A meticulous analysis of mergesort programs* Jyrki Katajainen**Y

!"$#
%'&)(+*-,$./102/43/1,65875:929<;=/158>?%:7@BAC7(DE/F(B@B@+G'5?H(J/LI KNM
OQPSR+T-U4VBWYXZR+Pu['WStS\vY]w1r^_xJ\JxX^T'\4`)T8WYR+R+['Vbm-a1Ugc+ngdeR+RB[-[?cRgyEf8UghjYW[:f-dePSiJR+R+VB[-jkdeXzWklQU4VY\q8]f-^_y$\XZT8U4R+d|['{~}m)UJgng1R+g[oof8hpg8['de1igRBVBjkgdeWY RWYjkT)UVYq1R+[srgf
"QUJgvk{eU4[-cYq1vY6[)jYWkdeWk`-W]`: Vb6[:y$]~\XzVBXzUd|{~Ug}8Wk1d|q8'fog~1X'4a11WY oUg'¡gWk¢4£U6{e1< 1f8¤EPkv1g¥ :rw4a1UgU4VY'VL`- cqLR+[CfSR+VBXzU['lgf
`:d|¦[)['c+§Cde{|Wk`-¨2v©'cª\gR«:jYj¬1WEWk©gXzm)ZR\1® 'cm)R+\J{~RjYº1WY6R+jz[=¯°\4\4c+]`'deR+VEqL[-RU4cl?[-lU4c{e\\Jl1]uXjkde±jT-²U4Wk³6m-VY´1deRjY²\4Wkµ2[-de¶1Xzj³+fE·:RE¸oR+T8{e³RR+¶+XzVY´1]~³\RB¹1VB['±XzWzµU4Xz[-dejS\cigRUR[)\jZ]8U{eU4Wkl1m)[-jYRE?RjYUg\4'VB`'WkF[-d|[-VB:R2nSR+jYVujzT'UzVBc\gU4jkn4{edeVBcBX=UJ`:T:Xz{eU{eRjv
WkXzde\4\1[-:jRBº {® m)m)RRB[ng\JjYU4\4{EVBWkded|jz[-nWY\¾QR2d|jY['WYU4WYR'ng{|deR+jkVBm»jº8Wk¿m-R°l¼Wkm-RRjYWT¼R+\g{| jYv~jkq1d|[)'\{eRQ[WkdeXzd|[:R+]~v~\8VB\4Xz`'Ug[-Wk½de\[:VBRBv{eWkUgm-WkRdeig\4VBRR2WkWYde\QcWkUm)VYRv
n4\4`-`'VXz]6R+VB['UgW=Xz¾pR2{e\g\4n VY q8¾º8ÆuÀÂRÁÇÃde¾8XÄpT'de{ejRXzUzR+{e\4['WYUJR+WkVde\48[-\4j`'[-]~\"V=]~Wk\4V=\Wkvkm-RU4ld|['U4WYR[-ngR+VY]Èv\4jY`'\VYVBvkWkd|[)U4nQlT:8VB\g\WY:WY{e\JR2XXÅv~`:d|T[
8XzWkm)\4R+R`'VB\[)ngVBR2'RjYRWk\4deÌcVBUW='{U4lsÑ:VB[-RÍF1Î n4Ígd|[)de¾_iJnJR+{ejz\J[Cn fU4 VBWkR¾Qm)R-ÏÐUgÉcYÁ¶1q1³YR2Ãµ¾8"·6ÄzÊY`:ËBU4¹gT½[-µ2²zÌ_dec'Wk\gmÒÎ|XwJÍgUT'¾p{ejYR{eRB\JgVYndedeWkR dejR¾Qj\ÏÐ]\]SRÁgT8Ãm'¾8RBdeVYÄ+cdef$m½XzVBR+U4R2['VBjkT8WYRjzRjkcm)Wk\dem'iJdeR+c[Â{emÂlgº WYjk\m-® \8m) RR
]~Wk\4m)VRzd|T'['VBWYR+UgVYc[-WkdeU4c{|UvXz{VBRR+XZ{eR\4iVBU4lQ[-ccRQ\JX\4T:]u`-\WY`:UgVWkdeU\[)[)Ujº{el1jkdejm-R+[?deXT'{eRXzR+['Wkd|[-n?{|d :VBUVBlÓVB\`)Wkd|[-Rj
Ô Õ'Öp×8Ø8ÙÚ=ÛÜC×¼Ý+ÙÖ
á87Þ å65<7,6ß:,éæ"ß:7775(B5)@+/=0B7@$@+í7,é5Qà)á8/1/1758@+58â>»7â4587@+><G'G1,éæã5<äêZ7Q7G:/1å6(B@+7>8@Bæ"G)74(uâ7,~5)/1/10Bâ0+@gâ47çJG'>î7g(B/1><,6â5),éè5<ãkG'êZâ4(BG'æ?0+58Gz/1@+0B,é0+è8@+,é0BG:7,6,65E58(ç)ê*'0BG174è<ã&-7Â@g/ý1ï*'þ»ð'7ñ&7Sòkó~><7ô'ÿ8(2õ÷/g/1ëöæñ+5z,6ð'58ãø4(+7ùéG'úgæ"ûüæì70B/,é@è80BG)0BG'>8GÂ0@$/1G:å6ãå6á8G:&=0B(G:A8@B(Bá<G'>80å67ß)(+0B,6758è8> ê7
0+è8,6@A<(BG <åé74æì,650+è87,65)0B7(+5o/1å8æ"7æG:(B&G1ãE/=â4G'æA<á80B7(pá858>87(p0Bè87SãG:å6åéG1ë,658ê=/F@B@+á8æA80+,6G'58@
'ýSH/F(Bè8(27"/g&),6ç)58ëA8á8è80,6âè?,6@zæÒê',6/gß:& 75»o7z,65î0Bè</175»G'/1(+,é(Bê:(,6/g5o&s/1å/F58/1(+>»(2/g0B&Qè<7, ãG'0+á<è80B7A8@Bá8AC0/1@Bâè87G:,6á8@Så60B>î,6ê'/1è)å60g@BýG C7A8(+G-><á8â7>Ç,é5î/F5
88ýSýSHHè8è8774(B*'77,6&Q@zá8585<G?,éß:,675)(Bã@+G:7=(BæÒí /F,é0B@,6G'0+5Âè87z/F@B@B@B7G)0âG1,~/Fã0B,675)>»0B7ëê:7,60B(BèÌ@gý 0Bè<7Q7å67æ75)0+@Jý =75<â7'çëS7>8GÓ58G'0zæÒ/F*'7
o8ýý S/FS5-G:G:&"ææ>8AoAo,6/F/F@B0+(B(B,é,6,65<@B@BG:G:â58580B,6@J@bG'ç5/Fæ"58o7G1>4ß'0Yæ"7ëu@gG1çJ7ß'/17475Â5<@> 0B/1è8o/(+717z@+70B,6å6âuè877æ/1(+G:7,é0+585)è8å60+&Qæ@=G'/174AC0B58,67>"â(2/1/F0B58è80B,6>7G',65<(å6G:@=*'ê'/17,6âJ&)å6å6/1@JG1å1ý ëuG:7Ao>74(2ãk/1G'0+(,6G'0B58è<@7G'75zå67,6æ5)0B7475-ê:0+7@J(Bý @0/1*'7
8ý â/gG:ß'5Â58/F,é@B,6å~05-/ /10+8å5)76ê'0=7740+,é(Z5",6æâg0B/17'G:5 ý 02/1C7åYý@+0BG:(B7>Ì,65ÒG:587æ7æ"G'(B&å6G)âJ/10+,éG:5Â/158>Â0+è87(+7÷/F(B7 ä åéG)âJ/F0B,6G'5<@
0+C7,é=æ"@+<7 G'(B(B~G'0+@Bæ774>?7'/1ç,6@B57'@+ý á8êoæý6ç äA<0Bå6',6G'G'çê 5 )7åéG:â4,éê0B0C,6ãkG'G'ä 5 å6på6<G10Bëý ,6æ@o0+7 ý èo/10EBG1ç'ëu/FG:5-74(&ß'77@Bß'(gG:74ç(B5Ò0Bë,658,6,650Bêè8æ"G:á8k70=ä 0Bè<0+è8G-0B,6>z,6æ"@ZæQ/17@+á8,e@BãE@+á80o,6æ"5)á<0B@BA8747u0Bê',6/F7G:0(+5½@båé7gä/F/1(B@B7=,60 5-@+0+æÒ7kê'ä/F74åé(Båéå @zG:~ê @BâJM74/17'ä5 ç
7'ý êCýéç 1ç<A8AEý M ý M
NQVBU4RVBjYcYRBmÂ['WYrRÌFUJºWzWkm)RQVB»~WYU4{|deU4[ ^\[:]~RBVBR+[)c2R\4[ p{enJ\4VYdeWkm-XzjU[)s^_\JXT'{eRgdeWklgf \JXzRgfWYU{elgf
ÆSaL`'\:T:º T¼\4gVBxgWYx R1ÇÍJw÷T-U4Ã6VBT'WkVBde\ UY{|eRl cW 'Yl ^\gWkm)XRT'`-PSWYUUg[:Wkdedejk\4m [-U4ÆS{ UJWk{e`:ngVB\UVY{ZdeWkm)aFXcBdeR+dec2[)j c21R Ä+º RjYRU4VBcYm ^_\`:[-c+d|{`'[)'R+Vc\['WkVBUgcW
!"# $
%
.--/10#&(
+
2:2
2
% '&( )
*+,&
% 43
877'9
71; 17
=<
?>
@3
!
