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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)Add)Mod)Mul)
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}9t|9t	}:ttttt tdtd tdtd t||||};t|;t
}<ttttt tdtd tdtd t||||}=t|=t}>tttdtdtd	tdttt tdtd tdtd   t t|||||6||7}?t|?t}@tttdtdtd	tdttt tdtd tdtd   t t|||||6||7}At|At}Btttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|-}Ct|Ct}Dtttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|-}Et|Et}Ftttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|8}Gt|Gt}Htttdtdtd	tdttt tdtd tdtd   tdtd t|||||(|8}It|It}Jttttt tdtd tdtd t|||%|9}Kt|Kt}Lttttt tdtd tdtd t|||%|9}Mt|Mt}Ntttdtdtd	tdttt tdtd tdtd   t t|||||%|'}Ot|Ot}Ptttdtdtd	tdttt tdtd tdtd   t t|||||%|'}Qt|Qt}Rtttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|(|:|;	}St|St}Ttttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|(|:|;	}Ut|Ut}Vtttdtdtd	tdttt tdtd tdtd   t t|||||%|/|:}Wt|Wt}Xtttdtdtd	tdttt tdtd tdtd   t t|||||%|/|:}Yt|Yt}Ztttdtdtd	tdtt  tdtd t|||/|<|=}[t|[t}\tttdtdtd	tdtt  tdtd t|||/|<|=}]t|]t}^ttttt tdtd t t||%|>}_t|_t}`ttttt tdtd t t||%|>}at|at}btttttt tdtd  t t|||%|9}ct|ct}dtttĐttt tdtd  t t|||%|9}et|et }fttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(t!t"	}gt|gt#}httttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(t!t$	}it|it%}jttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(t!t'
}kt|kt(}lttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(t!t)
}mt|mt*}nttttdtd tdtd ttt tdtd tdtd  t||||| |?}ot|ot+}pttttdtd tdtd ttt tdtd tdtd  t||||| |?}qt|qt,}rttttdtd t ttt tdtd tdtd  t||||| |}st|st-}tttttdtd t ttt tdtd tdtd  t||||| |}ut|ut.}vttttdtd tdtd ttt tdtd tdtd  t||||
|}wt|wt/}xttttdtd tdtd ttt tdtd tdtd  t||||
|}yt|yt0}zttttdtd ttt td	td tdtd t  t|||6|@|7|A}{t|{t1}|ttttdtd ttt td	td tdtd t  t|||6|@|7|A}}t|}t2}~ttttdtd ttt td	td tdtd t  t|||
|%|B|1|7}t|t3}ttttdtd ttt td	td tdtd t  t|||
|%|B|1|7}t|t4}ttttdtd ttt td	td tdtd t  t|||C|1|7|D}t|t5}ttttdtd ttt td	td tdtd t  t|||C|1|7|D}t|t6}ttttdtd ttt td	td tdtd t  t|||C|1|7|E|F}t|t7}ttttdtd ttt td	td tdtd t  t|||C|1|7|E|F}t|t8}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(||G	}t|t9}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(||G	}t|t:}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|(||7
}t|t;}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|(||7
}t|t<}ttttdtd ttt td	td tdtd t  t|||
|%|B|1|)|H	}t|t=}ttttdtd ttt td	td tdtd t  t|||
|%|B|1|)|H	}t|t>}ttttdtd ttt td	td tdtd t  t|||C|1|)|H|D}t|t?}ttttdtd ttt td	td tdtd t  t|||C|1|)|H|D}t|t@}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||(|-|4}t|tA}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||(|-|4}t|tB}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(|-|G	}t|tC}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||(|-|G	}t|tD}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|-|I
}t|tE}ttttdtd t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|-|I
}t|tF}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|(|8}t|tG}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|(|8}t|tH}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|8	}t|tI}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|(|8	}t|tJ}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(|J|K|L}t|tK}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|(|J|K|L}t|tL}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(|J|K|L}t|tM}ttt&t t tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|(|J|K|L}t|tN}ttttdtd tdtd ttt tdtd tdtd  t||||
|%|M}t|tO}ttttdtd tdtd ttt tdtd tdtd  t||||
|%|M}t|tP}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|%|'	}t|tQ}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   t  t||||||
|%|'	}t|tR}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||%|/|:|;|4
}t|tS}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||%|/|:|;|4
}t|tT}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|:
}t|ÐtU}ttttdtd tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|:
}t|ŐtV}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|ǐtW}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|ɐtX}ttttdtd tttd
td td	td tdtd tdtd  tttd
td td	td tdtd  t|||
|%|/|0|N}t|ːtY}ttttdtd tttd
td td	td tdtd  tttd
td td	td tdtd tdtd  t|||
|%|/|0|N}t|͐tZ}ttttdtd tttd
td td	td tdtd tdtd  tttd
td td	td tdtd  t|||/||?|N}t|ϐt[}ttttdtd tttd
td td	td tdtd  tttd
td td	td tdtd tdtd  t|||/||?|N}t|ѐt\}tttttd tdtd ttd	td  tdtd t||||O}t|Ӑt]}tttttd tdtd ttd	td  tdtd t||||O}t|Րt^}tttttd tdtd ttd	td  tdtd t t|||||}t|אt_}tttttd tdtd ttd	td  tdtd t t|||||}t|ِt`}tttttd
td t||P|Q}t|ېta}tttttd
td t||P|Q}t|ݐtb}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||R}t|ߐtc}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||R}t|td}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||S}t|te}ttttdtd tdtd tttd tdtd ttd	td  tdtd  t||||||S}t|tf}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|tg}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|th}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|ti}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|tj}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|tk}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||R	}t|tl}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|tm}ttttdtd tdtd t tttd tdtd ttd	td  tdtd  t|||||| ||S	}t|tn}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd  t||||||
|T}t|to}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd  t||||||
|T}t|tp}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd t  t||||||
||	}t|tq}ttttdtd tdtd tdtd tttd tdtd ttd	td  tdtd t  t||||||
||	}t|tr}ttttdtd tttd
td  t|
||:|P|U}t|ts} ttttdtd tttd
td  t|
||:|P|U}t|tt}ttttd	td tdtd tdtd tuttdtd tdtd  t||||| }t|tv}ttttd	td tdtd tdtd tuttdtd tdtd  t||||| }t|tw}tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}t|tx}tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}	t|	ty}
tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}t|tz}tttdtdtuttdtd tdtd  t ttd	td tdtd tdtd  t||||||||	}t|t{}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t|}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t}}ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||W| |
}t|t~}ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||W| |
}t|t}tttdttd	tdtuttdtd tdtd   ttdtd tdtd td   t|||||||W}t|t}tttdttd	tdtuttdtd tdtd   ttdtd tdtd td   t|||||||W}t|t}ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||W| ||X}t|t}ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||W| ||X}t|t}tttdttd	tdtuttdtd tdtd   ttdtd tdtd   t|||||||W}t|t} tttdttd	tdtuttdtd tdtd   ttdtd tdtd   t|||||||W}!t|!t}"ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||
|W|Y
}#t|#t}$ttttdtd tdtd t ttd	tdtuttdtd tdtd    t|||||||
|W|Y
}%t|%t}&ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||W|Z	}'t|'t}(ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||W|Z	})t|)t}*ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||
|W|-
}+t|+t},ttttd	tdtuttdtd tdtd   t ttdtd tdtd t  t|||||||
|W|-
}-t|-t}.ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||W|[| |}/t|/t}0ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||W|[| |}1t|1t}2ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||!| 	}3t|3t}4ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd    t|||||||!| 	}5t|5t}6ttttdtd tdtd ttd	tdtuttdtd tdtd   td  t|||||||!}7t|7t}8ttttdtd tdtd ttd	tdtuttdtd tdtd   td  t|||||||!}9t|9t}:ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||!|-| 
};t|;t}<ttttd	tdtuttdtd tdtd   t ttdtd tdtd tdtd  t|||||||!|-| 
}=t|=t}>ttttdtd tdtdtd	tdtut  td
td  t|||
|%|#|$}?t|?t}@ttttdtd tdtdtd	tdtut  td
td  t|||
|%|#|$}At|At}Bttttdtd tdtd tdtd tdtdtd	tdtuttdtd tdtd   td
td  t|||||||
|%|&
}Ct|Ct}Dttttdtd tdtd tdtd tdtdtd	tdtuttdtd tdtd   td
td  t|||||||
|%|&
}Et|Et}Ftttdtdtd	tdtutt tdtd tdtd   tdtd t|||||/|\|(}Gt|Gt}Htttdtdtd	tdtutt tdtd tdtd   tdtd t|||||/|\|(}It|It}Jtttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|.}Kt|Kt}Ltttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|.}Mt|Mt}Ntttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|:|;	}Ot|Ot}Ptttdtdtd	tdtutt tdtd tdtd   tdtd t|||||%|/|:|;	}Qt|Qt}Rtttdtdtd	tdtut  tdtd t|||/|<|=}St|St}Ttttdtdtd	tdtut  tdtd t|||/|<|=}Ut|Ut}Vttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}Wt|Wt}Xttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}Yt|Yt}Zttttdtd tutt tdtd tdtd td  t|||
|%|^}[t|[t}\ttttdtd tutt tdtd tdtd td  t|||
|%|^}]t|]t}^ttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|_	}_t|_t}`ttttdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t|||||
|%|/|_	}at|at}bttt&t tdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t||||||
|%|/|5
}ct|ct}dttt&t tdtd tdtdtd	tdtutt tdtd tdtd   tdtd  t||||||
|%|/|5
}et|et}fttt&t tdtd tdtdtd	tdtut  tdtd  t||||
|/|<|=}gt|gt}httt&t tdtd tdtdtd	tdtut  tdtd  t||||
|/|<|=}it|it}jttttdtd tdtttd
td td	td tdtd  tdtd  tuttd
td td	td tdtd tdtd  t|||/| ||`|a}kt|kt}lttttdtd tdtttd
td td	td tdtd  tdtd  tdtuttd
td td	td tdtd  tdtd  t|||/| ||`|a}mt|mt}ntttuttd tdtd ttd	td  tdtd td
td t||||%|b}ot|ot}ptttdtuttd tdtd ttd	td  tdtd  td
td t||||%|b}qt|qt}rttttdtd tdtd tuttd tdtd ttd	td  tdtd  t||||||c}st|st}tttttdtd tdtd tuttd tdtd ttd	td  tdtd  t||||||c}ut|ut}vttttdtd tdtd tdtd tuttd tdtd ttd	td  tdtd td
td  t||||||
|%|d	}wt|wt}xttttdtd tdtd tdtd tdtuttd tdtd ttd	td  tdtd  td
td  t||||||
|%|d	}yt|yt}zttttdtd tdtd tdtd tttd	td tdtd  t||||| }{t|{t}|ttttdtd tdtd tdtd tttd	td tdtd  t||||| }}t|}t}~ttttdtd tdtd tdtd tttd	td tdtd td  t||||| |}t|t}ttttdtd tdtd tdtd tttd	td tdtd td  t||||| |}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t|||||||e}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t|||||||e}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||e|	}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||e|	}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t||||||}t|t}ttttdtd tdtd tdtttd	td tdtd  t  t||||||}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||}t|t}ttttdtd tdtd t tdtttd	td tdtd  t  t|||||||}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  t  t|||||
|%|L}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  t  t|||||
