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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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}Mttttdtdtttd
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}Xt|Xt}Ytttd
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}Zt|Zt}[tttdtttdtdtttdtd tdtd   tttdtd tdtd   t|||||1}\t|\t}]tttdtttdtdtttdtd tdtd   tttdtd tdtd   t|||||1}^t|^t}_tttd
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|7
}`t|`t}atttd
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|7
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|
}dt|dt}etttd
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}ft|ft}gtttd
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}ht|ht}itttd
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}jt|jt}ktttd
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}lt|lt}mtttd
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}nt|nt}otttd
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||:|;}xt|xt }ytttd
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||<|;}zt|zt!}{tttd
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|7||}|t||t"}}tttd
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}t|t@}tttd
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}t|tA}tttttdtdtttdtd tdtd   ttd
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}4t|4t}5tttttdtdtttdtd tdtd   ttdtdtd
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tdtttdtd tdtd   t  t|||.|+|||L|1|V|
|N||d}nt|nt}ottttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|1|V||N|d}pt|pt}qttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|1|V||N|d}rt|rt}sttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|1|V|||!|f}tt|tt}uttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|1|V|||!|f}vt|vt}wttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|1|V|||f}xt|xt}yttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|1|V|||f}zt|zt}{ttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd    t|||.|+||||L|1|V}|t||t}}ttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd    t|||.|+||||L|1|V}~t|~t}tttttdtdtttdtd tdtd   ttdtdtd
tdtttdtd tdtd    t|||.|+|||L|1|V
}t|t}tttttdtdtttdtd tdtd   ttdtdtd
tdtttdtd tdtd    t|||.|+|||L|1|V
}t|t}ttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+|||||L|1|V}t|t}ttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+|||||L|1|V}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+|||L|3|V|
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tdtttdtd tdtd   t  t|||.|+|||L|3|V|
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tdtttdtd tdtd   t  t|||.|+||||L|3|V|;|g|h|i}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|3|V|;|g|h|i}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+|||L|3|V|
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tdtttdtd tdtd   t  t|||.|+|||L|3|V|
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tdtttdtd tdtd   t  t|||.|+|||L|3|V|
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tdtttdtd tdtd   t  t|||.|+|||L|3|V|
||7|;}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|3|V|;||k|l}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+||||L|3|V|;||k|l}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+|||L|3|V|
||7|m}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  t|||.|+|||L|3|V|
||7|m}t|t}tttdttdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd     t|||.|+|||L|3|V
}t|t}tttdttdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd     t|||.|+|||L|3|V
}t|t}ttttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd    t|||.|+|L|3|V}t|t}ttttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd    t|||.|+|L|3|V}t|t}tttdtdtdtdtttdtd tdtd   tdd  tdtdtd
tdtttdtd tdtd    t|||.|+|||L|3|V
}t|t}tttdtdtdtdtttdtd tdtd   tdd  tdtdtd
tdtttdtd tdtd    t|||.|+|||L|3|V
}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd    t|||.|+||||L|3|V|}t|t}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd    t|||.|+||||L|3|V|}t|t}tttRtd
tdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   t  t|||.|+|||||L|3|V}t|t}tttRtd
tdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   t  t|||.|+|||||L|3|V}t|t}tttd
tdtttdtd tdtd  t tdtdtdtdtttdtd tdtd   tdtd  t|||+||||	|	}t|t}tttd
tdtttdtd tdtd  t tdtdtdtdtttdtd tdtd   tdtd  t|||+||||	|	}t|t}tttd
tdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd   tdtd  t|||.|+|||||,|	|}t|t}tttd
tdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd   tdtd  t|||.|+|||||,|	|}t|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  tRtd
tdtttdtd tdtd   t  t|||.|+|||o|||,|n}t|tÃ}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  tRtd
tdtttdtd tdtd   t  t|||.|+|||o|||,|n}t|tă}tttdtdtttdtd tdtd  t tRtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtd  t|||.|+|||o|,|p||I}t|tŃ}tttdtdtttdtd tdtd  t tRtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtd  t|||.|+|||o|,|p||I}t|tƃ}tttdtdtttdtd tdtd t  t tRtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtd  t|||.|+|||o|||,|r|p|q}t|Đtȃ}tttdtttdtd tdtd  t tdtd t tRtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtd  t|||.|+|||o|||,|r|p|q}t|ƐtɃ}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   tdtd  tRtd
tdtttdtd tdtd   td	td  t|||.|+|||o||,|I}t|Ȑtʃ}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   tdtd  tRtd
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tdtttdtd tdtd   t  tdtttdtd tdtd  tdtd  t|||.|+||||	||s}t|ΐt̓}tttdtdtttdtd tdtd  t ttdtdtttdtd tdtd   tdtd  tRtd
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tdtttdtd tdtd   t  t|||.|+|||o|||,|	|}t|ԐtЃ}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  tRtd
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tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd    t|||.|+|||t|u|||J|1}t|ؐt҃}ttttdtdtttdtd tdtd   tdtd tRtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd    t|||.|+|||t|u|||J|1}t|ڐtӃ}tttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd    tdtdtdtdtttdtd tdtd    t|||.|+|||t|u|L
}t|ܐtԃ}tttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd    tdtdtdtdtttdtd tdtd    t|||.|+|||t|u|L
}t|ސtՃ}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u|L|||1}t|tփ}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u|L|||1}t|t׃}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u|L|||3}t|t؃}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u|L|||3}t|tك}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   tdtd  tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u||L|[}t|tڃ}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   tdtd  tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u||L|[}t|tۃ}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|1|
||}t|t܃}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|1|
||}t|t݃}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1|||v}t|tރ}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1|||v}t|t߃}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|1|
|N|7}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|1|
|N|7}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1||N|c}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1||N|c}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1||7}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1||7}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1||} t| t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|1||}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|1|w}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|1|w}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u||L|1|x}t|t}	ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd    t|||.|+|||t|u||L|1|x}
t|
t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|1|x}t|t}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|1|x}t|t}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3||	||y}t|t}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3||	||y}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3||	||z}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3||	||z}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|3|V|
|||d}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|3|V|
|||d}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|3|V|||d|{}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|3|V|||d|{}t|t}tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|3|V|
||b|d} t| t}!tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|3|V|
||b|d}"t|"t}#tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|3|V|||d|l}$t|$t}%tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u||L|3|V|||d|l}&t|&t}'tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|3|V|
|||b}(t|(t})tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|L|3|V|
|||b}*t|*t}+tttdtdtdtdtttdtd tdtd   ttdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd     t|||.|+|||t|u|L|3|V},t|,t}-tttdtdtdtdtttdtd tdtd   ttdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd     t|||.|+|||t|u|L|3|V}.t|.t}/tttdtdtdtdtttdtd tdtd   ttdtdtd
tdtttdtd tdtd    tdtdtdtdtttdtd tdtd    t|||.|+|||t|u|L|3|V}0t|0t}1tttdtdtdtdtttdtd tdtd   ttdtdtd
tdtttdtd tdtd    tdtdtdtdtttdtd tdtd    t|||.|+|||t|u|L|3|V}2t|2t }3tttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd    t|||.|+|||t|u||L|3|V}4t|4t}5tttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd    t|||.|+|||t|u||L|3|V}6t|6t}7tttdtdtdtdtttdtd tdtd   ttdtdtdtdtttdtd tdtd    ttdtdtd
tdtttdtd tdtd    t|||.|+|||t|u|L|3|V}8t|8t}9tttdtdtdtdtttdtd tdtd   ttdtdtdtdtttdtd tdtd    ttdtdtd
tdtttdtd tdtd    t|||.|+|||t|u|L|3|V}:t|:t};tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3|y}<t|<t}=tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3|y}>t|>t}?tttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3|z}@t|@t}Atttdtdtdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|u|||L|3|z}Bt|Bt}Cttttdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~||}	}Dt|Dt	}Ettttdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~||}	}Ft|Ft
}Gtttdtdtdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~||
}Ht|Ht}Itttdtdtdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~||
}Jt|Jt}Ktttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~||	}Lt|Lt}Mtttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~||	}Nt|Nt}Otttdtdtdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~||||1}Pt|Pt}Qtttdtdtdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~||||1}Rt|Rt}Stttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~||||1}Tt|Tt}Utttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~||||1}Vt|Vt}Wttttdtdtttdtd tdtd   tdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd    t|||||t|u|~|3|
}Xt|Xt}Yttttdtdtttdtd tdtd   tdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd    t|||||t|u|~|3|
}Zt|Zt}[ttttdtdtttdtd tdtd   tdtdtttdtd tdtd td   tttdtd tdtd  t|||t|u|~|}\t|\t}]ttttdtdtttdtd tdtd   tdtdtttdtd tdtd td   tttdtd tdtd  t|||t|u|~|}^t|^t}_ttttdtdtttdtd tdtd td   tttdtd tdtd  t|||t|~|}`t|`t}attttdtdtttdtd tdtd td   tttdtd tdtd  t|||t|~|}bt|bt}cttttdtdtttdtd tdtd   tdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd    t|||||t|u|~||3|}dt|dt}ettttdtdtttdtd tdtd   tdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd    t|||||t|u|~||3|}ft|ft}gttttdtdtttdtd tdtd td   ttdtdtttdtd tdtd    t|||||t|~||3|
}ht|ht}ittttdtdtttdtd tdtd td   ttdtdtttdtd tdtd    t|||||t|~||3|
}jt|jt}ktttdtdtdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~||||3}lt|lt}mtttdtdtdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~||||3}nt|nt}otttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   t  t|||||t|~||||3}pt|pt}qtttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   t  t|||||t|~||||3}rt|rt }stttdtdtdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~|||[}tt|tt!}utttdtdtdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||||t|u|~|||[}vt|vt"}wtttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~|||[
}xt|xt#}ytttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  t|||||t|~|||[
}zt|zt$}{ttttdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~|||}}|t||t%}}ttttdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~|||}}~t|~t&}tttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~|L|V||}t|t'}tttdtdtdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~|L|V||}t|t(}tttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~|L|V||}t|t)}tttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~|L|V||}t|t*}ttttdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|V|v}t|t+}ttttdtdtttdtd tdtd   tdtdtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|V|v}t|t,}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~||L|V|v}t|t-}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~||L|V|v}t|t.}ttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|1|}t|t/}ttttdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|1|}t|t0}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~||L|1|}t|t1}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~||L|1|}t|t2}ttttdtdtttdtd tdtd   tdtd tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|1|O|||V}t|t3}ttttdtdtttdtd tdtd   tdtd tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|1|O|||V}t|t4}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~||L|1|O|||V}t|t5}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~||L|1|O|||V}t|t6}ttttdtdtttdtd tdtd   tdtd tdtdtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~|||L|1|O|}t|t7}ttttdtdtttdtd tdtd   tdtd tdtdtd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~|||L|1|O|}t|t8}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~|||L|1|O|}t|t9}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tdtdtd
tdtttdtd tdtd   td	td  t|||.|+|||t|~|||L|1|O|}t|t:}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~|L|3|V|
|P|}t|t;}tttdtdtdtdtttdtd tdtd   t tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~|L|3|V|
|P|}t|t<}tttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~|L|3|V|
|P|}t|t=}tttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   t  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~|L|3|V|
|P|}t|t>}tttdtdtdtdtttdtd tdtd   tdtd tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|3|V||P|}t|t?}tttdtdtdtdtttdtd tdtd   tdtd tdtdtd
tdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    t|||.|+|||t|u|~||L|3|V||P|}t|t@}tttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~||L|3|V||P|}t|tA}tttdtdtdtdtttdtd tdtd td   tdtdtdtdtttdtd tdtd   tdtd  tdtdtd
tdtttdtd tdtd   t  t|||.|+|||t|~||L|3|V||P|}t|tB}tttdtdtdtdtttdtd tdtd   t tdtdtd
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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  x_m_r  n_r   replacement3401r  replacement3402replacement3403replacement3404replacement3405replacement3406replacement3407replacement3408replacement3409replacement3410replacement3411replacement3412replacement3413replacement3414replacement3415replacement3416replacement3417replacement3418replacement3419replacement3420replacement3421replacement3422replacement3423replacement3424replacement3425replacement3426replacement3427replacement3428replacement3429replacement3430replacement3431replacement3432replacement3433replacement3434replacement3435replacement3436replacement3437replacement3438replacement3439replacement3440replacement3441replacement3442replacement3443r  replacement3444replacement3445replacement3446replacement3447replacement3448replacement3449replacement3450replacement3451replacement3452replacement3453p_replacement3454replacement3455replacement3456replacement3457replacement3458replacement3459replacement3460replacement3461replacement3462replacement3463replacement3464replacement3465a_replacement3466replacement3467replacement3468replacement3469replacement3470replacement3471replacement3472replacement3473replacement3474replacement3475replacement3476replacement3477replacement3478replacement3479replacement3480replacement3481replacement3482replacement3483replacement3484replacement3485replacement3486replacement3487replacement3488replacement3489replacement3490replacement3491replacement3492replacement3493replacement3494replacement3495replacement3496replacement3497replacement3498replacement3499replacement3500replacement3501replacement3502replacement3503replacement3504replacement3505replacement3506replacement3507replacement3508replacement3509replacement3510replacement3511replacement3512replacement3513replacement3514replacement3515replacement3516replacement3517replacement3518replacement3519replacement3520replacement3521replacement3522replacement3523replacement3524replacement3525replacement3526replacement3527replacement3528replacement3529replacement3530replacement3531replacement3532replacement3533replacement3534replacement3535replacement3536replacement3537replacement3538replacement3539replacement3540replacement3541replacement3542replacement3543replacement3544replacement3545replacement3546replacement3547replacement3548replacement3549replacement3550replacement3551replacement3552replacement3553c_replacement3554replacement3555replacement3556replacement3557replacement3558replacement3559replacement3560replacement3561replacement3562replacement3563replacement3564replacement3565replacement3566replacement3567replacement3568replacement3569replacement3570replacement3571replacement3572replacement3573replacement3574replacement3575replacement3576replacement3577replacement3578replacement3579replacement3580replacement3581With3582With3583replacement3584replacement3585replacement3586replacement3587replacement3588replacement3589replacement3590replacement3591replacement3592replacement3593replacement3594replacement3595replacement3596replacement3597replacement3598replacement3599replacement3600replacement3601replacement3602replacement3603replacement3604replacement3605replacement3606replacement3607replacement3608replacement3609replacement3610replacement3611replacement3612replacement3613replacement3614replacement3615replacement3616replacement3617replacement3618replacement3619replacement3620replacement3621replacement3622replacement3623replacement3624replacement3625replacement3626replacement3627replacement3628replacement3629replacement3630replacement3631replacement3632replacement3633replacement3634replacement3635replacement3636replacement3637replacement3638replacement3639replacement3640replacement3641replacement3642replacement3643replacement3644replacement3645replacement3646replacement3647replacement3648replacement3649replacement3650replacement3651replacement3652replacement3653replacement3654replacement3655replacement3656replacement3657replacement3658replacement3659replacement3660replacement3661replacement3662replacement3663replacement3664replacement3665replacement3666replacement3667replacement3668replacement3669q_replacement3670replacement3671replacement3672replacement3673replacement3674replacement3675replacement3676replacement3677replacement3678replacement3679replacement3680replacement3681replacement3682replacement3683replacement3684replacement3685replacement3686replacement3687replacement3688replacement3689replacement3690replacement3691replacement3692replacement3693replacement3694replacement3695replacement3696replacement3697replacement3698replacement3699replacement3700replacement3701replacement3702replacement3703replacement3704replacement3705replacement3706replacement3707A_replacement3708replacement3709replacement3710replacement3711replacement3712replacement3713replacement3714replacement3715replacement3716replacement3717replacement3718replacement3719replacement3720replacement3721replacement3722replacement3723replacement3724replacement3725replacement3726replacement3727replacement3728replacement3729replacement3730replacement3731replacement3732replacement3733replacement3734replacement3735replacement3736replacement3737replacement3738replacement3739replacement3740replacement3741replacement3742replacement3743replacement3744replacement3745replacement3746replacement3747replacement3748replacement3749replacement3750replacement3751replacement3752replacement3753replacement3754replacement3755replacement3756replacement3757replacement3758replacement3759replacement3760replacement3761replacement3762replacement3763replacement3764replacement3765replacement3766replacement3767replacement3768replacement3769replacement3770replacement3771replacement3772replacement3773replacement3774replacement3775replacement3776replacement3777replacement3778replacement3779replacement3780replacement3781replacement3782replacement3783replacement3784replacement3785replacement3786replacement3787replacement3788replacement3789replacement3790replacement3791replacement3792replacement3793replacement3794replacement3795replacement3796replacement3797replacement3798replacement3799replacement3800replacement3801replacement3802replacement3803replacement3804replacement3805replacement3806replacement3807replacement3808replacement3809replacement3810replacement3811replacement3812replacement3813With3814With3815With3816With3817With3818With3819With3820With3821replacement3822replacement3823replacement3824replacement3825replacement3826replacement3827With3828With3829replacement3830replacement3831With3832With3833replacement3834replacement3835With3836With3837replacement3838replacement3839replacement3840replacement3841replacement3842replacement3843replacement3844replacement3845replacement3846replacement3847n2_With3848With3849replacement3850replacement3851replacement3852replacement3853With3854With3855replacement3856replacement3857replacement3858replacement3859replacement3860replacement3861replacement3862replacement3863replacement3864replacement3865replacement3866replacement3867replacement3868replacement3869replacement3870replacement3871replacement3872replacement3873replacement3874replacement3875replacement3876replacement3877replacement3878replacement3879With3880With3881replacement3882replacement3883replacement3884replacement3885replacement3886replacement3887u_v_replacement3888replacement3889replacement3890replacement3891replacement3892replacement3893replacement3894replacement3895replacement3896replacement3897replacement3898replacement3899replacement3900replacement3901replacement3902replacement3903replacement3904replacement3905e_replacement3906replacement3907replacement3908replacement3909replacement3910replacement3911replacement3912replacement3913d_replacement3914replacement3915replacement3916replacement3917replacement3918replacement3919(  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  