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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)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGamma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  G/usr/lib/python3/dist-packages/sympy/integrals/rubi/rules/hyperbolic.py
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}9t|9t	}:ttttt tdtd tdtd t||||};t|;t
}<ttttt tdtd tdtd t||||}=t|=t}>tttdtdtd	tdttt tdtd tdtd   t t|||||6||7}?t|?t}@tttdtdtd	tdttt tdtd tdtd   t t|||||6||7}At|At}Btttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|-}Ct|Ct}Dtttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|-}Et|Et}Ftttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|8}Gt|Gt}Htttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|8}It|It}Jttttt tdtd tdtd t|||%|9}Kt|Kt}Lttttt tdtd tdtd t|||%|9}Mt|Mt}Ntttdtdtd	tdttt tdtd tdtd   t t|||||%|'}Ot|Ot}Ptttdtdtd	tdttt tdtd tdtd   t t|||||%|'}Qt|Qt}Rtttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|(|:|;	}St|St}Ttttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|(|:|;	}Ut|Ut}Vtttdtdtd	tdttt tdtd tdtd   t t|||||%|/|:}Wt|Wt}Xtttdtdtd	tdttt tdtd tdtd   t t|||||%|/|:}Yt|Yt}Ztttdtdtd	tdtt  tdtd t|||/|<|=}[t|[t}\tttdtdtd	tdtt  tdtd t|||/|<|=}]t|]t}^ttttt tdtd t t||%|>}_t|_t}`ttttt tdtd t t||%|>}at|at}btttttt tdtd  t t|||%|9}ct|ct}dtttĐttt tdtd  t t|||%|9}et|et }fttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(t!t"	}gt|gt#}httttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(t!t$	}it|it%}jttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(t!t'
}kt|kt(}lttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(t!t)
}mt|mt*}nttttdtd tdtd ttt tdtd tdtd  t||||| |?}ot|ot+}pttttdtd tdtd ttt tdtd tdtd  t||||| |?}qt|qt,}rttttdtd t ttt tdtd tdtd  t||||| |}st|st-}tttttdtd t ttt tdtd tdtd  t||||| |}ut|ut.}vttttdtd tdtd ttt tdtd tdtd  t||||
|}wt|wt/}xttttdtd tdtd ttt tdtd tdtd  t||||
|}yt|yt0}zttttdtd ttt td	td tdtd t  t|||6|@|7|A}{t|{t1}|ttttdtd ttt td	td tdtd t  t|||6|@|7|A}}t|}t2}~ttttdtd ttt td	td tdtd t  t|||
|%|B|1|7}t|t3}ttttdtd ttt td	td tdtd t  t|||
|%|B|1|7}t|t4}ttttdtd ttt td	td tdtd t  t|||C|1|7|D}t|t5}ttttdtd ttt td	td tdtd t  t|||C|1|7|D}t|t6}ttttdtd ttt td	td tdtd t  t|||C|1|7|E|F}t|t7}ttttdtd ttt td	td tdtd t  t|||C|1|7|E|F}t|t8}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(||G	}t|t9}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(||G	}t|t:}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|(||7
}t|t;}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|(||7
}t|t<}ttttdtd ttt td	td tdtd t  t|||
|%|B|1|)|H	}t|t=}ttttdtd ttt td	td tdtd t  t|||
|%|B|1|)|H	}t|t>}ttttdtd ttt td	td tdtd t  t|||C|1|)|H|D}t|t?}ttttdtd ttt td	td tdtd t  t|||C|1|)|H|D}t|t@}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||(|-|4}t|tA}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||(|-|4}t|tB}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(|-|G	}t|tC}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(|-|G	}t|tD}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|-|I
}t|tE}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|-|I
}t|tF}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|(|8}t|tG}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|(|8}t|tH}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|8	}t|tI}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|8	}t|tJ}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(|J|K|L}t|tK}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(|J|K|L}t|tL}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(|J|K|L}t|tM}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(|J|K|L}t|tN}ttttdtd tdtd ttt tdtd tdtd  t||||
|%|M}t|tO}ttttdtd tdtd ttt tdtd tdtd  t||||
|%|M}t|tP}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|%|'	}t|tQ}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|%|'	}t|tR}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||%|/|:|;|4
}t|tS}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||%|/|:|;|4
}t|tT}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|:
}t|ÐtU}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|:
}t|ŐtV}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|ǐtW}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|ɐtX}ttttdtd tttd
td td	td tdtd tdtd  tttd
td td	td tdtd  t|||
|%|/|0|N}t|ːtY}ttttdtd tttd
td td	td tdtd  tttd
td td	td tdtd tdtd  t|||
|%|/|0|N}t|͐tZ}ttttdtd tttd
td td	td tdtd tdtd  tttd
td td	td tdtd  t|||/||?|N}t|ϐt[}ttttdtd tttd
td td	td tdtd  tttd
td td	td tdtd tdtd  t|||/||?|N}t|ѐt\}tttttd tdtd ttd	td  tdtd t||||O}t|Ӑt]}tttttd tdtd ttd	td  tdtd t||||O}t|Րt^}tttttd tdtd ttd	td  tdtd t t|||||}t|אt_}tttttd tdtd ttd	td  tdtd t t|||||}t|ِt`}tttttd
td t||P|Q}t|ېta}tttttd
td t||P|Q}t|ݐtb}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||R}t|ߐtc}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||R}t|td}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||S}t|te}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||S}t|tf}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|tg}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|th}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|ti}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|tj}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|tk}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|tl}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|tm}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|tn}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd  t||||||
|T}t|to}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd  t||||||
|T}t|tp}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd t  t||||||
||	}t|tq}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd t  t||||||
||	}t|tr}ttttdtd tttd
td  t|
||:|P|U}t|ts} ttttdtd tttd
td  t|
||:|P|U}t|tt}ttttd	td tdtd tdtd tuttdtd tdtd  t||||| }t|tv}ttttd	td tdtd tdtd tuttdtd tdtd  t||||| }t|tw}tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}t|tx}tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}	t|	ty}
tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}t|tz}tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}t|t{}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t|}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t}}ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||W| |
}t|t~}ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||W| |
}t|t}tttdttd	tdtuttdtd tdtd   ttdtd tdtd td   t|||||||W}t|t}tttdttd	tdtuttdtd tdtd   ttdtd tdtd td   t|||||||W}t|t}ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||W| ||X}t|t}ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||W| ||X}t|t}tttdttd	tdtuttdtd tdtd   ttdtd tdtd   t|||||||W}t|t} tttdttd	tdtuttdtd tdtd   ttdtd tdtd   t|||||||W}!t|!t}"ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||
