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pQr2H U VX //BM; i?2 MQKBM iBp2 bm{t U V i i?2 2M/ Q7 i?2 `QQi rQ`/ U V `2bmHib M2r rQ`/ U VX Hi?Qm;? T?QM2iB+ HHv Ub22 i?2 b2[m2M+2 Q7 AS bvK#QHbV i?2`2 Bb MQ +? M;2 7i2` //BiBQM Q7 i?2 M2r bm{t- i?2`2 Bb +? M;2 BM i?2 Q`i?Q;` T?vX h? i Bb- 7i2` +Hm##BM;- i?2 pQr2Hb U V M/ U V `2 +? M;2/ iQ U V- b2KB@pQr2H Y pQr2H K i` X h?2 M2ti b2+iBQM /Bb+mbb2b `mH2@# b2/ TT`Q +? iQ bi2KKBM;- 7Q+mbBM; QM bb K2b2X
9X SS_P*>@R, _lG1@"a1. SS_P*> b K2MiBQM2/ #Qp2- M bb K2b2 `QQi + M i F2 b2`B2b Q7 bm{t2b b2[m2MiB HHvX aQ- Qm` }`bi BK Bb iQ }M/ i?2 T`Q# #H2 b2[m2M+2 Q7 bm{t2b i? i rQ`/ +QMi BMbX q2 K Mm HHv +QHH2+i2/ HH TQbbB#H2 bm{t2b M/ + i2;Q`Bx2/ i?2K BMiQ bBt # bB+ ;`QmTb- pBxX- + b2 K `F2` U*JV UMQKBM iBp2- ++mb iBp2- HQ+ iBp2- ;2MBiBp2- BMbi`mK2Mi H M/ / iBp2V- THm` H K `F2` USJV- /2}MBi2M2bb K `F2` U.JV- 2KT? iB+ K `F2` U1JV- p2`# K `F2`b UoJV M/ Qi?2`bX h?2 Qi?2` + i2;Q`B2b +QMi BM FBMb?BT MQmM K `F2`b- /p2`#B H K F2`b M/ /2`Bp iBQM H bm{t2bX h #H2 AA b?Qrb bQK2 bm{t2b rBi? i?2B` +QmMibX h?2 `mH2 2M;BM2 ;2M2` i2b HBbi Q7 bm{t2bX Ai Bb KQ/mH2 i? i ;2M2` i2b HH T`Q# #H2 bm{t b2[m2M+2b i? i K v #2 ii +?2/ iQ `QQi- # b2/ QM i?2 {t iBQM `mH2b BM+Q`TQ` i2/ BM i?2 2M;BM2X h?2 `mH2 2M;BM2 mb2b +QHH2+iBQM Q7 `mH2b i? i T`Q/m+2b p HB/ HBbi Q7 bm{t2b BM b2[m2M+2X h?2 `mH2 2M;BM2 Bb `2bTQMbB#H2 7Q` ;2M2` iBM; i?2 T`QT2` b2[m2M+BM; Q7 bm{tU2bVX "v T`QT2` b2[m2M+BM;- r2 K2 M i? i i?2 bm{t2b Kmbi #B/2 #v KQ`T?Qi +iB+ `mH2b 7Q` bb K2b2X 6Q` 2t KTH2- i?2 //BiBQM Q7 THm` H K `F2` 7i2` + b2 K `F2` rBHH ;2M2` i2 M BMp HB/ b2[m2M+2 7Q` bb K2b2X q2 ? p2 Q#b2`p2/ i? i MQ BM~2+iBQMb `2 ii +?2/ iQ i?2 p2`# `QQi Q` MQmM `QQi 7i2` i?2 2KT? iB+ K `F2`X h?2 7QHHQrBM; 2t KTH2b BHHmbi` i2 bm+? {t iBQM `mH2b i? i i?2 `mH2 2M;BM2 mb2b iQ ;2M2` i2 i?2 bm{t HBbiX h?2 }`bi 2H2p2M- 1t KTH2b U8@R8V- BHHmbi` i2 MQKBM H bm{t iBQMX h?2 rQ`/ U , K MV Bb i?2 `QQi BM 1t KTH2b 8 i?`Qm;? R8 M/ i?2 rQ`/ U , iQ /QV Bb i?2 `QQi BM 1t KTH2b Re M/ RdX
U8V `QQi Y SJ 1t KTH2, → AS, UK MVY UTHm` H K `F2`VX UeV `QQi Y *J → 1t KTH2, → AS, UK MVY U;2MBiBp2 + b2 K `F2`VX UdV `QQi Y .J → 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`VX U3V `QQi Y 1J → 1t KTH2, → AS, UK MVY U2KT? iB+ K `F2`VX UNV `QQi Y SJ Y *J→ 1t KTH2, → AS, UK MVY UTHm` H K `F2`VY U;2MBiBp2 + b2 K `F2`VX →
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URyV `QQi Y SJ Y 1J 1t KTH2, → AS, UK MVY UTHm` H K `F2`VY U2KT?2iB+ K `F2`VX URRV `QQi Y *J Y 1J→ 1t KTH2, → AS, UK MVY U;2MBiBp2 + b2 K `F2`VY U2KT? iB+ K `F2`VX URkV `QQi Y .J Y *J→ 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`VY U;2MBiBp2 + b2 K `F2`VX URjV `QQi Y .J Y 1J→ 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`VY U2KT? iB+ K `F2`VX UR9V `QQi Y SJ Y *J→ Y 1J 1t KTH2, → AS, UK MVY UTHm` H K `F2`V → Y U ++mb iBp2 + b2 K `F2`VY U2KT? iB+ K `F2`VX UR8V `QQi Y .J Y *J Y 1J 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`V → Y U ++mb iBp2 + b2 K `F2`VY U2KT? iB+ K `F2`VX UReV `QQi Y oJ 1t KTH2, → st AS, UiQ /QVY UT bi i2Mb2 K `F2`- 1 T2`bQMVX URdV `QQi Y oJ Y→ 1J 1t KTH2, → st AS, UiQ /QVY UT bi i2Mb2 K `F2`- 1 T2`bQMV → Y U2KT? iB+ K `F2`VX UR3V `QQi Y Qi?2`b 1t KTH2, → st AS, UiQ ;QVY U1 T2`bQM K `F2`VY UQi?2` bm{tV →
q2 +QM}`K2/ R9 U1t KTH2b 8@R3V bm+? `mH2b M/ ;2M2` i2/ R3-RN9 bm{t b2[m2M+2b 7Q` bb K2b2X h?2b2 `mH2b `2 BKTH2K2Mi2/ mbBM; C p _1 T +F ;2X 1t KTH2b N i?`Qm;? R8 M/ 1t KTH2b Rd M/ R3 ? p2 b2[m2M+2b Q7 irQ Q` KQ`2 bm{t2b r?2`2 b 1t KTH2b 8 i?`Qm;? 3 M/ Re ? p2 QMHv QM2 bm{t 2 +?- ii +?2/ iQ i?2 `QQiX h?2 bm{t HBbi ;2M2` i2/ #v i?2 `mH2 2M;BM2 +QMi BMb i?2 bm{t2b U V- U V M/ U V BM 1t KTH2b 8- e M/ R8- `2bT2+iBp2HvX h?2 `mH2 2M;BM2 rQ`Fb rBi? HH ;` KK iB+ H + i2;Q`B2bX Ai ;2M2` i2b HBbi Q7 bm{t b2[m2M+2bX h?2 HBbi Bb `` M;2/ BM MQM@BM+`2 bBM; Q`/2` Q7 i?2 H2M;i? Q7 i?2 b2[m2M+2- bQ i? i BM i?2 M2ti T? b2 i?2 HQM;2bi TQbbB#H2 bm{t b2[m2M+2 BM M BMTmi rQ`/ + M #2 B/2MiB}2/ mbBM; b2[m2MiB H HQQF@mT Q7 i?2 HBbiX 6Q` BMbi M+2- H2i mb +QMbB/2` i?2 rQ`/ U V U1t KTH2 RV M/ bbmK2 i?2 bm{t b2[m2M+2 HBbi ? b i?2 2Mi`B2b U V- U V- U V- U V M/ U V BM i? i Q`/2`X b2[m2MiB H HQQF@ mT rBHH vB2H/ i?2 b2;K2Mi iBQM U V- r?2`2 b i?2 b2;K2Mi iBQM U V Bb KQ`2 TT`QT`B i2X >2M+2 i?2 HBbi Bb `` M;2/ BM MQM@BM+`2 bBM; Q`/2` Q7 H2M;i? Q7 i?2 bm{t b2[m2M+2bX h?2 BMTmi rQ`/b `2 T bb2/ i?`Qm;? i?2 bm{t HQQF@ mT T`Q+2bbX 6Q` M BMTmi rQ`/ Q7 H2M;i? Lw- K i+?BM; Bb ii2KTi2/ QMHv rBi? i?2 bm{t b2[m2M+2b r?Qb2 H2M;i? Bb H2bb i? M Lw 1X Mv K i+? 7QmM/ BM i?2 HBbi- rBHH b2T ` i2 i?2 rQ`/ K i+?2/ T `i b +QKTQM2MiX −
