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Throughput Optimal Packet Size Selection

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Œ |` o KMVV:KA{H†LN o | o GAGŽ|L]OGŽ`bG o tN o W(` o ]b€r{bV qbq Lk] ‹ H†{ o N or‘  o F:€n{ q F:€nO o KLkG’G o ]KVj]>FBGALk] ‹ | o
tN o W(` o ]€r“H†{bLk| o dbL•” o N o ](K q F €nO o KAGƒF N o G o ]KƒVj]–dbL•” o N o ](K.tN o W(` o ]b€TL o GTY—U\`bN‰KM{ o NTS^KA{ o N o F:N o F
|kLaCLkK o d˜](`ba ‘"o N™V:t q F:€nO o KšGIL› o GTYZœ o.q NAV q VjG o FGI€n{ o db`|L] ‹ F:| ‹ V:NALkKA{bažKMV€n{bVVjG o KA{ o.q F:€nO o K
GIL› o KANMF:]bGIaˆL•KAK o dŸVhg o N o F €n{-tN o W(` o ]b€ -F:GCFt`]b€rKALVj]¡V:tfKM{ o €n{\F:]b] o |†€TVj]dbLkKALVj]bGrS¢Lk]ŸVjNAd o N™KMV
aˆF0£LaCL› o KM{NAVj` ‹ { q `KfL]<F Œ |k` o KAVV:KA{ q L€rVj] o KsY
¤p`bN¥€TVj]KMNIL ‘ `KMLV:]bG¦L]§KM{bLkG q F qyo N8F:N o F G8tVj|k|VhH†GTY&œ o¨ NAG‰KŽd o g o |V q F.N o ] o HJF:|vKA{ o V:NI ‘ F:G o d
aˆF KM{ o aˆF KMLk€sF:|yaˆVd o |7V:t q F:€nO o KfKMNMF ]bGAaCLGIGALV:].L]…F&tN o W(` o ]b€r<{V qbq Lk] ‹ GIGIK o a©|LkO o F Œ |k` o KAVV KM{
q Lk€TVj] o KsY3œ o `G o KM{bLkGfaCVd o |'KAVˆGI{bVhHªKM{\F0K ‹ Lkg o ]…KA{ o V ‘ _ o € KML•g o V:taˆF0£LaCL›rL] ‹ KA{ o KM{bNIVj` ‹ { q `K
V:t!KM{ o G‰GIK o a6S\KA{ o d o €rLGALkVj]6F ‘ V:`KwKM{ o¥q F €nO o K^| o ] ‹ KM{.KAV ‘yo KMNMF ]bGAaCLkKIK o d.tVjN†F ‹ L•g o ]…tN o W(` o ]€r
LkGpFˆKA{bN o GA{bVj|kd ‘ F:G o d q NIV€ o GAGrY¦œ o KA{ o ] q NAVhgLd o F ]§F:| ‹ V:NALkKA{ba«KA{\F K¦d o K o NAaCL] o GRKM{ o G o V q KMLkašF:|
KA{bN o GA{bVj|kdbG or¬ €rL o ]KA|kƒtV:N¦F ‹ Lkg o ]§GIG‰K o a­`b]bd o N8€ o N‰KnF:Lk]§F:GAGI`ba q KMLV:]bGTY¥œ o GI{bVhH®KA{ o V q KALaˆF:|•¯
L•K„V:tfKM{bLkGF:| ‹ VjNAL•KM{bažH†LkKA{bVj`K`GAL] ‹ G‰KnF:]d\F:NAd¡V q KALaCL›TF KMLkVj]ZK o €n{b]LW(` o GˆGALk]b€ o L•KLG™]bV:K€r| o F:N
KA{\F K^KA{ o G o K o €n{b]bLW(` o GpHJV:`b|d ‘yo F qq |Lk€sF ‘ | oŽ‹ Lkg o ]ƒKM{ o t`b]b€ KMLV:]bGpL]g:Vj|kg o d'Y¥xfGAL] ‹ GALka&`b|}F0KMLV:]bGTS
H o V ‘ G o NIg o KM{\F K†KA{bLG†GIKANMF K oT‹ …| o F:dbGwKAVˆGIL ‹ ]bL ¨ €sF ](KA|k ‘yo KIK o NfKA{bNAVj` ‹ { q `K^F:Gf€TVja q F:N o d<KMVCV:KM{ o N
‘ F G o |kL] o GIKANMF K oT‹ L o G o g o ]ZLktKA{ o F:GIGA`ba q KALVj]bG^ašF:d o KMV q NAVhg o V q KMLaˆF:|kLkK„<F:N o N o |}F0£ o d'Y¦œ o KA{ o ]
o £K o ]bd<Vj`N°N o GA`b|•KMG°KMV™a’`b|kKAL q | o F:€ KML•g o GI|}Fsg o GfLk].F q Lk€TVj] o KsY‚„].KM{LG°€TF:G o SH o GI{bVhH%KA{\F KwGI€n{ o db`|•¯
Lk] ‹ F:|kVj] ‹ H†L•KM{ q F €nO o KCGIL› o G o | o € KMLV:]>€sF:]>GIL ‹ ]bL ¨ €sF ](KA|kZLa q NIV+g o KM{ o GIGIK o a±KA{bNAVj` ‹ { q `KTY§=V
Vj`N8O(]bVhH†| o d ‹jo S!KA{bLG¥LkG¥KA{ o™¨ NAG‰K&F0KAK o a q K¦KMV…L]KMNIVdb`€ o F:dg F:]b€ o d q NAV ‘ F ‘ L|kLG‰KML€&F:N ‹ `a o ](KAG¦tVjN
V q KMLaCL›rL] ‹ KM{ o KA{bNAVj` ‹ { q `KfV:t Œ |k` o KAVV:KA{*KMNAF:]bGAaCLGIGALkVj]bGTY
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w{ o N o {bF:G¢N o € o ]KM|• ‘"oro ]ˆKAN o a o ]bdbVj`bG3Lk](K o N o GIK¢L]CF qq |Lk€sF KALVj]bG4V:t Œ |k` o KAVV KM{™H†LN o | o GAGK o €n{b]bVj|½¯
V ‹ jY Œ |k` o KAVV KM{*LkG°F’|kV+H°¯ q VhH o NrS|VhH°¯¾€TVjG‰K°GA{VjNIKwNAF:] ‹jo H†LN o | o GAGJ€rVjaCa&`b]bLk€sF KALVj]CGIGIK o aÀ¿ÂÁbSÄÃS•ÅjÅTÆY
‚¾K o ]bF ‘ | o G’GIašF:|k| q VjNIKMF ‘ | o d o gL€ o GŽKAVƒ€TV:]b] o € K’KAV o F:€n{V:KA{ o NŽF:]bd˜€TVjaCa&`b]bLk€sF K o L]˜F:]F:d¯„{bV€
tF:GI{bLV:]&H†LkKM{™]VjaˆLk]\F:|G qyoTo dG¢V:ty` q KMV™ÅRX ‘q GTY Œ |k` o KAVV KM{'ÇÈG|VhH¡NMF:] ‹jo8É K„ q Lk€sF:|k|kˆÅhÊ:ašË4F:]bd|VhH
€rVjGIK†aˆF:O o L•KwGA`LkKnF ‘ | o F GRF&GIL] ‹ | o ¯¾{bV q €TF ‘ | o N oTq |F:€ o a o ]KsSbGI`b€n{BF:G o |LkaˆLk]\F KMLk] ‹ KM{ o H†LkN o tNAV:aÌF
qyo NIGAVj]\F | q VjNIKMF ‘ | o NMF:dLV q |}Fs o N°KMV’KA{ o { o F d q {bVj] o GTY3‚„]bd`bGIKANI<F:]bF:|kGIKAG°{\Fsg o¦o GIKALaˆF K o dšKM{\F0K¦ÅhÍ
aCL|k|LV:] ‘ |` o KMVV:KM{d o gL€ o G¦H o N o GA{bL qbqyo d§L]ZÎ:Ê:ÊÅjS'a oTo KML] ‹.o F:NI|L o NRtVjN o €TF:GIKAGTS!F:]bd q N o dbLk€rK¦KM{bF K
ÏÑÐ'Ò0Ó4Ô7Õ Ö×†Õ ØbÙjÚ Ù+ÛÜÖ×MÛ Ö'Ô7ÛrÝ1ÝÞ+ß0ß ÕrÖàÓIáRâäãpß0Û Öà1åsæfç=Ù+èCérÖÛ ãrà1ê!ç!ëì+í‰î}ìrï ð ñ ò
HJVjNI|dH†Lkd o¥‘ …Î:ÊjÊó’KA{ o N o H†Lk|| ‘yo Vhg o NpÃ:ô:ÊaCL|k|LkVj]ˆ] o H Œ |` o KMVV:KM{<d o gLk€ o GRGI{bL qbqyo d¿õÍ ÆY
Œ |k` o KAVV:KA{’`bG o GtN o W(` o ]€r&{V qbq Lk] ‹ F:]bd’V q"o NMF K o GLk]ŽKA{ o `b]b|kL€ o ]bG o dÎYÈÁ(ö¥÷R›¢‚‰EbX ‘ F:]bd7S:H†{bL€n{
LG¦F:|kGAV*`G o d ‘ B‚Ñu3u3u%ô:ÊÎY•ÅjÅ&NMF dbLVjG^F:G^H o |k|F:GpV KM{ o Npd o gLk€ o G¦GI`b€n{ZF:GpaCL€rNAVhH°Fsg o V+g o ]bGrS ‘ F ‘ 
aˆVj]LkKMV:NAG o KM€ YŽw{(`bGrS1LkKp€TF:] ‘"o’o £ q"o €rK o d§KM{\F K^KM{ o tN o W(` o ]b€TL o G¥L]ƒKA{bLG ‘ F:]bdBH†Lk|| ‘"o GI` ‘ _ o €rK o d
KMVšLk]K o N‰t o N o ]b€ o tNAV:a©V:KM{ o NRGIVj`bNI€ o GRL]ƒF:dbdbL•KMLV:]<KAV ‘yo Lk] ‹ GA` ‘ _ o €rK o dKMVKM{ o g F ‹ F:NIL o G†V:t=H†LN o | o GAG
