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Z
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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)Add)Mod)Mul)
EulerGamma)FloatIInteger)Pow)S)Abssign)sqrt)Integral)AndOr)simplifyWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  H/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rules/secant.py
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tttttdtdtttd
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}<tttttdtdtttdtd tdtd   tttdtd tdtd  tŃ||||| }=tɐ|=t}>ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ||||| ||*|+	}?tɐ|?t}@ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ||||| ||*|+	}Atɐ|At}Btttdttdtdtttdtd tdtd   tttdtd tdtd   tŃ||||| }Ctɐ|Ct}Dtttdttdtdtttdtd tdtd   tttdtd tdtd   tŃ||||| }Etɐ|Et}Ftttdtttdtdtttdtd tdtd   tttdtd tdtd   tŃ||||| }Gtɐ|Gt}Htttdtttdtdtttdtd tdtd   tttdtd tdtd   tŃ||||| }Itɐ|It}Jttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ||||| ||,|+	}Ktɐ|Kt}Lttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ||||| ||,|+	}Mtɐ|Mt}Nttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||| ||,}Otɐ|Ot}Pttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||| ||,}Qtɐ|Qt}Rttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||| |-}Stɐ|St}Tttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||| |-}Utɐ|Ut}Vttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||| ||,}Wtɐ|Wt}Xttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||| ||,}Ytɐ|Yt}Zttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||| |-}[tɐ|[t}\ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||| |-}]tɐ|]t}^ttttd
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}itɐ|it!}jtttttdtdtttdtd tdtd   ttd
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}tɐ|t0}tttd
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}tɐ|t1}tttd
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tdtttdtd tdtd  t ttdtdtttdtd tdtd    tŃ|||||| ||8	}tɐ|t@}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tŃ|||||| ||8	}tɐ|tA}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tŃ||||||| }tɐ|tB}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tŃ||||||| }tɐ|tC}tttd
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tdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    tŃ|||||| }tɐ|tE}tttd
tdtttdtd tdtd  t tttdtdtttdtd tdtd    tŃ|||||| ||&|
}tɐ|tF}tttd
tdtttdtd tdtd  t tttdtdtttdtd tdtd    tŃ|||||| ||&|
}tɐ|tG}tttd
tdtttdtd tdtd  t tttdtdtttdtd tdtd    tŃ|||||| ||8|
}tɐ|tH}tttd
tdtttdtd tdtd  t tttdtdtttdtd tdtd    tŃ|||||| ||8|
}tɐ|tI}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ||||||| ||&|5|9}tɐ|tJ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ||||||| ||&|5|9}tɐ|tK}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ|||||||| ||#||.}tɐ|tL}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ|||||||| ||#||.}tɐ|tM}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ|||||||| ||#||:}tɐ|ÐtN}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ|||||||| ||#||:}tɐ|ŐtO}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   t  tŃ|||||||| ||#}tɐ|ǐtP}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   t  tŃ|||||||| ||#}tɐ|ɐtQ}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   t  tŃ|||||||| ||$}tɐ|ːtR}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   t  tŃ|||||||| ||$}tɐ|͐tS}tttttdtdtttdtd tdtd   tttdtd tdtd  tŃ|||||%}tɐ|ϐtT}tttttdtdtttdtd tdtd   tttdtd tdtd  tŃ|||||%}tɐ|ѐtU}ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ|||||%|||+	}tɐ|ӐtV}ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ|||||%|||+	}tɐ|ՐtW}tttdttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||%}tɐ|אtX}tttdttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||%}tɐ|ِtY}tttdtttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||%}tɐ|ېtZ}tttdtttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||%}tɐ|ݐt[}ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ|||||%|||+	}tɐ|ߐt\}ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ|||||%|||+	}tɐ|t]}ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ||||||%|;}tɐ|t^}ttttdtdtttdtd tdtd   t tttdtd tdtd  tŃ||||||%|;}tɐ|t_}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||%||<}tɐ|t`}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||%||<}tɐ|ta}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||%||}tɐ|tb}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||%||}tɐ|tc}tttdtttdtdtttdtd tdtd   tttdtd tdtd td   tŃ|||||%}tɐ|td}tttdtttdtdtttdtd tdtd   tttdtd tdtd td   tŃ|||||%}tɐ|te}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||||%}tɐ|tf}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||||%}tɐ|tg}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||%||}tɐ|th}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ|||||%||}tɐ|ti}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||||%|=}tɐ|tj}ttttdtdtttdtd tdtd   t tttdtd tdtd td  tŃ||||||%|=}tɐ|tk}tttd
