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A & & & & q66;;q!   # # # # q66;;q!$  3 & & & & & &rc d tttzdttttzdz ttttzz ksJtttz dtttt zdz tttt zz ksJtttzt zdttttztt zttz ttz tt z dttttzztttt zztttt zzz ksJtdtzdttdzdz ttzdttdzzdz z ksJtdtzdttdz ddttzz z ksJtdtzdttdzdz ttzdttdzzdz z ksJtdtzt dz z dttdz dttdzzzdttdzzzdttzz dz ttdzdttdzzzdttdzzz dttzz dzz ksJttddtddzzdtdzz ttdd tdztddzzddtddzzzz dS) NTrrhriryrkrmrnro) r+rrrtogetherrerr5r0rrrrtest_cot_expansionr#/s* q1u::  $  ' ' 0 0 2 2 QA SVVc!ff_- / / / / q1u::  $  ' ' 0 0 2 2 AsA2wwSVVc1"gg-7/ / / / / q1uqy>> d + + 4 4 6 6 QAs1vv A &Q /#a&& 8 c!ffSVVm c!ffSVVm +c!ffSVVm ; = > > > > qs88??? % % . . 0 0 QQA#a&&!) a0 2 2 2 2 qs88??? % %QAqQxL)@ @ @ @ @ qs88??? % % . . 0 0 A A s1vv5 Q{Q50 0 0 0 0 qsRTz?? ! !t ! , , 3 3 5 5 Q Qs1vvqy[ 1SVVQY;.3q669A= q6619qQ{ "Qs1vvqy[ 01SVV8 ;a ?:A A A A Aa"s1vvqy.1SVV84555a"SVV)c!ffai/"qQ{2BCDDDDDrc@ttt ttt tksJtttj dz tjdz tt tksJtttjdz tjdz tttjdz ttjdz ksJdS)Nryrn)r+rrrrrrrtest_cot_AccumBoundsr%Cs {B3## $ $ RC(<(< < < < < {AD57ADF++ , , RC0D0D D D D D {146146** + +{3qtAv;;ADQRF /T/T T T T T T Trcttttdz dz ksJttddS)NrkrhcPttdSr)r+rrrrrrz test_cot_fdiff..Krr)r+rrrGr?rrrtest_cot_fdiffr(IsL q66<<>>c!ffaiZ!^ + + + + 6677777rc ttttsJtdd}t|tjusJttjtjusJttjtjusJttj tj usJttj tj usJtddd}t|tztjusJt| tztjusJttdz dtz ksJtt dz dtz ksJtttddzddtzz ksJtttddzd dtzz ksJtt ttksJtt ttttz tttdzz z ksJtt ttttz tksJtt tttt dttztz z dttztdzz ztz ksJtt tttttz ttksJt!tt ttd d ksJt!tt tttd t d  d z ksJttd tdzd z z tdzdz zt%td zzksJttt(t)d tksJtttt+tttz t-td fdksJttdjdusJtd djdusJt|tzdjdusJttjJtddd}ttjJt|jdusJtt2|zjdusJtt2dzjdusJttjJt|jdusJdS)NsTzerorP)rLrWrkrlrrrjrrhryrnrmrrFrxr)rJrWd)rr/rrrrInfinityrNegativeInfinityNaNComplexInfinityrr rr*r.r7r9r8rr2rCrArrr r)r*rPr-s r test_sincr3Ns( d1ggt $ $$$ $sA 77ae       qv % % % % " # #qv - - - - ;;!%     ! 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" " " 88 t # # # # "::  % % % % #;; $ & & & & 77  $ $ $ 88  % % % % % %rcp tttusJtjtdksJttt tzksJtt t tzksJtt t usJtddksJtdtdz ksJtdt dz ksJttddz tdz ksJttd dz t dz ksJttddz tdz ksJttd dz t dz ksJttdtdz dz tdz ksJttdtdz dz  t dz ksJttj td z ksJttddt d z ksJttdtdz dz tdz ksJttdtdz  dz t dz ksJttddz dz td z