Towards dynamic randomized algorithms in computational geometry
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(68) . h jl q n q muh p n{t 4x}h x q & nm vCn q zrxÄvWms¥ p m p ¥n p zn p n{t }m p ¥3n{ts¥hbm q k v hAv*hbt Pm p ¥ ¥x}h x q mwYjlhb¢ltux v \`URq mvYnx{w²x prq x}tozh q klx}hx q mow}n{t!wyh jl q xµ4vwymux p wyxi¤ q k5n q k8nbv £ilmow Pt zrxixµtshbj5x{zvWm p wyx
(69) m q v q nj`j xÄnxÄz m p \ UÀ\ fik5n hiv' q k`x{vWmv fik5n %$ ! m p "µ_ %$ \ klmv zrx ixµtshbj x pPq k5nbvntsx{nbz;x{nwÀklxÄz n klmu¥bktuxix}t4h v*hbjlk`mov q mow}n q muh p ¤ q k8n q v*h x q m xÄvAwyton{m vAx ix p hbx t q klx q klx}hbx q mw}nt nbvWj5x{w q h Aq klx x}toz (m p h-zrxµ q hhb¢ q nm p n p hj q m nt wyh jltux}|rm q b¤{m q< n ¢ x p xÄwyx{vvn& q hzrx{v*ms¥ p ixµ wyh jltsmw}n q x{z n{ts¥bhm q k v²¤r5v*m p ¥zln q nv q 5w q lx{v Ak`hivWx m j`tsx x pPq n q m h p movAzrm )gwy`t q}\ klhl¥bk q klxw²h pPq mu¢l q msh p h vW5w-k x{vWx{n{-w-klx{vAmovY¢5x ih p zEntut"£ilx{v q muh p ¤5m q wµn p ¢5x 5v*x lt ¤ h q m x q h q m xi¤ q h q nixn p m prq x}x{v q m pO hxxÄntsmv q mow3nvWj5x{w q v \:U q mov
(70) ntut q klx hx q `xnbv4m q ntov*h Pmsx}tzlvAn qq -nw q m ix q klx}hbx q mw}ntj`hb¢`tsx v²¤5n p z q klx x q klhPz`v n{xv q mutstmu¥bhhb8v \ klmvYn{jljltumsx{v q h-n p zrh m }x{zgn{ts¥bhm q k v²¤lm pPq hPzr5wyx{zgm pq klx x}tz ¢ \ "\ ton{ `vWh p m p "}_ $b ton $ ! \ k`xv q 5,z Eh 4q klmv rm p z h £ilx{v q msh p v@k5nbv
(71) jlh ¥x{vvWm ixµt m prq x}x{v q x{z q klx3x{vWx{n{-w-klx}vy¤5m q x ix p -n{movWxÄz ljOn p m jlx{vv*m ix@x prq kr5v*monv n h p ¥ q klx
(72) wyh p m q i¤ prq mst(m q ¢5x{w}n x4h p x
(73) h :q k`x klh q vWl¢ #*xÄw q v4~RvWh x q m x{v q hih klh qYq h q nv q xi¤ q klhl¥bk-nwym p ¥mvYv q m ltn q m p ¥ «h "q klx
(74) tonv q4q <h ix{nv \ X n p zrh m Än q muh p n ihbmoz`v q klx5vWxh wyh jltumow}n q x{zEzln q nv q 5w q lx{v²¤!n p z mv@¥bm Pm p ¥ jlhih h m q v3x )wymux p w i¤ h q klxgj5hbm prq h Pmsx
(75) Hh @q klx}hx q mow}n{tAwyh jltsxµ|rm q nbv <x}tst nv=j`-nbw q mowµnt!x{v*lt q v \URq4 5v q ¤5klh x ixµ}¤l¢5x p h q mowyxÄz q k5n q ¤(m p tsm q x}n q lxi¤ q k`hbl¥k q klx x jlk5nbv*mov3mv h q x p jl q h p jlnbw q mow}n{tYx )wymux p w i¤m q mv h p t x pPq muh p xÄz n p z;vWx}tzrh x}|Pj5x}m x pPq n{tst q x{v q x{z \ & p;q klx wyh pPq n& i¤ q klmv 'x )gwymux p w Omovh p t xµ|rj5x{w q x{z; nvwytnbvv*mow}n{t4n ix}-n{¥bx w}nbv*x n p nt lv*movnvvW x{vvWh x jlhb¢5n{¢lmstumov q mowzrmov q mu¢l q msh p h p zln q nP¤-n p zrh m }x{zn p n{t `vWmv n ix}n¥bxÄv q klxgw²h jltux}|Pm q gh p n{tst<j h vv*ms¢ltux plp m p ¥iv3h @q klxgn{ts¥bhm q k E\:URp nbw q ¤ q klx plp m p ¥gh Aq klxntu¥bhm q k k8nbv
(76) n-n p zrh nvWj5x{w q ¤(¢l q
(77) p x}m q klxµ q klxwyh p ¥bln q msh p h zln q nP¤ p h q k`xYx{vWlt q h q klx
(78) n{ts¥bhm q k ¤ q k8n q x n{m p vj`lx}t zrx q x} m p mov q mwCn p z¥m ix{v n p p m£ `x
(79) n p zgx}|`nbw q v*hbts q msh p\ X n p zrh m µx{z n p nt lv*mov4%n ixµ-n¥x{vYh p ntst!j5hivvWms¢`tsx plp m p ¥ivYh q klxn{ts¥hbm q k ¤ ¢l q v q 5zrmux{v q klx <hb-v q w}nbv*xz`n q n \ h p vWx{£ilx pPq t i¤lm q mov@nx{n{tsmov q mw hPzrx}t!h n p n{t `vWmv3 m p jlnbw q mowyx ¤ q klxm pPq x}x{v q m p ¥ zln q n nx h q x p j5hbm prq v x{nvWlx{z h p h¢ #*x{w q v²¤n p z q k`x}ms zrmv q ms¢` q muh p mv n h ¢5x}m p ¥ klh hb¥x p x}h5vy¤h h ix}m rm p ¥On p jlhb¢5n{¢lmstum q nvvW j q muh p m p v*j5nbw²x \ k`xj hm pPq v Amstuth p t g¢5xnvvW x{z q h¢5x3m p zrx}j5x p zPx prq h p xh n p h q klx} \<X n p zrh m Än q muh p mov3m prq x}xÄv q m p ¥ h q k`movj hm pPq h Pmsx m @q klmovx}|Pj xÄw q x{z wyh jltux}|rm q mv¢5x qq x} q k8n pq klx <hb-v q w}nbv*xOwyh jltsx}|Pm q Oh °q klxE¢5x{v q zrx q x} m p mov q mw n{ts¥bhm q k v p h p ¤"hbm xÄ£ 5n{tR¤ Aklx p0q klxnts¥hbm q k v
(80) nxv*m jltux}~ AklmwÀk mo
(81) v ixµ h q x pgq k`x3wµnbvWx \ URprq hPzr8wym p ¥v*h x°£ 5n prq m q msx{vAx}j`x{v*x prq m p ¥ q klxwyh jltux}|rm q h q klxxÄvWlt q m pEq klx pn nt lv*movmv
(82) ntov*hEj5hivv*ms¢ltuxi¤!n p zOtsx{nzlv q hEntu¥bhm q k v q k8n q n{xh q j` q vWx p vWm q m ix q hEn wyxµ q n{m p x}| q x pPq}\ . . .