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9XRX _2bmHib M/ .Bb+mbbBQM AM i?Bb 2tT2`BK2Mi- r2 mb2 T `i Q7 i?2 1JAGG13 bb K2b2 +Q`Tmb Q7 bBx2 Rkj-d8j rQ`/bX KQM; i?2b2- k8-RRR rQ`/b `2 mMB[m2 UBM+Hm/BM; BM~2+i2/ M/ `QQi rQ`/bVX 6Q` 2t KTH2- U , K MV- U , K2MV M/ U , i?2 K MV `2 +QMbB/@ 2`2/ b2T ` i2 rQ`/b- Hi?Qm;? i?2 b2+QM/ M/ i?2 i?B`/ rQ`/b `2 BM~2+i2/ 7Q`Kb Q7 i?2 }`bi rQ`/X q2 7QmM/ i? i 8X38 Bb i?2 K2 M rQ`/ H2M;i? 7Q` i?2 +Q`TmbX q2 K Mm HHv 2p Hm i2 i?2 QmiTmiX PM2 ?B;?Hv 2/m+ i2/ M/ M iBp2 bT2 F2`b Bb 2KTHQv2/ b K Mm H 2p Hm iQ` M/ 7QmM/ 8dW Q7 i?2 rQ`/b `2 +Q``2+iHv bi2KK2/ #v TT`Q +? RX aQK2 Q#b2`p iBQMb 7`QK i?2b2 2tT2`BK2Mib i? i 2tTH BM i?2 HQr ++m` +v `2 2MmK2` i2/ #2HQrX X am{t2b bm+? b U V- U V M/ U V r2`2 b2T ` i2/ 7`QK rQ`/b bm+? b U , bQK2V- U , bQK2V M/ U , M22/V Hi?Qm;? i?2b2 rQ`/b `2 MQi BM~2+i2/X h #H2 AAA b?Qrb 7Qm` ivT2b Q7 2``Q`b 7QmM/ mbBM; i?2 TT`Q +?X b /2}M2/ BM h #H2 AAA- hvT2@A M/ hvT2@AA 2``Q`b `2 bBKBH ` BM i?2 b2Mb2 i? i i?2v `2 #Qmi bBM;H2 bm{t2b- #mi i?2 }`bi QM2 Bb #Qmi bBM;H2 H2ii2` bm{t2b M/ i?2 b2+QM/ QM2 Bb #Qmi KmHiB@H2ii2` bm{t2bX hvT2@AAA M/ hvT2@Ao `2 /m2 iQ i?2 K2`;BM; Q7 irQ bm{t2bX Hi?Qm;? i?2 b2[m2M+2 Bb +Q``2+i- i?2 2``Q` Bb BM i?2 B/2MiB}+ iBQM Q7 bm{t #QmM/ `B2bX
h #H2 AAAX M HvbBb Q7 2``Q` ivT2b Q7 TT`Q +? RX AMTmi rQ`/ :2M2` i2/ bi2K *Q``2+i bi2K hvT2 Q7 2``Q` W hvT2@A 2``Q`, 6QmM/ bBM;H2 H2ii2` bm{t i i?2 2M/ Q7 i?2 BMTmi rQ`/ ( U V U V U V U V- BM i?2 2t KTH2) M/ `2KQp2/ ( b 8R ;2MBiBp2 + b2 K `F2`- BM i?2 2t KTH2) Hi?Qm;? i?2 rQ`/ Bb MQi BM~2+i2/X hvT2@AA 2``Q`, 6QmM/ KmHiB@ H2ii2` bm{t ( U V- BM i?2 2t@ KTH2) i i?2 2M/ Q7 i?2 BMTmi rQ`/ U V jy U V U V M/ `2KQp2/ ( b /2}MBiBp2 K `F2` U V Bb BM i?2 bm{t HBbi)X >2`2 i?2 BMTmi rQ`/ Bb `QQi rQ`/X hvT2@AAA 2``Q`, 6QmM/ bm{t b2@ [m2M+2 ( U V- BM i?2 2t KTH2) ;2M2` i2/ #v i?2 `mH2 2M@ U V ;BM2 M/ `2KQp2/X q?2i?2` QMHv i?2 Rd U V U V H bi H2ii2` U V Bb i?2 BM~2+iBQM H T `i BM i?2 BMTmi rQ`/- U V Bb MQiX hvT2@Ao 2``Q`, AMTmi Bb `2/mTHB+ iBp2 U +QKKQM T?2@ MQK2MQM (##B RN38) BM AM/B M H M;m ;2bV rQ`/ rBi? ?vT?2MX h?2 bi2KK2` 7QmM/ bm{t b2[m2M+2 k U V U V U V U V i i?2 2M/ Q7 i?2 b2+QM/ T `i Q7 i?2 `2/mTHB+ iBp2 rQ`/ M/ `2KQp2/ BiX "mi i?2 }`bi T `i Bb HbQ BM~2+i2/ M/ i?2`27Q`2- b?QmH/ #2 bi2KK2/ b r2HHX
"X h?2 2``Q` ` i2 7Q` BM~2+i2/ rQ`/b rBi? bm{t H2M;i? ;`2 i2` i? M 9 Bb H2bb i? M RW r?2`2 b i?2 2``Q` ` i2 7Q` BM~2+i2/ rQ`/b rBi? bm{t H2M;i? 2[m H iQ R Bb i?2 ?B;?2bi- 8eWX Ai Bb +H2 ` 7`QK i?Bb 2tT2`BK2Mi i? i i?2 2``Q` ` i2 /2+`2 b2b rBi? BM+`2 bBM; bm{t H2M;i?X b i?2 2``Q` ` i2 Q7 bBM;H2 +? ` +i2` bm{t2b Bb i?2 ?B;?2bi- QM2 TQbbB#H2 bQHmiBQM iQ BM+`2 b2
8?iiT,ffrrrX2KBHH2XH M+bX +XmFf
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8X SS_P*>@k, .A*hAPL_u GPPE@lS@"a1. SS_P*> Ai Bb +H2 ` i? i mbBM; i?2 `mH2 b2i /2p2HQT2/ BM i?2 T`2pBQmb b2+iBQM- r2 r2`2 MQi #H2 iQ 2ti` +i HH bi2Kb 7`QK i?2 BMTmi rQ`/bX PM HQQFBM; +HQb2Hv i i?2 hvT2@A M/ hvT2@AA 2``Q`b- r2 }M/ i? i i?2 BMTmib `2 `QQi rQ`/b- #mi i?2 2M/ H2ii2`UbV mM7Q`imM i2Hv K i+? bQK2 p HB/ bm{t2b 7`QK i?2 bm{t HBbiX AM h #H2 AAA- r2 b22 i? i i?2 BMTmi rQ`/ i? i + mb2b hvT2@A 2``Q`- Bb `QQi rQ`/ Bib2H7X h?2 2M/ H2ii2` Q7 i?2 BMTmi rQ`/- U V Bb i?2 ;2MBiBp2 + b2 K `F2` M/ Bb BM i?2 bm{t HBbiX >2M+2- i?2 bi2KK2` b2T ` i2b U V 7`QK - T`Q/m+BM; r`QM; bi2K X aBKBH `Hv- Qm` H;Q`Bi?K `2KQp2b U V b bm{t 7`QK HH rQ`/b i? i 2M/ BM 2p2M i?Qm;? K Mv bm+? rQ`/b `2 BM/BpBbB#H2X hvT2@AA 2``Q` Bb bBKBH ` iQ hvT2@A 2``Q`- 2t+2Ti i?2 MmK#2` Q7 H2ii2`b T`2b2Mi BM i?2 bm{tX h?2 MmK#2` Q7 rQ`/b i? i + mb2 hvT2@AA 2``Q`b Bb 72r2` #mi bm+? rQ`/b Q++m` 7`2[m2MiHv BM i?2 i2tiX hQ ? M/H2 i?2b2 irQ ivT2b Q7 2t+2TiBQMb- QM2 r v Bb iQ K BMi BM rQ`/ HBbi U?2M+27Q`i?- + HH2/ /B+iBQM `vV r?2`2 KQbi 7`2[m2Mi bi2Kb Q` `QQib `2 F2TiX 6Q` 2t KTH2- rQ`/b 2M/BM; rBi? Mv +? ` +i2` HBbi2/ BM h #H2 o- bm+? b U , `B+2V- U , pQB+2V- U VV M/ 2t+2TiBQM H `QQi rQ`/b Ubm+? b U , bQK2V- U , bQK2V M/ U , M22/VV `2 biQ`2/ BM i2ti }H2- QM2 rQ`/ T2` HBM2X h?mb BM i?Bb TT`Q +?- }`bi 2 +? rQ`/ Bb +?2+F2/ ; BMbi i?2 /B+iBQM `v Ui? i Bb- rQ`/b biQ`2/ BM i?2 i2ti }H2V iQ #2 bi2KK2/X 7i2` i? i r2 TTHv TT`Q +? RX h?2 K BM /p Mi ;2 Q7 i?2 TT`Q +? Bb i? i Bi KBMBKBx2b Qp2`@bi2KKBM; U`2KQpBM; iQQ K Mv H2ii2`b b bm{tV M/ mM/2`@bi2KKBM; U`2KQpBM; 72r2` H2ii2`b b bm{tV 2``Q`b (+X7X h #H2 sA)X
8XRX S`2T ` iBQM Q7 /B+iBQM `v q2 /2p2HQT 7`2[m2Mi `QQi rQ`/ HBbi 7`QK i?2 2MiB`2 1JAGG1 bb K2b2 +Q`Tmb U TT`QtB@ K i2Hv kXe KBHHBQM rQ`/bVX Hi2`M iBp2Hv- i?2 /B+iBQM `v K v +QKT`Bb2 QMHv i?Qb2 rQ`/b i? i +H b? rBi? i?2 bm{t2b- i?mb K v BKT`Qp2 i?2 b2 `+? 2{+B2M+vX lbBM; Svi?QM T`Q;` K- r2 2ti` +i i?2 mMB[m2 rQ`/b UBM+Hm/BM; BM~2+i2/ M/ `QQi rQ`/bV M/ i?2B` 7`2[m2M+B2b 7`QK i?2 +Q`Tmb BM H2tB+Q;` T?B+ Q`/2` iQ 2 b2 i?2 B/2MiB}+ iBQM Q7 i?2 `QQibX q2 K Mm HHv 2t@ i` +i M/ `` M;2 i?2 `QQi rQ`/b # b2/ QM 7`2[m2M+vX 6B;m`2 R BHHmbi` i2b Qm` 2tT2`BK2Mi iQ pBbm HBx2 i?2 BKT +i Q7 i?2 bBx2 Q7 /B+iBQM `v +Qp2` ;2 BM bi2KKBM;X q2 +?QQb2 8yyy- Ryyyy- R8yyy- kyyyy M/ k8yyy KQbi 7`2[m2Mi `QQi rQ`/b M/ i2bi rBi? i?2 +Q`Tmb /2b+`B#2/ BM a2+iBQM 9XRX q2 7QmM/ ++m` +B2b Q7 ee- dj- dd- 3y M/ 3RW `2bT2+iBp2Hv- r?2M K2`;2/ rBi? TT`Q +? RX h?Bb b?Qrb bi2KKBM; ++m` +v BM+`2 b2b b i?2 bBx2 Q7 i?2 /B+iBQM `v BM+`2 b2b- Hi?Qm;? b 2tT2+i2/ i?2 BM+`2 b2 bi `ib iQ H2p2H QzX q2 HbQ 2t KBM2 i?2 ++m` +v UBX2X- i?2 MmK#2` Q7 `QQi rQ`/bV Q7 bi2KKBM; rBi?Qmi +QK#BMBM; rBi? TT`Q +? RX