ksJttddz dz t d z ksJttddz tdz td z ksJttddz tdz t d z ksJd D]k}t|dz |dzdzD]N}t||dkr8tt|tz|z |tz|z ksJOltttdtdtdzz z ksJtd djdusJtdjdusJtt$jJtdt zt t'dzksJttdddjdusJttdddjdusJtt*jJtttddtddtzksJtttddtddtz ksJt-tt/tsJdS)Nrhrrkriryrmrlr|rnrpr~rlrnr|rpr~皙?FrTrjrrr)r'r rr;rr rrr"rrr rr6r.rrrrHr is_positiverMr>r*)rrPs r test_asinr8sj 99     :1 % % % % 88r"u     99"     99     77a<<<< 77bd???? 88s1u     Q ??bd " " " " a  s1u $ $ $ $ Q ??bd " " " " a  s1u $ $ $ $ a$q''k1_%% & &"Q$ . . . . q477{Ao&&& ' 'B3q5 0 0 0 0 <<2a4     Q RCE ) ) ) ) a$q''k""A% & &"Q$ . . . . $q477{##$Q& ' 'B3q5 0 0 0 0 a1a BrE ) ) ) ) $q''A+q ! !bSV + + + + a1d4jj( ) )RU 2 2 2 2 $q''A+tDzz) * *rc"f 4 4 4 433Aw1q)) 3 3A1ayyA~~C"QKK((AbDF2222 3 77<<??aQAX. . . . . e $ $ $ , 4 4 4 4 88 u $ $ $ $ 77? " " " 1::!E!HH $ $ $ $ A / / / ;t C C C C Q% 0 0 0 < E E E E 77  & & & HQNN## $ $Q"(< < < < < HROO$$ % %!Q")< < < < < T3q66 " """ """rctttddttdzdz zdtdzzdz zdtdzzdz zttdzzksJttdt}|dtdzzdz ksJttdt|ddtdzzdz ksJdS) Nrrryrnrlrrrp)r'rr9r8rt5s rtest_asin_seriesr=s 77>>!Q " " AqDF Qq!tVBY1a4+a1gg5 6 6 6 6 a  Q " "B 1a4???? 77  q!R + +qAvcz 9 9 9 9 9 9rc ttttksJttdzttdz ksJttdz tt dz ksJtdtz tdtt tztdz ztt dzz ksJtdtz tdt t tzdtzdz z tt dzzksJtttzdztdttdz ksJtt tzdztdtdksJtttzdz tdtd ksJtt tzdz tdt tdzksJtt tdzztzdz tdt dz tt dt dz zzksJtt tdzztzdz tdt dz tt dt dz zzksJdS)Nrhrkcdirriry)r'rrrr rr"rrrtest_asin_leading_termrAs 77 " "1 % % * * * * A;; & &q ) )RT 1 1 1 1 A;; & &q ) )bSU 2 2 2 2 !99 $ $QQ $ / /1SVV8bd?Qs1vvX3M M M M M !99 $ $QR $ 0 0QBs1vvI"Q4F3q664Q Q Q Q Q !a== ( ( ( 3 3rDGG| C C C C 1q>> ) )!! ) 4 4Q ? ? ? ? !a== ( ( ( 3 3Qx ? ? ? ? 1q>> ) )!! ) 4 4d1gg E E E E 1a4! a 0 0 0 ; ;s1uqQQUVWQXQX[IYIYGY?Y Y Y Y Y 1a4! a 0 0 0 < <A#aRVWXRYRYkJZJZHZ@Z Z Z Z Z Z Zrc Xtttt tttzt dtdzz zzksJttt dt tdt dtdzz zz zksJttttj dz ttz ksJtttdtt tdz dzdztz zksJttttdtz  tdz zksJttttdtz ksJdS)Nrhrk)r'rrrr r"r(r#rrr$r&rr%rrrtest_asin_rewriterCs| 77??3  A2c!A#QAX*>&?&?#? ? ? ? ? 77??4 Ad1a$q1a4x...@+A&B&B$B B B B B 77??4 ADFT!WW$4 4 4 4 4 77??4 AdD!Q$OOa,?+B&C&C$C C C C C 77??4 T!A#YYJA$5 5 5 5 5 77??4 D1II - - - - - -rcttdtdtdzz z ksJt t ddS)NrhrkcPttdSr)r'rrrrrrz!test_asin_fdiff..tAww}}Q'7'7r)r'rrr"rGr?rrrtest_asin_fdiffrGsO 77==??aQAX. . . . . 