|L]OGrYš‚„]ZKM{bLkG q F q"o N¦H o €TVj]b€ o ]KMNAF K o Vj] q NAVhgLdbLk] ‹ GAVj|k`KMLkVj]bGptVjN o ]bF ‘ |Lk] ‹<or¬ €TL o ]KŽ€TVjaCa&`b]bL½¯
€sF KALVj] ‘yo K„H oTo ] Œ |` o KMVV:KM{§d o gL€ o GŽLk]KM{ o tF:€ o V t°GA`€n{L]K o NIt o N o ]b€ o YšefF KM{ o N¦KM{\F ]˜aCLkKAL ‹ F KAL] ‹
KM{ o G ofo ” o €rKAG ‘ &L]b€rN o F G o d o NINAVjN€rVjNAN o € KMLV:]'SLa q NAVhg o d q VhH o N3€TV:](KANAVj|SVjNV:KA{ o N|kV+H o Nѯ„|Fh o NK o €n{¯
]bLW(` o GTSH o €rVj]bGALkd o Nv{bVhH–GA€n{ o db`b|kL] ‹’q F:€nO o K°KMNAF:]bGIaˆLkGAGALkVj]bGvF:]bdšaˆVdbLktøLk] ‹ KM{ o | o ] ‹ KM{ˆV:t q F €nO o K
KMNMF ]bGAaCLGIGALV:]bGRLk]ƒN o G q Vj]bG o KMVCKM{ o €T`bNIN o ](Kp€n{\F:]b] o |=€rVj]bdbL•KMLkVj]bGf€sF:] ‘yo `bG o dBKMVšLka q NAVhg o GIGIK o a
KM{bNIVj` ‹ { q `KsY
w{ of‘ F:GIL€wLd o F¦V:tyKM{ o†q F qyo N3LkG3F:GtVj||kV+H†GrY=[ Œ |k` o KAVV KM{€ o || É VjN4ùyúûnü0ý7þ ÿ}Ë4€rVj]bGILGIKAG3V:t'F ÿ„þ d o gL€ o F:]bd ` q KMVG o g o ]F:€ KMLkg o :þ SJH†L•KM{ F:||†€TV:aˆa&`]bL€TF KMLkVj]>KnF:O(L] ‹q |F:€ o Vj]b|k ‘yo K„H oTo ]
KM{ o ašF GIK o N8F:]bd§KM{ o GA|Fhg o GrY*wLa o LG¥dbL•gLkd o dZL]KAV…GI|V:KAG8F:]bd§KM{ o ašF GIK o N¥€TVj]KMNIVj|G¦H†{bLk€n{GI|}Fsg o
€sF:]6€TVjaCa&`b]bLk€sF K o F:]bd…L]<H†{bL€n{…KMLka o GI|V:KTY Œ |` o KMVV:KM{…`bG o Gpà CdbL•” o N o ](KftN o W(` o ]b€rL o GRdb`NAL] ‹ L•KMG
tN o W(` o ]b€r6{bV qq L] ‹ G o W(` o ]b€ o Y†w{ o ašF:G‰K o NTÇÈG ¨ £ o d Œ |` o KMVV:KA{6F dbdbN o GAGRd o K o NAaCL] o G†KM{ o {bV qbq L] ‹
G o W(` o ]b€ o `bG o d>H†LkKA{bL]KA{ o*q Lk€TVj] o K 3KM{(`bG o F:€n{>KMLka o GA|kV:K&Lk]>F ‹ Lkg o ] q Lk€TVj] o K&{bF:GF q F:N‰KMLk€T`b|F:N
tN o W(` o ]b€rB`bG o dL]6KA{\F K^GA|V KsY†[°K¥F:] ‹ Lkg o ]ƒKALa oŽo F:€n{BtN o W(` o ]b€ B€TF:]B{\Fsg o FšdbLk” o N o ]KpW(`\F |LkK„:S
L]*K o NAaCG°V:t Œ L•K†uNANAV:NweRF0K oÉ Œ u3e^ËÜS\F:GAGIV€rL}F K o d*H†L•KM{.LkKTY‚¾t KM{ o Œ uvetVjNwF q F:N‰KMLk€T`b|F:NvtN o W(` o ]b€r
€sF:] ‘yo’o GIKMLkašF0K o d7SyKA{ o aˆF:GIK o NR€sF:]B€n{VVjG o KM{ o | o ] ‹ KA{BV:tKA{ o&q F:€nO o K¦G o ]K¥Vhg o N^KM{\F0KRtN o W(` o ]€rjY
‚„](KA`bLkKALkg o |k:SwGA{bV:NIK o N q F €nO o KAG<F:N o G o ](K*V+g o NštN o W(` o ]b€TL o G*H†LkKA{ {bL ‹ { Œ uve GAVF:GˆKAVN o db`b€ o KM{ o
q NAV ‘ F ‘ L|kLkK„…KM{\F0K¦KM{ o §F:N o |kVjGIKTY™U\`bNIKA{ o NrS1KM{ o Œ u3e®KAV o F:€n{ZGA|}Fsg o aˆFs ‘yo dbLk” o N o ]KŽF:]bdKMLka o ¯
g:F NIL] ‹ Swd oTqyo ]bdL] ‹ V:]LkKAGˆdbLkGIKMF:]b€ o tNAVja KM{ o aˆF:GIK o N*F ]bdV:KA{ o NCtF:€rKAVjNAGrY%‚¾t¦KM{ o Œ u3e©KMV>F
q F:NIKAL€r`b|}F:N8GA|Fsg o €TF:] ‘"oˆo G‰KMLaˆF K o d'S4KA{ o aˆF:GIK o NŽ€sF:]>€n{bVVjG o {bVhH KMVBGI€n{ o db`| o €TV:aˆa&`]bL€TF KMLkVj]
H†LkKM{§KM{bF K8GA|}Fsg o F KŽF ‹ Lkg o ]ZKMLa o Yw{(`bGŽGA|}Fsg o G¥H†{bL€n{˜{\Fsg o F<{bL ‹ { Œ u3e—F0K8KA{ o aˆV:a o ](K8aˆFs
‘"o K o a q VjNAF:NALk|k§GIOL qbqyo d>L]tFsg:VjN&V:tfGA|Fsg o G&H†L•KM{ŸFB|kV+H Œ u3e¥S=KA{`G™N o d`b€TLk] ‹§q F:€nO o K|VjGIG™F:]bd
L]b€rN o F GAL] ‹ KA{bNAV:` ‹ { q `KsY
Œ |k` o KAVV:KA{ q F:€nO o KMG8F:N o N o GIKMNIL€ K o dKAV ‘"o V:t3KA{bN oro | o ] ‹ KM{bGrS1]\F:a o |•ÅjS'Í*VjN8óˆKMLka o GA|V KMGTYŽU\VjN
€TVj]b] o €rKALVj]| o GIG¦d\F KMFšH o €rVj]bGALkd o NRH†{\F K¥F:N o €sF || o dBL] Œ |` o KMVV:KM{ m ÷ q F:€nO o KMGrY m ÷8Å q F:€nO o KMG¥V:t
| o ] ‹ KM{ƒÍ ‘ LkKAG^F:N o G o ]Kp`GAL] ‹ ŎKALa o GA|kV:KsS m ÷^Í q F:€nO o KMG^V:t°Å jÎjÎ ‘ LkKMGf`bGIL] ‹ ÍKALa o GI|V:KAGTSyF:]bd
m ÷pó q F:€nO o KMGV:tyÎ ôÃ:Ê ‘ LkKAG=`bGIL] ‹ ófKMLka o GI|V:KAGTY4¤¦]€ o FfKMLa o GA|kV:K!LG!€n{bVjG o ]F K!KM{ o GIKnF NIKV tF q F €nO o K
KMNMF ]bGAaCLGIGALV:]'S"KA{ o’o ](KALN o&q F:€nO o K¥LGRG o ](K8F0K^KM{ o tN o W` o ]b€ V:tKM{ o’¨ NAG‰KpKMLka o GA|kV:KpLkNAN o G qyo € KML•g o V:t
KM{ o | o ] ‹ KA{V:t¥KM{ oBq F:€nO o KsS^F:]bd–F] o H tN o W(` o ]b€rLG*`bG o d–Vj]b|•ŸtVjNˆKA{ o ] o £K q F:€nO o KsY@ö¦Lkg o ]
KM{ o’¨ £ o dVhg o NI{ o F dZV t q F:€nO o K¥{ o F d o NIG¦Fš|V:] ‹jo N q F:€nO o K¥LkG^aCVjN o8or¬ €TL o ]K¦Lk]ƒK o NAaCG^V:t3`bG o NpdbF KnF
KM{bNIVj` ‹ { q `KsYB‚„]F:dbdbL•KMLV:]˜KMV…KM{ o V+g o NI{ o F:dŸ€rVj]bGALkd o NAF KMLkVj]bGrS=KM{ o*o ” o € K™V:t†€n{bVVjGALk] ‹ KA{ o*q F €nO o K
| o ] ‹ KM{*Lk]*N o G q Vj]bG o KMV’KA{ o Œ u3e–€sF:] ‘yo g o NIšGAL ‹ ]bL€TF:]K°Lk]ˆK o NAaCG°V:t'KA{ o KA{bNAVj` ‹ { q `KwF KAKMF:L] o d*Vj]
F:€T€rVj`b]K°V:tyKM{ o €n{\F NMF:€ K o NILG‰KML€rG¢V t"KA{ o tN o W(` o ]b€rC€n{\F:]] o | H o `bG o F¥GALka q | owo £F:a q | o KAVŽLk||k`bGIKANMF K o
KM{bLkGTY
! ³ ŠJVj]GALd o NCF Œ |` o KMVV:KM{>d o gL€ o [ÌKANMF:]bGIaˆL•KAKAL] ‹ KAVZF§d o gL€ o Œ S`bGALk] ‹ Vj]b|k˜K„HJV
tN o W(` o ]b€r§€n{bF:]b] o |GTS1]bF:a o |k# "%$^F:]&d "'sS7H†L•KM{§F:GIGAV€TLF K o d Œ u3e®V:t†Åh)Ê ()*¥F ]bd>Åh)Ê (,+¥N o G qyo € KML•g o |•jY
] "$vF:]b/d "0'sYvŠJVj]bGILd o N¢KA{ opo ” o € K°V:t1KA{ o tV:||VhH†Lk] ‹
- o K°KM{ o tN o W(` o ]b€ *G o W(` o ]€ o F:|•K o NI]\F K o^‘yo K„H oTo .
