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Z
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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)Add)Mod)Mul)
EulerGamma)FloatIInteger)Pow)S)Abssign)sqrt)Integral)AndOr)simplifyWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  T/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rules/inverse_hyperbolic.py
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tttdtd   tdtdtdtdtttdtd   tdtd  t|||||||||| |}(t|(t})tttttd
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||| ||!
}*t|*t}+tttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t|||||||||| ||!|#},t|,t}-tttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t|||||||||| ||!}.t|.t}/tttdtdtdtdtttdtd   tdtd tttd
 tdtd  tdd
   t||||
||| |	}0t|0t}1tttdtdtdtdtttdtd   tdtd tttdtd  tdd
  tttdtd  tdd
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||| ||$|"}4t|4t}5tttttd
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||| ||$|%}6t|6t }7tttttdtd  t tttdtd  t  tdtdtdtdtttdtd   tdtd  t|||||||||| ||$|%|&}8t|8t!}9tttttdtd  t tttdtd  t  tdtdtdtdtttdtd   tdtd  t|||||||||| ||$|%}:t|:t"};tttdtdtdtdtttdtd   tdtd tttd
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|||}<t|<t#}=tttdtdtdtdtttdtd   tdtd tttd
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|||}>t|>t$}?tttttd
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||'|| ||"}@t|@t%}Atttttd
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||'|| |
}Bt|Bt&}Ctttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   t  t||||||||'||| ||#}Dt|Dt'}Etttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   t  t||||||||'||| |}Ft|Ft(}Gtttttd
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||||(|)
}Ht|Ht)}Itttttd
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||||	}Jt|Jt*}Ktttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t|||||||||||*|+}Lt|Lt+}Mtttttd
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||||(|,
}Nt|Nt,}Otttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t|||||||||||(|}Pt|Pt-}Qtttttd
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||-|.}Rt|Rt.}Stttttd
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|||-|"|0
}Vt|Vt0}Wtttttd
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|||/|"|0
}Xt|Xt1}Ytttttd
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|||'|1	}Zt|Zt2}[tttttd
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|||'|"	}\t|\t3}]tttttdtd  tdtd tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t|||||||||'|2}^t|^t4}_tttttdtd  t t5ttdtd  t  tdtdtdtdtttdtd   tdtd  t||||
||6|7||'|3|4|5}`t|`t6}atttttd
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|||'||5
}bt|bt7}cttttdtdtdtdtttdtd   tdtd  tttd
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|||}dt|dt8}ettttdtdtdtdtttdtd   tdtd  tttd
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|||}ft|ft9}gttttttd
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||'|| ||8|"}ht|ht:}ittttttd
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|||}pt|pt>}qtttdtdtdtdtttdtd   tdtd ttttd
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|||}rt|rt?}sttttdtd t@ tttd
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||6||'|| ||9|	|"}tt|ttA}uttttdtd t@ tttd
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|||}|t||tE}}tttttd
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|||}~t|~tF}ttttdtd t@ tttd
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||6|||:
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||6|||:
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||6|||
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||6|||
}t|tJ}tttt@ tttd
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|||#|;|<|}t|tK}tttt@ tttdtd  t  tttdtd  t  tdtdtdtdtttdtd    t||||||||||#|;|<||}t|tL}tttt@ tttd
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||6||=||!|>|"}t|tO}ttttdtd t@ t
tttd
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||6||?||>}t|tP}ttttdtd t@ t
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||6||=||!|>}t|tR}ttttdtd t@ tttdtd  t  tttdtd  t  tdtdtdtdtttdtd   tdtd  t||||||||6|||=||!|>|#}t|tS}ttttdtd t@ tttd
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tttd
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||6|'||?||>|B|"}t|tY}ttttdtd t@ tttd
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||6|'||?||>|B}t|tZ}ttttdtd t@ tttdtd  t  tttdtd  t  tdtdtdtdtttdtd   tdtd  t||||||||6|'|||?||>|B|&}t|t[}ttttdtd t@ tttdtd  t  tttdtd  t  tdtdtdtdtttdtd   tdtd  t||||||||6|'|||?||>|B}t|t\}ttttdtd t@ tttd
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||6||?||$|C|"}t|t]}ttttdtd t@ tttd
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tttd
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|||||B
}t|tg}tttt@ tdtdtdtdtttdtd   tdtd  t
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tttd
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||6||'|| ||I|"}t|Ԑtq}ttttdtd td	td tttd
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|||||
}t|t}}ttttd	td tttdtd  tdtd  tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t|||||||||||&|L||+}t|t~}ttttd	td tttd
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t|
t}ttttdtd td	td tttdtd  t  t5ttdtd  t  tdtdtdtdtttdtd   tdtd  t||||
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tttdtd   t5ttdtd  t@  tdtdtdtdtttdtd   tdtd  t||||||||6|7|||B||||^}Bt|Bt}Ctttttd
 tdtd  t t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7||B|*||}Dt|Dt}Etttttdtd  t tttdtd  t  t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||||||6|7|||B|*|||}Ft|Ft}Gtttttd
 tdtd  t t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7||B|_|||^}Ht|Ht}Itttttdtd  t tttdtd  t  t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||||||6|7|||B|_||||^}Jt|Jt}Kttt5ttdtd  td	td tdtdtdtdtttdtd   t  t
tttd
 tdtd   t||||
||6|7||B||[| |}Lt|Lt}Mttt5ttdtd  td	td tdtdtdtdtttdtd   t  t
tttdtd  t
tttdtd    t||||||||6|7|||B|||[| |}Nt|Nt}Ottt5ttdtd  td	td tdtdtdtdtttdtd   tdtd  t
tttd
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||6|7|||B||`}Pt|Pt}Qttt5ttdtd  td	td tdtdtdtdtttdtd   tdtd  t
tttdtd  t
tttdtd    t||||||||6|7||||B|||`}Rt|Rt}Stttttd
 tdtd  t t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7||B|Z||}Tt|Tt}Utttttdtd  t tttdtd  t  t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||||||6|7|||B|Z|||}Vt|Vt}Wtttttd
 tdtd  t t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7|||B|#|}Xt|Xt}Ytttttd
 tdtd  t t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7|||B|#}Zt|Zt}[tttttdtd  t tttdtd  t  t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||||||6|7||||B|#|}\t|\t}]tttdtdtdtdtttdtd   tdtd tttdtd tdtd td	td tdtd  t
tttd
 tdtd   t||||
||6|7|T||||}^t|^t}_tttdtdtdtdtttdtd   tdtd tttdtd tdtd td	td tdtd  t
tttdtd  t
tttdtd    t||||||||6|7|T||||||}`t|`t}atttttd
 tdtd  t tdtdtdtdtttdtd   tdtd  tttdtd tdtd td	td tdtd  t||||
||6|7|T||||#|}bt|bt}ctttttd
 tdtd  t tdtdtdtdtttdtd   tdtd  tttdtd tdtd td	td tdtd  t||||
||6|7|T||||#}dt|dt}etttttdtd  t tttdtd  t  tdtdtdtdtttdtd   tdtd  tttdtd tdtd td	td tdtd  t||||||||6|7|T|||||#|}ft|ft}gtttttdtd  t@ t5ttdtd  t@  tdtdtdtdtttdtd    t||||
||6|7|a	}ht|ht}itttttdtd  t@ t5ttdtd  t@  tdtdtdtdtttdtd    t||||
||6|7|a	}jt|jt}ktttttdtd  td	td t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7||B
}lt|lt}mtttttdtd  td	td t5ttdtd  td	td  tdtdtdtdtttdtd   tdtd  t||||
||6|7||B
}nt|nt}ottttdtdtdtdtttdtd    t||||bttÃ}pt|ptă}qttttdtdtdtdtttdtd    t||||bttŃ}rt|rtƃ}sttttttd
 tdtd  t  tdtdtdtdtttdtd   t  t||||
|||U||#ttǃ}tt|ttȃ}uttttttdtd  t  tttdtd  t  tdtdtdtdtttdtd   t  t|||||||||U|||#ttɃ}vt|vtʃ}wttt5tttd
 tdtd  t tdtd  td	td tdtdtdtdtttdtd   tdtd  tdtd t||||
||6|7|U||*|ctt˃}xt|xt̃}yttt5tttdtd  t tttdtd  t  tdtd  td	td tdtdtdtdtttdtd   tdtd  tdtd t||||||||6|7|U|||*|ctt̓}zt|zt΃}{ttttttdtd tdtd  t||d|ttЃ}|t||tу}}ttttttdtd tdtd  t||d|tt҃}~t|~tӃ}tttϐttdtdtttdtd   tdtd  t||||d|}t|tՃ}tttϐttdtdtttdtd   tdtd  t||||d|}t|tփ}tttϐtttd
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||d|||#
}t|tۃ}tttϐttdtdtttdtd   tdtd  tttdtd  t  tttdtd  t  t||||||||d||||#}t|t܃}tttdtdtdtdtttdtd   tdtd tdtd t|||||}t|t݃}tttdtdtdtdtttdtd   tdtd tdtd t|||||}t|tރ}tttdtdtdtdttttdtd    tdtd t||||
||e}t|t}tttdtdtdtdttttdtd    tdtd t||||
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||6|||f
}t|t}ttttdtd tdtd td	td tdtdtdtdttttdtd    tdtd  t||||
||6|||f
}t|t}tttdtdtdtdttttdtd    tdtd ttd
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||6|i|j|k|||'|g|h}t|t}ttttdtd tdtd td	td tdtdtdtdttttdtd    tdtd  ttd
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||6|i|j|k|||'|l|h}t|t}ttt
tdtdtdtdttttd
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tdtdtdtdtttd
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||	|u|w|v
}t|ސt}ttttdtd tdtd td	td tdtdtdtdtt   t||||
||	|u|w|v
}t|t}ttt	tdtdtdtdtt   t|||u|xtt
}t|t}ttt	tdtdtdtdtt   t|||u|ytt}t|t}ttttdtdtt t|z|{}t|t}ttttd	td ttdtdtt  t|||z|{}t|t}ttttdtdtt t|z|{}t|t}ttttd	td ttdtdtt  t|||z|{}t|t}tttdtdtdtdtttdtd   tdtd t||||}t|t}tttdtdtdtdtttdtd   tdtd t||||}t|t}tttdtdtdtdtttdtd   t t|||||}}t|t}tttdtdtdtdtttdtd   t t|||||}}t|t}tttdtdtdtdtttdtd   tdtd tttdtd   t||||
||~|}t|t}tttdtdtdtdtttdtd   tdtd tttdtd   t||||
||~|}t|t}tttttdtd tttdtd   t||
|||}t|t}tttttdtd ttdtd tdtd  t||
||}t|t}tttttdtd ttdtd tdtd  t||
||}t|t}ttttdtdtttdtd   ttdtd tdtd  t||||
||} t| t}ttttdtdtttdtd   ttdtd tdtd  t||||
||}t|t}ttttdtd tdtd tdtd tdtdtdtdtttdtd    t||||
||'|8}t|t }ttttdtd tdtd tdtd tdtdtdtdtttdtd    t||||
||'|8}t|t!}tttdtdtdtdtttdtd   t t t||||z|n}t|t"}	tttdtdtdtdtttdtd   t t t||||z|n}
t|
t#}ttttd	td tdtdtdtdtttdtd   t  t|||||z|n|	}t|t$}ttttd	td tdtdtdtdtttdtd   t  t|||||z|n|	}t|t%}tttttdtd  tdtd tdtdtdtdtttdtd   tdtd  t||||
||V}t|t&}tttttdtd  tdtd tdtdtdtdtttdtd   tdtd  t||||
||V}t|t'}ttttdtd tdtd tdtd tdtdtdtdtttdtd   t  t||||
|||'|}	}t|t(}ttttdtd tdtd tdtd tdtdtdtdtttdtd   t  t||||
|||'|}	}t|t)}ttttd	td tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||~||||[
}t|t*}ttttd	td tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||~||||[
}t|t+}tttdtdtdtdtttdtd   tdtd ttttdtd    t||||
||~|}t|t,}tttdtdtdtdtttdtd   tdtd ttttdtd    t||||
||~|}t|t-}tttt@ tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||~||||>
} t| t.}!tttt@ tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||~||||>
}"t|"t/}#ttttd	td tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||"||
}$t|$t0}%ttttd	td tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||"||
}&t|&t1}'ttttd	td ttdtd tdtd tdtd  tdtdtdtdtttdtd   tdtd  t||||
||||'|
}(t|(t2})ttttd	td ttdtd tdtd tdtd  tdtdtdtdtttdtd   tdtd  t||||
||||'|
}*t|*t3}+tttttd
 tdtd  tdtd tdtdtdtdtttdtd    t||||
||||!	},t|,t4}-tttttd
 tdtd  tdtd tdtdtdtdtttdtd    t||||
||||!	}.t|.t5}/tttttd
 tdtd  tdtd tdtdtdtdtttdtd   t  t||||
||| |!|n
}0t|0t6}1tttttd
 tdtd  tdtd tdtdtdtdtttdtd   t  t||||
||| |!|n
}2t|2t7}3tttdtttd
 tdtd  tdtdtdtdtttdtd     t||||
||}4t|4t8}5tttdtttd
 tdtd  tdtdtdtdtttdtd     t||||
||}6t|6t9}7tttdtdtdtdtttdtd   tdtd tttd
 tdtd   t||||
||||	}8t|8t:}9tttdtdtdtdtttdtd   tdtd tttd
 tdtd   t||||
||||	}:t|:t;};tttdtdtdtdtttdtd   t
tttd
 tdtd   t||||
|||}<t|<t<}=tttdtdtdtdtttdtd   t
tttd
 tdtd   t||||
|||}>t|>t=}?tttdtdtdtdtttdtd   tdtd t
tttd
 tdtd   t||||
||||	}@t|@t>}Atttdtdtdtdtttdtd   tdtd t
tttd
 tdtd   t||||
||||	}Bt|Bt?}Ctttdtdtdtdtttdtd   tdtd t
tttd
 tdtd   t||||
||||	}Dt|Dt@}Etttdtdtdtdtttdtd   tdtd t
tttd
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||||	}Ft|FtA}Gtttdtdtdtdtttdtd   tdtd tttd
 tdtd  td
  t||||
||| |	}Ht|HtB}Itttdtdtdtdtttdtd   tdtd tttd
 tdtd  td
  t||||
||| |	}Jt|JtC}Ktttdtdtdtdtttdtd   tttd
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   t||||
||}Lt|LtD}Mtttdtdtdtdtttdtd   tttd
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   t||||
||}Nt|NtE}Otttttd
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||||$|%
}Pt|PtF}Qtttttd
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||||$|%
}Rt|RtG}Stttdtdtdtdtttdtd   t tttd
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   t||||
||| |n	}Tt|TtH}Utttdtdtdtdtttdtd   t tttd
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   t||||
||| |n	}Vt|VtI}Wtttttd
 tdtd  t tdtdtdtdtttdtd   t  t||||
||| |$|n|%}Xt|XtJ}Ytttttd
 tdtd  t tdtdtdtdtttdtd   t  t||||
||| |$|n|%}Zt|ZtK}[tttttd
 tdtd  t tdtdtdtdtttdtd   t  t||||
||| |$|
}\t|\tL}]tttttd
 tdtd  t tdtdtdtdtttdtd   t  t||||
||| |$|
}^t|^tM}_tttttd
 tdtd  t tdtdtdtdtttdtd   tdtd  t||||
|||||)
}`t|`tN}atttttd
 tdtd  t tdtdtdtdtttdtd   tdtd  t||||
|||||,
}bt|btO}ctttttd
 tdtd  t tdtdtdtdtttdtd   tdtd  t||||
|||||"
}dt|dtP}etttttd
 tdtd  t tdtdtdtdtttdtd   tdtd  t||||
|||||5
}ft|ftQ}gtttttdtd ttd
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||}ht|htR}itttttdtd ttd
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||}jt|jtS}kttttdtdtttdtd   ttd
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||}lt|ltT}mttttdtdtttdtd   ttd
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||}nt|ntU}ottttd
 tdtd tdtd tdtd tdtdtdtdtttdtd    t||||
||}pt|ptV}qttttd
 tdtd tdtd tdtd tdtdtdtdtttdtd    t||||
||}rt|rtW}stttttd
 tdtd  tdtd tdtdtdtdtttdtd   tdtd  t||||
||"|}tt|ttX}utttttd
 tdtd  tdtd tdtdtdtdtttdtd   tdtd  t||||
||"|}vt|vtY}wttttd
 tdtd tdtd tdtd tdtdtdtdtttdtd   tdtd  t||||
|||'|1	}xt|xtZ}yttttd
 tdtd tdtd tdtd tdtdtdtdtttdtd   tdtd  t||||
|||'|1	}zt|zt[}{tttt@ tdtdtdtdtttdtd   tdtd  tttd
 tdtd   t||||
||?||C	}|t||t\}}tttt@ tdtdtdtdtttdtd   tdtd  tttd
 tdtd   t||||
||?||C	}~t|~t]}tttt@ tdtdtdtdtttdtd   tdtd  tttd
 tdtd   t||||
||?||>	}t|t^}tttt@ tdtdtdtdtttdtd   tdtd  tttd
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||?||>	}t|t_}ttttdtdtdtdtttdtd   tdtd  tttd
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|||}t|t`}ttttdtdtdtdtttdtd   tdtd  tttd
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|||}t|ta}ttttdtdtdtdtttdtd   t  tttd
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|||}|	}t|tb}ttttdtdtdtdtttdtd   t  tttd
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|||}|	}t|tc}tttt@ tdtdtdtdtttdtd   tdtd  tttd
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|||?||C
}t|td}tttt@ tdtdtdtdtttdtd   tdtd  tttd
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|||?||C
}t|te}tttdtdtdtdtttdtd   tdtd ttttd
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||| |	}t|tf}tttdtdtdtdtttdtd   tdtd ttttd
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||| |	}t|tg}tttt@ tdtdtdtdtttdtd   tdtd  tttd
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|||?||>
}t|th}tttt@ tdtdtdtdtttdtd   tdtd  tttd
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|||?||>
}t|ti}tttt@ tdtdtdtdtttdtd   t  tttd
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|||| |
}t|tj}tttt@ tdtdtdtdtttdtd   t  tttd
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|||| |
}t|tk}ttttd	td tdtdtdtdtttdtd    tttd
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||B|}t|tl}ttttd	td tdtdtdtdtttdtd    tttd
 tdtd   t||||
||B|}t|tm}ttttttd
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||'|| ||8}t|tn}ttttttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||'|| ||8}t|to}ttttdtdtdtdtttdtd   t  tttd
 tdtd  td
  t||||
||| ||o
}t|tp}ttttdtdtdtdtttdtd   t  tttd
 tdtd  td
  t||||
||| ||o
}t|tq}ttttd
 tttd
 tdtd  t  tdtdtdtdtttdtd    t||||
||||$|
}t|tr}ttttd
 tttd
 tdtd  t  tdtdtdtdtttdtd    t||||
||||$|
}t|ts}ttttd
 tdtdtdtdtttdtd   tdtd  tttd
 tdtd  td
  t||||
||| |	}t|tt}ttttd
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 tdtd  td
  t||||
||| |	}t|tu}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd    t||||
|||||$
}t|tv}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd    t||||
|||||$
}t|tw}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd   t  t||||
||||| |$|n}t|tx}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd   t  t||||
||||| |$|n}t|ty}ttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   t  t||||
|||'||| |}t|tz}ttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   t  t||||
|||'||| |}t|t{}ttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||'||9| ||	}t|t|}ttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||'||9| ||	}t|t}}tttt@ t
tttd
 tdtd   tdtdtdtdtttdtd    t||||
||||	}t|t~}tttt@ t
tttd
 tdtd   tdtdtdtdtttdtd    t||||
||||	}t|t}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd   tdtd  t||||
|||||"|}t|Đt}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd   tdtd  t||||
|||||"|}t|Ɛt}tttt@ tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||||!||}t|Ȑt}tttt@ tttd
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|||||!||}t|ʐt}tttt@ tdtdtdtdtttdtd   tdtd  t
tttd
 tdtd   t||||
|||?||C
}t|̐t}tttt@ tdtdtdtdtttdtd   tdtd  t
tttd
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|||?||C
}t|ΐt}tttdtdtdtdtttdtd   tt
tttd
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|||}t|Аt}tttdtdtdtdtttdtd   tt
tttd
 tdtd    t||||
|||}t|Ґt}tttdtdtdtdtttdtd   t tt
tttd
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||||	}t|Ԑt}tttdtdtdtdtttdtd   t tt
tttd
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||||	}t|֐t}tttdtdtdtdtttdtd   tdtd tt
tttd
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||||	}t|ؐt}tttdtdtdtdtttdtd   tdtd tt
tttd
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||||	}t|ڐt}tttdtdtdtdtttdtd   tdtd ttd
 t
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||| |	}t|ܐt}tttdtdtdtdtttdtd   tdtd ttd
 t
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||| |	}t|ސt}tttt@ tdtdtdtdtttdtd   tdtd  t
