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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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||||M|Y	}t|t̓}tttĐtttd	td tdtd  t  t|||||M|Y|Z}t|t΃}tttĐttdtd  tttd	td tdtd  t  t|||M|[|\|]|^}t|tσ}tttĐttdtd tdtd  tttd	td tdtd  t  t|||||M|_|W|]	}t|tЃ}tttĐtttd	td tdtd  t  t|||M|_|W|]}t|tу}tttĐttt tdtd  t  t|||M|[|W|XtҐtӃ}t|tԃ}tttĐtttd	td tdtd  t  t|||M|[|W|X|`}t|tՃ}tttttd tdtd  ttd tdtd  ttdtd  tttd tdtd  tdd   t|||
|||K|a}t|tփ}tttttd tdtd  ttd tdtd  tttd tdtd  tdd   t|||
||K|a}t|t׃}tttttd tdtd  ttdtd  tttd tdtd  tdd   t|||
||K|a} t| t؃}ttttd ttd tdtd ttdtd  tdtd  tttd tdtd  tdd   t|||||L|b}t|tك}ttttd ttd tdtd tdtd  tttd tdtd  tdd   t||||L|b}t|tڃ}tttttd tdtd  ttd tdtd  ttd tdtd  ttd tdtd  tttd tdtd  tdd   t|||
|||K|L|b|a
}t|tۃ}tttttd tdtd  ttd tdtd  ttd tdtd  tttd tdtd  tdd   t|||
||K|L|b|a	}t|t܃}	tttĐtttd	td tdtd  t  t|||M|[|W|XtҐt݃}
t|
tރ}tttĐtt  tttd	td tdtd  t  t|||M|[|W|X|c}t|t߃}tttĐttdtd  ttt tdtd  t  t||||U|[|tҐt}t|t}tttttdtd  tttd tdtd   t|||e|f|d}t|t}tttttdtd  tttd tdtd   t|||e|f|g|h}t|t}tttttdtd  tttd tdtd   t|||e|f|g|i}t|t}tttttd tdtd  ttdtd  tttd tdtd   t|||e|f|l|j|k}t|t}ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|m}t|t}ttttttdtd   tttd tdtd   t|||f|l|n}t|t}tttttd tdtd  tttd tdtd   t|||e|l|o}t|t}ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|p}t|t}ttttttdtd   tttd tdtd   t|||f|l|q} t| t}!tttttd tdtd  tttd tdtd   t|||e|l|r}"t|"t}#ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|s}$t|$t}%ttttttdtd   tttd tdtd   t|||f|l|t}&t|&t}'tttttd tdtd  tttd tdtd   t|||e|l|u}(t|(t})ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|v}*t|*t}+ttttttdtd   tttd tdtd   t|||f|l|w},t|,t}-tttttd tdtd  tttd tdtd   t|||e|l|x}.t|.t}/ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|y}0t|0t}1ttttttdtd   tttd tdtd   t|||f|l|z}2t|2t}3tttttd tdtd  tttd tdtd   t|||e|l|{}4t|4t}5ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l||}6t|6t}7ttttttdtd   tttd tdtd   t|||f|l|}}8t|8t}9ttttd tdtd tdtd tttd tdtd   t|||e|l|~}:t|:t};ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|}<t|<t}=ttttttdtd   tttd tdtd   t|||f|l|}>t|>t}?tttttd tdtd  tttd tdtd   t|||e|l|}@t|@t}Attttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|}Bt|Bt}Cttttttdtd   tttd tdtd   t|||f|l|}Dt|Dt}Ettttd tdtd tdtd tttd tdtd   t|||e|l|}Ft|Ft}Gttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|}Ht|Ht }Ittttttdtd   tttd tdtd   t|||f|l|}Jt|Jt}Ktttttd tdtd  tttd tdtd   t|||e|l|}Lt|Lt}Mttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|}Nt|Nt}Otttttdtd tdtd  tttd tdtd   t|||f|l|}Pt|Pt}Qtttttd tdtd  tttd tdtd   t|||e|l|}Rt|Rt}Sttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|}Tt|Tt}Uttttttdtd   tttd tdtd   t|||f|l|}Vt|Vt}Wtttttd tdtd  tttd tdtd   t|||e|l|}Xt|Xt}Yttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|g||tҐt	
}Zt|Zt
}[ttttttdtd   tttd tdtd   t|||f|l||tҐt}\t|\t}]tttttd tdtd  tttd tdtd   t|||e|l||tҐt}^t|^t}_ttttd tdtd ttdtd  tdtd tttd tdtd   t|||e|f|l|g||tҐt
}`t|`t}attttttdtd   tttd tdtd   t|||f|l||tҐt}bt|bt}ctttttd tdtd  tttd tdtd   t|||e|l||tҐt}dt|dt}etttĐttdtd tdtd  ttt tdtd   t|||||M||tҐt	}ft|ft}gtttĐttt tdtd   t|||M||tҐt}ht|ht}itttttdtd  ttttd tdtd   t||||
||}jt|jt}ktttttdtd  ttttd tdtd   t||||
||}lt|lt}mtttttdtd  ttttd tdtd   t||||
||}nt|nt}otttttdtd  ttttd tdtd   t||||
||}pt|pt}qtttttd tdtd  ttttd tdtd   t||||
|}rt|rt}stttttd tdtd  ttttd tdtd   t||||
|}tt|tt}utttttd tdtd  ttttd tdtd   t||||
|}vt|vt }wtttttd tdtd  ttttd tdtd   t||||
|}xt|xt!}ytttĐttttt tdtd    t|||M|[|}zt|zt"}{tttĐttdtd tdtd  ttt tdtd  t  t||||||M||	}|t||t#}}tttĐttt tdtd  t  t||||M||}~t|~t$}tttĐttt tdtd  t  t||||M|[|}t|t%}tttĐttdtd tdtd  ttt tdtd   t|||||M|}t|t&}tttĐttt tdtd   t|||M|}t|t'}tttĐttdtd t  ttt tdtd  t  t|||||M|[|||tҐt(}t|t)}tttĐttdtd tdtd  ttt tdtd  t  t||||||M|[tҐt*	}t|t+}tttĐttt tdtd  t  t||||M|[tҐt,}t|t-}tttĐttdtd  ttt tdtd  t  t||||M||}t|t.}tttĐttdtd tdtd  ttt tdtd  t  t|||||M||}t|t/}tttĐttdtd t  ttt tdtd  t  t||||||M||	}t|t0}tttĐttdtd  ttt tdtd  t  t|||||M|}t|t1}tttĐttt tdtd  t  t||||M|}t|t2}tttĐtt t  ttt tdtd  t  t||||||M|}t|t3}tttĐttdtd  ttt tdtd  t  t||||||U||	}t|t4}tttĐtt t  ttt tdtd  t  t|||||||U||
}t|t5}tttttdtd tdtd  ttt tdtd  tdtd  t|||e|f||||V	}t|t6}tttĐttdtd tdtd  ttt tdtd  tdtd  t|||||||}t|t7}tttĐttt tdtd  tdtd  t|||||}t|t8}tttĐttdtd  tttd	td tdtd  t  t|||||||}t|t9}tttĐtttd	td tdtd  t  t||||||}t|t:}tttĐttdtd tdtd  t;ttd	td tdtd  tdtd  t<ttd	td tdtd  tdtd  t|||||||||M||}t|t=}tttĐt;ttd	td tdtd  tdtd  t<ttd	td tdtd  tdtd  t|||||||M||
}t|t>}tttĐttdtd tdtd  t;ttd	td tdtd  tdtd  t<ttd	td tdtd  tdtd  t|||||||||M|}t|t?}tttĐt;ttd	td tdtd  tdtd  t<ttd	td tdtd  tdtd  t|||||||M|	}t|t@}tttttd	td tdtd  tdtd tttd	td tdtd  tdtd  tttd	td tdtd  ttdtd tdtd   t||||
|||K|||||}t|tA}tttttd	td tdtd  tdtd tttd	td tdtd  tdtd  tttdtd tdtd   t||||
||K|||||}t|tB}ttttdtd tdtd tttd	td tdtd  tdtd  tttd	td tdtd  tdtd  tttd	td tdtd  ttdtd tdtd   t||||
|||K|L|||||||O}t|tC}ttttdtd tdtd tttd	td tdtd  tdtd  tttd	td tdtd  tdtd  tttdtd tdtd   t||||
||K|L|||||||O}t|tD}tttttdtd tdtd  ttt tdtd  tdtd  tt tdtd tdtd tdtd  t||||
|e|f||||||V}t|tE}tttFtdtd tttdtd  t tdtd tdtd t  t||||
||||	}t|tG}tttĐttdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||||||U|V
}t|tH}tttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd  tdtd  t||||
||||M|
}t|tI}tttĐtttd	td tdtd  ttdtd tdtd  tdtd  t||||||M|}t|tJ}tttttd	td tdtd  ttdtd tdtd  tdtd tttd	td tdtd  ttdtd tdtd   t||||
|||||||}t|tK}tttttdtd tdtd  tttd	td tdtd  ttdtd tdtd  tdtd  t||||
||||||}t|tL}Ðttttdtd tdtd tttd	td tdtd  ttdtd tdtd  tdtd  tttd	td tdtd  ttdtd tdtd   t||||
|||K|||||||O}Đt|ĐtM}Őttttdtd tdtd tttdtd tdtd   tttd	td tdtd  ttdtd tdtd  tdtd  t||||
||K|||||||O}Ɛt|ƐtN}ǐtttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd  t  t||||
|||||M||Ń}Ȑt|ȐtO}ɐtttĐtttd	td tdtd  ttdtd tdtd  t  t|||||||M||Ń
}ʐt|ʐtP}ːtttĐttdtd  ttt tdtd  ttdtd tdtd  t  t||||||||U||}̐t|̐tQ}͐tttĐtt tdtd  ttt tdtd  ttdtd tdtd  t  t||||
|||||U||}ΐt|ΐtR}ϐtttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd  t  t||||
|||||M|Y}Аt|АtS}ѐtttĐtttd	td tdtd  ttdtd tdtd  t  t|||||||M|Y|Z
}Ґt|ҐtT}Ӑttttt tdtd  ttdtd tdtd  tdtd ttt tdtd  ttdtd tdtd  ttdtd tdtd   t||||
|||K|||||||Ƀ}Ԑt|ԐtU}Րttttt tdtd  ttdtd tdtd  tdtd tttdtd tdtd  ttdtd tdtd   t||||
||K|||||||˃}֐t|֐tV}אttttt tdtd  ttdtd tdtd  tdtd ttt tdtd  ttdtd tdtd   t||||
||K|||||||̃}ؐt|ؐtW}ِtttttdtd tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||
|K|||||||̓}ڐt|ڐtX}ېttttdtd tttdtd tdtd  ttd
td tdtd  ttdtd tdtd   tttd	td tdtd  ttdtd tdtd  tdd   t||||||K|L|||||||||J}ܐt|ܐtY}ݐtttt tdtd tttdtd tdtd  ttd
td tdtd  ttdtd tdtd   tttd	td tdtd  ttdtd tdtd  tdd   t||||
|||K|L|||||||||J}ސt|ސtZ}ߐtttĐttt[ tdtd  tt tdtd  t  t|||||M||[|W|XtҐt\}t|t]}tttttd tdtd  ttd tdtd  ttdtd  tttd tdtd  ttd tdtd  tdd   t||||
|||K||҃
}t|t^}tttttd tdtd  ttd tdtd  tttd tdtd  ttd tdtd  tdd   t||||
||K||҃	}t|t_}tttttd tdtd  ttdtd  tttd tdtd  ttd tdtd  tdd   t||||
||K||҃	}t|t`}ttttd ttd tdtd ttd tdtd  ttdtd  tdtd  tttd tdtd  ttd tdtd  tdd   t||||||K|L|||ԃ}t|ta}ttttd ttd tdtd ttd tdtd  tdtd  tttd tdtd  ttd tdtd  tdd   t|||||K|L|||ԃ
}t|tb}tttttd tdtd  ttd tdtd  ttd tdtd  ttd tdtd  tttd tdtd  ttd tdtd  tdd   t||||
|||K|L|||Ճ}t|tc}tttttd tdtd  ttd tdtd  ttd tdtd  tttd tdtd  ttd tdtd  tdd   t||||
|||L|||փ}t|td}tttĐttt[ tdtd  tt tdtd  t  t|||||M||[|W|XtҐte}t|tf}tttĐtt  ttt[ tdtd  tt tdtd  t  t|||||M||[|W|X|ctҐtg}t|th}tttĐttdtd  ttt[ tdtd  tt tdtd  t  t||||||U||[|tҐti}t|tj}tttĐttdtd tdtd  ttt[ tdtd  ttd	td tdtd   t||||
|||U||[|׃}t|tk}tttĐttt[ tdtd  ttd	td tdtd   t|||||U||[|؃	}t|tl}tttĐtttd tdtd  ttdtd  t  t||||M||ِtҐtm}t|tn}tttĐtttd tdtd  ttdtd  t  t||||M|||ېtҐto	}t|tp}tttĐtttd tdtd  ttdtd  t  t||||M|||ܐtҐtq	}t|tr}tttĐttdtd tdtd  ttt[ tdtd  ttd	td tdtd  t  t||||
||||U||[tҐts} t| tt}tttĐttt[ tdtd  ttd	td tdtd  t  t||||||U||[tҐtu
}t|tv}tttĐttdtd tdtd  ttt[ tdtd  tt tdtd  t  t||||
||||M||[|݃}t|tw}tttĐttt[ tdtd  tt tdtd  t  t||||||M||[|݃
}t|tx}tttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd   t||||
|||M||[
}t|ty}	tttĐtttd	td tdtd  ttdtd tdtd   t|||||M||[}
t|
tz}tttĐttdtd  ttt tdtd  ttdtd tdtd  t  t||||||M|||
}t|t{}tttĐttdtd tdtd  ttt tdtd  ttdtd tdtd  t  t||||
|||M|||}t|t|}tttĐttdtd t  ttt tdtd  ttdtd tdtd  t  t||||
||||M|||}t|t}}tttĐttdtd  ttt tdtd  ttdtd tdtd  t  t|||||||M||
}t|t~}tttĐttt tdtd  ttdtd tdtd  t  t||||||M||	}t|t}tttĐtt t  ttt tdtd  ttdtd tdtd  t  t||||
|||M|||ރ}t|t}tttĐtt t  ttt tdtd  ttdtd tdtd  t  t||||
|||M|||߃}t|t}tttĐtt t  ttt tdtd  ttdtd tdtd  t  t||||
||||M||}t|t}tttĐttdtd  ttt tdtd  ttdtd tdtd  t  t||||||||U|||}t|t}tttĐtt t  ttt tdtd  ttdtd tdtd  t  t||||
||||U|||}t|t}tttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd   t||||
||||M|ƃ
} t| t}!tttĐtttd	td tdtd  ttdtd tdtd   t||||||M|ƃ}"t|"t}#tttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd  t  t||||
||||M|
}$t|$t}%tttĐtttd	td tdtd  ttdtd tdtd  t  t||||||M|}&t|&t}'tttĐttdtd tdtd  tttd	td tdtd  ttdtd tdtd  tdtd  t||||
|||||
}(t|(t})tttĐtttd	td tdtd  ttdtd tdtd  tdtd  t|||||||}*t|*t}+tttĐttdtd  ttt tdtd  ttdtd tdtd  tdtd  t|||||||||
},t|,t}-tttĐttt tdtd  ttdtd tdtd  tdtd  t||||||||	}.t|.t}/ttttdtd tdtd ttd	td tdtd  t t||||||||	}0t|0t}1ttttdtd tdtd ttd	td tdtd  t t||||||||W|X
}2t|2t}3ttttdtd tdtd ttd	td tdtd  t t|||||||||
}4t|4t}5ttttdtd tdtd ttd	td tdtd  t t||||||]|}6t|6t}7ttttdtd tdtd ttd	td tdtd  t t||||||]|}8t|8t}9ttttdtd tdtd ttd	td tdtd  t t||||||X|}:t|:t};ttttdtd tdtd ttd	td tdtd  t t||||||X}<t|<t}=ttttdtd tdtd ttd	td tdtd  t t|||||||}>t|>t}?tttdtttd tdtd ttd	td tdtd   t||||}@t|@t}Attttdtd tdtd ttd	td tdtd  t t|||||||}Bt|Bt}Ctttdtttdtd tdtd ttd	td tdtd   t||||}Dt|Dt}Ettttdtd tdtd ttd	td tdtd  t t||||||||	}Ft|Ft}Gttttdtd tdtd ttd	td tdtd  t t|||||||}Ht|Ht}Ittttdtd tt tdtd ttdtd tdtd  t  t||||||||||V}Jt|Jt}Kttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t|||||||||||}Lt|Lt}Mttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||||W|X|}Nt|Nt}Ottttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||||||}Pt|Pt}Qtttt tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||||}Rt|Rt}Sttttdtd tt tdtd ttdtd tdtd  t  t|||||||||||}Tt|Tt}Utttt tdtd tt tdtd ttdtd tdtd  t  t||||||||||||}Vt|Vt}Wttttdtd t ttdtd tdtd ttd	td tdtd  t  t||||||||]|
}Xt|Xt}Yttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t|||||||||]|}Zt|Zt}[ttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||X|
}\t|\t}]ttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t|||||||||X
}^t|^t}_ttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t|||||||||||}`t|`t}attttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||||}bt|bt}cttttdtd tt tdtd ttdtd tdtd  t  t||||||||||O||}dt|dt}etttt tdtd tt tdtd ttdtd tdtd  t  t|||||||||||O||}ft|ft}gttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||| |}ht|ht}ittttdtd tttdtd tdtd ttd	td tdtd   t||||||}jt|jt}kttttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||| |}lt|lt}mtttt tdtd tt tdtd ttdtd tdtd  t  t|||||||||| }nt|nt}ottttdtd tdtd ttdtd tdtd ttd	td tdtd  t  t||||||||||}pt|pt}qttttdtd ttdtd tdtd ttd	td tdtd  tdtd  t|||||||}rt|rt}sttttdtd ttt tdtd  tdtd  tt tdtd ttd td tdtd  t  t||||
||||||||||||}tt|tt}utttt tdtd tttd	td tdtd  tdtd  tt tdtd ttd td tdtd  t  t||||
|||||||||||||}vt|vt}wttttdtd tdtd tttd	td tdtd   ttd!td tdtd ttdtd tdtd  t  t||||
|||||||||||}xt|xt}yttttdtd tdtd tttd	td tdtd   ttd!td tdtd ttdtd tdtd  t  t||||
||||||||	|X|
|}zt|zt}{ttttdtd tdtd tttd	td tdtd   ttd!td tdtd ttdtd tdtd  t  t||||
||||||||||||}|t||t}}ttttdtd tdtd tttd	td tdtd   ttd!td tdtd ttdtd tdtd  t  t||||
||||||||||}~t|~t}ttttdtd tttd	td tdtd  tdtd  tt tdtd ttd td tdtd  t  t||||
|||||||||||O||}t|t}tttt tdtd tttd	td tdtd  tdtd  tt tdtd ttd td tdtd  t  t||||
||||||||||||O||}t|t}ttttdtd tdtd tttd	td tdtd  tdtd  ttd!td tdtd ttdtd tdtd  t  t||||
||||||||||}t|t}tttĐtt tdtd ttdtd tdtd  t  t||||||U|||||}t|t}tttĐttdtd  tt tdtd ttdtd tdtd  t  t|||||||U||||}t|t}tttĐtt tdtd  tt tdtd ttdtd tdtd  t  t|||||||U||||||}t|t}tttĐtt tdtd  tt tdtd ttdtd tdtd  t  t||||||||U||||}t|t}tttĐttdtd  tt tdtd ttdtd tdtd  t  t||||U|||tҐt	}t|t}tttĐttdtd tdtd  tt tdtd ttdtd tdtd  t  t||||||M|||tҐt}t|t}tttĐttdtd  tt tdtd ttdtd tdtd  t  t|||||||U|||||}t|t}tttĐtt t  tt tdtd ttdtd tdtd  t  t|||||||U|||||||}t|t}tttĐtt t  tt tdtd ttdtd tdtd  t  t||||||||U|||||}t|tÃ}tttĐttdtd tdtd  tt tdtd ttdtd tdtd  t  t||||||||||}t|tă}tttĐtt tdtd ttdtd tdtd  t  t||||||||	}t|tŃ}ttttd tdtd ttdtd  tdtd t t|||
||}t|tƃ}ttttd tdtd ttdtd  tdtd t t|||
||}t|tǃ}ttttd tdtd ttdtd  tdtd t t|||
|ِ|tҐtȃ}t|tɃ}ttttd tdtd ttdtd  tdtd t t|||
|ِ|}t|tʃ}ttttd tdtd ttdtd  tdtd t t|||
|||}t|t˃}ttttd tdtd ttdtd  tdtd t t|||
|||tҐt̃}t|t̓}ttttd tdtd ttdtd  tdtd t t|||
|||}t|t΃}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
|||||	}t|tσ}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
|||||	}t|tЃ}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
||||ِ|tҐtу
}t|t҃}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
||||ِ|	}t|tӃ}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
||||||
}t|tԃ}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
||||||tҐtՃ}t|tփ}ttttdtd tdtd tdtd ttd tdtd ttdtd  tdtd t  t|||
||||||
}t|t׃}ttttd tdtd ttd tdtd  tdtd t t|||
||}t|t؃}ttttd tdtd ttd tdtd  tdtd t t|||
||}t|tك}ttttd tdtd ttd tdtd  tdtd t t|||
|ِ|tҐtڃ}t|tۃ}ttttd tdtd ttd tdtd  tdtd t t|||
|ِ|}t|t܃}ttttd tdtd ttd tdtd  tdtd t t|||
|||}t|t݃}ttttd tdtd ttd tdtd  tdtd t t|||
|||tҐtރ}t|t߃}Ðttttd tdtd ttd tdtd  tdtd t t|||
|||}Đt|Đt}Őttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
|||||	}Ɛt|Ɛt}ǐttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
|||||	}Ȑt|Ȑt}ɐttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
||||ِ|tҐt
}ʐt|ʐt}ːttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
||||ِ|	}̐t|̐t}͐ttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
||||||
}ΐt|ΐt}ϐttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
||||||tҐt}Аt|Аt}ѐttttdtd tdtd tdtd ttd tdtd ttd tdtd  tdtd t  t|||
||||||
}Ґt|Ґt}Ӑttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
|||}Ԑt|Ԑt}Րttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
|||}֐t|֐t}אttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
|| |}ؐt|ؐt}ِttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
|| |}ڐt|ڐt}ېttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
|ِ| |tҐt	}ܐt|ܐt}ݐttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
|ِ| |}ސt|ސt}ߐttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
||||	}t|t}ttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
||||	}t|t}ttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
||| |	}t|t}ttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
||| |tҐt
}t|t}ttttd tdtd ttd tdtd  ttdtd  tdtd t t||||
||| |	}t|t}tttt t||!|"}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
||||||}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
||||||}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
||||| |}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
||||| |}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
||||ِ| |tҐt}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
||||ِ| |}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
|||||||}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
|||||||}t|t }ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
|||||| |}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
|||||| |tҐt}t|t}ttttdtd tdtd tdtd ttd tdtd ttd tdtd  ttdtd  tdtd t  t||||
|||||| |} t| t}ttttdtd ttdtd  t||||#|$}t|t}tttttd tdtd  tttd tdtd  ttdtd  ttttd tdtd  ttd tdtd  ttd tdtd  ttdtd    t||||
|||K|%|&|'}t|t}tttttd tdtd  tttd tdtd  ttdtd  ttttd tdtd  ttd tdtd  ttd tdtd  ttdtd    t||||
|||K|%|&|(}t|t}ttttd tdtd ttd tdtd  ttd tdtd  ttdtd  tdtd t t||||
|||)|*|+
}t|t	}	tttt t||,|-|*|+tҐt
}
t|
t}tttttd tdtd ttd tdtd  ttd tdtd  ttdtd  tdtd t  t||||
||||)|.
}t|t}ttttt  t|||,|-|.tҐt}t|t}tttttd tdtd  ttd tdtd  ttd tdtd  ttdtd  t t||||
||/|0}t|t}tttt t||,|-|0tҐt}t|t}ttttd td"td ttd tdtd  ttdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||e|f|l|4|1|2|3}t|t}ttttd td"td ttdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||e|f|4|1|2|3
}t|t}ttttdtd ttd td"td ttd tdtd  ttdtd  tdtd  tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||e|f|l|4||1|2|3}t|t}ttttdtd ttd td"td ttdtd  tdtd  tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||e|f|4||1|2|3}t|t}ttttd tdtd ttdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||
||e|f|l|5|6|7}t|t}ttttd tdtd tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||
||e|l|8|9|:}t|t}ttttd tdtd ttdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||
||e|f|l|5|6|;} t| t}!ttttd tdtd tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||
||e|l|8|9|<}"t|"t}#ttttd td"td ttd tdtd  ttdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||
||e|f|l|4|=|>}$t|$t}%ttttd td"td ttdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd  ttdtd   t||||
||e|f|4|?|@}&t|&t}'ttttttdtd tdtd tdtd tttdtd tdtd tdtd   t||||
||||A	}(t|(t})ttttttdtd tdtd tdtd tttdtd tdtd tdtd   t||||
||||B	}*t|*t}+ttttttdtd tdtd tdtd tttdtd tdtd tdtd   t||||
|||C|D	},t|,t}-tttdtdttd	td tdtd tttdtd tdtd tdtd tdtd   t||||
||E|F}.t|.t}/ttttdtd ttd	td tdtd tttdtd tdtd tdtd tdtd   t||||
|||E|G	}0t|0t }1tttdtttd tdtd  tttd tdtd ttdtd  tdtd   t|||
|||h}2t|2t!}3tttdtttd tdtd  tttd tdtd tdtd   t|||
||h}4t|4t"}5tttdtttd tdtd  tttd tdtd ttdtd  tdtd   t|||
|||i}6t|6t#}7tttdtttd tdtd  tttd tdtd tdtd   t|||
||i}8t|8t$}9tttdtttdtd  ttttd tdtd  ttd tdtd    t||||
||H}:t|:t%};tttdttttd tdtd  tttdtd    t|||
||I}<t|<t&}=tttdtttdtd  td ttttd tdtd  ttd tdtd    t||||
||J|K}>t|>t'}?tttdtttdtd  td ttttd tdtd  ttd tdtd    t||||
||J|L}@t|@t(}Atttdttttd tdtd  tttdtd  td   t|||
||M}Bt|Bt)}Ctttttd tdtd  tttd tdtd  ttttd tdtd  ttd tdtd    t||||
||e|f|N|O
}Dt|Dt*}Etttttd tdtd  ttttd tdtd  tttd tdtd    t|||
||e|f|N|O	}Ft|Ft+}Gtttttd tdtd  ttttd tdtd  ttd tdtd  tttd tdtd  ttd tdtd    t||||
|||e|f|P|Q}Ht|Ht,}Itttttd tdtd  ttttd tdtd  tttd tdtd  ttd tdtd    t|||
|||e|f|P|Q
}Jt|Jt-}Ktttttd tdtd  tttd tdtd  ttttd tdtd  ttd tdtd    t||||
||e|f|P|Q
}Lt|Lt.}Mttttttd tdtd  ttd tdtd  tttd tdtd   t||||
||R|S}Nt|Nt/}Ottttttd tdtd  ttd tdtd  tttd tdtd   t||||
||R|T}Pt|Pt0}Qtttdtttdtd  ttttd tdtd   ttttd tdtd    t||||
|||U}Rt|Rt1}Sttttdtd tdtd tttdtd tttd tdtd ttdtd  tdtd tdtd  tdtd  t||||
|||K|L|V|W}Tt|Tt2}Uttttttd td tdtd tdtd  td	td ttdtd tdtd tdtd  t||K|L||||||'|X|Y}Vt|Vt3}Wttttdtd tttd tdtd ttdtd  tdtd tdtd  tdtd t tdtd tdtd tdtd t||||
|||K|L||Z|}Xt|Xt4}Yttttdtd ttttd tdtd  tdtd  tdtd t tdtd tdtd tdtd t|||
|||K|L||Z|}Zt|Zt5}[ttttttdtd  t tdtd tdtd tdtd t||K|L|||'|(|[|
}\t|\t6}]ttttdtd tttd tdtd tdtd tdtd  td	td ttdtd tdtd tdtd  t|||||K|L||Z|
}^t|^t7}_ttttdtd t8ttd td#td  tdtd  ttdtd ttttd tdtd  tdtd  td	td  t|||||K|_||Z|\|]|^}`t|`t9}attttdtd tttd tdtd ttdtd  tdtd tdtd  tdtd td	td ttd td#td ttdtd  tdtd tdtd  t||||
|||K|L|_||Z|\|`|a|^}bt|bt:}cttt8ttd td#td  tdtd ttdtd ttttd tdtd  tdtd  tdtd td	td  t|||
|||K|_||Z|\|a|^}dt|dt;}ettttdtd tttd tdtd ttdtd  tdtd tdtd  tdtd td	td ttd td#td ttdtd  tdtd tdtd  t||||
|||K|L|_||Z|\|`|ސ|b}ft|ft<}gttt8ttd td#td  tdtd ttdtd ttttd tdtd  tdtd  tdtd td	td  t|||
|||K|_||Z|\|ސ|b}ht|ht=}ittttdtd tttd tdtd ttdtd  tdtd tdtd  tdtd td	td ttd td#td ttdtd  tdtd tdtd  t||||
|||K|L|_||Z|\|`|ߐ|b}jt|jt>}kttt8ttd td#td  tdtd ttdtd ttttd tdtd  tdtd  tdtd td	td  t|||
|||K|_||Z|\|ߐ|b}lt|lt?}mttttdtd ttttd td tdtd tdtd  td	td  t|||||||c|d|e
}nt|nt@}otttdtttd	td tdtd  tttd tdtd tttd	td tdtd  tdtd tdtd    t||||
||f}pt|ptA}qttttttttd tdtd  tdtd  t||||
|g}rt|rtB}stttttd tdtd tttttd tdtd   tdtd  tttttd tdtd    t||||
|h|i}tt|ttC}uttttttdtd ttttd tdtd  tdtd   tdtd tttttd tdtd    t||||
||h|j}vt|vtD}wtttttd tdtd ttttd tdtd  tdtd  ttttd tdtd   t||||
|k}xt|xtE}yttttdtd tdtd tdtd tttd tdtd ttttd tdtd    ttttd tdtd   t||||
||l|m}zt|ztF}{tttdttttd tdtd  tttdtd    t||||
||n}|t||tG}}tttdttttd tdtd  tttdtd    t||||
||o}~t|~tH}tttdttttd tdtd  tttdtd    t||||
||n}t|tI}tttdttttd tdtd  tttdtd    t||||
||o}t|tJ}tttttdtd  ttttd tdtd  tttdtd    t||||
||||ntҐtK
}t|tL}ttttdtd tdtd ttttd tdtd  tttdtd    t||||
