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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)Add)Mod)Mul)
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}@tttttdtd tdtd tttdtd tdtd  t|||||}At|At}Btttttdtd tdtd tttdtd tdtd  t|||||}Ct|Ct}Dtttttdtd tdtd tttdtd tdtd  t|||||}Et|Et}Ftttdtdtttdtd tdtd  t tttdtd tdtd td  t||||||||	}Gt|Gt}Htttdtdtttdtd tdtd  t tttdtd tdtd td  t||||||||	}It|It}Jtttdtdtttdtd tdtd  tdtd tttdtd tdtd tdtd  t|||||||||
}Kt|Kt}Ltttdtdtttdtd tdtd  td	td tttdtd tdtd tdtd  t|||||||||
}Mt|Mt}Ntttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t||||||||||||}Ot|Ot}Ptttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t||||||||||||}Qt|Qt}Rtttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  t  t||||||||||||}St|St}Ttttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  t  t||||||||||||}Ut|Ut}Vtttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t||||||||||||| |!}Wt|Wt}Xtttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t||||||||||||| |!}Yt|Yt}Ztttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t|||||||||||"||#|$|!}[t|[t}\tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t|||||||||||"||#|$|!}]t|]t}^tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t|||||||||||%|"|&|!}_t|_t}`tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t|||||||||||%|"|&|!}at|at}btttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t|||||||||||%|'|#|(|!}ct|ct}dtttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t  t|||||||||||%|'|#|(|!}et|et}ftttdtdtttdtd tdtd  t tttdtd tdtd  t|||||||||)|*|+}gt|gt }htttdtdtttdtd tdtd  t tttdtd tdtd  t|||||||||)|*|+}it|it!}jtttdtdtttdtd tdtd  t tttdtd tdtd  t|||||||||)||+}kt|kt"}ltttdtdtttdtd tdtd  t tttdtd tdtd  t|||||||||)||+}mt|mt#}ntttttdtd tdtd t$tttdtd tdtd  t||||||}ot|ot%}ptttttdtd tdtd t$tttdtd tdtd  t||||||}qt|qt&}rtttdtdtttdtd tdtd  t tttdtd tdtd  t||||||||||+}st|st'}ttttdtdtttdtd tdtd  t tttdtd tdtd  t||||||||||+}ut|ut(}vtttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  t  t|||||||||||}wt|wt)}xtttdtdtttdtd tdtd  td	td tdtdtttdtd tdtd  t  t|||||||||||}yt|yt*}ztttdtdtttdtd tdtd  t tttdtd tdtd td  tttdtd tdtd td  t||||||||	}{t|{t+}|tttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  td	td  tttdtd tdtd tdtd  t|||||||||||}}t|}t,}~tttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t||||||||||||||,}t|t-}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t.  tdtdtttdtd tdtd  t  t||||||||||||||,}t|t/}tttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t||||||||||||||-|(}t|t0}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t.  tdtdtttdtd tdtd  t  t|||||||||||||.||/|0}t|t1}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t.  tdtdtttdtd tdtd  t  t|||||||||||||.||/|0}t|t2}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||"||1|/|0|2}t|t3}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||"||1|/|0|2}t|t4}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t.  tdtdtttdtd tdtd  t  t||||||||||||3|"|4|/|0}t|t5}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  t.  tdtdtttdtd tdtd  t  t||||||||||||3|"|4|/|0}t|t6}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||%|"|5|0}t|t7}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||%|"|5|0}t|t8}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||6|'|7|*|5|0}t|t9}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||6|'|7|*|5|0}t|t:}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||6|'|7||1|(|0}t|t;}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||6|'|7||1|(|0}t|t<}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||%|'|1|(|0}t|t=}tttdtdtttdtd tdtd  t tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||%|'|1|(|0}t|t>}tttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  td	td  tdtdtttdtd tdtd  t  t|||||||||||||}t|t?}tttdtdtttdtd tdtd  tdtd tttdtd tdtd  t||||||||8	}t|t@}tttAttdtd tdtd  tdtd tB t t|||||9|:|;}t|tC}tttdtAttdtd tdtd  tdtd tB  t|||||9|<|=}t|tD}tttdtAttdtd tdtd  tdtd tB  t|||||9|>|=}t|tE}tttFttdtd tdtd  tAttdtd tdtd  tdtd tB  t||||||?|:|=	}t|tG}tttAttdtd tdtd  tdtd t. t||||||9|@|	}t|tH}tttAttdtd tdtd  tdtd t tdtd td	td t|||||||9|@|
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}t|t|}ttttAttdtd tdtd tdtd  tdtd tz  t|||||M|>|E|BtJt}
}t|t~}tttttJt}t|t}tttttJt}t|t}tttdtdtdtdtttdtd tdtd td   tdtdtttdtd tdtd td   tdtd tdtd t|||||||N}t|t}tttdtdtdtdtttdtd tdtd td   tdtdtttdtd tdtd td   tdtd tdtd t|||||||O}t|t}tttdtdtdtdtttdtd tdtd td   tdtdtttdtd tdtd td   tdtd tdtd t|||||||O}t|t}tttt t|PtJt}t|t}ttttt  t|PtJt}t|t}tttttdtd  t||Q|PtJt}t|t}tttttdtd  ttd	td  t|||Q|PtJt}t|t}tttAttdtd tdtd  tdtd t. tdtd t||||||9|@|	}t|t}tttAttdtd tdtd  tdtd t tdtd td	td tdtd t|||||||9|@|
}t|t}tttt|RtJt}t|t}tttdtttdtd tdtd  td	td tdtd tdtdtttdtd tdtd td	td   t tdtd t|||||S}t|t}tttdtttdtd tdtd  td	td tdtd tdtttdtd tdtd  td	td tdtd  t tdtd t|||||S}t|t} ttttAttdtd tdtd  tB tAttdtd tdtd  tdtd  td	td  t||||||U|9|:|T
}t|t}ttttAttdtd tdtd  tB tAttdtd tdtd  tdtd  tAttdtd tdtd  tdtd  td	td  t|||||||U|W|9|:|T|V}t|t}ttttAttdtd tdtd  tdtd tAttdtd tdtd  tdtd  tB td	td  t|||||||U|9|:|X}t|t}tttdtdtttdtd tdtd  tdtdtttdtd tdtd   td	td tdtd t||||||Y}t|t}tttt|Z}	t|	t}
tttBtz t tdtd t||||[}t|t}tttzt t tdtd t||||[}t|t}tttztdtd ttd	td  t tdtd t|||||\}t|t}tttt|PtJt}t|t}tttt|R|]tJt}t|t}tttt|P}t|t}ttttdtd tdtd tdtd tttdtd tdtd td	td  tttdtd tdtd  t||||||^|_}t|t}ttttdtd tdtd tdtd tttdtd tdtd  tttdtd tdtd td	td  t||||||^|_}t|t}ttttdtd tdtd tdtd tttdtd tdtd td	td  tttdtd tdtd tdtd  t||||||`}t|t}ttttdtd tdtd tdtd tttd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  tttdtd tdtd td	td  t||||||`}t|t} ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tttdtd tdtd tdtd  t||||||a|%|b	}!t|!t}"ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tdtttdtd tdtd  tdtd  t||||||a|%|b	}#t|#t}$ttttdtd tdtd tdtd tttdtd tdtd td	td  tttdtd tdtd td  t||||||^|_}%t|%t}&ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tttdtd tdtd td  t||||||^|_}'t|'t}(ttttdtd tdtd tdtd tttdtd tdtd t  tttdtd tdtd  t||||||})t|)t}*ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tttdtd tdtd t  t|||||||}+t|+t},ttttdtd tdtd tdtd tdtttdtd tdtd  t  tttdtd tdtd  t||||||}-t|-t}.ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tdtttdtd tdtd  t  t|||||||}/t|/t}0ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tttdtd tdtd tdtd  t|||||||^|c	}1t|1t}2ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tdtttdtd tdtd  tdtd  t|||||||^|c	}3t|3t}4ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tdtttdtd tdtd  td	td  t|||||%|:}5t|5t}6ttttdtd tdtd tdtd tdtttdtd tdtd  td	td  tdtttdtd tdtd  tdtd  t|||||S|%|b|d	}7t|7t}8tttAtz tFt  ttdtd  t||||e|f|g|h|i	}9t|9t}:tttBtdtdtttdtd tdtd   td	td ttdtd tdtd tdtd  tttdtd tdtd  t||||||||^|_
};t|;t}<tttBtdtdtttdtd tdtd   td	td ttdtd tdtd tdtd  tttdtd tdtd  t||||||||^|_
}=t|=t}>tttBtdtdtttdtd tdtd   td	td ttdtd tdtd tdtd  tttdtd tdtd td  t||||||||^|_
}?t|?t}@tttBtdtdtttdtd tdtd   td	td ttdtd tdtd tdtd  tttdtd tdtd td  t||||||||^|_
}At|At}BtttBtdtdtttdtd tdtd   td	td ttdtd tdtd tdtd  tttdtd tdtd  tttdtd tdtd  t||||||||^|_
}Ct|Ct}DtttBtdtdtttdtd tdtd   td	td ttdtd tdtd tdtd  tttdtd tdtd tttdtd tdtd   t||||||||^|_
}Et|Et}Fttttdtd tdtd tdtd tttdtd tdtd tdtd  tttdtd tdtd tdtd  t|||||||J|j	}Gt|Gt}Httttdtd tdtd tdtd tttdtd tdtd tdtd  tttdtd tdtd tdtd  t|||||||J|j	}It|It}Jttttdtd tdtd tdtd tttdtd tdtd tdtd  tttdtd tdtd tdtd  t||||||||J	}Kt|Kt}LtttAttdtd tdtd  tFttdtd tdtd   ttdtd tdtd tdtd  t||||||||k|l|J||m}Mt|Mt}NtttAttdtd tdtd tdtd  tttdtd tdtd  t|o||||||n}Ot|Ot}PtttAttdtd tdtd tdtd  tttdtd tdtd  t|o||||||n}Qt|Qt}RtttAttdtd tdtd tdtd  tttdtd tdtd t.  t|o||||||p|q|r
}St|St}TtttAttdtd tdtd tdtd  tttdtd tdtd t  t|o||||||s|%|"
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}gt|gt̃}htttAttdtd tdtd tdtd  tdtttdtd tdtd  t.  t|o||||||p|q|4