|W|Y
}#t|#t}$ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||
|W|Y
}%t|%t}&ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||W|Z	}'t|'t}(ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||W|Z	})t|)t}*ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||
|W|-
}+t|+t},ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||
|W|-
}-t|-t}.ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||W|[| |}/t|/t}0ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||W|[| |}1t|1t}2ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||!| 	}3t|3t}4ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||!| 	}5t|5t}6ttttdtd tdtd ttd	tdtuttdtd tdtd   td  t|||||||!}7t|7t}8ttttdtd tdtd ttd	tdtuttdtd tdtd   td  t|||||||!}9t|9t}:ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||!|-| 
};t|;t}<ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||!|-| 
}=t|=t}>ttttdtd tdtdtd	tdtut  td
td  t|||
|%|#|$}?t|?t}@ttttdtd tdtdtd	tdtut  td
td  t|||
|%|#|$}At|At}Bttttdtd tdtd tdtd tdtdtd	tdtuttdtd tdtd   td
td  t|||||||
|%|&
}Ct|Ct}Dttttdtd tdtd tdtd tdtdtd	tdtuttdtd tdtd   td
td  t|||||||
|%|&
}Et|Et}Ftttdtdtd	tdtutt tdtd tdtd   tdtd t|||||/|\|(}Gt|Gt}Htttdtdtd	tdtutt tdtd tdtd   tdtd t|||||/|\|(}It|It}Jtttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|.}Kt|Kt}Ltttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|.}Mt|Mt}Ntttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|:|;	}Ot|Ot}Ptttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|:|;	}Qt|Qt}Rtttdtdtd	tdtut  tdtd t|||/|<|=}St|St}Ttttdtdtd	tdtut  tdtd t|||/|<|=}Ut|Ut}Vttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}Wt|Wt}Xttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}Yt|Yt}Zttttdtd tutt tdtd tdtd td  t|||
|%|^}[t|[t}\ttttdtd tutt tdtd tdtd td  t|||
|%|^}]t|]t}^ttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|_	}_t|_t}`ttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|_	}at|at}bttt&t tdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t||||||
|%|/|5
}ct|ct}dttt&t tdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t||||||
|%|/|5
}et|et}fttt&t tdtd tdtdtd	tdtut  tdtd  t||||
|/|<|=}gt|gt}httt&t tdtd tdtdtd	tdtut  tdtd  t||||
|/|<|=}it|it}jttttdtd tdtttd
td td	td tdtd  tdtd  tuttd
td td	td tdtd tdtd  t|||/| ||`|a}kt|kt}lttttdtd tdtttd
td td	td tdtd  tdtd  tdtuttd
td td	td tdtd  tdtd  t|||/| ||`|a}mt|mt}ntttuttd tdtd ttd	td  tdtd td
td t||||%|b}ot|ot}ptttdtuttd tdtd ttd	td  tdtd  td
td t||||%|b}qt|qt}rttttdtd tdtd tuttd tdtd ttd	td  tdtd  t||||||c}st|st}tttttdtd tdtd tuttd tdtd ttd	td  tdtd  t||||||c}ut|ut}vttttdtd tdtd tdtd tuttd tdtd ttd	td  tdtd td
td  t||||||
|%|d	}wt|wt}xttttdtd tdtd tdtd tdtuttd tdtd ttd	td  tdtd  td
td  t||||||
|%|d	}yt|yt}zttttdtd tdtd tdtd tttd	td tdtd  t||||| }{t|{t}|ttttdtd tdtd tdtd tttd	td tdtd  t||||| }}t|}t}~ttttdtd tdtd tdtd tttd	td tdtd td  t||||| |}t|t}ttttdtd tdtd tdtd tttd	td tdtd td  t||||| |}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t|||||||e}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t|||||||e}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||e|	}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||e|	}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t||||||}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t||||||}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  t  t|||||
|%|L}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  t  t|||||
|%|L}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||-| 	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||-| 	}t|tÃ}ttttdtd tdtt td
td  t|
|%|#|$}t|tă}ttttdtd tdtt td
td  t|
|%|#|$}t|tŃ}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  t|||||
|%|f}t|tƃ}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  t|||||
|%|f}t|tǃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||/|\|(}t|tȃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||/|\|(}t|tɃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|.}t|tʃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|.}t|t˃}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|:|;	}t|t̃}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|:|;	}t|t̓}tttdtdtd	tdtt  tdtd t|||/|<|=}t|t΃}tttdtdtd	tdtt  tdtd t|||/|<|=}t|tσ}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}t|tЃ}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}t|tу}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|_	}t|t҃}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|_	}t|tӃ}ttt&t tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|5
}t|tԃ}ttt&t tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|5
}t|tՃ}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|Ðtփ}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|Őt׃}ttttdtd tdtttd
td td	td tdtd  t  tttd
td td	td tdtd  t|||/| ||`|g}t|ǐt؃}ttttdtd tdtttd
td td	td tdtd  t  tttd
td td	td tdtd  t|||/| ||`|g}t|ɐtك}ttttdtd tdtd tdtd tttd	td tdtd td
td  tttd	td tdtd  t|||||%| |h}t|ːtڃ}ttttdtd tdtd tdtd tttd	td tdtd  tttd	td tdtd td
td  t|||||%| |h}t|͐tۃ}ttttdtd tdtd tdtd tttd	td tdtd td
td  tttd	td tdtd tdtd  t|||||
|i}t|ϐt܃}ttttdtd tdtd tdtd tttd	td tdtd td
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|i}t|ѐt݃}ttttdtd tdtd tdtd tdtuttd	td tdtd  tdtd  tttd	td tdtd td
td  t|||||
|i}t|Ӑtރ}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tuttd	td tdtd tdtd  t|||||%|j| |	}t|Րt߃}ttttdtd tdtd tdtd tdtttd	td tdtd  td
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td  tttd	td tdtd td  t|||||%| |h}t|ِt}ttttdtd tdtd tdtd tdtuttd	td tdtd  td
td  tttd	td tdtd td  t|||||%| |h}t|ېt}ttttdtd tdtd tdtd tuttd	td tdtd t  tttd	td tdtd  t|||||
|k}t|ݐt}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tuttd	td tdtd t  t|||||
|%|k}t|ߐt}ttttdtd tdtd tdtd tdtuttd	td tdtd  t  tttd	td tdtd  t|||||
|k}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtuttd	td tdtd  t  t|||||
|%|k}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tuttd	td tdtd tdtd  t|||||%|/| |l	}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtuttd	td tdtd  tdtd  t|||||%|/| |l	}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtttd	td tdtd  td
td  t||||| |}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtttd	td tdtd  tdtd  t|||||6| ||m	}t|t}tttt tt  ttdtd  t|
|%|/|n|o|p|q|r	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd  t|||||||%| |h
}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd  t|||||||%| |h
}t|t}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd td  t|||||||%| |h
}t|t}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd td  t|||||||%| |h
}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tuttdtd tdtd  tttdtd tdtd  t|||||||%| |h