8XkX _2bmHib M/ .Bb+mbbBQM 6Q` i?Bb TT`Q +? r2 mb2 rQ`/ HBbi Q7 bBx2 k8-yyy `QQi rQ`/bX b Q#pBQmb- i?2 Q#i BM2/ `2bmHib BM h #H2 Ao `2 M BKT`Qp2K2Mi Qp2` i?2 }`bi TT`Q +?X q2 mb2 b2i Q7 ? M/@+` 7i2/
h #H2 AoX _2bmHi Q#i BM2/ mbBM; /B+iBQM `v rBi? TT`Q +? kX *Q``2+iHv bi2KK2/ 3RW .B+iBQM `v rQ`/b 98W AM+Q``2+iHv bi2KK2/ RNW ai2KK2/ b MQ BM~2+iBQM kjW ai2KK2/ b bBM;H2 +? ` +i2` BM~2+iBQM 8dW ai2KK2/ b KmHiBTH2 BM~2+iBQM kyW
`mH2b b /Bb+mbb2/ 2 `HB2` M/ /B+iBQM `v b /Bb+mbb2/ BM i?Bb b2+iBQM iQ bi2K M/ Q#i BM M ++m` +v Q7 M2 `Hv 3RWX L2 `Hv RNW Q7 i?2 rQ`/b `2 biBHH MQi bi2KK2/ T`QT2`HvX KQM; i?2
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80
75
70
65
60
55
50
45 Stemming accuracyStemming
40
35 Using Approach 1 Without using Approach 1 30
5000 10000 15000 20000 25000 Dictionary size
6B;X RX AKT +i Q7 ++m` +v rBi? BM+`2 bBM; /B+iBQM `v bBx2
BM+Q``2+iHv bi2KK2/ rQ`/b- kjW Q7 i?2 rQ`/b `2 K `F2/ `QQi rQ`/b Hi?Qm;? i?2v TQbb2bb BM~2+iBQMX h? i Bb- i?2 `mH2b 7 BH iQ 2ti` +i BM~2+iBQM 7`QK bm+? rQ`/bX PM HQQFBM; +HQb2Hv i i?2 BM+Q``2+iHv bi2KK2/ rQ`/b i? i `2 K `F2/ b MQ BM~2+iBQM- r2 }M/ i?2b2 `2 KQbiHv bBM;H2 +? ` +i2` BM~2+iBQMb ii +?2/ iQ i?2 `QQi rQ`/X P7 i?2 rQ`/b i? i `2 BM+Q``2+iHv bi2KK2/- 8dW `2 BM+Q``2+iHv bi2KK2/ b bBM;H2 +? ` +i2` BM~2+iBQMX .B;;BM; /22T2`- r2 }M/ i? i i?2b2 rQ`/b `2 MQi BM i?2 /B+iBQM `v M/ KQbi Q7 i?2K `2 T`QT2` MQmMb r?Qb2 2M/ H2ii2`b `2 mM7Q`imM i2Hv i?2 b K2 b bQK2 bBM;H2 H2ii2` bm{tX h?2 +QKKQM TT2 ` M+2 Q7 bBM;H2 H2ii2` bm{t2b b KQ`T?QHQ;B+ H BM~2+iBQMb + mb2b i?2 ` TB/ /QrM7 HH Q7 i?2 ++m` +v BM TT`Q +? kX q2 }M/ i? i- KQM; i?2 ;2M2` i2/ bm{t2b- RR bm{t2b `2 bBM;H2 H2ii2` bm{t2b M/ KQ`2 i? M 8yW Q7 i?2 BM~2+iBQMb BM bb K2b2 `2 bBM;H2 H2ii2` bm{t2bX am+? bBM;H2 H2ii2` h #H2 oX aBM;H2 H2ii2` bm{t2b BM bb K2b2 rBi? 2t KTH2b Q7 BM~2+i2/ rQ`/b M/ `QQi rQ`/b 2M/BM; rBi? i? i H2ii2` am{t * i2;Q`v AM~2+i2/ rQ`/b _QQi rQ`/b U V +[mBbBiBp2 K `F2` f U V U V 2nd T2`bQM T`2b2Mi i2Mb2 K `F2` U V GQ+ iBp2 K `F2` U V U V U V :2MBiBp2 K `F2` U V U V U V S`2b2Mi T `iB+BTH2 f LQKBM iBp2 K `F2` U V U V U V }MBi2 p2`# K `F2` U U V U V }MBi2 p2`# K `F2` f LQKBM iBp2 K `F2` U V U V U V }MBi2 p2`# K `F2` U V U V
KQ`T?QHQ;B+ H BM~2+iBQMb + mb2 K#B;mBiv r?BH2 T`2/B+iBM; i?2 mM/2`HvBM; `QQi rQ`/bX h?Bb TT`Q +? 2HBKBM i2b i?2 hvT2@AA 2``Q`b iQ ;`2 i 2ti2Mi M/ 7` +iBQM Q7 i?2 hvT2@A 2``Q`bX 7` +iBQM Q7 i?2 hvT2@A 2``Q`b biBHH 2tBbib- T `iB+mH `Hv r?2M i?2 bi2KK2` }M/b M mMb22M rQ`/ i? i 2M/b rBi? K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2iX E22TBM; i?Bb BM KBM/ Qm` ;Q H M2ti Bb iQ 7m`i?2` BKT`Qp2 T`QT2` bi2KKBM; Q7 mMb22M rQ`/b M/ BM+`2 b2 ++m` +vX q2
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/2b+`B#2 >B//2M J `FQp JQ/2H BM a2+iBQM e iQ ? M/H2 bBM;H2 H2ii2` BM~2+iBQMb H27i Qmi #v i?2 T`2pBQmb irQ TT`Q +?2bX eX SS_P*>@j, >u"_A. SS_P*> h #H2 oA K F2b M BKTQ`i Mi Q#b2`p iBQM r?2M r2 HQQF i ` M/QKHv TB+F2/ M2rb `iB+H2b BM 1M;HBb?- bb K2b2- "2M; HB M/ >BM/BX 1 +? +QHH2+iBQM Bb TT`QtBK i2Hv k-yyy rQ`/bX KQM; K DQ` AM/B M H M;m ;2b- "2M; HB Bb +HQb2bi iQ bb K2b2 BM i2`Kb Q7 bTQF2M M/ r`Bii2M 7Q`KbX >BM/B Bb +HQb2Hv `2H i2/ H M;m ;2 b r2HH- #mi r`Bii2M mbBM; /Bz2`2Mi b+`BTi- i?2 .2p M ; `B a+`BTiX h?2 7Qm`i? +QHmKM ;Bp2b i?2 MmK#2` Q7 mMB[m2 BM~2+i2/ rQ`/bX
h #H2 oAX ` M/QK bm`p2v QM Q++m``2M+2 Q7 bBM;H2 H2ii2` bm{t- KmHiBTH2 bm{t M/ KmHiBTH2 bm{t 2M/@rBi? bBM;H2 H2ii2` bm{tX a2Mi2@ qQ`/b AM~2+iBQM ivT2 G M;m ;2 aQm`+2 Q7 i2ti @M+2b hQi H lMB[m2 aBM;H2 Ja JmHiBTH2 1M;HBb? 3k kyRk 39j yeX33W yyXyyWN R3X8yW hBK2b Q7 AM/B Ry bb K2b2 Rjk kRe9 RkNj k3XkRW yNX9NW RjXyeW . BMBF C M b /? ` MRR "2M; HB kyk kky8 Rk9e RdXNdW ydXkkW R3XjdW M M/ # x ` S i`BF Rk >BM/B RRe kRek dN8 RkXydW yjXR9W RkX3kW . BMBF C ; ` MRj
q2 Q#b2`p2 i? i KQM; i?2b2 H M;m ;2b- bb K2b2 ? b i?2 ?B;?2bi 7`2[m2M+v Q7 bBM;H2 H2ii2` BM~2+iBQM H bm{t2bX h?Bb #2?QQp2b mb iQ /2p2HQT M H;Q`Bi?K iQ BKT`Qp2 i?2 ++m` +v Q7 /2i2+iBM; bBM;H2 H2ii2` bm{t2b iQ #mBH/ #2ii2` bi2KK2` 7Q` bb K2b2X (J2Hm++B M/ P`BQ kyyj) mb2 >JJb 7Q` bi2KKBM; }p2 /Bz2`2Mi H M;m ;2b- pBxX- .mi+?- 1M;HBb?- 6`2M+?