!¡)[\>F<br />

+ !¡),>2&a%'&,%5Ã + .3!K‘4L./ ¡./{ %¡./@1Á + Ie9&p+2A1Ž.B!;F%¡./@<br />

Fs.B!*%"!K,½¾¦67Fs%'-,!./§Á<br />

+43Q4/-E%2&¦I<br />

Èe9&¨!¡%"%'-G-A%9%'¡./:.354L4D@&438!17K+43,!w1¡4/-E%2&PÝI<br />

+K–¯-®H•F–¯-®<br />

À È€;w,8-¨%'&a&A+,%2& !.3!j%2&,%j%'&Q!¡%"C%'-0-%p&438!p17N+4BC,!¨194/-E%'&±¦¡#£O9<br />

,"—=¿éA•5º7±3¼—l¯”º7®<br />

+ .3!KNÊ#–Ž67Fsy%'-,!h.D<br />

O|+':…%2&,%9%'&(!*%"%'-0-%9&438!179+4BC,!91£4D-E%'&^¦¤-kTI£¹(!2!¡)09Ã<br />

= '&|%'&,C%VÃ + .B!akT-6!*%'-+cÊ#–Ž67Fsy%'-,!h.DfC1 Ã = I‹~<br />

1Z4/-E%'&é¦1-ŠT#K,8m4D-%‹Ã<br />

!.3!-#Z%'&-'oFsA.3!¡%F!Qù½¾Ž67Fsy%'-,!h.D Á = 1j4/-E%'&馭!¡),>2&‹%'&,%‹Ã = .3!Q<br />

%'&@./,8),>F%¡./­&A+,%2&<br />

¡./{ %¡./?C1 Á = IK~@%'&jÏA:-"!¡H}o++./EQæƒ-0t#,%'&-2jFs.B!*%"!…G+43øÁ + %'&,C%K.3!wF§Á + .3!H`T-6!¡%'-+Ú½¾¦67Fs%'-,!./?1<br />

4L./<br />

× ~}›‡~‚ Ø2ÙZˆ~¥"ƒˆ÷‡~|~¥kÚ~‡~ˆ¯}~z‡~‚ Ø'ÙZˆ~¥tƒˆ?Úh‚©‡~|~|~z,|"‹<br />

ÿ JI<br />

.3!…>F0+4/-%'I<br />

¨././54!¡)'&Q%'&,C% È<br />

¿ â3V =L â3V + #,,8<br />

¿ S—9šš í —`´*µ0µ)š5Y ô â3V + #,C,8<br />

¿ S—9š!µ0· í —9š!š-Y ô â3V + #OK&-'.—9šµ0·=.3!w%'&Z43!¡%…8F4/-%'-Z18±w.DÚÁ + #,C,8<br />

¿ !¡%'-+a./ùÁ + ./A%'-F>F%"!9O9./%'&—9š!š<br />

â ÿ + #Ã + .3!¨a4L./ ¡./{ %¡./i1Á + IQÏk88./%¡./¦#HÁ + .3!¨?Fs%'-,!./k1Á = !./,>F<br />

Fs%'-,8./E<br />

Á = IaR >F,8ƒ#—9šš088!1±¨!./,>F»—9ššH>'&./-: !,±‘./ùà = IŽ./,54L4/#¡F,!¡%'2),>F%¡./¦#<br />

â V + !2%¡.3!§, !9%'&p%2&.DF8g>F,8./%¡./o1¡%2&€;w¹…6ß sy%'-,!h.DPæƒ-0aI ' s)(|s)* s<br />

Á = #y.D%w&,!4/-E%'&D¦E-|TI ' s;(.s;*!s<br />

Õ§G@


!¡-%p./?%'&.3!‘+,+,-¨OK!Z¡./E./,54L4/_8 !'>F*.DF1b-'-,>Fa+,+=-"!<br />

}@A!¡%p19%'&0O9'q@+'<br />

UUT5#T UU“yY"Ia†?%2&,qo¹…,8_¸M&.L4z./+,!^1bj&.3!¨?>F%'¡./F% I‰KNOK'%'p%2&H>F8p17K%'&N+4BC-"!p,8a&F4/+, 8?>F,8),>F%…%'&NFsy+=-¡./0-%"!-I9†?¨543!¡<br />

+'Äh<br />

%'&,qa%'&p%'&2-H0),!'-:.D-O9-"!;179%'&F./…Fs,>FF4L4D-%j>F0G-A%"!$I<br />

Æ IwS"T UUÛY"I­Ž.D,8./Ex4D !¡%g>F,!¡%'F5./ 8|+43,!Q,8i+%¡./54j+,C"54L4/F4jFsy >F)%¡./,!<br />

