Hierarchical Cubes for Range-Sum Queries Chee ... - Semantic Scholar


 


 !"#%$&('*)+, -.%
 /10324257698;:=/0=?@: 69?@:=:BADCFE1GIHJ8K?@:=:BADLBADCMON PBk=QS\bRUegTWlJVYQSXYVmZ[iYenQSXpoq\X3]J]W^s^;rt_`eu]JiYZ[dS]JRb\habiYegXY\wQSvyV=x9cbTJdfegzwQSeu\hiD]{dSQj\ i | dfowdm}hTW\~ oTW\b\beuiS€‚IdSijƒ „*egi…dWƒ Qjzwa ˆ† ‡ICJ‰wŠb?@‹Œ‰ ]Weu i3^[VmiDTWRŒTW\\bQjdSŽ{en–IQfšUv—QjiDabz›=Z˜™ozbabVmTWTWQjX…VY\bTˆoŽ{QjiYdfiœababZq]W™Œ^@Q1i‘df]‚]{„*lJ\{}bQjX…V@QSe“Ž{V…TWQ ab’gb]JXYiDaU}bQjiQ&’“Q7lžd”iYTJXYQS’“Q7ah’gz•QjQjdfidSXYQSeg^Ÿ]J’g]{\ iV QjdfQ7T{iYdmi}iYzwahegZ[dm}%QS\hiYabe“]{QS\4V…e“ƒ Q7i \(egi›QfX… ¡]ˆdfegRbQSVY\Q7Xœdf]{TJZ RbRbRhV…aw]{XYT{QFdm}[TˆXY]RbV…RhQfVYšb]J¢ v Z[™bdfahawQS™UX\hQ&iY„*eg]J£ e“˜ XY\h}%TJ_’“¤”e T¥Xp~`oI„*RbTJVY}b\hQSeuz¦šbdm}¥¢+iYe“§jeuVmiqQ`TW\bTJTFŽ{i¨QfdfXYv}bahiDQ`™UabQZ©]JV…]Je“Ž{iD^Be“XY\hX…]{}bTJVYQ7’{Q9z+zbi…TWTWegX…\ªZ[T3QdSQ7abTJzw™Œdmen} Q v ™XYŒdf}hQjQ•’“Q«QjƒtiDlžegTJ§Sk=’“QOaUiY]JT‚e“\h^®XYŽ1Q7X…z­}bT QT‚XO˜ iYab_BT(™w~KvdSdf]{TJabiD\™ŒX=oFQX…}hV…dfTJT‚eg\bV…XIdSŽJabegQSiIZqvyiYeg\habiYdSzwZ¬VYQSeg™ŒRŒQjQSabz›\UQSzwV…™QSo&o¡\XOdSXYTJ}h]W\ Q ^ XYl‚}hTWabQSV…QSegoV…TJoJ\TWƒˆXV…Q¯3]W^lJ]‚Qj„œRbVYVYoQSQSl{šbdfQS¢F]V7ip~KX…dfT1’“abo(™ŒzwXYQjV…](i•Tž„*ZqdSTW™UTW’gTJegQj\{dmz1°1XmTW±*eg]W\4^ QSƒB’u˜T‚±3X…_œe“Qjl{i[dfQ Qjeu\i ˜ XYV…’gXYoJQf}hšb~TW¢T X XY_`}habegi*™ŒQjRhiqVY]{£²™b± ’“˜QjZ_ƒ¤I}hT{iI™UQjQS\1RbV…]JRŒ]{iYQjzX…]TW’g“QjleuT‚X…Q ³]W\´^¥dfXYab}b™ŒeuiµQ¹RhVYQjTJRbRUVYQjQ7VjiD~¶Qj\X…„`T‚QX…e“]{Rb\hV…iº]JRŒdj]{TWiY’g“Q·Q7z»T¸¯=\he“QjQSV…„ TJV…dm}bdf’ueuTJdSi…TJi ’ zV…w_`QjQSabiYšhab™Œ\b’nQjXmQjiji&zˆ~b„*iY™}b}bo]‚eu„¼dmXp}„`]FX…egi*}h]{T‚™UXVDTJX…iY}bT%Qj]Jz›Ž{RU]J]JTW\h\VYTJXYT[eu’dfzwabzbQj’ue“TWZ[iYVegŽJQS\U\›dSiDab^Ÿeg™Œ]JV…TJ\hQºZ[ijƒ%zwQSQj„œiY–B]JegŽJahV…\° V XYdSdS}hTJTJQ’“\gXYQj]‚’gzo¡lJQjX…™UV…}bQSTJQ(XD’“X…;¯=QS„*V=e“Qje“\bV…abTJ\hQjV…QSdmVYV7o}h¿qvyegdjabenTWX RŒ’;zh\b½T‚]WXYX TWQI\U]JX…z\bV…T{’g_`o1zwabQS}h™U]JTJÀQi•XY£¾T9}h¯BTJ½*iY\›e“Ž{_Rh\b¤VYenšhQSegivv ^ŸlQje“df]{XYaheglJi=QjTJ’“o¡RbRb™hV…aw]{ÀŒT{Qjdm}bVYQ7Qjz¨ij~hƒ ™babXBe“XOdjTW\­TW’uiY]¡™UQ Z[]JV…QQf^Áv ÍƲžÓžÕžÐÑ7ÐDÂDë(ÅÃhÄmÙsÇÊ̫Ų×pūƲϔÇÈÄmÄmÕS՞ÉÊÆOÌ«Ë¡ÇÊպڟÛ̫͞тÚuΞܟąÝ7ÎWÆ«ÞDÄmϔßf҂žàmÆ«ÄmÐpá”Ì«Ñâ”ÐFã­Òfì”Ë(ägŲÃhϔƲå‘͞ӞκÚ=Ðæ®Ô®ÇÊ՞ç4ąўƫÄm͞ÇÊŲϔ̾ÑWƫՂèBŲÄmÇÈÄmÉ;ÄmÉ Õ7ÖSÑ­×DąÇÊí*ÐpƲ՞ӞÉÊ×pÇÈЕąÐƲé*Ðp؂ÌϔÐDé`͞Ξ՞ūÒWўϔÐDąì”ŲƫūÌBÇÊÄmϔéÏmÕ ê ä“ÓSƾƫÎ{ò æ®î ï”Í7ïYƲçӞç4ϔÅYçKó ÌUð ×pΞÌYÅ«ð çÐpÌ«ÇÊÐpÌ«ÕfהÆ4ð ÐpўÄmўÍWўï”ŲñsÐpÅ«Ì«ÄmÌYì”îwÓjôs͂Ðpï…΂ўÄm҂ŲąƲí*é*ÉÊÐpÇÈÕSąƌƲÐpÏmÌYêð ÓfÚÁÆ«Õ7é*ê“Ï”ÉnÅ«èyé3ð ąƲÇÊ×pÌYõSö®Õ7Ç Ü ÷ùÐpúDÅ«ûÌ²üœÇ ÆÁËBýnþyþyÏmý“êbÿ æ¨Æ²ÁӞÿ Ðp՞yÌYÿ õ‚ø®ÐphÉÊÈýÄmÌ@7ÿäÁÙsŲÐDÐpúy×pú ÐYèð 4ÿ”û ”û ;ÿ jý“þ*ü uúYûý 4ýnþ ”7ûý“û¾ú ú uÁý ú yú¦ÿ”Wüœÿû¾ÿ ü…ýúD7fû úúYý ý 7uýgú ÿ yÿ Jú ý“úY[þ 7”ýú uû²þú Wÿ ÁUú ü ySÿ 7ú;ú ”fÿ”ûû û ý ”ý“þ uWÿûý Wÿuý «Ágúú ý yú¦pÿ”ýnûþ ý múfÿ hüú yÿ ”Wý ÿ yÿ ýnþ Iÿ 77úDúYûûüœhýný“þyþþyú ý“®ÿ =ÿÿ”û Áÿ=žû²ú ú JúDû ý“þ f®û û¾ú ú 7ýnû²úDþ ”pþú«úú {ÿ”û;þ jú Yý 7úDûüœýnþyþyý“ÿ yû²ÿ”ü 7ú fÿ Uüœú
    