KM{bN oTo KMNMF ]bGAaCLGIGALV:]¡G‰KMNAF K or‹ L o 2G 1…[ KANMF:]GAaCLkKMGCF:|k| q F:€nO o KAG*F:G m ÷pó q F:€nO o KA2G ^L•K™KMNAF:]bGAaCLkKAG m ÷pó
q F:€nO o KMG°V:]ˆtN o W(` o ]b€ 3 "%$3F ]bd m ÷8ÅRVj4] "'VjN3LkK3KANMF:]bGIaˆL•KMG m ÷8ÅRVj4] "%$F:]bd m ÷^ó¥V:4] "0'hY‚¾Kv€sF:] ‘"o
GA{bVhH†]§KM{\F K¦F m ÷pó q F €nO o K8G o ]K¥Vj&] "%$ o £ qyo NIL o ]b€ o GŽF.z=F:€nO o KŽu3NINAVjNpeRF K o<É z3u3eRËRV:t¢Ê5Y :ÁšH†{bLk| o
F m ÷^ó q F:€nO o K&G o ]K’Vj6] "0' o £ qyo NIL o ]b€ o G&F…zvu3e V:tJÊYÄÎ %Á 7 KM{ o €rVjNAN o G q Vj]dbL] ‹ g F:|` o GptVjN8F m ÷ŽÅ
q F €nO o KšF:N o ÊYÄÍjÊZF ]bd ÊYÄÊjÍY>w{ o N o tVjN o SJKA{ o KM{bNIVj` ‹ { q `KH†LkKA{ŸKA{ o<¨ NAG‰KˆG‰KMNAF K or‹ >LGCÍójÃYÄÎ
‘ (K o G qyo N’G o € S4H†LkKA{˜KM{ o G o €TVj]dLG8ÎjÃ:ÍY9 ‘ K o G qyo NŽG o €*F:]bdó Á%jóYÄô ‘ (K o G q"o N’G o €ˆH†L•KM{˜KA{ o
KA{bLNId.GIKMNAF K or‹ jY
w{ oCo £F:a q | o Lk]bdbL€TF K o G¦KM{\F K ‘ ˆ_I`bdL€TLkVj`bGI|kF d\F q KAL] ‹ KM{ oCq F:€nO o K&| o ] ‹ KA{§KAV6€n{bF:]b] o |v€rVj]bdbL½¯
KALVj]bGrSH o €TF:]<L]b€rN o F:G o KM{ o KA{bNAV:` ‹ { q `KRV t=KA{ o GIGIK o a GAL ‹ ]bL ¨ €sF:]KA|kjY÷ o ]€ o S ‹ L•g o ]<KA{ o¥q N o €TLkVj`bG
]\F0KM`bN o V:t ‘ F:]bdH†LdKA{L]F<H†LkN o | o GIGŽ] o K„H¢VjNAOSH o F:Lka­KMV q NAVhgLd o F:| ‹ VjNILkKM{aˆGpKA{\F K8€sF:]€n{bVV:G o
KA{ oRq F:€nO o Kw| o ] ‹ KM{GvGIV™F:G3KMVŽF:€n{bL o g o KM{ o ašF+£LkašF | ‘ F:]bdH†LdKA{ˆtVjNKM{ o^‹ L•g o ]ˆ€n{\F:]b] o |y€TVj]bdLkKMLkVj]bGrY
w{ opq NIV ‘ | o a@V:t1€n{VVjGIL] ‹Žq F:€nO o K†| o ] ‹ KA{bG¢Lk]š|kVjGAG‰ˆ€n{bF:]b] o |G°{\F G ‘yoTo ]šL]g o GIKML ‹ F K o dšH†Lkd o |•™tVjN
G‰G‰K o aˆGJH†L•KM{*V:]b|kVj] o tN o W` o ]b€ *V:t'KANMF:]GAaCLGAGILVj]B¿äóSÄô ÆYw{ o F La@L] q N o gLVj`bG¢HJVjNIOˆ{bF:GJ|F:N ‹jo |k
‘yoTo ]*KMV’KANMF:d o V:”6KA{ o Vhg o NA{ o F:d<V:t q F:€nO o K†{ o F:d o NAG°H†LkKA{šKM{ o z3uve¥SLY o YkSKM{\F0K°GAaˆF:|k| q F:€nO o KMG†{\Fsg o
aCVjN o V+g o NI{ o F:dCKM{\F ]C|kVj] ‹jo NVj] o G ‘ `K3{\Fsg o F:]Lk]b€TN o F:G o d q NAV ‘ F ‘ L|kLkK„8V:t"GA`b€r€ o GAGIt`|yKANMF:]bGIaˆLkGAGILVj]'Y
¤p`bNH¢VjNAO™dbL•” o NAG3Vj]ˆF:€T€rVj`b]K¢V:t7KA{ o tV€r`bGJF ]bd o £ q |VjL•KnF KALVj]™V t7KM{ o ]bF KM`bN o V t7tN o W(` o ]b€ C{bV qbq Lk] ‹
G‰G‰K o aˆG†GA`€n{BF:G Œ |k` o KAVV KM{'Yw{(`bGrS\H o €TV:]bGALkd o NwKM{ o €TF:G o H†{ o N or‘ .KA{ o¥o ]KMLkN o¦q F €nO o KRLGJG o ]KRVj]
FGALk] ‹ | o tN o W(` o ]€rƒH†L•KM{…dbLk” o N o ]K q F:€nO o KMG ‘yo Lk] ‹ G o ]KpV:]ƒdbL•” o N o ]KRtN o W(` o ]b€TL o GrYR÷ o ]b€ o SyH o €sF:]
aCLkKAL ‹ F K o KA{ o3o ” o € KMG V:t€n{\F:]b] o |€TVj]dbLkKALVj]bG ‘ ¦G o | o €rKAL] ‹ KA{ oq F:€nO o K=| o ] ‹ KM{¦KMV ‘yo KMNAF:]bGAaCLkKIK o d¦V+g o N
FŽtN o W(` o ]b€r*F:GwFŽt`b]€rKMLkVj]*V:t1KA{ o tN o W(` o ]€r*€n{bF:]b] o |'€TVj]dbLkKALVj]bGrY[^GJL||k`bGIKANMF K o dCL]šKA{ opo £bF a q | o
o F:NA|kL o NrS ‘ Bd o €TLkdbL] ‹ KMV.G o ]bdZ|}F:N ‹jo N q F:€nO o KMG8Vhg o N ‹ VVdBtN o W` o ]b€ €n{\F:]b] o |G8F:]dGAaˆF:|| q F:€nO o KMG
Vhg o N ‘ F:dtN o W(` o ]€r>€n{\F ]b] o |kGTSH o €sF:]>Lk]b€TN o F:G o KM{ o tNAF:€rKALVj]V:t†KMLa o KM{ o G‰G‰K o a o £ qyo NAL o ]b€ o G
‹ VVdšKMNAF:]bGAaCLGIGALkVj]*€TV:]bdbLkKALVj]GwF:]bd.KM{ o N or‘ .ašF+£LkaˆLk› o KM{ o¦‘ F:]bdH†LkdKM{…F KIKnF:Lk] o d ‘ šKA{ o GIG‰K o a…Y
U\N o W(` o ]b€ *{bV qbq L] ‹ L] Œ |k` o KAVV KM{*a o F:]GJKM{\F0KJKM{ o Œ u3etVjN o F:€n{.tN o W(` o ]b€ <F:]bd o F:€n{.KMLka o GA|kV:K
{\F GŽKMV ‘yo €rVj]bGILd o N o d7S ‘ `K&KM{LG&F |GAV6a o F:]bG’KA{\F KŽKM{ o G o ]bd o N™{\F:G’aˆVjN o €n{bV:L€ o GTY‚„]ŸF:ddbLkKALVj]'S
q F €nO o K3| o ] ‹ KM{bG€TF:]b]bV K ‘"o €n{VjG o ]ˆF N ‘ L•KMNMF NAL|• ‘ `K3F N o N o GIKANALk€rK o d&KMV¦G q"o €TL ¨bo d™g F:|` o GTY4U4L]\F ||k:S0KA{ o
aˆF:GIK o Nѯ„GA|Fsg o N o |}F KALVj]GA{bL q L] Œ |k` o KAVV KM{ q Lk€TVj] o KMG¥a o F:]bGpKA{\F K¦KA{ o ašF GIK o N¦€sF:]§GI€n{ o db`| o H†{bL€n{
GI|}Fsg o GˆN o € o Lkg o VjN™KMNAF:]bGIaˆL•KL]tVjNIašF0KMLV:]'SH†{\F K q F:€nO o KAG*| o ] ‹ KM{GˆF N o `bG o d ‘ >KM{ o aˆF:GIK o NCF:]bd
H†{bLk€n{-KALa o GI|V:KAGšF N o `bG o d tVjNˆF˜GA|Fsg o KA{(`bG*F:|k|VhH†L] ‹§¨ ] o Nѯ ‹ NAF:L] o d-€rVj]KMNIVj|RVhg o NˆKA{ o GIGIK o a
KA{bNAVj` ‹ { q `KTY
w{ o.q F qyo N’LG&VjN ‹ F:]bLk› o dŸF:G’tVj|k|VhH†GTY‚„]KA{ o tVj||kVhH†L] ‹ G o €rKMLkVj]>H o d o g o |V q FBaˆF KM{ o aˆF KMLk€sF:|
aCVd o |bV:t"KM{ o†q NIV ‘ | o a@F:]dš`bGIL] ‹ KM{bLkG3aˆVd o | q NAV q VjG o F:]CV q KALaˆF:|bF | ‹ VjNILkKA{ba €rVj]bGILd o NAL] ‹Ž‘ V:KM{ˆF
GIL] ‹ | o GA|Fsg o¥q L€rVj] o KfF:]bd…F™a&`b|kKAL q | o GI|}Fsg o¥q Lk€TVj] o KsY3‚„]<G o €:Y¢Í&H o¥q N o G o ]K^Vj`NwGALa’`b|}F KALVj]ˆaˆVd o |
F:]dZN o GI`b|kKAG¥tV:NpKM{ o GALk] ‹ | o GA|}Fsg o €TF:G o S4F G¥H o |k|3F:GptVjNpKA{ o a&`b|kKAL q | o GI|}Fsg o €sF:G o Y™œ oCo ]bd˜H†L•KM{ZF