|%|L}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|V	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||-| 	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||-| 	}t|tÃ}ttttdtd tdtt td
td  t|
|%|#|$}t|tă}ttttdtd tdtt td
td  t|
|%|#|$}t|tŃ}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  t|||||
|%|f}t|tƃ}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  t|||||
|%|f}t|tǃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||/|\|(}t|tȃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||/|\|(}t|tɃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|.}t|tʃ}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|.}t|t˃}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|:|;	}t|t̃}tttdtdtd	tdttt tdtd tdtd   tdtd t|||||%|/|:|;	}t|t̓}tttdtdtd	tdtt  tdtd t|||/|<|=}t|t΃}tttdtdtd	tdtt  tdtd t|||/|<|=}t|tσ}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}t|tЃ}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|]|(
}t|tу}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|_	}t|t҃}ttttdtd tdtdtd	tdttt tdtd tdtd   tdtd  t|||||
|%|/|_	}t|tӃ}ttt&t tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|5
}t|tԃ}ttt&t tdtd tdtdtd	tdttt tdtd tdtd   tdtd  t||||||
|%|/|5
}t|tՃ}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|Ðtփ}ttt&t tdtd tdtdtd	tdtt  tdtd  t||||
|/|<|=}t|Őt׃}ttttdtd tdtttd
td td	td tdtd  t  tttd
td td	td tdtd  t|||/| ||`|g}t|ǐt؃}ttttdtd tdtttd
td td	td tdtd  t  tttd
td td	td tdtd  t|||/| ||`|g}t|ɐtك}ttttdtd tdtd tdtd tttd	td tdtd td
td  tttd	td tdtd  t|||||%| |h}t|ːtڃ}ttttdtd tdtd tdtd tttd	td tdtd  tttd	td tdtd td
td  t|||||%| |h}t|͐tۃ}ttttdtd tdtd tdtd tttd	td tdtd td
td  tttd	td tdtd tdtd  t|||||
|i}t|ϐt܃}ttttdtd tdtd tdtd tttd	td tdtd td
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|i}t|ѐt݃}ttttdtd tdtd tdtd tdtuttd	td tdtd  tdtd  tttd	td tdtd td
td  t|||||
|i}t|Ӑtރ}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tuttd	td tdtd tdtd  t|||||%|j| |	}t|Րt߃}ttttdtd tdtd tdtd tdtttd	td tdtd  td
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td  tttd	td tdtd td  t|||||%| |h}t|ِt}ttttdtd tdtd tdtd tdtuttd	td tdtd  td
td  tttd	td tdtd td  t|||||%| |h}t|ېt}ttttdtd tdtd tdtd tuttd	td tdtd t  tttd	td tdtd  t|||||
|k}t|ݐt}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tuttd	td tdtd t  t|||||
|%|k}t|ߐt}ttttdtd tdtd tdtd tdtuttd	td tdtd  t  tttd	td tdtd  t|||||
|k}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtuttd	td tdtd  t  t|||||
|%|k}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tuttd	td tdtd tdtd  t|||||%|/| |l	}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtuttd	td tdtd  tdtd  t|||||%|/| |l	}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtttd	td tdtd  td
td  t||||| |}t|t}ttttdtd tdtd tdtd tdtttd	td tdtd  td
td  tdtttd	td tdtd  tdtd  t|||||6| ||m	}t|t}tttt tt  ttdtd  t|
|%|/|n|o|p|q|r	}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd  t|||||||%| |h
}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd  t|||||||%| |h
}t|t}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd td  t|||||||%| |h
}t|t}ttttd	tdtuttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd td  t|||||||%| |h
}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tuttdtd tdtd  tttdtd tdtd  t|||||||%| |h
}t|t}ttttd	tdtttdtd tdtd   td
td ttdtd tdtd tdtd  tttdtd tdtd tuttdtd tdtd   t|||||||%| |h
}t|t}ttttdtd tdtd tdtd tttd	td tdtd tdtd  tttdtd tdtd tdtd  t|||||||s|4	}t|t}ttttdtd tdtd tdtd tttd	td tdtd tdtd  tttdtd tdtd tdtd  t|||||||s|4	}t|t}ttttdtd tdtd tdtd tttd	td tdtd tdtd  tttdtd tdtd tdtd  t|||||||
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}t|t}tttttd	td tdtd tdtd  tttdtd tdtd t  t|y||||||z||
}	t|	t}
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}t|t}tttttd	td tdtd tdtd  tdtttdtd tdtd  t  t|y||||||~||
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}&tttttd	td tdtd tdtd  tdtttdtd tdtd  td
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}At|At}Btttttd	td tdtd tdtd  ttdtd  tttdtd tdtd td
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}Ct|Ct}Dtttttd	td tdtd tdtd  tttdtd tdtd tdtd  tttdtd tdtd td
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}Et|Et}Ftttttd	td tdtd tdtd  ttdtd  tttdtd tdtd tdtd  tttdtd tdtd td
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}Gt|Gt}Htttttd	td tdtd tdtd  tttdtd tdtd   tttdtd tdtd   t|y||||||V|o|
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td tdtd   t||||%|}at|at-}bttttdtdtd	tdt#ttd
td tdtd   t||||%|}ct|ct.}dttttdtdtd	tdt#ttd
td tdtd   t t||||%|1|7|}et|et/}fttttdtdtd	tdt#ttd
td tdtd   t t||||%|1|7|}gt|gt0}httttdtdtd	tdt#ttd
td tdtd   t t||||%|1|)|H|	}it|it1}jttttdtdtd	tdt#ttd
td tdtd   t t||||%|1|)|H|	}kt|kt2}lttttdtdtd	tdt#ttd
td tdtd   t t||||%|/|}mt|mt3}nttttdtdtd	tdt#ttd
td tdtd   t t||||%|/|}ot|ot4}pttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/||N|J
}qt|qt5}rttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/||N|J
}st|st6}tttttdtd ttdtdtd	tdt#ttd
td tdtd   tdtd  t||||
|%|'|}ut|ut7}vttttdtd ttdtdtd	tdt#ttd
td tdtd   tdtd  t||||
|%|'|}wt|wt8}xttttdtd ttdtdtd	tdt#ttd
td tdtd    t||||
|%||J}yt|yt9}zttttdtd ttdtdtd	tdt#ttd
td tdtd    t||||
|%||J}{t|{t:}|ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|7|J
}}t|}t;}~ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|7|J
}t|t<}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|)|H|J}t|t=}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%||1|)|H|J}t|t>}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/|}t|t?}ttttdtd ttdtdtd	tdt#ttd
td tdtd   t  t||||
|%|/|}t|t@}tttdttd	tdt#ttd
td tdtd   tdtd t||}t|tA}tttdttd	tdt#ttd
td tdtd   tdtd t||}t|tB}tttdttdtdtd	tdt#ttd
td tdtd    t||||%|}t|tC}tttdttdtdtd	tdt#ttd
td tdtd    t||||%|}t|tD}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|/||g}t|tE}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|/||g}t|tF}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|7||	}t|tG}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|7||	}t|tH}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|)|}t|tI}tttdttdtdtd	tdt#ttd
td tdtd    t t||||%|1|)|}t|tJ}tttdttdtdtd	tdt#ttd
td tdtd    tdtd t||||%|/|}t|tK}tttdttdtdtd	tdt#ttd
td tdtd    tdtd t||||%|/|}t|tL}ttttdtd tdttd	tdt#ttd
td tdtd   tdtd  t||}t|tM}ttttdtd tdttd	tdt#ttd
td tdtd   tdtd  t||}t|tN}ttttdtd tOtdtdtd	tdt#ttd
td tdtd    t||||
|%|}t|tP}ttttdtd tQtdtdtd	tdt#ttd
td tdtd    t||||
|%|}t|tR}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|/||J|g
}t|tS}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|/||J|g
}t|tT}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|7||
}t|tU}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|7||
}t|tV}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|)|	}t|tW}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    t  t||||
|%|1|)|	}t|tX}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    tdtd  t||||
|%|/|}t|tY}ttttdtd tdttdtdtd	tdt#ttd
td tdtd    tdtd  t||||
|%|/|}t|tZ}ttt#ttd	td tdtd tttdtd t#ttd	td tdtd   t|||1|}t|t[}ttt#ttd	td tdtd tttdtd t#ttd	td tdtd   t|||1|}t|t\}ttt#ttd	td tdtd ttt tdtd t#ttd	td tdtd   t||||}t|t]}ttt#ttd	td tdtd ttt tdtd t#ttd	td tdtd   t||||}t|t^}ttttdtd t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||
|%|0|1|}t|t_}ttttdtd t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||
|%|0|1|}t|Ðt`}tttt t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||||}t|Őta}tttt t#ttd	td tdtd  tttd
td tdtd t#ttd	td tdtd   t|||||}t|ǐtb}ttttdtdttdtd tdtd  td
td t||||}t|ɐtc}ttttdtdttdtd tdtd  td
td t||||}t|ːtd}tttttd	td tdtd tdtd ttdtd tdtd  td
td t||||||}t|͐te}tttttd	td tdtd tdtd ttdtd tdtd  td
td t||||||}t|ϐtf}tttttd
td t||}t|ѐtg}tttttd
td t||}t|Ӑth}tttdtdtttdtd  tttdtd  t|p}t|Րti}tttdtdtttdtd  tĐttdtd  t|p}t|אtj}tttttdtd tttdtd  t|s|}t|ِtk}tttttdtd tĐttdtd  t|s|}t|ېtl}ttttdtd tttdtd  tttdtd  t||}t|ݐtm}ttttdtd tttdtd  tĐttdtd  t||}t|ߐtn}tttdtdtttdtd  tĐttdtd  t|p|(}t|to}tttttdtd tĐttdtd  t|s|}t|tp}ttttdtd tttdtd  tĐttdtd  t||}t|tq}tttttuttd
td  t|||}t|tr}tttdtut td
td tt t|||}t|ts}tttdtut td
td tt t|||}t|tt}tttttuttd
td  t|||}t|tu}tttdtĐt td
td tt t|||}t|tv}tttdtt td
td tt t|||}t|tw}tttdtt td
td tt t|||}t|tx}tttdtĐt td
td tt t|||}t|ty}ttttd	tdtttdtd tdtd  tttdtd tdtd   td
td ttdtd tdtd tdtd  t|||||||
|%|&
}t|tz}ttttdtd ttd	tdtttdtd tdtd td   t  t||||||C|||
}t|t{}ttttdtd ttd	tdtttdtd tdtd td   t  t||||||C|||
}t|t|}ttttdtd tdtd tdtd ttttdtd  t td	td tdtd tdtd  t|||||||%| |1
}t|t}}ttttdtd tdtd tdtd tĐtttdtd  t td	td tdtd tdtd  t|||||||%| |1
}t|t~} ttttdtd tdtd tdtd tdtdtd	tdtttdtd tdtd td   tdtdtttdtd tdtd td    t|||||||| ||}t|t}ttttdtd tdtd tdtd ttdtdtuttdtd tdtd td   tttdtd tdtd td   t||||||| }t|t}ttttdtd tdtd tdtd tdtdtttdtd tdtd td  td	td tdtdtuttdtd tdtd td   tttdtd tdtd td   t|||||||| ||}t|t}ttttdtd tdtd tdtd ttd	tdtuttdtd tdtd td   tttdtd tdtd td   t||||||| }t|t}ttttdtd tdtd tdtd tdtdtttdtd tdtd td  td	tdtuttdtd tdtd td   tdtd tttdtd tdtd td   t|||||||| ||}	t|	t}
ttttdtd tdtd tdtd tttdtd tdtd  ttd	tdtttdtd tdtd    t||||||| }t|t}ttttdtd tdtd tdtd tttdtd tdtd  ttd	tdtttdtd tdtd    t||||||| }t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||}t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||W}t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||}t|t}ttttdtd tdtd tdtd tttdtd tdtd t  ttd	tdtttdtd tdtd    t||||||| |||!}t|t}ttttdtdtttdtd tdtd   ttdtd tdtd  ttd	tdtttdtd tdtd   td  t|||||||||
}t|t}ttttdtdtttdtd tdtd   ttdtd tdtd  ttd	tdtttdtd tdtd   td  t|||||||||
}t|t}ttttd	tdtut  td
td tdtt tdtd  t|||C||}t|t}ttttd	tdtut  td
td tdtt tdtd  t|||C||}t|t}tttdtdtttd	td tdtd tdtd  tttdtd tdtd td
td  t|||||V}t|t} tttdtdtttd	td tdtd tdtd  tttdtd tdtd td
td  t|||||V}!t|!t}"tttdtĐtttdtd  tttd	td tdtd   t||||||}#t|#t}$tttdttttdtd  tttd	td tdtd   t||||||}%t|%t}&tttutttdtd  tuttd	td tdtd  t||||||}'t|'t}(tttdtutttdtd  tuttd	td tdtd   t||||||})t|)t}*tttdtdtt td	tdtt  td
