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mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmHZHmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmÐZÐmĐZĐmŐZŐmƐZƐmǐZǐmZmȐZȐmɐZɐmʐZʐmːZːm̐Z̐m͐Z͐mΐZΐmϐZϐmАZАmѐZѐmҐZҐmӐZӐmԐZԐmՐZՐm֐Z֐mאZאmؐZؐmِZِmڐZڐmېZېmܐZݐmސZߐmZmZmZ ddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZ ddlmZmZ dd	lmZmZmZmZmZmZmZm Z  dd
lmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZ ddlmZmZmZmZmZmZmZ ddlmZ dd dD \ZZZZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6dd dD \Z7Z8Z9Z:Z;Z<Z=Z>Z?Z@ZAZBZCZDZEZFZ?Z@ZGZHZIZJZKZLZMZNZOZPZQZRed\	ZSZTZUZVZWZXZYZZZ[dZ\dZ]dZ^dd Z_dd Z`dd Zadd Zbdd Zcdd  Zdd!d" Zed#d$ Zfd%d& Zgd'd( Zhd)d* Zid+d, Zjd-d. Zkd/d0 Zld1d2 Zmd3d4 Znd5d6 Zod7d8 Zpd9d: Zqd;d< Zrd=d> Zsd?d@ ZtdAdB ZudCdD ZvdEdF ZwdGdH ZxdIdJ ZydKdL ZzdMdN Z{dOdP Z|dQdR Z}dSdT Z~dUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddĄ ZddƄ ZddȄ Zddʄ Zdd̄ Zdd΄ ZddЄ Zdd҄ ZddԄ Zddք Zdd؄ Zddڄ Zdd܄ Zddބ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  ZԐdd ZՐdd Z֐dd Zאdd Zؐd	d
 Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX Z dYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Z	dkdl Z
dmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z dd Z!dd Z"dd Z#dd Z$dd Z%dd Z&dd Z'dd Z(dd Z)dd Z*dd Z+dd Z,dd Z-dd Z.dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd Z5dÐdĄ Z6dŐdƄ Z7dǐdȄ Z8dɐdʄ Z9dːd̄ Z:d͐d΄ Z;dϐdЄ Z<dѐd҄ Z=dӐdԄ Z>dՐdք Z?dאd؄ Z@dِdڄ ZAdېd܄ ZBdݐdބ ZCdߐd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd  ZTdd ZUdd ZVdd ZWdd ZXd	d
 ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd  Zdd!d" Zed#d$ Zfd%d& Zgd'd( Zhd)d* Zid+d, Zjd-d. Zkd/d0 Zld1d2 Zmd3d4 Znd5d6 Zod7d8 Zpd9d: Zqd;d< Zrd=d> Zsd?d@ ZtdAdB ZudCdD ZvdEdF ZwdGdH ZxdIdJ ZydKdL ZzdMdN Z{dOdP Z|dQdR Z}dSdT Z~dUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdÐdĄ ZdŐdƄ ZdǐdȄ Zdɐdʄ Zdːd̄ Zd͐d΄ ZdϐdЄ Zdѐd҄ ZdӐdԄ ZdՐdք Zdאd؄ Zdِdڄ Zdېd܄ Zdݐdބ ZÐdߐd ZĐdd ZŐdd ZƐdd Zǐdd ZȐdd Zɐdd Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd  ZԐdd ZՐdd Z֐dd Zאdd Zؐd	d
 Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX Z dYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Z	dkdl Z
dmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z dd Z!dd Z"dd Z#dd Z$dd Z%dd Z&dd Z'dd Z(dd Z)dd Z*dd Z+dd Z,dd Z-dd Z.dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd Z5dÐdĄ Z6dŐdƄ Z7dǐdȄ Z8dɐdʄ Z9dːd̄ Z:d͐d΄ Z;dϐdЄ Z<dѐd҄ Z=dӐdԄ Z>dՐdք Z?dאd؄ Z@dِdڄ ZAdېd܄ ZBdݐdބ ZCdߐd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd  ZTdd ZUdd ZVdd ZWdd ZXd	d
 ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd  Zdd!d" Zed#d$ Zfd%d& Zgd'd( Zhd)d* Zid+d, Zjd-d. Zkd/d0 Zld1d2 Zmd3d4 Znd5d6 Zod7d8 Zpd9d: Zqd;d< Zrd=d> Zsd?d@ ZtdAdB ZudCdD ZvdEdF ZwdGdH ZxdIdJ ZydKdL ZzdMdN Z{dOdP Z|dQdR Z}dSdT Z~dUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdÐdĄ ZdŐdƄ ZdǐdȄ Zdɐdʄ Zdːd̄ Zd͐d΄ ZdϐdЄ Zdѐd҄ ZdӐdԄ ZdՐdք Zdאd؄ Zdِdڄ Zdېd܄ Zdݐdބ ZÐdߐd ZĐdd ZŐdd ZƐdd Zǐdd ZȐdd Zɐdd Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd  ZԐdd ZՐdd Z֐dd ZdS (  z
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGammaWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  I/usr/lib/python3/dist-packages/sympy/integrals/rubi/rules/inverse_trig.py
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||	|c|e|d
}t|tփ}ttܐttdtdtdtdtߐt   t|||c|ftt؃}t|tك}ttܐttdtdtdtdtt   t|||c|gttڃ}t|tۃ}ttܐtttdtd tdtd tdtd tdtd t||||}t|t݃}tttdtdtdtdtttdtd   tdtd t||||}t|t߃}ttܐtttdtd tdtd tdtd t t|||||h}t|t}tttdtdtdtdtttdtd   t t|||||h}t|t}ttܐtttdtd tdtd tdtd tdtd tttdtd   t||||
||i|}t|t}tttdtdtdtdtttdtd   tdtd tttdtd   t||||
||i|}t|t}ttܐtttdtd tttdtd   t||
||j|k}t|t}ttܐtttdtd ttdtd tdtd  t||
||l}t|t}ttܐtttdtd ttdtd tdtd  t||
||l}t|t}ttܐttttdtd tdtd  ttdtd tdtd  t||||
||m}t|t}ttܐttdtdtttdtd   ttdtd tdtd  t||||
||m}t|t}ttttdtd tdtd tdtd tttdtd tdtd tdtd  t||||
|||(}t|t}ttttdtd tdtd tdtd tdtdtdtdtttdtd    t||||
|||(}t|t}ttܐtttdtd tdtd tdtd t t t||||n|^}t|t}tttdtdtdtdtttdtd   t t t||||n|^}t|t}ttttd	td tttdtd tdtd tdtd t  t|||||n|^|	}t|t}ttttd	td tdtdtdtdtttdtd   t  t|||||n|^|	}t|t}tttttdtd  tdtd tttdtd tdtd tdtd tdtd  t||||
||E}t|t}tttttdtd  tdtd tdtdtdtdtttdtd   tdtd  t||||
||E}t|t}ttttdtd tdtd tdtd tttdtd tdtd tdtd tdtd  t||||
||||"	}t|t}ttttdtd tdtd tdtd tdtdtdtdtttdtd   tdtd  t||||
||||"	}t|t}ttttd	td tttdtd tdtd tdtd tdtd  tttdtd   t||||
||i||o|J
}t|t}ttttd	td tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||i||o|J
}t|Đt}ttܐtttdtd tdtd tdtd tdtd ttttdtd    t||||
||i|}t|Ɛt}tttdtdtdtdtttdtd   tdtd ttttdtd    t||||
||i|}t|Ȑt}tttt$ tttdtd tdtd tdtd tdtd  tttdtd   t||||
||i||o|0
}t|ʐt}tttt$ tdtdtdtdtttdtd   tdtd  tttdtd   t||||
||i||o|0
}t|̐t}ttttd	td tttdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
||| ||p
}t|ΐt}ttttd	td tttdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||| ||p
}t|Аt}ttttd	td ttdtd tdtd tdtd  tttdtd tdtd tdtd tdtd  t||||
|||||q
}t|Ґt}ttttd	td ttdtd tdtd tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||||q
}t|Ԑt}tttttd
 tdtd  tdtd tttdtd tdtd tdtd  t||||
||r|s|	}t|֐t}tttttd
 tdtd  tdtd tdtdtdtdtttdtd    t||||
||r|s|	}t|ؐt}tttttd
 tdtd  tdtd tttdtd tdtd tdtd t  t||||
||r|||^
}t|ڐt}tttttd
 tdtd  tdtd tdtdtdtdtttdtd   t  t||||
||r|||^
}t|ܐt }tttdtttd
 tdtd  tttdtd tdtd tdtd   t||||
||r}t|ސt}tttdtttd
 tdtd  tdtdtdtdtttdtd     t||||
||r}t|t}ttܐtttdtd tdtd tdtd tdtd tttd
 tdtd   t||||
|||r|	}t|t}tttdtdtdtdtttdtd   tdtd tttd
 tdtd   t||||
|||r|	}t|t}ttܐtttdtd tdtd tdtd ttttd
 tdtd   t||||
||r|}t|t}tttdtdtdtdtttdtd   ttttd
 tdtd   t||||
||r|}t|t}ttܐtttdtd tdtd tdtd tdtd ttttd
 tdtd   t||||
||r||	}t|t}tttdtdtdtdtttdtd   tdtd ttttd
 tdtd   t||||
||r||	}t|t}ttܐtttdtd tdtd tdtd tdtd ttttd
 tdtd   t||||
||r||	}t|t	}tttdtdtdtdtttdtd   tdtd ttttd
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||r||	}t|t
}ttܐtttdtd tdtd tdtd tdtd tttd
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  t||||
||r| |	}t|t}tttdtdtdtdtttdtd   tdtd tttd
 tdtd  td
  t||||
||r| |	}t|t}ttܐtttdtd tdtd tdtd tttd
 tdtd  tdd
   t||||
||r}t|t}tttdtdtdtdtttdtd   tttd
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||r}t|t}tttttd
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||r|s||
}t|t}tttttd
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||r|s||
}t|t}ttܐtttdtd tdtd tdtd t tttd
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||r| |^	}t|t}tttdtdtdtdtttdtd   t tttd
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||r|||^|}t|t}tttttd
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||r|||
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||r|||
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|||r|t|
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t|
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|||r|t|
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|||r|t| 
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|||r|t|%
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||l}t|t}ttܐttttdtd tdtd  ttd
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||m}t|t}ttܐttdtdtttdtd   ttd
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||m}t|t}ttttd
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||u}t|t}ttttd
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||u}t|t }tttttd
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|| |}t|t!}tttttd
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|| |} t| t"}!ttttd
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||||"	}"t|"t#}#ttttd
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||||"	}$t|$t$}%tttt$ tttdtd tdtd tdtd tdtd  tttd
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||/||5	}&t|&t%}'tttt$ tdtdtdtdtttdtd   tdtd  tttd
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||/||5	}(t|(t&})tttt$ tttdtd tdtd tdtd tdtd  tttd
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||/||0	},t|,t(}-ttttttdtd tdtd tdtd tdtd  tttd
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||r|/||5
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||r|/||0
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||r|/||0
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  t||||
||r| ||_
}Nt|Nt9}Ottttdtdtdtdtttdtd   t  tttd
 tdtd  td
  t||||
||r| ||_
}Pt|Pt:}Qttttd
 tttd
 tdtd  t
  tttdtd tdtd tdtd  t||||
||r|s||w
}Rt|Rt;}Sttttd
 tttd
 tdtd  t
  tdtdtdtdtttdtd    t||||
||r|s||w
}Tt|Tt<}Uttttd
 tttdtd tdtd tdtd tdtd  tttd
 tdtd  td
  t||||
||r| |	}Vt|Vt=}Wttttd
 tdtdtdtdtttdtd   tdtd  tttd
 tdtd  td
  t||||
||r| |	}Xt|Xt>}Ytttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd  t||||
||r|x|s|
}Zt|Zt?}[tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd    t||||
||r|x|s|
}\t|\t@}]tttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd t  t||||
|||r|x|||^}^t|^tA}_tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   t  t||||
|||r|x|||^}`t|`tB}attttd	td tttd
 tdtd  tdtd  tttdtd tdtd tdtd t  t||||
||||r|x| |}bt|btC}cttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   t  t||||
||||r|x| |}dt|dtD}ettttd	td tttd
 tdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
||||r|)| ||	}ft|ftE}gttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||||r|)| ||	}ht|htF}itttt$ ttttd
 tdtd   tttdtd tdtd tdtd  t||||
|||r|y	}jt|jtG}ktttt$ ttttd
 tdtd   tdtdtdtdtttdtd    t||||
|||r|y	}lt|ltH}mtttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
|||r|| |z}nt|ntI}otttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
|||r|| |z}pt|ptJ}qtttt$ tttd
 tdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
|||r|s|||{}rt|rtK}stttt$ tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||r|s|||{}tt|ttL}utttt$ tttdtd tdtd tdtd tdtd  ttttd
 tdtd   t||||
||r|/||5
}vt|vtM}wtttt$ tdtdtdtdtttdtd   tdtd  ttttd
 tdtd   t||||
||r|/||5
}xt|xtN}yttܐtttdtd tdtd tdtd tttttd
 tdtd    t||||
||r|}zt|ztO}{tttdtdtdtdtttdtd   tttttd
 tdtd    t||||
||r|}|t||tP}}ttܐtttdtd tdtd tdtd t tttttd
 tdtd    t||||
||r||	}~t|~tQ}tttdtdtdtdtttdtd   t tttttd
 tdtd    t||||
||r||	}t|tR}ttܐtttdtd tdtd tdtd tdtd tttttd
 tdtd    t||||
||r||	}t|tS}tttdtdtdtdtttdtd   tdtd tttttd
 tdtd    t||||