 
       % & (') &*  
 
 ! " #  $ #
   +,  -
.
/  01 32547689    :,
 ; Q1 RPzb‹5£ QS' Œ \b]J‡fXY' £Q' ¤ XY}bQ1' Rh£TJ¤VYQjeu\i(X›T]J^ ’“QjlJTˆQS’“bdfvyQj¤f°ˆ’“~¦8dS„*HtQS’g}bB™QSV…„*o Qe“XY ‰} … UŠ' £ Q ¤S~ƒ eu£ i*' 8zwsQSQSe“\bŽ{O5]JabNBXYV…Q7Q z(W c›€™‚ iDo ¤”}h~œ]‚^Ÿ„3]JV iIhTJ \  QS~b¢b„*TWZ[}bQjRbVY’g@Q Q•ƒ ]J^œdf}bahQŒ ™UH Q¡’gŒ QSlJzwc£ QjHwQ7’*df¤ ]{]W9Z ^¦QRŒTF]{ƒ dfiYe“QjXY’“egG]J\H ^Ÿeui¦]JVBzwTWQj\dS]JZ[RU]qiDQ7zbz­T‚Xm„*Tqe“XYdf}ab™ŒXYQJ}hƒœQ ³™U\ TJiYsQfe“vŽ{iDabQ7V…{Q ahQSh\h£¾TdSQ¤”~hU XY}bQzhT‚X…Tq] dSab^Ÿ™Œ]{QV ^Ÿ^ŸQj]JabT{ahVYdmXYV}}bQjzwVqegZ[Rh¡QSTW\hVYVmXYiYTWe“e“XY\b]{eg°\4]Jv\h~;qQj„*z¥iD}hahege“™w\dmvy} X…dS] abRh™Œ^ŸTW]{QjVYabijXYƒVe“XY;eg]JTJ\hdmi} XYVm}hTWVmQ\bTW\b°zhv°T‚qvX…9TiDahiYdf™wabahvy™w™UdSvabQ›df™Œabe“Q™Œ\X…Qjeg] ii ÎƲžÓžÅ²ÐKÐDŽ×pÅ«ÐpÐpўÓ7׏ÐpÆyÐ Ì;Ämþy՞Ämü ì”ÉÊUÍ7ÉÈÏmÄmƲúYŮӞþ Ðp̾ÅKÆ«yŲú×p͞ÐD׏ÉÊÆ«ÇÊ͞Ì@Õ*ŲÇÊÐ@Ä@VÕ ÏmÌ«‘“Í7êbÒ7’ƫӞÜÁƲ×pӞÐ@͞Н̲ÒW̲͞EÐ Ò7é3‘¦ÜÁÄm×p͞ūÉÊ ÐÒWÐDê“̾ДÐDƑŲð ÌU×pÐpƲÉÊÏ@UÆ«ÇÊӞÌsЮ͞×p՞ÐD•Ç ÉʔSW͞ÇÊНGÕ Ñž‘¦ÍžÆ«Ð`ӞƫąÏÆ À

· ¡[ÞÞ£

Av

iv

ýz

í

v

Æ*Ç


Æ ®
Æ

D­®:ò@ò:ò@® Æ ­

È õö

Ã

3z

z Ã

ÈÃ Æ

ÈBÃ

?z Ã

v

Ç

Æ

v%ë

Ã


Æ

­

%Û

z

Ï

!ä ¡[Π ä ß ­® #¯=®:ò@ò@ò:® #±

*v

±

z !Ï

Æ

±

Æ

Æ

­

±

Æ

Æ

­

Æ

ž‰Ÿ

D­ ?Ï

Ã

)z

±

Ç

­

Æ

,Ï

¯

˜ !Œ

­


Æ

D­

.z

¯ #Ï

-Ï

÷

z

÷

‘ !Œ

z

¤z

%z

ôÊ ž7¡[Ÿß à

Ç

­ ® ¯ ®:ò@ò@ò:® ± Ç v D­® V¯=®:ò@ò@ò@® "± Æ
Æ ýz ÃÁÈÒà v “Ï Þ¡5à"¡[Þ )à Bz Ã9Â Û d‘ ?yÜ? ýÛ A‘

ÆáÇ

Â

Ã

˜7®.˜7®.˜

iâ}ÜÒâ

‘


  V F>

«Œ 3˜?Üþ˜

‘

)˜

Æ!÷

–

–˜—š™œ›œŸžœ œ¡ ™

— › 

(0,0)

ž  

(0,2)

¡

(2,0)

(2,2)

(0,3) (1,2) (1,3) (2,1)(3,0) (3,1)

segŽJabV…Q b¿ @¢bTWZ[Rb’gQO]W^;_`ab™ŒQP=Q7df]JZ[RŒ]{iYenX…e“]{\4ƒ

(b) Hierarchical Organization

(a) B = { , }

Û ¡ ÞÞ · [ à

(2,3) (3,2) (3,3) (0,1)(1,0) (1,1)

< b2 , b1 >

Decomposition

43

39

HB

Data Cube

Prefix Cube

RPA

< b3 , b2 , b1 >

19

28

HR

.......

