+ Bi<^RIt^RIt^RIt^RIt^RIt^RItR.t]PPt ]PPt ]P!R R7R4t ]P!R]P]P ,4tR RltRt]P!R]P(]P,4P*t]P!R ]P(]P,4P*t!R R]P04tR#) NFraction)maxsizec\VR\4p\\\V44V,4pV^8dTMV)pVR8XdR#T# \d \ pL*i;i))pow_PyHASH_MODULUShashabs ValueError _PyHASH_INF) numerator denominatordinvhash_results&& /usr/lib/python3.14/fractions.py_hash_algorithmrse2;O4(T#i.)D011nU5&F22)6)+ sAA"!A"a \A\s* # optional whitespace at the start, (?P[-+]?) # an optional sign, then (?=\d|\.\d) # lookahead for digit or .digit (?P\d*|\d+(_\d+)*) # numerator (possibly empty) (?: # followed by (?:\s*/\s*(?P\d+(_\d+)*))? # an optional denominator | # or (?:\.(?P\d*|\d+(_\d+)*))? # an optional fractional part (?:E(?P[-+]?\d+(_\d+)*))? # and optional exponent ) \s*\z # and optional whitespace to finish cV^8dV^ V,,pMV^ V),,p\W^, ,V4wrEV^8XdV^,^8Xd VR,pV'dV^8MV^8pV\V43#)rr)divmodr )ndexponent no_neg_zeroqrsigns&&&& r_round_to_exponentrIsx1} R\ R(] !Av, "DAAv!a%1* R1q5QUD Q<cDV^8Xd R^^V, 3#\\V44\V4rC\V4\V4, WC8*,pWR, p\WV4wrx\\V44V^,8XdV^ ,pV^, pWxV3#)rF)strr lenr) rrfiguresstr_nstr_dmrr significands &&& r_round_to_figuresr)fs" AvaW$$s1v;A5 E SZ5>2A{H*1:D 3{ ! + A  h &&r ay (?: (?P.)? (?P[<>=^]) )? (?P[-+ ]?) # Alt flag forces a slash and denominator in the output, even for # integer-valued Fraction objects. (?P\#)? # We don't implement the zeropad flag since there's no single obvious way # to interpret it. (?P0|[1-9][0-9]*)? (?P[,_])? a (?: (?P.)? (?P[<>=^]) )? (?P[-+ ]?) (?Pz)? (?P\#)? # A '0' that's *not* followed by another digit is parsed as a minimum width # rather than a zeropad flag. (?P0(?=[0-9]))? (?P[0-9]+)? (?P[,_])? (?:\. (?=[,_0-9]) # lookahead for digit or separator (?P[0-9]+)? (?P[,_])? )? (?P[eEfFgG%]) caa]tRt^toR/tR0V3Rllt]R4t]R4t]R4t ]V3Rl4t Rt Rt R1Rlt ]R 4t]R 4tR tR tR tRtRtR2RltRt]!]]P24wttRt]!]]P:4wttRt ]!] ]PB4wt"t#Rt$]!]$]PJ4wt&t'Rt(]!](]PRR4wt*t+Rt,]!],]-R4wt.t/Rt0]!]0]PbR4wt2t3R3Rlt4R3Rlt5Rt6Rt7Rt8]Pr3Rlt:Rt;R tR#t?R$t@R%tAR&tBR'tCR(tDR)tER*tFR+tGR,tHR-tIR.tJVtKV;tL#)4rcx<\\V` V4pVEf \V4\JdWn^VnV#\V\P4'd%VPVnVPVnV#\V\4'g)\V\4'g2\VR4'd VP4wVnVnV#\V\4'Ed;\ P#V4pVf\%RV,4h\ VP'R4;'gR4pVP'R4pV'd \ V4pM^pVP'R4pV'dEVP)RR4p^ \+V4,pW,\ V4,pW',pVP'R 4pV'd5\ V4pV^8dV^ V,,pMV^ V),,pVP'R 4R 8XdV)pM\-R 4h\V4\u;Jd\V4JdMMM\V\P4'd[\V\P4'd;VPVP,VPVP,r!M \-R 4hV^8Xd\/RV,4h\0P2!W4p V^8dV )p W,pW),pWnW#nV#)Nas_integer_ratioz Invalid literal for Fraction: %rnum0denomdecimal_expr-zXargument should be a string or a Rational instance or have the as_integer_ratio() methodz+both arguments should be Rational instancesFraction(%s, 0))superr__new__typeint _numerator _denominator isinstancenumbersRationalrrfloathasattrr,r"_RATIONAL_FORMATmatchr groupreplacer# TypeErrorZeroDivisionErrormathgcd) clsrrselfr'r/r0scaler3g __class__s &&& rr7Fraction.__new__s>Xs+C0  I#%"+$%! Iw'7'788"+"5"5$-$9$9! Y..!)T229&8995>5O5O5Q2!2 Is++$**959$%G%.&/00 5 5#6 ("%e*K"#Kggi0G")//#r": "CL 0$-$5G $D #, ''%.C!#h!8%S0I'2t83K776?c)!* I !QRR)_ 8tK'8 8 G$4$455 {G$4$4 5 5##k&=&==%% (=(==# 12 2 ! #$5 $AB B HHY , ?A  #' r c\V4\JdVPV^4#\V\P 4'd'VPVP VP4#\V\4'g)\V\4'g1\VR4'dVP!VP4!#\R4h)rr,zLargument should be a Rational instance or have the as_integer_ratio() method) r8r9_from_coprime_intsr<r=r>rrr?r@r,rE)rInumbers&&r from_numberFraction.from_number9s <3 ))&!4 4  0 0 1 1))&*:*:F.>@A A%%q'9'9';<>r cF<\\V` V4pWnW#nV#N)r6rr7r:r;)rIrrobjrMs""" rrPFraction._from_coprime_intsis&Hc*3/"& r c VP^8H#rr;rJs&r is_integerFraction.is_integerus  A%%r c2VPVP3#rbr:r;rhs&rr,Fraction.as_integer_ratioys !2!233r c V^8d \R4hVPV8:d \V4#Rwr#rEVPVPrvWg,pW8V,,p W8dM&WEW(V,,V 3wr#rEYvW,, rvKEW, V,p ^V,W:V,,,VP8:d\P WE4#\P W*V,,W:V,,4#)rz$max_denominator should be at least 1)rrrr)r r;rr:rP) rJmax_denominatorp0q0p1q1rraq2ks && rlimit_denominatorFraction.limit_denominators@ Q CD D    /D> !# 1 11AbDB#R"Wb0NBBeq  " $ Q3R4=D-- -..r6 6..rB$wR4@ @r cVP#rb)r:rts&rrFraction.numerators ||r cVP#rbrgrzs&rrFraction.denominators ~~r cnVPP: RVP: RVP: R2#)(z, rV)rMrXr:r;rhs&r__repr__Fraction.__repr__s*#~~66#0A0AC Cr cVP^8Xd\VP4#VP: RVP: 2#)r/)r;r"r:rhs&r__str__Fraction.__str__s4    !t' '"oot/@/@A Ar cVR,;'gRpVR,;'gRpVR,R8XdRMVR,p\VR,4p\VR,;'gR 4pVR ,;'gRpVPVPrV ^8g V'd\ V4V R W 2p M\ V4V p V^8dRMTp W&\ V 4, \ V 4, ,p VR8XdW,V ,#VR 8XdW,V ,#VR 8Xd/\ V 4^,p V RV V ,V ,WR,#W,V ,#)fill align>rr4r2alt minimumwidthr. thousands_sepr<^N)boolr9r:r;r r#)rJrBrrpos_signalternate_formrrrrbodyrpaddinghalfs&& r_format_generalFraction._format_generalsMV}##g%%#v#-25=eEl+5077C8 o.44"  1 11 q5N!fm_-Qq.ABD!fm_-D!esT2SY>? C<>D( ( c\;( ( c\w<1$D5D>D(4/'%.