pattern3401rule3401pattern3402rule3402pattern3403rule3403pattern3404rule3404pattern3405rule3405pattern3406rule3406pattern3407rule3407pattern3408rule3408pattern3409rule3409pattern3410rule3410pattern3411rule3411pattern3412rule3412pattern3413rule3413pattern3414rule3414pattern3415rule3415pattern3416rule3416pattern3417rule3417pattern3418rule3418pattern3419rule3419pattern3420rule3420pattern3421rule3421pattern3422rule3422pattern3423rule3423pattern3424rule3424pattern3425rule3425pattern3426rule3426pattern3427rule3427pattern3428rule3428pattern3429rule3429pattern3430rule3430pattern3431rule3431pattern3432rule3432pattern3433rule3433pattern3434rule3434pattern3435rule3435pattern3436rule3436pattern3437rule3437pattern3438rule3438pattern3439rule3439pattern3440rule3440pattern3441rule3441pattern3442rule3442pattern3443rule3443pattern3444rule3444pattern3445rule3445pattern3446rule3446pattern3447rule3447pattern3448rule3448pattern3449rule3449pattern3450rule3450pattern3451rule3451pattern3452rule3452pattern3453rule3453pattern3454rule3454pattern3455rule3455pattern3456rule3456pattern3457rule3457pattern3458rule3458pattern3459rule3459pattern3460rule3460pattern3461rule3461pattern3462rule3462pattern3463rule3463pattern3464rule3464pattern3465rule3465pattern3466rule3466pattern3467rule3467pattern3468rule3468pattern3469rule3469pattern3470rule3470pattern3471rule3471pattern3472rule3472pattern3473rule3473pattern3474rule3474pattern3475rule3475pattern3476rule3476pattern3477rule3477pattern3478rule3478pattern3479rule3479pattern3480rule3480pattern3481rule3481pattern3482rule3482pattern3483rule3483pattern3484rule3484pattern3485rule3485pattern3486rule3486pattern3487rule3487pattern3488rule3488pattern3489rule3489pattern3490rule3490pattern3491rule3491pattern3492rule3492pattern3493rule3493pattern3494rule3494pattern3495rule3495pattern3496rule3496pattern3497rule3497pattern3498rule3498pattern3499rule3499pattern3500rule3500pattern3501rule3501pattern3502rule3502pattern3503rule3503pattern3504rule3504pattern3505rule3505pattern3506rule3506pattern3507rule3507pattern3508rule3508pattern3509rule3509pattern3510rule3510pattern3511rule3511pattern3512rule3512pattern3513rule3513pattern3514rule3514pattern3515rule3515pattern3516rule3516pattern3517rule3517pattern3518rule3518pattern3519rule3519pattern3520rule3520pattern3521rule3521pattern3522rule3522pattern3523rule3523pattern3524rule3524pattern3525rule3525pattern3526rule3526pattern3527rule3527pattern3528rule3528pattern3529rule3529pattern3530rule3530pattern3531rule3531pattern3532rule3532pattern3533rule3533pattern3534rule3534pattern3535rule3535pattern3536rule3536pattern3537rule3537pattern3538rule3538pattern3539rule3539pattern3540rule3540pattern3541rule3541pattern3542rule3542pattern3543rule3543pattern3544rule3544pattern3545rule3545pattern3546rule3546pattern3547rule3547pattern3548rule3548pattern3549rule3549pattern3550rule3550pattern3551rule3551pattern3552rule3552pattern3553rule3553pattern3554rule3554pattern3555rule3555pattern3556rule3556pattern3557rule3557pattern3558rule3558pattern3559rule3559pattern3560rule3560pattern3561rule3561pattern3562rule3562pattern3563rule3563pattern3564rule3564pattern3565rule3565pattern3566rule3566pattern3567rule3567pattern3568rule3568pattern3569rule3569pattern3570rule3570pattern3571rule3571pattern3572rule3572pattern3573rule3573pattern3574rule3574pattern3575rule3575pattern3576rule3576pattern3577rule3577pattern3578rule3578pattern3579rule3579pattern3580rule3580pattern3581rule3581pattern3582rule3582pattern3583rule3583pattern3584rule3584pattern3585rule3585pattern3586rule3586pattern3587rule3587pattern3588rule3588pattern3589rule3589pattern3590rule3590pattern3591rule3591pattern3592rule3592pattern3593rule3593pattern3594rule3594pattern3595rule3595pattern3596rule3596pattern3597rule3597pattern3598rule3598pattern3599rule3599pattern3600rule3600pattern3601rule3601pattern3602rule3602pattern3603rule3603pattern3604rule3604pattern3605rule3605pattern3606rule3606pattern3607rule3607pattern3608rule3608pattern3609rule3609pattern3610rule3610pattern3611rule3611pattern3612rule3612pattern3613rule3613pattern3614rule3614pattern3615rule3615pattern3616rule3616pattern3617rule3617pattern3618rule3618pattern3619rule3619pattern3620rule3620pattern3621rule3621pattern3622rule3622pattern3623rule3623pattern3624rule3624pattern3625rule3625pattern3626rule3626pattern3627rule3627pattern3628rule3628pattern3629rule3629pattern3630rule3630pattern3631rule3631pattern3632rule3632pattern3633rule3633pattern3634rule3634pattern3635rule3635pattern3636rule3636pattern3637rule3637pattern3638rule3638pattern3639rule3639pattern3640rule3640pattern3641rule3641pattern3642rule3642pattern3643rule3643pattern3644rule3644pattern3645rule3645pattern3646rule3646pattern3647rule3647pattern3648rule3648pattern3649rule3649pattern3650rule3650pattern3651rule3651pattern3652rule3652pattern3653rule3653pattern3654rule3654pattern3655rule3655pattern3656rule3656pattern3657rule3657pattern3658rule3658pattern3659rule3659pattern3660rule3660pattern3661rule3661pattern3662rule3662pattern3663rule3663pattern3664rule3664pattern3665rule3665pattern3666rule3666pattern3667rule3667pattern3668rule3668pattern3669rule3669pattern3670rule3670pattern3671rule3671pattern3672rule3672pattern3673rule3673pattern3674rule3674pattern3675rule3675pattern3676rule3676pattern3677rule3677pattern3678rule3678pattern3679rule3679pattern3680rule3680pattern3681rule3681pattern3682rule3682pattern3683rule3683pattern3684rule3684pattern3685rule3685pattern3686rule3686pattern3687rule3687pattern3688rule3688pattern3689rule3689pattern3690rule3690pattern3691rule3691pattern3692rule3692pattern3693rule3693pattern3694rule3694pattern3695rule3695pattern3696rule3696pattern3697rule3697pattern3698rule3698pattern3699rule3699pattern3700rule3700pattern3701rule3701pattern3702rule3702pattern3703rule3703pattern3704rule3704pattern3705rule3705pattern3706rule3706pattern3707rule3707pattern3708rule3708pattern3709rule3709pattern3710rule3710pattern3711rule3711pattern3712rule3712pattern3713rule3713pattern3714rule3714pattern3715rule3715pattern3716rule3716pattern3717rule3717pattern3718rule3718pattern3719rule3719pattern3720rule3720pattern3721rule3721pattern3722rule3722pattern3723rule3723pattern3724rule3724pattern3725rule3725pattern3726rule3726pattern3727rule3727pattern3728rule3728pattern3729rule3729pattern3730rule3730pattern3731rule3731pattern3732rule3732pattern3733rule3733pattern3734rule3734pattern3735rule3735pattern3736rule3736pattern3737rule3737pattern3738rule3738pattern3739rule3739pattern3740rule3740pattern3741rule3741pattern3742rule3742pattern3743rule3743pattern3744rule3744pattern3745rule3745pattern3746rule3746pattern3747rule3747pattern3748rule3748pattern3749rule3749pattern3750rule3750pattern3751rule3751pattern3752rule3752pattern3753rule3753pattern3754rule3754pattern3755rule3755pattern3756rule3756pattern3757rule3757pattern3758rule3758pattern3759rule3759pattern3760rule3760pattern3761rule3761pattern3762rule3762pattern3763rule3763pattern3764rule3764pattern3765rule3765pattern3766rule3766pattern3767rule3767pattern3768rule3768pattern3769rule3769pattern3770rule3770pattern3771rule3771pattern3772rule3772pattern3773rule3773pattern3774rule3774pattern3775rule3775pattern3776rule3776pattern3777rule3777pattern3778rule3778pattern3779rule3779pattern3780rule3780pattern3781rule3781pattern3782rule3782pattern3783rule3783pattern3784rule3784pattern3785rule3785pattern3786rule3786pattern3787rule3787pattern3788rule3788pattern3789rule3789pattern3790rule3790pattern3791rule3791pattern3792rule3792pattern3793rule3793pattern3794rule3794pattern3795rule3795pattern3796rule3796pattern3797rule3797pattern3798rule3798pattern3799rule3799pattern3800rule3800pattern3801rule3801pattern3802rule3802pattern3803rule3803pattern3804rule3804pattern3805rule3805pattern3806rule3806pattern3807rule3807pattern3808rule3808pattern3809rule3809pattern3810rule3810pattern3811rule3811pattern3812rule3812pattern3813rule3813pattern3814rule3814pattern3815rule3815pattern3816rule3816pattern3817rule3817pattern3818rule3818pattern3819rule3819pattern3820rule3820pattern3821rule3821pattern3822rule3822pattern3823rule3823pattern3824rule3824pattern3825rule3825pattern3826rule3826pattern3827rule3827pattern3828rule3828pattern3829rule3829pattern3830rule3830pattern3831rule3831pattern3832rule3832pattern3833rule3833pattern3834rule3834pattern3835rule3835pattern3836rule3836pattern3837rule3837pattern3838rule3838pattern3839rule3839pattern3840rule3840pattern3841rule3841pattern3842rule3842pattern3843rule3843pattern3844rule3844pattern3845rule3845pattern3846rule3846pattern3847rule3847pattern3848rule3848pattern3849rule3849pattern3850rule3850pattern3851rule3851pattern3852rule3852pattern3853rule3853pattern3854rule3854pattern3855rule3855pattern3856rule3856pattern3857rule3857pattern3858rule3858pattern3859rule3859pattern3860rule3860pattern3861rule3861pattern3862rule3862pattern3863rule3863pattern3864rule3864pattern3865rule3865pattern3866rule3866pattern3867rule3867pattern3868rule3868pattern3869rule3869pattern3870rule3870pattern3871rule3871pattern3872rule3872pattern3873rule3873pattern3874rule3874pattern3875rule3875pattern3876rule3876pattern3877rule3877pattern3878rule3878pattern3879rule3879pattern3880rule3880pattern3881rule3881pattern3882rule3882pattern3883rule3883pattern3884rule3884pattern3885rule3885pattern3886rule3886pattern3887rule3887pattern3888rule3888pattern3889rule3889pattern3890rule3890pattern3891rule3891pattern3892rule3892pattern3893rule3893pattern3894rule3894pattern3895rule3895pattern3896rule3896pattern3897rule3897pattern3898rule3898pattern3899rule3899pattern3900rule3900pattern3901rule3901pattern3902rule3902pattern3903rule3903pattern3904rule3904pattern3905rule3905pattern3906rule3906pattern3907rule3907pattern3908rule3908pattern3909rule3909pattern3910rule3910pattern3911rule3911pattern3912rule3912pattern3913rule3913pattern3914rule3914pattern3915rule3915pattern3916rule3916pattern3917rule3917pattern3918rule3918pattern3919rule3919r  r  r  tangent   sv    
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   C   sl   t td| tt||  td|td  |td |td  tdd    ||t| ||  |S r	  r  r  r+   r   r  r	  r  r  r  r       lr  c              	   C   sN   t | |  t| t|||   ||  tdt|||   |   ||S Nr  r  r   r  r  r  r  r  r  r  r  r	  r  r  r  r       Nr  c              	   C   sN   t | |  t| t|||   ||  tdt|||   |   ||S r!	  r  r   r  r  r  r#	  r  r  r  r    r$	  r  c              	   C   s   t |td |td  | td |td   t| t|||   |td  |t|||   |td   || t|| t|||   |td   |t|||   |td   | td | |td   | S Nr  r	  r  r  r   r  r  r  r	  r  r  r  r       r  c              	   C   s   t |td |td  | td |td   t| t|||   |td  |t|||   |td   || t|| t|||   |td   |t|||   |td   | td | |td   | S r&	  r  r  r   r  r  r  r	  r  r  r  r    r)	  r  c              	   C   s   t |td || td  |td  t| t|||   | |t|||   |td   || t|| t|||   |  |t|||   |td   ||td   | S r&	  r(	  r	  r  r  r  r       r  c              	   C   s   t |td || td  |td  t| t|||   | |t|||   |td   || t|| t|||   |  |t|||   |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d   || t| t|||   | |t|||   |td   || |  | S Nr  r  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d   || t| t|||   | |t|||   |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|||   |td   || t| t|||   | |t|||   |td   || || td   | S Nr  r  r(	  r	  r  r  r  r       r  c              	   C   s   t |td |td || td   t| t|||   | |t|||   |td   || t| t|||   | |t|||   |td   || || td   | S r-	  r*	  r	  r  r  r  r     r.	  r   c              	   C   s   t | td || td  | t| t|||   |td  |t|||   |  ||t|| t|||   |  |t|||   |td   ||  | S r&	  r(	  r	  r  r  r  r       r  c              	   C   s   t | td || td  | t| t|||   |td  |t|||   |  ||t|| t|||   |  |t|||   |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|||   |td   |t|||   |td   | td | || td   | S Nr  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|||   |td   |t|||   |td   | td | || td   | S r0	  r*	  r	  r  r  r  r    r1	  r  c              
   C   sl   t td| tt|||  | td |td  | td tdd    ||| t|||   |S r	  r	  r  r  r  r  r  r	  r  r  r  r    r 	  r  c              
   C   sn   t td| tt|||  | td |td  | td tdd    ||| t|||   | S r	  r	  r2	  r  r  r  r    r	  r  c              	   C   sf  t | tdtdt|td tdd     |tdt|td tdd   td   | t|||   td t|td tdd     |t|||   tdt|td tdd     t|||  td t|td tdd    | tt| | ||  td|td  | td tdd    ||t|||  |S r	  )	r  r  r%   r  r&   r  r  r+   r   r	  r  r  r  r    s   h r  c              	   C   sh  t | tdtdt|td tdd     |tdt|td tdd   td   | t|||   td t|td tdd     |t|||   tdt|td tdd     t|||  td t|td tdd    | tt| | ||  td|td  | td tdd    ||t|||  | S r	  )	r  r  r%   r  r&   r  r  r+   r   r	  r  r  r  r    s   j r  c              	   C   s   t td| t|||    t| | t|||   t|  ttd| t|||    |  |t|||   |  ||S r!	  )r  r  r  r&   r   r  r	  r  r  r  r	  
     r	  c              	   C   s   t td| t|||    t| | t|||   t|  ttd| t|||    |  |t|||   |  ||S r!	  )r  r  r  r&   r   r  r	  r  r  r  r
    r3	  r
  c                 C   sX   t | t|||   | |t|||   |  t|t|||   | |  ||S Nr  r  r   r	  r  r  r  r       Xr  c                 C   sL   t | t|||   | |t|||   |td   || |  | S r!	  r	  r	  r  r  r  r    r	  r  c                 C   sJ   t | t|||   | |t|||   |td   || |  |S r!	  r	  r	  r  r  r  r    r	  r  c              
   C   sn   t | | tt| | |td  |td td |td tdd    ||tdt|||   |S Nr	  r  r  )r  r+   r   r  r  r	  r  r  r  r    r	  r  c              
   C   sp   t | | tt| | |td  |td td |td tdd    ||tdt|||   | S r7	  )r  r+   r   r  r  r	  r  r  r  r  "     pr  c              	   C   s^   t td| tt| | | |td td |td td   ||t|||  |S r	  r  r  r+   r   r  r#	  r  r  r  r  &     ^r  c              
   C   sh   t td| tt| | | |td td |td td   ||tdt|||   | S r	  r9	  r#	  r  r  r  r  *     hr  c              	   C   s   t | 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   | S Nr  r'	  r  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d   || t| td | t|||   |td   |t|||   |td   || |td   | S r<	  r(	  r	  r  r  r  r  2  r)	  r  c              	   C   s   t || td |td |td   t| t|||   | |t|||   |td   || t| t|||   | |t|||   |td   || |td   | S r-	  r*	  r	  r  r  r  r  6  r+	  r  c              	   C   s   t || td |td |td   t| t|||   | |t|||   |td   || t| t|||   | |t|||   |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d   || t|| t|||   |  |t|||   |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d   || t|| t|||   |  |t|||   |td   ||  | S r&	  r(	  r	  r  r  r  r  B  r+	  r  c              	   C   s   t |td |td  || td  t| t|||   | |t|||   |td   || t|| t|||   |  |t|||   |td   ||| td   | S r&	  r*	  r	  r  r  r  r  F  r.	  r  c              	   C   s   t |td |td  || td  t| t|||   | |t|||   |td   || t|| t|||   |  |t|||   |td   ||| td   | S r&	  r(	  r	  r  r  r  r  J  r.	  r  c              	   C   s   t || td | td |  t| t|||   |td  |t|||   |  ||t| t|||   | |t|||   |td   || |  | S r-	  r*	  r	  r  r  r  r  N  r/	  r  c              	   C   s   t || td | td |  t| t|||   |td  |t|||   |  ||t| t|||   | |t|||   |td   || |  | S r-	  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d   |t|||   |td   || || td   | S Nr  r'	  r	  r  r*	  r	  r  r  r  r  V  r1	  r  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   | S r=	  r(	  r	  r  r  r  r  Z  r1	  r  c              
   C   sz   t tt|||  t| t|||   tt|||    ttdtt|||  tt|||    ||S r!	  )r  r  r  r  r  r   r  r  r  r  r	  r  r  r  r  ^     zr  c              
   C   sz   t tt|||  t| t|||   tt|||    ttdtt|||  tt|||    ||S r!	  )r  r  r  r  r  r   r  r>	  r  r  r  r  b  r?	  r  c              	   C   sr   t t| t|||   tt|||   tt|||   ttt|||  tt|||   ||S r4	  )r  r  r  r  r  r   r>	  r  r  r  r   f     rr   c              	   C   sr   t t| t|||   tt|||   tt|||   ttt|||  tt|||   ||S r4	  )r  r  r  r  r  r   r>	  r  r  r  r!  j  r@	  r!  c                 C   s   t | ||  | t|||   |   |t|||   |   |t|||   |  t|t|||   | t|||  | |   ||S r4	  )r  r  r  r  r   r	  r  r  r  r"  n     r"  c                 C   s   t | ||  | t|||   |   |t|||   |   |t|||   |  t|t|||   | t|||  | |   ||S r4	  )r  r  r  r  r   r	  r  r  r  r#  r  rA	  r#  c              
   C   s   t | t|||   | |t|||   |td   t|||  td |td |td  tdd    t|td tdd  |td |td  tdd  |td tdd  t|||  td  || |td   |S Nr  r  r  )r  r  r  r  r5   r  r	  r  r  r  r$  v  s   r$  c              
   C   s   t | t|||   | |t|||   |td   t|||  td |td |td  tdd    t|td tdd  |td |td  tdd  |td tdd  t|||  td  || |td   | S rB	  )r  r  r  r  r5   r  r	  r  r  r  r%  z     r%  c              	   C   st   t t|||  |  t| | t|||   t|  tt|||  |  |  |t|||   |  ||S r4	  r  r  r&   r   r  r	  r  r  r  r&  ~     tr&  c              	   C   st   t t|||  |  t| | t|||   t|  tt|||  |  |  |t|||   |  ||S r4	  r  r  r&   r   r  r	  r  r  r  r'    rE	  r'  c	           	   	   C   s   t |td |td  || | td  t| |t|||   |  | |t|||   |td   || t|| |t|||   |  |  |t|||   |td   ||| | td   | S r&	  r*	  	r  r  r  r  r  r  r  r  r	  r  r  r  r)       r)  c	           	   	   C   s   t |td |td  || | td  t| |t|||   |  | |t|||   |td   || t|| |t|||   |  |  |t|||   |td   ||| | td   | S r&	  r(	  rG	  r  r  r  r*    rH	  r*  c	           	   	   C   s   t || | td |td |td   t| |t|||   |  | |t|||   |td   || t| |t|||   |  | |t|||   |td   || |td   | S r-	  r*	  rG	  r  r  r  r+       r+  c	           	   	   C   s   t || | td |td |td   t| |t|||   |  | |t|||   |td   || t| |t|||   |  | |t|||   |td   || |td   | S r-	  r(	  rG	  r  r  r  r,    rI	  r,  c                 C   sr   t | td t| t|||   |td  || t| | t|||   |td   ||td   | S Nr  r'	  r	  r  r  r   r  r  r  r  r  r  r	  r  r  r  r-    r@	  r-  c                 C   sr   t | td t| t|||   |td  || t| | t|||   |td   ||td   | S rJ	  rK	  rL	  r  r  r  r.    r@	  r.  c                 C   sr   t | td t| t|||   |td  || t| t|||   |td  | | |td   | S Nr'	  r  r  rK	  rL	  r  r  r  r/    r@	  r/  c                 C   sr   t | td t| t|||   |td  || t| t|||   |td  | | |td   | S rM	  rK	  rL	  r  r  r  r0    r@	  r0  c                 C   s&   t ttt| ||  || | S r4	  )r  logr   r  r  r  r	  r  r  r  r1       &r1  c                 C   s$   t ttt| ||  || |S r4	  )r  rN	  r   r  rO	  r  r  r  r2    s   $r2  c              
   C   sJ   t | | tt|| | td |td   ||| t|||   |S Nr  r  r+   r   r  r  rL	  r  r  r  r3    r	  r3  c              
   C   sL   t | | tt|| | td |td   ||| t|||   | S rQ	  rR	  rL	  r  r  r  r4    r	  r4  c                 C   sr   t td|  | tt|||  ||t|| td |td   | t|td t|||   | | S rQ	  rK	  r  r  r  r  r	  r  r  r  r6    r@	  r6  c                 C   sz   t td|  | ttdt|||   ||t|| td |td   | t|td |t|||    | S Nr  r  rK	  rS	  r  r  r  r7    r?	  r7  c              	   C   sx   t td|  t| |t|||    |td  ||t|| |t|||    |td   ||td   | S Nr  r	  rK	  r  r  r  r  r  r	  r  r  r  r8       xr8  c              	   C   sx   t td|  t| |t|||    |td  ||t|| |t|||    |td   ||td   | S rU	  rK	  rV	  r  r  r  r9    rW	  r9  c              	   C   s|   t tdtd|   t| |t|||    |td  ||t| | |t|||    |  td| | |  | S r-	  rK	  rV	  r  r  r  r:       |r:  c              	   C   s|   t tdtd|   t| |t|||    |td  ||t| | |t|||    |  td| | |  | S r-	  rK	  rV	  r  r  r  r;    rX	  r;  c                 C   s\   t td | | tttdtd|  |td   ||t| |t|||    |S rT	  r  r  r+   r   r  r  rS	  r  r  r  r<       \r<  c                 C   sZ   t td| | tttdtd|  |td   ||t| |t|||    |S rT	  rY	  rS	  r  r  r  r=       Zr=  c              
   C   sH   t || tt| | |td  | |  |||t|||   | S r	  rR	  rV	  r  r  r  r>    s   Hr>  c              
   C   sF   t || tt| | |td  | |  |||t|||   |S r	  rR	  rV	  r  r  r  r?       Fr?  c              	   C   s   t | |t|||    |td  | td td|  | t|||    |td   |t|| |t|||    |td   ||td   | S Nr'	  r  r	  r   r  r  r  rV	  r  r  r  r@       r@  c              	   C   s   t | |t|||    |td  | td td|  | t|||    |td   |t|| |t|||    |td   ||td   | S r]	  r^	  rV	  r  r  r  rA    r_	  rA  c              
   C   s   t td| td |td   t| |t|||    | |t|||    |td   ||t|| |t|||    |td   || td |td   |td   | S r-	  rK	  rV	  r  r  r  rB       rB  c              
   C   s   t td| td |td   t| |t|||    | |t|||    |td   ||t|| |t|||    |td   || td |td   |td   | S r-	  rK	  rV	  r  r  r  rC    r`	  rC  c              
   C   s~   t || td |td   t|  t|||   | | |t|||     ||t| | | td |td   | S rQ	  rK	  rS	  r  r  r  rD       ~rD  c              
   C   s~   t || td |td   t|  t|||   | | |t|||     ||t| | | td |td   | S rQ	  rK	  rS	  r  r  r  rE    ra	  rE  c              
   C   sN   t || tt| | | |td |td   |||t|||   |S rQ	  rR	  rV	  r  r  r  rF    r$	  rF  c              
   C   sP   t || tt| | | |td |td   |||t|||   | S rQ	  rR	  rV	  r  r  r  rG       PrG  c                 C   sP   t | t|t|||   | ||t||t|||   |  ||  | S r4	  )r  r   r  r  r  r  r  r  r  r  r	  r  r  r  rH    rb	  rH  c                 C   sP   t | t|t|||   | ||t||t|||   |  ||  | S r4	  )r  r   r  r  rc	  r  r  r  rI    rb	  rI  c              
   C   sv   t | td|  ||  tt| | |td td  | | |td | td   |||t|||   |S rU	  r9	  r	  r  r  r  rJ       vrJ  c              
   C   sx   t | td|  ||  tt| | |td td  | | |td | td   |||t|||   | S rU	  r9	  r	  r  r  r  rK  
  rW	  rK  c                 C   sJ   t ||t|||   |  | |t|||    |  | | |  |S r4	  )r  r  r  r  r  r  r  r  r  r  r	  r  r  r  rL    r	  rL  c                 C   sL   t ||t|||   |  | |t|||    |  | | |  | S r4	  )r  r  r  re	  r  r  r  rM    r	  rM  c                 C   sz   t td |  ||  tttd|  |td  td  ||tdt| |t|||    t|||    |S rT	  r  r  r+   r   r  r  r  r  r  r  r  r	  r  r  r  rN    r?	  rN  c                 C   sx   t td|  ||  tttd|  |td  td  ||tdt| |t|||    t|||    |S rT	  r  r  r+   r   r  r  r  rg	  r  r  r  rO    rW	  rO  c              
   C   s   t | td|td   t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S rU	  r*	  re	  r  r  r  rP       rP  c              
   C   s   t | td|td   t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S rU	  r(	  re	  r  r  r  rQ  "  ri	  rQ  c              
   C   s   t td|td  |  t|t|||   |td  | |t|||    |td   ||ttd|td  |t|||   |td   | |t|||    |td   || |td   | S r<	  r*	  re	  r  r  r  rR  &  s   rR  c              
   C   s   t td|td  |  t|t|||   |td  | |t|||    |td   ||ttd |td  |t|||   |td   | |t|||    |td   || |td   | S r<	  r(	  re	  r  r  r  rS  *  rH	  rS  c              	   C   s   t | | tdt|  |t|||   td t|   | |t|||    t|  | |t|||    t|  t| |t|||    |  ||S rQ	  )r  r  r%   r  r&   r  r   re	  r  r  r  rT  .     rT  c              	   C   s   t | | tdt|  |t|||   td t|   | |t|||    t|  | |t|||    t|  t| |t|||    |  ||S rQ	  )r  r  r%   r  r&   r  r   re	  r  r  r  rU  2  rj	  rU  c                 C   sV   t td| |t|||   |  | |t|||    |td   ||  |S rU	  )r  r  r  r  re	  r  r  r  rV  6     VrV  c                 C   sX   t td | |t|||   |  | |t|||    |td   ||  |S rU	  )r  r  r  r  re	  r  r  r  rW  :  r6	  rW  c              
   C      t | |td|  td  || td  t|t|||   | | |t|||    |td   ||t||t|||   |  | |t|||    |td   ||| td   | S rJ	  r*	  re	  r  r  r  rX  >     rX  c              
   C      t | |td|  td  || td  t|t|||   | | |t|||    |td   ||t||t|||   |  | |t|||    |td   ||| td   | S rJ	  r(	  re	  r  r  r  rY  B  rm	  rY  c                 C   s   t td | |td  | tt|td | td |td |td    ||t| |t|||    t|t|||    |S N   r  rf	  r  r  r  r  r  r	  r  r  r  rZ  F  s   rZ  c                 C   s   t td| |td  | tt|td | td |td |td    ||t| |t|||    t|t|||    |S ro	  rh	  rq	  r  r  r  r[  J     r[  c              
   C   s   t |td |td|  td  |td |  t|t|||   |td  | |t|||    |td   || ttd| |t|||   |  | |t|||    |td   ||  | S rJ	  r*	  re	  r  r  r  r\  N  rH	  r\  c              
   C   s   t |td |td|  td  |td |  t|t|||   |td  | |t|||    |td   || ttd | |t|||   |  | |t|||    |td   ||  | S rJ	  r(	  re	  r  r  r  r]  R     r]  c              
   C   s   t | ||  |td |  t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S rU	  r*	  re	  r  r  r  r^  V     r^  c              
   C   s   t | ||  |td |  t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S rU	  r(	  re	  r  r  r  r_  Z  rt	  r_  c              
   C   rl	  rJ	  r*	  re	  r  r  r  r`  ^  rm	  r`  c              
   C   rn	  rJ	  r(	  re	  r  r  r  ra  b  rm	  ra  c                 C   s   t |t| |t|||    t| |t|||     t|||    tt|t|||   t| |t|||     ||S r4	  )r  r  r  r  r   rq	  r  r  r  rb  f     rb  c                 C   s   t |t| |t|||    t| |t|||     t|||    tt|t|||   t| |t|||     ||S r4	  )r  r  r  r  r   rq	  r  r  r  rc  j  ru	  rc  c              
   C   s   t |td |td  |td |td|    t|t|||   |td  | |t|||    |td   || ttd|td  |t|||   |td   | |t|||    |td   || |td|    | S r<	  r*	  re	  r  r  r  rd  n  rC	  rd  c              
   C   s   t |td |td  |td |td|    t|t|||   |td  | |t|||    |td   || ttd |td  |t|||   |td   | |t|||    |td   || |td|    | S r<	  r(	  re	  r  r  r  re  r  s   re  c              
   C   s   t |td |td  | || td   t|t|||   |td  | |t|||    |td   ||t|td |t|||   |td   | |t|||    |td   || || td   | S r=	  r*	  re	  r  r  r  rf  v     rf  c              
