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lmZmZmZ ddlmZ ddlmZ ddlmZmZ ddlmZ ddlmZ ddlmZmZ ddlmZ ddlm Z  ddlmZmZ ddlmZmZmZmZm	Z	m
Z
mZmZ ddlmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZmZmZmZmZmZm Z  ddlm!Z" dd dD \Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6Z7Z8Z9Z:Z;Z<Z=Z>Z?Z@ZAdd dD \ZBZCZDZEZFZGZHZIZJZKZLZMZNZOZPZQZJZKZRZSZTZUZVZWZXZYZZZ[Z\Z]ed\	Z^Z_Z`ZaZbZcZdZeZfdZgdZhdZid d! Zjd"d# Zkd$d% Zld&d' Zmd(d) Znd*d+ Zod,d- Zpd.d/ Zqd0d1 Zrd2d3 Zsd4d5 Ztd6d7 Zud8d9 Zvd:d; Zwd<d= Zxd>d? Zyd@dA ZzdBdC Z{dDdE Z|dFdG Z}dHdI Z~dJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ Zddń ZddǄ ZddɄ Zdd˄ Zdd̈́ Zddτ Zddф Zddӄ ZddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zِd d Zڐdd Zېdd Zܐdd Zݐdd	 Zސd
d Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM Z dNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Z	d`da Z
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d Z_dd Z`dd Zadd Zbdd Zcdd Zddd Zedd Zfdd Zgdd Zhdd Zid d! Zjd"d# Zkd$d% Zld&d' Zmd(d) Znd*d+ Zod,d- Zpd.d/ Zqd0d1 Zrd2d3 Zsd4d5 Ztd6d7 Zud8d9 Zvd:d; Zwd<d= Zxd>d? Zyd@dA ZzdBdC Z{dDdE Z|dFdG Z}dHdI Z~dJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ ZdĐdń ZdƐdǄ ZdȐdɄ Zdʐd˄ Zd̐d̈́ Zdΐdτ ZdАdф ZdҐdӄ ZÐdԐdՄ ZĐd֐dׄ ZŐdؐdل ZƐdڐdۄ Zǐdܐd݄ ZȐdސd߄ Zɐdd Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd ZԐdd ZՐdd Z֐dd Zאdd Zؐdd Zِd d Zڐdd Zېdd Zܐdd Zݐdd	 Zސd
d Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM Z dNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Z	d`da Z
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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)Add)Mod)Mul)
EulerGamma)FloatIInteger)Pow)S)Abssign)sqrt)Integral)AndOr)simplifyWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  N/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rules/inverse_trig.py
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||	|c|e|d
}t|tփ}ttܐttdtdtdtdtߐt   t|||c|ftt؃}t|tك}ttܐttdtdtdtdtt   t|||c|gttڃ}t|tۃ}ttܐtttdtd tdtd tdtd tdtd t||||}t|t݃}tttdtdtdtdtttdtd   tdtd t||||}t|t߃}ttܐtttdtd tdtd tdtd t t|||||h}t|t}tttdtdtdtdtttdtd   t t|||||h}t|t}ttܐtttdtd tdtd tdtd tdtd tttdtd   t||||
||i|}t|t}tttdtdtdtdtttdtd   tdtd tttdtd   t||||
||i|}t|t}ttܐtttdtd tttdtd   t||
||j|k}t|t}ttܐtttdtd ttdtd tdtd  t||
||l}t|t}ttܐtttdtd ttdtd tdtd  t||
||l}t|t}ttܐttttdtd tdtd  ttdtd tdtd  t||||
||m}t|t}ttܐttdtdtttdtd   ttdtd tdtd  t||||
||m}t|t}ttttdtd tdtd tdtd tttdtd tdtd tdtd  t||||
|||(}t|t}ttttdtd tdtd tdtd tdtdtdtdtttdtd    t||||
|||(}t|t}ttܐtttdtd tdtd tdtd t t t||||n|^}t|t}tttdtdtdtdtttdtd   t t t||||n|^}t|t}ttttd	td tttdtd tdtd tdtd t  t|||||n|^|	}t|t}ttttd	td tdtdtdtdtttdtd   t  t|||||n|^|	}t|t}tttttdtd  tdtd tttdtd tdtd tdtd tdtd  t||||
||E}t|t}tttttdtd  tdtd tdtdtdtdtttdtd   tdtd  t||||
||E}t|t}ttttdtd tdtd tdtd tttdtd tdtd tdtd tdtd  t||||
||||"	}t|t}ttttdtd tdtd tdtd tdtdtdtdtttdtd   tdtd  t||||
||||"	}t|t}ttttd	td tttdtd tdtd tdtd tdtd  tttdtd   t||||
||i||o|J
}t|t}ttttd	td tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||i||o|J
}t|Đt}ttܐtttdtd tdtd tdtd tdtd ttttdtd    t||||
||i|}t|Ɛt}tttdtdtdtdtttdtd   tdtd ttttdtd    t||||
||i|}t|Ȑt}tttt$ tttdtd tdtd tdtd tdtd  tttdtd   t||||
||i||o|0
}t|ʐt}tttt$ tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||i||o|0
}t|̐t}ttttd	td tttdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
||| ||p
}t|ΐt}ttttd	td tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||| ||p
}t|Аt}ttttd	td ttdtd tdtd tdtd  tttdtd tdtd tdtd tdtd  t||||
|||||q
}t|Ґt}ttttd	td ttdtd tdtd tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||||q
}t|Ԑt}tttttd
 tdtd  tdtd tttdtd tdtd tdtd  t||||
||r|s|	}t|֐t}tttttd
 tdtd  tdtd tdtdtdtdtttdtd    t||||
||r|s|	}t|ؐt}tttttd
 tdtd  tdtd tttdtd tdtd tdtd t  t||||
||r|||^
}t|ڐt}tttttd
 tdtd  tdtd tdtdtdtdtttdtd   t  t||||
||r|||^
}t|ܐt }tttdtttd
 tdtd  tttdtd tdtd tdtd   t||||
||r}t|ސt}tttdtttd
 tdtd  tdtdtdtdtttdtd     t||||
||r}t|t}ttܐtttdtd tdtd tdtd tdtd tttd
 tdtd   t||||
|||r|	}t|t}tttdtdtdtdtttdtd   tdtd tttd
 tdtd   t||||
|||r|	}t|t}ttܐtttdtd tdtd tdtd ttttd
 tdtd   t||||
||r|}t|t}tttdtdtdtdtttdtd   ttttd
 tdtd   t||||
||r|}t|t}ttܐtttdtd tdtd tdtd tdtd ttttd
 tdtd   t||||
||r||	}t|t}tttdtdtdtdtttdtd   tdtd ttttd
 tdtd   t||||
||r||	}t|t}ttܐtttdtd tdtd tdtd tdtd ttttd
 tdtd   t||||
||r||	}t|t	}tttdtdtdtdtttdtd   tdtd ttttd
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||r||	}t|t
}ttܐtttdtd tdtd tdtd tdtd tttd
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  t||||
||r| |	}t|t}tttdtdtdtdtttdtd   tdtd tttd
 tdtd  td
  t||||
||r| |	}t|t}ttܐtttdtd tdtd tdtd tttd
 tdtd  tdd
   t||||
||r}t|t}tttdtdtdtdtttdtd   tttd
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||r}t|t}tttttd
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||r|s||
}t|t}tttttd
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||r|s||
}t|t}ttܐtttdtd tdtd tdtd t tttd
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||r| |^	}t|t}tttdtdtdtdtttdtd   t tttd
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||r|||^|}t|t}tttttd
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||r|||
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||r|||
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|||r|t|
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t|
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|||r|t|
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|||r|t| 
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|||r|t|%
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||l}t|t}ttܐttttdtd tdtd  ttd
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||m}t|t}ttܐttdtdtttdtd   ttd
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||m}t|t}ttttd
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||u}t|t}ttttd
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||u}t|t }tttttd
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|| |}t|t!}tttttd
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|| |} t| t"}!ttttd
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||||"	}"t|"t#}#ttttd
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||||"	}$t|$t$}%tttt$ tttdtd tdtd tdtd tdtd  tttd
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||/||5	}&t|&t%}'tttt$ tdtdtdtdtttdtd   tdtd  tttd
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||/||5	}(t|(t&})tttt$ tttdtd tdtd tdtd tdtd  tttd
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||/||0	},t|,t(}-ttttttdtd tdtd tdtd tdtd  tttd
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||r|/||5
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||r|/||0
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||r|/||0
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  t||||
||r| ||_
}Nt|Nt9}Ottttdtdtdtdtttdtd   t  tttd
 tdtd  td
  t||||
||r| ||_
}Pt|Pt:}Qttttd
 tttd
 tdtd  t
  tttdtd tdtd tdtd  t||||
||r|s||w
}Rt|Rt;}Sttttd
 tttd
 tdtd  t
  tdtdtdtdtttdtd    t||||
||r|s||w
}Tt|Tt<}Uttttd
 tttdtd tdtd tdtd tdtd  tttd
 tdtd  td
  t||||
||r| |	}Vt|Vt=}Wttttd
 tdtdtdtdtttdtd   tdtd  tttd
 tdtd  td
  t||||
||r| |	}Xt|Xt>}Ytttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd  t||||
||r|x|s|
}Zt|Zt?}[tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd    t||||
||r|x|s|
}\t|\t@}]tttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd t  t||||
|||r|x|||^}^t|^tA}_tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   t  t||||
|||r|x|||^}`t|`tB}attttd	td tttd
 tdtd  tdtd  tttdtd tdtd tdtd t  t||||
||||r|x| |}bt|btC}cttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   t  t||||
||||r|x| |}dt|dtD}ettttd	td tttd
 tdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
||||r|)| ||	}ft|ftE}gttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||||r|)| ||	}ht|htF}itttt$ ttttd
 tdtd   tttdtd tdtd tdtd  t||||
|||r|y	}jt|jtG}ktttt$ ttttd
 tdtd   tdtdtdtdtttdtd    t||||
|||r|y	}lt|ltH}mtttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
|||r|| |z}nt|ntI}otttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
|||r|| |z}pt|ptJ}qtttt$ tttd
 tdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
|||r|s|||{}rt|rtK}stttt$ tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||r|s|||{}tt|ttL}utttt$ tttdtd tdtd tdtd tdtd  ttttd
 tdtd   t||||
||r|/||5
}vt|vtM}wtttt$ tdtdtdtdtttdtd   tdtd  ttttd
 tdtd   t||||
||r|/||5
}xt|xtN}yttܐtttdtd tdtd tdtd tttttd
 tdtd    t||||
||r|}zt|ztO}{tttdtdtdtdtttdtd   tttttd
 tdtd    t||||
||r|}|t||tP}}ttܐtttdtd tdtd tdtd t tttttd
 tdtd    t||||
||r||	}~t|~tQ}tttdtdtdtdtttdtd   t tttttd
 tdtd    t||||
||r||	}t|tR}ttܐtttdtd tdtd tdtd tdtd tttttd
 tdtd    t||||
||r||	}t|tS}tttdtdtdtdtttdtd   tdtd tttttd
 tdtd    t||||
||r||	}t|tT}ttܐtttdtd tdtd tdtd tdtd ttd
 ttttd
 tdtd    t||||
||r| |	}t|tU}tttdtdtdtdtttdtd   tdtd ttd
 ttttd
 tdtd    t||||
||r| |	}t|tV}tttt$ tttdtd tdtd tdtd tdtd  ttttd
 tdtd   t||||
||r|/||0||}t|tW}tttt$ tdtdtdtdtttdtd   tdtd  ttttd
 tdtd   t||||
||r|/||0||}t|tX}tttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