‘ NIL o t1dbLGI€T`bGIGALkVj]<F:]bd*€rVj]b€r|`bGILVj]bGrYœ o VjaˆL•K q NAVV:tGJV t!F:||KM{ o VjN o aˆG¢L]šKA{bLG q F qyo N¢db` o KMV’|}F:€nOV:t
G q F:€ o Y3w{ o G o F:N o Fhg F:Lk|}F ‘ | o Lk]…Fd o KnF L| o d.g o NIGALkVj]6V t=KA{bLG q F q"o NRF0KŽ¿½ÅhÊ0ÆY
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¤p`bN ‹ VF:|\LkG3KAV q NAVhgLd o F q F:€nO o K°GALk› o G o | o € KMLkVj]šF | ‹ VjNILkKA{ba~KA{\F Kv€sF ]šaˆF0£LaCL› o KM{ o KM{bNIVj` ‹ { q `K
Lk]F Œ |` o KMVV:KA{ q L€rVj] o KsYŽUV:NpGALka q |kL€rLkK„jS\H o €TVj]GALd o N¦Vj] o HJFsBd\F0KnFšKMNAF:]bG‰t o NptNAV:a KA{ o ašF GIK o N
KAV˜KM{ o GA|Fhg o YU\VjNCKM{bLkG q `N q VjG o H oƒ¨ NIGIK.d o g o |V q F˜ašF KA{ o aˆF KAL€sF |waˆVd o |†tVjNC€sF q KM`bNIL] ‹ KA{ o
KA{bNAVj` ‹ { q `K8V q KMLaCL›TF KMLkVj] q NIV ‘ | o a Lk]ZKA{ o Œ |` o KMVV:KM{§GA€ o ]\F NALVY.E` ‘ G o W(` o ]KM|k:S4H ošo £ q |kVjLkK¦KA{ o
aCVd o |7KAV ‹:o ] o NMF K o F:]…V q KALaˆF:|7GIVj|`KMLV:]*KMVKM{ o¥q NIV ‘ | o aÌV:t=L]K o N o GIKsYJug o ]…KM{bV:` ‹ {<H o €TVj]GALd o N
KA{ o G q"o €TL ¨ €’€TF:G o V:t Œ |k` o KAVV KM{…L]<KM{bLkG q F q"o NTS\KM{ o aˆVd o |'H o d o g o |V q F qbq |kL o G†KAV*F:].tN o W(` o ]€r
{bV qbq L] ‹ GIG‰K o a~H†{ o N o F^GIL] ‹ | o¢q F:€nO o K3a&`bGIK ‘"o KMNAF:]bGAaCLkKIK o d’Vj]™FRGAL] ‹ | o tN o W` o ]b€ jYœ o L]bL•KMLF:||•
€rVj]bGALkd o N¢F q L€TV:] o KvH†LkKA{*F’GIL] ‹ | o GA|}Fsg o Vj]b|•jY - F K o N3H oRo £K o ]bd*KM{LGvaˆVd o |\KAV’€TV:]bGALkd o NJF q Lk€TVj] o K
H†L•KM{<a&`b|•KML q | o GI|}Fsg o GTY
:1³²\³3GŽ¼»j¸"µ 0¶ ?IHˆ¼¶J-¸yµ ? F%KL
œ o H†Lk|| ¨ NAG‰K o £ q |}F L]*KM{ o aCVd o |7F:]bd<GA` ‘ G o W(` o ]KM|k&_I`bG‰KML•tø*LkKTY3ŠJVj]bGILd o NfF Œ |` o KMVV:KM{ q Lk€TVj] o K
H†LkKM{…F™GALk] ‹ | o GA|}Fsg o Y3w{ o ašF GIK o NwV:t!KM{ o¥q Lk€TVj] o K†LGwN o G q Vj]bGIL ‘ | o tVjN°KMNAF:]bGIaˆL•KAKMLk] ‹&q F €nO o KAGfKAV™KM{ o
GA|}Fsg o `bGIL] ‹ tN o W(` o ]€rZ{bV qbq L] ‹ Y™w{ o aˆF:GIK o N¦€TF:]˜€n{VVjG o tNIVja KA{bN oro dbLk” o N o ]K q F:€nO o K’| o ] ‹ KM{bG
]\F:a o |kšÍ ‘ LkKMGrS7Å jÎjÎ ‘ LkKAGwF:]bd…Î ôÃ:Ê ‘ L•KMGTYw{ o G o¥q F €nO o KAG†V€r€T` q .Vj] o SKA{bN oro VjN ¨ g o¦‘ |` o KMVV:KM{
GA|V KM2G o F:€n{ƒGA|V K^V:t| o ] ‹ KM#{ ÎjóCaCL€rNAVjG o €rVj]bdbGrYfœ o F:GIGA`ba o KA{\F KfKM{ o N o F:N o a&`b|kKAL q | o G o GAGALkVj]bG É F K
| o F GIK4KA{bN oro Ë1tNAVja FfašF:G‰K o N!KAV o g o NIŽGA|Fsg o H†L•KM{’F:]&L] ¨ ]bLkK o GA` qbq |k8V:t\d\F0KnFftV:N o F:€n{™G o GAGALkVj]'Y4uvF €n{
G o GIGALkVj]`bG o G8F.GALk] ‹ | o™‘ F:G or‘ F:]bd q F:€nO o KŽGAL› o LY o Y m ÷^óS m ÷^Í<F:]d m ÷8ÅjY&w{bLkG¥LG¢_I`bG‰KML ¨bo d§GALk]b€ o
Vj`bNwV ‘ _ o €rKALkg o LkG°KMV™d o K o NIaˆLk] o KM{ o ašF0£Lka&`ba@KM{bNIVj` ‹ { q `K q V:GAGAL ‘ | o Yw{(`bG†KM{bLkGJKMNAF:]bGA|F K o G°KMVCF:]
`b]b|LkaˆL•K o dŽGI` qbq |•’V:t o F:€n{ q F:€nO o KK„ qyo Y3E or‹ a o ]KnF KALVj]’LGF GAGA`a o d&KMVpV€T€r`bNF K=KM{ o - Î:ŠJ[pz§|}Fs o NTY
- o KwKM{ o¦q NAV ‘ F ‘ L|kLkK„CV:t!GA`b€r€ o GAGIt`|!KANMF:]bGIaˆLkGAGILVj]*V t o F:€n{ ‘ LkKJL]<F ‹ Lkg o ] q F €nO o K ‘yBo MÉ Œ EOe NÑË Yœ o
F:GAGI`ba o KM{\F0K M LGvF8NMF:]bdVja®g F:NALF ‘ | o H†LkKM{C€T`a&`b|}F0KMLkg o dbLG‰KMNAL ‘ `KALVj]&t`b]€rKMLkVj] ‹ Lkg o ] ‘ Q P RÉ M ËÜY4[^|k|
‘ LkKAGwV:t=F q F:€nO o KRF:N o F:GIGA`ba o d.KAV™{\Fsg o KM{ o GAF:a o Œ EeH†{L| o KM{ o Œ EeªF:GAGIV€rL}F K o d*H†L•KM{.dbL•” o N o ]K
q F:€nO o KMG^F:N o a&`KA`\F:|k|kˆL]bd orq"o ]bd o ](KTY3[ q F:€nO o K^LkGw€TVjNINA` q K o d6Lkt o g o ]BFGALk] ‹ | op‘ LkK†LkGwL] o NINAVjNrY
‡RVhH H o _I`bG‰KMLktø…KM{ o aCVd o |YŽ[ q F €nO o KŽLGRKMNMF ]bGAaCLkKIK o d§Vj]ZF*GIL] ‹ | o tN o W(` o ]b€ §LNIN o G q"o €rKALkg o V:t
LkKMG¦| o ] ‹ KM{'Y8w{ o Œ Ee®F:GAGIV€rL}F K o dBH†LkKA{§F ‘ LkK^d oTqyo ]bdGŽG‰KMNAV:] ‹ |k6Vj]BKA{ o tN o W` o ]b€ ZF:GpKMNAF:]bGAaCLGѯ
GALV:]>€TVj]bdLkKMLkVj]bG&€TF:] ‘"ošq VVjN&Lk]Vj] o tN o W(` o ]€r>H†{bLk| o KA{ o ašFs ‘"o*‹ VVd>L]>F ]bV:KM{ o NTY˜‚¾t†KM{ o
tN o W(` o ]b€TL o GwF N o NMF:]bdVja g F:NALF ‘ | o GTSjKA{ o ]šKA{ o Œ Ee“LGvF:|kGAV8NMF:]bdVja6Y4‚„] Œ |k` o KAVV:KA{'StN o W` o ]b€rL o G¢L]
KM{ o tN o W(` o ]b€rš{bV qbq Lk] ‹ G o W(` o ]b€ o F:N o^‹jo ] o NAF K o d ‘ šF q G o `bdVjNMF:]dbVja—]`a ‘"o N ‹jo ] o NAF KMVjN¢G oro d o d
‘ 6KM{ o ašF:G‰K o NAGpF dbdbN o GAG¥F:]d€T|V€nOYpw{(`bGpKM{ o tN o W(` o ]b€rL o G¦€TVj]bG‰KML•KM`K o TF S q G o `bdV ¯„NAF:]bdbVja g F:NAL½¯
F ‘ | Vo U F:]bdKA{bLG&aCV:KALkg F K o GŽKA{ o F ‘ Vhg o aCVd o |Y§÷fV+H o g o N™H o HJVj`|dŸ|LkO o KAVa o ]KMLV:]KM{\F0K™GALk]b€ o
KM{ o tN o W(` o ]b€TL o G¦F N o8‹jo ] o NMF K o d ‘ 6Fˆzv‡~G o W` o ]b€ o S1F:|k|'KM{ o tN o W(` o ]b€rL o Gp€sF:] ‘"o O(]bVhH†]§F:{ o F:dƒV:t
KMLa o Y=‚¾t'KM{ o Œ EefG¢F:GAGIV€rL}F K o dH†LkKA{CKA{ o G o tN o W(` o ]b€rL o G°F:N o O(]bVhH†].F:{ o F:dšF:GH o ||SKA{ o ]CKM{ ofo ]KMLkN o
