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+d, . +4,q +e {,q.4 i +q, +e, = . q.4 Qrz/ xvlqj wkh lqgxfwlrq k|srwkhvlv/ zh kdyh ]e i +w, gw @ d q[ 4 n@3 k l 4 +{ d,n.4 i +n, +d, . +4,n +e {,n.4 i +n, +e, . +n . 4,$ S1 FHURQH/ V1V1 GUDJRPLU/ M1 URXPHOLRWLV/ DQG M1 VXQGH 7 5 ]e 4 7 4 . +{ w,q.4 i +q.4, +w, gw q$ q . 4 d l 4 k q.4 +q, q.4 +q, +{ d, i +d, . +e {, i +e, . q.4 q[ 4 4 k l +{ d,n.4 i +n, +d, . +4,n +e {,n.4 i +n, +e, @ +n . 4,$ n@3 ]e 4 q.4 +q.4, +{ w, i +w, gw . +q . 4,$ d dqg wkh lghqwlw| +516, lv suryhg1 Wklv frpsohwhv wkh surri1 Wkh iroorzlqj fruroodu| lv xvhixo lq sudfwlfh1 Fruroodu| 51 Zlwk wkh deryh dvvxpswlrqv iru i dqg U> zh kdyh wkh sduwlfxodu lghqwlwlhv +zklfk fdq dovr eh rewdlqhg e| xvlqj Wd|oru*v irupxod zlwk wkh lqwhjudo uhpdlqghu, ]e q[ 4 +4,n +e d,n.4 i +n, +e, +n . 4,$ n@3 d ]e +4,q . +w d,q i +q, +w, gw> q$ d ]e q[ 4 4 +e d,n.4 i +n, +d, i +w, gw @ +n . 4,$ n@3 d ]e 4 . +e w,q i +q, +w, gw> q$ d +518, i +w, gw @ +519, dqg wkh lghqwlw| +vhh dovr ^46`, ]e +51:, i +w, gw @ d q[ 4 n@3 4 +n . 4,$ ed 5 n.4 k 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wkh _shuwxuehg uljkw uhfwdqjoh uxoh% ]e ]e 33 4 4 5 3 +5145, i +w, gw @ +e d, i +e, +e d, i +e, . +w e,5 i +w, gw= 5 5 d d e / zh fdswxuh wkh _shuwxuehg wudsh}rlg uxoh% ^46` lll, Ilqdoo|/ iru { @ d. 5 ]e +5146, i +w, gw @ d 3 +e d,5 3 i +d, . i +e, +e d, . i +d, i +e, 5 ; 4 . 5 5 ]e 33 d.e i +w, gw= w 5 d 61 YA|j}iB, YAj`B,|jt Xvlqj wkh lqwhjudo uhsuhvhqwdwlrq e| Wkhruhp 4/ zh fdq suryh wkh iroorzlqj lqhtxdolw| 9 S1 FHURQH/ V1V1 GUDJRPLU/ M1 URXPHOLRWLV/ DQG M1 VXQGH Wkhruhp 61 Ohw i = ^d> e` $ U eh d pdsslqj vr wkdw wkh ghulydwlyh i +q4, +q 4, lv devroxwho| frqwlqxrxv rq ^d> e`1 Wkhq e ] q[ 4 4 k l +614, i +w, gw +{ d,n.4 i +n, +d, . +4,n +e {,n.4 i +n, +e, +n . 4,$ n@3 d ; k l + q , A ni n4 A +{ d,q.4 . +e {,q.4 li i +q, 5 O4 ^d> e` > A +q.4,$ A A A A A ? ni +q, ns k +{d,qt.4 .+e{,qt.4 l 4t li s A 4> 4s . 4t @ 4 q$ qt.4 A A A A dqg i +q, 5 Os ^d> e` > A A A + q , A = ni n4 4 e q +e d, . { d. q$ 5 5 iru doo { 5 ^d> e` = Surri1 Xvlqj wkh uhsuhvhqwdwlrq +514, dqg wkh surshuwlhv ri wkh prgxoxv/ zh kdyh e ] q[ 4 4 k l i +w, gw +{ d,n.4 i +n, +d, . +4,n +e {,n.4 i +n, +e, +n . 