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}tɐ|tl} tttd
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}tɐ|tm}tttd
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tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tŃ||||||%|||6|}tɐ|tr}tttd
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}tɐ|tt}tttd
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}tɐ|tu}tttd
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tdtttdtd tdtd  t ttdtdtttdtd tdtd    tŃ||||||%||E	})tɐ|)t}*tttdttd
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}/tɐ|/t}0tttd
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}1tɐ|1t}2ttttd
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}7tɐ|7t}8tttd
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}9tɐ|9t}:tttttdtdtttdtd tdtd   ttd
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}?tɐ|?t}@tttd
tdtttdtd tdtd  t tttdtdtttdtd tdtd    tŃ||||||%||!|
}Atɐ|At}Bttttd
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tdtttdtd tdtd   t  tŃ|||||||||g|N|9|l}}tɐ|}t.}~ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tŃ|||||||||g|c|m|l}tɐ|t/}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tŃ|||||||||g|c|m|l}tɐ|t0}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tŃ|||||||||g||;}tɐ|t1}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tŃ|||||||||g||;}tɐ|t2}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tŃ|||||||||X
}tɐ|t3}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tŃ|||||||||X
}tɐ|t4}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   td	td  tŃ|||||||||n
}tɐ|t5}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   td	td  tŃ|||||||||n
}tɐ|t6}tttd
tdtttdtd tdtd  t tdtdtdtdtttdtd tdtd   tdtd  tŃ||||||||N	}tɐ|t7}tttd
tdtttdtd tdtd  t tdtdtdtdtttdtd tdtd   tdtd  tŃ||||||||N	}tɐ|t8}tttd
tdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd   tdtd  tŃ|||||||||P|}tɐ|t9}tttd
tdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd   tdtd  tŃ|||||||||P|}tɐ|t:}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||||`| |3|o}tɐ|t;}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||||`| |3|o}tɐ|t<}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||||`| |p|o|q|r}tɐ|t=}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||||`| |p|o|q|r}tɐ|t>}tttttd
tdtttdtd tdtd   tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||`| 	}tɐ|t?}tttttd
tdtttdtd tdtd   tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||`| 	}tɐ|t@}ttttdtdtttdtd tdtd   tdtd tttd
tdtttdtd tdtd    tttdtd tdtd  tŃ||||||||`| |s}tɐ|tA}ttttdtdtttdtd tdtd   tdtd tttd
tdtttdtd tdtd    tttdtd tdtd  tŃ||||||||`| |s}tɐ|tB}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||`| |t||,}tɐ|tC}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||`| |t||,}tɐ|tD}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||`| |t|-|u}tɐ|tE}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||`| |t|-|u}tɐ|tF}ttttd
tdtttdtd tdtd   td	td tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||`| |X
}tɐ|tG}ttttd
tdtttdtd tdtd   td	td tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||`| |X
}tɐ|tH}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||`| |X|,|+}tɐ|tI}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ|||||||`| |X|,|+}tɐ|tJ}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ||||||||`| |v|w|x}tɐ|tK}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   td	td  tttdtd tdtd  tŃ||||||||`| |v|w|x}tɐ|tL}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||`| |c
}tɐ|tM}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||`| |c
}tɐ|tN}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||`| |y}tɐ|tO}ttttdtdtttdtd tdtd   t ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||`| |y}tɐ|tP}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||||`| }tɐ|ÐtQ}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||||`| }tɐ|ŐtR}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   tdtd  ttd
tdtttdtd tdtd   td	td  tŃ|||||||O||P|`| |v|w|x}tɐ|ǐtS}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   tdtd  ttd
tdtttdtd tdtd   td	td  tŃ|||||||O||P|`| |v|w|x}tɐ|ɐtT}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  ttd
tdtttdtd tdtd   t  tŃ|||||||O|P|`| |c}tɐ|ːtU}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  ttd
tdtttdtd tdtd   t  tŃ|||||||O|P|`| |c}tɐ|͐tV}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  ttd
tdtttdtd tdtd   t  tŃ|||||||O|||P|`| }tɐ|ϐtW}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   t  ttd
tdtttdtd tdtd   t  tŃ|||||||O|||P|`| }tɐ|ѐtX}ttttdtdtttdtd tdtd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g| 
}tɐ|ӐtY}ttttdtdtttdtd tdtd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g| 
