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Z
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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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM Z dNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Z	d`da Z
dbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z dd Z!dd Z"dd Z#dd Z$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dd Z6dd Z7dd Z8dd Z9dd Z:ddÄ Z;dĐdń Z<dƐdǄ Z=dȐdɄ Z>dʐd˄ Z?d̐d̈́ Z@dΐdτ ZAdАdф ZBdҐdӄ ZCdԐdՄ ZDd֐dׄ ZEdؐdل ZFdڐdۄ ZGdܐd݄ ZHdސd߄ 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$d% Zld&d' Zmd(d) Znd*d+ Zod,d- Zpd.d/ Zqd0d1 Zrd2d3 Zsd4d5 Ztd6d7 Zud8d9 Zvd:d; Zwd<d= Zxd>d? Zyd@dA ZzdBdC Z{dDdE Z|dFdG Z}dHdI Z~dJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ ZdĐdń ZdƐdǄ ZdȐdɄ Zdʐd˄ Zd̐d̈́ Zdΐdτ ZdАdф ZdҐdӄ ZÐdԐdՄ ZĐd֐dׄ ZŐdؐdل ZƐdڐdۄ Zǐdܐd݄ ZȐdސd߄ Zɐdd Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd ZԐdd ZՐdd Z֐dd Zאdd Zؐdd Zِd d Zڐdd Zېdd Zܐdd Zݐdd	 Zސd
d Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM Z dNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Z	d`da Z
dbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdz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$dd Z%dd Z&dd Z'dd Z(dd Z)dd Z*dd Z+dd Z,dd Z-dd Z.dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd Z5dd Z6dd Z7dd Z8dd Z9dd Z:ddÄ Z;dĐdń Z<dƐdǄ Z=dȐdɄ Z>dʐd˄ Z?d̐d̈́ Z@dΐdτ ZAdАdф ZBdҐdӄ ZCdԐdՄ ZDd֐dׄ ZEdؐdل ZFdڐdۄ ZGdܐd݄ ZHdސd߄ ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXdd ZYd d ZZdd Z[dd Z\dd Z]dd	 Z^d
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	d Zߐ	d	d Z	d	d Z	d	d Z	d	d Z	d	d Z	d	d Z	d	d Z	d	d Z	d	d Z	d	d Z	d 	d! Z	d"	d# Z	d$	d% Z	d&	d' Z	d(	d) Z	d*	d+ Z	d,	d- Z	d.	d/ Z	d0	d1 Z	d2	d3 Z	d4	d5 Z	d6	d7 Z	d8	d9 Z	d:	d; Z	d<	d= Z	d>	d? Z	d@	dA Z	dB	dC Z	dD	dE Z	dF	dG Z	dH	dI Z	dJ	dK Z	dL	dM Z 	dN	dO Z	dP	dQ Z	dR	dS Z	dT	dU Z	dV	dW Z	dX	dY Z	dZ	d[ Z	d\	d] Z	d^	d_ Z		d`	da Z
	db	dc Z	dd	de Z	df	dg Z	dh	di Z	dj	dk Z	dl	dm Z	dn	do Z	dp	dq Z	dr	ds Z	dt	du Z	dv	dw Z	dx	dy Z	dz	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	d	d Z6	d	d Z7	d	d Z8	d	d Z9	d	d Z:	d	dÄ Z;	dĐ	dń Z<	dƐ	dǄ Z=	dȐ	dɄ Z>	dʐ	d˄ Z?	d̐	d̈́ Z@d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)Add)Mod)Mul)
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 tt||||||,|Z}tu|tG}tqtrttwdtxdtztttwdtxd twdtxd   twdtxd txdt(tttwdtxd twdtxd  twdtxd  tt||||||,|Z}tu|tH}tqtrtwdtxdt(tttwdtxd twdtxd  twdtxd ttwdtxdtytttwdtxd twdtxd   twdtxd  tt|||||8|9|,|_	} tu| tI}tqtrtwdtxdt(tttwdtxd twdtxd  twdtxd ttwdtxdtztttwdtxd twdtxd   twdtxd  tt|||||8|9|,|_	}tu|tJ}tqtrttwdtxdtytttwdtxd twdtxd   t~ t(tttwdtxd twdtxd txd  tt||||||,}tu|tK}tqtrttwdtxdtztttwdtxd twdtxd   t~ t(tttwdtxd twdtxd txd  tt||||||,}tu|tL}tqtrttwdtxdtytttwdtxd twdtxd   t~ t(tttwdtxd twdtxd txd  tt|||||,|||e	}tu|tM}	tqtrttwdtxdtztttwdtxd twdtxd   t~ t(tttwdtxd twdtxd txd  tt|||||,|||e	}
tu|
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}tu|t)}tqtrtwd
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}tu|t*}tqtrtwd
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}tu|t+}tqtrtwd
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}tu|t,}Ðtqtrtwdtxdtztttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   twdtxd  tftwd
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}Ntu|Ntr}Otqtrtwd
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txdtztttwdtxd twdtxd  t twdtxdtytttwdtxd twdtxd  t  ttwdtxdtztttwdtxd twdtxd   t~  tt||||||8||9|&|V}Rtu|Rtt}Stqtrtwd
txdtytttwdtxd twdtxd  t twdtxdtztttwdtxd twdtxd  t  ttwdtxdtytttwdtxd twdtxd   t~  tt||||||8||&|:|;|}Ttu|Ttu}Utqtrtwd
txdtztttwdtxd twdtxd  t twdtxdtytttwdtxd twdtxd  t  ttwdtxdtztttwdtxd twdtxd   t~  tt||||||8||&|:|;|}Vtu|Vtv}Wtqtrtwdtxdtztttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||8|9|&|||A}Xtu|Xtw}Ytqtrtwdtxdtytttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||8|9|&|||A}Ztu|Ztx}[tqtrtwdtxdtztttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||8||9|&|ă
}\tu|\ty}]tqtrtwdtxdtytttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||8||9|&|ă
}^tu|^tz}_tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt||||||||&|
}`tu|`t{}atqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt||||||||&|
}btu|bt|}ctqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||||&||
}dtu|dt}}etqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||||&||
}ftu|ft~}gtqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt||||||||&|B
}htu|ht}itqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt||||||||&|B
}jtu|jt}ktqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd t  tt|||||||&|d|:
}ltu|lt}mtqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd t  tt|||||||&|d|:
}ntu|nt}otqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd t  tt||||||||&|d|}ptu|pt}qtqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd t  tt||||||||&|d|}rtu|rt}stqtrtwd
txdtytttwdtxd twdtxd  t twdtxdtztttwdtxd twdtxd  t  ttwdtxdtytttwdtxd twdtxd   t~  tt||||||8||9|&|_|Ń}ttu|tt}utqtrtwd
txdtztttwdtxd twdtxd  t twdtxdtytttwdtxd twdtxd  t  ttwdtxdtztttwdtxd twdtxd   t~  tt||||||8||9|&|_|Ń}vtu|vt}wtqtrtwd
txdtytttwdtxd twdtxd  t twdtxdtztttwdtxd twdtxd  t  ttwdtxdtytttwdtxd twdtxd   t~  tt|||||||9|&|:
}xtu|xt}ytqtrtwd
txdtztttwdtxd twdtxd  t twdtxdtytttwdtxd twdtxd  t  ttwdtxdtztttwdtxd twdtxd   t~  tt|||||||9|&|:
}ztu|zt}{tqtrtwd
txdtytttwdtxd twdtxd  t twdtxdtztttwdtxd twdtxd  t  ttwdtxdtytttwdtxd twdtxd   t~  tt||||||||9|&|}|tu||t}}tqtrtwd
txdtztttwdtxd twdtxd  t twdtxdtytttwdtxd twdtxd  t  ttwdtxdtztttwdtxd twdtxd   t~  tt||||||||9|&|}~tu|~t}tqtrtwdtxdtztttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  ttwd
txdtytttwdtxd twdtxd   tt||||||8|,|||ƃ}tu|t}tqtrtwdtxdtytttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  ttwd
txdtztttwdtxd twdtxd   tt||||||8|,|||ƃ}tu|t}tqtrtwdtxdtztttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  ttwd
txdtytttwdtxd twdtxd   tt|||||8|,||H|ǃ
}tu|t}tqtrtwdtxdtytttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  ttwd
txdtztttwdtxd twdtxd   tt|||||8|,||H|ǃ
}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt||||||||,|ȃ
}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt||||||||,|ȃ
}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt||||||,|||
}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt||||||,|||
}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||||,||||ʃ}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||||,||||ʃ}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||||,||||˃}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||||,||||˃}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||||,||c|)||̃}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||||,||c|)||̃}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt|||||||,||c|)||˃}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt|||||||,||c|)||˃}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt||||||||,||c|o||˃}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt||||||||,||c|o||˃}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd txd  tt||||||||,||||||B}tu|t}tqtrtwd
txdtztttwdtxd twdtxd  t ttwdtxdtztttwdtxd twdtxd   t~  tytttwdtxd twdtxd txd  tt||||||||,||||||B}tu|t}tqtrtwd
txdtytttwdtxd twdtxd  t ttwdtxdtytttwdtxd twdtxd   t~  tztttwdtxd twdtxd t  tt||||||,||Ӄ	}tu|t}tqtrtwd
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}tu|t}tqtrtwd
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txdtytttwdtxd twdtxd   t  tt|||||||||i|,|}|||}4tu|4tg}5tqtrtwdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd   t~  twdtxdtwd
txdtztttwdtxd twdtxd   t  tt|||||||||i|,|}|||}6tu|6th}7tqtrtwdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtwdtxdtytttwdtxd twdtxd   t~  twdtxdtwd
txdtytttwdtxd twdtxd   t  tt||||||||||i|,|}|||}8tu|8ti}9tqtrtwdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd   t~  twdtxdtwd
txdtztttwdtxd twdtxd   t  tt||||||||||i|,|}|||}:tu|:tj};tqtrtwdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtwd
txdtytttwdtxd twdtxd     tt|||||||||i|,|}}<tu|<tk}=tqtrtwdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtwd
txdtztttwdtxd twdtxd     tt|||||||||i|,|}}>tu|>tl}?tqtrtwdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtwdtxdtytttwdtxd twdtxd   t~  twdtxdtwd
txdtytttwdtxd twdtxd    tt||||||||||i|,|}}@tu|@tm}Atqtrtwdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd   t~  twdtxdtwd
txdtztttwdtxd twdtxd    tt||||||||||i|,|}}Btu|Btn}Ctqtrtwdtxdtwdtxdtytttwdtxd twdtxd   ttwdtxdtwdtxdtytttwdtxd twdtxd    twdtxdtwd
txdtytttwdtxd twdtxd   t  tt|||||||||i|,|}|)|}Dtu|Dto}Etqtrtwdtxdtwdtxdtztttwdtxd twdtxd   ttwdtxdtwdtxdtztttwdtxd twdtxd    twdtxdtwd
txdtztttwdtxd twdtxd   t  tt|||||||||i|,|}|)|}Ftu|Ftp}Gtqtrt\twdtxdtytttwdtxd twdtxd   tttwdtxdtytttwdtxd twdtxd   ttytttwdtxd twdtxd   tt|||||||||
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txdtytttwdtxd twdtxd   twd	txd  tt|||||||||||i|,|}}Ttu|Ttw}Utqtrtwdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd   t~  twdtxdtwd
txdtztttwdtxd twdtxd   twd	txd  tt|||||||||||i|,|}}Vtu|Vtx}Wtqtrttwdtxdtytttwdtxd twdtxd   twdtxd tftwd
txdtytttwdtxd twdtxd   twd	txd  twdtxdtwdtxdtytttwdtxd twdtxd   t  tt|||||||||||9|j|&}Xtu|Xty}Ytqtrttwdtxdtztttwdtxd twdtxd   twdtxd tftwd
txdtztttwdtxd twdtxd   twd	txd  twdtxdtwdtxdtztttwdtxd twdtxd   t  tt|||||||||||9|j|&}Ztu|Ztz}[tqtrtwdtxdtytttwdtxd twdtxd  twdtxd twdtxdtytttwdtxd twdtxd  twdtxdtytttwdtxd twdtxd txd    tt|||||||}\tu|\t{}]tqtrtwdtxdtztttwdtxd twdtxd  twdtxd twdtxdtztttwdtxd twdtxd  twdtxdtztttwdtxd twdtxd txd    tt|||||||}^tu|^t|}_tqtrt\twdtxdtytttwdtxd twdtxd txd   tytttwdtxd twdtxd twdtxd  tt|||||}`tu|`t}}atqtrt\twdtxdtztttwdtxd twdtxd txd   tztttwdtxd twdtxd twdtxd  tt|||||}btu|bt~}ctqtrtwdtxdtytttwdtxd twdtxd  t~ t\twdtxdtytttwdtxd twdtxd txd    tt|||||||}dtu|dt}etqtrtwdtxdtztttwdtxd twdtxd  t~ t\twdtxdtztttwdtxd twdtxd txd    tt|||||||}ftu|ft}gtqtrtwdtxdtytttwdtxd twdtxd  t~ t\twdtxdtytttwdtxd twdtxd txd    tt|||||||}htu|ht}itqtrtwdtxdtztttwdtxd twdtxd  t~ t\twdtxdtztttwdtxd twdtxd txd    tt|||||||}jtu|jt}ktqtrtwdtxdtytttwdtxd twdtxd  twdtxd t\twdtxdtytttwdtxd twdtxd txd    tt|||||||f}ltu|lt}mtqtrtwdtxdtztttwdtxd twdtxd  twdtxd t\twdtxdtztttwdtxd twdtxd txd    tt|||||||f}ntu|nt}otqtrttwdtxdtytttwdtxd twdtxd   twdtxd twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt|||||||||
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}rtu|rt}stqtrttwdtxdtytttwdtxd twdtxd   twdtxd twdtxdtwdtxdtytttwdtxd twdtxd txd    tt||||||||	}ttu|tt}utqtrttwdtxdtztttwdtxd twdtxd   twdtxd twdtxdtwdtxdtztttwdtxd twdtxd txd    tt||||||||	}vtu|vt}wtqtrttwdtxdtytttwdtxd twdtxd   twdtxd twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt||||||||||{}xtu|xt}ytqtrttwdtxdtztttwdtxd twdtxd   twdtxd twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtztttwdtxd twdtxd txd    tt||||||||||{}ztu|zt}{tqtrttwdtxdtytttwdtxd twdtxd   twdtxd twdtxdtwdtxdtytttwdtxd twdtxd txd    tt|||||||||{
}|tu||t}}tqtrttwdtxdtztttwdtxd twdtxd   twdtxd twdtxdtwdtxdtztttwdtxd twdtxd txd    tt|||||||||{
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}tu|t}tqtrttwdtxdtztttwdtxd twdtxd   t~ twdtxdtwdtxdtztttwdtxd twdtxd txd    tt|||||||||&
}tu|t}tqtrtwdtxdtwdtxdtytttwdtxd twdtxd   t~ twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt||||||||||,}tu|t}tqtrtwdtxdtwdtxdtztttwdtxd twdtxd   t~ twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtztttwdtxd twdtxd txd    tt||||||||||,}tu|t}tqtrttwdtxdtytttwdtxd twdtxd   t~ twdtxdtwdtxdtytttwdtxd twdtxd txd    tt|||||||||,
}tu|t}tqtrttwdtxdtztttwdtxd twdtxd   t~ twdtxdtwdtxdtztttwdtxd twdtxd txd    tt|||||||||,
}tu|t}tqtrtwdtxdtwdtxdtytttwdtxd twdtxd   twdtxd twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt|||||||||f
}tu|t}tqtrtwdtxdtwdtxdtztttwdtxd twdtxd   twdtxd twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtztttwdtxd twdtxd txd    tt|||||||||f
}tu|t}tqtrttwdtxdtytttwdtxd twdtxd   twdtxd twdtxdtwdtxdtytttwdtxd twdtxd txd    tt||||||||f	}tu|t}tqtrttwdtxdtztttwdtxd twdtxd   twdtxd twdtxdtwdtxdtztttwdtxd twdtxd txd    tt||||||||f	}tu|t}tqtrtwdtxdtytttwdtxd twdtxd t  t~ twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt||||||||9|
}tu|t}tqtrtwdtxdtztttwdtxd twdtxd t  t~ twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtztttwdtxd twdtxd txd    tt||||||||9|
}tu|t}tqtrtwdtxdtytttwdtxd twdtxd t  t~ twdtxdtwdtxdtytttwdtxd twdtxd txd    tt|||||||9|	}tu|t}tqtrtwdtxdtztttwdtxd twdtxd t  t~ twdtxdtwdtxdtztttwdtxd twdtxd txd    tt|||||||9|	}tu|t}tqtrtwdtxdtwdtxdtytttwdtxd twdtxd   t~ twdtxdtwd
txdtytttwdtxd twdtxd    twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt||||||||||i|,||}tu|t}tqtrtwdtxdtwdtxdtztttwdtxd twdtxd   t~ twdtxdtwd
txdtztttwdtxd twdtxd    twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtztttwdtxd twdtxd txd    tt||||||||||i|,||}tu|t}tqtrtwdtxdtwdtxdtytttwdtxd twdtxd txd   twdtxdtwdtxdtytttwdtxd twdtxd   t~  twdtxdtwd
txdtytttwdtxd twdtxd    tt|||||||||i|,||}tu|t}tqtrtwdtxdtwdtxdtztttwdtxd twdtxd txd   twdtxdtwdtxdtztttwdtxd twdtxd   t~  twdtxdtwd
txdtztttwdtxd twdtxd    tt|||||||||i|,||}tu|t}tqtrtftwd
txdtytttwdtxd twdtxd   twdtxdtwdtxdtytttwdtxd twdtxd   twdtxd  twdtxdtwdtxdtytttwdtxd twdtxd   twdtxdtytttwdtxd twdtxd txd    tt|||||||||||i|,|f}tu|t}tqtrtftwd
txdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd   twdtxd  twdtxdtwdtxdtztttwdtxd twdtxd   twdtxdtztttwdtxd twdtxd txd    tt|||||||||||i|,|f}tu|t}tqtrtftwd
txdtytttwdtxd twdtxd   twdtxdtwdtxdtytttwdtxd twdtxd txd    twdtxdtwdtxdtytttwdtxd twdtxd   twdtxd  tt||||||||||i|,|f}tu|t}tqtrtftwd
txdtztttwdtxd twdtxd   twdtxdtwdtxdtztttwdtxd twdtxd txd    twdtxdtwdtxdtztttwdtxd twdtxd   twdtxd  tt||||||||||i|,|f}tu|t}tqtrttwdtxdtytttwdtxd twdtxd   t~ twdtxdtwd
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} tu
| tσ
}tqtrtttwd
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}tu
|tЃ
}tqtrttwdtxdtytttwdtxd twdtxd   t tttwd
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|tу
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|t҃
}tqtrtstwdtxd twdtxdtwdtxdtytӃ  twd	txd  tt|||||M|N
}tu
|tԃ
}	tqtrtstwdtxd twdtxdtwdtxdtztӃ  twd	txd  tt|||||M|N
}
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|
tՃ
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}tu
|tփ
}tqtrtttwd
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|t׃
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|t؃
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}tu
|tك
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|tڃ
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|tۃ
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|t܃
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|tރ
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}tu
|t߃
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} tu
| t
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|"t
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|$t
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|(t
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|*t
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|,t
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|.t
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|0t
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|2t
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|4t
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|8t
}9tqtrtttwdtxd twdtxd tttt twdtxd  twdtxd  tztttwd
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|Lt
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|Vt
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|Xt
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|Zt
}[tqtrtwdtxdtwdtxdtytst twd
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|\t
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}^tu
|^t
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|t
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|t
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|t
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|t
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|t
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|t
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|t
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|t 
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|t"
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|t#
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|t$
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|t%
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|t&
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|t'
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|t2
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|t3
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|t4
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|t5
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|t6
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|t7
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|Đt8
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|Ɛt9
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|Ȑt:
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|ʐt;
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|̐t<
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|ΐt=
}ϐtqtrtttwdtxd twdtxd twdtxdtwdtxdtytst twd
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|Аt>
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|Ґt?
}Ӑtqtrttt twdtxd twdtxdtwdtxdtyts  twdtxd  tt|||||9|Z|[
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|Ԑt@
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}֐tu
|֐tA
}אtqtrtttwdtxd tytttwd	txd twdtxd twdtxd twdtxd  tztttwd	txd twdtxd twdtxd  tt|||||9|R|Y
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|ؐtB
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|ڐtC
}ېtqtrtttwdtxd tytttwd	txd twdtxd twdtxd twdtxd  tztttwd	txd twdtxd twdtxd  tt|||9||^|Y
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|ܐtD
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|ސtE
}ߐtqtrtytttxd twdtxd tttwdtxd  twdtxd tt||||@
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|tF
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|tG
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|tH
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|tI
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|tJ
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75rule2375pattern2376rule2376pattern2377rule2377pattern2378rule2378pattern2379rule2379pattern2380rule2380pattern2381rule2381pattern2382rule2382pattern2383rule2383pattern2384rule2384pattern2385rule2385pattern2386rule2386pattern2387rule2387pattern2388rule2388pattern2389rule2389pattern2390rule2390pattern2391rule2391pattern2392rule2392pattern2393rule2393pattern2394rule2394pattern2395rule2395pattern2396rule2396pattern2397rule2397pattern2398rule2398pattern2399rule2399pattern2400rule2400pattern2401rule2401pattern2402rule2402pattern2403rule2403pattern2404rule2404pattern2405rule2405pattern2406rule2406pattern2407rule2407pattern2408rule2408pattern2409rule2409pattern2410rule2410pattern2411rule2411pattern2412rule2412pattern2413rule2413pattern2414rule2414pattern2415rule2415pattern2416rule2416pattern2417rule2417pattern2418rule2418pattern2419rule2419pattern2420rule2420pattern2421rule2421pattern2422rule2422pattern2423rule2423pattern2424rule2424pattern2425rule2425pattern2426rule2426pattern2427rule2427pattern2428rule2428pattern2429rule2429pattern2430rule2430pattern2431rule2431pattern2432rule2432pattern2433rule2433pattern2434rule2434pattern2435rule2435pattern2436rule2436pattern2437rule2437pattern2438rule2438pattern2439rule2439pattern2440rule2440pattern2441rule2441pattern2442rule2442pattern2443rule2443pattern2444rule2444pattern2445rule2445pattern2446rule2446pattern2447rule2447pattern2448rule2448pattern2449rule2449pattern2450rule2450pattern2451rule2451pattern2452rule2452pattern2453rule2453pattern2454rule2454pattern2455rule2455pattern2456rule2456pattern2457rule2457pattern2458rule2458pattern2459rule2459pattern2460rule2460pattern2461rule2461pattern2462rule2462pattern2463rule2463pattern2464rule2464pattern2465rule2465pattern2466rule2466pattern2467rule2467pattern2468rule2468pattern2469rule2469pattern2470rule2470pattern2471rule2471pattern2472rule2472pattern2473rule2473pattern2474rule2474pattern2475rule2475pattern2476rule2476pattern2477rule2477pattern2478rule2478pattern2479rule2479pattern2480rule2480pattern2481rule2481pattern2482rule2482pattern2483rule2483pattern2484rule2484pattern2485rule2485pattern2486rule2486pattern2487rule2487pattern2488rule2488pattern2489rule2489pattern2490rule2490pattern2491rule2491pattern2492rule2492pattern2493rule2493pattern2494rule2494pattern2495rule2495pattern2496rule2496pattern2497rule2497pattern2498rule2498pattern2499rule2499pattern2500rule2500pattern2501rule2501pattern2502rule2502pattern2503rule2503pattern2504rule2504pattern2505rule2505pattern2506rule2506pattern2507rule2507pattern2508rule2508pattern2509rule2509pattern2510rule2510pattern2511rule2511pattern2512rule2512pattern2513rule2513pattern2514rule2514pattern2515rule2515pattern2516rule2516pattern2517rule2517pattern2518rule2518pattern2519rule2519pattern2520rule2520pattern2521rule2521pattern2522rule2522pattern2523rule2523pattern2524rule2524pattern2525rule2525pattern2526rule2526pattern2527rule2527pattern2528rule2528pattern2529rule2529pattern2530rule2530pattern2531rule2531pattern2532rule2532pattern2533rule2533pattern2534rule2534pattern2535rule2535pattern2536rule2536pattern2537rule2537pattern2538rule2538pattern2539rule2539pattern2540rule2540pattern2541rule2541pattern2542rule2542pattern2543rule2543pattern2544rule2544pattern2545rule2545pattern2546rule2546pattern2547rule2547pattern2548rule2548pattern2549rule2549pattern2550rule2550pattern2551rule2551pattern2552rule2552pattern2553rule2553pattern2554rule2554pattern2555rule2555pattern2556rule2556pattern2557rule2557pattern2558rule2558pattern2559rule2559pattern2560rule2560pattern2561rule2561pattern2562rule2562pattern2563rule2563pattern2564rule2564pattern2565rule2565pattern2566rule2566pattern2567rule2567pattern2568rule2568pattern2569rule2569pattern2570rule2570pattern2571rule2571pattern2572rule2572pattern2573rule2573pattern2574rule2574pattern2575rule2575pattern2576rule2576pattern2577rule2577pattern2578rule2578pattern2579rule2579pattern2580rule2580pattern2581rule2581pattern2582rule2582pattern2583rule2583pattern2584rule2584pattern2585rule2585pattern2586rule2586pattern2587rule2587pattern2588rule2588pattern2589rule2589pattern2590rule2590pattern2591rule2591pattern2592rule2592pattern2593rule2593pattern2594rule2594pattern2595rule2595pattern2596rule2596pattern2597rule2597pattern2598rule2598pattern2599rule2599pattern2600rule2600pattern2601rule2601pattern2602rule2602pattern2603rule2603pattern2604rule2604pattern2605rule2605pattern2606rule2606pattern2607rule2607pattern2608rule2608pattern2609rule2609pattern2610rule2610pattern2611rule2611pattern2612rule2612pattern2613rule2613pattern2614rule2614pattern2615rule2615pattern2616rule2616pattern2617rule2617pattern2618rule2618pattern2619rule2619pattern2620rule2620pattern2621rule2621pattern2622rule2622pattern2623rule2623pattern2624rule2624pattern2625rule2625pattern2626rule2626pattern2627rule2627pattern2628rule2628pattern2629rule2629pattern2630rule2630pattern2631rule2631pattern2632rule2632pattern2633rule2633pattern2634rule2634pattern2635rule2635pattern2636rule2636pattern2637rule2637pattern2638rule2638pattern2639rule2639pattern2640rule2640pattern2641rule2641pattern2642rule2642pattern2643rule2643pattern2644rule2644pattern2645rule2645pattern2646rule2646pattern2647rule2647pattern2648rule2648pattern2649rule2649pattern2650rule2650pattern2651rule2651pattern2652rule2652pattern2653rule2653pattern2654rule2654pattern2655rule2655pattern2656rule2656pattern2657rule2657pattern2658rule2658pattern2659rule2659pattern2660rule2660pattern2661rule2661pattern2662rule2662pattern2663rule2663pattern2664rule2664pattern2665rule2665pattern2666rule2666pattern2667rule2667pattern2668rule2668pattern2669rule2669pattern2670rule2670pattern2671rule2671pattern2672rule2672pattern2673rule2673pattern2674rule2674pattern2675rule2675pattern2676rule2676pattern2677rule2677pattern2678rule2678pattern2679rule2679pattern2680rule2680pattern2681rule2681pattern2682rule2682pattern2683rule2683pattern2684rule2684pattern2685rule2685pattern2686rule2686pattern2687rule2687pattern2688rule2688pattern2689rule2689pattern2690rule2690pattern2691rule2691pattern2692rule2692pattern2693rule2693pattern2694rule2694pattern2695rule2695pattern2696rule2696pattern2697rule2697pattern2698rule2698pattern2699rule2699pattern2700rule2700pattern2701rule2701pattern2702rule2702pattern2703rule2703pattern2704rule2704pattern2705rule2705pattern2706rule2706pattern2707rule2707pattern2708rule2708pattern2709rule2709pattern2710rule2710pattern2711rule2711pattern2712rule2712pattern2713rule2713pattern2714rule2714pattern2715rule2715pattern2716rule2716pattern2717rule2717pattern2718rule2718pattern2719rule2719pattern2720rule2720pattern2721rule2721pattern2722rule2722pattern2723rule2723pattern2724rule2724pattern2725rule2725pattern2726rule2726pattern2727rule2727pattern2728rule2728pattern2729rule2729pattern2730rule2730pattern2731rule2731pattern2732rule2732pattern2733rule2733pattern2734rule2734pattern2735rule2735pattern2736rule2736pattern2737rule2737pattern2738rule2738pattern2739rule2739pattern2740rule2740pattern2741rule2741pattern2742rule2742pattern2743rule2743pattern2744rule2744pattern2745rule2745pattern2746rule2746pattern2747rule2747pattern2748rule2748pattern2749rule2749pattern2750rule2750pattern2751rule2751pattern2752rule2752pattern2753rule2753pattern2754rule2754pattern2755rule2755pattern2756rule2756pattern2757rule2757pattern2758rule2758pattern2759rule2759pattern2760rule2760pattern2761rule2761pattern2762rule2762pattern2763rule2763pattern2764rule2764pattern2765rule2765pattern2766rule2766pattern2767rule2767pattern2768rule2768pattern2769rule2769pattern2770rule2770pattern2771rule2771pattern2772rule2772pattern2773rule2773pattern2774rule2774pattern2775rule2775pattern2776rule2776pattern2777rule2777pattern2778rule2778pattern2779rule2779pattern2780rule2780pattern2781rule2781pattern2782rule2782pattern2783rule2783pattern2784rule2784pattern2785rule2785pattern2786rule2786pattern2787rule2787pattern2788rule2788pattern2789rule2789pattern2790rule2790pattern2791rule2791pattern2792rule2792pattern2793rule2793pattern2794rule2794pattern2795rule2795pattern2796rule2796pattern2797rule2797pattern2798rule2798pattern2799rule2799pattern2800rule2800pattern2801rule2801pattern2802rule2802pattern2803rule2803pattern2804rule2804pattern2805rule2805pattern2806rule2806pattern2807rule2807pattern2808rule2808pattern2809rule2809pattern2810rule2810pattern2811rule2811pattern2812rule2812pattern2813rule2813pattern2814rule2814pattern2815rule2815pattern2816rule2816pattern2817rule2817pattern2818rule2818pattern2819rule2819pattern2820rule2820pattern2821rule2821pattern2822rule2822pattern2823rule2823pattern2824rule2824pattern2825rule2825pattern2826rule2826pattern2827rule2827pattern2828rule2828pattern2829rule2829pattern2830rule2830pattern2831rule2831pattern2832rule2832pattern2833rule2833pattern2834rule2834pattern2835rule2835pattern2836rule2836pattern2837rule2837pattern2838rule2838pattern2839rule2839pattern2840rule2840pattern2841rule2841pattern2842rule2842pattern2843rule2843pattern2844rule2844pattern2845rule2845pattern2846rule2846pattern2847rule2847pattern2848rule2848pattern2849rule2849pattern2850rule2850pattern2851rule2851pattern2852rule2852pattern2853rule2853pattern2854rule2854pattern2855rule2855pattern2856rule2856pattern2857rule2857pattern2858rule2858pattern2859rule2859pattern2860rule2860pattern2861rule2861pattern2862rule2862pattern2863rule2863pattern2864rule2864pattern2865rule2865pattern2866rule2866pattern2867rule2867pattern2868rule2868pattern2869rule2869pattern2870rule2870pattern2871rule2871pattern2872rule2872pattern2873rule2873pattern2874rule2874pattern2875rule2875pattern2876rule2876pattern2877rule2877pattern2878rule2878pattern2879rule2879pattern2880rule2880pattern2881rule2881pattern2882rule2882pattern2883rule2883pattern2884rule2884pattern2885rule2885pattern2886rule2886pattern2887rule2887pattern2888rule2888pattern2889rule2889pattern2890rule2890pattern2891rule2891pattern2892rule2892pattern2893rule2893pattern2894rule2894pattern2895rule2895pattern2896rule2896pattern2897rule2897pattern2898rule2898pattern2899rule2899pattern2900rule2900pattern2901rule2901pattern2902rule2902pattern2903rule2903pattern2904rule2904pattern2905rule2905pattern2906rule2906pattern2907rule2907pattern2908rule2908pattern2909rule2909pattern2910rule2910pattern2911rule2911pattern2912rule2912pattern2913rule2913pattern2914rule2914pattern2915rule2915pattern2916rule2916pattern2917rule2917pattern2918rule2918pattern2919rule2919pattern2920rule2920pattern2921rule2921pattern2922rule2922pattern2923rule2923pattern2924rule2924pattern2925rule2925pattern2926rule2926pattern2927rule2927pattern2928rule2928pattern2929rule2929pattern2930rule2930pattern2931rule2931pattern2932rule2932pattern2933rule2933pattern2934rule2934pattern2935rule2935pattern2936rule2936pattern2937rule2937pattern2938rule2938pattern2939rule2939pattern2940rule2940pattern2941rule2941pattern2942rule2942pattern2943rule2943pattern2944rule2944pattern2945rule2945pattern2946rule2946pattern2947rule2947pattern2948rule2948pattern2949rule2949pattern2950rule2950pattern2951rule2951pattern2952rule2952pattern2953rule2953pattern2954rule2954pattern2955rule2955pattern2956rule2956pattern2957rule2957pattern2958rule2958pattern2959rule2959pattern2960rule2960pattern2961rule2961pattern2962rule2962pattern2963rule2963pattern2964rule2964pattern2965rule2965pattern2966rule2966pattern2967rule2967pattern2968rule2968pattern2969rule2969pattern2970rule2970pattern2971rule2971pattern2972rule2972pattern2973rule2973pattern2974rule2974pattern2975rule2975pattern2976rule2976pattern2977rule2977pattern2978rule2978pattern2979rule2979pattern2980rule2980pattern2981rule2981pattern2982rule2982pattern2983rule2983pattern2984rule2984pattern2985rule2985pattern2986rule2986pattern2987rule2987pattern2988rule2988pattern2989rule2989pattern2990rule2990pattern2991rule2991pattern2992rule2992pattern2993rule2993pattern2994rule2994pattern2995rule2995pattern2996rule2996pattern2997rule2997pattern2998rule2998pattern2999rule2999pattern3000rule3000pattern3001rule3001pattern3002rule3002pattern3003rule3003pattern3004rule3004pattern3005rule3005pattern3006rule3006pattern3007rule3007pattern3008rule3008pattern3009rule3009pattern3010rule3010pattern3011rule3011pattern3012rule3012pattern3013rule3013pattern3014rule3014pattern3015rule3015pattern3016rule3016pattern3017rule3017pattern3018rule3018pattern3019rule3019pattern3020rule3020pattern3021rule3021pattern3022rule3022pattern3023rule3023pattern3024rule3024pattern3025rule3025pattern3026rule3026pattern3027rule3027pattern3028rule3028pattern3029rule3029pattern3030rule3030pattern3031rule3031pattern3032rule3032pattern3033rule3033pattern3034rule3034pattern3035rule3035pattern3036rule3036pattern3037rule3037pattern3038rule3038pattern3039rule3039pattern3040rule3040pattern3041rule3041pattern3042rule3042pattern3043rule3043pattern3044rule3044pattern3045rule3045pattern3046rule3046pattern3047rule3047pattern3048rule3048pattern3049rule3049pattern3050rule3050pattern3051rule3051pattern3052rule3052pattern3053rule3053pattern3054rule3054pattern3055rule3055pattern3056rule3056pattern3057rule3057pattern3058rule3058pattern3059rule3059pattern3060rule3060pattern3061rule3061pattern3062rule3062pattern3063rule3063pattern3064rule3064pattern3065rule3065pattern3066rule3066pattern3067rule3067pattern3068rule3068pattern3069rule3069pattern3070rule3070pattern3071rule3071pattern3072rule3072pattern3073rule3073pattern3074rule3074pattern3075rule3075pattern3076rule3076pattern3077rule3077pattern3078rule3078pattern3079rule3079pattern3080rule3080pattern3081rule3081pattern3082rule3082pattern3083rule3083pattern3084rule3084pattern3085rule3085pattern3086rule3086pattern3087rule3087pattern3088rule3088pattern3089rule3089pattern3090rule3090pattern3091rule3091pattern3092rule3092pattern3093rule3093pattern3094rule3094pattern3095rule3095pattern3096rule3096pattern3097rule3097pattern3098rule3098pattern3099rule3099pattern3100rule3100pattern3101rule3101pattern3102rule3102pattern3103rule3103pattern3104rule3104pattern3105rule3105pattern3106rule3106pattern3107rule3107pattern3108rule3108pattern3109rule3109pattern3110rule3110pattern3111rule3111pattern3112rule3112pattern3113rule3113pattern3114rule3114pattern3115rule3115pattern3116rule3116pattern3117rule3117pattern3118rule3118pattern3119rule3119pattern3120rule3120pattern3121rule3121pattern3122rule3122pattern3123rule3123pattern3124rule3124pattern3125rule3125pattern3126rule3126pattern3127rule3127pattern3128rule3128pattern3129rule3129pattern3130rule3130pattern3131rule3131pattern3132rule3132pattern3133rule3133pattern3134rule3134pattern3135rule3135pattern3136rule3136pattern3137rule3137pattern3138rule3138pattern3139rule3139pattern3140rule3140pattern3141rule3141pattern3142rule3142pattern3143rule3143pattern3144rule3144pattern3145rule3145pattern3146rule3146pattern3147rule3147pattern3148rule3148pattern3149rule3149pattern3150rule3150pattern3151rule3151pattern3152rule3152pattern3153rule3153pattern3154rule3154pattern3155rule3155pattern3156rule3156pattern3157rule3157pattern3158rule3158pattern3159rule3159pattern3160rule3160pattern3161rule3161pattern3162rule3162pattern3163rule3163pattern3164rule3164pattern3165rule3165pattern3166rule3166pattern3167rule3167pattern3168rule3168pattern3169rule3169pattern3170rule3170pattern3171rule3171pattern3172rule3172pattern3173rule3173pattern3174rule3174pattern3175rule3175pattern3176rule3176pattern3177rule3177pattern3178rule3178pattern3179rule3179pattern3180rule3180pattern3181rule3181pattern3182rule3182pattern3183rule3183pattern3184rule3184pattern3185rule3185pattern3186rule3186pattern3187rule3187pattern3188rule3188pattern3189rule3189pattern3190rule3190pattern3191rule3191pattern3192rule3192pattern3193rule3193pattern3194rule3194pattern3195rule3195pattern3196rule3196pattern3197rule3197pattern3198rule3198pattern3199rule3199pattern3200rule3200pattern3201rule3201pattern3202rule3202pattern3203rule3203pattern3204rule3204pattern3205rule3205pattern3206rule3206pattern3207rule3207pattern3208rule3208pattern3209rule3209pattern3210rule3210pattern3211rule3211pattern3212rule3212pattern3213rule3213pattern3214rule3214pattern3215rule3215pattern3216rule3216pattern3217rule3217pattern3218rule3218pattern3219rule3219pattern3220rule3220pattern3221rule3221pattern3222rule3222pattern3223rule3223pattern3224rule3224pattern3225rule3225pattern3226rule3226pattern3227rule3227pattern3228rule3228pattern3229rule3229pattern3230rule3230pattern3231rule3231pattern3232rule3232pattern3233rule3233pattern3234rule3234pattern3235rule3235pattern3236rule3236pattern3237rule3237pattern3238rule3238pattern3239rule3239pattern3240rule3240pattern3241rule3241pattern3242rule3242pattern3243rule3243pattern3244rule3244pattern3245rule3245pattern3246rule3246pattern3247rule3247pattern3248rule3248pattern3249rule3249pattern3250rule3250pattern3251rule3251pattern3252rule3252pattern3253rule3253pattern3254rule3254pattern3255rule3255pattern3256rule3256pattern3257rule3257pattern3258rule3258pattern3259rule3259pattern3260rule3260pattern3261rule3261pattern3262rule3262pattern3263rule3263pattern3264rule3264pattern3265rule3265pattern3266rule3266pattern3267rule3267pattern3268rule3268pattern3269rule3269pattern3270rule3270pattern3271rule3271pattern3272rule3272pattern3273rule3273pattern3274rule3274pattern3275rule3275pattern3276rule3276pattern3277rule3277pattern3278rule3278pattern3279rule3279pattern3280rule3280pattern3281rule3281pattern3282rule3282pattern3283rule3283pattern3284rule3284pattern3285rule3285pattern3286rule3286pattern3287rule3287pattern3288rule3288pattern3289rule3289pattern3290rule3290pattern3291rule3291pattern3292rule3292pattern3293rule3293pattern3294rule3294pattern3295rule3295pattern3296rule3296pattern3297rule3297pattern3298rule3298pattern3299rule3299pattern3300rule3300pattern3301rule3301pattern3302rule3302pattern3303rule3303pattern3304rule3304pattern3305rule3305pattern3306rule3306pattern3307rule3307pattern3308rule3308pattern3309rule3309pattern3310rule3310pattern3311rule3311pattern3312rule3312pattern3313rule3313pattern3314rule3314pattern3315rule3315pattern3316rule3316pattern3317rule3317pattern3318rule3318pattern3319rule3319pattern3320rule3320pattern3321rule3321pattern3322rule3322pattern3323rule3323pattern3324rule3324pattern3325rule3325pattern3326rule3326pattern3327rule3327pattern3328rule3328pattern3329rule3329pattern3330rule3330pattern3331rule3331pattern3332rule3332pattern3333rule3333pattern3334rule3334pattern3335rule3335pattern3336rule3336pattern3337rule3337pattern3338rule3338pattern3339rule3339pattern3340rule3340pattern3341rule3341pattern3342rule3342pattern3343rule3343pattern3344rule3344pattern3345rule3345pattern3346rule3346pattern3347rule3347pattern3348rule3348pattern3349rule3349pattern3350rule3350pattern3351rule3351pattern3352rule3352pattern3353rule3353pattern3354rule3354pattern3355rule3355pattern3356rule3356pattern3357rule3357pattern3358rule3358pattern3359rule3359pattern3360rule3360pattern3361rule3361pattern3362rule3362pattern3363rule3363pattern3364rule3364pattern3365rule3365pattern3366rule3366pattern3367rule3367pattern3368rule3368pattern3369rule3369pattern3370rule3370pattern3371rule3371pattern3372rule3372pattern3373rule3373pattern3374rule3374pattern3375rule3375pattern3376rule3376pattern3377rule3377pattern3378rule3378pattern3379rule3379pattern3380rule3380pattern3381rule3381pattern3382rule3382pattern3383rule3383pattern3384rule3384pattern3385rule3385pattern3386rule3386pattern3387rule3387pattern3388rule3388pattern3389rule3389pattern3390rule3390pattern3391rule3391pattern3392rule3392pattern3393rule3393pattern3394rule3394pattern3395rule3395pattern3396rule3396pattern3397rule3397pattern3398rule3398pattern3399rule3399pattern3400rule3400r  r  r  sine   s         NNddddHHNNVVXX``ddnnnnjjllnnttppppppllllllpppppppnnvvvvvvppnn      
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   C   sD   t td | t|||   |t| |t|||      |S rY  r  r  r  r  r  r  r  r  r  r       Dr  c              
   C   sB   t td| t|||   |t| |t|||      |S rY  r  r  r  r  r  r  r  r  r  r       Br  c              	   C   s   t | td| td  | t| |t|||    |td  ||t|| |t|||    |td   t|||   ||  | S Nr  rK  rt  r  r  r  r  r       r  c              	   C   s   t | td| td  | t| |t|||    |td  ||t|| |t|||    |td   t|||   ||  | S r  rw  r  r  r  r  r    r  r  c                 C   s4   t t|||  || t|||   |   | S rC  r  r  r  r  r  r  r  r    s   4r  c                 C   s2   t t|||  || t|||   |   |S rC  r  r  r  r  r  r  r  r       2r  c                 C   sl   t td | tttdtd|  |td   |||t|||   t| |t|||     |S rW  r  r  r+   r   r  r  r  r  r  r  r  r       lr  c                 C   sj   t td| tttdtd|  |td   |||t|||   t| |t|||     |S rW  r  r  r+   r   r  r  r  r  r  r  r  r       jr  c              	   C   s   t |td | td| td   t| |t|||    |td  ||t|| |t|||    |  t|||   | | td| td   | S rp  rt  r  r  r  r  r       r  c              	   C   s   t |td | td| td   t| |t|||    |td  ||t|| |t|||    |  t|||   | | td| td   | S rp  rw  r  r  r  r  r    r  r  c                 C   s   t td|tdd   | |tdd    | ttdd tdd | tdd tdd |t|||   td|     t|||   |t| |t|||      | S Nr  r  rK  r  )r  r  r5   r  r  r  r  r  r  r  r    r  r  c                 C   s   t td|tdd   | |tdd    | ttdd tdd | tdd tdd |t|||   td|     t|||   |t| |t|||      |S r  )r  r  r5   r  r  r  r  r  r  r  r  	  r  r  c              	   C      t | t| td|t|||   |   t|   | |t|||    t|  ttd|t|||   |   | ||S rF  r  r%   r  r  r&   r   r  r  r  r  r    rk  r  c              	   C   r  rF  r  r%   r  r  r&   r   r  r  r  r  r    rk  r  c                 C   s^   t tdt| |  tt td |td  || td  td| | |   | |S r|  r  r  r  r<   r}  r  r  r  r  r    rI  r  c                 C   sP   t tdt| |  t|td || td  td| | |   | |S rY  )r  r  r  r<   r  r  r  r  r        Pr   c                 C   s^   t tdt| |  tttd |td  || td  td | | |   | |S r|  r  r  r  r  r  r    rI  r  c                 C   s^   t tdt| |  tttd |td  || td  td | | |   | |S rY  r  r  r  r  r  r  !  rI  r  c              
   C   v   t t| |t|||    t| |t|||    | |   tt| | |  |t|||   | |   ||S rC  r  r  r  r  r  r  %     vr  c              
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  D  r  r
  c              
   C   s   t t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d  | |S Nr  r  r  r   r  r}  r  r  r+   r   r  r  r  r  rE  r  r  r  r  r  I  s   4r  c              
   C   s   t t|td || td  |}ttd| | tttd| |td  |td  |  td| | |   ||t|td || td  | |S rW  r   r  r  r  r+   r   r  r  r  r  r  N  s   &~r  c              
   C   s   t t|td || td  |}ttd| | tttd| | |td |td  | |    ||t|td || td  | |S rW  r  r  r  r  r  r  S  s   &rr  c                 C   s^   t tdtt td |td  || td  td| | |   |t| |   |S r|  r  r  r=   r}  r  r  r  r  r  r  X  rI  r  c                 C   sP   t tdt|td || td  td| | |   |t| |   |S rY  )r  r  r=   r  r  r  r  r  r  \  r  r  c                 C   s^   t tdtttd |td  || td  td | | |   |t| |   |S r|  r  r  r  r  r  r  `  rI  r  c                 C   s^   t tdtttd |td  || td  td | | |   |t| |   |S rY  r  r  r  r  r  r  d  rI  r  c                 C   ~   t t| |t|||    | |  t| |t|||     ttdt| | |  |t|||   | |    ||S rF  r  r  r  r  r  r  h     ~r  c                 C   r  rF  r  r  r  r  r  r  l  r  r  c                 C   s   t td| td |td  |td   t| |t|||    |td  t| |td  ||td  t|||    | ||t|| |t|||    |td   t|||   || td |td   |td   | S rp  rt  r  r  r  r  r  p     r  c                 C   s   t td| td |td  |td   t| |t|||    |td  t| |td  ||td  t|||    | ||t|| |t|||    |td   t|||   || td |td   |td   | S rp  rw  r  r  r  r  r  t  r  r  c              
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   C   st   t ||  | tt| | |td tdd   | | ||td  tdd    |||t|||   |S r  r  r+   r   r  r  r  r  r  r  r  r  rE  r  r  r  r    rP  r  c              
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   C   `   t | | td|  t|t|||   td| |  | |t|||    |   ||S rY  r  r  r   r  r  r  r  r  r  r  r  r  rE  r  r  r  r     rf  r   c              
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   C      t || td | td| | td   t|t|||   | | |t|||    |td   ||t||t|||   |td   | |t|||    |  | | | td| | td   | S rp  rT  r  r  r  r  r$       r$  c              
   C      t || td | td| | td   t|t|||   | | |t|||    |td   ||t||t|||   |td   | |t|||    |  | | | td| | td   | S rp  rR  r  r  r  r  r%    r  r%  c                 C   sb   t ||t|||   |td   | |t|||    |td   || |td   |S rd  re  r  r  r  r  r&    rs  r&  c                 C   sd   t ||t|||   |td   | |t|||    |td   || |td   | S rd  rG  r  r  r  r  r'    rr  r'  c              
   C      t | td| | td  ||  t|t|||   | | |t|||    |td   ||t||t|||   |td   | |t|||    |td   || ||   | S Nr  rK  r  rT  r  r  r  r  r(    rX  r(  c              
   C      t | td| | td  ||  t|t|||   | | |t|||    |td   ||t||t|||   |td   | |t|||    |td   || ||   | S r  rR  r  r  r  r  r)    rX  r)  c              
   C   s   t | || td  |td |td   t|t|||   |td  | |t|||    |td   ||t||t|||   |td   | |t|||    |  | | | |td   | S rJ  rT  r  r  r  r  r*    rS  r*  c              
   C   s   t | || td  |td |td   t|t|||   |td  | |t|||    |td   ||t||t|||   |td   | |t|||    |  | | | |td   | S rJ  rR  r  r  r  r  r+    rS  r+  c              
   C   s   t |td td| | td  |td |td   t|t|||   |td  | |t|||    |td   ||ttd | |t|||   |td   | |t|||    |td   || |td   | S rQ  rT  r  r  r  r  r,    r  r,  c              
   C   s   t |td td| | td  |td |td   t|t|||   |td  | |t|||    |td   ||ttd| |t|||   |td   | |t|||    |td   || |td   | S rQ  rR  r  r  r  r  r-       r-  c                 C   \  t | t| |t|||     tt|||  td  | t|||   |  |t|||     ttt|||  td t|t|||    ||t |t| |t|||     tt|||  td  | t|||   |  |t|||     tt|||  t|t|||   tt|||  td   || S rF  rZ  r  r  r  r  r  rE  r  r  r  r.       ^ r.  c                 C   r  rF  r  r  r  r  r  r   r  r  r  r  r/    r  r/  c              
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   C   s   t |td |td  | ||   t|t|||   |td  | |t|||    |td   ||t||t|||   |td   | |t|||    |td   || ||   | S rU  rT  r  r  r  r  r2       r2  c              
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   C      t |tdt|  |t|||   t|  |t|||   t|  t|t|||   |  | |t|||    |  ||S rY  r  r  r%   r  r&   r   r  r  r  r  r  rf       rf  c              
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  r  r  r  r  r|       r|  c              	   C   s   t td|  t| |t|||    | |  |td  t|||   ||   t|||   ||t| |t|||    | t|||   | | S rF  r  r  r  r  r  r}    r  r}  c              
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   C   s  t |t|||   | td  |t|||   |td   | |t|||    |td tdd    | |t|||    |td tdd    ||  tt|| | | | td tdd    | | ||td  tdd    |||t|||   |S r  )r  r  r  r  r+   r   r  r  r  r  r  0      r  c              
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   C   st   t td| tt|| | | |  |td |td  | td tdd    |||t|||   |S rJ  rL  r  r  r  r  r  8  rP  r  c              
   C   sv   t td| tt|| | | |  |td |td  | td tdd    |||t|||   | S rJ  rO  r  r  r  r  r  <  r  r  c              	   C   r  rC  r   r  r  r  r  r  @  r  r  c              	   C   r  rC  r  r  r  r  r  r  D  r  r  c                 C   Z   t tdt|||  td  | |t|||    |  t|||  td  |S rp  r  r  r  r  r  r  H     Zr  c                 C   r  rp  r  r  r  r  r  r  L  r  r  c                 C   s&  t tdtd| td  | |td   t| |t|||    |td  ttd| td  | | |td  t|||    |td |td  |td   td| td  |td | |td   t|||  td   | t|||  td  || t| |t|||    |td  t|||   td|  | t|||  td   | t| |t|||    |td  td| td  |td |td    t|||   td| td  | | |td  t|||  td   | S Nr  r  r  r  r  rK  rt  r  r  r  r  r  P      * r  c                 C   s&  t tdtd| td  | |td   t| |t|||    |td  ttd| td  | | |td  t|||    |td |td  |td   td| td  |td | |td   t|||  td   | t|||  td  || t| |t|||    |td  t|||   td|  | t|||  td   | t| |t|||    |td  td| td  |td |td    t|||   td| td  | | |td  t|||  td   | S r  rw  r  r  r  r  r  T  r  r  c                 C   s  t tdtd| td   t| |t|||    | ttd| td  | | | t|||    |td |td  |td   td| td  |td | |td   t|||  td   | t|||  td  || t| |t|||    |td  t|||   td|  | t|||  td   | t|| |t|||    |td   |td  t|||   td| td  | t|||  td   | S Nr  r  r     r  rK  r  rt  r  r  r  r  r  X      r  c                 C   s  t tdtd| td   t| |t|||    | ttd| td  | | | t|||    |td |td  |td   td| td  |td | |td   t|||  td   | t|||  td  || t| |t|||    |td  t|||   td|  | t|||  td   | t|| |t|||    |td   |td  t|||   td| td  | t|||  td   | S r   rw  r  r  r  r  r  \  r"  r  c                 C   s  t tdtd| td  |td  | |td   t| |t|||    | ttd| td  td| td  |td  | |td   | | | td| td  |td | |td    t|||    |td | |td  |td	  |td   td
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   C   s   t t|t|||   tt|||   tt|||   ttt|||  | |t|||    tt|||    ||S rC  )r  r  r  r  r  r   r  r  r  r  r  x  r]  r  c              
   C   s   t t|t|||   tt|||   tt|||   ttt|||  | |t|||    tt|||    ||S rC  )r  r  r  r  r  r   r  r  r  r  r  |  r]  r  c              
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   C   s   t td| tt| td | |td |  | ||   t|||    |||t|||     ||t|td t|||   ||  | S rp  )r  r  r   r  r  r  r0  r  r  r  r    r  r  c                 C      t ||  | ||   ttd| |t|||     ||t ||  | ||   ttd||t|||     || S rF  r  r   r  r  r0  r  r  r  r       r  c                 C   rH  rF  r  r   r  r  r0  r  r  r  r    rJ  r  c              	   C   X   t |t| t|||   | ||t ||  t| t|||   |td  || S rF  r  r   r  r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c              	   C   rL  rF  r  r   r  r  rN  r  r  r  r    r  r  c                 C   sH   t || |t|||    |  t|||   ||td   | S rF  rB  r  r  r  r  r  r  r  rE  r  r  r  r    s   Hr  c                 C   sF   t || |t|||    |  t|||   ||td   |S rF  rC  rP  r  r  r  r    r~  r  c              	   C   s   t | | | || |td   | | td| td   t| |t|||    |td  ||t| |t|||    | |  | ||   t|||   | | td| td   | S rp  rt  rP  r  r  r  r     r  r  c              	   C   s   t | | | || |td   | | td| td   t| |t|||    |td  ||t| |t|||    | |  | ||   t|||   | | td| td   | S rp  rw  rP  r  r  r  r  $  r  r  c              	   C   s   t | | | || |td   ||td   t| |t|||    | ||t|| |t|||    |  t|||   ||td   | S rF  rt  rP  r  r  r  r  (  r  r  c              	   C   s   t | | | || |td   ||td   t| |t|||    | ||t|| |t|||    |  t|||   ||td   | S rF  rw  rP  r  r  r  r  ,  r  r  c                 C   r   t || tt| |t|||    ||t |  | ||  | ttdt| |t|||     || S rF  r  r   r  r  r  r0  r  r  r  r  0  rN  r  c                 C   rQ  rF  r  r   r  r  r  r0  r  r  r  r  4  rN  r  c                 C   s   t td|td  t| |t|||    |td  t| | |td  || |  | | | || |td   t|||    | ||t|| |t|||    |  t|||   ||td   | S rd  rt  rP  r  r  r  r  8     r  c                 C   s   t td|td  t| |t|||    |td  t| | |td  || |  | | | || |td   t|||    | ||t|| |t|||    |  t|||   ||td   | S rd  rw  rP  r  r  r  r  <  rT  r  c                 C   s  t td| td |td  |td   t| |t|||    |td  t|td | | ||   |td |  | ||   t|||    | ||t| |t|||    |td  |  | ||   t|||   || td |td   |td   | S rp  rt  rP  r  r  r  r  @       r  c                 C   s  t td| td |td  |td   t| |t|||    |td  t|td | | ||   |td |  | ||   t|||    | ||t| |t|||    |td  |  | ||   t|||   || td |td   |td   | S rp  rw  rP  r  r  r  r  D  rU  r  c              	   C   s   t |t|||   |ttdt|||    tt|||  td   ttttd|| |  | ||  |  ttd|| |   ||t|||  |S rF  r  rP  r  r  r  r  H     r  c              	   C   s   t |t|||   |ttdt|||    tt|||  td   ttttd|| |  | ||  |  ttd|| |   ||t|||  | S rF  r  rP  r  r  r  r  L     r  c              
   C   r   t || t| |t|||    |td  ||t |  | ||  | t| |t|||    | || S rF  rM  rP  r  r  r  r  P  rN  r  c              
   C   rX  rF  rO  rP  r  r  r  r  T  rN  r  c              	   C   @   t t|t|||   | | |t|||    |  ||S rC  r  r  r  r  r  r  r  r  rE  r  r  r  r  X     @r  c              	   C   rY  rC  r  rZ  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d  t|||     || t|| |t|||    |  t|||   | | td| td   | S rp  rt  r  r  r  r  r  `  rh  r  c              
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  t td||td   t| |t|||    | t||td |td  |td |td    || | td| | |td    t|||    | ||t|td | |t|||    |td   t|||   || |td   | S rp  rt  rP  r  r  r  r  x      r  c                 C   
  t td||td   t| |t|||    | t||td |td  |td |td    || | td| | |td    t|||    | ||t|td | |t|||    |td   t|||   || |td   | S rp  rw  rP  r  r  r  r  |  r_  r  c	           	      C   s  t |td ||td  | | ||    t| |t|||    |td  ||t|||    |td   t| | |td  || |td|  td   |  | |td|  td  || |td   t|||    | ||t|td | |t|||    |td   ||t|||    |td   |  | ||   t|||   || |td  | | ||    | S Nr  r  r  r'  rK  rt  r8  r  r  r  r        r  c	           	      C   s  t |td ||td  | | ||    t| |t|||    |td  ||t|||    |td   t| | |td  || |td|  td   |  | |td|  td  || |td   t|||    | ||t|td | |t|||    |td   ||t|||    |td   |  | ||   t|||   || |td  | | ||    | S ra  rw  r8  r  r  r  r    rb  r  c	           	      C   s|  t td|||   t| |t|||    |td  ||t|||    |  t| td | ||  | | | |td   |td | |td   ||  | td| td|  td  || |td    t|||    | ||t|td | |t|||    |td   ||t|||    |td   t|||   || ||   | S Nr  r  r  r  rK  rt  r8  r  r  r  r       ~ r  c	           	      C   s|  t td|||   t| |t|||    |td  ||t|||    |  t| td | ||  | | | |td   |td | |td   ||  | td| td|  td  || |td    t|||    | ||t|td | |t|||    |td   ||t|||    |td   t|||   || ||   | S rc  rw  r8  r  r  r  r    rd  r  c	           	      C   s4  t td| | td| td   t| |t|||    |td  ||t|||    |td   t| | | || |td   || || td  t|||    | || t|| |t|||    |  ||t|||    |  t|||   | | td| td   | S rJ  rt  r8  r  r  r  r       6 r  c	           	      C   s4  t td| | td| td   t| |t|||    |td  ||t|||    |td   t| | | || |td   || || td  t|||    | || t|| |t|||    |  ||t|||    |  t|||   | | td| td   | S rJ  rw  r8  r  r  r  r    re  r  c	           	      C   s  t td| | td| td   t| |t|||    |td  ||t|||    |td   t| | | || td  ||td |td  |td |td     || | || td  || ||    t|||    | ||t| |t|||    | ||t|||    |td   |  | ||   t|||   | | td| td   | S r  rt  r8  r  r  r  r        r  c	           	      C   s  t td| | td| td   t| |t|||    |td  ||t|||    |td   t| | | || td  ||td |td  |td |td     || | || td  || ||    t|||    | ||t| |t|||    | ||t|||    |td   |  | ||   t|||   | | td| td   | S r  rw  r8  r  r  r  r    rf  r  c	           	      C   sp  t td| td| td  |  | ||    t| |t|||    |td  ||t|||    |  t|  | td| | td  || |td   || || td  t|||    | ||t|td | |t|||    |  ||t|||    |td   t|||   | | td| td  |  | ||    | S rp  rt  r8  r  r  r  r       r r  c	           	      C   sp  t td| td| td  |  | ||    t| |t|||    |td  ||t|||    |  t|  | td| | td  || |td   || || td  t|||    | ||t|td | |t|||    |  ||t|||    |td   t|||   | | td| td  |  | ||    | S rp  rw  r8  r  r  r  r    rg  r  c                 C   s  t || |  t||t|||    |td  t|  | | || |td   |  | | || |td   t|||    | || t||t|||    |td  |  | ||   t|||   | | | |t|||      | S Nr  rK  r  r   r  r  r  r  r<  r  r  r  r    r  r  c                 C   s  t || |  t||t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   C   s   t || |  | ||    t||t|||    | | | ||td  t|||     ||t|td ||t|||    |td   t|||   | | | |t|||     |  | ||    | S rp  ri  r<  r  r  r  r    r  r  c              
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  r  r  c                 C   s   t td|  | tttdtd|td  |td | | ||     |||t|||   t| |t|||    t||t|||      |S rW  r  r0  r  r  r  r  $  r  r  c	           	      C   sF  t td|||   t| |t|||    | ||t|||    |td   t||td  ||  || | | || |td     || | | || |td|  td    t|||    | ||t|| |t|||    |  ||t|||    |td   t|||   |||   | S r  rt  r8  r  r  r  r  (     H r  c	           	      C   sF  t td|||   t| |t|||    | ||t|||    |td   t||td  ||  || | | || |td     || | | || |td|  td    t|||    | ||t|| |t|||    |  ||t|||    |td   t|||   |||   | S r  rw  r8  r  r  r  r  ,  r}  r  c	           	   	   C   s   t | | t|||   |ttdt|||    tt|||  td   tttd|| |   |tdd   |||  |  ttd|| |    ||t|||  |S r^  r  r8  r  r  r  r  0     r  c	           	   	   C   s   t | | t|||   |ttdt|||    tt|||  td   tttd|| |   |tdd   |||  |  ttd|| |    ||t|||  | S r^  r  r8  r  r  r  r  4  r  r  c                 C   s   t ||| |  t|||   |t| |t|||     t| |t|||      tt| | | td|  | |tdd    t| ||| |t|||    | S r  )r  r  r  r  r+   r   r  rZ  r  r  r  r  8  r  r  c                 C   s   t ||| |  t|||   |t| |t|||     t| |t|||      tt| | | td|  | |tdd    t| ||| |t|||    |S r  )r  r  r  r  r+   r   r  rZ  r  r  r  r	  <  r  r	  c              
   C      t || t| |t|||   t|   |t|||   t|  t|t|||   | | |t|||    |  ||S rC  rm  rZ  r  r  r  r
  @  rv  r
  c              
   C   r  rC  ro  rZ  r  r  r  r  D  rv  r  c              
   C      t | t| td|t|||   |   t|   | |t|||    t|  t|t|||   | td|t|||   |   |  ||S rF  r  rZ  r  r  r  r  H  r  r  c              
   C   r  rF  r  rZ  r  r  r  r  L  r  r  c	           	   
   C   s   t | td t|||   |t| |t|||     t| |t|||      tt| ||  |tdd   |||  |  t| ||   ||t|||  |S r  rr  r8  r  r  r  r  P  r\  r  c	           	   
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   C   st   t td | ttt|||  |t|||   td  | ||   | ||    |t| ||    |S rW  )r  r  r=   r	  r  r  r  rq  r  r  r  r@    rP  r@  c              
   C   sr   t td| ttt|||  |t|||   td  | ||   | ||    |t| ||    |S rW  )r  r  r=   r	  r  r  r  rq  r  r  r  rA    rN  rA  c                 C   ~   t tt|||  t| t|t|||    ttdtt|||  t| t| |t|||      ||S rF  )r  r  r  r  r   r  rq  r  r  r  rB     r  rB  c                 C   r  rF  )r  r  r  r  r   r  rq  r  r  r  rC  $  r  rC  c                 C   s   t td ttd t|||  td   t| td  ttt| |t|||    t|t|||   t| | | td  | |  | |   t| | | td t|||   | | t| td |td    |S rW  )r  r  r  r  r=   r	  r  r  rq  r  r  r  rD  (  r  rD  c                 C   s   t tdtt|||  td   t| td  ttt| |t|||    t|t|||   t| | | td  | |  | |   t| | | td | | t| td |td   t|||    |S rY  )r  r  r  r  r=   r	  r  r  rq  r  r  r  rE  ,  r  rE  c                 C   s   t td t| tdtdt|||     | |   t| tdtdt|||     | |   ttt| |t|||    t|t|||   t| | | td  | |  | |   t| | | td t|||   | |  |S rW  )r  r  r  r  r=   r	  r  r  rq  r  r  r  rF  0  r  rF  c                 C   s   t tdt| tdtdt|||     | |   t| tdtdt|||     | |   ttt| |t|||    t|t|||   t| | | td  | |  | |   t| | | td | | t|||    |S rW  )r  r  r  r  r=   r	  r  r  rq  r  r  r  rG  4  r>  rG  c                 C   z   t t| t|||   t|t|||    ttdt| t|||   t| |t|||      ||S rF  r  rq  r  r  r  rH  8  r  rH  c                 C   r  rF  r  rq  r  r  r  rI  <  r  rI  c                 C   s|  t tdttdt|||   |  | ||   | | ||t|||       t|  | ||   t|||  td  | | ||t|||       ||t|||     ttt| |t|||    t|| | |  td t||t|||     | | ||  | | ||    ||  | ||   t|| | |  td t|||    |S rW  )r  r  r  r  r=   r	  r  r  r0  r  r  r  rJ  @  rd  rJ  c                 C   s~  t td ttdt|||   |  | ||   | | ||t|||       t|  | ||   t|||  td  | | ||t|||       ||t|||     ttt| |t|||    t|| | |  td t||t|||     | | ||  | | ||    ||  | ||   t|| | |  td t|||    |S rW  )r  r  r  r  r=   r	  r  r  r0  r  r  r  rK  D  r  rK  c                 C      t t|  |t|||    t| |t|||     ttdt|  |t|||    t||t|||      ||S rF  r  r0  r  r  r  rL  H  r  rL  c                 C   r  rF  r  r0  r  r  r  rM  L  r  rM  c                 C      t |td|  tt|t|||   | td| t|||     t| |t|||     ||t | | td|  tt|t|||   t| |t|||     || S rY  r  r  r   r  r  rq  r  r  r  rN  P  r  rN  c                 C   r  rY  r  r  r   r  r  rq  r  r  r  rO  T  r  rO  c	           	      C   s  t td|||   t| |t|||    |td  ||t|||    |td   t| td | | ||  || | | | || |td     || | | td| | td  || |   t|||  td   | | ||  | | td| |   || | | || || td     t|||    | ||t|| |t|||    |td   ||t|||    |  t|||   |||   | S Nr  r  rK  r  rt  r8  r  r  r  rP  X      rP  c	           	      C   s  t td|||   t| |t|||    |td  ||t|||    |td   t| td | | ||  || | | | || |td     || | | td| | td  || |   t|||  td   | | ||  | | td| |   || | | || || td     t|||    | ||t|| |t|||    |td   ||t|||    |  t|||   |||   | S r  rw  r8  r  r  r  rQ  \  r  rQ  c	           	      C      t || t| |t|||    |td  ||t|||    |td   ||t |  | ||  | t| |t|||    |td  ||t|||    |  || S r  rM  r8  r  r  r  rR  `  r  rR  c	           	      C   r  r  rO  r8  r  r  r  rS  d  r  rS  c	           	      C   >   t | |t|||    | ||t|||    |  |S rC  r   r  r8  r  r  r  rT  h  r  rT  c	           	      C   r  rC  r   r  r8  r  r  r  rU  l  r  rU  c
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   C   s   t ||  | tt| |	 | |td |	td  |td tdd    |||	 |  |  |	|	|t|||	   |	 S r  r  r  r  r  r  rg    r\  rg  c	           	   
   C      t | t|t|||   | |t|||   |  ||t || t|t|||   |td  |t|||   |  || S rF  r7  	r  r  r  r  r  r  r  r  rE  r  r  r  rh    rv  rh  c	           	   
   C   r  rF  r9  r  r  r  r  ri    rv  ri  c	           	   
   C      t |td |  t|t|||   | |t|||   |td   ||t |td ||  t|t|||   |td  |t|||   |td   || S Nr  r  r  r  r  r  r  r  rj    rW  rj  c	           	   
   C   r  r  r  r  r  r  r  rk    rW  rk  c              
   C   r   t | | ||  |td |   t|t|||
   td| |	  ||t|||
    | |   |
|
S rY  r  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  rl    rN  rl  c              
   C   r  rY  r  r  r  r  r  rm    rN  rm  c
           