65
BA
5
â/1G:5Cæ/1?7å6A8&)á8@B4,6(B0+@Jê',6çC5874/1êo@BG'A8ý (+ACü07J/1,6>8@(+770/1>Â/1@,6,6å6,é5Â7æ">Â/Ao>8G:(B747(B@BAC0â/1G'(+5)(+,éA<00 0B,6)&,65 G'5Ì0+Þ è8G17QG'ã å6è8>8CG,6@+'@B0B0B0+,60+G'58G'(B7æ&Ì/1 G15<á8ã>ÒA?@Bß:G:æ"G'(B0+57,é(B5<ê:=ê½774@Bá8/FG:@æÒ(B0J@B/FçCG:580+(BG'5 0+ê',é5<74êÒ0B_è8,6/F75Ì(z@=0B7Jëè8/F,67Q(B0Bå6èÌ&Òè<,é/Q/F@+0B@ 0BG:,6æ"(B&Ì,é5<G1<ê ã ý
HæG)74>o(Bê'/g74&»@BG'5)(+á80 æ@B77(+7:G'ç)á87'@ý êoß'ý6/1ç (B,~/F)5-ç10+A<@AEGFý ã=0Bè87 o/F@B,64âçà)æ"á8770Bá<è<7=G-æ>Ð74/1(B(+ê'774@B*)G'58(+0G1ë
5EBç1çN,6ã5 G'Y(A8å~,6/158â@B70/1æ"58â477'(Bê:ç70+@BG'G:A (BY0 >8G1@Bë77:5 ç
7'ß'ý74êo(Bý6@Bç ,6G:
58@=çCGF5oã/1æ0+á874(B(2ê'/F74å@BæG'(+740 (Bê'~@+747@B7G'(+0 )ç @B77'_ç$/17'5<ý êo>ý6ç 0Bè<71(BçC7A8ãk7AE(Bý 75<â7@,650+è8ç87@+/17@z@BëSá87(+å6ß'å7/1&)@z@ G'ýC0+Hè87è8(7z/F>8>o7/1ß:A87å60+G',6ß'A 7
æâJ/F74åéå65-70p> ,é5Q)&0+è8.z,6@u5)á8AC0+/1è AC7(u1,6@ ç)A8C/AE1@Bý 74>ÒG:5 oG:B0Bý0+G'æ Yá8Aæ7(+ê'7@+G'(+0Jç:G'(S@B0B(/1,6ê'è)0æ"7(Bê:7@BG:(B0u/F@u,60ë/1@
ê'(ùéð/1æ"ï@J@Zý'æQYô5ÓFá<ùâ2âgèÌG'ï5)ó6/1ï 0B@(/1G'0+@+è8(0Z,6@Zå60+,6G0BAC0+/1å6F7ACï 17G:(ûèsö,6/F@òk5oð'/ /1òkCGóå6&)'1á8@Bù,60z@ :z@Bô G:,61@(Bù0+g0B,é5<ïG óÈêoï /Fç5o~,6G:0z/1( å6,6&)@°8,@B7?6/ ê oGY/1G':å6@BèÂá8G?0z/10+0B5oè8è8/F77Qå6&-â0+@+G:,6,6æ@58@B,6ç<0580B/1êè85)70/15Cê'ã /1/1G)å6â/1&)0+å$@BG',6,é(+@z5Ç@G1û,6ãu5»úgA80Bò(+óè<G 7
(B0B á<è<587 58(B,6á8585<êQ580B,658,6æ"êQ7'0Bç1,6æ7@+7:Aoý 7â4,È/Få6åé&"0Bè87zâG:58@B0/15)0,650+è87zåé7g/1>8,658ê0B7(+æ!GFã0+è87ãá858â0+,6G'574ÿ-A<(B7@+@B,658ê
/0B1,6@+æ"@B,6H7ê'5<GG1@Zã=ã /1//"â4,éâA8å6G:,6(B02@BG:/F0ê'0Bãk7(2G'/F0+(æè8/17=å6,6åæ"@A80B7(Bè80B,6,6æ"74â5 á8,é0+å6@+,6G:ß',éá8æ"7=@A8G:/1å6Ao5o&?74/F(20Båé/1è8&)0+7@+,6,éG'@p@B58á8G1@æ ãEGFA8ã_(+GFG'0+ãuè8ê'0B7z(è8/17Qá8æ"58â4@J>8G'ç174@B/(B0+å6@æ"&),éG15<G)ãêQ>80B7è<âå8G'7Qèoæ"/FA8@A8(B,6á80BæG 0B74,6o70+(J,éý8zß:H7z>8è<7G'C7ZAC587(+7á8(2>/F580B580+,6G'èo,65858/1ê @0
7A8ÿ)á87(+âAoá<G:0B@B77'>ý YG'5 5Ðè</Ì,é@"Ao7J/1/1(+0B(+,6å6â& á8å~CG/1-(G:,6*)58@ A8á80g)ýç u/1(+Z,6G'.zá85)@á8â0+G'è @+0Qá8æ@B74G)> >870+è8å6@7 èo/gß'"7! o7æ47G)5 >87A8å(+G'ëACè8G'74@B(B747Â>Ð0+ãè8G'7Â(â0BG:è<@B,é0@
G10BèCãZ/1#/ 0ë,6"å6!!å o7/FÂ@B@+æ?7æ /18å>867 & )&å~î/F580Bê'èCáo/1/F0Qê'7,658,6@B580+@B(B0+á8(Bâ4á80Bâ,6G'0+,65EG'çp5î,65874âà-å6áCá8/1>8å6,6@58êÌ0Bè<0B7Òè85)7Óá8(Bæ 7ãC774(B7(z58G1â4ã=7 æ"0+G»7æ0Bè8G:7Â(B&?,658(B7@+0Bã7(+á8(B74â580B,6âG:75 @
,6æQ0B@+á87å6å 0Bã2,6ý)A8Hå6,6èoâJ/F/10B0S,6G',6@J5zç)ë0+è8/17z@Sâ>8G'7 @+o058,é74@S>ÒG'5<0+G 7=C7G'=(S0B0YëS745½G/FãG:58(u>Qæ"0BèCG'/1@+0S0G1,658ã@B/z0+(B>8á8,6âß)0+,6,6@BG',6G'585@gç80Y7ëSÿ)7âå67ß'A<7'0=$ý Y0B5èC/1è80S,6@0Bè8å~/F7z0B7â(G:@BoG0)G1G:ã*-/ @
/æ")74ææç 7G'æ"(+=G'&(+.Z,6&Q'@ 5)(B&á87740+ã(B74èîGo(Bý7èo58/Fâ4@7Qá<,é@z@B7G:> 587'/ÓçC@Bë,6æè87A8(+å67J7/1( @0+æè877æ"âG'G'@+(+0Z&%YGF(Bãu7ã0B7è<(B77458G:âAo77(æ"/1G)0+,é>8G:758å@z,65î0Bèoë/F0=è<>8,éâG"è»580+G'è80z7?(+â7G'ã7@+(z0Q0BG1G ã
,68á588ê 0g.zç, 5)ãá8B/"ý 0BèQê:,éG-/1@G)5Câ>Â/1G:å658&)ëSâ@BG'å67á8(+>Q@B@+(0,éæ?G: âJ58/1/F@5)@B&=7ëS7@+o7G'(B7S(BèC0+0B,6/gèC58ß-/1êz,60G:A8á8à)(B(zá8G:,6ê',éâ2@z(2*)/F,6@+ææG'(B@$AC0,éG',65@(+02è80B/Fè8,65-@7S0gâç8ãYå~/1G:/1@B@+580+@B77,6@Bâ @+0è8oGæ"G')á<G:70Båé*>Ìè8G'G)á85>z@+@B7QãkG:G'è8(B(0B7J,6,65-/158A<0+ê7@B(B/FG'5C58(+/10>å)@B@+@B,67JG:58/1(Bâ40B(+7,6â58è,6ê 0
>8G)7@Y5"580BG'è80,6@S(+7Aoà)/1á8AC,6(B77(/FëS5-7Z&Qâ474G'ÿ-æ0+(2A</åé74@+æAo/17â5)7°0.zãG'5-(á<,60B0B*è@) G:@Ao(B7474(2@B/1á80+å6,60BG'@ 5E)&ý /F5o/1å6&)@B,658ê/Få6@BG?û ùéòkó +$ûúgñõ:ú ïAoð'/FñAoòk7ç(ëëSè87,6âãkèÌá8(Bëb0+è8/F7@Z(B7gæ"/1G'(Bå6(+,67Z7(z/15CâG:/158å6&)@B@B,67=>87/(+758>î7ë 0+G ,6æo7A<åéê'74G)æG)7> 5)02G:/F580Bå6,6&"G'5ãG'G1(zãE70Bè<ÿ)7=0B74,6(B55oY/FA8åuå~/1@+âG'7(B0+æ,6 587êo(+,ý ê'Y75»@+G'0B(Bè<07/1å6ãê:á<Gåéå
(B)&,60+è8ß'æ/F5 >8Þ 7ß:77å6å6>8G'7AC( 7> /1)&@pzâ,6.°0B7/F>Q02/,6534/1,65875z%ý -70á8/1(SåYâý G'
5<oâ/1å6á858@B>z,6G'0+5<è8@u7b/1/F(+>o7/1>8A<,0BK,6ß'77(+7æ5)074(Bãkê'(BG'74@Bæ G'(+0B0Eè8ß'G:/F@B(B7,~/1G15)ã0C.ZA85)(BG:á8Ao0+èEG:$ý@B7Y>5
G'æá<74((Bê'âG'74@B@+G'0(+æ0uG),6@S>80B74è8å-7æQã á</Fåé@B0+0+,67ëb@B0/g&,65 æ"YA87å~(B/1ê:â77@BG:@B(BG:0(B0B,6@,6580Bêè87SæãY74/10B@Bè80+7G)@B>E0pç'æ/F587>Ò0+è8/FG)>o>/1ãA<G:0B(,6ß',é5)70+æ7ê'77(+(pê'@B7G'@+G'(+0B(B,60S58,6êC@uç1â4,6G'5æ A<ACåÈ/F7â(0 7 ,670Bÿ),6ß'A87zå~/1ë5C/1,60B0Bè ,6G:oG5:G10Bã0BG:0Bæè874Y@Bá87zA(B7æ"@+á87(Bå60Bê:@7@B,éG:@S(B0B0èC0+/1G'0ê'0B74è<0B7Zè87,6(z585<ë7,6(u0Bè?å6G)0+G'è8A"7G1/1ã><æß'/175)(+ê'02/F7@+ê'G'7z(B0SG1ã ,6@uC7G:,65858å6ê&Q@B/1å6>o,6ê'/Fè)A80B0Bå6,6&ß:7'æý G:(B5 7
âå67G:@B@B@0Bå6ã&?(B740Bà-èCá</175Â5)0B0+å6èo&-/1ý 0G1ãuà)á8,6â*)@BG'(+0 8á<0=0Bè<7G:á80B7(å6G-G:A?G1ãuæQá8å60+,éë/g&æ7(+ê'7@+G'(B0,6@7ÿ)7âá80+7>
G1)ã=7â40+0BHè8,6G'7è85 7z(+7A80B@Bè8(B0G:7 GFê'ã+(2/F0Bð:è<æñ7Zïæ"ò AC0,é/15<1ACêQï7úz(=åÈ/FAC,658@S7ê'(YG'ãkáCG'(B/1ê)(Bê'æ?/17:58ç/1,&58âJ74/1â4>½7=å6å67G1/F> ã@æQãkö G' á8å6å6ñBå6G1#ú0Bë,6ë.@J/gý$ç& Y/15 oG58:)>î0B70+â4/FG'0B5 æ,6G'/15Yá8@+@BAQG)ëuâæ",~7z/170+(B,675)ê:>î0B7(B@BG)â4G:G'>8(B@B0á<0â,6@b7æ/F/G)5o>8@B/1á74å6&)å 8@/ý @B+74Y7>5 0
á8,65 58><)77(â0+0B,éè8G:,65 @âoG:ý)@BH0Eè8æ"7G)(+>877@BåYá<ýåéH0+@Zè87/F(B0+7zè87@BG'á8(+æ"70BæÒ,6âJ/F/F(Bå8, /1&5o7>Q/Fåé,6&)5 @+,é¼@C7,6@â0Bo/,6G:F5â*'7>z@Bá87A 7)&H_z/ /S8å6@B7 7(+,é74ý@GFã87ÿ)Ao7(+,6æ75)0B@
.
&
)+
1#/ '& ?
+
% @ &
6
4+#
1'/ &
&(
6
&
1#-/1'&(
8
8
*
+10 ,&
+1 &
+,& =
*
&(
&
6
$
$
$
?- $
@
%
)
)
ÜÙ:× ÙÚ
H è87æ"G)>8ë7è8å),6G1âãEèââG:G:æ58@BA8,6á<@+0B02@S/10+G1,6ãG'5/öá8@+ñ+7ð2õ:>ñ00+:è8û(BG:ç8á8ûê'úgè<ûG'á8ð:ñ00+è8/F,658@>÷Ao/°/FAoâ7G'(på6å6,é7@Sâ0+/,éG:=5Q/FG158ã>8G'ñBúYæ õ:ó6ïòúgââñï'7@+ý @ Â/(B741ê'â,6è8@B,60+5877(
,6/F/F5Q5858>>0Bè</0+7Zè8æ"(+777ê'G'æ,6á<@+0BG:0BA87(B&á8(+@J0åéý G)@+YâJè85"/FG'0B0Bá<,6è8G'åé>Â7 5zC7âJ/F/Fåé@+ê'5G ,658@+C70B5<G:z,é(B5<A87=ê(B/1G)GF5>8ãEá<,é0B5)âè80+77z7>Ìê'â7G:0B(gè8æý17HA8(+7'á8è8ý 07/1/10+â,éG:0+áo5/10+å)è8â7zG:æ,658A8A8á8á<0S02/1,60+@u,6G'@+0B58G'@E(+/F7(B>?7S,6âJ5/1(+æ(B,6747æ>G'G'(+á8&-0 ç
å~/F/1@B5<@B74ê'Hæ áoè8/F8å7"ê'6&7 æÒå~/1/1Bâ5<ýè8ê'=,6áo58/Få67åê'770+è8ÿ)ãk77QG'â(=A8á</(+0B,é7æ"A8@Q(+,6A870B@B,6(+ß'7G'5)7ê:0((2G: /1>oAoæ"/g74&(2@z/1'ë0+,6G'(B,6580B@0+7GF5îA8ãb(+,6G-A<5Óâ4á87ö (B@B7 @+G'ñB(#ú èo. /g)ß:çë7=è80+A<,6âè8Aoè»77,65<(,6@>8â,6/?G:ÿ á8@+5)á 0B8@ý 7B(+74AoB0Q/1ý'(+HG10Bã=@è<70B,éè<5î77 ÿ)/F75 â,6@Qá<0B7,658G'â45ÂG'á8GFã(/17Jê'/174â> èÌ0BA8G»(B,6æâG:,6æ0+,éß:Ao7=/F(BG:7"Ao70Bè8(/1,6@Ò0+,éG:/F5?@B@+á8,é@zæ/1A8@+@B0+á8,6G'æ"5î7ë>Â,60B0+G"èî020B/Fè<*'7 7/1G:â580+7áo/1á8å58,6â0G'@+G10Bã@"0B,6G1æã 7:ý8HG:è8Ao774(2(+/17J0+/1,6G'><587(@
æ"7J/1H@+á8è8(B7"7> >o/1)&0/?SæÒ7/F5)580Bå6,67A8&?á8å~7/10=0+7/1> åYý )&»A8G:á<5Ò(B/7 ß'Å/F(BA8,67(B0YG:&Qê'(2G1/FãæâG'@æ"/1(+A87 á80+ó~7ô<(Bò@gúYý õ:úJñï 4ç ð:ô)ïò :ô8ò~ïç/F58>