}tɐ|ՐtZ}ttttdtdtttdtd tdtd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g|%
}tɐ|אt[}ttttdtdtttdtd tdtd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g|%
}tɐ|ِt\}tttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd   tttdtd tdtd   tŃ|||||||g| 	}tɐ|ېt]}tttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd   tttdtd tdtd   tŃ|||||||g| 	}tɐ|ݐt^}tttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd   tttdtd tdtd   tŃ|||||||g|%|k
}tɐ|ߐt_}tttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd   tttdtd tdtd   tŃ|||||||g|%|k
}tɐ|t`}tttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd   tttdtd tdtd   tŃ|||||||g|%|j
}tɐ|ta}tttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd   tttdtd tdtd   tŃ|||||||g|%|j
}tɐ|tb}tttdtdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g| 
}tɐ|tc}tttdtdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g| 
}tɐ|td}tttdtdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g|%
}tɐ|te}tttdtdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd    tŃ|||||||O|g|%
}tɐ|tf}tttdtttdtdtttdtd tdtd   ttd
tdtttdtd tdtd    tttdtd tdtd   tŃ|||||||g|i	}tɐ|tg}tttdtttdtdtttdtd tdtd   ttd
tdtttdtd tdtd    tttdtd tdtd   tŃ|||||||g|i	}tɐ|th}tttdtttdtdtttdtd tdtd   ttd
tdtttdtd tdtd    tttdtd tdtd   tŃ|||||||g|%|j
}tɐ|ti}tttdtttdtdtttdtd tdtd   ttd
tdtttdtd tdtd    tttdtd tdtd   tŃ|||||||g|%|j
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tdtttdtd tdtd     tŃ|||||||O|g| 
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}Otɐ|Ot}Ptttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    ttdtdtttdtd tdtd    tŃ|||||||||
}Qtɐ|Qt}Rttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||}Stɐ|St}Tttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||}Utɐ|Ut}Vttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||| |}Wtɐ|Wt}Xttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||| |}Ytɐ|Yt}Zttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||| |||,}[tɐ|[t}\ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||| |||,}]tɐ|]t}^ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||| ||-}_tɐ|_t}`ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||| ||-}atɐ|at}bttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||%||<}ctɐ|ct}dttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||%||<}etɐ|et}fttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||%||}gtɐ|gt}httttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||%||}itɐ|it}jttttdtdtttdtd tdtd   tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||%|	}ktɐ|kt}lttttdtdtttdtd tdtd   tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||%|	}mtɐ|mt}nttttdtdtttdtd tdtd   tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||%|	}otɐ|ot}pttttdtdtttdtd tdtd   tttdtdtttdtd tdtd   tttdtd tdtd   tŃ|||||||%|	}qtɐ|qt}rttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||%||;}stɐ|st}tttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ||||||||%||;}utɐ|ut}vttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||||%
}wtɐ|wt}xttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd  tŃ|||||||||%
}ytɐ|yt}zttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd td  tŃ|||||||| ||,}{tɐ|{t}|ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd td  tŃ|||||||| ||,}}tɐ|}t}~ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd td  tŃ||||||||%||}tɐ|t}ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd td  tŃ||||||||%||}tɐ|t}ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd td  tŃ|||||||||=
}tɐ|t}ttttdtdtttdtd tdtd   ttdtdtttdtd tdtd   t  tttdtd tdtd td  tŃ|||||||||=
}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||| |3|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||| |3|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| |3||}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| |3||}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||| |3|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||| |3|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ|||||||||| |}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ|||||||||| |}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ||||||||| |||8}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ||||||||| |||8}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ|||||||||| ||q}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ|||||||||| ||q}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||| ||*|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||| ||*|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||*|}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||*|}tɐ|tÃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||| ||,|}tɐ|tă}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||| ||,|}tɐ|tŃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||,|}tɐ|tƃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||,|}tɐ|tǃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||}tɐ|tȃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||}tɐ|tɃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||8}tɐ|tʃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| ||8}tɐ|t˃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| }tɐ|t̃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||| }tɐ|t̓}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||!