   
   C   ~   t | | td  || td   t| |t|||	    ||td   ||t|||	    ||td    |	|	S rY  r  r  r  r  r  rn    r  rn  c
           
   
   C   r  rY  r  r  r  r  r  ro    r  ro  c	           	   
   C   v   t |t|||   t| |t|||    t||t|||      t|t|||   |td  ||S rk  r@  	r  r  r  r  r  r  r  r  rE  r  r  r  rp    r  rp  c	           	   
   C   r  rk  rA  r  r  r  r  rq    r  rq  c              
   C      t | t| |t|  |td t|   |t|||
   td t|   | |t|||
    t|  ||t|||
    t|  t|t|||
   td| |	  ||t|||
     |
|
S rY  r  r%   r  r  r&   r  r   r  r  r  r  rr    rh  rr  c              
   C   r  rY  r  r%   r  r  r&   r  r   r  r  r  r  rs    rh  rs  c                 C   s   t ||t|||
   |	td   | |t|||
    |td   ||t|||
    |  || || td   |
S rd  re  r  r  r  r  rt    r\  rt  c                 C   s   t ||t|||
   |	td   | |t|||
    |td   ||t|||
    |  || || td   |
 S rd  rG  r  r  r  r  ru    rk  ru  c              
   C   8  t |td| |	 td  |td| |	 td   t|t|||
   |	 | |t|||
    |td   ||t|||
    |td   |
|
 ttd | |t|||
   |	td   | |t|||
    |td   ||t|||
    |  || td| |	 td   |
 S r  rT  r  r  r  r  rv    rc  rv  c              
   C   6  t |td| |	 td  |td| |	 td   t|t|||
   |	 | |t|||
    |td   ||t|||
    |td   |
|
 ttd| |t|||
   |	td   | |t|||
    |td   ||t|||
    |  || td| |	 td   |
 S r  rR  r  r  r  r  rw    rb  rw  c              
   C     t | td| |	 td  || |	  t|t|||
   |	 | |t|||
    |td   ||t|||
    |  |
|
t||t|||
   |	td   | |t|||
    |td   ||t|||
    |  || || |	   |
 S r  rT  r  r  r  r  rx    r  rx  c              
   C     t | td| |	 td  || |	  t|t|||
   |	 | |t|||
    |td   ||t|||
    |  |
|
t||t|||
   |	td   | |t|||
    |td   ||t|||
    |  || || |	   |
 S r  rR  r  r  r  r  ry    r  ry  c
           
      C      t | t| |t|  |td t|   |t|||	   td t|   | |t|||	    t|  ||t|||	    t|  t|t|||	   td| |  |	|	S rY  r  
r  r  r  r  r  r  r  r  r  rE  r  r  r  rz     r  rz  c
           