||r|}||5|~}t|tY}tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
||r|}||5|~}t|tZ}tttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
||r|}||N|~}t|t[}tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
||r|}||N|~}t|t\}ttttd	td tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
||r|1|||}t|t]}ttttd	td tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
||r|1|||}t|t^}ttttd	td tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
|||r|||}t|t_}ttttd	td tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
|||r|||}t|t`}ttttd	td tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
|||r||| }t|ta}ttttd	td tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
|||r|||%}t|tb}tttttd
 tdtd tdtd tdtd  tttdtd tdtd tdtd  t||||
|||(}t|tc}tttttd
 tdtd tdtd tdtd  tdtdtdtdtttdtd    t||||
|||(}t|td}ttttd	td ttd
 tdtd tdtd tdtd  tttdtd tdtd tdtd  t||||
||||	}t|te}ttttd	td ttd
 tdtd tdtd tdtd  tdtdtdtdtttdtd    t||||
||||	}t|tf}ttttd	td tttd
 tdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
||| ||
}t|tg}ttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||| ||
}t|th}ttttd	td ttttdtd tdtd   tttd
 tdtd  tdtd  t||||
||||	}t|ti}ttttd	td ttdtdtttdtd    tttd
 tdtd  tdtd  t||||
||||	}t|tj}ttttd	td ttd
 tdtd tdtd tdtd  tttdtd tdtd tdtd tdtd  t||||
|||||q
}t|tk}ttttd	td ttd
 tdtd tdtd tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||||q
}t|tl}ttܐtttdtd tdtd tdtd tdtd tmt tttd
 tdtd   t||||
||r| ||
}t|tn}tttdtdtdtdtttdtd   tdtd tot tttd
 tdtd   t||||
||r| ||
}t|tp}ttܐtttdtd tdtd tdtd tdtd tmt tttd
 tdtd   t||||
||r| ||
}t|tq}tttdtdtdtdtttdtd   tdtd tot tttd
 tdtd   t||||
||r| ||
}t|tr}ttܐtttdtd tdtd tdtd tdtd tt tttd
 tdtd   t||||
||r| ||
}t|ts}tttdtdtdtdtttdtd   tdtd tt tttd
 tdtd   t||||
||r| ||
}t|tt}ttܐtttdtd tdtd tdtd tdtd tt tttd
 tdtd   t||||
||r| ||
}t|tu}tttdtdtdtdtttdtd   tdtd tt tttd
 tdtd   t||||
||r| ||
}t|Đtv}ttܐtttdtd tdtd tdtd tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|Ɛtx}tttdtdtdtdtttdtd   tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|Ȑty}ttܐtttdtd tdtd tdtd tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|ʐtz}tttdtdtdtdtttdtd   tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|̐t{}tttdtttd
 tdtd  tttdtd tdtd tdtd  tdtdtdtdtttdtd     t||||
||r}t|ΐt|}ttܐtttdtd tdtd tdtd tdtd tdtdtdtdtttdtd   td	td  tttd
 tdtd   t||||
||r|S|	}t|Аt}}ttܐtttdtd tdtd tdtd td	td tdtdtdtdtttdtd   tdtd  tttd
 tdtd   t||||
||r|S|	}t|Ґt~}ttܐtttdtd tttdtd tdtd   t|||
|n|}t|Ԑt}ttܐtttdtd tttdtd tdtd   t|||
|n|}t|֐t}ttܐtttdtd tdtd tdtd tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ؐt}tttdtdtdtdtttdtd   tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ڐt}ttttd	td tttdtd tdtd tdtd  tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ܐt}ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ސt}ttttd	td tttdtd tdtd tdtd  tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|t}ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|t}ttttd	td tttdtd tdtd tdtd  tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|4|
}t|t}ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|4|
}t|t}ttttttdtd tdtd tdtd td
  tdtdtdtdttttd
 tdtd     t||||
||&|'|	}t|t}ttttdtdtdtdtttdtd   td
  tdtdtdtdttttd
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||&|'|	}t|t}ttܐtttttdtd  t||}t|t}ttttd	td tttttdtd   t|||}t|t}ttܐttttdtd tdtd t|||}t|t}ttttd	td ttttdtd tdtd  t||||}t|t}ttܐtttdtd  tdtd tdtd ttttdtd tdtd  t|||
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}t|t݃}ttttdtd tdtd t$ tܐtttdtd  tdtd tdtd t  t||||
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}t|tރ}ttttdtd tdtd t$ tdtdtdtdtސtttdtd    t  t||||
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||&||	}t|t
}ttttdtd tdtd td	td ttdtdtdtdtttdtd tdtd    t||||
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sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r   r  r  r  r	  x_r   replacement5034r  replacement5035n_replacement5036replacement5037replacement5038replacement5039replacement5040replacement5041replacement5042replacement5043replacement5044replacement5045replacement5046replacement5047replacement5048replacement5049replacement5050replacement5051replacement5052replacement5053r  d_replacement5054replacement5055replacement5056replacement5057replacement5058replacement5059With5060With5061replacement5062replacement5063replacement5064replacement5065replacement5066replacement5067replacement5068replacement5069p_replacement5070replacement5071replacement5072replacement5073replacement5074replacement5075replacement5076replacement5077replacement5078replacement5079With5080With5081replacement5082replacement5083replacement5084replacement5085f_replacement5086replacement5087replacement5088replacement5089replacement5090replacement5091replacement5092replacement5093m_replacement5094replacement5095replacement5096replacement5097replacement5098replacement5099With5100With5101With5102With5103With5104With5105replacement5106replacement5107replacement5108replacement5109replacement5110replacement5111replacement5112replacement5113replacement5114replacement5115replacement5116replacement5117replacement5118replacement5119replacement5120replacement5121replacement5122replacement5123replacement5124replacement5125replacement5126replacement5127replacement5128replacement5129replacement5130replacement5131replacement5132replacement5133replacement5134replacement5135replacement5136replacement5137replacement5138replacement5139replacement5140replacement5141replacement5142replacement5143With5144With5145replacement5146replacement5147replacement5148replacement5149replacement5150replacement5151replacement5152replacement5153replacement5154replacement5155replacement5156replacement5157replacement5158replacement5159Px_With5160With5161replacement5162replacement5163With5164With5165With5166With5167With5168With5169replacement5170replacement5171With5172With5173replacement5174replacement5175replacement5176replacement5177replacement5178replacement5179replacement5180replacement5181replacement5182replacement5183replacement5184replacement5185replacement5186replacement5187replacement5188replacement5189logreplacement5190replacement5191replacement5192replacement5193With5194With5195replacement5196replacement5197u_r   With5198replacement5198With5199replacement5199With5200replacement5200With5201replacement5201With5202replacement5202With5203replacement5203RFx_With5204replacement5204With5205replacement5205a_replacement5206replacement5207With5208replacement5208With5209replacement5209replacement5210replacement5211replacement5212replacement5213c_replacement5214replacement5215replacement5216replacement5217replacement5218replacement5219replacement5220replacement5221replacement5222replacement5223replacement5224replacement5225replacement5226replacement5227replacement5228replacement5229replacement5230replacement5231replacement5232replacement5233replacement5234replacement5235replacement5236replacement5237replacement5238replacement5239replacement5240replacement5241replacement5242replacement5243replacement5244replacement5245replacement5246replacement5247replacement5248replacement5249replacement5250replacement5251replacement5252replacement5253replacement5254v_With5255replacement5255With5256replacement5256r>   replacement5257r
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  r  r  r  pattern5034rule5034pattern5035rule5035pattern5036rule5036pattern5037rule5037pattern5038rule5038pattern5039rule5039pattern5040rule5040pattern5041rule5041pattern5042rule5042pattern5043rule5043pattern5044rule5044pattern5045rule5045pattern5046rule5046pattern5047rule5047pattern5048rule5048pattern5049rule5049pattern5050rule5050pattern5051rule5051pattern5052rule5052pattern5053rule5053pattern5054rule5054pattern5055rule5055pattern5056rule5056pattern5057rule5057pattern5058rule5058pattern5059rule5059pattern5060rule5060pattern5061rule5061pattern5062rule5062pattern5063rule5063pattern5064rule5064pattern5065rule5065pattern5066rule5066pattern5067rule5067pattern5068rule5068pattern5069rule5069pattern5070rule5070pattern5071rule5071pattern5072rule5072pattern5073rule5073pattern5074rule5074pattern5075rule5075pattern5076rule5076pattern5077rule5077pattern5078rule5078pattern5079rule5079pattern5080rule5080pattern5081rule5081pattern5082rule5082pattern5083rule5083pattern5084rule5084pattern5085rule5085pattern5086rule5086pattern5087rule5087pattern5088rule5088pattern5089rule5089pattern5090rule5090pattern5091rule5091pattern5092rule5092pattern5093rule5093pattern5094rule5094pattern5095rule5095pattern5096rule5096pattern5097rule5097pattern5098rule5098pattern5099rule5099pattern5100rule5100pattern5101rule5101pattern5102rule5102pattern5103rule5103pattern5104rule5104pattern5105rule5105pattern5106rule5106pattern5107rule5107pattern5108rule5108pattern5109rule5109pattern5110rule5110pattern5111rule5111pattern5112rule5112pattern5113rule5113pattern5114rule5114pattern5115rule5115pattern5116rule5116pattern5117rule5117pattern5118rule5118pattern5119rule5119pattern5120rule5120