q F:€nO o Kf| o ] ‹ KM{.G o W(` o ]€ o €sF:] ‘yo d o K o NIaˆLk] o d.`bGIL] ‹ F&d o K o NAaCL]LGIKAL€RV q KMLkaˆLk›sF KALVj]7Y=÷fVhH o g o NrS\KM{ o
tN o W(` o ]b€r G o W` o ]b€ o G<F:N o `bGI`\F:|k|k>|kVj] ‹ F:]bd €rVj]KnF:Lk] G o g o NMF:|RdbLk” o N o ]KCtN o W(` o ]b€TL o GrYw{(`bGˆKM{ o
V q KMLkaˆLk›sF KALVj]6H†L|| ‘yo €TVja q `KMF KMLkVj]\F:|k|k6L]K o ]bGAL•g o Y Œ o GILd o G8KA{ o GIKMV:NMF ‹jo V:t¢KM{ o N o GA`b|•KMGŽF:]bdZKM{ o
KnF ‘ | o |kVV:O` q H†L|k| F:|GIVšN o W(`bLN o GI` ‘ GIKMF:]KMLF:|=G q F:€ o Y¦X…VjN o La q V:NIKnF ](KA|k:S Œ Ee LGf]bV:K^Fšd o K o NIaˆLk]¯
LGIKAL€*t`b]€rKMLkVj]ŸV:tftN o W(` o ]b€r¡GIL]b€ o KA{ o KMNAF:]bGAaCLGIGALkVj]>€TVj]dbLkKALVj]bGŽg:F NIH†L•KM{>KMLka o tVjN&KA{ o GMF:a o
tN o W(` o ]b€r:Y w{(`bGCKM{ o Œ Ee LG]bV:KO(]bVhH†]F { o F:d¡V:tfKMLka o.o g o ]-Lkt†KM{ o tN o W(` o ]€rŸG o W(` o ]b€ o LGrY
÷ o ]€ o KM{ o¦q N o gLV:`bGwO(]bVhH†| o d ‹jo V:t KM{ o tN o W(` o ]€r<G o W(` o ]b€ o aˆFs*]bV K ‘"o `bG o t`b|Yw{bLGwaCV:KALkg F K o G
Vj`bN¦aCVd o |=H†{bLk€n{ZF:GAGI`ba o GpKM{\F0K¦KM{ o tN o W(` o ]€TL o G8F:N o NAF:]bdbV:a g F:NALF ‘ | o GTS7F:]bd§GA` ‘ G o W` o ]KM|•KM{ o
F:GAGIV€rL}F K o d Œ Ee†G†F:N o F:|kGAV™NMF ]bdbVja—g:F NAL}F ‘ | o GTY4œ o dbV]bV:KfF:GIGA`ba o F:].G qyo €rL ¨ €¥€n{\F:NAF:€rK o NILGIKAL€¦V:t
KM{ o €T`a&`b|}F0KMLkg o dbLG‰KMNIL ‘ `K o d.t`b]b€ KMLkVj]6V t=KA{ o NMF:]bdVja g F:NIL}F ‘ | Bo MÉ Œ EeRË Y
[ q F:€nO o KwLGKANMF:]bGIaˆL•KAK o dšV:]*F¥GAL] ‹ | o tN o W(` o ]b€ *Lk]bd oTqyo ]d o ]K°V t'LkKAG¢| o ] ‹ KM{'Yw{ o | o ] ‹ KA{ˆV:t7KM{ o
q F:€nO o K4LkG1F K aCVjGIK óJGA|V KMG É XÍ WkÅ+Î:óJaˆGMË Y w{(`bG!KANMF:]GAaCLGAGILVj]^€TVj]bdLkKMLkVj]bG1F GAGAV€TLF K o dpH†LkKA{ŽFJtN o W(` o ]b€r
dbV¥]bV:K3€n{\F:] ‹jo GAL ‹ ]bL ¨ €sF:]KM|•’Lk]FpGA{bV:NIK3db`bNAF KMLkVjY] jKA{bLGLkG o G q"o €TL}F ||k8GIV¥H†{ o ]C€TVj]bGILd o NALk] ‹ H†LN o | o GAG
d o gL€ o G&KA{\F K’F:N o ]bV:K&aCV ‘ Lk| o Y.w{bLGŽaˆV:KALkg F K o G¥KM{ o F:GAGI`ba q KMLV:]V:twKA{ o GAF:a o Œ Ee@tVjNŽF:|| ‘ L•KMG
L]–F q F:€nO o KsY œ o F:GIGA`ba o KM{bF K*KM{ o Œ Ee†G*tVjN*dbL•” o N o ]K q F €nO o KAGƒF N o a&`KM`\F:|k|k¡L]d oTqyo ]bd o ]KsY
w{bLGRF:GAGI`ba q KMLkVj]<LG†aˆV KMLkg F K o d ‘ .KM{ o tF:€ KfKA{\F KfdbL•” o N o ]K q F:€nO o KAGpF:N o KANMF:]GAaCLkKAK o d…L]<dbL•” o N o ]K
tN o W(` o ]b€TL o GvF:]bd&KANMF:]GAaCLGAGILVj]Ž€TVj]dbLkKALVj]bG=ašFs ‘"o W`LkK o dbLk” o N o ]KtVjN4dbLk” o N o ]K4tN o W(` o ]€TL o GTY3‡fV:K o
KM{\F K ‘ `NAGIK„§|kVjGAG o G¥HJV:`b|d ‘yo N o F:|kLG‰KML€’L]KM{ o F ‘ G o ]b€ o V t¢tN o W(` o ]€rZ{bV qbq L] ‹ YC÷fV+H o g o N’F:G¦KM{ o
tN o W(` o ]b€TL o GfKMV ‘"o `G o d…tVjN°KMNAF:]bGIaˆLkGAGALkVj]<F:N o8‹:o ] o NMF K o d6F:GfF q G o `dbVjNMF ]bdbVja©](`ba ‘yo N†G o W(` o ]€ o S
F:GAGI`baˆLk] ‹ L]bd oTqyo ]bd o ]K q F €nO o KR|V:GAG o G†LG4_I`bGIKAL ¨\o d'Y
œ o F:GAGI`ba o KM{bF K.F KˆKM{ oƒ‘"or‹ L]b]L] ‹ V:t8FGA|kV:KsS¢KM{ o aˆF:G‰K o NˆO(]bVhH†G*KM{ o Œ Ee ‹ V+g o NI]bL] ‹ KM{ o
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‘ L•KMG&V tRKA{ o.q F:€nO o KCKMV ‘"o KANMF:]GAaCLkKAK o d>Lk]ŸKA{ o GA|kV:KsSvF:]d¡`G o GKM{LG&O(]bVhH†| o d ‹jo L]Ÿd o €TLkdbL] ‹ KA{ o
q F €nO o K8| o ] ‹ KA{'YŽœ o `bG o KA{bLG¦F GAGA`a q KALVj]aˆF:Lk]b|k<tVjN¥F:]bF:|k(KMLk€sF:| o F G o Y™w{LG¥F:GIGA`ba q KMLkVj]LG¦]V:K
] o € o GAGMF NI*tVjN¢KM{ opo £ o €T`KMLV:]…V t!KA{ opq NIV q VjG o d6F | ‹ VjNILkKA{ba.KA{ o F:| ‹ VjNAL•KM{ba@€TF:] ‘"o^o £ o €r`K o d ‘ F:G o d
Vj] o G‰KMLaˆF K o GfV:t€n{\F ]b] o |=€TVj]dbLkKALVj]bGfF:|kGAVbY°œ o HJVj`|dF:|kGAVC|LkO o KMVCN o aˆF:NIO*KM{\F KfKM{ o F:GIGA`ba q KMLkVj]
N oT‹ F:NIdbL] ‹ O(]bVhH†| o d ‹jo V t1€n{\F:]b] o |7€rVj]bdbL•KMLkVj]bGv{\F:G ‘yoTo ]*aˆF:d ofo |G o H†{ o N o F G¢H o ||¾¿cS9 ÆYU4Lk]\F:|k|kjS H o
F:|kGAVCF:GIGA`ba o KM{\F K†KA{ o N o g o NAG o €n{\F ]b] o |1tNIVja«KM{ o GI|}Fsg o KMVKM{ o aˆF:GIK o NwLkGf]Vj]¯„|kVjGAG‰jYvw{bLG†€TF:] ‘yo
_I`bG‰KML ¨\o d§Vj]KM{ o™‘ F:GALkG¦V:tvKM{ o GIašF:|k|4GIL› o V t¢KA{ o F:€nO(]bVhH†| o d ‹jo a o ]K q F:€nO o KMG8G o ]KŽV:]§KA{ o N o g o NAG o
€n{\F ]b] o |JL]€TF:G o V tRV:] o HJFh€TVjaCa&`b]L€sF0KMLV:]ZtNIVja KA{ o aˆF:GIK o N’KAVƒKM{ o GA|Fhg o Y˜¤p`bN&aCVd o |v€sF:]
‘yoˆo £K o ]d o d>KMV6€sF K o N¥KMV…K„HJVƒHJFs€rVjaCa&`b]bLk€sF KALVj]bG¦H†L•KM{F…|VjGIGI§N o g o NAG o €n{\F:]b] o |Y - F K o NTS!H o
H†Lk||4N o |F0£BKA{ o G o F:GIGA`ba q KALVj]bG¥Lk]ZV:`bN¦GALka&`b|}F0KMLV:]bGTY™‡fVhH H o d o aˆV:]bGIKANMF K o {V+H®KM{bLkG¦aˆVd o |4€sF:]
‘yo `bG o d…KAV q NAVhgLd o F™KA{bNAV:` ‹ { q `K†V q KMLkašF | q F €nO o KR| o ] ‹ KA{.€n{bVjL€ o F:| ‹ V:NALkKA{ba…S(H†{L€n{<LG°GILa q | o KMV
Lka q | o a o ]KsY