Ï

^Ÿ]{VsQ7TJdm}zbe“Z[QS\UiDeg]J\4ƒ

(b) Hierarchical Band Mapping

Üi

Ç

H

Ë Ê

ÆÇ ÈÉ

Û

É È

48

se“Ž{abV…Q h¿@P=Q7iDegŽJ\­cRhT{dfQI^Ÿ]JV ˜ VYQ7df]{Z RhawXYQ7z_`ab™ŒQjijƒ ^Ÿ]JV3 iDXY’gŽJQj]{R VYe“[XY}hdjZTW\›™UQO^Ÿ]{ab\hØ z›QS’uiYQS„*eu}biOQjXYVY}hQ Q¡Zq«ƒ TWeg\1TJ’“Ž{]JV…enX…}bZµX…] QSe“X;l‚TJe“\’“ahl{TW]JXY°JQQ7i TF V…’gŽJTJ]{\bVYŽJe“QSXYvy}biYZ abZ PÚabQSV…o>Û·ahiDeg\b Ž9Ã9ƒ Ø ³XY\º]V…iDXYQSQj„*R V…enX…JQ ~ Ûµeg\XY]FT[ df]J’g Qjd”X…e“]{\]J^B’g]djTW’RbV…Qfšb¢&[ VmTW\hŽJQfviYabZ·{ahQSV…e“Q7i XY™Û8]FoÝàT T{dSßáVYdS]Qj]JÛi…X iDeg\b]{ƒ ŽV bXY’g]JQj}hV=TWQ^IQjdfTJdSQjdmQS’“}’gä*ÃâÍe“B\ e:â Ã9yÛ8ƒ ~KÝã–=X…}bXYßã}hQSo\QSV…Û „*â egiYdS~bQJTWe“å~^a\ â╙UdS\bQ]JQSV…QjQ7VYlžzbQ7TJi¦iD’“RŒaUX…]J]­T‚\UXY™ŒQ7zbz Qi QSiYabl‚TJZ ’“ahTWabXYQjQ7VYz[egQje“i\[7X…XYQS}bV…Q`Z[TJi;zbzw]W^4e“XYT¦eg]Jdf\U]{TW’“’JgQjV…dfQSXY„*eg]JV…\qe“XYeg]J\b^Žœ’g]w^Ÿ]JdS V TJ✒bRbeui4V…QfRŒšbQS¢[VY^Ÿ]JV…TJV…Z[\bŽJQjQSz v BÖ IJ¼Â + Ø siYabe“Ž{Z©abV…{Q ahQSV…iYo }b]‚ah„3iYegiœ\bX…Ž}bQTW\ªTW’gŽJ¯=]{±3VYe“_ÙXY}hZ[Ã9iœƒ ^Ÿ]{ V*’“QSŽ{l‚]JTWV…’genahX…}bTWZXYeg\bŽ¡T[PÚ V…TJ\bŽJQSv egiD\XYQSiDRUXYi QjRh•i XY•] XY[] TWhV…QIƒ 3]{Z[]WX…enQIXYXYXYQj}hz4TWƒ X3en1^ õ}hTJi*T }bQje“Ž{}{X3]J^ b~wXY}bQj\ ’gVmQjTWd”\bX…Ž{e“]{Qf\viDab]JZ ^ Ø {’g]wV…ahdSQSQSTW„*V…’oV…enVmX…^ŸTWQj]JiI\hVŽJTQ7QfTJvVmdmiYTW}1ab\bZ Ž{VmQfTWv\b{iD°ahahv ZQSV…e“iYQ7abiSab™w~QjvVYdf„*oLabe“™ŒXYÛ } Q¡egeg\]J\ˆXY\h]›Ã·Q T(’gXY]wdS}hdS]JTWTJ’“Xv’ sIJ¼e“ Ž{abÀI V…Q qiD}h]‚„3i:XY}bÖ Q