ö8GFãEð'ó~0Bô<è8ò,6úg@ñß'ï /1(+,~/8å6 7,6$ý @kã_@B0+/G'(Bß'74/1>Ò(+,È,6/ 5"8å6G'7=58,67z@SG1>8ã7 o0Bè8587z74>Ò(+70+ê'G ,6@BC70+7z(B@gG1ç8ã0+0Yèo&-/1AC07 ,6@Jç)0+è8ç:7ëu/17â/F0+áo@B@B/1á<åæ0Y&)7=AC0+7zèo,é/1@0S!0B#"è<$7Z#ß'%&/F!å6#á87
,65(+Ð7ý ê',6A8@+åéá80B@+7GQ(+(+7 @JAoçCG:,Y,6A8ý5-7:(B0+ýéG:7ç:ê'(0B(2è<ß'/F7/1æ,6(+(=,~/,60Y@_8å&)/Ao677z@B@g7ç),6à)'@ ëá8!è874#"G'58$@+â7Z#7=%&â4GF!G'ão#5)AC(0BG'7@B5)@+0, 8å,é5<68&>8ý å~,6âJ/ /1C70+7å6@=åé74/>@Bå6G-0/1âg/10B740Bæ,6G:575),60B5@gý1æ"D77æ0)G:ç(B&)*ç'ç/1+ (+C77ZS*:587A8G'00
58/F5874â4> 7@B3½@/1/Ì(+,éå6å~&Â/ C7><,éå=@+0BGF,658ãâ@B0zG'æ",65)70B7ê:@+027/1(z0+7ß'æ/1(+74,È/5-8å0"67,65î@Jç 0B,è<7Â/15<A8.> (BG:-?ê'(â/1G:æ 58@B0á8/1585)>80B@g70ç ("/ 7ÿ)/175<â2> á80+1Â,6G'AC5EG'ýS,65)H0Bè877Â(zß'A</1(B(+,6,~æ/ 8å,60B6,67ß:@g7 ç
@+02/10+7æ745-0+@G1ãA8á8(B7 /F(B7zå6,é@+0B7> C7å6G1ëý
''ý AC5$G'ð ,6#5)6Ð0B7ï>?ò :0+òG úgû-&>úJô8/Q8ò ,65-70+):G9;(+7ê'&,6/@+0B<7= (?å6)G)ý /1>8@?0Bè<7 ,65)0B7ê:7(Â@+0BG'(+7>ì/10Ó0Bè87»æ"7æG:(B&»å6G)âJ/10+,éG:5
8?ý å6@oG)òkâJð'/1ñ+0+úÂ,6G'ï5ò 'ACòkúJG'û,65)úg0B74ô8>Ò2ò 0+7AG B/C)&9:/*ý <= @+0BG:(B7@?0Bè<7Ò,65)0B74ê'7(ã(BG:æ (B7ê:,6@B0B74( * /F00+è87Âæ"7æG:(B&
8ý'0+DÌè87zðFEgãúQG:(BïJæ ò 'òk7úJ):û9Kúgô8òG,L<7=)C,é@9:AC*G'<@+="@B, 8åâ6G'7'A<ý ,é74@=0Bè<7,65)0B7ê:7(ãk(BG'æ (B74ê',6@B0+7(H*Ò0+GQ(B7ê:,6@B0B74(I)ý =å6@+G
o'ý 0+Mz,é74ñ5-óOò 0?N<ûGFã÷úgò0+ó è87 ïò ,6:5)ò0Búg74ûê'7úJ(+ô8@ÂHò ,675 ):(+9C7ê'*(,6@B0+PQ7(B@R+* <=z/1@+580BG'>C(+7+ @S0B,6è85)0B7GÇ@Bá8(BæÌ7ê:ç1,é@+>80B,7K(R74(B) 758>8â477'ACç)7A858(B>8G),6>858á<ê â0uG'G:5;(à)PTá8G S 8'ý æ"bUVX0ñ 7:WZ5)Y[ô 0]W NÓë W],6ï0B\_òèÇ^'ýòkå~úJ/ ûC7åé@+úJGåô<ò 0+3'è8ç77zëceãè8G:7(BdZ(Bæ")g7j@ fmfh7)CS *L9;ijUBn[,:"!WZk#o[PJ!Wk49]+9 3l<`WZ<=n = WZ/Fo 8(58W 298>\/F^ 587ý â):è8=79Cå6@z@BGÌâ*aG:0B58è<PQ>87,60B-ãk,6G'G'<(B5C=æ"/1/Få6@2å6(B&Q7z70BACGQceG'@B0B@+è<d, ,C78å6@+7'fh02ý /10+*L7 i
8Hý 3'"!r ýk# !ûk4ö"3lïò<'=òkúg/Fû588> úgô87'ò 7ce"sk#dZ!);k4fp3l<-L= iq8("!/1k#58!âè8k474@3l<á8=Q58â/1G:(+758>8AC,6G'0B,6@BG:@+5o, 8å/16å67'å6&ý 0BGz0Bè<7u@+02/10+7æ745-0$ë,60Bèå~/ C7å
8'ý tûöò ïò :òúgûúJô8Gò 7<=>8G)7@58G'0+è8,658êoý
H/F>8è)>8á8(B@74@BA<@Bá874@J(B7,ý Yì0,6@@+027J/F/10B@+7&æ"0B7GQ5)0B0+@Q(2/F/158(B@B7"å~/1@B0+,67zæ0BA<è8åé7&?58G:â(BG:æ?5-/10+(Bå G:å@B@B0B02(+/Fá80Bâ70+æ"á8(B775)@0B@,é5),60+5-Gß:A8G'á<å6ß)(B,67 58êÒzý /F0æG:@B0z0Bè8(+77
(+>87J74/1Aoå6Y7,65Q0Y5<&->80BçFè<@â7G'G'æ"5o/1A8A8@+,6á8,éAoâ0B774æ"å6(B,6@58G),6/1>858(B7ê7å)G10Bæè8ãoG:70+è8(Bâ477uG'â@B,658G:0Sæ@+G10BãE(+A8á8/1å6,6âå6âJå80B/1,6A<G:0+á8758>Q(B@u7 @B/1Ç,65<58>â4A87ZâJ(+,é/10+æ"âè8è87Z,60B,658,6/Fß'êzâ70B@$GFáCão,6/1@_0Båè8/F(B7S@Bá<@+58>oá858/Fæ02,658/87ê>QýgH0+0+,éGè8æ"74o7(B77G1ã0BG:ãè8(B/77'çFA8@0B/1(Bè8æG:7ê'7:(âý/1G:Yæ@B5 0
ê:0+,é,éæ"ß:77'5 ý Y)&0Âæ0+è8,6ê'7Qè)æ0 C7G)>87ACå$G'âJ@+/1@B5Ì, 8å6G'75<0Båé& G?C7ê'Q700B(+/7J/1æ0+7G'>î(+7/1/1@â4â/1á85»(2/F/10BA<7QA8(B7G1@+0Bÿ),6,6æÒæÒ/F/F0B0B7,6G'GF5"ãuG10Bãuè<70+è8(+7Qá858758ÿ8,6/158âê"00B(B,6á8æ585<7 ,é)&5<ê
,6/F5@B@Bë,6ê:è<58,é,6â58èÂê=/1/ 5"+G'úgACóeõ 7N<(2/FòC0B0B,6G=G'5?74ß',67@ (+&C7A8,658(B,6êQæ"7,éÿ)0+,67ß'â7á8G'0+AC7>E7(ý /10B,6G:5Eç1/1å60Bè8G:á8ê'è0Bè8,6@$@B0B,6å6å',6ê:58G'(+7@E0+è87uâ4G'5)0B7ÿ)0
*
?
% -& :$)
)
+1 .
%
% +0&
?
&
?
%
?
+
+
+
+
6
?
+
*
CGû-úJG:û.z*)@ð'5)ñá8 0BB)èÐñ+ç ú 4èoúJ/Fñ+@QúJëôá8è<@Bú747>5Âûðâ/Â6'G:ú4æ@+ù,6æAo0B/Fè8A8(B7zå6,67Q58âêG:ß'@B/10B0=(+è8,~GF7/1ã5)A<07(2ß:/1GF7â4ãZ(B0B&?,60+âJè8å6/1G-7Âå$/F7ëS>Òâ7/F,658ê',6è)7>?580B7@Bâ40B>Ð&ÂG:(BG1A87ãá<@+(B>8027 , /FK0B77(Bæ"7æ"5)705)G)0>8A87(B,éåS@G:ê',éG:5Ð(258/F7'æè8ç<,6@Q@gëýè8(+Y775Òâ(B77gè<5)/1,é0@@
0Bæè<7g7/1â@BG'á<@+(B07@G1ãEá8/1@Bå67å)>ÌG'0+,65?è870B(è8A87(+@+,6æG'(+,60B0B,6,658ß'êQ74@å6,6,é0B5)7ß:(G'/1å60Bß)á<,é(B5<7ê/FG'(B587å6&0+è8(+77ê'5),6@Bá80+æ 7(BC7@S,6(@G1&7ã (B:GCúý' H2è<ð:7uûâöå~/F'@Bñ4@Bó6,6ïâJð'/Fô)å8ïê'G)/FG)58>8>Â580B74è<@B7@
5)æá874æ (Bê'C774@B(G'(+G10ãA8ú(Bù6G:úJûê'(2úg/Fô8æò@gûç <áðF8Egú0$ï'ãý(BG:Y5Qæ0+0Bè8è877@+ãG'7=å6A8å6G1(+ëG'ê:,658(2/1ê=æ"ëS@E7=0+@+è80B7uá8>85)&Qá8æ G:58C7å6&(0+G1è8ãC7zæA87á8æ"(+7 G'(BÐ&(Bâ7G:ãk@B70(B7GF5<ãEâß'7/1@J(Bç),6*:G:7á8& @
âG:æYAo5Ç/F(BG',6(B@B><G:758(Q@b0B/FGÌ58>?æÒ7/Få6*'7æ7G'745-á80S(æA8(BG1G:ß:ê'7(@S/1âJæ/1@(+(Bæ,67>?G'(+G'7á8(+07Jâg/1/1>o5 / 8åo767'ç(BëS7J/F7>8,6ëåé&Q,6å6åuâg/1å~å6/1â0+á87å~(/10+G'75î> á<~â@B7?ãý80BHè8/ 7?8å6/17 (+(2/g& ý
@B0B&)è<5)702â/FG:.ÿ @B0z7 G1ãS 0Bè8==7,6å658G-@+/10B>Ó7J/F@B>Q02/FG10Bã70Bæ"è8775)AC0 G',675)):0B749 (@B&)5) 02/F.ÿ=/17A@z$d ëu74V åé!åi /F=C@=ý 0Bè<â7âG'@+0B(+G'>8(+,6587ê@+020+/FGZ0B7G:æ"á8(75)âG:0 @B07 æ"G) 8>87åY9 ç
*7 â=,6@,670Y5)ëS0QGo0+ý (2/15<G1@Bëuå~/1740+ß',é7G:(g5îço,,6ã5)0B0BGÌè87QA8/1á8(+(+(27 /g&z,6ý@zH/1è<ââ7Ò74@BA<@B(B74G'>»ê:(2@B/F7æà)á8@75)0+G 0+,È/FC7å6?åé&)ç)A8,6(B07@+,67@=5)AC0B7G'> @B@+, â8åG'65)7020B/FGQ,65î>8G?ß'74/(B&»æãkG:7(Bë 7
@B>807/15)0+07æ@B027/F5)0B0+7@æ"0B7èo5)/F0B0u@=â/FG:(Bá87zå6>ë(Bo7,60Bz0+775?ÿ)7G'â45"á80B0B7è8>Ó7,é@5Q/1ACæ"/17=(2/Få6,6å658åé747'å ç:ý Y,é5?5G:G'(Bá<>8(u7A8((+0+G'GQê:(2@B/1è8æ G1ë >8ë7@Bè8â47(B,6(BA870B0B,6G:è8587z@7,6ÿ)587>8â7á<AC0B,67G'5 5 æ,6ê:è-0 C7587 C0ã(+G'æüAo/1(/1å6å67å6,6@Bæì,65"0Bè87èo/1(+>8ëb/F(B7 ~A<,éAC7å6,658,658êoçF,é5<@B0B(+á8â0+,éG:5Ao/F(2/Fåéå67å6,6@Bæ ý
? Ù!Ø :× LÜ [ $Ø JÙ!Ø Ö=0Ü ÐÙ 2eEØ L)ÙØ)× =Ø8Ù SØ [e
G10BDè<ãE747=00+è8å~/17=@+C7@0=/17æ"/1å675Q7uæ/1@+74,(+&45-(27'/g0pý)&,éþ»0+GF@ZãN7ò ä"'@2óÈ/g7ùB&å6ýF7D 0Bæ"èo/F7ù65)0ò0Bó0B+@è<%0B'7 G oC7ø(+ð:@B0Sò@BòkG:7ð'å6(Bû 70Bæ74 >E7ö ý 5)<0ûá8GFúg(+ãN0Bñõ:è8/°ú7@Bï(gá ð:ç-o/ñ/FòEF@B(B@+@+(á8G'/gæ(+&Q0B@S7SG10B0Bã è8èo7/F0G'7(å67æ,6@,67@/15)58,60+0BG:@@ 0B,6è8N<5Q74ú #(uAo6/1/1@+(+/1@B(275</g@g>& ý
Y58,60B,~/Fåéå6&)ç17J/Fâ2è?7å67æ"75)0uGFã ,é@S0Bè<G'á8ê:è-0S0BGãkG'(Bæ /@+G'(B0+7>Â@+á o/1(+(2/g&QGFã@B, &7G'587'ý Y5?7J/Fâè
öâG:158ïï@B70Bâ4è<á870B,6ß'@Bá7o/@B1á (+o/(2F/g(B&)(@÷/g&-/F@ (B7"7ê'ÿ)(BâG:7á8A8AC070B>îè87z0+G'å~ê'/174@+0u0Bè8G:758(7=@Bëá<â2è<èÇ,éâè"0Bèoæ/F0,6ê'7gè)/10 âèîC7=ê:@+(BæÒG'á</1A»å6å67â( G'58ç)@+/g,6ã@B0+0B7@(uG1ëãè<ç,é@2â/gè?&)ç 0Bè<7
@B@BáG:(Bo/0+17(+> (2/g@+&)á @o/F,65 (B(274/gß'&)7@(+,é&Â@ê'(B(+7G'><á8á8A»â7/1>Ó(+7ã(BG:æ YëbäÌ/g&Â0+G æ"7ä (Bê:7>?1ýCã(+HG'è8æ 745Â?0B0+è8G 7( ýCG'å6H7è8GF,6ã@zÒë/g/F&Â58> 0Bè8?7,é5)@á8@+æë,6C70Bâè8(z7G1> ã
7(B/174å65<7Ao>æ"7J/F0B7è<0B5)770B><@S@2åé/1&»,é5Qæ"æ"@+7G'G1A8(+ß'0B(B77G)@>?â740BG'è8@B(+@7Q>8,67@+@(gæÒ(Bý)74/FHAoåéè8å67J7/F7=@+0B0=è87>?7gGF/1ãbá8(B0+0S5)è80+G17Q,éãEåCè80+G'è87J5</F7=åé>8&â4@G'G'58G158@+ã70B(B@B/1á<á 0âo/0BFæ,6G'(B(G'5?/g@+&0,6@(+0+7è8æÒ7=@B/Fæ"è8,é5<(+7,6@J(B58ç1ê:*)â7S,éG:5<ã5)á8ê0258/1@Bâ,6á 580+o/,6,6G'5815Eê(+(2ç:/F/gëåé&)åCè8@0B,6è<â0BèG 7
0B,6æè<7ZA8G:å67á8æ"0BA<7á85)002/F&40BG',6G'58587z@g,6ç'5 /15<>Òý$Y/155C0B/1è<å6&)7=@Bãk7zG'å60Bå6è8G17ë,éAo5<7êZ(ãëSG'(+7=æÒA</F(B587@+â77=5)GF0=ã@B0BG:è8æ7@+77,6æ,6æA<A8(BG1(+G1ß'ß'747æ>Q7,65)æ"0B@A8G1å67ß:æ7(u75)0+70ÿ)/100BCG,6G1)58G'@g* ý
?+1 !1 &
1
=
)
+
*
*
)
$
6
'&
)
#"
#"
)
%
)
!