}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd tuttdtd tdtd   t|||||||%| |h
}t|t}ttttdtd tdtd tdtd tttd	td tdtd tdtd  tttdtd tdtd tdtd  t|||||||s|4	}t|t}ttttdtd tdtd tdtd tttd	td tdtd tdtd  tttdtd tdtd tdtd  t|||||||s|4	}t|t}ttttdtd tdtd tdtd tttd	td tdtd tdtd  tttdtd tdtd tdtd  t|||||||
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}t|t}tttttd	td tdtd tdtd  tttdtd tdtd t  t|y||||||z||
}	t|	t}
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}t|t}tttttd	td tdtd tdtd  tdtttdtd tdtd  t  t|y||||||~||
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}&tttttd	td tdtd tdtd  tdtttdtd tdtd  td
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}At|At}Btttttd	td tdtd tdtd  ttdtd  tttdtd tdtd td
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}Ct|Ct}Dtttttd	td tdtd tdtd  tttdtd tdtd tdtd  tttdtd tdtd td
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}Et|Et}Ftttttd	td tdtd tdtd  ttdtd  tttdtd tdtd tdtd  tttdtd tdtd td
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}Gt|Gt}Htttttd	td tdtd tdtd  tttdtd tdtd   tttdtd tdtd   t|y||||||V|o|
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td tdtd   t||||%|}at|at-}bttttdtdtd	tdt#ttd
td tdtd   t||||%|}ct|ct.}dttttdtdtd	tdt#ttd
td tdtd   t t||||%|1|7|}et|et/}fttttdtdtd	tdt#ttd
td tdtd   t t||||%|1|7|}gt|gt0}httttdtdtd	tdt#ttd
td tdtd   t t||||%|1|)|H|	}it|it1}jttttdtdtd	tdt#ttd
td tdtd   t t||||%|1|)|H|	}kt|kt2}lttttdtdtd	tdt#ttd
td tdtd   t t||||%|/|}mt|mt3}nttttdtdtd	tdt#ttd
td tdtd   t t||||%|/|}ot|ot4}pttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/||N|J
}qt|qt5}rttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/||N|J
}st|st6}tttttdtd ttdtdtd	tdt#ttd
td tdtd   tdtd  t||||
|%|'|}ut|ut7}vttttdtd ttdtdtd	tdt#ttd
td tdtd   tdtd  t||||
|%|'|}wt|wt8}xttttdtd ttdtdtd	tdt#ttd
td tdtd    t||||
|%||J}yt|yt9}zttttdtd ttdtdtd	tdt#ttd
td tdtd    t||||
|%||J}{t|{t:}|ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|7|J
}}t|}t;}~ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|7|J
}t|t<}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|)|H|J}t|t=}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|)|H|J}t|t>}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/|}t|t?}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/|}t|t@}tttdttd	tdt#ttd
td tdtd   tdtd t||}t|tA}tttdttd	tdt#ttd
td tdtd   tdtd t||}t|tB}tttdttdtdtd	tdt#ttd
td tdtd    t||||%|}t|tC}tttdttdtdtd	tdt#ttd
td tdtd    t||||%|}t|tD}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|/||g}t|tE}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|/||g}t|tF}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|7||	}t|tG}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|7||	}t|tH}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|)|}t|tI}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|)|}t|tJ}tttdttdtdtd	tdt#ttd
td tdtd    tdtd t||||%|/|}t|tK}tttdttdtdtd	tdt#ttd
td tdtd    tdtd t||||%|/|}t|tL}ttttdtd tdttd	tdt#ttd
td tdtd   tdtd  t||}t|tM}ttttdtd tdttd	tdt#ttd
td tdtd   tdtd  t||}t|tN}ttttdtd tOtdtdtd	tdt#ttd
td tdtd    t||||
|%|}t|tP}ttttdtd tQtdtdtd	tdt#ttd
td tdtd    t||||
|%|}t|tR}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|/||J|g
}t|tS}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|/||J|g
}t|tT}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|7||
}t|tU}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|7||
}t|tV}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|)|	}t|tW}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|)|	}t|tX}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    tdtd  t||||
|%|/|}t|tY}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    tdtd  t||||
|%|/|}t|tZ}ttt#ttd	td tdtd tttdtd t#ttd	td tdtd   t|||1|}t|t[}ttt#ttd	td tdtd tttdtd t#ttd	td tdtd   t|||1|}t|t\}ttt#ttd	td tdtd ttt tdtd t#ttd	td tdtd   t||||}t|t]}ttt#ttd	td tdtd ttt tdtd t#ttd	td tdtd   t||||}t|t^}ttttdtd t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||
|%|0|1|}t|t_}ttttdtd t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||
|%|0|1|}t|Ðt`}tttt t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||||}t|Őta}tttt t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||||}t|ǐtb}ttttdtdttdtd tdtd  td
td t||||}t|ɐtc}ttttdtdttdtd tdtd  td
td t||||}t|ːtd}tttttd	td tdtd tdtd ttdtd tdtd  td
td t||||||}t|͐te}tttttd	td tdtd tdtd ttdtd tdtd  td
td t||||||}t|ϐtf}tttttd
td t||}t|ѐtg}tttttd
td t||}t|Ӑth}tttdtdtttdtd  tttdtd  t|p}t|Րti}tttdtdtttdtd  tĐttdtd  t|p}t|אtj}tttttdtd tttdtd  t|s|}t|ِtk}tttttdtd tĐttdtd  t|s|}t|ېtl}ttttdtd tttdtd  tttdtd  t||}t|ݐtm}ttttdtd tttdtd  tĐttdtd  t||}t|ߐtn}tttdtdtttdtd  tĐttdtd  t|p|(}t|to}tttttdtd tĐttdtd  t|s|}t|tp}ttttdtd tttdtd  tĐttdtd  t||}t|tq}tttttuttd
td  t|||}t|tr}tttdtut td
td tt t|||}t|ts}tttdtut td
td tt t|||}t|tt}tttttuttd
td  t|||}t|tu}tttdtĐt td
td tt t|||}t|tv}tttdtt td
td tt t|||}t|tw}tttdtt td
td tt t|||}t|tx}tttdtĐt td
td tt t|||}t|ty}ttttd	tdtttdtd tdtd  tttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|%|&
}t|tz}ttttdtd ttd	tdtttdtd tdtd td   t  t||||||C|||
}t|t{}ttttdtd ttd	tdtttdtd tdtd td   t  t||||||C|||
}t|t|}ttttdtd tdtd tdtd ttttdtd  t td	td tdtd tdtd  t|||||||%| |1
}t|t}}ttttdtd tdtd tdtd tĐtttdtd  t td	td tdtd tdtd  t|||||||%| |1
}t|t~} ttttdtd tdtd tdtd tdtdtd	tdtttdtd tdtd td   tdtdtttdtd tdtd td    t|||||||| ||}t|t}ttttdtd tdtd tdtd ttdtdtuttdtd tdtd td   tttdtd tdtd td   t||||||| }t|t}ttttdtd tdtd tdtd tdtdtttdtd tdtd td  td	td tdtdtuttdtd tdtd td   tttdtd tdtd td   t|||||||| ||}t|t}ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd td   tttdtd tdtd td   t||||||| }t|t}ttttdtd tdtd tdtd tdtdtttdtd tdtd td  td	tdtuttdtd tdtd td   tdtd tttdtd tdtd td   t|||||||| ||}	t|	t}
ttttdtd tdtd tdtd tttdtd tdtd  ttd	tdtttdtd tdtd    t||||||| }t|t}ttttdtd tdtd tdtd tttdtd tdtd  ttd	tdtttdtd tdtd    t||||||| }t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||}t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||W}t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||}t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||!}t|t}ttttdtdtttdtd tdtd   ttdtd tdtd  ttd	tdtttdtd tdtd   td  t|||||||||
}t|t}ttttdtdtttdtd tdtd   ttdtd tdtd  ttd	tdtttdtd tdtd   td  t|||||||||
}t|t}ttttd	tdtut  td
td tdtt tdtd  t|||C||}t|t}ttttd	tdtut  td
td tdtt tdtd  t|||C||}t|t}tttdtdtttd	td tdtd tdtd  tttdtd tdtd td
td  t|||||V}t|t} tttdtdtttd	td tdtd tdtd  tttdtd tdtd td
td  t|||||V}!t|!t}"tttdtĐtttdtd  tttd	td tdtd   t||||||}#t|#t}$tttdttttdtd  tttd	td tdtd   t||||||}%t|%t}&tttutttdtd  tuttd	td tdtd  t||||||}'t|'t}(tttdtutttdtd  tuttd	td tdtd   t||||||})t|)t}*tttdtdtt td	tdtt  td