TW’gŽJ]{VYe“XY}bZ¶XY]¡ZqTJe“\X…TJe“\­TJ\­¯=±3_æà ]‚V…QSlJ„*QjVYV…’uenTWX…RUQjiKiT¦„*VmenTWX…\h}dŽJQfÛ[viYƒ abZ  ’gŽJab]JQjV…VYe“oÜXY}bÛ Z e“\X…]PÚ Tdf]{’“gQjdfXYeg]J\[]W^4’g]wdSØTJ’ eg \¥ƒ3V…½œQjiYo›RŒ]Jzb\hQfšhiYQ›\be“XYXY]&eg]J\9T1]WiD^;eg\b¯=Ž{’“±3QSvy_BdSQS~h’gXY*}babQ•RŒabzhRŒT‚zhXYQT‚XYegQ•\¥]WXY^K}bT¡Q­iYzhe“\hT‚ŽJX…’gTFQdSzbabT‚™ŒXmTQ RbV…PQfšbÚ ¢FVmTW\bŽ{QfviDahZ Ø abQSX…V…]=egQj]Ji™b™X…oTWeg\šhVmTBipX iDQSe“X®\]Wl{^b]J’g°]we“dS\hTJŽ ’{Vm TW’g\bŽJŽ{]JQfV…ve“XYiD}bahZZ dfdfahah™U™UQILQ df† QS’gMe“B\ %(ødSTJ\X…}hT‚T‚ÀX¡QjdfdSX`]J\]{X…\bTJ’“o•e“\hXYÍi }h%sQBƒ dfQj’“ui`}bQe“\qV…X…]}b]WQ=XqVmdfTWQS\h’g°{*vyegZ o\ iY† ab™wegiv VmiYabTWab\bZ»QSŽ{V…egQfQjviOabiDabQS£¾ZV…iDegXYQjQji R ab£¾QjžiDVYXY¤”oQS~bRUTJe“i\\hXYz¡q]¦X…X…T¦}b] QSdS\›]J’g¤ “^Ÿ Q7abd”Û8VYXYXYegÝ }h]JQS\ Þ£V*Û ]WV…^Œ[QS’“„*¤I]wV…djdSenTW]JX…’be“\\bRbX…Ž V…TJQfe“Qj\hšhT{iO¢dm}(TJV…TJ’“s’g\b]wXYŽJdS}hTJQSQ v’ XYeue“X`zw}hQSQ•df\]{TWXYVYe“’gV…šhŽJQjQ7]{iYz¡RUVYe“]{XYeg}h\›\hZ¶zbiDisXYQj}hX…R]TJ\hdfJzwQj~w’“’gTJsQ\h%9abzqR£¾iDe“zbXXYT‚Qj\hX…RhQSQji Qji=zhOXYiK]qTJX…\hX…]•z }b™ŒQ{QO¤f\hƒ@ab]JcRŒ\wXYvyzhQSVYT‚RU]XY]Ji Q7X=z¡OdfXY]{QS] \b’gu’“i=Boqeg]We“\ ^^ ’gTJ]zhdjzwTWQj’4zˆRhVY£¾QSiYšbab¢™wX…VmV…TWT{\bd”X…Ž{QjQfzhviD¤=ab^ŸZ ]JV{XYah}bQSQ¡V…e“TJQ7\hiiD„*„œ}bQS]{VIiYX…Q¦]:VYQ7Û[iDahƒ ’nXmi*}bTWQqV…QOzwQfXY]qXmTW™Œeg’ Qi '†te“\£TJ\h†&z9euTJi*VYT‚QÀ™UQjTJdfiYXYQjQ7zz(]{™\­o[XYX…}h}bQQ¦abRbRV…]JzbRŒT‚QSX…VYQIXpo›]J^‘XYdS}hQSTW’gXO%Ten\b^@]JTW\w\hvyz(V…]]J]J\hXB’“dfo¡Qje“’“^ 6