}tɐ|t΃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||!}tɐ|tσ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%|||}tɐ|tЃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%|||}tɐ|tу}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||B}tɐ|Ðt҃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||B}tɐ|ŐtӃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||}tɐ|ǐtԃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||}tɐ|ɐtՃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%|||}tɐ|ːtփ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%|||}tɐ|͐t׃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||}tɐ|ϐt؃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||}tɐ|ѐtك}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||!}tɐ|Ӑtڃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||%|||!}tɐ|Րtۃ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%||||}tɐ|אt܃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%||||}tɐ|ِt݃}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%||!}tɐ|ېtރ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ||||||||||%||!}tɐ|ݐt߃}ttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd  tttdtdtttdtd tdtd     tŃ|||||||||%
}tɐ|ߐt}ttttdtdtttdtd tdtd   ttd
tdtttdtd tdtd  tttdtdtttdtd tdtd     tŃ|||||||||%
}tɐ|t}ttttd
tdtttdtd tdtd  ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ|||||||||%
}tɐ|t}ttttd
tdtttdtd tdtd  ttdtdtttdtd tdtd    tttdtdtttdtd tdtd    tŃ|||||||||%
}tɐ|t}ttttdtdtttdtd tdtd   tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd   tŃ|||||||||%
}tɐ|t}ttttdtdtttdtd tdtd   tttdtdtttdtd tdtd    ttd
tdtttdtd tdtd   tŃ|||||||||%
}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd    tŃ||||||||||%}tɐ|t}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    ttdtdtttdtd tdtd    tŃ||||||||||%}tɐ|t}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||||%}tɐ|t}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    ttdtdtttdtd tdtd   t  tŃ|||||||||||%}tɐ|t}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtd  tŃ||||||||||P|`| |}tɐ|t}ttttdtdtttdtd tdtd   tdtd ttd
tdtttdtd tdtd   td	td  tdtdtdtdtttdtd tdtd   tdtd  tŃ||||||||||P|`| |}tɐ|t}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||
}tɐ|t}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||
}tɐ|t}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd td    tŃ|||||||}tɐ|t} tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd td    tŃ|||||||}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd td    tŃ||||||||	}	tɐ|	t}
tttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  tdtdtttdtd tdtd td    tŃ|||||||}tɐ|t}tttdtdtttdtd tdtd  tdtd tdtdtttdtd tdtd  tdtdtttdtd tdtd td    tŃ|||||||}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}tttdtdtttdtd tdtd  tdtd ttdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||	}tɐ|t}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd td    tŃ|||||||}tɐ|t}ttttdtdtttdtd tdtd   tdtdtdtdtttdtd tdtd td    tŃ|||||||}tɐ|t}tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   ttdtdtttdtd tdtd    tŃ||||||||	}tɐ|t}tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   ttdtdtttdtd tdtd    tŃ||||||||	}tɐ|t}tttdtdtdtdtttdtd tdtd td   ttdtdtttdtd tdtd    tŃ|||||||}tɐ|t } tttdtdtdtdtttdtd tdtd td   ttdtdtttdtd tdtd    tŃ|||||||}!tɐ|!t}"ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||| ||,}#tɐ|#t}$ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||| ||,}%tɐ|%t}&ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tŃ||||||| ||,
}'tɐ|'t}(ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tŃ||||||| ||,
})tɐ|)t}*ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||| |-}+tɐ|+t},ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||| |-}-tɐ|-t}.ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tŃ|||||||| |-
}/tɐ|/t}0ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tŃ|||||||| |-
}1tɐ|1t	}2ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||%|
}3tɐ|3t
}4ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||%|