tttd
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|||?||>|}t|t}tttt@ tdtdtdtdtttdtd   tdtd  t
tttd
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|||?||>|}t|t}tttt@ tttd
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||||$|C|}t|t}tttt@ tttd
 tdtd  t  tdtdtdtdtttdtd   tdtd  t||||
||||$|C|}t|t}tttt@ tttd
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||||$|^|}t|t}tttt@ tttd
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||||$|^|}t|t}ttttd	td tttd
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|||=|$||}t|t}ttttd	td tttd
 tdtd  t  tdtdtdtdtttdtd   tdtd  t||||
|||=|$||}t|t}ttttd	td tttd
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||||||)}t|t}ttttd	td tttd
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||||||,}t|t}ttttd	td tttd
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||||||"}t|t}ttttd	td tttd
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||||||5}t|t}tttttd
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||'|8}t|t}tttttd
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||'|8}t|t}ttttd	td ttd
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|||'|	}t|t}ttttd	td ttd
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|||'|	}t|t}ttttd	td tttd
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|||"||
} t| t}ttttd	td tttd
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|||"||
}t|t}ttttd	td ttdtdtttdtd    tttd
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|||'|	}t|t}ttttd	td ttdtdtttdtd    tttd
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|||'|	}t|t}ttttd	td ttd
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||||'|
}t|t}	ttttd	td ttd
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||||'|
}
t|
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd tt tttd
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||| ||
}t|t}tttdtdtdtdtttdtd   tdtd ttt tttd
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||'|| ||}t|t}tttdtdtdtdtttdtd   tdtd ttt tttd
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||'|| ||}"t|"t}#tttdtttd
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||}$t|$t}%tttdtdtdtdtttdtd   td	td tdtdtdtdtttdtd   tdtd  tttd
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|||c|	}(t|(t})tttttdtd tttdtd tdtd   t|||
|z|}*t|*t}+tttttdtd tttdtd tdtd   t|||
|z|},t|,t}-tttdtdtdtdtttdtd   tdtdtdtdtttd
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||6|7|	}.t|.t}/tttdtdtdtdtttdtd   tdtdtdtdtttd
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||6|7|	}6t|6t}7ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||6|7|	}8t|8t}9ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||6|7|B|
}:t|:t};ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||6|7|B|
}<t|<t}=ttttdtdtdtdtttdtd   td
  tdtdtdtdtt5ttd
 tdtd     t||||
||6|7|	}>t|>t}?ttttdtdtdtdtttdtd   td
  tdtdtdtdtt5ttd
 tdtd     t||||
||6|7|	}@t|@t}Attttdtdtttdtd  t||}Bt|Bt}Cttttd	td ttdtdtttdtd   t|||}Dt|Dt}Etttttttdtd  t|||}Ft|Ft}Gttttd	td tttttdtd   t||||}Ht|HtÃ}Itttttdtd  tdtd ttdtdtttdtd   t|||
|'|||K}Jt|Jtă}Ktttttdtd  tdtd ttdtd tdtd td	td  ttdtdtttdtd   t|||
||6||'||||K}Lt|LtŃ}Mtttttdtd  tdtd tdtd ttdtdtttdtd   t|||
||'||}Nt|Ntƃ}Otttttdtd  tdtd tdtd ttdtdtttdtd   t|||
||'||}Pt|Ptǃ}Qttttdtdt  tdtd tdtd ttdtdtttdtd   t|||
|||"}Rt|Rtȃ}Sttttdtdt  t tdtd tttttdtd   t|||
|'||5||	}Tt|TtɃ}Uttttdtdt  t tdtd tttttdtd   t|||
|'||5||	}Vt|Vtʃ}Wttttdtdt  t tdtd ttdtdtttdtd   t|||
||'||5}Xt|Xt˃}Ytttttttdtd  tttd
 tdtd  tdd
   t|||
|||}Zt|Zt̃}[tttttd
 tdtd  t tttttdtd   t|||
||||$|||K}\t|\t̓}]ttttdtdtttdtd  tttd
 tdtd   t|||
|||}^t|^t΃}_tttttd
 tdtd  tdtd ttdtdtttdtd   t|||
|'||"||	}`t|`tσ}atttttd
 tdtd  tdtd tttttdtd   t|||
|'||"||	}bt|btЃ}ctttttd
 tdtd  tdtd ttdtdtttdtd   t|||
||'||}dt|dtу}etttttd
 tdtd  tdtd tttttdtd   t|||
|'|||}ft|ft҃}gtttttd
 tdtd  tdtd tttttdtd   t|||
|'|||}ht|htӃ}itttttd
 tdtd  t ttdtdtttdtd   t|||
||'||}jt|jtԃ}kttttttttdtd   tttd
 tdtd  tdd
   t|||
|||}lt|ltՃ}mttttttd
 tdtd  t  tttttdtd   t|||
||||$||K
}nt|ntփ}ottttd
 tttd
 tdtd  tdtd  tttttdtd   t|||
||||}pt|pt׃}qttttd
 tttd
 tdtd  t  tttttdtd   t|||
||||$|||K}rt|rt؃}sttttd	td tttd
 tdtd  tdtd  ttdtdtttdtd   t|||
||'||||
}tt|ttك}uttttd	td tttd
 tdtd  tdtd  tttttdtd   t|||
||'||||
}vt|vtڃ}wttttd	td tttd
 tdtd  tdtd  ttdtdtttdtd   t|||
|||'||	}xt|xtۃ}yttttd	td tttd
 tdtd  tdtd  tttttdtd   t|||
||'|||	}zt|zt܃}{ttttd	td tttd
 tdtd  tdtd  tttttdtd   t|||
||'|||	}|t||t݃}}ttttd	td tttd
 tdtd  t  ttdtdtttdtd   t|||
|||'|||
}~t|~tރ}ttttttd
 tdtd  tdtd  ttdtdtttdtd   t|||
||'||}t|t߃}ttttttd
 tdtd  t  tttttdtd   t|||
||'|||	}t|t}ttttttd
 tdtd  t  ttdtdtttdtd   t|||
||'|||	}t|t}ttttdtdttd
   tdtd tdtd ttdtdtttdtd   t|||
|||"}t|t}ttttdtdttd
   t tdtd tttttdtd   t|||
|'||5||	}t|t}ttttdtdttd
   t tdtd tttttdtd   t|||
||'||5||
}t|t}ttttdtdttd
   t tdtd ttdtdtttdtd   t|||
||'||5|	}t|t}ttttdtdttttdtd  tdtd  t|||||}t|t}tttt@ ttttttdtd  tdtd   t||||W| |}t|t}ttttdtd tdtd td	td ttdtdttttdtd  tdtd   t||||
||||	}t|t}tttttd
 tdtd  ttdtd  tdtd tdtd ttdtdttttdtd    t||||
|||'|||}t|t}tttttd
 tdtd  ttdtd  tdtd tdtd ttdtdttttdtd    t||||
|||'|||}t|t}tttdtdttdtdttdtdttdtd tdtd    t|||||}t|t}tttdtdtttttdtd   t||}t|t}ttttdtdtttdtd  t||}t|t}ttttd	td ttdtdtttdtd   t|||B}t|t}tttttttdtd  t|||}t|t}ttttd	td tttttdtd   t||||B}t|t}tttt@ ttdtdtttdtd   t||||G}t|t}tttt@ tttttdtd   t|||||G}t|t}tttttdtd  tdtd ttdtdtttdtd   t|||
||'|||	}t|t}tttttdtd  tdtd tdtd ttdtdtttdtd   t|||
||||"}t|t}tttttdtd  t tdtd ttdtdtttdtd   t|||
||'|||5	}t|t}ttttdtdt  tdtd ttdtdtttdtd   t|||
|'||||K	}t|t}ttttd	td ttdtdt  tdtd  ttdtdtttdtd   t|||
|'|||B||K
}t|t}ttttdtdt  tdtd ttdtdtttdtd   t|||
||'|||	}t|t}ttttd	td ttdtdt  tdtd  ttdtdtttdtd   t|||
||'||||B
}t|t}tttt@ ttdtdt  tdtd  ttdtdtttdtd   t|||
|||'||||G}t|t}ttttdtdt  t tdtd ttdtdtttdtd   t|||
||'|||	}t|t}ttttdtdtttdtd  tttd
 tdtd   t|||
|||}t|t}tttttttdtd  tttd
 tdtd  tdd
   t|||
|||}t|t}tttttd
 tdtd  t ttdtdtttdtd   t|||
|||||$|%||}t|t}ttttttttdtd   tttd
 tdtd  tdd
   t|||
|||}t|t}ttttttd
 tdtd  t  ttdtdtttdtd   t|||
||||||%||}t|t }ttttd
 tttd
 tdtd  tdtd  ttdtdtttdtd   t|||
|||||ă	}t|Đt}ttttd
 tttd
 tdtd  t  ttdtdtttdtd   t|||
||||||||}t|Ɛt}ttttd	td tttd
 tdtd  t  ttdtdtttdtd   t|||
||||B|||"}t|Ȑt}tttttd
 tdtd  tdtd tdtd ttdtdtttdtd   t|||
||||"}t|ʐt}tttttd
 tdtd  t tdtd ttdtdtttdtd   t|||
||'|||5	}t|̐t}ttttdtdttd
   tdtd tdtd ttdtdtttdtd   t|||
||'||||ǃ
}t|ΐt}ttttdtdttd
   tdtd ttdtdtttdtd   t|||
||'||||ȃ
}t|Аt}ttttd	td ttdtdttd
   tdtd  ttdtdtttdtd   t|||
||'|||||B}t|Ґt}tttt@ ttdtdttd
   tdtd  ttdtdtttdtd   t|||
|||'|||||G}t|Ԑt	}ttttdtdttd
   t tdtd ttdtdtttdtd   t|||
||'|||	}t|֐t
}tttdtdttttttdtd  tdtd   t||||}t|ؐt}ttttdtdttttdtd  tdtd  t|||||}t|ڐt}tttt@ ttttttdtd  tdtd   t||||W| |}t|ܐt}ttttdtd tdtd td	td ttdtdttttdtd  tdtd   t||||
||||	}t|ސt}tttttd
 tdtd  ttdtd  tdtd tdtd ttdtdttttdtd    t||||
|||'||||}t|t}tttttd
 tdtd  ttdtd  tdtd tdtd ttdtdttttdtd    t||||
|||'||||}t|t}tttdtdttdtdttdtdttdtd tdtd    t|||||}t|t}tttdtdtdtdttttdtd    tdtd t||||
|}t|t}tttdtdtdtdttttdtd    tdtd t||||
|}t|t}tttdtdtdtdttttdtd    t t||||
||}}t|t}tttdtdtdtdttttdtd    t t||||
||}}t|t}ttttdtd tdtd td	td tdtdtdtdttttdtd    tdtd  t||||
||6|||
}t|t}ttttdtd tdtd td	td tdtdtdtdttttdtd    tdtd  t||||
||6|||
}t|t}ttttdtd tdtd t@ tdtdtdtdttttdtd    t  t||||
||6|||}
}t|t}ttttdtd tdtd t@ tdtdtdtdttttdtd    t  t||||
||6|||}
}t|t}tttdtdtdtdttttdtd    tdtd ttd
 tdtd ttdtd  tdtd tdtd  t||||
|i|j|k||'|l|h}t|t}tttdtdtdtdttttdtd    tdtd ttd
 tdtd ttdtd  tdtd tdtd  t||||
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 tdtd ttdtd  tdtd tdtd  t||||
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||||'|
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sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  x_r   replacement6087r  replacement6088n_replacement6089replacement6090replacement6091replacement6092replacement6093replacement6094replacement6095replacement6096replacement6097replacement6098replacement6099replacement6100replacement6101replacement6102replacement6103replacement6104replacement6105replacement6106r  d_replacement6107d1_d2_replacement6108replacement6109replacement6110replacement6111replacement6112With6113With6114replacement6115replacement6116replacement6117replacement6118replacement6119replacement6120replacement6121replacement6122p_replacement6123replacement6124replacement6125replacement6126replacement6127replacement6128replacement6129replacement6130replacement6131replacement6132replacement6133replacement6134replacement6135replacement6136replacement6137With6138With6139replacement6140replacement6141replacement6142replacement6143replacement6144f_replacement6145replacement6146replacement6147replacement6148replacement6149replacement6150replacement6151replacement6152replacement6153replacement6154m_replacement6155replacement6156replacement6157replacement6158replacement6159replacement6160replacement6161replacement6162With6163With6164With6165With6166With6167With6168replacement6169replacement6170replacement6171replacement6172replacement6173replacement6174replacement6175replacement6176replacement6177replacement6178replacement6179replacement6180replacement6181replacement6182replacement6183replacement6184replacement6185replacement6186replacement6187replacement6188replacement6189replacement6190replacement6191replacement6192replacement6193replacement6194replacement6195replacement6196replacement6197replacement6198replacement6199replacement6200replacement6201replacement6202replacement6203replacement6204replacement6205replacement6206replacement6207replacement6208replacement6209replacement6210replacement6211replacement6212replacement6213replacement6214replacement6215replacement6216replacement6217replacement6218replacement6219replacement6220replacement6221replacement6222replacement6223With6224With6225replacement6226replacement6227replacement6228replacement6229replacement6230replacement6231replacement6232replacement6233replacement6234replacement6235replacement6236replacement6237replacement6238replacement6239replacement6240Px_With6241With6242replacement6243replacement6244With6245With6246With6247With6248With6249With6250replacement6251replacement6252With6253With6254replacement6255replacement6256replacement6257replacement6258replacement6259replacement6260replacement6261replacement6262replacement6263replacement6264replacement6265replacement6266replacement6267replacement6268replacement6269replacement6270replacement6271logreplacement6272replacement6273replacement6274replacement6275replacement6276With6277With6278replacement6279replacement6280u_r   With6281replacement6281With6282replacement6282With6283replacement6283With6284replacement6284With6285replacement6285With6286replacement6286RFx_With6287replacement6287With6288replacement6288a_replacement6289replacement6290With6291replacement6291With6292replacement6292replacement6293replacement6294replacement6295replacement6296c_replacement6297replacement6298replacement6299replacement6300replacement6301replacement6302replacement6303replacement6304replacement6305replacement6306replacement6307replacement6308replacement6309replacement6310replacement6311replacement6312replacement6313replacement6314replacement6315replacement6316replacement6317replacement6318replacement6319replacement6320replacement6321replacement6322replacement6323replacement6324replacement6325replacement6326replacement6327replacement6328replacement6329replacement6330replacement6331replacement6332replacement6333replacement6334replacement6335replacement6336replacement6337v_With6338replacement6338With6339replacement6339expreplacement6340replacement6341replacement6342replacement6343r  replacement6344r  replacement6345replacement6346replacement6347replacement6348replacement6349replacement6350replacement6351replacement6352replacement6353replacement6354replacement6355replacement6356replacement6357replacement6358replacement6359replacement6360replacement6361replacement6362replacement6363replacement6364replacement6365replacement6366replacement6367replacement6368replacement6369replacement6370replacement6371replacement6372replacement6373replacement6374replacement6375replacement6376replacement6377replacement6378replacement6379replacement6380replacement6381replacement6382replacement6383replacement6384replacement6385replacement6386replacement6387replacement6388replacement6389r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h6704With6705replacement6706replacement6707replacement6708replacement6709replacement6710replacement6711replacement6712replacement6713replacement6714replacement6715replacement6716replacement6717replacement6718replacement6719replacement6720replacement6721replacement6722replacement6723replacement6724replacement6725replacement6726replacement6727replacement6728replacement6729replacement6730replacement6731replacement6732replacement6733replacement6734replacement6735replacement6736replacement6737replacement6738replacement6739With6740replacement6740With6741replacement6741(
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``````^^zzzzzzzzz~~~~~~~xxxxLLRRVVFFTTtdd^^\^^db^`\\^^^ddbb^^`@@tttt\\nnrrJJ.B.BVVNNttFLLdd||RRddxx~~tt~~ttxxxx~~||TTllxxxx~~TT<P4Hlzzxjjrfhdvltjjljjvt~~zjtrt|VXl@<P4HJBnztnn|tdftjx|x|XVXl^^VVZZRR66LLJJ``ttvvZZ::^^^^^^^^>>FFppxx^^^^^^^^ttNN((NNLL\\``ll006644FFHHvv.6>..BRRBBttLL              h r  c              	   C   s   t || | t|| |t||   |td   t|td |td  td  || t|| |t||   |  | S Nr4  r'  r"  )r  r   r  r  r  r  r   r!  r#  r$  xr  r  r  r7  J     r7  c              	   C   s   t || | t|| |t||   |td   t|| td t|| td   || t|| |t||   |  | S Nr4  r"  )r  r   r  r  r  r  r  r  r  r  r8  N     r8  c              	   C   s   t |||td   t|| |t||   |td   t|td |td  td  || t| |t||   |td  t|td |td  td  || |td   | S Nr"  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d   || t| |t||   |td  t|| td  t|| td  || |td   | S Nr"  r4  r  r  r   r  r  r  r  r  r  r  r;  V     r;  c              
   C   sN   t td||  tt|| t| | ||   ||| |t||   |S Nr"  r  r  r+   r   r  r  r  r  r  r  r<  Z     Nr<  c              
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   C   s\  t ||| |td   t||td  | |t||   |td   t|td |td  td  || t ||td  ||td   t||td  | |t||   |td   t|td |td  td  || t|| | |t||   |td   t|td |td  td  || |td   | S r  r  r  r  r  r  rF       ^ rF  c              
   C   sf  t ||| |td   t||td  | |t||   |td   t|| td t|| td   ||t ||td  ||td   t||td  | |t||   |td   t|| td t|| td   || t|| | |t||   |td   t|| td  t|| td  || |td   | S r  r  r  r  r  r  rG    s   h rG  c                 C   sP   t || td  tt| ||  | t||  t| ||t|| |S Nr4  r  r  r+   r   r  r  r  r  r  r  r  rH    r  rH  c                 C   sP   t || td  tt| ||  | t| t||  ||t|| |S r#  r  r  r+   r   r  r  r  r  r  r  r  rI    r  rI  c                 C   *   t || | | |t||   |  |S r  r   r  r  r  r  r  rJ       *rJ  c                 C   r&  r  r   r  r  r  r  r  rK    r(  rK  c                 C   s.   t t| |t||   || t|  |S r  )r  r  r  r  r   r!  r#  r%  r(  r  r  r  r  rM    r  rM  c                 C   s4   t t| |t||   || t| |   |S r  )r  r  r  r  )r   r!  r#  r  r  r"  r#  r  r  r  r  rP       4rP  c                 C   sB   t | |t||   |td  || t| |td   |S r  )r  r  r  r  r   r!  r#  r%  r(  r$  r  r  r  r  rQ       BrQ  c	           	      C   sH   t | |t||   |td  || t| |  |td   |S r  )r  r  r  r  	r   r!  r#  r  r  r"  r#  r$  r  r  r  r  rR       HrR  c              	   C   s   t t|td |td  td t|||td    t| |t||   | t|td |td  td  ||S Nr'  r"  r  r  r  r   r  r,  r  r  r  rS    r	  rS  c	           	   	   C   s   t t|| td t|| td  t|||  t|||    t| |t||   | t|| td t|| td   ||S r
  r  r  r  r   r  r.  r  r  r  rT    s   rT  c              
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   C      t |||td   | |}t|| tt|t|| td t|| td   ||| t| |t||   || S Nr'  r4  r"  r  r  r  r   r-  r  r  r5  r  r  r  rV       brV  c              
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   C   sJ  t t|||td   tdt|td |td  td   t| |t||   | t|td |td  td  ||t || | t|||td    tdt|td |td  td   t|| |t||   |td   || t|| |t||   |  t|||td    td | S r;  r  r  r  r   r  r  r,  r  r  r  rX    s   L rX  c	           	   
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   C   s  t td| | td| td  t| |t||   | |||td   |td   ||t || |t|  | |||td   t|  |td |td  td t|   td| td  t|| |t||   |td   |td |td  td |tdd    || t|| |t||   |  |||td   |  td| td  | S r;  r  r  r   r  r%   r&   r  r=  r  r  r  rZ    s    rZ  c
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   C   s  t td| | | td| td  t| |t||	   | |||	  |td   |||	  |td   |	|	t || | | | |tdd    t|||	   t|||	   td| td t||	 td  t||	 td   t|	| |t||	   |td   |td |	td  td |tdd    |	|	 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
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   C   s  t td| | | td| td  t| |t||	   | |||	  |td   |||	  |td   |	|	t || | | | t|  |||	  t|  |||	  t|  ||	 td t|   ||	 td t|   td| td  t|	| |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t|	| |t||	   |  |||	  |  |||	  |  td| td  |	 S r;  r  r  r   r  r%   r&   r  rB  r  r  r  r\    s    r\  c              
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   C   s  t td| td td| | |td   t| |t||	   | |||	  |td   |||	  |td   |	|	t || | | | |tdd    t||	 td  t||	 td  tdt|||	   t|||	   |td   t|	| |t||	   |td   |td |	td  td |tdd    |	|	 t|	| |t||	   |  |||	  |td   |||	  |td   td| | |td   |	 S rG  r  rB  r  r  r  rb        rb  c
           