||||ntҐtM
}t|tN}tttttdtd  ttttd tdtd  tttdtd    t||||
||||otҐtO
}t|tP}ttttdtd tdtd ttttd tdtd  tttdtd    t||||
||||otҐtQ
}t|tR}tttttdtd  ttttd tdtd  tttdtd    t||||
||||ntҐtS
}t|tT}ttttdtd tdtd ttttd tdtd  tttdtd    t||||
||||ntҐtU
}t|tV}tttttdtd  ttttd tdtd  tttdtd    t||||
||||otҐtW
}t|tX}ttttdtd tdtd ttttd tdtd  tttdtd    t||||
||||otҐtY
}t|tZ}ttttdtd ttt tdtd  tttt tdtd  tdtd   t||||
||||p|
}t|t[}tttdtdttt tdtd  tttt tdtd  tdtd   t||||
|||p}t|t\}ttttt tdtd  tttd tdtd  tt[ tdtd  tt tdtd   t||||
|e|f||||q|r}t|t]}ttttdtd tttd	td tdtd   ttt[ tdtd  ttd td tdtd  ttd	td tdtd   t||||
|e|f||||s|t|u}t|t^}ttttt[ tdtd  tt tdtd  t tt8tt_   tt[ tdtd  tt tdtd   t||||
|||K|||||}t|t`}ttttt[ tdtd  tt tdtd  t ttt[ tdtd  tt tdtd   t||||
||||||}t|ta}ttttt[ tdtd  tt tdtd  t tt8tt_   tt tdtd   t||||
||K|||||}t|tb}ttttt[ tdtd  tt tdtd  t tt8tt_   tt[ tdtd   t||||
||K|||||}t|tc}ttttt[ tdtd  ttt[ tdtd  tt tdtd  t  t||||
|||||
}t|td}tttt8tt_   ttt[ tdtd  tt tdtd  t  t||||
|K|||||}t|te}ttttt[ tdtd  t tt8tt_   tt[ tdtd  tt tdtd   t|||
|||K||||}t|tf}ttttt[ tdtd  t ttt[ tdtd  tt tdtd   t|||
|||||	}t|tg}ttttt[ tdtd  t tt8tt_   tt tdtd   t|||
||K||||
}t|th}ttttd tdtd ttd tdtd  tdtd tttd tdtd  ttd tdtd  ttd tdtd   t||||
|||K|v|w|x|y|z|{}t|ti}ttttd tdtd tdtd tttd tdtd  ttd tdtd  ttd tdtd   t|||
|||K|||}|x|~}t|tj}ttttt  t|W|X||,|||tҐtk	}t|tl}g |||||||||||||||||||||||||||||||||Ñ|ő|Ǒ|ɑ|ˑ|͑|ϑ|ё|ӑ|Ց|ב|ّ|ۑ|ݑ|ߑ|||||||||||||||||||||	||||||||||||!|#|%|'|)|+|-|/|1|3|5|7|9|;|=|?|A|C|E|G|I|K|M|O|Q|S|U|W|Y|[|]|_|a|c|e|g|i|k|m|o|q|s|u|w|y|{|}|||||||||||||||||||||||||||||||||||Ñ|ő|Ǒ|ɑ|ˑ|͑|ϑ|ё|ӑ|Ց|ב|ّ|ۑ|ݑ|ߑ|||||||||||||||||||||	||||||||||||!|#|%|'|)|+|-|/|1|3|5|7|9|;|=|?|A|C|E|G|I|K|M|O|Q|S|U|W|Y|[|]|_|a|c|e|g|i|k|m|o|q|s|u|w|y|{|}|||||||||||||||||||||||||||||||||||Ñ|ő|Ǒ|ɑ|ˑ|͑|ϑ|ё|ӑ|Ց|ב|ّ|ۑ|ݑ|ߑ|||||||||||||||||||||	||||||||||||!|#|%|'|)|+|-|/|1|3|5|7|9|;|=|?|A|C|E|G|I|K|M|O|Q|S|U|W|Y|[|]|_|a|c|e|g|i|k|m|o|q|s|u|w|y|{|}|||||||||||||||||||||||||||S )$Nr   (  cons800cons2cons3cons8cons52cons4cons5cons20cons19cons801cons29cons50cons127cons54cons802cons27cons803cons804cons151cons805cons502cons806cons650cons807cons808cons21cons48cons809cons810cons70cons811cons812cons813cons814cons815cons816cons817cons818cons819cons820cons821cons822cons823cons454cons824cons825cons826cons827cons828cons829cons830cons831cons832cons833cons834cons835cons836cons837cons838cons839cons840cons841cons842cons843cons844cons845cons846cons847cons848cons849cons850cons851cons852cons853cons854cons210cons211cons66cons855cons68cons856cons857cons466cons858cons859cons860cons55cons13cons139cons861cons862cons150cons246cons165cons863cons523cons864cons865cons866cons86cons867cons36cons37cons868cons470cons471cons869cons870cons38cons871cons872cons873cons874cons875cons876cons877cons878cons879cons880cons881cons882cons883cons884cons885cons886cons887cons888cons889cons890cons891cons892cons893cons894cons895cons896cons897cons898cons899cons900cons901cons902cons903cons904cons905cons906cons676cons907cons483cons908cons909cons484cons910cons911cons912cons913cons914cons915cons916cons917cons918cons87cons33cons96cons919cons198cons369cons358cons491cons543cons25cons920cons556cons921cons554cons57cons496cons59cons60cons61cons62cons922cons923cons924cons925cons926cons597cons73cons927cons588cons89cons130cons928cons929cons930cons931cons932cons47cons316cons228cons933cons934cons935cons936cons937cons938cons939cons940cons941cons942cons943cons944cons945cons946cons947cons948cons284cons949cons65cons721cons950cons951cons952cons75cons953cons704cons149cons954cons955cons798cons956cons957cons958cons959cons960cons961cons962cons963cons964cons965cons966cons967cons968cons71cons969cons970cons971cons972cons973cons974cons975cons976cons977cons514cons978cons979cons980cons981cons982cons669cons983cons984cons799cons985cons986cons987cons988cons989cons990cons95cons90cons991cons992cons993cons994cons995cons996cons997cons998cons999cons1000cons40cons1001cons1002cons1003cons1004cons1005cons1006cons1007cons1008cons1009cons1010cons1011cons1012cons385cons1013cons1014cons1015cons1016cons1017cons1018cons1019cons1020cons359cons1021cons248cons1022cons1023cons1024cons1025cons1026cons1027cons1028cons1029cons1030cons1031cons1032cons1033cons1034cons1035cons1036cons1037cons1038cons1039cons1040cons1041cons1042cons1043cons1044cons1045cons299cons1046cons1047cons1048cons1049cons1050cons707cons384cons1051cons1052cons699cons711cons155cons1053cons1054cons1055cons1056cons1057cons1058cons1059cons1060cons1061cons226cons1062cons517cons1063cons1064cons1065cons1066cons1067cons1068cons1069cons1070cons1071cons1072cons1073cons45cons481cons482cons1074cons1075cons1076cons1077cons1078cons1079cons1080cons1081cons1082cons1083cons1084cons1085cons1086cons1087cons1088cons1089cons1090cons1091c   bapmnredfur!  qhg            BCA   r  r  r(  sjkr/  r  r  (m   sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  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  x_n_r  r  q_r   replacement1476replacement1477a_p_c_s_replacement1478replacement1479replacement1480With1481With1482u_With1483With1484replacement1485replacement1486m_replacement1487replacement1488replacement1489replacement1490replacement1491replacement1492replacement1493replacement1494v_replacement1495w_replacement1496z_replacement1497replacement1498replacement1499replacement1500replacement1501replacement1502replacement1503replacement1504replacement1505replacement1506replacement1507replacement1508replacement1509replacement1510replacement1511replacement1512replacement1513replacement1514replacement1515replacement1516replacement1517replacement1518replacement1519e_replacement1520d_replacement1521Pq_With1522replacement1523replacement1524replacement1525replacement1526replacement1527replacement1528replacement1529replacement1530replacement1531With1532With1533With1534r   With1535replacement1535replacement1536replacement1537replacement1538replacement1539replacement1540replacement1541replacement1542replacement1543With1544replacement1544With1545With1546replacement1546A_replacement1547With1548With1549replacement1550With1551B_With1552With1553With1554With1555With1556With1557With1558With1559With1560With1561With1562With1563With1564With1565With1566With1567With1568With1569With1570With1571With1572With1573With1574replacement1575replacement1576replacement1577With1578With1579With1580With1581With1582With1583With1584replacement1584With1585replacement1585With1586replacement1586With1587replacement1587With1588replacement1588With1589replacement1589With1590replacement1590With1591replacement1591r  With1592With1593With1594With1595With1596With1597replacement1598replacement1599replacement1600With1601With1602replacement1603replacement1604replacement1605With1606replacement1606With1607replacement1607With1608replacement1608With1609With1610With1611With1612With1613replacement1614replacement1615replacement1616replacement1617replacement1618replacement1619replacement1620replacement1621a1_a2_replacement1622replacement1623replacement1624replacement1625replacement1626replacement1627replacement1628replacement1629replacement1630Px_With1631replacement1632replacement1633replacement1634replacement1635replacement1636replacement1637replacement1638replacement1639replacement1640replacement1641replacement1642replacement1643replacement1644replacement1645replacement1646replacement1647replacement1648replacement1649replacement1650n2_With1651replacement1651replacement1652replacement1653replacement1654replacement1655replacement1656replacement1657replacement1658With1659replacement1659With1660replacement1660With1661replacement1661replacement1662replacement1663With1664replacement1664With1665replacement1665With1666replacement1666With1667replacement1667With1668replacement1668With1669With1670replacement1671replacement1672With1673With1674With1675With1676With1677replacement1678replacement1679replacement1680replacement1681replacement1682With1683With1684replacement1685replacement1686replacement1687replacement1688replacement1689replacement1690replacement1691replacement1692replacement1693replacement1694replacement1695replacement1696replacement1697replacement1698replacement1699replacement1700replacement1701replacement1702replacement1703replacement1704replacement1705replacement1706replacement1707replacement1708replacement1709replacement1710replacement1711replacement1712replacement1713replacement1714replacement1715replacement1716replacement1717replacement1718replacement1719replacement1720replacement1721replacement1722replacement1723replacement1724j_replacement1725replacement1726replacement1727replacement1728replacement1729replacement1730replacement1731replacement1732replacement1733With1734replacement1735replacement1736replacement1737With1738replacement1738With1739replacement1739replacement1740replacement1741replacement1742replacement1743replacement1744replacement1745replacement1746With1747replacement1747With1748replacement1749With1750replacement1750With1751replacement1752replacement1753With1754replacement1754With1755replacement1756With1757replacement1757With1758replacement1759replacement1760With1761replacement1761With1762replacement1763With1764replacement1764With1765replacement1766replacement1767With1768replacement1768With1769replacement1770With1771replacement1771With1772replacement1773replacement1774With1775replacement1776With1777replacement1777replacement1778replacement1779With1780With1781With1782replacement1782With1783replacement1784replacement1785With1786With1787replacement1788With1789replacement1789replacement1790replacement1791With1792With1793With1794replacement1794With1795replacement1796f_replacement1797replacement1798replacement1799With1800replacement1800replacement1801With1802replacement1802replacement1803With1804replacement1804With1805With1806With1807With1808With1809With1810With1811With1812replacement1813replacement1814replacement1815replacement1816replacement1817replacement1818replacement1819With1820With1821With1822With1823replacement1824replacement1825replacement1826replacement1827replacement1828replacement1829replacement1830replacement1831replacement1832replacement1833replacement1834With1835replacement1836replacement1837replacement1838replacement1839replacement1840replacement1841replacement1842g_replacement1843replacement1844replacement1845replacement1846replacement1847replacement1848replacement1849replacement1850replacement1851replacement1852replacement1853replacement1854replacement1855replacement1856With1857With1858With1859With1860With1861replacement1861With1862replacement1862With1863replacement1863With1864replacement1864With1865replacement1865With1866replacement1866With1867replacement1867With1868replacement1868replacement1869replacement1870replacement1871replacement1872n3_replacement1873replacement1874replacement1875replacement1876replacement1877replacement1878replacement1879replacement1880replacement1881With1882With1883With1884replacement1884(  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  pattern1476rule1476pattern1477rule1477pattern1478rule1478pattern1479rule1479pattern1480rule1480pattern1481rule1481pattern1482rule1482pattern1483rule1483pattern1484rule1484pattern1485rule1485pattern1486rule1486pattern1487rule1487pattern1488rule1488pattern1489rule1489pattern1490rule1490pattern1491rule1491pattern1492rule1492pattern1493rule1493pattern1494rule1494pattern1495rule1495pattern1496rule1496pattern1497rule1497pattern1498rule1498pattern1499rule1499pattern1500rule1500pattern1501rule1501pattern1502rule1502pattern1503rule1503pattern1504rule1504pattern1505rule1505pattern1506rule1506pattern1507rule1507pattern1508rule1508pattern1509rule1509pattern1510rule1510pattern1511rule1511pattern1512rule1512pattern1513rule1513pattern1514rule1514pattern1515rule1515pattern1516rule1516pattern1517rule1517pattern1518rule1518pattern1519rule1519pattern1520rule1520pattern1521rule1521pattern1522rule1522pattern1523rule1523pattern1524rule1524pattern1525rule1525pattern1526rule1526pattern1527rule1527pattern1528rule1528pattern1529rule1529pattern1530rule1530pattern1531rule1531pattern1532rule1532pattern1533rule1533pattern1534rule1534pattern1535rule1535pattern1536rule1536pattern1537rule1537pattern1538rule1538pattern1539rule1539pattern1540rule1540pattern1541rule1541pattern1542rule1542pattern1543rule1543pattern1544rule1544pattern1545rule1545pattern1546rule1546pattern1547rule1547pattern1548rule1548pattern1549rule1549pattern1550rule1550pattern1551rule1551pattern1552rule1552pattern1553rule1553pattern1554rule1554pattern1555rule1555pattern1556rule1556pattern1557rule1557pattern1558rule1558pattern1559rule1559pattern1560rule1560pattern1561rule1561pattern1562rule1562pattern1563rule1563pattern1564rule1564pattern1565rule1565pattern1566rule1566pattern1567rule1567pattern1568rule1568pattern1569rule1569pattern1570rule1570pattern1571rule1571pattern1572rule1572pattern1573rule1573pattern1574rule1574pattern1575rule1575pattern1576rule1576pattern1577rule1577pattern1578rule1578pattern1579rule1579pattern1580rule1580pattern1581rule1581pattern1582rule1582pattern1583rule1583pattern1584rule1584pattern1585rule1585pattern1586rule1586pattern1587rule1587pattern1588rule1588pattern1589rule1589pattern1590rule1590pattern1591rule1591pattern1592rule1592pattern1593rule1593pattern1594rule1594pattern1595rule1595pattern1596rule1596pattern1597rule1597pattern1598rule1598pattern1599rule1599pattern1600rule1600pattern1601rule1601pattern1602rule1602pattern1603rule1603pattern1604rule1604pattern1605rule1605pattern1606rule1606pattern1607rule1607pattern1608rule1608pattern1609rule1609pattern1610rule1610pattern1611rule1611pattern1612rule1612pattern1613rule1613pattern1614rule1614pattern1615rule1615pattern1616rule1616pattern1617rule1617pattern1618rule1618pattern1619rule1619pattern1620rule1620pattern1621rule1621pattern1622rule1622pattern1623rule1623pattern1624rule1624pattern1625rule1625pattern1626rule1626pattern1627rule1627pattern1628rule1628pattern1629rule1629pattern1630rule1630pattern1631rule1631pattern1632rule1632pattern1633rule1633pattern1634rule1634pattern1635rule1635pattern1636rule1636pattern1637rule1637pattern1638rule1638pattern1639rule1639pattern1640rule1640pattern1641rule1641pattern1642rule1642pattern1643rule1643pattern1644rule1644pattern1645rule1645pattern1646rule1646pattern1647rule1647pattern1648rule1648pattern1649rule1649pattern1650rule1650pattern1651rule1651pattern1652rule1652pattern1653rule1653pattern1654rule1654pattern1655rule1655pattern1656rule1656pattern1657rule1657pattern1658rule1658pattern1659rule1659pattern1660rule1660pattern1661rule1661pattern1662rule1662pattern1663rule1663pattern1664rule1664pattern1665rule1665pattern1666rule1666pattern1667rule1667pattern1668rule1668pattern1669rule1669pattern1670rule1670pattern1671rule1671pattern1672rule1672pattern1673rule1673pattern1674rule1674pattern1675rule1675pattern1676rule1676pattern1677rule1677pattern1678rule1678pattern1679rule1679pattern1680rule1680pattern1681rule1681pattern1682rule1682pattern1683rule1683pattern1684rule1684pattern1685rule1685pattern1686rule1686pattern1687rule1687pattern1688rule1688pattern1689rule1689pattern1690rule1690pattern1691rule1691pattern1692rule1692pattern1693rule1693pattern1694rule1694pattern1695rule1695pattern1696rule1696pattern1697rule1697pattern1698rule1698pattern1699rule1699pattern1700rule1700pattern1701rule1701pattern1702rule1702pattern1703rule1703pattern1704rule1704pattern1705rule1705pattern1706rule1706pattern1707rule1707pattern1708rule1708pattern1709rule1709pattern1710rule1710pattern1711rule1711pattern1712rule1712pattern1713rule1713pattern1714rule1714pattern1715rule1715pattern1716rule1716pattern1717rule1717pattern1718rule1718pattern1719rule1719pattern1720rule1720pattern1721rule1721pattern1722rule1722pattern1723rule1723pattern1724rule1724pattern1725rule1725pattern1726rule1726pattern1727rule1727pattern1728rule1728pattern1729rule1729pattern1730rule1730pattern1731rule1731pattern1732rule1732pattern1733rule1733pattern1734rule1734pattern1735rule1735pattern1736rule1736pattern1737rule1737pattern1738rule1738pattern1739rule1739pattern1740rule1740pattern1741rule1741pattern1742rule1742pattern1743rule1743pattern1744rule1744pattern1745rule1745pattern1746rule1746pattern1747rule1747pattern1748rule1748pattern1749rule1749pattern1750rule1750pattern1751rule1751pattern1752rule1752pattern1753rule1753pattern1754rule1754pattern1755rule1755pattern1756rule1756pattern1757rule1757pattern1758rule1758pattern1759rule1759pattern1760rule1760pattern1761rule1761pattern1762rule1762pattern1763rule1763pattern1764rule1764pattern1765rule1765pattern1766rule1766pattern1767rule1767pattern1768rule1768pattern1769rule1769pattern1770rule1770pattern1771rule1771pattern1772rule1772pattern1773rule1773pattern1774rule1774pattern1775rule1775pattern1776rule1776pattern1777rule1777pattern1778rule1778pattern1779rule1779pattern1780rule1780pattern1781rule1781pattern1782rule1782pattern1783rule1783pattern1784rule1784pattern1785rule1785pattern1786rule1786pattern1787rule1787pattern1788rule1788pattern1789rule1789pattern1790rule1790pattern1791rule1791pattern1792rule1792pattern1793rule1793pattern1794rule1794pattern1795rule1795pattern1796rule1796pattern1797rule1797pattern1798rule1798pattern1799rule1799pattern1800rule1800pattern1801rule1801pattern1802rule1802pattern1803rule1803pattern1804rule1804pattern1805rule1805pattern1806rule1806pattern1807rule1807pattern1808rule1808pattern1809rule1809pattern1810rule1810pattern1811rule1811pattern1812rule1812pattern1813rule1813pattern1814rule1814pattern1815rule1815pattern1816rule1816pattern1817rule1817pattern1818rule1818pattern1819rule1819pattern1820rule1820pattern1821rule1821pattern1822rule1822pattern1823rule1823pattern1824rule1824pattern1825rule1825pattern1826rule1826pattern1827rule1827pattern1828rule1828pattern1829rule1829pattern1830rule1830pattern1831rule1831pattern1832rule1832pattern1833rule1833pattern1834rule1834pattern1835rule1835pattern1836rule1836pattern1837rule1837pattern1838rule1838pattern1839rule1839pattern1840rule1840pattern1841rule1841pattern1842rule1842pattern1843rule1843pattern1844rule1844pattern1845rule1845pattern1846rule1846pattern1847rule1847pattern1848rule1848pattern1849rule1849pattern1850rule1850pattern1851rule1851pattern1852rule1852pattern1853rule1853pattern1854rule1854pattern1855rule1855pattern1856rule1856pattern1857rule1857pattern1858rule1858pattern1859rule1859pattern1860rule1860pattern1861rule1861pattern1862rule1862pattern1863rule1863pattern1864rule1864pattern1865rule1865pattern1866rule1866pattern1867rule1867pattern1868rule1868pattern1869rule1869pattern1870rule1870pattern1871rule1871pattern1872rule1872pattern1873rule1873pattern1874rule1874pattern1875rule1875pattern1876rule1876pattern1877rule1877pattern1878rule1878pattern1879rule1879pattern1880rule1880pattern1881rule1881pattern1882rule1882pattern1883rule1883pattern1884rule1884r  r  r  miscellaneous_algebraic   s         * zf$Jd~$LfJ$^Lfh$J$^LLff$J:T  hvXdt|j\tZX\dhpbddhlhlhlhlhlhxhlhxhltlhltxtx~PjjjjrrrrR|NNrD|VfzpfLbjfXtZ
 :     8 @ | |vtvvr||~~zzzxzvz~|z~vrpzpr|r|zz||(P    :>6" <  " t~< : : jvvvvD         r  c              	   C   s\   t ||||  td |   tt| ||||    | |||||  td|  |S Nr  r  r  r+   r   )r  r  r  r  r  r  xr  r  r  r  h     \r  c              
   C   st   t ||td  |||  |td  |   tt|| | ||||    |  |||||  td|  |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  l     tr  c                 C   s   t || |||   |
  | |||||   |  |	  | |||   | |
   ||||   |	 |   t|| | |||   ||
   ||||   |	|   ||S Nr  r   )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  p     r  c	           	      C   s   t || | | t|||S r  r  	r  r  r  r  r  r  r  r  r  r  r  r  r  t     r  c	           	      C   s8   t ||| |||    |  ||||   |   |S r  )r   r  r  r  r  r  x     8r  c           	   
   C   s   t |}t|| |  | ||   | tt|||td  td  |  | |||   tdtd|    || |||   tdtd|    |||| |||    ||||    td|  |S Nr  r4   r  r+   r   r  )	r  r  r  r  r  r  r  r  r  r  r  r  r  |  s   r  c	           
   