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sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  x_r  r  r  r   replacement5646r  replacement5647m_replacement5648replacement5649replacement5650replacement5651replacement5652replacement5653replacement5654replacement5655n_replacement5656replacement5657replacement5658replacement5659replacement5660replacement5661replacement5662replacement5663replacement5664replacement5665replacement5666replacement5667replacement5668replacement5669a_replacement5670replacement5671replacement5672replacement5673replacement5674replacement5675replacement5676replacement5677replacement5678replacement5679replacement5680replacement5681replacement5682replacement5683u_v_replacement5684replacement5685replacement5686replacement5687replacement5688replacement5689p_replacement5690replacement5691replacement5692replacement5693replacement5694replacement5695replacement5696replacement5697replacement5698replacement5699replacement5700replacement5701replacement5702replacement5703replacement5704replacement5705replacement5706replacement5707replacement5708replacement5709replacement5710replacement5711replacement5712replacement5713replacement5714replacement5715With5716With5717replacement5718replacement5719replacement5720replacement5721replacement5722replacement5723replacement5724replacement5725replacement5726replacement5727replacement5728replacement5729c_replacement5730replacement5731r   With5732replacement5732With5733replacement5733e_With5734replacement5734With5735replacement5735replacement5736replacement5737replacement5738replacement5739replacement5740replacement5741replacement5742replacement5743replacement5744replacement5745replacement5746replacement5747replacement5748replacement5749With5750With5751replacement5752replacement5753replacement5754replacement5755replacement5756replacement5757replacement5758replacement5759With5760With5761replacement5762replacement5763With5764With5765replacement5766replacement5767replacement5768replacement5769replacement5770replacement5771replacement5772replacement5773replacement5774replacement5775replacement5776replacement5777replacement5778replacement5779replacement5780replacement5781replacement5782replacement5783replacement5784replacement5785replacement5786replacement5787replacement5788replacement5789replacement5790replacement5791replacement5792replacement5793replacement5794replacement5795replacement5796replacement5797replacement5798replacement5799replacement5800replacement5801replacement5802replacement5803replacement5804replacement5805replacement5806replacement5807replacement5808replacement5809r  replacement5810replacement5811replacement5812replacement5813replacement5814replacement5815replacement5816replacement5817replacement5818replacement5819replacement5820replacement5821replacement5822replacement5823replacement5824replacement5825replacement5826replacement5827replacement5828replacement5829replacement5830replacement5831With5832With5833replacement5834replacement5835replacement5836replacement5837replacement5838replacement5839replacement5840replacement5841replacement5842replacement5843replacement5844replacement5845replacement5846replacement5847replacement5848replacement5849replacement5850replacement5851replacement5852replacement5853replacement5854replacement5855replacement5856replacement5857replacement5858replacement5859replacement5860replacement5861replacement5862replacement5863replacement5864replacement5865replacement5866replacement5867replacement5868replacement5869replacement5870replacement5871replacement5872replacement5873replacement5874replacement5875replacement5876replacement5877replacement5878replacement5879replacement5880replacement5881replacement5882replacement5883replacement5884replacement5885replacement5886replacement5887replacement5888replacement5889replacement5890replacement5891replacement5892replacement5893replacement5894replacement5895replacement5896replacement5897replacement5898replacement5899replacement5900replacement5901replacement5902replacement5903replacement5904replacement5905replacement5906replacement5907replacement5908replacement5909replacement5910replacement5911replacement5912replacement5913replacement5914replacement5915replacement5916replacement5917replacement5918replacement5919replacement5920replacement5921replacement5922With5923With5924replacement5925With5926F_G_w_replacement5927replacement5928replacement5929replacement5930replacement5931replacement5932replacement5933replacement5934replacement5935replacement5936replacement5937replacement5938replacement5939replacement5940replacement5941replacement5942replacement5943replacement5944replacement5945replacement5946replacement5947replacement5948replacement5949replacement5950replacement5951replacement5952replacement5953replacement5954replacement5955replacement5956replacement5957replacement5958replacement5959f_replacement5960replacement5961replacement5962replacement5963replacement5964replacement5965h_replacement5966replacement5967replacement5968With5969With5970replacement5971replacement5972H_replacement5973replacement5974replacement5975replacement5976logreplacement5977replacement5978replacement5979replacement5980r  replacement5981replacement5982replacement5983replacement5984replacement5985replacement5986replacement5987replacement5988replacement5989replacement5990replacement5991replacement5992replacement5993replacement5994replacement5995replacement5996replacement5997replacement5998replacement5999replacement6000replacement6001replacement6002replacement6003replacement6004replacement6005replacement6006replacement6007replacement6008replacement6009replacement6010replacement6011replacement6012replacement6013replacement6014replacement6015replacement6016replacement6017replacement6018r  replacement6019r  replacement6020replacement6021replacement6022replacement6023replacement6024replacement6025replacement6026replacement6027replacement6028replacement6029replacement6030replacement6031replacement6032replacement6033replacement6034replacement6035replacement6036replacement6037replacement6038replacement6039replacement6040With6041With6042replacement6043replacement6044replacement6045replacement6046replacement6047replacement6048replacement6049replacement6050replacement6051replacement6052replacement6053replacement6054replacement6055replacement6056replacement6057replacement6058replacement6059replacement6060replacement6061replacement6062replacement6063replacement6064replacement6065b_replacement6066replacement6067replacement6068replacement6069replacement6070replacement6071replacement6072replacement6073replacement6074replacement6075A_replacement6076replacement6077replacement6078replacement6079replacement6080replacement6081replacement6082replacement6083replacement6084replacement6085replacement6086(-  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  pattern5646rule5646pattern5647rule5647pattern5648rule5648pattern5649rule5649pattern5650rule5650pattern5651rule5651pattern5652rule5652pattern5653rule5653pattern5654rule5654pattern5655rule5655pattern5656rule5656pattern5657rule5657pattern5658rule5658pattern5659rule5659pattern5660rule5660pattern5661rule5661pattern5662rule5662pattern5663rule5663pattern5664rule5664pattern5665rule5665pattern5666rule5666pattern5667rule5667pattern5668rule5668pattern5669rule5669pattern5670rule5670pattern5671rule5671pattern5672rule5672pattern5673rule5673pattern5674rule5674pattern5675rule5675pattern5676rule5676pattern5677rule5677pattern5678rule5678pattern5679rule5679pattern5680rule5680pattern5681rule5681pattern5682rule5682pattern5683rule5683pattern5684rule5684pattern5685rule5685pattern5686rule5686pattern5687rule5687pattern5688rule5688pattern5689rule5689pattern5690rule5690pattern5691rule5691pattern5692rule5692pattern5693rule5693pattern5694rule5694pattern5695rule5695pattern5696rule5696pattern5697rule5697pattern5698rule5698pattern5699rule5699pattern5700rule5700pattern5701rule5701pattern5702rule5702pattern5703rule5703pattern5704rule5704pattern5705rule5705pattern5706rule5706pattern5707rule5707pattern5708rule5708pattern5709rule5709pattern5710rule5710pattern5711rule5711pattern5712rule5712pattern5713rule5713pattern5714rule5714pattern5715rule5715pattern5716rule5716pattern5717rule5717pattern5718rule5718pattern5719rule5719pattern5720rule5720pattern5721rule5721pattern5722rule5722pattern5723rule5723pattern5724rule5724pattern5725rule5725pattern5726rule5726pattern5727rule5727pattern5728rule5728pattern5729rule5729pattern5730rule5730pattern5731rule5731pattern5732rule5732pattern5733rule5733pattern5734rule5734pattern5735rule5735pattern5736rule5736pattern5737rule5737pattern5738rule5738pattern5739rule5739pattern5740rule5740pattern5741rule5741pattern5742rule5742pattern5743rule5743pattern5744rule5744pattern5745rule5745pattern5746rule5746pattern5747rule5747pattern5748rule5748pattern5749rule5749pattern5750rule5750pattern5751rule5751pattern5752rule5752pattern5753rule5753pattern5754rule5754pattern5755rule5755pattern5756rule5756pattern5757rule5757pattern5758rule5758pattern5759rule5759pattern5760rule5760pattern5761rule5761pattern5762rule5762pattern5763rule5763pattern5764rule5764pattern5765rule5765pattern5766rule5766pattern5767rule5767pattern5768rule5768pattern5769rule5769pattern5770rule5770pattern5771rule5771pattern5772rule5772pattern5773rule5773pattern5774rule5774pattern5775rule5775pattern5776rule5776pattern5777rule5777pattern5778rule5778pattern5779rule5779pattern5780rule5780pattern5781rule5781pattern5782rule5782pattern5783rule5783pattern5784rule5784pattern5785rule5785pattern5786rule5786pattern5787rule5787pattern5788rule5788pattern5789rule5789pattern5790rule5790pattern5791rule5791pattern5792rule5792pattern5793rule5793pattern5794rule5794pattern5795rule5795pattern5796rule5796pattern5797rule5797pattern5798rule5798pattern5799rule5799pattern5800rule5800pattern5801rule5801pattern5802rule5802pattern5803rule5803pattern5804rule5804pattern5805rule5805pattern5806rule5806pattern5807rule5807pattern5808rule5808pattern5809rule5809pattern5810rule5810pattern5811rule5811pattern5812rule5812pattern5813rule5813pattern5814rule5814pattern5815rule5815pattern5816rule5816pattern5817rule5817pattern5818rule5818pattern5819rule5819pattern5820rule5820pattern5821rule5821pattern5822rule5822pattern5823rule5823pattern5824rule5824pattern5825rule5825pattern5826rule5826pattern5827rule5827pattern5828rule5828pattern5829rule5829pattern5830rule5830pattern5831rule5831pattern5832rule5832pattern5833rule5833pattern5834rule5834pattern5835rule5835pattern5836rule5836pattern5837rule5837pattern5838rule5838pattern5839rule5839pattern5840rule5840pattern5841rule5841pattern5842rule5842pattern5843rule5843pattern5844rule5844pattern5845rule5845pattern5846rule5846pattern5847rule5847pattern5848rule5848pattern5849rule5849pattern5850rule5850pattern5851rule5851pattern5852rule5852pattern5853rule5853pattern5854rule5854pattern5855rule5855pattern5856rule5856pattern5857rule5857pattern5858rule5858pattern5859rule5859pattern5860rule5860pattern5861rule5861pattern5862rule5862pattern5863rule5863pattern5864rule5864pattern5865rule5865pattern5866rule5866pattern5867rule5867pattern5868rule5868pattern5869rule5869pattern5870rule5870pattern5871rule5871pattern5872rule5872pattern5873rule5873pattern5874rule5874pattern5875rule5875pattern5876rule5876pattern5877rule5877pattern5878rule5878pattern5879rule5879pattern5880rule5880pattern5881rule5881pattern5882rule5882pattern5883rule5883pattern5884rule5884pattern5885rule5885pattern5886rule5886pattern5887rule5887pattern5888rule5888pattern5889rule5889pattern5890rule5890pattern5891rule5891pattern5892rule5892pattern5893rule5893pattern5894rule5894pattern5895rule5895pattern5896rule5896pattern5897rule5897pattern5898rule5898pattern5899rule5899pattern5900rule5900pattern5901rule5901pattern5902rule5902pattern5903rule5903pattern5904rule5904pattern5905rule5905pattern5906rule5906pattern5907rule5907pattern5908rule5908pattern5909rule5909pattern5910rule5910pattern5911rule5911pattern5912rule5912pattern5913rule5913pattern5914rule5914pattern5915rule5915pattern5916rule5916pattern5917rule5917pattern5918rule5918pattern5919rule5919pattern5920rule5920pattern5921rule5921pattern5922rule5922pattern5923rule5923pattern5924rule5924pattern5925rule5925pattern5926rule5926pattern5927rule5927pattern5928rule5928pattern5929rule5929pattern5930rule5930pattern5931rule5931pattern5932rule5932pattern5933rule5933pattern5934rule5934pattern5935rule5935pattern5936rule5936pattern5937rule5937pattern5938rule5938pattern5939rule5939pattern5940rule5940pattern5941rule5941pattern5942rule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\\dd^^\\ZZ\\rrppnn<<bbjjjj<<``nnbbHH0088``VV^^VVXXVVXXZZXX~~~~||``ddRRXX((vvvv~~~~~~~~>>jj||zzzz||~~zz^^nnnnppJJZZffdlxxhhrrjjpphhnnxxDDllllnnHHddDrrzz||||xx:44JVVddbbll\\ddffbbzzrrzz||vv^^ddllnnllttpprrvvzzTTxx&&JJ>>PPL>P4<<4::::rr^^``\d\         * r@  c                 C   j   t || | t| ||  |td  t|||   || t| ||  | t|||   | | S Nr  r   r  r  r  r  r  r  r  r  xr  r  r  r        jr   c                 C   rA  rB  r  r   r  r  r  rE  r  r  r  r    rG  r  c                 C      t |||td   t| ||  |td  t|||   || t| ||  |td  t|||   ||td   | S Nr  r  r  r   r  r  r  rE  r  r  r  r       r  c                 C   rI  rJ  r  r  r   r  r  r  rE  r  r  r  r    rL  r  c                 C      t t|||  | |S Nr  r  r  r  r  r  rF  r  r  r  r       r  c                 C   rN  rO  r  r  rQ  r  r  r  r    rR  r  c                 C   s   t t|  | ||  | tt| | | ||  | ||   ||t t|  | ||  | tt| | | ||  | ||   || S rO  r  r  r   r  rQ  r  r  r  r       r  c                 C   s   t t|  | ||  | tt| | | ||  | ||   ||t t|  | ||  | tt| | | ||  | ||   || S rO  rT  rQ  r  r  r  r    rU  r  c              	   C   sp   t tdd t| ||  | t| ||   || t tdd t| ||  | t|||   || S Nr  r  r  r  r   exprE  r  r  r  r	       pr	  c              	   C   sn   t tdd t| ||  | t| ||   ||t tdd t| ||  | t|||   || S rV  rW  rE  r  r  r  r
       nr
  c                 C   s   t | td |td  | t| t|||   |td  |||   || t|| t|||   |  |td |td   | t| | t|||   |td   |||   t|||   ||  | S Nr  rC  rM  r  r  r  r  r  r  rF  r  r  r  r    s   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 r[  rK  r]  r  r  r  r    s   r  c              	   C   sn  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 r[  rM  r  r  r  r  r  r  r  rF  r  r  r  r       p 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 r[  rK  r^  r  r  r  r       n r  c                 C   .   t t| ||  | t|||  | ||S rO  r   rd  r  r  r  r  r  r  r  rF  r  r  r  r        .r  c                 C   ra  rO  r   rd  r  rc  r  r  r  r    rd  r  c              
   C   s   t || ||td   tt| ||  |td  t|||  |td  t|||   ||| t| ||  |td  t|||  |  ||td   | S Nr  rC  r  r  r   rd  r  r  r  rc  r  r  r  r       r  c              
   C   s   t || ||td   tt| ||  |td  t|||  t|||  |td   ||| t| ||  |td  t|||  |  ||td   | S rf  rg  rc  r  r  r  r    rh  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  rC  r\  rM  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 ri  rK  r^  r  r  r  r    rj  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 Nr  r  rM  r]  r  r  r  r    s    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 rk  rK  r]  r  r  r  r        r  c              	   C   s  t |td | td |td   t| t|||   |td  |||  |  || t |td | |td  | td |td  |td  |td   t| t|||   |t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 ri  rM  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| 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 ri  rK  r^  r  r  r  r  $  s    r  c	           	   	   C   6   t t|||  | | |t|||    | ||S rO  r   r   r  	r  r  r  r  r  r  r  r  rF  r  r  r  r  (     6r  c	           	   	   C   rm  rO  r   r   r  ro  r  r  r  r  ,  rp  r  c	           	   	   C   sl   t td|  | t|||  | tt |  td|  |td  || td  td|   ||S Nr     r  r  r   r  Piro  r  r  r  r  0     l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 rr  )r  r  r%   r  r&   r  ru  r   ro  r  r  r  r  4     r  c	           	   	   C   sV   t td|  | t|||  | t|td || td  td|   ||S Nr  r  r  r   r  ro  r  r  r  r  8     Vr  c	           	   	   C   sX   t td |  | t|||  | t|td || td  td|   ||S rx  r  r  r   r  ro  r  r  r  r   <     X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 rx  )r  r  r%   r  r&   r   ro  r  r  r  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 rx  )r  r  r%   r  r&   r  r   ro  r  r  r  r"  D  rh  r"  c              
   C   sx   t tdt|||  | t|||   td |  t|||   |ttd| td| |    |  ||S )Nr\  r  rW  r  r  r  r  r  r  r  rF  r  r  r  r#  H     xr#  c              
   C   sv   t tdt|||  | t|||   td|  t|||   |ttd| td| |    |  ||S rx  rW  r~  r  r  r  r$  L  s   vr$  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 Nr  rC  r  r  r   r  r  r  r~  r  r  r  r%  P       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  r  r  r   r  r  r  r~  r  r  r  r&  T  r  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 Nr  r  rC  r  ro  r  r  r  r'  X      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 r  r  ro  r  r  r  r(  \  r  r(  c                 C   .   t | |tt||  | t|||  |S rO  r   r  r2  r  r  r  r  r  vrF  r  r  r  r+  `  rd  r+  c                 C   r  rO  r   r  r2  r  r  r  r  r,  d  rd  r,  c	           	      C   2   t | |t|||    | |||  |  |S rO  r   r  ro  r  r  r  r-  h     2r-  c	           	      C   r  rO  r   r  ro  r  r  r  r.  l  r  r.  c                 C   .   t tt|||  | |||   | ||S rO  rn  r  r  r  r  r  r  rF  r  r  r  r/  p  rd  r/  c                 C   r  rO  rq  r  r  r  r  r0  t  rd  r0  c              	   C     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 rJ  r  r  r  r  r  r2  x      r2  c              	   C   r  rJ  r  r  r  r  r  r3  |  r  r3  c                 C   r  rO  rn  r  r  r  r  r4    rd  r4  c                 C   r  rO  rq  r  r  r  r  r5    rd  r5  c                 C   8   t |||  | ||   | |  t|||   |S rO  r  r  r  r  r  r6       8r6  c                 C   r  rO  r  r  r  r  r  r7    r  r7  c                 C   *   t | |||   | t|||   |S rO  r  r  r  r  r  r8       *r8  c                 C   r  rO  r  r  r  r  r  r9    r  r9  c	           	      C   :   t tt|||  || | | |||   |  ||S rO  rn  	r  r  r  r  r  r  r  r  rF  r  r  r  r:       :r:  c	           	      C   r  rO  rq  r  r  r  r  r;    r  r;  c	           	      C      t |||  || |td   t| |||   |td  t|||   || t|| | |||   |td   t|||   || |td   | S rJ  rK  r  r  r  r  r<       r<  c	           	      C   r  rJ  rM  r  r  r  r  r=    r  r=  c              	   C   $  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 rJ  r  r  r  r  r  r  r  r  rF  r  r  r  r>       & r>  c              	   C   r  rJ  r  r  r  r  r  r?    r  r?  c                 C   6   t tt|||  || | |||   |  ||S rO  rn  r  r  r  r  r@    rp  r@  c                 C   r  rO  rq  r  r  r  r  rA    rp  rA  c                 C   <   t ||||   | ||   | |  t|||   |S rO  r  r  r  r  r  rB       <rB  c                 C   r  rO  r  r  r  r  r  rC    r  rC  c	           	      C   6   t || | | |||   |  t|||   |S rO  r  r  r  r  r  rD    rp  rD  c	           	      C   r  rO  r  r  r  r  r  rE    rp  rE  c              	   C   X   t tdd tt|  |||   || t tdd tt| |||   || S rV  rW  r  r  r  rF  r  r  r  rF    r|  rF  c              	   C   V   t tdd tt|  |||   ||t tdd tt| |||   || S rV  rW  r  r  r  r  rG    rz  rG  c              	   C   ,   t t| |t||||     | ||S rO  rb  r  r  r  r  rH       ,rH  c              	   C   r  rO  re  r  r  r  r  rI    r  rI  c              	   C   F   t t| |t||||      | |td  ||td|  S rk  )r+   r   r  r  r  r  r  r  rJ       FrJ  c              	   C   r  rk  )r+   r   r  r  r  r  r  r  rK    r  rK  c                 C   ^   t |}t|tt||td  | |t|||||      |  |||td|  |S NrC  r  r4   r  r+   r   r  r  r  r  r  r  r  r  rF  kr  r  r  rL       VrL  c                 C   r  r  r4   r  r+   r   r  r  r  r  r  r  rM    r  rM  c              	   C   r  rV  rW  r  r  r  r  rN    r|  rN  c              	   C   r  rV  rW  r  r  r  r  rO    rz  rO  c              	   C   r  rO  rb  r  r  r  r  rP    r  rP  c              	   C   r  rO  re  r  r  r  r  rQ    r  rQ  c                 C   J   t tdt||td tt| |t||||     | ||||S rJ  r  r  r3   r+   r   r  r  r  r  r  r  r  r  rF  r  r  r  rR       JrR  c                 C   r  rJ  r  r  r3   r+   r   r  r  r  r  r  rS    r  rS  c                 C   &   t | |t||||     | |S rO  r  r  r  r  r  rT       &rT  c                 C   r  rO  r  r  r  r  r  rU    r  rU  c                 C       t | |tt||  | |S rO  r  r  r  r  r  rF  r  r  r  rV  