   
   C   s  t td| td td| | |td   t| |t||	   | |||	  |td   |||	  |td   |	|	t || | | | t|  |||	  t|  |||	  t|  ||	 td t|   ||	 td t|   td|td   t|	| |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t|	| |t||	   |  |||	  |td   |||	  |td   td| | |td   |	 S rG  rD  rB  r  r  r  rc    s    rc  c                 C   sB   t td||  tt| ||  | t| ||t|| |S r  r  r,  r  r  r  rd    r-  rd  c                 C   sD   t td||  tt| ||  | t| ||t|| | S r  r  r,  r  r  r  re       Dre  c              	   C   s&  t || |  td| td  ||td   t|| |t||   |td   || td |tdd    || td |tdd    || t| | | |t||   |td   || td |tdd    || td |tdd    || |td   | S r;  r<  r=  r  r  r  rf       ( rf  c              	   C   sP  t ||t|  |||td   t|  td| td  |td |td  td t|   ||td   t|| |t||   |td   |td |td  td |tdd    || t| |t||   |td  |||td   |  t|td |td  td  || |td   | S r;  r  r%   r  r&   r   r  r  r  r=  r  r  r  rg       R rg  c
           
   	   C   sl  t || | |tdd    t|||	   t|||	   td| td  ||td  t||	 td  t||	 td   t|	| |t||	   |td   |td |	td  td |tdd    |	|	 t| |t||	   |td  |||	  |  |||	  |  t||	 td  t||	 td  || |td   |	 S r  r  r  r  r   r  r  rB  r  r  r  rh    s   n rh  c
           
   	   C   s  t || | t|  |||	  t|  |||	  t|  td| td  ||	 td t|   ||	 td t|   ||td   t|	| |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t| |t||	   |td  |||	  |  |||	  |  t||	 td  t||	 td  || |td   |	 S r;  r  r%   r&   r  r   r  r  r  rB  r  r  r  ri   	  s    ri  c              	   C   sR   t || | tt| ||  | t|td| td   ||t|| |S r0  )r  r+   r   r  r  r  r=  r  r  r  rj  	     Rrj  c              	   C   sT   t | | | tt| ||  | t|td| td   ||t|| |S r0  r  r+   r   r  r  r  r=  r  r  r  rk  	     Trk  c
           
   	   C   sX   t | | | | tt| ||	  | t|	td| td   |	|	t||	 |	S r0  rR  rB  r  r  r  rl  	     Xrl  c                 C   s   t ||tdd   t|||td    t|td |td  td  t| |t||   | |td |td  td |  ||S r  )r  r  r  r   r  r=  r  r  r  rm  	     rm  c
           
      C   s   t | | |tdd   t|||	   t|||	   t||	 td t||	 td   t| |t||	   | ||	 td |  ||	 td |  |	|	S r  )r  r  r  r   r  rB  r  r  r  rn  	     rn  c              
   C   r3  r0  r4  r5  r  r  r  ro  	  r6  ro  c              
   C   r7  r8  r9  r5  r  r  r  rp  	  r:  rp  c                 C   :   t t| |t||   | |||td   | ||S Nr'  r   r   r  r  r=  r  r  r  rq  "	     :rq  c                 C   rW  rX  r   r   r  r  r=  r  r  r  rr  &	  rZ  rr  c                 C   6   t | |t||   | |||td   |  |S rX  r   r  r  r=  r  r  r  rs  *	     6rs  c                 C   r\  rX  r   r  r  r=  r  r  r  rt  .	  r^  rt  c
           
      C   s>   t | |t||	   | |||	  |  |||	  |  |	S r  r)  rB  r  r  r  ru  2	     >ru  c
           
   	   C   s   t |||	  t| |||	  t|  || || |	td   t|   t| |t||	   | || || |	td   |  |	|	S rX  r  r&   r  r   r  )
r   r!  r#  r%  r(  r,  r+  r$  r)  r  r  r  r  rw  6	     rw  c                 C   s   t | t| |||td   t|  || td t|   || td t|   t| |t||   | || td |  || td |  ||S r8  r  r%   r  r&   r   r  r=  r  r  r  rx  :	     rx  c                 C   s>   t td| tt| ||  | t| ||t|| |S r  r  r  r+   r   r  r  r,  r  r  r  ry  >	  r`  ry  c                 C   s>   t td| tt| ||  | t| ||t|| |S r  r  r  r+   r   r  r  r,  r  r  r  rz  B	  r`  rz  c                 C   s   t || | |  td| |td   t| |t||   |td  || td |tdd    || td |tdd    || t| |t||   | |||td   |td   td| |td   | S r;  r<  r=  r  r  r  r{  F	     r{  c                 C   s$  t ||t|  | |||td   t|  |td |td  td t|   td| |td   t| |t||   |td  |td |td  td |tdd    || t| |t||   | |||td   |td   td| |td   | S r;  r  r%   r  r&   r   r  r  r=  r  r  r  r|  J	     & r|  c
           
      C   sT  t || | | t|  |||	  t|  |||	  t|  ||	 td t|   ||	 td t|   td| |td   t| |t||	   |td  |td |	td  td |tdd    |	|	 t| |t||	   | |||	  |td   |||	  |td   td| | |td   |	 S r  r  r%   r&   r  r   r  r  rB  r  r  r  r}  N	  s   V r}  c
           
      C   sd  t || | | t|  |||	  t|  |||	  t|  ||	 td t|   ||	 td t|   td| |td   t| |t||	   |td  ||	 td |tdd    ||	 td |tdd    |	|	 t| |t||	   | |||	  |td   |||	  |td   td| | |td   |	 S r  rj  rB  r  r  r  r~  R	  s   f r~  c                 C   sF   t td| tt| ||  | t|t|  ||t|| |S r  r$  r,  r  r  r  r  V	     Fr  c                 C   sH   t td| tt| ||  | t|t|  ||t|| | S r  r%  r,  r  r  r  r  Z	  r/  r  c
           
   	   C   s
  t || | | |  ||td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	t||	 |td  | |t||	   |  |||	td   |td   || |td   |	 S r  r<  
r   r!  r#  r%  r(  r,  r&  r$  r)  r  r  r  r  r  ^	      r  c
           
   	   C   sD  t || |t|  | |||	td   t|  |td |	td  td t|   ||td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |td   || |td   |	 S r;  rh  rl  r  r  r  r  b	  s   F r  c              	   C   sr  t || |	 | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   ||td   t|| |td  | |t||   |	td   |td |td  td |
tdd    ||t|| |td  | |t||   |	  |||  |
td   |||  |
td   || | |td   | S r  rj  r   r!  r#  r  r  r"  r#  r,  r&  r$  r)  r  r  r  r  r  f	     t r  c              	   C   s  t || |	 | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   ||td   t|| |td  | |t||   |	td   || td |
tdd    || td |
tdd    ||t|| |td  | |t||   |	  |||  |
td   |||  |
td   || | |td   | S r  rj  rn  r  r  r  r  j	      r  c              	   C   s   t |t| |t||   |||td   |td   | ||t || ||  td|  t|td |td  td |tdd   || t| |t||   |||td   |  td|  | S r8  )r  r   r  r  r  r   r!  r#  r%  r(  r)  r  r  r  r  r  n	  rE  r  c              	   C   s   t |t| |t||   |||td   |td   | ||t || | |  td|  t|| td |tdd   || td |tdd    || t| |t||   |||td   |  td|  | S r8  )r  r   r  r  r  rq  r  r  r  r  r	  rg  r  c	           	   	   C   s@  t td| | |td |td   t|| |td  | |t||    |||td   |td   || t || ||  ||td   t|| |td  |td |td  td |tdd    || t|| |td  | |t||    |||td   |  ||td   | S r;  )r  r  r   r  r  	r   r!  r#  r%  r(  r,  r&  r)  r  r  r  r  r  v	  s   B r  c	           	   	   C   sR  t td| | |td |td   t|| |td  | |t||    |||td   |td   || t || | |  ||td   t|| |td  || td |tdd    || td |tdd    || t|| |td  | |t||    |||td   |  ||td   | S r;  r<  rr  r  r  r  r  z	  s   T r  c	           
   
   C      t || | |||td   |  |}	t|| tt|	t|td |td  td  ||| t| |t||   |	| S r0  r4  
r   r!  r#  r%  r(  r,  r&  r)  r  r.  r  r  r  r  ~	     *^r  c	           
   
   C      t || | |||td   |  |}	t|| tt|	t|| td t|| td   ||| t| |t||   |	| S r8  r9  rt  r  r  r  r  	     *br  c           	      C   s   t || |td |td  td |  |}t|| | |t||    ||t|| ||  tt|t|td |td  td  ||| S r0  )r  r  r  r  r   r-  r  	r   r!  r#  r%  r(  r&  r)  r  r.  r  r  r  r  	  s   2lr  c
                 C   s   t |	| ||	 td |  ||	 td |  |	}
t| | | | |t||	    |
|	t|| | | |  tt|
t||	 td t||	 td   |	|	|	 S r
  )r  r  r  r  r   r-  r  r   r!  r#  r  r  r"  r#  r&  r)  r  r.  r  r  r  r  	  s   6|r  c           	   
   C   s  t || |td |td  td |  |}t|| ||tdd    t|||td    t|td |td  td  tt|t|td |td  td  ||| t| |t||   t|| |||td   |  || S r;  )r  r  r  r  r   r-  r  rx  r  r  r  r  	  s   2r  c
              