- Ai HB M M/ aT MBb?X h?2v /2bB;M i?2B` TT`Q +? iQ bi2KKBM; BM i2`Kb Q7 M >JJ rBi? bi i2b 7Q` irQ bm#@T`Q+2bb2b Q` /BbDQBMi b2ib, bi i2b BM i?2 T`2}t@b2i i? i `2 +QMbB/2`2/ iQ #2 i?2 bi2Kb M/ bi i2b BM i?2 bm{t@b2i i? i TQbbB#Hv ;2M2` i2 i?2 bm{t b2[m2M+2 B7 i?2 rQ`/ ? b QM2X Pm` T`Q#H2K Bb #Bi /Bz2`2MiX q2 BMi2M/ iQ /2pBb2 KQ/2H iQ H2 `M iQ +H bbB7v bBM;H2 H2ii2` bm{t2b QMHvX Pm` rQ`F Bb }`bi Q7 Bib FBM/ 7Q` bQK2 Q7 i?2 +QMbB/2`2/ H M;m ;2bX lb2 Q7 bm{t Bb ;Qp2`M2/ #v bvMi +iB+ T`BM+BTH2b Q7 H M;m ;2 i? i K v bT`2 / Qp2` M 2MiB`2 b2Mi2M+2X aBM+2 >JJ Bb r2HH FMQrM 7Q` b2[m2M+2 H #2HHBM;- Bi Bb bmBi #H2 + M/B/ i2 7Q` 2tT2`BK2Mib HBF2 Qm`bX Pm` +QM+2Ti Bb p2`v bBKTH2X q2 /`QT i?2 bBM;H2 Q++m``2M+2 Q7 i?2 bBM;H2 H2ii2` bm{t b2i 7`QK i?2 bm{t HBbi ;2M2` i2/ #v i?2 `mH2 2M;BM2X q2 +QHH2+i HH i?2 rQ`/b- r?Qb2 2M/ +? ` +@ i2` K i+?2b K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2i- BM/2T2M/2Mi Q7 BM~2+iBQM H BM7Q`K iBQMX h?Bb +QHH2+iBQM +QMi BMb QMHv i?Qb2 rQ`/b- r?B+? `2 MQi BM i?2 /B+iBQM `v M/ rQ`/b i? i `2 MQi +Qp2`2/ #v i?2 `mH2 2M;BM2X h?Bb rQ`/ HBbi Bb b2Mi b BMTmi iQ i?2 >JJ i` BMBM; KQ/2H iQ +H bbB7vX h?2 i bF /2b+`B#2/ ?2`2 Bb M 2ti2MbBQM Q7 Qm` T`2pBQmb rQ`F (a ? `B 2i HX kyRj)X eXRX h?2 >JJ KQ/2H amTTQb2 w0- w1- - wn 1 `2 i?2 rQ`/b Q7 +Q`TmbX 1 +? rQ`/ wi + M #2 bTHBi b pi si- ··· − ◦ r?2`2 pi Bb `QQi rQ`/c si M BM~2+iBQM H Q` /2`Bp iBQM H bm{tc M/ i?2 +QM+ i2M iBQM QT2` iBQM #2ir22M irQ bi`BM;bX G2i S #2 i?2 b2i Q7 BM~2+iBQM H bm{t2b BM◦ i?2 H M;m ;2 mM/2` +QMbB/2` iBQM BM+Hm/BM; i?2 2KTiv bi`BM; !X 6Q` Mv rQ`/- w p s B7 s = !- r2 b v i? i ≡ ◦
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h #H2 oAAX M 2t KTH2 b2Mi2M+2 KQ/2HH2/ mbBM; Qm` ;2M2` iBp2 KQ/2H Q7 i?2 i2ti 7Q` KQ`T?QHQ;B+ H BM~2+iBQMbX
w w0 w1 w2 w3 w4 w5 w6 rQ`/b p s @ ! ! @ ! @ @ @ @ @ @ q J L L J L J J
h?2`27Q`2- 7Q` +Q`Tmb ;2M2` i2/ #v G- i?2 T`Q#H2K Q7 /2+B/BM; B7 rQ`/ Bb KQ`T?QHQ;@ B+ HHv BM~2+i2/ #QBHb /QrM iQ /2i2`KBMBM; i?2 bi i2 Q7 G UN Q` MV i i?2 2t +i KQK2Mi Q7 ;2M2` iBM; i?2 rQ`/X q2 +QMbi`m+i M >JJ@# b2/ H;Q`Bi?K iQ T`2/B+i i?2 bi i2b Q7 G +Q``2bTQM/BM; iQ i?2 rQ`/b Q7 Mv ;Bp2M +Q`TmbX h?2`27Q`2- i?2 T`Q#H2K ? b irQ K BM bT2+ib, (a) 2biBK iBM; i?2 >JJ T ` K2i2`b rBi? i` BMBM; +Q`Tmb M/ (b) TTHvBM; i?2 + HB#` i2/ H;Q`Bi?K QM i2bi +Q`Tmb iQ /2i2+i KQ`T?QHQ;B+ HHv BM~2+i2/ rQ`/bX Pm` >JJ 7Q` i?2 ;2M2` iQ` G + M #2 /2}M2/ b 7QHHQrbX BX S Bb i?2 HT? #2i i? i +QMbBbib Q7 i?2 b2i Q7 BM~2+iBQMb i? i ;2M2` iQ` G + M ;2M2` i2X BBX Q = N,M Bb i?2 b2i Q7 TQbbB#H2 bi i2b Q7 GX BBBX A =({ a ) Bb} i?2 Q Q K i`Bt Q7 bi i2 i` MbBiBQM T`Q# #BHBiB2b Q7 GX k! | |×| | BpX E =(ek(s)) Bb i?2 Q S K i`Bt i? i +QMi BMb i?2 2KBbbBQM T`Q# #BHBiB2b Q7 BM~2+iBQMb UQ` i?2 HT? #2i BM| i?2|× >JJV| | 7`QK SX AM Q`/2` iQ +QKTmi2 i?2 QTiBK H T i?- r2 mb2 i?2 oBi2`#B H;Q`Bi?K (oBi2`#B RNed)X h?2 ;Q H Q7 i?2 H;Q`Bi?K Bb iQ +QKTmi2 i?2 T`Q# #BHBiv fk(i) Q7 i?2 KQbi T`Q# #H2 T i? 2M/BM; BM bi i2 k i wi 7Q` 2p2`v TQbbB#H2 bi i2 kX AM Qm` + b2- i?2 bi i2b `2 2Bi?2` N Q` MX q2 FMQr i? i i?2 BM ++m` +v Q7 i?2 T`2pBQmb K2i?Q/ +QK2b KQbiHv 7`QK bBM;H2 H2ii2` BM~2+iBQMbX 6Q` KmHiBTH2 H2ii2` BM~2+iBQMb- i?2 K#B;mBiv Q7 #2BM; i`m2 BM~2+iBQM p2`bmb +QBM+B/2Mi H K i+? Q7 i?2 rQ`/ rBi? i?2 b2i Q7 BM~2+iBQMb Bb bB;MB}+ MiHv HQrX q2 /2MQi2 #v S1 M/ Sm i?2 b2i Q7 bBM;H2 H2ii2` M/ KmHiB@H2ii2` BM~2+iBQMb- `2bT2+iBp2HvX AM Q`/2` iQ
14qqh, qQ`/ iQ rQ`/ h` MbH iBQM 151h, TT`QtBK i2 1M;HBb? h` MbH iBQM
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ě qQ`/b rBi? KmHiB@H2ii2` BM~2+iBQM (Msm)X 6Q` 2t KTH2, U 4 , iQ r`Bi2 Y 7mim`2 i2Mb2 K `F2`VX ě qQ`/b rBi? bBM;H2 +? ` +i2` BM~2+iBQM (Ms1)X 6Q` 2t KTH2, U , ;2 Y ;2MBiBp2 K `F2`VX ě qQ`/b rBi? MQ BM~2+iBQM- BX2X- `QQi rQ`/b (Ne)X 6Q` 2t KTH2, U , bm++2bb7mHVX ě qQ`/b i? i ? p2 MQ BM~2+iBQM #mi 2M/ rBi? K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2i (Ns1)X h?2b2 `2 `QQi rQ`/b i? i 2M/ rBi? bBM;H2 H2ii2` bm{t b2iX 6Q` 2t KTH2, U , r?Qb2VX h #H2 oAAA ;Bp2b /2i BHb Q7 bm{t2b T`2b2Mi BM i?2 i` BMBM; b2iX Ai Bb +H2 ` 7`QK h #H2 oAAA i? i i?2 MmK#2` Q7 rQ`/b rBi? bBM;H2 H2ii2` BM~2+iBQM UjyXjdW BM i?2 i` BMBM; / i V Bb KQ`2 i? M i?2 MmK#2` Q7 rQ`/b rBi? KmHiB@H2ii2` BM~2+iBQM UR8XyeW BM i?2 i` BMBM; / i VX AMi2`2biBM;Hv b K2MiBQM2/ 2 `HB2`- rQ`/b rBi? bBM;H2 H2ii2` bm{t (Ms1) M/ rQ`/b i? i mM7Q`imM i2Hv 2M/ rBi? Mv K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2i (N") +`2 i2 T`Q#H2KbX AM i?2 i` BMBM; b2i- r2 ? p2 R-e3e UNjeYd8yV bm+? rQ`/b- r?B+? Bb KQ`2 i? M 8yW U89XedWV Q7 i?2 i` BMBM; / i M/ R-e3k rQ`/b (N" Y Ns1) `2 +im H MQM@BM~2+i2/ rQ`/bX AM //BiBQM iQ R-e3e UNjeYd8yV
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h #H2 AsX aBM;H2 H2ii2` bm{t 7`2[m2M+v U6V BM i?2 bb K2b2 i` BMBM; +Q`TmbX am{t am{t + i2;Q`v hQi H 6 UWV U V :2MBiBp2 K `F2` 8Ne RNXjj U V GQ+ iBp2 K `F2` kj3 ydXdk U V +[mBbBiBp2 K `F2`f2nd T2`bQM T`2b2Mi i2Mb2 K `F2` 33 ykX38 U V LQKBM iBp2 K `F2`fLQM@}MBi2 p2`# K `F2` jee RRX3d U V 6BMBi2 p2`# K `F2` jyy yNXdj U V LQKBM iBp2 K `F2`f 6BMBi2 p2`# K `F2` kde y3XN8 U V 6BMBi2 p2`# K `F2` jk yRXj3 rQ`/b i? i TQbb2bb Mv QM2 K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2i i i?2 2M/- r2 ? p2 kRy KQ`2 rQ`/b BM i?2 i` BMBM; }H2- rBi? KmHiBTH2 bm{t2b i? i 2M/ rBi? Mv QM2 K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2iX lbBM; TT`Q +? R M/ TT`Q +? k- r2 + M ? M/H2 KmHiBTH2 +? ` +i2` BM~2+iBQM r2HHX h?2 bi iBbiB+b Q7 bBM;H2 +? ` +i2` BM~2+iBQM BM i?2 i` BMBM; b2i Bb ;Bp2M BM h #H2 AsX 6`QK i?2 bi iBbiB+b- Bi Bb +H2 ` i? i i?2 ;2MBiBp2 + b2 K `F2` URNXjjWV Bb i?2 KQbi 7`2[m2Mi KQM; i?2 bBM;H2 H2ii2` bm{t2bX AM bb K2b2- r2 ? p2 RR bm{t2b BM i?2 bBM;H2