      rV  c                 C   r  rO  r  r  r  r  r  rW    r  rW  c                 C      t t| ||  | |S rO  rP  r  r  rF  r  r  r  rX    rR  rX  c                 C   r  rO  rS  r  r  r  r  rY    rR  rY  c                 C   sL   t t| tt|||  | ||t t| tt|||  | || S rO  rT  r  r  r  r  r[       Lr[  c                 C   sL   t t| tt|||  | ||t t| tt|||  | || S rO  rT  r  r  r  r  r\    r  r\  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  rF  r0  r  r  r  r]  "     (r]  c           	      C   ^   |t d | }tt d| tt||t d  | |t|||    |  |||| |S rf  )r  r  r+   r   r  r  r  r  r  r^  +     Nr^  c           	      C   r  r  r  r  r  r  r  r_  1  r  r_  c           	      C   r  rf  )r  r  r+   r   r  r  r  r  r  r`  :  r  r`  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 r  r  
r  r  r  r  r  r  r  r  rF  r0  r  r  r  rb  @  r  rb  c	           
      C   l   |t d | }	t|t| |t|   || t|  t|| | |t||||     |  ||S rJ  )r  r  r%   r&   r   r  r  r  r  r  rc  I     \rc  c	           
      C   r  r  r  r  r  r  r  rd  O  r  rd  c	           
      C   r  rJ  )r  r  r%   r&   r   r  r  r  r  r  re  X  r  re  c              	   C      t || || td  ||  t|| ||  t| |||    || t||td  || || td   t| |||    ||  | S rf  r  r  r   r  r  r  r  r  r  r  rF  r  r  r  rf  ^     rf  c              	   C   r  rf  r  r  r   r  r  r  r  r  r  rg  b  r  rg  c              	   C      t |||   | |td  t|| ||  t| |||    || t|| |td  t| |||    ||td   | S rJ  rK  r  r  r  r  rh  f     rh  c              	   C   r  rJ  rM  r  r  r  r  ri  j  r  ri  c              
   C   p   t tdd t|| | t|  |||    || t tdd t|| | t| |||    || S rV  rW  r  r  r  r  rj  n  rY  rj  c              
   C   n   t tdd t|| | t|  |||    ||t tdd t|| | t| |||    || S rV  rW  r  r  r  r  rk  r  rZ  rk  c              	   C   s   t || | |td  tt| |||   |td  t| |||    ||t|td|  t| |||   |  |td  | S r  r  r  r  r  r  r  rF  r  r  r  rl  v  rU  rl  c              	   C   s   t || | |td  tt| |||   t| |||   |td   ||t|td|  t| |||   |  |td  | S r  r  r  r  r  r  rm  z  rU  rm  c              	   C   s   t |td | t|| t| |||   |td   || tt| |||   | |td | |td   | t|| t| |||   |td   t| |||    || |  | S NrC  r\  r  rM  r  r  r  r  rn  ~     rn  c              	   C   s   t |td | t|| t| |||   |td   ||tt| |||   | |td | |td   | t|| t| |||    t| |||   |td   || |  | S r  rK  r  r  r  r  ro    s   ro  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 NrC  r\  r  r  rM  r  r  r  r  rp    s    rp  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 r  rK  r  r  r  r  rq    s    rq  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 ri  rM  r  r  r  r  rr        rr  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 ri  rK  r  r  r  r  rs    r  rs  c	           
      C   |   t |}	t|	| tt||	|td  td  | |t||||   ||	|      |  |||| td|	  |S rf  r  
r  r  r  r  r  r  r  r  rF  r  r  r  r  rt       trt  c	           
      C   r  rf  r  r  r  r  r  ru    r  ru  c	           	   
   C   6   t t|| | | |t||||     | ||S rO  rb  r  r  r  r  rv    rp  rv  c	           	   
   C   r  rO  re  r  r  r  r  rw    rp  rw  c              	   C   s   t |td |td  t|| t| |||   |td   || tt| |||   |td  |td | |td  |td   | t|| t| |||   |td   t| |||    || |td   | S rk  rM  r  r  r  r  rx    s   rx  c              	   C   s   t |td |td  t|| t| |||   |td   ||tt| |||   |td  |td | |td  |td   | t|| t| |||    t| |||   |td   || |td   | S rk  rK  r  r  r  r  ry       ry  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 rk  rM  r  r  r  r  rz    s    rz  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 rk  rK  r  r  r  r  r{    s    r{  c              
   C   L   t t|| td  | |t||||      |  ||td|  S Nr\  r  )r+   r   r  r  r  r  r  r  r|    r  r|  c              
   C   r  r  )r+   r   r  r  r  r  r  r  r}    r  r}  c	           
      C      t |}	t|	| tt||	 |td  td  | |t||||   ||	 |      |  |||| td |	  | S rf  r  r  r  r  r  r~       |r~  c	           
      C   r  rf  r  r  r  r  r  r    r  r  c	           	      C   l   t || | td| |  tt|| td  | |t||||      |  ||td| | S Nr  r\  r  r  r+   r   r  r  r  r  r  r    rv  r  c	           	      C   r  r  r  r  r+   r   r  r  r  r  r  r    rv  r  c           	      C   j   t |}t|tt|||td  td  | |t|||||      |  |||td|  |S rf  r  	r  r  r  r  r  r  r  rF  r  r  r  r  r       br  c           	      C   r  rf  r  r  r  r  r  r    r  r  c	           	      C   \   t |t| |t|   || t|  t|| | |t||||     |  ||S rO  r  r%   r&   r   r  r  r  r  r  r       \r  c	           	      C   r  rO  r  r%   r&   r   r  r  r  r  r  r    r  r  c                 C   ^   t td|td  tt| |t|||||td       | ||||td  |S rJ  r  r  r  r  r  r       ^r  c                 C   r  rJ  r  r  r  r  r  r    r  r  c	           	      C   r  rO  r  r  r  r  r  r    r  r  c	           	      C   r  rO  r  r  r  r  r  r    r  r  c              
   C   r  rV  rW  r  r  r  r  r    rY  r  c              
   C   r  rV  rW  r  r  r  r  r    rZ  r  c	           	   
   C   r  rO  rb  r  r  r  r  r    rp  r  c	           	   
   C   r  rO  re  r  r  r  r  r     rp  r  c	           	      C   h   t t||td| td  tt| |t||||     | |t||td |  ||||S Nr  rC  r   )r  r3   r  r+   r   r  	r  r  r  r  r  r  r  r  rF  r  r  r  r       hr  c	           	      C   r  r  )r  r3   r  r+   r   r  r  r  r  r  r    r  r  c
           
   	   C   2   t ||	 | | |t||||     |  |	S rO  r  
r  r  r  r  r  r  r  r  r  rF  r  r  r  r    r  r  c
           
   	   C   r  rO  r  r  r  r  r  r    r  r  c                 C   ,   t || | | |tt||  |  |S rO  r  r  r  r  r  r  r  rF  r  r  r  r    r  r  c                 C   r  rO  r  r  r  r  r  r    r  r  c                 C   :   t t| |||   |td  || |td   |S rJ  r  r  r  r  r  r  r  r    r  r  c                 C   r  rJ  r  r  r  r  r  r  r  r     r  r  c              	   C      t || td || |td   t|||  t| |||   |td   || t||| td  t| |||   |td   || |td   | S rJ  r  r  r  r  r  r  $     r  c              	   C   r  rJ  r  r  r  r  r  r  (  r  r  c              
   C   sp   t tdd tt|  ||  ||td   || t tdd tt| ||  ||td   || S rV  rW  r  r  r  rF  r  r  r  r  ,  rY  r  c              
   C   sn   t tdd tt|  ||  ||td   ||t tdd tt| ||  ||td   || S rV  rW  r  r  r  r  r  0  rZ  r  c                 C   0   t tt| ||  ||td   | ||S rx  r   rd  r  r  r  r  r  r  rF  r  r  r  r  4     0r  c                 C   r  rx  r   rd  r  r  r 	  r  r  r  r  8  r	  r  c                 C      t tt|||  |S rO  r  r  r  rF  r  r  r  r  <     r  c                 C   r	  rO  r  r	  r  r  r  r  @  r	  r  c                 C   6   t |t| ||  ||td    td|  |S rx  r  r  r  r  r  r  rF  r  r  r  r  D  rp  r  c                 C   r	  rx  r  r	  r  r  r  r  H  rp  r  c              	   C      t || td| |  td|  tt| ||  ||td   || t|t| ||  ||td    td|  | S rx  rM  r	  r  r  r  r  L  rL  r  c              	   C   r	  rx  rK  r	  r  r  r  r  P  rL  r  c              
   C      t |td |td  td|  t|||  |td  t| ||  ||td    || t||||  |td   t| ||  ||td    td|  | S r[  r  r  r  r  r  r  r  rF  r  r  r  r  T     r  c              
   C   r		  r[  r  r
	  r  r  r  r  X  r	  r  c                 C     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 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|||  |td  t| ||  ||td    || t|||  |td  t| ||  ||td    ||td   | S rk  rK  r
	  r  r  r  r  d  r	  r  c              
   C   r	  rk  rM  r
	  r  r  r  r  h  r	  r  c                 C   (  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 rk  rK  r
	  r  r  r  r  l     * r  c                 C   r	  rk  rM  r
	  r  r  r  r  p  r	  r  c                 C   6   t |||  | t| ||  ||td    |S rx  r   r  r  r
	  r  r  r  r  t  rp  r  c                 C   r	  rx  )r   r  r  r
	  r  r  r  r  x  rp  r  c              	   C   >   t t|||  | t| ||  ||td   | ||S rx  r  r  r  r  r  r  r  r  rF  r  r  r  r  |     >r  c              	   C   r	  rx  r	  r	  r  r  r  r    r	  r  c                 C   &   t t|||  tt|||  |S rO  )r   r2  r  r  r  r  r  rF  r  r  r  r    r  r  c                 C   r	  rO  )r   r2  r  r	  r  r  r  r    r  r  c                 C   s   t tdt| ||  | ttd| td| |   ttd| td| |  td  ||t| ||  |td  ||td   | S rk  r  r  r   rX  r  r  r  r  r  r  rF  r  r  r  r       r  c              	   C   s   t tdt| ||  | ttd| td| |   tdttd| td| |    || t| ||  |td  ||td   | S rk  r	  r	  r  r  r  r    r  r  c              	   C   s   t |td t|t|||   |td  | ||  |  ||t || | ||td   t|t|||   |td  | ||  |td   || t||t|||   |td   | ||  |  ||td   | S Nr  r\  rC  r  r  r   r  r  r  r  r  r  r  r  r  rF  r  r  r  r    r  r  c              	   C   s   t |td t|t|||   |td  | ||  |  ||t || | ||td   t|t|||   |td  | ||  |td   || t||t|||   |td   | ||  |  ||td   | S r	  r	  r	  r  r  r  r    r  r  c              	   C   s   t |td t|t|||   |td  | ||  |  ||t || || |td   t|t|||   |td  | ||  |td   || t|t|||   |td  | ||  |  || |td   | S Nr\  r  r  rC  r	  r	  r  r  r  r    r  r  c              	   C   s   t |td t|t|||   |td  | ||  |  ||t || || |td   t|t|||   |td  | ||  |td   || t|t|||   |td  | ||  |  || |td   | S r	  r	  r	  r  r  r  r    r  r  c	           	   	   C   rm  rO  r   r   r  ro  r  r  r  r    rp  r  c	           	   	   C   6   t t|||  | | |t|||    | ||S rO  r	  ro  r  r  r  r    rp  r  c              
   C   s   t | | | td| |  t|||  |td  | |t|||     ||t|||  |td  td|  | |td   | t| |||  |  td| | | |t|||      | S Nr  rC  r  r	  r~  r  r  r  r       r  c              
   C   s   t | | | td| |  t|||  |td  | |t|||     ||t|||  |td  td|  | |td   | t| |||  |  td| | | |t|||      | S r!	  r	  r~  r  r  r  r    r"	  r  c              
   C   s   t || |  tttd| td| |  |||   ||t |||  tttd| td| |  |||   || ttd|| |t|||     |||    | S rk  r  r   r  r  r  r  r  r  r  r  r  r  r  rF  r  r  r  r       r  c              
   C   s   t || |  tttd| td| |  |||   || t |||  tttd| td| |  |||   || ttd|| |t|||     |||    | S rk  r#	  r$	  r  r  r  r       r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     ||t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S rk  r	  r~  r  r  r  r    r  r  c              