pattern5121rule5121pattern5122rule5122pattern5123rule5123pattern5124rule5124pattern5125rule5125pattern5126rule5126pattern5127rule5127pattern5128rule5128pattern5129rule5129pattern5130rule5130pattern5131rule5131pattern5132rule5132pattern5133rule5133pattern5134rule5134pattern5135rule5135pattern5136rule5136pattern5137rule5137pattern5138rule5138pattern5139rule5139pattern5140rule5140pattern5141rule5141pattern5142rule5142pattern5143rule5143pattern5144rule5144pattern5145rule5145pattern5146rule5146pattern5147rule5147pattern5148rule5148pattern5149rule5149pattern5150rule5150pattern5151rule5151pattern5152rule5152pattern5153rule5153pattern5154rule5154pattern5155rule5155pattern5156rule5156pattern5157rule5157pattern5158rule5158pattern5159rule5159pattern5160rule5160pattern5161rule5161pattern5162rule5162pattern5163rule5163pattern5164rule5164pattern5165rule5165pattern5166rule5166pattern5167rule5167pattern5168rule5168pattern5169rule5169pattern5170rule5170pattern5171rule5171pattern5172rule5172pattern5173rule5173pattern5174rule5174pattern5175rule5175pattern5176rule5176pattern5177rule5177pattern5178rule5178pattern5179rule5179pattern5180rule5180pattern5181rule5181pattern5182rule5182pattern5183rule5183pattern5184rule5184pattern5185rule5185pattern5186rule5186pattern5187rule5187pattern5188rule5188pattern5189rule5189pattern5190rule5190pattern5191rule5191pattern5192rule5192pattern5193rule5193pattern5194rule5194pattern5195rule5195pattern5196rule5196pattern5197rule5197pattern5198rule5198pattern5199rule5199pattern5200rule5200pattern5201rule5201pattern5202rule5202pattern5203rule5203pattern5204rule5204pattern5205rule5205pattern5206rule5206pattern5207rule5207pattern5208rule5208pattern5209rule5209pattern5210rule5210pattern5211rule5211pattern5212rule5212pattern5213rule5213pattern5214rule5214pattern5215rule5215pattern5216rule5216pattern5217rule5217pattern5218rule5218pattern5219rule5219pattern5220rule5220pattern5221rule5221pattern5222rule5222pattern5223rule5223pattern5224rule5224pattern5225rule5225pattern5226rule5226pattern5227rule5227pattern5228rule5228pattern5229rule5229pattern5230rule5230pattern5231rule5231pattern5232rule5232pattern5233rule5233pattern5234rule5234pattern5235rule5235pattern5236rule5236pattern5237rule5237pattern5238rule5238pattern5239rule5239pattern5240rule5240pattern5241rule5241pattern5242rule5242pattern5243rule5243pattern5244rule5244pattern5245rule5245pattern5246rule5246pattern5247rule5247pattern5248rule5248pattern5249rule5249pattern5250rule5250pattern5251rule5251pattern5252rule5252pattern5253rule5253pattern5254rule5254pattern5255rule5255pattern5256rule5256pattern5257rule5257pattern5258rule5258pattern5259rule5259pattern5260rule5260pattern5261rule5261pattern5262rule5262pattern5263rule5263pattern5264rule5264pattern5265rule5265pattern5266rule5266pattern5267rule5267pattern5268rule5268pattern5269rule5269pattern5270rule5270pattern5271rule5271pattern5272rule5272pattern5273rule5273pattern5274rule5274pattern5275rule5275pattern5276rule5276pattern5277rule5277pattern5278rule5278pattern5279rule5279pattern5280rule5280pattern5281rule5281pattern5282rule5282pattern5283rule5283pattern5284rule5284pattern5285rule5285pattern5286rule5286pattern5287rule5287pattern5288rule5288pattern5289rule5289pattern5290rule5290pattern5291rule5291pattern5292rule5292pattern5293rule5293pattern5294rule5294pattern5295rule5295pattern5296rule5296pattern5297rule5297pattern5298rule5298pattern5299rule5299pattern5300rule5300pattern5301rule5301pattern5302rule5302pattern5303rule5303pattern5304rule5304pattern5305rule5305pattern5306rule5306pattern5307rule5307pattern5308rule5308pattern5309rule5309pattern5310rule5310pattern5311rule5311pattern5312rule5312pattern5313rule5313pattern5314rule5314pattern5315rule5315pattern5316rule5316pattern5317rule5317pattern5318rule5318pattern5319rule5319pattern5320rule5320pattern5321rule5321pattern5322rule5322pattern5323rule5323pattern5324rule5324pattern5325rule5325pattern5326rule5326pattern5327rule5327pattern5328rule5328pattern5329rule5329pattern5330rule5330pattern5331rule5331pattern5332rule5332pattern5333rule5333pattern5334rule5334pattern5335rule5335pattern5336rule5336pattern5337rule5337pattern5338rule5338pattern5339rule5339pattern5340rule5340pattern5341rule5341pattern5342rule5342pattern5343rule5343pattern5344rule5344pattern5345rule5345pattern5346rule5346pattern5347rule5347pattern5348rule5348pattern5349rule5349pattern5350rule5350pattern5351rule5351pattern5352rule5352pattern5353rule5353pattern5354rule5354pattern5355rule5355pattern5356rule5356pattern5357rule5357pattern5358rule5358pattern5359rule5359pattern5360rule5360pattern5361rule5361pattern5362rule5362pattern5363rule5363pattern5364rule5364pattern5365rule5365pattern5366rule5366pattern5367rule5367pattern5368rule5368pattern5369rule5369pattern5370rule5370pattern5371rule5371pattern5372rule5372pattern5373rule5373pattern5374rule5374pattern5375rule5375pattern5376rule5376pattern5377rule5377pattern5378rule5378pattern5379rule5379pattern5380rule5380pattern5381rule5381pattern5382rule5382pattern5383rule5383pattern5384rule5384pattern5385rule5385pattern5386rule5386pattern5387rule5387pattern5388rule5388pattern5389rule5389pattern5390rule5390pattern5391rule5391pattern5392rule5392pattern5393rule5393pattern5394rule5394pattern5395rule5395pattern5396rule5396pattern5397rule5397pattern5398rule5398pattern5399rule5399pattern5400rule5400pattern5401rule5401pattern5402rule5402pattern5403rule5403pattern5404rule5404pattern5405rule5405pattern5406rule5406pattern5407rule5407pattern5408rule5408pattern5409rule5409pattern5410rule5410pattern5411rule5411pattern5412rule5412pattern5413rule5413pattern5414rule5414pattern5415rule5415pattern5416rule5416pattern5417rule5417pattern5418rule5418pattern5419rule5419pattern5420rule5420pattern5421rule5421pattern5422rule5422pattern5423rule5423pattern5424rule5424pattern5425rule5425pattern5426rule5426pattern5427rule5427pattern5428rule5428pattern5429rule5429pattern5430rule5430pattern5431rule5431pattern5432rule5432pattern5433rule5433pattern5434rule5434pattern5435rule5435pattern5436rule5436pattern5437rule5437pattern5438rule5438pattern5439rule5439pattern5440rule5440pattern5441rule5441pattern5442rule5442pattern5443rule5443pattern5444rule5444pattern5445rule5445pattern5446rule5446pattern5447rule5447pattern5448rule5448pattern5449rule5449pattern5450rule5450pattern5451rule5451pattern5452rule5452pattern5453rule5453pattern5454rule5454pattern5455rule5455pattern5456rule5456pattern5457rule5457pattern5458rule5458pattern5459rule5459pattern5460rule5460pattern5461rule5461pattern5462rule5462pattern5463rule5463pattern5464rule5464pattern5465rule5465pattern5466rule5466pattern5467rule5467pattern5468rule5468pattern5469rule5469pattern5470rule5470pattern5471rule5471pattern5472rule5472pattern5473rule5473pattern5474rule5474pattern5475rule5475pattern5476rule5476pattern5477rule5477pattern5478rule5478pattern5479rule5479pattern5480rule5480pattern5481rule5481pattern5482rule5482pattern5483rule5483pattern5484rule5484pattern5485rule5485pattern5486rule5486pattern5487rule5487pattern5488rule5488pattern5489rule5489pattern5490rule5490pattern5491rule5491pattern5492rule5492pattern5493rule5493pattern5494rule5494pattern5495rule5495pattern5496rule5496pattern5497rule5497pattern5498rule5498pattern5499rule5499pattern5500rule5500pattern5501rule5501pattern5502rule5502pattern5503rule5503pattern5504rule5504pattern5505rule5505pattern5506rule5506pattern5507rule5507pattern5508rule5508pattern5509rule5509pattern5510rule5510pattern5511rule5511pattern5512rule5512pattern5513rule5513pattern5514rule5514pattern5515rule5515pattern5516rule5516pattern5517rule5517pattern5518rule5518pattern5519rule5519pattern5520rule5520pattern5521rule5521pattern5522rule5522pattern5523rule5523pattern5524rule5524pattern5525rule5525pattern5526rule5526pattern5527rule5527pattern5528rule5528pattern5529rule5529pattern5530rule5530pattern5531rule5531pattern5532rule5532pattern5533rule5533pattern5534rule5534pattern5535rule5535pattern5536rule5536pattern5537rule5537pattern5538rule5538pattern5539rule5539pattern5540rule5540pattern5541rule5541pattern5542rule5542pattern5543rule5543pattern5544rule5544pattern5545rule5545pattern5546rule5546pattern5547rule5547pattern5548rule5548pattern5549rule5549pattern5550rule5550pattern5551rule5551pattern5552rule5552pattern5553rule5553pattern5554rule5554pattern5555rule5555pattern5556rule5556pattern5557rule5557pattern5558rule5558pattern5559rule5559pattern5560rule5560pattern5561rule5561pattern5562rule5562pattern5563rule5563pattern5564rule5564pattern5565rule5565pattern5566rule5566pattern5567rule5567pattern5568rule5568pattern5569rule5569pattern5570rule5570pattern5571rule5571pattern5572rule5572pattern5573rule5573pattern5574rule5574pattern5575rule5575pattern5576rule5576pattern5577rule5577pattern5578rule5578pattern5579rule5579pattern5580rule5580pattern5581rule5581pattern5582rule5582pattern5583rule5583pattern5584rule5584pattern5585rule5585pattern5586rule5586pattern5587rule5587pattern5588rule5588pattern5589rule5589pattern5590rule5590pattern5591rule5591pattern5592rule5592pattern5593rule5593pattern5594rule5594pattern5595rule5595pattern5596rule5596pattern5597rule5597pattern5598rule5598pattern5599rule5599pattern5600rule5600pattern5601rule5601pattern5602rule5602pattern5603rule5603pattern5604rule5604pattern5605rule5605pattern5606rule5606pattern5607rule5607pattern5608rule5608pattern5609rule5609pattern5610rule5610pattern5611rule5611pattern5612rule5612pattern5613rule5613pattern5614rule5614pattern5615rule5615pattern5616rule5616pattern5617rule5617pattern5618rule5618pattern5619rule5619pattern5620rule5620pattern5621rule5621pattern5622rule5622pattern5623rule5623pattern5624rule5624pattern5625rule5625pattern5626rule5626pattern5627rule5627pattern5628rule5628pattern5629rule5629pattern5630rule5630pattern5631rule5631pattern5632rule5632pattern5633rule5633pattern5634rule5634pattern5635rule5635pattern5636rule5636pattern5637rule5637pattern5638rule5638pattern5639rule5639pattern5640rule5640pattern5641rule5641pattern5642rule5642pattern5643rule5643pattern5644rule5644pattern5645rule5645r  r  r  inverse_trig   s	    v T