4,$ n@3 d ]e 4 m{ wmq i +q, +w, gw @= U= q$ d Revhuyh wkdw 5 4 U 7 q$ @ @ 6 ]e m{ wmq gw8 i +q, d +q, i q$ 4 4 5 e 6 ] ]e q q 7 +{ w, gw . +w {, gw8 d d & +q, % q.4 q.4 i 4 +{ d, . +e {, q$ q.4 dqg wkh uvw lqhtxdolw| lq +614, lv suryhg1 Xvlqj Kroghu*v lqwhjudo lqhtxdolw|/ zh dovr kdyh U @ 3 e 4 s4 3 e 4 t4 ] ] 4 C +q, s D C qt m{ wm gwD i +w, gw q$ d d % &4 +{ d,qt.4 . +e {,qt.4 t 4 +q, > i q$ qt . 4 s zklfk suryhv wkh vhfrqg lqhtxdolw| lq +614,1 : Ilqdoo|/ ohw xv revhuyh wkdw U @ @ @ ]e 4 q +q, vxs m{ wm i +w, gw q$ w5^d>e` d &q % 4 vxs m{ wm i +q, q$ w5^d>e` 4 4 ^pd{ +{ d> e {,`q i +q, q$ q 4 +q, d . e 4 4 i +e d, . { q$ 5 5 4 dqg wkh wkhruhp lv frpsohwho| suryhg1 Wkh iroorzlqj fruroodu| lv xvhixo lq sudfwlfh1 Fruroodu| 61 Zlwk wkh deryh dvvxpswlrqv iru i dqg q/ zh kdyh wkh sduwlfxodu lqhtxdolwlhv e ] q[ 4 +4,n n .4 +n, +615, +e d, i +e, i +w, gw +n . 4,$ n@3 d ; i +q, n n4 A +e d,q.4 li i +q, 5 O4 ^d> e` > A A +q.4,$ A A A A ? ni +q, ns +ed,q. t4 P =@ li s A 4> s4 . 4t @ 4 q$ +qt.4,4@t A A A A dqg i +q, 5 Os ^d> e` > A A A = ni +q, n4 q q$ +e d, > dqg e ] q[ 4 4 n.4 +n, P i +w, gw +e d, i +e, +n . 4,$ n@3 d dqg +vhh dovr ^46`, e ] q[ 4 4 e d n.4 k l i +w, gw +616, i +n, +d, . +4,n i +n, +e, +n . 4,$ 5 n@3 d ; + q , ni n4 A A 5q +q.4,$ +e d,q.4 li i +q, 5 O4 ^d> e` > A A A A A ? ni +q, ns q. 4t li s A 4> 4s . 4t @ 4 q A 5 q$+qt.4,4@t +e d, A A A dqg i +q, 5 Os ^d> e` > A A + q , A = ni n4 +e d,q > 5q q$ uhvshfwlyho|= S1 FHURQH/ V1V1 GUDJRPLU/ M1 URXPHOLRWLV/ DQG M1 VXQGH ; Uhpdun 51 Li zh sxw q @ 4 lq +614,/ zh fdswxuh wkh lqhtxdolw| +617, e ] i +w, gw +{ d, i +d, . +e {, i +e, d l ; k 5 4 e i +4, A +e d,5 . { d. i 3 5 O4 ^d> e` > A 7 5 4 li A A A A ? 4 k t.4 .+e{,t.4 l t +{d, 3 ni n li s A 4> 4s . 4t @ 4 A s t.4 A A A A dqg i 3 5 Os ^d> e` > A 3 = 4 d . e +e d, . { 5 ni n4 > 5 iru doo { 5 ^d> e` > dqg/ lq sduwlfxodu/ d, wkh _ohiw uhfwdqjoh% lqhtxdolw| ; ni 3 n4 A A +e d,5 5 A e A A ] A ? 4 i +w, gw +e d, i +d, ni 3 n A +t.4,4s@t +e d,4. t A A d A A A = ni 3 n4 +e d, = li i 3 5 O4 ^d> e` > li i 3 5 Os ^d> e` > e, wkh _uljkw uhfwdqjoh% lqhtxdolw| ; ni 3 n4 A A +e d,5 A 5 e A A ] A ? 4 i +w, gw +e d, i +e, ni 3 n A +t.4,4s@t +e d,4. t A A d A A A = ni 3 n4 +e d, = li i 3 5 O4 ^d> e` > li i 3 5 Os ^d> e` > f, wkh _wudsh}rlg% lqhtxdolw| +618, e ] i +w, gw i +d, . i +e, +e d, 5 d ; 3 A ni n4 +e d,5 A li i 3 5 O4 ^d> e` > A 7 A A A A ? 