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H2ii2` bm{t b2iX h?2 H bi 7Qm` bm{t T B`b BM h #H2 As b?Qr i?2 pQr2H K i` M/ i?2 7mHH pQr2HX .2T2M/BM; QM mb2- i?2v +? M;2 i?2B` 7Q`K 7`QK 7mHH pQr2H iQ K i` Q` K i` iQ 7mHH pQr2HX b b?QrM BM h #H2 As- KQM; i?2 RR +? ` +i2`b- U V- U V M/ U V `2 K#B;mQmb- i? i Bb i?2 b K2 bvK#QHfH2ii2` Bb mb2/ iQ BM~2+i MQmMb b r2HH b p2`#bX eXjX _2bmHib M/ .Bb+mbbBQM h?2 bi2KKBM; ++m` +v 7QmM/ mbBM; TT`Q +? R Bb 8dW M/ mbBM; TT`Q +? k Bb 3kW M/ mb@ BM; i?2 ?v#`B/ TT`Q +? Bb N9WX h?2 +QKTH2i2 bi iBbiB+b 7Q` Qm` 2tT2`BK2Mib `2 ;Bp2M BM h @ #H2 sX (a? `K 2i HX kyy3) `2TQ`i2/ eNW 6@K2 bm`2 7Q` bm{t +[mBbBiBQM- r?2M i?2v i2bi2/ i?2B` mMbmT2`pBb2/ TT`Q +? rBi? jyy-yyy bb K2b2 rQ`/bX AM +QKT `BbQM rBi? (a? `K 2i HX kyy3)- i?2 `2bmHi T`Q/m+2/ #v TT`Q +? k rBi? `QQi rQ`/ HBbi Q7 QMHv k8-yyy 2Mi`B2b Bb +QMbB/2` #Hv #2ii2`X qBi? i?2 b K2 i2bi / i - r2 7QmM/ 38W +Q``2+i bi2Kb mbBM; JQ`@ 72bbQ` (*`2mix M/ G ;mb kyy8)X JQ`72bbQ` Bb M mMbmT2`pBb2/ H M;m ;2 BM/2T2M/2Mi iQQH Q7 7Qm` KQ`T?QHQ;v H2 `MBM; KQ/2Hb # b2/ QM `2+m`bBp2 KBMBKmK /2b+`BTiBQM H2M;i? (*`2mix M/ G ;mb kyyk)X Ai i F2b M mM MMQi i2/ +Q`Tmb b BMTmi M/ ;2M2` i2b KQ`T?2K2@HBF2 mMBib Q7 i?2 rQ`/b Q#b2`p2/ BM i?2 +Q`TmbX h?2 `2K BMBM; 2``Q`b BM Qm` +QK#BM2/ TT`Q +? `2 /m2 iQ B``2;mH ` mb2 Q7 bQK2 p2`#bX b K2MiBQM2/ 2 `HB2`- bb K2b2 p2`# KQ`T?QHQ;v Bb +QKTH2tX 6BM/BM; i?2 `QQi 7Q`K 7`QK BM~2+i2/ 7Q`Kb Q7 B``2;mH ` p2`#b HBF2 U , iQ ;QV Q` U , iQ ;QV Bb MQi TQbbB#H2 rBi? i?Bb bi2KK2`X Ai M22/b H2KK iBx2` iQ 2ti` +i i?2 `QQi- b i?2 r?QH2 7Q`K Q7 i?2 B``2;mH ` p2`# +? M;2b 7i2` BM~2+iBQMX >Qr2p2`- rBi? Qm` ?v@ #`B/ TT`Q +? r2 KBMBKBx2 i?2 2``Q` ` i2 iQ IRyWX 1K#2//BM; KQ`2 HBM;mBbiB+ FMQrH2/;2 mbBM; [m MiBi iBp2 `2bi`B+iBQMb HBF2 (SQ`i2` RN3yc GQpBMb RNe3) M/ #v T`QT2` ? M/HBM; Q7 +QKTQmM/ rQ`/b M/ ?vT?2M i2/ rQ`/b- r2 K v #2 #H2 iQ 7m`i?2` `2/m+2 i?2 2``Q` ` i2X AM Q`/2` iQ ;Bp2 ;HBKTb2 Q7 i?2 QmiTmi /Bz2`2M+2 KQM; TT`Q +?2b- r2 i #mH i2 i?2 bi2K
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2ti` +i2/ #v i?2 p `BQmb bi2KK2`b BM h #H2 sA 7Q` bQK2 rQ`/b +QMi BMBM; i?2 MQmM `QQi U , /` K VX q2 +QMbB/2` i?2 rQ`/ U V #2+ mb2 Bib H bi H2ii2` Bb K2K#2` Q7 bBM;H2 H2ii2` bm{t b2iX b Q#pBQmb- BM TT`Q +? R- Bb 2ti` +i2/ 7`QK i?2 2M/ Q7 i?2 `QQi rQ`/ U V T`Q/m+BM; r`QM; bi2K U V- Hi?Qm;? i?2 2ti` +i2/ bi2K Bb p HB/ K2 MBM;7mH rQ`/ BM bb K2b2X 7i2` BMi`Q/m+BM; i?2 rQ`/ HBbi BM TT`Q +? k- i?2 bi2KK2` `2+Q;MBx2b U V b `QQi rQ`/X JQ`72bbQ`- M mMbmT2`pBb2/ KQ/2H- `2TQ`ib U V M/ U , i?2 / `K V b `QQi rQ`/bX AM i?2 b2+QM/ 2t KTH2- i?2 2ti` +i2/ QmiTmi U V Bb MQi `QQi rQ`/- r?2`2 b BM i?2 }`bi 2t KTH2 Bi Bb `QQi rQ`/X h?2 mi?Q`b Q7 JQ`72bbQ` bi i2 i?2B` TT`Q +? b @dzh?2 ;2M2` H B/2 #2?BM/ i?2 JQ`72bbQ` KQ/2H Bb iQ /Bb+Qp2` b +QKT +i /2b+`BTiBQM Q7 i?2 / i b TQbbB#H2X am#@bi`BM;b Q++m``BM; 7`2[m2MiHv 2MQm;? BM b2p2` H /Bz2`2Mi rQ`/ 7Q`Kb `2 T`QTQb2/ b KQ`T?b M/ i?2 rQ`/b `2 i?2M `2T`2b2Mi2/ b +QM+ i2M iBQM Q7 KQ`T?bǴ (*`2mix M/ G ;mb kyy8)X JQ`72bbQ` /Q2b MQi mb2 H M;m ;2@bT2+B}+ `mH2bX " b2/ QM 2pB/2M+2 M/ T`Q# #BHBiv- Bi H2 `Mb iQ b2;K2Mi rQ`/b BMiQ p HB/ K2 MBM; #2 `BM; mMBibX h?2`27Q`2- BM + b2 Q7 1t KTH2b UBpV i?`Qm;? UpBBV Uh #H2 sAV- JQ`72bbQ` T`Q/m+2b i?2 r`QM; bi2K b Bi }M/b U V iQ #2 # b2 rQ`/ BM i?2 +Q`TmbX .m2 iQ i?2 +QMi`QHH2/ `mH2 b2[m2M+2- Qm` TT`Q +? k M/ TT`Q +? j T`Q/m+2 i?2 +Q``2+i bi2KX GBF2rBb2- r2 +QKT `2 i?2 QmiTmi Q7 i?2 bi2KK2`b BM i?2 b K2 h #H2 sA 7Q` bQK2 rQ`/b +QMi BMBM; i?2 p2`# `QQi U , iQ /QVX
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ai2KKBM; `2bQm`+2@TQQ` AM/B M H M;m ;2b ,R8 V V V V V V V V V iQ /QYk*SbhY1J V U V V V V /` K Y.JYL*J /` K YSGYG*J U V /` K YSGY:*J V U U /` K Y.JY:*J iQ /QYkSbh V U U V V /` K Y.J /` K Y.J U U V /` K YG*J /` K Y*J V U U V /` K V U iQ /QYkS`h V U *Q``2+i bi2KKBM; U U U U U U U U U U T2`bQM- +QM/BiBQM H T bi i2Mb2c nd VU 2 VU +[mBbBiBp2 + b2 K `F2`c V V V V → → V V V V V V JQ`72bbQ` U U U U U U U U U VU VU VU V V V V V V V V T2`bQM- T bi i2Mb2c k*Sbh V :2MBiBp2 + b2 K `F2`c *J V V nd → /` K 2 , TT`Q +? j U U U U U U U U U → , VU U VU VU U V V V V V V V V V ai2KK2` TT`Q +? k U U U U U U U U U U VU VU h #H2 sAX *QKT `BbQM Q7 bi2KKBM; #v /Bz2`2Mi TT`Q +?2b 7Q` bQK2 rQ`/bX LQKBM iBp2 + b2 K `F2`c :*J T2`bQM- T`2b2Mi i2Mb2c kSbh V V V V V → nd V 2 V V V SHm` H K `F2`c → V → TT`Q +? R U U U U U U U VU VU VU VU VU V V V V V V V GQ+ iBp2 + b2 K `F2`c L*J aQK2 rQ`/b +QMi BMBM; i?2 bb K2b2 MQmM `QQi U U U U U U U U U aQK2 rQ`/b +QMi BMBM; i?2 bb K2b2 p2`# `QQi U U U .2}MBiBp2 K `F2`c SG 1KT? iB+ K `F2`c kSbh → → → SHmb UYV bvK#QH BM/B+ i2b1J i?2 KQ`T?2K2 #QmM/ `B2bX G*J .J UBV aHX qQ`/ UpV UtV UBBV UBpV UpBV UBtV UtBV UBBBV UpBBV UtBBV UpBBBV