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sympy.integrals.rubi.constraintsr  r  r  r  r 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t5904replacement5905replacement5906replacement5907replacement5908replacement5909replacement5910replacement5911replacement5912replacement5913replacement5914replacement5915replacement5916replacement5917replacement5918replacement5919replacement5920replacement5921replacement5922With5923With5924replacement5925With5926F_G_w_replacement5927replacement5928replacement5929replacement5930replacement5931replacement5932replacement5933replacement5934replacement5935replacement5936replacement5937replacement5938replacement5939replacement5940replacement5941replacement5942replacement5943replacement5944replacement5945replacement5946replacement5947replacement5948replacement5949replacement5950replacement5951replacement5952replacement5953replacement5954replacement5955replacement5956replacement5957replacement5958replacement5959f_replacement5960replacement5961replacement5962replacement5963replacement5964replacement5965h_replacement5966replacement5967replacement5968With5969With5970replacement5971replacement5972H_replacement5973replacement5974replacement5975replacement5976logreplacement5977replacement5978replacement5979replacement5980r  replacement5981replacement5982replacement5983replacement5984replacement5985replacement5986replacement5987replacement5988replacement5989replacement5990replacement5991replacement5992replacement5993replacement5994replacement5995replacement5996replacement5997replacement5998replacement5999replacement6000replacement6001replacement6002replacement6003replacement6004replacement6005replacement6006replacement6007replacement6008replacement6009replacement6010replacement6011replacement6012replacement6013replacement6014replacement6015replacement6016replacement6017replacement6018r  replacement6019r  replacement6020replacement6021replacement6022replacement6023replacement6024replacement6025replacement6026replacement6027replacement6028replacement6029replacement6030replacement6031replacement6032replacement6033replacement6034replacement6035replacement6036replacement6037replacement6038replacement6039replacement6040With6041With6042replacement6043replacement6044replacement6045replacement6046replacement6047replacement6048replacement6049replacement6050replacement6051replacement6052replacement6053replacement6054replacement6055replacement6056replacement6057replacement6058replacement6059replacement6060replacement6061replacement6062replacement6063replacement6064replacement6065b_replacement6066replacement6067replacement6068replacement6069replacement6070replacement6071replacement6072replacement6073replacement6074replacement6075A_replacement6076replacement6077replacement6078replacement6079replacement6080replacement6081replacement6082replacement6083replacement6084replacement6085replacement6086(-  r  r  r  r  r 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\\dd^^\\ZZ\\rrppnn<<bbjjjj<<``nnbbHH0088``VV^^VVXXVVXXZZXX~~~~||``ddRRXX((vvvv~~~~~~~~>>jj||zzzz||~~zz^^nnnnppJJZZffdlxxhhrrjjpphhnnxxDDllllnnHHddDrrzz||||xx:44JVVddbbll\\ddffbbzzrrzz||vv^^ddllnnllttpprrvvzzTTxx&&JJ>>PPL>P4<<4::::rr^^``\d\         * r  c                 C   j   t || | t| ||  |td  t|||   || t| ||  | t|||   | | S Nr  r   r  r  r  r  r  r  r  r  xr  r  r  r       jr  c                 C   r  r  r  r   r  r  r  r  r  r  r  r    r  r  c                 C      t |||td   t| ||  |td  t|||   || t| ||  |td  t|||   ||td   | S Nr  r  r  r   r  r  r  r  r  r  r  r       r  c                 C   r  r  r  r  r   r  r  r  r  r  r  r  r    r  r  c                 C      t t|||  | |S Nr  r  r  r  r  r  r  r  r  r  r       r  c                 C   r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t t|  | ||  | tt| | | ||  | ||   ||t t|  | ||  | tt| | | ||  | ||   || S r  r  r  r   r  r  r  r  r  r       r  c                 C   s   t t|  | ||  | tt| | | ||  | ||   ||t t|  | ||  | tt| | | ||  | ||   || S r  r  r  r  r  r  r    r  r  c              	   C   sp   t tdd t| ||  | t| ||   || t tdd t| ||  | t|||   || S Nr  r  r  r  r   expr  r  r  r  r       pr  c              	   C   sn   t tdd t| ||  | t| ||   ||t tdd t| ||  | t|||   || S r  r  r  r  r  r  r       nr  c                 C   s   t | td |td  | t| t|||   |td  |||   || t|| t|||   |  |td |td   | t| | t|||   |td   |||   t|||   ||  | S Nr  r  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d  |||   ||t|| t|||   |  |td |td   | t| | t|||   |td   |||   t|||   ||  | S r  r  r  r  r  r  r    s   r  c              	   C   sn  t | td |td  | t| t|||   |td  |||  |  || t |td | |td  |td |td   t| t|||   | |||  |td   || t| | t|||   |td   |||  |  t|||   ||  | t|| | t|||   |  |||  |td   |td |td   | S r  r  r  r  r  r  r  r  r  r  r  r  r  r       p r  c              	   C   sl  t | td |td  | t| t|||   |td  |||  |  ||t |td | |td  |td |td   t| t|||   | |||  |td   || t| | t|||   |td   |||  |  t|||   ||  | t|| | t|||   |  |||  |td   |td |td   | S r  r  r  r  r  r  r       n r  c                 C   .   t t| ||  | t|||  | ||S r  r   rd  r  r  r  r  r  r  r  r  r  r  r  r       .r  c                 C   r  r  r   rd  r  r  r  r  r  r    r  r  c              
   C   s   t || ||td   tt| ||  |td  t|||  |td  t|||   ||| t| ||  |td  t|||  |  ||td   | S Nr  r  r  r  r   rd  r  r  r  r  r  r  r  r       r  c              
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  r  r  c                 C   s  t |td | td |td   t| t|||   |td  |||   || t|| t|||   |td   | td |td  |td  |td   | t| t|||   |td  |||   t|||   | | |td   | S Nr  r  r  r  r  r  r  r    s    r  c                 C   s
  t |td | td |td   t| t|||   |td  |||   ||t|| t|||   |td   | td |td  |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d | td |td   t| t|||   |td  |||  |  || t |td | |td  | td |td  |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d  |td   | S r  r  r  r  r  r  r    s    r  c              	   C   s  t |td | td |td   t| t|||   |td  |||  |  ||t |td | |td  | td |td  |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d  |td   | S r  r  r  r  r  r  r     s    r   c	           	   	   C   6   t t|||  | | |t|||    | ||S r  r   r   r  	r  r  r  r  r  r  r  r  r  r  r  r  r       6r  c	           	   	   C   r  r  r   r   r  r  r  r  r  r  "  r  r  c	           	   	   C   sl   t td|  | t|||  | tt |  td|  |td  || td  td|   ||S Nr     r  r  r   r  Pir  r  r  r  r  &     lr  c	           	   	   C   s   t td|  t| | |t|||    t|  tt |  td|  |td  || td  td t|   t|||  | tt |  td|  |td  || td  td|   ||S r  )r  r  r%   r  r&   r  r  r   r  r  r  r  r  *     r  c	           	   	   C   sV   t td|  | t|||  | t|td || td  td|   ||S Nr  r  r  r   r  r  r  r  r  r  .     Vr  c	           	   	   C   sX   t td |  | t|||  | t|td || td  td|   ||S r  r  r  r   r  r  r  r  r  r  2     Xr  c	           	   	   C   s   t td|  t| | |t|||    t|  t|td || td  td t|   t|||  | t|td || td  td|   ||S r  )r  r  r%   r  r&   r   r  r  r  r  r  6     r  c	           	   	   C   s   t td |  t| | |t|||    t|  t|td || td  td t|   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              