}it|it̓}jtttAttdtd tdtd tdtd  tdtttdtd tdtd  t.  t|o|||||||x|y|z}kt|kt΃}ltttAttdtd tdtd tdtd  tdtttdtd tdtd  t.  t|o|||||||x|y|z}mt|mtσ}ntttAttdtd tdtd tdtd  tdtttdtd tdtd  t.  t|o||||||{|q|r||}ot|otЃ}ptttAttdtd tdtd tdtd  tdtttdtd tdtd  t.  t|o||||||{|q|r||}qt|qtу}rtttAttdtd tdtd tdtd  tdtttdtd tdtd  td	td  t|o||||||:}st|st҃}ttttAttdtd tdtd tdtd  tdtttdtd tdtd  td	td  t|o||||||:}ut|utӃ}vtttAttdtd tdtd tdtd  tdtttdtd tdtd  td	td  t|o||||||@}wt|wtԃ}xtttAttdtd tdtd tdtd  tdtttdtd tdtd  td	td  t|o||||||@}yt|ytՃ}ztttAttdtd tdtd tdtd  ttdtdtttdtd tdtd   td	td  t|o||||||||}|~}{t|{t׃}|tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd   td	td  t|o|||||||||~}}t|}t؃}~tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd   td	td  t|o|||||||||~}t|tك}tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd   td	td  tttdtd tdtd tdtd  t|o||||||||}||}t|tڃ}tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd   td	td  tttdtd tdtd tdtd  t|o||||||||||}t|tۃ}tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd   td	td  tttdtd tdtd tdtd  t|o||||||||||}t|t܃}tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd    ttdtdtttdtd tdtd    t|o||||||||||}||}t|tރ}tttAttdtd tdtd tdtd  ttdtdtttdtd tdtd    ttdtdtttdtd tdtd    t|o||||||||||}||}t|t߃}tttAttdtd  tFtz  t|o|||f||}t|t}tttAttdtd tdtd tdtd  ttdtd  tttdtd tdtd td	td  t|o||||||%|b|
}t|t}tttAttdtd tdtd tdtd  ttdtd  tttdtd tdtd td	td  t|o||||||%|b|
}t|t}tttAttdtd tdtd tdtd  tttdtd tdtd tdtd  tttdtd tdtd td	td  t|o||||||||
}t|t}tttAttdtd tdtd tdtd  ttdtd  tttdtd tdtd tdtd  tttdtd tdtd td	td  t|o||||||||
}t|t}tttAttdtd tdtd tdtd  tFttdtd tdtd   tdttdtd tdtd   t|o|||||||f|
}t|t}tttAt ttztd	td  t|o|||}t|t}tttAt tĐtztd	td  t|o|||}t|t}tttAt ttztdtd  tĐtztd	td  t|o|||}t|t}ttttdtdtdtdtttd	td tdtd   t t|||||||}t|t}ttttdtdtdtdtttd	td tdtd   t t|||||||}t|t}ttttdtdtdtdtttd	td tdtd   tdtd t|||||;|}t|t}ttttdtdtdtdtttd	td tdtd   tdtd t|||||;|}t|t}ttttdtdtdtdtttd	td tdtd   t|||||}t|t}ttttdtdtdtdtttd	td tdtd   t|||||}t|t}ttttdtdtdtdtttd	td tdtd   t t|||||)||}t|t}ttttdtdtdtdtttd	td tdtd   t t|||||)||}t|t}ttttdtdtdtdtttd	td tdtd   t t|||||)|||	}t|t}ttttdtdtdtdtttd	td tdtd   t t|||||)|||	}t|t}ttttdtdtdtdtttd	td tdtd   t t||||||}t|t}ttttdtdtdtdtttd	td tdtd   t t||||||}t|t}ttttdtd ttdtdtdtdtttd	td tdtd   t  t|||||||||Q
}t|t}ttttdtd ttdtdtdtdtttd	td tdtd   t  t|||||||||Q
}t|t}ttttdtd ttdtdtdtdtttd	td tdtd   tdtd  t||||||;|}t|t}ttttdtd ttdtdtdtdtttd	td tdtd   tdtd  t||||||;|}t|t}ttttdtd ttdtdtdtdtttd	td tdtd    t||||||}t|t}ttttdtd ttdtdtdtdtttd	td tdtd    t||||||}t|t}ttttdtd ttdtdtdtdtttd	td tdtd   t  t||||||)||	}t|t}ttttdtd ttdtdtdtdtttd	td tdtd   t  t||||||)||	}t|Ðt}ttttdtd ttdtdtdtdtttd	td tdtd   t  t||||||)|||
}t|Őt}ttttdtd ttdtdtdtdtttd	td tdtd   t  t||||||)|||
}t|ǐt}ttttdtd ttdtdtdtdtttd	td tdtd   t  t|||||||}t|ɐt }ttttdtd ttdtdtdtdtttd	td tdtd   t  t|||||||}t|ːt}tttdttdtdtdtdtttd	td tdtd    t|||||}t|͐t}tttdttdtdtdtdtttd	td tdtd    t|||||}t|ϐt}tttdttdtdtdtdtttd	td tdtd    t t|||||||}t|ѐt}tttdttdtdtdtdtttd	td tdtd    t t|||||||}t|Ӑt}tttdttdtdtdtdtttd	td tdtd    t t|||||)|||	}t|Րt}tttdttdtdtdtdtttd	td tdtd    t t|||||)|||	}t|אt}tttdttdtdtdtdtttd	td tdtd    t t|||||)||}t|ِt}tttdttdtdtdtdtttd	td tdtd    t t|||||)||}t|ېt	}tttdttdtdtdtdtttd	td tdtd    tdtd t||||||}t|ݐt
}tttdttdtdtdtdtttd	td tdtd    tdtd t||||||}t|ߐt}ttttdtd ttdtdtdtdtttd	td tdtd    t||||||}t|t}ttttdtd ttdtdtdtdtttd	td tdtd    t||||||}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    t  t||||||||Q|
}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    t  t||||||||Q|
}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    t  t||||||)|||
}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    t  t||||||)|||
}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    t  t||||||)||	}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    t  t||||||)||	}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    tdtd  t|||||||}t|t}ttttdtd tdttdtdtdtdtttd	td tdtd    tdtd  t|||||||}t|t}tttttdtd tdtd tttdtd tttdtd tdtd   t|||)|*}t|t}tttttdtd tdtd tttdtd tttdtd tdtd   t|||)|*}t|t}tttttdtd tdtd ttt. tdtd tttdtd tdtd   t||||*}t|t}tttttdtd tdtd ttt. tdtd tttdtd tdtd   t||||*}t|t}ttttdtd tttdtd tdtd  tttd	td tdtd tttdtd tdtd   t||||||)|*}t|t}ttttdtd tttdtd tdtd  tttd	td tdtd tttdtd tdtd   t||||||)|*}t|t} ttttdtd tttdtd tdtd  tttd	td tdtd tttdtd tdtd   t|||||)|*|}t|t}tttt tttdtd tdtd  tttd	td tdtd tttdtd tdtd   t|||||)|*|}t|t}ttttdtdttdtd tdtd  td	td t||||}t|t}ttttdtdttdtd tdtd  td	td t||||}t|t}tttttdtd tdtd tdtd ttdtd tdtd  td	td t||||||}	t|	t }
tttttdtd tdtd tdtd ttdtd tdtd  td	td t||||||}t|t!}tttttd	td t||}t|t"}tttttd	td t||}t|t#}tttdtdttztdtd  tttdtd  t|g}t|t$}tttdtdtĐtztdtd  tĐttdtd  t|g}t|t%}ttttztdtd tttdtd  t||J}t|t&}tttĐtztdtd tĐttdtd  t||J}t|t'}ttttdtd ttztdtd  tttdtd  t||}t|t(}ttttdtd tĐtztdtd  tĐttdtd  t||}t|t)}tttdtdttztdtd  tĐttdtd  t|g|}t|t*}ttttztdtd tĐttdtd  t|J|}t|t+} ttttdtd ttztdtd  tĐttdtd  t||}!t|!t,}"ttttztttd	td  t|q|7|}#t|#t-}$tttdtt td	td tĐtz t|q|7|}%t|%t.}&tttdtt td	td ttz t|q|7|}'t|'t/}(tttĐtztttd	td  t|q|7|})t|)t0}*tttdtĐt td	td ttz t|q|7|}+t|+t1},tttdtt td	td tĐtz t|q|7|}-t|-t2}.tttdtt td	td ttz t|q|7|}/t|/t3}0tttdtĐt td	td tĐtz t|q|7|}1t|1t4}2tttBtdtdtttdtd tdtd  tttdtd tdtd   td	td ttdtd tdtd tdtd  t|||||||||
}3t|3t5}4ttttdtd tBtdtdtttdtd tdtd td   t.  t|||||||b||
}5t|5t6}6ttttdtd tBtdtdtttdtd tdtd td   t.  t|||||||b||
}7t|7t7}8ttttdtd tdtd tdtd tt8ttdtd  t. tdtd tdtd tdtd  t||||||||^|)
}9t|9t9}:ttttdtd tdtd tdtd tĐt8ttdtd  t. tdtd tdtd tdtd  t||||||||^|)
};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 t<tdtdtttd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tttdtd tdtd td   tttdtd tdtd td   t||||||||^||}At|At>}Bttttdtd tdtd tdtd t8tdtdtttdtd tdtd td   tttdtd tdtd td   t|||||||^}Ct|Ct?}Dttttdtd tdtd tdtd tdtdtttdtd tdtd td  tdtdtttdtd tdtd td   tdtd tttdtd tdtd td   t||||||||^||}Et|Et@}Fttttdtd tdtd tdtd tttdtd tdtd  tBtdtdtttdtd tdtd    t|||||||^|	}Gt|GtA}Httttdtd tdtd tdtd tttdtd tdtd  tBtdtdtttdtd tdtd    t|||||||^|	}It|ItB}Jttttdtd tdtd tdtd tttdtd tdtd  tBtdtdtttdtd tdtd    t|||||||^|	}Kt|KtC}Lttttdtd tdtd tdtd tttdtd tdtd  tBtdtdtttdtd tdtd    t|||||||^|	}Mt|MtD}Nttttdtd tdtd tdtd tttdtd tdtd t.  tBtdtdtttdtd tdtd    t|||||||^|:|r|}Ot|OtE}Pttttdtd tdtd tdtd tttdtd tdtd t.  tBtdtdtttdtd tdtd    t|||||||^|:|r|}Qt|QtF}Rttttdtd tdtd tdtd tttdtd tdtd t.  tBtdtdtttdtd tdtd    t|||||||^|:|r|}St|StG}Tttttdtd tdtd tdtd tttdtd tdtd t.  tBtdtdtttdtd tdtd    t|||||||^|:|r|}Ut|UtH}Vttttd
tdtttdtd tdtd   ttdtd tdtd  tBtdtdtttdtd tdtd   td  t||||||||	|
}Wt|WtI}Xttttd
tdtttdtd tdtd   ttdtd tdtd  tBtdtdtttdtd tdtd   td  t||||||||	|
}Yt|YtJ}ZtttBtdtdttz  td	td tdtĐtz tdtd  t|||||}[t|[tK}\tttBtdtdttz  td	td tdttz tdtd  t|||||}]t|]tL}^tttdtdtttdtd tdtd tdtd  tttdtd tdtd td	td  t|||||}_t|_tM}`tttdtdtttdtd tdtd tdtd  tttdtd tdtd td	td  t|||||}at|atN}btttdtĐt8ttdtd  tttdtd tdtd   t||||||}ct|ctO}dtttdtt8ttdtd  tttdtd tdtd   t||||||}et|etP}ftttt8ttdtd  tttdtd tdtd  t||||||}gt|gtQ}htttdtt8ttdtd  tttdtd tdtd   t||||||}it|itR}jtttdtdtĐtz tdtdttz  td	td tdtd t||||Y}kt|ktS}lg ||||||đ|Ƒ|ȑ|ʑ|̑|Α|Б|ґ|ԑ|֑|ؑ|ڑ|ܑ|ޑ||||||||||||||||| |||||
||||||||||| |"|$|&|(|*|,|.|0|2|4|6|8|:|<|>|@|B|D|F|H|J|L|N|P|R|T|V|X|Z|\|^|`|b|d|f|h|j|l|n|p|r|t|v|x|z|||~|||||||||||||||||||||||||||||||||||đ|Ƒ|ȑ|ʑ|̑|Α|Б|ґ|ԑ|֑|ؑ|ڑ|ܑ|ޑ||||||||||||||||| |||||
||||||||||| |"|$|&|(|*|,|.|0|2|4|6|8|:|<|>|@|B|D|F|H|J|L|N|P|R|T|V|X|Z|\|^|`|b|d|f|h|j|l|n|p|r|t|v|x|z|||~|||||||||||||||||||||||||||||||||||đ|Ƒ|ȑ|ʑ|̑|Α|Б|ґ|ԑ|֑|ؑ|ڑ|ܑ|ޑ||||||||||||||||| |||||