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dX 1sS1_AJ1Lha AL Ph>1_ GL:l:1a 7i2` Q#i BMBM; 2t+2HH2Mi `2bmHib BM bb K2b2- r2 2ti2M/ Qm` TT`Q +? iQ i?`22 Qi?2` H M@ ;m ;2b 7`QK 1 bi2`M AM/B X "2BM; bTQF2M BM i?2 b K2 `2;BQM i?2v b? `2 bK HH KQmMi Q7 +QKKQM pQ+ #mH `vX 6Q` 2 +? H M;m ;2- r2 ? p2 ;2M2` i2/ i?2 bm{t HBbi mbBM; i?2 `mH2 2M;BM2 M/ K Mm HHv /2p2HQT2/ `QQi rQ`/ HBbibX q2 K Mm HHv i ;;2/ j-kRk- k-89y M/ k-ekR rQ`/b mbBM; i?2 7Qm` i ;b K2MiBQM2/ 2 `HB2` 7Q` "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/Q `2bT2+iBp2Hv M/ i` BM2/ i?2K 7Q` i?2 ?v#`B/ KQ/2HX URV GBF2 bb K2b2- i?2 "2M; HB p2`# Bb +QKTH2t + i2;Q`v BM i2`Kb Q7 BM~2+iBQMX 6BMBi2 p2`#b BM "2M; HB `2 BM~2+i2/ 7Q` T2`bQM- i2Mb2- bT2+i- ?QMQ`- KQQ/ M/ 2KT? bBb (a `F ` M/ " M/vQT /?v v kyy3)X lMHBF2 i?2 p2`#- i?2 # b2 7Q`K Bb MQi +? M;2/ BM "2M; HB MQmM BM~2+iBQMbX lMHBF2 KQbi Qi?2` AM/B M H M;m ;2b- i?2`2 ? p2 #22M b2p2` H ii2KTib i bi2KKBM; "2M; HB i2tib (J DmK/2` 2i HX kyydc a `F ` M/ " M/vQT /?v v kyy3c S BF M/ S `mB kyRRc S BF 2i HX kyRR)X >Qr2p2`- MQM2 Q7 i?2b2 bi2KK2`b `2 Tm#HB+Hv p BH #H2X 7i2` K Mm H p HB/ iBQM Q7 i?2 `mH2b ;2M2` i2/ #v i?2 `mH2 2M;BM2- r2 7QmM/ Rk-98e bm{t b2[m2M+2b mbBM; RR `mH2bX h?2 7QHHQrBM; `2 i?2 `mH2b mb2/ BM `mH2 2M;BM2X U V `QQi Y SJ 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`V U#V `QQi Y *J → 1t KTH2, → AS, U#QQFVY U;2MBiBp2 + b2 K `F2`V U+V `QQi Y .J → 1t KTH2, → AS, U#QQFVY U/2}MBiBp2 K `F2`V U/V `QQi Y 1J → 1t KTH2, → AS, U#QQFVY U2KT? iB+ K `F2`V U2V `QQi Y SJ Y→ *J 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`VY U+ b2 K `F2`V U7V `QQi Y SJ Y 1J→ 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`VY U2KT? iB+ K `F2`V U;V `QQi Y *J Y 1J→ 1t KTH2, → AS, U#QQFVY U+ b2 K `F2`VY U2KT? iB+ K `F2`V U?V `QQi Y .J Y→ *J 1t KTH2, → AS, U#QQFVY U/2}MBiBp2 K `F2`V Y U+ b2 K `F2`V UBV `QQi Y .J Y→ 1J 1t KTH2, → AS, U#QQFVY U/2}MBiBp2 K `F2`V Y U2KT? iB+ K `F2`V UDV `QQi Y SJ Y→ *J Y 1J 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`VY U+ b2 K `F2`VY U2KT? iB+ K `F2`V → UFV `QQi Y oJ 1t KTH2, → AS, UiQ FMQrVY UT`2b2Mi i2Mb2- ?QMQ`B}+ K `F2`V lbBM; QMHv i?2 bm{t→ bi`BTTBM; TT`Q +?- r2 Q#i BM2/ 8eW ++m` +vX q2 BKT`Qp2 i?2 ++m` +v iQ 3RW QM //BM; 7`2[m2Mi rQ`/ HBbi Q7 bBx2 jy-Ry8X 6`QK +Q`Tmb M HvbBb- r2
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}M/ N bBM;H2 H2ii2` K#B;mQmb bm{t2b Ub22 TT2M/Bt *V `2bTQMbB#H2 7Q` /2+HBM2 BM i?2 bi`2M;i? Q7 i?2 `mH2@# b2/ TT`Q +?X q2 Q#i BM M2 `Hv RyW BKT`Qp2K2Mi Qp2` TT`Q +? k QM TTHvBM; i?2 ?v#`B/ TT`Q +?- r?2M i2bi2/ QM R8yk rQ`/bX UkV "Bb?MmT`Bv J MBTm`B Bb M AM/Q@`v M H M;m ;2 bTQF2M BM bb K- h`BTm` M/ J @ MBTm` Q7 AM/B b r2HH b BM avH?2i `2;BQM Q7 " M;H /2b? M/ bQK2 M2 `#v `2;BQMb Q7 "m`K - rBi? `2K `F #H2 BM~m2M+2 7`QK bb K2b2- "2M; HB M/ J2Bi2BReX ++Q`/BM; iQ (aBM? RN3k)- BM jy-yyy "Bb?MmT`Bv J MBTm`B rQ`/ HBbi- HKQbi 9-yyy r2`2 Q7 J2Bi2B Q`B;BMX Hi?Qm;? i?2 `QQib #Q``Qr2/ 7`QK J2Bi2B + MMQi i F2 {t /B`2+iHv- bQK2 "Bb?@ MmT`Bv J MBTm`B `QQi rQ`/b ii +? 7i2` J2Bi2B `QQib 7Q`KBM; +QKTQmM/ rQ`/bc bm{t2b K v #2 ii +?2/ iQ bm+? +QKTQmM/ rQ`/bX (aBM? RN3k) HbQ `2TQ`i2/ i? i i?2 bi #H2 2H2K2Mib Q7 i?2 H M;m ;2 bm+? b /2+H2MbBQM H 2M/BM;b- +QMDm; iBQM Hb M/ T`QMQKBM H 7Q`Kb Q7 "Bb?MmT`Bv J MBTm`B `2 Q7 AM/Q@`v M Q`B;BM M/ `2 +HQb2Hv `2H i2/ iQ b@ b K2b2- "2M; HB M/ P`Bv X KQM; i?B`iv }p2 T`BM+BT H T?QM2K2b- "Bb?MmT`Bv J MBTm`B ? b 2B;?i pQr2Hb- ir2Miv }p2 +QMbQM Mib M/ irQ b2KB@pQr2HbX h?2 KQbi BKTQ`i Mi 7 +i #Qmi i?2 H M;m ;2b Bb i?2 7Q`K iBQM Q7 rQ`/b bi `iBM; rBi? M b H bQmM/b HBF2 U VX 7i2` K Mm H p HB/ iBQM Q7 i?2 `mH2b ;2M2` i2/ #v i?2 `mH2 2M;BM2- r2 7QmM/ 3-eN9 bm{t b2[m2M+2b mbBM; Ry `mH2bX h?2 7QHHQrBM; `2 i?2 `mH2b mb2/ BM `mH2 2M;BM2X U V `QQi Y SJ 1t KTH2, → AS, UK MVY UTHm` H K `F2`V U#V `QQi Y *J → 1t KTH2, → AS, UK MVY U+ b2 K `F2`V U+V `QQi Y .J → 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`V U/V `QQi Y 1J → 1t KTH2, → AS, UK MVY U2KT? iB+ K `F2`V U2V `QQi Y SJ Y *J→ 1t KTH2, → AS, UK MVY UTHm` H K `F2`VY U+ b2 K `F2`V U7V `QQi Y SJ Y 1J→ 1t KTH2, → AS, UK MVY UTHm` H K `F2`VY U2KT? iB+ K `F2`V U;V `QQi Y *J Y 1J → 1t KTH2, → AS, UK MVY U+ b2 K `F2`VY U2KT? iB+ K `F2`V U?V `QQi Y .J Y *J→ 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`V Y U+ b2 K `F2`V UBV `QQi Y .J Y 1J→ 1t KTH2, → AS, UK MVY U/2}MBiBp2 K `F2`V Y U2KT? iB+ K `F2`V UDV `QQi Y oJ → 1t KTH2, → AS, UiQ /QVY UT bi i2Mb2 K `F2`V lbBM; QMHv i?2 bm{t→ bi`BTTBM; TT`Q +? r2 Q#i BM2/ 8jW ++m` +vX q2 BKT`Qp2/ i?2 ++m` +v iQ ddW- QM //BM; 7`2[m2Mi rQ`/ HBbi Q7 bBx2 Ry-j8yX 6`QK +Q`Tmb M HvbBb- r2
16J2Bi2B Q` J22i2B Bb K BMHv bTQF2M BM i?2 LQ`i?@2 bi AM/B M bi i2 Q7 J MBTm` M/ #2HQM;b iQ i?2 hB#2iQ@ "m`K M H M;m ;2 7 KBHvX
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ,R3 LX a ? `B 2i HX