   C   s   t td| | | | |td   t|||  |td  | |t|||     ||t|||  |td  || |t|||     |td   | t||||  |td   ||td  |td  |td   | S rk  r	  r~  r  r  r  r    r  r  c                 C   s   t tdtd|   tttd| td| |  |||   ||t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S rV  r  r  r   r  r  r  r]  r$	  r  r  r  r    r%	  r  c                 C   s   t tdtd|   tttd| td| |  |||   || t tdtd|  tttd| td| |  |||   || tt|||  td|  |  | S rV  r'	  r$	  r  r  r  r    r&	  r  c              	   C   s   t tdtd|   t|||  | ttd |  |||   |  ||t|||  |td  td|  | |td   | S rV  r	  r~  r  r  r  r       r  c              	   C   s   t tdtd|   t|||  | ttd |  |||   |  || t|||  |td  td|  | |td   | S rV  r	  r~  r  r  r  r    r  r  c	           	      C   s   t t|||  | ttd| td| |   td|  ttd| td| |  td|    tdtd|    |  ||S rk  r   r   r  r  r  ro  r  r  r  r       r  c	           	      C   s   t t|||  | ttd| td| |  td|  ttd| td| |  td|    tdtd|    |  ||S rk  r)	  ro  r  r  r  r    r  r  c	           	   	   C   sb   t t|||  | tdtd|   ttd |  |||   | td|    |  ||S rV  r   r   r  rX  ro  r  r  r  r       br  c	           	   	   C   sb   t t|||  | tdtd|   ttd |  |||   | td|    |  ||S rV  r+	  ro  r  r  r  r    r,	  r  c	           
      C   sn   t | |t|||    | |}	t|| tt|||  |td  |	||| t|||  | |	| S rB  r  r  r  r   r  
r  r  r  r  r  r  r  r  rF  r  r  r  r  r       "Lr  c	           
      C   sn   t | |t|||    | |}	t|| tt|||  |td  |	||| t|||  | |	| S rB  r-	  r.	  r  r  r  r    r/	  r  c              
   C   s   t td| t|||  | | td |td  | | td ttd | td| |     || t|||  |td  || |  |td   | S rk  r	  r~  r  r  r  r       r  c              
   C   s   t td| t|||  | | td |td  | | td ttd| td| |     ||t|||  |td  || |  |td   | S rk  r	  r~  r  r  r  r       r  c              
   C   s  t td|| td |td    ttd |  | | td|  | | |  ||  | |t|||     || t|||  td td| | td |td    | t||||   || |t|||     | td |td    | S rV  r	  r$	  r  r  r  r        r  c              
   C   s  t td|| td |td    ttd |  | | td|  | | |  ||  | |t|||     || t|||  td td| | td |td    | t||||   || |t|||     | td |td    | S rV  r	  r$	  r  r  r  r    r2	  r  c	           	   
   C   s   t t|||  | td | | td |td  | | td ttd | td| |     td| |   |  ||S rk  r+	  ro  r  r  r  r       r  c	           	   
   C   s   t t|||  | td| | td |td  | | td ttd| td| |     td| |   |  ||S rk  r+	  ro  r  r  r  r  	     r  c                 C   r  rO  r   r  r2  r  r  r  r  r  	  rd  r  c                 C   s.   t | |tt||  | t|||  |S rO  r5	  r  r  r  r  r  
	  rd  r  c	           	      C   r  rO  r   r  ro  r  r  r  r  	  r  r  c	           	      C   s2   t | |t|||    | |||  |  |S rO  r6	  ro  r  r  r  r  	  r  r  c                 C   sV   t td| tt|tdtd|   | |t|||    |  |||| |S rf  r  r  r+   r   r  r  r  r  r  r  	  rz  r  c                 C   V   t td| tt|tdtd|   | |t|||    |  |||| |S rf  r7	  r  r  r  r  r  	  rz  r  c                 C   s&   t | |t||||     | |S rO  r6	  r  r  r  r  r  	  r  r  c                 C   &   t | |t||||     | |S rO  r6	  r  r  r  r  r  "	  r  r  c                 C   r  rJ  r  r  r3   r+   r   r  r  r  r  r  r  &	  r  r  c                 C   J   t tdt||td tt| |t||||     | ||||S rJ  r:	  r  r  r  r  r  *	  r  r  c                 C   r  rO  r5	  r  r  r  r  r  .	  r  r  c                 C       t | |tt||  | |S rO  r5	  r  r  r  r  r  2	  r  r  c                 C   sZ   t td| tt|td|td |   | |t|||    |  |||| |S rf  r7	  r  r  r  r  r  6	     Zr  c                 C   Z   t td| tt|td|td |   | |t|||    |  |||| |S rf  r7	  r  r  r  r  r  :	  r=	  r  c              	   C   s   t || td ||  t|||  t| |||    ||t|| | t||| td  t| |||    ||  | S rJ  r	  r  r  r  r  rF  r  r  r  r  >	  rL  r  c              	   C   s   t || td ||  t|||  t| |||    ||t|| | t||| td  || t| |||     | S rJ  r	  r?	  r  r  r  r  B	  rL  r  c              	   C   s.   t || | |t||||     |  |S rO  r6	  r  r  r  r  r  F	  rd  r  c              	   C   .   t || | |t||||     |  |S rO  r6	  r  r  r  r  r  J	  rd  r  c	           	      C   r  rO  r  r%   r&   r   r  r  r  r  r  r  N	  r  r  c	           	      C   \   t |t| |t|   || t|  t|| | |t||||     |  ||S rO  rA	  r  r  r  r  r  R	  r  r  c                 C   r  rO  r5	  r  r  r  r  r  V	  r  r  c                 C   ,   t || | | |tt||  |  |S rO  r5	  r  r  r  r  r  Z	  r  r  c              
   C      t || td || |  t|||  tdt| |||    |  ||t||| td  tdt| |||    |  || |  | S rJ  r  r  r  r  r  r  r  rF  r  r  r  r  ^	  r	  r  c              
   C   rD	  rJ  r  rE	  r  r  r  r  b	  r	  r  c                 C   s*   t t| ||  ||td   | |S rx  r   r  r  r 	  r  r  r  r  f	  r  r  c                 C   s2   t tdt| ||  ||td    | |S rV  r   r  r  r 	  r  r  r  r  j	  r  r  c              
   C   s   t | | td| |  td|  tt| ||  ||td   ||t|tt| ||  ||td    td|  | S rx  )r  r  r   r  r  r]  r  r	  r  r  r  r  n	  r(	  r  c              
   C   s   t | | td| |  td|  ttdt| ||  ||td    ||t|tt| ||  ||td    td|  | S rk  )r  r  r   r  r  r]  r  r	  r  r  r  r  r	  s   r  c                 C   s:   t |||  | t| ||  ||td   |  |S rx  rF	  r	  r  r  r  r  v	  r  r  c              	   C   sB   t |||  | tdt| ||  ||td    |  |S rV  rG	  r	  r  r  r  r  z	     Br  c                 C   s   t t| | | t|||  |td  tt t| ||   td  || t t| | | t|||  |td  ttt| ||   td  || ttd|||  |  tt| ||   | | S NrC  r  r  )r  r  r   r  r]  rX  r  r>   r  r  r  r  r  rF  r  r  r  r  ~	     r  c              
   C   s   t || | t|||  |td  ttdt| ||    || t || | t|||  |td  tt| ||  td  || ttd |||  |  tt| ||   | | S rI	  )r  r   r  r]  rX  r  r  rJ	  r  r  r  r  	     r  c                 C   sj   t || | t|||  |td  t| ||   || t|||  | t| ||   | | S rB  r  r   r  r  r  rJ	  r  r  r  r  	  rG  r  c                 C   sh   t || | t|||  |td  t| ||   ||t|||  | |t| ||    | S rB  rM	  rJ	  r  r  r  r  	  r  r  c              	   C   s   t |td |td  t|||  tdt| ||   |td   ||t|tdt| ||   |td   |td |td  |td   | t|||  tdt| ||   |td   t| ||   ||td   | S Nr\  rC  r  r  r  r  r   r  r  r  r  r  r  r  r  rF  r  r  r  r  	  s   r  c              	   C   s   t |td |td  t|||  tdt| ||   |td   || t|tdt| ||   |td   |td |td  |td   | t|||  tdt| ||   |td   ||td  t| ||    | S rN	  r  r  r   r  r  r  rP	  r  r  r  r  	  s   r  c              
   C   s  t |td |td  t|||  | tdt| ||   |td   ||t |td | |td  |td |td  |td   t|||  |td  tdt| ||   |td   || t|||  | tdt| ||   |td   t| ||   ||td   | t|| |||  |td   tdt| ||   |td   |td |td  |td   | S rN	  rO	  r  r  r  r  r  r  rF  r  r  r  r  	  s    r  c              
   C   s  t |td |td  t|||  | tdt| ||   |td   || t |td | |td  |td |td  |td   t|||  |td  tdt| ||   |td   || t|||  | tdt| ||   |td   ||td  t| ||    | t|| |||  |td   tdt| ||   |td   |td |td  |td   | S rN	  rQ	  rR	  r  r  r  r  	  s    r  c              	   C   s   t |td | t|||  tdt| ||   |td   ||t|tdt| ||   |  |td |td   | t|||  tdt| ||   |td   t| ||   ||  | S rV  rK  rP	  r  r  r  r  	  s   r  c              	   C   s   t |td | t|||  tdt| ||   |td   || t|tdt| ||   |  |td |td   | t|||  tdt| ||   |td   t| ||   ||  | S rV  rM  rP	  r  r  r  r  	  rw  r  c              
   C   sl  t |td | t|||  | tdt| ||   |td   ||t |td | |td  |td |td   t|||  |td  tdt| ||   |  || t|||  | tdt| ||   |td   t| ||   ||  | t|| |||  |td   tdt| ||   |  |td |td   | S Nr  r  rC  r\  rK  rR	  r  r  r  r  	  r`  r  c              
   C   sn  t |td | t|||  | tdt| ||   |td   || t |td | |td  |td |td   t|||  |td  tdt| ||   |  || t|||  | tdt| ||   |td   t| ||   ||  | t|| |||  |td   tdt| ||   |  |td |td   | S rS	  rM  rR	  r  r  r  r  	  r_  r  c                 C   `   t tdt| ||   | t| ||  |  t|||  | t| ||  |   ||S rJ  )r  r  r  r   rR	  r  r  r  r  	     `r  c                 C   rT	  rJ  )r  r  r  r   rR	  r  r  r  r  	  rU	  r  c	           	   	   C   r 	  rO  rq  ro  r  r  r  r  	  rp  r  c	           	   	   C   r 	  rO  rn  ro  r  r  r  r  	  rp  r  c	           	      C   L   t t|||  | | t|||   | | t|||  |   ||S rO  rq  ro  r  r  r  r  	  r  r  c	           	      C   rV	  rO  rn  ro  r  r  r  r  	  r  r  c                 C   .   t tdtt|| | t|||   |S rJ  )r   r  r  r2  r	  r  r  r  r  	  rd  r  c                 C   rW	  rJ  )r   r  r  r2  r	  r  r  r  r  	  rd  r  c                 C   2   t |||  | tdt| ||   |  |S rJ  )r   r  r  rR	  r  r  r  r   	  r  r   c                 C   rX	  rJ  )r   r  r  rR	  r  r  r  r  	  r  r  c                 C   r8	  rf  r  r  r  r  r  r  	  rz  r  c                 C   r8	  rf  r  r  r  r  r  r  	  rz  r  c                 C   r9	  rO  r  r  r  r  r  r  	  r  r  c                 C   r9	  rO  r  r  r  r  r  r  	  r  r  c                 C   r;	  rJ  r  r  r  r  r  r  	  r  r  c                 C   r;	  rJ  r  r  r  r  r  r  	  r  r  c                 C   r<	  rO  r  r  r  r  r  r  	  r  r  c                 C   r<	  rO  r  r  r  r  r  r	  	  r  r	  c                 C   r>	  rf  r  r  r  r  r  r
  	  r=	  r
  c                 C   r>	  rf  r  r  r  r  r  r  	  r=	  r  c              	   C   r@	  rO  r  r  r  r  r  r  	  rd  r  c              	   C   r@	  rO  r  r  r  r  r  r  
  rd  r  c	           	      C   rB	  rO  r  r  r  r  r  r  
  r  r  c	           	      C   rB	  rO  r  r  r  r  r  r  

  r  r  c                 C   rC	  rO  r  r  r  r  r  r  
  r  r  c                 C   rC	  rO  r  r  r  r  r  r  
  r  r  c              
   C      t || td || |td   t|||  tdt| |||    |td   ||t||| td  tdt| |||    |td   || |td   | S rf  r  r  r  r  r  r  
     r  c              
   C   rY	  rf  r  r  r  r  r  r  
  rZ	  r  c                 C      t || ||td   t|||  |td  t| ||  |td   || t|||  | t| ||  |td   ||td   | S rf  r  rR	  r  r  r  r  
  r  r  c                 C   r[	  rf  r  rR	  r  r  r  r  "
  r  r  c                 C   sB   t t|||  | t| ||  | t| ||  |  ||S rO  r   rd  r  r  r  r  r  r  r  &
  rH	  r  c                 C   s   t |||  | t| ||  |  t| ||  |td   |t |||  | t| ||  |td   t| ||  |  | S )Nr\  )r   r  r  r  r  r  r  r  r  *
  r  r  c                 C   s   t |||  | tdt| ||   |  t| ||  |td   |t |||  | tdt| ||   |td   t| ||  |  | S r  )r   r  r  r  r  r  r  r  r  .