      C   r  rY  r  r  r  r  r  r{    r  r{  c                 C   sv   t ||t|||
   |	td   | |t|||
    |  ||t|||
    |  | | | ||   |
S rF  re  r  r  r  r  r|    r  r|  c                 C   sx   t ||t|||
   |	td   | |t|||
    |  ||t|||
    |  | | | ||   |
 S rF  rG  r  r  r  r  r}    r  r}  c              
   C     t || |	 td | td| |	 td   t|t|||
   |	 | |t|||
    |td   ||t|||
    |  |
|
t||t|||
   |	td   | |t|||
    |  ||t|||
    |  | | | td| |	 td   |
 S rp  rT  r  r  r  r  r~        r~  c              
   C     t || |	 td | td| |	 td   t|t|||
   |	 | |t|||
    |td   ||t|||
    |  |
|
t||t|||
   |	td   | |t|||
    |  ||t|||
    |  | | | td| |	 td   |
 S rp  rR  r  r  r  r  r    r  r  c              
   C   r  r  rT  r  r  r  r  r    rc  r  c              
   C   r  r  rR  r  r  r  r  r    rb  r  c              
   C   r  r  rT  r  r  r  r  r     r  r  c              
   C   r  r  rR  r  r  r  r  r  $  r  r  c              
   C   r  rp  rT  r  r  r  r  r  (  r  r  c              
   C   r  rp  rR  r  r  r  r  r  ,  r  r  c              
   C      t | t| |t|  |td t|   |t|||
   td t|   | |t|||
    t|  ||t|||
    t|  t|t|||
   td| |	  ||t|||
    | |   |
|
S rY  r  r  r  r  r  r  0  r  r  c              
   C   r  rY  r  r  r  r  r  r  4  r  r  c
           
      C   s`   t ||t|||	   |td   | |t|||	    |  || || td   |	 S rF  re  r  r  r  r  r  8  rf  r  c
           
      C   s^   t ||t|||	   |td   | |t|||	    |  || || td   |	S rF  rG  r  r  r  r  r  <  rI  r  c
           
   
   C   s   t || | | || || td    | |td  |td   t|t|||	   |td  | |t|||	    |td   |	|	t|t|||	   |td  | |t|||	    |  | | ||   | | | |td   |	 S rJ  rT  r  r  r  r  r  @     r  c
           
   
   C   s   t || | | || || td    | |td  |td   t|t|||	   |td  | |t|||	    |td   |	|	t|t|||	   |td  | |t|||	    |  | | ||   | | | |td   |	 S rJ  rR  r  r  r  r  r  D  r  r  c
           
   
   C      t | | | || || td   ||| td   t|t|||	   | | |t|||	    |  |	|	t||t|||	   |td   | |t|||	    |  || || td   |	 S rF  rT  r  r  r  r  r  H     r  c
           
   
   C      t | | | || || td   ||| td   t|t|||	   | | |t|||	    |  |	|	t||t|||	   |td   | |t|||	    |  || || td   |	 S rF  rR  r  r  r  r  r  L  r  r  c              
   C   s  t td|td td| td   t| |t|||    |td  td|  | |td  ||  || td| td  t|||     ||ttd| |t|||    |td   |  | ||   t|||   |td | td| td   | S r  rt  rP  r  r  r  r  P  rU  r  c              
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d| td |td  |td  |td  |td  || td  || td   t|t|||   |td  | |t|||    |  t| td |td  |td  |td  |td  | td |td  |td  td| td  || td  || td   | | | | td |td  |td  |td || td  || td    t|||    |td || td  || td  || td  || td   | td |td  |td  |td  |td  | td |td  |td  |td  || td  td| td|  td   |td || td  || td  || td  || td   t|||  td   | ||t|t|||   |td  | |t|||    |td   t|||   | | | |td   | t|t|||   |td  | |t|||    |td   t|||   ||td  | || td   | t||t|||   |td   | |t|||    |td   || td  t|||   | td |td  | |td  |td   | t| |t|||   |td   | |t|||    |td   |td  t|||   |td |td  | || td  || td   | S r  rw  rZ  r  r  r  r    r  r  c	           	   	   C   l   t t|t|||   | tdt|||  td  |td   | |t|||    |  ||S rp  r   rI  r  r  r  r  r  r  r    r  r  c	           	   	   C   r	  rp  r   rI  r  r  r  r  r  r  r    r  r  c              
   C   N   t t|t|||   | t|||  | | |t|||     ||S rC  r  r  r  r  r  r  r  r  rE  r  r  r  r       Nr  c              
   C   r  rC  r  r  r  r  r  r    r  r  c	           	      C   Z  t |td |  t|t|||   | |t|||   |td   ||t ||td  | td |  t|t|||   |td  |t|||   |td   || t |td | td |td   | td |td   t|t|||   |td  |t|||   |td   | |t|||     || S r  r  r  r  r  r  r       \ r  c	           	      C   r  r  r  r  r  r  r  r    r  r  c	           	      C     t |td | |  t|t|||   | |t|||   |td   |  t|||   |  ||t |td | td |td   | | |  t|t|||   |td  |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d |td  t|t|||   | |t|||   |td   | |t|||     ||t |td | td |td   |td  t|t|||   | |t|||   |td   | |t|||     || 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   j  t | |td  | td |td   t|t|||   |td  |t|||   |  ||t || | td |td   t|t|||   |td  |t|||   |  || t | td |td  |td | td |td    t|t|||   |td  |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d |td   t|t|||   |td  |t|||   |  |  t|||   |  || t | | | |td | td |td    t|t|||   |td  |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d |td | td |td    t|t|||   | |t|||   |td   | |t|||     || t td| td |td   t|t|||   | |t|||   |  | |t|||     || S rW  r  r  r  r  r  r    r>  r  c	           	      C   r  rW  r  r  r  r  r  r    r>  r  c                 C   s   t td ttd | | tt|td ttd|td |td   |td | |  |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dttd | | tt|td ttd|td |td   |td | |  |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   z   t tt|||  t|t|||    tt|t|||   | |t|||    tt|||    ||S rC  r  r  r  r   r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c              
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   C   z   t tt|||  t|t|||    tt|t|||   | |t|||    tt|||    ||S rC  r  r  r  r  r  r    r  r  c              
   C   r  rC  r  r  r  r  r  r    r  r  c	           	      C      t || t|t|||   |td  |t|||   |  ||t | | | t|t|||   |td  |t|||   |  | |t|||     || S rk  )r  r   r  r  r  r  r  r  r  r    rW  r  c	           	      C   r  rk  )r  r   r  r  r  r  r  r  r  r    rW  r  c	           	      C      t td|  t|t|||   | |t|||   |  ||t || |  t|t|||   |td  |t|||   |  | |t|||     || S rF  r  r  r  r  r  r    rl  r  c	           	      C   r  rF  r  r  r  r  r  r    rl  r  c
           
   
   C   r  rC  r  r  r  r  r  r    r  r  c
           
   
   C   r  rC  r  r  r  r  r  r    r  r  c
           
      C     t |td |  t|t|||	   | |t|||	   |td   | |t|||	    |td   |	|	t ||td  | td |  t|t|||	   |td  |t|||	   |td   | |t|||	    |td   |	|	 t |td | td |td   | td |td   t|t|||	   |td  |t|||	   |td   | |t|||	    |  |	|	 S r  r  r  r  r  r  r  
      r  c
           
      C   r   r  r  r  r  r  r  r    r!  r  c
           
   
   C   T   t | td|  t| |t|||	    |  ||t|||	    |  |	|	S rY  r  r  r  r  r  r    r4  r  c
           
   
   C   r"  rY  r  r  r  r  r  r     r4  r   c              
   C   |   t | | td|  t|t|||
   td| |	  | |t|||
    |   ||t|||
    |  |
|
S rY  r  r  r  r  r  r    r  r  c              
   C   r#  rY  r  r  r  r  r  r    r  r  c	           	   
   C   n   t |td t| |t|||    | |t|||    |td   ||t|||    |  ||S r	  r  r8  r  r  r  r  "  rn  r  c	           	   
   C   r$  r	  r  r8  r  r  r  r  &  rn  r  c
           
   
   C   s   t | | t|||	   |ttdt|||	    tt|||	  td   tttd||	 |   |td tdd   td||	 |   ||td  tdd    |||	  |  |	|	t|||	  |	S rJ  r  r  r  r  r  r  *  rT  r  c
           
   
   C   s   t | | t|||	   |ttdt|||	    tt|||	  td   tttd||	 |   |td tdd   td||	 |   ||td  tdd    |||	  |  |	|	t|||	  |	 S rJ  r  r  r  r  r  r  .  r  r  c
           
   
   C   s   t | td|  t|||	   |t| |t|||	     t| |t|||	      tt| ||	  |td tdd   | ||	  ||td  tdd    |||	  |  |	|	t|||	  |	S r  rr  r  r  r  r  r  2  r  r  c
           
   
   C   s   t | td|  t|||	   |t| |t|||	     t| |t|||	      tt| ||	  |td tdd   | ||	  ||td  tdd    |||	  |  |	|	t|||	  |	 S r  rt  r  r  r  r  r  6  rS  r  c              
   C   Z   t t|t|||
   |	 | |t|||
    | ||t|||
    |  |
|
S rC  r  r  r  r  r  r	  :  r  r	  c              
   C   r%  rC  r  r  r  r  r  r
  >  r  r
  c              
   C   s  t | | | |t|||
   |	td   tdt|||
   tdd |	td    t|||
  td tdd |	td    | tttd||
 |   |	td tdd   td||
 |   ||	td  tdd    |||
  |  |
|
t|||
  |
S r  r  r  r  r  r  r  B  r  r  c              
   C   s  t | | | |t|||
   |	td   tdt|||
   tdd |	td    t|||
  td tdd |	td    | tttd||
 |   |	td tdd   td||
 |   ||	td  tdd    |||
  |  |
|
t|||
  |
 S r  r  r  r  r  r  r  F  r  r  c              
   C   s  t ||t|||
   |	td   | |t|||
    tdd |	td    | |t|||
    tdd |	td    | tt| ||
  |	td tdd   | ||
  ||	td  tdd    |||
  |  |
|
t|||
  |
S r  r  r  r  r  r  r  J  r  r  c              
   C   s  t ||t|||
   |	td   | |t|||
    tdd |	td    | |t|||
    tdd |	td    | tt| ||
  |	td tdd   | ||
  ||	td  tdd    |||
  |  |
|
t|||
  |
 S r  r  r  r  r  r  r  N  r  r  c	           	      C   ^   t tdt|||  td  | |t|||    |  ||t|||    |  |S rp  r  r8  r  r  r  r  R  rI  r  c	           	      C   r&  rp  r  r8  r  r  r  r  V  rI  r  c
           
   	   C   p   t ttdt|||	  td  |td  | |t|||	    |  ||t|||	    |  |	|	S rp  r   rI  r  r  r  r  r  r  r  Z  rD  r  c
           
   	   C   r'  rp  r   rI  r  r  r  r  r  r  r  ^  rD  r  c              	   C   \   t t|t|||
   |	 | |t|||
    |  ||t|||
    |  |
|
S rC  r  r  r  r  r  r  b  r  r  c              	   C   r*  rC  r  r  r  r  r  r  f  r  r  c                 C   V   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S rC  r   r  r  r  r  r  r  r  j  r  r  c                 C   r+  rC  r   r  r  r  r  r  r  r  n  r  r  c              
   C      t |tdt|	  |t|||
   t|	  |t|||
   t|	  t|t|||
   |	  | |t|||
    |  ||t|||
    |  |
|
S rY  r  r  r  r  r  r  r     r  c              
   C   r.  rY  r  r  r  r  r  r  v  r/  r  c                 C      t || tt| |t|||    t|t|||    ||t || | tt| |t|||    t|t|||   ||t|||      || S rC  r  r  r  r  r  r  r  r  rE  r  r  r  r  z  r/  r  c                 C   r0  rC  r  r1  r  r  r  r  ~  r/  r  c                 C      t || tt|t|||   t| |t|||     ||t |  | ||  | tt|t|||   t| |t|||    ||t|||      || S rC  r  r1  r  r  r  r    r\  r  c                 C   r2  rC  r  r1  r  r  r  r    r\  r  c                 C   s   t td | | tttd| | ||  || |td    |||t|||   t|t|||   t| |t|||      |S rW  r  r1  r  r  r  r    r  r  c                 C   s   t td| | tttd| | ||  || |td    |||t|||   t|t|||   t| |t|||      |S rW  r  r1  r  r  r  r    r  r  c              	   C   s\   t t| | ttt|||  t|||  td  | |  | |   ||  | S rF  )r  r  r<   r	  r  r  r  r0  r  r  r  r    r  r  c              	   C   sZ   t t| | ttt|||  t|||  td  | |  | |   ||  |S rF  )r  r  r<   r	  r  r  r  r0  r  r  r  r     r  r   c                 C   s  t t|t|||   ||t|||     t| |t|||     tt|t|||   ||t|||     |  | ||  | | ||    || t|t|||    t|td | |t|||     ||t|||    | | ||      | S rY  )r  r  r  r<   r	  r  r  r1  r  r  r  r!    r  r!  c                 C   s  t t|t|||   ||t|||     t| |t|||     tt|t|||   ||t|||     |  | ||  | | ||    || t|t|||    t|td | |t|||     ||t|||    | | ||      |S rY  )r  r  r  r<   r	  r  r  r1  r  r  r  r"    r  r"  c                 C      t | | ttdt|t|||   t| |t|||      ||t |  | ||  ||  tt|t|||   t| |t|||    ||t|||      || S rF  r{  r1  r  r  r  r#    r~  r#  c                 C   r3  rF  r|  r1  r  r  r  r$    r~  r$  c                 C      t td| tt| |t|||    t|||   ||t || tt| |t|||    ||t|||     || S rF  r  r0  r  r  r  r%    rv  r%  c                 C   r4  rF  r  r0  r  r  r  r&    rv  r&  c                 C      t | | ttdt| |t|||    t|||    ||t |  | ||  | ttdt| |t|||    ||t|||      || S rF  r{  r0  r  r  r  r'    r  r'  c                 C   r5  rF  r|  r0  r  r  r  r(    r  r(  c                 C      t | | |  | ||   ttdt|t|||   t| |t|||      || t || |  | ||   tt| |t|||    t|t|||   ||t|||      || S rF  r{  r1  r  r  r  r)    r  r)  c                 C   r6  rF  r|  r1  r  r  r  r*    r  r*  c                 C   s  t tdttd t|||  td   t|t|||    t| t|||   | | |   ttd| ||  tttdttdtdt|||     td td|  | |   t|||   |t| |t|||     ||   |S rW  )r  r  r  r  r  r;   r	  r1  r  r  r  r+    r  r+  c                 C   s  t td tt|||  td   t|t|||    t| t|||   | | |   ttd| ||  tttdttdtdt|||     td td|  | |   |t| |t|||     ||  t|||    |S rW  )r  r  r  r  r  r;   r	  r1  r  r  r  r,    r.  r,  c                 C      t ||  | ||   ttdt|t|||   t| |t|||      ||t ||  | ||   tt| |t|||    t|t|||   ||t|||      || S rF  r{  r1  r  r  r  r-    rX  r-  c                 C   r7  rF  r|  r1  r  r  r  r.    rX  r.  c                 C      t td| ttdt|t|||   t| |t|||      ||t |||  tt|t|||   t| |t|||    ||t|||      || S rF  r  r1  r  r  r  r/    r  r/  c                 C   r8  rF  r  r1  r  r  r  r0    r  r0  c                 C      t td||  | ||    t|  | ||  || t|||    t| |t|||    t|||    ||t |td ||  | ||    tt| |t|||    ||t|||     || S rp  r  r  r   r  r  r0  r  r  r  r1    rT  r1  c                 C   r9  rp  r  r  r   r  r  r0  r  r  r  r2    rT  r2  c                 C      t td| ttdt| |t|||    t|||    ||t || ttdt| |t|||    ||t|||      || S rF  r  r0  r  r  r  r3    rx  r3  c                 C   r<  rF  r  r0  r  r  r  r4    rx  r4  c                 C      t td| tt| |t|||    t||t|||     t|||   ||t || tt| |t|||    t||t|||     || S rF  r  r0  r  r  r  r5    r/  r5  c                 C   r=  rF  r  r0  r  r  r  r6    r/  r6  c                 C   s   t td |  | tttd|  | |td  td  ||t|||  t| |t|||    t||t|||      |S rW  r  r0  r  r  r  r7    r1  r7  c                 C   s   t td|  | tttd|  | |td  td  ||t|||  t| |t|||    t||t|||      |S rW  r  r0  r  r  r  r8    r  r8  c                 C      t | | tt||t|||    t| |t|||    t|||    ||t |  | ||  | ttdt| |t|||    t||t|||      || S rF  rR  r0  r  r  r  r9    r  r9  c     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   C   sz   t t|||  t| |t|||    t||t|||      ttdt|||  t|||    ||S rF  r@  r0  r  r  r  r=  
  r  r=  c              
   C   sz   t t|||  t| |t|||    t||t|||      ttdt|||  t|||    ||S rF  rA  r0  r  r  r  r>    r  r>  c                 C      t td|  tt| |t|||    t||t|||    t|||    ||t ||  ttdt| |t|||    t||t|||      || S rF  r  r0  r  r  r  r?    rW  r?  c                 C   r?  rF  r  r0  r  r  r  r@    rW  r@  c              	   C   sj   t t| |t|||    t||t|||     t|||   ttdt|||   ||S rF  )r  r  r  r  r   r  r  r0  r  r  r  rA    r  rA  c              	   C   sb   t t| |t|||    t||t|||     t|||   tt|||  ||S rC  )r  r  r  r  r   r  r0  r  r  r  rB    rs  rB  c                 C      t |tt| |t|||    t||t|||    t|||    ||t |tt| |t|||    t||t|||     || S rC  r  r0  r  r  r  rC  "  r  rC  c                 C   r@  rC  r  r0  r  r  r  rD  &  r  rD  c
           
   	   C   sN   t | | ||  t| |t|||	    ||  t|||	  |  |	|	S rC  )r  r   r  r  r  r  r  r  rE  *  r  rE  c
           
   	   C   sV   t | | ||  t| |t|||	    ||  tdt|||	   |  |	|	S rF  )r  r   r  r  r  r  r  r  r  rF  .  r  rF  c              	   C   s   t t| |t|||
    t| |t|||
     |t|||
    tt||
 |	 | ||
  |tdd    |||
  |  t| ||
   |
|
t|||
  |
S NrK  r  r  r  r  r  r  rG  2  r\  rG  c              	   C   s   t t| |t|||
    t| |t|||
     |t|||
    tt||
 |	 | ||
  |tdd    |||
  |  t| ||
   |
|
t|||
  |
 S rA  r  r  r  r  r  rH  6  r  rH  c              	   C   \   t t|t|||
   |	 | |t|||
    |  ||t|||
    |  |
|
S rC  r  r  r  r  r  rI  :  r  rI  c              	   C   rB  rC  r  r  r  r  r  rJ  >  r  rJ  c                 C   V   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S rC  r  r  r  r  r  rK  B  r  rK  c                 C   rC  rC  r  r  r  r  r  rL  F  r  rL  c              	   C   p   t |||  t|t|||
   | | |	  | t|||
   | |  |t|||
   | |  |
|
S rC  r  r  r  r  r  rM  J  rD  rM  c              	   C   rD  rC  r  r  r  r  r  rN  N  rD  rN  c              
   C      t |t|||
   |	 |t|||
   |	  t|t|||
   |	  | |t|||
    |  ||t|||
    |  |
|
S rC  r  r  r  r  r  rO  R  r  rO  c              
   C   rE  rC  r  r  r  r  r  rP  V  r  rP  c              
   C   h   t || t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S rC  r  r  r  r  r  rQ  Z     hrQ  c              
   C   rF  rC  r  r  r  r  r  rR  ^  rG  rR  c
           
      C   `   t ||t|||	    | | t|||	   | |  tdt|||	   | |   |	S rF  r  r  r  r  r  rS  b  rf  rS  c
           
      C   rH  rF  r  r  r  r  r  rT  f  rf  rT  c              	   C      t |t|||
   |	 tdt|||
   |	  t||t|||
    | | t|||
   | |  tdt|||
   | |	   |
|
S rF  )r  r  r  r   r  r  r  r  rU  j  rx  rU  c              	   C   rI  rF  )r  r  r  r   r  r  r  r  rV  n  rx  rV  c              
   C      t |t|||
   | ||t|||
    |  |t|||
   | |   t|t|||
   | |	  | |t|||
    |  |t|||
   | |  |
|
S rC  r  r  r  r  r  rW  r  r\  rW  c              
   C   rJ  rC  r  r  r  r  r  rX  v  r\  rX  c              	   C   p   t |||  t|t|||
   | | |	  | t|||
   | |  |t|||
   | |  |
|
S rC  r  r  r  r  r  rY  z  rD  rY  c              	   C   rK  rC  r  r  r  r  r  rZ  ~  rD  rZ  c              
   C      t |t|||
   |	 |t|||
   |	  t|t|||
   |	  | |t|||
    |  ||t|||
    |  |
|
S rC  r  r  r  r  r  r[    r  r[  c              
   C   rL  rC  r  r  r  r  r  r\    r  r\  c              
   C   h   t || t|t|||
   | |	  ||t|||
    |  | t|||
   | |  |
|
S rC  r  r  r  r  r  r]    rG  r]  c              
   C   rM  rC  r  r  r  r  r  r^    rG  r^  c
           
      C   X   t | |t|||	    | |t|||	   | |  t|||	  | |   |	S rC  r  r  r  r  r  r_    r  r_  c
           
      C   rN  rC  r  r  r  r  r  r`    r  r`  c              	   C      t |t|||
   |	 t|||
  |	  t| |t|||
    | |t|||
   | |  t|||
  | |	   |
|
S rC  r  r  r  r  r  ra    rv  ra  c              	   C   rO  rC  r  r  r  r  r  rb    rv  rb  c              
   C      t |t|||
   | | |t|||
    |  | t|||
   | |   t|t|||
   | |	  ||t|||
    |  | t|||
   | |  |
|
S rC  r  r  r  r  r  rc    r\  rc  c              
   C   rP  rC  r  r  r  r  r  rd    r\  rd  c	           	   	   C   T   t t| |t|||    ||t|||    |  t|||  |  ||S rC  r  	r  r  r  r  r  r  r  r  rE  r  r  r  re    r4  re  c	           	   	   C   rQ  rC  r  rR  r  r  r  rf    r4  rf  c              
   C   p   t || ||  t| |t|||
    ||t|||
    | |	   t|||
  td|   |
|
S rY  r7  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  rg    rD  rg  c              
   C   rS  rY  r9  rT  r  r  r  rh    rD  rh  c
           
      C   j   t ||t|||	    | | | || t|||	  td   | | ||  t|||	     |	S rY  r  
r  r  r  r  r  r  r  r  r  rE  r  r  r  ri    r  ri  c
           
      C   rU  rY  r  rV  r  r  r  rj    r  rj  c	           	      C      t | | ||  td| |  tt||t|||    t||t|||     ||t | | ||  td| |  tt||t|||    t||t|||     || S rY  r  	r  r  r  r  r  r  r  r  rE  r  r  r  rk       rk  c	           	      C   rW  rY  r  rX  r  r  r  rl    rY  rl  c                 C   sh   t |||t|||
    |  ||t|||
    |	  t|||
   |||	 td   |
 S rF  rB  rT  r  r  r  rm    rG  rm  c                 C   sf   t |||t|||
    |  ||t|||
    |	  t|||
   |||	 td   |
S rF  rC  rT  r  r  r  rn       frn  c
           
      C      t || tt||t|||	    ||t|||	    |td   |	|	t |  | ||  | tt||t|||	    ||t|||	    |  |	|	 S rF  rR  
r  r  r  r  r  r  r  r  r  rE  r  r  r  ro    rv  ro  c
           
