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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGammaWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  D/usr/lib/python3/dist-packages/sympy/integrals/rubi/rules/tangent.py
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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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   C   sn   t td| tt||  td|td  |td |td  tdd    ||t| ||  | S Nr  r  r  r  r  r+   r   r  r  r  r  r  r  r  r  r  r       nr  c              
   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 r  r  r  r  r  r  r    r	  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  r
  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    r  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 r  )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  r  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  (  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|||   |td   || t| t|||   | |t|||   |td   || |td   | S r  r   r  r  r  r  r  0  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  4  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  8  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|||   |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   D  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  H  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  L  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 r  r   r  r  r  r  r  P  r	  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  T     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  X  r  r  c              	   C   sr   t t| t|||   tt|||   tt|||   ttt|||  tt|||   ||S r  )r  r  r  r  r  r   r  r  r  r  r  \     rr  c              	   C   sr   t t| t|||   tt|||   tt|||   ttt|||  tt|||   ||S r  )r  r  r  r  r  r   r  r  r  r  r  `  r  r  c                 C   s   t | ||  | t|||   |   |t|||   |   |t|||   |  t|t|||   | t|||  | |   ||S r  )r  r  r  r  r   r  r  r  r  r  d     r  c                 C   s   t | ||  | t|||   |   |t|||   |   |t|||   |  t|t|||   | t|||  | |   ||S r  )r  r  r  r  r   r  r  r  r  r	  h  r  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
  l  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 r  )r  r  r  r  r5   r  r  r  r  r  r  p     r  c              	   C   st   t t|||  |  t| | t|||   t|  tt|||  |  |  |t|||   |  ||S r  r  r  r&   r   r  r  r  r  r  r  t     tr  c              	   C   st   t t|||  |  t| | t|||   t|  tt|||  |  |  |t|||   |  ||S r  r  r  r&   r   r  r  r  r  r  r  x  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  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|||   |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   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 r"  r#  r$  r  r  r  r    r  r  c                 C   sr   t | td t| t|||   |td  || t| t|||   |td  | | |td   | S Nr  r  r  r#  r$  r  r  r  r    r  r  c                 C   sr   t | td t| t|||   |td  || t| t|||   |td  | | |td   | S r%  r#  r$  r  r  r  r    r  r  c                 C   s&   t ttt| ||  || | S r  )r  logr   r  r  r  r  r  r  r  r       &r  c                 C   s$   t ttt| ||  || |S r  )r  r&  r   r  r'  r  r  r  r    s   $r  c              
   C   sJ   t | | tt|| | td |td   ||| t|||   |S Nr  r  r+   r   r  r  r$  r  r  r  r    r  r  c              
   C   sL   t | | tt|| | td |td   ||| t|||   | S r)  r*  r$  r  r  r  r    r  r  c                 C   sr   t td|  | tt|||  ||t|| td |td   | t|td t|||   | | S r)  r#  r  r  r  r  r  r  r  r  r    r  r  c                 C   sz   t td|  | ttdt|||   ||t|| td |td   | t|td |t|||    | S Nr  r  r#  r+  r  r  r  r    r  r  c              	   C   sx   t td|  t| |t|||    |td  ||t|| |t|||    |td   ||td   | S Nr  r  r#  r  r  r  r  r  r  r  r  r  r       xr  c              	   C   sx   t td|  t| |t|||    |td  ||t|| |t|||    |td   ||td   | S r-  r#  r.  r  r  r  r    r/  r  c              	   C   s|   t tdtd|   t| |t|||    |td  ||t| | |t|||    |  td| | |  | S r  r#  r.  r  r  r  r        |r   c              	   C   s|   t tdtd|   t| |t|||    |td  ||t| | |t|||    |  td| | |  | S r  r#  r.  r  r  r  r!    r0  r!  c                 C   s\   t td | | tttdtd|  |td   ||t| |t|||    |S r,  r  r  r+   r   r  r  r+  r  r  r  r"       \r"  c                 C   sZ   t td| | tttdtd|  |td   ||t| |t|||    |S r,  r1  r+  r  r  r  r#       Zr#  c              
   C   sH   t || tt| | |td  | |  |||t|||   | S r  r*  r.  r  r  r  r$    s   Hr$  c              
   C   sF   t || tt| | |td  | |  |||t|||   |S r  r*  r.  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  r.  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 r5  r6  r.  r  r  r  r'    r7  r'  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  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d   || td |td   |td   | S r  r#  r.  r  r  r  r)    r8  r)  c              
   C   s~   t || td |td   t|  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|  t|||   | | |t|||     ||t| | | td |td   | S r)  r#  r+  r  r  r  r+    r9  r+  c              
   C   sN   t || tt| | | |td |td   |||t|||   |S r)  r*  r.  r  r  r  r,    r  r,  c              
   C   sP   t || tt| | | |td |td   |||t|||   | S r)  r*  r.  r  r  r  r-       Pr-  c                 C   sP   t | t|t|||   | ||t||t|||   |  ||  | S r  )r  r   r  r  r  r  r  r  r  r  r  r  r  r  r.    r:  r.  c                 C   sP   t | t|t|||   | ||t||t|||   |  ||  | S r  )r  r   r  r  r;  r  r  r  r/    r:  r/  c              
   C   sv   t | td|  ||  tt| | |td td  | | |td | td   |||t|||   |S r-  r  r  r  r  r  r0       vr0  c              
   C   sx   t | td|  ||  tt| | |td td  | | |td | td   |||t|||   | S r-  r  r  r  r  r  r1     r/  r1  c                 C   sJ   t ||t|||   |  | |t|||    |  | | |  |S r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r2    r  r2  c                 C   sL   t ||t|||   |  | |t|||    |  | | |  | S r  )r  r  r  r=  r  r  r  r3    r  r3  c                 C   sz   t td |  ||  tttd|  |td  td  ||tdt| |t|||    t|||    |S r,  r  r  r+   r   r  r  r  r  r  r  r  r  r  r  r  r4    r  r4  c                 C   sx   t td|  ||  tttd|  |td  td  ||tdt| |t|||    t|||    |S r,  r  r  r+   r   r  r  r  r?  r  r  r  r5    r/  r5  c              