     r  c              	   C      t || ||  t|||  |td  tdt| ||   |  ||t|||  | tdt| ||   |  ||  | S r  rD  r  r  r  r  r  2
  r3	  r  c              	   C   r^	  r  rH  r  r  r  r  r  6
  r3	  r  c                 C   r[	  rf  r	  rR	  r  r  r  r  :
  r  r  c              	   C   s   t || ||td   t|||  |td  tdt| ||   |td   ||t|||  | tdt| ||   |td   ||td   | S rf  r	  rR	  r  r  r  r  >
  r0	  r  c                 C   s   t |||  | t| ||  |td   t| ||  td  | t |||  | t| ||  |td   t| ||   | S )Nr\     )r   r  r  r  r  r  r  r  r  r  rF  r  r  r  r  B
  r*	  r  c                 C   s   t |||  | tdt| ||   |  t| ||  |td   |t |||  | tdt| ||   |td   t| ||  |td   | S Nr  r\  r  )r   r  r  r  r  r  r  r  r  F
  r1	  r  c                 C   s   t |||  | tdt| ||   |td   t| ||  td  |t |||  | tdt| ||   |td   t| ||   | S )Nr  r\  r_	  )r   r  r  r  r`	  r  r  r  r  J
  r]	  r  c                 C   s   t |||  | tdt| ||   |  tdt| ||   |td   |t |||  | tdt| ||   |td   tdt| ||   |td   | S ra	  )r   r  r  r  r  r  r  r  r   N
  s   r   c           	      C   s~   t tdt| ||   | t| ||  |  |}t|| t||||  |td   || t|||  | || S rf  )r  r  r  r  r  r   	r  r  r  r  r  r  r  rF  r  r  r  r  r!  R
  s   6Hr!  c           	      C      t tdt| ||   | tdt| ||   |  |}t|| t||||  |td   || t|||  | || S rf  )r  r  r  r  r  r   rb	  r  r  r  r"  W
     >Hr"  c              	   C   sR   t td| t|||  | tdttd|  td| |   |  ||S rk  r{  rR	  r  r  r  r#  \
     Rr#  c           	      C   rc	  rf  )r  r  r  r  r  r   rb	  r  r  r  r$  `
  rd	  r$  c	           	      C   s8   t t||| | t|||  |t|||  |S rO  r   r2  )	FGr  r  r  r  r  wrF  r  r  r  r(  e
  r  r(  c	           	   	   C      t || || |td   t| |t|||    |td  |||  |td   || t| |t|||    |td  |||  |  || |td   | S rf  r  ro  r  r  r  r)  i
     r)  c	           	   	   C   rj	  rf  r  ro  r  r  r  r*  m
  rk	  r*  c	           	   	   C   rj	  rf  r	  ro  r  r  r  r+  q
  rk	  r+  c	           	   	   C      t || || |td   t| |t|||    |td  |||  |td   ||t| |t|||    |td  |||  |  || |td   | S rf  r	  ro  r  r  r  r,  u
     r,  c	           	   	   C   rl	  rf  r  ro  r  r  r  r-  y
  rm	  r-  c	           	   	   C   rl	  rf  r  ro  r  r  r  r.  }
  rm	  r.  c
           
      C   B   t t|||	  | t| ||	  | t|||	  |  |	|	S rO  rb  
r  r  r  r  r  r  r  r  r  rF  r  r  r  r/  
  rH	  r/  c
           
      C   rn	  rO  re  ro	  r  r  r  r0  
  rH	  r0  c
           
      C   sB   t t|||	  | t| ||	  | t|||	  |  |	|	S rO  r\	  ro	  r  r  r  r1  
  rH	  r1  c                 C   sD   t t|||  | ||||  |
  | |||  |	|| ||S rO  )r   rc  )rg	  rh	  r  r  r  r  r  r  r  r  r  rF  r  r  r  r2  
  s   Dr2  c                 C      t | ||||    | t|||   |td  |td  t| td  |td   |t | ||||    | | t|  t|||   |td  |td  t| td  |td   | S rx  )r  r  r  r]  r  rg	  r  r  r  r  r  rF  r  r  r  r3  
     r3  c                 C   rp	  rx  )r  r  r  r]  r  rq	  r  r  r  r4  
  rr	  r4  c                 C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    t|||  |td   || t| ||||    | | t|  t|||  |  |td  |td  t| td  |td |td    | t| ||||    | | t|||  |td   t|||   |td  |td  t| td  |td |td    | S r[  r  r  r]  r   r  r  r  rg	  r  r  r  r  r  r  rF  r  r  r  r5  
      r5  c                 C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    t|||  |td   ||t| ||||    | | t|  t|||  |  |td  |td  t| td  |td |td    | t| ||||    | | t|||   t|||  |td   |td  |td  t| td  |td |td    | S r[  r  r  r]  r   r  r  r  rt	  r  r  r  r6  
  r  r6  c                 C   s   t | ||||    t|||  |td   t|||   ||td   |t | ||||    | | t|  t|||  |td   |td |td  |td   | S rV  )r  r  r  r  r]  rt	  r  r  r  r7  
  s   r7  c                 C   s   t | ||||    t|||   t|||  |td   ||td   | t | ||||    | | t|  t|||  |td   |td |td  |td   | S rV  )r  r  r  r  r]  rt	  r  r  r  r8  
  s   r8  c                 C   sj  t |td  |td  t| td  |td |td td   |td |td  |td   t| ||||    t|||  |td   || t| ||||    t|||  |td   t|||   ||td   | t| ||||    | | t|  t|||  |td   |td |td  |td   | S rk  rs	  rt	  r  r  r  r9  
  s   l r9  c                 C   sh  t |td  |td  t| td  |td |td td   |td |td  |td   t| ||||    t|||  |td   ||t| ||||    t|||   t|||  |td   ||td   | t| ||||    | | t|  t|||  |td   |td |td  |td   | S rk  rv	  rt	  r  r  r  r:  
  s   j r:  c              	   C      t ttd| td| |  td |  t||||    t|||  |  t| ||||    ttd| td| |  td |  t| |||    ||S r  )r  rX  r  r  r   rt	  r  r  r  r;  
  r	  r;  c              	   C   rw	  rk  )r  rX  r  r  r   rt	  r  r  r  r<  
  r	  r<  c                 C   sz   t t| ||||    ttd| td| |  td |  ttd| td| |  td |   ||S r!	  r   r   rX  r  rt	  r  r  r  r=  
     zr=  c                 C   sz   t t| ||||    ttd| td| |  td |   ttd| td| |  td |  ||S r!	  rx	  rt	  r  r  r  r>  
  ry	  r>  c              	   C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    tdt|||   |td   ||t| ||||    | | tdt|||   |  t|  |td  |td  t| td  |td |td    | t| ||||    | | tdt|||   |td   t|||   |td  |td  t| td  |td |td    | S rk  rv	  rt	  r  r  r  r?  
  s    r?  c              	   C   s  t |td | |td  |td  |td  t| td  |td |td    t| ||||    tdt|||   |td   || t| ||||    | | tdt|||   |  t|  |td  |td  t| td  |td |td    | t| ||||    | | tdt|||   |td   t|||   |td  |td  t| td  |td |td    | S rk  rs	  rt	  r  r  r  r@  
  s    r@  c                 C   s   t | ||||    tdt|||   |td   t|||   ||td   |t | ||||    | | tdt|||   |td   t|  |td |td  |td   | S Nr  rC  r\  r  )r  r  r  r  r]  rt	  r  r  r  rA  
     rA  c                 C   s   t | ||||    tdt|||   |td   t|||   ||td   | t | ||||    | | tdt|||   |td   t|  |td |td  |td   | S rz	  )r  r  r  r  r]  rt	  r  r  r  rB  
  r"	  rB  c              	   C   s  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dt|||   |td   t|||   ||td   | t| ||||    | | tdt|||   |td   t|  |td |td  |td   | S Nr  r\  rC  r  rv	  rt	  r  r  r  rC  
  s    rC  c              	   C   s  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dt|||   |td   t|||   ||td   | t| ||||    | | tdt|||   |td   t|  |td |td  |td   | S r|	  rs	  rt	  r  r  r  rD  
  s    rD  c              
   C   s   t td| | ||||     t||| t|  td|  |td  || t|  td|  |td  td ttd| td| |    t||||    || t|  ||   |S rk  r  r  r5   r]  rX  rt	  r  r  r  rE  
  rL	  rE  c              
   C   s   t td| | ||||     t||| t|  td|  |td  || t|  td|  |td  td ttd| td| |   t||||    || t|  ||   |S )Nr\  r  r  r}	  rt	  r  r  r  rF  
  r  rF  c              
   C   s   t ttd| td| |  td | tdt|||   |  t| |||    tt| ||||    ttd| td| |  td |   t||||    |||S rk  )r  rX  r  r  r   r-  rt	  r  r  r  rG  
  s   rG  c              
   C   s   t tdttd | td| |   | tdt|||   |  t||||    tt| ||||    tdttd | td| |   |   t| |||    |||S rV  )r  r  rX  r  r   r-  rt	  r  r  r  rH  
  s   rH  c
           
   	   C   st   t td| ||  t| ||||	    tt | td|  |td  ||	 td  td|   |	|	S rr  rt  
rg	  r  r  r  r  r  r  r  r  rF  r  r  r  rJ  
  s   trJ  c
           
   	   C   ^   t td| ||  t| ||||	    t|td ||	 td  td|   |	|	S rx  ry  r~	  r  r  r  rK  
  r  rK  c
           
   	   C   r	  rx  r{  r~	  r  r  r  rL  
  r  rL  c              	   C   s`   t ||	 t| ||||
    tt | td|  |td  ||
 td  |  |
|
S )Nrs  r  )r  r   r  ru  r  rg	  r  r  r  r  r  r  r  r  r  rF  r  r  r  rM  
  rU	  rM  c              	   C   sJ   t ||	 t| ||||
    t|td ||
 td  |  |
|
S rx  )r  r   r  r  r	  r  r  r  rN  
  r  rN  c              
   C   sR   t ||	 t| ||||
    tdt|td ||
 td   |  |
|
S rV  )r  r   r  r  r	  r  r  r  rO  
  re	  rO  c              
   C      t td|	 t| ||||
    t|||
   ||t|||
     |
|
t| ||||
    ||	t|||
     ||t|||
     |
 S rx  r  r  r   r  r  rg	  r  r  r  r  r  r  r  hr  rF  r  r  r  rQ    r]	  rQ  c              
   C   r	  rx  r  r  r   r  r  r	  r  r  r  rR    r]	  rR  c                 C   s*   t | |t||  |t|||  |S rO  rf	  )rg	  rh	  r  r  r  r  rF  r  r  r  rS  	  r  rS  c	           
      C   d   t | ||||    t|||  |  |}	t|t|	||td   || t|	||  | S rB  )r  r  r  r   r  r  
rg	  r  r  r  r  r  r  r  rF  r  r  r  r  rT       .6rT  c	           
      C   r	  rB  )r  r  r  r   r  r  r	  r  r  r  rU    r	  rU  c                 C   sF   t t| ||||
    t|||
  | t|||
  |	  |
|
S rO  r\	  r	  r  r  r  rV    r  rV  c                 C   sN   t t| ||||    ||
  t|||  | t|||  |	  ||S rO  r\	  )rg	  r  r  r  r  r  r  r  r  r  r  rF  r  r  r  rW    s   NrW  c                 C   sF   t t| ||||
    ||||
  | ||||
  |	  |
|
S rO  )r   rh  )rg	  rh	  Hr  r  r  r  r  r  r  rF  r  r  r  rY    r  rY  c                 C      t t| | t|| ||S rO  )r   rh  r  rg	  r  r  r  rF  r  r  r  rZ  #     rZ  c                 C   r	  rO  )r   rh  r  r	  r  r  r  r[  '  r	  r[  c                 C   s*   t t| | t|| t||  ||S rO  )r   rh  r  r  )rg	  r  r  r  r  rF  r  r  r  r\  +  r  r\  c                 C   s<   t |||  |  td |||  |   td  | |S rx  r   r  r  r  r  r  rF  r  r  r  r^  /  r  r^  c                 C   s<   t |||  |  td |||  |   td  | |S rx  r	  r	  r  r  r  r_  3  r  r_  c                 C   s   t ||td  t| |t|||    |td   |td  | t |t| |t|||    |td   || |td  t| |t|||      | S rk  r  r  r  r]  r  r  r  r  r  r  rF  r  r  r  r`  7  rh  r`  c              
   C   s   t ||td  t| |t|||    |td   |td  |t |t| |t|||    |td   t| |t|||     || |td   | S rk  r  r  r  r]  r  r	  r  r  r  ra  ;  r}  ra  c              
   C      t |tt| |t|||     t|||  td|  ttd|   td  tt|||  td|  ttd|   td | ||S )Nrs  r  rC  )r  r  r  r]  r  rX  r   r 	  r  r  r  rb  ?  r  rb  c              
   C   r	  )Nrs  r  r  )r  r  r  r]  r  rX  r   r 	  r  r  r  rc  C  r  rc  c                 C   s   t t|||  td||   t| | | |  td| | |  |||  td ||   t|  | | |  td| | |   | ||S rV  r+	  r	  r  r  r  rd  G  r]	  rd  c                 C   s   t t|||  td||   t| | | |  td |||  td ||   t|  | | |  td  | ||S rV  r+	  r	  r  r  r  re  K  r4	  re  c              
   C      t |t| |t|||     |td |td  td  | t || | t| |t|||     |td |td  td  | S r  )r  r  r]  r  r  r 	  r  r  r  rf  O     rf  c              