(
+* ,&'-
$&
8
)"
/.
)
*
)"
0&
:
'"
13254
687:9<;=7:>?+@9BA
AC9ED;=F GHDJILKNMEI!O9EKNA
Y5»0YëSGYëb/g&CG'0B0+G'æ á8AÓæ7(+ê'7@+G'(B0gçG'(*8(+,67Po&îò +ð0+ %?ûúgñõ:ú4ïð:ñòkço0YëSG?@Bá)C/1(B(/g&)@/1(+7
æ74(Bê'74> /10/Q0+,6æ7'ý)$)74>8ê'7ë,6â* +) çCA8A$ý / &EACG',65)0B7>ÌG'á800Bèo/F0z,é0,6@Z/1><ß'/15)02/Fê'7G:á8@
0B0BGè<7Z(B70ß:/17,6å6(B@@+7G1ã0Bè80Bè877G:@B(Bá>8C/74(u1(BGF(ãE/g7&)å6@7æë7,éå65)å)0+ãk@á858,65Qâ0+7,éß'G:75Ò(+&Q/F@b@B7/â4G'@B7585)>"0+,é@B5<á 7o/åF7(Bå6(7/gæ&-ý1745-H0Sè<@2,é@p/gß)ëb,658/g&êG:0Bè85877=æÒACG'/F,6ÿ-5),60Bæ74(á80Bæ7@+G10Jã ý
=0Bè<G17=ëS(B774ß:@B7á8(Jå60Bç$,60B58è8ê,6@@BG:æ(B0+7,é0+5<è8êG)æ> 7ë0+è8,6å6G)å>58G:,6@S05858G7â4å6G'75<@B@ê'/17(B(,6å6@+&»02/ (B8å746027'/1ý',65»þ»0+7è8A<7(B7G:@+(B7>85)70=(/zG1ã>8, 7Kà)74áo(B/F75)åu0S7å6G'7A8æ"0+,é7æ"5)0B, @g&JçE/10+,Y,éý G:7'5ý6ç
ëè8,6Yâ5Âè?/QA8(B5<7G'@+7(B(Bæ?ß:7/1@zå0+@B70ÿ)/ 08,CG6å6-,60YG:&*?/1A858(B>?G:ê',6(2@/F7æ ß'745Ò@B7æ"7:çG'7'(+7=ý êo7 ý6âç ),6çC7AE5)0ý 0+èo/15?/0Bæè<774(B(Bê'7ß:7z7GF(Bãu@/10Yå$ëuæGQ7@+0+á è8o/G)F>E(B(2ý /g&)@,é@
/1â4âG'æ"A8å6,é@+è87>,65/=å6G)G'Aëè87(+7=0+è87=@+æÒ/1å6å67@+0GFã0+è870YëSGè87J/F>8@,6@æG1ß:7>,65)0BGz0Bè<7=G'á<0BA8á80
&G:587'ç10+è87,65-ß:G'å6ß'74>Z,658><,éâ47@u/1(+7uá<Ao>o/F0B7>Q/1â4âG'(+>8,658ê'å6&)çL/F58>/F00+è87S758>QG1ãC7J/1âè,é0+7(2/F0B,6G'5,60
,6@0B74@B0B74>ëè870+è87(7,60+è87(GFã0+è87=@+á o/1(+(2/g&)@,6@7ÿ)èo/Fá8@B0+7>Eý =G1ëS7ß'74(Jç:>8á8(B,658êG'587,60B74(2/10+,6G'5
)
)
:
)
#&(
#
)
Y z£
sY k Ìîk Y "¤ '¥1¢g
8'¢g)}£¤ Ó' ¥1¢g Ó
'¥1¢g Ð£ s "¤ 8'¢g
ss Y Ó
'¥gg'Y " ¤ '¥1¢g ÷£ î
¢1¥ ')}B£ s Ó
'¥1¢g Ð£ s ÓY "¤ ¢1¥ '
s " ¤ Ó '¥1¢g
'¥gg' ÷£ î Y
o ' [QR+¯cBdeR+['WWk\vkU4lXzRBVBngRgº
G:0+758@Bå60+&Q@u0B,6è8@S7@Bá8ACACG'7@+( ,6C0B,6á8G'G'5?á8G1@gç8ã/1G:5858>Q7zâgG1/1ã5 0Bè8C77Zè8/g7Jß:/1G'><,6>8@J7ç8> 5<G')&0 CGæ"'0+G'èE(+7uç8,6âJ@/F(Bá87ACãká8>oå/F0BA87(B>EG:ý<ê'H(/1è8æ7(+æ"7ã,eG'58(+êC7'ý çG:5858G'7z0+G1è8ã7(S0Bè8ëb74/g@B&7
GF/FãE58>?@BAC0B7è877>85Ó,658ëê(Bá8,60BA70+/è87=@+7A<Ao(B/FG'(2ê:/1(20+/F7æ â4G-,6@S><7z0BGãG'â(è8740+â2è8*"7A80YëS(B,6GQG:(Ao0BG:G@B@+0B, è8<å7é7å6G-âJG:/1AQ@+7ë@Jý è8,6âãkèQ0B7G1(ãE0B0Bè8è<,67Z@=0,60/1,6,6å6@@,é58@SG"@Bæ?åéG:58/1å6ê'å6747((
58?G74:â7(B7@B@G1/1ß:(+7&î(Jç)0BëSGÓ7Z0B/F7A8@+0QA8å6ë& è8)770B><è<ê'77(ë0+,6è8â7* ) @S7458(B>îá<åé7GFã=0B)è8ç)7"A$@Bý á o/F(B(/g0BèC&»/1ë0S,é580+Gè»,60B58è85<7"7(uå~/1å6G)(Bê:G'7A"(@B0è8/1G:,6á8åå6,6>@7(+ß:7J/17(âè877458>E> ý
ë,60Bè?/3á8æ"AQ@B02/F0B7æ"75)0Jý)Hè874@B7,é><7J/1@=/F(B7z,6æA8å67æ"75)0B7>,65 $,6êoý /1@Sãá85<â0B,6G'5 ý
GF@+á ãuo/0BY1è85 (+7Q(2/g(&)/1@J58/ý ê:k?7QãuG'0B(Bè8(z7à)7Q58á8ß'G:,6(+/F0J7ýåéá<>E7ç$G10BGFëuè8ã 77ß:(B77(Jãkç$7(B/175Ì5<â77å6 7æG:á87,60B5)@Z@+0z,é(+><7J,67@z/1> /158(B7C7(ß'/g74& ã(G:?(Bá87Q@BâJ740+/1>îè85 7Q, C7ãu0B÷7,60z@+/g0,éß:@ëG'ã,6è8(+>8G'770+æ > è87)&58( Â7,6@+0BG'è8(+74 0B(,658G1,6ê?@zãG'0B0Bè8è8á8770
o(+@B0uä 7å67æ745-0+@u/15<>Q0Bè87(+7J/gãk0B7(,658@+7(B0+,é5<ê0Bè87å~/F@B07å67æ"75)0,65)0BGz,60B@A8(+G'AC7(SåéG)âJ/F0B,6G'5$ý
S7å6&7æ"<,7é5)5C0u/1(Bæ"&ÓG1@Bß'7J7/F@(Bâ/1èÐ(+7z0B0Bè8G ,6@C7(+Z7à)><á8G',658(B7'7@ý G'58å6& ~å6G'ê M ä zâG'æ"Ao/1(+,6@BG'5<@JçE/Lã0B7(ëè8,6â2èî/F0æG:@B0ä
á8@+7@âG'â5<G'758>AC@+@+,67á>858o/7>8(1,658(+0+(2êQè8/g7&)G:ý 5ÒâJY/F50+@Bè87Q0+7è8ë7 (+è87Cå~74(B/1(B@B0B70,6ß:,60+7Z58è8587G:74(B(0>8/174å6G),6(=åG'G1G1AzããGF0B0Bã è8è877 02o/1(B,6@+å6@J0çJç)/@B0+á è8âo/7G:(+1æ7(+(2Ao/1/g/F(+&Ì7(B,6,é@B0Y@G:ëu5ZåÈGQ/F,6(B@$@+ê:&)Ao7æ(z7(æ0BãèoG'74(+/F0Bæ5»(B,67â0B>èoâJ/F0B/FG=0@B7><G1@g7ãýâD0B,6>8è87770
ã7(+å6G'7æ"æ 7ë5)0è8â,6â2G'è»æ"@+7á @$o/ã(BFG:(Bæì(2/g&»0Bè</175»@B774âåé74G:æ58>75)@+0zá o/@Bè8F(BG:(2á8/gå6&)> ç'/o7"0B74æ@B0SG1,éß:@p7Ao>Â7(0BãGÓG'(+0Bæè87"7>QG'á8/10p0+A80Bá8è807&7G:5<58>Q7Ò0BG/F58@+7>E7=ç,, ãoã0+0Bèoè8/1,6@0
@+á o/1(+(2/g&",é@74ÿ-èC/1á8@+0B7>ÂG:(58G'0gý)Hè)á8@Jç<0Bè87â4G'@B0GFãG'587z,60B7(/10+,éG:5,6@ oß:7ZG:(@B,6ÿç8A8(+G1ß),é><7>
! " # $ % & # ')( * *'+( " -, $ /. !')( * *'+( # $ 0. 1
.
"
'
'
''& " #2 3 2 !')( * *'+( # , $ /% 3 2 ')( * *'+( " $ 4. " 1
.