Ò

24

42

32

34

40 102

23

egs\ e“Ž{sabegV…ŽJQ abV…bQ ¿ J@ƒ ¢bTWZ[Rb’gQ[]W^*T¯=½3_%^Ÿ]{VOXY}bQ¡PIT‚XmT9_`ab™ŒQ AÖ IJ¼Â  XYdf}UQj}b’“T‚Q*XI]Jdf^Ÿ^ ]{]JÃ\hV iD˜ XYeuV…i_ªahdfd”]{QfX…¢bZ e“]{dfRh\QjawRwTWXYXI’gQ7ŽJXYz¡]{}hVY’gTWe“]XYX=dj}bXYTWZ%}h’g“Q•oq^Ÿ]{Rb„*V@V…e“TWQfXYšh\•}›¢¯BV…QjVm±3TWiYRUˆ_\hQ7ŽJÃd”QfXœviYeuXYabi‘]•Z¶iDXYeg}bZ[egQO\9e“’udfTWQ7QjVsTJ’“wdmX…×}] i RhTJyVYƒ Qj\{XKVmT‚X…}bQSVKXY}hTJ\q„*enX…}qVYQ7iDRŒQjdfXKXY]OX…}bQBdSQS’g£ ¤ Û

2

30

8

42

13

54

23

47

Û

”

y AŒ Bz

ÒÛ

· ùVŸ-£:ß@¥$Ð=ßÎùVŸ

Òâ

yŽ ’

À?½

_Þ VùQÎß ä ¦

—Q®F—‰®:ò@ò:ò®F—

_Þ VùQÎß ä ¦

:ë y– #ì

«˜

«˜

½

¡ BÎLß:¡ µ ùCÐ ž‰Þ

½

³

æŽ ’

•

µ ù*Ð ž‰Þ ½

h½

Û

Ž ’

Û

¥$¡5©

z

Ï

¥-¡5©

· ¢

˜

y–

¡ dÎß:¡T¢

³

¹

)˜ ½ ¡ BÎLß:¡ µ ùCÐ ž‰Þ

Û

½

Ê Å$ž7ß:¡

3Þ Vù"Îß ä ¦



³

½

ª

¡ BÎLß¡ µ ùCÐ žQÞ ½ bz

³

ÉÏ

áz

˜

A˜

_â
ë

}Ï

680

y‘

#â

B•

f£ ¤ % ' ƒ  £p  p IJ+ç ³\•abQSXYV…}boeuiKe“\hiYŽhQj~bd”X…TWe“\U]{z\4~Wab„œRQzbTWRbXYVYegQ7\biDŽ¡Qj\TWX‘\ TJ’“Ž{vy]JzbV…e“enZ[X…}bQSZq\UiDieg]J^Ÿ]{\hVKTJ’4df]{¯=\h½3ipX…_AVYaUà d”XYƒeg\bŽU~

 RP‹5Œ v ‡ '

ü

ü

Ρ5ž‰Ð ä ÎÐTž‰Þ

À

žQŸ-Å

· ¥-Ñ,¡[£

À

·

í

o;X[O5N:U \
] îŠ< ï R$ ð N@U;\.R c-OQPp5o+ ï n“ñ ò-óô*õJô6ö¿÷ øFWMùDmV\­ú+ódûýüäþ6ÿ
(û ©ÿPüyû "ÿPþ  aû
©û  õ !$#&% u ô % Ž (ô ')'*'©ô %,+-4ûüäþ .ü ) /10µþ­.ü 2 " .ü (345©ÿ 6*©*ü 7Z þ 689%,:1!=*:@? A\)ô '*'*'Z.ô =):B? Ž .ô =*:@? u C  ö !>Bò E u ú F u ô E Ž Gú F Ž *ô '*'*'ô E + Gú F + ÷1ûüäþ D þ­ÿ ).ü 45I34  H K mV\Dù mV\"*ú L9ûüäþ .ü ) /1H.MJ 6© þ  H þ65ÿ 2Þ.ü 4I345 H û ©ü .ü 4568NP&þ ,OP!RQTS*UGVXWY ÷ [)\>!P# ] u 8ô ] Ž *ô '*'*'Z8ô ]^G-_05¿.ü 2, &/J þ ` H þ­ÿacb Z$ .ü 40d6*450üEûýÿÍI ó P&þ  feG H ý&þ ghaû £i ö  b­j ÷ Lk!P#-7 l ÷ ZO[NR p5P:]@ò q u ú r u .ô q Ž ú r Ž )ô '('*'©.ô q + Gú r + 2÷ st5 H  qYu!kqfþ v5#&E u5.ô w uG-5ô r*ux!k8ûýyÿ #&FGu$.ô w u{z|=.u ? nu } Z þ­5ÿ Nw~!o@ò w .ô w )ô '*'*'©ô w + ÷1ûý ü ².ü q þ ©cü 6**Mûÿ9]€:c7  ÷ LD!‚L„ƒ…#&u O_:†Ž-7 ‡ ÷ NR=\
mVN@WˆL_7 í o;X[O[N@U;\.] îŠ< ï R(¶ ð N:U \.R c-OQPp[o;M²d ï nMñ ò-óôyõ ô¤öë÷ Fø WMD ù mV\"úÀó ûüäþ­h ÿ €†(Mû  ÿPüyû "ÿP þ  aû 
5Mû    õ !P#&% u .ô % Ž *ô '*')'©ô %+y-4ûüäþ .ü ) /Š0Pþ­.ü ) ‰ .ü (345©ÿ 6*©*ü 7Z þ 689%:p!=*:@? A\*ô ')'('©.ô =*:@? Ž ô =):B? u C  ö !>Bò E u ú F u 8ô E Ž ú F Ž *ô '*'*'©8ô E + Gú F + ÷1ûüäþ H þ­ÿ ).ü 4 D