||r||	}t|tT}ttܐtttdtd tdtd tdtd tdtd ttd
 ttttd
 tdtd    t||||
||r| |	}t|tU}tttdtdtdtdtttdtd   tdtd ttd
 ttttd
 tdtd    t||||
||r| |	}t|tV}tttt$ tttdtd tdtd tdtd tdtd  ttttd
 tdtd   t||||
||r|/||0||}t|tW}tttt$ tdtdtdtdtttdtd   tdtd  ttttd
 tdtd   t||||
||r|/||0||}t|tX}tttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
||r|}||5|~}t|tY}tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
||r|}||5|~}t|tZ}tttt$ tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
||r|}||N|~}t|t[}tttt$ tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
||r|}||N|~}t|t\}ttttd	td tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
||r|1|||}t|t]}ttttd	td tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
||r|1|||}t|t^}ttttd	td tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
|||r|||}t|t_}ttttd	td tttd
 tdtd  t
  tttdtd tdtd tdtd tdtd  t||||
|||r|||}t|t`}ttttd	td tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
|||r||| }t|ta}ttttd	td tttd
 tdtd  t
  tdtdtdtdtttdtd   tdtd  t||||
|||r|||%}t|tb}tttttd
 tdtd tdtd tdtd  tttdtd tdtd tdtd  t||||
|||(}t|tc}tttttd
 tdtd tdtd tdtd  tdtdtdtdtttdtd    t||||
|||(}t|td}ttttd	td ttd
 tdtd tdtd tdtd  tttdtd tdtd tdtd  t||||
||||	}t|te}ttttd	td ttd
 tdtd tdtd tdtd  tdtdtdtdtttdtd    t||||
||||	}t|tf}ttttd	td tttd
 tdtd  tdtd  tttdtd tdtd tdtd tdtd  t||||
||| ||
}t|tg}ttttd	td tttd
 tdtd  tdtd  tdtdtdtdtttdtd   tdtd  t||||
||| ||
}t|th}ttttd	td ttttdtd tdtd   tttd
 tdtd  tdtd  t||||
||||	}t|ti}ttttd	td ttdtdtttdtd    tttd
 tdtd  tdtd  t||||
||||	}t|tj}ttttd	td ttd
 tdtd tdtd tdtd  tttdtd tdtd tdtd tdtd  t||||
|||||q
}t|tk}ttttd	td ttd
 tdtd tdtd tdtd  tdtdtdtdtttdtd   tdtd  t||||
|||||q
}t|tl}ttܐtttdtd tdtd tdtd tdtd tmt tttd
 tdtd   t||||
||r| ||
}t|tn}tttdtdtdtdtttdtd   tdtd tot tttd
 tdtd   t||||
||r| ||
}t|tp}ttܐtttdtd tdtd tdtd tdtd tmt tttd
 tdtd   t||||
||r| ||
}t|tq}tttdtdtdtdtttdtd   tdtd tot tttd
 tdtd   t||||
||r| ||
}t|tr}ttܐtttdtd tdtd tdtd tdtd tt tttd
 tdtd   t||||
||r| ||
}t|ts}tttdtdtdtdtttdtd   tdtd tt tttd
 tdtd   t||||
||r| ||
}t|tt}ttܐtttdtd tdtd tdtd tdtd tt tttd
 tdtd   t||||
||r| ||
}t|tu}tttdtdtdtdtttdtd   tdtd tt tttd
 tdtd   t||||
||r| ||
}t|Đtv}ttܐtttdtd tdtd tdtd tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|Ɛtx}tttdtdtdtdtttdtd   tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|Ȑty}ttܐtttdtd tdtd tdtd tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|ʐtz}tttdtdtdtdtttdtd   tdtd twt
t tttd
 tdtd   t||||
|||r| ||}t|̐t{}tttdtttd
 tdtd  tttdtd tdtd tdtd  tdtdtdtdtttdtd     t||||
||r}t|ΐt|}ttܐtttdtd tdtd tdtd tdtd tdtdtdtdtttdtd   td	td  tttd
 tdtd   t||||
||r|S|	}t|Аt}}ttܐtttdtd tdtd tdtd td	td tdtdtdtdtttdtd   tdtd  tttd
 tdtd   t||||
||r|S|	}t|Ґt~}ttܐtttdtd tttdtd tdtd   t|||
|n|}t|Ԑt}ttܐtttdtd tttdtd tdtd   t|||
|n|}t|֐t}ttܐtttdtd tdtd tdtd tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ؐt}tttdtdtdtdtttdtd   tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ڐt}ttttd	td tttdtd tdtd tdtd  tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ܐt}ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|ސt}ttttd	td tttdtd tdtd tdtd  tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|t}ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|	}t|t}ttttd	td tttdtd tdtd tdtd  tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|4|
}t|t}ttttd	td tdtdtdtdtttdtd    tdtdtdtdtttd
 tdtd tdtd    t||||
||&|'|4|
}t|t}ttttttdtd tdtd tdtd td
  tdtdtdtdttttd
 tdtd     t||||
||&|'|	}t|t}ttttdtdtdtdtttdtd   td
  tdtdtdtdttttd
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||&|'|	}t|t}ttܐtttttdtd  t||}t|t}ttttd	td tttttdtd   t|||}t|t}ttܐttttdtd tdtd t|||}t|t}ttttd	td ttttdtd tdtd  t||||}t|t}ttܐtttdtd  tdtd tdtd ttttdtd tdtd  t|||
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}t|t݃}ttttdtd tdtd t$ tܐtttdtd  tdtd tdtd t  t||||
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}t|tރ}ttttdtd tdtd t$ tdtdtdtdtސtttdtd    t  t||||
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||&||	}t|t
}ttttdtd tdtd td	td ttdtdtdtdtttdtd tdtd    t||||
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zvv~~xx~~xxxx||||||||~~nnvv~~LLRR||VVFFTTrrdd^^ZZZ^^^^^bbbbbb^^^``@@ttppjjffrrJJVVNNrrDLLdd||RRdd~~vv||rr||ppvvvv~~||zzTTll~~vv~~~~||ttzzTT2F>Rzzxjjrprbltbbltt~vvzrtrt|VXl@2F>R@Lztnf|tbpttx|x|XVXl^^VVZZRR66BBJJ``ttvvBB::^^^^^^^^>>FFppxx^^^^^^^^ttNNP((88((NNLL\\``ll006644FFHHvvllttLL             R r  c              	   C   s   t || | t|| |t||   |td   t|td  |td  td  || t|| |t||   |  | S Nr	  r  r  )r  r   r	  r  r  r  r  r  r  r  xr  r  r  r       r  c              	   C   s   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  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  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 r  r  r  r   r  r  r  r  r  r  r  r       r  c              
   C   N   t td||  tt|| t| | ||   ||| |t||   |S Nr  r  r  r+   r   r  r	  r  r  r  r  r       Nr  c              
   C   r  r  r  r  r+   r   r  r  r  r  r  r  r    r  r  c                 C   s.   t t| ||  | t| ||t|| S N)r+   r   r  r	  r  r  r  r  r       .r  c                 C   s0   t t| ||  | t| ||t||  S r  )r+   r   r  r  r  r  r  r  r       0r  c              	   C   s   t || | ||td   t|| |td  | |t||   |td   t|td  |td  td  || t|| |td  | |t||   |  ||td   | S Nr  r	  r  r  r  r  r  r  r  r  r  r  r  r  r       r  c              	   C   s   t || | ||td   t|| |td  | |t||   |td   t|td  |td  td  ||t|| |td  | |t||   |  ||td   | S r  r  r  r  r  r  r       r  c              	   C   s   t || | |td  t||td  | |t||   |td   t|td  |td  td  || t||td  | |t||   |  |td  | S r  r  r  r  r  r  r  r  r  r  r  r       r  c              	   C   s   t || | |td  t||td  | |t||   |td   t|td  |td  td  ||t||td  | |t||   |  |td  | S r  r  r  r  r  r  r       r  c                 C   s   t || td  ||td   ttt| ||  |td  ||td t|td   t||td   |||t|| | t|| | |t||   |td   t|td  |td  td  || |td   | S Nr	  r  r  )	r  r  r+   r   rd  r  r	  r  r  r  r  r  r  r       r  c                 C   s   t || td  ||td   ttt| ||  |td  ||td t|td   t||td   |||t|| | t|| | |t||   |td   t|td  |td  td  || |td   | S r  )	r  r  r+   r   rd  r  r  r  r  r  r  r  r  r    r  r  c              
   C   sb  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  r    s   d r  c              
   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  r    s   b r  c                 C   sP   t || td  tt| ||  | t||  t| ||t|| |S Nr	  r  r  r+   r   r  r  r	  r  r  r  r  r       Pr  c                 C   sR   t || td  tt| ||  | t| t||  ||t|| | S r  r  r  r+   r   r  r  r  r  r  r  r  r        Rr   c                 C   *   t || | | |t||   |  |S r  r   r	  r  r  r  r  r!       *r!  c                 C   r  r  r   r  r  r  r  r  r"    r  r"  c                 C   s.   t t| |t||   || t|  |S r  )r  r  r	  r  r  r  r  r  r  r  r  r  r  r$    r  r$  c                 C   s0   t t| |t||   || t|  | S r  )r  r  r  r  r  r  r  r  r%    r  r%  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  r&       Br&  c                 C   sD   t | |t||   |td  || t| |td   | S r  )r  r  r  r  r  r  r  r  r'       Dr'  c              	   C      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  r(       r(  c              	   C   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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*  c              
   C   |   t |||td   | |}t|| 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+  ,     ^r+  c              
   C   sP  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 Nr  r  r	  r  r  r  r   r	  r  r  r  r  r  r,  1     R r,  c              
   C   sP  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  r-  5  r  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||   |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  r  r  r   r  r  r  r  r.  9      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||   |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  r/  =  r  r/  c              
   C   s   t || | t| t|| |t||   |td   |||td    || t|| |t||   |  |t|||td     | S Nr	  r  )r  r  r   r	  r  r  r  r  r  r  r0  A     r0  c              
   C   s   t || | t| t|| |t||   |td   |||td    ||t|| |t||   |  |t|||td     | S r  )r  r  r   r  r  r  r  r  r  r  r1  E     r1  c              
   C   s   t || | t|td  |td  td  |t|||td     t|| |t||   |td   |td  |td  td  || t|| |t||   |  |t|||td     | S r  r  r  r  r  r  r2  I  s   r2  c              
   C   s   t || | t|td  |td  td  |t|||td     t|| |t||   |td   |td  |td  td  ||t|| |t||   |  |t|||td     | S r  r  r  r  r  r  r3  M     r3  c              
   C   s  t td| 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| |td   | S Nr  r  r  r	  r  r  r  r  r  r5  Q      r5  c              
   C   s  t td| 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| |td   | S r  r  r  r  r  r  r6  U  r  r6  c                 C   sB   t td||  tt| ||  | t| ||t|| |S r  r  r  r  r  r  r7  Y  r  r7  c                 C   sD   t td||  tt| ||  | t| ||t|| | S r  r  r  r  r  r  r8  ]  r  r8  c              	   C   sT  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  r9  a  s   V r9  c              	   C   sV  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  r:  e  s   X r:  c              	   C   sR   t || | tt| ||  | t|td| td   ||t|| |S r  )r  r+   r   r  r  r	  r  r  r  r  r;  i  r  r;  c              	   C   sT   t || | tt| ||  | t|td| td   ||t|| | S r  )r  r+   r   r  r  r  r  r  r  r  r<  m     Tr<  c                 C      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  r=  q     r=  c                 C   r  r  )r  r  r  r   r  r  r  r  r  r>  u  r  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@  c                 C   :   t t| |t||   | |||td   | ||S Nr  r   r   r	  r  r  r  r  r  rA       :rA  c                 C   r  r  r   r   r  r  r  r  r  r  rB    r  rB  c                 C   6   t | |t||   | |||td   |  |S r  r   r	  r  r  r  r  r  rC       6rC  c                 C   r  r  r   r  r  r  r  r  r  rD    r  rD  c
           