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  r  r  r  r*       r*  c              
   C   N   t td||  tt|| t| | ||   ||| |t||   |S Nr  r  r  r+   r   r  r	  rv
  r  r  r  r+       Nr+  c              
   C   r
  r
  r  r  r+   r   r  r  rv
  r  r  r  r,    r
  r,  c                 C   s.   t t| ||  | t| ||t|| S N)r+   r   r  r	  rv
  r  r  r  r-       .r-  c                 C   s0   t t| ||  | t| ||t||  S r
  )r+   r   r  r  rv
  r  r  r  r.       0r.  c              	   C   s   t || | ||td   t|| |td  | |t||   |td   t|td  |td  td  || t|| |td  | |t||   |  ||td   | S Nr  r   r  r{
  r  r  r  r  r  r  rw
  r  r  r  r/       r/  c              	   C   s   t || | ||td   t|| |td  | |t||   |td   t|td  |td  td  ||t|| |td  | |t||   |  ||td   | S r
  r}
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  r  r  r  r0       r0  c              	   C   s   t || | |td  t||td  | |t||   |td   t|td  |td  td  || t||td  | |t||   |  |td  | S r
  r{
  r  r  r  r  r  rw
  r  r  r  r1       r1  c              	   C   s   t || | |td  t||td  | |t||   |td   t|td  |td  td  ||t||td  | |t||   |  |td  | S r
  r}
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  r  r  r  r2       r2  c                 C   s   t || td  ||td   ttt| ||  |td  ||td t|td   t||td   |||t|| | t|| | |t||   |td   t|td  |td  td  || |td   | S Nr   r  r  )	r  r  r+   r   rd  r  r	  r  r  r
  r  r  r  r3       r3  c                 C   s   t || td  ||td   ttt| ||  |td  ||td t|td   t||td   |||t|| | t|| | |t||   |td   t|td  |td  td  || |td   | S r
  )	r  r  r+   r   rd  r  r  r  r  r
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  r4  c              
   C   sb  t ||| |td   t||td  | |t||   |td   t|td  |td  td  || t ||td  ||td   t||td  | |t||   |td   t|td  |td  td  || t|| | |t||   |td   t|td  |td  td  || |td   | S r
  r{
  r
  r  r  r  r5    s   d r5  c              
   C   s`  t ||| |td   t||td  | |t||   |td   t|td  |td  td  ||t ||td  ||td   t||td  | |t||   |td   t|td  |td  td  || t|| | |t||   |td   t|td  |td  td  || |td   | S r
  r}
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  r  r  r  r6    s   b r6  c                 C   sP   t || td  tt| ||  | t||  t| ||t|| |S Nr   r  r  r+   r   r  r  r	  r
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  r  r  r+   r   r  r  r  r
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  r
  r   r  r
  r  r  r  r:    r
  r:  c                 C   s.   t t| |t||   || t|  |S r
  )r  r  r	  r  r  r  r  r  r  rw
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  r<  c                 C   s0   t t| |t||   || t|  | S r
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  r=  c                 C   sB   t | |t||   |td  || t| |td   |S r
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  r  r  r  r>  !     Br>  c                 C   sD   t | |t||   |td  || t| |td   | S r
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  r  r  r  r?  %     Dr?  c              	   C      t t|td  |td  td t|||td    t| |t||   | t|td  |td  td  ||S Nr  r  r  r  r  r   r	  r
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  r
  r  r  r  r   r  r
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   C   ~   t |||td   | |}t|| tt|t|td  |td  td  ||| t| |t||   || S r
  r  r  r  r   r-  r  r	  r  r  r  r  r  r  rw
  r  r  r  r  rB  1     `rB  c              
   C   |   t |||td   | |}t|| tt|t|td  |td  td  |||t| |t||   || S r
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   C   sP  t t|||td   tdt|td  |td  td   t| |t||   | t|td  |td  td  ||t || | t|||td    tdt|td  |td  td   t|| |t||   |td   || t|| |t||   |  t|||td    td | S Nr  r  r   r  r  r  r   r	  r  r
  r  r  r  rD  ;     R rD  c              
   C   sP  t t|||td   tdt|td  |td  td   t| |t||   | t|td  |td  td  ||t || | t|||td    tdt|td  |td  td   t|| |t||   |td   || t|| |t||   |  t|||td    td | S r
  r  r  r  r   r  r  r
  r  r  r  rE  ?  r
  rE  c              
   C   s  t td| | td| td  t| |t||   | |||td   |td   ||t || |t|  | |||td   t|  |td  |td  td t|   td| td  t|| |t||   |td   |td  |td  td |tdd    || t|| |t||   |  |||td   |  td| td  | S r
  r  r  r   r	  r%   r&   r  r  r  r  r  r  r  r  rw
  r  r  r  rF  C      rF  c              
   C   s  t td| | td| td  t| |t||   | |||td   |td   ||t || |t|  | |||td   t|  |td  |td  td t|   td| td  t|| |t||   |td   |td  |td  td |tdd    || t|| |t||   |  |||td   |  td| td  | S r
  r  r  r   r  r%   r&   r  r
  r  r  r  rG  G  r
  rG  c              
   C   s   t || | t| t|| |t||   |td   |||td    || t|| |t||   |  |t|||td     | S Nr   r  )r  r  r   r	  r  r  r
  r  r  r  rH  K     rH  c              
   C   s   t || | t| t|| |t||   |td   |||td    ||t|| |t||   |  |t|||td     | S r
  )r  r  r   r  r  r  r
  r  r  r  rI  O     rI  c              
   C   s   t || | t|td  |td  td  |t|||td     t|| |t||   |td   |td  |td  td  || t|| |t||   |  |t|||td     | S r
  r
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  r  r  r  rJ  S  s   rJ  c              
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   	   C   F   t t| |t||	   | ||	 | |||	td   |  |	|	S r
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  || || |td   t|
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  r  r  r  r  r  r  r  r  r  r  r  rw
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  r  r  r  r  r  	  r  r  c                 C   sB   t t| ||  | t| || |t|   ||t|| S r
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  r{
  r
  r  r  r  r  	     r  c              	   C   s   t || | ||td   t| |t||   |td  |||  |td   t|td  |td  td  ||t| |t||   | |||  |td   ||td   | S r
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  r  r  r  r  	  r~
  r  c                 C   4   t t| |t||   | |||  |  ||S r
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  r  r  r  r  	     4r  c                 C   r  r
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  r  r  r  r  	     \r  c              	   C   s^   t || td  tt| ||  | || |t|  |  t| ||t|| | S r
  )r  r  r+   r   r  r  r  r
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   C   sj   t | |}t|| tt|t|td  |td  td  ||| t||t||   || S r
  r  r  r   r-  r  r  r	  r+  r  r  r  rw
  r  r  r  r  r  	  s   
`r  c              
   C   sh   t | |}t|| tt|t|td  |td  td  |||t||t||   || S r
  r  r  r   r-  r  r  r  r  r  r  r  r  	  s   
^r  c                 C   (   t t| ||t||   |  ||S r
  r  r+  r  r  r  r  rw
  r  r  r  r  	     (r  c                 C   r  r
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  r  r  r  r  r  	  r  r  c           	   
   C   sz   t | |||  |  |}t|| tt|t|td  |td  td  ||| t||t||   || S r
  r  	r+  r  r  r  r  r  r  rw
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   C   sx   t | |||  |  |}t|| tt|t|td  |td  td  |||t||t||   || S r
  r  r  r  r  r  r  	  s   ^r  c              
   C   s   t |||
  | |||
  |	  |
}t|| | tt|| |t||
   |td   t|td  |
td  td  |
|
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   | ||
 S ru
  )r  r  r   r-  r	  r  r  r  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  r  	  s   &r  c              
   C   s   t |||
  | |||
  |	  |
}t|| | tt|| |t||
   |td   t|td  |
td  td  |
|
|
t| |t||
   | ||
 S ru
  )r  r  r   r-  r  r  r  r  r  r  r  r  	  s   &r  c              
   C   s   t |||
  ||
td   |	 |||
  td  |
}t|| | tt|| |t||
   |td   t|td  |
td  td  |
|
|
 t| |t||
   | ||
 S r
  )r  r  r  r   r-  r	  r  r  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  r  	  s   :r  c              
   C   s   t |||
  ||
td   |	 |||
  td  |
}t|| | tt|| |t||
   |td   t|td  |
td  td  |
|
|
t| |t||
   | ||
 S r
  )r  r  r  r   r-  r  r  r  r  r  r  r  	  s   :r  c	           	      C   8   t t| ||t||   |  |||  |  ||S r
  r  	r+  r  r  r  r  r  r  r  rw
  r  r  r  r  	     8r  c	           	      C   r  r
  r
  r  r  r  r  r  
  r  r  c
              