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sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  u_r  r  r  x_r  r   replacement4688r  replacement4689replacement4690replacement4691replacement4692replacement4693replacement4694replacement4695replacement4696A_replacement4697replacement4698replacement4699replacement4700replacement4701replacement4702replacement4703replacement4704replacement4705replacement4706replacement4707replacement4708replacement4709replacement4710n1_n2_replacement4711replacement4712replacement4713replacement4714replacement4715replacement4716replacement4717replacement4718replacement4719replacement4720replacement4721replacement4722replacement4723replacement4724replacement4725replacement4726replacement4727replacement4728replacement4729replacement4730replacement4731replacement4732replacement4733replacement4734replacement4735replacement4736replacement4737replacement4738replacement4739replacement4740replacement4741replacement4742replacement4743replacement4744replacement4745replacement4746replacement4747replacement4748replacement4749replacement4750replacement4751replacement4752replacement4753replacement4754replacement4755replacement4756replacement4757replacement4758p_replacement4759replacement4760replacement4761replacement4762m_replacement4763replacement4764replacement4765replacement4766replacement4767replacement4768replacement4769replacement4770replacement4771replacement4772replacement4773replacement4774replacement4775replacement4776replacement4777replacement4778r  replacement4779replacement4780replacement4781replacement4782replacement4783replacement4784replacement4785replacement4786replacement4787n_replacement4788replacement4789replacement4790replacement4791replacement4792replacement4793replacement4794replacement4795replacement4796replacement4797replacement4798replacement4799replacement4800replacement4801replacement4802replacement4803replacement4804replacement4805F_a_replacement4806replacement4807replacement4808G_replacement4809With4810With4811r   With4812replacement4812With4813replacement4813With4814replacement4814With4815replacement4815With4816replacement4816With4817replacement4817With4818replacement4818With4819replacement4819With4820replacement4820With4821replacement4821With4822replacement4822With4823replacement4823replacement4824H_replacement4825With4826replacement4826With4827replacement4827With4828replacement4828With4829replacement4829With4830replacement4830With4831replacement4831With4832replacement4832With4833replacement4833With4834replacement4834With4835replacement4835v_With4836replacement4836With4837replacement4837With4838replacement4838With4839replacement4839replacement4840replacement4841replacement4842y_With4843replacement4843w_With4844replacement4844With4845replacement4845z_With4846replacement4846With4847With4848With4849replacement4849replacement4850replacement4851replacement4852replacement4853replacement4854replacement4855replacement4856With4857With4858With4859With4860replacement4860With4861replacement4861With4862replacement4863replacement4864replacement4865replacement4866replacement4867replacement4868replacement4869replacement4870replacement4871replacement4872replacement4873replacement4874replacement4875With4876With4877replacement4878With4879replacement4880replacement4881replacement4882replacement4883replacement4884replacement4885replacement4886replacement4887replacement4888replacement4889replacement4890replacement4891replacement4892replacement4893replacement4894replacement4895replacement4896replacement4897replacement4898replacement4899replacement4900replacement4901replacement4902replacement4903replacement4904replacement4905replacement4906replacement4907replacement4908replacement4909replacement4910replacement4911replacement4912f_replacement4913replacement4914replacement4915replacement4916replacement4917replacement4918h_replacement4919replacement4920replacement4921With4922With4923replacement4924replacement4925replacement4926replacement4927replacement4928replacement4929logreplacement4930replacement4931replacement4932replacement4933replacement4934replacement4935replacement4936replacement4937replacement4938replacement4939replacement4940replacement4941replacement4942replacement4943replacement4944replacement4945replacement4946replacement4947replacement4948replacement4949replacement4950replacement4951replacement4952replacement4953replacement4954replacement4955replacement4956replacement4957replacement4958replacement4959replacement4960replacement4961replacement4962replacement4963replacement4964replacement4965replacement4966replacement4967replacement4968replacement4969replacement4970replacement4971replacement4972replacement4973replacement4974replacement4975replacement4976replacement4977replacement4978replacement4979replacement4980replacement4981replacement4982replacement4983replacement4984replacement4985With4986With4987replacement4988replacement4989replacement4990replacement4991replacement4992replacement4993replacement4994replacement4995replacement4996replacement4997replacement4998replacement4999replacement5000replacement5001replacement5002replacement5003replacement5004replacement5005replacement5006replacement5007c_replacement5008replacement5009replacement5010b_replacement5011replacement5012replacement5013replacement5014replacement5015replacement5016replacement5017replacement5018replacement5019replacement5020replacement5021replacement5022replacement5023replacement5024replacement5025replacement5026replacement5027replacement5028replacement5029replacement5030replacement5031replacement5032replacement5033(m  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  pattern4688rule4688pattern4689rule4689pattern4690rule4690pattern4691rule4691pattern4692rule4692pattern4693rule4693pattern4694rule4694pattern4695rule4695pattern4696rule4696pattern4697rule4697pattern4698rule4698pattern4699rule4699pattern4700rule4700pattern4701rule4701pattern4702rule4702pattern4703rule4703pattern4704rule4704pattern4705rule4705pattern4706rule4706pattern4707rule4707pattern4708rule4708pattern4709rule4709pattern4710rule4710pattern4711rule4711pattern4712rule4712pattern4713rule4713pattern4714rule4714pattern4715rule4715pattern4716rule4716pattern4717rule4717pattern4718rule4718pattern4719rule4719pattern4720rule4720pattern4721rule4721pattern4722rule4722pattern4723rule4723pattern4724rule4724pattern4725rule4725pattern4726rule4726pattern4727rule4727pattern4728rule4728pattern4729rule4729pattern4730rule4730pattern4731rule4731pattern4732rule4732pattern4733rule4733pattern4734rule4734pattern4735rule4735pattern4736rule4736pattern4737rule4737pattern4738rule4738pattern4739rule4739pattern4740rule4740pattern4741rule4741pattern4742rule4742pattern4743rule4743pattern4744rule4744pattern4745rule4745pattern4746rule4746pattern4747rule4747pattern4748rule4748pattern4749rule4749pattern4750rule4750pattern4751rule4751pattern4752rule4752pattern4753rule4753pattern4754rule4754pattern4755rule4755pattern4756rule4756pattern4757rule4757pattern4758rule4758pattern4759rule4759pattern4760rule4760pattern4761rule4761pattern4762rule4762pattern4763rule4763pattern4764rule4764pattern4765rule4765pattern4766rule4766pattern4767rule4767pattern4768rule4768pattern4769rule4769pattern4770rule4770pattern4771rule4771pattern4772rule4772pattern4773rule4773pattern4774rule4774pattern4775rule4775pattern4776rule4776pattern4777rule4777pattern4778rule4778pattern4779rule4779pattern4780rule4780pattern4781rule4781pattern4782rule4782pattern4783rule4783pattern4784rule4784pattern4785rule4785pattern4786rule4786pattern4787rule4787pattern4788rule4788pattern4789rule4789pattern4790rule4790pattern4791rule4791pattern4792rule4792pattern4793rule4793pattern4794rule4794pattern4795rule4795pattern4796rule4796pattern4797rule4797pattern4798rule4798pattern4799rule4799pattern4800rule4800pattern4801rule4801pattern4802rule4802pattern4803rule4803pattern4804rule4804pattern4805rule4805pattern4806rule4806pattern4807rule4807pattern4808rule4808pattern4809rule4809pattern4810rule4810pattern4811rule4811pattern4812rule4812pattern4813rule4813pattern4814rule4814pattern4815rule4815pattern4816rule4816pattern4817rule4817pattern4818rule4818pattern4819rule4819pattern4820rule4820pattern4821rule4821pattern4822rule4822pattern4823rule4823pattern4824rule4824pattern4825rule4825pattern4826rule4826pattern4827rule4827pattern4828rule4828pattern4829rule4829pattern4830rule4830pattern4831rule4831pattern4832rule4832pattern4833rule4833pattern4834rule4834pattern4835rule4835pattern4836rule4836pattern4837rule4837pattern4838rule4838pattern4839rule4839pattern4840rule4840pattern4841rule4841pattern4842rule4842pattern4843rule4843pattern4844rule4844pattern4845rule4845pattern4846rule4846pattern4847rule4847pattern4848rule4848pattern4849rule4849pattern4850rule4850pattern4851rule4851pattern4