   C   s   t | td|td   t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S r-  r  r=  r  r  r  r6       r6  c              
   C   s   t | td|td   t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S r-  r   r=  r  r  r  r7    rA  r7  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  r=  r  r  r  r8    s   r8  c              
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   C      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>  4     r>  c              
   C      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?  8  rE  r?  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  r>  r  r  r  r  r  r  r  r  r  r@  <  s   r@  c                 C   s   t td| |td  | tt|td | td |td |td    ||t| |t|||    t|t|||    |S rG  r@  rI  r  r  r  rA  @     rA  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 r"  r  r=  r  r  r  rB  D  r   rB  c              
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   C   s   t | ||  |td |  t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S r-  r  r=  r  r  r  rD  L     rD  c              
   C   s   t | ||  |td |  t|t|||   |td  | |t|||    |td   ||t||t|||   |  | |t|||    |  | | |  | S r-  r   r=  r  r  r  rE  P  rL  rE  c              
   C   rD  r"  r  r=  r  r  r  rF  T  rE  rF  c              
   C   rF  r"  r   r=  r  r  r  rG  X  rE  rG  c                 C   s   t |t| |t|||    t| |t|||     t|||    tt|t|||   t| |t|||     ||S r  )r  r  r  r  r   rI  r  r  r  rH  \     rH  c                 C   s   t |t| |t|||    t| |t|||     t|||    tt|t|||   t| |t|||     ||S r  )r  r  r  r  r   rI  r  r  r  rI  `  rM  rI  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  r=  r  r  r  rJ  d  r  rJ  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   r=  r  r  r  rK  h  s   rK  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  r=  r  r  r  rL  l     rL  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   r=  r  r  r  rM  p  rN  rM  c              
   C      t || | |td|    t|t|||   | | |t|||    |td   ||t| |t|||   |  | |t|||    |  || |td|    | S r,  r  r=  r  r  r  rN  t     rN  c              
   C      t || | |td|    t|t|||   | | |t|||    |td   ||t| |t|||   |  | |t|||    |  || |td|    | S r,  r   r=  r  r  r  rO  x  rP  rO  c              
   C   rD  r"  r  r=  r  r  r  rP  |  rE  rP  c              
   C   rF  r"  r   r=  r  r  r  rQ    rE  rQ  c              
   C   rO  r,  r  r=  r  r  r  rR    rP  rR  c              
   C   rQ  r,  r   r=  r  r  r  rS    rP  rS  c              
   C   s   t |t|||   | | |t|||    | td   | |t|||    | td   t| |t|||    |td  | |t|||    |td |   ||S r)  )r  r  r  r  r   r=  r  r  r  rT       rT  c              
   C   s   t |t|||   | | |t|||    | td   | |t|||    | td   t| |t|||    |td  | |t|||    |td |   ||S r)  )r  r  r  r  r   r=  r  r  r  rU    rR  rU  c              
   C   sr   t td||  tttd|td |td   |td td  | | |  |||t|||   |S r  r  r  r  r  r  rV    r  rV  c              
   C   st   t td||  tttd|td |td   |td td  | | |  |||t|||   | S r  r  r  r  r  r  rW    r  rW  c                 C   s   t |td tt|||   | |t | td |td  t|||   | | t td|  | t|||   | | S r)  )r  r  r  r  r  r?  r  r  r  rX       rX  c                 C   s   t |td tt|||   | | t | td |td  t|||   | | t td|  | t|||   | | S r)  )r  r  r  r  r  r?  r  r  r  rY       rY  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  r;  r  r  r  rZ       rZ  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   r;  r  r  r  r[    rU  r[  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  r?  r  r  r  r\    r  r\  c              
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   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  r=  r  r  r  rb    rK  rb  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 rZ  )r  r  r%   r  r&   r+   r   r  r=  r  r  r  rc       rc  c                 C   s   t td | | tt|td | td |td  |td   ||t|t|||   t| |t|||     |S rG  )r  r  r+   r   r  r  r  rI  r  r  r  rd    r  rd  c                 C   s   t td| | tt|td | td |td  |td   ||t|t|||   t| |t|||     |S rG  )r  r  r+   r   r  r  r  rI  r  r  r  re    s   re  c              
   C   s   t td|t| |t|||     t| |t|||     t|||    tt| |t|||    t|t|||    ||S r  )r  r  r  r  r  r   rI  r  r  r  rf       rf  c              
   C   s   t td|t| |t|||     t| |t|||     t|||    tt| |t|||    t|t|||    ||S r  )r  r  r  r  r  r   rI  r  r  r  rg    r\  rg  c              
   C   sp   t |t|||   | |t|||   |  t|t|||   |  | |t|||    |  ||S r  )r  r  r   r  r=  r  r  r  rh    r  rh  c              
   C   sp   t |t|||   | |t|||   |  t|t|||   |  | |t|||    |  ||S r  )r  r  r   r  r=  r  r  r  ri    r  ri  c              
   C   sl   t || tt|| | | |  |td |td  | td td   |||t|||   |S r-  r*  r  r  r  r  rj    r  rj  c              
   C   sn   t || tt|| | | |  |td |td  | td td   |||t|||   | S r-  r*  r  r  r  r  rk    r  rk  c                 C   s6   t | |t|||    | t|||  |  |S r  )r   r  r  r  r  r  r  rl       6rl  c                 C   s6   t | |t|||    | t|||  |  |S r  )r   r  r  r  r  r  r  rm    r]  rm  c                 C   s\   t | t|||   |t|||    | t|||  |  t|||  |   |S r  r   r  r  r  r  r  r  rn    r2  rn  c                 C   s\   t | t|||   |t|||    | t|||  |   t|||  |  |S r  r   r  r  r  r  r  r  ro    r2  ro  c              
   C   sx   t t|||  | t| |t|||   t|  tt|||  | |  | |t|||    |  ||S r  r  r=  r  r  r  rp    r/  rp  c              