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   C   sv   t tdt|||  | t|||   td|  t|||   |ttd| td| |    |  ||S r  r  r  r  r  r  r  B  s   vr  c                 C   s  t | | td |td   t|||  | | |t|||     ||t || | || td |td    t|||  |td  t|||   | |t|||     || t||||  |  t|||   || |t|||     | td |td    | S Nr  r  r  r  r   r  r  r  r  r  r  r  r  F       r  c                 C   s  t | | td |td   t|||  | | |t|||     ||t || | || td |td    t|||  |td  t|||   | |t|||     || t||||  |  t|||   || |t|||     | td |td    | S r  r  r  r   r  r  r  r  r  r  r  r  J  r  r  c	           	   
   C   s  t | | td |td   t| |t|||    |td  |||  |  ||t ||td  | td |td  |td   t| |t|||    |td  |||  |  t|||   || t || | || td |td   |td   t| |t|||    |td  |||  |td   t|||   || t|| |t|||    |td   |||  |  t|||   || td |td   |td   | S Nr  r  r  r  r  r  r  r  r  N      r  c	           	   
   C   s  t | | td |td   t| |t|||    |td  |||  |  ||t ||td  | td |td  |td   t| |t|||    |td  |||  |  t|||   || t || | || td |td   |td   t| |t|||    |td  |||  |td   t|||   || t|| |t|||    |td   |||  |  t|||   || td |td   |td   | S r  r  r  r  r  r  r  R  r  r  c                 C   .   t | |tt||  | t|||  |S r  r   r  r2  r  r  r  r  r  vr  r  r  r  r  V  r  r  c                 C   r  r  r   r  r2  r  r  r  r  r  Z  r  r  c	           	      C   2   t | |t|||    | |||  |  |S r  r   r  r  r  r  r  r  ^     2r  c	           	      C   r   r  r   r  r  r  r  r  r  b  r  r  c                 C   .   t tt|||  | |||   | ||S r  r  r  r  r  r  r  r  r  r  r  r  r  f  r  r  c                 C   r  r  r  r  r  r  r  r  j  r  r  c              	   C     t ||| |td   t|td|  | |||   |td   t|||   || t td| || |td   t||  | |||   |td   t|||   || t|td|  | |||   |td   t|||   || |td   | S r  r  r  r  r  r  r  n      r  c              	   C   r  r  r  r  r  r  r  r  r  r  r  c                 C   r  r  r  r  r  r  r  r  v  r  r  c                 C   r  r  r  r  r  r  r  r  z  r  r  c                 C   8   t |||  | ||   | |  t|||   |S r  r  r  r  r  r  r  ~     8r  c                 C   r  r  r  r  r  r  r  r    r	  r  c                 C   *   t | |||   | t|||   |S r  r  r  r  r  r  r       *r  c                 C   r
  r  r  r  r  r  r  r     r  r   c	           	      C   :   t tt|||  || | | |||   |  ||S r  r  	r  r  r  r  r  r  r  r  r  r  r  r  r!       :r!  c	           	      C   r  r  r  r  r  r  r  r"    r  r"  c	           	      C      t |||  || |td   t| |||   |td  t|||   || t|| | |||   |td   t|||   || |td   | S r  r  r  r  r  r  r#       r#  c	           	      C   r  r  r  r  r  r  r  r$    r  r$  c              	   C   $  t ||| |td   t||| td  | |||   |td   t|||   || t || td || |td   t|||  | |||   |td   t|||   || t||| td  | |||   |td   t|||   || |td   | S r  r  r  r  r  r  r  r  r  r  r  r  r  r%       & r%  c              	   C   r  r  r  r  r  r  r  r&    r  r&  c                 C   6   t tt|||  || | |||   |  ||S r  r  r  r  r  r  r'    r  r'  c                 C   r  r  r  r  r  r  r  r(    r  r(  c                 C   <   t ||||   | ||   | |  t|||   |S r  r  r  r  r  r  r)       <r)  c                 C   r  r  r  r  r  r  r  r*    r  r*  c	           	      C   6   t || | | |||   |  t|||   |S r  r  r  r  r  r  r+    r  r+  c	           	      C   r  r  r  r  r  r  r  r,    r  r,  c              	   C   X   t tdd tt|  |||   || t tdd tt| |||   || S r  r  r  r  r  r  r  r  r  r-    r  r-  c              	   C   V   t tdd tt|  |||   ||t tdd tt| |||   || S r  r  r  r  r  r  r.    r  r.  c              	   C   ,   t t| |t||||     | ||S r  r  r  r  r  r  r/       ,r/  c              	   C   r  r  r  r  r  r  r  r0    r  r0  c              	   C   F   t t| |t||||      | |td  ||td|  S r  )r+   r   r  r  r  r  r  r  r1       Fr1  c              	   C   r  r  )r+   r   r  r  r  r  r  r  r2    r  r2  c                 C   ^   t |}t|tt||td  | |t|||||      |  |||td|  |S Nr  r  r4   r  r+   r   r  r  r  r  r  r  r  r  r  kr  r  r  r3       Vr3  c                 C   r  r   r4   r  r+   r   r  r  r"  r  r  r  r4    r$  r4  c              	   C   r  r  r  r  r  r  r  r5    r  r5  c              	   C   r  r  r  r  r  r  r  r6    r  r6  c              	   C   r  r  r  r  r  r  r  r7    r  r7  c              	   C   r  r  r  r  r  r  r  r8    r  r8  c                 C   J   t tdt||td tt| |t||||     | ||||S r  r  r  r3   r+   r   r  r  r  r  r  r  r  r  r  r  r  r  r9       Jr9  c                 C   r&  r  r  r  r3   r+   r   r  r(  r  r  r  r:    r)  r:  c                 C   &   t | |t||||     | |S r  r  r(  r  r  r  r;       &r;  c                 C   r+  r  r  r(  r  r  r  r<    r,  r<  c                 C       t | |tt||  | |S r  r  r  r  r  r  r  r  r  r  r=         r=  c                 C   r-  r  r  r.  r  r  r  r>    r/  r>  c                 C      t t| ||  | |S r  r  r  r  r  r  r  r  r?    r  r?  c                 C   r0  r  r  r1  r  r  r  r@    r  r@  c                 C   sL   t t| tt|||  | ||t t| tt|||  | || S r  r  r  r  r  r  rB       LrB  c                 C   sL   t t| tt|||  | ||t t| tt|||  | || S r  r  r  r  r  r  rC    r2  rC  c           	      C   V   t |ttttfrdS |td | }tt|tt	|tdt
|tdr)dS dS NFr  r   T
isinstanceintr  floatr  r  r  r   r  r#   rQ   	r  r  r  r  r  r  r  r  r  r  r  r  rD       (rD  c           	      C   ^   |t d | }tt d| tt||t d  | |t|||    |  |||| |S r  )r  r  r+   r   r  r9  r  r  r  rE  !     NrE  c           	      C   r3  r4  r5  r9  r  r  r  rF  '  r:  rF  c           	      C   r;  r  )r  r  r+   r   r  r9  r  r  r  rG  0  r<  rG  c	           
      C   V   t |ttttfrdS |td | }	tt|	tt	|tdt
|	tdr)dS dS r4  r5  
r  r  r  r  r  r  r  r  r  r  r  r  r  rI  6  r:  rI  c	           
      C   l   |t d | }	t|t| |t|   || t|  t|| | |t||||     |  ||S r  )r  r  r%   r&   r   r  r>  r  r  r  rJ  ?     \rJ  c	           
      C   r=  r4  r5  r>  r  r  r  rK  E  r:  rK  c	           
      C   r?  r  )r  r  r%   r&   r   r  r>  r  r  r  rL  N  r@  rL  c              	   C      t || || td  ||  t|| ||  t| |||    || t||td  || || td   t| |||    ||  | S r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  rM  T     rM  c              	   C   rA  r  r  r  r   r  r  rC  r  r  r  rN  X  rD  rN  c              	   C      t |||   | |td  t|| ||  t| |||    || t|| |td  t| |||    ||td   | S r  r  rC  r  r  r  rO  \     rO  c              	   C   rF  r  r  rC  r  r  r  rP  `  rG  rP  c              