(83) a. . . x <x}xgj5n{ q mowyltnt Om pPq x}x{v q x{z m p zrxÄvWms¥ p m p ¥ z, p n mowntu¥bhbm q k v m p jl-nw q mowyxi¤ q klxzln q n h n j`hb¢`tsx n{xh q x p nw}£ `msxÄz jlh¥bxÄvvWmix}t \URq mv@hb¢rmuhb5v*t p h q x{nbv*h p n{¢ltsx q hx{wyh jl q x q klx Aklhtsx
(84) x{v*lt q x{nbw-k q m x4n p x zln q n mvCm p vWx} q x{z \ kP5v ~ vWx m z, p n mw"vw-klx x{vnx p x{wyx{vvn{ \ x4v q 5z, ¢ h q k q klxµhbx q mowµnt`wyh j`tsx}|Pm q n p z jlnbw q mow}n{tx )wymux p w Eh @q klxgntu¥bhm q k v \ klmv q k`x{vWmvv prq klx{vWm }x{v@hb` <hb `v3m p q klmv xµtoz \ URp;q klx -v q wÀk5n{j q xµ}¤ q klxOzrx 5p m q msh p vn p z nm p jlhbj5x} q msx{vh wytonvv*mow}n{t
(85) v q 5w q lx{vm p h jl q n q muh p n{
(86) t 4x}h x q & nxEx{w}n{tstsxÄz(¤nbv <x}tstnbvn p zln x prq nt q hihbt zr5ntum q Aklh vWx
(87) jlxÄvWx pPq n q msh p mov p x
(88)
(89) ¤5n p z AklmwÀkntstuh 4v5v q hjl@h ix x}tut p h p x{vWlt q v"m p n n plp xµ q k5n q mov hxAm pPq `m q m ix q k5n pq klx@5v*5nt5h p x \lZ tst p xÄwyx{vvn& ¢5nbw ¥hb p z h q klx
(90) p zrx}v q n p zrm p ¥h hl4ntu¥bhbm q k v Amstut(¢5x hb p z m pgq klmovAw-k5nj q x} \ ] x Pmsh5vx{v*lt q vÆh p -n p zrh m }xÄz=m p wyx x pPq n{tbn{ts¥hbm q k vnx<jlxÄvWx pPq x{z@m p k5n{j q x}@e \ k`hivWxn{ts¥hbm q k vAnx q klx h p xÄv q k5n q@ n ixÄz q klx ¢5x}¥bm plp m p ¥h x{vWxÄn-w-klx{vm p q klmov x}tz \ klx gn{x°v q n q mwb¤ q klhb`¥bkEm p wyx x prq nt ¤b¢5x{w}n8vWx q klx ntut n ix5vWx h q klx h ,p . mow q 4-n{jlk¤nv q 5w q lx q k8n q@p xµx{zlv q klx p h Atsx{zr¥x3h n{tst!zln q nnvYx{n{t nbv q klx m p m q montum {n q muh p v q x}j \:U q 8v q ¢5x p h q mwyx{z q k5n q \ "\ tn `vWh p ntvWh <hb ixÄz ngtsh q h p zrm rmzrx n p z wyh p £ilx}n{ts¥hbm q k vy¤ q k5n q w}n plp h q ¢ xx}| q x p zrxÄz q hOn ,z p n mowvw-klx xi¤ n p z q kP5v Amstst p h q ¢ xzrx ixµtshbj5x{z3k`x}x \ x@n{tov*h3jlx{vWx pPq v*x ix}-n{t x q k`hPzlvh n p nt lv*mov²¤ zr`x q h \ "\ ton lv*h p ¤ \ lt `tsx °n p z X\ fix}mozPx}t \ klx x}ton{ p n x}x
(91) movm prq hPzr5w²x{zm p k8nj q x} aP\5URq mvy¤~ j`x klmov q hmowµntst i¤rhl v q vWx m z p n mowv q 8w q lx
(92) [ $bdP¤
(93) [ ! \iURq ntstuh 4v q klxwyh p v q 5w q muh p h q klx x}tn p n q mon p ¥b`ton q msh p h ngvWx q h j5hbm prq vWm q x{v²¤(m p n p OzPm x p vWmsh p ¤ Am q k`hb q jlx}tsm m p n{ p h Atsx{zP¥bx h q klmvv*x q}\ klx x}ton{ p n x}x mvwyh j5n{x{z q h n v*m mutonv q 5w q `xi¤ p "µ_b_ c¢ "\ \ 4lmu¢5nbv²¤ 3\ A\ @p q k¤5n p * jlhbj5hiv*x{z m # z \ fik5nms \ k5n{j q x} v*klh 4vCklh q klx@¢5nvWmwmzrx{n@h q klx x}tn p n x}x4tsxÄnbzlv q h°zrx{v*ms¥ p m p ¥ n ix}& 3¥x p x}nt v q 5w q lx ¤ q klx UR,p . lx p wy2x 4-n{jlk¤Pntutsh Am p ¥ q klx@v*x m ,z p n mow"w²h p v q 8w q msh p h p x}h5v@¥bx}h x q mowv q 8w q lx{v \ xw}n p hbl¥klt vn q k5n q q klmv3v q 8w q lx n{jljltsmux{v q h q k`xvn x