   C   sx   t t|||  | t| |t|||   t|  tt|||  | |  | |t|||    |  ||S r  r  r=  r  r  r  rq   	  r/  rq  c                 C   s^   t | t|||   |t|||    | t|||  |  t|||  ||   |S r  r^  r  r  r  r  r  r  r  r  r  r  r  rr  	  r  rr  c                 C   s^   t | t|||   |t|||    | t|||  ||   t|||  |  |S r  r_  r`  r  r  r  rs  	  r  rs  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  ru  	     `ru  c	           	   	   C   s`   t | | ||  t||t|||    | |  tdt|||   td|   ||S r  r  ra  r  r  r  rv  	  rb  rv  c	           	   	   C   sZ   t | | | tt| ||  |td  |||  |td   ||t|||  |S r  r*  ra  r  r  r  rw  	  r3  rw  c	           	   
   C   sd   t | | | tt| ||  |td  |||  |td   ||tdt|||   | S Nr  r  r*  ra  r  r  r  rx  	     drx  c                 C   s<   t || | ||   |t || t|||   | | S r  r  r  r  r  r  r  r  r  r  r  r  r  ry  	     <ry  c                 C   s<   t || | ||   |t || |t|||    | S r  re  rf  r  r  r  rz   	  rg  rz  c                 C   sf   t | | ||  tt|||  ||t|| | ||   | t|| t|||   | | S r  r  r   r  r  rf  r  r  r  r{  $	     fr{  c                 C   sn   t | | ||  ttdt|||   ||t|| | ||   | t|| |t|||    | S r  r  r   r  r  r  rf  r  r  r  r|  (	  r  r|  c              	   C   s   t | | ||  td|  |  t| |t|||    |td  ||t| |t|||    | |  | ||   td|  | |  | S r,  r#  r  r  r  r  r  r  r  r  r  r  r  r}  ,	     r}  c              	   C   s   t | | ||  td|  |  t| |t|||    |td  ||t| |t|||    | |  | ||   td|  | |  | S r,  r#  rk  r  r  r  r~  0	  rl  r~  c              	   C   sh   t | | ||  | t| |t|||    | ||t|| |t|||    |  ||  | S r  rh  rk  r  r  r  r  4	  r  r  c              	   C   sh   t | | ||  | t| |t|||    | ||t|| |t|||    |  ||  | S r  rh  rk  r  r  r  r  8	  r  r  c              	   C   s   t | |t|||    |td  t| | ||  | | ||  t|||    | |t|| |t|||    |  ||  | S r  r6  rk  r  r  r  r  <	  rJ  r  c              	   C   s   t | |t|||    |td  t| | ||  | | ||  t|||    | |t|| |t|||    |  ||  | S r  r6  rk  r  r  r  r  @	  rJ  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  r#  rk  r  r  r  r  D	     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  r#  rk  r  r  r  r  H	  rm  r  c              
   C   sD   t |tt| t|||   |t|||    | ||  |S r  )r  r&  r   r  r  rf  r  r  r  r  L	     Dr  c              
   C   sF   t |tt| t|||   |t|||    | ||  | S r  )r  r&  r   r  r  rf  r  r  r  r  P	  r4  r  c              
   C   s   t |  | ||  | td |td   t|  t|||   | | |t|||     ||t|| | ||   | td |td   | S r)  r#  rf  r  r  r  r  T	     r  c              
   C   s   t |  | ||  | td |td   t|  t|||   | | |t|||     ||t|| | ||   | td |td   | S r)  r#  rf  r  r  r  r  X	  ro  r  c                 C   s   t td |td  | tttd| |td  td| |   ||||t|||    t| t|||    |S 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ttd| |td  td| |   ||||t|||    t| t|||    |S r,  rp  rq  r  r  r  r  `	  r9  r  c                 C   s^   t td|td  | tttd| | ||td    ||t| t|||   |S r,  r1  rq  r  r  r  r  d	  r  r  c                 C   s`   t td |td  | tttd| | ||td    ||t| t|||   |S r,  r1  rq  r  r  r  r  h	  rb  r  c                 C   sb   t td| tt| | ||td   | td |td   ||t| t|||   |S Nr  rH  r1  rq  r  r  r  r  l	     br  c                 C   sd   t td | tt| | ||td   | td |td   ||t| t|||   |S rs  r1  rq  r  r  r  r  p	  rd  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  rH  rp  rf  r  r  r  r  t	  rP  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 ru  rp  rf  r  r  r  r  x	     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 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d|  t| | ||  ||  |  | ||  ||  t|||    t| |t|||     || ttdtd|  t| | ||  ||  |  | ||  ||  t|||    t| |t|||     || S r,  rw  rx  r  r  r  r  	  ry  r  c              
   C   sV   t || | tt| || |  | || |td   |||t|||   |S r)  r*  rk  r  r  r  r  	  rC  r  c              
   C   sX   t || | tt| || |  | || |td   |||t|||   | S r)  r*  rk  r  r  r  r  	  r  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  	  r  r  c              	   C   sX   t |t| t|||   | ||t ||  t| t|||   |td  || S r  rz  r{  r  r  r  r  	  r  r  c              
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   C   s   t |  | ||  td |td  ttd| |t|||     ||t |td | tt|||  || t|| |  | td| |   |td  | S r,  r#  rf  r  r  r  r  	     r  c              
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   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  r#  ra  r  r  r  r  	     r  c	           	   
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   C   s   t | | ||  td|td   t| |t|||    |td  ||t|||    |td   || t| | |t|||    |  ||t|||    |  td| | |  | S r  r#  ra  r  r  r  r  	  rX  r  c	           	   
   C   s   t | | ||  td|td   t| |t|||    |td  ||t|||    |td   || t| | |t|||    |  ||t|||    |  td| | |  | S r  r#  ra  r  r  r  r  	  rX  r  c	           	   
   C   s   t tdtd|   t| |t|||    |td  ||t|||    |  ||t| | |t|||    |  ||t|||    |td   td| | |  | ||    | S r  r#  ra  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  r#  ra  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  ra  r  r  r  r  	  rU  r  c	           	   
   C   s   t | | | ||   t| |t|||    | ||t|||    |td   ||t|| |t|||    |  ||t|||    |td   || |td |td    | S r  r  ra  r  r  r  r  	  rU  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  r#  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  r#  r  r  r  r  r  	  r  r  c                 C   s$  t tdtd| td   t||t|||    |td  t| |td  | |td  |td   || | |  || | |td  || |   t|||    | ||t||t|||    |td  |  | ||   td|  | | |t|||      | S Nr  r  r  r  r#  r  r  r  r  r  	     & r  c                 C   s$  t tdtd| td   t||t|||    |td  t| |td  | |td  |td   || | |  || | |td  || |   t|||    | ||t||t|||    |td  |  | ||   td|  | | |t|||      | S 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  rf  r  r  r  r  	  rr  r  c                 C   s   t ||  | ||   ttd| |t|||     ||t ||  | ||   ttd||t|||     || S r  r  rf  r  r  r  r  	  rr  r  c                 C   s   t tdtd|  |  | ||    t||t|||    | t| | |td  ||  || | t|||    | ||t| ||t|||    |td   td| | |t|||     |  | ||    | S 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  r#  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  r#  ra  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  r#  ra  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 r)  r  r  r   r  r  rf  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 r)  r  rf  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 r)  r  rf  r  r  r  r  