   	   C      t |||	  t| |||	  t|  || || |	td   t|   t| |t||	   | || || |	td   |  |	|	S r  r  r&   r  r   r	  
r  r  r  r  r  r  r  r  r   r  r  r  r  rF       rF  c
           
   	   C   r  r  r  r&   r  r   r  r  r  r  r  rG    r  rG  c                 C   s@   t td| tt| ||  | t| ||t|| | S r  r  r  r+   r   r  r	  r  r  r  r  rH       @rH  c                 C   s>   t td| tt| ||  | t| ||t|| |S r  r  r  r+   r   r  r  r  r  r  r  rI       >rI  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  rJ    s   ( rJ  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  rK       * rK  c                 C   sF   t td| tt| ||  | t|t|  ||t|| |S r  r  r  r  r  r  rL       FrL  c                 C   sH   t td| tt| ||  | t|t|  ||t|| | S r  r  r  r  r  r  rM       HrM  c
           
   	   C   sH  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  r  
r  r  r  r  r  r  r  r  r   r  r  r  r  rO    s   J rO  c
           
   	   C   sF  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  r  r  r  r  r  rP    s   H rP  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 Nr  r	  r  )r  r   r	  r  r  r  r  r  r  r  r   r  r  r  r  rQ    r  rQ  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 r  )r  r   r  r  r  r  r  r  r  rR    r  rR  c	           	   	   C   sB  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  rS       D rS  c	           	   	   C   sB  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  rT    r  rT  c	           
   
   C      t || | |||td   |  |}	t|| 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  r  r  rU       *`rU  c	           
   
   C      t || | |||td   |  |}	t|| tt|	t|td  |td  td  |||t| |t||   |	| S r  r  r  r  r  r  rV       *^rV  c           	      C   s   t || |td  |td  td |  |}t|| | |t||    ||t|| ||  tt|t|td  |td  td  ||| S r  )r  r  r  r	  r   r-  r  	r  r  r  r  r  r  r   r  r  r  r  r  rW       4nrW  c           	      C   s   t || |td  |td  td |  |}t|| | |t||    ||t|| ||  tt|t|td  |td  td  ||| S r  )r  r  r  r  r   r-  r  r  r  r  r  rX    r  rX  c           	   
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   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	           	   
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           
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   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  r  r  r  r  r  r]        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  r  r  r  r  r  r^    r  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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  r  r  r  r  r  rq  A	      rq  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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  r  r  r  r  r  rr  E	  r  rr  c
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   	   C   sf  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  r  r  r  r  r  rs  I	  s   h rs  c
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   C   sZ  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  r  r  r  r  r  rw  Y	  s    ^ rw  c
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   C   sX  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  r  r  r  r  r  rx  ]	  s    \ rx  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  ry  a	     lry  c	           	   	   C   sn   t || td  ||  tt| ||  | t|td| td   t||  ||t|| | S r  r  r  r  r  r  rz  e	     nrz  c	           	   	   C      t |t| |||td   t|  |td  |td  td t|   t|| | |t||   |  |td  |td  td |  ||S r  r  r%   r  r&   r   r	  r  r  r  r  r{  i	     r{  c	           	   	   C   r  r  r  r%   r  r&   r   r  r  r  r  r  r|  m	  r  r|  c
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      C   B   t ||	 | | |t||	   |  |||	td   |  |	S r  r  r  r  r  r  r  	  r  r  c
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   C   sj   t | |}t|| 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  r  r  r  r  r  	  s   
`r  c              
   C   sh   t | |}t|| 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   r0  r  r*  r1  r  r  r  r  	  r2  r  c           	   
   C   sz   t | |||  |  |}t|| 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  r  r  	  s   `r  c           	   
   C   sx   t | |||  |  |}t|| tt|t|td  |td  td  |||t||t||   || S r  r/  r3  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  	  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  r4  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 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   :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 r  )r  r  r  r   r-  r  r  r5  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   r6  r  r*  r7  r  r  r  r  	  r8  r  c
              
   C   s   t |||	td   | |||	  |  |	}
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  	  s   .fr  c
              
   C   s   t |||	td   | |||	  |  |	}
t|| tttdt|td  |	td  td  |
|	|	|	t| |t||	   |
|	 S r  )r  r  r  r   r  r  r9  r  r  r  r   
  s   .dr  c                 C   J   t t| |t||
   | |||
td   |	  |||
  | |
|
S r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  
     Jr  c                 C   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  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  r  r=  r  r  r  r  
  s    r  c              	   C   n   t t| |t||
   | t|||
td    |||
td   |	tdd   |||
  |  |
|
S Nr  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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   |	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  !
  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  c
           