(94) jlh¢ltsx v h AklmwÀk q klx h ,p . mw q Ynjlk Anvjlx Pmshb8vWt 5vWx{z ¤ ¢l q m q ntutsh 4vAm p v*x} q msh p v \ <h Pm p z`v h wyh jltsx}|Pm q On p nt lv*movnxgjlx{vWx prq x{z(¤ AklmwÀk0klhtoz p zrx},k Pj5h q klx{vWxÄv v*m muton q h q klhiv*xgv q n q x{z hb°n p n{t }m p ¥Entu¥bhm q k v@5v*m p ¥ q klx h ,p . mw q 4-n{jlk \ klx j5hivvWmu¢lmstum q h x @h rm p ¥ q klx{v*x wyh p zPm q muh p vAmovAn{tov*hv q 8zrmsx{z \ fix ix}-n{t(n{jljltumow}n q msh p vn{xzrx ix}tuhbj5x{z \ klx5vWx4h !q klx UR,p . lx p wyx Ynjlk hb4n p v xµm p ¥ x{£ `x{v q v Am q kn¥bhihPzEwyh jltux}|rm q 3movAn{tov*hzrmvwy8vvWxÄz \ |Pj xµm x prq nt5xÄvWlt q v hb4w²h jl q m p ¥wyh p ix}|kPltutovm p zrm x p vWmuh p v a n p z l¤5n p z x tn p n q mon p ¥bltn q msh p vYm p zrm x p v*msh p vAen p z a ¤ vWklh q klx3j`-nbw q mowµntx )wymsx p w h q klx n{ts¥bhm q k v \ URp k5nj q x}4r¤ q klx
(95) mozrxÄnh q klx x}ton{ p n x}x@mvjlmow ix{zljn¥ nm p ¤5n p zgx p ton{¥x{z q h¢5xnjljltumsx{z q h q klxwµnbvWxh klms¥klx}4hb-zPx}-v ¦ hh p hbmzrmn¥-n vy¤5m p n p zrm x p vWmuh p v \ . .
(96)
(97) . klmvAw}nbv*x zrhix{v p h q 5q m prq h q klx -n x
(98) h h k5n{j q x} \5 |rj5x}m x pPq n{tlxÄvWlt q vAnx. v*klh p\ klx p? k5nj q x}Ad 5p n{tst n ix{v q klx An q h An{-zlv q klxz, p n m {n q msh p h q klx URp,. x p wy2x 4-nj`k \ klx4¥bx p x}-n{t5vw-klx x hzrx}tux q m p ¥
(99) n@zln q n@movwytux{n \bURq AmutstP¢5x4vWx}x p h pq <h x}|`n jltsx{v x}ton{ p n q mon p ¥bltn q muh p h j hm pPq vWm q x{v
(100) n p zOn-n p ¥bx x prq vYh tsm p xvWx}¥ x prq v m pq k`x@jlton p x q k5n q<q klx zrx q nmutovn{xi¤Pklh xixµ}¤i-n q klx} q x{w-k p mw}nt \ klmov<w}n plp h q ¢5x%n ihmozrxÄz(¤ p tsx{vv@n q
(101) q klxjlmwyxh xnbv*m ix3h movvWmuh p v \ klx q k`x}hbx q mw}nt:wyh jltsx}|Pm q mv p x ix} q klx}tux{vvx}|`wyx}tstux pPq ¤in p z q klx nts¥hbm q k mov ix}& 'x )gwymux pPq m p jl-nw q mwyx \ URp j8n-n{tstux}t q hghbl h `vh p U p . lx p w²x Ynjlk ¤"ntsh q h n q klhbvk5n ixzrx{v*ms¥ p x{z v*x ix}-n{t5h q k`x}Av q 8w q lx{v \PZ £ `mow 3jlx{vWx pPq n q muh p h !q klx{v*x <hb lv²¤ h v q t ix}& x{w²x prq ¤ p k8nj q x} \ Amutst(¢5x hb p zgm * . .
(102)
(103)
(104) .
(105) d.
(106) .
(107) . . . . RU p q klmov
(108) w-k5nj q x}}¤ <xjlxÄvWx pPq
(109) q klxgzPx 5p m q msh p v
(110) n p z n{m p jlhbj5x} q msxÄvh A p zln x prq nt v q 8w q lx{v"m p4 h j` q n q msh p nt 4x}h x q &i¤ hb Aklmow-knts¥hbm q k vh wyh p v q 5w q msh p vnx jlx{vWx prq x{z m pq k`x hbtutsh Am p ¥°wÀk8nj q x}-v \ k`x
(111) wyh jltsx}|Pm q
(112) h !q klx@¢5x{v q p h p zPx q x} m p` mv q mw
(113) nts¥hbm q k vCmvYn{tovWh¥bmix p\ hiv q h :q k`x3xÄvWlt q vAnx q n ix p h zrx%$ i¤ xµk $ `¤ ] f $ ! ¤ Aklxµx hbxzrx q n{mstvwµn p ¢ x hb p z(¤x{vWj5x{w²montut wyh p w²x} p m p ¥ntu¥bhbm q k vy¤ q k8n q Amutst p h q ¢ x v q 5zrmux{zklx}x \ rz x p h q x{v q klx b zrm x p v*msh p nt 5wytumozrx{n p v*j5nbw²xi¤ Am q kvw}n{ton<jlhPzP5w q ¤Pn p z 5wytumozrxÄn p zrmv q n p wyx \ x} v@vW5w-kOnbv &ix} q mow}n{t ¤ -n{¢5hix ¤ ¢ xµtsh ¤ Amstut¢5xh q x p 5v*x{z q k`x
(114) ixµ q mw}nt zrmsx{w q msh p mvj5n{-n{tstsxµt q h q klx tonbv q n{|rmvh ¤5n p z m q vh q k`hb¥bh p nt krj5x}jlton p x
(115) mov q kr5vk`hbm }h pPq n{t \ >. . . . E . . . . . . . klx ¿-i± E¨`´!"! h n 5p m q xvWx q. h & j5hm pPq vh ¤zrx p h q xÄz nv ~ B -¤w}n p ¢5x x{£ilmbn{tsx pPq tzrx 5p x{zm pgq klx htstsh Am p ¥ Angnv # q klx v n{tstux{v q wyh p ix}|vWx q wyh prq nm p m p ¥ B ¤ # q klx
(116) m pPq x}vWx{w q msh p h ntut!wyh p ix}|vWx q vAwyh pPq n{m p m p ¥ B ¤ # q klx