4 ni 3 ns +e d,4. t li i 3 5 Os ^d> e` > 5+t .4,4@t A A A A A A A = ni 3 n4 +e d, = 5 < Uhpdun 61 Li zh sxw q @ 5 lq +614,/ zh jhw wkh lqhtxdolw| e ] i +w, gw +{ d, i +d, +e {, i +e, +619, d l 3 3 4k +{ d,5 i +d, +e {,5 i +e, 5 ; 33 k l i 33 A 6 6 A 4 A +e d, li i 5 O4 ^d> e` > . +e {, A 9 A A A A A ? 33 k 4 i 5t.4 .+e{,5t.4 l t s +{d, li s A 4> s4 . 4t @ 4 A 5 5t.4 A A 33 A A dqg i 5 Os ^d> e` > A 33 A A A = i 4 4 d.e 5 > 5 5 +e d, . { 5 iru doo { 5 ^d> e` > dqg/ lq sduwlfxodu= d, wkh _shuwxuehg ohiw uhfwdqjoh% lqhtxdolw| e ] 3 4 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{,q.4 @ = > 5 = +5q . 4, +e d, +e d, +q . 4, Ixuwkhu vlpsolfdwlrq ri wkh deryh uhvxow e| pxowlso|lqj wkurxjkrxw e| e d q$ jlyhv ] 4 e +{ w,q i +q, +w, gw q$ d +717, +q4, +{ d,q.4 . +4,q +e {,q.4 i +e, i +q4, +d, +q . 4,$ ed 4 M +{> q, > 5 q$ zkhuh +718, M 5 +{> q, @ q 5q.4 5 . E 5q.4 5 +q . 4, +D . E, D +5q . 4, +q . 4, 5 r +5q . 4, Dq.4 . +4,q E q.4 4 zlwk D @ { d> E @ e {= Qrz/ iurp +718,/ +5q . 4, +q . 4,5 M 5 +{> q, @ q5 +D . E, D5q.4 . E 5q.4 k 5 l q . +5q . 4, +D . E, D5q.4 . E 5q.4 Dq.4 . +4, E q.4 @ q5 +D . E, D5q.4 . E 5q.4 q . +5q . 4, DE D5q . E 5q 5Dq.4 +4, E q.4 5 @ q5 +D . E, D5q.4 . E 5q.4 . +5q . 4, DE ^Dq +E,q ` Qrz/ vxevwlwxwlrq ri D @ { d> E @ e { dqg wkh idfw wkdw D . E @ e d jlyhv M +{>q s5q, .4 > dv suhvhqwhg lq +716,1 Vxevwlwxwlrq ri lghqwlw| +514, lqwr +717, L +{> q, @ +q.4, jlyhv +715, dqg wkh uvw sduw ri wkh wkhruhp lv wkxv suryhg1 Wkh xsshu erxqg lv rewdlqhg e| wdnlqj hlwkhu L +d> q, ru L +e> q, vlqfh L +{> q, lv frqyh{1 Khqfh wkh wkhruhp lv frpsohwho| suryhg1 S1 FHURQH/ V1V1 GUDJRPLU/ M1 URXPHOLRWLV/ DQG M1 VXQGH 45 Fruroodu| 71 Ohw wkh frqglwlrqv ri Wkhruhp 7 krog1 Wkhq wkh iroorzlqj uhvxow krogv q 4 4 e d n.4 k 4 ] e l [ i +n, +d, . +4,n i +n, +e, +719, i +w, gw e d d +n . 4,$ 5 n@3 q ed ^4 . +4,q ` i +q4, +e, i +q4, +d, 5 +q . 4,$ ed ; 5q q.4 ? q.4 > q hyhq 4 ed 4 s = 5 q$ 5 5q . 4 = 5> q rgg e Surri1 Wdnlqj { @ d. 5 lq +715, jlyhv +715,/ zkhuh L d.e >q 5 4 s @ +q . 4, 5q . 4 ed 5 q.4 q r4 5 5 7q5 . +5q . 4, ^4 . +4,q ` = H{dplqlqj wkh deryh h{suhvvlrq iru q hyhq ru q rgg uhdglo| jlyhv wkh uhvxow +719,1 Uhpdun 71 Iru q hyhq/ wkhq wkh wklug whup lq wkh prgxoxv vljq ydqlvkhv dqg wkxv wkhuh lv qr shuwxuedwlrq wr wkh wudsh}rlgdo uxoh +719,1 Wkhruhp 81 Ohw wkh frqglwlrqv ri Wkhruhp 7 eh vdwlvhg1 Ixuwkhu/ vxssrvh wkdw i +q, lv glhuhqwldeoh dqg eh vxfk wkdw +q.4, i =@ vxs i q.4 +w, ? 