   	   C   s\   t || td  t| tt| ||	  | || |t|	  |  |	|	t||	 |	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  1
  r,  r  c              	   C   n   t t| |t||
   | t|||
td    |||
td   |	tdd   |||
  |  |
|
S r  r  r;  r  r  r  r  5
  r  r  c              	   C   rC  r  r   r;  r  r  r  r  9
  r  r  c                 C      t |t|	 |||
td   t|	  |td  |
td  td t|	   t| |t||
   | |||
  |  |td  |
td  td |	  |
|
S r  r  r;  r  r  r  r  =
     r  c                 C   rD  r  r  r;  r  r  r  r  A
  rE  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  E
     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  rF  r  r  r  r  I
  r  r  c              	   C      t |t|
 |||td   t|
  |td  |td  td t|
   t| |t||   |	 |td  |td  td |
  t||||  |   ||S r  )r  r%   r  r&   r   r	  r  r$  r  r  r  r  M
  r  r  c              	   C   rH  r  )r  r%   r  r&   r   r  r  r$  r  r  r  r  Q
  r  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  U
  s   &f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  rI  r  r  r  r  Z
  s   &dr  c
           
      C   D   t t| |t||	   | |||	  |  |||	  |  |	|	S r  r(  r=  r  r  r  r  _
  r  r  c
           
      C   rJ  r  r*  r=  r  r  r  r  c
  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  g
     

r  c              
   C   sj   t ||}t|| tt|t|td  |td  td  ||| t| |t||   || S r  r-  rQ  r  r  r  r  p
  s   
`r  c                 C   rK  rL  rM  rQ  r  r  r  r  v
  rS  r  c              
   C   sh   t ||}t|| tt|t|td  |td  td  |||t| |t||   || S r  r/  rQ  r  r  r  r  
  s   
^r  c	           
      C   `   t |ttttfrdS t| ||t||   |  |||td   |  |}	t|	r.dS dS NFr  T	rN  rO  r  rP  r  r   r	  r  r)   
r  r  r  r  r  r  r  r   r  r  r  r  r  r  
     :r  c	           
      C   D   t | ||t||   |  |||td   |  |}	t|	|S r  r   r	  r  r   rW  r  r  r  r  
     :
r  c	           
      C   rT  rU  	rN  rO  r  rP  r  r   r  r  r)   rW  r  r  r  r  
  rX  r  c	           
      C   rY  r  r   r  r  r   rW  r  r  r  r  
  r[  r  c              	   C   l   t |ttttfrdS t| ||t||   |	  |||||td   |
   |  |}t|r4dS dS rU  rV  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  
     Fr  c              	   C   P   t | ||t||   |	  |||||td   |
   |  |}t||S r  rZ  r_  r  r  r  r  
     F
r  c              	   C   r^  rU  r\  r_  r  r  r  r  
  r`  r  c              	   C   ra  r  r]  r_  r  r  r  r  
  rb  r  c                 C   >   t |ttttfrdS tt|| | | |}t|rdS dS rL  )rN  rO  r  rP  r  r   r	  r)   r  r  r  r  r  r  r  r  r  
     r  c                 C   "   t t|| | | |}t||S r  )r   r	  r   rd  r  r  r  r  
     
r  c                 C   rc  rL  )rN  rO  r  rP  r  r   r  r)   rd  r  r  r  r  
  re  r  c                 C   rf  r  )r   r  r   rd  r  r  r  r  
  rg  r  c                 C   r0  r  r(  r  r  r  r  r  r  r  r  r  r  
  r2  r  c                 C   r0  r  r*  rh  r  r  r  r  
  r2  r  c                 C   V   t |ttttfrdS t|||td   | t|| |  | |}t|r)dS dS rU  )	rN  rO  r  rP  r  r   r  r	  r)   r  r  r  r  r  r   r  r  r  r  r  r  
     0r  c                 C   :   t |||td   | t|| |  | |}t||S r  )r   r  r	  r   rj  r  r  r  r  
     0
r  c                 C   ri  rU  )	rN  rO  r  rP  r  r   r  r  r)   rj  r  r  r  r  
  rk  r  c                 C   rl  r  )r   r  r  r   rj  r  r  r  r  
  rm  r  c	           	   	   C   >   t t|||td   | | ||t||   |  ||S r  )r   r   r  r	  	r  r  r  r  r  r  r  r   r  r  r  r  r    r  r  c	           	   	   C   rn  r  )r   r   r  r  ro  r  r  r  r  	  r  r  c                 C   "   t || |t||   |  |S r  r  r  r  r  r  r  r  r  r  r  r       "r  c                 C   rp  r  r  rq  r  r  r  r    rr  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    r  r  c                 C   rs  r  r  r  r+   r   r  ru  r  r  r  r    r  r  c	           	   	   C   `   t td| tt| |t|  | || | | | ||  |  |  |||||  |S r  rt  r   r  r  r  r       `r  c	           	   	   C   rw  r  rv  r   r  r  r  r  !  rx  r  c
           
   
   C   j   t td| tt||t|	  | ||	td  |td  ||td   |  |	|	|||	  |	S r  rt  
r  r  r  r  r  r  r  r  r   r  r  r  r  r  %  r  r  c
           