  rA  r  c                 C   s   t td|  tt| |t|||    t||t|||     ||t ||  tt| |t|||    | t|||   |  t||t|||     || S r)  r  rf  r  r  r  r  
  rA  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  r#  ra  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  r#  ra  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  rH  r  r  r  r   r  r  r  rk  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 r  r  rk  r  r  r  r  *
  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  r#  ra  r  r  r  r  .
     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  r#  ra  r  r  r  r  2
  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  r#  ra  r  r  r  r  6
     > 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  r#  ra  r  r  r  r  :
  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  r#  ra  r  r  r  r  >
     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  r#  ra  r  r  r  r  B
  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  r#  ra  r  r  r  r  F
  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  r#  ra  r  r  r  r  J
  r  r  c                 C   s   t | | | ||   t| |t|||    | ||t || | ||   t| |t|||    | | t|||   |  ||t|||     || S r  r  r   r  rk  r  r  r  r  N
     r  c                 C   s   t | | | ||   t| |t|||    | ||t || | ||   t| |t|||    | | t|||   |  ||t|||     || S r  r  rk  r  r  r  r  R
  r  r  c                 C   s   t ||  tt| |t|||    | t|||   |  t||t|||     ||t | | ||  |  tt| |t|||    t||t|||     || S r  r  r   r  r  rf  r  r  r  r  V
  rP  r  c                 C   s   t ||  tt| |t|||    | t|||   |  t||t|||     ||t | | ||  |  tt| |t|||    t||t|||     || S r  r  rf  r  r  r  r  Z
  rP  r  c	           	   
   C   sj   t | | | tt| | |td  ||| |  |  | | |td   |||t|||   |S Nr  r  r*  ra  r  r  r  r  ^
     jr  c	           	   
   C   sl   t | | | tt| | |td  ||| |  |  | | |td   |||t|||   | S r  r*  ra  r  r  r  r  b
  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  r#  ra  r  r  r  r  f
       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  r#  ra  r  r  r  r  j
  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  r#  ra  r  r  r  r  n
      r  c	           	      C   s  t td||| td   t| |t|||    |td  ||t|||    |  t| td | || td  |t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  r#  ra  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  r#  ra  r  r  r  r  v
      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  r#  ra  r  r  r  r  z
  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  r#  ra  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  r#  ra  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  r#  ra  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  r#  ra  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  r#  ra  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  rk  r  r  r  r  
  r  r  c	           	   
   C   sb   t || tt| | | ||| |  |  |td |td   |||t|||   |S r)  r*  ra  r  r  r  r  
  rt  r  c	           	   
   C   sd   t || tt| | | ||| |  |  |td |td   |||t|||   | S r)  r*  ra  r  r  r  r  
  rd  r  c              	   C   sL   t || t|t|||   | |  | t|||   | |  ||S r  r  r=  r  r  r  r  
  r  r  c              	   C   sL   t || t|t|||   | |  | t|||   | |  ||S r  r  r=  r  r  r  r  
  r  r  c
           
   
   C   s   t |t| ||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  r  c
           
   
   C   s   t |t| ||t|||	   |  t|  |t|||	   | t|   t|t|||	   ||  | |t|||	    |  |	|	S r  r  r  r  r  r  r  
  r  r  c                 C   sV   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  
  rC  r  c                 C   sV   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S r  r  r  r  r  r  r  
  rC  r  c              	   C   sp   t |||  t|t|||
   | | |	  | t|||
   | |  |t|||
   | |  |
|
S r  r  r  r  r  r  r  
  r  r  c              	   C   sp   t |||  t|t|||
   | | |	  | t|||
   | |  |t|||
   | |  |
|
S r  r  r  r  r  r  r  
  r  r  c              
   C   s   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  
  ro  r  c              
   C   s   t |tdt|||   |
  |	 |t|||   |	 |
   t|t|||   |	|
  | |t|||    |  ||t|||    |  ||S r  r  r  r  r   r  r  r  r  r  
  r7  r  c              
   C   sh   t || t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r  r  r  r  r  r  r  
  r  r  c              
   C   sh   t || t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r  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  
  rb  r  c
           
      C   sX   t ||t|||	    | | t|||	   | |  t|||	  | |   |	S r  r  r  r  r  r  r  
  r  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  
  ro  r  c              	   C   s   t |t|||
   |	 t|||
  |	  t||t|||
    | | t|||
   | |  t|||
  | |	   |
|
S r  r  r  r  r  r  r  
  rT  r  c              
   C   s   t |t|||
   | ||t|||
    |  |t|||
   | |   t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r  r  r  r  r  r  r  
     r  c              
   C   s   t |t|||
   | ||t|||
    |  |t|||
   | |   t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S r  r  r  r  r  r  r    r  r  c              	   C   sf   t || | 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    ri  r  c              
   C   sp   t || | tt| ||
  |||
  |td   |||
  |	td   |
|
tdt|||
   |
 S rc  r*  r  r  r  r  r  
  r  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    ro  r  c	           	   
   C   s   t td| tt| | | | | | || | ||    t|||    |||t|||     ||t || | ttdt|||   || S r  r  r  r  r  r  r    r7  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  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|||	    |td  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|||	    |	 |	|	t||t|||	    |td  | | ||   | | ||   || |td |td   |td   |	 S r  r#  r  r  r  r  r    r  r  c
           