}M/ Ry bBM;H2 H2ii2` K#B;mQmb bm{t2b Ub22 TT2M/Bt *V `2bTQMbB#H2 7Q` /2+HBM2 BM i?2 bi`2M;i? Q7 i?2 `mH2@# b2/ TT`Q +?X q2 Q#i BM M2 `Hv RyW BKT`Qp2K2Mi Qp2` TT`Q +? k QM TTHvBM; i?2 ?v#`B/ TT`Q +?- r?2M i2bi2/ QM R-8Ry rQ`/bX UjV "Q/Q- iQM H H M;m ;2 rBi? irQ iQM2b #2HQM;b iQ i?2 hB#2iQ@"m`K M H M;m ;2 7 KBHvX Ai Bb bTQF2M K BMHv BM LQ`i?@2 bi AM/B M/ ? b p2`v +HQb2 `2b2K#H M+2 iQ _ #? - : `Q- .BK b M/ EQF#Q`QFRdX KQM; Bib kk T?QM2K2b- Bi ? b bBt pQr2Hb M/ bBti22M +QMbQM Mi bQmM/bX h?2 mb2 Q7 i?2 ?B;? # +F mM`QmM/2/ pQr2H T?QM2K2 U V Bb p2`v 7`2[m2Mi BM "Q/QX 7i2` K Mm H p HB/ iBQM Q7 i?2 `mH2b ;2M2` i2/ #v i?2 `mH2 2M;BM2 r2 7QmM/ e-j99 bm{t b2[m2M+2b mbBM; RR `mH2bX h?2 7QHHQrBM; `2 i?2 `mH2b mb2/ BM `mH2 2M;BM2X U V `QQi Y SJ 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`V U#V `QQi Y *J → 1t KTH2, → AS, U#QQFVY U;2MBiBp2 + b2 K `F2`V U+V `QQi Y .J → 1t KTH2, → AS, U#QQFVY U/2}MBiBp2 K `F2`V U/V `QQi Y 1J → 1t KTH2, → AS, U#QQFVY U2KT? iB+ K `F2`V U2V `QQi Y SJ Y→ *J 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`VY U;2MBiBp2 + b2 K `F2`V U7V `QQi Y SJ Y 1J→ 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`VY U2KT? iB+ K `F2`V U;V `QQi Y *J Y 1J→ 1t KTH2, → AS, U#QQFVY U;2MBiBp2 + b2 K `F2`VY U2KT? iB+ K `F2`V U?V `QQi Y *J Y .J→ 1t KTH2, → AS, U#QQFVY U;2MBiBp2 + b2 K `F2`VY U/2}MBiBp2 K `F2`V UBV `QQi Y .J Y 1J→ 1t KTH2, → AS, U#QQFVY U/2}MBiBp2 K `F2`VY U2KT? iB+ K `F2`V UDV `QQi Y SJ Y *J→ Y 1J 1t KTH2, → AS, U#QQFVY UTHm` H K `F2`VY U;2MBiBp2 + b2 → K `F2`VY U2KT? iB+ K `F2`V UFV `QQi Y oJ 1t KTH2, → AS, UiQ ;QVY UT`2b2Mi T2`72+i i2Mb2 K `F2`V lbBM; QMHv i?2 bm{t→ bi`BTTBM; TT`Q +?- r2 Q#i BM2/ 98W ++m` +vX q2 BKT`Qp2/ i?2 ++m` +v iQ dRW QM //BM; 7`2[m2Mi rQ`/ HBbi Q7 bBx2 N-8ykX 6`QK +Q`Tmb M HvbBb- r2 }M/ Ry bBM;H2 H2ii2` K#B;mQmb bm{t2b Ub22 TT2M/Bt *V `2bTQMbB#H2 7Q` /2+HBM2 BM i?2 bi`2M;i? Q7 `mH2@# b2/ TT`Q +?X q2 +?B2p2 M2 `Hv RRW BKT`Qp2K2Mi Qp2` TT`Q +? k QM TTHvBM; i?2 ?v#`B/ TT`Q +?- r?2M i2bi2/ QM R-8yN rQ`/bX
17HH 7Qm` H M;m ;2b `2 bTQF2M BM /Bz2`2Mi TH +2b Q7 LQ`i?@2 bi AM/B - #2HQM; iQ i?2 hB#2iQ@"m`K M H M@ ;m ;2 7 KBHv M/ `2 pmHM2` #H2 H M;m ;2b ++Q`/BM; iQ lL1a*PX
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ai2KKBM; `2bQm`+2@TQQ` AM/B M H M;m ;2b ,RN
h?2 Q#i BM2/ `2bmHib 7Q` HH i?2 H M;m ;2b `2 b?QrM BM h #H2 sAAX h?2 H M;m ;2b mb2/ BM i?2 bim/v- 2t+2Ti "2M; HB- biBHH H +F ;QQ/ # H M+2/ +Q`TQ` X lbBM; Qm` `mH2 2M;BM2 r2 T`Q/m+2 Rk-98e- 3-eN9 M/ e-j99 bm{t b2[m2M+2b 7Q` "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/Q- `2bT2+iBp2HvX "2BM; p2`# }M H H M;m ;2b- i?2 BMp2biB; i2/ H M;m ;2b ? p2 +QKTH2t KQ`T?QHQ;v 7Q` i?2 p2`#X h?2 bK HH bBx2 Q7 i?2 `QQi rQ`/ HBbi K v #2 i?2 `2 bQM #2?BM/ i?2 HQr ++m` +v BM "Bb?MmT`Bv J MBTm`B M/ "Q/QX q2 K v #2 #H2 iQ BKT`Qp2 i?2 ++m` +v #v BM+`2 bBM; i?2 /B+iBQM `v bBx2 M/ rBi? KQ`2 BMbB;?ib iQ i?2 H M;m ;2b BM /2bB;MBM; i?2 `mH2b mb2/ #v i?2 `mH2 2M;BM2X h?2b2 irQ H M;m ;2b `2 pmHM2` #H2 b K2MiBQM2/ 2 `HB2` M/ HBM;mBbiB+ 2tT2`iBb2 Bb /B{+mHi iQ }M/X 6Q` K Mm H 2p Hm iBQM- r2 2KTHQv QM2 2p Hm iQ` 7Q` 2 +? H M;m ;2c i?2 2p Hm iQ`b `2 ?B;?Hv 2/m+ i2/ M/ M iBp2 bT2 F2` Q7 i?2 H M;m ;2X q2 +QKT `2 Qm` `2bmHi rBi? mMbmT2`pBb2/ TT`Q +?2b bm+? b (. b;mTi M/ L; kyyd)-
h #H2 sAAX _2bmHib Q#i BM2/ 7Q` bb K2b2- "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/Q mbBM; p `BQmb TT`Q +?2bX G M;m ;2 aGa RUWV .a kUWV aaa jUWV bb K2b2 R3-RN9 8d k8-yyy 3R RR N9 "2M; HB Rk-98e 8e jy-Ry8 39 3 N9 "Bb?MmT`Bv J MBTm`B 3-eN9 8j Ry-j8y dd Ry 3d "Q/Q e-j99 98 N-8yk dR RR 3k R TT`Q +? Rc k TT`Q +? kc j >v#`B/ TT`Q +? aGa→ am{t HBbi bBx2c .a→ .B+iBQM `v aBx2c→ aaa aBM;H2 bm{t bBx2 → → →
(. b M/ " M/vQT /?v v kyRy) M/ (a? `K 2i HX kyy3) M/ i?2 +QKT `BbQMb `2 ;Bp2M BM h #H2 sAAAX 6`QK i?2 i #H2- Bi Bb +H2 ` i? i Qm` TT`Q +? rQ`F r2HH rBi? HQr `2bQm`+2 H M;m ;2b- T `iB+mH `Hv QM2b 7`QK AM/B X q2 HbQ +QKT `2 Qm` `2bmHib rBi? i?2b2 Q#i BM2/ #v JQ`72bbQ`X h?2 Q#i BM2/ `2bmHib `2 b?QrM BM h #H2 sAAA rBi? Rkj-d8j- Rjy-8Rk- 9k-83y M/ 9y-Ryj rQ`/b 7Q` bb K2b2- "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/Q- `2bT2+iBp2HvX q2 ? p2 iQ K2MiBQM ?2`2 i? i i?2 +Q`TQ` mb2/ 7Q` "Bb?MmT`Bv J MBTm`B M/ "Q/Q `2 MQi # H M+2/X 6Q` "Bb?MmT`Bv J MBTm`B- i2tib `2 +QHH2+i2/ 7`QK #HQ;b M/ qBFBT2/B - r?2`2 b 7Q` "Q/Q r2 ? p2 K Mm HHv ivT2/ 9y-Ryj rQ`/b 7Q` Qm` rQ`FX AM h #H2 sAAA- i?2 `2bmHib Q#i BM2/ BM Qm` 2tT2`BK2Mib rBi? JQ`72bbQ` M/ i?2 ?v#`B/ TT`Q +? `2 T`2b2Mi2/X Pi?2` i?`22 `2bmHib b?QrM `2 7`QK i?2 `2bT2+iBp2 `2TQ`ibX aBM+2 i?2 / i b2ib U M/ H M;m ;2bV 7Q` i?2 /Bz2`2Mi TT`Q +?2b `2 MQi i?2 b K2- bK HH p `B iBQMb BM i?2 [m HBiv Q7 i?2 QmiTmi K v #2 B;MQ`2/X
h #H2 sAAAX *QKT `BbQM Q7 Qm` `2bmHi rBi? Qi?2` TT`Q +? bb K2b2 "2M; HB "Bb?MmT`Bv "Q/Q TT`Q +? JQ`72bbQ`(*`2mix M/ G ;mb kyy8) 3RW 3yW 3RW d3W lMbmT2`pBb2/ (. b;mTi M/ L; kyyd) @ 39W @ @ lMbmT2`pBb2/ (. b M/ " M/vQT /?v v kyRy) @ d9XyeW @ @ E@K2 Mb *Hmbi2`BM; (a? `K 2i HX kyy3) 38W @ @ @ lMbmT2`pBb2/ Pm` ?v#`B/ TT`Q +? N9W N9W 3dW 3kW >v#`B/