4= 4 5 w ^d>e` Wkhq ed 4 mSW +{,m s i +q.4, L +{> q, > 4 q$ 45 zkhuh SW +{, lv wkh shuwxuehg wudsh}rlgdo w|sh uxoh jlyhq e| wkh ohiw kdqg vlgh ri +715, dqg L +{> q, lv dv jlyhq e| +716,1 +71:, Surri1 Ohw i> j = ^d> e` $ U eh devroxwho| frqwlqxrxv dqg i 3 > j3 eh erxqghg1 Wkhq Fkhe|fkhy*v lqhtxdolw| krogv +vhh ^48/ s1 53:`, mW +i> j,m 5 +e d, 45 vxs mi 3 +w,m vxs mj 3 +w,m = 5 w ^d>e` 5 w ^d>e` Pdwlf/ Shfdulf dqg Xmhylf ^49` xvlqj d suhpdwxuh Ju xvv w|sh dujxphqw suryhg wkdw s +e d, +71;, mW +i> j,m s vxs mj3 +w,m W +i> i,= 45 w5^d>e` Wkxv/ dvvrfldwlqj i +q, +, zlwk j +, dqg +{ w,q zlwk i lq +71;, uhdglo| surgxfhv +71:, zkhuh L +{> q, lv dv jlyhq e| +716,1 Wkhruhp 91 Ohw wkh frqglwlrqv ri Wkhruhp 7 eh vdwlvhg1 Ixuwkhu/ vxssrvh wkdw i +q, lv orfdoo| devroxwho| frqwlqxrxv rq +d> e, dqg ohw i +q.4, 5 O5 +d> e, = Wkhq ed +q.4, 4 +71<, mSW +{,m L +{> q, > i 5 q$ zkhuh SW +{, lv wkh shuwxuehg wudsh}rlgdo w|sh uxoh jlyhq e| wkh ohiw kdqg vlgh ri +715, dqg L +{> q, lv dv jlyhq lq +716,1 46 Surri1 Wkh iroorzlqj uhvxow zdv rewdlqhg e| Oxsdv +vhh ^48/ s1 543`,1 Iru i> j = +d> e, $ U orfdoo| devroxwho| frqwlqxrxv rq +d> e, dqg i 3 > j3 5 O5 +d> e, > wkhq mW +i> j,m zkhuh # nkn5 =@ 4 ed ] d e +e d,5 3 ni n5 nj3 n5 > 5 5 mk +w,m $ 45 iru k 5 O5 +d> e, = Pdwlf/ Shfdulf dqg Xmhylf ^49` ixuwkhu vkrz wkdw mW +i> j,m +7143, +e d, 3 s nj n5 W +i> i,= q Qrz/ dvvrfldwlqj i +q, +, zlwk j +, dqg +{ w, zlwk i lq +7143, jlyhv +71<,/ zkhuh L +{> q, lv irxqg lq +716,1 Uhpdun 81 Uhvxowv +71:, dqg +71<, duh qrw uhdglo| frpsdudeoh wr wkdw rewdlqhg lq Wkhruhp 7 vlqfh wkh erxqg qrz lqyroyhv wkh ehkdylrxu ri i +q.4, +, udwkhu wkdq i +q, +, = 81 VV,WB|NA YA 6jiWB, YA|j}iB|NA Frqvlghu wkh sduwlwlrq Lp = d @ {3 ? {4 ? === ? {p4 ? {p @ e ri wkh lqwhuydo ^d> e` dqg wkh lqwhuphgldwh srlqwv @ + 3 > ===> p4 ,> zkhuh m 5 ^{m > {m .4 ` +m @ 3> ===> p 4,= Sxw km =@ {m.4 {m dqg &+k, @ pd{ ikm mm @ 3> ===> p 4j = Lq ^4`/ wkh dxwkruv frqvlghuhg wkh iroorzlqj jhqhudol}dwlrq ri wkh wudsh}rlg iru0 pxod 4 knm .4 % i +n, +{m , . +4,n i +n, +{m.4, & p 4 q[ [ +814, Wp>q +i> Lp , =@ +n . 