      C   s>  t td|td |td   t||t|||	    |td  t| | | | | |  || |  || |  |  | | | | |  || |  || |  t|||	    |	 |	|	t||t|||	    |td  | | ||   | | ||   || |td |td   |td   |	 S r  r#  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  &     r  c
           
   	   C   s   t ||t|||	    | t| | ||  | | ||  t|||	    |	 |	t|| ||t|||	    |td   || |td   |	 S r  r  r  r  r  r  r  *  r  r  c                 C   s  t |||	td  || ||    t||t|||
    |td  ||t|||
    |	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  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|||
    |
 |
|
 t|td ||t|||
    |td   ||t|||
    |	td   |  | ||   || |	td  || ||    |
 S r  r#  r  r  r  r  r  2  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  r#  r  r  r  r  r   6     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  r#  r  r  r  r  r  :  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  r#  r  r  r  r  r  >     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  r#  r  r  r  r  r  B  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  r#  r  r  r  r  r  F     ~ 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  r#  r  r  r  r  r  J  r  r  c                 C   s$  t td|||	   t||t|||
    | ||t|||
    |	td   t| | | ||	  ||| |	 || |    | | | ||	  || | |	 || |    t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S r  r#  r  r  r  r  r  N  r  r  c                 C   s$  t td|||	   t||t|||
    | ||t|||
    |	td   t| | | ||	  ||| |	 || |    | | | ||	  || | |	 || |    t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S 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d   t| | | |	td  || |   ||| |	td  || |    ||  | ||   ||	 td  t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | | ||   ||td |td   |	td   |
 S r  r#  r  r  r  r  r  V      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  r#  r  r  r  r  r	  Z  r  r	  c              	   C   sR   t || | tt|||
  |td  |||
  |	  |
|
t|||
  |
S r  r*  r  r  r  r  r
  ^     Rr
  c              
   C   s\   t || | tt|||
  |td  |||
  |	  |
|
tdt|||
   |
 S rc  r*  r  r  r  r  r  b  r2  r  c
           
      C   s   t | | ||  || ||   t||t|||	    | |	|	t |  | ||  || ||   t||t|||	    ||t|||	    |  ||t|||	     |	|	 S r  r  r  r  r  r  r  f  r  r  c
           
      C   s   t | | ||  || ||   t||t|||	    | |	|	t |  | ||  || ||   t||t|||	    ||t|||	    |  ||t|||	     |	|	 S r  r  r  r  r  r  r  j  r  r  c                 C   s   t || t||t|||
    ||t|||
    |  ||t|||
    |	  |
|
 t | | ||  | t||t|||
    | ||t|||
    |	  |
|
 S r  r  r  r  r  r  r  n  rR  r  c                 C   s   t || t||t|||
    ||t|||
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    |	  |
|
 t | | ||  | t||t|||
    | ||t|||
    |	  |
|
 S r  r  r  r  r  r  r  r  rR  r  c              	   C   Z   t | td | tt|||
  | |||
  |	  | ||
   |
|
t|||
  |
S r)  r  r  r  r  r  r  v  r3  r  c              
   C   d   t | td | tt|||
  | |||
  |	  | ||
   |
|
tdt|||
   |
 S r,  r  r  r  r  r  r  z  rd  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 r,  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 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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  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  r#  r  r  r  r  r    r  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|||
    || |td  | | ||   || ||	  | | ||    t|||
  td   |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   || ||	   |
 S Nr  r  r  r  r#  r  r  r  r  r        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|||
    || |td  | | ||   || ||	  | | ||    t|||
  td   |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   || ||	   |
 S r  r#  r  r  r  r  r    r  r  c                 C   s  t td||td |td   |td   t||t|||
    |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  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|||
  td   ||td  | | | ||   ||| ||     t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	  | | ||   ||td |td   |td   |
 S r  r#  r  r  r  r  r    r  r  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  r#  r  r  r  r  r        " r  c                 C   s  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t| ||t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  r#  r  r  r  r  r    r  r  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  r#  r  r  r  r  r       x r  c                 C   sv  t td||	  t||t|||
    |td  ||t|||
    |	td   t| | | ||	  ||| |	 || |    ||	 | | | | | |  || |  || |   t|||
    | | | ||	  ||| | || |	    t|||
  td   |
 |
|
t|||t|||
    |  ||t|||
    |	  |||	   |
 S r  r#  r  r  r  r  r    r  r  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 r)  r#  r  r  r  r  r    r  r  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 r)  r#  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 r,  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 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tdt|||	  td  ||t|||	    |  ||t|||	     |	|	t td|td |td   t||t|||	    | t| | ||  | | ||  t|||	    |	 |	|	 S r  r#  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 r,  )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  r)  r  r  r  r  r  r'    r3  r'  c              
   C   r  r,  r  r  r  r  r  r(    rd  r(  c                 C   r  r,  r|  r  r  r  r  r)    r  r)  c                 C   r  r,  r|  r  r  r  r  r*    r  r*  c              
   C   s:   t | ||  tt|| | |||t|||   |S 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|||   | S r  r  r  r  r  r  r,    rg  r,  c	           	      C   sh   t |td t||t|||    |td  t|| ||  || t|||    | ||S Nr  r  r#  	r  r  r  r  r  r  r  r  r  r  r  r  r-    r  r-  c	           	      C   sh   t |td t||t|||    |td  t|| ||  || t|||    | ||S r  r#  r  r  r  r  r.    r  r.  c              