#
'
'
''& # #2 5
687:9 #;
3
%
P
%$
!<=A?&@>=
)
=
)
#&
+1
G
)
)
<>=?&@>=
DB CB4 )
FE
)
"
H<>=?&@>=
)
0BâèCG:A-/10z&),6Ao58G:êQ,65-0+è80+77z(B@7å67/1æ(B77á85)@+0+7@>»0BGQ,6580B@Bè<0+7Z7J/1G:>Ìá80BG1A<ãbá8/F0'(B&(/gG'&Â5<7âá8,6@(+@BoG'ß:(+7@Jý ACY75 (0+7è8å677æ@B7475-âG:0gý58>qc!k#%Yå6G)G'AÂ0+è87â4G'@B0G1ã
@Bæ74â,6@+G'Y@B585Ð,658>»ê=7J@+/F/1á â2å6o/èÐ0+G'Fê'GF(B(274ãZ/g0B0Bè8&Óè<77,é(g@zý1H~@+å6è8G'è8G'ê 7S(+M 0BG1ä7ß'(7(0+æ"/1èoå6/1å)75Ó(Bâê:G'0B,6@+58è80ê7 âJ/1oACá8(B/1@+@+@B07@+> 7@B@á )&o/0+è810B(+7è<(2(+7/g7Â@B&Â7,6@G:@+(=Ao/170ëâ4,Èè8æ/F7å8G'(+æ7Q@+0740Bè8(BG:ê'7Q58747?@@+7,6æâ@$G:7A858(+(B>ê'G:7?Ao@+G:áë(Bo/è80BF,67G:(B(+5o(27Â/g/1&Óå)0Bè<0B,éG 7@
ç)ëè8,6â2è?,6@ ä 4ý Y5½/58G:(BæÒ/Fåoâg/1@B7z0+è87@Bá o/1(+(2/g&)@ o74,é5<êæ"7(Bê:7>Â/1(B7zGFã0Bè<7
ã@258G:/FG:(æ(BæÒ/170/F@+å,æ&æ7'G'ý7@+(+0þ ê'èC7è<@/17å 5,6ã=@=0Bâ4âè8G'å67J7?58/F@+7(B,éå6><å6&?77æ"(B58,675875)ß'ê?0B74@Q(Z0Bè<,6æ"75î@BG'7"7g(+/17Z58âG'0+èÐèo(+æÒ/1æ5Ì/17å(+ä ê'æ",6587(BêÂ:ê:ý87AoH@z/F@Bè8G'@g7458ý (Bå67&)<ãç8á8G:0+(B(Bè80+7'è87çN70B74(Bè8ÿ-æ"70+(2G'G1/?(+ß'7'70+ç(70B/1@Bè80zå6å7?,6â@z5)G:58@Bá80z7æ ââJ74C7/1@Bá<@2(/F@B7(BG1&> ã
)&AC7(Yã0+G:è8(B7æ?58/1G:58(BâæÒ7z/FGFåoã æ"CG7'(B0Bê:0+7G'@Sæ,é@ á8CGA"'æá<587>8(+ê'77> @+G')&(+0,é@ :ä :åéG:ä=ê å6M G:äê ä kä ký<ä HýG@Bá<æ!á8A$ç)0Bè87 +pð'ñïò 0 Fïú
M
*
)
-
)
% E
132
9EF$K
;7:>?J@#9EACA
9BD;F G+DJIKNMBI!O 9BKNA
1G0B<G ãG'á80Y~ëS((å6G' Goëêç/g@+& ä á 1oGo/ç<:1ë(+0B(20+è8/gG'7&)æ (B@7QYá8,6äÓ5ÌAQ>87Jæ"7/158â7è»(BG:ê:0B7æ7@B@zG:740B(B(Bè<0Jê'ç)77:G:ý@B(uH,&@+è87,6æ,6@zG1ãA8(Bå670B& è<>87á<ð â,6758@Qñ A80á80B+è<0z$7Q/1@5-ûá<7Júg/Fæ ñ(Bõ:o7å6,6ú7ï(z(Jð'ý,GFñ4Yòãb5?ç:Aoæ0B/Fè87@B7(+@+ê'7,6@z7æ@pãA8(+ãG:G'å67á8æ æQ(Jç)74,65-åé58G:0@+ê/10B0+M 7J,é/FäG:>5
G17ÿ8ãS/1ãæ"G:á8A8"( å6Y7'ëbç/g0+&"è87æè87(+7gê'/17>8@,60zâ,6G'@=á<,6åéæ> ACC7G'(+02*:/F75-A8000+,6G 5îo/?58>ÌA<(B0B,6G'è8(+7,é0Yæ&Ì,6à)58á8,6æQ7á8á87æüã(BG1G:ãSæ 0Bè8ë7è8ã,6G'âá<èî(Z0+è<è87J7Q/1>8@Bæ?@ã/1/Få6å6@B70g@Bý 0z87G:å (
7@2/Fæ"æ75)70Z@Bá ,6@o/F/1(Bå6(ë/g/g&&)@=,6@(B,67458æ@B7G1(+ß'0B747>E>Óç,é/15)580+G>»0+/gè8ã70+7A8((+7J,éG:/F(Bâ,6è 0Y&Q(+7à)æá87G1á8ß'7:/Fý å/"(/158â70+ëü,éâg/17åEå6774æ"ÿ-AC75)7(+0 ,éæ", ãb75)/10B5)@g& ç87'ýãêo(BG:ý6ç:æ 0Bè80BG:è<@B77
âJA8/Fá8(B(+(BAo,67G:>Ç@B7zG',6á8@u0 /15Q-&Óá<58.°G'/F(+02>8/734(B/174,6>Ò587å65»,6@B0g7ç'074ß'/17åY5"ý 0B è8BçG:á8,658ê'>8èQ,6âJë/1,60+0B7èQ0+0+èoè8/1,60@u@+0B0Bè8(+7 á8âC70Bá<@B(B07z>o0Bè8/F027/?5)@+á80Bæ (Bá<o7â40B(á8(+G17"ãE7ãå6G'7(zæ"0B7è<5),é@0
â@Bè<G:æG1ëîAo/F0BèC(B,6/1@B0G:58/@ã /Fë@B,é0+å67å8(,658,éæ"â4(BA87J/Få67@Bæ7ãk74(B5-G'0æü/10+,é/ G1CG5',6á8@E0SG ä=<02å6/1G:,6ê 58M 74ä">0B, ãoG /A8 '(BäG:ê'å6G'(2/Fê æM ä@Bý 0Y/15Q0B7S0+è8,6@E7=á8A8@+(+77>Q@B740B5-G0S(B7Aoæ"/FAo77æ (SC7ëS7(
0Bâè<èo7/15<(+ê'77å~/1> 0B,6/Fß:â7âG:G'(B(+>8>8,6758(zê:G1åé&Qãu0+ëè8è<7z7ã5ÂG:á8/(=è8è<7J7J/1/1>?>8,6@g@çCá8,é5<AC@B>o0B/17g/10+7>Ì>EG1ý ãá8@B,658ê?/Q>o/F02/@B0B(+á8â0+á8(B7'ý$Hè87@+02/F0B7,é@
ë,6@è8@B7è<(+G'7z@(B0+0B,675è8(70Y0Bëu5-èCGá</1æ 5Qëo70B/gè<&z(p7=æG1G'ãE70+(+è8æê'7774(+@+(B@JG'ê'ý:(+74H0J>ç1è8,6@B7=5á âo/7JG:/F1@Bâ(+0SèQ(2/gG1æ&)ã@u0B7è8,6(+@74ê'@B,6å67z587@+ê=@B@ACAC0B7/1èoâ@B/F,~@/15åC0+è8ãæG'7á<(B747((Bê',6G'74@_(g@/Fç),60,e@ãCæâãG:å6G'7Já8@+/1(J0E(+ç:å6G:&0B58è8A87u7z(+@+G'å~Ao/1AC74@+G'0â(+,~@B0B/1á ,6åCG'o/æ5o1/F(+7å8(2(+/gê'0B&G 7
0Bè<7@Bá 5<C/
G'1 (B(Bæ?(/g&)/1ç8å$@=ëæ/1è8(B,677â(+è?ê'G17ã,é@ 0+ê'è8G)7z7@ä@2/F0Bæý<è8H(+7=G'è8á8@+7,ê:&(+è7'7ãý G'ð(+7'çCñzëusö 7zN 1âïG:ú458ï âE75),65 0+(2/10+èo7/1@+G:"7 5?!+0B#ç è8!H7S5<G'U(Bæ?$ /1åC$ æ$ 7(+^ ê'ç)70+@è8ë7è<775<(B> 7
G1èo%ã /gß:!7=@+7á å6o/7æ"1(+7(25)/g&)0B@S@åéèo7ã/10J@ ýC7èC7/15Ç@B7 (B7J/F(Bâ7è8><7á8>Eâç70+@èo0B/1G 0â,6G'@ A)&),6&58ê!,65G1ãë0Bè8è<,67âè@Bá 0+o/è817=(+â4(2G'/g&)@B0@ GFC7ã0+,6è8587zêÂ,éæ"5<5877(B(Sê:7åé>»G)G:@BAQ0+,6,éåé@ å
oß:7ZAC7(7å67æ75)0g'ý èC/1@B7 ,6@/0YëSG Yëb/g&Qæ"7(Bê:7'ç:0Bè87z,658587(å6G)G'A"G1ãëè8,6â2è"âG'@+0B@z/10SæG'@+0
@B/1,6â4ÿÂâG'ACæ"7(A8å67,éå6@+7è8æ7>"745-7 0gâýD,67705)0Bá<å6&)@ý 58G1ëìâ4G'58@+,é><7(è8G1ëü/0+è8(B747 ë/g&Ìæ7(+ê'7'çC,Yý 7'ý6(ç _èo/1@+7 âg/15 C7
0ãB/Fè<@B7è8Y@+,65îG'á 5$o//?ý1H0+(+è8(2è8/g(B7&)74(+7@ 7 ãëC7G:(B/g,67'&»58ç:êQëuææ"7p74(B>87ê'(B77ê:@Bâ470B(B>?è<, o77,é@(B7Âè<@Bæ?7/1(B(+/177 å6å6G:7ò 58N8@Bå60gñ+&Zú2ý ú 0+è8åé7Så$1ï0BâJè8ú/1ï"74@+@B7u>87ë7âJACè8/1774@+58(B77S>8@z,60BâJ58è8/1êÌ7S5 02G'/FC75»,éå)ëGFèoãoè8/F0B,658è8â>8è»7Så670BG1>?è<ã,é,6(+0B5Â>è<7/Q@Bá 02@Bo//F,6æ"1,6åé(+@,é(2å~/g/FG1& (ã
,6ê'@u,6ß:@+7æÒ5?/F,éåé5 å67($0+,éêCèoý/1Q5"/F0Bè8@=7/ G'<å0Béè<G)7â(*0Y><ëu,ÈG/Fê'02(/1/1,6å6æ @Jý:ýFHHè8è877 A88å(B6G:G)ê'â(2*-/F@æ ëã,6(20+/FèÒê'â4æG'58745-@+70â0á8/10+*),éß:,6587ê5)âJá8/Fæ (B7zC7G1(BãE@0+è8@+è8,6@uG'á8âJ/Få6> @B7C7,é@
A8å~/1â4DN77>Â*0 A8)è),ç &)+@Bç8,6âJ/1/F5<åé>å6&Q)Q/gã>80+775<(G'7J0B/F7zâ2èÓ0+è8G'7z0Bè8è<7J7/1(><,6@5ÒG10+ãè870+è8o7 5oo/F(BåE@+A80Jç<(+G'@Bê'7â(G:/158æÌ>Eý çC/158>"0Bè8,6(B>"@Bá C/1(B(/g&-ç)(+7@BAC7â 0B,6ß:7å6&-ý Y5?0Bè<7ZA<(BG'ê:(2/Fæ 0YëuGQ,65)ß'/1(+,~/15)0B@u/F(B7æ?/1,65)02/F,é5<7>
)
H*
8
*
-
@
)
'&
)
% -
)
)
E
?
0 1 )
+
@
)
» ¤ î Y ' ¥1¢g î
¤ '¥1¢g
O
'B} £ Ð Ì Ì
' +} £ » Â
» ¤ '¥1¢g » Y "¤ '¥1¢g
'¥1¢g
Q¤ '
'¥1¢g S "¤ '
£ Ó Ì
£ Ó Â
»
»
"¤ '¥1¢g "¤ '¥1¢g
¤ ¥
¥
o8 [QR+¯cBdeR+['WWkm:VBRRBvkU4lXzR+VBnJR_m-R+[÷Wkm)RS{eUJjYWSjk`')UVYVBU4lm)UJjSWkm-RjYXzU4{|eR2jYWSWYU4d|{~º
'8ýSýSA8A8(+(+,6,6G'G'((0B0BGQGQ0+0+è8è87z7z77ÿ)ÿ)77ââá8á80+0+,6,6G'G'5Â5ÂGFGFãã 8å8å66G)G)ââ**M:çç )) n o ++ç8ý/F58>
)GQ0+è87G'á80+âG'æ"7ZGFã0Bè870+7@B0+@,65 8å6G-â*)@ /F58> >870+7(Bæ",é5<7@=ëè8,6âèÂGFã_0+è877å67æ75)0+@
)ç+QG'()Q,é@0+G C7zæG1ß:7>0+G0+è87zG'á80+A8á80'&G:M 587'ý ã0B7(0+è87z0B7@+0âG'5)0+(BG'å@+ë,60Bâè87@0BG 8å6G-â*
0+0+ 7è8;@B7z0zç G',6á85 )0+ç A8 á8M 0''G'ç:&!( G'G:( 58 7' ý ý8:ý%HYè85"747J(B7/1ãâG:è(B7'GFçNãE0B0Bè8è8774@Bâ7 G'<å@+0zéG)G1âã*)0B@ è8C7ß',67=58@+58027/F(0B7å6æ"G-G:7AÂ5)0B,6@u@=/F@+,é(Bÿ?7=74ACÿ-774(=â74á8åé0B7474æ> 7o75)0=ãG'æ"(+7ZG1ß'/z7>?58740+ë G
0+0+è8G»7@B(BD&)774æ/F0(Bæ"á87 @70Bð (+o &-5oñ ç$/1ëuå6å61&»7?ïú4@+âïZ0BG:á8>858>874@B&Ð,6Ao>877G:5<( 58>8å6,6&î58èoêQ0B/Fè<G'@B7Â75?âJÌë/1è8@+ë7Â,6âè8èë74(BGFè87Óã7(+ã0BG'7 è<á87Z0+(Qè8@+á7?@+áo/å~o/F/1F(B@B(2(B0"/g(2&)/g@B&)@á @?C/èo1/F/1(B@u(B(7 /g0+è8&îo77z,6@Q,6@B58æ?7ê»ÿ)/1å6èoæ"å6/F77@Bá8(B0@Bê:0+077/1>E> ,6åYý ý C=(BG1@Bá8ë0g7 ý
5)á8æ 8åD6C7G)740â2(B*»),658ç ><ê+,È/Fç,é5<ê')(>8çJ/1/F,6âJæ 58/1>0+ã7*zG'@=(>8/170Bê)è<5</1,éG',6@50B7SAo0+0B/Fè8è<(B77u0B,6G'âè8(+á<7g>8åÈ/17/F>8((@GFãkG1ãG'ã8á80B0+è<(( è8 7 7ë8åãk/gG'6&»G)á8â2($æ*)@B@7á (+,6o/ê'5F7Q(B0+(è8,6@/g7 &-ê'@go,6ý 5Cß'Y7/155Çå0+A8è8,6(+5 7G'ê'A8$((+,6/1G'êoæÌê'ý (<ý/1ýæHãè8(7/1ê:8åæ6G-7â5)* 0
GFã $,6êoý 0+è87ãG'å6å6G1ë,658ê,65)ß'/1(B,~/F5-0+@u/1(+7æÒ/F,65-0/1,6587>
88'ýSýSýSA8A8A8(+(+(+,6,6,6G'G'G'(((0B0B0BG""G"G #'M çç /1)) 5<> n o +Ò +?/Fç58/158)> >) n ) n+n /F*58*ç > ç8/1) 58> o *ç
oýSA8(+,6G'(0B"G ;; /F58> ; ç ) o +?/158>> ) o *ý
*! * " # . ')( " $ /% ,
$ /.