v

· ùVŸ-£:ß@¥$Ð=ßÎùVŸAÖ_Þ VùQÎß ä ¦

IJ+ç

sT­e“¯BŽ{ab½*V…Q_ F^ŸV…]JiD}bZ]‚„3T­iqzbT TWX…‚TvyiDdfX…ahTJ™UŽJQQ TW’gƒŽJ]{³VY\1e“XY}hXY}bZ·Q^Ÿšh]JV…ViDXdS]JiD\hX…TWiDŽ{XYV…Q9ahdf£¾iDXYXYeg\bQjRŽ ^ŸiY7]JQj¤fV¡df~]{XYXY\h}b}bz9Q[euiiDRbX…djV…TJTWQfŽJ\tšhQ›¢9™Œ£¾dfiDQabXYQS™Œ^ŸRU]JQ[abi \U]Wq^zˆX…]e“\ºeg{i¦c¤”~Q7dS]Jd”XYX…}h\he“Q[iD]{XY\ V…¯Bah½3bd”ƒX…_%1Qjz e“eu\iI£¾TWzb\QSŸV…¤”TWe“l{ƒ%’gŽJQj]{z³VY\ˆ^Ÿe“XYV…XY}b]J}hZZ Q XYXY}h}hQOQ›dS\h]J]J\h\wiDvyXYVYV…]ah]JdfX[XYQjdSz(QS’gRbijV…ƒˆQfšb–B¢\ˆdSabTW™Œ\¥Q¦e“™Z[o¡RbT{’gzQSZ[pahQjiD\{XYegXm\bT‚Ž X…e“]{XY}b\ Q¦\bl‚]JTJXY’“Q{ab~KQ7iœXY}h]WQ ^ XY]J}hVmzwQ¦QjRbVq}e“o\tiYeudS„*TW}b’4eudSdm’“}¥aUipXYX…}bQSQ V…e“\bdfŽ[QS’gu]Ji^TWXY}hV…QQdfZ[QS]’guzbiœenXYšh]qQ7ztZ[e“iD\h}he“]JZ[abeg’u§Sz¥Q¦Qfh³ ¢wèJRb–•’g]Jƒ e“X BÖ IJ+ç+ Ø siYabe“Ž{Z¶abV…Q abQSOV…o¡iD}bah]‚iY„3eg\bisŽ X…TJ}b\›Q=TJ¯B’“½3Ž{]J_BV…enƒ X…}bZq’gŽJi]JV…^Ÿ]{e“XYVK}bQSZ l‚TJ’“ahTWXYeg\bŽ¦TOV… TJ\bŽJQSv ¯XY=Ø }h½3Q;_ TW\hÃ9iY„œQSƒIl‚QS½œTWV¦’go(aheuiT‚X…X…}bT­QjQ•iKiYzbabTQfZ[RbšhZ[VY\bQSe“TWšbXYXYeg¢[]Jeg]J\9V…\1TJ]W\b]W^;ŽJ^3QS¯=TWvy½iYXabZ ZZq]TWipRhabX RbQjQe“VY\hÜo Ž dfÛ Qj£ s’“ahKTWiYl‚™he“TJ\b’“Q’“ŽabQ77TJiS¤”\ ~ƒ ahTW\UTW’gŽJXYz Q`]{¯BVYT3e“±3XYV…}hTJ_BZ \b~žŽJXY£QS}bvyQ3piYabVmZªTW\h؎JabQfvQjiYVYaboIZ ahiYeue“i¨\habX…Ž=QS}bV…QKTWo\Zqeuis¯BTWšheg½*\V…_BiDTWXKƒ‚’gŽJV…cQS]{eg„*Z[VYe“V…XYe“en}b’uXYTWZºXYV…QS’“\ oBXY]3XYeg\{] QjX…l‚˜ ]¦TW_’“T v dfJ]{¤f’“ƒ gQjdfXYeg]J\¡]J^4RbV…Qfšb¢qVmTW\bŽ{QfviDabZ¹abQSV…egQj&i ÛqÝéßêÛ [ £¾iDXYQjR :Ö IJ+çÀI ¯=\ ½3_?abRùzbT‚e“^UX…Q TW\h]Jz^;]JT(\bzh’go¦T‚X…e“T(^hXYdf}habQœ™Œl‚Q[TJ’“dfabQSQœ’gåeg\•%FdfT‚QjÀ’“Qjd”' XmegiBi‘T›zwQjdfVYQjeglJ’“ Q7z¦' aheg\ iYe“\hTJ\Ž XYXY}hV…abQ¡QIl‚^ŸTW]J’gVBabQq¯=½3e“\FA_ dSQSÃ9’ga¿ %®ƒ }bQ[^Ÿ]J’g“]‚„*eg\bŽ›Xp„œ]RbVY]{RUQjVDX…e“Q7i¦TWV…Q £ ˜ ž¤ X…}b}bQ•Q=TJab\hRŒdfzhQ7T‚ipX…XY]JQ*V=]JdS^ QS%’g iBT‚À]WQj^ df' X…i TJ'VYQe“^¨TWTJÀŒ\hQ7z[d”X…]JQj\hz’“o•™o(en^@XY£ }bžQ ¤‘\bab]JR\hzbQ*T‚X…]WQ ^ ]J1^ %s~bTW\hz£ {ë¤ % ' ƒ £ ˜ {¤¡³y£¾J^e“\h%tdS’“ìaUzw¦®e“\h£ 'Ž ¤f~' ¤XY}bTWQjV…\Q¦\bT‚À]{\bQjd”Q=X…]JQjz(^¨XY™}bo¡QOXYzw}hQjQ¦i…dfabQjRŒ\hzhzbT‚TJXY\{Q¦X]Jdf^sQj’“dSui;QS’g]J^ %®' ƒ RbRb˜ egV…V…\b]J]JŽ%RŒRŒQSQS£VYVYsXpXpo­o­TW™b£ £ ’g˜ ˜ Q 77¤”ž¤;ƒ ¤”^Ÿ~O]J’gTW}h]‚\hQS„3zºegV*iœRbRb^ŸVYV…VY]]J]{RŒ]JZ>^¾QSi*VYXYXpTW}ho%V…QQI£zw˜Ž{Qfe“{šhl{¤¡\hQS\(eneuX…ie“QS]{’uT\›iDQj]J„*df]{^‘}bVY¯BQS]{V…’“½+QuTWZqV…o¥«TWƒ Rb]Wv^ Û