7788888rc  tttusJtttusJtjt dksJtt t t zksJtt t t zksJtdtdz ksJttj tdz ksJttddttddzksJtddksJtdtksJttddz tdz ksJttd dz ttddzksJtddD]a}t|D]M}t||dkr5tt|tz|z |tz|z ksJtt|tz|z  t|tz|z z ksJtt|tz|z tdz t!t|tz|z z ksJtt|tz|z  tdz t!t|tz|z  z ksJOctdt ztdz t!dt zz ksJtt"t"dtdt"dzz z ksJtd jd usJtd jd usJtt(jJttdd d jd usJttdd d jd usJttddd jd usJtt,jJtdt,ztdt,zksJtdt0ztdt0zksJttddttddksJttddttddksJtt,t0t zztt,t0t zz ksJtt2tt/t2ksJdS)Nrhrrkryrirmrlrr6TrjFrrrrpro)r#r rrr;rr rrrr r"rr6r*r.r'rrrrHr7rMrrPre)rnums r test_acosrJs, 99     99     :1 % % % % 88qt     992     77bd???? <<2a4     Q Bx1~~$5 5 5 5 5 77a<<<< 88r>>>> Q ??bd " " " " a  r(1a..0 0 0 0 01b\\KK88 K KC3{{aCBqMM**c"fQh6666SR]]N++rCF1H}<<<<CBqMM**bdT#c"fQh--5H5H.HHHHHSR]]N++r!tdCBqMM>6J6J/JJJJJ  K !991tAaCyy( ( ( ( ( 77<<??ba!Q$h/ / / / / 99  $ $ $ $ 88 u $ $ $ $ 77? " " " A / / / ;t C C C C Q% 0 0 0 < D D D D A / / / ;u D D D D 77  & & & A;; " "d26ll 2 2 2 2 Q<< ! ! # #tBF|| 3 3 3 3 A   ) ) + +tHQNN/C/C C C C C Q * * , ,Xb!__0E0E E E E E AaC== " " $ $Q1W 5 5 5 5 77    $y||"4"4 4 4 4 4 4 4rcttttdz ksJttdztt dt t zksJttdz ttksJtdtz tdt t tzt t dzzksJtdtz tdt t tzdtzzt t dzz ksJtt tzdztdtd ksJtt tzdztdtdksJtt tzdz tdtdksJtt tzdz tddtztdz ksJtt tdzztzdz tdtt t t ddzzzksJtt tdzztzdz tdtt t t ddzzzksJdS)Nrkrhr?rirjry)r#rrrr"r rrrrtest_acos_leading_termrL s 77 " "1 % %A - - - - A;; & &q ) )T!WWT1"XX-= = = = = A;; & &q ) )R / / / / !99 $ $QQ $ / /A2c!ff9qQx3G G G G G !99 $ $QR $ 0 0Ac!ffHqtOaAh4N N N N N !a== ( ( ( 3 3Qx ? ? ? ? 1q>> ) )!! ) 4 4Q ? ? ? ? !a== ( ( ( 3 3tBxx ? ? ? ? 1q>> ) )!! ) 4 4"tBxx G G G G 1a4! a 0 0 0 ; ;rAc$q''TU+FVFVDV?V V V V V 1a4! a 0 0 0 < <Qs4PQ77UV;GWGWEW@W W W W W W Wrctttddtdz tz tdzdz z dtdzzdz z dtdzzd z z t tdzzksJtttddtdz t ttddz ksJttdt}|d tdzzdz ksJttdt|dd tdzzd z ksJttdttdz ksJttdttjusJdS) Nrr|rkryrnrlrrrr:ror{) r#rr9rr8r'rrrr;s rtest_acos_seriesrNs 77>>!Q " " 1q1a46AadF2I%!Q$s 2Qq!tWW< = = = = 77>>!Q " "bdT!WW^^Aq!-D-D&D D D D D a  Q " "B AqD     77  q!R + +r!Q$ws{ : : : : 77  q! $ $1 , , , , 77  q! $ $ . . . . . .rc ttttdz t tt tzt dtdzz zzzksJttttt t tdzzdzzdz tt dtdzz tz zksJtdttj dz ksJtdttdtksJttttj dz ttz ksJtttdtt tdz dzdztz ztdz zksJttttdtz ksJttttdtz  tdz zksJdS)Nrkrhrjr?)r#rrrrr r"r(rrr'r$r&r%rrrtest_acos_rewriterQ%s  77??3  2a4!C!d1q!t8nn0D,E,E*E#E E E E E 77??4 B4B==(81(<$=a$?