   C   s   t |||	td   | |||	  |  |	}
t|| tttdt|td  |	td  td  |
|	|	|	 t| |t||	   |
|	 S r
  )r  r  r  r   r  r	  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  r  
  s   .fr  c
              
   C   s   t |||	td   | |||	  |  |	}
t|| tttdt|td  |	td  td  |
|	|	|	t| |t||	   |
|	 S r
  )r  r  r  r   r  r  r  r  r  r  r  

  s   .dr  c                 C   J   t t| |t||
   | |||
td   |	  |||
  | |
|
S r
  r
  r  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  
     Jr  c                 C   r  r
  r
  r  r  r  r  r  
  r  r  c
           
   	   C   s  t td|| t| |td   t| |t||	   |td  |||	  |td   || | td| | |	  || |	td  |td    |	|	 t| |t||	   |td  |||	td    |||	  |  || t| |td   |	 S r
  r
  
r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  
      r  c
           
   	   C   s  t td|| t| |td   t| |t||	   |td  |||	  |td   || | td| | |	  || |	td  |td    |	|	t| |t||	   |td  |||	td    |||	  |  || t| |td   |	 S r
  r
  r  r  r  r  r  
  s    r  c              	   C   n   t t| |t||
   | t|||
td    |||
td   |	tdd   |||
  |  |
|
S Nr  r   r
  r  r  r  r  r  
  r
  r  c              	   C   r  r   r   r  r  r  r  r  #
  r
  r  c                 C   s^  t td|| t| |td   tt| |t||
   |td  |||
  |td   |||
td   |	tdd   || | || |
 td|	 td   || |
td  |td|	  td    |
|
|
 t| |t||
   |td  |||
td   |	tdd    |||
  |  || t| |td   |
 S r
  )r  r  r  r   r   r	  r  r  r  r  r  r  '
  s   ` r  c                 C   s\  t td|| t| |td   tt| |t||
   |td  |||
  |td   |||
td   |	tdd   || | || |
 td|	 td   || |
td  |td|	  td    |
|
|
t| |t||
   |td  |||
td   |	tdd    |||
  |  || t| |td   |
 S r
  )r  r  r  r   r   r  r  r  r  r  r  r  +
  r
  r  c
           
      C   s   t || || t| |td   t| |t||	   |td  |||	  |td   |	|	 t| |t||	   |td  |||	  |  || t| |td   |	 S r
  r
  r  r  r  r  r  /
     r  c
           
      C   s   t || || t| |td   t| |t||	   |td  |||	  |td   |	|	t| |t||	   |td  |||	  |  || t| |td   |	 S r
  r
  r  r  r  r  r  3
     r  c
           
   	   C   s\   t || td  t| tt| ||	  | || |t|	  |  |	|	t||	 |	S r
  r
  r  r  r  r  r  7
  r  r  c
           
   	   C   s^   t || td  t| tt| ||	  | || |t|	  |  |	|	t||	 |	 S r
  r
  r  r  r  r  r  ;
  r  r  c              	   C   n   t t| |t||
   | t|||
td    |||
td   |	tdd   |||
  |  |
|
S r
  r
  r  r  r  r  r  ?
  r
  r  c              	   C   r#  r
  r   r  r  r  r  r  C
  r
  r  c                 C      t |t|	 |||
td   t|	  |td  |
td  td t|	   t| |t||
   | |||
  |  |td  |
td  td |	  |
|
S r
  r
  r  r  r  r  r  G
     r  c                 C   r$  r
  r
  r  r  r  r  r  K
  r%  r  c                 C   s   t || || t| |	td   t| |t||
   |	td  |||
   |
|
 t| |t||
   |	td  t||||
  |   || t| |	td   |
 S r
  )r  r  r  r   r	  r  r  r  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  O
     r  c                 C   s   t || || t| |	td   t| |t||
   |	td  |||
   |
|
t| |t||
   |	td  t||||
  |   || t| |	td   |
 S r
  )r  r  r  r   r  r  r  r&  r  r  r  r  S
  r
  r  c              	   C      t |t|
 |||td   t|
  |td  |td  td t|
   t| |t||   |	 |td  |td  td |
  t||||  |   ||S r
  )r  r%   r  r&   r   r	  r  r  r  r  r  r  W
  r
  r  c              	   C   r(  r
  )r  r%   r  r&   r   r  r  r  r  r  r  r  [
  r
  r  c	           
   
   C   s   t |||  | |||  |  |}	t|| tttdt|td  |td  td  |	||| t| |t||   |	| S rz
  )r  r  r   r  r  r	  
r  r  r  r  r  r  r  r  rw
  r  r  r  r  r  _
  s   &fr  c	           
   
   C   s   t |||  | |||  |  |}	t|| tttdt|td  |td  td  |	|||t| |t||   |	| S rz
  )r  r  r   r  r  r  r)  r  r  r  r  d
  s   &dr  c
           
      C   D   t t| |t||	   | |||	  |  |||	  |  |	|	S r
  r  r  r  r  r  r  i
  r
  r  c
           