4,$ 5 m @3 n@3 dqg suryhg wkh iroorzlqj wkhruhp= Wkhruhp :1 Ohw i = ^d> e` $ U eh vxfk wkdw lw*v ghulydwlyh i +q4, lv devroxwho| frqwlqxrxv rq ^d> e`1 Wkhq zh kdyh ]e +815, i +w, gw @ Wp>q +i> Lp , . Up>q +i> Lp , > d zkhuh wkh uhplqghu Up>q +i> Lp , vdwlvhv wkh hvwlpdwh +816, mUp>q +i> Lp ,m dqg Fq =@ 4 p4 Fq +q, [ q.4 i +q . 4,$ 4 m@3 km > 55u.4 4 55u li q @ 5u li q @ 5u . 41 S1 FHURQH/ V1V1 GUDJRPLU/ M1 URXPHOLRWLV/ DQG M1 VXQGH 47 Qrz/ ohw xv ghqh wkh hyhq pruh jhqhudol}hg txdgudwxuh irupxod k n.4 +n, 4 m {m i +{m , +n . 4,$ m @3 n@3 l n.4 +n, n i +{m .4 , > . +4, {m.4 m Wp>q +i> > Lp , = @ p [4 q[4 zkhuh {m > m +m @ 3> ===> p 4, duh dv deryh1 Wkh iroorzlqj wkhruhp krogv1 Wkhruhp ;1 Ohw i eh dv lq Wkhruhp :1 Wkhq zh kdyh wkh irupxod ]e +817, p>q +i> > Lp , > i +w, gw @ Wp>q +i> > Lp , . U d zkhuh wkh uhplqghu vdwlvhv wkh hvwlpdwh +818, Up>q +i> > Lp , ; 4 k +q, pS q.4 q.4 l A 4 A i A > { . { m m .4 m m A + q .4,$ 4 m@3 A A A A A A A A % & 4t ? pS 4 pS 4 qt .4 qt .4 4 = @ +q, m {m {m .4 m . > A q$+qt.4,4@t i s A m @3 m @3 A A A A A A A q A 4 A {m .{m .4 4 i +q, A &+k, . pd{ = q$ m = 5 4 5 m @3>===>p 4 Surri1 Dsso| wkh lqhtxdolw| +614, rq wkh vxelqwhuydo ^{m > {m .4 ` wr jhw {]m.4 q 4 4 [ i +w, gw +n . 4,$ n@3 {m l k n.4 +n, n.4 +n, i +{m , . +4,n {m.4 m i +{m .4 , m {m ; k q.4 q.4 l 4 A > vxs i +q, +w, m {m . {m .4 m A +q.4,$ A A w5^{m >{m .4 ` A A A A A A $ s4 # A 4 A {U m .4 ? s +m {m ,qt.4 .+{m.4 m ,qt.4 t 4 +q, +v, gv i > q$ qt .4 A {m A A A A A $ # A A lq k {U m .4 A A 4 4 k . {m .{m.4 = A + q , A i +v, gv m = q$ m 5 5 {m 48 Vxpplqj ryhu m iurp 3 wr p 4 dqg xvlqj wkh jhqhudol}hg wuldqjoh lqhtxdolw|/ zh kdyh Up>q +i> > Lp , p4 {]m.4 q 4 4 [ [ i +w, gw +n . 4,$ n@3 m @3 {m l k n.4 +n, n.4 +n, i +{m , . +4,n {m .4 m i +{m .4 , m {m ; pS 4 k q.4 q.4 l A 4 A > vxs i +q, +w, m {m . {m .4 m A A + q .4,$ A m @3 w5^{m >{m .4 ` A A A A A A A 4 A ? pS 4 # {Um.4 +q, s $ s +m {m ,qt.4.+{m.4m ,qt.4 t4 4 = @ i +v, gv > q$ qt .4 A m @3 { A m A A A A A $ # A A lq k m .4 p4 {U A A 4 S 4 k . {m {m.4 = + q , A i +v, gv A m m = q$ 5 5 m @3 Dv 5 vxs w ^{m >{m .4 ` {m +q, +q, i +w, i / wkh uvw lqhtxdolw| lv reylrxv1 4 Xvlqj wkh glvfuhwh Kroghu lqhtxdolw|/ zh kdyh p [4 3 4 E C +qt . 4,4@t m @3 {m 5 p [4 9 4 9 7 4 @t +qt . 