ö¥L•g o ]…KA{ o Œ Ee M tVjN°KM{ o tN o W(` o ]b€ …Vj]…H†{L€n{6F q F €nO o KRLGwKAV ‘yo KMNMF ]bGAaCLkKIK o d7SKM{ o aˆF:GIK o N†V:t
KA{ o&q Lk€TVj] o K¦d o €TLd o GpKM{ o™q F:€nO o K¥| o ] ‹ KM_{ d eÉ M Ë ‘ L•KMGTS'F:G¦Fšt`b]b€ KMLkVj]BV:t3KM{ o Œ Ee¥S1F KRKM{ o™‘yoT‹ Lk]b]bLk] ‹
V:t!KM{ o8q F:€nO o K^KMNAF:]bGIaˆLkGAGALkVj]'Yw{ o aˆF:GIK o N†{\F:GwKA{bN oro €n{bV:L€ o GwtVjON d eÉ M Ë°F:G†dbLkGA€T`GAG o d ‘yo tVjN o Y¢EL]€ o
Œ EefGCV:tpdLk” o N o ]K q F €nO o KAG.F:N o a’`KM`\F ||kL]bd oTqyo ]bd o ]KsSw| o ] ‹ KA{bGˆV tpdbL•” o N o ]K q F:€nO o KMG*F:N o F:|kGAV
a&`KM`\F:|k|kŸLk]bd oTqyo ]d o ]KsY~w{(`bG.KM{ oq F:€nO o K…KANMF:]GAaCLGAGILVj] q NAV€ o GAG<LGšFN o ] o HJF:| q NIV€ o GAGrSRH†L•KM{
KA{ o GIGIK o aÀN o ] o H†Lk] ‹ LkKAG o |•t°F0tøK o N o g o NI q F:€nO o K8KMNAF:]bGAaCLGIGALkVj] ¿ Å+Î0ÆY’œ o H†Lk||]V+H o g:VjO o N o ] o HJF:|
N o HJF:NAd§KM{ o VjNIƒKMV<€n{\F:NAF:€rK o NALk› o KM{ o KM{bNIVj` ‹ { q `K8V:t°F ](F:N ‘ L•KMNAF:NI q F:€nO o KŽ| o ] ‹ KM{§G o | o €rKMLkVj]§NA`b| o
d RÉ M Ë W - o KKM{ o €T`a&`b|}F0KMLkg o dbLkGIKMNIL ‘ `KMLV:]’t`b]b€ KMLV:]™€TVjNIN o G q V:]bdbL] ‹ KAVpKM{ o Œ Ee ‘yo d o ]bV K o d ‘  P RÉ M ËÜY
w{ o ]'SKM{ o Fsg o NMF ‹jo db`NMF KALVj]V:t7F8GI$ L] ‹ | o N o ] o HJF:| qyo NALkVd™LkGKM{ o Fsg o NMF ‹jo | o ] ‹ KA{CV t'F q F:€nO o KvH†{bL€n{
H o d o ]bV:K o F:G df eÉ M Ë S gihdf RÉ M kË j_lnm o df eÉ M qË p,P RÉ M rË W=‡fV:K o KM{bF QK df RÉ M Ë8F:]Td d RÉ M Ë¥F:N o €T|kVjG o |k§N o |}F K o dZtVjN
Œ |k` o KAVV KM{>H†LkKAD{ dRf KMF:O(L] ‹ KM{ o g F:|k` o GV:t’9Y Î:ó aˆG o € S^ÅjYäôÃjó aCG o €…F:]bd-ÍYkÅhÎjó aCG o €.tVjN d^g F:|k` o GV:t
Í S4Å jÎjΚF:]bd˜Î:ôjÃ:Ê ‘ L•KMGpN o G qyo € KML•g o |•jY8w{(`bGTS Vj]b€ o KM{ o ašF:G‰K o Npd o €rLd o sG d ‘ F G o d§Vj] M S d¢f LkGpF:|kGAV
F:`KMVjaˆF KMLk€sF:|k|kd o K o NAaCL] o d ‘ F:G o dƒVj]<KM{ o €n{bV:L€ o V:t d„Y3w{ o N o LkGRF™N o HJF:NAdƒF:GAGIV€rL}F K o d.H†LkKA{ o g o N‰
q F €nO o KJKMNMF ]bGAaCLGIGALV:]'Y4‚¾t1KA{ opq F:€nO o Kw{bF:tG d ‘ LkKAGTS(KM{ o ]*KM{ o N o H°F:NId.LBG d L•t F:|k|KA{ o^‘ LkKMG¢V:t'KA{ opq F:€nO o K
N o F:€n{KM{ o N o € o Lkg o NvGA`b€r€ o GIGIt`b|k|kCF:]dˆÊ¥Lkt"F K3| o F:G‰KvVj] ow‘ L•K3N o F €n{ o GvKM{ o N o € o Lkg o N3L] o NINAVjNrYw{(`bGvKA{ o
o £ qyo € K o d>N o HJF:NIdtVjNŽF q F:€nO o K’L8G d eÉ M Ë MuRv wx Y<‡fV+H¥S ‹ Lkg o ]˜KA{ o €r`b$ a&`b|F KML•g o dbLG‰KMNIL ‘ `KALVj]t`b]€rKMLkVj]
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KA{bLG ‘ ’F GAGA`aˆLk] ‹ KA{\F K4F q F:€nO o KV t\| o ] ‹ KMI{ d\LG=F:GAGIV€rL}F K o dŽH†L•KM{’F^N o H°F:NId&V:Øt d ‘ L•KMG=F:G!|Vj] ‹ F:G × ‘ LkKAG
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V:t4KA{bLG†GA|Fsg o S`bGIL] ‹ KM{ o V q KMLkašF:|7GIKMNAF K or‹ .Lk]…KA{ o GAL] ‹ | o GI|}Fsg o €sF:G o Y°X6VjN o G qyo €rL ¨ €TF:||•jSKA{ o V q KML½¯
ašF:| q F:€nO o K8| o ] ‹ KM{KA{bN o GA{bVj|kdbGptVjN o F:€n{§GA|Fhg o F:N o&q N o ¯¾€TVja q `K o dZF:G qyo NpKA{ o f¤pfEZF:| ‹ VjNILkKM{a6S
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GA|}Fsg o LGv€n{bVjG o ]'SL]KM`LkKML•g o |k&KA{bNAVj` ‹ { q `K¢LGvV q KALaCL› o dLkt"KM{ oRq F:€nO o K°| o ] ‹ KA{šLkGvG o | o €rK o d<F:G qyo N3KM{ o
V q KMLkašF |GIKANMF K oT‹ ŽtVjN4KA{ o GA|}Fsg o Yw{(`bG3KM{ o KMF:GAOŽLGKAV¦€n{bVV:G o KM{ o GI|}Fsg o V q KMLaˆF:|k|kjY1‚„]KA`bLkKALkg o |k:SjKM{ o
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q F qyo NvF qbq |kL o G4KMV ‹jo ] o NIL€°H†LkN o | o GIG€n{\F:]b] o |GvF:]bd]bV K3G qyo €TL ¨ €sF ||k8KMV Œ |` o KMVV:KM{'SjF:]bdCF:G3GA`b€n{CdbV o G
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N o € o L•g o NfG o | o €rKMLkVj]<GIKANMF K oT‹ .KA`bNA]bG†Vj`KwKMV ‘"o Lkd o ]KMLk€sF:|7L] ‘ V KM{'Y
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o £ q |}F L]Z|}F K o NTYCw{ o dbLk” o N o ]K ‘yo ]€n{bašF NAO§F:| ‹ VjNAL•KM{baCGp`bG o dZtVjN¥€TVja q F:NILGAV:]F:N o F:|GIV o £ q |}F:Lk] o d
|}F K o NTYœ o `bG o X6F KM|F ‘ tVjNJKM{ o G o GALka&`b|F KMLkVj]bGTY=[GALk] ‹ | o^q L€rVj] o K†€rVj]bGILGIKAL] ‹ V tF™aˆF:GIK o N†F:]bd<dbL•t}¯
t o N o ]KRGI|}Fsg o G†LGw€TN o F K o d'Yœ o dbV]bV:K†€rVj]bGALkd o N°KA{ o¥q L€rVj] o K°tVjNAaˆF KALVj] q {\F:G o Lk].Vj`bNwGALka&`b|F KMLkVj]bGTY
‚„]6F ||"KA{ o GALka&`b|F KMLkVj]ˆN o GI`b|kKAGTSKA{ o KM{bNIVj` ‹ { q `K†GA{V+H†]…LG¢KM{ o Fsg o NMF ‹:o V+g o N¥ÅhʒKANAL}F |GTS(H†{ o N o¥o F:€n{
KMNALF:|7€rVj]bGILGIKAGwV:tvÅ jÊjÊ Œ |` o KMVV:KM{*GI|V:KAGTYœ o €TVj]GALd o N†F™efFh| o L ‹ { o NANIVjN°aCVd o |"tV:NJKM{ o tN o W(` o ]b€r
€n{\F:]b] o |GfL]…F:|k|"KM{ o¥¨b‹ `bN o GTY
w{ o KA{ o VjN o KAL€sF |!aCVd o | d o g o |kV qyo dBLk]6KM{ o’q N o gLVj`G^G o €rKALVj]BLkGR`G o d6KMV*d o K o NAaCL] o F:]ƒV q KMLkašF:|