   C   s$  t |	| ||	 td |  ||	 td |  |	}
t|| | | |tdd    t|||	   t|||	   t||	 td t||	 td   tt|
t||	 td t||	 td   |	|	|	 t| |t||	   t|	| |||	  |  |||	  |  |	|	 S r  )r  r  r  r  r   r-  r  ry  r  r  r  r  	  s   6r  c
           
   
   C   s~  t td| | |td |td   t||	 |td  | |t||	   |  |||	td   |td   |	|	 t || | | |  ||td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |  ||td   |	 S r;  r<  rl  r  r  r  r  	      r  c	           	   
   C   s  t |td t|||td    |td |td  t|td |td  td   t|| |td  | |t||   |  t|td |td  td  || t || | t|||td    ||td  t|td |td  td   t|| |td  | |t||   |td   || t|| |td  | |t||   |  t|||td    ||td   | S r;  r  r  r  r   r  r  	r   r!  r#  r%  r(  r,  r&  r$  r  r  r  r  r  	      r  c              
   C   s  t |td t|||
   t|||
   |td |td  t||
 td  t||
 td   t||
 |td  | |t||
   |	  t||
 td t||
 td   |
|
 t || |	 t|||
   t|||
   ||td  t||
 td  t||
 td   t||
 |td  | |t||
   |	td   |
|
 t||
 |td  | |t||
   |	  t|||
   t|||
   ||td   |
 S r;  rO  r   r!  r#  r  r  r"  r#  r,  r&  r$  r  r  r  r  r  	  rJ  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d t|   ||td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |  ||td   |	 S r;  rA  rl  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 || |	 | | |
tdd    t|||   t|||   ||td  t|| td  t|| td   t|| |td  | |t||   |	td   |td |td  td |
tdd    || t|| |td  | |t||   |	  |||  |
  |||  |
  ||td   | S r;  r  rn  r  r  r  r  	      r  c
           
   
   C   s  t td| | |td|  td  t||	 | | |t||	   |  |||	td   |td   |	|	t || | | |  ||td|  td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |  ||td|  td   |	 S r;  r<  rl  r  r  r  r  	  s    r  c	           	   
   C   s  t t|||td   |td t|td |td  td   t|| | | |t||   |  t|td |td  td  ||t || | t|||td    ||td  t|td |td  td   t|| |t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|||
  t|||
   |td t||
 td  t||
 td   t||
 | | |t||
   |	  t||
 td t||
 td   |
|
 t || |	 t|||
   t|||
   ||td  t||
 td  t||
 td   t||
 |td  | |t||
   |	td   |
|
 t||
 |td  | |t||
   |	  t|||
   t|||
   ||td   |
 S r8  r?  r~  r  r  r  r  	  rC  r  c
           
   
   C   s  t td| | |td|  td  t||	 | | |t||	   |  |||	td   |td   |	|	t || |t|  | |||	td   t|  |td |	td  td t|   ||td|  td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |  ||td|  td   |	 S r;  rA  rl  r  r  r  r  	      r  c              
   C   s  t td| | |
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td   |||  |
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tdd    || t|| |td  | |t||   |	  |||  |
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  td   | S r;  r  rn  r  r  r  r  	  s    r  c
           
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   C   s  t |td |td|  td  |td |td   t||	 |td  | |t||	   |  |||	td   |  |	|	t || | | |  ||td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |td   || |td   |	 S rG  r<  rl  r  r  r  r  	  s    r  c
           
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   C   s  t |td |td|  td  |td |td   t||	 |td  | |t||	   |  |||	td   |  |	|	 t || |t|  | |||	td   t|  |td |	td  td t|   ||td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t||	 |td  | |t||	   |  |||	td   |td   || |td   |	 S rG  rA  rl  r  r  r  r  	  s    r  c              
   C   s  t |td |td|
  td  |td |td   t|| |td  | |t||   |	  |||  |
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tdd    || t|| |td  | |t||   |	  |||  |
td   |||  |
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   C   s  t |td |td|
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tdd    || td |
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td   || | |td   | S rG  rD  rn  r  r  r  r  	       r  c
           
   
   C   s  t |td |td  td| |td   t||	 |td  | |t||	   |  |||	td   |td   |	|	 t || | | |  td| |td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t|||	 |td   | |t||	   |  |||	td   |td   td| |td   |	 S Nr'  r4  r"  r3  r<  rl  r  r  r  r  	  s    r  c
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   C   s  t |td |td  td| |td   t||	 |td  | |t||	   |  |||	td   |td   |	|	 t ||t|  | | |||	td   t|  |td |	td  td t|   td| |td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t|||	 |td   | |t||	   |  |||	td   |td   td| |td   |	 S r  rA  rl  r  r  r  r  	  s    r  c              
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td   | S r  rD  rn  r  r  r  r  	  s    " r  c              
   C   s.  t |td |td  td| | |
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tdd    || t||| |td   | |t||   |	  |||  |
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   C   s  t |td|
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td   t|| |td  | |t||   |	td   |td |td  td |
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td   |||  |
td   td| | | |
td   | S rG  rD  rn  r  r  r  r  	  r  r  c              
   C   s$  t |td|
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td   t|| | | |t||   |	  |||  |
td   |||  |
td   ||t || |	 | | t|
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td   t|| |td  | |t||   |	td   || td |
tdd    || td |
tdd    || t|| |td  | |t||   |	  |||  |
td   |||  |
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td   | S rG  rD  rn  r  r  r  r  	  s    ( r  c	           	   
   C   s\  t |td |td  |td |  t|| |td  | |t||   |  t|||td    || t || | t|td |td  td  || t|||td     t|| |td  | |t||   |td   || t||| |td   | |t||   |  t|||td    ||  | S Nr'  r4  r3  r"  r  r|  r  r  r  r  	  r"  r  c              
   C   s  t |td |td  |td |  t||
 |td  | |t||
   |	  t|||
  t|||
    |
|
t || |	 t|||
   t|||
   || | | t||
 td  t||
 td   t||
 |td  | |t||
   |	td   |
|
 t|||
 |td   | |t||
   |	  t|||
   t|||
   || |  |
 S r  r  r~  r  r  r  r  	  rp  r  c                 C   sP   t || td  t| tt| ||  | t||  ||t|| |S r#  r  r  r  r+   r   r  r  r   r!  r#  r%  r(  r&  r$  r  r  r  r  r  	  r  r  c
           
      C   sV   t || td  t| |  tt| ||	  | t|	|  |	|	t||	 |	S r#  r  r  r  r+   r   r  r  )
r   r!  r#  r  r  r"  r#  r&  r$  r  r  r  r  r   
     Vr  c              
   C   s`  t || |td  | |t||    ttdd |td tdd  |td tdd  |td  |td   t|| |td   |t || || |td   tttd|td td |td td t|td tdd  |td td |td  |td   t||td  |td  |td   | S )Nr"  r'  r*  )r  r  r  r5   r  r  r   r   r!  r#  r%  r(  r,  r&  r  r  r  r  r  
  rH  r  c
           
      C   s  t || ||	 |td   tttd|td td |td td t|td tdd  |td td |td |	td   |td t| |  |td  |td   |	t ||	 |td  | |t||	    t|td  |	td  td  ttdd |td tdd  |td tdd  |td |	td   |t|||	   t|||	   |td   |	 S Nr'  r"  r*  )r  r  r  r   r  r  r5   )
r   r!  r#  r  r  r"  r#  r,  r&  r  r  r  r  r  
  s    r  c	           	   	   C      t t|td |td  td t|||td    t|| | | |t||   |  t|td |td  td  ||S r0  r1  r|  r  r  r  r  
     r  c              	   C      t t||
 td t||
 td  t|||
  t|||
    t||
 | | |t||
   |	  t||
 td t||
 td   |
|
S r
  r2  r~  r  r  r  r  
     r  c
           
   
   C   s  t |td |td  |td |td|  td   t||	 |td  | |t||	   |  |||	td   |  |	|	t || | | |  ||td|  td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t|||	 |td   | |t||	   |  |||	td   |td   ||td|  td   |	 S r  r<  rl  r  r  r  r  
  r}  r  c
           
   
   C   s  t |td |td  |td |td|  td   t||	 |td  | |t||	   |  |||	td   |  |	|	 t ||t|  | | |||	td   t|  |td |	td  td t|   ||td|  td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t|||	 |td   | |t||	   |  |||	td   |td   ||td|  td   |	 S r  rA  rl  r  r  r  r  
      r  c              
   C   s  t |td |td  |td |td|
  td   t|| |td  | |t||   |	  |||  |
  |||  |
  ||t || |	 | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   ||td|
  td   t|| |td  | |t||   |	td   |td |td  td |
tdd    || t||| |td   | |t||   |	  |||  |
td   |||  |
td   || |td|
  td   | S r  rD  rn  r  r  r  r  
  s      r  c              
   C   s,  t |td |td  |td |td|
  td   t|| |td  | |t||   |	  |||  |
  |||  |
  ||t || |	 | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   ||td|
  td   t|| |td  | |t||   |	td   || td |
tdd    || td |
tdd    || t||| |td   | |t||   |	  |||  |
td   |||  |
td   || |td|
  td   | S r  rD  rn  r  r  r  r   
  s    0 r  c
           
   	   C   s*  t || | |  || |td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	t||	 | | |t||	   |td   |||	td   |  t||	 td  t||	 td  || |td   |	 S r  r  r  r   r  r  r  rl  r  r  r  r  $
     , r  c
           
   	   C   s`  t |t| | | |||	td   t|  |td |	td  td t|   || |td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t||	 | | |t||	   |td   |||	td   |  t|td |	td  td  || |td   |	 S r;  rM  rl  r  r  r  r  (
  rH  r  c              	   C   s  t || | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   || |	td   t|| |td  | |t||   |	td   |td |td  td |
tdd    ||t|| | | |t||   |	td   |||  |
  |||  |
  t|| td  t|| td  || |	td   | S r  rP  rn  r  r  r  r  ,
  s    r  c              	   C   s  t || | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   || |	td   t|| |td  | |t||   |	td   || td |
tdd    || td |
tdd    ||t|| | | |t||   |	td   |||  |
  |||  |
  t|| td  t|| td  || |	td   | S r  rP  rn  r  r  r  r  0
      r  c	           	   	   C   s   t || || t| |td   t|| |td  | |t||   |td   || t|| | | |t||   |td   || t| |td   | S r  r>  r|  r  r  r  r  4
  r  r  c              	   C   s   t || || t| |  |	td   t||
 |td  | |t||
   |	td   |
|
 t||
 | | |t||
   |	td   || t| |  |	td   |
 S r  r?  r~  r  r  r  r  8
     r  c	           	   	   C   r  r0  r1  r|  r  r  r  r  <
  r  r  c              	   C   r  r
  r2  r~  r  r  r  r  @
  r  r  c
           
   
   C   s  t || | |  || |td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	t || |  |td|  td  || |td   t||	 |td  | |t||	   |td   ||	 td |tdd    ||	 td |tdd    |	|	 t||	 | | |t||	   |td   |||	td   |  t||	 td  t||	 td  || |td   |	 S r  r  rl  r  r  r  r  D
  r  r  c
           
   
   C   sP  t |t| | | |||	td   t|  |td |	td  td t|   || |td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t ||t|  |||	td   t|  |td |	td  td t|   |td|  td  || |td   t||	 |td  | |t||	   |td   |td |	td  td |tdd    |	|	 t||	 | | |t||	   |td   |||	td   |  t|td |	td  td  || |td   |	 S r;  rM  rl  r  r  r  r  H
  s    T r  c              
   C   s  t || | | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   || |	td   t|| |td  | |t||   |	td   |td |td  td |
tdd    ||t || | t|
  |||  t|
  |||  t|
  || td t|
   || td t|
   |td|
  td  || |	td   t|| |td  | |t||   |	td   |td |td  td |
tdd    || t|| | | |t||   |	td   |||  |
  |||  |
  t|| td  t|| td  || |	td   | S r  rP  rn  r  r  r  r  L
  s     r  c	           	   	   C   sl   t || td  ||  tt| ||  | t||  t|td| td   ||t|| |S r  r$  	r   r!  r#  r%  r(  r&  r$  r)  r  r  r  r  r  P
  s   lr  c	           	   	   C   sn   t || td  | |  tt| ||  | t|td| td   t||  ||t|| |S r  r%  r  r  r  r  r  T
     nr  c              	   C   sr   t || td  | | |	  tt| ||
  | t|
td|	 td   t|
|  |
|
t||
 |
S r  r%  r   r!  r#  r  r  r"  r#  r&  r$  r)  r  r  r  r  r  X
     rr  c	           	   	   C   s   t |t| |||td   t|  |td |td  td t|   t|| | |t||   |  |td |td  td |  ||S r0  r  r%   r  r&   r   r  r  r  r  r  r  \
     r  c              	   C   s   t | | t|	 |||
  t|	  |||
  t|	  ||
 td t|	   ||
 td t|	   t|
| | |t||
   |  ||
 td |	  ||
 td |	  |
|
S r
  r  r%   r&   r  r   r  r  r  r  r  r  `
     r  c
           
   	   C   sj   t t| |t||	   | t|||	td    ||	 | |||	td   |tdd    |	|	S r0  r   r   r  r  r  rl  r  r  r  r  d
     jr  c                 C   s   t t| |t||   |	 t|||  t|||    || | |||  |
tdd    |||  |
tdd    ||S r  r   r   r  r  r  rn  r  r  r  r  h
  r  r  c              	   C   s$  t || ||td  |td   t|| |td  ||td  ||td  |td    t|| td t|| td   || t||| |td   | |t||    ||td   | t||| |td   | |t||    |td |td   | S )Nr"  r*  r'  r4  r  r  r   r  r  r  r  r  r  r  r  l
  ri  r  c              	   C   s   t || td| |td   t|||td   |td  t|td |td  td  || t| |t||   |||td   |td   td| |td   | S r0  )r  r  r   r  r  r  rq  r  r  r  r  p
  r  r  c              	   C   s   t || td| |td   t|||td   |td  t|| td t|| td   || t| |t||   |||td   |td   td| |td   | S r;  r  rq  r  r  r  r  t
  r  r  c	           
   
   C   rs  r0  r4  rt  r  r  r  r  x
  ru  r  c	           
   
   C   rv  r8  r9  rt  r  r  r  r  }
  rw  r  c
           
   	   C   F   t t| |t||	   | ||	 | |||	td   |  |	|	S rX  rY  rl  r  r  r  r  
  rk  r  c
           
   	   C   r  rX  r[  rl  r  r  r  r  
  rk  r  c
           
      C   B   t ||	 | | |t||	   |  |||	td   |  |	S rX  r]  rl  r  r  r  r  
  r-  r  c
           
      C   r  rX  r_  rl  r  r  r  r  
  r-  r  c                 C   sJ   t || | | |t||   |	  |||  |
  |||  |
  |S r  r)  rn  r  r  r  r  
     Jr  c              	   C   s   t |||  t|
 |||  t|
  || || |td   t|
   t|| | | |t||   |	  || || |td   |
  ||S rX  ra  r   r!  r#  r%  r(  r,  r+  r-  r&  r$  r)  r  r  r  r  r  
     r  c
           
   	   C   s   t | t| |||	td   t|  ||	 td t|   ||	 td t|   t||	 | | |t||	   |  ||	 td |  ||	 td |  |	|	S r8  rc  rl  r  r  r  r  
     r  c                 C   B   t t| ||  | t| || |t|   ||t|| S r  )r+   r   r  r  r  r,  r  r  r  r  
  r-  r  c                 C   r  r  )r+   r   r  r  r  r,  r  r  r  r  
  r-  r  c              	   C   s   t || | ||td   t| |t||   |td  |||  |td   t|td |td  td  || t| |t||   | |||  |td   ||td   | S r  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d   | S r  r  r  r  r  r  r  
  r  r  c                 C   4   t t| |t||   | |||  |  ||S r  r   r   r  r  r  r  r  r  
  r+  r  c                 C   r  r  r   r   r  r  r  r  r  r  
  r+  r  c              	   C   \   t || td  tt| ||  | || |t|  |  t| ||t|| |S r#  r$  r  r  r  r  r  
     \r  c              	   C   r  r#  r  r  r+   r   r  r  r  r  r  r  r  r  
  r  r  c              
   C   sh   t | |}t|| tt|t|td |td  td  ||| t||t||   || S r0  r  r  r   r-  r  r  r  r+  r   r!  r#  r  r.  r  r  r  r  
  s   
^r  c              
   C   s   t | |}t|| t|td  |td  td  t|| td t|| td   tt|t|td  |td  td  ||| t||t||   || S r;  r  r  r  r  r   r-  r  r  r  r  r  r  
  s   
r  c                 C   (   t t| ||t||   |  ||S r  r  r+  r   r!  r#  r$  r  r  r  r  r  
     (r  c                 C   r  r  r  r  r  r  r  r  
  r  r  c           	   
   C   sx   t | |||  |  |}t|| tt|t|td |td  td  ||| t||t||   || S r0  r  	r+  r   r!  r#  r%  r(  r&  r  r.  r  r  r  r  
  s   ^r  c           	   
   C   s   t | |||  |  |}t|| t|td  |td  td  t|| td t|| td   tt|t|td  |td  td  ||| t||t||   || S r;  r  r  r  r  r  r  
  s   r  c              
   C   s   t |||
  | |||
  |	  |
}t|| | tt|| |t||
   |td   t|td |
td  td  |
|
|
 t| |t||
   | ||
 S r  )r  r  r   r-  r  r  r  r   r!  r#  r%  r(  r,  r+  r&  r$  r)  r  r.  r  r  r  r  
     &r  c              
   C   s   t |||
  | |||
  |	  |
}t|| | tt|| |t||
   |td   t||
 td t||
 td   |
|
|
 t| |t||
   | ||
 S r
  )r  r  r   r-  r  r  r  r  r  r  r  r  
  s   &r  c              
   C   s   t |||
  ||
td   |	 |||
  td  |
}t|| | tt|| |t||
   |td   t|td |
td  td  |
|
|
 t| |t||
   | ||
 S r8  )r  r  r  r   r-  r  r  r   r!  r#  r%  r(  r,  r+  r-  r$  r)  r  r.  r  r  r  r  
  s   :r  c              
   C   s   t |||
  ||
td   |	 |||
  td  |
}t|| | tt|| |t||
   |td   t||
 td t||
 td   |
|
|
 t| |t||
   | ||
 S r8  )r  r  r  r   r-  r  r  r  r  r  r  r  
  s   :r  c	           	      C   8   t t| ||t||   |  |||  |  ||S r  r  	r+  r   r!  r#  r%  r(  r&  r$  r  r  r  r  r  
     8r  c	           	      C   r  r  r  r  r  r  r  r  
  r  r  c
              