      C   r[  rF  rS  r\  r  r  r  rp    rv  rp  c              
   C   s  t | | ||	 td  || ||	   || td| td   t||t|||
    |td  ||t|||
    |	  |
|
t||t|||
    | ||t|||
    |	  | | ||   t|||
   || td| td   |
 S rp  rt  rT  r  r  r  rq    r  rq  c              
   C   s  t | | ||	 td  || ||	   || td| td   t||t|||
    |td  ||t|||
    |	  |
|
t||t|||
    | ||t|||
    |	  | | ||   t|||
   || td| td   |
 S rp  rw  rT  r  r  r  rr    r  rr  c              
   C   s   t |  | ||	 td  || ||	   |||	 td   t||t|||
    | ||t|||
    |	  |
|
 t|||t|||
    |  ||t|||
    |	  t|||
   |||	 td   |
 S rF  rt  rT  r  r  r  rs    r  rs  c              
   C   s   t |  | ||	 td  || ||	   |||	 td   t||t|||
    | ||t|||
    |	  |
|
 t|||t|||
    |  ||t|||
    |	  t|||
   |||	 td   |
 S rF  rw  rT  r  r  r  rt    r  rt  c                 C   s   t ||t|||
    | ||t|||
    |	td   |  | ||   t|||
   ||td |td   |	td   |
S rp  rG  rT  r  r  r  ru    r  ru  c                 C   s   t ||t|||
    | ||t|||
    |	td   |  | ||   t|||
   ||td |td   |	td   |
 S rp  re  rT  r  r  r  rv    r  rv  c                 C   s  t |||	td  || ||    t||t|||
    |td  ||t|||
    |	td   t| | | ||	 td  ||| |td  || |	td     | | | ||	 td  || | |	td  || |    t|||
    |
 |
|
 t|td ||t|||
    |td   ||t|||
    |	td   |  | ||   t|||
   || |	td  || ||    |
 S Nr  rK  r  r  rt  rT  r  r  r  rw        rw  c                 C   s  t |||	td  || ||    t||t|||
    |td  ||t|||
    |	td   t| | | ||	 td  ||| |td  || |	td     | | | ||	 td  || | |	td  || |    t|||
    |
 |
|
 t|td ||t|||
    |td   ||t|||
    |	td   |  | ||   t|||
   || |	td  || ||    |
 S r]  rw  rT  r  r  r  rx    r^  rx  c                 C   s  t td|||	 td   t||t|||
    |td  ||t|||
    |	  t| | | ||	 td  ||| |td  || |	td     | | | ||	 td  || | td| |	  || |    t|||
    |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   t|||
   || ||	 td   |
 S r^  rt  rT  r  r  r  ry        ry  c                 C   s  t td|||	 td   t||t|||
    |td  ||t|||
    |	  t| | | ||	 td  ||| |td  || |	td     | | | ||	 td  || | td| |	  || |    t|||
    |
 |
|
t|| ||t|||
    |td   ||t|||
    |	td   t|||
   || ||	 td   |
 S r^  rw  rT  r  r  r  rz    r_  rz  c                 C   st  t td|| td| td   t||t|||
    |td  ||t|||
    |	td   t| || |	 || |td    ||| | || |	    || | ||	 td  || ||	    t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	  | | ||   t|||
   || td| td   |
 S rJ  rt  rT  r  r  r  r{    r  r{  c                 C   st  t td|| td| td   t||t|||
    |td  ||t|||
    |	td   t| || |	 || |td    ||| | || |	    || | ||	 td  || ||	    t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	  | | ||   t|||
   || td| td   |
 S rJ  rw  rT  r  r  r  r|    r  r|  c                 C   s  t td|td| td  | | ||    t||t|||
    |td  ||t|||
    |	  t| | | td| |	 td  || |td    ||| | || |	td     || | ||   ||	 td  t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	td   | | ||   t|||
   || td| td  | | ||    |
 S rp  rt  rT  r  r  r  r}  
      r}  c                 C   s  t td|td| td  | | ||    t||t|||
    |td  ||t|||
    |	  t| | | td| |	 td  || |td    ||| | || |	td     || | ||   ||	 td  t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	td   | | ||   t|||
   || td| td  | | ||    |
 S rp  rw  rT  r  r  r  r~    r`  r~  c
           
   
   C   s   t td | | ||t|||	    |td   t|||	   || t||t|||	     td| td   |	S r  r;  r\  r  r  r  r    rk  r  c
           
   
   C   s   t td| | ||t|||	    |td   t|||	   || t||t|||	     td| td   |	S r  r=  r\  r  r  r  r    r\  r  c
           
      C   sT  t | | | td| td  |td | | |td  ||    td| |td  || ||    tt||t|||	    ||t|||	    |td   |	|	t|td ||t|||	    |td   |  | ||   t|||	   || t||t|||	     |td  || ||    |	 S ro  rm  r\  r  r  r  r       V r  c
           
      C   sT  t | | | td| td  |td | | |td  ||    td| |td  || ||    tt||t|||	    ||t|||	    |td   |	|	t|td ||t|||	    |td   |  | ||   t|||	   || t||t|||	     |td  || ||    |	 S ro  rn  r\  r  r  r  r    ra  r  c
           
      C   s,  t | | | td| td  |td | | |td  ||    || td| td   tt||t|||	    ||t|||	    |  |	|	ttd | | ||t|||	    |td   t|||	   || t||t|||	     td| td   |	 S ro  rm  r\  r  r  r  r  "  s   . r  c
           
      C   s*  t | | | td| td  |td | | |td  ||    || td| td   tt||t|||	    ||t|||	    |  |	|	ttd| | ||t|||	    |td   t|||	   || t||t|||	     td| td   |	 S ro  rn  r\  r  r  r  r  &  r  r  c	           	      C      t || tt||t|||    t||t|||     ||t | | ||  | ttdt||t|||    t||t|||      || S rF  rR  rX  r  r  r  r  *  r/  r  c	           	      C   rb  rF  rS  rX  r  r  r  r  .  r/  r  c                 C   sR  t td|||	 td   t||t|||
    | ||t|||
    |	td   t| | | ||	 td  ||| | || |	    | | | ||	 td  ||| | || |	    t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	  t|||
   |||	 td   |
 S rd  rt  rT  r  r  r  r  2     T r  c                 C   sR  t td|||	 td   t||t|||
    | ||t|||
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  td   | | || || ||	    || td|  | ||   ||	 td   t|||
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 S r  rt  rT  r  r  r  r  b       r  c                 C   s  t td|||	 td   t||t|||
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    |	  t| |td  | ||	 td  || || |	td  || |td     || | | ||	 td  || | td| |	  || |     t|||
  td   | | || || ||	    || td|  | ||   ||	 td   t|||
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 |
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t|| ||t|||
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   || ||	 td   |
 S r  rw  rT  r  r  r  r  f  rh  r  c                 C      t || |td  tt|t|||   t||t|||     ||t| | | | ||  t|||    |t|||   tdd  t||t|||      | S r  r  r  r  r  r  r  r  r  rE  r  r  r  r  j  rV  r  c                 C   ri  r  r  rj  r  r  r  r  n  rV  r  c	           	      C      t || tt||t|||    t||t|||     ||t | | ||  | tt||t|||    ||t|||    tdd   || S r  rR  rX  r  r  r  r  r  r/  r  c	           	      C   rk  r  rS  rX  r  r  r  r  v  r/  r  c                 C   s  t ||td |td   t| | ||  | | ||  t|||    |t|||   tdd  t||t|||      ||ttd| | ||   t|||   |t|t|||    t||t|||     |td |td    | S r  r  r  r  r  r  r  r  r  rE  r  r  r  r  z  r  r  c                 C   s  t ||td |td   t| | ||  | | ||  t|||    |t|||   tdd  t||t|||      ||ttd | | ||   t|||   |t|t|||    t||t|||     |td |td    | S r  r  rl  r  r  r  r  ~  r  r  c                 C   s  t td |  t|tdtdt|||     ||   t|tdtdt|||     ||   ||  ttt||t|||    t|t|||   t|| | td  ||  ||   t|| | td t|||   ||td  |  |S rW  )r  r  r  r  r<   r	  r  r  rj  r  r  r  r    r  r  c                 C   s  t td|  t|tdtdt|||     ||   t|tdtdt|||     ||   ||  ttt||t|||    t|t|||   t|| | td  ||  ||   t|| | td ||td  | t|||    |S rW  )r  r  r  r  r<   r	  r  r  rj  r  r  r  r    r  r  c                 C      t t| t|||   t|t|||    t| |t|||    | t|||   tdd  t||t|||      || S r  r  rj  r  r  r  r    r  r  c                 C   rm  r  r  rj  r  r  r  r    r  r  c	           	      C   s  t td |  t| | ||  t|||  td  ||t|||    ||    ttdt|||    | | ||   ||t|||    ||    ||t|||     ||  ttt||t|||    t|| ||  td t||t|||     || ||  || ||    || | ||  td  t|| ||  td t|||    |S rW  )r  r  r  r  r<   r	  r  r  rX  r  r  r  r    s    r  c	           	      C   s  t td|  t| | ||  t|||  td  ||t|||    ||    ttdt|||    | | ||   ||t|||    ||    ||t|||     ||  ttt||t|||    t|| ||  td t||t|||     || ||  || ||    || | ||  td  t|| ||  td t|||    |S rW  )r  r  r  r  r<   r	  r  r  rX  r  r  r  r    s    r  c	           	      C      t t| |t|||    t||t|||     t| |t|||    ||t|||    tdd  t| |t|||      ||S r  r  rX  r  r  r  r       r  c	           	      C   rn  r  r  rX  r  r  r  r    ro  r  c	           	      C      t | | ||  ttdt||t|||    t||t|||      ||t | | ||  ||  tt|||  td ||t|||    tdd  t||t|||      || S r  r{  rX  r  r  r  r    r  r  c	           	      C   rp  r  r|  rX  r  r  r  r    r  r  c                 C   s  t td|td |td  |td   t||t|||
    |td  ||t|||
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  td   | |td  | | ||   ||td  | | ||    t|||
    |
 |
|
t||t|||
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 S rJ  rt  rT  r  r  r  r    r"  r  c                 C   s  t td|td |td  |td   t||t|||
    |td  ||t|||
    |	td   t||td  | | ||   ||	 | | ||    || | ||   ||	 td  t|||
  td   | |td  | | ||   ||td  | | ||    t|||
    |
 |
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   ||td |td   |td   |
 S rJ  rw  rT  r  r  r  r    r"  r  c                 C   s   t td|td |td  |td  | | ||    t||t|||
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    |	  t|| | | ||   ||	 td  || | | ||   ||	 td  t|||
  td   |td | | ||   | | ||    | | ||  || |td  || |td    t|||
    |
 |
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t||t|||
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   ||td |td   |td  | | ||    |
 S r  rt  rT  r  r  r  r        $ r  c                 C   s   t td|td |td  |td  | | ||    t||t|||
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    |	  t|| | | ||   ||	 td  || | | ||   ||	 td  t|||
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    |
 |
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   ||td |td   |td  | | ||    |
 S r  rw  rT  r  r  r  r    rq  r  c	           	      C      t | | ||  | | ||   ttd||t|||     ||t |  | ||  | | ||   ttd||t|||     || S rF  rI  rX  r  r  r  r    r  r  c	           	      C   rr  rF  rK  rX  r  r  r  r    r  r  c
           
      C   re  rC  r  rV  r  r  r  r    r\  r  c
           
      C   re  rC  r  rV  r  r  r  r    r\  r  c
           
      C   s  t tdtd| td  t||t|||	    |td  t| | | td| td  |td| | | ||    | td| td  || ||   |td| td  || ||    t|||	    | | | td| td  ||| td| | |    t|||	  td   |	 t||t|||	     |	|	ttd | t||t|||	     ||t|||	    |  t|||	   |td| td   |	 S Nr  r  r  rK  rx  r\  r  r  r  r    s    r  c
           
      C   s  t tdtd| td  t||t|||	    |td  t| | | td| td  |td| | | ||    | td| td  || ||   |td| td  || ||    t|||	    | | | td| td  ||| td| | |    t|||	  td   |	 t||t|||	     |	|	ttd| t||t|||	     ||t|||	    |  t|||	   |td| td   |	 S rs  ry  r\  r  r  r  r    s    r  c              
   C   sj   t td|  ttdtt|||  t|||  td   ||  ||   |t||   |S Nr  rK  r  )r  r  r;   r	  r  r  r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c              
   C   sh   t td|  ttdtt|||  t|||  td  ||  ||   |t||   |S rt  )r  r  r;   r	  r  r  r  ru  r  r  r  r    rG  r  c                 C   ~   t tt|||  t|t|||    t| |t|||    t||t|||    tt|||    ||S rC  r  rl  r  r  r  r    r  r  c                 C   rv  rC  r  rl  r  r  r  r    r  r  c	           	      C      t || tt||t|||    t||t|||     ||t |  | ||  | ttdt||t|||    t||t|||      || S rF  rR  rX  r  r  r  r    rv  r  c	           	      C   rw  rF  rS  rX  r  r  r  r    rv  r  c                 C   V   t | |t|||
    ||t|||
    |  ||t|||
    |	  |
S rC  r  rT  r  r  r  r    r  r  c                 C   rx  rC  r  rT  r  r  r  r    r  r  c              	   C   s   t t||t|||    t||t|||     |t|||    tt| ||  |
 |||  |tdd    |||  |	tdd    ||t|||  |S rA  r  r  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r    r\  r  c              	   C   s   t t||t|||    t||t|||     |t|||    tt| ||  |
 |||  |tdd    |||  |	tdd    ||t|||  | S rA  r  ry  r  r  r  r    r  r  c              
   C   N   t td| t|t|||   |td  | |t|||     ||S rF  r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c              
   C   rz  rF  r  r{  r  r  r  r    r  r  c              
   C   sp   t td| tttd|td  |td tdd   | ||td   |  ||t|||  | S rJ  rO  r  r  r  r  r  rE  r  r  r  r    rD  r  c              
   C   sn   t td| tttd|td  |td tdd   | ||td   |  ||t|||  |S rJ  rL  r|  r  r  r  r    rn  r  c                 C   sN   t | |t|||   |td   t|||   || |td   |S rF  rG  r  r  r  r  r  r  rE  r  r  r  r  
  r  r  c                 C   sP   t | |t|||   |td   t|||   || |td   | S rF  re  r}  r  r  r  r    r  r  c                 C   s   t | |td  ||td   |td |td   t|t|||   |td  ||t| |t|||   |td   t|||   || |td   | S rW  rt  r}  r  r  r  r    rW  r  c                 C   s   t | |td  ||td   |td |td   t|t|||   |td  ||t| |t|||   |td   t|||   || |td   | S rW  rw  r}  r  r  r  r    rW  r  c                 C   s   t | |td  ||td   |td  t|t|||   | ||t||t|||   |td   t|||   || |td   | S rW  rt  r}  r  r  r  r    r  r  c                 C   s   t | |td  ||td   |td  t|t|||   | ||t||t|||   |td   t|||   || |td   | S rW  rw  r}  r  r  r  r    r  r  c	           	      C   h   t |td t||t|||    |td  t|| ||  || t|||    | ||S r	  r  	r  r  r  r  r  r  r  r  rE  r  r  r  r  "  rG  r  c	           	      C   r~  r	  r  r  r  r  r  r  &  rG  r  c                 C   ^   t ||td  t||t|||    |td  t| |t|||    | ||S rW  r  r  r  r  r  r  r  r  rE  r  r  r  r  *  rI  r  c                 C   r  rW  r  r  r  r  r  r  .  rI  r  c	           	   
   C      t |t||t|||    | t|||  td td  ||t | | t||t|||    | t|||  td  || S rp  rM  r  r  r  r  r  2  r  r  c	           	   
   C   r  rp  rO  r  r  r  r  r  6  r  r  c              
   C      t |t||t|||    | t|||  td td  ||t | | t||t|||    | t|||  td  || S rp  rM  r  r  r  r  r  :  r  r  c              
   C   r  rp  rO  r  r  r  r  r  >  r  r  c	           	      C   s  t td|td td| td   t||t|||    |td  t| | |td  || td| td  t|||    ||| ||    | ||t||t|||    | | | ||  ||   t|||   || td| td   | S rp  rt  r  r  r  r  r  B  r  r  c	           	      C   s  t td|td td| td   t||t|||    |td  t| | |td  || td| td  t|||    ||| ||    | ||t||t|||    | | | ||  ||   t|||   || td| td   | S rp  rw  r  r  r  r  r  F  r  r  c                 C   s  t td|td td| td   t||t|||    |td  t| | |td  || |  || td| td  t|||    | ||t|| |  ||t|||    |  t|||   || td| td   | S rp  rt  r  r  r  r  r  J  r  r  c                 C   s  t td|td td| td   t||t|||    |td  t| | |td  || |  || td| td  t|||    | ||t|| |  ||t|||    |  t|||   || td| td   | S rp  rw  r  r  r  r  r  N  r  r  c	           	      C   s  t td||td |td   |td   t||t|||    |td  t||td  | | ||  ||   | |td  || |  ||td   ||td  | | ||  ||    t|||    | ||t||t|||    |td  | |td  || |  ||td    t|||   || |td |td   |td   | S rp  rt  r  r  r  r  r  R      r  c	           	      C   s  t td||td |td   |td   t||t|||    |td  t||td  | | ||  ||   | |td  || |  ||td   ||td  | | ||  ||    t|||    | ||t||t|||    |td  | |td  || |  ||td    t|||   || |td |td   |td   | S rp  rw  r  r  r  r  r  V  r  r  c                 C   sV  t td||td |td   |td   t||t|||    |td  t|| | |  |td  | |td  ||td   |td | |  |td   t|||    | ||t||t|||    |td  | |td  ||td    t|||   || |td |td   |td   | S rp  rt  r  r  r  r  r  Z  r  r  c                 C   sV  t td||td |td   |td   t||t|||    |td  t|| | |  |td  | |td  ||td   |td | |  |td   t|||    | ||t||t|||    |td  | |td  ||td    t|||   || |td |td   |td   | S rp  rw  r  r  r  r  r  ^  r  r  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td   || |td  ||  t|||    | ||t|||t|||    |td   t|||   || |td   | S rp  rt  r  r  r  r  r  b     r  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td   || |td  ||  t|||    | ||t|||t|||    |td   t|||   || |td   | S rp  rw  r  r  r  r  r  f  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 rp  rt  r  r  r  r  r  j  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 rp  rw  r  r  r  r  r  n  r  r  c	           	   
   C      t |t|||   | |  |t|||  |  |  t|t|||   ||  | |t|||    |t|||  td    ||S rY  r  r  r   r  	r  r  r  r  r  r  r  r  rE  r  r  r  r  r  r  r  c	           	   
   C   r  rY  r  r  r   r  r  r  r  r  r  v  r  r  c              
   C      t |t|||   | |  |t|||  |  |  t|t|||   ||  | |t|||  td    ||S rY  r  r  r  r  r  r  r  r  rE  r  r  r  r  z  rJ  r  c              
   C   r  rY  r  r  r  r  r  r  ~  rJ  r  c                 C   sb  t td|td |td |td   |	td   t||t|||
    |	td  t| | | |td |td   |	td  t|||
  td  ||	td  |  | || ||   || ||  | | ||      || |td | || | |	td   |td | |	td    | | ||  | |td  |	td  ||td |td |	td       t|||
    |
 |
|
 t||t|||
    |	td  | | ||   | |td  || |  ||td    t|||
   |td | |td |td   |	td   |
 S rp  rt  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r        f r  c                 C   sb  t td|td |td |td   |	td   t||t|||
    |	td  t| | | |td |td   |	td  t|||
  td  ||	td  |  | || ||   || ||  | | ||      || |td | || | |	td   |td | |	td    | | ||  | |td  |	td  ||td |td |	td       t|||
    |
 |
|
 t||t|||
    |	td  | | ||   | |td  || |  ||td    t|||
   |td | |td |td   |	td   |
 S rp  rw  r  r  r  r  r    r  r  c
           
      C   s  t td|td |td |td   |td   t||t|||	    |td  t|| | |td |td   |td  t|||	  td  ||td  | | || ||   || | | ||      | | ||  | |td  |td  ||td |td |td      t|||	    |	 |	|	t||t|||	    |td  | |td  ||td    | | ||   t|||	   |td | |td |td   |td   |	 S rp  rt  
r  r  r  r  r  r  r  r  r  rE  r  r  r  r        r  c
           
      C   s  t td|td |td |td   |td   t||t|||	    |td  t|| | |td |td   |td  t|||	  td  ||td  | | || ||   || | | ||      | | ||  | |td  |td  ||td |td |td      t|||	    |	 |	|	t||t|||	    |td  | |td  ||td    | | ||   t|||	   |td | |td |td   |td   |	 S rp  rw  r  r  r  r  r    r  r  c                 C   sf  t td||	td   t||t|||
    |	 t| | | |	td  || |  ||| |	td  || |	td  ||	td      t|||
    td| | | ||	td  || ||    t|||
  td   |
 |
|
t|| ||t|||
    |	td   t|||
   t|||
   || |	td   |
 S r  rt  r  r  r  r  r       h r  c                 C   sf  t td||	td   t||t|||
    |	 t| | | |	td  || |  ||| |	td  || |	td  ||	td      t|||
    td| | | ||	td  || ||    t|||
  td   |
 |
|
t|| ||t|||
    |	td   t|||
   t|||
   || |	td   |
 S r  rw  r  r  r  r  r    r  r  c
           
      C   sJ  t td||td   t||t|||	    | t| | | |td  || |  || | |td  ||td    t|||	    td| | | || | |td   t|||	  td   |	 |	|	t|| ||t|||	    |td   t|||	   t|||	   || |td   |	 S r  rt  r  r  r  r  r       L r  c
           
      C   sJ  t td||td   t||t|||	    | t| | | |td  || |  || | |td  ||td    t|||	    td| | | || | |td   t|||	  td   |	 |	|	t|| ||t|||	    |td   t|||	   t|||	   || |td   |	 S r  rw  r  r  r  r  r    r  r  c                 C   s  t tdtd| | | td|	 td   t||t|||    |	td  ||t|||    |
  t| |td |	td  |td td|	 |
 td    || | |	|
 td   ||td |	 |td |
td     || | td|	 |
  | | ||  |	|
 td    t|||    | || t||t|||    |	 ||t|||    |
td   | | ||  ||   t|||   td| | | td|	 td   | S Nr  r  rK  r  rt  r  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c                 C   s  t tdtd| | | td|	 td   t||t|||    |	td  ||t|||    |
  t| |td |	td  |td td|	 |
 td    || | |	|
 td   ||td |	 |td |
td     || | td|	 |
  | | ||  |	|
 td    t|||    | || t||t|||    |	 ||t|||    |
td   | | ||  ||   t|||   td| | | td|	 td   | S r  rw  r  r  r  r  r    r  r  c                 C   s  t tdtd| | | td| td   t||t|||
    |td  ||t|||
    |	  t| |td |td  |td td| |	 td    ||td | |td |	td     || | ||	 td  || td| |	    t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | | ||   t|||
   td| | | td| td   |
 S r  rt  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c                 C   s  t tdtd| | | td| td   t||t|||
    |td  ||t|||
    |	  t| |td |td  |td td| |	 td    ||td | |td |	td     || | ||	 td  || td| |	    t|||
    |
 |
|
 t||t|||
    | ||t|||
    |	td   | | ||   t|||
   td| | | td| td   |
 S r  rw  r  r  r  r  r    r  r  c                 C   s   t ||t|||
    |	 t| |t|||
    | |
 t||t|||
     |
ttd | ||t|||
    |	td   t|||
   || t||t|||
     td|	 td   |
 S r  )r   r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t ||t|||
    |	 t| |t|||
    | |
 t||t|||
     |
ttd| ||t|||
    |	td   t|||
   || t||t|||
     td|	 td   |
 S r  )r   r  r  r  r  r  r  r  r  r  r    rT  r  c
           
      C   s   t | | t||t|||	    | t||t|||	     |	|	ttd | ||t|||	    |td   t|||	   || t||t|||	     td| td   |	 S r  )r  r   r  r  r  r  r  r  r  r  r  r    r  r  c
           