q F €nO o K| o ] ‹ KM{G o | o €rKALVj]ŸF:| ‹ VjNILkKM{a6Y…w{ o aCVd o |¢LkG ‘ F:G o dŸVj]>F GAGA`a q KALVj]G&V:t†H†{bL€n{H o N o |}F0£
KA{ o F:GIGA`ba q KMLkVj]KA{\F K’KA{ o Œ u3e—tV:N&F q F NIKMLk€T`b|F:N¥tN o W(` o ]b€rLG&O(]bVhH†]'Yœ o €sF:|k|vKA{bLG Œ u3e N o ¯
|F0£F KMLkVj]'Y¥œ o €rVj]bGALkd o N¦KA{ o™q"o NItVjNIašF ]b€ o V:t3KA{ o V q KMLkašF |4F:| ‹ VjNILkKM{a €rVj]bGILd o NAL] ‹ V:]b|k q L€rVj] o KMG
H†L•KM{ƒa’`b|kKAL q | o GA|}Fsg o Gpdb` o KMVˆ|}F:€nO<V:tG q F:€ o Y^÷ o N o H o H†L|k|1L]g o GIKAL ‹ F K o KA{ o tVj|k|VhH†L] ‹ F | ‹ VjNILkKA{baˆG
F:G ‘yo ]€n{bašF NAO(GfKAV€TVja q F:N o H†LkKM{<KM{ o V q KMLkašF:|"F:| ‹ VjNAL•KM{baCGTY
ò*¸yº=µ!¹·+L¸ ó=¼Æ
µ ôÓõ ÔI·+·0ö¹ J Õ 1!w{ o ašF GIK o N!KANMF:]GAaCLkKMG!Vj]b|• m ÷†£ É H†{ o N o ¼<l Å ynXÍ yÜójË q F:€nO o KMG
KAV o F:€n{šGI|}Fsg o Lk]ˆF¥NAV:`b]bdCNAV ‘ Lk]™tF:GA{bLkVj]™H†LkKA{bVj`K3N oT‹ F:NIdCKAV¦KM{ o €n{\F:]] o |€TV:]bdbLkKALVj]™tVjN o F:€n{šGI|}Fsg o Y
w{(`bG†KM{bLkGwGIKANMF K oT‹ .LkGwV ‘ |kLkgLVj`G ‘ V KM{<L]<N or‹ F:NIdbGwKMV€n{bVVjGALk] ‹q F:€nO o Kp| o ] ‹ KA{…F:]bd<GA€n{ o db`b|kL] ‹ Y
ò*¸yº=µ!¹ ·0ظ ó=¼µ ¸ ¶h¼ ÔI·+·+¸ ¶ Õ 18w{ o ašF:G‰K o N8KANMF:]bGIaˆL•KMG¦KMV o F:€n{GA|}Fsg o Lk]F6G‰KMNIL€rK8NIVj`b]bd
NIV ‘ L]§tF:GI{bLVj]7S ‘ `K’€n{bVVjG o G’KM{ oˆq F:€nO o K™GIL› o KMV…KMNMF ]bGAaCLkK ‘ F:G o d>Vj]ZKM{ o €n{\F:]b] o |J€rVj]bdbL•KMLkVj]bG¥KMV
KA{\F K†GA|Fsg o Y3w{ o aˆF:GIK o NwLG°KA{(`bGRV ‘ |L•gLkVj`bGvH†LkKM{…N o G qyo € KfKAVˆGI€n{ o d`b|Lk] ‹ Y
4
4
7
Multiple slaves, known BER, one way optimal size retransmissions
x 10
9
Four slaves with unknown lossy forward channel
x 10
optimal
rropt
rrdh5
rrdh3
rrdh1
8
6
7
6
4
Throughput (bytes/sec)
Throughput (bytes/sec)
5
optimal
rropt
rrdh5
rrdh3
rrdh1
3
5
4
3
2
2
1
1
0
2
2.5
3
3.5
4
4.5
5
No of slaves in the piconet
5.5
6
6.5
7
0
0.2
0.4
0.6
Parameter value
0.8
1
−3
x 10
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„‚ ].U4L ‹ `bN o ÅfH o GI{bVhH“KM{ oR‘"o {\FsgLVjNvV:t'KA{ o dbL•” o N o ](K¢GIKANMF K oT‹ L o GJF:GJF8t`b]b€rKALVj]CV:t'KA{ o ](`ba ‘"o NJV:t
GI|}Fsg o GwL]*KM{ o¦q L€rVj] o KTY3‡RV:K o KM{bF KwL]*KA{bLG ¨\‹ `bN o SKA{ o ](`ba ‘yo NwV:t!GA|Fsg o GwLk]*KM{ o¦q L€TV:] o KwLkG q |kV:KAK o d
Vj]8KM{ o £¯„F0£LG=`b]b|LkO o V:KM{ o N ¨b‹ `bN o GTY‚„]&KA{bLG!€sF G o H o F:GIGA`ba o FRNAFs| o L ‹ {’€n{\F ]b] o |H†LkKM{’F q F:NAF:a o K o N
V:tÎYkÅ £7Ås)Ê (,+hY4w{ o ](`ba ‘yo NV t\GA|Fhg o GLk]ŽKA{ oJq Lk€TVj] o KLkG!g F:NIL o dŽtNAV:a®ÎwKMVpÃY4w{ o V q KMLkašF |(F:| ‹ V:NALkKA{ba
{\F G¢KM{ o^‘yo GIK q"o NItVjNIašF ]b€ o V:t F:|k|\KM{ o GIKMNAF K or‹ L o G¢€rVj]bGILd o N o d.LkNAN o G qyo € KML•g o V t'KM{ o ](`ba ‘yo NJV t1GA|Fhg o G
Lk]˜KM{ ošq Lk€TVj] o KsY…[^]>Lk](K o N o GIKAL] ‹ V ‘ G o NIg F KALVj]˜KM{bVj` ‹ {LkGŽKM{bF K’KA{ ošqyo N‰tVjNAaˆF:]b€ o V:t°KA{ o V q KMLkašF:|
Lk]b€TN o F:G o G^H†L•KM{BF ]BL]b€rN o F:G o Lk]6KA{ o ](`ba ‘yo NRV:t3GA|Fhg o GrYpw{ o V:KA{ o NRGIKANMF K oT‹ L o G^Lk]b€T|k`bdbLk] ‹ NINAV q K^dbV
]bV K°GA{V+H%F:]*Lka q NAVhg o a o ](KJL]*G‰GIK o a qyo NItV:NAaˆF:]b€ o H†LkKM{*F:].L]b€rN o F:G o Lk]šKM{ o ]`a ‘"o N°V:t GI|}Fsg o GTY
w{(`bGrS`bGIL] ‹ KM{ o V q KMLaˆF:|GIKMNAF K or‹ jS(H†LkKA{CK„H¢V’GI|}Fsg o GvKA{ o ašF0£Lka&`ba KAV:KnF |bKM{bNIVj` ‹ { q `K¢F KAKMF:L] o dˆLkG
ó5Y 0£"ÅhÊ + ‘ K o G qyo N¢G o €TVj]bd*H†{ o N o F:GJKA{ o aˆF0£La&`a®KMV:KMF:|\KM{bNIVj` ‹ { q `KwF0KAKnF L] o dCH†L•KM{*G o g o ].GA|Fhg o G
LküG Yäô 0£"ÅhÊ + ‘ (K o G q"o NG o €rVj]bYd F:]Lk]b€TN o F:G o V:t"F ‘ Vj`KwÅ+à qyo N4€ o ]KTYœ–LkKM{’aˆVjN o GA|Fsg o GrSKM{ o V q KMLkašF:|
G‰KMNMF0K oT‹ .{\F:GfF ‹ N o F K o N†€n{bVjL€ o V:tGI|}Fsg o GwH†{bL€n{<KMNAF:]bGA|F K o GwKMV ‘"o KAK o N†GIGIK o a qyo NItV:NAaˆF:]b€ o Y
œ o ] o £Kw€rVj]bGILd o N¢N o |}F+£bF0KMLV:]šÍSLY o Y•SF:GAGI`ba o KM{\F0KJKM{ o €n{\F:]] o | Œ u3eLkG¢]bV KJO(]bVhH†] ‘ `KJ{\F:GvKMV
‘yo¥o GIKALaˆF K o d'Y°w{ o €n{\F:]b] o | Œ u3e LkG o GIKALaˆF K o dƒF G o £ q |}F:Lk] o d o F:NI|L o NTY¢‚„]BU4L ‹ `bN o Î&H o GA{V+HKA{ o
KA{bNAVj` ‹ { q `K¢g o NAGA`G°€n{\F:]b] o |'W(`\F:|kLkK„™H†{ o ]*KM{ o V q KALaˆF:|F:| ‹ VjNAL•KM{ba `bG o G°€n{\F:]b] o | o GIKMLkašF0KMLV:]'Y!œ o
€rVj]bGALkd o N’FƒGA€ o ]\F NALV6H†{ o N oT‘ KM{ o dbL•” o N o ]K™GI|}Fsg o G&{\Fsg o GI|L ‹ {KM|kBdbLk” o N o ]K™€n{\F:]] o |¢€TVj]bdLkKMLkVj]bGrY
w{ o LkKA{GI|}Fsg o {\F:G™F…€n{\F:]b] o | ‹ L•g o ] ‘ efFs| o L ‹ {˜dLGIKANAL ‘ `KMLkVj]§H†LkKM{F q F:NAF:a o K o N äÎý H†{ o N o ý
LG&KM{ o.q F:NMF a o K o N’V:tRKA{ o NMFs| o L ‹ {>dLGIKANAL ‘ `KMLkVj]>F:G ‹ Lkg o ] o F:NI|L o N&F:]d¡LkG q |kV:KAK o dŸVj]KM{ o £(¯„F0£LG
V:tRKA{ o*¨\‹ `N o Y˜œ o G oTo KM{\F0K™KM{ o V q KMLaˆF:|¢F:| ‹ VjNAL•KM{ba qyo N‰tVjNAaCG ‘"o KAK o N™`b]bd o NCF:||vN or‹ La o GŽKM{\F:]