$tAPQSTPTH~~VWGWBXBX$X X X X X 77??4 ADF * * * * 99  T " "d3ii&7&7&<&< < < < < 77??4 ADFT!WW$4 4 4 4 4 77??4 BtT1a4%!)__q-@!,C'D'D$Dr!t$K K K K K 77??4 D1II - - - - 77??4 T!A#YYJA$5 5 5 5 5 5 5rcttdtdtdzz z ksJt t ddS)NrirhrkcPttdSr)r#rrrrrrz!test_acos_fdiff..2rFr)r#rrr"rGr?rrrtest_acos_fdiffrT0sO 77==??ba!Q$h/ / / / / 7788888rc  tttusJtjtdksJttt dz ksJtt t dz ksJtt tt dz t dz ksJtddksJtdt dz ksJttdt dz ksJtdtdz t tddzksJttddtdzz t dz ksJttddtdzdz z  t d z ksJttddtdzdz zt tdd zksJtd tdzt d z ksJtdtdzt tdd zksJtd tdz t td d zksJd D]k}t|dz |dzdzD]N}t||dkr8tt|t z|z |t z|z ksJOlttt dz ksJtttddtdzzz ksJttjdusJtd t"zt" t%dzksJt'tt)tsJtt)tddtddt dz zksJt+tddjdusJtt.t0t2t4t6t8t:t<t>t@f D]}|js|j!|j"t|j"usJ|j#t|j#usJ|j$t|j$usJ|j%t|j%usJ|j&t|j&usJn|j't|j"usJ|j(t|j#usJ|j)t|j$usJ|j*t|j%usJ|j+t|j&usJ|j't|j'usJ|j(t|j(usJ|j)t|j)usJ|j*t|j*usJ|j+t|j+usJdS)Nrhrkrrmryror|rlrprjr~r{r5TriF),r(r rr;rrrrr"r rr6r0rrrHrr rr>r+r$rrMrPnpnnrVrXrZenpennr^r is_nonzeror7 is_negativeis_nonpositiveis_nonnegativeis_extended_nonzerois_extended_positiveis_extended_negativeis_extended_nonpositiveis_extended_nonnegative)rrIr*s r test_atanrc5s 99     :1 % % % % 88r!t     99A     99 RCE2a400 0 0 0 0 77a<<<< 77bd???? 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AZZRUU #SAZZ]41;;>%A%(AZZ]41;;>%A&BC"Q%%jj[bee $c"Q%%jj!mDAKKN&Bbee**a-RUU Q6'78 9 9 9 9 9 q66==d= # #qQx / / / / qs88??? % %Ac!ffHSVVO)< < < < < q66 "d * * * * q66>T ! ! ! ! q66  & & & r77 5 ( ( ( ( q66 ! ! # #s1vv - - - - q5 ! ! ! +u 4 4 4 4 q66 t # # # # r!te $ $ $ .$ 6 6 6 6 #a&&!1 * * * QAXM!OaRTA ob001a"Q$h]Q1I3N3NN O O O O #a&&!Q ' ' ' aC!A#I!Q$s "R1WU] 2Qq!tWW < = = = = q66;;q>>c!ffWSVV^ + + + + q66  a # #q ( ( ( ( q66  a # #qAvcz 1 1 1 1 q66  a # #r!Q$wu} 4 4 4 4 666677777rc tdd}t|tusJtttusJtddksJtdtksJtt tdz ksJtt tdz ksJtttdz ksJtt ttdd zttd d zksJtdtd zttdd zksJtdtd z td z ksJttd dtdzz td z ksJttd dtdzz ttd d zksJttddtd zd z zttd dzksJttddtd zd z z ttddzksJttdtd z ttddzksJdD]a}t|D]M}t||dkr5tt |tz|z |tz|z ksJtt |tz|z  t|tz|z z ksJtt|tz|z tdz tt|tz|z z ksJtt|tz|z  tdz tt|tz|z  z ksJOctttdtdztddtdzz z zz ksJttt