(117) m pPq x}vWx{w q msh p h ntutk5nt vWj5nwyx{v4wyh pPq n{m p m p ¥ B \ klx4w²h jl q n q msh p h q klxAwyh p ixµ|kPltutimov"n@w²x prq -n{trjlhb¢ltux m p h jl q n q msh p nt 4x}h x q i¤n p z m q k5nbv¢5x}x p nbv q t °v q 5zrmsxÄz(¤ p h q h p t ¢5x{w}n8vWx4h m q v j`-nbw q mowµnt`njljltumow}n q muh p v²¤ ¢l q n{tovWh¢5x{wµn5v*x3m q mvAn3jlxµtsm m p n{ hb4v*hbt rm p ¥n3tuh q h h q klx}4£ilx{v q msh p v \ tonvv*mow}n{t n q k`x n q mow}n{tYx{vW`t q v h w²h p ix}| j5hbt rk`x{zr-n0n{tstsh 5v q h;v q n q x q klx htstsh Am p ¥jlhj5x} q E~tsx q 5vx{w}n{tst q k5n q n 0 nwyx
(118) movAn nbwyx
(119) h zrm x p v*msh p 0 4 B. y¶ ÀÀ· ¹%$iÃ&$ klx p ¢5x}h 0 o nbwyx{vgn p z q klx p ¢5x}h m p wymzrx p yw xÄv ¢5x q <x}x p 0 o nbw²x{vn p z 0 "² nwyx{vh ~ B nx('*) &+-,/. ~02351 46 789 : ¤ hb c 0 <;"b\ k`x{vWx
(120) ¢5hb p zlv@nx nbv j q h q mow}n{tst q ms¥k qµ\ URp j5n q mwylton{}¤lm p ¢5h q kEzPm x p vWmsh p ven p z a ¤ q klmv p ¢5x}<movtsm p x{n{ \ klx¢ xµk5n rmuhblh
(121) q klxwyh jltsx}|Pm q Eh > ~ B
(122) k5nvntvWhO¢ xµx p v q 5zrmux{z p zrxµk j5h q klx{v*x{v h q klxzrmv q ms¢l q msh p v@h q klxj5hbm prq v@h B \ lhb
(123) x}|`n j`tsxi¤lm q klxj hm pPq v
(124) nx w-klhiv*x p m p zrx}j5x p zPx prq t h n p hb nt5zrmv q ms¢` q muh p ¤ q k`x pq k`xYx}|Pj5x{w q x{zv*m }x4h ~ B m=v '?>²~ tuhb¥ & 1A@C3EB D \.
(125) .
(126) . . " . . . klx
(127) jlhb¢ltux h w²h jl q m p ¥ q k`x
(128) wyh p ix}|kr`tst wyh p vWmov q vm p w²h jl q m p ¥ q klx
(129) j5hbt Pklx zrh pq k5n q m qC hb vy¤Pm \ x \rq klx wyh j`tsx q x@zrxÄvwymsj q msh p h m q v¢5hb p zln& \. x q 5v@v q n{ q Am q kOn -v q hb¢5v*x} n q msh p\!U pEq klx3j`ton p xi¤(m q movYx{nv q hvWx}x q k5n q
(130) q klmv jlhb¢ltux movAn q tux{nbv q nbvAwyh jltux}|nbv4vWh q m p ¥ & p ¢5x}vA ltsx q 5v q nix q klx
(131) j5hbm prq vh p n j5n{-n{¢ hton Am q ? k ix} q mow}n{tn|Pmov²¤ q klx p q klxw²h p ix}|kPltut(mov q k`xj5ht P¥bh p h xÄz¢, q klx{v*x & j5hbm prq vy¤ ©o±g· ¨5 i¸r²@ i¯Àªµ¿µ©«ª-ªµr-\5 nbw-k n{ts¥hbm q k wyh j` q m p ¥ q klx
(132) wyh p ix}|kPltst h & j5hbm pPq vk8nbv q kP5vAn @~ & tsh¥ & q m x@wyh jltux}|rm q \ & j q m nt v q n q mw
(133) nts¥hbm q k vCx}|Pmov q m p zrm x p v*msh p vCen p z ar\ URp klms¥klx}zPm x p vWmsh p vy¤ X
(134) \ fixµmozrx}t f x}m $ " ! k5nbv"¥bm ix p n p n{ts¥hbm q k Aklhiv*x@w²h jltux}| m q mov ' ) & tuhb¥ & & 0 1 3 B 4 : ¤ AklmwÀkmv"hbj q m n{t hCx ix p zrm x p vWmuh p e \ klxv q hb-n{¥bx mv=m p ' ) & 0 31 4 : \ klxn{ts¥hbm q k mvYm p wyx x prq nt ¤l¢l q
(135) q klxn p nt `vWmv@mov
(136) n h q m }x{zgh p q klx & m p vWx} q muh p v \ Zq x}4vWx ixµ-nt ixÄn-vh p v*5w}wyxÄvv `tx{vWx{n{-w-k5vh p 5p zrm p ¥n p hbj q m ntn{ts¥hbm q k h@n p gzPm x p vWmsh p vy¤ [@\ k5n}x}tutsx@k5nvx{wyx pPq t ¥bm ix p vW8wÀkn p ntu¥bhbm q k k8n ,_ " ! \ ZYp nts¥hbm q k Ak`hivWx°wyh jltsx}|Pm q m=v '3~ & tshb¥ & ¤ Aklx}x mv q klx°vWm }x
(137) h q klx h q jl q ¤ q k5n q mov q k`x p ¢5x}h nwyx q vh q k`x3w²h p ix}|kPltutR¤rmvAzrx{vwymu¢ xÄzm p f x}m $d ! \ URpEq klx jlton p xi¤ zrx q x} m p mov q mwYh pl tsm p xn{ts¥hbm q k vYn{x p h p ¤ Am q kEhj q m nt!wyh jltux}|Pm q ' ~ tsh¥ & j5x}Am p vWx} q muh p ~Rv*x}x hbAx}|`n j`tsx Z@ f $ ! \ .