852rule4852pattern4853rule4853pattern4854rule4854pattern4855rule4855pattern4856rule4856pattern4857rule4857pattern4858rule4858pattern4859rule4859pattern4860rule4860pattern4861rule4861pattern4862rule4862pattern4863rule4863pattern4864rule4864pattern4865rule4865pattern4866rule4866pattern4867rule4867pattern4868rule4868pattern4869rule4869pattern4870rule4870pattern4871rule4871pattern4872rule4872pattern4873rule4873pattern4874rule4874pattern4875rule4875pattern4876rule4876pattern4877rule4877pattern4878rule4878pattern4879rule4879pattern4880rule4880pattern4881rule4881pattern4882rule4882pattern4883rule4883pattern4884rule4884pattern4885rule4885pattern4886rule4886pattern4887rule4887pattern4888rule4888pattern4889rule4889pattern4890rule4890pattern4891rule4891pattern4892rule4892pattern4893rule4893pattern4894rule4894pattern4895rule4895pattern4896rule4896pattern4897rule4897pattern4898rule4898pattern4899rule4899pattern4900rule4900pattern4901rule4901pattern4902rule4902pattern4903rule4903pattern4904rule4904pattern4905rule4905pattern4906rule4906pattern4907rule4907pattern4908rule4908pattern4909rule4909pattern4910rule4910pattern4911rule4911pattern4912rule4912pattern4913rule4913pattern4914rule4914pattern4915rule4915pattern4916rule4916pattern4917rule4917pattern4918rule4918pattern4919rule4919pattern4920rule4920pattern4921rule4921pattern4922rule4922pattern4923rule4923pattern4924rule4924pattern4925rule4925pattern4926rule4926pattern4927rule4927pattern4928rule4928pattern4929rule4929pattern4930rule4930pattern4931rule4931pattern4932rule4932pattern4933rule4933pattern4934rule4934pattern4935rule4935pattern4936rule4936pattern4937rule4937pattern4938rule4938pattern4939rule4939pattern4940rule4940pattern4941rule4941pattern4942rule4942pattern4943rule4943pattern4944rule4944pattern4945rule4945pattern4946rule4946pattern4947rule4947pattern4948rule4948pattern4949rule4949pattern4950rule4950pattern4951rule4951pattern4952rule4952pattern4953rule4953pattern4954rule4954pattern4955rule4955pattern4956rule4956pattern4957rule4957pattern4958rule4958pattern4959rule4959pattern4960rule4960pattern4961rule4961pattern4962rule4962pattern4963rule4963pattern4964rule4964pattern4965rule4965pattern4966rule4966pattern4967rule4967pattern4968rule4968pattern4969rule4969pattern4970rule4970pattern4971rule4971pattern4972rule4972pattern4973rule4973pattern4974rule4974pattern4975rule4975pattern4976rule4976pattern4977rule4977pattern4978rule4978pattern4979rule4979pattern4980rule4980pattern4981rule4981pattern4982rule4982pattern4983rule4983pattern4984rule4984pattern4985rule4985pattern4986rule4986pattern4987rule4987pattern4988rule4988pattern4989rule4989pattern4990rule4990pattern4991rule4991pattern4992rule4992pattern4993rule4993pattern4994rule4994pattern4995rule4995pattern4996rule4996pattern4997rule4997pattern4998rule4998pattern4999rule4999pattern5000rule5000pattern5001rule5001pattern5002rule5002pattern5003rule5003pattern5004rule5004pattern5005rule5005pattern5006rule5006pattern5007rule5007pattern5008rule5008pattern5009rule5009pattern5010rule5010pattern5011rule5011pattern5012rule5012pattern5013rule5013pattern5014rule5014pattern5015rule5015pattern5016rule5016pattern5017rule5017pattern5018rule5018pattern5019rule5019pattern5020rule5020pattern5021rule5021pattern5022rule5022pattern5023rule5023pattern5024rule5024pattern5025rule5025pattern5026rule5026pattern5027rule5027pattern5028rule5028pattern5029rule5029pattern5030rule5030pattern5031rule5031pattern5032rule5032pattern5033rule5033r  r  r  miscellaneous_trig   s~    
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XX\\\\PPXX^^^~~~~ff||Z\\|VtVVVVX\X\XXfVVVVZZZZZZrr"(4Jd44RFrr||~~~~zz<66Nffll\\ffhhdd||ppzz||xxddnnppnnttppvv||TTxx&&LL@@RRN@R4<<4<<<<vvbb``X``       rC  c              	   C   s   t |t| ||   | |t| ||   |   |t| ||   |  t|t| ||   ||  |t| ||   |   t| ||S Nr  r  r  r  r   rH  r  r  r  r  r  r  r  xr  r  r  r       r  c              	   C      t |t| ||   | |t| ||   |   |t| ||   |  t|t| ||   | |t| ||   | |   t| ||S rD  rE  rF  r  r  r  r    rH  r  c              	   C   s   t |t| ||   | |t| ||   |  |t| ||   |   t|t| ||   | |  |t| ||   |  t| ||S rD  rE  rF  r  r  r  r    rH  r  c              	   C   s   t |t| ||   | |t| ||   |  |t| ||   |   t|t| ||   |  |t| ||   ||   t| ||S rD  rE  rF  r  r  r  r    rH  r  c                 C   `   t |t| ||   | |t| ||   |  t|t| ||   | |  t| ||S rD  r  r  r   rH  rF  r  r  r  r       `r  c              	   C   s   t |t| ||   |  |t| ||   |  |t| ||   |  t|t| ||   | |t| ||   |   t| ||S rD  r  r  r  r  r   rH  r  r  r  r  r  rG  r  r  r  r       r  c              	   C   s   t |t| ||   | |t| ||   |   |t| ||   |  t|t| ||   |  |t| ||   |  t| ||S rD  rM  rN  r  r  r  r    rO  r  c                 C   \   t |t| ||   | |t| ||   |  t|t| ||   |  t| ||S rD  r  r  r   rH  rN  r  r  r  r       \r  c                 C   rP  rD  rK  rN  r  r  r  r	    rR  r	  c              	   C   N   t |t|t|||   |td  | t|||   |  t| ||S Nr  r   r  r  rH  r  r  r  r  r  r  r  rG  r  r  r  r       Nr  c              	   C   rS  rT  r  r   r  r  rH  rW  r  r  r  r    rX  r  c                 C   6   t | t|||   | t| t|||   |S rD  r   r  rH  r  r  r  r  r  rG  r  r  r  r       6r  c                 C   rZ  rD  r   r  rH  r\  r  r  r  r    r]  r  c	           	   
   C   r   t |td t|t|||   |td  | t|||  td  |t|||    |  t| ||S Nr  r  r  r   r  rH  	r  r  r  r  r  r  r  r  rG  r  r  r  r       rr  c	           	   
   C   r_  r`  r  r  r   r  rH  rc  r  r  r  r    rd  r  c              	   C   ^   t |td t|t|||   |td  | t|||  td  |  t| ||S r`  rb  r  r  r  r  r  r  r  rG  r  r  r  r       ^r  c              	   C   rf  r`  re  rg  r  r  r  r    rh  r  c                 C   Z   t | t|||  td  |t|||    | t| t|||  td  |S Nr  r   r  r  rH  r  r  r  r  r  r  rG  r  r  r  r       Zr  c                 C   ri  rj  r   r  r  rH  rl  r  r  r  r    rm  r  c                 C   F   t | t|||  td  | t| t|||  td  |S rj  rk  r  r  r  r  r  rG  r  r  r  r       Fr  c                 C   ro  rj  rn  rp  r  r  r  r    rq  r  c                 C   R   t | t|||   |t|||  td   | t| t|||   |S rj  rk  rl  r  r  r  r       Rr  c                 C   rr  rj  rn  rl  r  r  r  r    rs  r  c
           
      C   V   t | |t|||	    |t|||	  td   t| t|||	  |  |	S rj  rk  
r  r  r  r  r  r  r   r!  r  rG  r  r  r  r       Vr  c
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      C   rt  rj  rn  ru  r  r  r  r    rv  r  c                 C   rJ  rD  r  r  r   rH  rF  r  r  r  r    rL  r  c              	   C   rI  rD  rE  rF  r  r  r  r    rH  r  c                 C   rP  rD  rw  rN  r  r  r  r    rR  r  c                 C   \   t |t| ||   | |t| ||   |  t|t| ||   |  t| ||S rD  rw  rN  r  r  r  r     rR  r   c              	   C   rS  rT  r  r   r  r  rH  rW  r  r  r  r!    rX  r!  c              	   C   N   t |t|t|||   |td  | t|||   |  t| ||S rT  ry  rW  r  r  r  r"  #  rX  r"  c                 C   rZ  rD  r   r  rH  r\  r  r  r  r#  '  r]  r#  c                 C   6   t | t|||   | t| t|||   |S rD  r{  r\  r  r  r  r$  +  r]  r$  c	           	   
   C   r_  r`  r  r  r   r  rH  rc  r  r  r  r%  /  rd  r%  c	           	   
   C   r   t |td t|t|||   |td  | t|||  td  |t|||    |  t| ||S r`  r}  rc  r  r  r  r&  3  rd  r&  c              	   C   rf  r`  r}  rg  r  r  r  r'  7  rh  r'  c              	   C   ^   t |td t|t|||   |td  | t|||  td  |  t| ||S r`  r}  rg  r  r  r  r(  ;  rh  r(  c                 C   ri  rj  r   r  r  rH  rl  r  r  r  r)  ?  rm  r)  c                 C   Z   t | t|||  td  |t|||    | t| t|||  td  |S rj  r  rl  r  r  r  r*  C  rm  r*  c                 C   ro  rj  r  rp  r  r  r  r+  G  rq  r+  c                 C   F   t | t|||  td  | t| t|||  td  |S rj  r  rp  r  r  r  r,  K  rq  r,  c                 C   rr  rj  r  rl  r  r  r  r-  O  rs  r-  c
           
      C   rt  rj  r  ru  r  r  r  r.  S  rv  r.  c
           