   C   s   t |}	t||	 |  | ||   | tt||	|td  td  |  | |||	   td|td |    || |||	   td|td |    |||| |||    ||||    td|	  |S r  r  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   r  c
                 C   s,  t |}
t||
 |  | ||   | ttt|	|
|td  td  |  | ||	|
   tdtd|    || ||	|
   tdtd|    t|t|	|  | ||	|
   td|  || ||	|
   td |   |  |	|	|	|| ||	|    |||	|    td|
  |	S r  r4   r  r+   r   r-  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   & r  c                 C   s4  t |}t|| |  | ||   | ttt|
||td  td  |  | ||
|   td|td |    || ||
|   td|td |    t|	t|
|  | ||
|   td|  || ||
|   td |   |  |
|
|
|| ||
|    |||
|    td|  |
S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   . r  c                 C   s<   t |tt| |||   | |td  |||| | S Nr  r  r+   r   r  )r  r  r  r  r  r  r  r  r  r       <r  c              	   C   sN   t ||td  tt|| td  | |||   |  |||| | S Nr  r  )r  r  r  r  r  r  r  r  r  r  r       Nr  c              	   C   sZ   t ||| |  || |  tt|| td  | |||   |  |||| | S )Nr  r  r  r  r  r  r  r  r  r  r  r  r  r       Zr  c              	   C   sP   t |tt| |||   ||td|    | |td  |||| | S r  r  r  r  r  r  r  r!  r  r  r  r  r  r       Pr  c	           	   
   C   sb   t ||td  tt|| td  | |||   ||td|    |  |||| | S Nr  r  r  r  	r  r  r  r  r  r  r!  r  r  r  r  r  r       br  c
           
   
   C   sn   t |||	 |  ||	 |  tt|	| td  | ||	|   ||	td|    |  |	|	||	 |	 S Nr  r  r  
r  r  r  r  r  r  r  r!  r  r  r  r  r  r       nr  c              	   C   sb   t |tt| |||   ||td |   |td|    | |td  |||| | S r  r  r  r  r  r  r    r	  r  c	           	   
   C   st   t ||td  tt|| td  | |||   ||td |   |td|    |  |||| | S r 	  r  r	  r  r  r  r    r  r  c
           
   
   C   s   t |||	 |  ||	 |  tt|	| td  | ||	|   ||td |   |	td|    |  |	|	||	 |	 S r	  r  r	  r  r  r  r       r  c                 C      t t|||  |S r  r   r2  )r  r  r  r  r  r  r       r  c                 C   "   t t|||  t|||  |S r  r	  )r  r  r  vr  r  r  r  r       "r  c                 C   0   t t|||  t|||  t|||  |S r  r	  r  r  r  r  r	  wr  r  r  r  r       0r  c	           	      C   s>   t t|||  t|||  t|||  t|||  |S r  r	  )	r  r  r  r  r  r	  r	  r  zr  r  r  r       >r  c                 C   r	  r  r	  r  r  r  r  r  r  r    r		  r  c                 C   r
	  r  r	  r  r  r  r	  r  r  r  r  r    r	  r  c                 C   r	  r  r	  r	  r  r  r  r    r	  r  c                 C   r
	  r  r	  r  r  r  r	  r  r  r  r  r    r	  r  c                 C   r	  r  r	  r	  r  r  r  r    r		  r  c                 C       t | | | t|||  |S r  r	  )r  r  r  r  r  r  r  r  r        r  c                 C   r
	  r  r	  r	  r  r  r  r    r	  r  c                 C   s*   t ||  t|||  t|||  |S r  r	  )r  r  r  r  r	  r  r  r  r  r       *r  c                 C   r	  r  r	  )r  r  r  r  r	  r	  r  r  r  r  r    r	  r  c                 C   s8   t ||  t|||  t|||  t|||  |S r  r	  )r  r  r  r  r  r	  r  r	  r  r  r  r    r  r  c                 C   r	  r  r	  r	  r  r  r  r    r		  r  c                 C      t ||  t|||  |S r  r	  r  r  r  r  r  r  r  r       r  c                 C   r	  r  r	  r	  r  r  r  r    r		  r  c                 C   r	  r  r	  )r  r  r  r  r  r  r  r  r     r	  r   c                 C   "   t t||| t|||   |S r  r	  r	  r  r  r  r    r	  r  c                 C   r	  r  r	  r	  r  r  r  r     r	  r  c                 C   *   t ||  t|||  t|||  |S r  r	  r  r  r  r  r  r	  r  r  r  r    r	  r  c                 C   r	  r  r	  r	  r  r  r  r    r	  r  c                 C   r	  r  r	  r	  r  r  r  r    r		  r  c                 C   r	  r  r	  r	  r  r  r  r    r	  r  c                 C   s   t t|||  t|| |S r  r	  )r  r  r  r	  r  r  r  r    r  r  c                 C   s&   t ||  t|||  t|| |S r  r	  )r  r  r  r  r	  r  r  r  r    s   &r  c                 C   sx   t td|  | td|  | |
|td    td| | |
|td    | | | t| ||
|     |
 S Nr  r  r  r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
    s   xr
  c              
   C   s   t ||  || |  t|| ||||td    ||td| td    |||    | |||   tdd   ||S )Nr  r  r  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r        r  c                 C   s   t |}t|| tt||| | td  | | | |||  |  |  t| t|| | || |   |||||  td|  |S Nr  r  r4   r  r+   r   r  r   r  )r)  r  r  r  r  r  r  r  r  r  r  r  $  s   r  c                 C   sj   t td|td  tt|||||td     | t||td  | | ||||td  |S r  r  r  r+   r   r  r)  r  r  r  r  r  r  r  r  r  r  )     jr  c                 C   s   t ||||   | t| ||td  t| ||td   | |t||||   |td  t| ||td  || |td   | S r#	  )r   r2  r  r   r  r)  r  r  r  r  r  r  r  r  r  -     r  c                 C   0   t t| || |  ||||   |  ||S r  r   r   r)  r  r  r  r  r  r  r  r  r  r  r  1  r	  r  c                 C   $   t t| ||||   |  ||S r  r+	  r(	  r  r  r  r  5     $r  c              	   C   s^   t td| tt|td|td |   |||  |  t|| | | |||| |S r  r%	  r&	  r  r  r  r  9     ^r  c                 C   T   t |t| |t|   || t|  t| ||  ||||   |  ||S r  r  r%   r&   r   r,	  r  r  r  r  =     Tr  c                 C   s   t td|| |td   t||||   |td  t| | || t| ||||   |td   || |td   | S r  )r  r  r   r  r  r&	  r  r  r  r  A  s   r  c                 C   sL   t td| t|| |td  ||||   |  t| | | ||S r  r  r  r   r2  )r)  r  r  r  r  r  r  r  r  r  r  r  E     Lr  c                 C   s,   t |||||   |  t| | | |S r  r	  r(	  r  r  r  r  I     ,r  c              
   C   s   t | ||  |}t|| | t|||  ||||   |td   t||| td   | || t|||||   |  | S Nr  )r  r  r   r  r2  r  )r)  r  r  r  r  r  r  r  r  r  r  r  M  s   zr  c           
   
   C   s   t | |}td}	t|| | t|| | ||||   |td   t||	 t| ||	 |	| ||  td  t|	td| ||t|| | ||||   |  t||	td  t| ||	 |	| ||  td  t|	td| | S Nr  r  r  r   	r   r  r  r   r  r  r   r   r  )
r)  r  r  r  r  r  r  r  r  r  r  r  r  r  R  s   
r  c              
   C   s   t | |}td}t|| | t||||   |td  t|| t| || |||  td  t|td| ||t||||   | t||td  t| || |||  td  t|td| | S r7	  r8	  r)  r  r  r  r  r  r  r  r  r  r  r  X  s   
r  c                 C   sB   t |ttttfrdS t| |}td}t||td rdS dS )NFr  r  T)	
isinstanceintr  floatr  r   r  r#   r  r9	  r  r  r  r  ^     
r  c                 C   s  t | |}td}ttd|| |td   t||||   |td  t|| |||td   td  t| || t|td|td  ||t||||   |td  |t| || || t	| || t| ||  |   || | |td   | S )Nr  r  r   r  )
r   r  r  r  r   r  r   r   r  r2  r9	  r  r  r  r  h  s   
r  c              	   C   s   t td|| |td   t||||   |td  t| | |td  t| | | | ||t| | ||||   |td   || |td   | S r  )r  r  r   r2  r  r  r(	  r  r  r  r  o     r  c              	   C   sp   t td|  | td|  | |  td| | |td   td|  | t| ||td     | S r	  r 	  )r  r  r  r  r  r  r  r  r  r  r  s     pr  c              	   C   s@   t |td| |  td| t| ||td     | S r	  r 	  )r  r  r  r  r  r  r  r  r  r  w     @r  c              	   C   sP   t |td|  | || |   td|  | t| ||td     | S r	  r 	  )r  r  r  r  r  r  r  r  r  r   {  r  r   c              	   C   sH   t |td| |td   td| t| ||td     | S Nr  r  r  r 	  )r  r  r  r  r  r  r  r  r  r!       Hr!  c              	   C   s2   t ||td  |t| ||td     |S )Nr  r  r 	  )r  r  r  r  r  r  r  r  r"       2r"  c              	   C   sh   t | | td|  | |td   td| | |  td|  | t| ||td     | S rA	  r 	  )r  r  r  r  r  r  r  r  r  r  r  r#       hr#  c              	   C   sF   t || | |td  ||   | | t| ||td     |S r	  r 	  )r  r  r  r  r  r  r  r  r  r  r$       Fr$  c           	      C   s   t |ttttfrdS t| |}t| |t|td | td   ||||   |}t	| |t|td | td   ||||   |}t
||rOdS dS )NFr  r  Tr:	  r;	  r  r<	  r  r   r  r  r  r  rR   	r)  r  r  r  r  r  r  QRr  r  r  r%    s   
88
r%  c           	   	   C   sN  t | |}t| |t|td | td   ||||   |}t| |t|td | td   ||||   |}t|t|d |  d  || |d   t||||   |d  t|| | |d  || |d   t|| | | ||t	||t|d |  d   | ||||   |d   || |d   | S r#	  )
r   r  r  r  r  r  r   r2  r  r  rG	  r  r  r  r&    s   
88r&  c           
      C   s  t | |}t| | |t|td | td   ||  ||||   |}t| | |t|td | td   ||  ||||   |}	t|t|d |  d  || |d   t|| ||||   |d   t|| ||   |d  t|t	|  t	||d   d  t
|	|t	 | tt	d|d  | ||t|	|t|d |  d   | ||||   |d   |d | |d   | S )Nr  r  r   r  r   r  r  r  r  r  r   r2  r  r  r   r   r  )
r)  r  r  r  r  r  r  r  rH	  rI	  r  r  r  r'    s
   
DD r'  c                 C   s>   t |ttttfrdS t|td |}t|tdrdS dS NFr  Tr:	  r;	  r  r<	  r  r   r  r$   r)  r  r  r  r  r  r  r  r  r  r  r(       r(  c                 C   s   t |td |}ttd| tt|td|td |   |||||    |  t| t||td|   |||| |S r  r   r  r  r+   r   r   r  rM	  r  r  r  r)    s   rr)  c              	   C   sR   t |td | ttd| td | | |  |td |td    ||S Nr  r  r  r  r  r   )r  r  r  r  r  r  r  r  r+       Rr+  c              	   C   s   t t|| td}tt|| td}t|td| |  t|td|  | ||   || |  | ||    |td || |  |td |td    ||t||  | ||   td| |  ttd|||   || S Nr  r  r  rx   r  r  r4   r  r   r  r  r  r  r  r  r  r  r  r  r,    s   r,  c              	   C   s   t t| | td}tt| | td}t|td| |  t|td |  | ||   || | | ||    |td || |  |td |td    || t|| | ||   td| |  ttd|||   || S rS	  rT	  rU	  r  r  r  r-    s   r-  c                 C   s0   t |td | ttd|||   || S Nr  r  rQ	  r  r  r  r  r  r  r  r  r  r.    r	  r.  c              	   C   s   |t dd  |t dd   }t|| tt d||  ||t|||  | tt d|t d ||  |t d   || S Nr  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r/        dr/  c              	   C   s   |t dd  |t dd   }t|| tt d||  ||t| ||  | tt d|t d ||  |t d   || S rX	  rY	  r  r  r  r  r  r  r  r  r  r1    r[	  r1  c              	   C   s   |t dd  |t dd   }t|| tt d||  ||t|| | tt d|t d ||  |t d   || S rX	  rY	  r  r  r  r  r  r  r  r  r  r2    s    `r2  c              	   C   s   | t dd  | t dd   }t|| tt d||  ||t|||  | tt d|t d ||  |t d   || S rX	  rY	  rZ	  r  r  r  r3       $dr3  c              	   C   s   | t dd  | t dd   }t|| tt d||  ||t| ||  | tt d|t d ||  |t d   || S rX	  rY	  r\	  r  r  r  r4    r^	  r4  c              	   C   s   | t dd  | t dd   }t|| tt d||  ||t|| | tt d|t d ||  |t d   || S rX	  rY	  r]	  r  r  r  r5    s   $`r5  c              	   C   s   | t dd  |t dd   }t|| tt d||  || t|||  | tt d|t d ||  |t d   || S rX	  rY	  rZ	  r  r  r  r6       "fr6  c              	   C   s   | t dd  |t dd   }t|| tt d||  || t| ||  | tt d|t d ||  |t d   || S rX	  rY	  r\	  r  r  r  r7    r_	  r7  c              	   C   s   | t dd  |t dd   }t|| tt d||  || t|| | tt d|t d ||  |t d   || S rX	  rY	  r]	  r  r  r  r8       "br8  c              	   C   s   |t dd  | t dd   }t|| tt d||  || t|||  | tt d|t d ||  |t d   || S rX	  rY	  rZ	  r  r  r  r9    r_	  r9  c              	   C   s   |t dd  | t dd   }t|| tt d||  || t| ||  | tt d|t d ||  |t d   || S rX	  rY	  r\	  r  r  r  r:    r_	  r:  c              	   C   s   |t dd  | t dd   }t|| tt d||  || t|| | tt d|t d ||  |t d   || S rX	  rY	  r]	  r  r  r  r;    r`	  r;  c              	   C   sx   || t dd  }t|| tt d||  ||t|||  | tt d|t d ||  |t d   || S rX	  rY	  rZ	  r  r  r  r<       dr<  c              	   C   sx   || t dd  }t|| tt d||  ||t| ||  | tt d|t d ||  |t d   || S rX	  rY	  r\	  r  r  r  r=    ra	  r=  c              	   C   st   || t dd  }t|| tt d||  ||t|| | tt d|t d ||  |t d   || S rX	  rY	  r]	  r  r  r  r>    s   `r>  c              	   C   sv   t || td}t|| ttd||  ||t|||  | ttd|td ||  |td   || S rP	  r  r  r  r   rZ	  r  r  r  r?       dr?  c              	   C   sv   t || td}t|| ttd||  ||t| ||  | ttd|td ||  |td   || S rP	  rb	  r\	  r  r  r  r@    rc	  r@  c              	   C   sr   t || td}t|| ttd||  ||t|| | ttd|td ||  |td   || S rP	  rb	  r]	  r  r  r  rA  !  s   `rA  c              	   C   s|   | | t dd  }t|| tt d||  || t|||  | tt d|t d ||  |t d   || S rX	  rY	  rZ	  r  r  r  rB  &     frB  c              	   C   s|   | | t dd  }t|| tt d||  || t| ||  | tt d|t d ||  |t d   || S rX	  rY	  r\	  r  r  r  rC  +  rd	  rC  c              	   C   sx   | | t dd  }t|| tt d||  || t|| | tt d|t d ||  |t d   || S rX	  rY	  r]	  r  r  r  rD  0  s   brD  c              	   C   sz   t | | td}t|| ttd||  || t|||  | ttd|td ||  |td   || S rP	  rb	  rZ	  r  r  r  rE  5     frE  c              	   C   sz   t | | td}t|| ttd||  || t| ||  | ttd|td ||  |td   || S rP	  rb	  r\	  r  r  r  rF  :  re	  rF  c              	   C   sv   t | | td}t|| ttd||  || t|| | ttd|td ||  |td   || S rP	  rb	  r]	  r  r  r  rG  ?  s   brG  c              	   C   sT   t |t|td |||td    ||t| ||  |||td    | S Nr  r  r!	  rW	  r  r  r  rH  D  r2	  rH  c              
   C   sT   t | t||||td    ||t |t|td |||td    || S Nr  r  r!	  )r  r  r  r  r  r  r  r  rI  H  r2	  rI  c              
   C   sX   t | ttd|||td    ||t |t|td |||td    || S rX	  r!	  )r  r  r  r  r  r  r  r  rJ  L     XrJ  c                 C   s^   || t dd  }t|t d | t| || |  |t d ||  |t d   ||S rX	  rY	  rZ	  r  r  r  rK  P     JrK  c                 C   sV   || t dd  }t||t d  | t||t d ||  |t d   ||S rX	  rY	  r\	  r  r  r  rL  U  s   BrL  c                 C   s^   || t dd  }t|t d | t| || |  |t d ||  |t d   ||S rX	  rY	  r]	  r  r  r  rM  Z  ri	  rM  c                 C   s`   | | t dd  }t|| t| | || ||    |t d ||  |t d   ||S rX	  rY	  rZ	  r  r  r  rN  _  s   JrN  c                 C   sX   | | t dd  }t| |t d  | t||t d ||  |t d   ||S rX	  rY	  r\	  r  r  r  rO  d  s   BrO  c                 C   sT   | | t dd  }t| | | t|| |t d ||  |t d   ||S rX	  rY	  r]	  r  r  r  rP  i  s   >rP  c                 C   sR   t |ttttfrdS || tdd  }t| ||  ||td   r'dS dS NFr  r  r  Tr:	  r;	  r  r<	  r  r  r   rZ	  r  r  r  rQ  n  s    rQ  c              
   C   s   || t dd  }t|t d|  t|t d|  ||  ||t d    || ||  t d| |t d     |t d ||  |t d   ||t|| ||  ||t d    t d|  tt d||  || S rX	  rY	  rZ	  r  r  r  rR  w  s   rR  c                 C   sN   t |ttttfrdS || tdd  }t| | ||td   r%dS dS rj	  rk	  r\	  r  r  r  rS  }  s   rS  c              
   C   s   || t dd  }t|t d|  t|| | ||t d    || | t d| |t d     |t d ||  |t d   ||t|| | ||t d    t d|  tt d||  || S rX	  rY	  r\	  r  r  r  rT    s   rT  c                 C   sJ   t |ttttfrdS || tdd  }t| ||td   r#dS dS rj	  rk	  r]	  r  r  r  rU    s   rU  c              
   C   s   || t dd  }t|t d|  t|t d|  ||t d    || t d| |t d     |t d ||  |t d   ||t|| ||t d    t d|  tt d||  || S rX	  rY	  r]	  r  r  r  rV    s   rV  c                 C   sT   t |ttttfrdS | | tdd  }t| ||  ||td   r(dS dS rj	  rk	  rZ	  r  r  r  rW    s    rW  c              
   C   s   | | t dd  }t|t d|  t|t d|  ||  ||t d    || ||  t d| |t d     |t d ||  |t d   ||t|| ||  ||t d    t d|  tt d||  || S rX	  rY	  rZ	  r  r  r  rX    s   rX  c                 C   sP   t |ttttfrdS | | tdd  }t| | ||td   r&dS dS rj	  rk	  r\	  r  r  r  rY    s   rY  c              
   C   s   | | t dd  }t|t d|  t| | | ||t d    || | t d| |t d     |t d ||  |t d   ||t|| | ||t d    t d|  tt d||  || S rX	  rY	  r\	  r  r  r  rZ    s   rZ  c                 C   sL   t |ttttfrdS | | tdd  }t| ||td   r$dS dS rj	  rk	  r]	  r  r  r  r[    s   r[  c              
   C   s   | | t dd  }t|t d|  t|t d|  ||t d    || t d| |t d     |t d ||  |t d   ||t|| ||t d    t d|  tt d||  || S rX	  rY	  r]	  r  r  r  r\    s   r\  c              
   C   s   t |ttttfrdS t|t  || t|   ||td  t| |t|td   t| |t  ||||    t	ttd|td td }t
|rQdS dS NFr  r   r  Tr:	  r;	  r  r<	  r  r  iir  r   r   r)   r)  r  r  r  r  r  r  r	  r  r  r  r]    s   r]  c              
   C   s   t |t  || t|   ||td  t| |t|td   t| |t  ||||    tttd|td td }t||S Nr  r   r  r  rn	  r  r   r   r   ro	  r  r  r  r^    s   
r^  c              
   C   s   t |ttttfrdS t|t ||td  t| |t|td   t| |t  ||||    t	ttd|td td }t
|rHdS dS rl	  rm	  r)  r  r  r  r  r	  r  r  r  r_    s   nr_  c              
   C   sx   t |t ||td  t| |t|td   t| |t  ||||    tttd|td td }t||S rp	  rq	  rr	  r  r  r  r`    s   n
r`  c                 C   s  t t||  td}tt||  td}ttd| |td  t| ||td    | |td  || |tdttd     |ttdtdd  | | t|td |td  || |  |td  || |tdttd   td   ttdttd  || |  tt|| |tdttd   || |tdttd    tdtdttd   |td t||| |  || |tdttd   td   t| ||td     | S Nr  r  r  r  ir   r  r  r   r  r  r<   r	  r  r  r  r  r  r  r  r  r  r  ra    s    ra  c                 C   s   t t||  td}tt||  td}t|| t|| |tdttd   t| ||td    ||t|| || tdttd   | ttdt| ||td    || S Nr  r  r   r  r  r   r  r   r  ru	  r  r  r  rb       rb  c                 C   s  t t||  td}tt||  td}ttd| |td  t| ||td    | |td  || |tdttd     |ttdtdd  | | t|td |td  || |  |td  || |tdttd   td   tttdtd  || |  tt|| |tdttd   || |tdttd    tdtdttd   |td t| || |  || |tdttd   td   t| ||td     | S rs	  rt	  ru	  r  r  r  rc    s    rc  c                 C   s   t t||  td}tt||  td}t|| t|| |tdttd   t| ||td    ||t|| || tdttd   | ttdt| ||td    || S rv	  rw	  ru	  r  r  r  rd    rx	  rd  c                 C   sR  t t||  td}tt||  td}t||td  | tdttd  t| ||td    td|  |td  ||td  tdttd  |   |ttdtdd  | | | t|td |td  || |td   |td  ||td  tdttd  | td   ||td  |  tt||td  tdttd  | ||td  tdttd  |  ttdtd tdd   td|td  t||td  ||td  |  ||td  tdttd  | td   t| ||td     | S )Nr  r  r  r  r  )r   r  r  r   r  r  r<   r  ru	  r  r  r  re    s
    * re  c                 C   s   t ||  td}t|td|td   ttd|td  |td  ttd td t| ||td    ||ttd| |td  |tdttd   td|td   ttdt| ||td    || S )Nr  r  r  r  r  )r  r  r  r   r  r  r  r  r  r  r  r  r  r  rf    s   rf  c              
   C   sr  t || |td  t|||td   td  || |td    t|td  | ||td    ||td  |td    tttttd|td  td| | |td   ttd|td  |td   || |td   td tdtdttd   tttdtd t| ||td    |||td     | S )Nr  r  r  r  r  )r  r  r  r=   r	  r  r  r  r  r  r  r  r  rg  	  s   t rg  c                 C   s   t | t||  td | tdt||  td  t|td  t||  td td t| ||td    || t |t||  td | tdt||  td  t|td t||  td td t| ||td    || S )Nr  r  r  r  )r  r  r  r   r  rz	  r  r  r  rh    s   rh  c              
   C   sr   t t| |tdttd|t||||     ||tt| t| |td | |t||||    | S )Nr   r  )r  r   r  r   r  r2  r)  r  r  r  r  r  r  r  ri       rri  c                 C   s   t | |}td}	td}
tt||	  || |	|   ||||   |  t||
| td  t| ||	|
| td   t|
tdtdtd|	 |  |   t|	td|td td |S Nr  r  r  r   r  r  r   r  r   r  r  r   r   )r)  r  r  r  r  r  r  r  r  r  r  r  r  r  rj    s   
rj  c           	      C   s   t | |}td}td}tt|| ||||   |  t||| td  t| |||| td   t|tdtdtd| |  |   t|td|td td |S r}	  r~	  )	r)  r  r  r  r  r  r  r  r  r  r  r  rk    s   
rk  c                 C   s   t t| ||td t||td  ||||   |  ||t||||   | t| ||td  t| ||td   | | S r6	  )r  r   r  r   r2  r(	  r  r  r  rl  #  s   rl  c                 C   s,   t t| || |  ||||    ||S r  r+	  )r)  r  r  r  r  r  r  r  r  r  rm  '  r5	  rm  c                 C   s    t t| ||||    ||S r  r+	  r{	  r  r  r  rn  +  r	  rn  c           	      C   s6   t |ttttfrdS t| |td}t|rdS dS )NFr   T)r:	  r;	  r  r<	  r  r   r  r   	r)  r  r  r  r  r  r  r  Pq0r  r  r  ro  /  s   ro  c           	      C   s  t | |td}ttdtd| | |td   t|| |td  ||||   |  ttd | | ||td   |||td   td  td| | |  |td  |  | ||t||| |td   ||||   |td   || |td   | S )Nr   r  r  r  )r   r  r  r   r2  r  r	  r  r  r  rp  8  s    rp  c           
   