      C   s   t | | t||t|||	    | t||t|||	     |	|	ttd| ||t|||	    |td   t|||	   || t||t|||	     td| td   |	 S r  )r  r   r  r  r  r  r  r  r  r  r  r    rX  r  c                 C   sf  t td|| |	|
 td   t||t|||    |	 ||t|||    |
  t| | | |	|
 td  ||| |	 || |
td     || | |	|
 td  || | td|	 td   t|||    | ||t|||t|||    |	  ||t|||    |
td   t|||   || |	|
 td   | S rp  rt  r  r  r  r  r    r  r  c                 C   sf  t td|| |	|
 td   t||t|||    |	 ||t|||    |
  t| | | |	|
 td  ||| |	 || |
td     || | |	|
 td  || | td|	 td   t|||    | ||t|||t|||    |	  ||t|||    |
td   t|||   || |	|
 td   | S rp  rw  r  r  r  r  r    r  r  c                 C   sJ  t td|| ||	 td   t||t|||
    | ||t|||
    |	  t| | | ||	 td  || | td| td  t|||
    ||| | || |	td     |
 |
|
t|||t|||
    |  ||t|||
    |	td   t|||
   || ||	 td   |
 S rp  rt  r  r  r  r  r    r  r  c                 C   sJ  t td|| ||	 td   t||t|||
    | ||t|||
    |	  t| | | ||	 td  || | td| td  t|||
    ||| | || |	td     |
 |
|
t|||t|||
    |  ||t|||
    |	td   t|||
   || ||	 td   |
 S rp  rw  r  r  r  r  r    r  r  c                 C   s  t td|td|	 td  | | ||    t||t|||    |	td  ||t|||    |
  t| || |	td  || td|	 |
 td    ||| |
td  || |	    ||| |	 || |
td     || | |	|
 td  || td|	 td    || | ||   |	|
 td   t|||    | ||t||t|||    |	 ||t|||    |
td   | | ||  ||   t|||   |td|	 td  | | ||    | S rJ  rt  r  r  r  r  r         r  c                 C   s  t td|td|	 td  | | ||    t||t|||    |	td  ||t|||    |
  t| || |	td  || td|	 |
 td    ||| |
td  || |	    ||| |	 || |
td     || | |	|
 td  || td|	 td    || | ||   |	|
 td   t|||    | ||t||t|||    |	 ||t|||    |
td   | | ||  ||   t|||   |td|	 td  | | ||    | S rJ  rw  r  r  r  r  r    r  r  c                 C   s  t td|td| td  | | ||    t||t|||
    |td  ||t|||
    |	  t| || |td  || td| |	 td    ||| | || |	td     | | | ||	 td  || | ||	 td  || td| td     t|||
    |
 |
|
t|| |  ||t|||
    |  ||t|||
    |	td   t|||
   |td| td  | | ||    |
 S rJ  rt  r  r  r  r  r        r  c                 C   s  t td|td| td  | | ||    t||t|||
    |td  ||t|||
    |	  t| || |td  || td| |	 td    ||| | || |	td     | | | ||	 td  || | ||	 td  || td| td     t|||
    |
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   |td| td  | | ||    |
 S rJ  rw  r  r  r  r  r    r  r  c                 C   s  t td|| |td |td   |
td   t||t|||    |	 ||t|||    |
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td    ||  | ||   |	|
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td     | ||t||t|||    |	 ||t|||    |
td   | |td  || |  ||td    t|||   || |td |td   |
td   | S rp  rt  r  r  r  r  r    r  r  c                 C   s  t td|| |td |td   |
td   t||t|||    |	 ||t|||    |
td   t| | || |	 || |
td    || |td |	td  |td |
td    ||  | ||   |	|
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td     | ||t||t|||    |	 ||t|||    |
td   | |td  || |  ||td    t|||   || |td |td   |
td   | S rp  rw  r  r  r  r  r    r  r  c                 C   s  t td|| |td |td   |	td   t||t|||
    | ||t|||
    |	td   t| | || | || |	td    || || | || |	td     || |td  ||	 td  ||td |td  |td |	td      t|||
    |
 |
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t||t|||
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    |	td   | |td  ||td    t|||
   || |td |td   |	td   |
 S rp  rt  r  r  r  r  r    r  r  c                 C   s  t td|| |td |td   |	td   t||t|||
    | ||t|||
    |	td   t| | || | || |	td    || || | || |	td     || |td  ||	 td  ||td |td  |td |	td      t|||
    |
 |
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   || |td |td   |	td   |
 S rp  rw  r  r  r  r  r    r  r  c                 C   sj  t td|| |	|
 td   t||t|||    |	 ||t|||    |
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td     || | |	|
 td  ||| |	 || |	td     t|||    | ||t|||t|||    |	  ||t|||    |
td   t|||   || |	|
 td   | S rp  rt  r  r  r  r  r    r  r  c                 C   sj  t td|| |	|
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td     || | |	|
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td   t|||   || |	|
 td   | S rp  rw  r  r  r  r  r    r  r  c                 C   sN  t td|| ||	 td   t||t|||
    | ||t|||
    |	  t| | | ||	 td  ||| | || |	td     ||| | || |td    t|||
    |
 |
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   || ||	 td   |
 S rp  rt  r  r  r  r  r    r  r  c                 C   sN  t td|| ||	 td   t||t|||
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    |	  t| | | ||	 td  ||| | || |	td     ||| | || |td    t|||
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   || ||	 td   |
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td   t||t|||    |	td  ||t|||    |
td   t| | || |
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td    ||  | ||   |	|
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td  || |	    | | |td |td |
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td   | |td  || |  ||td    t|||   || |td |td   |
td   | S rJ  rt  r  r  r  r  r         r  c                 C   s  t td||td |td   |
td   t||t|||    |	td  ||t|||    |
td   t| | || |
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td    ||  | ||   |	|
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td  || |	    | | |td |td |
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td   | |td  || |  ||td    t|||   || |td |td   |
td   | S rJ  rw  r  r  r  r  r    r  r  c                 C   sp  t td||td |td   |	td   t||t|||
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 |
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 S rJ  rt  r  r  r  r  r  
      t r  c                 C   sp  t td||td |td   |	td   t||t|||
    |td  ||t|||
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 S rJ  rw  r  r  r  r  r    r  r  c                 C   s  t td||	|
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td   t|||   || |	|
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td  || |	    | || || |	|
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 td   t|||    || | |	|
 td  ||| |	 || |	td     t|||  td   | ||t|||t|||    |	  ||t|||    |
td   t|||   || |	|
 td   | S rJ  rw  r  r  r  r  r    r  r  c                 C   s  t td|||	 td   t||t|||
    |td  ||t|||
    |	  t| | | ||	 td  ||| | || |td    t|||
  td   ||| |	td  || |    | | | ||	 td  ||| || ||	 td     t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	td   t|||
   || ||	 td   |
 S rJ  rt  r  r  r  r  r        r  c                 C   s  t td|||	 td   t||t|||
    |td  ||t|||
    |	  t| | | ||	 td  ||| | || |td    t|||
  td   ||| |	td  || |    | | | ||	 td  ||| || ||	 td     t|||
    |
 |
|
t|||t|||
    |  ||t|||
    |	td   t|||
   || ||	 td   |
 S rJ  rw  r  r  r  r  r    r  r  c	           	      C      t td| t| | || ||  t|||    t|t|||   ||t|||    tdd    ||t |||  tt|t|||   t||t|||     || S r  r:  	r  r  r  r  r  r  r  r  rE  r  r  r  r  "  rY  r  c	           	      C   r  r  r;  r  r  r  r  r  &  rY  r  c                 C      t td| t| | || t|||    t|t|||   ||t|||    tdd    ||t |||  tt|t|||   t||t|||     || S r  r:  r  r  r  r  r  r  r  rE  r  r  r  r  *  rV  r  c                 C   r  r  r;  r  r  r  r  r  .  rV  r  c
           
      C      t |td t| |td  ||td   ||| td| |   t|||	    ||t|||	    tdd  t||t|||	      |	|	t ||td  tt||t|||	    t||t|||	     |	|	 S Nr  r  r  r:  
r  r  r  r  r  r  r  r  r  rE  r  r  r  r  2  r  r  c
           
      C   r  r  r;  r  r  r  r  r	  6  r  r	  c	           	      C      t |td t| |td  ||td   td| | | t|||    ||t|||    tdd  t||t|||      ||t ||td  tt||t|||    t||t|||     || S r  r:  	r  r  r  r  r  r  r  r  rE  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d |td  |	td  | | ||    t||t|||    |	td  ||t|||    |
  t||	|
 td  | |td  || |  ||td    ||	|
 td  | |td  || |  ||td    t|||  td   |	td | | ||   | | ||  ||    || |td  || |  ||td    |	td | | ||   | | ||  ||    t|||    | ||t||t|||    |	td  ||t|||    |
td   | |td  || |  ||td    t|||   ||td |td   |	td  | | ||    | S r  rt  r  r  r  r  r  B       r  c                 C   s  t td|td |td  |	td  | | ||    t||t|||    |	td  ||t|||    |
  t||	|
 td  | |td  || |  ||td    ||	|
 td  | |td  || |  ||td    t|||  td   |	td | | ||   | | ||  ||    || |td  || |  ||td    |	td | | ||   | | ||  ||    t|||    | ||t||t|||    |	td  ||t|||    |
td   | |td  || |  ||td    t|||   ||td |td   |	td  | | ||    | S r  rw  r  r  r  r  r  F  r  r  c                 C   sN  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t|| |  |td  | | ||   || |td  ||td    ||	 td   || |td  ||td    ||	 td  t|||
  td   || |  |td  | | ||   || |td  ||td     t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	td   | |td  ||td    t|||
   ||td |td   |td  | | ||    |
 S r  rt  r  r  r  r  r  J      R r  c                 C   sN  t td|td |td  |td  | | ||    t||t|||
    |td  ||t|||
    |	  t|| |  |td  | | ||   || |td  ||td    ||	 td   || |td  ||td    ||	 td  t|||
  td   || |  |td  | | ||   || |td  ||td     t|||
    |
 |
|
t||t|||
    |td  ||t|||
    |	td   | |td  ||td    t|||
   ||td |td   |td  | | ||    |
 S r  rw  r  r  r  r  r  N  r  r  c
           
      C      t | |td  || |  ||td   || | ||    ttd||t|||	     |	|	t | |td  || |  ||td   || | ||    ttd||t|||	     |	|	 t||	 ||  |	 S rW  r  r  r  r  r  r  R  r  r  c
           
      C   r  rW  r  r  r  r  r  r  V  r  r  c	           	      C      t | |td  ||td   || | ||    ttd||t|||     ||t | |td  ||td   || | ||    ttd||t|||     || t|| ||  | S rW  r  r  r  r  r  r  Z  r  r  c	           	      C   r  rW  r  r  r  r  r  r  ^  r  r  c
           
      C      t td||  tt|  | | || |  | | | || |  || |  t|||	    |	t||t|||	    ||t|||	      |	|	 t |||  tt||t|||	    |	|	 S rF  r  r  r   r  r  r  r  r  r  r  r  b  rS  r  c
           
      C   r  rF  r  r  r   r  r  r  r  r  r  r  r  f  rS  r  c	           	      C      t td||  tt|  | | || |  || | || |  t|||    |t||t|||    ||t|||      || t |||  tt||t|||    || S rF  r  r  r  r  r  r  j  r  r  c	           	      C   r  rF  r  r  r  r  r  r  n  r  r  c
           
      C   s`  t tdtd|  tttd|  | | || | ||    td| | | ||| ||    t|||	  td   td|| | || | ||     t|||	    |	||t|||	    tdd  t||t|||	      |	|	t|t||t|||	     t|||	   || t||t|||	      |	 S r  r  r  r   r  r  r  r  r  r  r  r  r  r     b r  c
           
      C   s`  t tdtd|  tttd|  | | || | ||    td| | | ||| ||    t|||	  td   td|| | || | ||     t|||	    |	||t|||	    tdd  t||t|||	      |	|	t|t||t|||	     t|||	   || t||t|||	      |	 S r  r  r  r   r  r  r  r  r  r  r  r  r  v  r  r  c	           	      C   sF  t tdtd|  tttd|  | | || | ||    ||| ||   t|||  td   td|  | | || |   t|||    |||t|||    tdd  t||t|||      ||t|t||t|||     t|||   || t||t|||      | S r  r  r  r  r  r  r  z  r}  r  c	           	      C   sF  t tdtd|  tttd|  | | || | ||    ||| ||   t|||  td   td|  | | || |   t|||    |||t|||    tdd  t||t|||      ||t|t||t|||     t|||   || t||t|||      | S r  r  r  r  r  r  r  ~  r}  r  c                 C   r   t ||t|||    |	 ||t|||    |
  | |t|||    |t|||  td    |S rY  r  r  r  r  r  r    rN  r  c                 C   r  rY  r  r  r  r  r  r    rN  r  c                 C   ^   t | |t|||
  td   ||t|||
    |  ||t|||
    |	  |
S rY  r  r  r  r  r  r    rI  r  c                 C   r  rY  r  r  r  r  r  r    rI  r  c              
   C      t |t|||   | |
  |t|||  |
  |  t|t|||   ||
  ||t|||    |	  | |t|||    |t|||  td    ||S rY  r  r  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r     rW  r   c              
   C   r  rY  r  r  r  r  r  r!    rW  r!  c              
   C      t |t|||
   | |	  |t|||
  |	  |  t|t|||
   ||	  | |t|||
  td    ||t|||
    |  |
|
S rY  r  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r"    r  r"  c              
   C   r  rY  r  r  r  r  r  r#    r  r#  c                 C   sB   t | | t|||   |t|||    |  || |  |S rC  r  r  r  r  r  r$    r  r$  c                 C   s   t td| tt| td |td  |td  |td tdd   |||  t|||   |t|||    | S rJ  r  r  r+   r   r  r  r  r  r  r  r%    r\  r%  c              	   C   s   t | td |td  |td  | t| t|||   |t|||    |td  ||t|  t|||   |t|||    | t|||   |t|||    |td   ||  | S rg  rT  r  r  r  r  r&    r  r&  c                 C   sr   t td| tttd| td |td  |td   |||  t|||   |t|||    | S rp  r  r  r  r  r  r'    rN  r'  c              	   C   sF   t t|||  | | | t|||   |t|||      |S rC  r  r  r  r  r  r(    r~  r(  c              	   C   s   t |td | td |td  |td   t| t|||   |t|||    |td  ||t|  t|||   |t|||    | t|||   |t|||    |td   || td |td   |td   | S rW  rT  r  r  r  r  r)    s   r)  c                 C   sL   t | td |td  |td  tt|||  t| | | ||S rY  )r  r  r   r  r>   r  r  r  r  r*       Lr*  c                 C   s   t | t|||   |t|||    t| td |td   |  | t|||   |t|||    |  tt|||  t| | | ||S rY  )r  r  r  r  r  r   r>   r  r  r  r  r+    ro  r+  c              	   C   s   t td| t| t|||   |t|||    |td  t|||  td|   ||t| | t|||   |t|||    |td   t|||  td|   ||td   | S r  rT  r  r  r  r  r  r  rE  r  r  r  r,    r  r,  c              	   C   s   t td|  t| t|||   |t|||    |td  t|||  td|   ||t|| t|||   |t|||    |td   t|||  td|   ||td   | S r  rT  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|||    |  t|||  |   td| | |  | S rJ  rT  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|||    |  t|||  |   td|  | |  | S rJ  rT  r  r  r  r  r/    r  r/  c                 C   s   t | | t|||   |t|||    |  ttd||td | t|||   | td|   t|||  |   td| | |  |S rp  r  r  r  r5   r  r  r  r  r  r  r0    r  r0  c                 C   s   t || t|||   |t|||    |  ttd||td | |t|||    td|    t|||  |   td|  | |  | S rp  r  r  r  r  r  r1    r  r1  c                 C   s"   t | t|||   | | |S rC  r   r  r  r  r  r  r2       "r2  c                 C   s"   t | |t|||    | |S rC  r  r  r  r  r  r3    r  r3  c              
   C   sx   t td| tt|| | ||  |  |td td | td |td  td   ||t|||  |S rJ  r  r  r+   r   r  r  r  r  r  r4    r  r4  c              
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   C   s   t | td t| t|||   |t|||    |td  t|||   ||t || td  t| t|||   |t|||    |td  || t| t|||   |t|||    |td  | | |td   | S r  rT  r  r  r  r  r:    r  r:  c              
   C   s   t |td t| t|||   |t|||    |td  t|||   ||t | |td  t| t|||   |t|||    |td  || t| t|||   |t|||    |td  || |td   | S r  rT  r  r  r  r  r;    r  r;  c              
   C   s6  t | td t| t|||   |t|||    |td  t|||  |  ||t td| t| t|||   |t|||    |td  t|||  |td   || t | td |td  t| t|||   |t|||    |td  t|||  |td   || S )Nr  r  rK  r  r  r  r  r  r  r<    rb  r<  c              
   C   s6  t td|  t| t|||   |t|||    |td  t|||  |td   ||t |td t| t|||   |t|||    |td  t|||  |  || t | td |td  t| t|||   |t|||    |td  t|||  |td   || S rQ  r  r  r  r  r  r=    rb  r=  c              
   C   s   t | | td |td   t|  t|||   |t|||    | t|||   |t|||     || t|| | td |td   | S rY  rR  r  r  r  r  r>  
  r  r>  c              
   C   s   t || td |td   t|  t|||   |t|||    | t|||   |t|||     ||t| | | td |td   | S rY  rR  r  r  r  r  r?    ro  r?  c              
   C   s  t | td | td |td   tt|||  |td  | t|||   |t|||     ||t || td |td   tt|||  |td  || t| t|||  |td   || td |td   |td   | S r  rR  r  r  r  r  r  rE  r  r  r  r@    r  r@  c                 C   s  t | | td |td   tt|||  |td  ||t |td | td |td   tt|||  |td  | t|||   |t|||     || t|t|||  |td   || td |td   |td   | S rg  rT  r  r  r  r  rA    r  rA  c              
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   C   s  t | | td |td   t| t|||   |t|||    |td  t|||  |  t|||  |td   ||t || td |td   t| t|||   |t|||    |td  t|||  |td   t|||  |  || t | | | td |td   t| t|||   |t|||    | t|||  |td   t|||  |td   || S ri  r  r  r  r  r  rL  B  r  rL  c              
   C   sn   t td | t|||   |t|||     |t| |t|||    |t|||      |S rY  r;  r  r  r  r  r  rE  r  r  r  rM  F  rn  rM  c              	   C   s   t | td| td  | t| |t|||    |t|||    |td  ||t| t|||   |t|||    | |t|||    |t|||    |td   ||  | S r  rT  r  r  r  r  r  r  rE  r  r  r  rN  J  s   rN  c              	   C   sT   t |  t|||   | || | t|||   |t|||      | S rC  r  r  r  r  r  rO  N  r4  rO  c              
   C   L   t tdt| t|td |td  t|||  t||    |S rp  r   r  r  r  r>   r  r  r  r  rP  R  r  rP  c              	   C   s   t |td | td| td   t| |t|||    |t|||    |td  ||t| t|||   |t|||    | |t|||    |t|||    |  | | td| td   | S rp  rT  r  r  r  r  rQ  V  r  rQ  c                 C   sR   t |||  ttt| | | |||t|||   |t|||    |S rC  )r  r+   r   r  r  r  r  r  r  r  rR  Z  r  rR  c              	   C   sD   t t| t|td |td  t|||  t||   |S rY  )r   r  r  r  r>   r  r  r  r  rS  ^  r  rS  c                 C   s  t t| |t|||    |t|||    t| |t|||    |t|||    | t|td |td     tt| | t|td |td    t|td |td  t|||  t||  | t|td |td     ||S rY  r  r  r  r  r  r   r>   r  r  r  r  rT  b  r  rT  c                 C   sP  t td| t| |t|||    |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|||    | |t|||    |t|||    |td   ||  | S r  rT  r  r  r  r  rU  f  s   R rU  c                 C   s   t tdt|td || td   |}t|| tttd| || |   ||td|t|td || td    | S rp  )r   r  r  r  r+   r   r  r  r  r  r  rE  r  r  r  r  rV  j  s   .\rV  c              
   C   s   t tttd |td  || td  |}t|| tttd| || |   ||tttd |td  || td  | |S r  r  r  r  r  r  rW  o  s   2^rW  c                 C   s   t tdtttd |td  || td   |}t|| tttd| || |   ||td|tttd |td  || td    | S )Nr  r  r  )r   r  r  r}  r  r+   r   r  r  r  r  rX  t  s   :hrX  c              
   C   s   t t|td || td  |}ttd| | tttd| | td| | |  |td |td  | |    ||t|td || td  | |S rW  r  r  r  r  r  rY  y  s   &rY  c                 C   sZ   t |||  tttd|t| |   |||t|||   |t|||    |S rF  )r  r+   r   r  r  r  r  r  r  r  r  rZ  ~  r  rZ  c              
   C   r  rp  r  r  r  r  r  r[    r  r[  c                 C   s  t t| |t|||    |t|||    | t|td |td    t| |t|||    |t|||     ttdt| | t|td |td    t|td |td  t|||  t||  | t|td |td      ||S rW  r  r  r  r  r  r\    r  r\  c                 C   s   t td| td |td  |td   tt| |t|||    |t|||    ||ttd| t|||   |t|||     |t| |t|||    |t|||     | td |td  |td    | S rp  r  r  r  r  r  r]    r  r]  c              
   C   sd  t td|td | td |td  |td    t| |t|||    |t|||    |td  | |td  ||td  t|||    ||td  t|||     ||t|t|||   |t|||    | |t|||    |t|||    |td   ||td  | td |td  |td    | S rp  rT  r  r  r  r  r^    s   f r^  c	           	      C   sF  t |td|  | ||  ||   td|td   |t td |  | |td  |td || ||    |td || ||    tt||t|||    |t|||    | td|td  | | |  | t || ||  |t|||   |t|||     td| | | |  | S rY  )r  r  logr   r  r  	r  r  r  r  r  r  r  r  rE  r  r  r  r_    r}  r_  c                 C   s  t |td|  | ||   td|td   |t |t|||   td| |  | t td|  | | ||td   ||td   tt||t|||    |t|||    | td|td  | |  | t || t|||   td| | |  | S rY  )r  r  r  r  r   r  r  r  r  r  r  r  r  rE  r  r  r  r`    rU  r`  c                 C   s   t |td|  | ||   td|td   |t |t|||   td| |  | t td |  | | ||td   ||td   tt||t|||    |t|||    | td|td  | |  | t || t|||   td| | |  | S rY  )r  r  r  r  r   r  r  r  r  r  r  r  r  rE  r  r  r  ra    r  ra  c	           	   
   C   s   t ||| ||   |td |td   |t || ||  t||t|||    |t|||     ||td |td    | S rY  r  r  r  r  r  r  r  r  r  rb    r  rb  c              
   C   s   t || | |td |td   |t || t||t|||    |t|||     ||td |td    | S rY  r  r  r  r  r  rc    rk  rc  c              
   C   s   t || | |td |td   |t || t||t|||    |t|||     ||td |td    | S rY  r  r  r  r  r  rd    rk  rd  c	           	   
   C   s  t | |td |td   ||| ||    |td |td   ttd||t|||    |t|||     ||t||| ||   |td |td   | t|| ||  t||t|||    |t|||     ||td |td    | S rW  r  r  r   r  r  r  r  r  r  r  r  re    r  re  c              
   C   s  t | |td |td   || |  |td |td   ttd||t|||    |t|||     ||t|| t||t|||    |t|||     ||td |td    | t|| |||   ||td |td    | S rW  r  r  r  r  r  rf    r  rf  c              
   C   s  t | |td |td   || |  |td |td   ttd||t|||    |t|||     ||t|| |||   ||td |td    | t|| t||t|||    |t|||     ||td |td    | S rW  r  r  r  r  r  rg    r  rg  c
           
      C   s   t ||t|||	    |t|||	    | || t|||	   ||  || t|||	    ||   || |td   |	S rF  rC  
r  r  r  r  r  r  r  r  r  rE  r  r  r  rh    r]  rh  c	           	      C   sl   t || t|||   ||  ||t|||    |t|||    |  || |td   | S rF  rC  	r  r  r  r  r  r  r  r  rE  r  r  r  ri    r  ri  c	           	      C   sj   t || t|||   ||  ||t|||    |t|||    |  || |td   |S rF  rB  	r  r  r  r  r  r  r  r  rE  r  r  r  rj    r  rj  c
           