~9>2qy!¡%2'g#<br />

IŠÏONv°¡¼ •F®F®"¿±¨—AÂC¯\¼*ëèºb\®HPƒ®"•F¼—,¿Q(vé°¡¼ À ®F–—SRQ¼°UT ¯z\A¼ À ¼—<br />

.B!a&,C"8-Q%'&,|O9o%'&)E&%<br />

#¹¨I/#¦R8-¡43,8ƒ#£R,I/#ƒ€Š†`F4B8ƒ#¦¨IŽS"T UUTY"I9e9&jF’¦ >F%Z1v!¡%'-+67"8-…2-+' !¡-%"%¡./,!w<br />

~9''-%2%<br />

>'&¦It'-+¦I,UT-6ÝW6Ýn?#ƒ;w.D:ƒI=1¡†_!*&.DE%'¦# Æ 0+)%'-pRA>2./-,>F0Z-+% I<br />

+4BC.DE=IveŽ<br />

# ¹¨I/#€i†?F438ƒ#A¨ISFT UU‡YFIA¸'%*.BX4D67"8-+43./E,Èß:54/),%¡./Ej+=A!'!./2./-,>FHE5./,!-I<br />

~9''-%2%<br />

°"º7± Wv•5±3–²X,F—,º7® ²¨²L±z® —=•"®5#XY[ZSFTY"#ƒVAT d TT “I<br />

V<br />

&-¦#,¸£IƒSFT UÇUYFIC`p® é°"±B¯”º7±¨•GPu–í À ²L±¨—AÂa¼—a+K–•Tº7°¡–•T1b,°¡®"®$¯”I£¸&¦I«¨I%'& !h.B!$#uZ-+% It1 Æ G+)%'-<br />

Æ<br />

Æ ¹HI<br />

RA>2.D-,>F#ŽR%"17"8>;w./:uIB#ƒR%"17"8ƒ#<br />

4L4L./,!-#ŽÐHI/#€Ô¸M'5#AæIƒSFT UU“YFI¦¹p>'&./-:.DEQ%2&Z1b),>F%¡./,X4z./%¡Q1£§4/%'-(>F,8.D%*.D,!9./P^+,'%¡.354<br />

Æ<br />

IZÏcNv°¡¼ •F®F®"¿±¨—AÂC¯(¼*ëHºb\A®1b,®5—,ºb\¦dp–º7±¨¼—,–²/e¼—$ë”®5°¡® —,•F®j¼— V °Fº7± W9• ±¨–²f,"—=º7® ²¨²z±B½<br />

"8-Z+4BC-<br />

"5O917"8ƒ#\gI/#,€¬~9q- #t¹HIŽS"T UUC‡Y"I9ߣs+,-¡./0-%"54' !¡)4/%"!Z@%'&HC++4z.3>-%*.D?1v!'%*.B!h§u


UU‡F%'¡./F%')2 !=1b¦+43./E,È£¹l1b254L./{ %¡./<br />

ˆp¨'&¦I V °Fº7±B½<br />

Ẑ¡1'#ƒÞpI¦SFT<br />

±¨–²\,"—=º7® ²¨²z±L®5—,•F® #[^XZ$#uUV d T ÝUI<br />

Wv•<br />

UÇVY"Ip¸£43./E?!p!¡ ">2&¦ÈZ¹ÑŒ),%¡./%"%¡./:C++'A>2&¦I V °"º7± Wv•5±3–²r,"—=º7® ²¨²z±L®5—,•F® #"]¡]#<br />

Ẑ¡1'#¦ÞpIMS"T<br />

d ÇÇtI ?W<br />

">2&P!¡%'F%'-E./ !-IwÏcNv°¡¼ •F®F®"¿±¨—AÂC¯(¼*ë^ºb\®<br />

æ¦EC4D-#¦¸£I£S"T5UU“Y"IwR!¡%'-%*.B>¨,8@,!*y!¡%2-%¡.3>j!*<br />

°F—,–º7±3¼—=–²le¼—$ë”®5°h®5—,•F®j¼— V ,?Nv²L–—=—,±¨—AÂPu³5¯”º7®5íN¯”I<br />

n±3°2¯”ºl,F—,º7®<br />

!¡%'-5#u¨I/#=€ÔÞ9A!*-A‘4L./ p+43./E,I9ÏcNv°¡¼5•"®F®"¿±3—¯…¼¡ë<br />

}o>F¹K4L4/<br />

°¡® —=•"®p¼— V °Fº7± Wv• ±¨–²f,F—,º7® ²¨²L±z® —=•"®5I<br />

ºb\A®Gd(±¨—,ºb\d(–º7±3¼—=–²Ce¼—-ë-®<br />

!./,#XgIB#y€ŠZ2)00,8ƒ#,}lI=S"T UUT Y"I Æ 0¨./%'0-%K!¡%'"C%'-E./ !M.D@+43./E,ȹ<br />