   C   s   t |ttttfrdS t| |}t| ||}	tt|||  | t	d t
| | t	dttt	d| t||t	d t	d|   rIdS dS NFr  r   r  Tr:	  r;	  r  r<	  r  r   r   r  r   r  rR   r  r   
r)  r  r  r  r  r  r  r  r  Pqqr  r  r  rq  >  s   
brq  c           
      C   s  t | |}t| ||}	td||||  | d   t|| | ||||   |  t|	 | || |   || | d  || |	||    |||  | d   | ||t|	||| d   || || | d   ||||   |d   ||||  | d   | S r  r   r   r  r   r2  r  r	  r  r  r  rr  H  s   
rr  c              
   C   s   t |ttttfrdS t| |}t| ||}tt|| | t	d t
| | t	dttt	d| t||t	d t	d|   rGdS dS r	  r	  r)  r  r  r  r  r  r  r	  r  r  r  rs  O  s   
^rs  c                 C   s   t | |}t| ||}td||| | d   t||||   | t| | || |   | | d  || |||    || | d   | ||t||| | d   ||||   |d   ||| | d   | S r  r	  r	  r  r  r  rt  Y  s   
rt  c                 C   st   t | |}tt|| | td  ||||    |  t|| t| t|td|  | ||td|  S )Nr  r  r   r+   r   r  r2  r   r  )r)  r  r  r  r  r  r  r  r  r  r  ru  `  s   
jru  c           
      C   s   t |}t| |}	t|| tt|| ||	 td  td  ||||   || |    |  t|||	  t| t|||  |  | |||| td |  | S r  	r4   r   r  r+   r   r  r2  r   r  )
r)  r  r  r  r  r  r  r  r  r  r  r  r  rv  e  s   
rv  c           	      C   s   t | |}t|| | td| |  tt|| | td  ||||    |  t|| t| t|td|  | ||td| | S r  r   r  r  r+   r   r2  r   r  )	r)  r  r  r  r  r  r  r  r  r  r  r  rw  k  s   
rw  c                 C   sr   t |}t|tt|||td  td  |||||    |  t| t|||  |||td|  |S r  r$	  rM	  r  r  r  rx  p  s   jrx  c                 C   sf   t |}t|tt||td  |||||    |  t| t|||  |||td|  |S r#	  r$	  )r)  r  r  r  r  r  r  r  r  r  ry  u  s   ^ry  c                 C   r0	  r  r1	  r,	  r  r  r  rz  z  r2	  rz  c                 C   s~   t td|td  tt|||||td     | tt|| | |t||||td    ||||td  |S r  r  r  r+   r   r   r  r  r&	  r  r  r  r{  ~  s   ~r{  c                 C   r0	  r  r1	  r,	  r  r  r  r|    r2	  r|  c              	   C   sL   t | t||||   | ||t |t|| ||||   |  || S r  r  )r  r  r  r  r  r  r  r  r  r  r  r}    r4	  r}  c                 C   r*	  r  r+	  r,	  r  r  r  r~    r	  r~  c                 C   r-	  r  r+	  r(	  r  r  r  r    r.	  r  c	           	   	   C   s\   t || ||   t||td tt|| ||||   |  t|| | ||||S r  )r  r   r  r+   r   r  )	r)  r  r  r  r  r  r  r	  r  r  r  r  r    r  r  c              	   C   sJ   t tdt||td tt||||   | t|| | ||||S r  )r  r  r   r+   r   r  )r)  r  r  r  r  r	  r  r  r  r  r    s   Jr  c
           
      C   s:   t | ||	 |  || || |	td|    |  |	S r  r   r  
r)  r  r  r  r  r  r  r  r  r  r  r  r  r    s   :r  c                 C   s.   t | || || |td|    |  |S r  r	  r)  r  r  r  r  r  r  r  r  r  r  r    s   .r  c
           
   	   C   s   t |||	|   t| |||	|   t|  || || |	td|    t|   t| ||	 |  || || |	td|    |  |	|	S r  r  r&   r  r   r	  r  r  r  r       r  c              	   C   s   t ||||   t| ||||   t|  || || |td|    t|   t| || || |td|    |  ||S r  r	  r	  r  r  r  r    s   r  c                 C   sN   t ||
 | ||
|   |	td   |||
|   |	td   | |  |
S r  r  r  )r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r    r  r  c
           
      C   sN   t ||	 | ||	|   |td   |||	|   |td   | |  |	S r  r	  )
r  r  r  r  r  r  r  r!  r  r  r  r  r  r    r  r  c                 C   sn   t ||| |td   | |||	   |td   ||||	   |td   | | | |td   |S r  r	  )r  r  r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r    r	  r  c                 C   sn   t ||| |td   | |||   |
td   ||||   |
td   | | | |td   |S r  r	  )r  r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r    r	  r  c              	   C   st   t | t|||
|   | |||
|   |	  |
|
t |t|
| |||
|   |  |||
|   |	  |
|
 S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c	           
      C   s   t |}	t|	| ttt||	td  ||||	|    |  t| t|| | ||	 |  |  ||||||  td|	  |S r#	  r  )
r+  r  r  r  r  r  r  r  r  r  r  r  r  r       r  c	           	   	   C   sR   t td| tt|||  ||td   | t|| | | |||| |S Nr  r  r%	  	r)  r  r  r  r  r  r!  r  r  r  r  r  r    rR	  r  c
           
      C   D   t t| ||	 |  |||	|   ||	td|    |  |	|	S r  r   r   r  
r)  r  r  r  r  r  r  r!  r  r  r  r  r  r       Dr  c                 C   8   t t| ||||   ||td|    |  ||S r  r	  r)  r  r  r  r  r!  r  r  r  r  r  r    r  r  c
           
      C   sB   t ||	 | ||	|   ||	td|    |td   |  |	S rV	  r	  
r  r  r  r  r  r  r  r!  r  r  r  r  r  r       Br  c	           	      C   sB   t || | |||   ||td|    |td   |  |S rV	  r	  	r  r  r  r  r  r  r!  r  r  r  r  r  r    r	  r  c                 C   sb   t ||| |td   | |||   ||td|    |
td   | | |td   |S r	  r	  )r  r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r    r	  r  c                 C   sb   t |||
 |td   | ||
|   ||
td|    |	td   | | |td   |
S r	  r	  )r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r    r	  r  c
           
      C   s   t td| t|  |td| |	|   td t|   |||	|   ||	td|    t|  t| ||	 |  |td| |	|   td|   |	|	S Nr  r  r  r  r%   r&   r   r	  r  r  r  r       r  c                 C   s   t td| t|  |td| ||   td t|   ||||   ||td|    t|  t| |td| ||   td|   ||S r	  r	  r	  r  r  r  r       r  c	           	   
   C   sn   t td| tt|td|td |   |||  ||td   |  t|| | | |||| |S Nr  r  r  r%	  r	  r  r  r  r    r	  r  c
           
   	   C   T   t |	|  ||	 |  t| |	|  |||	|   ||	td|    |  |	|	S r  r!	  r	  r  r  r  r    r2	  r  c
           
   	   C   s`   t td| t||	 |td  |||	|   ||	td|    |  t| |	 |	 |	|	S r	  r3	  r	  r  r  r  r       `r  c                 C   s@   t |||||   ||td|    |  t| | | |S r  )r   r  r2  r	  r  r  r  r    r@	  r  c                 C   s   t |td|  | |td |  | td| | |
  td| |     | ||td   ||td   |
td   td| td   |S Nr  r  r  r  r	  r  r  r  r  r  r  r  r  r!  r(  r  r  r  r  r  r    r	  r  c                 C   s   t |
td|  | |
td td| | |	 td| |     | ||
td   ||
td   |	td   td| td   |
S r	  r	  r  r  r  r  r  r  r  r!  r(  r  r  r  r  r  r       r  c                 C   s   t |
td|  | |
td |  | td| | |	  td| |     | ||
td   ||
td   |	td   td| td   |
S r	  r	  r  r  r  r  r  r  r  r!  r(  r  r  r  r  r  r    r	  r  c
           
      C   s   t |	td|  | |	td td| | | td| |     | ||	td   ||	td   |td   td| td   |	S r	  r	  
r  r  r  r  r  r  r!  r(  r  r  r  r  r  r  	  r	  r  c              	   C   s   t td| ||  | | td| |   td| td |  | ||    td| ||td   td |  | |td    || td |  | |td   t| |||   ||td|      | S r	  r 	  )r  r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r  r  r  	  s   r  c              
   C   s   t ||  || |  t|| ||||	td    ||td|	 td    ||td|	     | |||	   ||td|	    tdd   ||S rf	  r!	  )r  r  r  r  r  r  r  r  r  r  r!  r  r  r  r  r  r  r  r  	     r  c           
      C   sB   t |ttttfrdS t| |}td}	t|td| rdS dS )NFr  r  T)	r:	  r;	  r  r<	  r  r   r  rP   r  
r)  r  r  r  r  r!  r  r  r  r  r  r  r  r  	  r=	  r  c           
      C   s  t | |}td}	ttd|| |td  td | | |td    t||||   ||td|    |td  t|||	|   td | t| ||	|  |t| ||	   |	|td| td   td  ||	 | | |	td  t| ||	|  td | | |	td| |td   td  |td |	||td   td   t| ||	    t|	td|td  ||t|||||   ||td|    |td   t|||	|   td | t| ||	|  |t| ||	   ||	 | | t| ||	|  td | | |td  t| ||	    t|	td|td  || |td  td | | |td    | S )Nr  r  r  r  r  r   r  )	r   r  r  r  r   r  r   r   r  r	  r  r  r  r  	  s
   
  r  c              	   C   s   t ||td  | | td| |   |td |  | ||    || td |  | |td    |td |  | |td   t| ||td   ||td     | S r	  r 	  r  r  r  r  r  r  r  r  r  r  r  r   	     r  c              	   C   s   t td|  | | || | |td   || td |  | |td    |td |  | |td   t| ||td   ||td     |S r	  r 	  )r  r  r  r  r  r  r  r  r  r  r  $	  s   r  c              	   C   s   t || | td|td  | |td   || td |  | |td    |td |  | |td   t| ||td   ||td     | S r	  r 	  )r  r  r  r  r  r  r  r  r  r  r  (	  r>	  r  c              	   C   s   t td| td  | | | | | | |td   | | |td  td |  | |td    | | td |  | |td   t| ||td   ||td     |S rA	  r 	  )r  r  r  r  r  r  r  r  r  r  r  r  ,	     r  c              	   C   sB   t ||td  |t| ||td   ||td     |S )Nr  r  r  r 	  )r  r  r  r  r  r  r  r  r  r  r  0	  r	  r  c	           	   	   C   s   t td| td  | | | | | | |td   | | |td  td |  | |td    || | td |  | |td    | | td |  | |td   t| ||td   ||td     |S rA	  r 	  	r  r  r  r  r  r  r  r  r  r  r  r  r  4	     r  c              	   C   s   t td| td  | | | | | | |td   | | |td  td |  | |td    || | td |  | |td    | | td |  | |td   t| ||td   ||td     |S rA	  r 	  )r  r  r  r  r  r  r  r  r  r  r  r  8	  r	  r  c                 C   s   t |ttttfrdS t| |}t| || t|td | td   ||||   ||td|    |}	t	| || t|td | td   ||||   ||td|    |}
t
|td| rkdS dS NFr  r  r  TrF	  r)  r  r  r  r  r!  r  r  r  rH	  rI	  r  r  r  r  <	  s   
PPr  c                 C   s$  t | |}t| || t|td | td   ||||   ||td|    |}	t| || t|td | td   ||||   ||td|    |}
t|| t|d |  d  || |d  d| | |d    t||||   ||d|    |d  t|	| | |d  d| | |d   t||t	|   d| t
|
|t	|  |t
|
|t	   t	|d| d   d  |t	 | | t	d  t
|
|t	|  d| | t	d| |d   d  |d t	||d   d   t
|
|t	    tt	d|d  | ||t||| t|d |  d   ||||   ||d|    |d   t||t	|   d| t
|
|t	|  |t
|
|t	   |t	 | | t
|
|t	|  d| | |d  t
|
|t	    tt	d|d  || |d  d| | |d    | S Nr  r  r  r  r  r   rJ	  r	  r  r  r  r  G	  s   
PP ~ r  c	                 C   s   t |ttttfrdS t| |}	t| | ||  || t|	td | td   ||||   ||td|    |}
t	| | ||  || t|	td | td   ||||   ||td|    |}t
|	td| rwdS dS r	  rF	  r)  r  r  r  r  r  r!  r  r  r  rH	  rI	  r  r  r  r  O	  s   
\\r  c	                 C   sR  t | |}	t| | ||  || t|	td | td   ||||   ||td|    |}
t| | ||  || t|	td | td   ||||   ||td|    |}t|| t|	d |  d  || |d  d| | |d    t|| ||||   ||d|    |d   t|
| ||   |d  d| | |d   t||t	| |   dt
||t	|  |t
||t	 |   t	|d| d   d  |t	|  | t	d  t
||t	|  d| t	d| |d   d  |d t	||d   d  |  t
||t	    tt	d|d  | ||t||| t|	d |  d   ||||   ||d|    |d   t||t	|   d| t
||t	|  |t
||t	   |t	 | | t
||t	|  d| | |d  t
||t	    tt	d|d  |d | |d  d| | |d    | S r	  rJ	  r	  r  r  r  r  Z	  s   
\\  r  c	           
      C   s>   t |ttttfrdS t|td |}	t|	tdrdS dS rK	  rL	  
r)  r  r  r  r  r  r!  r  r  r  r  r  r  r  b	  rN	  r  c	           
      C   s   t |td |}	ttd|	 tt|td|td |	   |||||	    ||td| |	    |  t| t||td|	   ||||	 |S r	  rO	  r	  r  r  r  r  k	  s   r  c	           	      C   @   t t| || |  ||||   ||td|     ||S r  r	  	r)  r  r  r  r  r  r  r!  r  r  r  r  r  q	  r@	  r  c                 C   4   t t| ||||   ||td|     ||S r  r	  r)  r  r  r  r  r!  r  r  r  r  r  u	     4r  c                 C   V   t |ttttfrdS t| |}t| ||}ttd| | td tdr)dS dS NFr  r  r   T	r:	  r;	  r  r<	  r  r   r   r#   r  r)  r  r  r  r  r  r  r	  r  r  r  r  y	     
"r  c                 C   s   t | |}t| ||}tdt|||  ||d   | td|  |||  |d| |   |||  ||d   | d    | ||t|||  t|||  ||d    d | S )N      ?r  r  )r   r   r  r   r2  r  logr	  r  r  r  r  	  s   
r  c                 C   r	  r	  r	  r	  r  r  r  r  	  r	  r  c                 C   s   t | |}t| ||}t|||  ||d   | t| |||d   |||  ||d   | d    | |t|||  t|d| |  dt|||  ||d    t|d   | S Nr  r	  )r   r   r   r2  r  r  r  r  r	  r  r  r  r  	  s   
r  c                 C   r	  r	  r	  r	  r  r  r  r  	  r	  r  c                 C   s   t | |}t| ||}t|||  ||d   | t| || |d   |||  ||d   | d    | |t|| |  t|d| |  dt|||  ||d    t| d   | S r	  )r   r   r   r2  r  r>   r  r  r	  r  r  r  r  	  s   
r  c
                 C   s   t |	ttttfrdS t| |	}
t| |	|
}tt|
t	d| t
|t	d| |  |
 t	d t	dttt	d| tt|t	dtt	d| t||
t	d t	d|   r^dS dS NFr  r  r   r  Tr:	  r;	  r  r<	  r  r   r   r  rR   r  r$   r  r   r#   r)  r  r  r  r  r  r  r!  r  r  r  r	  r  r  r  r  	  s   
r  c
                 C   sR  t | |	}
t| |	|
}t||	 | |||	|   ||	d|    |  t| ||	|
   |||	d| |
   |d|  |
 d  ||	| |
   |||d   |
 d    ||d| |  |
 d    |	 |	t||d| |
 d   ||	 |d|  |
 d   |||	|   ||	d|    |d   ||d| |  |
 d   |	 S Nr  r  r  r   r   r   r2  r  r	  r  r  r  r  	  s   
> r  c           
      C   s   t |ttttfrdS t| |}t| ||}	tt|t	d| t
t	d| | | t	d t	dttt	d| tt|t	dtt	d| t||t	d t	d|   r\dS dS r	  r	  
r)  r  r  r  r  r!  r  r  r  r	  r  r  r  r  	  s   
r  c           
   