(138) . . . . . . . EE ^ %T . 9 5Ag 3'5 ²1A-)8 - . klx ii±li©4¸i©o}ii h nvWx q. !#". h & j5hbm prq vy¤"wµntstux{z ªµ©s·Wª ¤!m p mvn ¥x}h x q mow v q 8w q lx5v*x{z q h=vWhbtix{z@jlh{|Pm m q @£ilx}msx{v²¤{vW5w-knv q klxwytsh vWx{v qp }x ms¥kr¢5hbvh nY¥m ix p v*m q x ¤rhb q k`x3w²tshiv*x{v q j8nmsAh vWm q x{v \ klmvv q 5w q `xk5nbv
(139) ¢ xµx p j`tsx pPq m ltst gv q 5zrmsxÄz³m pEq klxtsm q x}n q `xi¤ n p z xv q n q x{z hl hb lv Am q km q}\ \iZ lx p k5n x}x{w²x prq t zrx ih q x{z2n ix}& wyh j`tsx q xv*l ix q h
(140) m q Z l _" ! ¤m p Aklmow-k3klxA¥m ix{v q k`x4njljltumow}n q muh p v²¤ q klxAj`hbj5x} q mux{vy¤n p znYtuh q h ntu¥bhm q k v h@wyh jl q m p ¥ q klx zrmn¥-n \ lhb4x{nbw-kvWm q x 4(¤ q klx ii±li©"¿y !! ~ 45h 4mov q k`x3v*x q h j hm pPq vm p q k5n q nx wytuhiv*x} q h 4 q k5n pq hn p h q klx}4v*m q x
(141) h B \ %$. B. ('. '. &$. ~ 4 . *),+.-0/. 5 1. /. B. #2. 4 +. 3. ~ 45
(142) -. 54. . ~. 6-. +5. . 73.
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(145) x}|PjlxÄvvWxÄz nv@ '. ~ 4 . *).
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(147) . . . . ~ 4 (5 . Aklxµx ~ 4 (5 mov q klxk8nt v*j5nbw²x tum m q x{zg¢, q k`x¢lmov*x{w q m p ¥k,Pj5x}jltn p xh 4 n p z 5 ¤ wyh prq nm p m p ¥ 4 \ klx ¦ hh p hbm<zrmon{¥bn h B mov q k`xj5n{ q m q muh p m p ¥ h hb x{z ¢ q klx ¦ hbh p hm wyxµtstovh q klx vWm q x{v \ klxj5hbm pPq v@h B n{xnbvv* x{z q hg¢ xm p ¥x p x}nt"j5h vWm q msh p p h ej hm pPq v
(148) nx wyh vWjlk`x}mw}nt \iURpq klmv"w}nbv*xi¤ q kl+x ixµ q mwyx{vh q klx4zrmn¥-n n{x q klx4w²x prq x}-v!h q klxvWj`klx}xÄv j5nvv*m p ¥ q klhbl¥k ev*m q x{v \ y¶ ÀÀ· ¹%$iÃ" klxOw²h jltux}|Pm q Eh q k`x ¦ hh p hbm
(149) zPmon¥-n h n v*x q h j5hm pPq vAm p mv=' ) & 31 : \ &. URpgq klx a zrm x p vWmuh p n{t w}nbv*xi¤ q klmvAwyh jltsx}|Pm q movA£i5nbzrn q mow \ klx ° ! i´P±li¹ ·R²©oi±bi´! b· ©oi± mov q klxzr5n{t¥b-n{jlk0h q klx ¦ hh p hbm<zrmon{¥bn q <h v*m q xÄvCh B n{x@tum p ix{z3¢n p x{zP¥bx4h !q k`x q mon p ¥bltn q muh p m n p zh p tm q klx}muxÄvWj5x{w q m ix wyxµtstov4nxnz#nbw²x prqµ\ klx x}tn p n q mn p ¥lton q muh p mov@nj5n{ q m q muh p h m p vWm jltumowyx{v Aklh vW4 x ix} q mow²x{vYn{x q klxgv*m q xÄv \URq vn q mov x{v q klx htstuh Am p ¥ j`hbj5x} q i¤ Aklmow-k zPx 5p x{v@m q p mo£ilx}t k`xv*jlklx}x{v@wymu-wy vwyms¢lm p ¥ q klxv*m j`tsmow²x{vCh Aq k`x x}ton{ p n q mn p ¥lton q msh p zPh p h q w²h pPq nm p n p gvWm q x
(150) m pgq k`x}ms<m pPq x}mshb \ klmvYjlhj5x} q En{tstuh 4v45v q hzrx{vWmu¥ p n ixµ vWm jltsx
(151) m p wyx x pPq nt n{ts¥bhm q k E\ klmv n{ts¥bhm q k mov@zr`x q h 4x}x p n p z fimu¢5vWh p f`@ $ ! hb q klx q hgzrm x p v*msh p nt:w}nbv*xi¤ n p z m q k8nbv3¢5x}x p ¥bx p x}-n{tsm µx{z q hEn p Ozrm x p v*msh p v [ h $ " ! \!Z v n p m p wyx x pPq n{t"n{ts¥bh m q k vy¤im q mov p h q x )wymsx pPq m p q klx <hb-v q w}nbv*x rm q vAwyh jltsx}|Pm q
(152) mov ' ~ & m pq klx@j`ton p n w}nvWx n p ? z ' ) & 31 89 : m p zrm x p vWmuh p l\ k`xOn q klhbv vWk`h q k5n qgq klxOwyh jltsx}|Pm q w}n p ¢5x
(153) m jl@h ix{z q hn p x}|Pj5x{w q x{zw²hiv q h '?> & 9 8 B1 D hklh hb¥x p x}h5vzrmv q ms¢` q muh p v \ h <x ix}}¤ q klx
(154) jlhih mov p h q x{n{tst h n{tR¤ q k`x k Pj h q klxÄvWx{v4nx p h q ix} jlx{wymov*x n p z q klxj5x} hb n p w²x{v q x p z q h¢5xj5hihbxµ hb°zrx}¥x p x}n q xzrmv q ms¢l q msh p v
(155) vW5w-k nbvj5hm pPq v h p vW` nbw²x{v \ klxgn{ts¥hbm q k wyh p vWmv q v
(156) m p m p vWxµ q m p ¥ q klxj hm pPq v
(157) m p q l p ¤!n p z m p lj zln q m p ¥ q klx q movm p vWx} q x{z ¤ q klx vWm jltumowyx{v v q 8w q lx n q x}x{nbw-k m p vWxµ q muh p\ klx p n p x
(158) j hm pP r p q p q Aklh vWxwymu-wy vwyms¢5x{zv*jlklx}xwyh nm v 8v ¢5xx h ixÄz(¤ q klx zrh p h q ¢5x}tuh p ¥ q h q klx q mn p ¥lton q msh p n p hbx \ klx p msh p h Aq klx{v*xv*m jltumowyxÄvmov@ngvWm jlt gwyh p`p x{w q x{z .