      C   ^   t | |t|||	    |t|||	  td   tdt|||	   |  t| |	S Nr  r  r  ru  r  r  r  r/  W  rh  r/  c                 C   `   t |t| ||   | |t| ||   |  t|t| ||   | |  t| ||S rD  rK  rF  r  r  r  r0  [  rL  r0  c                 C   r  rD  rQ  rF  r  r  r  r1  _  rL  r1  c              	   C   s   t |t| ||   | |t| ||   |  |t| ||   |   t|t| ||   |  |t| ||   ||   t| ||S rD  rE  rF  r  r  r  r2  c  rH  r2  c              	   C   s   t |t| ||   | |t| ||   |  |t| ||   |   t|t| ||   | |  |t| ||   |  t| ||S rD  rE  rF  r  r  r  r3  g  rH  r3  c              	   C   s   t |t| ||   | |t| ||   |   |t| ||   |  t|t| ||   | |t| ||   | |   t| ||S rD  rE  rF  r  r  r  r4  k  rH  r4  c              	   C   s   t |t| ||   | |t| ||   |   |t| ||   |  t|t| ||   ||  |t| ||   |   t| ||S rD  rE  rF  r  r  r  r5  o  rH  r5  c                 C   rx  rD  rK  rN  r  r  r  r6  s  rR  r6  c                 C   rx  rD  rQ  rN  r  r  r  r7  w  rR  r7  c              	   C   s   t |t| ||   | |t| ||   |   |t| ||   |  t|t| ||   |  |t| ||   |  t| ||S rD  rM  rN  r  r  r  r8  {  rO  r8  c              	   C   s   t |t| ||   |  |t| ||   |  |t| ||   |  t|t| ||   | |t| ||   |   t| ||S rD  rM  rN  r  r  r  r9    rO  r9  c              	   C   rz  rT  rY  rW  r  r  r  r:    rX  r:  c              	   C   rz  rT  rV  rW  r  r  r  r;    rX  r;  c                 C   r|  rD  r^  r\  r  r  r  r<    r]  r<  c                 C   r|  rD  r[  r\  r  r  r  r=    r]  r=  c	           	   
   C   r~  r`  re  rc  r  r  r  r>    rd  r>  c	           	   
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      C   r  r  rk  ru  r  r  r  rG    rh  rG  c                 C   sl   t t| | |||   td| td|   |t t| | |||   td| td|   | S rj  r  r  r  r  r  r  r  rG  r  r  r  rH       lrH  c                 C   sl   t t| | |||   td| td|   |t t| | |||   td| td|   | S rj  r  r  r  r  r  rI    r  rI  c                 C   sn   t t| | |||   td| td|   | t t| | |||   td| td|   | S rj  r  r  r  r  r  r  r  rJ       nrJ  c              	   C   sl   t tdd t|t|||   | ||t tdd t|t|||   | t|||   || S Nr  r  r  r  r   r  r  r  r  r  r  r  r  rG  r  r  r  rL    r  rL  c              	   C   sl   t tdd t|t|||   | ||t tdd t|t|||   | t|||   || S r  r  r  r  r  r  rM    r  rM  c                 C   P   t td| ||   t|t| ||   ||  t| ||  |  ||S rj  r  r  r   r  r  )r  r  r  r  r  r  r  rG  r  r  r  rN       PrN  c                 C   r  rj  r  )r  r  r  r  r  r  r  rG  r  r  r  rO    r  rO  c	           	      C   sn   t |td |t| ||   |td   |t|||   |td   td| | |td   |S Nr  ra  r  )r  r  r  r  	r  r  r  r  r  r  r  r  rG  r  r  r  rQ    r  rQ  c	           	      C   sp   t |td |t| ||   |td   |t|||   |td   td| | |td   | S r  )r  r  r  r  r  r  r  rR    s   prR  c	           	      C   sL   t |t| ||   | |t|||   |td   || |  | S Nr  )r  r  r  r  r  r  r  r  rS       LrS  c	           	      C   sJ   t |t| ||   | |t|||   |td   || |  |S r  r  r  r  r  r  rT       JrT  c	           	   	   C   s   t |td || td  td|td  |td   t|t| ||   |td  |t|||   |td   ||t|td |t| ||   |td   |t|||   |td   td| | |td   | S N   rU  r  r  ra  r  r  r   r  r  r  r  r  r  r  rU       rU  c	           	   	   C   s   t |td || td  td|td  |td   t|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  r  r  r  rV    r  rV  c	           	   	   C   s   t |td |td|  td  td|td  |td   t|t| ||   |td  |t|||   |td   ||t|t| ||   | |t|||   |td   td| | |td   | S Nr  r  r  ra  r  r  r  r  r  rW       rW  c	           	   	   C   s   t |td |td|  td  td|td  |td   t|t| ||   |td  |t|||   |td   ||t|t| ||   | |t|||   |td   td| | |td   | S r  r  r  r  r  r  rX    r  rX  c	           	   	   C   s   t |td || td  |td|   t|t| ||   |td  |t|||   |  ||t|td |t| ||   |td   |t|||   |td   td| | |td|    | S Nr  rU  ra  r  r  r  r  r  r  rY       rY  c	           	   	   C   s   t |td || td  |td|   t|t| ||   |td  |t|||   |  ||t|td |t| ||   |td   |t|||   |td   td| | |td|    | S r  r  r  r  r  r  rZ    r  rZ  c	           	   	   C   s   t |td|  td |td || td   t|t| ||   |td  |t|||   |  ||t|t| ||   | |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d || td   t|t| ||   |td  |t|||   |  ||t|t| ||   | |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|t|||   |td  t| ||   ||ttd|t|||   |  t| ||   |td| td   | S Nr  r  rU  r  r  r  r  r  r]       r]  c                 C   s   t td| | td| td  t|t|||   |td  t| ||   ||ttd |t|||   |  t| ||   |td| td   | S r  r  r  r   r  r  r  r  r  r  r  r^    s   r^  c                 C   s   t td| td td| |td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           
   	   C   sb   t td| ||   ||   t|t| ||	   ||  |t| ||	   ||   |	|	S rj  r  
r  r  r  r  r  r  r  r  r  rG  r  r  r  rh  3     brh  c                 C   sz   t ||t| ||
   |td   |t| ||
   |td   |t|||
   |	  || ||	 td   |
S NrU  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rG  r  r  r  ri  7  s   zri  c                 C   s|   t ||t| ||
   |td   |t| ||
   |td   |t|||
   |	  || ||	 td   |
 S r  )r  r  r  r  r  r  r  r  rk  ;     |rk  c                 C   s|   t |t| ||
   |td  |t| ||
   |td   |t|||
   |	  || | ||	 td   |
 S r  r  r  r  r  r  rl  ?  r  rl  c              	   C   s,  t |td ||	 td  td|td  ||	 td   t|t| ||
   |td  |t| ||
   |  |t|||
   |	td   |
|
t|td |t| ||
   |td   |t| ||
   |  |t|||
   |	td   td| | ||	 td   |
 S r  r  r  r  r  r  rm  C     . rm  c              	   C   s,  t |td ||	 td  td|td  ||	 td   t|t| ||
   |td  |t| ||
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   |	td   |
|
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 S Nr  rU  r  ra  r  r  r  r  r  rq  S      rq  c              	   C   s  t |td ||	 td  |td ||	 td   t|t| ||
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 S r  r  r  r  r  r  rz  w  r  rz  c              	   C   s   t |t| ||
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|
S rD  r  r  r  r  r  r{  {  rO  r{  c                 C   sd   t |t| ||   |td  |td  t| ||  |td   || |td   | S r  r  )r  r  r  r  r  r  rG  r  r  r  r|       dr|  c                 C   s&   t ||| |||  |   | |S rD  )r   )Fr  r  r  r  r  r  rG  r  r  r  r    s   &r  c                 C   s   t td||  tttdtdtdtd t |  | |||  td  t| | |td    |tttd|td |S )Nr  r  rU  r  )r  r  r  r   kr  r   r  r  r  r  r  r  rG  r  r  r  r    rO  r  c              	   C   s0   t ttd||| |||  |    ||S r  r   rI  r  r  r  r  r  r       0r  c	           	   
   C   sB   t t||||  | td||| |||  |    ||S r  r  )	r  Gr  r  r  r  r  r  rG  r  r  r  r       Br  c                 C   s   t | |||  }t|t| |||  t|  |t|| |t|   t||| t|   tt||||  ||S rD  rH  r  r%   r&   r   r   )r  r  r  r  r  r  rG  vr  r  r  r    s   nr  c           	      C   sh   t | |||  }t|t| ||| |  t|  || | t|   t|| ||  ||S rD  rH  r  r%   r&   r   )	r  r  r  r  r  r  r  rG  r  r  r  r  r    s   Tr  c                 C   Z   t |ttttfrdS tt||||   |}tt||||   | ||dr+dS dS NFT
isinstanceintr  floatr  r   r  rm  r  r  r  r  r  rG  r  r  r  r  r       "r  c                 C   r   t t||||   |}t|||  ttttdt||||   | ||||t||||   | |S r  r   r  r  r+   r   r  r  r  r  r  r  r       Xr  c                 C   r  r  r  r  r  r  r  r   r  rm  r  r  r  r  r    r  r  c                 C   t   t t||||   |}t|||  ttttdt||||   | ||||t||||   | | S r  r   r  r  r+   r   r  r  r  r  r  r  r       Zr  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   z   t t||||   |}ttd||  ttttd| 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    r  r  c                 C   |   t t||||   |}ttd||  ttttd| t||||   | ||||t||||   | | S r  r   r  r  r  r+   r   r  r  r  r  r  r       br  c                 C   r  r  r  r  r  r  r  r   r  rm  r  r  r  r  r    r  r  c                 C   r  r  r   r  r  r+   r   r  r  r  r  r  r  r    r  r  c                 C   sZ   t |ttttfrdS tt|| ||   |}tt|| ||   | ||dr+dS dS r  r  r  r  r  r  rG  r  r  r  r  r    r  r  c                 C   sr   t t|| ||   |}t|||  ttttdt|| ||   | ||||t|| ||   | |S r  r  r  r  r  r  r    r  r  c                 C   sj   t |ttttfrdS ttdt||||    |}ttd|t||||     ||dr3dS dS NFr  T	r  r  r  r  r  r   r  r  rm  r  r  r  r  r       "*r  c                 C   s   t tdt||||    |}t|||  ttttdtd|t||||     ||||td|t||||     | S r  r   r  r  r  r+   r   r  r  r  r  r  r        "jr  c                 C   sj   t |ttttfrdS ttdt|| ||    |}ttd|t|| ||     ||dr3dS dS r  r  r  r  r  r  r    r  r  c                 C   s   t tdt|| ||    |}t|||  ttttdtd|t|| ||     ||||td|t|| ||     | S r  r  r  r  r  r  r    r  r  c              	   C   s   t |ttttfrdS tt||||   |}ttt||||   | ||dt	t