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      C   s  t td||td   t||t|||	    |t|||	    |td  t| |td  |td  || || ||    | | | |td  |||td  ||td   || |    t|||	    | | | |td  ||| | ||td   ||td     t|||	    |	 |	|	t||t|||	    |t|||	    | || t|||	   ||  || t|||	    ||   || |td   |	 S r^  rT  r  r  r  r  ro    s    ro  c	           	      C   s~  t td||td   t||t|||    |t|||    |td  t| |td  |td  || | |  | | | |td  || | |  t|||    | | | |td  ||td  |  ||td  |  t|||    | ||t|| t|||   ||  ||t|||    |t|||    |  || |td   | S r^  rT  r  r  r  r  rp    r  rp  c	           	      C   s~  t td||td   t||t|||    |t|||    |td  t| |td  |td  || | |  | | | |td  || | |  t|||    | | | |td  ||td  |  ||td  |  t|||    | ||t|| t|||   ||  ||t|||    |t|||    |  || |td   | S r^  rT  r  r  r  r  rq    r  rq  c	           	      C   s   t || tt||t|||    |t|||    ||t | | ||  | ttdt||t|||    |t|||     || S rF  )r  r   r  r  r  r  r  r  r  r  rr    rx  rr  c	           	   	   C   s   t || ||  |  | ||  t|||    |  | ||  t|||    |||t|||    |t|||     |td |td  |td    |S rY  rB  r  r  r  r  rs    rV  rs  c              	   C   s   t | | t|||   ||  |  | ||  t|||    |||t|||    |t|||     |td |td  |td    | S rY  rB  r  r  r  r  rt    ro  rt  c              	   C   s   t | | t|||   ||  |  | ||  t|||    |||t|||    |t|||     |td |td  |td    |S rY  rC  r  r  r  r  ru    r  ru  c	           	   
   C   s(  t | | ||  ||  |td |td  |td   ttd||t|||    |t|||     ||t|| ||  |  | ||  t|||    |  | ||  t|||    |||t|||    |t|||     |td |td  |td    | S rW  rT  r  r  r  r  rv       * rv  c              
   C   s  t | | ||  |td |td  |td   ttd||t|||    |t|||     ||t| | t|||   ||  |  | ||  t|||    |||t|||    |t|||     |td |td  |td    | S rW  rT  r  r  r  r  rw    r  rw  c              
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      C   s  t td|td |td |td  |td    t||t|||	    |t|||	    |td  t|td | | ||  ||   |td |  | ||   t|||	    |td |  | ||   t|||	    |	 |	|	t||t|||	    |t|||	    |td  || ||  |  | ||  t|||	    |  | ||  t|||	     ||td  |td |td  |td    |	 S rp  rT  r  r  r  r  ry    s    ry  c	           	      C   s  t td|td |td |td  |td    t||t|||    |t|||    |td  t|  | |td  t|||   |td | | ||    |td |  | ||   t|||    | ||t||t|||    |t|||    |td  | | t|||   ||  |  | ||  t|||     ||td  |td |td  |td    | S rp  rT  r  r  r  r  rz        rz  c	           	      C   s  t td|td |td |td  |td    t||t|||    |t|||    |td  t|  | |td  t|||   |td | | ||    |td |  | ||   t|||    | ||t||t|||    |t|||    |td  | | t|||   ||  |  | ||  t|||     ||td  |td |td  |td    | S rp  rT  r  r  r  r  r{    r  r{  c                 C   B   t t|||  | t|||   | |t|||     |S rC  r,  r  r  r  r  r|    r  r|  c                 C   r  rC  r-  r  r  r  r  r}  
  r  r}  c                 C   6   t | t|||   | |t|||    | |S rC  r,  r  r  r  r  r~       6r~  c                 C   r  rC  r-  r  r  r  r  r    r  r  c              	   C   s   t | |t|||    |t|||    | | t|||   | |t|||    |   t|||  |  t| t|||   | |t|||    | ||S rC  )r  r  r  r  r   r  r  r  r  r    rW  r  c              	   C   s   t | |t|||    |t|||    | | t|||   | |t|||    |   t|||  |  t| t|||   | |t|||    | ||S rC  )r  r  r  r  r   r  r  r  r  r    rW  r  c                 C   8   t | t|||   | |t|||    |  |S rC  r,  r  r  r  r  r  r  r  rE  r  r  r  r    r  r  c                 C   r  rC  r-  r  r  r  r  r  "  r  r  c              	   C   s   t | |t|||    |t|||    |  | t|||   | |t|||    |  tdt|||   |  t| t|||   | |t|||    |  ||S rF  )r  r  r  r  r  r   r  r  r  r  r  &  r  r  c              	   C   s   t | |t|||    |t|||    |  | t|||   | |t|||    |  tdt|||   |  t| t|||   | |t|||    |  ||S rF  )r  r  r  r  r  r   r  r  r  r  r  *  r  r  c                 C   s   t | td| td  td|  t| t|||  td  |td  ||t| t|||  td  | td| | t|||    | S r  r
  r  r  r  r  rE  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|||   td| |  | S r  r  r  r  r  r  r  2  r  r  c                 C   s   t td|td  | td| td   t| t|||  td  |td  ||t| t|||  td  |td  | | td| td  t|||    | S rW  r
  r  r  r  r  r  6  r  r  c                 C   s   t td|td  | td| td   t| t|||  td  |td  ||t| t|||  td  |td  t|||   | | td| td   | S rW  r  r  r  r  r  r  :  r  r  c                 C   .   t | | tt|||  td|  ||S rY  rO  r  r  r  r  r  rE  r  r  r  r  >     .r  c                 C   r  rY  rM  r  r  r  r  r  B  r  r  c                 C   &   t | t|||  td  | |S rY  r  r  r  r  r  r  F     &r  c                 C   r  rY  r  r  r  r  r  r  J  r  r  c              	   C   s   t t|||  |}t|| tt| |td |td  | |   | |td |td  td | td   ||t|||  | |S ri  r   r  r  r+   r   r  r  r  r  r  r  rE  r  r  r  r  r  N     r  c              	   C   s   t t|||  |}t|| tt|td |td  td | td  | |td  |td  |  | |  ||t|||  | |S ri  r  r  r  r  r  r  S  r  r  c              	   C   sP   t td|  ttd|  |ttd| td| |    | | ||S rY  r  r  r  r  r  r  X  r  r  c              	   C   sP   t td|  ttd|  |ttd| td| |    | | ||S rY  r  r  r  r  r  r  \  r  r  c                 C   &   t | |t|||  |   | |S rC  r  r  r  r  r  r  r  rE  r  r  r  r  `  r  r  c                 C   r  rC  r  r  r  r  r  r  d  r  r  c                 C   s   t tdt|||   |}t|| tt|td |td  td | | td td  t| |td |td  td |td   | ||  ||td|t|||    | S rJ  r   r  r  r  r+   r   r2  r  r  r  r  r  r  rE  r  r  r  r  r  h  s   r  c                 C   s   t t|||  |}t|| tt|td |td  td | | td td  t| |td |td  td |td   | ||  ||t|||  | |S ri  r   r  r  r+   r   r  r2  r  r  r  r  r  m  s   r  c                 C   6   t | | tt|t|||  td|   ||S rY  )r  r   rH  r  r  r  r  r  r  r  rD  rE  r  r  r  r  r  r  r  c                 C   r  rY  )r  r   rH  r  r  r  r  r  r  r  v  r  r  c                 C   l   t | t|||  td  | t|||  td |   tt|t|||  td|   ||S rY  )r  r  r  r   rH  r  r  r  r  r  z  r  r  c                 C   r  rY  )r  r  r  r   rH  r  r  r  r  r  ~  r  r  c           	      C   s   t tdt|||   |}t|| tt|td |td  td | td || td  td  t| |td |td  td |td   | ||  ||td|t|||    | S rJ  r  	r  r  r  r  r  r  r  rE  r  r  r  r  r    s   r  c           	      C   s   t t|||  |}t|| tt|td |td  td | td || td  td  t| |td |td  td |td   | ||  ||t|||  | |S ri  r  r  r  r  r  r    s   r  c           	      C   s   t t|||  |}t|| tt|td  |td  td |td tdd   t| ||td  |td  td |td    ||  ||t|||  | | S ri  )r   r  r  r+   r   r  r2  r  r  r  r  r    s   r  c           	      C   s   t t|||  |}t|| tt|td  |td  td |td tdd   t| ||td  |td  td |td    ||  ||t|||  | |S ri  )r   r  r  r+   r   r  r2  r  r  r  r  r    s   r  c                 C   @   t t| |t|||  |   | t|||  |  ||S rC  r  r  r  r  r  r    r[  r  c                 C   r  rC  r  r  r  r  r  r    r[  r  c           	      C   s   t t|||  |}t|| tt|td |td  td | td || td  td  t| |td |td  td |td   |||  ||   ||  ||t|||  | |S ri  r  r  r  r  r  r    s   r  c           	      C   s   t tdt|||   |}t|| t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|||    | S rJ  r  r  r  r  r  r    s   r  c                 C   R   t tdt|||  td  |td  | |t|||  |   |  |S rp  r  r  r  r  r  r    r  r  c                 C   r  rp  r  r  r  r  r  r    r  r  c              	   C   X   t ttdt|||  td  |td  | |t|||  |   |  ||S rp  r(  r  r  r  r  r    r  r  c              	   C   r  rp  r)  r  r  r  r  r    r  r  c	           
   	   C   s   t t|||  |}	t|	| tt| |||	 | |   | |	td  |td  td |td tdd    ||t|||  |	 |S ri  r   r  r  r+   r   r  
r  r  r  r  r  r  r  r  rE  r  r  r  r  r    r  r  c	           
   	   C   s   t t|||  |}	t|	| tt| |||	 | |   | |	td  |td  td |td tdd    ||t|||  |	 | S ri  r   r  r  r+   r   r  r  r  r  r  r    s   r  c	           
   	   C   s   t t|||  |}	t|	|td  | tt|| | |||	 | |   |  |	td  |td  td | td tdd    ||t|||  |	 |S rJ  r   r  r  r  r+   r   r  r  r  r  r    s   r  c	           
   	   C   s   t t|||  |}	t|	|td  | tt|| | |||	 | |   |  |	td  |td  td | td tdd    ||t|||  |	 | S rJ  r   r  r  r  r+   r   r  r  r  r  r    s   r  c           	      C   s   t t|||  |}t||td  | tt|| |td |td  td | | td td   t| |td |td  td |td   |||  ||   ||  ||t|||  | |S rJ  r   r  r  r  r+   r   r2  r  r  r  r  r    s   r  c           	      C   s   t tdt|||   |}t||td  | tt|| |td |td  td | | td td   t| |td |td  td |td   |||  ||   ||  ||td|t|||    | S rJ  r  r  r  r  r  r    s   r  c           	      C   s   t t|||  |}t||td  | tt|| |td |td  td | td  t| |td |td  td |td   |||  ||   | |  |td |td  td  ||t|||  | |S rp  r  r  r  r  r  r    s   r  c           	      C   s  t tdt|||   |}t||td  | tt|| |td |td  td | td  t| |td |td  td |td   |||  ||   | |  |td |td  td  ||td|t|||    | S rp  r  r  r  r  r  r    s   r  c
                 C   s  t tdt|||	   |	}
t|
| t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d  td | td |td     | |	|  |	|	td|
t|||	    |	 S rJ  r  r  r  r  r  r  r  r  r  r  rE  r  r  r  r  r    s   r  c
                 C   s  t t|||	  |	}
t|
| tt|
td |	td  td | td || td  td  t| |
td |	td  td |td   ||
td |	td  td | td |td     | |	|  |	|	t|||	  |
 |	S ri  r  r  r  r  r  r    s   r  c
                 C   s"  t tdt|||	   |	}
t|
| t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d  td |td |td     |	|  |	|	td|
t|||	    |	 S rJ  r  r  r  r  r  r    s    r  c
                 C   s  t t|||	  |	}
t|
| tt|
td |	td  td | td || td  td  t| |
td |	td  td |td   ||
|  |	|   ||
td |	td  td |td |td     |	|  |	|	t|||	  |
 |	S ri  r  r  r  r  r  r    s   r  c	           	   	   C   R   t td|  ||   t|td| t|||  |   td|  ||S Nr  r  r  	r  r  r  r  r  r  r!  r  rE  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d|    |  tt|td| t|||  |   td|   ||S rY  )r  r  r  r   rD  r  r  r  r  r    rW  r  c	           	   
   C   r  rY  )r  r  r  r   rD  r  r  r  r  r     rW  r  c           	      C      t td |  | |td  td}ttd| | ttd|td| t|||  |   |  ||ttd| | ttd|td| t|||  |   |  || S r  r  r  r  r   r  	r  r  r  r  r  r  r!  rE  r  r  r  r  r       (r  c           	      C   r  r  r  r  r  r   r  r  r  r  r  r  	  r  r  c
           
   	   C   f   t td|  ||   t|td| t|||	  |   td|  t|||	  |  |	|	S r  r  
r  r  r  r  r  r  r  r!  r  rE  r  r  r  r    rZ  r  c
           
   	   C   r  r  r  r  r  r  r  r    rZ  r  c
           
   	   C      t |td| t|||	  |   td |  | |t|||	  |   |t|||	  td|    |  t|td| t|||	  |   td|  t|||	  |  |	|	S rY  r  r  r  r   r  r  r  r  r    r  r  c
           
   	   C   r  rY  r  r  r  r   r  r  r  r  r    r  r  c
                 C   s   t tdt|||	   |	}
t|
| tt|
td |	td  td | td ||  td  t| |	td td |  ||	td td |td    | |	|  |	|	td|
t|||	    |	 S rJ  r  r  r  r  r  r  r  r  r!  r  rE  r  r  r  r  r    s   r  c
                 C   s   t t|||	  |	}
t|
| tt|
td |	td  td | td ||  td  t| |	td td |  ||	td td |td    | |	|  |	|	t|||	  |
 |	S ri  r  r  r  r  r  r  #  s   r  c
           
      C   `   t t| |t|||	  |   |t|||	  td|    | t|||	  |  |	|	S rY  r
  r  r  r  r  r  (  rf  r  c
           
      C   r  rY  r  r  r  r  r  r  ,  rf  r  c              
   C   s   t t|||
  |
}t|| tt|td  |
td  td |td tdd   | ||| |
 |   ||| |
 td|    |	  |
|
t|||
  | |
S ri  r  r  r  r  r  r  r  r  r  r!  r  rE  r  r  r  r  r  0  s   r  c              
   C   s   t t|||
  |
}t|| tt|td  |
td  td |td tdd   | ||| |
 |   ||| |
 td|    |	  |
|
t|||
  | |
 S ri  r  r   r  r  r  r  5  s   r  c
           
   	   C   f   t td|  ||   t|td| t|||	  |   td|  t|||	  |  |	|	S r  r  r  r  r  r  r  :  rZ  r  c
           
   	   C   r  r  r  r  r  r  r  r  >  rZ  r  c
           
   	   C      t |td| t|||	  |   td |  | |t|||	  |   |t|||	  td|    |  t|td| t|||	  |   td|  t|||	  |  |	|	S rY  )r  r  r  r   r  r  r  r  r  r  B  r  r  c
           
   	   C   r  rY  )r  r  r  r   r  r  r  r  r  r  F  r  r  c
                 C   s   t tdt|||	   |	}
t|
|td  | tt|	| |
td |	td  td | td ||  td   t| |	td td |  ||	td td |td    | |	|  |	|	td|
t|||	    |	 S rJ  r  r  r  r  r  r  J  s   r  c
                 C   s   t t|||	  |	}
t|
|td  | tt|	| |
td |	td  td | td ||  td   t| |	td td |  ||	td td |td    | |	|  |	|	t|||	  |
 |	S rJ  r  r  r  r  r  r  O  s   r  c
           
   	   C   x   t ttdt|||	  td  |td  | |t|||	  |   |t|||	  td|    |  |	|	S rp  r(  r  r  r  r  r  T  r  r  c
           
   	   C   r  rp  r)  r  r  r  r  r  X  r  r  c              
   C   s   t t|||
  |
}t||td  | tt|
| |td  |
td  td | td tdd    | ||| |
 |   ||| |
 td|    |	  |
|
t|||
  | |
S rJ  r  r   r  r  r  r  \     r  c              
   C   s   t t|||
  |
}t||td  | tt|
| |td  |
td  td | td tdd    | ||| |
 |   ||| |
 td|    |	  |
|
t|||
  | |
 S rJ  r  r   r  r  r  r  a     r  c
           
   	   C   r  r  r  r  r   r  r  r  r  r  r  r  f  rZ  r  c
           
   	   C   n   t td|  ||   t|td| t|||	  |   td|  tdt|||	   |  |	|	S r  r  r  r   r  r  r  r  r  r  r  j  rn  r  c
           
   	   C   r  rY  r  r  r  r   r  r  r  r  r  r  n  r  r  c
           
   	   C      t |td| t|||	  |   td |  | |t|||	  |   |t|||	  td|    |  t|td| t|||	  |   td|  tdt|||	   |  |	|	S rW  r  r  r  r   r  r  r  r  r  r  r  rX  r  c
                 C   s   t t|||	  |	}
t|
|td  | tt|	| |
td |	td  td | | td   t| |	td td |  ||	|  |	td td |td    ||	td|    |	|  |	|	t|||	  |
 |	S rJ  r  r  r  r  r  r  v     r  c
                 C   s   t tdt|||	   |	}
t|
|td  | tt|	| |
td |	td  td | | td   t| |	td td |  ||	|  |	td td |td    ||	td|    |	|  |	|	td|
t|||	    |	 S rJ  r  r  r  r  r  r  {     r  c
           
   	   C      t ttdt|||	  td  | td  | |t|||	  |   |t|||	  td|    |  t|||	  |  |	|	S rp  r(  r  r  r  r  r    r1  r  c
           
   	   C   r  rp  r)  r  r  r  r  r    r1  r  c              
   C   s   t t|||
  |
}t||td  | tt|
|  |td  |
td  td |td tdd    | ||| |
 |   ||| |
 td|    |	  |
|
t|||
  | |
S rJ  r  r   r  r  r  r    r  r  c              
   C   s   t t|||
  |
}t||td  | tt|
|  |td  |
td  td |td tdd    | ||| |
 |   ||| |
 td|    |	  |
|
t|||
  | |
 S rJ  r  r   r  r  r  r    r  r  c
           
   	   C   r  r  r  r  r  r  r  r    rn  r  c
           
   	   C   r  r  r  r  r  r  r  r    rZ  r  c
           
   	   C   r
  rW  r	  r  r  r  r  r    rX  r  c
           
   	   C   r  rY  r  r  r  r  r  r    r  r  c
                 C   s   t tdt|||	   |	}
t|
|td  | tt|	| |
td |	td  td | | td   t| |
td |	td  td |  ||
td |	td  td |td    | |	|  |	|	td|
t|||	    |	 S rJ  r  r  r  r  r  r    r  r  c
                 C   s   t t|||	  |	}
t|
|td  | tt|	| |
td |	td  td | | td   t| |
td |	td  td |  ||
td |	td  td |td    | |	|  |	|	t|||	  |
 |	S rJ  r  r  r  r  r  r    r  r  c
           
   	   C      t ttdt|||	  td  |td  | |t|||	  |   |t|||	  td|    |  t|||	  |   |	|	S rp  r(  r  r  r  r  r    r1  r  c
           