   C   s   t |td |td  | || td   t|t|||   |td  | |t|||    |td   ||t|td |t|||   |td   | |t|||    |td   || || td   | S r=	  r(	  re	  r  r  r  rg  z  rv	  rg  c              
   C      t || | |td|    t|t|||   | | |t|||    |td   ||t| |t|||   |  | |t|||    |  || |td|    | S rT	  r*	  re	  r  r  r  rh  ~     rh  c              
   C      t || | |td|    t|t|||   | | |t|||    |td   ||t| |t|||   |  | |t|||    |  || |td|    | S rT	  r(	  re	  r  r  r  ri    rx	  ri  c              
   C   rl	  rJ	  r*	  re	  r  r  r  rj    rm	  rj  c              
   C   rn	  rJ	  r(	  re	  r  r  r  rk    rm	  rk  c              
   C   rw	  rT	  r*	  re	  r  r  r  rl    rx	  rl  c              
   C   ry	  rT	  r(	  re	  r  r  r  rm    rx	  rm  c              
   C   s   t |t|||   | | |t|||    | td   | |t|||    | td   t| |t|||    |td  | |t|||    |td |   ||S rQ	  )r  r  r  r  r   re	  r  r  r  rn       rn  c              
   C   s   t |t|||   | | |t|||    | td   | |t|||    | td   t| |t|||    |td  | |t|||    |td |   ||S rQ	  )r  r  r  r  r   re	  r  r  r  ro    rz	  ro  c              
   C   sr   t td||  tttd|td |td   |td td  | | |  |||t|||   |S r	  r9	  r	  r  r  r  rp    r@	  rp  c              
   C   st   t td||  tttd|td |td   |td td  | | |  |||t|||   | S r	  r9	  r	  r  r  r  rq    rE	  rq  c                 C   s   t |td tt|||   | |t | td |td  t|||   | | t td|  | t|||   | | S rQ	  )r  r  r  r  r  rg	  r  r  r  rr       rr  c                 C   s   t |td tt|||   | | t | td |td  t|||   | | t td|  | t|||   | | S rQ	  )r  r  r  r  r  rg	  r  r  r  rs       rs  c              
   C   s   t td|td  t|t|||   | | td |td  | | |td  t|||    |td   ||t||t|||   |  | |t|||     ||td   | S r-	  r*	  rc	  r  r  r  rt       rt  c              
   C   s   t td|td  t|t|||   | | td |td  | | |td  t|||    |td   ||t||t|||   |  | |t|||     ||td   | S r-	  r(	  rc	  r  r  r  ru    r}	  ru  c              
   C   sr   t td| tttd| td |td  |td   |||  t|||   | t|||   | S r-	  )r  r  r+   r   r  r  rg	  r  r  r  rv    r@	  rv  c              
   C   sp   t td| tttd| td |td  |td   |||  t|||   | t|||   |S r-	  )r  r  r+   r   r  r  rg	  r  r  r  rw    r8	  rw  c                 C   s   t |td |td  t|t|||   |td  | |t|||     || t |td | td |td   |td  t|t|||   |td  | |t|||     || S Nr  r'	  r  r  r   r  r  rc	  r  r  r  rx       rx  c                 C   s   t |td |td  t|t|||   |td  | |t|||     || t |td | td |td   |td  t|t|||   |td  | |t|||     || S r~	  r  r  r   r  r  rc	  r  r  r  ry    r	  ry  c                 C   s   t |td |td | td |td    t|t|||   |td  | |t|||     ||t td| td |td   t|t|||   | | |t|||     || S rT	  r	  rc	  r  r  r  rz    rm	  rz  c                 C   s   t |td |td | td |td    t|t|||   |td  | |t|||     ||t td| td |td   t|t|||   | | |t|||     || S rT	  r	  rc	  r  r  r  r{    rm	  r{  c              
   C   s   t |tdt|td   |t|||   tdt|td    t|||  td t|td    ||  tttd|td |td   |td td  | | |  |||t|||   |S Nr  r'	  r  r	  )r  r  r%   r  r&   r+   r   r  re	  r  r  r  r|    rs	  r|  c              
   C   s   t |tdt|td   |t|||   tdt|td    t|||  td t|td    ||  tttd|td |td   |td td  | | |  |||t|||   | S r	  )r  r  r%   r  r&   r+   r   r  re	  r  r  r  r}       r}  c                 C   s   t td | | tt|td | td |td  |td   ||t|t|||   t| |t|||     |S ro	  )r  r  r+   r   r  r  r  rq	  r  r  r  r~    r3	  r~  c                 C   s   t td| | tt|td | td |td  |td   ||t|t|||   t| |t|||     |S ro	  )r  r  r+   r   r  r  r  rq	  r  r  r  r    s   r  c              
   C   s   t td|t| |t|||     t| |t|||     t|||    tt| |t|||    t|t|||    ||S r!	  )r  r  r  r  r  r   rq	  r  r  r  r       r  c              
   C   s   t td|t| |t|||     t| |t|||     t|||    tt| |t|||    t|t|||    ||S r!	  )r  r  r  r  r  r   rq	  r  r  r  r    r	  r  c              
   C   sp   t |t|||   | |t|||   |  t|t|||   |  | |t|||    |  ||S r4	  )r  r  r   r  re	  r  r  r  r    r8	  r  c              
   C   sp   t |t|||   | |t|||   |  t|t|||   |  | |t|||    |  ||S r4	  )r  r  r   r  re	  r  r  r  r    r8	  r  c              
   C   sl   t || tt|| | | |  |td |td  | td td   |||t|||   |S rU	  rR	  r	  r  r  r  r    r 	  r  c              
   C   sn   t || tt|| | | |  |td |td  | td td   |||t|||   | S rU	  rR	  r	  r  r  r  r    r	  r  c                 C   s6   t | |t|||    | t|||  |  |S r4	  )r   r  r  r	  r  r  r  r       6r  c                 C   s6   t | |t|||    | t|||  |  |S r4	  )r   r  r  r	  r  r  r  r    r	  r  c                 C   s\   t | t|||   |t|||    | t|||  |  t|||  |   |S r4	  r   r  r  r	  r  r  r  r    rZ	  r  c                 C   s\   t | t|||   |t|||    | t|||  |   t|||  |  |S r4	  r   r  r  r	  r  r  r  r  	  rZ	  r  c              
   C   sx   t t|||  | t| |t|||   t|  tt|||  | |  | |t|||    |  ||S r4	  rD	  re	  r  r  r  r  	  rW	  r  c              
   C   sx   t t|||  | t| |t|||   t|  tt|||  | |  | |t|||    |  ||S r4	  rF	  re	  r  r  r  r  
	  rW	  r  c                 C   s^   t | t|||   |t|||    | t|||  |  t|||  ||   |S r4	  r	  r  r  r  r  r  r  r  r	  r  r  r  r  	  r:	  r  c                 C   s^   t | t|||   |t|||    | t|||  ||   t|||  |  |S r4	  r	  r	  r  r  r  r  	  r:	  r  c	           	   	   C   s`   t | | ||  t||t|||    | |  tdt|||   td|   ||S r-	  r"	  	r  r  r  r  r  r  r  r  r	  r  r  r  r  	     `r  c	           	   	   C   s`   t | | ||  t||t|||    | |  tdt|||   td|   ||S r-	  r%	  r	  r  r  r  r  	  r	  r  c	           	   	   C   sZ   t | | | tt| ||  |td  |||  |td   ||t|||  |S r	  rR	  r	  r  r  r  r  	  r[	  r  c	           	   
   C   sd   t | | | tt| ||  |td  |||  |td   ||tdt|||   | S Nr	  r  rR	  r	  r  r  r  r  "	     dr  c                 C   s<   t || | ||   |t || t|||   | | S r4	  r  r  r  r  r  r  r  r  r	  r  r  r  r  &	     <r  c                 C   s<   t || | ||   |t || |t|||    | S r4	  r	  r	  r  r  r  r  *	  r	  r  c                 C   sf   t | | ||  tt|||  ||t|| | ||   | t|| t|||   | | S r4	  r  r   r  r  r	  r  r  r  r  .	     fr  c                 C   sn   t | | ||  ttdt|||   ||t|| | ||   | t|| |t|||    | S r!	  r  r   r  r  r  r	  r  r  r  r  2	  r	  r  c              	   C   s   t | | ||  td|  |  t| |t|||    |td  ||t| |t|||    | |  | ||   td|  | |  | S rT	  rK	  r  r  r  r  r  r  r  r	  r  r  r  r  6	     r  c              	   C   s   t | | ||  td|  |  t| |t|||    |td  ||t| |t|||    | |  | ||   td|  | |  | S rT	  rK	  r	  r  r  r  r  :	  r	  r  c              	   C   sh   t | | ||  | t| |t|||    | ||t|| |t|||    |  ||  | S r4	  r	  r	  r  r  r  r  >	  r;	  r  c              	   C   sh   t | | ||  | t| |t|||    | ||t|| |t|||    |  ||  | S r4	  r	  r	  r  r  r  r  B	  r;	  r  c              	   C   s   t | |t|||    |td  t| | ||  | | ||  t|||    | |t|| |t|||    |  ||  | S r	  r^	  r	  r  r  r  r  F	  rr	  r  c              	   C   s   t | |t|||    |td  t| | ||  | | ||  t|||    | |t|| |t|||    |  ||  | S r	  r^	  r	  r  r  r  r  J	  rr	  r  c                 C   s   t td| td |td   t| |t|||    |td  t| | ||  |  | ||  t|||    | ||t| |t|||    |td  |  | ||   || td |td   |td   | S r-	  rK	  r	  r  r  r  r  N	     r  c                 C   s   t td| td |td   t| |t|||    |td  t| | ||  |  | ||  t|||    | ||t| |t|||    |td  |  | ||   || td |td   |td   | S r-	  rK	  r	  r  r  r  r  R	  r	  r  c              
   C   sD   t |tt| t|||   |t|||    | ||  |S r4	  )r  rN	  r   r  r  r	  r  r  r  r  V	     Dr  c              
   C   sF   t |tt| t|||   |t|||    | ||  | S r4	  )r  rN	  r   r  r  r	  r  r  r  r  Z	  r\	  r  c              
   C   s   t |  | ||  | td |td   t|  t|||   | | |t|||     ||t|| | ||   | td |td   | S rQ	  rK	  r	  r  r  r  r  ^	     r  c              
   C   s   t |  | ||  | td |td   t|  t|||   | | |t|||     ||t|| | ||   | td |td   | S rQ	  rK	  r	  r  r  r  r  b	  r	  r  c                 C   s   t td |td  | tttd| |td  td| |   ||||t|||    t| t|||    |S rT	  r  r  r+   r   r  r  r  r  r  r  r  r	  r  r  r  r  f	     r  c                 C   s~   t td|td  | tttd| |td  td| |   ||||t|||    t| t|||    |S rT	  r	  r	  r  r  r  r  j	  ra	  r  c                 C   s^   t td|td  | tttd| | ||td    ||t| t|||   |S rT	  rY	  r	  r  r  r  r  n	  r:	  r  c                 C   s`   t td |td  | tttd| | ||td    ||t| t|||   |S rT	  rY	  r	  r  r  r  r  r	  r	  r  c                 C   sb   t td| tt| | ||td   | td |td   ||t| t|||   |S Nr  rp	  rY	  r	  r  r  r  r  v	     br  c                 C   sd   t td | tt| | ||td   | td |td   ||t| t|||   |S r	  rY	  r	  r  r  r  r  z	  r	  r  c                 C   s   t td |td  | tttdtd |  |td  td| | |  |td   ||td |  | ||  || t|||    t| |t|||     |S Nr  r  rp	  r	  r	  r  r  r  r  ~	  rx	  r  c                 C   s   t td|td  | tttdtd |  |td  td| | |  |td   ||td |  | ||  || t|||    t| |t|||     |S r	  r	  r	  r  r  r  r  	     r  c                 C   s  t | td |td  td}ttdtd|  t| | ||  ||  |  | ||  ||  t|||    t| |t|||     || ttdtd|  t| | ||  ||  |  | ||  ||  t|||    t| |t|||     || S rT	  r  r  r  r   r  r  r  r  r  r  r  r  r	  r  r  r  r  r  	     "r  c                 C   s  t | td |td  td}ttdtd|  t| | ||  ||  |  | ||  ||  t|||    t| |t|||     || ttdtd|  t| | ||  ||  |  | ||  ||  t|||    t| |t|||     || S rT	  r	  r	  r  r  r  r  	  r	  r  c              
   C   sV   t || | tt| || |  | || |td   |||t|||   |S rQ	  rR	  r	  r  r  r  r  	  rk	  r  c              
   C   sX   t || | tt| || |  | || |td   |||t|||   | S rQ	  rR	  r	  r  r  r  r  	  r6	  r  c              	   C   sX   t |t| t|||   | ||t ||  t| t|||   |td  || S r!	  r  r   r  r  r  r  r  r  r  r  r	  r  r  r  r  	  r6	  r  c              	   C   sX   t |t| t|||   | ||t ||  t| t|||   |td  || S r!	  r	  r	  r  r  r  r  	  r6	  r  c              
   C   s   t |td t| td  t| |t|||    | tt|||   td  ||t |td t| td  t| |t|||    | t t|||   td  || S rT	  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|||    | |t|||    |  ||t |td t| td  ttdtt|||    | |t|||    |  || S rT	  r	  r	  r  r  r  r  	  r`	  r  c                 C   s  t tdtd| td   t| |t|||    |td  t| |td  | |td   td| | |  td| |td  t|||    | ||t|| |t|||    |  | | ||  td  td| td  | |  | S rB	  rK	  r	  r  r  r  r  	      r  c                 C   s  t tdtd| td   t| |t|||    |td  t| |td  | |td   td| | |  td| |td  t|||    | ||t|| |t|||    |  | | ||  td  td| td  | |  | S rB	  rK	  r	  r  r  r  r  	  r	  r  c              
   C   s   t |  | ||  td |td  ttd| |t|||     ||t |td | tt|||  || t|| |  | td| |   |td  | S rT	  rK	  r	  r  r  r  r  	     r  c              
   C   s   t |  | ||  td |td  ttd| |t|||     ||t |td | ttdt|||   || t|| |  | td| |   |td  | S rT	  rK	  r	  r  r  r  r  	  r	  r  c                 C   s>  t td| td |td   t| |t|||    |td  t| |td  | |td   td| | |  td |  | | ||td   ||td   t|||    | ||t| |t|||    |td  |  | ||  td  || | td |td   |td   | S r-	  rK	  r	  r  r  r  r  	     @ r  c                 C   s>  t td| td |td   t| |t|||    |td  t| |td  | |td   td| | |  td |  | | ||td   ||td   t|||    | ||t| |t|||    |td  |  | ||  td  || | td |td   |td   | S r-	  rK	  r	  r  r  r  r  	  r	  r  c              	   C   s   t | |t|||    | t|td td| | t|||    |td  | |t|td | |t|||    |td   || |td   | S rT	  r   r  r  r  r	  r  r  r  r  	     r  c              	   C   s   t | |t|||    | t|td td| | t|||    |td  | |t|td | |t|||    |td   || |td   | S rT	  r	  r	  r  r  r  r  	  r	  r  c                 C   s   t td |  | | tttdtd | td  |td  | |  ||   ||t||t|||    t| |t|||     |S rT	  rY	  r	  r  r  r  r  	  r	  r  c                 C   s   t td|  | | tttdtd | td  |td  | |  ||   ||t||t|||    t| |t|||     |S rT	  rY	  r	  r  r  r  r  	  rA	  r  c	           	   
   C   s   t td| td  | | ||   t| |t|||    |td  ||t|||    |td   ||t| | | |t|||    |td   ||t|||    |td   ||td  | | ||    | S Nr  r	  r  rK	  r	  r  r  r  r  	     r  c	           	   
   C   s   t td| td  | | ||   t| |t|||    |td  ||t|||    |td   ||t| | | |t|||    |td   ||t|||    |td   ||td  | | ||    | S r	  rK	  r	  r  r  r  r  	  r	  r  c	           	   
   C   s   t | | ||  td|td   t| |t|||    |td  ||t|||    |td   || t| | |t|||    |  ||t|||    |  td| | |  | S r0	  rK	  r	  r  r  r  r  	  r	  r  c	           	   
   C   s   t | | ||  td|td   t| |t|||    |td  ||t|||    |td   || t| | |t|||    |  ||t|||    |  td| | |  | S r0	  rK	  r	  r  r  r  r  	  r	  r  c	           	   
   C   s   t tdtd|   t| |t|||    |td  ||t|||    |  ||t| | |t|||    |  ||t|||    |td   td| | |  | ||    | S r-	  rK	  r	  r  r  r  r  	     r  c	           	   
   C   s   t tdtd|   t| |t|||    |td  ||t|||    |  ||t| | |t|||    |  ||t|||    |td   td| | |  | ||    | S r-	  rK	  r	  r  r  r  r  	  r	  r  c	           	   
   C   s   t | | | ||   t| |t|||    | ||t|||    |td   ||t|| |t|||    |  ||t|||    |td   || |td |td    | S r-	  r  r   r  r  r  r	  r  r  r  r  	  r}	  r  c	           	   
   C   s   t | | | ||   t| |t|||    | ||t|||    |td   ||t|| |t|||    |  ||t|||    |td   || |td |td    | S r-	  r	  r	  r  r  r  r  	  r}	  r  c                 C   s0  t tdtd|  |  | ||    t||t|||    |td  t| | | |td  ||td   ||td  |  ||td  |  | ||   t|||    | ||t||t|||    | | | ||   td| | |t|||     |  | ||    | S r	  rK	  r  r  r  r  r  r  r  r	  r  r  r  r  	     2 r  c                 C   s0  t tdtd|  |  | ||    t||t|||    |td  t| | | |td  ||td   ||td  |  ||td  |  | ||   t|||    | ||t||t|||    | | | ||   td| | |t|||     |  | ||    | S r	  rK	  r	  r  r  r  r  	  r	  r  c                 C   s$  t tdtd| td   t||t|||    |td  t| |td  | |td  |td   || | |  || | |td  || |   t|||    | ||t||t|||    |td  |  | ||   td|  | | |t|||      | S Nr  r  r'	  r	  rK	  r	  r  r  r  r  	     & r  c                 C   s$  t tdtd| td   t||t|||    |td  t| |td  | |td  |td   || | |  || | |td  || |   t|||    | ||t||t|||    |td  |  | ||   td|  | | |t|||      | S r	  rK	  r	  r  r  r  r  	  r	  r  c                 C   s   t ||  | ||   ttd| |t|||     ||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|||     ||t ||  | ||   ttd||t|||     || S r!	  r	  r	  r  r  r  r  
  r	  r  c                 C   s   t tdtd|  |  | ||    t||t|||    | t| | |td  ||  || | t|||    | ||t| ||t|||    |td   td| | |t|||     |  | ||    | S r	  rK	  r	  r  r  r  r  
     r  c                 C   s   t tdtd|  |  | ||    t||t|||    | t| | |td  ||  || | t|||    | ||t| ||t|||    |td   td| | |t|||     |  | ||    | S r	  rK	  r	  r  r  r  r  
  r	  r  c	           	      C   s  t | ||td  | | ||    t| |t|||    |td  ||t|||    |td   t||  | |td|  td  || |td    | td  | || td  | | | |td   |td | |td   t|||    | ||t| td | |t|||    |td   ||t|||    |td   |  | ||   || |td  | | ||    | S Nr  r'	  r  r	  rK	  r	  r  r  r  r  
      r  c	           	      C   s  t | ||td  | | ||    t| |t|||    |td  ||t|||    |td   t||  | |td|  td  || |td    | td  | || td  | | | |td   |td | |td   t|||    | ||t| td | |t|||    |td   ||t|||    |td   |  | ||   || |td  | | ||    | S r	  rK	  r	  r  r  r  r  
  r	  r  c                 C   s   t td| td  | | ||   tt| |t|||    ||t | |td |td   td| | |  | |td |td    t| |t|||    t| |t|||     ||t|||     || S rQ	  r  r  r   r  r  r	  r  r  r  r  
  r	  r  c                 C   s   t td| td  | | ||   tt| |t|||    ||t | |td |td   td| | |  | |td |td    t| |t|||    t| |t|||     ||t|||     || S rQ	  r	  r	  r  r  r  r  
  r	  r  c                 C   s   t td|  tt| |t|||    t||t|||     ||t ||  tt| |t|||    | t|||   |  t||t|||     || S rQ	  r	  r	  r  r  r  r   
  ri	  r  c                 C   s   t td|  tt| |t|||    t||t|||     ||t ||  tt| |t|||    | t|||   |  t||t|||     || S rQ	  r	  r	  r  r  r  r  $
  ri	  r  c	           	      C   sR  t | ||| td   t| |t|||    |td  ||t|||    |  t| | |td|   || |td   | | |td  || td| td|  td   t|||    | ||t|td | |t|||    |td   ||t|||    |td   || || td   | S Nr	  r'	  r  r  r	  r  rK	  r	  r  r  r  r  (
     T r  c	           	      C   sR  t | ||| td   t| |t|||    |td  ||t|||    |  t| | |td|   || |td   | | |td  || td| td|  td   t|||    | ||t|td | |t|||    |td   ||t|||    |td   || || td   | S r	  rK	  r	  r  r  r  r  ,
  r	  r  c                 C   s  t tdtd| td  |  t| |t|||    |td  ttd|  | | | | td| td  t|||    ||  | t||t|||     ||t|| |t|||    |  t||t|||     td|  | |  | S Nr  rp	  r  r  r  r   r  r  r  r	  r  r  r  r  0
      r  c                 C   s  t tdtd| td  |  t| |t|||    |td  ttd|  | | | | td| td  t|||    ||  | t||t|||     ||t|| |t|||    |  t||t|||     td|  | |  | S r	  r	  r	  r  r  r  r  4
  r	  r  c	           	      C   sr  t tdtd| td  |  t| |t|||    |td  ||t|||    |td   t|| | | || |td    ||  | || td  || || td    t|||    || | |td  || |    | ||t| |t|||    | ||t|||    |td   |  | ||   td|  | |  | S r	  rK	  r	  r  r  r  r  8
     t r  c	           	      C   sr  t tdtd| td  |  t| |t|||    |td  ||t|||    |td   t|| | | || |td    ||  | || td  || || td    t|||    || | |td  || |    | ||t| |t|||    | ||t|||    |td   |  | ||   td|  | |  | S r	  rK	  r	  r  r  r  r  <
  r	  r  c	           	      C   s<  t tdtd|  | |  | ||    t| |t|||    |td  ||t|||    |  t|  | td| | td  || |  || || td  t|||    | ||t| | |t|||    |  ||t|||    |td   td| | |  | ||    | S r-	  rK	  r	  r  r  r  r  @
     > r  c	           	      C   s<  t tdtd|  | |  | ||    t| |t|||    |td  ||t|||    |  t|  | td| | td  || |  || || td  t|||    | ||t| | |t|||    |  ||t|||    |td   td| | |  | ||    | S r-	  rK	  r	  r  r  r  r  D
  r	  r  c	           	      C   sT  t td| || td   t| |t|||    | ||t|||    |td   t|  |td  || td  ||  | |td|  td  || |   t|||    || | |td  || |    | || t|| |t|||    |  ||t|||    |td   ||| td   | S Nr  r	  r'	  r  rK	  r	  r  r  r  r  H
     V r  c	           	      C   sT  t td| || td   t| |t|||    | ||t|||    |td   t|  |td  || td  ||  | |td|  td  || |   t|||    || | |td  || |    | || t|| |t|||    |  ||t|||    |td   ||| td   | S r	  rK	  r	  r  r  r  r  L
  r	  r  c	           	      C   s>  t td| |td |td   |td   t| |t|||    | ||t|||    |td   t|  | |td  | | || td  t|||    || |  | || t|| |t|||    |  ||t|||    |td   ||td |td   |td   | S r-	  rK	  r	  r  r  r  r  P
  r	  r  c	           	      C   s>  t td| |td |td   |td   t| |t|||    | ||t|||    |td   t|  | |td  | | || td  t|||    || |  | || t|| |t|||    |  ||t|||    |td   ||td |td   |td   | S r-	  rK	  r	  r  r  r  r  T
  r	  r  c                 C   s   t | | | ||   t| |t|||    | ||t || | ||   t| |t|||    | | t|||   |  ||t|||     || S r4	  r  r   r  r	  r  r  r  r  X
     r  c                 C   s   t | | | ||   t| |t|||    | ||t || | ||   t| |t|||    | | t|||   |  ||t|||     || S r4	  r	  r	  r  r  r  r  \
  r	  r  c                 C   s   t ||  tt| |t|||    | t|||   |  t||t|||     ||t | | ||  |  tt| |t|||    t||t|||     || S r4	  r  r   r  r  r	  r  r  r  r  `
  rx	  r  c                 C   s   t ||  tt| |t|||    | t|||   |  t||t|||     ||t | | ||  |  tt| |t|||    t||t|||     || S r4	  r	  r	  r  r  r  r  d
  rx	  r  c	           	   
   C   sj   t | | | tt| | |td  ||| |  |  | | |td   |||t|||   |S Nr	  r  rR	  r	  r  r  r  r  h
     jr  c	           	   
   C   sl   t | | | tt| | |td  ||| |  |  | | |td   |||t|||   | S r	  rR	  r	  r  r  r  r  l
  r 	  r  c	           	      C   s  t td||td |td   |td   t| |t|||    |td  ||t|||    |td   t| td | |  | |td  || |td    |td |  | ||   | | |td  || |td     || | |  | td| |   || td  |td |td |td  |td |td      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d |td   |td   | S Nr  r  r'	  r	  r  rK	  r	  r  r  r  r  p
       r  c	           	      C   s  t td||td |td   |td   t| |t|||    |td  ||t|||    |td   t| td | |  | |td  || |td    |td |  | ||   | | |td  || |td     || | |  | td| |   || td  |td |td |td  |td |td      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d |td   |td   | S r	  rK	  r	  r  r  r  r  t
  r	  r  c	           	      C   s  t td||| td   t| |t|||    |td  ||t|||    |  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d| td  |td   || td  t|||    | ||t|td | |t|||    |td   ||t|||    |td   || || td   | S Nr  r	  r	  r  r  r'	  r	  rK	  r	  r  r  r  r  x
      r  c	           	      C   s  t td||| td   t| |t|||    |td  ||t|||    |  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d| td  |td   || td  t|||    | ||t|td | |t|||    |td   ||t|||    |td   || || td   | S r	  rK	  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d   t| |td  |td  | |td  |td   || | || td   |||  |  | ||   t|||  td   |td td |  | | ||td   ||td    t|||    | ||t| |t|||    |td  ||t|||    |td   |  | ||   || td |td   |td   | S r	  rK	  r	  r  r  r  r  
      r  c	           	      C   s  t td| td |td  |td   t| |t|||    |td  ||t|||    |td   t| |td  |td  | |td  |td   || | || td   |||  |  | ||   t|||  td   |td td |  | | ||td   ||td    t|||    | ||t| |t|||    |td  ||t|||    |td   |  | ||   || td |td   |td   | S r	  rK	  r	  r  r  r  r  
  r	  r  c	           	      C   st  t td| td |td  |td   t| |t|||    |td  ||t|||    |td   t| | |td  || |  || || td  t|||  td   |td |  | ||   t|||    | ||t|| |t|||    |td   ||t|||    |  || td |td   |td   | S r	  rK	  r	  r  r  r  r  
     v r  c	           	      C   st  t td| td |td  |td   t| |t|||    |td  ||t|||    |td   t| | |td  || |  || || td  t|||  td   |td |  | ||   t|||    | ||t|| |t|||    |td   ||t|||    |  || td |td   |td   | S r	  rK	  r	  r  r  r  r  
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      r  c	           	      C   s  t td| td |td  |td  |  | ||    t| |t|||    |td  ||t|||    |  t| |td  |  | ||   |td | || td   |td | || td  t|||  td   ||td  |  | ||   t|||    | ||t|td | |t|||    |td   ||t|||    |td   || td |td   |td  |  | ||    | S r-	  rK	  r	  r  r  r  r  
  r	  r  c	           	      C   s  t td|| td  t| |t|||    |td  ||t|||    |td   t| td | || td  || | | || |td     || | td| | td  || |   t|||  td   || td | td | td|  | |  |td |   t|||    | ||t|| |t|||    |td   ||t|||    |  ||| td   | S r	  rK	  r	  r  r  r  r  
      r  c	           	      C   s  t td|| td  t| |t|||    |td  ||t|||    |td   t| td | || td  || | | || |td     || | td| | td  || |   t|||  td   || td | td | td|  | |  |td |   t|||    | ||t|| |t|||    |td   ||t|||    |  ||| td   | S r	  rK	  r	  r  r  r  r  
  r	  r  c                 C   s.  t |td | td |td  |  | ||    t|  t|||   | | |t|||     ||t |td |td |td  |  | ||    t| t|||   | ||t|||     || t|| | ||   | td |td  |td |td    | S rQ	  rK	  r	  r  r  r  r  
     0 r  c                 C   s.  t |td | td |td  |  | ||    t|  t|||   | | |t|||     ||t |td |td |td  |  | ||    t| t|||   | ||t|||     || t|| | ||   | td |td  |td |td    | S rQ	  rK	  r	  r  r  r  r  
  r	  r  c                 C   s  t ||  | ||   |td |td   tt|||  td td t| |t|||    ||t|||      || t td|td |td   tt| | ||  |  | ||  t|||    |t| |t|||     || S rT	  r  r  r   r  r  r  r	  r  r  r  r  
      r  c                 C   s  t ||  | ||   |td |td   ttdt|||  td  t| |t|||    ||t|||      || t td|td |td   tt| | ||  |  | ||  t|||    |t| |t|||     || S r,	  r	  r	  r  r  r  r  
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     X r  c                 C   sV  t |  | ||  td |td |td   ttdt|||  td  t| |t|||    ||t|||      ||t td|td |td   tt| td | td|  | |  |td |  | td  | td|  | |  |td |  t|||    |t| |t|||     || S r,	  r	  r	  r  r  r  r  
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     r  c                 C   s   t |td |td |td   ttdt|||  td  | |t|||    |  ||t|||     ||t td|td |td   t| |t|||    | ||t|||     || S r,	  r	  r	  r  r  r  r  
  r	  r  c	           	   
   C   sb   t || tt| | | ||| |  |  |td |td   |||t|||   |S rQ	  rR	  r	  r  r  r  r  
  r	  r  c	           	   
   C   sd   t || tt| | | ||| |  |  |td |td   |||t|||   | S rQ	  rR	  r	  r  r  r  r  
  r	  r  c              	   C   sL   t || t|t|||   | |  | t|||   | |  ||S r4	  r	  re	  r  r  r  r  
  r	  r  c              	   C   sL   t || t|t|||   | |  | t|||   | |  ||S r4	  r	  re	  r  r  r  r  
  r	  r  c
           