   C   p   t tdd t|| | t|  |||    || t tdd t|| | t| |||    || S r  r  rC  r  r  r  rQ  d  r  rQ  c              
   C   n   t tdd t|| | t|  |||    ||t tdd t|| | t| |||    || S r  r  rC  r  r  r  rR  h  r  rR  c              	   C   s   t || | |td  tt| |||   |td  t| |||    ||t|td|  t| |||   |  |td  | S r   r  r  r  r  r  r  r  r  r  r  rS  l  r  rS  c              	   C   s   t || | |td  tt| |||   t| |||   |td   ||t|td|  t| |||   |  |td  | S r   r  rJ  r  r  r  rT  p  r  rT  c              	   C   s   t |td | t|| t| |||   |td   || tt| |||   | |td | |td   | t|| t| |||   |td   t| |||    || |  | S Nr  r  r  r  rJ  r  r  r  rU  t     rU  c              	   C   s   t |td | t|| t| |||   |td   ||tt| |||   | |td | |td   | t|| t| |||    t| |||   |td   || |  | S rK  r  rJ  r  r  r  rV  x  s   rV  c              
   C   s  t |td | t|| t| |||   |td   || t |td|  td || td  |td |td  |td   t||td|   t| |||   |  || t||td|  td  || td  t| |||   |  |td |td  |td   | t||| td  t| |||   |td   t| |||    || |  | S Nr  r  r  r  r  rJ  r  r  r  rW  |  s    rW  c              
   C   s  t |td | t|| t| |||   |td   ||t |td|  td || td  |td |td  |td   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   || |  | S rM  r  rJ  r  r  r  rX    s    rX  c              
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r  r  r  r  r  r  r  r  r  r#  r  r  r  r[       tr[  c	           
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   C   6   t t|| | | |t||||     | ||S r  r  r  r  r  r  r]    r  r]  c	           	   
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   C   rH  r  r  rC  r  r  r  rq    r  rq  c              
   C   rI  r  r  rC  r  r  r  rr    r  rr  c	           	   
   C   rR  r  r  r  r  r  r  rs    r  rs  c	           	   
   C   rR  r  r  r  r  r  r  rt    r  rt  c	           	      C   h   t t||td| td  tt| |t||||     | |t||td |  ||||S Nr  r  r   )r  r3   r  r+   r   r  	r  r  r  r  r  r  r  r  r  r  r  r  ru       hru  c	           	      C   re  rf  )r  r3   r  r+   r   r  rg  r  r  r  rv    rh  rv  c
           
   	   C   2   t ||	 | | |t||||     |  |	S r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  rw    r  rw  c
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   	   C   ri  r  r  rj  r  r  r  rx    r  rx  c                 C   ,   t || | | |tt||  |  |S r  r  r  r  r  r  r  r  r  r  r  r  ry  
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   C   s   t || |  tttd| td| |  |||   || t |||  tttd| td| |  |||   || ttd|| |t|||     |||    | S r  r  r  r  r  r  r       r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     ||t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S r  r  r  r  r  r  r    rS  r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     ||t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S r  r  r  r  r  r  r    rS  r  c                 C   s   t tdtd|   tttd| td| |  |||   ||t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S r  r  r  r   r  r  r  rD  r  r  r  r  r    r  r  c                 C   s   t tdtd|   tttd| td| |  |||   || t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S r  r  r  r  r  r  r    r  r  c              	   C   s   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  c              	   C   s   t tdtd|   t|||  | ttd |  |||   |  || t|||  |td  td|  | |td   | S r  r  r  r  r  r  r    rG  r  c	           	      C   s   t t|||  | ttd| td| |   td|  ttd| td| |  td|    tdtd|    |  ||S r  r   r   r  r  r  r  r  r  r  r       r  c	           	      C   s   t t|||  | ttd| td| |  td|  ttd| td| |  td|    tdtd|    |  ||S r  r  r  r  r  r  r    rG  r  c	           	   	   C   sb   t t|||  | tdtd|   ttd |  |||   | td|    |  ||S r  r   r   r  r  r  r  r  r  r       br  c	           	   	   C   sb   t t|||  | tdtd|   ttd |  |||   | td|    |  ||S r  r  r  r  r  r  r    r  r  c	           
      C   sn   t | |t|||    | |}	t|| tt|||  |td  |	||| t|||  | |	| S r  r  r  r  r   r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r       "Lr  c	           
      C   sn   t | |t|||    | |}	t|| tt|||  |td  |	||| t|||  | |	| S r  r  r  r  r  r  r    r  r  c              
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   C      t || td || |  t|||  tdt| |||    |  ||t||| td  tdt| |||    |  || |  | S r  rB  r  r  r  r  r  r  r  r  r  r  r  T	  r  r  c              
   C   r  r  rE  r  r  r  r  r  X	  r  r  c                 C   s*   t t| ||  ||td   | |S r  r   r  r  ru  r  r  r  r  \	  r  r  c                 C   s2   t tdt| ||  ||td    | |S r  r   r  r  ru  r  r  r  r  `	  r  r  c              
   C   s   t | | td| |  td|  tt| ||  ||td   ||t|tt| ||  ||td    td|  | S r  )r  r  r   r  r  rD  r  r|  r  r  r  r  d	  r  r  c              
   C   s   t | | td| |  td|  ttdt| ||  ||td    ||t|tt| ||  ||td    td|  | S r  )r  r  r   r  r  rD  r  r|  r  r  r  r  h	  s   r  c                 C   s:   t |||  | t| ||  ||td   |  |S r  r  r  r  r  r  r  l	  r  r  c              	   C   sB   t |||  | tdt| ||  ||td    |  |S r  r  r  r  r  r  r  p	     Br  c                 C   s   t t| | | t|||  |td  tt t| ||   td  || t t| | | t|||  |td  ttt| ||   td  || ttd|||  |  tt| ||   | | S Nr  r  r  )r  r  r   r  rD  r  r  r>   r  r  r  r  r  r  r  r  r  r  t	     r  c              
   C   s   t || | t|||  |td  ttdt| ||    || t || | t|||  |td  tt| ||  td  || ttd |||  |  tt| ||   | | S r  )r  r   r  rD  r  r  r  r  r  r  r  r  x	     r  c                 C   sj   t || | t|||  |td  t| ||   || t|||  | t| ||   | | S r  r  r   r  r  r  r  r  r  r  r  |	  r  r  c                 C   sh   t || | t|||  |td  t| ||   ||t|||  | |t| ||    | S r  r  r  r  r  r  r  	  rh  r  c              	   C   s   t |td |td  t|||  tdt| ||   |td   ||t|tdt| ||   |td   |td |td  |td   | t|||  tdt| ||   |td   t| ||   ||td   | S Nr  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  	  s   r  c              	   C   s   t |td |td  t|||  tdt| ||   |td   || t|tdt| ||   |td   |td |td  |td   | t|||  tdt| ||   |td   ||td  t| ||    | S r  r  r  r   r  r  r  r  r  r  r  r  	  s   r  c              
   C   s  t |td |td  t|||  | tdt| ||   |td   ||t |td | |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|| |||  |td   tdt| ||   |td   |td |td  |td   | S r  r  r  r  r  r  r  r  r  r  r  r  r  	  s    r  c              
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  r  r  c                 C   r  r  r  rl  r  r  r  r  
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   C      t || td || |td   t|||  tdt| |||    |td   ||t||| td  tdt| |||    |td   || |td   | S r  rB  rJ  r  r  r  r  
     r  c              