   
   C   ry  r  rv  rz  r  r  r  r  )  r  r  c              
   C      t td| tt||t|  |
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   C   l   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   r  r  r  r  r  r+   r   r  r  r  r  r  r    r  r  c                 C   sd   t td| tt||||   t|t||  | t||   t| ||t| ||  |S r  )	r  r  r+   r   r   r  r  r  r	  r  r  r  r  r  r  r  r  r  r  r       dr  c                 C   sf   t td| tt||||   t|t||  | t||   t| ||t| ||  | S r  )	r  r  r+   r   r   r  r  r  r  r  r  r  r  r       fr  c                 C   s  t |t| td |td  td|  | t|||td     |td |   t|td  | td |td  td|  | t|||td     |td |    t|td|  t|||td    ||   t|||td   t| td |td  td|  | t|||td     |td |    || t|t| |t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d  td|  | t|||td     |td |   t|td  | td |td  td|  | t|||td     |td |    t|td|  t|||td    ||   t|||td   t| td |td  td|  | t|||td     |td |    ||t|t| |td  |t|||td      | S r  )r  r  r  r   r  r  r~  r  r  r  r    s    r  c                 C   sF   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    r  r  c                 C   sD   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  r  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  r       r  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  c                 C   rK  rL  rM  r  r  r  rR  r  wr  r  r  r    rS  r  c              
   C   s^   t ||}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  r    s   
Tr  c                 C   rK  rL  rM  r  r  r  r  r    rS  r  c              
   C   s\   t ||}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  r    s   
Rr  c              	   C   s~   t || | t|| |t||   |td   |td |td  td  || t|| |t||   |  | S r  )r  r   r>   r  r  r  r  r  r  r       ~r  c              	   C   s|   t || | t|| |t||   |td   |td |td  td  ||t|| |t||   |  | S r  )r  r   r
  r  r  r  r  r  r  r       |r  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  r  c              	   C   s   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  r	    r  r	  c              	   C   s   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  r
    rG  r
  c              
   C   s   t tttdt t|  |||   t|  | |  | td|  |t tttdt t|  |||   t|  | |  | td|  | t t| | | t|||   | | S r  )r  r  r  r  r>   r  r  r  r  r  r  r  r  r       r  c                 C   sv   t ttd ttt |  | td |||   ||t ttd ttt|  | td |||   || S r  r  r  r  r   r  r  r  r  r  r       vr  c              	   C   st   t ttd tttdt| |   |||   ||t ttd tttdt| |   |||   || S r  r  r  r  r  r  r       t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   s   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>   r  r  r  r  r    r  r  c                 C   s   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
  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d |td  td  || ttd| |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   s   t td| | | t| |t||   |td  ttdtdt | | t    |td |td  td  ||ttd| |t||   |  ttdtdt | | t    | S r  )r  r  r   r
  r  r  r  r  r  r  r  r       r  c              	   C   s   t || | |td  t||td  | |t||   |td   |td |td  td  || t||td  | |t||   |  |td  | S r  r  r  r   r>   r  r  r  r  r  r       r  c              	   C   s   t || | |td  t||td  | |t||   |td   |td |td  td  ||t||td  | |t||   |  |td  | S r  r  r  r   r
  r  r  r  r  r  r    rE  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||   | |||  |  |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 || t||td  | |t||   |  |||   || S r  r  r  r   r>   r  r  r  r  r  +  r  r  c              
   C   r  r  r  r  r   r
  r  r  r  r  r  /  r  r  c              	   C   s   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  3  r  r  c              	   C   s   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  7     r  c              
   C   |   t td| t|| | |t||   |  ||t || t||td  | |t||   |  |||   || S r  r  r  r  r  r  r  ;  r  r  c              
   C   r  r  r  r  r  r  r  r  ?  r  r  c	           	      C   <   t t|| | |t||   |  |||  |  ||S r  r  r  r  r  r  r   C  r  r   c	           	      C   r  r  r  r  r  r  r  r!  G  r  r!  c	           	      C   6   t || | |t||   |  |||  |  |S r  r  r  r  r  r  r"  K  r  r"  c	           	      C   r  r  r  r  r  r  r  r#  O  r  r#  c              	   C   s   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  r  r  r  r  r$  S     r$  c              	   C   s   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  r  r  r  r  r%  W  r  r%  c              
   C   s  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  r	  r  r  r  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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 r  r  r  r  r  r  r'  _  r  r'  c                 C   s0   t tt| |t||   ||| |  |S r  )r  r  r   r>   r  r  r  r  r(  c  r  r(  c                 C   s2   t tt| |t||   ||| |  | S r  )r  r  r   r
  r  r  r  r  r)  g     2r)  c                 C   s>   t | |t||   |td  || | |td   |S r  )r  r>   r  r  r  r  r  r*  k  r  r*  c                 C   s@   t | |t||   |td  || | |td   | S r  )r  r
  r  r  r  r  r  r+  o  r  r+  c              
   C   s   t t| ttdt tt| | td  tt | | td   |t|  |t t| ttdttt| | td  tt | | td   |t|  | t td t | |t||    ttt| | td tt | | td   |t|  | S r  )r  r  r  r  r  r>   r  r  r  r  r,  s     " r,  c              
   C   s"  t t| ttdt tt| | td  tt | | td   |t|  | t t| ttdttt| | td  tt | | td   |t|  | t td t | |t||    ttt| | td tt | | td   |t|  | S r  )r  r  r  r  r  r
  r>   r  r  r  r  r-  w     $ 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.  {  r  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/    r  r/  c              	   C      t t|td |td  td t|||td    t| |t||   | t|td |td  td  ||S r  r  r  r  r   r>   r  r  r  r  r0    r  r0  c              	   C   r  r  r  r  r  r   r
  r  r  r  r  r1    r  r1  c              	   C   s   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 r  r  r  r  r  r  r2    s   r2  c              	   C   s   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 r  r  r  r  r  r  r3    s   r3  c              
   C   sd   t ||| t|||td     |t || |t||    |t|||td     | S r  )r  r  r  r>   r  r  r  r  r4    r  r4  c              
   C   sf   t ||| t|||td     | t || |t||    |t|||td     | S r  )r  r  r  r
  r  r  r  r  r5    r  r5  c              	   C   s  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  r  r  r  r  r6    r>  r6  c              	   C   s  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 r  r  r  r  r  r  r7    r>  r7  c              
   C   s   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  r	  r  r  )r  r  r   r>   r  r  r  r  r  r  r8       r8  c              
   C   s   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 r  )r  r  r   r
  r  r  r  r  r  r  r9    r  r9  c              
   C   s  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  r	  r  r  r  r  r  r  r  r:        r:  c              
   C   s  t td| td td| |td   t| |t||   | |||td   |t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 r  r  r  r  r  r  r;    r  r;  c              	   C   s   t td| |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<    s   r<  c              	   C   s   t td| |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=    r&  r=  c              	   C   sT   t || | tt| ||  | t|td | td   ||t|| |S Nr  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  r  r  r  r   r>   r  r  r  r  r?    r  r?  c              	   C   sV   t || | tt| ||  | t|td | td   ||t|| | S r  )r  r+   r   r  r  r
  r  r  r  r  r@    s   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|| | S Nr  r  r  )r  r  r  r+   r   r  r
  r  r  r  r  rA    rG  rA  c              
   C   s   t ttd ttt |  | td |||td    ||t ttd ttt|  | td |||td    || S r  r  r  r  r  r  rB    r  rB  c              
   C   s   t ttd tttdt| |   |||td    ||t ttd tttdt| |   |||td    || S r  r  r  r  r  r  rC    r  rC  c              
   C   X   t | ttd|||td    ||t |tt|| |||td    || S r  r  r   r  r>   r  r  r  r  rD       XrD  c              
   C   r  r  r  r   r  r
  r  r  r  r  rE    r  rE  c              	   C   sx   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  rF    s   ZrF  c              	   C   sv   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  rG    s   XrG  c                 C   <   t t| |t||   | |||td   |  ||S r  r   r   r>   r  r  r  r  r  rH    r  rH  c                 C   r  r  r   r   r
  r  r  r  r  r  rI    r  rI  c                 C   r  r  r   r>   r  r  r  r  r  rJ    r  rJ  c                 C   r  r  r   r
  r  r  r  r  r  rK    r  rK  c              
   C      t td| t||td  | |t||   |  ||t || t||td  | |t||   |  |||td    || S Nr  r  r  r  r  r  r  r  rL       rL  c              
   C   r  r  r  r  r  r  r  rM    r  rM  c              
   C      t td| t|| | |t||   |  ||t || t||td  | |t||   |  |||td    || S r  r  r  r  r  r  rN    r  rN  c              
   C   r  r  r  r  r  r  r  rO    r  rO  c                 C   s   t td||  t| |t||   | | | t  || tt| |t||   |td   || |td   | S r  )r  r  r   r>   r  r  r  r  r  r  rP       rP  c                 C   s   t td||  t| |t||   | | | t  || tt| |t||   |td   || |td   | S r  )r  r  r   r
  r  r  r  r  r  r  rQ  	  r  rQ  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  rR       rR  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  rS    r  rS  c              
   C   r  r  r  r  r  r  r  rT    r  rT  c              
   C   r  r  r  r  r  r  r  rU    r  rU  c                 C   sx   t t| t| |t||   | ||| t   ||tt| |t||   |td   || |td   | S r  )r  r  r   r>   r  r  r  r  r  r  rV       xrV  c                 C   sx   t t| t| |t||   | ||| t   ||tt| |t||   |td   || |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  rX  %  r  rX  c              
   C   r  r  r  r  r  r  r  rY  )  r  rY  c              	   C   s   t ||| | |td   t||td  | |t||   |td   || t|| | |t||   |td   || | |td   | S r  r  r  r  r  r  rZ  -  r  rZ  c              	   C   s   t ||| | |td   t||td  | |t||   |td   ||t|| | |t||   |td   || | |td   | S r  r  r  r  r  r  r[  1  r%  r[  c              	   C   :   t t| |t||   || |||td    ||S r  r  r  r  r  r  r  r  r  r  r  r  r\  5  r  r\  c              	   C   r  r  r  r  r  r  r  r]  9  r  r]  c              	   C   s   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^  =  rA  r^  c              	   C   s   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_  A  rB  r_  c              	   C   sR  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`  E     T r`  c              	   C   sR  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 r  r  r  r  r  r  ra  I  r  ra  c              	   C   s$  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  r  r  r  r  rb  M     & rb  c              	   C   s$  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 r  r  r  r  r  r  rc  Q  r  rc  c              	   C   s  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  r	  r  r  r  r  r  r  r  rd  U  s    rd  c              	   C   s  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 r  r  r  r  r  r  re  Y  s    re  c              	   C   s  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 Nr	  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  rf  ]      rf  c              	   C   s  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 r  r  r  r  r  r  rg  a  r  rg  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||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  rh  e      rh  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||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  ri  i  r  ri  c	           	   	   C   s   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  rj  m  r  rj  c	           	   	   C   s   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  rk  q  r  rk  c	           	   	   C   s   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  rl  u  r  rl  c	           	   	   C   s   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  rm  y  r  rm  c                 C   s   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 r  r  r  r   r>   r  r  r  r  r  r  rn  }     rn  c                 C   s   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 r  r  r  r   r
  r  r  r  r  r  r  ro    r  ro  c	           	      C   D   t t|| | |t||   |  |||td   |  ||S r  r  r  r  r  r  rp    r  rp  c	           	      C   r  r  r  r  r  r  r  rq    r  rq  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  rr    r  rr  c	           	   
   C   r  r@  )r  r   r
  r  r  r  r  r  rs    r  rs  c                 C   s$  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 Nr	  r  r  r  r  r  r  r  rt    r  rt  c                 C   s$  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 r  r  r  r  r  r  ru    r  ru  c              
   C   s  t td | |t||    ttt| | td tt | | td   t| |t t| ttdtt| | td  tt | | td   t| | t t| ttdtt| | td tt | | td   t| | S r  )r  r  r>   r  r  r  r  r  r  r  r  rv       
 rv  c              
   C   s  t td | |t||    ttt| | td tt | | td   t| |t t| ttdtt| | td  tt | | td   t| | t t| ttdtt| | td tt | | td   t| | S r  )r  r  r
  r  r  r  r  r  r  r  r  rw    r  rw  c                 C   sB   t tdt| tt| ||  | t| ||t|| |S r  )r  r  r  r+   r   r  r>   r  r  r  r  rx    r  rx  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  ry    r  ry  c              
   C      t t|td |td  td t|||td    t| |t||   | |t|td |td  td   ||S r  r  r  r  r  r  rz    r  rz  c              
   C   r  r  r  r  r  r  r  r{    r  r{  c                 C   s   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|    r  r|  c                 C   s   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}    r  r}  c                 C   s0  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~       2 r~  c                 C   s0  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      t td| t||td  | |t||   |  |||td   |td   ||t || t||td  | |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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   r  r  r  r  r  r  r  r    r  r  c	           	   
   C   sP  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    r  r  c	           	   
   C   sN  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    s   P 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  r  r  r  r  r  r    r  r  c	           	   	   C   st   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  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 r  )r  r  r  r+   r   r  r  r
  r  r  r  r  r    r  r  c                 C   s   t || td| |td   t|||td   |td  |td |td  td  || t| |t||   |||td   |td   td| |td   | S r  r  r  r  r  r  r    r  r  c                 C   s   t || td| |td   t|||td   |td  |td |td  td  ||t| |t||   |||td   |td   td| |td   | S r  r  r  r  r  r  r    r  r  c           	   	   C   s   t || |||td   |  |}t|| tt||td |td  td  ||| t| |t||   || S r  )r  r  r  r   r-  r>   r  r  r  r  r    s   &Zr  c           	   	   C   s~   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    s   &Xr  c	           	   	   C   B   t 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   h   t | t|| |||td   |  ||t |t|| |||td   |  t||  || S r  r  r  r  r  r  r       hr  c              
   C   r  r  r  r  r  r  r  r    r  r  c	           	      C   >   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dd t| |t||   | ttd|  |||td    || t tdd t| |t||   | t|td  |||td    || S r  r  r  r   r>   r  r  r  r  r  r  r  r  r  r  r  r  r       r  c              
   C      t tdd t| |t||   | tttdtd|  | |||td    || t tdd t| |t||   | tttdtd|  | |||td    || S r  r  r  r   r
  r  r-  r  r  r  r  r    r  r  c              
   C   r  r  r  r  r  r  r  r    r  r  c              
   C   r  r  r  r  r  r  r  r  #  r  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    || tt| |t||   |  ttdttd|  td| |  | S r  r  r  r  r   r>   r  r   r  r  r  r  r  r  '  rA  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    ||tt| |t||   |  ttdttd|  td| |  | S r  r  r  r  r   r
  r  r   r  r  r  r  r  r  +  rB  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    ||tt| |t||   |  ttdttd|  td| |  | S r  r  r  r  r  r  r  /  rB  r  c              	   C   s   t t| | td t| |t||   |td  ttdttd|  |||td    || tt| |t||   |  ttdttd|  td| |  | S r  r  r  r  r  r  r  3  rA  r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    ||tt| |t||   |  t|td | td| |  | S r  r  r  r  r   r>   r  r  	r  r  r  r  r  r  r   r  r  r  r  r  r  7  r  r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    || tt| |t||   |  t|td | td| |  | S r  r  r  r  r   r
  r  r  r  r  r  r  r  ;     r  c	           	   	   C   s   t t| | td t| |t||   |td  t|td | |||td    || t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d | |||td    ||tt| |t||   |  t|td | td| |  | S r  r   r  r  r  r  r  C  r  r  c                 C   sn   t t| |t||   t| |t||    || | td|  |t||   |t||     |S r  )r  r  r>   r
  r  r  r  r  r  r  G  r  r  c              	   C   s   t ||td  t| |t||   |td  | |t||   |td   |||td    ||t| |t||   | | |t||   |td   || | |td   | S r  r  r  r   r>   r
  r  r  r  r  r  r  K  r  r  c              	   C   s   t ||td  t| |t||   |td  | |t||   |td   |||td    ||t| |t||   |td  | |t||   |  || | |td   | S r  r  r  r  r  r  r  O  r  r  c              	   C   s~   t ttd ttt |  | td ||||    ||t ttd ttt|  | td ||||    || S r  r  r  r  r  r  r  r  r  r  r  S  r  r  c              	   C   s|   t ttd tttdt| |   ||||    ||t ttd tttdt| |   ||||    || S r  r  r  r  r  r  r  W  r  r  c                 C   s   t || t|||t|||td      |td |td  td  || t td| | t|td | |t||    |||td    || t|| |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  c                 C   s   t || t|||t|||td      |td |td  td  ||t td| | t|td | |t||    |||td    || t|| |t||    ||t|||td      | S r  )r  r   r  r  r
  r  r  r  r  r  r  _  s   r  c	           	      C   s$  t || |td  t||td  ||t|||td      |td |td  td  || t 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  c  r  r  c	           	      C   s"  t || |td  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d  | |t||    ||t|||td      |td  | S r  )r  r  r   r  r
  r  r  r  r  r  r  g  r  r  c	           
   