   
   C   s   t |t| ||t|||	   |  t|  |t|||	   | t|   t|t|||	   ||  | |t|||	    |  |	|	S r4	  r  r%   r  r&   r   
r  r  r  r  r  r  r  r  r  r	  r  r  r  r  
  rA	  r  c
           
   
   C   s   t |t| ||t|||	   |  t|  |t|||	   | t|   t|t|||	   ||  | |t|||	    |  |	|	S r4	  r	  r	  r  r  r  r  
  rA	  r  c                 C   sV   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S r4	  r   r  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  r  
  rk	  r  c                 C   sV   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S r4	  r	  r	  r  r  r  r   
  rk	  r   c              	   C   sp   t |||  t|t|||
   | | |	  | t|||
   | |  |t|||
   | |  |
|
S r4	  r	  r	  r  r  r  r  
  r8	  r  c              	   C   sp   t |||  t|t|||
   | | |	  | t|||
   | |  |t|||
   | |  |
|
S r4	  r	  r	  r  r  r  r  
  r8	  r  c              
   C   s   t |t|||   |	 |
  |t|||  |
  |	  t|t|||   |	|
  | |t|||    |  ||t|||    |  ||S r4	  r5	  r  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  r  
  r	  r  c              
   C   s   t |tdt|||   |
  |	 |t|||   |	 |
   t|t|||   |	|
  | |t|||    |  ||t|||    |  ||S r!	  r  r  r  r   r	  r  r  r  r  
  r_	  r  c              
   C   sh   t || t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r4	  r	  r	  r  r  r  r  
  r;	  r  c              
   C   sh   t || t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r4	  r	  r	  r  r  r  r  
  r;	  r  c
           