   C   r  r  rE  rJ  r  r  r  r  
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  rD  r  c                 C   r  r  rB  r  r  r  r  r  
  rD  r  c                 C   sB   t t|||  | t| ||  | t| ||  |  ||S r  r   rd  r  r  r  r  r  r  r  
  r  r  c                 C   s   t |||  | t| ||  |  t| ||  |td   |t |||  | t| ||  |td   t| ||  |  | S )Nr  )r   r  r  r  r  r  r  r  r   
  rG  r  c                 C   s   t |||  | tdt| ||   |  t| ||  |td   |t |||  | tdt| ||   |td   t| ||  |  | S rY  )r   r  r  r  r  r  r  r  r  $
     r  c              	   C      t || ||  t|||  |td  tdt| ||   |  ||t|||  | tdt| ||   |  ||  | S r   r  r  r  r  r  r   (
  r  r   c              	   C   r  r   r  r  r  r  r  r  ,
  r  r  c                 C   r  r  r  r  r  r  r  r  0
  rD  r  c              	   C   s   t || ||td   t|||  |td  tdt| ||   |td   ||t|||  | tdt| ||   |td   ||td   | S r  r  r  r  r  r  r  4
  r  r  c                 C   s   t |||  | t| ||  |td   t| ||  td  | t |||  | t| ||  |td   t| ||   | S )Nr     )r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  8
  r  r  c                 C   s   t |||  | tdt| ||   |  t| ||  |td   |t |||  | tdt| ||   |td   t| ||  |td   | S Nr  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 |||  | tdt| ||   |td   t| ||   | S )Nr  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 |||  | tdt| ||   |td   tdt| ||   |td   | S r  )r   r  r  r  r  r  r  r  r  D
  s   r  c           	      C   s~   t tdt| ||   | t| ||  |  |}t|| t||||  |td   || t|||  | || S r  )r  r  r  r  r  r   	r  r  r  r  r  r  r  r  r  r  r  r  r  H
  s   6Hr  c           	      C      t tdt| ||   | tdt| ||   |  |}t|| t||||  |td   || t|||  | || S r  )r  r  r  r  r  r   r  r  r  r  r	  M
     >Hr	  c              	   C   sR   t td| t|||  | tdttd|  td| |   |  ||S r  r  r  r  r  r  r
  R
     Rr
  c           	      C   r  r  )r  r  r  r  r  r   r  r  r  r  r  V
  r  r  c	           	      C   s8   t t||| | t|||  |t|||  |S r  r   r2  )	FGr  r  r  r  r  wr  r  r  r  r  [
  r	  r  c	           	   	   C      t || || |td   t| |t|||    |td  |||  |td   || t| |t|||    |td  |||  |  || |td   | S r  rE  r  r  r  r  r  _
     r  c	           	   	   C   r  r  rB  r  r  r  r  r  c
  r  r  c	           	   	   C   r  r  r  r  r  r  r  r  g
  r  r  c	           	   	   C      t || || |td   t| |t|||    |td  |||  |td   ||t| |t|||    |td  |||  |  || |td   | S r  r  r  r  r  r  r  k
     r  c	           	   	   C   r  r  rB  r  r  r  r  r  o
  r  r  c	           	   	   C   r  r  rE  r  r  r  r  r  s
  r  r  c
           
      C   B   t t|||	  | t| ||	  | t|||	  |  |	|	S r  r  
r  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  c
           
      C   sB   t t|||	  | t| ||	  | t|||	  |  |	|	S r  r  r  r  r  r  r  
  r  r  c                 C   sD   t t|||  | ||||  |
  | |||  |	|| ||S r  )r   rc  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  
  s   Dr  c                 C      t | ||||    | t|||   |td  |td  t| td  |td   |t | ||||    | | t|  t|||   |td  |td  t| td  |td   | S r  )r  r  r  rD  r  r  r  r  r  r  r  r  r  r  r  r  
     r  c                 C   r  r  )r  r  r  rD  r  r  r  r  r  r  
  r  r  c                 C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    t|||  |td   || t| ||||    | | t|  t|||  |  |td  |td  t| td  |td |td    | t| ||||    | | t|||  |td   t|||   |td  |td  t| td  |td |td    | S r  r  r  rD  r   r  r  r  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| td  |td |td    t| ||||    t|||  |td   ||t| ||||    | | t|  t|||  |  |td  |td  t| td  |td |td    | t| ||||    | | t|||   t|||  |td   |td  |td  t| td  |td |td    | S r  r  r  rD  r   r  r  r  r  r  r  r  r  
  rN  r  c                 C   s   t | ||||    t|||  |td   t|||   ||td   |t | ||||    | | t|  t|||  |td   |td |td  |td   | S r  )r  r  r  r  rD  r  r  r  r  r  
  s   r  c                 C   s   t | ||||    t|||   t|||  |td   ||td   | t | ||||    | | t|  t|||  |td   |td |td  |td   | S r  )r  r  r  r  rD  r  r  r  r  r  
  s   r  c                 C   sj  t |td  |td  t| td  |td |td td   |td |td  |td   t| ||||    t|||  |td   || t| ||||    t|||  |td   t|||   ||td   | t| ||||    | | t|  t|||  |td   |td |td  |td   | S r  r  r  r  r  r  r   
  s   l r   c                 C   sh  t |td  |td  t| td  |td |td td   |td |td  |td   t| ||||    t|||  |td   ||t| ||||    t|||   t|||  |td   ||td   | t| ||||    | | t|  t|||  |td   |td |td  |td   | S r  r  r  r  r  r  r!  
  s   j r!  c              	   C      t ttd| td| |  td |  t||||    t|||  |  t| ||||    ttd| td| |  td |  t| |||    ||S r  )r  r  r  r  r   r  r  r  r  r"  
  r  r"  c              	   C   r  r  )r  r  r  r  r   r  r  r  r  r#  
  r  r#  c                 C   sz   t t| ||||    ttd| td| |  td |  ttd| td| |  td |   ||S r  r   r   r  r  r  r  r  r  r$  
     zr$  c                 C   sz   t t| ||||    ttd| td| |  td |   ttd| td| |  td |  ||S r  r  r  r  r  r  r%  
  r  r%  c              	   C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    tdt|||   |td   ||t| ||||    | | tdt|||   |  t|  |td  |td  t| td  |td |td    | t| ||||    | | tdt|||   |td   t|||   |td  |td  t| td  |td |td    | S r  r  r  r  r  r  r&  
  s    r&  c              	   C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    tdt|||   |td   || t| ||||    | | tdt|||   |  t|  |td  |td  t| td  |td |td    | t| ||||    | | tdt|||   |td   t|||   |td  |td  t| td  |td |td    | S r  r  r  r  r  r  r'  
  s    r'  c                 C   s   t | ||||    tdt|||   |td   t|||   ||td   |t | ||||    | | tdt|||   |td   t|  |td |td  |td   | S Nr  r  r  r  )r  r  r  r  rD  r  r  r  r  r(  
     r(  c                 C   s   t | ||||    tdt|||   |td   t|||   ||td   | t | ||||    | | tdt|||   |td   t|  |td |td  |td   | S r  )r  r  r  r  rD  r  r  r  r  r)  
  r  r)  c              	   C   s  t |td  |td  t| td  |td |td td   |td |td  |td   t| ||||    tdt|||   |td   ||t| ||||    tdt|||   |td   t|||   ||td   | t| ||||    | | tdt|||   |td   t|  |td |td  |td   | S Nr  r  r  r  r  r  r  r  r  r*  
  s    r*  c              	   C   s  t |td  |td  t| td  |td |td td   |td |td  |td   t| ||||    tdt|||   |td   || t| ||||    tdt|||   |td   t|||   ||td   | t| ||||    | | tdt|||   |td   t|  |td |td  |td   | S r  r  r  r  r  r  r+  
  s    r+  c              
   C   s   t td| | ||||     t||| t|  td|  |td  || t|  td|  |td  td ttd| td| |    t||||    || t|  ||   |S r  r  r  r5   rD  r  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d| td| |   t||||    || t|  ||   |S )Nr  r  r  r  r  r  r  r  r-  
  rL  r-  c              
   C   s   t ttd| td| |  td | tdt|||   |  t| |||    tt| ||||    ttd| td| |  td |   t||||    |||S r  )r  r  r  r  r   r-  r  r  r  r  r.  