   C   s   t || ||t|||td      |}	t|| tt|	|td |td  td  ||| t| |t||   |	| S r  )r  r  r  r  r   r   r>   rI  r  r  r  r  k  s   .Zr  c	           
   
   C   s   t || ||t|||td      |}	t|| tt|	|td |td  td  |||t| |t||   |	| S r  )r  r  r  r  r   r   r
  rI  r  r  r  r  p  s   .Xr  c	           
   
   C      t || | |t||    |}	ttd| | tt|	| |||td    ||| t||t|||td     |	| S r  )r  r>   r  r  r   r   r  rI  r  r  r  r  u     "fr  c	           
   
   C   r  r  )r  r
  r  r  r   r   r  rI  r  r  r  r  z  r  r  c                 C   s:  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 r  )r  r   r>   r  r  r  r  r  r  r  r    s   < r  c                 C   s8  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 r  )r  r   r
  r  r  r  r  r  r  r  r    s   : r  c                 C   s   t t |  | td t| td tdd   t|  | td t | 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  r  c                 C   s   t || t |  | td t| td tdd    t|  | td t | 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   sR   t t |  | td t| td  t|  | td t | td   |S r  r   r  r  r
  r  r  r  r    r  r  c                 C   sZ   t || t |  | td t| td   t|  | td t | td   |S r  r  r  r  r  r  r       Zr  c                 C   sz   t || t|td|| |  |  t |  | td t| td   t|  | td t | td   ||S r  r  r   r  r  r  r  r  r  r   r  r  r  r  r  r       zr  c                 C   sf   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   sL   t || t|||   || | td |  t|t| |   ||S r  r  r   r  r  r>   r  r  r  r  r    s   Lr  c                 C   s   t td|td  ||  t|tdt| |   t | td   tdt| |   t| td   td|||   |  ||S r  r  r  r   r  r  r  r  r  r    r  r  c                 C   sf   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   sv   t || |||  |  || | td |   t|||   || | td |  t|t| |   ||S r  r  r  r   r  r>   r  r  r  r  r    r  r  c              	   C   sZ   t | | | t|t| |   | | t|||td    |td td   |S r  )r  r  r>   r  r  r  r  r  r  r    r  r  c              	   C   s  t t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   r  r>   r  r  r  r  r  r   r  r  r  r  r    s    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   C   s*  t tdt|   || td   || td   | tt|td t |  td|td t |   | td   t |  | td |td t |  t|  | td   |  ||t | | ||   td t| td  t| | ||   td t | td   |S )Nr  r	  r  r  r  r  r  r  r+   r   r  r  r  r  r    s   , r  c                 C   s   t |||  | t |  | t| | |  td t| td   t|  | t| | |  td t | td   |S r  r  r  r  r  r  r    r  r  c	           	      C   s   t || td td  | t|t |  t| |  td t| td |   t|  t| |  td t | td |   ||S r  r  r  r  r  r  r    r  r  c	           	   	   C      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 r  r  r  r  r  r  r    r&  r  c                 C   *   t |t|t| | || |    |S r  )r   r  r
  rq  r  r  r  r  #  r  r  c              	   C   s<   t tdt| td  t|t| t| |   ||S 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d   tdt| |   t | 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  r  +  r  r  c              	   C   s   t t|| td  tdt| |   t| td tdd    tdt| |   t | td tdd    ttd|td | td    ||td|  S Nr  r  r  r"  r  r  r  r  r  /  r  r  c                 C   sn   t ttdt| |   t| td  tdt| |   t | td   |td  ||td|  S r  r+   r   r  r  r
  r  r  r  r  3  r  r  c                 C   l   t t|| td  tdt| |   |td   tdt| |   | td   ||td|  S r#  r$  r  r  r  r  r  7  r  r  c                 C   s   t || td| |  tt|| td  tdt| |   t| td tdd    tdt| |   t | td tdd    ttd|td | td    ||td| | S r  )r  r  r+   r   r  r  r  r  r  r  r  ;  r&  r  c                 C   r%  r#  r$  r  r  r  r  r  ?  r  r  c              	   C   sJ   t || t|||  |||  td |  t|t| |   ||S r  r  r   r  r  r
  r  r  r  r  r  C  r<  r  c              	   C   sv   t ||  |||  |  |||  td |   t|||  |||  td |  t|t| |   ||S r  r  r  r   r  r
  r  r  r  r  r  G  r  r  c              	   C   s   t || tt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  r  r  r  r  K  r  r  c              	   C   s   t || tt|| td  tdt| |   t| td   tdt| |   t | td   td|| |  |  ||td| | S r#  r(  r  r  r  r  r  O  r  r  c              	   C   s`   t td|||   |  |||  |  ttd|||   | t|t| |   ||S r  r'  r  r  r  r  r  S  rx  r  c              	   C   s   t || ||  td| |  tt|| td  tdt| |   t| td   tdt| |   t | td   td|| |  |  ||td| | S r  r  r  r+   r   r  r  r  r  r  r  W  r  r  c              	   C   sd   t td|||   |  |||  |  t|td|||   |  t|t| |   ||S r  r'  r  r  r  r  r  [  r  r  c                 C   s(   t t|t| |  | | |  | S r  )r  r  r
  r  r  r  r  r  _  r2  r  c              	   C   s^   t |  | | t|t| |   | | t|||td    |td td   | S r  )r  r  r
  r  r  r  r  r  r  r  c  r,  r  c              	   C   s  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 r  r  r  r   r  r
  r  r  r  r  r  r  g  s    r  c              	   C   sl   t | | | td t|t| |   | td | t|||td    |td td   | S r  )r  r  r  r
  r  r  r  r  r  r  k  r  r  c              	   C   s  t |td| td  | | |td td|td td     t|||td   |td  t|t| |   ||t|||td   |td  |  | | td|  td  t|t| |   | td | |td td|td td     | S )Nr  r  r  r  r*  r  r  r  r  r  o  s    r  c                 C   s   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  r  r  r  s  s   r  c              	   C   s(  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 td     | S )Nr  r  r  r  r  r*  r  r  r  r  r  w  r  r  c              	   C   s   t | | td  ||  tttdt| |td|  td  t||  t|td | td   ||t| | | S )Nr	  r  r  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 |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d    |   |||td   |  t||td|   tdtd| td |td    |  t|t| |   ||S r  r'  r  r  r  r  r    rG  r  c                 C   s   t || t|  td |   t||td |   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ttdt| |   t| td |  tdt| |   t | td |   |td  ||td| | S r  r(  r  r  r  r  r    r  r  c              	   C   s   t || tt|| td  tdt| |   t| td |   tdt| |   t | td |   ||td| | S r#  r(  r  r  r  r  r    r+  r  c              	   C   s   t || ||  td| |  tt|| td  tdt| |   t| 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d| td |td    |  |||td   |  t|tdtd| td |td    |  t|t| |   ||S r  r'  r  r  r  r  r    r  r  c                 C   sD   t tdt| td  t|t| t|| ||     ||S r  r  rq  r  r  r  r    r  r  c                 C   s   t t| | ||   t| td  tdt|| ||     t| td   t|  | t| | |  td t | td   tt|  | t| | |  td t | td  t|  | t| | |  td t| td   ||S r  r  r  r  r  r  r    s   r  c                 C   s(  t tdt|   || td   || td   | tt|td t |  td|td t |   | td   t|  | td |td t |  t |  | td   |  ||tdt|| ||     t| td  tdt|| ||     t | td   |S )Nr  r	  r  r  r  r  r  r  r  r  r    r  r  c                 C   s
  t t| | ||   t| td  tdt|| ||     t| td   t|  | t| | |  td t | td   t|||  | t|  | t| | |  td t | td   t|  | t| | |  td t| td   ||S r  r  r  r  r  r  r    s    r  c	           	      C   sj  t || td td  | t|  t| |  td t|  t| |   t| td   t|  t| |  t|  t| |  td  t| td   t |  t| |  td t| td   t|  t| |  td t | td   t|t |  t| |  td t | td |   t|  t| |  td t| td |   ||S r  )r  r  r  r   r  r  r  r  r       l r  c	           	   	   C   r   r  r'  r  r  r  r  r    r&  r  c                 C   r!  r  )r   r  r>   rq  r  r  r  r    r  r  c                 C   rs  r  r  r  r+   r   r>   ru  r  r  r  r    r  r  c                 C   rs  r  r  r  r+   r   r
  ru  r  r  r  r    r  r  c                 C   "   t | |t|||    | |S r  r  ru  r  r  r  r    rr  r  c                 C   r0  r  r  ru  r  r  r  r    rr  r  c	           	   	   C   rw  r  r.  r   r  r  r  r     rx  r   c	           	   	   C   rw  r  r/  r   r  r  r  r    rx  r  c	           	      C   2   t | |t|||    | |||  |  |S r  r  r   r  r  r  r    r  r  c	           	      C   r1  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.  rz  r  r  r  r    r  r  c
           