   C   s   t |||	td   | |||	  |  |	}
t|| tttdt|td |	td  td  |
|	|	|	 t| |t||	   |
|	 S r0  )r  r  r  r   r  r  )r   r!  r#  r%  r(  r,  r+  r&  r)  r  r.  r  r  r  r  
  s   .dr  c              
   C   s   t |||  |
 |||  |
  |||  |	  |}t|| tttdt|| td t|| td   |||| t| |t||   || S r  r  r  r   r  r  r  )r   r!  r#  r  r  r"  r#  r,  r+  r&  r)  r  r.  r  r  r  r  
  s   6hr  c                 C   sJ   t t| |t||
   | |||
td   |	  |||
  | |
|
S rX  rY  r   r!  r#  r%  r(  r,  r+  r&  r$  r)  r  r  r  r  r     r  r  c                 C   sR   t t| |t||   |
 |||  |  |||  |  |||  |	 ||S r  r  r   r!  r#  r  r  r"  r#  r,  r+  r&  r$  r)  r  r  r  r  r    rQ  r  c
           
   	   C   s  t td|| t| |td   t| |t||	   |td  |||	  |td   || | td| | |	  || |	td  |td    |	|	 t| |t||	   |td  |||	td    |||	  |  || t| |td   |	 S r  r{  
r   r!  r#  r%  r(  r,  r+  r&  r$  r  r  r  r  r        r  c              	   C   s.  t td|| t| |  |
td   t| |t||   |
td  |||  |	td   || | |	 td| | | |  || | |td  |	td    || t| |t||   |
td  |||  |	  || || |td    || t| |  |
td   | S r  rO  r   r!  r#  r  r  r"  r#  r,  r+  r&  r$  r  r  r  r  r       0 r  c              	   C   sn   t t| |t||
   | t|||
td    |||
td   |	tdd   |||
  |  |
|
S Nr'  r4  r  r  r  r  r  r    r  r  c                 C   s   t t| |t||   |
 t|||   t|||   |||  |tdd   |||  |tdd    |||  |	  ||S Nr4  r'  r  r  r  r  r  r       r  c                 C   s^  t td|| t| |td   tt| |t||
   |td  |||
  |td   |||
td   |	tdd   || | || |
 td|	 td   || |
td  |td|	  td    |
|
|
 t| |t||
   |td  |||
td   |	tdd    |||
  |  || t| |td   |
 S r  )r  r  r  r   r   r  r  r  r  r  r  r    s   ` r  c                 C   s  t td|| t| |  |
td   tt| |t||   |
td  |||  |	td   |||  |tdd   |||  |tdd    || | |	 || | | td| td   || | |td  |	td|  td    ||| t| |t||   |
td  |||  |tdd    |||  |tdd    |||  |	  || t| |  |
td   | S r  )r  r  r  r   r   r  r  r  r  r  r  r        r  c
           
      C   s   t || || t| |td   t| |t||	   |td  |||	  |td   |	|	 t| |t||	   |td  |||	  |  || t| |td   |	 S r  r>  r  r  r  r  r        r  c                 C   s   t ||	 || t| |  |
td   t| |t||   |
td  |||  |	td   || t| |t||   |
td  |||  |	  || t| |  |
td   | S r  r?  r  r  r  r  r  $  r  r  c
           
   	   C   s\   t || td  t| tt| ||	  | || |t|	  |  |	|	t||	 |	S r#  r  r  r  r  r  r  (  r  r  c              	   C   sb   t ||	 td  t| |  tt| ||  |
 || |t|  |	  ||t|| |S r#  r  r  r  r  r  r  ,     br  c              	   C   sn   t t| |t||
   | t|||
td    |||
td   |	tdd   |||
  |  |
|
S r0  r  r  r  r  r  r  0  r  r  c                 C   s   t t| |t||   |
 t|||  t|||    |||  |tdd   |||  |tdd    |||  |	  ||S r  r  r  r  r  r  r  4  r  r  c                 C   s   t |t|	 |||
td   t|	  |td |
td  td t|	   t| |t||
   | |||
  |  |td |
td  td |	  |
|
S r0  r  r  r  r  r  r  8  rd  r  c                 C   s   t | t|	 |||
td   t|	  ||
 td t|	   ||
 td t|	   t| |t||
   | |||
  |  ||
 td |	  ||
 td |	  |
|
S r8  rc  r  r  r  r  r  <     r  c                 C   s   t | | t| |||  t|  |||  t|  |td  |td  td t|   t| |t||   |
 |||  |	  || td |  || td |  ||S r;  r  r  r  r  r  r  @  r  r  c                 C   s   t || || t| |	td   t| |t||
   |	td  |||
   |
|
 t| |t||
   |	td  t||||
  |   || t| |	td   |
 S r  )r  r  r  r   r  r  r  )r   r!  r#  r%  r(  r,  r+  r-  r&  r$  r  r  r  r  r  D  r  r  c                 C   s   t ||
 || t| |  |td   t| |t||   |td  |||   || t| |t||   |td  t|	|||  |
   || t| |  |td   | S r  )r  r  r  r   r  r  r  )r   r!  r#  r  r  r"  r#  r,  r+  r-  r&  r$  r  r  r  r  r  H  r  r  c              	   C   s   t |t|
 |||td   t|
  |td |td  td t|
   t| |t||   |	 |td |td  td |
  t||||  |   ||S r0  )r  r%   r  r&   r   r  r  r  r  r  r  r  L     r  c              	   C   s   t | t|
 |||td   t|
  || td t|
   || td t|
   t| |t||   |	 || td |
  || td |
  t||||  |   ||S r8  )r  r%   r  r&   r   r  r  r  r  r  r  r  P  r  r  c              	   C   s   t | | t| |||  t|  |||  t|  || td t|   || td t|   t| |t||   | || td |  || td |  t|	|||  |
   ||S r
  )r  r%   r&   r  r   r  r  )r   r!  r#  r  r  r"  r#  r,  r+  r-  r&  r$  r)  r  r  r  r  r  T     r  c	           
   
   C   s   t |||  | |||  |  |}	t|| tttdt|td |td  td  |	||| t| |t||   |	| S r  )r  r  r   r  r  r  
r   r!  r#  r%  r(  r,  r+  r&  r  r.  r  r  r  r  X  s   &dr  c	           
   
   C   s   t |||  | |||  |  |}	t|| tttdt|| td t|| td   |	||| t| |t||   |	| S r  r  r  r  r  r  r  ]  s   &hr  c
           
      C   B   t t| |t||	   | |||	  | |||	  |  |	|	S r  r  r  r  r  r  r   b  r-  r   c
           
      C   r  r  r  r  r  r  r  r  f  r-  r  c                 C   2   t |ttttfrdS t||}t||rdS dS NFT
isinstanceintr  floatr  r  r   r   r!  r#  r.  r  vr  r  r  r  j     

r  c              
   C   sh   t ||}t|| tt|t|td |td  td  ||| t| |t||   || S r0  r  r  r  r  r  r  s  s   
^r  c                 C   r  r  r  r  r  r  r  r  y  r  r  c              
   C   s   t ||}t|| t|td  |td  td  t|| td t|| td   tt|t|td  |td  td  ||| t| |t||   || S r;  r  r  r  r  r  r    s   
r  c	           
      C   s`   t |ttttfrdS t| ||t||   |  |||td   |  |}	t|	r.dS dS NFr'  T	r  r  r  r  r  r   r  r  r)   
r+  r   r!  r#  r%  r(  r$  r)  r  r.  r  r  r  r    s   :r  c	           
      C   sD   t | ||t||   |  |||td   |  |}	t|	|S rX  r   r  r  r   r  r  r  r  r    s   :
r  c                 C   sh   t |
ttttfrdS t| ||t||
   |  |||
  |	  |||
  |	  |
}t|r2dS dS r  r  r  r  r  r  r   r  r)   r+  r   r!  r#  r  r  r"  r#  r$  r)  r  r.  r  r  r  r	    s   Br	  c                 C   sL   t | ||t||
   |  |||
  |	  |||
  |	  |
}t||
S r  r   r  r   r  r  r  r  r
    s   B
r
  c              	   C   sl   t |ttttfrdS t| ||t||   |	  |||||td   |
   |  |}t|r4dS dS r  r  r+  r   r!  r#  r%  r(  r,  r+  r&  r$  r)  r  r.  r  r  r  r    s   Fr  c              	   C   sP   t | ||t||   |	  |||||td   |
   |  |}t||S rX  r  r  r  r  r  r    s   F
r  c                 C   st   t |ttttfrdS t| ||t||   |  ||	|||  |  |||  |   |
  |}t|r8dS dS r  r  r+  r   r!  r#  r  r  r"  r#  r,  r+  r&  r$  r)  r  r.  r  r  r  r    s   Nr  c                 C   sX   t | ||t||   |  ||	|||  |  |||  |   |
  |}t||S r  r  r  r  r  r  r    s   N
r  c                 C   >   t |ttttfrdS tt|| | | |}t|rdS dS r  )r  r  r  r  r  r   r  r)   r2  r#  r$  r  r.  r  r  r  r       r  c                 C   "   t t|| | | |}t||S r  )r   r  r   r  r  r  r  r       
r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   r  r  r  r2  r   r!  r#  r$  r  r  r  r  r    r  r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   sV   t |ttttfrdS t|||td   | t|| |  | |}t|r)dS dS r  )	r  r  r  r  r  r   r  r  r)   r2  r#  r%  r(  r$  r)  r  r.  r  r  r  r    s   0r  c                 C   s:   t |||td   | t|| |  | |}t||S rX  )r   r  r  r   r  r  r  r  r    s   0
r  c	           
      C   s^   t |ttttfrdS t|||  | |||  |  t|| |  | |}	t|	r-dS dS r  r  
r2  r#  r  r  r"  r#  r$  r)  r  r.  r  r  r  r    s   8r  c	           
      C   sB   t |||  | |||  |  t|| |  | |}	t|	|S r  r  r  r  r  r  r    s   8
r  c	           	   	   C   s>   t t|||td   | | ||t||   |  ||S rX  )r   r   r  r  )	r2  r   r!  r#  r%  r(  r$  r)  r  r  r  r  r    r`  r  c              	   C   sF   t t|||
  |	 |||
  |	  | ||t||
   |  |
|
S r  r  )r2  r   r!  r#  r  r  r"  r#  r$  r)  r  r  r  r  r    rk  r  c                 C   "   t || |t||   |  |S r  r'  r   r!  r#  r$  r.  r  r  r  r  r       "r  c                 C   r  r  r)  r  r  r  r  r    r  r  c                 C   :   t td| tt| |t|  | |||||  |S r  r  r  r+   r   r  r   r!  r#  r%  r$  r  r  r  r  r     rZ  r   c                 C   r  r  r  r  r+   r   r  r  r  r  r  r!    rZ  r!  c	           	   	   C   `   t td| tt| |t|  | || | | | ||  |  |  |||||  |S r  r  r|  r  r  r  r"        `r"  c	           	   	   C   r  r  r  r|  r  r  r  r#  $  r  r#  c
           
   
   C   j   t td| tt||t|	  | ||	td  |td  ||td   |  |	|	|||	  |	S r  r  
r1  r0  r/  r   r!  r#  r%  r$  r)  r  r  r  r  r$  (  r  r$  c
           