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(161) v*m jltumowyxÄv@nx h¢ q n{m p xÄz ¢Otsm p rm p ¥ q h q klxx}tux x pPq vYh @ ~ ~ ms¥lx "\ " \ klmv n{ts¥bhm q k mv ix} vWm jltuxi¤Pn p zntstuh 4v5v q hjlh¥bx{vv*m ix}tnw}£ `msx p x zln q nP¤ AklmwÀk mv3h ¥x{n q jlnbw q mow}n{tm prq x}x{v q}\ hOm p w²x{nvWxm q vx)gw²msx p w'i¤nOzln q n v q 8w q lxg¥bm Pm p ¥ £ilmow Pt q klxvWx q ~ Ak8nbv q h¢5x h p z \ klmvYjlh¢ltsx k8nbv@¢5x}x pEq k`xv q n q m p ¥ j5hm pPq h hblAx{vWxÄn-w-klx{v@~ k5nj q x} a \. . . . . . ms¥lx "\ " URp vWxµ q m p ¥nvWm q x@m pgq klx x}ton{ p n q mon p ¥b`ton q msh p V }x h5vhbj q m nt5n{ts¥bhm q k v:nx p h p bh q k`xYjltn p n{<w}nbv*x \ klxYx{wyx pPq n{ts¥bh m q k ¢ [@\ k5n}x}tutsxi¤ h q klxwyh jl q n q msh p h ²w h p ix}|kPltstvy¤ p h &¥m ix{v¢zr5ntum q .
(162) "c.
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(165) n p w q muh p h q klx vWm }x h q k`x3zPmon¥-n E\ klmvk5nbvA¢5x}x p vWht ix{zm p q klx
(166) j5n q mwylton{4w}nbv*x Aklxµx q klx
(167) j5hbm prq vtumsx@m pgq <hjlton p x{v [ hbm $ $r¤ [ A_ " ! \ '+";5
(168) " 9 5A@Ag 3'5,. . = ; . . zrx p h q xÄv@ngvWx q h & vWm q x{v4m p ¥bx p x}-n{t"j5hiv*m q muh p m pEq klxjlton p x \ 4mix p n v*l¢5v*x q h j5hbm prq vh B ¤ q klx
(169) ¥x p x}ntsm }x{z ¦ hh p hbm!j ht P¥bh p h mov4zrx 5p xÄz nv@ ~ 4 B ~ 4
(170) ~ 4
(171) ~ <mov q klx3tuhPwy5vAh n j5hm pPq 4 q k5n q mv@wytsh vWx} q hx{nwÀk vWm q x
(172) h q k8n pEq hn p h q klxµ j5hbm prq m p B g\ klx
(173) h-zrx} 0 ¦ hbh p hbm!zPmon¥-n h B mov@~ zrx p h q x{vAwµn-zPm p n{tsm q 5 ' ~ B ~ B 0 7. x q 4 9 4 4¢5x q klx}xgvWm q x{v3h B ¤ q klx}muwymu-wy wyx pPq x²} ¤ ~ 4 9 4 4y q klx}ms hbj5x p wymu-wy zrmov \ fim p wyx q k`x j5hbm prq vnx m p ¥x p x}nt4j h vWm q msh p ¤ q klx}msw²ms-w² wymu-w-tsxzrh p h q j5nvv q k`hb`¥bkOn p gh q klx}
(174) v*m q x \ x q ¢5x q klxv*x q h vWm q x{vA¢ xµtsh p ¥bm p ¥ q h ~ 4 9 4 4y \ U 0 ¤ q klx p movAn ix} q x}|h ' 78 9 ~ B <n p z ' 78 ~ B 4 B. '. ). 1. +. 1. /. /. #2. 4. 3. '. #2. '. ). +. '. ). 3. . . '. ). . '. .
(175) mv q k`x4wyh h p j5hbm pPq"q hx}¥bmuh p v ~ 4 b-¤ ~ 4 bÆn p z ~ 4 b m p ' 789 ~ B \
(176) mv"w}ntutsx{z n ¿ ! ª{ R·R¹-¶5 {²À·* 9 m pq klmov"zPmon¥-n ~Rv*x}x4mu¥blx "b\ e \ 0mv q k`xEwyh h p j5hbm prqq h x}¥bmuh p v ~ 4 9 4 b¤ ~ 4 4 b°n p z ~ 4 4 9 bm p ' 78 ~ B \ mvn µi ·R¹-¶ ÀÀ·* m p q k`mov3zPmon¥-n ~Rv*x}x !ms¥b`x "b\ e \ #. '. +. '. 3. +. #. '. 3. +. 3. . 0'. '. '. +. '. 3. . +. 3. '. +. . 3. . . h v* n{m }xi¤"n p q mon p ¥btsx Aklhiv*x ixµ q mwyx{vn{xOvWm q x{vh . n p z Aklh vWxOhbj5x p wymu-wy zrmov
(177) wyh prq n m p v vWm q x{v"w²hbx{vWj5h p zlv q h~ ©«ª¸i´P!l· !n2ix} q x}|@h ¢5h q k ' 789 ~ B n p z ' 78 ~ B \ h p ix}vWx}t i¤bn p !ix} q x}|
(178) h ' 7 ~ B mv"zr5n{t q h n q mon p ¥btsx Ak`hivWxhbj5x p wymswy zrmv wyh prq nm p v 0 ; " h 0 ; evWm q x{vm p m q vm prq x}muhb \ 0. B. '. '. . '.