   
   C   r2  r  r/  rz  r  r  r  r    r  r  c              
   C      t td| tt||t|  |
 ||td  |td  ||td   |  || | | | ||  |  |	  |||||  |S r  r.  r|  r  r  r  r    r  r  c              
   C   r3  r  r/  r|  r  r  r  r    r  r  c              	   C   s   t ttd ttt |  t| |  td ||||    ||t ttd ttt|  t| |  td ||||    || S r  r  ru  r  r  r  r    r  r  c              	   C   s   t ttd tt| ||  t | ||   ||||    ||t ttd tt| ||  t | ||   ||||    || S r  r  ru  r  r  r  r	    r  r	  c                 C   &   t t| ||  ||||    |S r  r  ru  r  r  r  r
    r  r
  c                 C   r4  r  r  ru  r  r  r  r    r  r  c              	   C   s   t || t|| | td td|  | ||   |td |td|    td  || t|t| |||    | S r  )r  r   r  r  r>   r  r  r  r  r  r  r  r    r  r  c              	   C   s   t || t|| | td td|  | ||   |td |td|    td  ||t|t| |||    | S r  )r  r   r  r  r
  r5  r  r  r  r    r  r  c              	   C   s~   t ttd ttt |  t| ||   td | ||t ttd ttt|  t| ||   td | || S r  r  r5  r  r  r  r    r  r  c                 C   st   t ttd tttdt| |||     | ||t ttd tttdt| |||     | || S r  r  r5  r  r  r  r    r  r  c              	   C   s   t || |td  t|||  | td td|  | ||   |td |td|    td  || t||td  t| |||    |td  | 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d |td|    td  ||t||td  t| |||    |td  | S r  r  r6  r  r  r  r    r  r  c                 C   s   t ttd ttt |  t| ||||     td ||t ttd ttt|  t| ||||     td || S r  r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s|   t ttd tttdt| |||||       ||t ttd tttdt| |||||       || S r  r  r7  r  r  r  r    r  r  c                 C   s   t ttd t|| tt |  t| ||||     td  ||t ttd t|| tt|  t| ||||     td  || S r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t ttd t|| ttdt| |||||        ||t ttd t|| ttdt| |||||        || S r  r  r8  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   s2   t tt|| t| ||td    | |S r  )r  r  r>   r  r  r  r  r  r  r  r  r  r  '  r  r  c              
   C   s4   t tt|| t| ||td    | | S r  )r  r  r
  r  r  r9  r  r  r  r  +  r)  r  c              	   C   sF   t t|| t| ||td    |td  ||td   |S r  )r  r>   r  r  r  r  r  r  r  r  r  r  r  /  r  r  c              	   C   sH   t t|| t| ||td    |td  ||td   | S r  )r  r
  r  r  r:  r  r  r  r  3  r  r  c                 C   z   t t| ||td   t|||td    tt|| t| ||td    | t| ||td    ||S r  r  r  r  r  r  r  7  r  r  c                 C   r;  r  r  r  r  r  r  r  ;  r  r  c                 C   s@   t tdd t|t| ||t t|  td t||| S Nr  r  r  r  r  r   r>   r}  r  r  rR  r  r  r  r  r  r  ?  r  r  c                 C   sB   t tdd t|t| || t t|  td t||| S r<  r=  r>  r  r  r  r   C  r  r   c              
   C      t |ttttfrdS z/t||}ttt|t	t
|ttt||td t||t|tdtd   }W n ttfyF   Y dS w |rKdS dS NFr  r  T)rN  rO  r  rP  r  rQ  r  r6   r   r  r^   r>   r   r  r  r  r  	TypeErrorAttributeErrorr  r  rR  r  tmpresr  r  r  r!  G     
Tr!  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 r  )rQ  r  r  r  r3   r  r+   r   r-  r  r   r  r  rR  r  rD  r  r  r  r"  T  s   
r"  c              
   C   r?  r@  )rN  rO  r  rP  r  rQ  r  r6   r   r  r^   r?   r   r  r  r  r  rA  rB  rC  r  r  r  r#  Z  rF  r#  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 r  )rQ  r  r  r  r3   r  r+   r   r-  r  r   rG  r  r  r  r$  g  s   
r$  c              
   C   sv   t t| t||ttdt |  tdt | |   | t|   || t|t||t| ||     | S r  r  r  r   r  r  r  r>   r  r~  r  r  r  r%  m  r  r%  c              
   C   st   t t| t||ttdt |  tdt | |   | t|   ||t|t||t| ||     | S r  r  r  r   r  r  r  r
  r  r~  r  r  r  r&  q  r  r&  c              
   C   sx   t t| t|| ttdt |  tdt | |   | t|   || t|t||t| ||     | S r  rH  r~  r  r  r  r'  u  r  r'  c              
   C   sv   t t| t|| ttdt |  tdt | |   | t|   ||t|t||t| ||     | S r  rI  r~  r  r  r  r(  y  r  r(  c                 C   sh  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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  r>   r  r~  r  r  r  r)  }     j r)  c                 C   sj  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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  r
  r  r~  r  r  r  r*    r-  r*  c                 C   sj  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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  rJ  r~  r  r  r  r+    r-  r+  c                 C   sh  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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  rL  r~  r  r  r  r,    rK  r,  c              
   C   s   t t| ||td   t|||  |td  |ttdt |  tdt | |   | t|   || t|||  |td  t||t| ||     ||td   | S r  rJ  r  r  r  r  r-    r  r-  c              
   C   s   t t| ||td   t|||  |td  |ttdt |  tdt | |   | t|   ||t|||  |td  t||t| ||     ||td   | S r  rL  r  r  r  r  r.    r  r.  c              
   C   s   t t| ||td   t|||  |td  | ttdt |  tdt | |   | t|   || t|||  |td  t||t| ||     ||td   | S r  rJ  r  r  r  r  r/    s   r/  c              
   C   s   t t| ||td   t|||  |td  | ttdt |  tdt | |   | t|   ||t|||  |td  t||t| ||     ||td   | S r  rL  r  r  r  r  r0    r  r0  c                 C   s  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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  rJ  r  r  r  r  r1    r	  r1  c                 C   s  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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  rL  r  r  r  r  r2        r2  c                 C   s  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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  rJ  r  r  r  r  r3    rM  r3  c                 C   s  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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  rL  r  r  r  r  r4    r	  r4  c                 C   sR   t |t|ttd|  td| |   || t|tt| ||   | S r  r  r   r  r  r  r>   r  r  r  r  r  r  r  r5    r  r5  c                 C   sP   t |t|ttd|  td| |   ||t|tt| ||   | S r  r  r   r  r  r  r
  r  rO  r  r  r  r6    r  r6  c              	   C   sX   t |t|ttd|  td| |   ||t|ttdt| ||    | S r  rN  rO  r  r  r  r7    r  r7  c              	   C   sZ   t |t|ttd|  td| |   || t|ttdt| ||    | S r  rP  rO  r  r  r  r8    r  r8  c                 C   s   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  r  r  r  r  r  r  r  r  r9    r  r9  c                 C   s   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  rR  r  r  r  r:    r  r:  c              	   C   s   t |||td   t|||  |td  ttd|  td| |   ||t|||  |td  ttdt| ||    ||td   | S r  rQ  rR  r  r  r  r;    r,  r;  c              	   C   s   t |||td   t|||  |td  ttd|  td| |   || t|||  |td  ttdt| ||    ||td   | S r  rS  rR  r  r  r  r<    s   r<  c              
   C   sf   t |t||ttd|  td| |   | |  || t|t||t| ||     | S r  r  r   r  r  r  r>   r  r~  r  r  r  r=    r  r=  c              
   C   sd   t |t||ttd|  td| |   | |  ||t|t||t| ||     | S r  r  r   r  r  r  r
  r  r~  r  r  r  r>    r  r>  c              
   C   sh   t |t|| ttd|  td| |   | |  || t|t||t| ||     | S r  rT  r~  r  r  r  r?    r  r?  c              
   C   sf   t |t|| ttd|  td| |   | |  ||t|t||t| ||     | S r  rU  r~  r  r  r  r@    r  r@  c                 C   s   t t| | | t  t|ttd|  td| |   | | | | t ttd|  td| |    t  ||t t| || t  t|ttd|  td| |   || || t ttd|  td| |    t  || t|t||t| ||     | S r  r  r  r   r  r  r  r>   r  r~  r  r  r  rA    r  rA  c                 C   s"  t t| | | t  t|ttd|  td| |   | | | | t ttd|  td| |    t  || t t| || t  t|ttd|  td| |   || || t ttd|  td| |    t  || t|t||t| ||     | S r  r  r  r   r  r  r  r
  r  r~  r  r  r  rB    r  rB  c                 C   s"  t t| | | t  t|ttd|  td| |   | | | | t ttd|  td| |    t  || t t| || t  t|ttd|  td| |   || || t ttd|  td| |    t  || t|t||t| ||     | S r  rV  r~  r  r  r  rC    r  rC  c                 C   s   t t| | | t  t|ttd|  td| |   | | | | t ttd|  td| |    t  ||t t| || t  t|ttd|  td| |   || || t ttd|  td| |    t  || t|t||t| ||     | S r  rW  r~  r  r  r  rD    r  rD  c              
   C   s   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  r  r  r  rE    r  rE  c              
   C   s   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  r  r  r  rF    rE  rF  c              