dt||||    | t| |rCdS dS )NFTr  )r  r  r  r  r  r   r  r  rm  r^  r  rH  r  r  r  r  r  r  rG  r  r  r  r  r    s   Rr  c                 C   s   t t||||   |}t|td|  ||  ttt||  |td |td  td  t||||   | ||||t||||   | |S r  )r   r  r  r  r+   r   r  r  r  r  r  r    s   r  c              	   C   s   t |ttttfrdS ttdt||||    |}tt	td|t||||     ||dt
t|t||||   |  |rGdS dS r  )r  r  r  r  r  r   r  r  r  rm  r^  rH  r  r  r  r  r  $  s   "Rr  c                 C   s   t tdt||||    |}t|td|  ||  ttt||  |td |td  td  td|t||||     ||||td|t||||     | S r  r  r  r  r  r  r  -  s   "r  c              	   C   s   t |ttttfrdS z/t| |}ttdt| |}t	t
t|tttdt| || |dtt| |}W n ttfyF   Y dS w |rKdS dS r  )r  r  r  r  r  rj  r   r  r  r  r6   r   rm  r   r^  rH  	TypeErrorAttributeErrorr  rG  r  r  resr  r  r  r  3  s   
>r  c                 C   s   t | |}ttdt| |}tttt|ttdt| |t| t	||td t
tttd|td |td  td  td|t|  | |||td|t|  ||S r  )rj  r   r  r  r  r   r   r
   r  r3   r+   r   r  r  rG  r  r  r  r  r  r  A  s   
r  c              	   C   s   t |ttttfrdS z't| |}tt||}tt	t
|ttt||| |dtt| |}W n ttfy>   Y dS w |rCdS dS r  )r  r  r  r  r  rj  r   r  r  r6   r   rm  r   r^  rH  r  r  r  r  r  r  r  H  s   
6r  c                 C   s   t | |}tt||}tttt|tt||t|t||t	d t
ttt	d|t	d |t	d  t	d  t|| | |||t|| ||S r  )rj  r   r  r  r   r   r
   r  r3   r  r+   r   r  r  r  r  r  r  V  s   
r  c	           	      C   s8   t tt| |||  | ||||  |  ||S rD  r   rd  rH  )	r  r  r  r  r  r  r  r  rG  r  r  r  r  ]     8r  c                 C   sL   t tt| |||  |	 ||||  |
  ||||  |  ||S rD  r  )r  r  Hr  r  r  r  r  r  r  r  rrG  r  r  r  r  a  r  r  c                 C   X   t |ttttfrdS tt||||   |}tt||||   | ||r*dS dS r  r  r  r  r  r  r  e      r  c                 C   r  r  r  r  r  r  r  r  n  r  r  c                 C   r  r  r  r  r  r  r  r  t  r  r  c                 C   r  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    r  r  c                 C   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frdS tt||||   |}tt||||   | ||r*dS dS r  r  r  r  r  r  r    r  r  c                 C   s   t t||||   |}t|||  ttt|td  |td  td |td tdd   t||||   | ||||t||||   | |S r  r  r  r  r  r  r    s   r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   s   t t||||   |}t|||  ttt|td  |td  td | td tdd   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   s   t t||||   |}t|||  ttt|td  |td  td |td tdd   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   s   t t||||   |}t|||  ttt|td  |td  td | td tdd   t||||   | ||||t||||   | | S r  r  r  r  r  r  r    s   r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   s   t t||||   |}t|td|  ||  ttt||  |td  |td  td |td tdd    t||||   | ||||t||||   | |S Nr  r  rU  r  r  r  r  r  r    s   r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   s   t t||||   |}t|td|  ||  ttt||  |td  |td  td |td tdd    t||||   | ||||t||||   | | S r  r  r  r  r  r  r    s   r  c	           
      C   X   t |ttttfrdS tt||||   |}	tt||||   |	 ||r*dS dS r  r  
r  r  r  r  r  r  r  r  rG  r  r  r  r  r    r  r  c	           
   	   C   Z   t t||||   |}	t|tt|t||||   |  ||tt|| | S rD  )r   r  r  r   rH  r  r  r  r  r  r       @r  c	           
      C   r  r  r  r  r  r  r  r  
  r  r  c	           
   	   C   r  rD  )r   r  r  r   rH  r  r  r  r  r  r    r  r  c              	   C      t |ttttfrdS z$t| |}tt||}tt	t
|ttt||| t| |}W n ttfy;   Y dS w |r@dS dS r  )r  r  r  r  r  rj  r   r  r  r6   r   rm  r   r  r  r  r  r  r  r  r       
0r  c                 C   s   t | |}tt||}tttt|tt||t|t||t	d t
ttt	dt|| | t| |||t|| ||S r  )rj  r   r  r  r   r   r
   r  r3   r  r+   r   r  r  r  r  r  r  r  '  s   
pr  c              	   C   r  r  )r  r  r  r  r  rj  r   r  r  r6   r   rm  r   r  r  r  r  r  r  r  r  .  r  r  c                 C   s   t | |}tt||}tttt|tt||t| t||t	d t
ttt	dt|| | t| |||t|| ||S r  )rj  r   r  r  r   r   r
   r  r3   r  r+   r   r  r  r  r  r  r  r  <  s   
rr  c                 C      t | | | tt|||S rD  r  r   rH  r  r  r  r  r  r  r  rG  r  r  r  r  C     r  c                 C   r  rD  r  r  r  r  r  r  G  r  r  c                 C   r  rD  r  r  r  r  r  r  K  r  r  c              	   C   s`   t |ttttfrdS ztt|t| |}tt|}W n t	t
fy)   Y dS w |r.dS dS r  r  r  r  r  r  r  rH  r6   r   r  r  )r  rG  yr  r  r  r  r  r  O     r  c                 C   s0   t t|t| |}t|ttt|| |S rD  r  rH  r  r$  r   )r  rG  r  r  r  r  r  r  \  s   r  c              	   C   sd   t |ttttfrdS ztt|| t| |}tt|}W n t	t
fy+   Y dS w |r0dS dS r  r  )r  wrG  r  r  r  r  r  r  r  b  s   r  c                 C   s8   t t|| t| |}t|ttt|| | |S rD  r  )r  r   rG  r  r  r  r  r  r  o  s    r  c              	   C   s`   t |ttttfrdS ztt|t||}tt|}W n t	t
fy)   Y dS w |r.dS dS r  r  )r  r  rG  r  r  r  r  r  r  r  u  r  r  c                 C   s>   t t|t||}t|t|| td   | td  |S r  r  rH  r  r  )r  r  rG  r  r  r  r  r  r    s   *r  c              	   C   sr   t |ttttfrdS ztt|| t|||  |   |}tt|}W n t	t
fy2   Y dS w |r7dS dS r  r  )r  r  r  rG  r  zr  r  r  r  r  r    s   &r  c                 C   s`   t t|| t|||  |   |}t|t|| td  || td    | td  |S r  r  )r  r  r  rG  r  r  r  r  r  r  r    s   &:r  c           	      C   s   t | |||  }t|t| |||  t|  |t|| |t|   t||| t|   tt |t||||   ||S rD  r  )	r  r  r  r  r  r  r  rG  r  r  r  r  r    s   vr  c	           
      C   sp   t | |||  }	t|t| |||	 |  t|  ||	 | t|   t||	 ||  t | ||S rD  r  )
r  r  r  r  r  r  r  r  rG  r  r  r  r  r    s   \r  c              	   C   s|   t |ttttfrdS z t| |}tt||}tt	t
|ttt||| |}W n ttfy7   Y dS w |r<dS dS r  )r  r  r  r  r  rj  r   r  r  r6   r   rm  r   r  r  r  r  r  r  r    s   
(r  c              	   C   sl   t | |}tt||}t|t||d tttd|d |d  d  t|| | |||t|| |S r  )rj  r   r  r  r3   r+   r   r  r  r  r  r  r    s   
Tr  c                 C   N   t | t|||  |  | | tdt|||   ||   t| |S r  )r   r  r  r  rH  r  r  r  r  r  r  r  rG  r  r  r  r    rX  r  c                 C   r  r  )r   r  r  r  rH  r  r  r  r  r    rX  r  c
           
   	   C   sL   t t|||| |||	  | |    |  | |||	  ||   |	S rD  r   rH  )
r  r  r  r  r  r  r  r  r  rG  r  r  r  r    r  r  c              	   C   sj   t t|
||| |||  | |    || |||  | |	    |  | |||  ||   |S rD  r  )r  r  r  r  r  r  r  r  r  r  r  rG  r  r  r  r       jr  c              	   C   sf   t t|	|| |||
  |   | || |||
  | |    |  | |||
  ||   |
S rD  r  )r  r  r  r  r  r  r  r  r  r  rG  r  r  r  r       fr  c                 C   s0   t | t|  |||   |  | t| |S rD  )r   exprH  )r  r  r  r  r  r  rG  r  r  r  r    r  r  c                 C   s   t t| |S rD  )r   r  )r  rG  r  r  r  r    s   r  c                 C   sP   t |}t |}t| t| |t|   | | t|  t|||  ||S rD  r  )r  r  r  r  rG  uuvvr  r  r  r    s   @r  c                 C   sL   t |}t |}t||  t|  ||  t|  t||| |   ||S rD  rH  r  r&   r   )r  r  r  r  rG  r	  r
  r  r  r  r    s   <r  c           
      C   sz   t |}t |}t |}	t||  t|  |	| t|   ||  |	|  t|  t||| |   |	||   ||S rD  r  )
r  r  r  r  r  r   rG  r	  r
  wwr  r  r  r    s   br  c                 C   s0   t |ttttfrdS t| |}t|rdS dS r  )r  r  r  r  r  rI  r)   r  rG  r  r  r  r  r    s   
r  c                 C   s   t | |}t||S rD  )rI  r   r  r  r  r  r    s   

r  c                 C   s   t |ttttfrdS zbttttdtt	t
tttd|td ttt| |td |td  td  tt| |td ttt| |td | | ||}t| |}tt|td |}t|t}W n ttfyy   Y dS w |r~dS dS )NFr  r  T)r  r  r  r  r  r   r   r
   	ShowStepsStepCounterr  r   r  r  r   r  rj  r   r  r  )r  rG  r   r  r  r  r  r  r  r    s   
r  c                 C   s  t tttdttttttd|td t	t
t| |td |td  td  t
t| |td t	t
t| |td | | ||}t| |}t	t
|td |}ttd| t||d tttd|d |d  d  t
|d | | |||t
|d | ||S )NFr  r  )r   r   r