}5tɐ|5t}6ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tŃ|||||||%|	}7tɐ|7t}8ttttdtdtttdtd tdtd   tdtd tdtdtdtdtttdtd tdtd td    tŃ|||||||%|	}9tɐ|9t}:tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   tttdtdtttdtd tdtd    tŃ||||||||%	};tɐ|;t}<tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   tttdtdtttdtd tdtd    tŃ||||||||%	}=tɐ|=t}>tttdtdtdtdtttdtd tdtd td   tttdtdtttdtd tdtd    tŃ|||||||%}?tɐ|?t}@tttdtdtdtdtttdtd tdtd td   tttdtdtttdtd tdtd    tŃ|||||||%}Atɐ|At}Bttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||%|+|}Ctɐ|Ct}Dttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||%||}Etɐ|Et}Fttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tŃ|||||||%|+|
}Gtɐ|Gt}Httttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tŃ|||||||%|+|
}Itɐ|It}Jttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||%|;}Ktɐ|Kt}Lttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||%|;}Mtɐ|Mt}Nttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tŃ||||||||%|;
}Otɐ|Ot}Pttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tŃ||||||||%|;
}Qtɐ|Qt}Rtttdtdtttdtd tdtd  t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||	}Stɐ|St}Ttttdtdtttdtd tdtd  t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||	}Utɐ|Ut}Vtttdtdtttdtd tdtd  t tdtdtdtdtttdtd tdtd td    tŃ|||||||}Wtɐ|Wt}Xtttdtdtttdtd tdtd  t tdtdtdtdtttdtd tdtd td    tŃ|||||||}Ytɐ|Yt}Ztttdtdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||P|}[tɐ|[t}\tttdtdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||P|}]tɐ|]t}^tttdtdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd td    tŃ||||||||P|
}_tɐ|_t }`tttdtdtttdtd tdtd  t tdtd t tdtdtdtdtttdtd tdtd td    tŃ||||||||P|
}atɐ|at!}btttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||}ctɐ|ct"}dtttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||}etɐ|et#}ftttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd td    tŃ|||||||||
}gtɐ|gt$}htttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd td    tŃ|||||||||
}itɐ|it%}jtttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||}ktɐ|kt&}ltttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||}mtɐ|mt'}ntttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd td    tŃ|||||||||
}otɐ|ot(}ptttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd    tdtdtdtdtttdtd tdtd td    tŃ|||||||||
}qtɐ|qt)}rttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd  tŃ|||||||||| }stɐ|st*}tttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd  tŃ|||||||||| }utɐ|ut+}vttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd  tŃ||||||||| 
}wtɐ|wt,}xttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd  tŃ||||||||| 
}ytɐ|yt-}zttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd  tŃ||||||||||%}{tɐ|{t.}|ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd  tŃ||||||||||%}}tɐ|}t/}~ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd  tŃ|||||||||%
}tɐ|t0}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd  tŃ|||||||||%
}tɐ|t1}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd  tŃ|||||||||=
}tɐ|t2}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd  tŃ|||||||||=
}tɐ|t3}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd  tŃ||||||||=	}tɐ|t4}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd  tŃ||||||||=	}tɐ|t5}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||| ||,}tɐ|t6}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||| ||,}tɐ|t7}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||| ||,}tɐ|t8}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||| ||,}tɐ|t9}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||| |-|}tɐ|t:}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||| |-|}tɐ|t;}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||| |-|}tɐ|t<}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||| |-|}tɐ|t=}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||| |-||}tɐ|t>}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||| |-||}tɐ|t?}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||| |-||}tɐ|t@}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||| |-||}tɐ|tA}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd td  tŃ||||||||%||}tɐ|tB}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd td  tŃ||||||||%||}tɐ|tC}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd td  tŃ|||||||%||
}tɐ|tD}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd td  tŃ|||||||%||
}tɐ|tE}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd td  tŃ|||||||||%|=}tɐ|tF}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tttdtd tdtd td  tŃ|||||||||%|=}tɐ|tG}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd td  tŃ||||||||%|=
}tɐ|tH}ttttdtdtttdtd tdtd   t tdtdtdtdtttdtd tdtd td    tttdtd tdtd td  tŃ||||||||%|=