   C   sX   t ||td  t||t|||    ||t|||    |td   || S r,  r  r  r  r  r  r/    r  r/  c              
   C   sX   t ||td  t||t|||    ||t|||    |td   || S r,  r  r  r  r  r  r0    r  r0  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  r#  r  r  r  r  r1         r1  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  r#  r  r  r  r  r2    r  r2  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  r#  r  r  r  r  r3    r}  r3  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  r#  r  r  r  r  r4    r}  r4  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 r,  r#  r  r  r  r  r  r  r  r  r  r  r  r5       r5  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  r#  r  r  r  r  r6  
  r  r6  c                 C   sR   t | ttdt|||   ||t |tt|||  || t|| | S r  rj  r  r  r  r  r  r  r  r  r  r7    r  r7  c              	   C   sR   t | tt|||  ||t |ttdt|||   || t|| | S r  r  r  r  r  r  r8    r  r8  c                 C   sD   t | ttdt|||   ||t |tt|||  || S r  r  r  r  r  r  r  r  r  r  r9    rn  r9  c              	   C   sD   t | tt|||  ||t |ttdt|||   || S r  rz  r  r  r  r  r:    rn  r:  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 r,  r#  r  r  r  r  r;    r  r;  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  r#  r  r  r  r  r<  "  s    r<  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 r,  r#  r  r  r  r  r  r  r  r  r  r  r=  &  s   r=  c              
   C   s   t | |td  ||td   |td |td   ttdt|||  td  ||t|||     ||t || |  |td |td   ttdt|||   || t|| | |  |td |td   | S r  r#  r  r  r  r  r>  *  r  r>  c	           	      C   s  t td|t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  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  r#  r  r  r  r  r@  2  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  r#  r  r  r  r  rA  6  r  rA  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  r#  r  r  r  r  rB  :  r  rB  c	           	   	   C   s   t ||t|||    | t| |t|||    | | |t|||t|||    |td   || |td   | S r  r  r  r  r  r  rC  >  rS  rC  c	           	   	   C   s   t ||t|||    | t| |t|||    | | |t|||t|||    |td   || |td   | S r  r  r  r  r  r  rD  B  rS  rD  c              	   C   sp   t | | t||t|||    | ||t|||t|||    |td   || |td   | S r  r  r   r  r  r  r  r  r  r  rE  F  r  rE  c              	   C   sp   t | | t||t|||    | ||t|||t|||    |td   || |td   | S r  r  r  r  r  r  rF  J  r  rF  c              	   C   sF   t | | tt|||
  | |||
  |	  |
|
t|||
  |
S r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rG  N  r4  rG  c              
   C   sP   t | | tt|||
  | |||
  |	  |
|
tdt|||
   |
 S r  r*  r  r  r  r  rH  R  r:  rH  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  r#  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rI  V      rI  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  r#  r  r  r  r  rJ  Z  r  rJ  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  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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  r#  r  r  r  r  rL  b  r  rL  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  r#  r  r  r  r  rM  f  r  rM  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  r#  r  r  r  r  rN  j  r  rN  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  r#  r  r  r  r  rO  n  r  rO  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  r#  r  r  r  r  rP  r  r  rP  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  r#  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rQ  v      rQ  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  r#  r  r  r  r  rR  z  r  rR  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  r#  r  r  r  r  rS  ~      rS  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  r#  r  r  r  r  rT    r  rT  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  r#  r  r  r  r  rU        rU  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  r#  r  r  r  r  rV    r  rV  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  r#  r  r  r  r  rW        rW  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  r#  r  r  r  r  rX    r  rX  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  r#  r  r  r  r  rY    r  rY  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  r#  r  r  r  r  rZ    r  rZ  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  r#  r  r  r  r  r[       6 r[  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  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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  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|||    | | ||  || |
td  || |	    | || t||t|||    |	 ||t|||    |
td   | |td  || | ||     || |td |td   |
td   | S r  r#  r  r  r  r  r^    r  r^  c                 C   s  t td||td |td   |	td   t||t|||
    |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  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d      t|||
  td   || |  |	td  | | ||   t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | |td  ||td    || |td |td   |	td   |
 S r  r#  r  r  r  r  r`    r  r`  c                 C   s  t td||	|
 td   t||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  r#  r  r  r  r  ra        ra  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  r#  r  r  r  r  rb    r  rb  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  r#  r  r  r  r  rc    r  rc  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  r#  r  r  r  r  rd    r  rd  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  r#  r  r  r  r  re        R re  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  r#  r  r  r  r  rf    r  rf  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  r#  r  r  r  r  rg        : rg  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  r#  r  r  r  r  rh    r  rh  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 r)  r#  