   C   s  t | |}t| ||}	t||||   ||d|    | t| |	||   |	||d| |   d| | d  ||| |   ||d  | d    |d| | | d    | |t|	|d| | d   ||||   ||d|    |d   |d| | | d   | S r	  r	  r	  r  r  r  r  	  s   
 r  c
                 C   s   t | |	}
td}td}tt||  ||	 ||   |||	|   ||	td|    |  t|	||  t| |	|||   t|tdtd| |
 |   t|td|td |	S r}	  r~	  )r)  r  r  r  r  r  r  r!  r  r  r  r  r  r  r  r  r  	  s   
r  c                 C   s   t | |}td}	td}
tt||	 ||||   ||td|    |  t||
|  t| ||	|
|   t|
tdtd|	 | |   t|	td|td |S r}	  r~	  )r)  r  r  r  r  r!  r  r  r  r  r  r  r  r  r  	  s   
r  c	           	      C   r	  r  r   r   r  r	  r  r  r  r  	  r@	  r  c                 C   r	  r  r	  r	  r  r  r  r  	  r	  r  c	           
      C   s   t | |}	tt|| |	 td  ||||    ||td |    |  t||	 t| t|td|  | ||td|  S )Nr  r  r  r	  )
r)  r  r  r  r  r  r!  r  r  r  r  r  r  r  	  s   
r  c
                 C   s   t |}
t| |	}t|
| tt|	|
 || td  td  ||||   |	|
 |    ||td |   |	td |
 |    |  t|	|
|  t| t|	|	|
  |  |	 |	|	||	 td |
  |	 S r	  r	  )r)  r  r  r  r  r  r  r!  r  r  r  r  r  r  r  r  	  s   
r  c
                 C   s   t | |	}
t||	 | td|	 |  tt|	| |
 td  |||	|    ||	td |    |  t|	|
 t| t|	td|	  |	 |	|	td|	 |	 S r 	  r	  )r)  r  r  r  r  r  r  r!  r  r  r  r  r  r  r  	  s   
r  c	           
      C   s   t |}	t|	tt||	|td  td  ||||	|    ||td|	 |    |  t| t|||	  |||td|	  |S r	  r$	  r	  r  r  r  r  	  r	  r  c           	      C   s~   t |}t|tt||td  |||||    ||td| |    |  t| t|||  |||td|  |S )Nr  r  r  r$	  )	r)  r  r  r  r  r!  r  r  r  r  r  r  r  	  s   vr  c
           
   	   C   sf   t ||tdd   t||	  t|	 t| |	|  |||	|   ||	td|    |  |	|	S Nr  r  r  r  r  r   r	  r  r  r  r  	     fr  c
           
   	   C   sf   t ||tdd   t|	 t||	  t| |	|  |||	|   ||	td|    |  |	|	S r	  r	  r	  r  r  r  r  
  r	  r  c
           
   	   C   r	  r  r!	  r	  r  r  r  r  
  r2	  r  c	           	      C   s   t td|td  tt|||||td     ||td| |td     | tt|| | |t||||td    ||||td  |S r	  r	  r	  r  r  r  r  

  r	  r  c
           
   	   C   r	  r  r!	  r	  r  r  r  r  
  r2	  r  c	           
   	   C   s   t td | | |td  td}	ttd| |	 t| || |  |td| ||   |	  ||ttd| |	 t| || |  |td| ||   |	  || S r	  rb	  )
r)  r  r  r  r  r  r  r!  r  r  r  r  r  r  
  s   (r  c              	   C   s   t td | | |td  td}ttd| | t| |td| ||   |  ||ttd| | t| |td| ||   |  || S r	  rb	  )r)  r  r  r  r  r!  r  r  r  r  r  r  
  s   (tr  c
           
      C   r	  r  r	  r	  r  r  r  r  
  r	  r  c                 C   r	  r  r	  r	  r  r  r  r   
  r  r  c
           
      C   s>   t | ||	 |  |||	|   ||	td|    |  |	S r  r	  r	  r  r  r  r  $
  r	  r  c                 C   s2   t | ||||   ||td|    |  |S r  r	  r	  r  r  r  r  (
  rC	  r  c              
   C   sp   t || |	|   t|	|
td tt|
| |||
|   ||
td|    |  t|	| |
 |
|
|	|
S r	  )r  r3   r  r+   r   r  )r)  r  r  r  r  r  r!  r  r  r	  r  r  r  r  r  ,
  r?	  r  c	           	   	   C   s^   t tdt||td tt||||   ||td|    | t|| | ||||S r	  )r  r  r3   r+   r   r  )	r)  r  r  r  r  r!  r  r	  r  r  r  r  r  0
  r/	  r  c                 C   sT   t |td|  | ||  |||   |td   || |  |td   |S r  r	  r  r  r  r  r  r  r  r  r  r  4
  r2	  r  c                 C      t | ||  | td | | |  |td   t||  | ||  |||   |td   ||t|td|  | ||  |||   |td   | | |  |td   | S r  r  r  r   r  r	  r  r  r  r  8
  r	  r  c                 C   s   t || ||  | td  | || td   t|| |  | ||  |||   |  || t|td|  | ||  |||   |td   | || td   | S r  r	  r	  r  r  r  r  <
     r  c                 C   s   t || | |  || td  t|| | ||  |||   |td   || t|| ||  |||   |  || td  | S r  r	  r	  r  r  r  r  @
  s   r  c                 C   s   t | | | |  || td  t|| | ||  |||   |td   ||t|| ||  |||   |  || td  | S r  r	  r	  r  r  r  r  D
  r	  r  c                 C   s   t || | | td || |  |td   t||  | ||  |||   |td   || t|td|  | ||  |||   |td   || |  |td   | S r  r	  r	  r  r  r  r  H
  r	  r  c                 C   r	  r  r	  r	  r  r  r  r  L
  r	  r  c                 C   sn   t | t|| | ||  |||   |td   ||t|| ||  |||   |  || |   | S r6	  r  r   r  r  r	  r  r  r  r  P
  r	  r  c                 C   sh   t tdtd|  tttd|  |td  td  |||t| |td  |||    |S rV	  r  r  r+   r   r  )r  r  r  r  r  r  r  r  T
  rD	  r  c                 C   r	  r  r	  r	  r  r  r  r  X
  r	  r  c              	   C   s   t | | td|  td  ||td   t|||  t| ||  |||    || ttd |td|   t| ||  |||    ||td   | S r	  r  r  r   r  r  )r  r  r  r  r  r  r  r  r  \
  r  r  c              	   C   s   t || t|  | ||| |    t|   | ||  |||   t|  t|||  | ||| |    |  ||S r  )r  r&   r   r	  r  r  r  r  `
     r  c                 C   sF   t tdt||td tt| ||  |||   | ||||S r  )r  r  r3   r+   r   )r  r  r  r  r  r  r  r  r  r  r  d
  rE	  r  c                 C   s>   t td| tt| |||   ||  | |||| |S r  r  r  r  r  r  r  r  r  r  r  r  r  h
  r	  r  c                 C   sp   t ||td  || | | td   | ||  |||   |td   | | |  |td   | S r#	  r	  r  r  r  r  r  r  r  r  r  r  r  r  l
  r?	  r  c                 C      t || | | ||  | td  | | |  |td   t|| | |  | ||  |||   |td   ||t||td  || | | td   | ||  |||   |td   | | |  |td   | S r  r	  r	  r  r  r  r  p
     r  c                 C      t ||||   | | ||  | td  | || | td   t|| | | |  | ||  |||   |  || t||td  || | | td   | ||  |||   |td   | || | td   | S r  r	  r	  r  r  r  r  t
     r  c                 C   X   t |t| |t|   || t|  t|| | ||  |||   |  ||S r  r1	  r	  r  r  r  r  x
  rh	  r  c              	   C   sZ   t td| tt|td|td |   | |||   ||  |  |||| |S r  r  r	  r  r  r  r  |
  r  r  c                 C   r	  r  r1	  r	  r  r  r  r  
  rh	  r  c                 C   s   t |||   | | |  || | td  t|| ||  | ||  |||   |td   || t|| |td  | ||  |||   |  ||| | td   | S r  r	  r	  r  r  r  r  
  r	  r  c                 C   s   t | ||   | | |  |||  td  t|| ||  | ||  |||   |td   ||t|| |td  | ||  |||   |  ||||  td   | S r  r	  r	  r  r  r  r  
  s   r  c                 C   s   t || || | | | td  || |  |td   t|| ||  | ||  |||   |td   || t||td  || || td   | ||  |||   |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   s   t | || |   || | | | td  ||||  td   t|| || |  | ||  |||   |  || t||td  || || td   | ||  |||   |td   ||||  td   | S r  r	  r	  r  r  r  r  
  s   r  c                 C   r	  r  r	  r	  r  r  r  r  
  r	  r  c                 C   sf   t td|td  tt| |||td    ||||td     | ||||td  |S r  r  r	  r  r  r  r  
  r	  r  c                 C   r	  r  r1	  r	  r  r  r  r  
  rh	  r  c                 C   s   t | ||   t|| ||  | ||  |||   |td   ||t|| |td  | ||  |||   |  || | |   | S r#	  r	  r	  r  r  r  r  
  s   r  c                 C   sp   t td | |  tttd|  |td  td  ||||td  t| ||  |||    |S rV	  r	  )r  r  r  r  r  r  r  r  r  r  
  r?	  r  c                 C   r	  r  r	  r	  r  r  r  r  
  r	  r  c                 C   r	  r  r1	  r	  r  r  r  r  
  rh	  r  c              	   C   s   t |t| || t| t|   || t|  | ||| |    t|   | ||  |||   t|  t||| |  | ||| |    |  ||S r  r1	  r	  r  r  r  r  
  r	  r  c	           	   	   C   sX   t || ||   t||td tt|| | ||  |||   |  ||||S r  )r  r3   r  r+   r   )	r  r  r  r  r  r  r  r	  r  r  r  r  r  
  rh	  r  c              
   C   sr   t td| tt|
td|td |   |||
  |	  | |
||   ||
||    |  |
|
|
| |
S r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  
  r|	  r  c                 C   l   t |t| |t|   || t|  t|| ||||   |
  | ||  |||   |	  ||S r  r1	  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  
     lr  c                 C   st   t |||td   ||
 | | td   ||
|  ||
||    |	td   |||	 | td   |
S r#	  r	  r/  r  r  r  r  r  r  r  r  r  r  r  r  r  r  
  r  r  c              	   C   s(  t || || ||	 | td  || || |	||   td    || | |	td   t||
 | |  ||
|  ||
||    |	td   |
|
 t||td  ||
 | | td   | | ||   ||
|  ||
||    |	td   || | |	td   |
 S r  r	  r	  r  r  r  r  
  s   * r  c              	   C   s  t ||  || ||	 | td  || || |	||   td    |||	 | td   t||
 ||  ||
|  ||
||    |	  |
|
t|||td   ||
 | | td   ||
|  ||
||    |	td   |||	 | td   |
 S r  r	  r	  r  r  r  r  
  s    r  c              	   C   s  t || ||	 | td  || || |	||   td   ||| |	||   td   t||
 | ||
|  ||
||    |	  |
|
 t|||td   ||
 | | td   ||
|  ||
||    |	td   ||| |	||   td   |
 S r  r	  r	  r  r  r  r  
  s    r  c                 C   s   t td|td  tt|||
||td     |	 | |
||td    ||
||td     |  |
|
|
|td  |
S r  r  r	  r  r  r  r  
  s   r  c                 C   r	  r  r1	  r	  r  r  r  r  
  r	  r  c                 C   s   t |t| || t|	 t|   || t|  ||||   t|	   |||  ||||    t|	  t|||	 |  ||||   |	  ||||   |
  ||S r  r1	  )r/  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  
  r	  r  c                 C   s   t |}t|tt||td  ||||   ||||    |  tt|| | |t||||   |||td|  |S r#	  )r4   r  r+   r   r  r   r  r  )r)  r  r  r  r  r  r  r  r  r  r  r   
  s   zr   c              	   C   sj   t td| tt|td|td |   ||||   ||  |  t|| | | |||| |S r  r%	  r)  r  r  r  r  r  r  r  r  r  r  r  
  r'	  r  c	           	      C   v   t |t|t|t|  |t|t|   || t|t|  t| ||  |||  |||   |  ||S r  r  r  r  r  r   	r)  r  r  r  r  r  r  r  r  r  r  r  r  
     vr  c	           	      C   H   t ||  || |  t| ||  |||  |||   |  ||S r  r  r	  r  r  r  r  
  rB	  r  c           	      C   s>   t |ttttfrdS t|td |}t|tdrdS dS rK	  rL	  	r)  r  r  r  r  r  r  r  r  r  r  r  r  
  rN	  r  c           	      C   s   t |td |}ttd| tt|td|td |   ||||   ||||    |  t| t||td|   |||| |S r  rO	  r	  r  r  r  r  
  s   ~r  c	              
   C   s   t |ttttfrdS t| |}	t| ||	}
tt|	|t	d t
|||  |	 t	d t	dttt	d| t||	t	d t	d|   rKdS dS )NFr  r  r   r  T)r:	  r;	  r  r<	  r  r   r   r  rQ   r  r$   r  r   r)  r  r  r  r  r  r  r  r  r  r	  r  r  r  r     s   
fr  c	              	   C   s  t | |}	t| ||	}
t|| | |||  |||   |  t| |
| || |	   || |	 d  ||||  |	 d    |
||	   | |t|
|||	 d   || || |	 d   |||  |||   |d   ||||  |	 d   | S r  r	  r	  r  r  r  r  
  s   
r  c                 C   s   t td|td  tt||||td    ||||td     | tt|| | |t||||td    ||||td  |S r  r	  r	  r  r  r  r    r)	  r  c	           	      C   r	  r  r	  r	  r  r  r  r	    r	  r	  c	           	      C   r	  r  r  r	  r  r  r  r
    rB	  r
  c	           	      C   s8   t t| || |  |||  |||   |  ||S r  r+	  r	  r  r  r  r    r  r  c                 C   s,   t t| |||  |||   |  ||S r  r+	  )r)  r  r  r  r  r  r  r  r  r  r  !  r5	  r  c                 C   sr   t tdtd |  | td |   ttd|  ||  | td|  td| |  td|   ||S rg	  rQ	  r  r  r  r  r  r  r  r  r  %  r|	  r  c                 C   s,   t t| ||  ||td   | ||S Nr  r   r2  r  r	  r  r  r  r  )  r5	  r  c                 C   sL   t |ttttfrdS t| ||  ||td   }tt||r$dS dS NFr  T	r:	  r;	  r  r<	  r  r  r  r(   r   r  r  r  r  r  r  r  r  r  r  -      r  c                 C   sH   t | ||  ||td   }tt||| ttt|||||S r	  r  r  r  r   r   r  r   r	  r  r  r  r  6  s    (r  c                 C   s:  t td |  |td  tdttd | ttd| td  |td  td|td  |    td}ttdtd |  |td |   ttd | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   | td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td| | tdtdd  td| | tdtdd  |td    td|   |  ||S N   r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  <  s   x r  c                 C   s   t td|  ||  |  td|  td| |  td |   | ||  ||td   |  ttd|  ||  | td|  td| |  td|   ||S rg	  rQ	  r	  r  r  r  r  A  r  r  c                 C   sL   t |ttttfrdS tt| ||  ||td   |}t|r$dS dS r	  	r:	  r;	  r  r<	  r  r   r  r  r(   r	  r  r  r  r  E     &r  c                 C   sd   t t| ||  ||td   |}t| ||  ||td   | t|| tt||||S r	  r   r  r  r  r  r   r	  r  r  r  r  N  s   &>r  c                 C   s  t td |  |td  tdttd | ttd| td  |td  td|td  |    td}ttd | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |   td| | tdtdd  td| | tdtdd  |td    td|   |   | ||  ||td   |  ttd | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   | td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td| | tdtdd  td| | tdtdd  |td    td|   |  ||S r	  r  r  r  r  r  r   r	  r  r  r  r  T  s
   x  V r  c                 C   s   t tdtd |  | td |   ttd|  ||  | td|  td| |  td|   |||  |  ||S rg	  rQ	  r  r  r  r  r  r  r  r  r  r  r  r  Y  r	  r  c                 C   s<   t t|||  | | ||  ||td   |  ||S r	  r	  r	  r  r  r  r  ]  r  r  c           	      C   sL   t |ttttfrdS t| ||  ||td   }tt||r$dS dS r	  r	  	r  r  r  r  r  r  r  r  r  r  r  r  r  a  r	  r  c           	      C   sX   t | ||  ||td   }tt||| t|||  | tt||| ||S r	  r	  r	  r  r  r  r  j  s    8r  c           	      C   sJ  t td |  |td  tdttd | ttd| td  |td  td|td  |    td}ttdtd |  |td |   t|||  | td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td| | tdtdd  td| | tdtdd  |td    td|   |  ||S r	  r	  	r  r  r  r  r  r  r  r  r  r  r  r  r  p  s   x r  c                 C   s   t td|  ||  |  td|  td| |  td |   | ||  ||td   |  ttd|  ||  | td|  td| |  td|   |||  |  ||S rg	  rQ	  r	  r  r  r  r  u  r	  r  c           	      C   sL   t |ttttfrdS tt| ||  ||td   |}t|r$dS dS r	  r	  r	  r  r  r  r  y  r	  r  c           	      C   st   t t| ||  ||td   |}t| ||  ||td   | t|| t|||  | t|| ||S r	  r	  r	  r  r  r  r    s   &Nr  c           	      C   s  t td |  |td  tdttd | ttd| td  |td  td|td  |    td}ttd | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |   td| | tdtdd  td| | tdtdd  |td    td|   |   | ||  ||td   |  t|||  | td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td | | tdtdd  td| | tdttdt   tdtdd  |td  tdttdt     td|   |  td| | tdtdd  td| | tdtdd  |td    td|   |  ||S r	  r	  r	  r  r  r  r    s
   x  f r  c                 C   st   t tdtd |  |td |   t|td| |  | td| td| |  td|   || S rg	  rQ	  r  r  r  r  r  r  r  r  r    r  r  c                 C   s4   t t| ||td   ||td   | ||S rf	  r	  r	  r  r  r  r     r	  r   c                 C   sT   t |ttttfrdS t| ||td   ||td   }tt||r(dS dS NFr  r  Tr	  r  r  r  r  r  r  r  r  r  r!       (r!  c                 C   sP   t | ||td   ||td   }tt||| ttt|||||S rf	  r	  r 
  r  r  r  r"    s   ((r"  c                 C   sb  t td |  |td  td|td   tdttd | ttd| td  |td  td|  |td     td}ttdtd |  |td |   t|td| |  tdtdd  td|td  tdtdd  |td    td|   | |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  ||S Nr	  r  r  r  r  r	  r  r  r  r  r  r  r  r  r  r#    s    r#  c                 C   s   t |td| |  |  td| td| |  td |   | ||td   ||td   |  t|td| |  | td| td| |  td|   ||S rg	  rQ	  r	  r  r  r  r$    r	  r$  c                 C   sT   t |ttttfrdS tt| ||td   ||td   |}t|r(dS dS r	  r	  r 
  r  r  r  r%       .r%  c                 C   st   t t| ||td   ||td   |}t| ||td   ||td   | t|| tt||||S rf	  r	  r 
  r  r  r  r&    s   .Fr&  c                 C   s  t td |  |td  td|td   tdttd | ttd| td  |td  td|  |td     td}t| ||td   ||td   | |td| |  tdtdd  td|td  tdtdd  |td    td|   |   |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |   |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |   t|td| |  tdtdd  td|td  tdtdd  |td    td|   | |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  ||S r
  r	  r
  r  r  r  r'    s
      r'  c                 C   s   t tdtd |  |td |   t|td| |  | td| td| |  td|   |||  |  || S rg	  rQ	  r  r  r  r  r  r  r  r  r  r  r  r(    r"	  r(  c                 C   sD   t t|||  | | ||td   ||td   |  ||S rf	  r	  r
  r  r  r  r)    r	  r)  c           	      C   sT   t |ttttfrdS t| ||td   ||td   }tt||r(dS dS r	  r	  	r  r  r  r  r  r  r  r  r  r  r  r  r*    r
  r*  c           	      C   s`   t | ||td   ||td   }tt||| t|||  | tt||| ||S rf	  r	  r
  r  r  r  r+    s   (8r+  c           	      C   sr  t td |  |td  td|td   tdttd | ttd| td  |td  td|  |td     td}ttdtd |  |td |   t|||  | |td| |  tdtdd  td|td  tdtdd  |td    td|   |  |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  ||S r
  r	  	r  r  r  r  r  r  r  r  r  r  r  r  r,    s    r,  c                 C   s   t |td| |  |  td| td| |  td |   | ||td   ||td   |  t|td| |  | td| td| |  td|   |||  |  ||S rg	  rQ	  r
  r  r  r  r-    s   r-  c           	      C   sT   t |ttttfrdS tt| ||td   ||td   |}t|r(dS dS r	  r	  r
  r  r  r  r.    r
  r.  c           	      C   s   t t| ||td   ||td   |}t| ||td   ||td   | t|| t|||  | t|| ||S rf	  r	  r
  r  r  r  r/    s   .Vr/  c           	      C   s  t td |  |td  td|td   tdttd | ttd| td  |td  td|  |td     td}t| ||td   ||td   | |td| |  tdtdd  td|td  tdtdd  |td    td|   |   |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |   |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |   t|||  | |td| |  tdtdd  td|td  tdtdd  |td    td|   |  |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  |td| |  tdtdd  td|td  tdttdt   tdtdd  |td  tdttdt     td|   |  ||S r
  r	  r
  r  r  r  r0    s
      r0  c                 C   sD   t td|  ||   ||   t|||  td|  ||S r	  rQ	  r  r  r  r  r  r  r  r  r  r1    r	  r1  c              	   C   s   t td|  ||   ||   tttd|  | | |td  |td |td   | |||td|  | |S r	  r  r
  r  r  r  r2    r	  r2  c                 C   s   t td | | | |td  td}ttd|  ||   ||   t||||   | ||||tdttdt   td    |  ||||tdttdt   td    |  ||S rP	  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r3    s   ,r3  c                 C   s<   t t| ||  ||td   ||td   | ||S rf	  r	  r
  r  r  r  r4    r  r4  c                 C   s\   t |ttttfrdS t| ||  ||td   ||td   }tt||r,dS dS r	  r	  r  r  r  r  r  r  r  r  r  r  r5       0r5  c                 C   sX   t | ||  ||td   ||td   }tt||| ttt|||||S rf	  r	  r
  r  r  r  r6    s   0(r6  c              
   C   s   t tdtd |  |td |   tttd|  |td  td| | |  td|td   td|td  |td   td| | td | | |td    | |||td|  | |S Nr  r  r	  	   r  r
  r  r  r  r7       r7  c                 C   sl   t |||  td |  | ||  ||td   ||td   |  t|||  td|  ||S rg	  rQ	  r
  r  r  r  r8    r	  r8  c              
   C   sd  t td |  | | |td  td}t|||  | |  |||  |tdttdt   td  |   |||  |tdttdt   td  |   | ||  ||td   ||td   |  t|||  | | |||  |tdttdt   td  |  |||  |tdttdt   td  |  ||S rP	  r  r  r  r  r  r   r