   r  r  r  r   r  r  r   r  rj  r  r  r3   r+   )r  rG  r   r  r  r  r  r  r  	  s   
fr  c                 C   s   t | }t||S rD  )rH  r   r  r  r  r  r  	  s   
r  c                 C      t || ||td   t|||  |td  t| ||  |td   || t|||  | t| ||  |td   ||td   | S Nr  rU  r  r  r  r  r  r  r  rG  r  r  r  r  	     r  c                 C   s   t || ||td   t|||  |td  t| ||  |td   ||t|||  | t| ||  |td   ||td   | S r  r  r  r   r  r  r  r  r  r  r  	  s   r  c                 C   sB   t t|||  | t| ||  | t| ||  |  ||S rD  r   rd  r  r  r  r  r  r  r  r  r  rG  r  r  r  r  	  r  r  c                 C   s   t |||  | t| ||  |  t| ||  |td   | t |||  | t| ||  |td   t| ||  |  | S )Nra  )r   r  r  r  r  r  r  r  r   	  rO  r  c                 C   s   t |||  | tdt| ||   |  t| ||  |td   |t |||  | tdt| ||   |td   t| ||  |  | S Nr  ra  )r   r  r  r  r  r  r  r  r  $	     r  c              	   C   s   t || ||  t|||  |td  tdt| ||   |  || t|||  | tdt| ||   |  ||  | S r  )r  r   r  r  r  r  r  r  r  r  (	     r  c              	   C   s   t || ||  t|||  |td  tdt| ||   |  ||t|||  | td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  r  r  0	  r  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	  s   r  c                 C   s   t |||  | t| ||  |td   t| ||  td  |t |||  | t| ||  |td   t| ||   | S )Nra  r  )r   r  r  r  r  r  r  r  r  r  rG  r  r  r  r  8	  s   r  c                 C   s   t |||  | tdt| ||   |  t| ||  |td   | t |||  | tdt| ||   |td   t| ||  |td   | S Nr  ra  r  )r   r  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| ||   | S )Nr  ra  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	     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  rG  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	  rs  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 rD  r   r2  )	r  r  r  r  r  r  r  r   rG  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  r  	r  r  r  r  r  r  r  r  rG  r  r  r  r  _	     r  c	           	   	   C   s   t || || |td   t| |t|||    |td  |||  |td   ||t| |t|||    |td  |||  |  || |td   | S r  r  r$  r  r  r  r  c	     r  c	           	   	   C   r#  r  r  r$  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$  r  r  r  r  k	  r&  r  c	           	   	   C   s   t || || |td   t| |t|||    |td  |||  |td   || t| |t|||    |td  |||  |  || |td   | S r  r  r$  r  r  r  r  o	  r%  r  c	           	   	   C   r'  r  r  r$  r  r  r  r  s	  r&  r  c
           
      C   B   t t|||	  | t| ||	  | t|||	  |  |	|	S rD  r   rd  r  
r  r  r  r  r  r  r  r  r  rG  r  r  r  r  w	  r  r  c
           
      C   r(  rD  r   rd  r  r*  r  r  r  r  {	  r  r  c
           
      C   sB   t t|||	  | t| ||	  | t|||	  |  |	|	S rD  r  r*  r  r  r  r  	  r  r  c                 C   sD   t t|||  | ||||  |
  | |||  |	|| ||S rD  )r   rc  )r  r  r  r  r  r  r  r  r  r  r  rG  r  r  r  r  	  s   Dr  c                 C   s   t | ||||    | t|||   |td |td  t| td  |td   | t | ||||    | | t|  t|||   |td |td  t| td  |td   | S rj  )r  r  r  r$  r  r  r  r  r  r  r  rG  r  r  r  r  	     r  c                 C   s   t | ||||    | t|||   |td |td  t| td  |td   |t | ||||    | | t|  t|||   |td |td  t| td  |td   | S rj  )r  r  r  r$  r  r,  r  r  r  r  	     r  c                 C   s  t |td | |td  |td |td  t| td  |td |td    t| ||||    t|||  |td   ||t| ||||    | | t|  t|||  |  |td |td  t| td  |td |td    | t| ||||    | | t|||  |td   t|||   |td |td  t| td  |td |td    | S Nr  rU  ra  r  r  r$  r   r  r  r  r  r  r  r  r  r  r  rG  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  r$  r   r  r  r  )r  r  r  r  r  r  r  rG  r  r  r  r  	  r2  r  c                 C   s   t | ||||    t|||  |td   t|||   ||td   |t | ||||    | | t|  t|||  |td   |td |td  |td   | S r  )r  r  r  r  r$  r1  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  r$  r1  r  r  r  r   	  s   r   c                 C   sf  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  r0  r1  r  r  r  r  	     h r  c                 C   sf  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  r3  r1  r  r  r  r  	  r4  r  c              	   C      t ttdt |||   td |  tt| |||    t|||  |  t| ||||    ttdt |||   td |  tt | |||    ||S r  )r  r  r  r  r  r   r1  r  r  r  r  	  r  r  c              	   C   r5  r  )r  r  r  r  r  r   r1  r  r  r  r  	  r  r  c                 C   s~   t t| tt| ||||    tdttdt |||    |  ttdt |||   td |   |||S r  r  r  r   r   r  r  r1  r  r  r  r  	  s   ~r  c                 C   s   t t | tt| ||||    tdttdt |||    |   ttdt |||   td |  |||S r  r6  r1  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  r3  r1  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  r0  r1  r  r  r  r  	  r7  r  c                 C      t | ||||    tdt|||   |td   t|||   ||td   |t | ||||    | | tdt|||   |td   t|  |td |td  |td   | S Nr  rU  ra  r  )r  r  r  r  r$  r1  r  r  r  r	  	  r.  r	  c                 C   r8  r9  )r  r  r  r  r$  r1  r  r  r  r
  	  r.  r
  c              	   C   s~  t |td |td  t| td  |td |td td   |td |td  |td   t| ||||    tdt|||   |td   ||t| ||||    tdt|||   |td   t|||   ||td   | t| ||||    | | tdt|||   |td   t|  |td |td  |td   | S Nr  ra  rU  r  r3  r1  r  r  r  r  	      r  c              	   C   s~  t |td |td  t| td  |td |td td   |td |td  |td   t| ||||    tdt|||   |td   ||t| ||||    tdt|||   |td   t|||   ||td   | t| ||||    | | tdt|||   |td   t|  |td |td  |td   | S r:  r0  r1  r  r  r  r  	  r;  r  c                 C   s   t td| | ||||     t|t | | t|  td|  |td  t | | t|  td|  |td  td ttdt |||     tt| |||    || t|  t| |   |S r  )r  r  r5   r  r$  r  r1  r  r  r  r  	  s   r  c                 C   s   t | ||||    td t |  t|t | | t|  td|  |td  t | | t|  td|  |td  td ttdt |||    tt| |||    || t|  t| |   |S r  )r  r  r  r5   r$  r  r1  r  r  r  r  	  s   r  c              
   C   s   t ttdt |||   td | tdt|||   |  tt | |||    tt| ||||    ttdt |||   td |   tt| |||    |||S r  )r  r  r  r  r  r   r-  r1  r  r  r  r  	  s   r  c                 C   s   t tdttd t |||    | tdt|||   |  tt| |||    tt| ||||    tdttd t |||    |   tt | |||    |||S r  )r  r  r  r  r  r   r-  r1  r  r  r  r  	  s   r  c
           
   	   C   st   t td| ||  t| ||||	    tt | td|  |td  ||	 td  td|   |	|	S )Nr  r  )r  r  r   r  Pi
r  r  r  r  r  r  r  r  r  rG  r  r  r  r  	  r  r  c
           
   	   C   ^   t td| ||  t| ||||	    t|td ||	 td  td|   |	|	S rj  r  r  r   r  r=  r  r  r  r  	  rh  r  c
           
   	   C   r>  rj  r  r=  r  r  r  r  	  rh  r  c              	   C   sb   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  rG  r  r  r  r  	  r  r  c              	   C   sJ   t ||	 t| ||||
    t|td ||
 td  |  |
|
S rj  )r  r   r  r  r@  r  r  r  r  	  r  r  c              
   C   sR   t ||	 t| ||||
    tdt|td ||
 td   |  |
|
S r  )r  r   r  r  r@  r  r  r  r  	  rs  r  c              
   C      t td|	 t| ||||
    t|||
   ||t|||
     |
|
t| ||||
    ||	t|||
     ||t|||
     |
 S rj  r  r  r  r  r  r  r  r  r  hr  rG  r  r  r  r  	  r  r  c              
   C   rA  rj  r  rB  r  r  r  r  	  r  r  c                 C   s*   t | |t||  |t|||  |S rD  r"  )r  r  r  r  r  r  rG  r  r  r  r  	     *r  c	           
      C   b   t | ||||    t|||  |  |}	t|t|	||td   || t|| |	| S rT  )r  r  r  r   r  
r  r  r  r  r  r  r  r  rG  r  r  r  r  r  
     .4r  c	           
      C   rE  rT  )r  r  r  r   r  rF  r  r  r  r  
  rG  r  c                 C   sF   t t| ||||
    t|||
  | t|||
  |	  |
|
S rD  r  r@  r  r  r  r  
  rq  r  c                 C   sN   t t| ||||    ||
  t|||  | t|||  |	  ||S rD  r  )r  r  r  r  r  r  r  r  r  r  r  rG  r  r  r  r  
  rX  r  c                 C   sF   t t| ||||
    ||||
  | ||||
  |	  |
|
S rD  )r   rh  )r  r  r  r  r  r  r  r  r  r  rG  r  r  r  r   
  rq  r   c                 C      t t| | t|| ||S rD  )r   rh  r  r  r  r  r  rG  r  r  r  r!  
  r  r!  c                 C   rH  rD  )r   rh  r  rI  r  r  r  r"  
  r  r"  c                 C   s*   t t| | t|| t||  ||S rD  )r   rh  r  r  )r  r  r  r  r  rG  r  r  r  r#  !