'
,
!
*')( $ /. '
,
( '
( $
?
.
0
)
)
'
* *')( 1 /. .
3
687:9
1
( ')( # 1 /. ( !
)
)
G
s » Y !¤ » '¥1 ¢g î
Â ""¤¤ ''¥1¥1¢g¢g ¤ '¥1¢g ! " # $ *.
. &
$ *.
% &
$ *%
. &
' }Ì£ Ó Ó
î "¤ '¥1¢g
'¥1¢g S "¤ ' £ Ì Ó
î
"¤ '¥1¢g Ó "¤ ' ' B}Ì£ Ó Ó
î "¤ '¥1¢g
'¥1¢g S "¤ ' ' £ Ì Ó
î ÂÓ ""¤ ¤ '¥ ¥1 ¢g ¤ '¥1¢g ')( *
" $ /% ,
$ /.
'
'
-,
$ /. &
,
( $
( *
.
( *
. & % &
')( 687 9
3
O
')( OYO
O~
O
')( , '+( ' ( $ %
$ % & ¥
C< [QR+¯°c+deR+['Wp]È\4`'VYvkU4lXzRBVBngRm)RB[Wkm)RS{eUJjYWpjk`'-U4VYVBUlm)UJjWkm)RjYXzU{|eRjYWWYU4d|{~º
,
( *
. &
'
! '
#
$ .
( , '+( '
$ %
! $ % & $
'
$
$
( ! '
#
$ .
,
')( *
" $ /% ' } £ » Ì
» Y Q¤ '¥1¢g '¥1¢g Q¤ ' £ Ó Ì
»
Q¤ '¥1¢g Â "¤ ' ' +} £ » Ì
» Y Q¤ '¥1¢g
'¥1¢g Q¤ ' ' Q£ » Â
» ÓÂ "?¤ ¤ '¥ ¥1 ¢g ¤ '¥1¢g O
( *')( *
$ . & $ /% &
O
! O
ã-ç0B7(Q/Óç 0B7 @+0Q,éçN5 G'( M ç ço ëçè< 7 (B7?ç /15Ì#)ç 7 å67;æ; ç$75)G'0(",é@z;æ""G1âß'G'75)>Â0+(B0+G'G?å0B@+è8ë7Q,60BG:âá8è80B7A8@"á<0B0 G &4G' 58; 7ç /F58->sç/F58'G'ç0+è87'ç(
0+7/F@Bâ0è»,6@S0B; âJ,6 æ/1(+7Q(B,67;B/1M>?5ÌG'7á8å670æ@+74G; 5-0+0èo,é/1@0S020B/1è<*:7°75Ì/ oGã1(+ß:G'7=æ ,65)0+ß'è8/17(+,Èå~/F/F5)@B0B0z@@Bè8á G:C/å61> (B(C7/g&-ãç$G'(+,Y7zý 7'0Bý6çoè8ë7zè<58775îÿ)00+,6è80B7Q74(2â/1G'0+5),6G'0+5(BG'@+åS02/F,6@(B0B,6@g5 ý
758 å6747âæ"7G:@B7( @5)/1 0(+& ;,é@p o7ç02/1@Bã,6*:G'ÿ?7(+57ZG'(ã@+(+02@BG'/F7æ (Bß:0B7,6/F5»585)êQ&@B00+G1/1è8ã0+770Bæè8587747ÿ-5)G'00+0+@Zè8,60+7æQ7((2á</F@+á0B@B,60 o/G'C715E(+Qý (2/g7&)ÿ)@J7ç:âG'á85<0+7åé&>»o,65ß'7=/1/F>8>8><>8,é0+,60B,6G',6G'5Â5C0+/1Gå)@B0B0è</170B740+æ7@B70g5)ý 0Bk@Sã/1/F(B5 7
)&Ao/F@B@gHç GG@B Sá8æ U á<$ A, $0Bè8 7S /$ CG~å61G'ß',ê 7E_âJä,eã/Få60B^âè<á8ç)7/1å~/1@B0S0+, &æ,éG:7=58G'GF@J@+ã0ç40+0Bä è8è877pâæ
G' 74@+;(B0Eê'G15874ãG:>Q(B/SæÒ@B58á /FG'o/å)(+FæÒæ(B(/17/gåg(+&-ê'ãk@pG'7á8@,é@ ((/1 ë(+ 7=/gý âJ&=Y/F5Qæ"(B(B0B7,6è87(B7 >"ê:7:G'0+,6á8@èQ0poGæ@B:Gá87(+580Bê'è8>8,67587,6> ê(
0+/FG'åéå$02/FAoå/1â@+G'@B7@+@z0=,6,6@@ :ä'ä å6G'ê kä ä ý8kHä è<ý 7(B)7,6ãk58G'â(B77:ç0Bè<0Bè877ââG:G'@B@+0z0=G1âJã/F@+á8Ao@B77â4> ,È/F-&å"æ0B74è8(B7ê'7458@=G'(+,6@=æÒG:/158åCå6æ& 74(Bê'kä74@çCG10Bß'è877(
+ð:ñïò 0FïúzAC7(ãG'(+æÒ/15<M â7zG1ãEãkG'á8(( ë/g&Qæ7(+ê'7@+G'(+0u,6@ 'äå6G'ê M ä ä ý
ÐGFã ,6$æ"$,6,6êoA8êoýå6ý7<æ"ç7/10Bè<5)580(B> 7/17"0BQ,6G:ß'>85/174(B,6@B,~@â/F(+5-/ , CG0+C7@'Qá8G10B0ã è<7$,6ãêoG:ý á8åé<,6("58YçEë74/1@/g58G1&>»ãæA<0+è8á8747Q(B(Bê'7 0Y74ëS@BG'G (+Yâ0=ëbG)>8A8/g7'&Â(+G'ç<æ"ê:â(2G'7/1(+(Bæ(Bê:77@+G:AoGF58G:ã å658&?$>8,6,6,é58êo5Óê"ý Ao'0B/1ý G(+-=0Jãý G:5<-á87Q(uá8âß'(G'/Fá8/1(Bå6â,~>»/10+áo5)ê:/10+G @ å
âJ/:/Fä=@Bå6â0Bå6G:74á8êAÌå~/10+ã"ä á8,éG:(B 580+è8@7@+(è8ä /FG1458ëüý >Ì0Bëèo7/F58(B0,6â0B7'7Q0+çè8/"0+7?è8A8ëu7(BG:G:ACê'(B7@B(2((0 /Fã æG'âg(+/1æÒ@Bã7?G'/1(z5<âG:7â,6æ7Qê:è-G1A80(ãå67ë7ÿ),6,6/gê'0Y&?è)&?"0 æYG1ëãz7/g(+7&Âê',6ê'7æè)@+G'"0 7Y(+(+ëb0Jê'ý0/g7&Ó@+G'/1æ(+â0*$7 ,6(+G:@ ê'57 Y@+0BG'è8(B/F70Y07,6@5)å67Jß'/1C774@+åé0G:å6G1Ao,6ë 5 7
0+ê:è8(2/17G'æ (+&M æÒ /g&Â@Bá<,65)Aoß'7/1(+å6,6,6G'>o(z/10+0B7QG"0B0Bè8èo7Ó/F0=@BG1,6æããA8G:å6á87Q("âYëG:@B/g0Q&æ"æG-74><(B7ê'å 74@BG', ãZ(+0J0Bç è<8á7Ò80=A<(B0+G'è8ê:7(2/F@+,æ &4758GFGÌã_0+å6è8G'587ê:(B77( @+á8oå60B0B@",658,éê5ÇA<0B(Bè8G7 A8(+G'ê:(2/1æ âJ/1âè87 4ý8Hè8,6@,6@B@+á87,6@>8,6@Bâ4á8@B@+7>Â,65?0Bè87ãá8å6åAo/FAo74(Jý
EØ8Ý EÖp× [
z!Ø -?
Û Y!× H>874GÂß'70+å67G'@BAC0"70B>Âè87?,65?0B0Bè<è<77G'(+A87(+0B7,6âJß)/F,6å=G'á8A8@(+7@B>87â,6â0+0B,6G',6G:5858@g@Qý <ëuG'7?(èo0Bè8/g7ß:7@2/1,6æ*:7A<G1åé74ãæâG:7æ5)0BAo74>/F(B0+,6@Bè8G:7?5?æëu77(+ê'èC7/g@+ß'G'7(B0Q/1å6A<@BGQ(BG',6ê:æ"(2/FA8æå67 @
æ"0+è8775)ã0Bá87å6>ÌåAoß'/17AC(+@B7,6(gG'ý85<H@Zè8GF7zãb@Bà)G:á8(B,60+â,é*)5<@BêQG:(BA80(BG:/Fê'58(2> /Fæè<7J@S/1,6A8æ@+G'A8(+å607æQë7è85)G'0+@+77Q>Qæ,6587â0+å6,6á8â>8á87 å6G'á8@z/15o/Få6&-@+7@/1(+7Qê',6ß'75Ì,65
'ýS0+0+7è8ÿ)70 CGæ-74G:(B*Âê'70YëS(BG:G á8Y0Bëb,658/g&7'ç<oG@B:77:0B0Bç8G:7'æ ý êoYý6á8ç A?)æç8A$7ý (+ê'7@+G'(+0Zëè<,éâè /gß:G',6>8@á85<587â7@+@2/F(B&»âG:A-&),658ê 6ãG:(
8ýS7,6æâA<4,éåé74745-æ075)0YëS02/FG0BY,6ëbG'5?/g&?á8æ@+7@Q74(Bê'/1(B74(@B/gG'&)(+0@Jço//1F58@B>î7>»/FG:ââ5»G'(+0B>8è8,67Q58êÂæ"0+7GÂ(Bê:0B7è8ã7"á858@B,6âæ0+,6A<G'åé5Ì7ê'â,6G'ß'@+705Ìæ",65 G-><$7,éåêCACý 7(Y$ãG:H(Bæ"è8,6@@
8ýS0Y@+æ"ëS7ß'G-G7><Y5Óëb7å/gG'0B&z(è8æ"7,6@,6ê'7ß:è)(B7ê:0(B7@+,6@B,é58G:G:@+(B5?0B0E(BAoG:á<A87â(0B0Bã,6,6G'G'æ"(+5<æ,@&47@,é5?>o/1,6ß'0B@7z@/ G:,6oG58(15<@Bß:7,67'ÿ(ç å6,68áG-588G:@+0AE0B(Bá8ý á<@Bâ,60B58,6êG'5<Ao@G:,6,é5-5?0+7,60B(B@S@ ,658=58â47â(G'(+å6>8G-G:,658AEêzý 0BGzG'á8(âG:@B0
o8ýSýS7,60Bâ74(24/1,é740+,65-ß'07ÂãG',6æá<"( A<Yëbåé74/gæ&7æ5)027/F(+0Bê',6G175»@+G'(+G10=ã/1à)@á8>8,6â7*)ß:@B7G'å6(+G'0AC70>Â/1*',6745 5Ð¼ã7(BâG:0Bæ ,6G:5 0+è8<7 ý 8çoG8á)8G'0*Çá<G1@Bã ,658¼êQ7>8ACê'G'74,65)ë0B,é7â(+* @ )ç
8ý CGA8/F58A$'>?0+ý 0BG'>8æ ,6ß- ,6/1á<@+,é58AÂG:> 58è8@ 7J/F-&A8@B G:(Bë0Q,6/10+èÒ@z>8@+è87@+, ãâ0B(B@g, C7ý > -& /1(Bå6@+@BG'5 Bç 8á<0(B7J/Få6, &4,é5<êÒæQá<åé0+,6A8å6,eâJ/F0B,6G'58@
/F(Båé(2å$/gæ&Â7/F(+58ê'> 7@+/"G'(+ëu0=G:A8(B(+*ÂG'ê'/1((+/1(2æ"/g&)@çoèo/F/g58ß'> 7(+0+7è80B7á<(B@5»/1æ/7ACãG'á<,65)580Bâ740B(=,6G:0B5oG?/1å60+,6è80Y& 7)@+0BG'è8(+70B&Ì7>Ì/1(BG'7á80+âJA8/1á8å6å60g7ç>Âëëè8,6,60BâèÌèÂ/1,6@Z5Â74,6,é580+A8è8á<7(0
GF0+è8ã_70+è8775)0+0Y,éëu(+7?GâJ/F/1(Bå6(2åS/g&)0BGÌ@zG10Bãè87"0+è8@B7G'(+âg0B/1,6å658åYêÓý8Hãá8è8587â4(+0Bá8,6G'585E58ý ,658=ê"74580B,6âæ7'çp7z0B,6è8@=7?æ"0B7J,6æ"/1@+7Qá8(B@B74AC> 75)/10Q@0B,é5»è870+è80B,67Âæ/17zå6å60+G)GâJ/170+ÿ),é7G:â5 á<0BGF7 ã
)
?