      C   s`   t ||t|||	    | | t|||	   | |  tdt|||	   | |   |	S r!	  r   r  r  r	  r  r  r  r  
  r	  r  c
           
      C   sX   t ||t|||	    | | t|||	   | |  t|||	  | |   |	S r4	  r	  r	  r  r  r  r	  
  r6	  r	  c              	   C   s   t |t|||
   |	 tdt|||
   |	  t||t|||
    | | t|||
   | |  tdt|||
   | |	   |
|
S r!	  )r  r  r  r   r	  r  r  r  r
     r	  r
  c              	   C   s   t |t|||
   |	 t|||
  |	  t||t|||
    | | t|||
   | |  t|||
  | |	   |
|
S r4	  r5	  r	  r  r  r  r    r|	  r  c              
   C   s   t |t|||
   | ||t|||
    |  |t|||
   | |   t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r4	  r5	  r	  r  r  r  r       r  c              
   C   s   t |t|||
   | ||t|||
    |  |t|||
   | |   t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r4	  r5	  r	  r  r  r  r    r	  r  c              	   C   sf   t || | tt| ||
  |||
  |td   |||
  |	td   |
|
t|||
  |
S r	  rR	  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  r    r	  r  c              
   C   sp   t || | tt| ||
  |||
  |td   |||
  |	td   |
|
tdt|||
   |
 S r	  rR	  r	  r  r  r  r    r8	  r  c	           	   
   C   s   t td| tt| | | | | | || | ||    t|||    |||t|||     ||t || | tt|||  || S r!	  r  r  r   r  r  	r  r  r  r  r  r  r  r  r	  r  r  r  r    r	  r  c	           	   
   C   s   t td| tt| | | | | | || | ||    t|||    |||t|||     ||t || | ttdt|||   || S r!	  r	  r	  r  r  r  r    r_	  r  c
           
      C   s   t tdtd| |  t||t|||	    |td  t| | | | | |  || |  td| | | t|||	    || |  |	 |	|	t||t|||	    | | | ||   || ||   td|td  | |  |	 S r-	  rK	  
r  r  r  r  r  r  r  r  r  r	  r  r  r  r        r  c
           
      C   s   t tdtd| |  t||t|||	    |td  t| | | | | |  || |  td| | | t|||	    || |  |	 |	|	t||t|||	    | | | ||   || ||   td|td  | |  |	 S r-	  rK	  r	  r  r  r  r  $  r	  r  c
           
      C   s>  t td|td |td   t||t|||	    |td  t| | | | | |  || |  || |  |  | | | | |  || |  || |  t|||	    |	 |	|	t||t|||	    |td  | | ||   | | ||   || |td |td   |td   |	 S r-	  rK	  r	  r  r  r  r  (  r	  r  c
           
      C   s>  t td|td |td   t||t|||	    |td  t| | | | | |  || |  || |  |  | | | | |  || |  || |  t|||	    |	 |	|	t||t|||	    |td  | | ||   | | ||   || |td |td   |td   |	 S r-	  rK	  r	  r  r  r  r  ,  r	  r  c
           
   	   C   s   t ||t|||	    | t| | ||  | | ||  t|||	    |	 |	t|| ||t|||	    |td   || |td   |	 S r!	  r	  r	  r  r  r  r  0     r  c
           
   	   C   s   t ||t|||	    | t| | ||  | | ||  t|||	    |	 |	t|| ||t|||	    |td   || |td   |	 S r!	  r	  r	  r  r  r  r  4  r	  r  c                 C   s  t |||	td  || ||    t||t|||
    |td  ||t|||
    |	td   t| | | ||	 td  ||| |	td  || |td     | | | ||	  ||| |td  || |	td     t|||
    |
 |
|
 t|td ||t|||
    |td   ||t|||
    |	td   |  | ||   || |	td  || ||    |
 S r	  rK	  r	  r  r  r  r  8      r  c                 C   s  t |||	td  || ||    t||t|||
    |td  ||t|||
    |	td   t| | | ||	 td  ||| |	td  || |td     | | | ||	  ||| |td  || |	td     t|||
    |
 |
|
 t|td ||t|||
    |td   ||t|||
    |	td   |  | ||   || |	td  || ||    |
 S r	  rK	  r	  r  r  r  r  <  r	  r  c                 C   sX  t td|||	   t||t|||
    |td  ||t|||
    |	  t| | | ||	  ||| |td  || |	td     ||td  | | ||   |||	  | | ||    t|||
    |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   || ||	   |
 S Nr  r	  rK	  r	  r  r  r  r  @     Z r  c                 C   sX  t td|||	   t||t|||
    |td  ||t|||
    |	  t| | | ||	  ||| |td  || |	td     ||td  | | ||   |||	  | | ||    t|||
    |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   || ||	   |
 S r	  rK	  r	  r  r  r  r  D  r	  r  c                 C   sH  t tdtd|td  |  t||t|||
    |td  ||t|||
    |	td   t| || | || |	   ||| |	 || |    ||  | ||	  || ||	    t|||
    |
 |
|
t||t|||
    | ||t|||
    |	  | | ||   td| | |  |
 S r	  rK	  r	  r  r  r  r  H     J r  c                 C   sH  t tdtd|td  |  t||t|||
    |td  ||t|||
    |	td   t| || | || |	   ||| |	 || |    ||  | ||	  || ||	    t|||
    |
 |
|
t||t|||
    | ||t|||
    |	  | | ||   td| | |  |
 S r	  rK	  r	  r  r  r  r  L  r	  r  c                 C   s|  t tdtd| | | | ||    t||t|||
    |td  ||t|||
    |	  t| | | td| |	 td  || |   ||| | || |	td     || | ||   ||	 td  t|||
    |
 |
|
t||t|||
    | ||t|||
    |	td   | | ||   td| | | | ||    |
 S r-	  rK	  r	  r  r  r  r  P     ~ r  c                 C   s|  t tdtd| | | | ||    t||t|||
    |td  ||t|||
    |	  t| | | td| |	 td  || |   ||| | || |	td     || | ||   ||	 td  t|||
    |
 |
|
t||t|||
    | ||t|||
    |	td   | | ||   td| | | | ||    |
 S r-	  rK	  r	  r  r  r  r  T  r	  r  c                 C   s$  t td|||	   t||t|||
    | ||t|||
    |	td   t| | | ||	  ||| |	 || |    | | | ||	  || | |	 || |    t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S r	  rK	  r	  r  r  r  r   X  r	  r   c                 C   s$  t td|||	   t||t|||
    | ||t|||
    |	td   t| | | ||	  ||| |	 || |    | | | ||	  || | |	 || |    t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S r	  rK	  r	  r  r  r  r!  \  r	  r!  c                 C   s  t td||td |td   |	td   t||t|||
    | ||t|||
    |	td   t| | | |	td  || |   ||| |	td  || |    ||  | ||   ||	 td  t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | | ||   ||td |td   |	td   |
 S r-	  rK	  r	  r  r  r  r"  `      r"  c                 C   s  t td||td |td   |	td   t||t|||
    | ||t|||
    |	td   t| | | |	td  || |   ||| |	td  || |    ||  | ||   ||	 td  t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | | ||   ||td |td   |	td   |
 S r-	  rK	  r	  r  r  r  r#  d  r	  r#  c              	   C   sR   t || | tt|||
  |td  |||
  |	  |
|
t|||
  |
S r	  rR	  r	  r  r  r  r$  h     Rr$  c              
   C   s\   t || | tt|||
  |td  |||
  |	  |
|
tdt|||
   |
 S r	  rR	  r	  r  r  r  r%  l  rZ	  r%  c
           