4, m @3 5 4 s4 s k qt.4 qt.4 l 4t +q, F m {m . {m .4 m i +v, gvD {]m .4 53 4 s4 6s 6 s4 {]m .4 9E : +q, s F : 9C : i +v, gvD : 7 8 8 {m p [4 k 7 m @3 @ qt.4 qt.4 l t4 m {m . {m.4 m 4 +qt . 4,4@t t 6 4t 8 5 6 4t 4 p 4 p [ [ qt.4 qt.4 +q, 7 8 m {m {m .4 m . i s m @3 m @3 dqg wkh vhfrqg lqhtxdolw| lq +818, lv suryhg1 Ilqdoo|/ ohw xv revhuyh wkdw p [4 3 4 q {m . {m .4 +q, F 4 gv k +v, . D i m m 5 5 {]m .4 4 E C q$ m @3 {m S1 FHURQH/ V1V1 GUDJRPLU/ M1 URXPHOLRWLV/ DQG M1 VXQGH 49 4 3 {]m .4 q p 4 [ {m . {m .4 4 +q, F E km . m pd{ i +v, gvD C m @3>===>p4 5 5 m @3 {m q 4 {m . {m .4 +q, km . pd{ m i m @3>===>p4 5 5 4 dqg wkh odvw sduw ri +818, lv suryhg1 Uhpdun 91 Dv +{ d, .+e d, +e d, iru 4/ { 5 ^d> e`/ wkhq zh uhpdun wkdw wkh uvw eudqfk ri +818, fdq eh erxqghg e| p4 4 +q, [ q.4 i +q . 4,$ 4 m@3 km = +819, Wkh vhfrqg eudqfk fdq eh xsshu erxqghg e| 4 q$+qt . 4,4@t +81:, 5 6 4t 4 p [ +q, 7 .4 8 kqt i m s m @3 dqg qdoo|/ wkh odvw eudqfk lq +818, fdq eh xsshu erxqghg e| 4 ^&+k,`q i +q, = +81;, q$ 4 p>q +i> > Lp , Qrwh wkdw doo wkh erxqgv surylghg e| +819,0+81;, duh xqlirup erxqgv iru U lq whupv ri wkh lqwhuphgldwh srlqwv 1 Wkh odvw lqhtxdolw| zh fdq jhw iurp +818, lv wkdw rqh iru zklfk zh kdyh m @ Frqvhtxhqwo|/ zh fdq vwdwh wkh iroorzlqj fruroodu| +vhh dovr ^46`,= {m .{m .4 1 5 Fruroodu| 81 Ohw i eh dv lq Wkhruhp ;1 Wkhq zh kdyh wkh irupxod ]e +81<, p>q +i> Lp , > i +w, gw @ Wp>q +i> Lp , . U d zkhuh +8143, Wp>q +i> Lp , @ p [4 q[4 m @3 n@3 4 5n.4 +n . 4,$ k l i +n, +{m , . +4,n i +n, +{m .4 , kqm .4 vdwlvhv wkh hvwlpdwh dqg wkh uhpdlqghu U ; 4 q.4 +q, pS A 4 A A q +q.4,$ i A 5 4 m@3 km > A A A A A ? A % & 4t pS 4 Up>q +i> Lp , 4 +q, A kqm .4 > A s A 5q q$+qt.4,4@t i A m @3 A A A A A A = 4 q i +q, = 5q q$ ^&+k,` 4 Uhpdun :1 Vlplodu uhvxowv fdq eh vwdwhg e| xvlqj wkh _shuwxuehg% yhuvlrqv hperg0 lhg lq Wkhruhpv 7/ 8 dqg 9/ exw zh rplw wkh ghwdlov1 4: -jujijAWjt do ,+,c 5 5 #+BW+ @?_ a +N,wWAW5c 5L4i t|hLt! |)Ti ?i^@*|it ? |4i _gihi?|@M*i 4@TT?}t @?_ @TT*U@|L?t c hiTh?| +BW +it +iT L**c VL*c L EbbHc DSS zzPD""2>z'[>f[>"xe{2> 55 #+BW+c ? |i |h@Ti3L_ ?i^@*|) uLh @MtL*|i*) UL?|?Lt 4@TT?}tc tM4| |i_ uLh d2o do 55 #+BW+c ? |i |h@Ti3L_ ^@_h@|hi uLh4*@ uLh 4@TT?}t Lu ML?_i_ @h@|L? @?_ @TT*U@|L?tc deo dDo tM4||i_ 55 #+BW+c ? |i |h@Ti3L_ uLh4*@ uLh wTtU|3@? 4@TT?}t @?_ @TT*U@|L?tc A@4!@?} a Lu @|c E? 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