   	   C   r  rp  r)  r  r  r  r  r    r1  r  c	           	   
   C   f   t td|  ||   t| |t|||    |td| t|||    td|   ||S r  r  r  r  r  r  r    rZ  r  c	           	   
   C   r  r  r  r  r  r  r  r    rZ  r  c	           	   
   C      t |td| t|||    td |  ||t|||    |t|||  td   |  t| |t|||    |td| t|||    td|   ||S rY  r  r  r  r  r  r    r  r  c	           	   
   C   r  rY  r  r  r  r  r  r    r  r  c           	      C      t td | | |td  td}t|td |  | ||  |  ttd|td| t|||    |  ||t|td |  | ||  |  ttd|td| t|||    |  || S r  r  	r  r  r  r  r  r  r  rE  r  r  r  r  r       (r  c           	      C   r  r  r  r  r  r  r  r    r  r  c	           	   	   C   \   t t| |t|||    ||t|||    |t|||  td   |  ||S rY  r
  r  r  r  r  r    r  r  c	           	   	   C   r  rY  r  r  r  r  r  r    r  r  c                 C   sh   t || | t| ||  |td  t|||   ||t| ||  | t|||   | | S rk  r5  r  r  r  r  r  rE  r  r  r  r    rG  r  c                 C   sj   t || | t| ||  |td  t|||   || t| ||  | t|||   | | S rk  r3  r  r  r  r  r    r  r  c                 C   s   t |||td   t| ||  |td  t|||   || t| ||  |td  t|||   ||td   | S rF  rw  r  r  r  r  r    r  r  c                 C   s   t |||td   t| ||  |td  t|||   ||t| ||  |td  t|||   ||td   | S rF  rt  r  r  r  r  r    rk  r  c                 C      t t|||  | |S rC  r  r  r  r  r  r  rE  r  r  r  r    rz  r  c                 C   r  rC  r  r  r  r  r  r  r    rz  r  c                 C   s   t t|  | ||  | tt| | | ||  | ||   ||t t|  | ||  | tt| | | ||  | ||   || S rC  r  r  r   r  r  r  r  r  r    r  r  c                 C   s   t t|  | ||  | tt| | | ||  | ||   || t t|  | ||  | tt| | | ||  | ||   || S rC  r  r  r  r  r  r    r  r  c              	   C   B   t td| ttt||td  | ||t| ||  |S rY  )r  r  r+   r   r  r  r  r  r  r  r    r  r  c              	   C   r  rY  )r  r  r+   r   r  r  r  r  r  r  r    r  r  c              	   C   s   t t|  | ||  | tt| | | ||  t| ||   ||t t|  | ||  | tt| | | ||  t| ||   || S rC  )r  r  r   r  r  r  r  r  r  r    rx  r  c              	   C   s   t t|  | ||  | tt| | | ||  t| ||   || t t|  | ||  | tt| | | ||  t| ||   || S rC  )r  r  r   r  r  r  r  r  r  r     r  r  c              
   C   sv   t ttd t| ||  | tt |||    ||t ttd t| ||  | tt|||    || S rY  r  r  r  r   expr  r  r  r  r     r  r  c              
   C   sv   t tdd t| ||  | tt |||    ||t tdd t| ||  | tt|||    || S rp  r  r  r   r  r  r  r  r  r  r  
   r  r  c                 C   s   t | td |td  | t| t|||   |td  |||   ||t|| t|||   |  |td |td   | t| | t|||   |td   |||   t|||   ||  | S rg  rt  r  r  r  r  r  r  rE  r  r  r  r     rh  r  c                 C   s   t | td |td  | t| t|||   |td  |||   ||t|| t|||   |  |td |td   | t| | t|||   |td   |||   t|||   ||  | S rg  rw  r   r  r  r  r     rh  r  c              	   C   sl  t | td |td  | t| t|||   |td  |||  |  ||t |td | |td  |td |td   t| t|||   | |||  |td   || t| | t|||   |td   |||  |  t|||   ||  | t|| | t|||   |  |||  |td   |td |td   | S rg  rt  r  r  r  r  r  r  r  rE  r  r  r  r        n r  c              	   C   sl  t | td |td  | t| t|||   |td  |||  |  ||t |td | |td  |td |td   t| t|||   | |||  |td   || t| | t|||   |td   |||  |  t|||   ||  | t|| | t|||   |  |||  |td   |td |td   | S rg  rw  r!  r  r  r  r     r"  r  c                 C   .   t t| ||  | t|||  | ||S rC  r   rd  r  r  r  r  r  r  r  rE  r  r  r  r     r  r  c                 C   r#  rC  r   rd  r  r%  r  r  r  r  "   r  r  c              
   C   s   t || ||td   tt| ||  |td  t|||  |td  t|||   ||| t| ||  |td  t|||  |  ||td   | S rd  r  r  r   rd  r  r  r  r%  r  r  r  r  &   rV  r  c              
   C   s   t || ||td   tt| ||  |td  t|||  t|||  |td   |||t| ||  |td  t|||  |  ||td   | S rd  r'  r%  r  r  r  r  *   rl  r  c              	   C   s  t |td |td  |td |td  |td   t| t|||   | |||  |td   || t | td |td  | |td  |td |td  |td   t| t|||   |td  |||  |td   || t| t|||   | |||  |td   ||td   | t| | | | t|||   |td   |||  |td   t|||   |td |td  |td   | S Nr  r  rK  r  rt  r!  r  r  r  r  .       r  c              	   C   s  t |td |td  |td |td  |td   t| t|||   | |||  |td   || t | td |td  | |td  |td |td  |td   t| t|||   |td  |||  |td   || t| t|||   | |||  |td   ||td   | t| | | | t|||   |td   |||  |td   t|||   |td |td  |td   | S r(  rw  r!  r  r  r  r  2   r)  r  c                 C   s
  t |td | td |td   t| t|||   |td  |||   ||t|| t|||   |td   | td |td  |td  |td   | t| t|||   |td  |||   t|||   | | |td   | S rW  rt  r   r  r  r  r   6   r_  r   c                 C   s
  t |td | td |td   t| t|||   |td  |||   ||t|| t|||   |td   | td |td  |td  |td   | t| t|||   |td  |||   t|||   | | |td   | S rW  rw  r   r  r  r  r  :   r_  r  c              	   C   s  t |td | td |td   t| t|||   |td  |||  |  ||t |td | |td  | td |td  |td  |td   t| t|||   |td  |||  |td   || t| t|||   |td  |||  |  t|||   | | |td   | t|| | t|||   |td   |||  |td   | td |td  |td  |td   | S r(  rt  r!  r  r  r  r  >       r  c              	   C   s  t |td | td |td   t| t|||   |td  |||  |  ||t |td | |td  | td |td  |td  |td   t| t|||   |td  |||  |td   || t| t|||   |td  |||  |  t|||   | | |td   | t|| | t|||   |td   |||  |td   | td |td  |td  |td   | S r(  rw  r!  r  r  r  r  B   r*  r  c	           	   	   C   6   t t|||  | | |t|||    | ||S rC  r   r   r  r8  r  r  r  r  F   r  r  c	           	   	   C   r+  rC  r   r   r  r8  r  r  r  r  J   r  r  c	           	   	   C   sl   t td|  | t|||  | tt |  td|  |td  || td  td|   ||S r|  )r  r  r   r  r}  r8  r  r  r  r  N   r  r  c	           	   	   C   s   t td|  t| | |t|||    t|  tt |  td|  |td  || td  td t|   t|||  | tt |  td|  |td  || td  td|   ||S r|  )r  r  r%   r  r&   r  r}  r   r8  r  r  r  r  R   rS  r  c	           	   	   C   V   t td|  | t|||  | t|td || td  td|   ||S rY  r  r8  r  r  r  r  V   r  r  c	           	   	   C   r.  rY  r  r8  r  r  r  r	  Z   r  r	  c	           	   	   C   s   t td|  t| | |t|||    t|  t|td || td  td t|   t|||  | t|td || td  td|   ||S rY  )r  r  r%   r  r&   r   r8  r  r  r  r
  ^   rl  r
  c	           	   	   C   s   t td|  t| | |t|||    t|  t|td || td  td t|   t|||  | t|td || td  td|   ||S rY  )r  r  r%   r  r&   r  r   r8  r  r  r  r  b   rl  r  c                 C   s   t tdt|||  | tt|||    td|  tt|||    t| ttdt |||     t|   ||S rY  r  rP  r  r  r  r  f   r\  r  c                 C   sz   t tdt|||  | tt|||    td|  tt|||    |ttdt |||     |  ||S rY  r  rP  r  r  r  r  j   r  r  c                 C   s  t | | td |td   t|||  | | |t|||     ||t || | || td |td    t|||  |td  t|||   | |t|||     || t||||  |  t|||   || |t|||     | td |td    | S r  rR  rP  r  r  r  r  n   rU  r  c                 C   s  t | | td |td   t|||  | | |t|||     ||t || | || td |td    t|||  |td  t|||   | |t|||     || t||||  |  t|||   || |t|||     | td |td    | S r  rT  rP  r  r  r  r  r   rU  r  c	           	   
   C   s  t | | td |td   t| |t|||    |td  |||  |  ||t ||td  | td |td  |td   t| |t|||    |td  |||  |  t|||   || t || | || td |td   |td   t| |t|||    |td  |||  |td   t|||   || t|| |t|||    |td   |||  |  t|||   || td |td   |td   | S ri  rR  r8  r  r  r  r  v       r  c	           	   
   C   s  t | | td |td   t| |t|||    |td  |||  |  ||t ||td  | td |td  |td   t| |t|||    |td  |||  |  t|||   || t || | || td |td   |td   t| |t|||    |td  |||  |td   t|||   || t|| |t|||    |td   |||  |  t|||   || td |td   |td   | S ri  rT  r8  r  r  r  r  z   r/  r  c                 C   .   t | |tt||  | t|||  |S rC  r   r  r2  r  r  r  r  rD  vrE  r  r  r  r  ~   r  r  c                 C   r0  rC  r   r  r2  r2  r  r  r  r     r  r  c	           	      C   2   t | |t|||    | |||  |  |S rC  r  r8  r  r  r  r     r  r  c	           	      C   r5  rC  r  r8  r  r  r  r     r  r  c                 C   .   t tt|||  | |||   | ||S rC  r,  r  r  r  r  r     r  r  c                 C   r6  rC  r-  r  r  r  r  r     r  r  c              	   C   s  t ||| |td   t|td|  | |||   |td   t|||   || t td| || |td   t||  | |||   |td   t|||   || t|td|  | |||   |td   t|||   || |td   | S rF  rT  r  r  r  r  r     r  r  c              	   C   s  t ||| |td   t|td|  | |||   |td   t|||   ||t td| || |td   t||  | |||   |td   t|||   || t|td|  | |||   |td   t|||   || |td   | S rF  rR  r  r  r  r  r     r  r  c                 C   r6  rC  r,  r  r  r  r  r     r  r  c                 C   r6  rC  r-  r  r  r  r  r     r  r  c                 C   8   t |||  | ||   | |  t|||   |S rC  r  r  r  r  r  r     r  r  c                 C   r7  rC  r  r  r  r  r  r     r  r  c                 C   *   t | |||   | t|||   |S rC  r  r  r  r  r  r        *r  c                 C   r8  rC  r  r  r  r  r  r      r9  r   c	           	      C   :   t tt|||  || | | |||   |  ||S rC  r,  	r  r  r  r  r  r  r  r  rE  r  r  r  r!     r  r!  c	           	      C   r:  rC  r-  r;  r  r  r  r"     r  r"  c	           	      C   s   t |||  || |td   t| |||   |td  t|||   || t|| | |||   |td   t|||   || |td   | S rF  rw  r;  r  r  r  r#     r  r#  c	           	      C   s   t |||  || |td   t| |||   |td  t|||   ||t|| | |||   |td   t|||   || |td   | S rF  rt  r;  r  r  r  r$     r  r$  c              	   C   s$  t ||| |td   t||| td  | |||   |td   t|||   || t || td || |td   t|||  | |||   |td   t|||   || t||| td  | |||   |td   t|||   || |td   | S rF  rT  r  r  r  r  r%     s   & r%  c              	   C   s"  t ||| |td   t||| td  | |||   |td   t|||   ||t || td || |td   t|||  | |||   |td   t|||   || t||| td  | |||   |td   t|||   || |td   | S rF  rR  r  r  r  r  r&     r,  r&  c                 C   6   t tt|||  || | |||   |  ||S rC  r,  r  r  r  r  r'     r  r'  c                 C   r<  rC  r-  r  r  r  r  r(     r  r(  c                 C   <   t ||||   | ||   | |  t|||   |S rC  r  r  r  r  r  r)        <r)  c                 C   r=  rC  r  r  r  r  r  r*     r>  r*  c	           	      C   6   t || | | |||   |  t|||   |S rC  r  r;  r  r  r  r+     r  r+  c	           	      C   r?  rC  r  r;  r  r  r  r,     r  r,  c                 C   b   t ttdtt tttd| ttdt  t| td  tdt| td  |S rW  )r  r  r  r}  r  r  r  rE  r  r  r  r-     rs  r-  c                 C   r@  rW  )r  r  r  r}  r  r  rA  r  r  r  r.     rs  r.  c              	   C   sL   t t| tt||td  ||t t| tt||td  || S rY  )r  r  r   r  r  ry  r  r  r  r/     r  r/  c              	   C   sN   t t| tt||td  || t t| tt||td  || S rY  )r  r  r   r  r  ry  r  r  r  r0     r  r0  c              	   C   f   t ttd ttt |  t| ||   ||t ttd ttt|  t| ||   || S rY  r  rq  r  r  r  r1     rZ  r1  c              	   C   f   t tdd ttt |  t| ||   ||t tdd ttt|  t| ||   || S rp  r  rq  r  r  r  r2     rZ  r2  c              	   C   ,   t t| |t||||     | ||S rC  r$  r  r  r  r  r3        ,r3  c              	   C   rD  rC  r&  r  r  r  r  r4  !  rE  r4  c              	   C   F   t t| |t||||      | |td  ||td|  S rW  )r+   r   r  r  r  r  r  r  r5  !  r~  r5  c              	   C   rF  rW  )r+   r   r  r  r  r  r  r  r6  
!  r~  r6  c                 C   ^   t |}t|tt||td  | |t|||||      |  |||td|  |S r  r4   r  r+   r   r  r  r  r  r  r  r  r  rE  r`  r  r  r  r7  !     Vr7  c                 C   rG  r  r4   r  r+   r   r  r  rI  r  r  r  r8  !  rJ  r8  c              	   C   rB  rY  r  rq  r  r  r  r9  !  rZ  r9  c              	   C   rC  rp  r  rq  r  r  r  r:  !  rZ  r:  c              	   C   rD  rC  r$  r  r  r  r  r;   !  rE  r;  c              	   C   rD  rC  r&  r  r  r  r  r<  $!  rE  r<  c                 C   J   t tdt||td tt| |t||||     | ||||S rF  )r  r  r3   r+   r   r  r  r  r  r  r  r  rD  rE  r  r  r  r=  (!  r  r=  c                 C   rL  rF  )r  r  r3   r+   r   r  rM  r  r  r  r>  ,!  r  r>  c                 C   &   t | |t||||     | |S rC  r  rM  r  r  r  r?  0!  r  r?  c                 C   rN  rC  r  rM  r  r  r  r@  4!  r  r@  c                 C       t | |tt||  | |S rC  r1  r  r  r  rD  rE  r  r  r  rA  8!      rA  c                 C   rO  rC  r4  rP  r  r  r  rB  <!  rQ  rB  c                 C      t t| ||  | |S rC  r  r  r  rE  r  r  r  rC  @!  rz  rC  c                 C   rR  rC  r  rS  r  r  r  rD  D!  rz  rD  c                 C   sL   t t| tt|||  | ||t t| tt|||  | || S rC  r  rq  r  r  r  rE  H!  r  rE  c                 C   sN   t t| tt|||  | || t t| tt|||  | || S rC  r  rq  r  r  r  rF  L!  r  rF  c           	      C   V   t |ttttfrdS |td | }tt|tt	|tdt
|tdr)dS dS NFr  r   T
isinstanceintr  floatr  r  r  r   r  r#   rQ   	r  r  r  r  r  r  r  rE  r0  r  r  r  rG  P!     (rG  c           	      C   ^   |t d | }tt d| tt||t d  | |t|||    |  |||| |S rd  )r  r  r+   r   r  rZ  r  r  r  rH  Y!     NrH  c           	      C   rT  rU  rV  rZ  r  r  r  rI  _!  r[  rI  c           	      C   r\  rd  )r  r  r+   r   r  rZ  r  r  r  rJ  h!  r]  rJ  c	           
      C   V   t |ttttfrdS |td | }	tt|	tt	|tdt
|	tdr)dS dS rU  rV  
r  r  r  r  r  r  r  r  rE  r0  r  r  r  rL  n!  r[  rL  c	           
      C   l   |t d | }	t|t| |t|   || t|  t|| | |t||||     |  ||S rF  )r  r  r%   r&   r   r  r_  r  r  r  rM  w!     \rM  c	           
      C   r^  rU  rV  r_  r  r  r  rN  }!  r[  rN  c	           
      C   r`  rF  )r  r  r%   r&   r   r  r_  r  r  r  rO  !  ra  rO  c              
   C   B   t td| ttt| ||td   ||||td  |S rY  rL  r  r  r  r  rE  r  r  r  rP  !  r  rP  c              
   C   rb  rY  rO  rc  r  r  r  rQ  !  r  rQ  c              	   C   s   t || || td  ||  t|| ||  t| |||    ||t||td  || || td   t| |||    ||  | S rd  r  r  r  r  r  r  rE  r  r  r  rR  !  rx  rR  c              	   C   s   t || || td  ||  t|| ||  t| |||    || t||td  || || td   t| |||    ||  | S rd  r  rd  r  r  r  rS  !  r  rS  c              	   C   s   t |||   | |td  t|| ||  t| |||    || t|| |td  t| |||    ||td   | S rF  rw  rd  r  r  r  rT  !  r  rT  c              	   C   s   t |||   | |td  t|| ||  t| |||    ||t|| |td  t| |||    ||td   | S rF  rt  rd  r  r  r  rU  !  r]  rU  c              
   C   ~   t ttd t|| | tt |  t| ||    ||t ttd t|| | tt|  t| ||    || S rY  r  rd  r  r  r  rV  !  r  rV  c              
   C   ~   t tdd t|| | tt |  t| ||    ||t tdd t|| | tt|  t| ||    || S rp  r  rd  r  r  r  rW  !  r  rW  c              	   C   s   t || | |td  tt| |||   |td  t| |||    ||t|td|  t| |||   |  |td  | S r  rR  r  r  r  r  r  rE  r  r  r  rX  !  r  rX  c              	   C   s   t || | |td  tt| |||   t| |||   |td   || t|td|  t| |||   |  |td  | S r  rR  rg  r  r  r  rY  !  r  rY  c              	   C   s   t |td | t|| t| |||   |td   ||tt| |||   | |td | |td   | t|| t| |||   |td   t| |||    || |  | S NrK  r  r  rt  rg  r  r  r  rZ  !  r  rZ  c              	   C   s   t |td | t|| t| |||   |td   ||tt| |||   | |td | |td   | t|| t| |||    t| |||   |td   || |  | S rh  rw  rg  r  r  r  r[  !  r  r[  c              
   C   s  t |td | t|| t| |||   |td   ||t |td|  td || td  |td |td  |td   t||td|   t| |||   |  || t||td|  td  || td  t| |||   |  |td |td  |td   | t||| td  t| |||   |td   t| |||    || |  | S NrK  r  r  r  rt  rg  r  r  r  r\  !  rf  r\  c              
   C   s  t |td | t|| t| |||   |td   ||t |td|  td || td  |td |td  |td   t||td|   t| |||   |  || t||td|  td  || td  t| |||   |  |td |td  |td   | t||| td  t| |||    t| |||   |td   || |  | S ri  rw  rg  r  r  r  r]  !  rf  r]  c              
   C   s  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   t||td|   t| |||   |td   || t||td  t| |||   |  |td  | t|| | ||| td   t| |||   |td   t| |||    |td || td   | S r(  rt  rg  r  r  r  r^  !  r  r^  c              
   C   s  t |td |td  |td  |td || td   t||td|   t| |||   |  || t |td |td  | |td  |td || td   t||td|   t| |||   |td   || t||td  t| |||   |  |td  | t|| | ||| td   t| |||    t| |||   |td   |td || td   | S r(  rw  rg  r  r  r  r_  !  r  r_  c	           
      C   |   t |}	t|	| tt||	|td  td  | |t||||   ||	|      |  |||| td|	  |S rd  rH  
r  r  r  r  r  r  r  r  rE  r`  r  r  r  r`  !     tr`  c	           
      C   rj  rd  rK  rk  r  r  r  ra  !  rl  ra  c	           	   
   C   6   t t|| | | |t||||     | ||S rC  r$  r;  r  r  r  rb  !  r  rb  c	           	   
   C   rm  rC  r&  r;  r  r  r  rc  !  r  rc  c              	   C   s   t |td |td  t|| t| |||   |td   ||tt| |||   |td  |td | |td  |td   | t|| t| |||   |td   t| |||    || |td   | S rW  rt  rg  r  r  r  rd  !  r  rd  c              	   C   s   t |td |td  t|| t| |||   |td   ||tt| |||   |td  |td | |td  |td   | t|| t| |||    t| |||   |td   || |td   | S rW  rw  rg  r  r  r  re  !  r  re  c              
   C   s  t |td |td  t|| t| |||   |td   ||t |td|  td || td  |td |td  |td  |td   t||td|   t| |||   |td   || t||| td  t| |||   |td   t| |||    || |td   | t||td|  td  || td  t| |||   |td   |td |td  |td  |td   | S rW  rt  rg  r  r  r  rf  !      rf  c              
   C   s  t |td |td  t|| t| |||   |td   ||t |td|  td || td  |td |td  |td  |td   t||td|   t| |||   |td   || t||| td  t| |||    t| |||   |td   || |td   | t||td|  td  || td  t| |||   |td   |td |td  |td  |td   | S rW  rw  rg  r  r  r  rg  !  rn  rg  c              
   C   L   t t|| td  | |t||||      |  ||td|  S r	  )r+   r   r  r  r  r  r  r  rh  !  r  rh  c              
   C   ro  r	  )r+   r   r  r  r  r  r  r  ri  !  r  ri  c	           
      C      t |}	t|	| tt||	 |td  td  | |t||||   ||	 |      |  |||| td |	  | S rd  rH  rk  r  r  r  rj  !     |rj  c	           
      C   rp  rd  rK  rk  r  r  r  rk  !  rq  rk  c	           	      C   l   t || | td| |  tt|| td  | |t||||      |  ||td| | S r  rL  r;  r  r  r  rl   "  r  rl  c	           	      C   rr  r  rO  r;  r  r  r  rm  "  r  rm  c           	      C   j   t |}t|tt|||td  td  | |t|||||      |  |||td|  |S rd  rH  	r  r  r  r  r  r  r  rE  r`  r  r  r  rn  "     brn  c           	      C   rs  rd  rK  rt  r  r  r  ro  "  ru  ro  c	           	      C   \   t |t| |t|   || t|  t|| | |t||||     |  ||S rC  r  r%   r&   r   r  r;  r  r  r  rp  "  r  rp  c	           	      C   rv  rC  r  r%   r&   r   r  r;  r  r  r  rq  "  r  rq  c                 C   ^   t td|td  tt| |t|||||td       | ||||td  |S rF  rL  r  r  r  r  rr  "  rI  rr  c                 C   ry  rF  rO  r  r  r  r  rs  "  rI  rs  c	           	      C   rv  rC  rw  r;  r  r  r  rt  ""  r  rt  c	           	      C   rv  rC  rx  r;  r  r  r  ru  &"  r  ru  c              
   C   re  rY  r  rd  r  r  r  rv  *"  r  rv  c              
   C   rf  rp  r  rd  r  r  r  rw  ."  r  rw  c	           	   
   C   rm  rC  r$  r;  r  r  r  rx  2"  r  rx  c	           	   
   C   rm  rC  r&  r;  r  r  r  ry  6"  r  ry  c	           	      C   h   t t||td| td  tt| |t||||     | |t||td |  ||||S Nr  rK  r   )r  r3   r  r+   r   r  	r  r  r  r  r  r  r  rD  rE  r  r  r  rz  :"  rG  rz  c	           	      C   rz  r{  )r  r3   r  r+   r   r  r|  r  r  r  r{  >"  rG  r{  c
           
   	   C   2   t ||	 | | |t||||     |  |	S rC  r  
r  r  r  r  r  r  r  r  rD  rE  r  r  r  r|  B"  r  r|  c
           
   	   C   r}  rC  r  r~  r  r  r  r}  F"  r  r}  c                 C   ,   t || | | |tt||  |  |S rC  r1  r  r  r  r  r  rD  rE  r  r  r  r~  J"  rE  r~  c                 C   r  rC  r4  r  r  r  r  r  N"  rE  r  c                 C   s:   t t| |||   |td  || |td   |S rF  r  r  r  rg  r  r  r  r  R"  r  r  c                 C   s<   t t| |||   |td  || |td   | S rF  r  r  r  rg  r  r  r  r  V"  r>  r  c              	   C   s   t || td || |td   t|||  t| |||   |td   || t||| td  t| |||   |td   || |td   | S rF  r  rg  r  r  r  r  Z"  rv  r  c              	   C   s   t || td || |td   t|||  t| |||   |td   ||t||| td  t| |||   |td   || |td   | S rF  r  rg  r  r  r  r  ^"  r/  r  c                 C   2   t t|td| |  td td|  |S r|  r  r  r  r  rE  r  r  r  r  b"  r  r  c                 C   r  r|  r  r  r  r  r  r  f"  r  r  c                 C   s   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t|td| |  td td|  || S r  r  r  r  r   r  r  r  r  r  r  j"  r  r  c                 C   s   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t|td| |  td td|  || S r  r  r  r  r  r  r  n"  rX  r  c                 C   0   t tt| ||  ||td   | ||S rY  r   rd  r  r  r  r  r  r  rE  r  r  r  r  r"     0r  c                 C   r  rY  r   rd  r  r  r  r  r  r  r  v"  r  r  c                 C      t tt|||  |S rC  r1  r  r3  rE  r  r  r  r  z"     r  c                 C   r  rC  r4  r  r  r  r  r  ~"  r  r  c                 C   s8   t |t| ||  ||td    td|  | S rY  r  r  r  r  r  r  "  r  r  c                 C   s6   t |t| ||  ||td    td|  |S rY  r  r  r  r  r  r  "  r  r  c              	   C   s   t | | td| |  td|  tt| ||  ||td   ||t|t| ||  ||td    td|  | S rY  rt  r  r  r  r  r  "  r  r  c              	   C   s   t | | td| |  td|  tt| ||  ||td   ||t|t| ||  ||td    td|  | S rY  rw  r  r  r  r  r  "  r  r  c              
   C   s   t |td |td  td|  t|||  |td  t| ||  ||td    ||t||||  |td   t| ||  ||td    td|  | S rg  r  r  r  r  r  r  r  rE  r  r  r  r  "  r  r  c              
   C   s   t |td |td  td|  t|||  |td  t| ||  ||td    || t||||  |td   t| ||  ||td    td|  | S rg  r  r  r  r  r  r  "  r  r  c                 C   s  t || td| |  td|  t|||  |td  t| ||  ||td    || t |td |td  td|  t|||  |td  t| ||  ||td    || t||||  |td   t| ||  ||td    td|  | S rg  rR  r  r  r  r  r  "  r  r  c                 C   s  t || td| |  td|  t|||  |td  t| ||  ||td    || t |td |td  td|  t|||  |td  t| ||  ||td    || t||||  |td   t| ||  ||td    td|  | S rg  rT  r  r  r  r  r  "  r  r  c              
   C   s   t td| |td |td   t|||  |td  t| ||  ||td    || t|||  |td  t| ||  ||td    ||td   | S rW  rw  r  r  r  r  r  "  r  r  c              
   C   s   t td| |td |td   t|||  |td  t| ||  ||td    ||t|||  |td  t| ||  ||td    ||td   | S rW  rt  r  r  r  r  r  "  r  r  c                 C   s(  t td| |td |td   t|||  |td  t| ||  ||td    || t || td| |  |td |td   t|||  |td  t| ||  ||td    || t|||  |td  t| ||  ||td    ||td   | S rW  rw  r  r  r  r  r  "  r  r  c                 C   s&  t td| |td |td   t|||  |td  t| ||  ||td    ||t || td| |  |td |td   t|||  |td  t| ||  ||td    || t|||  |td  t| ||  ||td    ||td   | S rW  rt  r  r  r  r  r  "  s   ( r  c                 C   6   t |||  | t| ||  ||td    |S rY  r  r  r  r  r  r  "  r  r  c                 C   r  rY  r  r  r  r  r  r  "  r  r  c              	   C   >   t t|||  | t| ||  ||td   | ||S rY  r  r  r  r  r  r  "  r  r  c              	   C   r  rY  r  r  r  r  r  r  "  r  r  c                 C   &   t t|||  tt|||  |S rC  )r   r2  r  r  r  rD  r3  rE  r  r  r  r  "  r  r  c                 C   r  rC  )r   r2  r  r  r  r  r  r  "  r  r  (A  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r}  r  B_C_F_G_H_r  r  r  r  rK  f_r  h_i_j_k_l_r  r  r  r  r_t_r  r  s_w_r  y_z_a1_a2_b1_b2_c1_c2_d1_d2_n1_r  e1_e2_f1_f2_g1_g2_n3_Pq_Pm_Px_Qm_Qr_Qx_jn_mn_non2_RFx_RGx_r  iiPqqQRrr  r`  rD  	_UseGamma	ShowStepsStepCounterrB  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  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$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  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/  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
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