r  r  r  r  r  r  r  r  r  r  r  r  r  ri        ri  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 r)  r#  r  r  r  r  rj    r  rj  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 r)  r#  	r  r  r  r  r  r  r  r  r  r  r  r  rk       p rk  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 r)  r#  r  r  r  r  rl    r  rl  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 r,  r#  r  r  r  r  rm       ( rm  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  r#  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d  ||t|||	     |	|	t td|td |td   t||t|||	    | t|| |  | | ||  t|||	    |	 |	|	 S r,  r#  r  r  r  r  ro    r  ro  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  r#  r  r  r  r  rp    r  rp  c              
   C   s   t td||  tt|| |	 ||| |  |
  | |td  || |  ||td    |td |td   |||t|||   |S r  r  r  r  r  r  rq    rl  rq  c              
   C   s   t td||  tt|| |	 ||| |  |
  | |td  || |  ||td    |td |td   |||t|||   | S r  r  r  r  r  r  rr    ro  rr  c              
   C   s   t td||  tt||
 | |||
 |  |	  | |td  ||
td    |td |
td   |
|
|t|||
   |
S r  r  r  r  r  r  rs    rM  rs  c              
   C   s   t td||  tt||
 | |||
 |  |	  | |td  ||
td    |td |
td   |
|
|t|||
   |
 S r  r  r  r  r  r  rt       rt  c                 C   .   t td|  tt|||  td ||S r  )r  r  r   r  r+  r  r  r  ru       .ru  c                 C   r  r  )r  r  r   r  r+  r  r  r  rv  
  r  rv  c              
   C   sj   t || |  ttd| |t|||  td   t|||  td   || t|| |  | S r  )r  r   r  r  r  r  r+  r  r  r  rw    r  rw  c              
   C   sj   t || |  ttd| |t|||  td   t|||  td   || t|| |  | S r  )r  r   r  r  r  r  r+  r  r  r  rx    r  rx  c              
   C   sV   t || tt| |||   | |td |td   |||t|||   |S r)  r*  r  r  r  r  r  r  r  r  r  r  r  ry    rC  ry  c              
   C   sX   t || tt| |||   | |td |td   |||t|||   | S r)  r*  r  r  r  r  rz    r  rz  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 r  r   r  r  r+   r   r  r2  	r  r  r  r  r  r  r  r  r  r  r  r  r}  (     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 r  r   r  r  r+   r   r  r2  r  r  r  r  r~  -     r~  c	           
   	   C   s   t t|||  |}	t|	| 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  2  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  7  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 r  r  r  r  r  r  r  <  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 r  r  r  r  r  r  r  A  r  r  c	           	   
   C   sb   t || tt|| | | |||   |  |td |td   |||t|||   |S r)  r*  	r  r  r  r  r  r  r  r  r  r  r  r  r  F  rt  r  c	           	   
   C   sd   t || tt|| | | |||   |  |td |td   |||t|||   | S r)  r*  r  r  r  r  r  J  rd  r  c	           	   	   C   sR   t td|  ||   t|td| t|||  |   td|  ||S rG  r  	r  r  r  r  r  r  r  r  r  r  r  r  r  N  r  r  c	           	   
   C   sZ   t td|  ||   t|td| tdt|||   |   td|  ||S NrH  r  r  r  r   r  r  r  r  R  r3  r  c	           	   	   C   s   t |td| t|||  |   td |  | |t|||  |   |t|||  td|    |  t|td| t|||  |   td|  ||S r)  r  r   r  r  r  r  V  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 r,  r  r   r  r  r  r  Z  rE  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  ^  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  c  s   (r  c              
   C   s   t || 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  h  rT  r  c              
   C   s   t || tt|
| |td |
td  | td td   | ||
|   ||
td|    |	  |
|
|t|||
   |
 S r-  r*  r  r  r  r  r  l  rM  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 r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  p  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 r  r  r  r  r  r  r  u  s   
 r  c              
   C   s   t ||td  | tt|td |
td  | td td  | ||
|   ||
td|    |	  |
|
|t|||
   |
S r  r  r  r  r  r  r  z  r  r  c              
   C   s   t ||td  | tt|td |
td  | td td  | ||
|   ||
td|    |	  |
|
|t|||
   |
 S r  r  r  r  r  r  r  ~  rJ  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 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d    ||	td|    |	|  |	|	t|||	  |
 |	 S r  r  r  r  r  r  r    s   r  c
           
   	   C   sf   t td|  ||   t|td| t|||	  |   td|  t|||	  |  |	|	S rG  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r    ri  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    r<  r  c
           
   	   C   s   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  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 r,  r  r  r  r  r  r    rN  r  c              
   C   sv   t || tt|
| | | ||
|   ||
td|    |	  |td |
td   |
|
|t|||
   |
S r)  r*  r  r  r  r  r    r<  r  c              
   C   sx   t || tt|
| | | ||
|   ||
td|    |	  |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|||	  |   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 r,  r  r  r  r  r  r    rU  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 r,  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 r,  r  r  r  r  r  r    s   r  c	           	   
   C   sf   t td|  ||   t| |t|||    |td| t|||    td|   ||S rG  r  	r  r  r  r  r  r  r  r  r  r  r  r  r    ri  r  c	           	   
   C   sf   t td|  ||   t| |t|||    |td| t|||    td|   ||S rG  r  r  r  r  r  r    ri  r  c	           	   
   C   s   t |td| t|||    td |  ||t|||    |t|||  td   |  t| |t|||    |td| t|||    td|   ||S r)  r  r  r  r  r  r    rL  r  c	           	   
   C   s   t |td| t|||    td |  ||t|||    |t|||  td   |  t| |t|||    |td| t|||    td|   ||S r)  r  r  r  r  r  r    rL  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  r  r	  r  r  r  r    r