0 :1
*
-
"
,
, $
%
)
)
!
#
.0
?
?
@
1
:
#&(
$
#
1#&
+
.
& !
-
$
+
kj d R Ã~XZWYRR+1VBWkng8R\1jY\\q-VBWÄÃ6deXWT'VB\4\vigRU-l Ä Ã6T¼Wk\4d|['\WYvkR+VBU4jBl ÄÃ6T8]~\4\4`'d|['VYWYvR+VBUjBl Ä Ã6degWY`'RBdeVBcUgq'WkjYdeig\RVBWÄ m-RU4T-jY\4VBW
WkdeXzrRzxJXzx$Ã~RXzxJXzxgjBx jÄ Í4J$JJgx x w ggx w ggx wCJgE:rÍr2x Egwgx'Íxr ÍNJ Jx
cXz\J\XigT-R2jj rr Í44JxJx$JxJxxgx ror g4JxJx$JxJxgxgx rCr JgxgxEgxgxgxgx r 'Jxgr xE1xgxJÍx wCr8xx1ÍFEr rCr 'rxrgr2
WkdeXzw4RzxJXzx$Ã~RXzxJXzxgjBx jÄ r gJ$gx Í ggx ÍFgrx gE:gr2x w4 Í4J'xr rJrw rox::r2r2x
cXz\J\XigT-R2jj EEggJxJpx$xJr xggxw EgÍ4JxJpx$xJr xgFxr $JÍgxgxExgr xgFxr r LJxgw xExgÍFxJr x wwg:Í4xrErrx $x'Í r 1Í JÍxw
WkdeXzÍ4RzxJXzx$Ã~RXzxJXzxgjBx jÄ g Fr2r wggx w4x rÍ1grx wx ro ggx rw Jgr JLxw wxEÍ4gr :Jr x Jxpr2 Exgr JJxÍ
cXz\J\XigT-R2jj 1Í4xJÍ px$xJrJxgr x E1Í4xJÍ x$pxJrJxgr x $LÍxgÍ xExgrgxgr x r2xpÍCxJr2x1xgxEw gxgxJxJx r2Í x11Í w1Jwxx r2$x gxgxw4xLÍ
Wkder8XzxgRzxJXzx$Ã~RXzxJXzxgjBx jÄ gLpÍNxrÍ4x g pr ggx J w gggx wJÍNJgr8 JJx 'r :r x1wx Jw E1x Íx
cXz\J\XigT-R2jj w4r xExgFxJr x$$xJÍ xgx w4r xExgFxJr x$$xJÍ gxgx wr x$xJ1xgr xEExgÍ gxgx w1r2x$rxJw1xgrxEwxggxJx x wrEw$Í4r gxgÍgxLw w wwJxw Jw x:r 14LwJwÍ
WkdewCXzxgRzxJXzx$Ã~RXzxJXzxgjBx jÄ r21w gLÍ LÍJÍw4x :r Í1grx 'r Í ggx ÍJÍNJgEÍgÍxx Ew4gEExgÍgÍxrLw$ÍJÍgrÍÍ:Jr2xx
cXz\J\XigT-R2jj 1wgxgLxJx$w xJJxgw x :1wr gxgLxJx$w xJJxgw x 'LwNr JxJ1xgxEw xggxgw x wJwNxJxgFxErxgwgxJÍJxÍ ÍCwJÍC gg gx1LÍJww LJw$JÍ x1w J
WkdeÍCXzxgRzxJXzx$Ã~RXzxJXzxgjBx jÄ ExgxLwÍ ggxw=w r prgw4xZw rrxggxr $J1w :Jr2xzw Í4:rr 4xLJxw1Í1r 'gr Egx:Jr2xx
cXz\J\XigT-R2jj r2rJxrÍxgxgxLxJx$w JxJgxgxrgrgrrwÍxgxgxLxJx$w JxJ1xgxÍzrgrgrrwNÍNxJxJx1xgxEw gxg1xgxÍzrgJr x$xJÍ xgxExgJxJx rÍgJwgr x1gÍx Jrrgwr2$prgÍ4x :r
$kc2«-\g§ XT-j : Wkm)RSRjk[1`'`-{eWYXj¼]~R+\VV\d|[']WYq1RRnglR+VZc\JjYX\4VBT)Wkd|U[-VYn:dejYº \4[-kXzjfCRUXZ[)j 'XzR+[)\ig\JRWYRj j=WkWkm)m-RzRS[1[1`)`-XX88R+RBVbVz\4\]]R+Xz{eRR2XzXzR+\4['VBWulQXzVBR+\]~igR+RVBjRBº [)cR2jf
;
9=77@77
9 717!717
;
9
9
1;;
9
9
9
97717!717
7
9 7177@77
=9
9
;@9
=9;
; 9=;
9 ;1;
17
7
9
9
;
@7
=9
7
7
7
99;
@7717!717
7
;
; 7@; !9 7
7
>
BA
;
7
;
!;1;
'9
7
=9
);
;
@;
'9
7
7 7177@77
; ; @9 ;
;
8;
BA
7
8;
@9 ;
7 =;; 9 ;
;17!7177@77
7
>
;1;!;'9
>
19 ;@7
=7 9
; 87@7
; !7177@77
7 9 =9 ;
;7@7717!717
7
5
7
7717!717
; !9 ;
;
9
=9
7
; @7717!717
87 9 9 =;
17;
9 9 =; 9
;1;;
;
!7177@77
7
9
;;
9 7'9
177@; 9=;
;;7
9
9
7 1;
9
1;@;
;
;
87
@9
9
19 7 ;
=7; 9
;
;;
'9
9 ;
; )7 @;
; 87
;
;
7@;
7 9
;
; @;
7
=9
7
;
@; 7
99
BA
ëS0BGQG'(Bæ?*"/1@B*:Ao7=/F0Bâè<77Z,6@Sâ4G'7æÿ)âACå6á8/1>8(B,67@+>EG'ý58@/1á8@S,6âã *)/F@B,6G'(b(+/F0=@/1Ao58G:>?@B@Bè8, 7g8å/167'A8ý @+G'(B0=/F(B7,6æ"A8å67æQ75)0B7>Q@+,6æ,6å~/1(Bå6&)çg,é5"G'(+>87(
)&(B7»ã70BY(B5»è874587"Hâ@B7/ &)<åâ@Bé0+G'7 7á8æ 5)Q0+ëS@JâJç)/F7æå6åê:7g,é, /1ß:@B7k_á<0+,(Bè87>?7 dFi:/1*ý@S HA8!,6(BæG:0+Ao7,éG:æ"@@B/F77>(B@B7AC)&,67Q5»5).z0 æ"5-)&,éá<å6å60B,6è@B0+7è8â4,67Q5 G'58ß'>8/1)@g(+,6ýCç'G'A$þ»á8ý @7ÒA</1(Bå6G'@+ê:GÒ(2/Fê:æ,6ß'çg@7Q0+è8/10B7=è<@5)7Òæ"á8æ"æ 7J/17C7@+æá8(S(BG:74(BG1> & ã
*'âJ/F74&(B(B,6â7G:>"æG'Aoá8/F0p(BG',6@B5QG:58/ @z)Aoá8745 (YãG:(B æH74>EçES/1@B5<0/1> 0B,60+G:è85 7Q5)ëá8æ ,60+èo74 (ZGFãb74åé74&æâ4åé7G)5)â0*æ"ã(B7G1à)ß'á87@g74ý58_â&ÿ-AC/175<(+> ,éæ"75)0B@zSëS&-70+7(B7@
G1HãSè8,é75)0+(+7á8(B585o58/F,6å58æêQ70+,6æ"æG'7(B@=&)ý:/F(Bþ»77/gß:á87@B(274/F> ê'70+@è87 GFã_Þ @+7ß'74(2/1å â4(+G'á8æ58@=A<ë,éå67,60+'( èÒ",6,5),0B74ëê'7,60+(+èÂ@=>8G'(A8/g0+ë,6æ5Â, &J(2/1/F0+58,6>8G'5G'æ"å67å6ß:&7ãå (+G'æý
0BA8è<(+7G'ê',6(5-/10+æ"7(B@uß'/Fèoå /gUß:7$ /1å6$ å C7 7$ä5Ó(Bá85Â^ ë)&,6Q0+èá8@B0B,6è<587ê@20B/Fè<æ7 7=Ð,658å6A<, 8(á820J/Fý (B&ãá85<â0B,6G'5 #-sk dFi:ý1Hè87z@BG:(B0B,658ê
+
$
)$ ?
0 1
E
"
. .'&
# % ?
0
+
!
"!
ëS0+è877=å6åYH0YçJëSè8ëG7è<Y7(+ëb(Bá8/g7J58&/F58@uæ,658â4G'7ê"(+á8ê'0B5),67æ0B@+,6G'5874(Bê@S0pãG'A8G'58(Bå6å6G:å6&G1ê'ë (2æ"/F0Bæ7è<æ7o/G:/11(B5o@+&=7/F(+>å67&-ãG:@+75,6(+@Z7$58/1,6ââ4êo74âý@=G'(+,6>8@æ?,6>858/17ê*:o70+58@GQ,60+0B0B7è<è8å6&7=7@20+@B/FG-,6ææG7S@BA<,6åéæ5)7á8A8âæ G'å67'@+o7ý 0z4<(æG'G1(G)ãE,6>858æ"7@Bå70æà)/158á8G:â4,6(B0B7'&7 ç
(+A87(+ã77>8(+,67â580+â@7@S(+7/1@B@EAC0+7è8â0+7S,éß:ß'77(+â@B,6G:G'@B50+@ ><G',6 :58äêåé@BG:74êà-á<äÐ75)0B/1,~58/1> å8/1â4 â'7ä@B@på6G'ëê ,é0+äèzçNAoëG:,éè85),60+â27è»(B@gâ4ý1G'H(B(+è877@BAC@+,éG'æ"5<A8>8å6@Q7E(Bâ7JG:/F@B@B0G:æ5o/G)8å>8674& å
ëSß:77(Bå6@+åo,é0+G:GQ5î0BGFè8ã=70Yæëu7JG /F ë@Bá8/g(+& 7>?æ"(B7á8(B5<ê:587@B,658G:(Bê0g0+çE,6>8æ74M 7@B@gA8ý ,60B7?á8,6,60Bâ@ *)@BC7G'(+0B00+7,6@u( M æ?C7/1@B(B(0 ê: ,6âg5o/1/1@Bå67 å6&zo7ëuèCG:(B/g@Bß-7z,6G:0+á8èo(J/1ý 5"=0Bå6è8@B7zGÌAC,65»G',65)0Bè80B7,6(@
âJ0+è8/F@B7z7'(Bçp7@Bå~/1,6æ0+,6ß'A<7 åé&Óo7â4G'èoá8/g5)ß)0+,éG:,é5<á8ê»(SG1æã70+æ"è87G'(B0Y&ÓëSG(B7A<ã74(B(BG'7ê:58(2â4/F7æ@Â@>8:G)à)7á8@Q,6â58*-G:@+G'0Q(+0ê',6,éß'@7?@+7/175Ð5Â/10+âGâá<æ?(2/1/1*:0+7Â7@BA8å6,6(+ê'7è)>80B,6âå6&0B,6G:ã75 ëS7GF( ã
æ"@+G'7(B0+æ,658G:ê (B&?A<(B(B7G'ãkê:7(2(B/F7æ5<â@7@?0B70B@+èo0B7/F>E5îý æ"S7G:(Bæê:7Ao@B/FG:(B(B70J>Çý <0BG»G'á<0Y"( ëSYëbG /gYëb&Ì/gæ&»7æ"(+ê'77(B@+ê:G'7(+@B0G:(B,6@0Qâ,60Qå67J,6/1@÷(+åé/&»oG0+:è8á87 0o7/Ó4@Bã 0Q/1â4G10BG'ãz(Q0Bè8GF7 ã
@+åé ,6ê:è-S0+ã G'å6/1&æ"@+0B8,A876(g,6ê:å6ç)7ê'ë(7(Sè8G:,6A8ãâ2G:0BèQ(,6æ",6ãk@SG', á8&g58/1((G'0B0pë,6G:0B/g5»G)&QGê-æãY/g/1ß'7((+7Óê'ã(+7@BG'á8@+æüG'(+(+A800B(Bè<,6â@B7=G',658æ"A8êÇ(+Ao7,6/1>8æ(+,67âA8>0B(+74G10+> GQß'70Bæ" èo/F75)0S0B ã@G'(S0BG 0Y0Bëuè8/FG 7zå6åëå6G1@B/gëSG'&Q(+70B("æ,6Y58G'74êÇ(+(B>8ê'A8774(B(S@BG:G'0Bê'(+7(20 (+/F4æ æý ,6@g@ ç
0+/ô8G oGð::òS0+á8è8,éæ"0u7@B/°A87Ó(Bã G1/1G'ß:âA80+7=0+G',é0+æ"(è8GF7, &Jã /10B740+ÿ-,é0+G:0G 58oG@J8)/ý ý G:Y=*Ò0QG1æ",éëS@77(B/Fß:ê:å67@B7(JGÌ@Bç)G:0+ëu(Bè80G:7=A8(B(+0B(+7èÇG'å~ê:/158(20BG',6/1ß:0+æ 7,658à-0Bê áCGQ/10+ACèoå6,67/10Y(&0QãG'GFâ4(+ãEG'æ æ0Bè8o7A<7,éå6A80+70B(B(7G:(zG'ê'A8(20+/Fèo0+æ,é/1æ"5?@, &J0Bëè</1/10+7@S,éG:,6,éæ585)@ß'A8/Fâ(+(BG1G:,~ß'á8/175)å6>> 0
0YG:ëSA8G0B,6Yæëb,/g&J&?/F0Bæ",6G'75$(Býê:7@BG:(B0zA8(BG:ê'(/1æ o/F@B7>»G:5 $,6êoý :çC7ß'75ÌãkG'(z0Bè87Qå~/F0B0B74(Zâ4G'æA<,éå67>Óë,é0+è8G'á<0
b?