  r  r  r  r9       ,: r9  c                 C   sd  t td | | | |td  td}t||||   |  ||||tdttdt   td    |   ||||tdttdt   td    |   | ||  ||td   ||td   |  t||||   | ||||tdttdt   td    |  ||||tdttdt   td    |  ||S rP	  r
  r

  r  r  r  r:  "  r
  r:  c                 C   s\   t |ttttfrdS tt| ||  ||td   ||td   |}t|r,dS dS r	  r	  r
  r  r  r  r;  '     6r;  c                 C   s   t t| ||  ||td   ||td   |}t| ||  ||td   ||td   | t|| tt||||S rf	  r	  r
  r  r  r  r<  0  s   6Nr<  c                 C   s,  t td |  |td  td| | |  td|td   tdttd | ttd| td  |td  td|  | | |  td|  |td   td|td  |  |td |td     td}t|td| |  tdtdd  td | | td|td   tdtdd  |td    td|   |  |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |td  ttdt    td|   |   |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |td  ttdt    td|   |   | ||  ||td   ||td   |  t|td| |  tdtdd  td | | td|td   tdtdd  |td    td|   | |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |td  ttdt    td|   |  |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |td  ttdt    td|   |  ||S 	Nr	  r  r
  r     r  r  r  r	  r

  r  r  r  r=  6  s      L r=  c                 C   r	  r  r	  r	  r  r  r  r>  ;  r		  r>  c	           	      C   sT   t td|  ||   ||   t|||  td|  |||  |  ||S r	  rQ	  	r  r  r  r  r  r  r  r  r  r  r  r  r?  ?  r2	  r?  c	           
   
   C   s   t td |  | | |td  td}	ttd|  ||   ||   t|||  | |||  |	 |  |||  |	tdttdt   td  |  |||  |	tdttdt   td  |  ||S rP	  r	
  
r  r  r  r  r  r  r  r  r  r  r  r  r  r@  C     ,r@  c	           
      C   s   t td | | | |td  td}	ttd|  ||   ||   t||||	   | ||||	tdttdt   td    |  ||||	tdttdt   td    |  |||  |  ||S rP	  r	
  r
  r  r  r  rA  H  r
  rA  c	           	      C   sL   t t|||  | | ||  ||td   ||td   |  ||S rf	  r	  r
  r  r  r  rB  M  r4	  rB  c	           
      C   s\   t |ttttfrdS t| ||  ||td   ||td   }	tt|	|r,dS dS r	  r	  
r  r  r  r  r  r  r  r  r  r  r  r  r  rC  Q  r
  rC  c	           
      C   sh   t | ||  ||td   ||td   }	tt|	|| t|||  | tt|	|| ||S rf	  r	  r
  r  r  r  rD  Z  s   08rD  c	           	   
   C   s   t tdtd |  |td |   tttd|  |td  td| | |  td|td   td|td  |td   td| | td | | |td    | |||td|  | |S r
  r  r
  r  r  r  rE  `  r
  rE  c	           	      C   s|   t |||  td |  | ||  ||td   ||td   |  t|||  td|  |||  |  ||S rg	  rQ	  r
  r  r  r  rF  d  s   |rF  c	           
   
   C   st  t td |  | | |td  td}	t|||  |	 |  |||  |	tdttdt   td  |   |||  |	tdttdt   td  |   | ||  ||td   ||td   |  t|||  | |||  |	 |  |||  |	tdttdt   td  |  |||  |	tdttdt   td  |  ||S rP	  r
  r
  r  r  r  rG  h     ,J rG  c	           
      C   st  t td | | | |td  td}	t||||	   |  ||||	tdttdt   td    |   ||||	tdttdt   td    |   | ||  ||td   ||td   |  t||||	   | ||||	tdttdt   td    |  ||||	tdttdt   td    |  |||  |  ||S rP	  r
  r
  r  r  r  rH  m  r
  rH  c	           
      C   s\   t |ttttfrdS tt| ||  ||td   ||td   |}	t|	r,dS dS r	  r	  r
  r  r  r  rI  r  r
  rI  c	           
      C   s   t t| ||  ||td   ||td   |}	t| ||  ||td   ||td   | t|	| t|||  | t|	| ||S rf	  r	  r
  r  r  r  rJ  {  s   6^rJ  c	           
      C   s<  t td |  |td  td| | |  td|td   tdttd | ttd| td  |td  td|  | | |  td|  |td   td|td  |  |td |td     td}	t|td| |  tdtdd  td | | td|td   tdtdd  |	td    td|	   |  |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |	td  ttdt    td|	   |   |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |	td  ttdt    td|	   |   | ||  ||td   ||td   |  t|||  | |td| |  tdtdd  td | | td|td   tdtdd  |	td    td|	   |  |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |	td  ttdt    td|	   |  |td| |  tdtdd  td | | tdttdt   td|td  tdttdt    tdtdd  t |	td  ttdt    td|	   |  ||S r
  r	  r
  r  r  r  rK    s      \ rK  c                 C   r
	  r  r	  r	  r  r  r  rL    r	  rL  c                 C   s   t | | t| | |td  | |  |td| td  td|  |  |td    tdt| |td  |  ||td   ||  ||td    t| td td|  |  td   |t| td td|  |  td  |S Nr  r  r  )r  r>   r  r  r  r	  r  r  r  rN    s   rN  c                 C   s   t | | t| | |td  | |  |td| td  td|  |  |td    tdt| |td  |  ||td   ||  ||td    t| td  td|  |  td   |t| td  td|  |  td  | S r
  )r  r  r  r  r  r	  r  r  r  rO    s    rO  c              
   C   s   t tt| || td|   |td td|td    ||td   |td |td|td  td|     | ||||td|  | S Nr  r     r  r  )r+   r   r-  r  r  r  r  r  r  r  r  r  r  r  rP    r	  rP  c                 C   s   t |ttttfrdS t||td}t||td}t||td}t||td}t||td}tttd| |td  td| | |  |td  t	|rXdS dS 	NFr   r  r  r  r  r  T
r:	  r;	  r  r<	  r  r3   r  r  r   r   r  r	  r  r  r  r  r  r  r  r  r  rQ       FrQ  c              
   C   s   t ||td}t ||td}t ||td}t ||td}t ||td}ttt||| td|   |td td|td    ||td   |td |td|td  td|     |  ||||td|  | S Nr   r  r  r  r  r  r
  )r3   r  r+   r   r-  r 
  r  r  r  rR    s   rR  c                 C   s   t tt| || td|   |td td|td    ||td   |td |td|td  td|     | t|t|| td|  |  ||||td|  | S r
  )r+   r   r-  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  rS    s   rS  c           	      C   s   t |ttttfrdS t||td}t||td}t||td}t||td}t||td}tttd| |td  td| | |  |td  t	|rXdS dS r
  r
  	r  r  r	  r  r  r  r  r  r  r  r  r  rT    r!
  rT  c           	      C   s  t ||td}t ||td}t ||td}t ||td}t ||td}ttt||| td|   |td td|td    ||td   |td |td|td  td|     |  t|t|| td|  |  ||||td|  | S r"
  )r3   r  r+   r   r-  r   r  r#
  r  r  r  rU    s   rU  c                 C   sN  t td | td  tt| td| td  |td  td| td  |  td| td  | |  td| td  |td  td |  | td|td     td|  |td  |  td|td    td |  | | td  | td |  | | td  ||td	| |td|    |S )
N   r  r
  r  r  @       r  r  r  r
  r  r  r  rV    s   P rV  c                 C   s   t |ttttfrdS t||td}t||td}t||td}t||td}t||td}tt|t|t	td|td  | td| | |  |td  r[dS dS r
  )
r:	  r;	  r  r<	  r  r3   r  r  r   r   r 
  r  r  r  rW    s   LrW  c                 C   s  t ||td}t ||td}t ||td}t ||td}t ||td}ttd |td  tt|td|td  |td  td|td  |  td|td  | |  td	|td  |td  td
 | | td|td     td| |td  |  td|td    td | | | td  |  td | | | td  ||td| |td|   |S )Nr   r  r  r  r  r$
  r
  r%
  r&
  r  )r3   r  r  r+   r   r 
  r  r  r  rX    s   P rX  c
              	   C   s  t td|td  td| |  |td  }
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d| |  |	td|  | td| |  ||  ||
    td| |	td  td|  |	||
    |	|	 S Nr  r  r  r  r  r  r  r   )r  r  r  r  r  r  r  r  r  r  r  r  r  r  rY    s   4X rY  c	           
   	   C   sj  t td|td  td| |  |td  }	ttd|	 t| | | |	  td| |  td| |  |td|  | ||  ||	    td| |td  td|  |||	    || ttd|	 t| | | |	  td| |  td| |  |td|  | ||  ||	    td| |td  td|  |||	    || S r'
  r(
  )
r  r  r  r  r  r  r  r  r  r  r  r  r  rZ    s   48 rZ  c              
   C   s  t td|td  td| |  |td  }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d| |  |
td|  | td| |  ||  ||     td| |
td  td|  |
||    |
|
 S r'
  r(
  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r[    s   4h r[  c
              
   C   sz  t td|td  td| |  |td  }
ttd|
 t|	| | | | |
  td| |  td| |  |	td|  | ||  ||
     td| |	td  td|  |	||
    |	|	 ttd|
 t|	| | | | |
  td| |  td| |  |	td|  | ||  ||
     td| |	td  td|  |	||
    |	|	 S r'
  r(
  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r\    s   4H r\  c	           
   
   C   s  t ||td | | |td   td| td |  | ||     td}	ttd |td  t| | ||  td| | |  |	  |	 |ttd|td  t|td|  | | td|  | |  td|td  |  td| | |  td|td  | |td   td| |td  | | td| |    td| | td|  | ||  td| |     |	td |  | |td     |	 | S Nr  r     r  r  r  r  r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r]    s   Vz r]  c           	   
   C   s  t |td |  |td  |td | | |td     td}ttd |td  t||td| |   |  | |ttd|td  t|| | td| | |td   td| | |td   td| | | ||     | |   | | S Nr  r  r  r  r+
  	r  r  r  r  r  r  r  r  r  r  r  r  r^    s   Jr^  c	           
   
   C   s  t | |td | | |td   td| td |  | ||     td}	ttd|td  t| | ||  td| | |  |	  |	 |ttd|td  t|td|  | | td|  | |  td|td  |  td| | |  td|td  | |td   td| |td  | | td| |    td| | td|  | ||  td| |     |	td |  | |td     |	 | S r)
  r  r  r  r>   r,
  r  r  r  r_    s   Xx r_  c           	   
   C   s  t | td |  |td  |td | | |td     td}ttd|td  t|| td| | |  |  | |ttd|td  t| |  | td| | |td   td| | |td   td| | | ||     | |   | | S r-
  r/
  r.
  r  r  r  r`    s   Lr`  c
           