      C   s   t | | ||  || ||   t||t|||	    | |	|	t |  | ||  || ||   t||t|||	    ||t|||	    |  ||t|||	     |	|	 S r4	  r	  r	  r  r  r  r&  p  r+	  r&  c
           
      C   s   t | | ||  || ||   t||t|||	    | |	|	t |  | ||  || ||   t||t|||	    ||t|||	    |  ||t|||	     |	|	 S r4	  r	  r	  r  r  r  r'  t  r+	  r'  c                 C   s   t || t||t|||
    ||t|||
    |  ||t|||
    |	  |
|
 t | | ||  | t||t|||
    | ||t|||
    |	  |
|
 S r4	  r	  r	  r  r  r  r(  x  rz	  r(  c                 C   s   t || t||t|||
    ||t|||
    |  ||t|||
    |	  |
|
 t | | ||  | t||t|||
    | ||t|||
    |	  |
|
 S r4	  r	  r	  r  r  r  r)  |  rz	  r)  c              	   C   Z   t | td | tt|||
  | |||
  |	  | ||
   |
|
t|||
  |
S rQ	  r9	  r	  r  r  r  r+    r[	  r+  c              
   C   d   t | td | tt|||
  | |||
  |	  | ||
   |
|
tdt|||
   |
 S rT	  r9	  r	  r  r  r  r,    r	  r,  c                 C      t | td t| td  t||t|||
    | ||t|||
    |	  tt|||
   td  |
|
t | td t| td  t||t|||
    | ||t|||
    |	  t t|||
   td  |
|
 S rT	  r	  r	  r  r  r  r-       r-  c                 C      t | td t| td  ttdtt|||
    ||t|||
    |  ||t|||
    |	  |
|
t | td t| td  ttdtt|||
    ||t|||
    |  ||t|||
    |	  |
|
 S rT	  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d   t| | | | | |	td  || |td    || | |td |td  |td |	td    |||	  |  | | | | |  || |     t|||
  td   ||	td  | | ||  | | ||   | | ||  || ||     t|||
    || | || | ||    || |	td  || |td     |
 |
|
 t||t|||
    |td  ||t|||
    |	td   |  | ||   | | ||   || |td |td   |	td   |
 S r	  rK	  r	  r  r  r  r/         r/  c                 C   s  t td||td |td   |	td   t||t|||
    |td  ||t|||
    |	td   t| | | | | |	td  || |td    || | |td |td  |td |	td    |||	  |  | | | | |  || |     t|||
  td   ||	td  | | ||  | | ||   | | ||  || ||     t|||
    || | || | ||    || |	td  || |td     |
 |
|
 t||t|||
    |td  ||t|||
    |	td   |  | ||   | | ||   || |td |td   |	td   |
 S r	  rK	  r	  r  r  r  r0    r	  r0  c                 C   s  t td|||	   t||t|||
    |td  ||t|||
    |	  t| |td  | ||	  || || |	td  || |td     |||	  td|  | | ||td |td     t|||
    || |td  | | ||   || ||	  | | ||    t|||
  td   |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   || ||	   |
 S Nr  r'	  r  r	  rK	  r	  r  r  r  r1        r1  c                 C   s  t td|||	   t||t|||
    |td  ||t|||
    |	  t| |td  | ||	  || || |	td  || |td     |||	  td|  | | ||td |td     t|||
    || |td  | | ||   || ||	  | | ||    t|||
  td   |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   || ||	   |
 S r	  rK	  r	  r  r  r  r2    r	  r2  c                 C   s  t td||td |td   |td   t||t|||
    |td  ||t|||
    |	td   t| | || |td  || |	   || || |	 || |td     || | | ||   ||	 td  t|||
  td   ||td  | | | ||   ||| ||     t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	  | | ||   ||td |td   |td   |
 S r	  rK	  r	  r  r  r  r3        r3  c                 C   s  t td||td |td   |td   t||t|||
    |td  ||t|||
    |	td   t| | || |td  || |	   || || |	 || |td     || | | ||   ||	 td  t|||
  td   ||td  | | | ||   ||| ||     t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	  | | ||   ||td |td   |td   |
 S r	  rK	  r	  r  r  r  r4    r	  r4  c                 C   s  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t| ||td  | | ||   |td | ||	 td    || || |	td  || |td     || | | ||   ||	 td  t|||
  td   |td | | ||   | | ||   t|||
    |
 |
|
t|||t|||
    |td   ||t|||
    |	td   | | ||   ||td |td   |td  | | ||    |
 S r-	  rK	  r	  r  r  r  r5        " r5  c                 C   s  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t| ||td  | | ||   |td | ||	 td    || || |	td  || |td     || | | ||   ||	 td  t|||
  td   |td | | ||   | | ||   t|||
    |
 |
|
t|||t|||
    |td   ||t|||
    |	td   | | ||   ||td |td   |td  | | ||    |
 S r-	  rK	  r	  r  r  r  r6    r	  r6  c                 C   sv  t td||	  t||t|||
    |td  ||t|||
    |	td   t| | | ||	  ||| |	 || |    ||	 | | | | | |  || |  || |   t|||
    | | | ||	  ||| | || |	    t|||
  td   |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S Nr  r	  r  rK	  r	  r  r  r  r7       x r7  c                 C   sv  t td||	  t||t|||
    |td  ||t|||
    |	td   t| | | ||	  ||| |	 || |    ||	 | | | | | |  || |  || |   t|||
    | | | ||	  ||| | || |	    t|||
  td   |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S r	  rK	  r	  r  r  r  r8    r	  r8  c	           	      C   sX  t || | ||   |td |td  | | ||    t| t|||   | ||t|||     ||t ||  | ||   |td |td  | | ||    t| t|||   | ||t|||     || t|| || ||   ||| ||     |td |td  |td |td    | S rQ	  rK	  r	  r  r  r  r9    r	  r9  c	           	      C   sX  t || | ||   |td |td  | | ||    t| t|||   | ||t|||     ||t ||  | ||   |td |td  | | ||    t| t|||   | ||t|||     || t|| || ||   ||| ||     |td |td  |td |td    | S rQ	  rK	  r	  r  r  r  r:    r	  r:  c	           	      C   sL  t |  | ||  | | ||   |td |td   tt|||  td td ||t|||    t||t|||      || t td|td |td   tt| || ||   || | ||    | | | ||   ||| ||    t|||    |t||t|||     || S rT	  r	  r	  r  r  r  r;       N r;  c	           	      C   sL  t |  | ||  | | ||   |td |td   ttdt|||  td  ||t|||    t||t|||      || t td|td |td   tt| || ||   || | ||    | | | ||   ||| ||    t|||    |t||t|||     || S r,	  r	  r	  r  r  r  r<    r	  r<  c
           
      C   s  t || | ||   |td |td   t||t|||	    | t|||	  td td  ||t|||	     |	|	t td|td |td   t||t|||	    | t| | ||  | | ||  t|||	    |	 |	|	 S rT	  rK	  
r  r  r  r  r  r  r  r  r  r	  r  r  r  r=    r	  r=  c
           
      C   s  t || | ||   |td |td   ttdt|||	  td  ||t|||	    |  ||t|||	     |	|	t td|td |td   t||t|||	    | t| | ||  | | ||  t|||	    |	 |	|	 S r,	  rK	  r	  r  r  r  r>    r	  r>  c	           	      C   s   t || tt|||  td td t||t|||    t||t|||      ||tt| | ||  | | ||  t|||    |t||t|||    t||t|||      | S rT	  )r  r   r  r  r  r  r	  r  r  r  r?    r	  r?  c	           	      C   s   t || ttdt|||  td  t||t|||    t||t|||      ||tt| | ||  | | ||  t|||    |t||t|||    t||t|||      | S )Nr  r'	  )r  r   r  r  r  r  r	  r  r  r  r@    r	  r@  c              	   C   r	  rQ	  r9	  r	  r  r  r  rA    r[	  rA  c              
   C   r	  rT	  r9	  r	  r  r  r  rB    r	  rB  c                 C   r	  rT	  r	  r	  r  r  r  rC    r	  rC  c                 C   r	  rT	  r	  r	  r  r  r  rD    r	  rD  c              
   C   s:   t | ||  tt|| | |||t|||   |S r4	  r  r+   r   r  r  r  r  r  r  r  r  r	  r  r  r  rE       :rE  c              
   C   s<   t | ||  tt|| | |||t|||   | S r4	  r	  r	  r  r  r  rF    r	  rF  c	           	      C   sh   t |td t||t|||    |td  t|| ||  || t|||    | ||S Nr'	  r  rK	  	r  r  r  r  r  r  r  r  r	  r  r  r  rG    r;	  rG  c	           	      C   sh   t |td t||t|||    |td  t|| ||  || t|||    | ||S r	  rK	  r	  r  r  r  rH    r;	  rH  c              
   C   sX   t ||td  t||t|||    ||t|||    |td   || S rT	  r	  r	  r  r  r  rI    r6	  rI  c              
   C   sX   t ||td  t||t|||    ||t|||    |td   || S rT	  r	  r	  r  r  r  rJ    r6	  rJ  c	           	      C   s  t tdtd|td  |  t||t|||    |td  t| | td| td  ||  ||  || |td  |td | | ||    t|||    | ||t||t|||    | | | ||  ||   t|||   td| | |  | S r	  rK	  r	  r  r  r  rK          rK  c	           	      C   s  t tdtd|td  |  t||t|||    |td  t| | td| td  ||  ||  || |td  |td | | ||    t|||    | ||t||t|||    | | | ||  ||   td| | | t|||    | S r	  rK	  r	  r  r  r  rL    r	  rL  c                 C   s  t tdtd|td  |  t||t|||    |td  t| | td| td  ||  | | |td  || |td   t|||    | ||t||t|||    | | | ||   t|||   td| | |  | S r	  rK	  r	  r  r  r  rM    r	  rM  c                 C   s  t tdtd|td  |  t||t|||    |td  t| | td| td  ||  | | |td  || |td   t|||    | ||t||t|||    | | | ||   td| | | t|||    | S r	  rK	  r	  r  r  r  rN    r	  rN  c              
   C   s   t | |td  || |  ||td   |td |td   tt|||  td td ||t|||     ||t|| | ||  ||   |td |td   | S rT	  rK	  r  r  r  r  r  r  r  r	  r  r  r  rO       rO  c              
   C   s   t | |td  || |  ||td   |td |td   ttdt|||  td  ||t|||     ||t|| | ||  ||   |td |td   | S r,	  rK	  r	  r  r  r  rP    r 
  rP  c                 C   sR   t | ttdt|||   ||t |tt|||  || t|| | S r!	  r	  r  r  r  r  r  r	  r  r  r  rQ    r	  rQ  c              	   C   sR   t | tt|||  ||t |ttdt|||   || t|| | S r!	  r	  r
  r  r  r  rR    r	  rR  c                 C   sD   t | ttdt|||   ||t |tt|||  || S r!	  r	  r  r  r  r  r	  r  r  r  rS     r	  rS  c              	   C   sD   t | tt|||  ||t |ttdt|||   || S r!	  r	  r
  r  r  r  rT  $  r	  rT  c                 C   s  t | | ||  ||  |td |td   tt|||  || t | |td  || |  ||td   |td |td   tt|||  td td ||t|||     || t|| | ||  ||   |td |td   | S rT	  rK	  r	  r  r  r  rU  (  r	  rU  c                 C   s  t | | ||  ||  |td |td   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 r,	  rK	  r	  r  r  r  rV  ,  s    rV  c              
   C   s   t | |td  ||td   |td |td   tt|||  td td ||t|||     ||t || |  |td |td   tt|||  || t|| | |  |td |td   | S rT	  rK	  r  r  r  r  r  r  r	  r  r  r  rW  0  s   rW  c              
   C   s   t | |td  ||td   |td |td   ttdt|||  td  ||t|||     ||t || |  |td |td   ttdt|||   || t|| | |  |td |td   | S r,	  rK	  r
  r  r  r  rX  4  r	  rX  c	           	      C   s  t td|td |td   t||t|||    |td  t|| || |   | | ||  ||  t|||    | ||t||t|||    |td  | |td  || |  ||td    || |td |td   |td   | S r-	  rK	  r	  r  r  r  rY  8      rY  c	           	      C   s  t td|td |td   t||t|||    |td  t|| || |   | | ||  ||  t|||    | ||t||t|||    |td  | |td  || |  ||td    || |td |td   |td   | S r-	  rK	  r	  r  r  r  rZ  <  r
  rZ  c                 C   s   t td|td |td   t||t|||    |td  t|| |  | | ||  t|||    | ||t||t|||    |td  | |td  ||td    || |td |td   |td   | S r-	  rK	  r	  r  r  r  r[  @  r	  r[  c                 C   s   t td|td |td   t||t|||    |td  t|| |  | | ||  t|||    | ||t||t|||    |td  | |td  ||td    || |td |td   |td   | S r-	  rK	  r	  r  r  r  r\  D  r	  r\  c	           	   	   C   s   t ||t|||    | t| |t|||    | | |t|||t|||    |td   || |td   | S r!	  r	  r	  r  r  r  r]  H  r{	  r]  c	           	   	   C   s   t ||t|||    | t| |t|||    | | |t|||t|||    |td   || |td   | S r!	  r	  r	  r  r  r  r^  L  r{	  r^  c              	   C   sp   t | | t||t|||    | ||t|||t|||    |td   || |td   | S r!	  r  r   r  r  r  r	  r  r  r  r_  P  r8	  r_  c              	   C   sp   t | | t||t|||    | ||t|||t|||    |td   || |td   | S r!	  r
  r	  r  r  r  r`  T  r8	  r`  c              	   C   sF   t | | tt|||
  | |||
  |	  |
|
t|||
  |
S r4	  r	  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  ra  X  r\	  ra  c              
   C   sP   t | | tt|||
  | |||
  |	  |
|
tdt|||
   |
 S r!	  rR	  r
  r  r  r  rb  \  rb	  rb  c                 C   s  t td||td |td    t||t|||
    |	td  t|| |td |td   t|||
  td  || | | ||  ||    || |td  || |  ||td     ||  | | | | |  || |  || |  || |  || |   t|||
    |
 |
|
t||t|||
    |	td  | | ||   | |td  || |  ||td    |td | |td |td   |	td   |
 S r-	  rK	  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  rc  `      rc  c                 C   s  t td||td |td    t||t|||
    |	td  t|| |td |td   t|||
  td  || | | ||  ||    || |td  || |  ||td     ||  | | | | |  || |  || |  || |  || |   t|||
    |
 |
|
t||t|||
    |	td  | | ||   | |td  || |  ||td    |td | |td |td   |	td   |
 S r-	  rK	  r
  r  r  r  rd  d  r
  rd  c
           
      C   s  t td||td |td    t||t|||	    |td  t|| |td |td   t|||	  td  || | | ||    || |td  ||td     ||  | | | | |  || |  || |   t|||	    |	 |	|	t||t|||	    |td  | |td  ||td    | | ||   |td | |td |td   |td   |	 S r-	  rK	  
r  r  r  r  r  r  r  r  r  r	  r  r  r  re  h      re  c
           
      C   s  t td||td |td    t||t|||	    |td  t|| |td |td   t|||	  td  || | | ||    || |td  ||td     ||  | | | | |  || |  || |   t|||	    |	 |	|	t||t|||	    |td  | |td  ||td    | | ||   |td | |td |td   |td   |	 S r-	  rK	  r	
  r  r  r  rf  l  r

  rf  c                 C   sL  t td||	td   t||t|||
    |	 t|  | | |	td  || |  ||	td  | | ||  ||   t|||
    || | |	td  || | |	td  ||    t|||
  td   |
 |
|
 t|| ||t|||
    |	td   t|||
   || |	td   |
 S r-	  rK	  r
  r  r  r  rg  p  r	  rg  c                 C   sL  t td||	td   t||t|||
    |	 t|  | | |	td  || |  ||	td  | | ||  ||   t|||
    || | |	td  || | |	td  ||    t|||
  td   |
 |
|
 t|| ||t|||
    |	td   || |	td  t|||
    |
 S r-	  rK	  r
  r  r  r  rh  t  r	  rh  c
           