ý–

þ˜

Òª

z

1ª

ô‘ ‘

A˜

Ž ’

ҏ

w

¥-¡5©

Û

_Þ VùQÎß ä ¦

¶z—

´ à‰ž‰Þ¥-ž7ß¡

½

³ ¢

¥$¡5©

Ï

îÀ

· ¢

_z

3Y4 H.J  fOi‹ŒƒO ŽïAR$ðN@U;\¤RTc*OQPp[o+ïn“ñÍò-ó
s õn“s öë÷27 b­÷ROi‹‰!P# -7O•Ž9!$# -7 L SVO l ÷ÉZO5NR=p5P:]–W m É o ÷ ,) H ûX\W ûýÿ8 þ ! ïs XP4 ÿ Z(­ ­©  ° b(±, "~{¡µ þ­ÿtþ­ÿyY  "~ #M $" þ­ÿ¥ÿPûM¥ ûü*Pë û þ 62¥ ûM©6 þ X¡40© ü /Ÿ H & þ­ÿ5 ) Vt4[  Z4 H û© ü*ä¡  g4 H H Vt©6 H û© ÿ6*© ü&x*g(s º ÿ¥ûMe H üyû J  ë / W ûü.6*­ ÿPüyûÿ \þ( ûü." ÿ`^ s ]5*0 µ4 þ Z(­ ­­  .gsú _`_(X 6ü* aûü.6 (t4T_4a6 J 62Pþ­ÿT_f56 g¥ü* H H.J ° l ± i #Jþ H M \h25 YÌ þ­ÿyc b,gµg þ H þ&P4 üª/Ÿ H V H ûÿ5 þ­ÿ5)  H û*$e ûýÿ) \h4z ûd &¿û © ÿ¥üyû" ÿµþ&' &²þ& þqûÿˆ¡  g54 H \h*•

H.J ”ºi V  e þ&© ÿg f( ú ¯G l ­ § b  Is h6) 0 H Z*­­ o  ° o c± V€4 i)· ÿ H Ls &~j b H þ*E þ&Bks biL b05µ0 þ ¥ û@6s þ­ÿ5:BADCEGIH a J ?LKMHONMPQGR+L5.8./S*,/S5T-0/2sµg þ  © ü l j© U o ­ sp›p4©6 ü." ÿFs b H û~*­ ÿµþts \þ J Z*­­ §  ° Z(¯ ‰± f