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(187) jlx{wyx{zPm p ¥x{vWlt q vAw}n p ¢ x x}| q x p zPx{z q hklmu¥bklx}4zPm x p Wv msh p v \ klx
(188) hbzrx} 0 ¦ hbh p hm!zrmon{¥b-n wyh p v*mov q vm p wyx}tstvCh zrm x p v*msh p vc 111 l\lq k`x
(189) ixµ . q mowyx{vh q klx zrmon{¥bn nx zr5n{t q h;vWm jltumowyx{v Ak`hivWx ix} q mwyx{vnx vWm q x{vh B \ x q 4 4 111 4 ¢5x " v*m q xÄv h B ¤ ~ 4 111 4 b q klx}muhbj5x p wymswy ¢5ntutR¤ m q 9 vwyx prq x}n p 8z 9 C q klxOvWl¢8vWx q h j5hbm prq vh 9 B wyh pPq n{8 m 9 p x{z m p ~ 4 9 111 4 89 b \U C EDR¤ q klx p mov<n ix} q x}|h ntut ¦ hbh p hmzrmn¥-n v ' ~ B hFDi " 0 GDi l\ 7 " 111 " m p # mov q klx wyh h p j hm pPqAq h q klx
(190) x}¥bmuh p v ~ C 4 b hb * '+H ~ B 4 5nbvAm pgq klx
(191) jlton p n4w}nvWxi¤ movAw}n{tstux{znwytsh vWx q rj5x2ix} q x}| \ 8 9 # URp ' H 8JI ~ B -¤ mv q k`x@wyh h p j5hbm prqq h q klxAx}¥msh p v ~ C LK Ak`x}x K n ¢5xn p Ev*l¢5vWx q h v*m }Nx MEh 4 9 111 4 89 CO gmov@m p wymozrx prq4q hO~ 1 B 4x}¥msh p v \U I " PM <x w}ntut n ¸i©o´P R·R¹-¶5 ²-·* {\ 4 b hb * # gmv q k`xwyh h p j5hbm prqq h q klx3x}¥bmuh p v ~ C 4 9 111 4 89 " 111 " 3m p '+H 8 ~ B 4 5nvm p zPm x p vWmsh p eP¤ mvAn n{ q Pj5x ix} q x}| \ hvW nm }xi¤{nwytuhiv*x q Pj5x ix} q x}| h n3klmu¥bklxµhbzrx} ¦ hh p hbm zrmon{¥b-n x n{m p v pm vW5w}w²x{vv*m ixzrmon{¥b-n v \ hbx ¥x p x}ntut i¤:Q n M o nbwyxgx nm p v@m p ; M0vW8w}wyx{vvWm ix zrmn¥-n v \ +. 3. . +. 3. '. ). '. +. 3. /#+. 3. '. '. '. +. 4. 3. 4. '. +. 6. 3. '. +. 3. 2. +. 3. /.
(192) "e.
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(195) zrx{n{t Am q k 0 wytsh vWx{v q j5hbm prq vj`hb¢`tsx v \ x}x x}x@$e ! ¥m ix{v q klx hbtstuh Am p ¥x{vWlt q y¶ ÀÀ· ¹%$iÃuÅ URpgq klx
(196) jltn p x ¤ q klx vWm }x
(197) h :q klx hbzrx} 0 ¦ hh p hbm!zrmn¥bn mov ' ~ 0 ~ & ; 0 \ k`x
(198) vWm }xYh h-zrx}v
(199) 0 ¦ hbh p hmzrmn¥-n v mv q kP5v ' ~ & 0 \ . klx-n p zrh vn j`tsm p ¥ q x{w-k p mo£ilxg~*fix{w q msh p e \^aP\ "
(200) vWk`h 4v q klx hbtstuh Am p ¥ hbv q w}nvWx. x{vWlt q m p zrm x p v*msh p. . f$ _ ! . y¶ ÀÀ· ¹%$ià RU p zPm x p vWmsh p er¤ q klx°vWm µx3h n{tst ¦ hh p hbm:zrmon{¥bn vYh h-zrxµ-v "@q h 0 m v=' ) 0 1 3 B & 0 1 3 B 4 : \ 6. 6. x}x4k5nvntvWh ¥bm ix pq klx -v q n{ts¥bhm q k Hq hwyh jl q Ax klms¥klx}hbzrx}-v ¦ hbh p hbm zrmn¥-n v h & vWm q x{vCm pq k`xj`ton p x \ klxhb-zPx} 0 zrmon{¥b-n mov<wyh p v q 5w q x{z h q k`x@hbzrx} 0 ; " zrmn¥-n m p ' ~ 0 ~ & ; 0 ituhb¥ & q m x \ klx4hbzrx}-v 0 zrmn¥-n vCn{x q kP5vwyh p v q 5w q x{z m p ' ~ 0 & tsh¥ & q m x \ Z f`f$ _ ! ¥bm i x=n q ms¥bk q xµ¢5hb p z h '3~ & tsh¥ & 0 & \ [@\ k5n}x}tstuxn p z 3\ zrxµtovW¢` plp x} < b$ ! k5ni xEzPxi x}tshj5x{z q <h i x}-v*msh p v h n ¢5x qq x}<ntu¥bhm q k hb<ton{¥bx 0 \ klx -v q h p xYk8nbvn ' ~ & tuhb¥ & 0 ~ & ; 0 ituhb¥ & q m x wyh jltux}|rm q i ¤ Am q kn ' ~ 0 ~ & ; 0 v q h-n¥xi¤ Aklmstux q klxvWx{w²h p z h p x p v m p '3~ & 0 ~ & ; 0 itsh¥ & q m x Am q k ' ~ & v q hb-n{¥bx \ 3\ zrx}tvW¢l plp x}µ¤ \ & X hl ix°n p z X
(201) \ fixµmozrx}t & f$ d ! 5vWx
(202) zP5ntum q g ~WfixÄw q muh p?b" \ P q hwyh p v q 5w q n{tst5hbzrx}v & ; " zrmn¥-n v m p ' ~ & 89 q m x@n p z v*j5nbwyx°wyh jltsx}|Pm q \ . . . . . . . . 9 5Ag 3'5 ³%--& l"',C<)5 B p h zrx p h q x{v4nv*x q h i¯ {¿²· ª 5j hm pPq vAhb4tsm p x vWx}¥ x pPq vy¤lm p 8wytsmzrx{n p vWj5nwyx \ klx ¦ hh p hbmzrmn¥-n h B mov4zrx 5p x{z m pq klxvn x Anlvnbv q klxjlxÄwyx{zrm p ¥wµnbvWx ¤ m q mv q klx q xÄvvWxµton q msh p h q k`xj`ton p xm prq hwyx}tutov
(203) ~ i<nbvvWhPwymn q xÄz Am q kvWx}¥ x pPq v B B ~ ~
(204) ~ i mu¥blx "b\^a v*klh 4vn p x}|ln jltux \ x q 5v p h ,zrx q n{mst q klxv q 5w q lx h @q klxzrmon{¥bn ¤ AklmwÀk Amutst(¢5x
(205) 5v*x lt hb
(206) fix{w q msh p \ ar\ ar\ "\ klx n|Pm n{t5x j q wymswytsx
(207) w²x prq x}xÄz n q n ix} q x}|h q k`xzrmn¥bn q hb8wÀklxÄv q klx}x h¢ #*x{w q v²¤5n p z q klx n{|rm n{t5x j q wymu-wytux@wyx prq x}x{zh p n p x{zr¥bx q hb5w-klx{v q hhb¢ #*xÄw q v \ ZYp x{zr¥x h q klmv@zrmn¥bn mvYj5n q h Aq klx¢lmvWx{w q m p ¥tsm p xh <q hghb¢ #*x{w q v 4 n p z 5 ¤n p z0m q v q <hEx}| q x m q msx{v@n{xx{£ `mozrmv q n prq
(208) h 4 ¤ 5 n p z 6 n p z h 4 ¤ 5 n p z . . . '. '. ). +.-0/. . 1. /. #2. +. /. 3. 6-. 4. 6-. 73.