      C   s.  t td||td   t||t|||	    | t|  | | |td  || |  ||td  | | ||   t|||	    || | |td  || |  t|||	  td   |	 |	|	 t|| ||t|||	    |td   t|||	   || |td   |	 S r-	  rK	  r	
  r  r  r  ri  x  r	  ri  c
           
      C   s.  t td||td   t||t|||	    | t|  | | |td  || |  ||td  | | ||   t|||	    || | |td  || |  t|||	  td   |	 |	|	 t|| ||t|||	    |td   || |td  t|||	    |	 S r-	  rK	  r	
  r  r  r  rj  |  r	  rj  c                 C   s  t tdtd| |	 | | ||    t||t|||    |	td  ||t|||    |
  t||  | td|	 |
 td  || |	  || |
td    || | |
td  ||	 | |     | | | |	|
 td  || | |	|
 td   || | |	|
 td  td| | |	    t|||    | ||t||t|||    |	 ||t|||    |
td   | | ||  ||   td| |	 | | ||    | S r	  rK	  r  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  rk        rk  c                 C   s  t tdtd| |	 | | ||    t||t|||    |	td  ||t|||    |
  t||  | td|	 |
 td  || |	  || |
td    || | |
td  ||	 | |     | | | |	|
 td  || | |	|
 td   || | |	|
 td  td| | |	    t|||    | ||t||t|||    |	 ||t|||    |
td   | | ||  ||   td| |	 | | ||    | S r	  rK	  r
  r  r  r  rl    r
  rl  c                 C   s  t tdtd| | | | ||    t||t|||
    |td  ||t|||
    |	  t||  | td| |	 td  || |	td    || | | |   | | | ||	 td  td| | | |  || | ||	 td   t|||
    |
 |
|
t|| |  ||t|||
    |  ||t|||
    |	td   td| | | | ||    |
 S r	  rK	  r
  r  r  r  rm        rm  c                 C   s  t tdtd| | | | ||    t||t|||
    |td  ||t|||
    |	  t||  | td| |	 td  || |	td    || | | |   | | | ||	 td  td| | | |  || | ||	 td   t|||
    |
 |
|
t|| |  ||t|||
    |  ||t|||
    |	td   td| | | | ||    |
 S r	  rK	  r
  r  r  r  rn    r
  rn  c                 C   s  t td|| |td |td   |
td   t||t|||    |	 ||t|||    |
td   t| | |
td  | | ||  ||   || |td |	 |td |
td    ||  | ||   |	|
 td    t|||    ||	 | |td  || |  ||td     | || t||t|||    |	 ||t|||    |
td   | |td  || |  ||td    || |td |td   |
td   | S r-	  rK	  r
  r  r  r  ro        ro  c                 C   s  t td|| |td |td   |
td   t||t|||    |	 ||t|||    |
td   t| | |
td  | | ||  ||   || |td |	 |td |
td    ||  | ||   |	|
 td    t|||    ||	 | |td  || |  ||td     | || t||t|||    |	 ||t|||    |
td   | |td  || |  ||td    || |td |td   |
td   | S r-	  rK	  r
  r  r  r  rp    r
  rp  c                 C   s  t td|| |td |td   |	td   t||t|||
    | ||t|||
    |	td   t| | |	td  | | ||   ||  |td  ||	 td  ||td | |td |	td      t|||
    || | |td  ||td     |
 |
|
 t||t|||
    | ||t|||
    |	td   | |td  ||td    || |td |td   |	td   |
 S r-	  rK	  r
  r  r  r  rq        rq  c                 C   s  t td|| |td |td   |	td   t||t|||
    | ||t|||
    |	td   t| | |	td  | | ||   ||  |td  ||	 td  ||td | |td |	td      t|||
    || | |td  ||td     |
 |
|
 t||t|||
    | ||t|||
    |	td   | |td  ||td    || |td |td   |	td   |
 S r-	  rK	  r
  r  r  r  rr    r
  rr  c                 C   sR  t td|| |	|
 td   t||t|||    |	 ||t|||    |
  t| | | |	|
 td  ||| |	 || |
td     | | | |	|
 td  ||	 | | ||    t|||    | ||t|||t|||    |	  ||t|||    |
td   || |	|
 td   | S r!	  rK	  r
  r  r  r  rs    r	  rs  c                 C   sR  t td|| |	|
 td   t||t|||    |	 ||t|||    |
  t| | | |	|
 td  ||| |	 || |
td     | | | |	|
 td  ||	 | | ||    t|||    | ||t|||t|||    |	  ||t|||    |
td   || |	|
 td   | S r!	  rK	  r
  r  r  r  rt    r	  rt  c                 C   s4  t td|| ||	 td   t||t|||
    | ||t|||
    |	  t| | | ||	 td  || | | ||   t|||
    ||| | || |	td     |
 |
|
t|||t|||
    |  ||t|||
    |	td   || ||	 td   |
 S r!	  rK	  r
  r  r  r  ru       6 ru  c                 C   s4  t td|| ||	 td   t||t|||
    | ||t|||
    |	  t| | | ||	 td  || | | ||   t|||
    ||| | || |	td     |
 |
|
t|||t|||
    |  ||t|||
    |	td   || ||	 td   |
 S r!	  rK	  r
  r  r  r  rv    r
  rv  c                 C   s<  t td||td |td   |
td   t||t|||    |	td  ||t|||    |
td   t| | | | |
td  || |	   || |td |	 |td |
td    ||  | ||   |	|
 td    t|||  td   ||
td  ||| ||   | | | | ||     t|||    | | ||  || |
td  || |	    | || t||t|||    |	 ||t|||    |
td   | |td  || | ||     || |td |td   |
td   | S r	  rK	  r
  r  r  r  rw        @ rw  c                 C   s<  t td||td |td   |
td   t||t|||    |	td  ||t|||    |
td   t| | | | |
td  || |	   || |td |	 |td |
td    ||  | ||   |	|
 td    t|||  td   ||
td  ||| ||   | | | | ||     t|||    | | ||  || |
td  || |	    | || t||t|||    |	 ||t|||    |
td   | |td  || | ||     || |td |td   |
td   | S r	  rK	  r
  r  r  r  rx    r
  rx  c                 C   s  t td||td |td   |	td   t||t|||
    |td  ||t|||
    |	td   t| | | | |	td  || |   || || |	td  || |    || |td  ||	 td  ||td | |td |	td      t|||
  td   || |  |	td  | | ||   t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | |td  ||td    || |td |td   |	td   |
 S r	  rK	  r
  r  r  r  ry         ry  c                 C   s  t td||td |td   |	td   t||t|||
    |td  ||t|||
    |	td   t| | | | |	td  || |   || || |	td  || |    || |td  ||	 td  ||td | |td |	td      t|||
  td   || |  |	td  | | ||   t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | |td  ||td    || |td |td   |	td   |
 S r	  rK	  r
  r  r  r  rz    r
  rz  c                 C   s  t td||	|
 td   t||t|||    |	td  ||t|||    |
  t| | | |	|
 td  ||| |
td  || |	    ||	|
 td  | | ||  ||   t|||    | | | |	|
 td  ||	 | | ||    t|||  td   | ||t|||t|||    |	  ||t|||    |
td   || |	|
 td   | S r	  rK	  r
  r  r  r  r{        r{  c                 C   s  t td||	|
 td   t||t|||    |	td  ||t|||    |
  t| | | |	|
 td  ||| |
td  || |	    ||	|
 td  | | ||  ||   t|||    | | | |	|
 td  ||	 | | ||    t|||  td   | ||t|||t|||    |	  ||t|||    |
td   || |	|
 td   | S r	  rK	  r
  r  r  r  r|    r
  r|  c                 C   st  t td|||	 td   t||t|||
    |td  ||t|||
    |	  t| | | ||	 td  || | | ||   t|||
  td   ||| |	td  || |    || | ||   ||	 td  t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	td   || ||	 td   |
 S r	  rK	  r
  r  r  r  r}    r	  r}  c                 C   st  t td|||	 td   t||t|||
    |td  ||t|||
    |	  t| | | ||	 td  || | | ||   t|||
  td   ||| |	td  || |    || | ||   ||	 td  t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	td   || ||	 td   |
 S r	  rK	  r
  r  r  r  r~    r	  r~  c                 C   sN  t td|td |td  |	td  | | ||    t||t|||    |	td  ||t|||    |
  t| ||	td  | | ||   |td | |	|
 td    || |td  ||| ||     |	|
 td  t|||  td   |	td | | ||   | | ||  ||   t|||    || ||  || |
td  || |	td     | ||t||t|||    |	td  ||t|||    |
td   | |td  ||| ||     ||td |td   |	td  | | ||    | S r-	  rK	  r
  r  r  r  r        R r  c                 C   sN  t td|td |td  |	td  | | ||    t||t|||    |	td  ||t|||    |
  t| ||	td  | | ||   |td | |	|
 td    || |td  ||| ||     |	|
 td  t|||  td   |	td | | ||   | | ||  ||   t|||    || ||  || |
td  || |	td     | ||t||t|||    |	td  ||t|||    |
td   | |td  ||| ||     ||td |td   |	td  | | ||    | S r-	  rK	  r
  r  r  r  r    r
  r  c                 C   s6  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t| ||td  | | ||   |td | ||	 td    || || |	td  || |td     || |td  ||td    ||	 td  t|||
  td   |td | | ||   | | ||   t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	td   | |td  ||td    ||td |td   |td  | | ||    |
 S r-	  rK	  r
  r  r  r  r        : r  c                 C   s6  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t| ||td  | | ||   |td | ||	 td    || || |	td  || |td     || |td  ||td    ||	 td  t|||
  td   |td | | ||   | | ||   t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	td   | |td  ||td    ||td |td   |td  | | ||    |
 S r-	  rK	  r
  r  r  r  r    r
  r  c
           
      C   s  t | |td  || |  ||td   |td |td  | | ||    t| t|||	   | ||t|||	     |	|	t | |td  || |  ||td   |td |td  | | ||    t| t|||	   | ||t|||	     |	|	 t|	|| | ||  ||   ||  | ||  ||     |td |td  |td |td    |	 S rQ	  rK	  
r  r  r  r  r  r  r  r  r  r	  r  r  r  r        r  c
           
      C   s  t | |td  || |  ||td   |td |td  | | ||    t| t|||	   | ||t|||	     |	|	t | |td  || |  ||td   |td |td  | | ||    t| t|||	   | ||t|||	     |	|	 t|	|| | ||  ||   ||  | ||  ||     |td |td  |td |td    |	 S rQ	  rK	  r
  r  r  r  r    r
  r  c	           	      C   sn  t | |td  ||td   |td |td  | | ||    t| t|||   | ||t|||     ||t | |td  ||td   |td |td  | | ||    t| t|||   | ||t|||     || t||| | ||   || | ||     |td |td  |td |td    | S rQ	  rK	  	r  r  r  r  r  r  r  r  r	  r  r  r  r       p r  c	           	      C   sn  t | |td  ||td   |td |td  | | ||    t| t|||   | ||t|||     ||t | |td  ||td   |td |td  | | ||    t| t|||   | ||t|||     || t||| | ||   || | ||     |td |td  |td |td    | S rQ	  rK	  r
  r  r  r  r    r
  r  c                 C   s&  t | |td  || |  ||td   |td |td   t||t|||
    |	 t|||
  td td  ||t|||
     |
|
t td|td |td   t||t|||
    |	 t|| || |   || || |   t|||
    |
 |
|
 S rT	  rK	  r
  r  r  r  r       ( r  c                 C   s&  t | |td  || |  ||td   |td |td   ttdt|||
  td  ||t|||
    |	  ||t|||
     |
|
t td|td |td   t||t|||
    |	 t|| || |   || || |   t|||
    |
 |
|
 S r,	  rK	  r
  r  r  r  r    r
  r  c
           
      C   s  t | |td  ||td   |td |td   t||t|||	    | t|||	  td td  ||t|||	     |	|	t td|td |td   t||t|||	    | t|| |  | | ||  t|||	    |	 |	|	 S rT	  rK	  r	
  r  r  r  r    r	  r  c
           
      C   s  t | |td  ||td   |td |td   ttdt|||	  td  ||t|||	    |  ||t|||	     |	|	t td|td |td   t||t|||	    | t|| |  | | ||  t|||	    |	 |	|	 S r,	  rK	  r	
  r  r  r  r    r	  r  c              
   C   s   t td||  tt|| |	 ||| |  |
  | |td  || |  ||td    |td |td   |||t|||   |S r-	  r9	  r
  r  r  r  r     r	  r  c              
   C   s   t td||  tt|| |	 ||| |  |
  | |td  || |  ||td    |td |td   |||t|||   | S r-	  r9	  r
  r  r  r  r    r	  r  c              
   C   s   t td||  tt||
 | |||
 |  |	  | |td  ||
td    |td |
td   |
|
|t|||
   |
S r-	  r9	  r
  r  r  r  r    ru	  r  c              
   C   s   t td||  tt||
 | |||
 |  |	  | |td  ||
td    |td |
td   |
|
|t|||
   |
 S r-	  r9	  r
  r  r  r  r       r  c                 C   .   t td|  tt|||  td ||S r-	  )r  r  r   r  rS	  r  r  r  r       .r  c                 C   r
  r-	  )r  r  r   r  rS	  r  r  r  r    r
  r  c              
   C   sj   t || |  ttd| |t|||  td   t|||  td   || t|| |  | S r-	  )r  r   r  r  r  r  rS	  r  r  r  r    r	  r  c              
   C   sj   t || |  ttd| |t|||  td   t|||  td   || t|| |  | S r-	  )r  r   r  r  r  r  rS	  r  r  r  r    r	  r  c              
   C   sV   t || tt| |||   | |td |td   |||t|||   |S rQ	  rR	  r  r  r  r  r  r  r  r	  r  r  r  r     rk	  r  c              
   C   sX   t || tt| |||   | |td |td   |||t|||   | S rQ	  rR	  r
  r  r  r  r  $  r6	  r  c	           
   	   C   s   t t|||  |}	t|	|td  | tt|| | |||	 | |   |  |	td |td  td | td td   ||t|||  |	 |S r	  )r   r  r  r  r+   r   
r  r  r  r  r  r  r  r  r	  r  r  r  r  r  (  s   r  c	           
      C   s   t tdt|||   |}	t|	|td  | tt|| | |||	 | |   |  |	td |td  td | td td   ||td|	t|||    | S r	  r   r  r  r  r+   r   r
  r  r  r  r  -  s   r  c           	      C   s   t t|||  |}t|| tt|| | |  |td  |td  td |td tdd    t| || |  ||td  |td  td |td    ||  ||t|||  | | S r0	  r   r  r  r+   r   r  r2  	r  r  r  r  r  r  r  r	  r  r  r  r  r  2     r  c           	      C   s   t t|||  |}t|| tt|| | |  |td  |td  td |td tdd    t| || |  ||td  |td  td |td    ||  ||t|||  | |S r0	  r   r  r  r+   r   r  r2  r"
  r  r  r  r  7     r  c	           
   	   C   s   t t|||  |}	t|	| tt| |||	 | |   | |	td |td  td |td td   ||t|||  |	 |S r0	  r   r  r  r+   r   r  r
  r  r  r  r  <  s   zr  c	           
      C   s   t tdt|||   |}	t|	| tt| |||	 | |   | |	td |td  td |td td   ||td|	t|||    | S r	  r 
  r
  r  r  r  r  A  s   r  c           	      C   s   t t|||  |}t|| tt|td  |td  td | td || td  tdd   t| |td  |td  td |td   ||| |   ||  ||t|||  | |S r0	  r$
  r"
  r  r  r  r  F  r%
  r  c           	      C   s   t t|||  |}t|| tt|td  |td  td | td || td  tdd   t| |td  |td  td |td   ||| |   ||  ||t|||  | | S r0	  r!
  r"
  r  r  r  r  K  r#
  r  c	           	   
   C   sb   t || tt|| | | |||   |  |td |td   |||t|||   |S rQ	  rR	  	r  r  r  r  r  r  r  r  r	  r  r  r  r  P  r	  r  c	           	   
   C   sd   t || tt|| | | |||   |  |td |td   |||t|||   | S rQ	  rR	  r'
  r  r  r  r  T  r	  r  c	           	   	   C   sR   t td|  ||   t|td| t|||  |   td|  ||S ro	  r	  	r  r  r  r  r  r  r!  r  r	  r  r  r  r  X  r	  r  c	           	   
   C   sZ   t td|  ||   t|td| tdt|||   |   td|  ||S Nrp	  r  r  r	  r(
  r  r  r  r  \  r[	  r  c	           	   	   C   s   t |td| t|||  |   td |  | |t|||  |   |t|||  td|    |  t|td| t|||  |   td|  ||S rQ	  r	  r(
  r  r  r  r  `  r/	  r  c	           	   
   C   s   t |td| tdt|||   |   td |  | |tdt|||   |   |tdt|||   td|    |  t|td| tdt|||   |   td|  ||S rT	  r	  r(
  r  r  r  r  d  rm	  r  c           	      C   s   t td |  | |td  td}ttd| | ttd|td| t|||  |   |  ||ttd| | ttd|td| t|||  |   |  || S r)
  r  r  r  r   r  	r  r  r  r  r  r  r!  r	  r  r  r  r  r  h  s   (r  c           	      C   s   t td |  | |td  td}ttd| | ttd|td| tdt|||   |   |  ||ttd| | ttd|td| tdt|||   |   |  || S r)
  r*
  r+
  r  r  r  r  m  s   (r  c              
   C   s   t || tt|
| |td |
td  | td td   | ||
|   ||
td|    |	  |
|
|t|||
   |
S rU	  rR	  r  r  r  r  r  r  r  r  r!  r  r	  r  r  r  r  r  r|	  r  c              
   C   s   t || tt|
| |td |
td  | td td   | ||
|   ||
td|    |	  |
|
|t|||
   |
 S rU	  rR	  r,
  r  r  r  r  v  ru	  r  c
                 C   s   t t|||	  |	}
t|
| tt|
|	 td | |  |
td  |	td  td |td tdd    t| |
|	 td|   ||
|	 |  |
td  |	td  td |td    ||
td  |	td  td |   |	|  |	|	t|||	  |
 |	 S r0	  r!
  r  r  r  r  r  r  r  r!  r  r	  r  r  r  r  r  z  s    r  c
                 C   s  t t|||	  |	}
t|
| tt|
|	 td | |  |
td  |	td  td |td tdd    t| |
|	 td|   ||
|	 |  |
td  |	td  td |td    ||
td  |	td  td |   |	|  |	|	t|||	  |
 |	S r0	  r$
  r-
  r  r  r  r    s   
 r  c              
   C   s   t ||td  | tt|td |
td  | td td  | ||
|   ||
td|    |	  |
|
|t|||
   |
S r	  r9	  r,
  r  r  r  r    r
  r  c              
   C   s   t ||td  | tt|td |
td  | td td  | ||
|   ||
td|    |	  |
|
|t|||
   |
 S r	  r9	  r,
  r  r  r  r    rr	  r  c
                 C   s   t t|||	  |	}
t|
| tt|
td  |	td  td |td ||  tdd   t| td|	td  |  ||	|  td|	td  |td    ||	td|    |	|  |	|	t|||	  |
 |	S r0	  r$
  r-
  r  r  r  r    s   r  c
                 C   s   t t|||	  |	}
t|
| tt|
td  |	td  td |td ||  tdd   t| td|	td  |  ||	|  td|	td  |td    ||	td|    |	|  |	|	t|||	  |
 |	 S r0	  r!
  r-
  r  r  r  r    s   r  c
           