  rD  r#  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  r$  r  r  r  r  r  r  rG  r  r  r  r%  %
  r  r%  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  r$  r  rK  r  r  r  r&  )
  r  r&  c                 C   s   t t|||  td||    t|  | | |  td| | |  |||  td ||   t| | | |  td| | |   | ||S r  r   r   r  r  rK  r  r  r  r'  -
  s   r'  c                 C   s   t t|||  td||    t|  | | |  td |||  td ||   t| | | |  td  | ||S r  rM  rK  r  r  r  r(  1
  s   r(  c              
   C   s   t |t| |t|||     |td |td  td  |t || | t| |t|||     |td |td  td  | S r  )r  r  r$  r  r  r  r  r  r  rG  r  r  r  r)  5
     r)  c              
   C   s   t |t| |t|||     |td |td  td  |t || | t| |t|||     |td |td  td  | S r  )r  r  r$  r  r  rN  r  r  r  r*  9
  rO  r*  c              
   C   sb  t |td |td  | |td  |td |td  |td  td  tt| |t|||    |td  ||t|t| |t|||    |  |td |td  |td  td  | t|| | | t| |t|||    |td   t| |t|||     |td |td  |td  td  | S r  r  r  r   r  r$  r  r  rK  r  r  r  r+  =
     d r+  c              
   C   sb  t |td |td  | |td  |td |td  |td  td  tt| |t|||    |td  ||t|t| |t|||    |  |td |td  |td  td  | t|| | | t| |t|||     t| |t|||    |td   |td |td  |td  td  | S r  r  r  r   r  r$  r  r  rK  r  r  r  r,  A
  rQ  r,  c                 C   sZ  t |td |td  |td td  td |td |td  |td  |td   tt| |t|||    |td  ||t|t| |t|||    |td   |td |td  |td  |td   | t|t| |t|||    |td   || |td  t| |t|||      | S r  r  r  r   r  r$  r  r  rK  r  r  r  r-  E
     \ r-  c              
   C   sZ  t |td |td  |td td  td |td |td  |td  |td   tt| |t|||    |td  ||t|t| |t|||    |td   |td |td  |td  |td   | t|t| |t|||    |td   t| |t|||     || |td   | S r  r  r  r   r  r$  r  r  rK  r  r  r  r.  I
  rT  r.  c              
   C   sX  t |td |||  tdt |   ttdt |   td |   t |||  t|   tt|   t|||  t |   tt |    |  t| t t | | | td  td| |  tdtt | | | td  td| |   |||  tdt |  ttdt |    t | | | td  |S r  r  r  r  r  r5   rK  r  r  r  r/  M
     Z r/  c              
   C   sN  t ||||  t|  tt|   |||  t |  tt |    |  td|||  tdt |   ttdt |   td |   t| t t | | | td  td| |  tdtt | | | td  td| |   |||  tdt |   ttdt |    t | | | td  |S r  r  r  r  r  r5   rK  r  r  r  r0  Q
  s   P r0  c                 C   s   t ||td  |td  t| |t|||    |td   |td |td   |t ||td  t| |t|||    |td   || |td  t| |t|||      | S r  rJ  r  r  r  r  r  r  rG  r  r  r  r1  U
  r.  r1  c              
   C   s   t ||td  |td  t| |t|||    |td   |td |td   |t ||td  t| |t|||    |td   t| |t|||     || |td   | S r  rL  rY  r  r  r  r2  Y
  r.  r2  c                 C   s   t td|  tt|| |||  |td ||    |td  t|  | | | |td   || |  |||  |td  ||   |td  t| | | | |td   || |   |  |||S r  r  r  r   r   r  rY  r  r  r  r3  ]
  r  r3  c                 C   s   t td|  tt|| |||  |td ||    t|  | | | |td   |||  |td  ||   t| | | | |td    |  |||S r  rZ  rY  r  r  r  r4  a
  r&  r4  c              
   C   s   t ||td  |td  t| |t|||     |td |td  |td td   |t || ||td   t| |t|||     |td |td  |td td   | S r  )r  r  r  r$  r  r  r  r  r  r  rG  r  r  r  r5  e
  r.  r5  c              
   C   s   t ||td  |td  t| |t|||     |td |td  |td td   |t || ||td   t| |t|||     |td |td  |td td   | S r  )r  r  r  r$  r  r[  r  r  r  r6  i
  r.  r6  c                 C   s  t |td |td  | |td  |td |td  |td  |td td   t|| t| |t|||    |td   ||t||td  |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 |td  |td  |td td   | S r  rP  rY  r  r  r  r7  m
      r7  c                 C   s  t |td |td  | |td  |td |td  |td  |td td   t|| t| |t|||    |td   ||t||td  |td  t| |t|||    |  |td |td  |td  |td td   | t|| | ||td   t| |t|||     t| |t|||    |td   |td |td  |td  |td td   | S r  rR  rY  r  r  r  r8  q
  r\  r8  c                 C   s  t |td |td  |td td  |td td  |td |td  |td  |td   t|| t| |t|||    |td   ||t||td  t| |t|||    |td   || |td  t| |t|||      | t||td  |td  t| |t|||    |td   |td |td  |td  |td   | S r  rS  rY  r  r  r  r9  u
      r9  c                 C   s  t |td |td  |td td  |td td  |td |td  |td  |td   t|| t| |t|||    |td   ||t||td  t| |t|||    |td   t| |t|||     || |td   | t||td  |td  t| |t|||    |td   |td |td  |td  |td   | S r  rU  rY  r  r  r  r:  y
  r]  r:  c              
   C   sp  t ||td  td |||  tdt |   ttdt |   td |   t |||  t|   tt|   t|||  t |   tt |    |  t| t t | | | | td  td| |  tdtt | | | | td  td| |   |||  tdt |  ttdt |    t | | | | td  |S r  rV  rY  r  r  r  r;  }
     r r;  c              
   C   sf  t ||td  |||  t|  tt|   |||  t |  tt |    |  td|||  tdt |   ttdt |   td |   t| t t | | | | td  td| |  tdtt | | | | td  td| |   |||  tdt |   ttdt |    t | | | | td  |S r  rV  rY  r  r  r  r<  
  r4  r<  c                 C   sj   t tdt| | |  t|||  td|  |||  td|  ttd|  | |   ||S r  r  r  r  r   rN  r  r  r  r=  
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  r  r>  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 Nra  r  rU  rL  rK  r  r  r  r?  
     r?  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`  rJ  rK  r  r  r  r@  
  ra  r@  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 Nr  ra  r  rU  rU  rK  r  r  r  rA  
     t rA  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d  t| |t|||      | S rb  rS  rK  r  r  r  rB  
  rc  rB  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  rR  rK  r  r  r  rC  
     | rC  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  rP  rK  r  r  r  rD  
  rd  rD  c              
   C   sX  t ||||  t|  tt|   |||  tdt |  ttdt |   td  |  td|||  tdt |   ttdt |   td |  t|t t| | | td  td| |  tdtt| | | td  td| |   |||  tdt |   ttdt |    t| | | td  |S r  rX  rK  r  r  r  rE  
  rW  rE  c              
   C   s`  t |t |||  t|   tt|   |||  tdt |   ttdt |   td  |  td |||  tdt |   ttdt |   td |  t|t t| | | td  td| |  tdtt| | | td  td| |   |||  tdt |  ttdt |    t| | | td  |S r  rX  rK  r  r  r  rF  
  s   b rF  c              
   C   s   t tdt| | | |td   t|| |||  |td |   |||  td|td  |  ttd|  | | |td    ||S r  r_  r[  r  r  r  rG  
  r  rG  c              
   C   s   t td| | t| | | |td   |td  t|| |||  |td |   |||  td|td  |   ttd|  | | |td    ||S r  r_  r[  r  r  r  rH  
  r&  rH  c                 C   s   t ||td  |td  tdt| |t|||     |td   |td |td   |t ||td  tdt| |t|||     |td   t| |t|||     || |td   | S Nr  ra  rU  rL  rY  r  r  r  rI  
  r  rI  c                 C   s   t ||td  |td  tdt| |t|||     |td   |td |td   |t ||td  tdt| |t|||     |td   || |td  t| |t|||      | S re  rJ  rY  r  r  r  rJ  
  r  rJ  c                 C   s  t |td |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dt| |t|||     |td   t| |t|||     || |td   | t||td  |td  tdt| |t|||     |td   |td |td  |td  |td   | S rb  rU  rY  r  r  r  rK  
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  r-  rT  c              	   C   s   t || t|| t|| |td   t| ||  t|| |   || tt| ||  t|| |  | |  | S rT  rh  r  r  r  r  r  rG  r  r  r  rU  
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   C   n   t td| ttt|| | || |  | ||   |  | |td  ||td|||   | S r  rq  r  r  r  r  r  r  rG  r  r  r  r[  
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   C   rt  r  rs  ru  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  rG  lstr  r  r  r]       
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  rz  r^  c                 C      t |t|| |   |S rD  )r   r  r  r  r  r  r   rG  r  r  r  r_       r_  c                 C   r{  rD  )r   r  r|  r  r  r  r`    r}  r`  c                 C   $   t tt||  t||  ||S rD  r)  r  r  r  r   rG  r  r  r  ra       $ra  c                 C   r~  rD  r+  r  r  r  r  rb    r  rb  c                 C   *   t t||  t|| t||  ||S rD  r)  r  r  r  r  r   rG  r  r  r  rc    rD  rc  c                 C   r  rD  r+  r  r  r  r  rd  #  rD  rd  c                 C   s0   t td|   t|ttd| |   ||S rj  r  )r  r  r  r   rG  r  r  r  re  '  r  re  c                 C   s$   t tt||  t||  ||S rD  r  r  r  r  r  rf  +  r  rf  c                 C   s*   t t||  t|| t||  ||S rD  r  r  r  r  r  rg  /  rD  rg  c                 C   sT   t t|| tt|| td  t| ||tt|t|| td   | S rT  )r  r  r   r  r  r  r  r   rG  r  r  r  rh  3  s   Trh  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  r  r  r  r  ri  7  r  ri  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  r  r  r  r  rj  ;  r  rj  c                 C   sV   t t|| tt|| td  t| || tt|t|| td   | S rT  )r  r  r   r  r  r  r  r  r  r  rk  ?  rv  rk  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  r  r  r  r  rl  C  r  rl  c                 C   sn   t t|| ttdt| | td  || t t|| ttdt| | td  t| || S r  r  r  r  r  r  rm  G  r  rm  c                 C   sl   t t|| ttdt| | td  t| ||t t|| ttdt| | td  || S r  r  r  r  r  r  rn  K  r  rn  c                 C   sn   t t|| ttdt| | td  t| || t t|| ttdt| | td  || S r  r  r  r  r  r  ro  O  r  ro  c	           	      C   sJ   t | |ttd| td| |   td  | |||  |  |S rj  )r   r  r  r$  r  r  r  rp  S  r  rp  c              
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           
   
   C   b   t || td  tt| | ||  ||	  | t| ||	|   |  |	|	|||	  |	S rT  rq  r  r  r  r  rt  _  r  rt  c
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   C   s   t || ||  tt|||  ||t|||     ||t||||   t|||   || ||t|||      | S rD  )r  r   r  r  r  	r  r  r  r  r  r  r  r  rG  r  r  r  r    r  r  c	           	   
   C   s   t || ||  tt|||  ||t|||     || t||||   t|||   || ||t|||      | S rD  )r  r   r  r  r  r  r  r  r  r    r  r  c                 C   "   t | t| |t|  | |S rD  )r   r  r  r  r  r  r  r  rG  r  r  r  r       "r  c                 C   r  rD  )r   r  r  r  r  r  r  r    r  r  c                 C   6   t t|t| ||  | t|||  |  ||S rD  r)  rF  r  r  r  r    r]  r  c                 C   r  rD  r+  rF  r  r  r  r    r]  r  c                 C   sx   t tdt|  | ||  |  tt|||  ||t tdt|  | ||  |  tt| ||  || S r  r  r  r  r   r  r  r  r  r  r    s   xr  c              	   C   s   t tdt|  | ||  |  ttdt| ||   ||t tdt|  | ||  |  ttdt|||   || S r  r  r  r  r  r  r    r  r  c              	   C   sf   t |t|  | ||  |  | ttdt| ||  t|||    ||t|| | | S r  )r  r  r   r  r  r  r  r  r  r    r  r  c              	   C   s^   t t|  | ||  | ttdt| ||  t|||    ||t|| | | S r  )r  r  r   r  r  r  r  r  r  r  r    rh  r  c                 C   s$   t || t|  | |  |  |S rD  )r   r  )r  r  r  r  r  rG  r  r  r  r    r  r  (  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r$  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r<  r
  B_C_r}  r  r  r~  rw  rs  d_e_r  g_r  i_j_k_l_rP  rj  rK  q_r_t_r  r  s_r  r   r  r  a1_a2_b1_b2_c1_c2_d1_d2_r  r  e1_e2_f1_f2_g1_g2_n3_Pq_Pm_Px_Qm_Qr_Qx_jn_mn_non2_RFx_RGx_r  iiPqqQRr  r  r  r  	_UseGammar  r  rC  r  r  r  r  r  r  r  r  r	  r  r  r  r  r  r  r  r  r  r  r  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  rL  rM  rN  rO  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  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/  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  rt  ru  rv  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  <module>   sZ              n"JjB.
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