@ @>D( (r c aa a!VR,;'gRpVR,;'gRpVR,R8XdRMVR,p\VR,4p\VR,4p\VR ,4p\VR ,;'gR 4pVR ,o!\VR ,;'gR4p VR,;'gRp VR,p V R9;'dV'*p V'*p V R9dRMRpVR8Xd VR 8XdRpV R9d=V )pV R8Xd V^,p\VPVPW4wppRpT pM{V R9d \ V ^4MV ^,p\ VPVPV4wpppV R9;'gV^8;'g VV,R#8*pV'd V^, MV)pV R8XdRpMV'dV VV,R 2pMRpVR V^, R2 pV'dRMTpVR\V4V, o V\V4V, RoV 'dSPR 4oV 'd S'gRMRpV 'd0V PV3Rl\^\S4^444oVS,V,pV'dSV\V4, \V4, pS PS!'d^V,^,^,MT4o S!'d[^\S 4^, ^,,pS RVRPV V!3R l\V\S 4^444,o S V,pW(\V4, \V4, ,pVR8XdVV,V,#VR!8XdVV,V,#VR"8Xd0\V4^,pVRVV,V,VVR,#VV,V,#)$rrrrrr4r2rrzeropadrr.r precision6frac_separatorspresentation_typegGEFGEe=TzfF%%FeEz+03drN.c3:<"TFpSW^,xK R#5iN).0pos frac_parts& r /Fraction._format_float_style..4s"&N1L#'0!G&<1Lsc3H<"TFpSSW^,,xK R#5irr)rrleadingrs& rrrDs)4SC C? C<T>D( ( c\$;( ( c\w<1$D5D>D(4/'$%.@ @'>D( (r c \V4;p'dVPV4#\V4;p'd(VR,e VR,fVPV4#\ RV: R\ V4P : 24h)rrzInvalid format specifier z for object of type )%_GENERAL_FORMAT_SPECIFICATION_MATCHERr#_FLOAT_FORMAT_SPECIFICATION_MATCHERrr r8rX)rJ format_specrBs"" r __format__Fraction.__format__Ws:+F F5 F''. .7 D D5 DW~%y)9)A//66' 7""&t*"5"5!8 :  r caaaVVV3RlpRSP,R,VnSPVnVVV3RlpRSP,R,VnSPVnW43#)cL<\V\4'd S!W4#\V\4'dS!V\V44#\V\4'dS!\V4V4#S'd)\V\4'dS!\V4V4#\ #rb)r<rr9r?complexNotImplemented)rtbfallback_operatorhandle_complexmonomorphic_operators&&rforward-Fraction._operator_fallbacks..forwards}!X&&+A11As##+Ax{;;Au%%(q155Jq'$:$:(q155%%r __cp<\V\P4'dS!\V4V4#\V\P4'dS!\ V4\ V44#S'd<\V\P 4'dS!\V4\ V44#\#rb) r<r=r>rRealr?Complexrr)rrtrrrs&&rreverse-Fraction._operator_fallbacks..reverses{!W--..+HQK;;Aw||,,(q58<<Jq'//$B$B(U1X>>%%r __r)rX__doc__)rrrrrsfff r_operator_fallbacksFraction._operator_fallbackshsgb & "3"<"<? HUG,,,r cVPVPr2\VPV,VPV,,W#,4#rb)rrr)rtrrrs&& r_mod Fraction._modns7 Br)akkB.>?IIr c(Ve\#\V\P4'Ed5VP^8XEdVP pV^8d9\ PVPV,VPV,4#VP^8d;\ PVPV),VPV),4#VP^8Xd%\RVPV),,4h\ PVP)V),VP)V),4#\V4\V4,#\V\\34'd\V4V,#\#)Nr5) rr<r=r>rrrrPr:r;rFr?r)rtrmodulopowers&&& r__pow__Fraction.__pow__usJ  ! ! a)) * *}}! A:#66q||u7L78~~7NPP\\A%#66q~~%7O78||v7MOO\\Q&+,=,-NNuf,D-EFF$66UF7R9: 5&7PRR Qx58++ E7+ , ,8q= ! !r cvVe\#VP^8Xd$VP^8dWP,#\V\P 4'd(\ VPVP4V,#VP^8XdWP,#V\V4,#rb) rr;r:r<r=r>rrrr?)rrtrs&&&r__rpow__Fraction.__rpow__s  ! ! >>Q 1<<1#4 $ $ a)) * *AKK71< < >>Q  $ $E!H}r cV\PVPVP4#rbrrPr:r;rzs&r__pos__Fraction.