   C   s   t |||td   t|||  |td  | ttd|  td| |   | |  || t|||  |td  t||t| ||     ||td   | S r  rX  r  r  r  r  rG    r  rG  c              
   C   s   t |||td   t|||  |td  | ttd|  td| |   | |  ||t|||  |td  t||t| ||     ||td   | S r  rY  r  r  r  r  rH    r  rH  c                 C   s  t t| | | t  ||td   t|||  |td  t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  || t|||  |td  t||t| ||     ||td   | S r  r  r  r  r   r  r  r>   r  r  r  r  r  rI        rI  c                 C   s  t t| | | t  ||td   t|||  |td  t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  || t|||  |td  t||t| ||     ||td   | S r  r  r  r  r   r  r  r
  r  r  r  r  r  rJ        rJ  c                 C   s  t t| | | t  ||td   t|||  |td  t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  || t|||  |td  t||t| ||     ||td   | S r  rZ  r  r  r  r  rK    r]  rK  c                 C   s  t t| | | t  ||td   t|||  |td  t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  || t|||  |td  t||t| ||     ||td   | S r  r\  r  r  r  r  rL  	  r[  rL  c                 C   sB   t t|t| | | td td  || t|t|  | S r  )r   r-  r  r  r  r>   r  r  r  r  rM    r  rM  c                 C   s@   t t|t| | | td td  ||t|t|  | S r  )r   r-  r  r  r  r
  r  r  r  r  rN    r  rN  c                 C   s   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  rO    r  rO  c                 C   s   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  rP    r  rP  c                 C   rK  rL  rM  r  r  r  r  rQ    rS  rQ  c                 C   sZ   t ||}t|tt|t|| |td td  ||| t| |t|  || S r  )r  r  r   r-  r  r  r>   r  r  r  r  rR  &  s   
PrR  c                 C   rK  rL  rM  r  r  r  r  rS  ,  rS  rS  c                 C   sX   t ||}t|tt|t|| |td td  |||t| |t|  || S r  )r  r  r   r-  r  r  r
  r  r  r  r  rT  5  s   
NrT  c              	   C   s~   t ttd tt|tt | td  | ||   ||t ttd tt|tt| td  | ||   || S r  r  )r  r  rR  r  r  r  r  r  rU  ;  r  rU  c                 C   sx   t t|t|  t|| | || t t|t| | t| | td td  || t|t|  t| | S r  )r   r-  r>   r  r  r  r  rR  r  r  r  r  r  rV  ?  r  rV  c                 C   sx   t t|t|| t|  | || t t|t| | t| | td td  || t|t| t|  | S r  )r   r-  r  r
  r  r  r  r^  r  r  r  rW  C  r  rW  c                 C   2   t |ttttfrdS t| |}t||rdS dS rL  rM  r  rR  r  r  zr  r  r  rX  G  rS  rX  c                 C   s~   t | |}tt|t| ||tt|t| t|| | || tt|t|| t| |td td  || S r  )r  r  r>   r  r   r-  r  r  r`  r  r  r  rY  P     
trY  c                 C   r_  rL  rM  r`  r  r  r  rZ  V  rS  rZ  c                 C   s~   t | |}tt|t| ||tt|t|| t| | || tt|t|| t| |td td  || S r  )r  r  r  r
  r   r-  r  r  r`  r  r  r  r[  _  rb  r[  c                 C   sf   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  r\  e  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  rd  r  r  r  r]  i  r  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^  m  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_  q  r  r_  c                 C   0   t t| |t||   | ||td|  S r  )r+   r   r  r  r9  r  r  r  r`  u  r  r`  c                 C   rh  r  )r+   r   r	  r  r9  r  r  r  ra  y  r  ra  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  rc  r:  r  r  r  rb  }  r  rb  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  re  r:  r  r  r  rc    r  rc  c              	   C   s`   t || td  tt| ||  | tdt| |td   t| ||t|| |S Nr	  r  r  r  r+   r   r  r  r  r  r  r  r  rd    rx  rd  c              	   C   sb   t || td  tt| ||  | tdt| |td   t| ||t|| | S ri  rg  r  r  r  r  re    r  re  c                 C   &   t || | |t||   |  |S r  r  r  r  r  r  rf    r  rf  c                 C   rk  r  r  r  r  r  r  rg    r  rg  c                 C   s   t |||td   | |}t|| | t|td |td   tt||t|td |td  td   ||| t| |t||   || S r@  r  r  r  r  r   r-  r  r  r  r  r  rh    s   rh  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  r  r  r  r  ri    s   ri  c                 C   b   t t|td | td  | |t||   |  ||td  | |  ||td|  S Nr  r  r  r+   r   r  r  r  r  r  r  rj    r  rj  c                 C   rn  ro  r+   r   r  r	  r  r  r  r  rk    r  rk  c              
   C   z   t t|td | tt|td | td  | |t||   |  ||td  | |  ||td| | S ro  r  r  r  r  r  rl    r  rl  c              
   C   rr  ro  r  r  r  r  r  rm    r  rm  c              
   C      t t|||td   |t||td  |   tt|td | td  | |t||   |  ||td  | |  ||td| | S ro  r  r  r  r  r  rn    r  rn  c              
   C   rs  ro  r  r  r  r  r  ro    r  ro  c                 C   r  r  r   r  r  r  r  r  r  rp    r  rp  c                 C   r  r  r   r  r  r  r  r  r  rq    r  rq  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  r  r  r  r  rr    r  rr  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  r  r  r  r  rs    r  rs  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@  rl  r  r  r  r  rt    s   &rt  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@  rm  r  r  r  r  ru    s   &ru  c	           	      C   f   t t|| td|  td  | |t||   |  ||td  | |  ||td|  S ro  rp  r  r  r  r  rv    r  rv  c	           	      C   rv  ro  rq  r  r  r  r  rw    r  rw  c	           	   
   C   ~   t t|td | tt|| td|  td  | |t||   |  ||td  | |  ||td| | S ro  r  r  r  r  r  rx    r  rx  c	           	   
   C   rw  ro  r  r  r  r  r  ry    r  ry  c	           	   
   C      t t|||td   |t||td  |   tt|| td|  td  | |t||   |  ||td  | |  ||td| | S ro  r  r  r  r  r  rz    r  rz  c	           	   
   C   rx  ro  r  r  r  r  r  r{    r  r{  c	           	      C   r  r  rt  r  r  r  r  r|    r  r|  c	           	      C   r  r  ru  r  r  r  r  r}    r  r}  c                 C   sj   t tdttdtd| ||  td   | ||    | t| ||  t| ||   | | S r  )r   r  r  r  r  rO  r  r  r  r~    r  r~  c                 C   sh   t tdttdtd| ||  td   | ||    |t| ||  t| ||   | | S r  )r   r  r  r  r  rO  r  r  r  r    r  r  c              	   C   sB   t td| tt|| t| t| ||t| ||  |S r  rf  r5  r  r  r  r    r  r  c              	   C   sD   t td| tt|| t|t|  ||t| ||  | S r  rg  r5  r  r  r  r    r  r  c                 C   s  t tttdtdttd| td   ttt| ||    |   | t tttdttd| td  td ttt| ||    |   | t tttdttdt t| ||     td | t ttdtdttd| td   ttt| ||    |   t| ||   | t ttdttd| td  td ttt| ||    |   t| ||   | t tttdt t| ||   td t| ||   | S r  )r  r  r  r  r  r  r  r  rO  r  r  r  r    r  r  c                 C   s  t tttdttdttd| td    tt t| ||    |   |t tttdtttd| td  td  tt t| ||    |   | t tttdttdt t| ||    td | t tt| ||  td  | t ttdttdttd| td    tt t| ||    |   t| ||   | t ttdtttd| td  td  tt t| ||    |   t| ||   | t ttdttdt t| ||    t| ||   | S r  )r  r  r  r  r  r  r  r  rO  r  r  r  r    s     r  c              
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   C   sb   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  )  r  r  c              
   C   s`   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  -  rx  r  c              
   C   s   t || ||td  t|td   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  1  rG  r  c              
   C   s   t || ||td  t|td   tt|||  |td  t|| |t|td td   |||t| |t|  |||  |td   ||td   | S rz  )r  r  r  r   r-  r  r  r  r  r  r  r  r  5  r  r  c                 C   rK  rL  rM  r  r  r  r  r  9  rS  r  c              
   C   sv   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  B  s   
lr  c                 C   rK  rL  rM  r  r  r  r  r  H  rS  r  c              
   C   st   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  Q  s   
jr  (  __doc__Zsympy.externalr   r   r   r   r   r   Z%sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r}  ZA_ZB_ZC_ZF_ZG_ZH_r  Zb_r  r#  Ze_rE  Zg_Zh_Zi_Zj_Zk_Zl_rN  r  r4  Zq_Zr_Zt_r  r   Zs_r  r  Zy_Zz_Za1_Za2_Zb1_Zb2_Zc1_Zc2_Zd1_Zd2_Zn1_Zn2_Ze1_Ze2_Zf1_Zf2_Zg1_Zg2_Zn3_ZPq_ZPm_r  ZQm_ZQr_ZQx_Zjn_Zmn_Znon2_r  ZRGx_r  iiZPqqQRrr  kr  Z	_UseGammaZ	ShowStepsZStepCounterr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rF  rG  rH  rI  rJ  rK  rL  rM  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  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/  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  <module>   sJ              nJjB.
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