KM{ o V ‘ |kLkgLVj`G°NANIdb{£…GIKANMF K oT‹ L o GwKM{bF KfG o ]d ¨ £ o d¯„| o ] ‹ KA{ q F:€nO o KAGTY°‚¾KfLG†V ‘ gLV:`bGwKM{\F K†KA{ o V q KMLkašF |
GIKMNAF K or‹  ‹ L•g o Gf` q tF:LNI] o GIGfLk] o £€n{\F:] ‹jo tVjNwKM{bLkG ‹ F:L]7Yv‚¾t4€n{\F:]b] o |•¯ ‘ F:G o dBGI€n{ o db`|L] ‹ LkGf]V:Kf`bG o d
Vj]F:€r€TVj`b]K¦V ttF:LNI] o GIG^€TV:]bGALkd o NAF KMLkVj]bGTSyNANIV q KpF:€n{bL o g o GpKM{ oŽ‘"o GIK qyo N‰tVjNAaˆF:]b€ o V ‘ KnF:Lk] o d ‘ ƒF:]
¨ £ o d¯¾| o ] ‹ KM{…GIKANMF K oT‹ *tV:N†F ‹ Lkg o ]<€n{\F:]b] o | W`bF:|L•K„jSbF ]bdƒF d\F q KAGwGAaCVV:KA{b|kCKMV€n{\F ] ‹jo L].€n{\F:]] o |
W`bF:|L•K„jY [^dbdL] ‹ €n{\F ]b] o |½¯ ‘ F G o d–GI€n{ o db`|L] ‹>q NAVhgLd o G<F:]F:dbdbL•KMLkVj]\F:|†L]€TN o F:G o Lk] KM{NAVj` ‹ { q `K
F:€TNIVjGAG†KM{ o8‘ VF:NAd7Yvœ o {\Fsg o €rVj]bGILd o N o d6aˆV:N o g F:NALF KMLkVj]bGwLk]…GILa&`|}F KALVj]bGJL]b€r|`bdbLk] ‹ N o |}F0£Lk] ‹ KM{ o
F:GAGI`ba q KMLV:]bGV:t"|VjGIG4tN oro N o g o NIG o €n{\F:]b] o |GvF:]bdGAF:a o GIL› owq F:€nO o KvN o KANMF:]GAaCLGAGILVj]GTY4w{ o G o N o GA`b|•KMG
F:N o ]bV:K†GI{bVhH†]6tVjNw|F:€nO*V:t=G q F:€ o Y
þ!/
³ ÿŽ¸"µ!» Öº ?s¼¸yµ
Œ |k` o KAVV:KA{Ž{bF:G ‘yoTo ]ŽKA{ o GI` ‘ _ o €rKV tba&`b€n{&F KAK o ]KMLkVj]Ž|F K o |k:Y Œ |` o KMVV:KM{¥`bG o G=tN o W(` o ]b€rŽ{bV qbq L] ‹
F:]bd™V qyo NAF K o GL]8KM{ o `]b|Lk€ o ]G o dCÎYäÁ(ö¥÷R›v‚‰EbX ‘ F ]bd'SjH†{bLk€n{&LG4F:|GIVp`bG o d ‘ ’‚Ñu3u3u3ôjÊÎY•ÅjÅwNMF dbLVjG=F:G
H o ||yF:GvV:KM{ o N¢d o gL€ o GvGA`b€n{.F G¢aCL€rNAVhH°Fsg o Vhg o ]bGTY3w{(`bGrSLkKv€TF:] ‘yofo £ q"o €rK o d*KM{bF K3KM{ o tN o W` o ]b€rL o G
L]¦KM{bLkG ‘ F:]bd¥H†L|k| ‘yo GA` ‘ _ o €rK o d’KAV†L]K o NIt o N o ]b€ o tNAVja V:KM{ o N GAVj`bNI€ o G=Lk]¥F:dbdbL•KMLV:]pKMV ‘"o L] ‹ GI` ‘ _ o €rK o d
KMV§KM{ o g F ‹ F NAL o G™V:tfH†LN o | o GAG™|Lk]bO(GTY>‚„]>KM{LG q F qyo N™H o €TVj]b€ o ]KMNAF K o Vj] q NIV+gLkdbL] ‹ GIVj|`KALVj]G’tVjN
o ]\F ‘ |L] ‹’or¬ €rL o ]Kw€rVjaCa&`b]bLk€sF KALVj] ‘yo K„H oTo ] Œ |k` o KAVV KM{šd o gL€ o GwL]CKM{ o tF:€ o V:t GA`€n{.L]K o NIt o N o ]b€ o Y
œ o €TV:]bGALkd o N!F Œ |` o KMVV:KA{ q L€rVj] o K!V qyo NAF KMLk] ‹ L]¦|kVjGAG‰¦€n{\F:]] o |(€TV:]bdbLkKALVj]G1F:]bd q NIV+gLkd o F:| ‹ V:NALkKA{baCG
KMVBaˆF0£LaCL› o KA{ o KA{bNAVj` ‹ { q `K’L]F q L€rVj] o K’H†LkKA{Vj] o VjN’aCVjN o GI|}Fsg o G ‘ ˜€n{bVVjGALk] ‹ KA{ o*q F €nO o K
| o ] ‹ KM{bGwKAV ‘yo KMNAF:]bGAaCLkKIK o d6F0KwKM{ o dbL•” o N o ]K†tN o W(` o ]b€rL o GTY
ò — ò ÿ ;
jÅ Y m Y Œ o NIKMG o O0F:GrY8ü0ýE úøý7þ›=ùyÿúƒ™úÉ:ÿúü0ý\Y[°KA{ o ]\FˆE€rL o ]KAL ¨ € S1ÅóY
ÎY@z=Y Œ {\F ‹ HJF KTS¢z!Y Œ {bF KAKMF:€n{\F:N‰FS3[’Y¥NILGI{b]\FS3F:]d¡E"Y
™Y==NIL q F KA{bLY§u]b{bF:]b€TLk] ‹ KM{NAVj` ‹ { q `K
Vhg o NJH†LN o | o GAGv|}F:]Gv`GAL] ‹ €n{\F:]] o |yGIKMF K o d oTqyo ]bd o ]K q F:€nO o KwGI€n{ o d`b|Lk] ‹ Y‚Ñu3u3u>‚„]tV€rVja©ÅY
ÍY Š°F:{b] o NAG.‚„]¯‰EKMF K…ö¦NAVj` q Y Œ |k` o KAVV:KA{Vhg o NIKnF O o G…ôjÊjÎYkÅ:År£¡H†LkKM{“Î:ÊjÊÅBGI{bL q a o ](KAG*Vj]KANMF:€nOY
û þ„ù\ü Üÿ ù ž “ ÿÿ ù øbøbø úøý7 ÿÎ:ÿ\ ûnü>%š ÿFqû ÿ!L• !"#•#,š ø %š2 “ ÿF™S
‡RVhg6Î:Ê:ÊÅjY
ÁbY Œ NAFh<iYF:]bdƒŠ^YÄUJYyE(KM`bNIašF:]7Y Œ |` o KMVV:KM>{ 13ŠJVj]b] o €rKfH†LkKA{…€TF ‘ | o GT—Y ÷ Mþ ý\ÿúûnþ ¡sƒ9ž$&%SyÎ:ÊjÊÅjY
óY ¤&YÄuw'Y o |k|k*F:]bd…UJY Œ F ‘ L€n{'Y3zNAV KMV€TVj|'V q KMLkaˆLk›sF KALVj]ˆ`bGALk] ‹ dLGA€rN o K o €n{\F:]b] o | GIKMF KMLkGIKMLk€:Y‚Ñu3u3u
‚‰Š°x^zvŠ^S"U4|V:N o ]€ o ‚¾KnF |kjS\¤¦€ K¥Å jôY
Y E"Y - `'S (’Y Œ {\F N ‹ {\Fsg F:]'SRF:]bd–e¥YJENALkO F ](KTY UF:LNCGA€n{ o db`b|kL] ‹ Lk] H†LN o | o GAG q F €nO o K<] o K„H¢VjNAO(GTY
ý Žþ ÿ ü ˖0úø)ý ˜:SyÃ É ÁË 1ÈÁ(Ã:0Í /Ájô S[^` ‹ Å Y
) ú¶ú¶ú !*,+- ’ q:7ý 2û ÿúü07ý Žü0.
ÃY Œ YyX6Lk|| o NwF:]dƒŠ^Y Œ LGAdLO(L}F:]7Y Œ |` o KMø VV:KA{…N o g o F:| o d'—Y ÷ Mþ ý\ÿúûnÈþ ¡Èƒ9ž&%S"Î:Ê:ÊÅjY
ôY@uwY=X6VdL}F:]bVY&[ GALa q | o F:| ‹ V:NALkKA{ba©tVjN¦V q KALaCL›rL] ‹ KA{ oq F:€nO o K&GIL› o Lk]ZF:NAW q NAV:KAV€rVj|G ‘ F:G o d
Vj]6F:€nO(]bVhH†| o d ‹jo a o ]KR{bLG‰KMVjN‰jY3zNAV€:Y\V tÍÅTGIKRŠJ‚‰EbE"S Œ F |kKMLkaˆV:N o x^E[’SyX6F:N¦Å ÃY
Y ¦Y3u` ‹jo ] o ‡ ‹ S3‚nYvEKMV:L€sFS¢F ]bd¡÷ŽY 17{\F:] ‹ Y>z4F €nO o KCtF:LkN&W(` o ` o L] ‹ F:| ‹ VjNAL•KM{baCG¥tVjN&H†LN o | o GAG
] o K„HJVjNIO(GRH†LkKA{<|V€sF KALVj]¯¾d oTqyo ]d o ]K o NINAVjNIGTY3‚Ñu3u3u‚„]tV€rVja…S7Å :ôY
ÅhÊY!E"YEF:GIHJF KMLSbUJY[^]0_I`a6SF:]bd<e¥YbijF:Lk]'Y ’Y“ Mü ”˜ “ Lù ”2ÿ =ùyÿƒú Ø÷—û –þ $ÿ 3ú É0þ 3'þ þnû ÿúü08ý œsü ù e”"þ ÿ„ühü0ÿ “ 8þ ÿ ü ˖ Y3{KAK q 15440HwHwH¥YäG o F:GrYä` q"o ]b]'Y o db'` 4*G‰H°F KA6L 4 q ` ‘ |Lk€sF KALVj]7Yä{KMa…S[^` ‹ Î:ÊjÊjÎY
ÅjÅjY Œ |k` o KAVV:KA{6ø E‚‰öY Œ |` o KMVV:KM{<G qyo €rL ¨ €TF KMLkVj]'Y{KAK q 1
440HwHwH¥Y ‘ |` o KMVV:KM{7Yä€rVja6SyÎ ÊjÊjÊY
Å+ÎY e¥YbœVj|•”47Y 3ÿÑühû “ ÿúû Z2ü ™þ úø)ý ˜4:Lý ™šÿ “ þ ’Y“ þnü r*kü œ8—”\þ ”þ Y3zN o ]KML€ o ¯„÷^F:|k|S7Å jô Y

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