      C   r*  r
  r
  r  r  r  r  r  m
  r
  r  c                 C   2   t |ttttfrdS t||}t||rdS dS NFT
isinstanceintr  floatr  r  r   r  r  r  r  rw
  vr  r  r  r  q
     

r  c              
   C   sj   t ||}t|| tt|t|td  |td  td  ||| t| |t||   || S r
  r  r1  r  r  r  r  z
  s   
`r  c                 C   r+  r,  r-  r1  r  r  r  r  
  r3  r  c              
   C   sh   t ||}t|| tt|t|td  |td  td  |||t| |t||   || S r
  r  r1  r  r  r  r  
  s   
^r  c	           
      C   `   t |ttttfrdS t| ||t||   |  |||td   |  |}	t|	r.dS dS NFr  T	r.  r/  r  r0  r  r   r	  r  r)   
r+  r  r  r  r  r  r  r  rw
  r  r  r  r  r  
     :r  c	           
      C   D   t | ||t||   |  |||td   |  |}	t|	|S r
  r   r	  r  r   r7  r  r  r  r  
     :
r  c	           
      C   r4  r5  	r.  r/  r  r0  r  r   r  r  r)   r7  r  r  r  r  
  r8  r  c	           
      C   r9  r
  r   r  r  r   r7  r  r  r  r  
  r;  r  c              	   C   l   t |ttttfrdS t| ||t||   |	  |||||td   |
   |  |}t|r4dS dS r5  r6  r+  r  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  r  
     Fr  c              	   C   P   t | ||t||   |	  |||||td   |
   |  |}t||S r
  r:  r?  r  r  r  r  
     F
r  c              	   C   r>  r5  r<  r?  r  r  r  r  
  r@  r  c              	   C   rA  r
  r=  r?  r  r  r  r  
  rB  r  c                 C   >   t |ttttfrdS tt|| | | |}t|rdS dS r,  )r.  r/  r  r0  r  r   r	  r)   r2  r  r  rw
  r  r  r  r  r  
     r  c                 C   "   t t|| | | |}t||S r
  )r   r	  r   rD  r  r  r  r  
     
r  c                 C   rC  r,  )r.  r/  r  r0  r  r   r  r)   rD  r  r  r  r  
  rE  r  c                 C   rF  r
  )r   r  r   rD  r  r  r  r  
  rG  r  c                 C   r  r
  r  r2  r  r  r  r  rw
  r  r  r  r  
  r  r  c                 C   r  r
  r
  rH  r  r  r  r  
  r  r  c                 C   V   t |ttttfrdS t|||td   | t|| |  | |}t|r)dS dS r5  )	r.  r/  r  r0  r  r   r  r	  r)   r2  r  r  r  r  r  rw
  r  r  r  r  r  
     0r  c                 C   :   t |||td   | t|| |  | |}t||S r
  )r   r  r	  r   rJ  r  r  r  r  
     0
r  c                 C   rI  r5  )	r.  r/  r  r0  r  r   r  r  r)   rJ  r  r  r  r     rK  r  c                 C   rL  r
  )r   r  r  r   rJ  r  r  r  r  	  rM  r  c	           	   	   C   >   t t|||td   | | ||t||   |  ||S r
  )r   r   r  r	  	r2  r  r  r  r  r  r  r  rw
  r  r  r  r    r
  r  c	           	   	   C   rN  r
  )r   r   r  r  rO  r  r  r  r    r
  r  c                 C   "   t || |t||   |  |S r
  r
  r  r  r  r  r  rw
  r  r  r  r       "r  c                 C   rP  r
  r
  rQ  r  r  r  r    rR  r  c                 C   :   t td| tt| |t|  | |||||  |S r
  r  r  r+   r   r	  r  r  r  r  r  rw
  r  r  r  r    r
  r  c                 C   rS  r
  r  r  r+   r   r  rU  r  r  r  r  #  r
  r  c	           	   	   C   `   t td| tt| |t|  | || | | | ||  |  |  |||||  |S r
  rT  r
  r  r  r  r  '     `r  c	           	   	   C   rW  r
  rV  r
  r  r  r  r  +  rX  r  c
           
   
   C   j   t td| tt||t|	  | ||	td  |td  ||td   |  |	|	|||	  |	S rz
  rT  
r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  /  r
  r  c
           
   
   C   rY  rz
  rV  rZ  r  r  r  r  3  r
  r  c              
   C      t td| tt||t|  |
 ||td  |td  ||td   |  || | | | ||  |  |	  |||||  |S rz
  rT  r  r  r  r  r  r  r  r  r  r  r  r  rw
  r  r  r  r  7  r
  r  c              
   C   r[  rz
  rV  r\  r  r  r  r  ;  r
  r  c                 C   s  t |t| |t|||td      |t tt| | t| td|   t| td|    tt|t|  t| |t|||td       t|| | tt|||td   td  tt|||td   td    | t tt| |t| td|   t| td|    tt|t|  t| |t|||td       t|| | tt|||td   td  tt|||td   td    | S r
  )	r  r  r	  r  Pir  r  r  r  r  r  r  r  rw
  r  r  r  r  ?  r
  r  c                 C   s  t td t| |t||td  td    tt||td  td td td  ||  |t tdtt tttdt|  t| |t||td  td     t| td|   tt||td  td td  || ttd|   | t tdtt tttdt|  t| |t||td  td     tt||td  td td  t| td|   || ttd|   | S r
  )	r  r  r  r  r  r]  r  r  r  r  r  r  rw
  r  r  r  r  C  s    r  c                 C   s  t tdt| |t||td  td    tt||td  td td td  ||  |t tdtt tttdt|  t| |t||td  td     t| td|   tt||td  td td  || ttd|   | t tdtt tttdt|  t| |t||td  td     t| td|   tt||td  td td  || ttd|   | S r
  )	r  r  r  r  r  r]  r  r  r  r_  r  r  r  r  G  s    r  c                 C   s  t td|td  | |td  t| |t|||td     |td  || t|| |t|||td     |  | ttd| | | |t|||td     |td   ttd | | |td  |td |td    ||  | S N   r  r   r"  r  r  r   r	  r  r  rU  r  r  r  r  K  r  r  c                 C   s  t td|td  | |td  t| |t|||td     |td  || t|| |t|||td     |  | ttd| | | |t|||td     |td   ttd | | |td  |td |td    ||  | S r`  r  r  r   r  r  r  rU  r  r  r  r  O  r  r  c                 C   s  t ||t| td|   t| td|    t|| |t|||td      td|   td| | tt|||td   td  tt|||td   td    | t ||t| td|   t| td|    t|| |t|||td      td|   td| | tt|||td   td  tt|||td   td    | S r
  )r  r  r  r  r  r	  r  r^  r  r  r  r  S  s    r  c                 C   s   t ttd| t| |t||td  td   td|   t| td|   td| t| |td    |t ttd| t| |t||td  td   td|   t| td|   td| t| |td    | S r
  )r  r  r  r  r  r  r  r  r_  r  r  r  r  W  s    r  c                 C   s   t ttd| t| |t||td  td   td|   t| td|   td| t||td    |t ttd| t| |t||td  td   td|   t| td|   td| t||td    | S r   )r  r  r  r  r  r  r  r  r_  r  r  r  r  [  s   r  c                 C   s  t tt| | t| td|   t| td|    tt| |t|||td     ttt||    t|| | tt|||td   td  tt|||td   td    | t tt| |t| td|   t| td|    tt| |t|||td     ttt||    t|| | tt|||td   td  tt|||td   td    | S r
  )	r  r  r]  r  r  r  r  r	  r  r^  r  r  r  r  _  s    r  c                 C   s>  t td tt|  tttdt|  t| |t||td  td     tt||td  td td  t| td|   ||  |t tdtt|  tttdt|  t| |t||td  td     t| td|   tt||td  td td  ||  | S r
  	r  r  r  r]  r  r  r  r  r  r_  r  r  r  r   c  s   @ r   c                 C   s<  t tdtt|  tttdt|  t| |t||td  td     t| td|   tt||td  td td  ||  |t tdtt|  tttdt|  t| |t||td  td     t| td|   tt||td  td td  ||  | S r
  rd  r_  r  r  r  r  g  s   > r  c                 C   s$  t ttd | | |td  |td |td   || | t| |t|||td       | t tt| || tdd   | t| td|   t| td|    tt|t|  t| |t|||td       | tt|||td   td  tt|||td   td   | t tt| || tdd   |t| td|   t| td|    tt|t|  t| |t|||td       | tt|||td   td  tt|||td   td   | S )Nr  ra  r  )	r  r  r  r	  r]  r  r  r  r  r^  r  r  r  r  k  s    ( r  c                 C   s  t t|td  |td  td| |td   || | t| |t||td  td     |t tdtt td| tdd   tttdt|  t| |t||td  td     t| td|   tt||td  td td  ||  | t tdtt td| tdd   tttdt|  t| |t||td  td     tt||td  td td  t| td|   ||  | S )Nr  ra  r  r  )	r  r  r  r  r]  r  r  r  r  r_  r  r  r  r  o  r
  r  c                 C   s  t t|td  |td  td| |td   || | t| |t||td  td     |t tdtt td| tdd   tttdt|  t| |t||td  td     t| td|   tt||td  td td  ||  | t tdtt td| tdd   tttdt|  t| |t||td  td     t| td|   tt||td  td td  ||  | S )Nr  ra  r   r  r  )	r  r  r  r  r]  r  r  r  r  r_  r  r  r  r  s  r
  r  c                 C   s  t || t| td|   t| td|    t|| |t|||td      td|   td|td  | tt|||td   td  tt|||td   td    |t ||t| td|   t| td|    t|| |t|||td      td|   td|td  | tt|||td   td  tt|||td   td    | t ttd | | |td  |td |td   td| | | | |t|||td       | S )Nr  ra  )r  r  r  r  r  r	  r  r  r^  r  r  r  r  w  s     r  c                 C   s  t t|td  |td  td| |td   td| | | | |t||td  td     |t ttd| t| |t||td  td   td|   t| td|   td|td  t| |td    | t ttd| t| |t||td  td   td|   t| td|   td|td  t| |td    | S )Nr  ra  r  )r  r  r  r  r  r  r  r  r_  r  r  r  r  {  s    r  c                 C   s  t t|td  |td  td| |td   td| | | | |t||td  td     |t ttd| t| |t||td  td   td|   t| td|   td|td  t||td    | t ttd| t| |t||td  td   td|   t| td|   td|td  t||td    | S )Nr  ra  r   )r  r  r  r  r  r  r  r  r_  r  r  r  r    s    r  c                 C   sZ  t tdtd|td  |td  |td   t| |t|||td     |td  || t|| |t|||td     |td   td|td  |td  |td   | t| |t|||td     |td  ttd | | |td  |td |td    td| | | |td   | S Nr  ra  r  rb  rU  r  r  r  r       \ r  c                 C   sZ  t tdtd|td  |td  |td   t| |t|||td     |td  || t|| |t|||td     |td   td|td  |td  |td   | t| |t|||td     |td  ttd | | |td  |td |td    td| | | |td   | S re  rc  rU  r  r  r  r	    rf  r	  c              	   C   s:   t td| tt|| t| ||t| ||  |S r
  r
  r  r  r  rw
  r  r  r  r
    r
  r
  c              	   C   s<   t td| tt|| t| ||t| ||  | S r
  r
  rg  r  r  r  r       <r  c                 C   *   t |t| | |||  |  |  |S r
  r   r  r  r  r  r  r  r  rw
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  r   r  rk  r  r  r  r    r
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   C   l   t t|  |td  | |  ttt|| ttd|td   ||t| |td  td |S r
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  r  r  r  r+   r   r  ro  r  r  r  r    r
  r  c                 C   sd   t td| tt||||   t|t||  | t||   t| ||t| ||  |S r
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  r  c                 C   s  t |t| td |td  td|  | t|||td     |td |   t|td  | td |td  td|  | t|||td     |td |    t|td|  t|||td    ||   t|||td   t| td |td  td|  | t|||td     |td |    ||t|t| |td  |t|||td      | S r
  )r  r  r  r   r  r  r^  r  r  r  r    s    r  c                 C   sF   t t|t| | ttd| td   || t|t|  | S rz
  )r   r-  r  r  r  r  r	  r  rw
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  r  c                 C   sD   t t|t| | ttd| td   ||t|t|  | S rz
  )r   r-  r  r  r  r  r  rt  r  r  r  r    r
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   C   s   t |||td   tt|||  |td  t|| ttd|td   ||| t| |t|  |||  |td   ||td   | S rz
  )r  r  r   r-  r  r  r  r	  r  r  r  r  r  r  rw
  r  r  r  r       r  c              
   C   s   t |||td   tt|||  |td  t|| ttd|td   |||t| |t|  |||  |td   ||td   | S rz
  )r  r  r   r-  r  r  r  r  ru  r  r  r  r    r  r  c                 C   r+  r,  r-  r  r  r  r2  rw
  wr  r  r  r    r3  r  c              
   C   s^   t ||}t|tt|t|| ttd|td   ||| t| |t|  || S rz
  )r  r  r   r-  r  r  r  r	  rw  r  r  r  r    s   
Tr  c                 C   r+  r,  r-  rw  r  r  r  r    r3  r  c              
   C   s\   t ||}t|tt|t|| ttd|td   |||t| |t|  || S rz
  )r  r  r   r-  r  r  r  r  rw  r  r  r  r    s   
Rr  c              	   C   s~   t || | t|| |t||   |td   |td |td  td  || t|| |t||   |  | S ru
  )r  r   r>   r  r  rv
  r  r  r  r       ~r  c              	   C   s|   t || | t|| |t||   |td   |td |td  td  ||t|| |t||   |  | S ru
  )r  r   r
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  r  r  r  r  r  r  )  r  r  c              
   C   r  rz
  r  r  r  r  r  r  -  r
  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    || tt| |t||   |  ttdttd|  td| |  | S r
  r  r  r  r   r>   r  r   r  r  r  r  r  r  1  r!  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    ||tt| |t||   |  ttdttd|  td| |  | S r
  r  r  r  r   r
  r  r   r  r  r  r  r  r  5  r"  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    ||tt| |t||   |  ttdttd|  td| |  | S r
  r  r  r  r  r  r  9  r"  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    || tt| |t||   |  ttdttd|  td| |  | S r
  r  r  r  r  r  r  =  r!  r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    ||tt| |t||   |  t|td | td| |  | S r
  r  r  r  r   r>   r  r  	r  r  r  r  r  r  r  r  rw
  r  r  r  r  A  r  r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    || tt| |t||   |  t|td | td| |  | S r
  r  r  r  r   r
  r  r  r  r  r  r  r  E     r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    || tt| |t||   |  t|td | td| |  | S r
  r  r  r  r  r  r  I  r  r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    ||tt| |t||   |  t|td | td| |  | S r
  r  r  r  r  r  r  M  r  r  c                 C   sn   t t| |t||   t| |t||    || | td|  |t||   |t||     |S r
  )r  r  r>   r
  r  r
  r  r  r  r  Q  r
  r  c              	   C   s   t ||td  t| |t||   |td  | |t||   |td   |||td    ||t| |t||   | | |t||   |td   || | |td   | S r
  r  r  r   r>   r
  r  r
  r  r  r  r  U  r
  r  c              	   C   s   t ||td  t| |t||   |td  | |t||   |td   |||td    ||t| |t||   |td  | |t||   |  || | |td   | S r
  r  r
  r  r  r  r  Y  r
  r  c              	   C   s~   t ttd ttt |  | td ||||    ||t ttd ttt|  | td ||||    || S r
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  r  r  r  r  ]  ry  r  c              	   C   s|   t ttd tttdt| |   ||||    ||t ttd tttdt| |   ||||    || S r
  r  r  r  r  r  r  a  rz  r  c                 C   s   t || t|||t|||td      |td |td  td  || t td| | t|td | |t||    |||td    || t|| |t||    ||t|||td      | S r
  )r  r   r  r  r>   r  r  r  r  r  r  r  r  rw
  r  r  r  r  e     r  c                 C   s   t || t|||t|||td      |td |td  td  ||t td| | t|td | |t||    |||td    || t|| |t||    ||t|||td      | S r
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  r  r  r  r  r  r  i  s   r  c	           	      C   s$  t || |td  t||td  ||t|||td      |td |td  td  || t td| | |td  t||td  | |t||    |||td    || t||td  | |t||    ||t|||td      |td  | S rz
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  r  r  r  r  m  r  r  c	           	      C   s"  t || |td  t||td  ||t|||td      |td |td  td  ||t td| | |td  t||td  | |t||    |||td    || t||td  | |t||    ||t|||td      |td  | S rz
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  r  r  r  r  r  r  q  r  r  c	           
   