   
   C   j   t td| tt||t|	  | ||	td  |td  ||td   |  |	|	|||	  |	S r  r  r  r  r  r  r%  ,  r  r%  c              
   C   s   t td| tt||t|  |
 ||td  |td  ||td   |  || | | | ||  |  |	  |||||  |S r  r  r1  r0  r/  r   r!  r#  r%  r(  r,  r&  r$  r)  r  r  r  r  r&  0  rb  r&  c              
   C      t td| tt||t|  |
 ||td  |td  ||td   |  || | | | ||  |  |	  |||||  |S r  r  r  r  r  r  r'  4  rb  r'  c                 C   s  t |t| |t|||td      |t tt| | t| td|   t| td|    tt| t|  t| |t|||td       t| | |tt|||td   td  tt|||td   td    | t tt| |t| td|   t| td|    tt| t|  t| |t|||td       t| | |tt|||td   td  tt|||td   td    | S rX  )	r  r  r  r  Pir  r  r  r  r   r!  r#  r%  r  r  r  r  r(  8  s    r(  c                 C   s
  t td|td  | |td  t| |t|||td     |td  ||t|| |t|||td     |  | ttd| | | |t|||td     |td   ttd| | |td  |td |td    ||  | S )N   r'  r4  r3  r  r  r   r  r  r  r  r  r  r  r)  <  rm  r)  c                 C   s~  t || t| td|   t| td|    t| |t|||td     td|   td| |tt|||td   td  tt|||td   td    |t ||t| td|   t| td|    t| |t|||td     td|   td| |tt|||td   td  tt|||td   td    | S rX  )r  r  r  r  r  r  r  r  r  r  r  r*  @  rz  r*  c                 C   s  t ttdtt | |td  t| td|  t| td|    tttdt| |t|||td      tdt|   tdt| |tt|||td   td  tt|||td   td    |t ttdtt | |td  t| td|   t| td|    tttdt| |t|||td      tdt|   tdt| |tt|||td   td  tt|||td   td    | S )Nr'  r4  r  r"  )	r  r  r  r  r  r  r  r  r  r  r  r  r  r+  D  r  r+  c                 C   s&  t ttd| | |td  |td |td   || | t| |t|||td       | t tt| | | tdd   | t| td|   t| td|    tt| t|  t| |t|||td       |tt|||td   td  tt|||td   td   | t tt| | | tdd   |t| td|   t| td|    tt| t|  t| |t|||td       |tt|||td   td  tt|||td   td   | S )Nr'  r  r*  )	r  r  r  r  r  r  r  r  r  r  r  r  r  r,  H  s    * r,  c                 C   s   t || t| td|   t| td|    t| |t|||td     td|   td|td  |tt|||td   td  tt|||td   td    |t ||t| td|   t| td|    t| |t|||td     td|   td|td  |tt|||td   td  tt|||td   td    | t ttd| | |td  |td |td   td| | | | |t|||td       | S )Nr'  r  )r  r  r  r  r  r  r  r  r  r  r  r  r-  L  s     r-  c                 C   sV  t tdtd|td  |td  |td   t| |t|||td     |td  ||t|| |t|||td     |td   td|td  |td  |td   | t| |t|||td     |td  ttd| | |td  |td |td    td| | | |td   | S )Nr"  r  r'  r  r  r  r  r  r.  P  s   X r.  c                 C   s  t tdt| |t||td  td    tt||td  td td td  ||  |t ttdtt t| t| td|   t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td| |  | t ttdtt t| t| td|  t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td| |  | S r0  )	r  r  r  r  r  r  r  r  r  r   r!  r%  r  r  r  r  r/  T  r  r/  c                 C   s  t tdt| |t||td  td    tt||td  td td td  ||  |t ttdtt t| t| td|   t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td| |  | t ttdtt t| t| td|  t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td| |  | S r  )	r  r  r  r  r  r  r  r  r  r  r  r  r  r0  X  r  r0  c                 C   sF  t td|td  | |td  t| |t|||td     |td  ||t|| |t|||td     |  | ttd| | | |t|||td     |td   td| | |td  |td |td    || t|||td   td  t|||td   td   | S )Nr  r'  r4  r3  r"  r  r  r  r  r  r1  \  s   H r1  c                 C   s   t ttd| t| |t||td  td   td|   t| td|   td| t||td    |t ttd| t| |t||td  td   td|   t| td|   td| t||td    | S r0  r  r  r  r  r  r  r  r  r  r  r  r  r2  `  s   r2  c                 C   s   t ttd| t| |t||td  td   td|   t| td|   td| t||td    | t ttd| t| |t||td  td   td|   t| td|   td| t||td    | S r  r  r  r  r  r  r  r  r  r  r  r  r  r3  d  s   r3  c                 C   s  t ttdtt t| td|   t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  tdt| | |  |t ttdtt t| td|  t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  tdt| | |  | S r0  	r  r  r  r  r  r  r  r  r  r  r  r  r  r4  h  r  r4  c                 C   s  t ttdtt t| td|   t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  tdt| | |  |t ttdtt t| td|  t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  tdt| | |  | S r  r  r  r  r  r  r5  l  r  r5  c                 C   s  t t||td  t||td  td  || | t| |t||td  td     | t ttdtt t| td|   t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td|tdd   | |  | t ttdtt t| td|  t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td|tdd   | |  | S r  	r  r  r  r  r  r  r  r  r  r  r  r  r  r6  p       r6  c                 C   s  t t||td  t||td  td  || | t| |t||td  td     | t ttdtt t| td|   t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td|tdd   | |  | t ttdtt t| td|  t| td|    tttdt| |t||td  td    tdt|   tt||td  td td  td|tdd   | |  | S )Nr'  r3  r4  r*  r  r  r  r  r  r7  t  r  r7  c                 C   s|  t ttd| t| |t||td  td   td|   t| td|   td|td  t||td    | t ttd| t| |t||td  td   td|   t| td|   td|td  t||td    | t t||td  t||td  td  td| | | | |t||td  td     | S )Nr'  r"  r  r  r  r  r  r  r8  x  s   ~ r8  c                 C   sz  t ttd| t| |t||td  td   td|   t| td|   td|td  t||td    |t ttd| t| |t||td  td   td|   t| td|   td|td  t||td    | t t||td  t||td  td  td| | | | |t||td  td     | S )Nr'  r4  r  r3  r  r  r  r  r  r9  |  s   | r9  c                 C   s  t tdtd|td  |td  |td   t| |t|||td     |td  ||t|| |t|||td     |td   td|td  |td  |td   | t| |t|||td     |td  td| |td  ||td    td| | |td  t|||td   td  t|||td   td   | S )Nr"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  r$  r)  r  r  r  r  r;    rZ  r;  c              	   C   s:   t td| tt|| t| ||t| ||  |S r  rf  r  r  r  r  r<    rZ  r<  c                 C   *   t |t| | |||  |  |  |S r  r   r  r   r!  r#  r&  r$  r.  r  r  r  r  r=    r(  r=  c                 C   r   r  r   r   r  r  r  r  r>    r(  r>  c              
   C   sj   t t| |td  | |  ttt|| t|td td  ||t| |td  td |S r;  r  r  r  r+   r   r  r!  r$  r  r  r  r  r?    r  r?  c              
   C   s   t tt| |td  td td tt| |td  td td  | |  ttt|| t|td t|td   ||t| |td  td |S r;  r  r  r  r+   r   r  r  r  r  r  r@       r@  c              	   C   B   t td| tt||||   t| ||t| ||  |S r  r  r   r!  r#  r,  r$  r  r  r  r  rA    r-  rA  c              	   C   r  r  r  r	  r  r  r  rB    r-  rB  c              	   C   \   t td| tt||||   |  | t||  |  t| ||t| ||  |S r  r$  r   r!  r#  r,  r&  r$  r  r  r  r  rC    r  rC  c              	   C   r
  r  r  r  r  r  r  rD    r  rD  c                 C   sF   t t|t| | t| td td  || t|t|  | S r0  )r   r-  r  r  r  r  r  r.  r  r  r  r  rE    rk  rE  c                 C   sN   t t|t| | t| td t| td   || t|t|  | S r
  )r   r-  r  r  r  r  r  r  r  r  r  rF    r  rF  c              	   C   s   t |||td   tt|||  |td  t|| t|td td  ||| t| |t|  |||  |td   ||td   | S r  )r  r  r   r-  r  r  r  r  r   r!  r#  r%  r&  r.  r  r  r  r  rG    r  rG  c              
   C   s   t |||td   tt|||  |td  t|| t|td t|td   ||| t| |t|  |||  |td   ||td   | S r  )r  r  r   r-  r  r  r  r  r  r  r  r  rH       rH  c                 C   r  r  r  r   r!  r.  r  r  wr  r  r  rJ    r  rJ  c              	   C   s^   t ||}t|tt|t|| t|td td  ||| t| |t|  || S r0  )r  r  r   r-  r  r  r  r  r  r  r  r  rK    s   
TrK  c                 C   r  r  r  r  r  r  r  rL    r  rL  c              
   C   sf   t ||}t|tt|t|| t|td t|td   ||| t| |t|  || S r
  )r  r  r   r-  r  r  r  r  r  r  r  r  rM    s   
\rM  c                 C   s&   t |t|td td  |  |S r0  r   r  r  r$  r.  r  r  r  r  rO       &rO  c                 C   s.   t ||  |t|td td  |  |S r0  r  r&  r$  r.  r  r  r  r  rP    r  rP  c                 C   s.   t |t|td t|td   |  |S r
  r  r  r  r  r  rQ    r  rQ  c                 C   s6   t ||  |t|td t|td   |  |S r
  r  r  r  r  r  rR    r^  rR  c              	   C      t || | t|| |t||   |td   |td  |td  td  || t|| |t||   |  | S r  )r  r   r  r  r  r  r  r  r  rS       rS  c              	   C   r  r  )r  r   r  r  r  r  r  r  r  rT    r  rT  c                 C      t | |t||   | |S r  r   r  r  r  r  r  rU       rU  c                 C   r  r  r   r  r  r  r  r  rV    r  rV  c              	   C      t || | | t| |t||   |td  ttd| |||    |td  |td  td  ||t| |t||   | ttd| |||    | | S r  r  r   r  r  r  r  r,  r  r  r  rW    r  rW  c              	   C   r  r  r  r   r  r  r  r  r,  r  r  r  rX    r  rX  c              	   C   s   t ttdt | |||   | | |  |td|  | t ttdt | |||   | | |  |td|  | t t|||  t| | |  | | S rX  )r  r  r  r  r  r#  r%  r(  r  r  r  r  rY    rd  rY  c                 C   sp   t tdd tt|  | td |||   || t tdd tt| | td |||   || S r  r  r  r   r  r  r  r  r  rZ       prZ  c              	   C   s~   t tdd tttdtd| |   |||   || t tdd tttdtd| |   |||   || S r  r  r  r  r  r  r[  
     ~r[  c                 C   J   t |tt|| |||   ||t| tt|||  | | | S r  )r  r   r  r  r  r   r*  r  r  r  r\    r  r\  c                 C   r"  r  )r  r   r  r  r  r   r*  r  r  r  r]    r  r]  c                 C      t || ||td   t|||  |td  |td  |td  td  || t| |t||   |||  |td   ||td   | S r  r  r  r   r  r  rq  r  r  r  r^    r  r^  c                 C   r#  r  r  r  r   r  r  rq  r  r  r  r_    r  r_  c              
   C      t td| | | t| |t||   |td  ttdtd| | td    |td  |td  td  || ttd| |t||   |  ttdtd| | td    | S r8  r  r  r   r  r  r  r  r  r  r`       r`  c              
   C   r&  r8  r  r  r   r  r  r  r  r  r  ra  "  r(  ra  c              	   C      t || | |td  t||td  | |t||   |td   |td  |td  td  || t||td  | |t||   |  |td  | S r  r'  r  r  r  r  rb  &  r  rb  c              	   C   r*  r  r)  r  r  r  r  rc  *  r  rc  c                 C   4   t t| |t||   | |||  |  ||S r  r   r   r  r=  r  r  r  rd  .  r+  rd  c                 C   r+  r  r   r   r  r=  r  r  r  re  2  r+  re  c                 C   .   t | |t||   | |||  |  |S r  r  r=  r  r  r  rf  6  r  rf  c                 C   r.  r  r  r=  r  r  r  rg  :  r  rg  c              
   C      t td| t||td  | |t||   |  ||t || t||td  | |t||   |  |||   || S r  r  r  r   r  r  r  r  r  rh  >     rh  c              
   C   r/  r  r  r  r   r  r  r  r  r  ri  B  r1  ri  c              	   C      t || | | t| |t||   |td  ttd| | |||    |td  |td  td  || t| |t||   | ttd| | |||    | | S r  r  r,  r  r  r  rj  F  r  rj  c              	   C   r3  r  r  r,  r  r  r  rk  J  r  rk  c              
   C   |   t td| t|| | |t||   |  ||t || t||td  | |t||   |  |||   || S r  r0  r  r  r  r  rl  N     |rl  c              
   C   r4  r  r2  r  r  r  r  rm  R  r5  rm  c	           	      C   <   t t|| | |t||   |  |||  |  ||S r  r,  r  r  r  r  rn  V     <rn  c	           	      C   r6  r  r-  r  r  r  r  ro  Z  r7  ro  c	           	      C   6   t || | |t||   |  |||  |  |S r  r  r  r  r  r  rp  ^  r^  rp  c	           	      C   r8  r  r  r  r  r  r  rq  b  r^  rq  c              	   C      t td| | td| td  t| |t||   |||td   |td   ||t|| |t||    |||td   |  td| td  | t||||td   |  td| | td| td   | S r;  r'  rq  r  r  r  rr  f     rr  c              	   C   r9  r;  r)  rq  r  r  r  rs  j  r:  rs  c              
   C     t td| | td| td  t| |t||   | |||td   |td   ||t |td | | |td  td| td| td   t| |t||   |td  |||td   |td   || t|| |t||   |  |||td   |  td| td  | t|| | |t||   |td   |||td   |  td| | td| td   | S Nr'  r"  r4  r3  r'  r=  r  r  r  rt  n      rt  c              