   	   C   s   t tdtd|  ttd |  | ||  |	td td | | td| |    td|	 td | | ||    |||	  ||	td   ||	td   ||	td    |	|	 t|t|||	  ||	td   ||	td   ||	td    td|  |	 S Nr  r  r  r  r  r  r   r  r	  )
r  r  r  r  r  r  r  r  r  r  r  r  r  ra    s   " ra  c	           	   	   C   s  t tdtd|  ttd |  | ||  td| | |td   td| td | | ||    |||  ||td   ||td   ||td    || t|t|||  ||td   ||td   ||td    td|  | S )Nr  r  r  r  r1
  )	r  r  r  r  r  r  r  r  r  r  r  r  rb    s    rb  c              	   C   sz   t | ||  | ||    t|t|||   | || t |||  | ||    t|t| ||   | || S r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  rc    s   zrc  c              	   C   sp   t |||  | ||    t|t|||   ||t |||  | ||    t|t| ||   || S r  r2
  r3
  r  r  r  rd    r?	  rd  c                 C   s   t |t|t| ||   | |td  ||td   |||td  ||td      ||t |t|t|||   | |td  ||td   |||td  ||td      || S r  r  r   r  r  r3
  r  r  r  re    s   re  c              
   C   s\   t td| |  t|t| ||td|     ||t || |  t|||  || S r	  )r  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  rf    r  rf  c                 C   s   t |t|| t| ||td|     | |td  |td|  ||td  |td     ||t |t|||  | |td  |td|  ||td  |td     || S r  r4
  r  r  r  r  rg  #  s   rg  c                 C   s   t t| | td}t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 |td     || S rP	  rx   r  r  r4   r  r   r  r  r  r  r  r  r  r  r  r  r  r  rh  '  s   rh  c                 C   s   t t| | td}t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 |td     || S rP	  r5
  r  r  r  r  r  r  r  r  r  r  ri  -  s   ri  c                 C   s   t t|  | td}t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 |td     || S rP	  r5
  r6
  r  r  r  rj  3  s   rj  c                 C   s   t t|  | td}t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 |td     || S rP	  r5
  r7
  r  r  r  rk  9  s   rk  c                 C   s   t |ttd|td |td |td   t| ||td   ||td     ||t |t||td |td |td   t| ||td   ||td     || S Nr  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  rl  ?  r	  rl  c                 C   s   t |ttdt| ||td   |td |td |td     ||t |t|t| ||td   |td |td |td     || S )Nr  r  r  r9
  r  r  r  r  r  r  r  r  rm  C  r	  rm  c              
   C   s  t || |td  ||td  |td   ||td    t|td |td |td   t| ||td   ||td    || t|td t| ||td   ||td    |||  | |td  ||td  |td   ||td     | S )Nr  r  r  r	  r:
  r  r  r  rn  G  s    rn  c                 C   s  t || |td  ||td  |td   ||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d    ttd|||  t| ||td   ||td     || t|td t| ||td   ||td    |||  | |td  ||td  |td   ||td     | S Nr  r  r  r  r	  r:
  r  r  r  ro  K  s    ro  c                 C   s0  t || |td  ||td    t|td |td |td   t| ||td    || t td| |td  | |td  ||td    ttdt| ||td   |||    || t|td t| ||td    |||  | |td  ||td     | S r<
  r	  r;
  r  r  r  rp  O  s   2 rp  c                 C   sp   t | tttd||td td | | ||     |||t|||td   ||td    |S r8
  r  r+   r   r  r  )r  r  r  r  r  r  r  r  r  r  r  rq  S  r?	  rq  c                 C   sV   t | tttdtd| | |td  |  |||t|||td    |S r8
  r=
  )r  r  r  r  r  r  r  r  r  r  rr  W  s   Vrr  c	           	      C   sh   t | tttd||td | | ||     |||t|||td   ||td    |S r8
  r=
  )	r  r  r  r  r  r  r  r  r  r  r  r  rs  [  rD	  rs  c                 C   sN   t | tttd|| |td  |  |||t|||td    |S r8
  r=
  )r  r  r  r  r  r  r  r  r  r  r  rt  _  r  rt  c                 C   s`   t | tttd| | |td  |  |||t|||td   ||td    |S r8
  r=
  )r  r  r  r  r  r  r  r  r  r  r  ru  c  r	  ru  c                 C   s   t | | tttdtd | |td  |td td |  | |td    td  |||t| ||td   ||td    |S r8
  r=
  r:
  r  r  r  rv  g     rv  c                 C   s  t td |  | |td  }tt td|  t | |  tt td| t | |  |td| |td   |  tdt | ||td   ||td    t|  | td   td| t|  | td  |tt td|  t ||  tt td| t ||  |td| |td   |  tdt | ||td   ||td    t|  | td   td| t|  | td  | S r	  )r  r  r  r  r  r>   )r  r  r  r  r  r  r  r  r  r  rw  k  s   " rw  c                 C   s   t | ttd| td |td |td   t|||td    t|||td     ||t |t|| td |td |td   t|||td    t|||td     || S r	  r9
  )r  r  r  r  r  r  r  r  r  r  rx  p  s   rx  c	           	      C   s  t tdt|||  |t| ||  ||td      td|td  | | | |td  td|td  | |td  |td   || | | |td  || |  td| |td     |td|  | |td  td|  | | |  td|td  | |  td| | |td     | | ||  t| ||  ||td    td | | td| |  || |     td|td  | |||    |S )Nr  r
  r  
         r 	  r	  r  r  r  ry  t  s    ry  c
           
      C   sB   t |||	  | | | tt||	 t| | | |	 |  |	S r  r   r  r2  )
r  r  r  r  r  r  r  r  r	  r  r  r  r  rz  x  r	  rz  c                 C   s   t tdtt|||
|   |	 |td | ||
td   |td |  | ||    |
| |td  td| |     ||td  td| |  td| |
  td  |
|
|||
  |t| ||
  ||
td     |
S r  r	  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r{  |  s   r{  c
           
      C   s   t tdtd|  tt|||	|   | | |td  |td  td| |	  |	td   ||	 td  |	|	|||	  |t| ||	td     |	S r	  r	  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r|    s   r|  c                 C   s2   t ||| tt|| t|| |   | |S r  rB
  )r  r  r  r  r  r  r	  r  r  r  r  r}    rC	  r}  c	           	      C   s   t td| td  || td   tt|| | td  | |td  |td   |  |td  | td| | |  ||td   |  |||| |t| ||td     |S )Nr  r  r  r	  )	r  r  r  r  r  r  r  r  r  r  r  r  r~    s   r~  c
           
      C   s   t tdtd | | td  || td   |td |   || |  tt|	td | | | td  |  |td  |	td  |  | |td  |	td  td| td   |	|	||	 |t| ||	td     |	S Nr  r  r  r  r	  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   r  c                 C   s*  t td|td |	   || |	  tt||
 ||td  td| |  td| |  td |	 td   |td | ||td   |td |  | ||    || |td  td| |    td|	 td   |||||  |t| ||  ||td     |S r	  r	  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   , r  c
           
      C   s   t tdtd | td  |td |   || |  | tt|	| | |	 td | td   | |td  |td  td| |	  |	td  td| td   |	|	|||	  |t| ||	td     |	S rC
  r	  
r  r  r  r  r  r  r  r  r  r  r  r  r  r    r	  r  c                 C   s   t || |	tdd   t|||  ||td    t| ||  ||td    t| ||  ||td   |	 |||  |t| ||  ||td     |
  ||S r	  r	  rD
  r  r  r  r    r	  r  c
           
      C   s   t || |tdd   t|||	td    t| ||	td    t| ||	td   | |||	  |t| ||	td     |  |	|	S r	  r	  rE
  r  r  r  r    r>
  r  c                 C   s   t || |	tdd   t| ||  ||td    t|||  ||td    t| ||  ||td   |	 |||  |t| ||  ||td     |
  ||S r	  r	  rD
  r  r  r  r    r	  r  c
           
      C   s   t || |tdd   t| ||	td    t|||	td    t| ||	td   | |||	  |t| ||	td     |  |	|	S r	  r	  rE
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  r  c	           	      C   s@   t | | tt|| t| | | | | t|||  |S r  rB
  )	r  r  r  r  r  r  r	  r	  r  r  r  r  r    r@	  r  c                 C   st   t td|  tttd| |td  td  |||t||td  || |||   td|     |S r	  r	  )r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t td|  | t| |t|||td      |t td|td  | |td  td| |t|||td     tdd    | S rf	  r 	  rz	  r  r  r  r    r	  r  c                 C   sj   t ttd| |  tttdttd|td |    ||| | |t|||td     |S rV	  )r  r  r  r+   r   rz	  r  r  r  r    r'	  r  c              
   C   s^   t t| | |td  || | t|||td     |t|||td     |S r  )r   r  r  r:
  r  r  r  r    r/	  r  c                 C   sp   t |tttdtd | |td  td  |||t||td  |t| ||td      |S r8
  r=
  rz	  r  r  r  r    r?	  r  c                 C   s   t tdd ttd  t|||  | tt| t| |td    ||t tdd ttd  t|||  | tt| t| |td    || S r	  )r  r  r  r   r  )r  r  r  r  r  r  r  r  r  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|| | |tdttd    ttdt| ||td    || S rv	  r  r  r  r  r   ry	  r  r  r  r       r  c                 C   s   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tdt| ||td    || S rv	  rF
  ry	  r  r  r  r       r  c                 C   s   t | |  td}t||| |tdttd    t| | ttd td t| ||td   |||    ||t||| |tdttd    ttdt| ||td    || S rv	  rF
  ry	  r  r  r  r    rH
  r  c                 C   s   t ||  td}t|| | |tdttd    t|| ttd td t| ||td   |||    ||t|| | |tdttd    ttdt| ||td    || S rv	  rF
  ry	  r  r  r  r    rG
  r  c                 C   V   t |ttttfrdS t||  td}t| | |tdttd   r)dS dS NFr  r  T	r:	  r;	  r  r<	  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r       &r  c                 C   s  t ||  td}ttdtdtdd   | t|td |td  ||  td || td ttd td   ttdttd  || td  |t|| td || td ttd td   t| ||td     tttdttd|td  t|td tdttd  td  | | |tdttd   || | |tdttd       ||| | td ttd || td ttd  |S Nr  r  r  r     r  r  r  r  r  r+   r   rL
  r  r  r  r    s    r  c                 C   rI
  rJ
  	r:	  r;	  r  r<	  r  r  r  r   r  rL
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  r  c                 C   s   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td    ttdt| ||td    || S rv	  rF
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  rK
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  r  r  r  r       $r  c                 C   s  t | |  td}ttd tdtdd   | t|td |td  ||  td | | td ttd td   ttdttd  | | td  |t| | td | | td ttd td   t| ||td     tttdttd|td  t|td tdttd  td  || |tdttd   ||| |tdttd       |||| td ttd | | td ttd  |S rN
  rP
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  r  r  r  r        r  c                 C   rS
  rJ
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  r  c                 C   s   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td    ttdt| ||td    || S rv	  rF
  rL
  r  r  r  r       r  c                 C   V   t |ttttfrdS t| |  td}t|| |tdttd   r)dS dS rJ
  rK
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  r  r  r  r    rT
  r  c                 C   s  t | |  td}ttdtdtdd   | t|td |td  ||  td | | ttd td td   tttdtd  | | td  |t| | td  | | ttd td td   t| ||td     tttdttd|td  t|td tdttd  td  || |tdttd   ||| |tdttd       ||| | td ttd || td ttd  |S rN
  rP
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  r  r  r  r    rU
  r  c                 C   rW
  rJ
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  r  r  r  r  #  rT
  r  c                 C   s   t | |  td}t| | ||  || |tdttd    t| | ttd td t| ||td   |||    ||t|| |tdttd   || |tdttd    ttdt| ||td    || S rv	  rF
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  r  r  r  r  ,  rV
  r  c                 C   V   t |ttttfrdS t||  td}t| | |tdttd   r)dS dS rJ
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  r  r  r  r  2  rM
  r  c                 C   s  t ||  td}ttd tdtdd   | t|td |td  ||  td || ttd td td   tttdtd  || td  |t|| td  || ttd td td   t| ||td     tttdttd|td  t|td tdttd  td  | | |tdttd   || | |tdttd       |||| td ttd | | td ttd  |S rN
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  r  r  r  r  ;  s    r  c                 C   rX
  rJ
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  rL
  r  r  r  r  A  rM
  r  c                 C   s   t ||  td}t| | ||  | | |tdttd    t|| ttd td t| ||td   |||    ||t| | |tdttd   | | |tdttd    ttdt| ||td    || S rv	  rF
  rL
  r  r  r  r  J  rR
  r  c                 C   s^   t td| tt|td|td |   |||  |t| ||     |||| |S r  r	  )r  r  r  r  r  r  r  r  r  r  r  r  P  r/	  r  c              
   C   s   t |t||  |td  |td  || ||    ||t | | t|t| |||   |  |td  |td  || ||     || S r  r9
  )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d | |td  |td td  |  |||| |td  |||    |S )Nr  r  r  r  )	r  r  r  r  r  r  r  r!  r  r  r  r  r  X  r	  r  c                 C   s   t | td || td  |td  tttd| td | |
td  || td td  |  |
|
|
|td  | || td  ||
|  |td    |
S rV	  r  )r  r  r  r  r  r  r  r  r  r!  r  r  r  r  r  \  s   r  c                 C   s  t td| | | |
td  td |  | |td    t| |||   ||td|    |
td  t| | | | ||   td|  | | | || td| |
td  td     |td | | ||
 | td   || | |td  | ||
td  td  td|  | | | |td  || |td|
 td  td     || | | ||   |td|
 td  td     | || t|| |||   ||td|    |
td   |  | | | ||   td|  | |  | ||    |td | |  || |  |td  | td|  | |  | ||    || | | ||       | | | |
td  td |  | |td    | S r0
  r	  r	  r  r  r  r  `  s     r  c
           
      C   s4  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d |  | | |td| td  td  || | ||   |td| td  td     |	 |	|	 t|	| ||	|   ||	td|    |td   |  | | td|  |  | ||    |td |  |	| td |  | | || | ||       | | |td  td |  | |td    |	 S r0
  r	  r	  r  r  r  r  d  s    8 r  c                 C   s  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d   |
| | |td  | ||	td  td  td|  | | | |td  || |td|	 td  td     ||td  | |td|	 td  td     |
 |
|
 t|
| ||
|   ||
td|    |	td   |  | | | ||   td|  |td  |  |td | |  |
| |  |td  | td|  | |  | ||    ||td  |     | | | |	td  td |  | |td    |
 S r0
  r	  r	  r  r  r  r  h  s     r  c                 C   s  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d   |
| td | td  | | |td  | |td  | ||	td  td   || | | ||   |td|	 td  td     |
 |
|
 t|
| ||
|   ||
td|    |	td   | td  | | td|  | |  | ||    |td | |  |
| td| td  | | | |td  |  || | | ||       | | | |	td  td |  | |td    |
 S r0
  r	  r	  r  r  r  r  l  s     r  c	           	      C   s  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d| td  td   | ||t|| |||   ||td|    |td   td |  |  | ||   |td |  |||  | | ||     | | |td  td |  | |td    | S r0
  r	  r	  r  r  r  r  p  s    r  c
           
      C   s  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d | | || | td   |	| td | td  | | |td  | |td  | ||td  td   ||td  | |td| td  td     |	 |	|	 t|	| ||	|   ||	td|    |td   | td  | | td|  |td  |  |td | |  |	| td| td  | | | |td  |  ||td  |     | | | |td  td |  | |td    |	 S r0
  r	  r	  r  r  r  r  t  s     r  c                 C   s  t td 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d| |	td  td     |
 |
|
 t|
 | ||
td|    |	td   td |  | |
|  |  | ||   td|  | |  | ||     td| td  |td  | |	td   |
 S r0
  r	  )r  r  r  r  r  r  r  r!  r(  r  r  r  r  r  r  x  s    r  c	           	      C   st  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d  td     | || t| | ||td|    |td   td |  | | ||  td|  |  | ||     td| td  | | |td   | S r0
  r	  )	r  r  r  r  r  r  r!  r  r  r  r  r  r  |  s   v r  c
           
      C   s  t td 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d  || |td| td  td     |	 |	|	 t|	 | ||	td|    |td   td |  |td  | td|  | |	|  |  | ||     td| td  |td  | |td   |	 S r0
  r	  )
r  r  r  r  r  r  r!  r(  r  r  r  r  r  r    s    r  c           
      C   s,  t td| td  |td  | | |td   |td |  | | td|td  |    || |  | td| |    td}t | | |td  |td|  | | td|td  |    td| | td | || |    || |  | td| |    td}	t|t|	td|  |  ||  | t|t|	td|  |  ||  | t|t||  | td| |   td| td  | |td  td| td  | | |  | |td  | |  ||td  | |  |td | |td  |  | td| |    ||td  td| td  |td  | | |td   || | |  td|td  | |     || td | td  | || |   td| td  | | | |  || |     ||  | S )Nr*
  r  r  r  r  r/
  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r    s
     r  c           	      C   sP  t td| td  |td  | | |td   td|td  | |  || |  | td| |    td}t td| td  |td  | | |td   td|td  | |  || |  | td| |    td}t|t|td|  |  ||  | t|t|td|  |  ||  | t|t|| |  | td| |   td| td  | | || |td  |  | td| |    |td td| td  |td  | | |td   td|td  | |     td| td  |td  |   ||  | S )Nr*
  r  r  r  r  r/
  )	r  r  r  r  r  r  r  r  r  r  r  r  r    s   ||Z r  c           	   	   C   s8  t |ttttfrdS z~t||}t||}t||||||   td t|||  }t||||||   td t|||  }t| |||   ||| td  || td  t	||   | |}t
ttdt|t|td t|||   tdtt|||}W n ttfy   Y dS w |rdS dS )NFr  r  T)r:	  r;	  r  r<	  r  r   r3   r  r   r  r  r  rP   rO   r   r  	TypeErrorAttributeError)	r  r  r	  r  r  r  r  r	  resr  r  r  r    s   

,,JFr  c                 C   s  t ||}t ||}t||||||   td t|||  }t||||||   td t|||  }t| |||   ||| td  || td  t||   | |}ttt|||| d   ||| d   ||| d   ||| d   t||  | | |S r  )	r   r3   r  r   r  r  r  r   r   )r  r  r	  r  r  r  r  r	  r  r  r  r    s   

,,J`r  (5  __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$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  expr  r	  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $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  Pir*  r0  C_F_G_H_r  b_r  r  r	  rM  r  h_i_r  k_l_r  r  r  r  r_t_r  r  r  r  r  y_r  r  r  b1_b2_c1_c2_d1_d2_n1_r  e1_e2_f1_f2_g1_g2_r  r  Pm_r  Qm_Qr_Qx_jn_mn_non2_RFx_RGx_r  rn	  r	  rH	  rI	  r  r  r  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  r  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r+  r,  r-  r.  r/  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  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  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  <module>   s              n"JjB.
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
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								