   	   C   sf   t td|  ||   t|td| t|||	  |   td|  t|||	  |  |	|	S ro	  r	  
r  r  r  r  r  r  r  r!  r  r	  r  r  r  r    r	  r  c
           
   
   C   sv   t td|  ||   t|td| tdt|||	   |   td|  tdt|||	   |  |	|	S r)
  r	  r.
  r  r  r  r    rd	  r  c
           
   	   C   s   t |td| t|||	  |   td |  | |t|||	  |   |t|||	  td|    |  t|td| t|||	  |   td|  t|||	  |  |	|	S rQ	  r	  r.
  r  r  r  r    r 
  r  c
           
   
   C   s   t |td| tdt|||	   |   td |  | |tdt|||	   |   |tdt|||	   td|    |  t|td| tdt|||	   |   td|  tdt|||	   |  |	|	S rT	  r	  r.
  r  r  r  r    rv	  r  c              
   C   sv   t || tt|
| | | ||
|   ||
td|    |	  |td |
td   |
|
|t|||
   |
S rQ	  rR	  r,
  r  r  r  r    rd	  r  c              
   C   sx   t || tt|
| | | ||
|   ||
td|    |	  |td |
td   |
|
|t|||
   |
 S rQ	  rR	  r,
  r  r  r  r    rW	  r  c
           
   	   C   sn   t td|  ||   t|td| t|||	  |   td|  tdt|||	   |  |	|	S r)
  r	  r.
  r  r  r  r    r	  r  c
           
   
   C   sn   t td|  ||   t|td| tdt|||	   |   td|  t|||	  |  |	|	S r)
  r	  r.
  r  r  r  r    r	  r  c
           
   	   C   s   t |td| t|||	  |   td |  | |t|||	  |   |t|||	  td|    |  t|td| t|||	  |   td|  tdt|||	   |  |	|	S rT	  r	  r.
  r  r  r  r    r}	  r  c
           
   
   C   s   t |td| tdt|||	   |   td |  | |tdt|||	   |   |tdt|||	   td|    |  t|td| tdt|||	   |   td|  t|||	  |  |	|	S rT	  r	  r.
  r  r  r  r    r	  r  c
                 C   s   t tdt|||	   |	}
t|
| tt|
|	 |td| |   | |
|	 td|   ||
|	 |   | |  |
td |	td  td  |	|	td|
t|||	    |	S r-	  r 
  r-
  r  r  r  r    s   r  c
              	   C   s   t t|||	  |	}
t|
| tt|
|	 |td| |   | |
|	 td|   ||
|	 |   | |  |
td |	td  td  |	|	t|||	  |
 |	 S rT	  r&
  r-
  r  r  r  r    s   r  c	           	   
   C   sf   t td|  ||   t| |t|||    |td| t|||    td|   ||S ro	  r	  	r  r  r  r  r  r  r  r  r	  r  r  r  r    r	  r  c	           	   
   C   sf   t td|  ||   t| |t|||    |td| t|||    td|   ||S ro	  r	  r/
  r  r  r  r    r	  r  c	           	   
   C   s   t |td| t|||    td |  ||t|||    |t|||  td   |  t| |t|||    |td| t|||    td|   ||S rQ	  r	  r/
  r  r  r  r    rt	  r  c	           	   
   C   s   t |td| t|||    td |  ||t|||    |t|||  td   |  t| |t|||    |td| t|||    td|   ||S rQ	  r	  r/
  r  r  r  r    rt	  r  c           	      C   s   t td | | |td  td}t|td |  | ||  |  ttdt|td| t|||    | | ||t|td |  | ||  |  ttdt|td| t|||    | | || S r)
  r  r  r  r   r  r  	r  r  r  r  r  r  r  r	  r  r  r  r  r       (r  c           	      C   s   t td | | |td  td}t|td |  | ||  |  ttdt|td| t|||    | | ||t|td |  | ||  |  ttdt|td| t|||    | | || S r)
  r0
  r1
  r  r  r  r    r2
  r  c	           	   	   C   s\   t t| |t|||    ||t|||    |t|||  td   |  ||S rQ	  r   rI  r  r  r/
  r  r  r  r    rZ	  r  c	           	   	   C   s\   t t| |t|||    ||t|||    |t|||  td   |  ||S rQ	  r3
  r/
  r  r  r  r    rZ	  r  c              	   C   s   t tdt t| ||  | ttdt |||    ttdt |||   td  || tt| ||  |td   ||td   | S rT	  r  r  r  r   expr  r  r  r  r  r  r	  r  r  r  r       r  c              
   C   s   t tdt t| ||  | ttdt |||    tdttdt |||     || tt| ||  |td   ||td   | S rT	  r4
  r6
  r  r  r  r    r7
  r  c              	   C   s   t | td t| t|||   |td  |||  |  || t | | | ||td   t| t|||   |td  |||  |td   || t| | t|||   |td   |||  |  ||td   | S rJ	  rK	  r  r  r  r  r  r  r  r	  r  r  r  r       r  c              	   C   s   t | td t| t|||   |td  |||  |  || t | | | ||td   t| t|||   |td  |||  |td   || t| | t|||   |td   |||  |  ||td   | S rJ	  rK	  r8
  r  r  r  r    r9
  r  c              	   C   s   t | td t| t|||   |td  |||  |  || t || | | |td   t| t|||   |td  |||  |td   || t| t|||   |td  |||  |  | | |td   | S Nr'	  r  r  r	  rK	  r8
  r  r  r  r    r9
  r  c              	   C   s   t | td t| t|||   |td  |||  |  || t || | | |td   t| t|||   |td  |||  |td   || t| t|||   |td  |||  |  | | |td   | S r:
  rK	  r8
  r  r  r  r    r9
  r  c	           	   	   C   s6   t t|||  | | |t|||    | ||S r4	  r   r   r  r	  r  r  r  r    r	  r  c	           	   	   C   s6   t t|||  | | |t|||    | ||S r4	  r;
  r	  r  r  r  r    r	  r  c              
   C   s   t | | | td| |  t|||  |td  | |t|||     ||t|||  |td  td|  | |td   | t| |||  |  td| | | |t|||      | S r	  rK	  r	  r  r  r  r  
  rI	  r  c              
   C   s   t | | | td| |  t|||  |td  | |t|||     || t|||  |td  td|  | |td   | t| |||  |  td| | | |t|||      | S r	  rK	  r	  r  r  r  r    r1	  r  c              
   C   s   t || |  tttd| td| |  |||   || t |||  tttd| td| |  |||   || ttd|| |t|||     |||    | S rT	  r  r   r  r  r  r  r  r	  r  r  r  r    r`	  r  c              
   C   s   t || |  tttd| td| |  |||   ||t |||  tttd| td| |  |||   || ttd|| |t|||     |||    | S rT	  r<
  r	  r  r  r  r    rz	  r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     ||t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S rT	  rK	  r	  r  r  r  r    r	  r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     || t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S rT	  rK	  r	  r  r  r  r    r9
  r  c                 C   s   t tdtd|   tttd| td| |  |||   ||t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S r-	  r  r  r   r  r  r  rN	  r	  r  r  r  r  "  rz	  r  c                 C   s   t tdtd|   tttd| td| |  |||   || t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S r-	  r=
  r	  r  r  r  r  &  r`	  r  c              	   C   s   t tdtd|   t|||  | ttd|  |||   |  ||t|||  |td  td|  | |td   | S r-	  r  r  r   r5
  r  r	  r  r  r  r  *  r|	  r  c              	   C   s   t tdtd|   t|||  | ttd |  |||   |  || t|||  |td  td|  | |td   | S r-	  r>
  r	  r  r  r  r  .  r
  r  c	           	      C   s   t t|||  | ttd| td| |  td|  ttd| td| |  td|    tdtd|    |  ||S rT	  r   r   r  r  r  r	  r  r  r  r  2  r
  r  c	           	      C   s   t t|||  | ttd| td| |  td|  ttd| td| |  td|    tdtd|    |  ||S rT	  r?
  r	  r  r  r  r  6  r
  r  c	           	      C   s`   t t|||  | ttd|  |||   | td|   tdtd|    |  ||S rT	  )r   r   r5
  r  r	  r  r  r  r  :  r	  r  c	           	   	   C   sb   t t|||  | tdtd|   ttd |  |||   | td|    |  ||S r-	  )r   r   r  r5
  r	  r  r  r  r  >  r	  r  c	           
      C   sn   t | |t|||    | |}	t|| tt|||  |td  |	||| t|||  | |	| S r	  r  r  r  r   r  
r  r  r  r  r  r  r  r  r	  ur  r  r  r  B     "Lr  c	           
      C   sn   t | |t|||    | |}	t|| tt|||  |td  |	||| t|||  | |	| S r	  r@
  rA
  r  r  r  r  G  rC
  r  c                 C   s   t tdt | t|||  | | td |td  | t|  td ttdt |||      || t|||  |td  || t|   |td   | S rT	  r4
  r	  r  r  r  r  L  r	  r  c                 C   s   t tdt | t|||  | | td |td  | t|  td ttdt |||      ||t|||  |td  || t|   |td   | S rT	  r4
  r	  r  r  r  r  P  r/	  r  c              
   C   s  t td|| td |td    ttd|  | | td|  | | |  ||  | |t|||     ||t|||  td td| | td |td    | t||||   || |t|||     | td |td    | S r-	  rK	  r	  r  r  r  r  T  s    r  c              
   C   s  t td|| td |td    ttd |  | | td|  | | |  ||  | |t|||     || t|||  td td| | td |td    | t||||   || |t|||     | td |td    | S r-	  rK	  r	  r  r  r  r  X  r	  r  c	           	      C   s   t t|||  | td t | | td |td  | t|  td ttdt |||      td| t|    |  ||S rT	  r   r   r  r  r5
  r	  r  r  r  r  \  rr	  r  c	           	      C   s   t t|||  | tdt | | td |td  | t|  td ttdt |||      td| t|    |  ||S rT	  rD
  r	  r  r  r  r  `  r
  r  c                 C   s.   t | |tt||  | t|||  |S r4	  r   r  r2  r  r  r  r  rB
  vr	  r  r  r  r  d  r
  r  c                 C   s.   t | |tt||  | t|||  |S r4	  rE
  rF
  r  r  r  r  h  r
  r  c	           	      C   s2   t | |t|||    | |||  |  |S r4	  r	  r	  r  r  r  r  l     2r  c	           	      C   s2   t | |t|||    | |||  |  |S r4	  r	  r	  r  r  r  r  p  rH
  r  c                 C   sV   t td| tt|tdtd|   | |t|||    |  |||| |S r	  r9	  r  r  r  r  r  r  r	  r  r  r  r  t  rk	  r  c                 C   sV   t td| tt|tdtd|   | |t|||    |  |||| |S r	  r9	  rI
  r  r  r  r  x  rk	  r  c                 C   s&   t | |t||||     | |S r4	  r	  rI
  r  r  r  r  |  rP	  r  c                 C   s&   t | |t||||     | |S r4	  r	  rI
  r  r  r  r    rP	  r  c                 C   sJ   t tdt||td tt| |t||||     | ||||S r!	  r  r  r3   r+   r   r  r  r  r  r  r  r  rB
  r	  r  r  r  r    r	  r  c                 C   sJ   t tdt||td tt| |t||||     | ||||S r!	  rJ
  rK
  r  r  r  r    r	  r  c                 C   s    t | |tt||  | |S r4	  rE
  r  r  r  rB
  r	  r  r  r  r        r  c                 C   s    t | |tt||  | |S r4	  rE
  rL
  r  r  r  r    rM
  r  c                 C   sZ   t td| tt|td|td |   | |t|||    |  |||| |S r	  r9	  r  r  r  r  r  r  r  r	  r  r  r  r    r[	  r  c                 C   sZ   t td| tt|td|td |   | |t|||    |  |||| |S r	  r9	  rN
  r  r  r  r    r[	  r  c              	   C   s   t || td ||  t|||  t| |||    || t|| | t||| td  t| |||    ||  | S r!	  rK	  r  r  r  r  r	  r  r  r  r    r|	  r  c              	   C   s   t || td ||  t|||  t| |||    ||t|| | t||| td  || t| |||     | S r!	  rK	  rO
  r  r  r  r    r{	  r  c              	   C   s.   t || | |t||||     |  |S r4	  r	  rN
  r  r  r  r    r
  r  c              	   C   s.   t || | |t||||     |  |S r4	  r	  rN
  r  r  r  r    r
  r  c	           	      C   s\   t |t| |t|   || t|  t|| | |t||||     |  ||S r4	  r  r%   r&   r   r  r'
  r  r  r  r    rZ	  r  c	           	      C   s\   t |t| |t|   || t|  t|| | |t||||     |  ||S r4	  rP
  r'
  r  r  r  r    rZ	  r  c                 C   s,   t || | | |tt||  |  |S r4	  rE
  r  r  r  r  r  rB
  r	  r  r  r  r       ,r  c                 C   s,   t || | | |tt||  |  |S r4	  rE
  rQ
  r  r  r  r    rR
  r  c              
   C   s   t || td || |  t|||  tdt| |||    |  || t||| td  tdt| |||    |  || |  | S r!	  )r  r  r   r  r  r  r  r  r  r  r  r	  r  r  r  r    r7
  r  c              
   C   s   t || td || |  t|||  tdt| |||    |  ||t||| td  tdt| |||    |  || |  | S r!	  )r  r  r   r  r  rS
  r  r  r  r    r	  r  c                 C   s*   t t| ||  ||td   | |S rQ	  r	  r  r  r  r  r	  r  r  r  r    s   *r  c                 C   s2   t tdt| ||  ||td    | |S r-	  r   r  r  rT
  r  r  r  r    rH
  r  c              	   C   s<   t |tt| ||  ||td    td|  | S rQ	  )r  rN	  r  r  r  r  r  r  r  r	  r  r  r  r    r	  r  c              	   C   s:   t |tt| ||  ||td    td|  |S rQ	  )r  rN	  r  r  rV
  r  r  r  r    r	  r  c              
   C   s   t | | td| |  td|  tt| ||  ||td   ||t|tt| ||  ||td    td|  | S rQ	  )r  r  r   r  r  rN	  r  rV
  r  r  r  r     ru	  r   c              
   C   s   t | | td| |  td|  ttdt| ||  ||td    ||t|tt| ||  ||td    td|  | S rT	  )r  r  r   r  r  rN	  r  rV
  r  r  r  r    r	  r  c                 C   s:   t |||  | t| ||  ||td   |  |S rQ	  r	  r  r  r  r  r  r  r  r	  r  r  r  r    r	  r  c              	   C   sB   t |||  | tdt| ||  ||td    |  |S r-	  rU
  rW
  r  r  r  r    s   B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  r5
  r  rN	  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  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  Pir*  B_C_F_G_H_r5  b_r  r  r  f_g_h_i_j_k_l_r  r  r(  r  r_t_r  r  s_w_r  y_z_a1_a2_b1_b2_c1_c2_d1_d2_n1_r  e1_e2_f1_f2_g1_g2_n3_Pq_Pm_Px_Qm_Qr_Qx_jn_mn_non2_RFx_RGx_r  iiPqqQRrr  krB
  	_UseGamma	ShowStepsStepCounterr	  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  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/  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  <module>   sz              n"JjB.
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