   C   r	  r  )r  r  r]  r  r  r 	  r  r  r  rg  S  r	  rg  c              
   C   sd  t |td |td  | |td  |td |td  |td  td  tt| |t|||    |td  || t|t| |t|||    |  |td |td  |td  td  | t|| | | t| |t|||    |td   t| |t|||     |td |td  |td  td  | S r[  r  r  r   r  r]  r  r  r	  r  r  r  rh  W  s   f rh  c              
   C   sb  t |td |td  | |td  |td |td  |td  td  tt| |t|||    |td  ||t|t| |t|||    |  |td |td  |td  td  | t|| | | t| |t|||     t| |t|||    |td   |td |td  |td  td  | S r[  r  r  r   r  r]  r  r  r	  r  r  r  ri  [  s   d ri  c                 C   s\  t |td |td  |td td  td |td |td  |td  |td   tt| |t|||    |td  || t|t| |t|||    |td   |td |td  |td  |td   | t|t| |t|||    |td   || |td  t| |t|||      | S r!	  r  r  r   r  r]  r  r  r	  r  r  r  rj  _  s   ^ rj  c              
   C   sZ  t |td |td  |td td  td |td |td  |td  |td   tt| |t|||    |td  ||t|t| |t|||    |td   |td |td  |td  |td   | t|t| |t|||    |td   t| |t|||     || |td   | S r!	  r  r  r   r  r]  r  r  r	  r  r  r  rk  c  s   \ rk  c              
   C   s  t |tdtd|||  td |   ttd |    |   |||  | t|  |||  |  t|    |  t| || | td  td| |  td|| | td td| |   |||  td |  ttd |    || | td  |S rk  r  r  rX  r5   r	  r  r  r  rl  g  s    rl  c              
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   C   s2  t ||td  tdtd|||  td |   ttd |    |   |||  | t|  |||  |  t|    |  t| || | | td  td| |  td|| | | td td| |   |||  td |  ttd |    || | | td  |S rV  r	  r	  r  r  r  rx    s   4 rx  c              
   C   s4  t ||td  tdtd|||  td |   ttd |    |   |||  | t|  |||  |  t|    |  t| || | | td  td| |  td|| | | td td| |   |||  td |   ttd |    || | | td  |S rV  r	  r	  r  r  r  ry    s   6 ry  c                 C   J   t td| t|||  |  |||  td|   td  | ||S rk  r  r  r   r	  r  r  r  rz    r  rz  c                 C   r	  r  r	  r	  r  r  r  r{    r  r{  c                 C   sn   t tdt|  | |  t|||  td|  |||  td|  ttd |  | |   ||S rk  r  r  rX  r   r 	  r  r  r  r|    rZ  r|  c                 C   sz   t td | | t|  | |  t|||  td|  |||  td|   ttd |  | |   ||S rk  r	  r 	  r  r  r  r}    ry	  r}  c                 C   s   t ||td  tdt| |t|||     |td   |td  |t |tdt| |t|||     |td   t| |t|||     || |td   | S Nr\  r  rC  r	  r	  r  r  r  r~    r&	  r~  c                 C   s   t ||td  tdt| |t|||     |td   |td  | t |tdt| |t|||     |td   || |td  t| |t|||      | S r	  r	  r	  r  r  r  r    s   r  c                 C   sr  t |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|||     |td   |td |td  |td  |td   | t|tdt| |t|||     |td   t| |t|||     || |td   | S r|	  r	  r	  r  r  r  r    s   t r  c                 C   st  t |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|||     |td   |td |td  |td  |td   | t|tdt| |t|||     |td   || |td  t| |t|||      | S r|	  r	  r	  r  r  r  r    s   v r  c                 C   sz  t |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|||     |  |td |td  |td  td  | t|| | | tdt| |t|||     |td   t| |t|||     |td |td  |td  td  | S r  r	  r	  r  r  r  r    s   | r  c                 C   s|  t |td |td  | |td  |td |td  |td  td  ttdt| |t|||     |td  || t|tdt| |t|||     |  |td |td  |td  td  | t|| | | tdt| |t|||     |td   t| |t|||     |td |td  |td  td  | S r  r	  r	  r  r  r  r    s   ~ r  c              
   C   s&  t td| | |||  | t|  |||  td|  ttd|   td  |  |||  td|  ttd|   td |  t||| | td td| |  td|| | td td| |   |||  td|   ttd|    || | td  |S rk  r	  r	  r  r  r  r    s   ( r  c              
   C   s"  t ||||  | t|  |||  td|  ttd|   td  |  td |||  td|   ttd|   td |  t||| | td td| |  td|| | td td| |   |||  td|  ttd|    || | td  |S r!	  )r  rX  r  r5   r	  r  r  r  r    s   $ r  c                 C   R   t td| t|| |||  |  |||  td|   td  |  ||S rk  r	  r  r  r  r  r  rF  r  r  r  r    re	  r  c                 C   r	  r  r	  r	  r  r  r  r    re	  r  c              
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   C   s>  t td| ||td   |||  | t|  |||  td|  ttd|   td  |  |||  td|  ttd|   td |  t||| | | td td| |  td|| | | td td| |   |||  td|   ttd|    || | | td  |S rk  r	  r	  r  r  r  r       @ r  c              
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   C   n   t td| ttt|| | || |  | ||   |  | |td  ||td|||   | S rV  r  r  r  r  r  r  r  rF  r  r  r  r  '  rZ  r  c              
   C   r	  rV  r  r	  r  r  r  r  +  rZ  r  c                 C   X   t ||}tt|t|td t|td |t|td t|td  |  |S Nr  r  rs  r_	  )r   r   r  r  r  r  r  rF  lstr  r  r  r  /     
Nr  c                 C   r	  r	  )r   r   r  r  r  r	  r  r  r  r  4  r	  r  c                 C      t |t|| |   |S rO  r  r  r  r  r  ri	  rF  r  r  r  r  9  rR  r  c                 C   r	  rO  r  r	  r  r  r  r  =  rR  r  c                 C   $   t tt||  t||  ||S rO  rb  r  r  r  ri	  rF  r  r  r  r  A     $r  c                 C   r	  rO  re  r	  r  r  r  r  E  r	  r  c                 C   *   t t||  t|| t||  ||S rO  rb  r  r  r  r  ri	  rF  r  r  r  r  I  r  r  c                 C   r	  rO  re  r	  r  r  r  r  M  r  r  c                 C   s0   t td|   t|ttd| |   ||S rx  r{  )r  r  r  ri	  rF  r  r  r  r  Q  r	  r  c                 C   s$   t tt||  t||  ||S rO  r\	  r	  r  r  r  r  U  r	  r  c                 C   s*   t t||  t|| t||  ||S rO  r\	  r	  r  r  r  r  Y  r  r  c                 C   sV   t t|| tt|| td  t| || tt|t|| td   | S rB  )r  r  r   r  r  r  r  ri	  rF  r  r  r  r  ]  rz  r  c                 C   sd   t t|| ttdt| | td  t| ||ttdt| | td  t| | S rf  )r  r  r   r  r  r  r	  r  r  r  r  a     dr  c                 C   sd   t t|| ttdt| | td  t| ||ttdt| | td  t| | S rf  r  r  r   r  r  r  r	  r  r  r  r  e  r	  r  c                 C   sV   t t|| tt|| td  t| || tt|t|| td   | S rB  )r  r  r   r  r  r  r	  r  r  r  r  i  rz  r  c                 C   sl   t t|| ttdt| | td  ||t t|| ttdt| | td  t| || S rf  r  r  r   r  r  r  r	  r  r  r  r  m  rv  r  c                 C   sl   t t|| ttdt| | td  ||t t|| ttdt| | td  t| || S rf  r	  r	  r  r  r  r  q  rv  r  c                 C   sl   t t|| ttdt| | td  t| ||t t|| ttdt| | td  || S rf  r	  r	  r  r  r  r  u  rv  r  c                 C   sl   t t|| ttdt| | td  t| ||t t|| ttdt| | td  || S rf  r	  r	  r  r  r  r  y  rv  r  c	           	      C   sJ   t | |ttd| td| |   td  | |||  |  |S rx  r	  ro  r  r  r  r  }  r  r  c              
   C   sX   t td|  t|| td|  |ttd| td| |    | |  ||S rx  ry  rR	  r  r  r  r    r|  r  c              
   C   sX   t td|  t|| td|  |ttd| td| |    | |  ||S rx  ry  rR	  r  r  r  r    r|  r  c
           
   
   C   b   t || td  tt| | ||  ||	  | t| ||	|   |  |	|	|||	  |	S rB  r  
r  r  r  r  r  r  r  r  r  rF  r  r  r  r    r,	  r  c
           
   
   C   r	  rB  r  r	  r  r  r  r    r,	  r  c	           	   
   C   ^   t tdt|||  | td|  | | || ttd| td| |     ||S rx  ry  	r  r  r  r  r  r  r  r  rF  r  r  r  r    r  r  c              
   C   R   t tdt|||  | | | | | ttd| td| |     ||S rx  ry  r  r  r  r  r  r  r  rF  r  r  r  r    re	  r  c	           	   
   C   r	  rx  ry  r	  r  r  r  r    r  r  c              
   C   r	  rx  ry  r	  r  r  r  r    re	  r  c	           	   
   C   r	  rx  ry  r	  r  r  r  r    r  r  c              	   C   s   t |||  | t|||   | |t|||    t| td |td  td  |t |||  | t|||   | |t|||    t| td |td  td  | t|||  |td  || |td   | S rk  r   rX  r  r  r  r~  r  r  r  r       r  c              	   C   s   t |||  | t|||   | |t|||    t| td |td  td  |t |||  | t|||   | |t|||    t| td |td  td  | t|||  |td  || |td   | S rk  r	  r~  r  r  r  r    r	  r  c	           	   	   C   s   t td|  t|||  | t|||  |td   ||t td| t|||  | t|||   t|||  |td   || S r  r	  ro  r  r  r  r       r  c	           	   	   C   s   t td|  t|||  | t|||  |td   ||t td| t|||  | t|||  |td   t|||   || S r  r	  ro  r  r  r  r    r	  r  c	           	      C   s
  t td| t|||  | t|||   t|||  |td   ||t | |td  t|||  | t|||  |td   || t | td |td  |td  t|||  | t|||  |td   | |t|||     || S ra	  r	  ro  r  r  r  r    rl  r  c	           	      C   s
  t td| t|||  | t|||  |td   t|||   ||t | |td  t|||  | t|||  |td   || t | td |td  |td  t|||  | t|||  |td   | |t|||     || S ra	  r	  ro  r  r  r  r    rl  r  c	           	   
   C      t || ||  tt|||  ||t|||     || t||||   t|||   || ||t|||      | S rO  )r  r   r  r  r  	Ar  r  r  r  r  r  r  rF  r  r  r  r    r(	  r  c	           	   
   C   r	  rO  )r  r   r  r  r  r	  r  r  r  r    r(	  r  c                 C   "   t | t| |t|  | |S rO  )r   r  r  r  r  r  r  r  rF  r  r  r  r       "r  c                 C   r	  rO  )r   r  r  r	  r  r  r  r    r	  r  c                 C   6   t t|t| ||  | t|||  |  ||S rO  rb  r  r  r  r  r  r  r  rF  r  r  r  r    rp  r  c                 C   r	  rO  re  r	  r  r  r  r    rp  r  c                 C   sx   t tdt|  | ||  |  tt|||  ||t tdt|  | ||  |  tt| ||  || S rJ  r  r  r  r   r  r  r  r  r  rF  r  r  r  r    r  r  c              	   C   s   t tdt|  | ||  |  ttdt| ||   ||t tdt|  | ||  |  ttdt|||   || S rJ  r	  r	  r  r  r  r    r3	  r  c              	   C   sh   t |t|  | ||  |  | ttdt| ||  t|||    || t|| | | S rJ  )r  r  r   r  r  r	  r  r  r  r    r  r  c              	   C   s^   t t|  | ||  | ttdt| ||  t|||    ||t|| | | S rJ  )r  r  r   r  r  r  r	  r  r  r  r    r  r  c                 C   s"   t || t| | |  |  |S rO  )r   rX  )r  r  r  r  r  rF  r  r  r  r    r	  r  ((  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rX  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  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  ru  r  B_C_r%  r&  rX  r  r  rZ  d_ra  rI  g_rP  i_j_k_l_r  r  r1  q_r_t_r)  r*  s_r'  r  y_z_a1_a2_b1_b2_c1_c2_d1_d2_n1_n2_e1_e2_f1_f2_g1_g2_n3_Pq_Pm_Px_Qm_Qr_Qx_jn_mn_non2_RFx_RGx_r  iiPqqQRrCr  r  	_UseGamma	ShowStepsStepCounterr@  r   r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r+  r,  r-  r.  r/  r0  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  r[  r\  r]  r^  r_  r`  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
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