t"t!tddtdzz z t"tz zztdz zksJttt$t%dtz  tdz zksJttt&t'dtz ksJttt(tdttdztz z zdz ttdzt)ttdzdz ztz zksJttt*tdttdztz z zdz ttdzt+dttdzdz z ztz zksJttttt tdz zksJt-t.ddS)NreTr+rhrrirkrrmryrlrnr|rprrrr~)ryrmrncPttdSr)r&rrrrrrztest_asec..1rFr)rr&rr rrr-r r"rr6r,r%rrrrr r'r#r(r$rGr?)rerrIs r test_asecr ssA 77c>>>> 99     77a<<<< 88r>>>> 88r!t     991     991     BxA&'' ( (Bx1~~,= = = = = DGG  8Aq>> 1 1 1 1 1 $q'' ??bd " " " " Q477]## $ $1 , , , , a!DGG)m$$$ % %HQNN): : : : : Q4771_%% & &"Xa__*< < < < < a!DGG)A+o&&& ' '2hq"oo+= = = = = Q$q''! " "b"b)9)9&9 9 9 9 9 KK88 K KC3{{aCBqMM**c"fQh6666SR]]N++rCF1H}<<<<CBqMM**bdT#c"fQh--5H5H.HHHHHSR]]N++r!tdCBqMM>6J6J/JJJJJ  K 77<<??aAd1qAv:&6&6!67 7 7 7 7 77??3  1Sa!AqD&j)9)9AaC)?%@%@#@2a4#G G G G G 77??4 T!A#YYJA$5 5 5 5 5 77??4 D1II - - - - 77??4  AQT 1 a$q!t**T$q!tax..-A-A"A!"CC D D D D 77??4  AQT 1 a$q!t**T!DANN2B-C-C"CA"EE F F F F 77??4 T!WWHr!tO 3 3 3 3 7788888rc^ttjjdusJt ddd}t|jdusJtt jJttjJt ddd}t|jdusJdS)NFrPT)rOrLrrJfinite)r&rrrrrrrH)rPrs rtest_asec_is_realr4s << 5 ( ( ( (sT4000A 77 #t + + + + 77? " " " 77? " " "st,,,A 77?e # # # # # #rc tdtz ttdz ksJttdztt dt tzksJttdz ttksJtttdt t tzt t dzzksJtttdt t tzdtzzt t dzz ksJtt tzdztdtdksJtt tzdztdtd ksJtt tzdz tddtztdz ksJtt tzdz tdtdksJtt tdzztztddz z tdtt t dt dz zzksJtt tdzztztddz z tdtt t dt dz zzksJdS)Nrhrkr?rirPry)r&rrrr"r rrrrrtest_asec_leading_termr>s !99 $ $Q ' '2a4 / / / / A;; & &q ) )T!WWT!WW_ < < < < A;; & &q ) )R / / / / 77 " "11 " - -!CFFQs1vvX1E E E E E 77 " "12 " . .!CFF(QrT/Ac!ffH2L L L L L !c ?? * *11 * 5 5c B B B B 1s   + +AA + 6 6499* D D D D !c ?? * *11 * 5 52T 9J J J J J 1s   + +AA + 6 6$t** D D D D 1a4! add1f$ % % 5 5aa 5 @ @B3qSWXYSZSZ{K[K[I[D[ [ [ [ [ 1a4! add1f$ % % 5 5ab 5 A AR!CPQTXYZT[T[P[L\L\J\E\ \ \ \ \ \ \rctttddtt dztt tzz ttdzzdz z dtztdzzdz z dtztdzzd z z d tztd zzd z z t tdzzksJttdt}|d tztdzzdz ksJttdt|ddtztdzzd z ksJdS)Nrrrkrmryrrlrnr#r|rror{)r&rr9r rr8r)t4s rtest_asec_seriesrOs2 77>>!Q " " #a&&1SVV8a1fQh&1QT"4 A#ad(2+ 1QT $ ')*1a4 1 1 1 1 1 a  Q " "B Aad2     77  q!R + +r!tAqDy| ; ; ; ; ; ;rc  tttusJtdtdz ksJtdt dz ksJttdksJtt dksJttdksJtdtusJtt ddtzksJtt ddtzksJtt d d dtzz ksJt tt tsJt tttsJtdtdz tdz ksJtt ttd dzt dz ksJttddtd zd z ztd z