   C   r;  r<  r)  r=  r  r  r  ru  r  r=  ru  c                 C   0   t tt| |t||   ||| |  |S r  )r  r  r   r  r*  r  r  r  rv  v     0rv  c                 C   r>  r  )r  r  r   r  r*  r  r  r  rw  z  r?  rw  c                 C   >   t | |t||   |td  || | |td   |S r  )r  r  r  r,  r  r  r  rx  ~  r`  rx  c                 C   r@  r  )r  r  r  r,  r  r  r  ry    r`  ry  c              
   C     t td | |t||    tt| | td t|| td   |t|  |t t| ttdt t| | td  t|| td   |t|  | t t| ttdtt| | td  t|| td   |t|  | S r0  )r  r  r  r>   r  r  r  r*  r  r  r  rz        rz  c              
   C   rA  r0  )r  r  r  r>   r  r  r  r*  r  r  r  r{    rB  r{  c                 C   sF   t td|t|  tt| ||  | t| ||t|| |S r  )r  r  r  r+   r   r  r  r,  r  r  r  r|    rk  r|  c              	   C   s|   t |ttdtd|td |td     t|||td    tt| ||  | t| ||t|| | S r  )r  r  r  r+   r   r  r  r,  r  r  r  r}    r5  r}  c              	   C      t t|td  |td  td t|||td    t| |t||   | t|td  |td  td  ||S r0  r  r  r  r   r  r,  r  r  r  r~    r  r~  c              	   C   rC  r0  r  r  r  r   r  r,  r  r  r  r    r  r  c              	   C      t || | td t|| |t||   |td   |||td   td  || t|| |t||   |  td| |||td     | t| |t||   |td  td| | |td  |td   | S r8  r'  r,  r  r  r  r       r  c              	   C   rF  r8  r)  r,  r  r  r  r    rG  r  c              
   C   f   t ||| t|||td     | t || |t||    |t|||td     | S rX  )r  r  r  r  r*  r  r  r  r       fr  c              
   C   rH  rX  )r  r  r  r  r*  r  r  r  r    rI  r  c              	   C     t td| td td| |td   t| |t||   |||td   |td   ||t||||td   |td   td| | |td td   | t|| |t||    |||td   |td   td| |td   | S Nr'  r*  r"  r  r'  rq  r  r  r  r    r  r  c              	   C   rJ  rK  r)  rq  r  r  r  r    r  r  c              
   C      t |td | |td  t| |t||   |td  |||td   tdd   ||t|| |t||   |  |t|||td     | t|| | |t||   |td   || t|||td     | S Nr'  r4  r3  r*  )r  r  r   r  r  r  r,  r  r  r  r    r:  r  c              
   C   rL  rM  )r  r  r   r  r  r  r,  r  r  r  r    r:  r  c              
   C     t td| td td| |td   t| |t||   | |||td   |td   ||t |td | |td  td|td td   t| |t||   |td  |||td   |  || t|| |t||   |  |||td   |td   td| |td   | t|| | |t||   |td   |||td   |td   td| | |td td   | S Nr'  r*  r"  r4  r  r3  r'  r=  r  r  r  r        r  c              
   C   rN  rO  r)  r=  r  r  r  r    rP  r  c              	   C      t td| |td  ||td   t|| |t||   |td   |||td   |  ||t| |t||   |td  |||td   |td   || | |td   | S r0  r'  r=  r  r  r  r       r  c              	   C   rQ  r0  r)  r=  r  r  r  r    rR  r  c              	   C   sT   t || | tt| ||  | t|td | td   ||t|| |S Nr'  r3  )r  r+   r   r  r  r  r=  r  r  r  r    rS  r  c                 C   s   t ||tdd   t|td  |td  td  t|||td    t| |t||   | |td  |td  td |  ||S r  r  r  r  r   r  r=  r  r  r  r       r  c              	   C   sX   t | | | tt| ||  | t|td | td   ||t|| | S rS  )r  r+   r   r  r  r  r=  r  r  r  r    rT  r  c              	   C   s   t || |tdd    t|td |td  td |td |td    t|||td    tt| ||  | t|td | td   ||t|| | S Nr"  r'  r4  r3  )r  r  r  r+   r   r  r  r=  r  r  r  r    r  r  c              
   C   s   t tdd tt|  | td |||td    || t tdd tt| | td |||td    || S r  r  r  r  r  r  r    r  r  c              
   C   s   t tdd tttdtd| |   |||td    || t tdd tttdtd| |   |||td    || S r  r  r  r  r  r  r    r  r  c              
   C   X   t | ttd|||td    ||t |tt|| |||td    || S r  r  r   r  r  r*  r  r  r  r    rT  r  c              
   C   rW  r  r  r   r  r  r*  r  r  r  r    rT  r  c              	   C   z   t |||td   | |}t|| tt||td  |td  td  ||| t| |t||   || S r0  )r  r  r  r   r   r  r5  r  r  r  r       \r  c              	   C   rZ  r0  )r  r  r  r   r   r  r5  r  r  r  r    r[  r  c                 C   <   t t| |t||   | |||td   |  ||S rX  r   r   r  r  r=  r  r  r  r    r7  r  c                 C   r\  rX  r   r   r  r  r=  r  r  r  r    r7  r  c                 C   r\  rX  r   r  r  r=  r  r  r  r     r^  r  c                 C   r\  rX  r   r  r  r=  r  r  r  r    r^  r  c              
   C      t td| t||td  | |t||   |  ||t || t||td  | |t||   |  |||td    || S Nr"  r3  r'  r0  r  r  r  r  r       r  c              
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   C      t td| t|| | |t||   |  ||t || t||td  | |t||   |  |||td    || S r  r0  r  r  r  r  r    r1  r  c              
   C   rd  r  r2  r  r  r  r  r    r1  r  c                 C   ~   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   re  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   | 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   | S r  r)  r,  r  r  r  r  $  r  r  c              
   C   ra  rb  r0  r  r  r  r  r  (  rc  r  c              
   C   ra  rb  r2  r  r  r  r  r  ,  rc  r  c                 C   |   t td| t| |t||   | ||| td   ||t| |t||   |td  || |td   | S r  r'  r,  r  r  r  r  0  r5  r  c                 C   rf  r  r)  r,  r  r  r  r  4  r5  r  c              
   C   rd  r  r0  r  r  r  r  r  8  r1  r  c              
   C   rd  r  r2  r  r  r  r  r  <  r1  r  c              	   C      t ||| | |td   t||td  | |t||   |td   || t|| | |t||   |td   || | |td   | S r  r'  r  r  r  r  r  @  r  r  c              	   C   rg  r  r)  r  r  r  r  r  D  r  r  c              	   C   :   t t| |t||   || |||td    ||S rX  r]  r   r!  r#  r%  r(  r&  r  r  r  r  r  H  rZ  r  c              	   C   rh  rX  r^  ri  r  r  r  r  L  rZ  r  c              	   C      t || td| |td   t| |t||   |td  |||td   |  ||t| |t||   | |||td   |td   td| |td   | S r;  r'  r=  r  r  r  r  P  r  r  c              	   C   rj  r;  r)  r=  r  r  r  r  T  r  r  c              	   C   N  t td|td |td  |td   t|| |t||   |td   |||td   td  ||t| |t||   |td  |td |td  td  |td | |||td    |td  |td   | t|| |t||   |td   || | |||td    |td   | S Nr  r'  r"  r'  r,  r  r  r  r  X     P r  c              	   C   rk  rl  r)  r,  r  r  r  r  \  rm  r  c              	   C   "  t tdtd|td  | |td   t| |t||   |||td   |td   ||t||||td   |td   td|td  | |td td   | t|| |t||    |||td   |td   td|td  | |td   | S Nr"  r'  r  r*  r'  rq  r  r  r  r  `     $ r  c              	   C   rn  ro  r)  rq  r  r  r  r  d  rp  r  c              	   C     t || td|  t|| |t||   |td   |||td   td  || t| |t||   |td  td| |td  |td  |td   | t|| |t||   |  td|td  | |||td     | S Nr'  r4  r"  r*  r'  r,  r  r  r  r  h  rB  r  c              	   C   rq  rr  r)  r,  r  r  r  r  l  rB  r  c              	   C     t |td |td | |  t||td  | |t||    |||td   |td   || t|||  |||td   |td   || |td   | t||td  | |t||    |||td   |td   |td | |  | S Nr4  r'  r3  r"  r'  r   r!  r#  r%  r(  r&  r)  r  r  r  r  r  p      r  c              	   C   rs  rt  r)  ru  r  r  r  r  t  rv  r  c	           	   
   C     t |td | |td  |td  t|| | |t||   |td   |||td   |  ||t |td |td | |  t||td  | |t||   |  |||td   |td   || t||td  | |t||   |  |||td   |td   |td | |  | t|| ||  | |t||   |td   |||td   |td   || |td   | S r  r'  r  r  r  r  r  x  rC  r  c	           	   
   C   rw  r  r)  r  r  r  r  r  |  rC  r  c	           	   	   C      t ||| |td   t||td  | |t||   |td   |||td   |  || t|| | |t||   |td   |||td   |td   || | |td   | S r  r'  r  r  r  r  r       r  c	           	   	   C   rx  r  r)  r  r  r  r  r    ry  r  c	           	   	   C      t || | |td  t||td  | |t||   |td   |||td   |  || t||td  | |t||   |  |||td   |td   ||td   | S r  r'  r  r  r  r  r    r  r  c	           	   	   C   rz  r  r)  r  r  r  r  r    r  r  c                 C      t ||td  t|| | |t||    t|||td    ||t || | |td  t||td  t|||td    || t||td  | |t||    t|||td    |td  | S r0  r  r  r   r  r  r  ri  r  r  r  r       r  c                 C   r{  r0  r  r  r   r  r  r  ri  r  r  r  r    r}  r  c	           	      C   D   t t|| | |t||   |  |||td   |  ||S rX  r]  r  r  r  r  r    rK  r  c	           	      C   r  rX  r^  r  r  r  r  r    rK  r  c	           	   
   C      t |t|| | |t||   |  |||td   |td   ||t |td | t||td  | |t||   |  |||td   |td   || S r  )r  r   r  r  r  r  r  r  r    r  r  c	           	   
   C   r  r  )r  r   r  r  r  r  r  r  r    r  r  c                 C   "  t |td |td |  t||td  | |t||   |  t|||td    ||t || ||  t||td  | |t||   |td   t|||td    || t||td  | |t||   |  t|||td    |td | |  | S Nr4  r'  r3  r|  r  r  r  r  r    rp  r  c                 C   r  r  r~  r  r  r  r  r    rp  r  c              
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   C      t t|td  |td  td t|||td    t| |t||   | |t|td  |td  td   ||S r0  rD  r,  r  r  r  r    r  r  c              
   C   r  r0  rE  r,  r  r  r  r    r  r  c                 C      t || | t| |t||   |td  |t|||td     ||t| |t||   | t|||td    ||  | S r  )r  r   r  r  r  r  r,  r  r  r  r    rb  r  c                 C   r  r  )r  r   r  r  r  r  r,  r  r  r  r    rb  r  c                 C   .  t |td |td  |td  t||td  | |t||   |  t|||td    ||t || | |td  t||td  | |t||   |td   t|||td    || t||td  | |t||   |  t|||td    ||td   | S r;  r|  r  r  r  r  r    r  r  c                 C   r  r;  r~  r  r  r  r  r    r  r  c	           	   
   C      t td| t||td  | |t||   |  |||td   |td   ||t || t||td  | |t||   |  |||td   |  || S rb  r0  r  r  r  r  r    r  r  c	           	   
   C   r  rb  r2  r  r  r  r  r    r  r  c	           	   
   C      t td| t|| | |t||   |  |||td   |td   ||t || t||td  | |t||   |  |||td   |  || S r  r0  r  r  r  r  r    rd  r  c	           	   
   C   r  r  r2  r  r  r  r  r    rd  r  c	           	   
   C   P  t ||| |td   t||td  | |t||   |td   |||td   |  || t ||td|  td  ||td   t||td  | |t||   |td   |||td   |  || t|| | |t||   |td   |||td   |td   || | |td   | S r  r'  r  r  r  r  r    rN  r  c	           	   
   C   r  r  r)  r  r  r  r  r    rN  r  c	           	   	   C   sr   t || td  ||  tt| ||  | t||  t|| td|  td   ||t|| |S r  )r  r  r+   r   r  r  r  r  r  r  r  r    r  r  c	           	   	   C   s   t ||tdd   t|td  |td  td  t|||td    t|| | |t||   |  |td  |td  td |  ||S r  rT  r  r  r  r  r       r  c	           	   	   C   sv   t || td  | |  tt| ||  | t|| td|  td   t||  ||t|| | S r  )r  r  r+   r   r  r  r  r  r  r  r  r       vr  c	           	   	   C   s   t ||  | | |tdd    t|td |td  td |td |td    t|||td    tt| ||  | t|| td|  td   t||  ||t|| | S rV  )r  r  r  r+   r   r  r  r  r  r  r  r  r    ry  r  c                 C      t || td| |td   t|||td   |td  |td  |td  td  || t| |t||   |||td   |td   td| |td   | S r0  r$  rq  r  r  r  r     r  r  c                 C   r  r0  r%  rq  r  r  r  r    r  r  c           	   	   C      t || |||td   |  |}t|| tt||td  |td  td  ||| t| |t||   || S r0  )r  r  r  r   r-  r  rx  r  r  r  r       &\r  c           	   	   C   r  r0  )r  r  r  r   r-  r  rx  r  r  r  r    r  r  c	           	   	   C   B   t t| |t||   | || |||td   |  ||S rX  r]  r  r  r  r  r    r-  r  c	           	   	   C   r  rX  r^  r  r  r  r  r    r-  r  c              
   C   h   t | t|| |||td   |  ||t |t|| |||td   |  t||  || S rX  rX  ru  r  r  r  r       hr  c              
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   
   C      t || ||t|||td      |}	t|| tt|	|td  |td  td  ||| t| |t||   |	| S r0  )r  r  r  r  r   r   r  r  r  r  r  r  ~     .\r  c	           
   