__pos__s**1<<HHr cX\PVP)VP4#rbr rzs&r__neg__Fraction.__neg__s**ALL=!..IIr ch\P\VP4VP4#rb)rrPr r:r;rzs&r__abs__Fraction.__abs__s"**3q||+>1 1r c<VPVP,#rbrlrzs&r __floor__Fraction.__floor__s||q~~--r c@VP)VP,)#rbrlrzs&r__ceil__Fraction.__ceil__s,,!..011r c|VfeVPp\VPV4wr4V^,V8dV#V^,V8d V^,#V^,^8XdV#V^,#^ \V4,pV^8d\ \ W,4V4#\ \ W, 4V,4#rb)r;rr:r rround)rJndigitsrfloor remaindershifts&& r __round__Fraction.__round__s ?!!A%dooq9 E1}q  Q"qy a qy CL  Q;E$,/7 7E$,/%78 8r cB\VPVP4#rb)rr:r;rhs&r__hash__Fraction.__hash__st0A0ABBr cz\V4\Jd'VPV8H;'dVP^8H#\ V\ P 4'd;VPVP8H;'dVPVP8H#\ V\ P4'dVP^8Xd VPp\ V\4'dQ\P!V4'g\P!V4'dRV8H#WP!V48H#\"#)r)r8r9r:r;r<r=r>rrrimagrealr?rGisnanisinfrZrrs&&r__eq__Fraction.__eq__s 7c><<1$<<1)< < a)) * *LLAKK/44NNamm3 5 a ) )affkA a  zz!}} 1 axLLO++" !r c\V\P4'd@V!VPVP,VP VP ,4#\V\4'dY\P!V4'g\P!V4'd V!RV4#V!WPV44#\#)r/) r<r=r>r:rr;rr?rGr2r3rZr)rJotherops&&&r_richcmpFraction._richcmps eW-- . .doo(9(99''%//9; ; eU # #zz%  DJJu$5$5#u~%$ 677! !r cBVPV\P4#rb)r9operatorltrs&&r__lt__Fraction.__lt__zz!X[[))r cBVPV\P4#rb)r9r<gtrs&&r__gt__Fraction.__gt__r@r cBVPV\P4#rb)r9r<lers&&r__le__Fraction.__le__r@r cBVPV\P4#rb)r9r<gers&&r__ge__Fraction.__ge__r@r c,\VP4#rb)rr:rzs&r__bool__Fraction.__bool__#sALL!!r cJVPVPVP33#rb)rMr:r;rhs&r __reduce__Fraction.__reduce__+s $2C2C DEEr cz\V4\8XdV#VPVPVP4#rbr8rrMr:r;rhs&r__copy__Fraction.__copy__.. : !K~~doot/@/@AAr cz\V4\8XdV#VPVPVP4#rbrT)rJmemos&&r __deepcopy__Fraction.__deepcopy__3rWr )r;r:rl)rN)i@B)Trb)MrX __module__ __qualname____firstlineno__ __slots__r7 classmethodrRrZr_rPrir,rwpropertyrrrrrrrrrr<add__add____radd__rsub__sub____rsub__rmul__mul____rmul__rtruediv __truediv__ __rtruediv__rfloordiv __floordiv__ __rfloordiv__rr __divmod__ __rdivmod__rmod__mod____rmod__rr r rrindexrrrr!r)r,r4r9r>rCrGrKrNrQrUrZ__static_attributes____classdictcell__ __classcell__)rM __classdict__s@@rrrs*/IiVBB* = = ? ?  &47ArC B )Df)P "l d D,D(,,?GX D,D(,,?GX =,D(,,?GX1(!4D(:J:J KKN#6iARARTY"ZL-- 2'65IJ J ,D(,,FGX "D IJN#..:2.2 94C"*",****"FB BBr i@)F) functoolsrGr=r<resys__all__ hash_infomodulusr infr lru_cachercompileVERBOSE IGNORECASErArr)DOTALL fullmatchrrr>rrr rrs    , --''mm  w'*(*@:: ZZ"-- !":$'P)+ 4YY )'Y&$')jj2&YY''&'Y'$,@Bw@Br