   C   s   t || ||t|||td      |}	t|| tt|	|td |td  td  ||| t| |t||   |	| S r
  )r  r  r  r  r   r   r>   r)  r  r  r  r  u  s   .Zr  c	           
   
   C   s   t || ||t|||td      |}	t|| tt|	|td |td  td  |||t| |t||   |	| S r
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  r)  r  r  r  r  z  s   .Xr  c	           
   
   C      t || | |t||    |}	ttd| | tt|	| |||td    ||| t||t|||td     |	| S r
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   
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  r  r  r   r   r  r)  r  r  r  r    r  r  c                 C   s:  t || t| |t||   ||t|||td      || t || | t|td | |t||    |td |td  td  || t||td  | |t||   td  td | t| |t||   td ||t|||td      |||td    td|  | S r
  )r  r   r>   r  r  r  r  r  r  r  r    s   < r  c                 C   s8  t || t| |t||   ||t|||td      ||t || | t|td | |t||    |td |td  td  || t||td  | |t||   td  td | t| |t||   td ||t|||td      |||td    td|  | S r
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  r  r  r  r  r  r  r  r    s   : r  c                 C   s   t t |  | td t| td tdd   t|  | td t | td tdd    t| td |td  td  |S rz
  r   r  r  r  r  r  rw
  r  r  r  r    r  r  c                 C   s   t || t |  | td t| td tdd    t|  | td t | td tdd    t| td |td  td  |S rz
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  r  r  r  r    r
  r  c                 C   sR   t t |  | td t| td  t|  | td t | td   |S rz
  r   r  r  r  r  r  r  r    r
  r  c                 C   sZ   t || t |  | td t| td   t|  | td t | td   |S rz
  r  r  r  r  r  r       Zr  c                 C   sz   t || t|td|| |  |  t |  | td t| td   t|  | td t | td   ||S rz
  r  r   r  r  r  r  r  r  r  r  rw
  r  r  r  r       zr  c                 C   sf   t ||||  |  t |  | td t| td   t|  | td t | td   |S rz
  r  r  r  r  r  r    rs  r  c              	   C   sL   t || t|||   || | td |  t|t| |   ||S r
  r  r   r  r  r>   r  r  r  r  r    s   Lr  c                 C   s   t td|td  ||  t|tdt| |   t | td   tdt| |   t| td   td|||   |  ||S ru
  r  r  r   r  r  r  r  r  r    r  r  c                 C   sf   t ||||  |  t |  | td t| td   t|  | td t | td   |S rz
  r  r  r  r  r  r    rs  r  c              	   C   sv   t || |||  |  || | td |   t|||   || | td |  t|t| |   ||S r
  r  r  r   r  r>   r  r  r  r  r    r  r  c              	   C   sZ   t | | | t|t| |   | | t|||td    |td td   |S r
  )r  r  r>   r  r  r  r  r  r  r    r  r  c              	   C   s  t td|td  td| td  ||td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  td |  | |td  |  t|t| |   | | |td td|td td     | S Nr  r  r  ra  r  r  r   r  r>   r  r  r  r  r  r  rw
  r  r  r  r    s     r  c                 C   s&   t t|t| |  | | |  |S r
  )r  r  r>   r  r  r  r  r       &r  c                 C   sf   t || t| td |td  td t | td |  t |  | td t|   ||S r
  r  r  r  r  r  r    rs  r  c                 C   sf   t || tt |  | td t| td |  t|  | td t | td |   ||S rz
  r  r   r  r  r  r  r  r  r    rs  r  c                 C   sf   t |t| td  t|||td   t | td |  t |  | td t|   ||S r
  r  r  r  r   r  r  r  r  r    rs  r  c                 C   sf   t |t | td  t|||td   t| td |  t|  | td t |   ||S r
  r  r  r  r  r  r    rs  r  c              	   C   s   t |t| |||td   t|  | td |td  td t|   t| td |td  td | t|t| |   ||S r
  r  r%   r  r&   r   r  r>   r  r  r  r  r    r
  r  c              	   C   sb   t |  | | td t|t| |   |t|||td    |td td   | S rz
  )r  r  r  r>   r  r  r  r  r  r       br  c              	   C   s   t | | | td| |td   t|||td   | t|t| |   || t|||td   |td  t|t| |   td| |td   | S r
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  )r  r  r  r>   r  r  r  r  r    r  r  c              	   C   s  t |td td|  td ||td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  td |  | |td  |  t|t| |   | | |td td|td td     | S )Nr  r"  ra  r  r  r  r  r  r  r    s    r  c                 C   sn   t || t|| | td |td  td t | td |   t |  | td t|   ||S r
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  r  c                 C   s   t |t| |||td   t|  t |  | td t|   t|  | td t|   t|t |  | td t| td |   t|  | td t | td |   ||S r
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  )r  r   r  r  r  r>   r  r  r  r  r    r  r  c              	   C   s   t |td|  |||td   |  t |  | td |   t|  | td |   t||td |   t |  | td |  t|  | td |  t|t| |   ||S r
  r  r  r  r   r  r>   r  r  r  r  r    r
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  r  rv
  r  r  r  r    r  r  c              
   C   s*  t tdt|   || td   || td   | tt|td t |  td|td t |   | td   t |  | td |td t |  t|  | td   |  ||t | | ||   td t| td  t| | ||   td t | td   |S )Nra  r   r  r  r"  r  r  r  r+   r   r
  r  r  r  r    s   , r  c                 C   s   t |||  | t |  | t| | |  td t| td   t|  | t| | |  td t | td   |S rz
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  )r   r  r
  rQ  r  r  r  r  -  r
  r  c              	   C   s<   t tdt| td  t|t| t| |   ||S r
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   C   s   t ttdt| |   t| td tdd   tdt| |   t | td tdd    |td ttd|td | td     ||td|  S rz
  r+   r   r  r  r  r  r  r  r  r  5  r  r  c              	   C   s   t t|| td  tdt| |   t| td tdd    tdt| |   t | td tdd    ttd|td | td    ||td|  S Nr"  r  r  r  r  r  r  r  r  9  r
  r  c                 C   sn   t ttdt| |   t| td  tdt| |   t | td   |td  ||td|  S rz
  r+   r   r  r  r  r  r  r  r  =  r
  r  c                 C   l   t t|| td  tdt| |   |td   tdt| |   | td   ||td|  S r  r  r  r  r  r  r  A  r
  r  c                 C   s   t || td| |  tt|| td  tdt| |   t| td tdd    tdt| |   t | td tdd    ttd|td | td    ||td| | S r  )r  r  r+   r   r  r  r  r  r  r  r  E  r  r  c                 C   r  r  r  r  r  r  r  r  I  r
  r  c              	   C   sJ   t || t|||  |||  td |  t|t| |   ||S r
  r  r   r  r  r
  r  r  r  r  r  M  r  r  c              	   C   sv   t ||  |||  |  |||  td |   t|||  |||  td |  t|t| |   ||S r
  r  r  r   r  r
  r  r  r  r  r  Q  r  r  c              	   C   s   t || tttdt| |   t| td  tdt| |   t | td   td|| |  |  |td  ||td| | S rz
  r  r+   r   r  r  r  r  r  r  r  U  r
  r  c              	   C   s   t || tt|| td  tdt| |   t| td   tdt| |   t | td   td|| |  |  ||td| | S r  r  r  r  r  r  r  Y  r  r  c              	   C   s`   t td|||   |  |||  |  ttd|||   | t|t| |   ||S r
  r  r  r  r  r  r  ]  rX  r  c              	   C   s   t || ||  td| |  tt|| td  tdt| |   t| td   tdt| |   t | td   td|| |  |  ||td| | S r  r  r  r+   r   r  r  r  r  r  r  a  r
  r  c              	   C   sd   t td|||   |  |||  |  t|td|||   |  t|t| |   ||S r
  r  r  r  r  r  r  e  rr  r  c                 C   s(   t t|t| |  | | |  | S r
  )r  r  r
  r  r  r  r  r  i  r  r  c              	   C   s^   t |  | | t|t| |   | | t|||td    |td td   | S r
  )r  r  r
  r  r  r  r  r  r  r  m  r  r  c              	   C   s  t td|td  td| td  ||td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  td|  | |td  |  t|t| |   | | |td td|td td     | S r  r  r  r   r  r
  r  r  r  r  r  r   q  s    r   c              	   C   sl   t | | | td t|t| |   | td | t|||td    |td td   | S rz
  )r  r  r  r
  r  r  r  r  r  r  u  r
  r  c              	   C   s  t |td| td  | | |td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  |  | | td|  td  t|t| |   | td | |td td|td td     | S )Nr  r  ra  r  r
  r  r  r  r  r  y  s    r  c                 C   s   t |||td   |td  td|  | |td  |  t|t| |   | td | |td  |td td   |S )Nr  r  r  )r  r  r  r
  r  r  r  r  r  }  s   r  c              	   C   s(  t |td td|  td | td | |td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  td|  | |td  |  t|t| |   | td | |td td|td td     | S )Nr  r"  ra  r  r  r
  r  r  r  r  r    r
  r  c              	   C   s   t | | td  ||  tttdt| |td|  td  t||  t|td | td   ||t| | | S )Nr   r  r  r"  )r  r  r+   r   r  r  r  r
  r  r  r  r  r       r  c              
   C   sf   t || t||td|   tdtd| td |td    |  t|t| |   ||S r
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   C   s   t |td |  tdtd| td |td    |   |||td   |  t||td|   tdtd| td |td    |  t|t| |   ||S r
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  r  c              	   C   s   t || tttdt| |   t| td |  tdt| |   t | td |   |td  ||td| | S rz
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  r	  c              	   C   s   t || tt|| td  tdt| |   t| td |   tdt| |   t | td |   ||td| | S r  r  r  r  r  r  r
    r  r
  c              	   C   s   t || ||  td| |  tt|| td  tdt| |   t| td |   tdt| |   t | td |   ||td| | S r  r	  r  r  r  r  r       r  c              
   C   s   t tdtd| td |td    |  |||td   |  t|tdtd| td |td    |  t|t| |   ||S rz
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  r  c                 C   s   t t| | ||   t| td  tdt|| ||     t| td   t|  | t| | |  td t | td   tt|  | t| | |  td t | td  t|  | t| | |  td t| td   ||S r
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  r  r  r  r    s   r  c                 C   s(  t tdt|   || td   || td   | tt|td t |  td|td t |   | td   t|  | td |td t |  t |  | td   |  ||tdt|| ||     t| td  tdt|| ||     t | td   |S )Nra  r   r  r"  r  r  r
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  r  c                 C   s
  t t| | ||   t| td  tdt|| ||     t| td   t|  | t| | |  td t | td   t|||  | t|  | t| | |  td t | td   t|  | t| | |  td t| td   ||S r
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  )r  r  r  r   r  r  r  r  r       l r  c	           	   	   C   r   r
  r  r  r  r  r  r    r  r  c                 C   r  r
  )r   r  r>   rQ  r  r  r  r    r
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  r  r  r+   r   r>   rU  r  r  r  r    r
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  r  r  r+   r   r
  rU  r  r  r  r    r
  r  c                 C   "   t | |t|||    | |S r
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  r  r  r  r    rX  r  c	           	   	   C   rW  r
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  r  r  r  r    r  r  c	           	      C   r  r
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  r  r  r  r    r  r  c
           