}r./A%'¦#,R,IB#,~'<br />

²ë-ºb\¥,F—,º7® °F—,–º7±3¼—=–²li¼±3—=ºLe¼—-ë-® °¡® —=•"®<br />

>F0+,"C%¡./:,54/!.3!-IQÏsN9°h¼5•"®F®F¿±3—¯¨¼¡ë\ºb\®cb¢®<br />

!./,#[gI/#Z')00,8ƒ#A}lI/#A€Ò¸&.L4L.D+,!$#,¹¨IS"T5UUT-'&¦Iw'-+¦IKUT-6ÝÇt#H¥K¹NR¹ ¹…0 !$#…¹ZÏÞ9 !* ">2&<br />

!¡%'"%2-E./<br />

!./,#XgIB#y€Š¸M&.L4z./+,!-#=¹¨I,SFT UU“YFI¦e¦%F54uF8-v:!-I+,'%*.BX4Ã"8-<br />

}r./A%'¦#,R,IB#yZ2)00,8ƒ#}lI/#~'<br />

°F—,–º7±¨¼—,–²<br />

+4BC.DE=Èv=>F%'"!M./Ó,)-,>2./Eg+=-¡1b',>FIÏHN9°h¼5•"®F®F¿±3—¯K¼¡ë¨ºb\A®abF\A±¨°h¿t,"—=º7®<br />

8,)4/% #ßwIS"T5UÇÇY"IR%'& !./{F./Ej+43,!%2&,%¡>F%"5./0>F%¡./,!ŽO9./%'&0>F%'Fsy%268-+,-,8-%F’¦ >F%"!-I<br />

¸£<br />

À éº7–º7±3¼—,–²f,F—,º7® ²¨²L±z® —=•"®5#hu#,ÛWn? d ÛV“I<br />

e¼í<br />

UU“YFIv¤wxA¤xpÈ,¹Ô!*),8ƒ#¦>F0+4/-%'#ƒ+,2%¡.354/67"8-p+43-p17<br />

¸£-F%¡./,!pC,8o%'-0+="54<br />

Þ9-E./-<br />

%¡./l./l4L./ +43,!^1(>F%¡./¦IoÏc‰K-2%'{-


UVWY"Ie9&p4L./ p,%')2j1+43,!-IÏHN9°¡¼ •F®"®F¿±¨—A¯Z¼¡ëHºb\A®nüéA°Fºb\¦,"—,º7®5°"—=–½<br />

RA>F-"8%¡.#ußwIƒS"T<br />

°¡® —=•"®p¼— V °"º7± Wv•5±3–²\,"—=º7® ²¨²L±z® —,•F® I<br />

º7±3¼—=–²fi¼±¨—,º?e¼—-ë-®<br />

UV ‡YFI_ÏA%2-'+43¦Èg¹ +43cE--"%¡./|!¡y!*%'- OK&.3>2&f>-|8 54…O9./%'&x.D%'-">F%¡./,!<br />

e£%'#¹HI9SFT<br />

>2&¦I '-+¦I}@-0p}@Ïh¸M6Þ96'T ÝU#8;w.D:ƒI1uß8.DF%¨-%hO92qy!-I@ÏN9°¡¼ •F®"®F¿±¨—A¯0¼¡ëQºb\A®.n± ë-ºb\H,"—=º7® °F—,–º7±¨¼—,–²<br />

e£%'#¹¨IS"T<br />

V °Fº7± W9• ±¨–²\,"—,º7®5²3²L±L® —=•"®5I<br />

iy¼±¨—,º©e¼—$ë”®5°h®5—,•F®p¼—<br />

54L4D>-%¡./¦IoÏNv°¡¼ •F®F®"¿±¨—AÂC¯H¼¡ëQºb\A®‚RQ¼°ƒT5ī\¼ À<br />

#ÞpIMS"T UVWY"Ip¹p>'&./-:./Eè!*-:-"54E543!p!./H)4/%"C-),!4/IaÏ3}o–•:\A±¨—,®t,"—=º7® ²¨²z±L®5—,•F®E‡I<br />

†_5438./E-<br />

ߣ4L4L.B!p‰Z'O9y8ƒ#æƒ%F8ƒI<br />

UV ‡YFIƒ†_'+43¦È¹­!¡y!*%'-¥1b9E--F%¡./E0+43,!-IeŽ >'&¦I2-+¦Iy}@-0aV,?t# Æ 0+)6<br />

†_2'-¦#¨I,SFT<br />

I/#=RA>2&AC4¡1¹…ÏF#;K./:ƒI,C1 ß8./F<br />

¼—c,"—,—=¼na –º7±ba ® V ÀÀ °¡¼5–•:\A®$¯\º7¼„Nv²L–—,—=±3—†…<br />

Pu•:\®"¿é²L±3—Â0–—=¿De¼—,º7°¡¼²LI<br />

Õ§Q Õ

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!