Û e Ø HH/è8<å7Ìé7 0Bè<87ýNG'þ»(+770B,6âJA8/Få~/Få 5Âo5<0BGÂ>8,6âg58/1ê'(B@?(+&ÂG1ãQG'á<0B0è<,é/"@?æAo/FG'Ao(+747( 0Bè</FG'58(BG:> á8ê'0+èÌè87Ì7ÿ)ãá8ACå67åz(B,6ß'æ74(B74@B5-,60G:/15 åÂ7ß'/1/F(+7»åéáC/1@Bá80B,6æ"G:5ÂæÒG1/Fã=(B, /1&å67å>Ð0Bè8,65 7
@+G'(B0+,658ê÷/Få6ê'G'(+,60Bè8æ"@å6,é@+0B7>?0+è87(B7 ~,658âå6á8>8,658ê0Bè<7,65-0+7(BA<åÈ/g&Që,60+è0Bè<7âG'æ"A8,6å67( 4ý
)
*
, ?
!
6
%
? #
,
4
6
ÐÜ ÖÙ $Ú eEÖp×!
ãHG:è8(u7 0+è8o7(+,6@B(0zè8/17á8å60+A)è8ãká8G'åE(âëSG:G'æá8æ"å6>?7å65),6*'0B@J7=ý 0+GQ0Bèo/F58* å6,é@+02/F,é('?GFKN/F0JçoDN77 z/1,6@BèEç8/F58>?HG'æ, /1@/15875
$!
Ø EÖ0Ü L
rJº =ËB²+º ² [)1'´gµR+VB¶ jYjY\· )[C² f ® gº · SUJngR+VY`':TC!¹ f¼"$a¼º'#&Æ%(d|{ejY'jY)J\4±_[of8¸-¶gU4[-µ" '±»º¶zUg·)XZ²+U4*[o)f8²Ba1¶1\4³,VB)uWkd|¶[--n°#d|[Q¶1±{|d ¸.[-:RU·/V1Wk´gdef XzuR^
gf'd|[VBR³jY¶gjÊf
w1ºÆuua)º)R:¿11deUJjY0EUg\4jY\4['RgVY<v 4fq8;"f'#RÆ=¶1jk{eº±_R20=l".¸ º f8'·~r `:²44³'1{|Í1de-jkf:m'T'´1d TC[-¶1³nº 61· ^)w ±3\g2X"µ J57T-gU46:)['º ·~lg³kf ¶ :RËUg/·16d|¶ [)Ân'fC·~9¶ QUJ8bjY²j"µ º fo|´ r Ì¹ :º :+)!¹ )3µ eµ+fEw[)îyEFdeWkde\[Cf
'º+=:C º² >EDEº'é²4¿GÉ R+['F"Wk{eÃYRr lgfJ:¿SrºÄp;Ç º'2 t:R+VYº ['den4m-U4[of1U[)Z^Sº=:º'i4U[$; lgq8f [=R+{eRXzRB['WYU4VBlZ^c\JjYWXz\1'R+{~f@?.A-6<B
'Í1ºº-M=a)º8º:^yEU4jYVYWk{edejYigjYd|{\e[CvY^f UJujYigWkVBR+\VBUJU4ng[-R+vQcUJPjYRSº;VBR\1jk`'\1{e<WYjf î\4H[ jk`'uVBRigU4RT-ljY\4\4VB]EWUg.f 'I7U46JT-* WkdeigR=K jY\4ÃYVBr Wkd|[-JnÄULw {e2)ngr\FVYdeº Wkm)Xzjf.$#&%N#¶1±Ê
'-º .¸=c\J'º X/·T'1º-`)O´ SWk'd|\4[-'{en',³ jYDd|Wk² [-d|)4[-jYµ WkRSVY`-U4P[-XzQ R+ÃYr['=:Wº'LfEigwg\Ä [zU4VBÆu'W=,rR+Y2`)YXZf4M$U4'['\º [C{|`)fXzR{eU4['w1[:f<d|VB[-R+n=T'VYU4d|[-['WYRc?\1Fd|[Sd|[-nR1¶\4]'TT'VBD\4¶':{eRAXz²jC']~±\V¹U4[=URB#{eR¶!cWkeVB²+\4Ë['·~²dec V R+¶1VBnJ<³ WLUgµBXzJf \M$[\{|N`)XzVBR2RjYjMf [S} 8g]~²\"µ VB|<´ zf-yN¶ +[-n4#{eU¶1[)±_8.¸ f$'r ·~g²J³µ:XYf:*T')To²BºC¶1r,³ ÍJ)Lw 2F¶ ZwFr+':º ·~¶1±=¹1·¹u¹ +A+'±²³ 6Ë+!¹ J+)!¹ )3µ eµ+f
%
E
3 #3
5 5
8717
3
;
5
8717
)3
:3
; 9 ;
;
877
;; '; 9
87
3
7 9
)3
7
8;
#
9
Ó^ T'VB\gn4VBUJX
q1U4RVYl dejY\4[-j R+Xz{eR\XziJRR+j['O W
c
J
\
X
T
Wk\vUlzXz\4R+VBVBjYnJWRjYc\4UJVBjYW R ¾p{e\gn ¾ ¾p{e\gn ¾
]~\4`'VYvUlXz\4R+VBVBjYngWR2cjY\4UJVBjYWR ¾p{e\gn ¾ x:Î Íg¾p{e\J n ¾
d|[:v~T'{eUgcRZXzR+\4VBVBngjYR2WjYc\4UJVBWjYR ¾p{e\gn ¾ ¾p{e\gn ¾
Ug'U4T-WkdeigR=Xz\4R+VBVBjYnJWRjYc\4UJVBjYW R ¾p{e\gn ¾ rgÎ Íg¾p{e\J n ¾
VBU4[-:\JXd R8 RjYgWS`'c2deUgcjYq'R jY \VBW ¾p{e\gn ¾ Ã¾8Ä
jYWYU4[-:UVB8m)RR2jYU4WST-c2jY\4UgVBjYRW ¾p{e\gn ¾ x:Î Íg¾p{e\Jn ¾
8\gWYWY\JXv~`:8TQRm-jYWSRUc2T)UgjYjY\R VBW ¾p{e\gn ¾ ¾p{e\gn ¾

# # T'VYT'deX`:VBdeWkR=deig^ RjY
ÍFÎ Íg¾{e\gn ¾
:Î wgÍJ¾p{e\gn ¾
:Î gÍJ¾p{e\gn ¾
1¾{e\gn ¾
1¾{e\gn ¾
1¾{e\gn ¾
rgr¾p{e\gn ¾
9
"!
# $ #
% ! &# ' (&)
$ #*+ ,#,$- (
/
. + ,#
##10 2
3)#/
, # 4 2 #, 10 652
527
BV R+Xz]~RBRVBXzR+[)\c2VBRl j w ¾p{e\gn ¾
¾_{e\gn ¾
w ¾p{e\gn ¾
¾p{e\gn ¾
-¾p{e\gn ¾
Ã~x:Î Í =Ï ÄY¾{e\gn ¾
Ã =ÏÓw ÄY¾{e\gn ¾
kjg$de`-jY«-WkU4§ d|['[-WkndeWkde\4<R]j=U® U4qLVBm-RRRl\J8XU4R+[-m-deWYUWYigRjY8de\J\4Xzº `'VRSd|\4[:]]È\4iVBUXzVYde\4UJ`-Wkdej\4[ÒjY\UgVBjYWkd|jY[)\1nQc+deUJT:WYVBR\JQn4VBUJdeXzWkmQjWkm'm)dej_R+[½qLRjYlg\4º VB® Wkd|m)[-RSn{e¾½\RBv{e\4RVBXz'R+R+['VuWYWYjR+foVBRXzUgjcYmÂd|[QcWk\m-[:R v
Fºu?ÃYr ºg=:Lº-ÄSSwg\4Í{|d E[ 2FwgU4Í [-' º º-a1R'ngRdecYq8f p`-R+`-R+vXzR+VBngR2jY\4VBWf+63¶1³B±=¹1· é¶9³k¶Ë+²µBµ3 1´ 8²·~·~²³µ P
:º =:)º'¹!to¶Ug$WYU #YU4¶1d|±[-¸.R+[o:f·/® L´ º' UgÃYjYr U[)gR+L[oÄpf)w UL[)2 gx:=:º º ® R+`:m-\4{eU'f)VBUgcWkdec2U4{8d|[:v~T'{eUgcRZXzR+VBngR2jY\4VBWfA¶1³<6Ë-R1¶'³Ê
:ºu¿SVBº R+;î['Wkº)dectR+<vR+SVY['Ude{|n4~m-fCU4y[ [-n4U4{eR[-\1\1PÒºB?^${|ºd 8jdef8WYcÆm'ºde=:Rgºef f)r *)²:º # ³¶+´1³¹1±±Q1´ 8¹L´ '¹´1²fw[)yEFdeWkde\[Cf
rx'ºPS'ºBy1deº'jYtS\4['[1v `);WkmoRjkfZ{eR*l)²-`:'³B{|·dejk¶m:Od|[¼#n¶1±^_¸.\JX'·T-²³7U4['lg³kf ¶Bp´1³kR2¹1Ug±=1d|±O[)n'Lf8´LQf M$UgjY\j{|`)ºefCXzr RzJ rJ'} º 1¹1±²)·~¹!J- ´1¶1³,6·)±µ+f
rgrJºPS'ºBy1deº'jYtS\4['[1v `);WkmoRjkf {eR*l)4² `:'³+{|de·ujkm:¶ d|:[¼n#¶1^_±\J.¸ X:T-·~²U4O³['lgf ³kp¶B´1R2³kUg¹11±=d|[)O± n'f8 1Q´g&fUgjYMEj\4ºefC{|`-r Xz4RQ'º:Z} '8¶1³+/· L´¹ '8²B¹1³kË L´Lf
rw1ºPMER+ºBVYy{eUgº'n'tSf)[1¿`)R+WkVYmo{|d Zf [ E uR+6¶1de'±Rµ{|o¹R+VBn' fSRBVBXz|µB.f U4>C['lgRfcWkr `'VBLRwFºÆu\gWYRj=d|[î^\gXT'`-WYR+V÷aFc+deRB[)cR <faLT'VYd|[-ngR+VYv
r'ºPS'ºBy1deº'jYtS\4['[1v `);WkmoRjkf {eR*l)²9`:'8'{|·~de¹jk3m:2d|[¼¶1³n ^_\JX³k¹+¸T-U4['I_lg¹gf µp²5R2Ug 1d|[)@n'ef8¹1·Q¶1Ug³BjY± jºefCr¶1³ g'#º ¶1± )¹1·~¶1³6¹!$#¶1±_¸.'·/1´gf
r 'º ¸.'º ·?²³º:R1Q¶\ :8³Ug)W¹! U[) P [ÃYr º'1wJRÄWYR+4VBxEjYjY2 \[C1f º p[\igRBVBigdeR»\4]oUg'U4T-WkdeigR=jY\4VBWkd|[-n:Zf *)² +Fµ2·~³k!¹ 6¹ 4#¶1±Ê
rÍ1ºPÉ¹1º =³k² º:'8¶UJ2WY·WYÉR+VB¹1jY³\4-² [ 6)U·~[)²³ ¹1=:ËB²º >$fgQº S\VBRBng[:U[-[RjYtjYlgU4f `']~#Xz¶1U4±_['.¸ ['·~²`:³ '{|dejk³ém)´FRB¹ VBjf 4a1¹1U4/· 6[ ¶ :VBU[)cB8bdejY²c"µ\:|fo´ ^5TU4{|d*] )º fo² r b:¹1³º gÊ
r'º ÃYr º8a1LR'Ä ngRLde2 cY1q8Í fu1ºoX^T'\4{eVYRVYXzdengR+RB['[)Wk1d|[-`)n X p `'de1c²q'± jY\VB W T:Ã VB\JLn4Ä_VBUgJXZ 'jº f4#¶1±±Q6ËB¹1· é¶:µ¶Q·)² $#&% r 1º Qº8Uga1jYjRºe'fCngr Rde:cYºq8Jf ´1¶1³ 6· )±µBf2w[-y$1deWkde\4[of S'FdejY\[:<v ;Rjk{eRlz`:'{|dejkm'd|[8n=^\gXT-U4['lgf RUJFd|[-n:f
9
8717
7
=<
5
8
8717
7
19 ';
5
>=
:9
3
(F
8; 3
3
=
:3
5
=9 5
@
;'9
7
9
R8
?
5
87
5
87'9
77
HG
77 69 99
P
87'9
A
<9
87
3
3
5
8717
LK
SI
(9 7
13
;
>M
CBED6B
JI
ON
CQ
LA
8771;
=5
;

Download Report

A meticulous analysis of mergesort programs* Jyrki Katajainen**Y

Paperzz.com

Your Paperzz