(209) .
(210) . "}a. " . . . mu¥blx "b\^a ¦ hh p hbm:zrmon{¥b-n h tsm p x
(211) vWx}¥ x pPq v. . . . . !ms¥b`x "b\ g zP¥bx~ 4. 52(62. i.
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(213) .
(214) . . . . {x{v*j5x{w q mix}t \ movAzPx 5p x{z¢ hb`@v*x}¥ x prq vn p z zrx p h q xÄz nv~ 4 52(62 i \PURq wyh p v*mov q v h j5hb q muh p vAh tsm p x{vn p zgj5nn¢5hbtnbv \ hzrx{vwymu¢ x q klx w}nvWx@h m p 5p m q x@x{zP¥bx{v²¤ x=nbzlz q klxv ¢5hbt \ klxxµ¥bmsh p ~ 4 52(62 ;wyhbx{v*j h p zlv q h n p p ¢5hb p zPx{z j5n{ q h Aq klx ¢lmvWx{w q m p ¥tsm p x3h 4 n p z 5 ~Rmu¥blx "b\ \ hbxµhixµ}¤ q hx p vWlxwyh plp x{w q mrm q i¤ x°nbzlz x{zP¥bx{vAn q m p 5p m q i¤ q k5n q Amutst ¢ h p zg p ¢5h p zrx{zgwyxµtstov4 q klx
(215) x{zr¥bx~ 4 (62 i!m p mu¥blx "\ mov q klxvWx q h wyx pPq xµ-v~Rn q m p 5p m q 4h 4q klxgw²ms-w²tsx{v~ Am q k m p 5p m q x-nzrms5v²¤ q k5n q mv tum p x{v- q k5n qq hb5w-k 4(¤n p z m q mvtsm m q x{zY¢ q k`x4wymswytsx{v q k5n q x{vWj5x{w q m ix}t q hb5w-k 6 n p z \ URp !ms¥b`x{v "\ gn p z "\ r¤ q k`xvWk8nbzrh xÄz j5n{ q v4nx q klx3m prq x}muhb-vh q k`x3x j q w²ms-w²tsx{v. . . . . . . $$$ . $ ). . . 6 6
(216) . , $1# : ' /, . . , ' ). $$$ . $ ).
(217) =6 6 . . . ms¥lx "\ g URp 5p m q x@x{zP¥bx{v. wyx prq x}x{zh p xÄzr¥bx \ URp v*h xn ¢lmu¥blh5v"w}nvWx{v²¤rton{¢5x}t~ 4 52(67 n%°zrx p h q x q h zrm x}x pPq x{zr¥x{vy¤ q k8n q AmutstP¢ x4zPmov q m p ¥lmov*klx{z3m p3q k`x hbtstuh Am p ¥ n `~ 4 57(62 i 8 n p z ~ 4 52(62 i~Rmu¥blx "b\ d \. klx¥x}h x q mw
(218) zr5nth q klx ¦ hbh p hmzrmon{¥bn h tum p x°vWx}¥ x pPq vmov q klxx{zP¥bx x p t n n q mn p ¥lton q msh p\ 4\ \ 'n{j '<nj $i ! ¥bm ixÄv3n p hbj q m n{t<nts¥hbm q k p`p m p ¥Em p ' ~ & tshb¥ & q hwyh jl q x q k`x ¦ hh p hbm:zrmon{¥b-n h tsm p x{vn p z j5hb q muh p vYh w²ms-w²tsx{v \.
(219) ". C .
(220) =6 6 . . . . . 6 6
(221) @. . . 6 6 . . . . . . . . 6 6 . . . . 6 6
(222) . .
(223) =6 6 . . . !ms¥b`x "b\ d ZY ¢`ms¥b`hb5vton¢5x}t~ 4 . 52(62. i. %T . . YZ p nn p ¥x x pPq mv q k`x@j5n q m q msh p h j5hb q muh p vYh kPj xµ-vW` nbw²x{v \. . . m p zr8wyx{z¢,n 5p m q xvWx q h kPj xµ-vW` nbw²x{v"hb. #55'C,C<)5 ; E+1"513%@: B mvn v*x q h k rj5x}jlton p vm p \
(224) klxE¥x p x}nt4j h vWm q msh p w²h p zrm q muh p vWx q v q k5n q n p " k,Pj5x}jltn p xÄvk5n ixx j q gm pPq x}vWx{w q msh p ¤v*hEnixµ q xµ| h 4q klxgn{-n p ¥bx x pPq ¢5x tuh p ¥ v q h x}|`nbw q t k rj5x}jlton p x{v \ klx
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