   
   C   j   t td| tt||t|	  | ||	td  |td  ||td   |  |	|	|||	  |	S rz
  r  rZ  r  r  r  r    r
  r  c
           
   
   C   r  rz
  r  rZ  r  r  r  r    r
  r  c              
   C      t td| tt||t|  |
 ||td  |td  ||td   |  || | | | ||  |  |	  |||||  |S rz
  r  r\  r  r  r  r    r
  r  c              
   C   r  rz
  r  r\  r  r  r  r    r
  r  c              	   C   s   t ttd ttt |  t| |  td ||||    ||t ttd ttt|  t| |  td ||||    || S r
  r  rU  r  r  r  r     r  r   c              	   C   s   t ttd tt| ||  t | ||   ||||    ||t ttd tt| ||  t | ||   ||||    || S r
  r  rU  r  r  r  r!    r  r!  c                 C   &   t t| ||  ||||    |S r
  r|  rU  r  r  r  r"    r  r"  c                 C   r  r
  r~  rU  r  r  r  r#    r  r#  c              	   C   s   t || t|| | td td|  | ||   |td |td|    td  || t|t| |||    | S r
  )r  r   r  r  r>   r  r  r  rw
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  r$  c              	   C   s   t || t|| | td td|  | ||   |td |td|    td  ||t|t| |||    | S r
  )r  r   r  r  r
  r  r  r  r  r%    r  r%  c              	   C   s~   t ttd ttt |  t| ||   td | ||t ttd ttt|  t| ||   td | || S r
  r  r  r  r  r  r&  	  ry  r&  c                 C   st   t ttd tttdt| |||     | ||t ttd tttdt| |||     | || S r
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  r  r  r  r(    r  r(  c              	   C   s   t || |td  t|||  | td td|  | ||   |td |td|    td  ||t||td  t| |||    |td  | S rz
  r  r  r  r  r  r)    r  r)  c                 C   s   t ttd ttt |  t| ||||     td ||t ttd ttt|  t| ||||     td || S r
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  r  r  r  r*    r
  r*  c                 C   s|   t ttd tttdt| |||||       ||t ttd tttdt| |||||       || S r
  r  r  r  r  r  r+    rz  r+  c                 C   s   t ttd t|| tt |  t| ||||     td  ||t ttd t|| tt|  t| ||||     td  || S r
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  r,  c                 C   s   t ttd t|| ttdt| |||||        ||t ttd t|| ttdt| |||||        || S r
  r  r  r  r  r  r-  %  r  r-  c                 C   ri  r
  r~  rk  r  r  r  r.  )  r
  r.  c                 C   ri  r
  r|  rk  r  r  r  r/  -  r
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   C   s2   t tt|| t| ||td    | |S r
  )r  r  r>   r  r  r  r  r  rw
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   C   s4   t tt|| t| ||td    | | S r
  )r  r  r
  r  r  r  r  r  r  r1  5  r	  r1  c              	   C   sF   t t|| t| ||td    |td  ||td   |S r
  )r  r>   r  r  r  r  r  r  rw
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  r2  c              	   C   sH   t t|| t| ||td    |td  ||td   | S r
  )r  r
  r  r  r  r  r  r  r3  =  r
  r3  c                 C   z   t t| ||td   t|||td    tt|| t| ||td    | t| ||td    ||S r
  r  r  r  r  r  r4  A  r  r4  c                 C   r  r
  r  r  r  r  r  r5  E  r  r5  c                 C   s@   t tdd t|t| ||t t|  td t||| S Nr  r  ra  r  r  r   r>   r]  r#  r  r2  rx  rw
  r  r  r  r7  I  r
  r7  c                 C   sB   t tdd t|t| || t t|  td t||| S r  r  r  r  r  r  r8  M  r
  r8  c              
   C      t |ttttfrdS z/t||}ttt|t	t
|ttt||td t||t|tdtd   }W n ttfyF   Y dS w |rKdS dS NFr  r  T)r.  r/  r  r0  r  rQ  r  r6   r   r  r^   r>   r   r  r  r  r  	TypeErrorAttributeErrorr  r  r2  rw
  tmpresr  r  r  r9  Q     
Tr9  c              
   C   s   t ||}tt|| tdt||td  |  tt|td|td ttttdt	| td|  td  t
||| |||||S r  )rQ  r  r  r  r3   r  r+   r   r-  r  r   r  r  r2  rw
  r$  r  r  r  r:  ^  s   
r:  c              
   C   r  r   )r.  r/  r  r0  r  rQ  r  r6   r   r  r^   r?   r   r  r  r  r  r!  r"  r#  r  r  r  r;  d  r&  r;  c              
   C   s   t ||}tt|| tdt||td  |  tt|td|td ttttdt	| td|  td  t
||| ||||| S r  )rQ  r  r  r  r3   r  r+   r   r-  r  r   r'  r  r  r  r<  q  s   
r<  c              
   C   sv   t t| t||ttdt |  tdt | |   | t|   || t|t||t| ||     | S r
  r  r  r   r  r  r  r>   r  r^  r  r  r  r=  w  r  r=  c              
   C   st   t t| t||ttdt |  tdt | |   | t|   ||t|t||t| ||     | S r
  r  r  r   r  r  r  r
  r  r^  r  r  r  r>  {  r  r>  c              
   C   sx   t t| t|| ttdt |  tdt | |   | t|   || t|t||t| ||     | S r
  r(  r^  r  r  r  r?    r  r?  c              
   C   sv   t t| t|| ttdt |  tdt | |   | t|   ||t|t||t| ||     | S r
  r)  r^  r  r  r  r@    r  r@  c                 C   sh  t |t | | td  t|ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  ||t |t| | td  t|ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|t||t| ||     | S rz
  r  r  r  r   r  r  r>   r  r^  r  r  r  rA       j rA  c                 C   sj  t |t | | td  t|ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  || t |t| | td  t|ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|t||t| ||     | S rz
  r  r  r  r   r  r  r
  r  r^  r  r  r  rB    r  rB  c                 C   sj  t |t | | td  t|ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  || t |t| | td  t|ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|t||t| ||     | S rz
  r*  r^  r  r  r  rC    r  rC  c                 C   sh  t |t | | td  t|ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  ||t |t| | td  t|ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|t||t| ||     | S rz
  r,  r^  r  r  r  rD    r+  rD  c              
   C   s   t t| ||td   t|||  |td  |ttdt |  tdt | |   | t|   || t|||  |td  t||t| ||     ||td   | S rz
  r*  r
  r  r  r  rE    r  rE  c              
   C   s   t t| ||td   t|||  |td  |ttdt |  tdt | |   | t|   ||t|||  |td  t||t| ||     ||td   | S rz
  r,  r
  r  r  r  rF    r  rF  c              
   C   s   t t| ||td   t|||  |td  | ttdt |  tdt | |   | t|   || t|||  |td  t||t| ||     ||td   | S rz
  r*  r
  r  r  r  rG    s   rG  c              
   C   s   t t| ||td   t|||  |td  | ttdt |  tdt | |   | t|   ||t|||  |td  t||t| ||     ||td   | S rz
  r,  r
  r  r  r  rH    r  rH  c                 C   s  t |t | | td  ||td   t|||  |td  ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  ||t |t| | td  ||td   t|||  |td  ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|||  |td  t||t| ||     ||td   | S rz
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  r  r  r  rI    r
  rI  c                 C   s  t |t | | td  ||td   t|||  |td  ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  || t |t| | td  ||td   t|||  |td  ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|||  |td  t||t| ||     ||td   | S rz
  r,  r
  r  r  r  rJ        rJ  c                 C   s  t |t | | td  ||td   t|||  |td  ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  || t |t| | td  ||td   t|||  |td  ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|||  |td  t||t| ||     ||td   | S rz
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  r  r  r  rK    r-  rK  c                 C   s  t |t | | td  ||td   t|||  |td  ttdt |  tdt | |   t | | t | | td ttdt |  tdt | |    td  ||t |t| | td  ||td   t|||  |td  ttdt |  tdt | |   t| | t| | td ttdt |  tdt | |    td  || t|||  |td  t||t| ||     ||td   | S rz
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  rL  c                 C   sR   t |t|ttd|  td| |   || t|tt| ||   | S r
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  rM  c                 C   sP   t |t|ttd|  td| |   ||t|tt| ||   | S r
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  r  r/  r  r  r  rN    r
  rN  c              	   C   sX   t |t|ttd|  td| |   ||t|ttdt| ||    | S r
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  rQ  c                 C   s   t |||td   t|||  |td  ttd|  td| |   ||t|||  |td  tt| ||   ||td   | S rz
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  r  r2  r  r  r  rR    r  rR  c              	   C   s   t |||td   t|||  |td  ttd|  td| |   ||t|||  |td  ttdt| ||    ||td   | S rz
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   C   sf   t |t||ttd|  td| |   | |  || t|t||t| ||     | S r
  r  r   r  r  r  r>   r  r^  r  r  r  rU    rs  rU  c              
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  r  r  r   r  r  r>   r  r
  r  r  r  r]    r  r]  c              
   C   s   t |||td   t|||  |td  |ttd|  td| |   | |  ||t|||  |td  t||t| ||     ||td   | S rz
  r  r  r   r  r  r
  r  r
  r  r  r  r^    r%  r^  c              
   C   s   t |||td   t|||  |td  | ttd|  td| |   | |  || t|||  |td  t||t| ||     ||td   | S rz
  r8  r
  r  r  r  r_    r
  r_  c              
   C   s   t |||td   t|||  |td  | ttd|  td| |   | |  ||t|||  |td  t||t| ||     ||td   | S rz
  r9  r
  r  r  r  r`    r  r`  c                 C   s  t t| | | t  ||td   t|||  |td  ttd|  td| |   | | | | t ttd|  td| |    t  ||t t| || t  ||td   t|||  |td  ttd|  td| |   || || t ttd|  td| |    t  || t|||  |td  t||t| ||     ||td   | S rz
  r  r  r  r   r  r  r>   r  r
  r  r  r  ra        ra  c                 C   s  t t| | | t  ||td   t|||  |td  ttd|  td| |   | | | | t ttd|  td| |    t  || t t| || t  ||td   t|||  |td  ttd|  td| |   || || t ttd|  td| |    t  || t|||  |td  t||t| ||     ||td   | S rz
  r  r  r  r   r  r  r
  r  r
  r  r  r  rb        rb  c                 C   s  t t| | | t  ||td   t|||  |td  ttd|  td| |   | | | | t ttd|  td| |    t  || t t| || t  ||td   t|||  |td  ttd|  td| |   || || t ttd|  td| |    t  || t|||  |td  t||t| ||     ||td   | S rz
  r:  r
  r  r  r  rc    r=  rc  c                 C   s  t t| | | t  ||td   t|||  |td  ttd|  td| |   | | | | t ttd|  td| |    t  ||t t| || t  ||td   t|||  |td  ttd|  td| |   || || t ttd|  td| |    t  || t|||  |td  t||t| ||     ||td   | S rz
  r<  r
  r  r  r  rd    r;  rd  c                 C   sB   t t|t| | | td td  || t|t|  | S r
  )r   r-  r  r  r  r>   rt  r  r  r  re    r
  re  c                 C   s@   t t|t| | | td td  ||t|t|  | S r
  )r   r-  r  r  r  r
  rt  r  r  r  rf    r
  rf  c                 C   s   t |||td   tt|||  |td  t|| |td td  ||| t| |t|  |||  |td   ||td   | S rz
  )r  r  r   r-  r  r  r>   ru  r  r  r  rg    r
  rg  c                 C   s   t |||td   tt|||  |td  t|| |td td  |||t| |t|  |||  |td   ||td   | S rz
  )r  r  r   r-  r  r  r
  ru  r  r  r  rh  #  r  rh  c                 C   r+  r,  r-  rw  r  r  r  ri  '  r3  ri  c                 C   sZ   t ||}t|tt|t|| |td td  ||| t| |t|  || S r
  )r  r  r   r-  r  r  r>   rw  r  r  r  rj  0  s   
Prj  c                 C   r+  r,  r-  rw  r  r  r  rk  6  r3  rk  c                 C   sX   t ||}t|tt|t|| |td td  |||t| |t|  || S r
  )r  r  r   r-  r  r  r
  rw  r  r  r  rl  ?  s   
Nrl  c              	   C   s~   t ttd tt|tt | td  | ||   ||t ttd tt|tt| td  | ||   || S r
  r  )r  r  r2  rx  rw
  r  r  r  rm  E  ry  rm  c                 C   sx   t t|t|  t|| | || t t|t| | t| | td td  || t|t|  t| | S r
  )r   r-  r>   r  r  r  r  r2  rx  rw
  r  r  r  rn  I  r  rn  c                 C   sx   t t|t|| t|  | || t t|t| | t| | td td  || t|t| t|  | S r
  )r   r-  r  r
  r  r  r  r>  r  r  r  ro  M  r  ro  c                 C   2   t |ttttfrdS t| |}t||rdS dS r,  r-  r  r2  rx  rw
  zr  r  r  rp  Q  r3  rp  c                 C   s~   t | |}tt|t| ||tt|t| t|| | || tt|t|| t| |td td  || S r
  )r  r  r>   r  r   r-  r  r  r@  r  r  r  rq  Z     
trq  c                 C   r?  r,  r-  r@  r  r  r  rr  `  r3  rr  c                 C   s~   t | |}tt|t| ||tt|t|| t| | || tt|t|| t| |td td  || S r
  )r  r  r  r
  r   r-  r  r  r@  r  r  r  rs  i  rB  rs  c                 C   sf   t td|  ttd|ttdtd| td |td      || t|t| |  | S rz
  r  r  r   r  r  r  r  rw
  r  r  r  rt  o  rs  rt  c                 C   sd   t td|  ttd|ttdtd| td |td      ||t|t| |  | S rz
  r  r  r   r  r  r  rD  r  r  r  ru  s  rr  ru  c                 C   sF   t td| tt| ||  | t| t| ||t|| |S r
  r  r  r+   r   r  r  r  rv
  r  r  r  rv  w  r
  rv  c                 C   sH   t td| tt| ||  | t|t|  ||t|| | S r
  r  r  r+   r   r  r  r  rv
  r  r  r  rw  {  r
  rw  c                 C   0   t t| |t||   | ||td|  S r
  )r+   r   r  r  r  r  r  r  rx    r
  rx  c                 C   rH  r
  )r+   r   r	  r  r  r  r  r  ry    r
  ry  c                 C   s   t |||td   t||td  ttdtd|td |td     || t||td  | |t||    |td  | S r
  rC  r  r  r  r  rz    r
  rz  c                 C   s   t |||td   t||td  ttdtd|td |td     ||t||td  | |t||    |td  | S r
  rE  r  r  r  r  r{    r
  r{  c              	   C   s`   t || td  tt| ||  | tdt| |td   t| ||t|| |S Nr   r  r  r  r+   r   r  r  r  r
  r  r  r  r|    rX  r|  c              	   C   sb   t || td  tt| ||  | tdt| |td   t| ||t|| | S rI  rG  r
  r  r  r  r}    r  r}  c                 C   &   t || | |t||   |  |S r
  rl  r
  r  r  r  r~    r  r~  c                 C   rK  r
  rj  r
  r  r  r  r    r  r  c                 C   s   t |||td   | |}t|| | t|td |td   tt||t|td |td  td   ||| t| |t||   || S r   r  r  r  r  r   r-  r  r
  r  r  r  r    s   r  c                 C   s   t |||td   | |}t|| | t|td |td   tt||t|td |td  td   |||t| |t||   || S r   r  r  r  r  r   r-  r  r
  r  r  r  r    s   r  c                 C   b   t t|td | td  | |t||   |  ||td  | |  ||td|  S Nr  r"  r  r+   r   r  r  r
  r  r  r  r    r  r  c                 C   rN  rO  r+   r   r  r	  r
  r  r  r  r    r  r  c              
   C   z   t t|td | tt|td | td  | |t||   |  ||td  | |  ||td| | S rO  rp  r
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  r
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  r
  rk  r  r  r  r  '  r
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   C   sb   t | t| td  tt|t| | | t| td td   ||| t|t|  | S r   )r  r  r  r   r-  r  r  r  rt  r  r  r  r  3  r  r  c              
   C   s`   t | t| td  tt|t| | | t| td td   |||t|t|  | S r   )r  r  r  r   r-  r  r  r  rt  r  r  r  r  7  rX  r  c              
   C   s   t || ||td  t|td   tt|||  |td  t|| |t|td td   ||| t| |t|  |||  |td   ||td   | S Nr  r  r   )r  r  r  r   r-  r  r  r  ru  r  r  r  r  ;  r'  r  c              
   C   s   t || ||td  t|td   tt|||  |td  t|| |t|td td   |||t| |t|  |||  |td   ||td   | S rZ  )r  r  r  r   r-  r  r  r  ru  r  r  r  r  ?  r
  r  c                 C   r+  r,  r-  rw  r  r  r  r  C  r3  r  c              
   C   sv   t ||}t|| t|td  tt|t|| |t|td td   ||| t| |t|  || S r   )r  r  r  r  r   r-  r  r  rw  r  r  r  r  L  s   
lr  c                 C   r+  r,  r-  rw  r  r  r  r  R  r3  r  c              
   C   st   t ||}t|| t|td  tt|t|| |t|td td   |||t| |t|  || S r   )r  r  r  r  r   r-  r  r  rw  r  r  r  r  [  s   
jr  (  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r]  A_B_C_F_G_H_r  b_r  r;  e_r]  g_h_i_j_k_l_rf  r(  rL  q_r_t_r  r  s_r6  r%  y_z_a1_a2_b1_b2_c1_c2_d1_d2_n1_n2_e1_e2_f1_f2_g1_g2_n3_Pq_Pm_r  Qm_Qr_Qx_jn_mn_non2_r  RGx_r  iiPqqQRrr  kr  	_UseGamma	ShowStepsStepCounterrt
  r&  r'  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r^  r_  r`  ra  rb  rc  rd  re  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  <module>   s`              n"JjB.
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																		