ksJttddtd zd z z t d z ksJtd t d z ksJttddtdzz t d z ksJttddtdzz ttdd zksJtdtd ztdz ksJttdtd z ttddzksJtt tdtdztddtdzz z zz ksJtt tt ttddtdzz z ttz zzksJtt ttdtz ksJtt t t!dtz  tdz zksJtt t"t#ttdzdz  tdz zttdzztz ksJtt t$t%dttdzdz z  tdz zttdzztz ksJtt t&t't tdz zksJt)t*ddS)Nrhrkrirryrormrrnrrlrjr|rpr{r~cPttdSr)r%rrrrrrztest_acsc..zrFr)r%r rrrr,r>rr-r"r rrrr r'r#r(r$r&rGr?rrr test_acscrXs 99     77bd???? 88s1u     88q==== 99>>>> 99>>>> 77c>>>> A<<27 " " " " A<<27 " " " " A<<1qt8 # # # # T3q66 " """ " T3q66 " """ " $q'' ??bd " " " " BxA&'' ( (RCE 1 1 1 1 Q4771_%% & &"Q$ . . . . a!DGG)A+o&&& ' 'B3q5 0 0 0 0 88s1u     a!DGG)m$$$ % %"Q . . . . Q477]## $ $8Aq>>(9 9 9 9 9 DGG  2 % % % % Q$q''! " "b"b)9)9&9 9 9 9 9 77<<??b!Q$tA!Q$J'7'7"78 8 8 8 8 77??3  A2c$q1QT6z*:*:QqS*@&A&A#A A A A A 77??4 D1II - - - - 77??4 T!A#YYJA$5 5 5 5 5 77??4 tAqD1H~~   A %tAqDzz1!3 4 4 4 4 77??4 d1T!Q$(^^+;&<&<%>#  #a&& ( ( ( ( q66>>$  3q66 ) ) ) ) q66>>#  !A#s1Q3xx#qbd))';"< < < < < q66>>#  !CFF( * * * * q66>>#  3qs88Q;?Qs1Q3xxZ"@ @ @ @ @ q66>>#  3qs88Q;?Qs1Q3xxZ"@ @ @ @ @ q66>>#  !CBqD5$A$A$A"A A A A A q66>>#  #qb2a4i%"@"@"@ @ @ @ @ q31 ~&&& ' ' / / 4 4 c2#a%!)c!GAqMM/222CA'!Q--/%@@@@AKPRRR R R R R R q66>>' " "d1ggtBqDzz'!&!:L:L/L&M M M M M q66>>' " " ' '1 - -Q 7 7 7 7 7 7rctdtz ttksJttdzttdz ksJttdz tt dz ksJtttdtt tztdz ztt dzz ksJtttdt t tzdtzdz z tt dzzksJtttzdztdtdksJtt tzdztdttdz ksJtttzdz tdt tdz ksJtt tzdz tdtd ksJtt tdzztzt ddz z tdt dz tt tddzzzksJtt tdzztzt ddz z tdt dz tt tddzzzksJdS)Nrhrkr?riryrPr)r%rrrr rrr"rrrtest_acsc_leading_termrs !99 $ $Q ' '1 , , , , A;; & &q ) )RT 1 1 1 1 A;; & &q ) )bSU 2 2 2 2 77 " "11 " - -3q66BqD1SVV81K K K K K 77 " "12 " . .1"SVV)ad1f2DqQx2O O O O O !c ?? * *11 * 5 5c B B B B 1s   + +AA + 6 6"tCyy. H H H H !c ?? * *11 * 5 5"tDzz9I I I I I 1s   + +AA + 6 6499* D D D D 1a4! add1f$ % % 5 5aa 5 @ @RCEAcRVWXRYRY\]R]N^N^L^D^ ^ ^ ^ ^ 1a4! add1f$ % % 5 5ab 5 A AbSUQsSWXYSZSZ]^S^O_O_M_E_ _ _ _ _ _ _rctttddt t dzt dz ztt tzzttdzzdz zdtztdzzdz zdtztdzzd z zd tztd zzd z zt tdzzksJttdt}|dtztdzzd z ksJttd t|dd tztd zzd z ksJdS) Nrrrkrmryrrlrnrrr|r)r%rr9r rrr8r)t6s rtest_acsc_seriesrs@ 77>>!Q " " 3q66 BqD1SVV8#a1fQh. 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