  s   r.  c              
   C   s   t tdttd | td| |   | tdt|||   |  t||||    tt| ||||    tdttd | td| |   |   t| |||    |||S r  )r  r  r  r  r   r-  r  r  r  r  r/  
  s   r/  c
           
   	   C   st   t td| ||  t| ||||	    tt | td|  |td  ||	 td  td|   |	|	S r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r1  
  s   tr1  c
           
   	   C   ^   t td| ||  t| ||||	    t|td ||	 td  td|   |	|	S r  r  r  r  r  r  r2  
  rd  r2  c
           
   	   C   r  r  r  r  r  r  r  r3  
  rd  r3  c              	   C   s`   t ||	 t| ||||
    tt | td|  |td  ||
 td  |  |
|
S )Nr  r  )r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r4  
  r  r4  c              	   C   sJ   t ||	 t| ||||
    t|td ||
 td  |  |
|
S r  )r  r   r  r  r  r  r  r  r5  
  r)  r5  c              
   C   sR   t ||	 t| ||||
    tdt|td ||
 td   |  |
|
S r  )r  r   r  r  r  r  r  r  r6  
  r  r6  c              
   C      t td|	 t| ||||
    t|||
   ||t|||
     |
|
t| ||||
    ||	t|||
     ||t|||
     |
 S r  r  r  r   r  r  r  r  r  r  r  r  r  r  hr  r  r  r  r  r8  
  r  r8  c              
   C   r  r  r  r  r   r  r  r  r  r  r  r9  
  r  r9  c                 C   s*   t | |t||  |t|||  |S r  r  )r  r  r  r  r  r  r  r  r  r  r:  
  r  r:  c	           
      C   d   t | ||||    t|||  |  |}	t|t|	||td   || t|	||  | S r  )r  r  r  r   r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r;       .6r;  c	           
      C   r  r  )r  r  r  r   r  r  r  r  r  r  r<    r  r<  c                 C   sF   t t| ||||
    t|||
  | t|||
  |	  |
|
S r  r  r  r  r  r  r=    r  r=  c                 C   sN   t t| ||||    ||
  t|||  | t|||  |	  ||S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r>    s   Nr>  c                 C   sF   t t| ||||
    ||||
  | ||||
  |	  |
|
S r  )r   rh  )r  r  Hr  r  r  r  r  r  r  r  r  r  r  r@    r  r@  c                 C      t t| | t|| ||S r  )r   rh  r  r  r  r  r  r  r  r  r  rA       rA  c                 C   r  r  )r   rh  r  r   r  r  r  rB    r  rB  c                 C   s*   t t| | t|| t||  ||S r  )r   rh  r  r  )r  r  r  r  r  r  r  r  r  rC  !  r  rC  c                 C   s<   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  | |S r  r  r  r  r  r  rF  )  r  rF  c                 C   s   t ||td  t| |t|||    |td   |td  | t |t| |t|||    |td   || |td  t| |t|||      | S r  r  r  r  rD  r  r  r  r  r  r  r  r  r  r  rG  -  r  rG  c              
   C   s   t ||td  t| |t|||    |td   |td  |t |t| |t|||    |td   t| |t|||     || |td   | S r  r  r  r  rD  r  r  r  r  r  rH  1  r  rH  c              
   C      t |tt| |t|||     t|||  td|  ttd|   td  tt|||  td|  ttd|   td | ||S )Nr  r  r  )r  r  r  rD  r  r  r   ru  r  r  r  rI  5  rD  rI  c              
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   C   s2  t ||td  tdtd|||  td |   ttd |    |   |||  | t|  |||  |  t|    |  t| || | | td  td| |  td|| | | td td| |   |||  td |  ttd |    || | | td  |S r  r  r  r  r  r  r_    s   4 r_  c              
   C   s4  t ||td  tdtd|||  td |   ttd |    |   |||  | t|  |||  |  t|    |  t| || | | td  td| |  td|| | | td td| |   |||  td |   ttd |    || | | td  |S r  r  r  r  r  r  r`    s   6 r`  c                 C   J   t td| t|||  |  |||  td|   td  | ||S r  r  r  r   r  r  r  r  ra    r)  ra  c                 C   r  r  r  r  r  r  r  rb    r)  rb  c                 C   sn   t tdt|  | |  t|||  td|  |||  td|  ttd |  | |   ||S r  r  r  r  r   ru  r  r  r  rc    r  rc  c                 C   sz   t td | | t|  | |  t|||  td|  |||  td|   ttd |  | |   ||S r  r  ru  r  r  r  rd    r  rd  c                 C   s   t ||td  tdt| |t|||     |td   |td  |t |tdt| |t|||     |td   t| |t|||     || |td   | S Nr  r  r  r  r  r  r  r  re    r  re  c                 C   s   t ||td  tdt| |t|||     |td   |td  | t |tdt| |t|||     |td   || |td  t| |t|||      | S r  r  r  r  r  r  rf    s   rf  c                 C   sr  t |td |td  |td td  td |td |td  |td  |td   ttdt| |t|||     |td  ||t|tdt| |t|||     |td   |td |td  |td  |td   | t|tdt| |t|||     |td   t| |t|||     || |td   | S r  r  r  r  r  r  rg    s   t rg  c                 C   st  t |td |td  |td td  td |td |td  |td  |td   ttdt| |t|||     |td  || t|tdt| |t|||     |td   |td |td  |td  |td   | t|tdt| |t|||     |td   || |td  t| |t|||      | S r  r  r  r  r  r  rh    s   v rh  c                 C   sz  t |td |td  | |td  |td |td  |td  td  ttdt| |t|||     |td  ||t|tdt| |t|||     |  |td |td  |td  td  | t|| | | tdt| |t|||     |td   t| |t|||     |td |td  |td  td  | S r  r  r  r  r  r  ri    s   | ri  c                 C   s|  t |td |td  | |td  |td |td  |td  td  ttdt| |t|||     |td  || t|tdt| |t|||     |  |td |td  |td  td  | t|| | | tdt| |t|||     |td   t| |t|||     |td |td  |td  td  | S r  r
  r  r  r  r  rj    s   ~ rj  c              
   C   s&  t td| | |||  | t|  |||  td|  ttd|   td  |  |||  td|  ttd|   td |  t||| | td td| |  td|| | td td| |   |||  td|   ttd|    || | td  |S r  r  r  r  r  r  rk    s   ( rk  c              
   C   s"  t ||||  | t|  |||  td|  ttd|   td  |  td |||  td|   ttd|   td |  t||| | td td| |  td|| | td td| |   |||  td|  ttd|    || | td  |S r  )r  r  r  r5   r  r  r  r  rl    s   $ rl  c                 C   R   t td| t|| |||  |  |||  td|   td  |  ||S r  r  r  r  r  r  r  r  r  r  r  rm    r  rm  c                 C   r  r  r  r  r  r  r  rn    r  rn  c              
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   C   n   t td| ttt|| | || |  | ||   |  | |td  ||td|||   | S r  rZ  r  r  r  r  r  r  r  r  r  r  r    r  r  c              
   C   r'  r  r[  r(  r  r  r  r  !  r  r  c                 C   X   t ||}tt|t|td t|td |t|td t|td  |  |S Nr  r  r  r  )r   r   r  r  r  r  r  r  Zlstr  r  r  r  %     
Nr  c                 C   r)  r*  )r   r   r  r  r  r+  r  r  r  r  *  r,  r  c                 C      t |t|| |   |S r  r  r  r  r  r  r  r  r  r  r  r  /  r  r  c                 C   r-  r  r  r.  r  r  r  r  3  r  r  c                 C   $   t tt||  t||  ||S r  r  r  r  r  r  r  r  r  r  r  7     $r  c                 C   r/  r  r  r0  r  r  r  r  ;  r1  r  c                 C   *   t t||  t|| t||  ||S r  r  r  r  r  r  r  r  r  r  r  r  ?  r  r  c                 C   r2  r  r  r3  r  r  r  r  C  r  r  c                 C   s0   t td|   t|ttd| |   ||S r  r  )r  r  r  r  r  r  r  r  r  G  rv  r  c                 C   s$   t tt||  t||  ||S r  r  r0  r  r  r  r  K  r1  r  c                 C   s*   t t||  t|| t||  ||S r  r  r3  r  r  r  r  O  r  r  c                 C   sV   t t|| tt|| td  t| || tt|t|| td   | S r  )r  r  r   r  r  r  r  r  r  r  r  r  r  S  r  r  c                 C   sd   t t|| ttdt| | td  t| ||ttdt| | td  t| | S r  )r  r  r   r  r  r  r4  r  r  r  r  W     dr  c                 C   sd   t t|| ttdt| | td  t| ||ttdt| | td  t| | S r  r  r  r   r  r  r  r4  r  r  r  r  [  r5  r  c                 C   sV   t t|| tt|| td  t| || tt|t|| td   | S r  )r  r  r   r  r  r  r4  r  r  r  r  _  r  r  c                 C   sl   t t|| ttdt| | td  ||t t|| ttdt| | td  t| || S r  r  r  r   r  r  r  r4  r  r  r  r  c  r  r  c                 C   sl   t t|| ttdt| | td  ||t t|| ttdt| | td  t| || S r  r7  r4  r  r  r  r  g  r  r  c                 C   sl   t t|| ttdt| | td  t| ||t t|| ttdt| | td  || S r  r6  r4  r  r  r  r  k  r  r  c                 C   sl   t t|| ttdt| | td  t| ||t t|| ttdt| | td  || S r  r7  r4  r  r  r  r  o  r  r  c	           	      C   sJ   t | |ttd| td| |   td  | |||  |  |S r  r  r  r  r  r  r  s  r)  r  c              
   C   sX   t td|  t|| td|  |ttd| td| |    | |  ||S r  r  r  r  r  r  r  w  r  r  c              
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           
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   C   b   t || td  tt| | ||  ||	  | t| ||	|   |  |	|	|||	  |	S r  rZ  
r  r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c
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   C   r8  r  r[  r9  r  r  r  r    r  r  c	           	   
   C   ^   t tdt|||  | td|  | | || ttd| td| |     ||S r  r  	r  r  r  r  r  r  r  r  r  r  r  r  r    rd  r  c              
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   r   r   r   r   r   r   r   r   r   r   r   r   r   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  rD  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
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