3X *PL*GlaAPL AM i?Bb rQ`F- r2 ? p2 T`2b2Mi2/ bi2KK2`b 7Q` i2tib BM bb K2b2- "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/QX HH `2 KQ`T?QHQ;B+ HHv `B+?- ;;HmiBM iBM; M/ `2H iBp2Hv 7`22 rQ`/ Q`/2` AM/B M H M;m ;2bX 6B`bi r2 mb2 `mH2@# b2/ TT`Q +? M/ Q#i BM 8dW- 8eW- 8jW M/ 98W bi2KKBM; ++m` +v- `2bT2+iBp2HvX L2ti- r2 // 7`2[m2Mi rQ`/ HBbi iQ i?2 `mH2@ # b2/ TT`Q +? M/ BM+`2 b2 i?2 ++m` +v bm#bi MiB HHv iQ 3RW- 39W- ddW M/ dRW 7Q` i?2 b K2 H M;m ;2b- `2bT2+iBp2HvX q2 7QmM/ i? i 7Q` i?2 H M;m ;2 b2i- /QKBM Mi 7` +iBQM Q7 bm{t2b `2 bBM;H2 H2ii2` M/ rQ`/b 2M/BM; bm+? bBM;H2 H2ii2`b +`2 i2 T`Q#H2Kb /m`BM; bm{t bi`BTTBM;X h?2`27Q`2- r2 T`QTQb2 M2r K2i?Q/ i? i +QK#BM2b i?2 `mH2@# b2/ H;Q`Bi?K 7Q` T`2/B+iBM; KmHiBTH2 H2ii2` bm{t2b M/ M >JJ@# b2/ H;Q`Bi?K 7Q` T`2/B+iBM; i?2 bBM;H2
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ,ky LX a ? `B 2i HX
H2ii2` bm{t2bX h?2 `2bmHiBM; H;Q`Bi?K mb2b i?2 bi`2M;i?b Q7 #Qi? H;Q`Bi?Kb H2 /BM; iQ Km+? ?B;?2` ++m` +v Q7 N9W +QKT `2/ iQ Dmbi 3kW 7Q` bb K2b2 M/ N9W- 3dW M/ 3kW 7Q` "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/Q- `2bT2+iBp2HvX Ai Bb TQbbB#H2 i? i M K2/ 2MiBiv `2+Q;MBiBQM- T`BQ` iQ bi2KKBM; Q` BM T ` HH2H K v ?2HTX h?Bb Bb #2+ mb2 K Mv 2``Q`b Q++m` rBi? PPo rQ`/b- HQi Q7 r?B+? `2 M K2/ 2MiBiB2bX >Qr2p2`- bBM+2 H M;m ;2b +QMbB/2`2/ U2t+2Ti "2M; HBc 2p2M "2M; HB `2b2 `+?2`b +QKTH BM Q7 H +F Q7 +Q`TQ` M/ iQQHbV `2 `2bQm`+2@ TQQ` H M;m ;2b- M K2/ 2MiBiv `2+Q;MBx2`b `2 MQi `2 /BHv p BH #H2 Hi?Qm;? i?2`2 Bb bQK2 Tm#HBb?2/ `2b2 `+? (1F# H M/ " M/vQT /?v v kyy3c a? `K 2i HX kyRk)X b 7mim`2 rQ`F- Bi rQmH/ #2 BMi2`2biBM; iQ 2tTHQ`2 i?2 TQbbB#BHBiv Q7 KQ/2HHBM; HH KQ`T?QHQ;B+ H T?2MQK2M mbBM; Qi?2` bm++2bb7mH i2+?MB[m2b bm+? b PTiBK HBiv h?2Q`v (S`BM+2 M/ aKQH2MbFv RNNj)- J tBKmK 1Mi`QTv JQ/2Hb (_ iM T `F?B RNNd) M/ *QM/BiBQM H _ M/QK 6B2H/b (G z2`iv 2i HX kyyR) M/ +QKT `BM; i?2 `2bmHib rBi? i?Qb2 Q7 Qm` TT`Q +?2bX
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ai2KKBM; `2bQm`+2@TQQ` AM/B M H M;m ;2b ,kR
TT2M/Bt , bb K2b2 LQmM AM~2+iBQM q2 7QmM/ 8-key BM~2+iBQM H 7Q`Kb 7Q` i?2 bb K2b2 MQmM `QQi U ,K MVX h #H2 sAo HBbib 72r Q7 i?2 BM~2+iBQM H 7Q`KbX h?2 b2+QM/ +QHmKM Bb i?2 BM~2+i2/ rQ`/- i?2 i?B`/ +QHmKM `2T`2b2Mib i?2 i` Mb+`B#2/ 7Q`K BM AS M/ i?2 7Qm`i? +QHmKM b?Qrb i?2 #`2 F@mT Q7 i?2 rQ`/ BMiQ p HB/ KQ`T?QHQ;B+ H mMBibX
h #H2 sAoX aQK2 BM~2+iBQM H 7Q`Kb 7Q` i?2 MQmM `QQi U ,K MV RX kX jX 9X 8X eX dX 3X NX RyX RRX RkX RjX R9X R8X ReX RdX R3X RNX kyX kRX kkX kjX k9X k8X keX kdX k3X kNX jyX jRX jkX jjX j9X j8X jeX jdX j3X jNX 9yX 9RX 9kX 9jX 99X 98X
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ,kk LX a ? `B 2i HX
TT2M/Bt ", bb K2b2 o2`# AM~2+iBQM q2 7QmM/ j3y BM~2+iBQM H 7Q`Kb 7Q` i?2 bb K2b2 p2`# `QQi U ,iQ #2VX h #H2 so HBbib 72r Q7 i?2 BM~2+iBQM H 7Q`KbX h?2 b2+QM/ +QHmKM Bb i?2 BM~2+i2/ rQ`/- i?2 i?B`/ +QHmKM `2T`2b2Mib i?2 i` Mb+`B#2/ 7Q`K BM AS M/ i?2 7Qm`i? +QHmKM b?Qrb i?2 #`2 F@mT Q7 i?2 rQ`/ BMiQ p HB/ KQ`T?QHQ;B+ H mMBibX
h #H2 soX aQK2 BM~2+iBQM H 7Q`Kb Q7 i?2 `QQi p2`# U , iQ #2V RX kX jX 9X 8X eX dX 3X NX RyX RRX RkX RjX R9X ReX RdX R3X RNX kyX kRX kkX kjX k9X k8X keX kdX k3X kNX jyX jRX jkX jjX j9X j8X jeX jdX j3X jNX 9yX 9RX
*J h` Mb +iBQMb QM bB M G M;m ;2 AM7Q`K iBQM S`Q+2bbBM;- oQHX o- LQX L- `iB+H2 - Sm#HB+ iBQM / i2, C Mm `v uuuuX ai2KKBM; `2bQm`+2@TQQ` AM/B M H M;m ;2b ,kj
TT2M/Bt *, K#B;mQmb bBM;H2 H2ii2` bm{t HBbi h #H2 soAX aBM;H2 H2ii2` bm{t2b BM "2M; HB- "Bb?MmT`Bv J MBTm`B M/ "Q/Q rBi? 2t KTH2b Q7 BM~2+i2/ rQ`/b M/ `QQi rQ`/b 2M/BM; rBi? i? i H2ii2`X am{t * i2;Q`v AM~2+i2/ rQ`/ _QQi rQ`/ G M;m ;2 , "2M; HB :2MBiBp2 *J U , ` BM Y :*JV U , K `F2iV h2Mb2 K `F2` U , 2 i Y hJV U , #QQFV h2Mb2 K `F2` U , iQ /Q Y hJV U , `Q /V GQ+ iBp2 *J U , #Qp2 Y G*JV U ?2fb?2V h2Mb2 K `F2` U , TB2+2 , RSSHV U , HBF2V
G M;m ;2 , "Bb?MmT`Bv J MBTm`B :2MBiBp2 *J U , 7`mBi Y :*JV U , T`2bbV h2Mb2 K `F2` U , `2+Q;MBx2 Y hJV U , b2H2+iV h2Mb2 K `F2` U , iQ #2 Y hJV U , ;` M/ 7 i?2`V h2Mb2 K `F2` U , iQ #2 Y hJV U , #m/V h2Mb2 K `F2` U , iQ r22T Y hJV U , `iV h2Mb2 K `F2` U , iQ #2 Y hJV U , mbV
G M;m ;2 , "Q/Q LQKBM iBp2 *J U , _ KYL*JV U , ?QM2biV LQKBM H bm{t U , iQ bH22TV L2; iBQM bm{t U , 2 iY/Q MQiV U , K MV o2`# H bm{t U , iQ +miYb2T ` i2V U , M K2 Q7 i`22V o2`# H bm{t U , rQ`FY}MBb? V 1KT? iB+ K `F2` U , vQmYQMHvV U , +? ` +i2`V /D2+iBp2 /2MQiBM; bm7@ U , ++2bb +`vBM;V U , rQK#V }t
L*J LQKBM iBp2 + b2 K `F2`c :*J :2MBiBp2 + b2 K `F2`c G*J GQ+ iBp2 + b2 K `F2`c hJ →h2Mb2 K `F2`c RSSH 6B`bi T2`bQM→ THm` H K `F2`c → → →
h #H2 soAAX am{t BM7Q`K iBQM BM i?2 i` BMBM; +Q`TQ` G M;m ;2 , "2M; HB hQi H W qQ`/b rBi? bBM;H2 H2ii2` bm{t2b (Ms1) 3e9 keXNy qQ`/b rBi? KmHiB@H2ii2` bm{t2b(Msm) eRk RNXy8 qQ`/b rBi? MQ bm{t (N!) Ry89 jkX3k _QQi rQ`/b i? i 2M/ rBi? Mv K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2i (Ns1) e3k kRXkj
G M;m ;2 , "Bb?MmT`Bv J MBTm`B qQ`/b rBi? bBM;H2 H2ii2` bm{t2b (Ms1) 8Re kyXjR qQ`/b rBi? KmHiB@H2ii2` bm{t2b (Msm) 889 kRX3R qQ`/b rBi? MQ bm{t (N!) N83 jdXdk _QQi rQ`/b i? i 2M/ rBi? Mv K2K#2` Q7 i?2 bBM;H2 H2ii2` bm{t b2i (Ns1) 8Rk kyXRe
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