  r  c	           	   	   C   s\   t t| |t|||    ||t|||    |t|||  td   |  ||S r)  r   rI  r  r  r  r  r  r  r    r2  r  c	           	   	   C   s\   t t| |t|||    ||t|||    |t|||  td   |  ||S r)  r  r  r  r  r  r    r2  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 r,  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 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 r"  r#  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 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 Nr  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 r  r#  r  r  r  r  r    r  r  c	           	   	   C   s6   t t|||  | | |t|||    | ||S r  r   r   r  ra  r  r  r  r    r]  r  c	           	   	   C   s6   t t|||  | | |t|||    | ||S r  r  ra  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  r#  rk  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  r#  rk  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 r,  r  r   r  r  r  r  r  rf  r  r  r  r    r8  r  c              
   C   s   t || |  tttd| td| |  |||   ||t |||  tttd| td| |  |||   || ttd|| |t|||     |||    | S r,  r  rf  r  r  r  r    rR  r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     ||t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S r,  r#  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d   ||td  |td  |td   | S r,  r#  rk  r  r  r  r    r  r  c                 C   s   t tdtd|   tttd| td| |  |||   ||t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S r  r  r  r   r  r  r  r&  rf  r  r  r  r    rR  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  rf  r  r  r  r    r8  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  rk  r  r  r  r     rT  r  c              	   C   s   t tdtd|   t|||  | ttd |  |||   |  || t|||  |td  td|  | |td   | S r  r  rk  r  r  r  r  $  r  r  c	           	      C   s   t t|||  | ttd| td| |  td|  ttd| td| |  td|    tdtd|    |  ||S r,  r   r   r  r  r  ra  r  r  r  r  (  r  r  c	           	      C   s   t t|||  | ttd| td| |  td|  ttd| td| |  td|    tdtd|    |  ||S r,  r  ra  r  r  r  r  ,  r  r  c	           	      C   s`   t t|||  | ttd|  |||   | td|   tdtd|    |  ||S r,  )r   r   r  r  ra  r  r  r  r  0  rb  r  c	           	   	   C   sb   t t|||  | tdtd|   ttd |  |||   | td|    |  ||S r  )r   r   r  r  ra  r  r  r  r  4  rt  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  8     "Lr  c	           
      C   sn   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 | t|||  | | td |td  | t|  td ttdt |||      || t|||  |td  || t|   |td   | S r,  r  rk  r  r  r  r  B  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 r,  r  rk  r  r  r  r  F  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  r#  rf  r  r  r  r  J  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  r#  rf  r  r  r  r  N  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 r,  r   r   r  r  r  ra  r  r  r  r  R  rJ  r  c	           	      C   s   t t|||  | tdt | | td |td  | t|  td ttdt |||      td| t|    |  ||S r,  r  ra  r  r  r  r  V  r  r  c                 C   s.   t | |tt||  | t|||  |S r  r   r  r2  r  r  r  r  r  vr  r  r  r  r  Z  r  r  c                 C   s.   t | |tt||  | t|||  |S r  r  r  r  r  r  r  ^  r  r  c	           	      C   s2   t | |t|||    | |||  |  |S r  r  ra  r  r  r  r  b     2r  c	           	      C   s2   t | |t|||    | |||  |  |S r  r  ra  r  r  r  r  f  r   r  c                 C   sV   t td| tt|tdtd|   | |t|||    |  |||| |S r  r  r  r  r  r  r  r  r  r  r  r  r  j  rC  r  c                 C   sV   t td| tt|tdtd|   | |t|||    |  |||| |S r  r  r!  r  r  r  r  n  rC  r  c                 C   s&   t | |t||||     | |S r  r  r!  r  r  r  r  r  r(  r  c                 C   s&   t | |t||||     | |S r  r  r!  r  r  r  r  v  r(  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  r  r  r  r  r  r  z  r  r  c                 C   sJ   t tdt||td tt| |t||||     | ||||S r  r"  r#  r  r  r  r  ~  r  r  c                 C   s    t | |tt||  | |S r  r  r  r  r  r  r  r  r  r  r        r  c                 C   s    t | |tt||  | |S r  r  r$  r  r  r  r    r%  r  c                 C   sZ   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    r3  r  c                 C   sZ   t td| tt|td|td |   | |t|||    |  |||| |S r  r  r&  r  r  r  r    r3  r  c              	   C   s   t || td ||  t|||  t| |||    || t|| | t||| td  t| |||    ||  | S r  r#  r  r  r  r  r  r  r  r  r    rT  r  c              	   C   s   t || td ||  t|||  t| |||    ||t|| | t||| td  || t| |||     | S r  r#  r'  r  r  r  r    rS  r  c              	   C   s.   t || | |t||||     |  |S r  r  r&  r  r  r  r    r  r  c              	   C   s.   t || | |t||||     |  |S r  r  r&  r  r  r  r    r  r  c	           	      C   s\   t |t| |t|   || t|  t|| | |t||||     |  ||S r  r  r%   r&   r   r  r  r  r  r  r    r2  r  c	           	      C   s\   t |t| |t|   || t|  t|| | |t||||     |  ||S r  r(  r  r  r  r  r    r2  r  c                 C   s,   t || | | |tt||  |  |S r  r  r  r  r  r  r  r  r  r  r  r  r       ,r  c                 C   s,   t || | | |t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dt| |||    |  || |  | S 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dt| |||    |  ||t||| td  tdt| |||    |  || |  | S r  )r  r  r   r  r  r+  r  r  r  r    ro  r  c                 C   s*   t t| ||  ||td   | |S r)  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  r,  r  r  r  r    r   r  c              	   C   s<   t |tt| ||  ||td    td|  | S r)  )r  r&  r  r  r  r  r  r  r  r  r  r  r  r    rg  r  c              	   C   s:   t |tt| ||  ||td    td|  |S 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t| ||  ||td    td|  | S r)  )r  r  r   r  r  r&  r  r.  r  r  r  r    rM  r  c              
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   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r&  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  ZPir  ZB_ZC_ZF_ZG_ZH_r  Zb_rt  r  r  Zf_Zg_Zh_Zi_Zj_Zk_Zl_r  r  r  r  Zr_Zt_r  r  Zs_Zw_r  Zy_Zz_Za1_Za2_Zb1_Zb2_Zc1_Zc2_Zd1_Zd2_Zn1_r  Ze1_Ze2_Zf1_Zf2_Zg1_Zg2_Zn3_ZPq_ZPm_ZPx_ZQm_ZQr_ZQx_Zjn_Zmn_Znon2_ZRFx_ZRGx_r  iiZPqqQRrr  kr  Z	_UseGammaZ	ShowStepsZ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  r  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  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
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