   C   r  r0  )r  r  r  r  r   r   r  r  r  r  r  r    r  r  c	           
   
   C      t || | |t||    |}	ttd| | tt|	| |||td    ||| t||t|||td     |	| S rX  )r  r  r  r  r   r   r  r  r  r  r  r       "fr  c	           
   
   C   r  rX  )r  r  r  r  r   r   r  r  r  r  r  r    r  r  c                 C   :  t || t| |t||   ||t|||td      ||t || | t|td | |t||    |td  |td  td  || t||td  | |t||   td  td | t| |t||   td ||t|||td      |||td    td|  | S r0  )r  r   r  r  r  r  r  r  r  r  r       < r  c                 C   r  r0  )r  r   r  r  r  r  r  r  r  r  r    r  r  c                 C   s~   t |  | td tdd |td   | | td |td tdd    t| td  |td  td  |S r  r   r  r  r   r$  r  r  r  r  r    r!  r  c                 C   s   t || |  | td tdd |td    | | td |td tdd    t| td  |td  td  |S r  r  r   r&  r$  r  r  r  r  r    r  r  c                 C   sB   t |  | td | td  | | td |td   |S r  r   r  r  r  r  r  r    r-  r  c                 C   sJ   t || |  | td | td   | | td |td   |S r  r  r  r  r  r  r     r  r   c                 C   sV   t || t|||  | |  | td  |td  td |td   ||S r0  r  r   r  r   r#  r%  r$  r)  r  r  r  r  r    r  r  c	           	      C   sf   t || t|||  | |  |||  |  | td  |td  td |td   ||S r0  r  )	r   r#  r%  r(  r,  r&  r$  r)  r  r  r  r  r    rI  r  c                 C   sj   t || t|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  c                 C   sV   t ||||  |  |  | td | td   | | td |td   |S r  r  r  r  r  r  r    r  r  c              	   C   sL   t || t|||   || | td |  t|t| |   ||S r  r  r   r  rN  r  r  r  r  r  r    s   Lr  c                 C   s   t td|td  ||  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    rc  r  c                 C   sV   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d |  t|t| |   ||S r  r  r  r   rN  r  r  r  r  r  r    r  r  c              	   C   \   t |  | | t|t| |   | | t|||td    |td td   |S r  )r  rN  r  r  r  r  r  r  r  r	    r  r	  c              	   C     t td|td  td| td  ||td td|td td     t|||td   |td  t|t| |   || t|||td   |td  td|  | |td  |  t|t| |   | | |td td|td td     | S Nr'  r"  r*  r  r  r  r   rN  r  r  r  r  r  r  r
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  c                 C   &   t t|t| |  | | |  |S r  )r  rN  r  r  r  r  r  r    r  r  c                 C   sZ   t || t| | td | | td  |td  td | td |   ||S r  r  r  r  r  r  r       Zr  c                 C   s\   t || t|  | td |  | td  |td  td |td |   ||S r  r  r  r  r  r  r    r  r  c                 C   sV   t || t|  | td | td |  | | td |td |   ||S r  r  r  r  r  r  r    r  r  c                 C   sT   t ||td  t|||td   | td |  | | td |  ||S r0  r  r  r  r  r  r    rS  r  c                 C   sX   t || td  t|||td   |td |  |  | td |   ||S r0  r  r  r  r  r  r    rT  r  c              	   C   s   t |t| |||td   t|  | td  |td  td t|   t| td  |td  td | t|t| |   ||S r0  r  r%   r  r&   r   rN  r  r  r  r  r  r       r  c              	   C   s`   t |  | | td t|t| |   |t|||td    |td td   |S Nr"  r'  r4  )r  r  rN  r  r  r  r  r  r  r    r  r  c              	   C   s   t | | | td| |td   t|||td   | t|t| |   || t|||td   |td  t|t| |   td| |td   | S r0  r  r  r  r  r  r    r  r  c                 C   sp   t |||td   |td  |  | | td  t|t| |   | | | |td td   |S r;  )r  r  rN  r  r  r  r  r  r    r   r  c              	   C   s  t |td td|  td ||td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  td|  | |td  |  t|t| |   | | |td td|td td     | S )Nr'  r  r"  r  r  r  r  r  r    rv  r  c                 C   sb   t || t|| | | 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  c                 C   sd   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|| |  | td | td |   | | td |td |   ||S r  r  r  r  r  r  r       ^r  c              	   C   s\   t ||td  t|| |||td   | td |   | | td |  ||S r0  r  r  r  r  r  r  
  r  r  c              	   C   s`   t || td  t|| |||td   |td |   |  | td |   ||S r0  r  r  r  r  r  r    r  r  c              	   C   s   t |t| |||td   t|  | td  |td  td t|   t|| | td  |td  td |  t|t| |   ||S r0  r  r  r  r  r  r    r  r  c                 C   sZ   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d   t|  |  | td t|   | | td t|   t||  | td | td |   | | td |td |   ||S r0  )r  r%   r  r&   r   r  r  r  r  r    r  r  c              	   C   s   t |t| |||td   t|  | td  |td  td t|   t|| td  |td  td |  t|t| |   ||S r0  r  r  r  r  r  r    r  r  c              	   C   sb   t || t||td |   | td  |td  td |  t|t| |   ||S r0  r  r  r  r  r  r  "  r  r  c              	   C   sb   t || t|tdtd| |   |  tdtd| |   |  t|t| |   ||S r  r  r  r  r  r  r   &  r  r   c              	   C   s   t |td|  |||td   |  |  | td |   | | td |   t||td |   |  | td |  | | td |  t|t| |   ||S r0  r  r  r  r  r  r!  *  r  r!  c              	   C   s   t |td|  |||td   |  ||td  | td |   t||td |   ||td  | td |  t|t| |   ||S r0  r  r  r  r  r  r"  .  r  r"  c                 C   sZ   t |  | || |  td | td  | | || |  td |td   |S r  r  r  r  r  r  r#  2  r  r#  c              
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   C   s   t ttd||   tdd |td   td||   |td tdd    |td ttd|td | td     ||td|  S r  r+   r   r  r  r  r  r  r  r*  N  r  r*  c              	   C   s   t t|| td  td||   tdd |td    td||   |td tdd    ttd|td | td    ||td|  S Nr3  r"  r'  r  r  r  r  r  r+  R  r  r+  c                 C   s^   t ttd||   | td  td||   |td   |td  ||td|  S r  r+   r   r  r  r  r  r  r,  V  r  r,  c                 C   sd   t t|| td  td||   | td   td||   |td   ||td|  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d |td    td||   |td tdd    ttd|td | td    ||td| | S rb  )r  r  r+   r   r  r  r  r  r  r.  ^  r  r.  c              	   C   s   t || td| |  tt|| td  td||   | td   td||   |td   ||td| | S rb  r  r  r  r  r  r/  b  r  r/  c                 C   sJ   t |||  | | | td  t|t| |   | |td   |S r  r  r  rN  r  r  r  r  r  r0  f  r  r0  c              	   C   sJ   t || t|||  |||  td |  t|t| |   ||S r  r  r   r  rN  r  r  r  r  r  r1  j  r  r1  c              	   C   sv   t ||  |||  |  |||  td |   t|||  |||  td |  t|t| |   ||S r  r  r  r   rN  r  r  r  r  r  r2  n  r  r2  c              	   C   sr   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  r3  r  r  r3  c              
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   C   s   t |td |  tdtd| td |td    |   |||td   |  t||td|   tdtd| td |td    |  t|t| |   ||S r0  r  r  r  r  r  rB    r  rB  c                 C   s|   t | td |  ||  t||td |   | | td | td |   | | td |td |   ||S r8  r  r  r  r  r  rC    r5  rC  c              	   C   sr   t || tttd||   | td |  td||   |td |   |td  ||td| | S r  r  r  r  r  r  rD    r  rD  c              	   C   sx   t || tt|| td  td||   | td |   td||   |td |   ||td| | S r  r  r  r  r  r  rE    r  rE  c              	   C   s   t || ||  td| |  tt|| td  td||   | td |   td||   |td |   ||td| | S rb  r  r  r  r  r  rF    rb  rF  c              
   C   s   t |t| tdtd| td |td    t|   |||td   t|  t|tdtd| td |td    |  t|t| |   ||S r  )r  r%   r  r&   r   rN  r  r  r  r  r  rG    rd  rG  c                 C   s>   t td|td  t|t|t|| ||     ||S r  r  r  r  r  r  rH    r`  rH  c                 C   s   t || ||   |td  tdtd|| ||     |td   | | || |  td | td   t| | || |  td | td  | | || |  td |td   ||S r;  r  r  r  r  r  rI    r  rI  c                 C   s  t td || td   || td   | tt|td|  |td|  td | td   | | |td|  |  | td   td |  ||tdtd|| ||     | td  tdtd|| ||     |td   |S )Nr  r4  r'  r3  r"  r  r  r  r  r  rJ        rJ  c                 C   s   t || ||   |td  tdtd|| ||     |td   | | || |  td | td   t|||  | | | || |  td | td   | | || |  td |td   ||S r;  r  r  r  r  r  rK    s   rK  c	           	      C   s  t |td| td   | | ||  td | ||   |td   | ||  | ||  td  |td   |  ||  td |td   | ||  td | td   t||  ||  td | td |   | ||  td |td |   ||S r  r  r  r  r  r  rL    s    rL  c	           	   	   C   r  r0  r  r  r  r  r  rM    r  rM  c                 C   r  r  )r   rN  r  r  r  r  r  rN    r(  rN  c                 C   r  r  r  r  r+   r   r  r  r  r  r  rO    rZ  rO  c                 C   r  r  r  r  r+   r   r  r  r  r  r  rP    rZ  rP  c                 C   "   t | |t|||    | |S r  r  r  r  r  r  rQ    r  rQ  c                 C   r  r  r  r  r  r  r  rR    r  rR  c	           	   	   C   r  r  r  r|  r  r  r  rS    r  rS  c	           	   	   C   r  r  r  r|  r  r  r  rT    r  rT  c	           	      C   2   t | |t|||    | |||  |  |S r  r  r|  r  r  r  rU       2rU  c	           	      C   r  r  r  r|  r  r  r  rV    r  rV  c
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   C   s2   t tt|| t| ||td    | |S rX  )r  r  r  r  r  r   r!  r#  r  r  r  r  rk  R  r  rk  c              
   C   s4   t tt|| t| ||td    | | S rX  )r  r  r  r  r  r  r  r  r  rl  V  r+  rl  c              	   C   sF   t t|| t| ||td    |td  ||td   |S r0  )r  r  r  r  r   r!  r#  r&  r  r  r  r  rm  Z  rk  rm  c              	   C   sH   t t|| t| ||td    |td  ||td   | S r0  )r  r  r  r  r  r  r  r  rn  ^  r/  rn  c                 C   z   t t| ||td   t|||td    tt|| t| ||td    | t| ||td    ||S rX  rD  ri  r  r  r  ro  b     zro  c                 C   r  rX  rE  ri  r  r  r  rp  f  r  rp  c              	   C   t   t |||td   | |}t| tttd| td  |td  td  |||| tt| | || S r0  )r  r  r  r   r  r   r#  r%  r$  r  r.  r  r  r  rq  j     Vrq  c              	   C   r  r0  )r  r  r  r   r  r  r  r  r  rr  o  r  rr  c              
   C      t |ttttfrdS z0t||}ttt|t	t
|ttt||td  t||t|tdtd   }W n ttfyG   Y dS w |rLdS dS NFr'  r"  T)r  r  r  r  r  rQ  r  r6   r   r  r^   rA   r   r  r  r  r  	TypeErrorAttributeErrorr$  r.  r  r  tmpresr  r  r  rs  t     
Vrs  c              
   C   s   t ||}tt|| tdt||td  |  tt|td|td ttttdt	| td|  td  t
||| |||||S rl  )rQ  r  r  r  r3   r  r+   r   r-  r  r   r$  r.  r  r  r  r  r  r  rt    s   
rt  c              
   C   r  r  )r  r  r  r  r  rQ  r  r6   r   r  r^   r@   r   r  r  r  r  r  r  r  r  r  r  ru    r  ru  c              
   C   s   t ||}tt|| tdt||td  |  tt|td|td ttttd t	|td  | td  t
||| |||||S rl  )rQ  r  r  r  r3   r  r+   r   r-  r  r   r  r  r  r  rv    s   
rv  c              
   C   d   t |t||ttd|  td| |   | |  ||t|t||t| ||     | S rX  r  r   rN  r  r  r  r  r  r  r  r  rw    r  rw  c              
   C   r  rX  r  r   rN  r  r  r  r  r  r  r  r  rx    r  rx  c              
   C   f   t |t|| ttd|  td| |   | |  ||t|t||t| ||     | S rX  r  r  r  r  r  ry    rI  ry  c              
   C   r  rX  r  r  r  r  r  rz    rI  rz  c                 C   0  t || | td  t|ttd|  td| |   | | | | td ttd|  td| |    td  ||t ||| td  t|ttd|  td| |   || || td ttd|  td| |    td  || t|t||t| ||     | S r  r  r  r   rN  r  r  r  r  r  r  r  r{       2 r{  c                 C   r  r  r  r  r   rN  r  r  r  r  r  r  r  r|    r  r|  c                 C   2  t || | td  t|ttd|  td| |   | | | | td ttd|  td| |    td  || t ||| td  t|ttd|  td| |   || || td ttd|  td| |    td  || t|t||t| ||     | S r  r  r  r  r  r  r}       4 r}  c                 C   r  r  r  r  r  r  r  r~    r  r~  c              
   C      t |||td   t|||  |td  |ttd|  td| |   | |  ||t|||  |td  t||t| ||     ||td   | S r  r  r  r  r  r  r    rV  r  c              
   C   r  r  r  r  r  r  r  r    rV  r  c              
   C      t |||td   t|||  |td  | ttd|  td| |   | |  ||t|||  |td  t||t| ||     ||td   | S r  r  r  r  r  r  r    r  r  c              
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   C   t   t t| t||ttdt |  tdt | |   | t|   ||t|t||t| ||     | S rX  r  r  r   rN  r  r  r  r  r  r  r  r  r       tr  c              
   C   r  rX  r  r  r   rN  r  r  r  r  r  r  r  r  r    r	  r  c              
   C   v   t t| t|| ttdt |  tdt | |   | t|   ||t|t||t| ||     | S rX  r  r  r  r  r  r    r  r  c              
   C   r  rX  r
  r  r  r  r  r    r  r  c                 C   p  t t| | t|  td  t|ttdt |  tdt | |   | t|  | t|  td ttdt |  tdt | |    td  ||t t| |t|  td  t|ttdt |  tdt | |   |t|  |t|  td ttdt |  tdt | |    td  || t|t||t| ||     | S r  r  r  r  r   rN  r  r  r  r  r  r  r  r  
  r@  r  c                 C   r  r  r  r  r  r   rN  r  r  r  r  r  r  r  r    r@  r  c                 C   r  t t| | t|  td  t|ttdt |  tdt | |   | t|  | t|  td ttdt |  tdt | |    td  || t t| |t|  td  t|ttdt |  tdt | |   |t|  |t|  td ttdt |  tdt | |    td  || t|t||t| ||     | S r  r  r  r  r  r  r    ro  r  c                 C   r  r  r  r  r  r  r  r    ro  r  c              
   C      t t| ||td   t|||  |td  |ttdt |  tdt | |   | t|   ||t|||  |td  t||t| ||     ||td   | S r  r  r  r  r  r  r       r  c              
   C   r  r  r  r  r  r  r  r    r  r  c              
   C      t t| ||td   t|||  |td  | ttdt |  tdt | |   | t|   ||t|||  |td  t||t| ||     ||td   | S r  r  r  r  r  r  r  "  r  r  c              
   C   r  r  r  r  r  r  r  r  &  r  r  c                 C     t t| | t|  td  ||td   t|||  |td  ttdt |  tdt | |   | t|  | t|  td ttdt |  tdt | |    td  ||t t| |t|  td  ||td   t|||  |td  ttdt |  tdt | |   |t|  |t|  td ttdt |  tdt | |    td  || t|||  |td  t||t| ||     ||td   | S r  r  r  r  r  r  r  *      r  c                 C   r  r  r  r  r  r  r  r  .  r  r  c                 C     t t| | t|  td  ||td   t|||  |td  ttdt |  tdt | |   | t|  | t|  td ttdt |  tdt | |    td  || t t| |t|  td  ||td   t|||  |td  ttdt |  tdt | |   |t|  |t|  td ttdt |  tdt | |    td  || t|||  |td  t||t| ||     ||td   | S r  r  r  r  r  r  r  2      r  c                 C   r  r  r  r  r  r  r  r  6  r  r  c                 C   B   t t|t| | td| td   || t|t|  | S r  )r   r-  r  r  r  r  r  r  r  r  r  :  r-  r  c                 C   r  r  )r   r-  r  r  r  r  r  r  r  r  r  >  r-  r  c              	   C      t |||td   tt|||  |td  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  B  rU  r  c              	   C   r  r  )r  r  r   r-  r  r  r  r  r  r  r  r  F  rU  r  c                 C   r  r  r  r  r  r  r  r  J  r  r  c              	   C   Z   t ||}t|tt|t|| td|td   ||| t| |t|  || S r  )r  r  r   r-  r  r  r  r  r  r  r  r  S     
Pr  c                 C   r  r  r  r  r  r  r  r  Y  r  r  c              	   C   r  r  )r  r  r   r-  r  r  r  r  r  r  r  r  b  r  r  c              	   C   s   t t| | td ttd| | td   ttdt|  | td t| | td   ||t|t| |  | S r  r  r  r  r   r  r   r#  r  r  r  r  r  h  r	  r  c                 C   sd   t td|  ttd|ttdtd| td |td      ||t|t| |  | S r  r  r  r   r  r  r  r  r  r  r  r  l  r  r  c                 C   sH   t td| tt| ||  | t| t| ||t|| | S r  r  r  r+   r   r  r  r   r  r  r  r  r  p  r/  r  c                 C   sH   t td| tt| ||  | t|t|  ||t|| | S r  r  r  r+   r   r  r  r  r  r  r  r  r  t  r/  r  c                 C   0   t t| |t||   | ||td|  S r  )r+   r   r  r  r  r  r  r  r  x  r?  r  c                 C   r   r  )r+   r   r  r  r  r  r  r  r  |  r?  r  c              	   C   s   t |t|| td  ttd|| td   |td  t|| t| | td t|| td   ||t||td  | |t||    |td  | S r  r  r  r  r  r  r    r  r  c                 C   s   t |||td   t||td  ttdtd|td |td     ||t||td  | |t||    |td  | S r  r  r  r  r  r  r    rb  r  c              	   C   sb   t || td  tt| ||  | tdt| |td   t| ||t|| | S r
  r  r  r+   r   r  r  r   r  r  r  r  r    r  r  c              	   C   sb   t || td  tt| ||  | tdt| |td   t| ||t|| | S r
  r  r  r  r  r  r    r  r  c                 C   &   t || | |t||   |  |S r  r  r  r  r  r  r    r  r  c                 C   r"  r  r  r  r  r  r  r    r  r  c              
   C   s   t |||td   | |}t|t|| td  ttd|| td   tt||t| | td  t|| td   |||t| |t||   || S r0  r  r  r  r  r   r-  r   r5  r  r  r  r    s   r  c                 C   s   t |||td   | |}t|| | t|td  |td   tt||t|td  |td  td   ||| t| |t||   || S r  r  r  r  r  r   r-  r  r5  r  r  r  r    s   r  c                 C   b   t t|td | td  | |t||   |  ||td  | |  ||td|  S Nr'  r3  r"  r+   r   r  r  r=  r  r  r  r    r  r  c                 C   r%  r&  r+   r   r  r  r=  r  r  r  r    r  r  c              
   C   z   t t|td | tt|td | td  | |t||   |  ||td  | |  ||td| | S r&  r  r=  r  r  r  r    r  r  c              
   C   r)  r&  r  r=  r  r  r  r    r  r  c              
   C      t t|||td   |t||td  |   tt|td | td  | |t||   |  ||td  | |  ||td| | S r&  r  r=  r  r  r  r    rU  r  c              
   C   r*  r&  r  r=  r  r  r  r    rU  r  c                 C   r\  rX  r   r   r  r=  r  r  r  r    r^  r  c                 C   r\  rX  r   r  r  r=  r  r  r  r    r^  r  c              	   C   s   t |t|| td  ttd|| td   td| |td   t|||td   |td  |t| | td  t|| td   ||t| |t||   |||td   |td   td| |td   | S r  r  rq  r  r  r  r    rF  r  c              
   C   s   t || | td| t|td  |td   |td   t|||td   |td  |t|td  |td  td   || t| |t||   |||td   |td   td| |td   | S r;  )r  r  r  r   r  r  rq  r  r  r  r    s   r  c           	   
   C   s   t || |||td   |  |}t|t|| td  ttd|| td   tt||t| | td  t|| td   |||t| |t||   || S r0  r#  rx  r  r  r  r    s   &r  c           	      C   s   t || |||td   |  |}t|| | t|td  |td   tt||t|td  |td  td   ||| t| |t||   || S r  r$  rx  r  r  r  r    r  r  c	           	      C   f   t t|| td|  td  | |t||   |  ||td  | |  ||td|  S r&  r'  r  r  r  r  r    rI  r  c	           	      C   r-  r&  r(  r  r  r  r  r    rI  r  c	           	   
   C   ~   t t|td | tt|| td|  td  | |t||   |  ||td  | |  ||td| | S r&  r  r  r  r  r  r    r!  r  c	           	   
   C   r.  r&  r  r  r  r  r  r    r!  r  c	           	   
   C      t t|||td   |t||td  |   tt|| td|  td  | |t||   |  ||td  | |  ||td| | S r&  r  r  r  r  r  r    r  r  c	           	   
   C   r/  r&  r  r  r  r  r  r    r  r  c	           	      C   r  rX  r+  r  r  r  r  r    r`  r  c	           	      C   r  rX  r,  r  r  r  r  r    r`  r  c                 C   sp   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   s`   t tdttd| ||  td  | ||    |t| ||  t| ||   | | S Nr"  r3  )r   r  r  r  r  r  r  r  r  r    r  r  c              	   C   sD   t td| tt|| t| t| ||t| ||  | S r  r  r  r  r  r  r    rK  r  c              	   C   sD   t td| tt|| t|t|  ||t| ||  | S r  r  r  r  r  r  r     rK  r  c              
   C   s  t ttdtdttd| td   tt| ||    |   t| ||   |t ttdttd| td  td tt| ||    |   t| ||   | t ttdttd t| ||    t| ||   | t ttdtdttd| td   tt| ||    |  | t ttdttd| td  td tt| ||    |  | t ttdttd t| ||    td | S r  )r  r  r  r  rN  r   r  r  r  r  r  r    r  r  c              
   C   s  t ttdtdt| td td  tt| ||   |   t| ||   |t ttdt| td td td tt| ||   |   t| ||   | t ttdttd t| ||    t| ||   | t ttdtdt| td td   tt| ||   |  | t ttdt| td td td  tt| ||   |  | t ttdttd t| ||   td | t t| ||  td | S r  )r  r  r  r  rN  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d    t|td t|td   ||td| ||   |t|| td  ||td   ||td   |  |td    t| ||   |td  | S r
  )r  r  r+   r   r  r  r   r   r!  r&  r  r  r  r  r    r  r  c              
   C   s  t || td  |td  tt|| td  |  | |td  |  | td |td    t|td td  ||td| ||   |t|| td  ||td   ||td   |  |td    t| ||   |td  | S r  )r  r  r+   r   r  r  r  r1  r  r  r  r    r  r  c              	   C   sd   t || td  tt|| |  tdt|  |  t| t| ||t| ||  | S r
  r!  r  r  r  r  r    r  r  c              	   C   sd   t || td  tt|| |  tdt|  |  t|t|  ||t| ||  | S r
  r  r  r  r  r  r    r  r  c                 C   r   r  r)  r  r  r  r  r    r(  r  c                 C   r   r  r'  r  r  r  r  r     r(  r  c                 C   s~   t td|  tt|  | td | | td  ||  | td   ||tt||  | t|tt| |  | S r  )r  r  r   r  r  r  rN  r   )r   r  r  r  r  r  $  r!  r  c              
   C   s   t ||  t||  ||t |t| ||  td  ttd| ||  td   |  t||  t|  ||  td t| ||  td   || t|tt| ||   | S r  )r  r   r  r  r  rN  r   r   r)  r  r  r  r  r  (  r  r  c                 C   sP   t td|  t||  ||tttd|td |  | td   | S r  r  r  r   r  r2  r  r  r  r  ,  r  r  c                 C   sR   t ttd| |td  ttd| |td  |  td|  |  |S r  r  r  r  r  r  r  0  rQ  r  c                 C   s.   t ttd|td  td|  |  |S r0  r  r  r  r  r  r  4  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  r2  r  r  r  r  8  r  r  c              
   C   s   t || |td   t|||  ||t |t| ||  td  t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  rN  r   r   r&  r)  r  r  r  r  r  <  r   r  c              	   C   sZ   t td|  t|||  ||t|| ttd|td |  | td    | S r  r3  r4  r  r  r  r  @  r  r  c                 C   sZ   t ||  ttd| |td  ttd| |td  |  td|  |  |S r  r  r  r  r  r  r  D  r  r  c                 C   s6   t ||  ttd|td  td|  |  |S r0  r  r  r  r  r  r  H  r^  r  c                 C   s   t ttd| td  | ttdtd|    ttdtd|     tt|t| | | ttd| td    |||t|t|  | S r  r  r  r  r   r-  r  r  r   r  r  r  r  r  L  r  r  c              
   C   sf   t | t| td   tt|t| | | t| td  td   ||| t|t|  | S r  r  r  r  r   r-  r  r  r  r  r  r  r  r  P  rI  r  c                 C   s   t |ttd|td   || ttdtd|   ttdtd|   |td   tt|||  |td  t|| |ttd|td    |||t| |t|  |||  |td   ||td   | S r  r5  r  r  r  r  r  T  rg  r  c              
   C   s   t || |t|td   |td   tt|||  |td  t|| |t|td  td   ||| t| |t|  |||  |td   ||td   | S r;  r6  r  r  r  r  r  X  r  r  c                 C   r  r  r  r  r  r  r  r  \  r  r  c                 C   s   t ||}t|ttd|td   |ttdtd|   ttdtd|    tt|t|| |ttd|td    |||t| |t|  || S r  )r  r  r  r  r   r-  r  r   r  r  r  r  r  e  s   
r  c                 C   r  r  r  r  r  r  r  r  k  r  r  c              
   C   sz   t ||}t|| t|td   tt|t|| |t|td  td   ||| t| |t|  || S r  )r  r  r  r  r   r-  r  r  r  r  r  r  r  t  s   
pr  (  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rN  r  r  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r  A_B_C_F_G_H_r  b_r  rL  e_rv  g_h_i_j_k_l_r  r9  r_  q_r_t_r  rI  s_w_r6  y_z_a1_a2_b1_b2_c1_c2_rN  rO  n1_n2_e1_e2_f1_f2_g1_g2_n3_Pq_Pm_r  Qm_Qr_Qx_jn_mn_non2_r  RGx_r  iiPqqQRrr/  kr.  	_UseGamma	ShowStepsStepCounterr  r7  r8  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rM  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  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  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rJ  rK  rL  rM  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  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  r  r  r  r  r  r  r  r  r  <module>   s              n"JjB.
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