}tɐ|tI}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||%||<|!}tɐ|tJ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||%||<|!}tɐ|tK}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||%||<|!}tɐ|tL}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||%||<|!}tɐ|tM}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%||<|}tɐ|tN}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%||<|}tɐ|tO}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%||<|}tɐ|tP}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%||<|}tɐ|tQ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||%|||}tɐ|ÐtR}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||%|||}tɐ|ŐtS}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||%|||}tɐ|ǐtT}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ||||||||%|||}tɐ|ɐtU}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%|||}tɐ|ːtV}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%|||}tɐ|͐tW}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%|||}tɐ|ϐtX}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%|||}tɐ|ѐtY}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%||}tɐ|ӐtZ}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%||}tɐ|Րt[}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%||}tɐ|אt\}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%||}tɐ|ِt]}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%||!}tɐ|ېt^}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||%||!}tɐ|ݐt_}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%||!}tɐ|ߐt`}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   t  tdtdtdtdtttdtd tdtd td    tŃ|||||||||%||!}tɐ|ta}tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  ttdtdtttdtd tdtd     tŃ|||||||||%
}tɐ|tb}tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  ttdtdtttdtd tdtd     tŃ|||||||||%
}tɐ|tc}tttdtdtdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  ttdtdtttdtd tdtd     tŃ||||||||%	}tɐ|td}tttdtdtdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  ttdtdtttdtd tdtd     tŃ||||||||%	}tɐ|te}tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  tttdtdtttdtd tdtd     tŃ|||||||||%
}tɐ|tf}tttdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  tttdtdtttdtd tdtd     tŃ|||||||||%
}tɐ|tg}tttdtdtdtdtttdtd tdtd td   ttd
tdtttdtd tdtd  tttdtdtttdtd tdtd     tŃ||||||||%	}tɐ|th}tttdtdtdtdtttdtd tdtd td   ttd
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tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||||}tɐ|tj}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||||}tɐ|tk}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd td    tŃ||||||||||}tɐ|tl}tttd
tdtttdtd tdtd  td	td ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd td    tŃ||||||||||}tɐ|tm}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||||N}tɐ|tn}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ|||||||||||N}tɐ|to}tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd td    tŃ||||||||||N}tɐ|tp} tttd
tdtttdtd tdtd  t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd td    tŃ||||||||||N}tɐ|tq}tttd
tdtttdtd tdtd  t tdtd t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||||P|}tɐ|tr}tttd
tdtttdtd tdtd  t tdtd t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd   tdtdtttdtd tdtd td    tŃ||||||||||||P|}tɐ|ts}tttd
tdtttdtd tdtd  t tdtd t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd td    tŃ|||||||||||P|}tɐ|tt}tttd
tdtttdtd tdtd  t tdtd t ttdtdtttdtd tdtd   tdtd  tdtdtdtdtttdtd tdtd td    tŃ|||||||||||P|}	tɐ|	tu}
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sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  x_m_r  n_r   replacement3920replacement3921replacement3922replacement3923replacement3924replacement3925replacement3926replacement3927replacement3928replacement3929replacement3930replacement3931replacement3932replacement3933replacement3934replacement3935replacement3936replacement3937replacement3938replacement3939replacement3940replacement3941replacement3942replacement3943a_replacement3944replacement3945r  replacement3946replacement3947replacement3948replacement3949replacement3950replacement3951replacement3952replacement3953replacement3954replacement3955replacement3956replacement3957replacement3958replacement3959replacement3960replacement3961replacement3962replacement3963replacement3964replacement3965replacement3966replacement3967replacement3968replacement3969replacement3970replacement3971replacement3972replacement3973replacement3974replacement3975replacement3976replacement3977replacement3978replacement3979replacement3980replacement3981replacement3982replacement3983replacement3984replacement3985replacement3986replacement3987replacement3988replacement3989replacement3990replacement3991replacement3992replacement3993replacement3994replacement3995replacement3996replacement3997replacement3998replacement3999replacement4000replacement4001replacement4002replacement4003replacement4004replacement4005replacement4006replacement4007replacement4008replacement4009replacement4010replacement4011replacement4012replacement4013replacement4014replacement4015replacement4016replacement4017replacement4018replacement4019replacement4020replacement4021replacement4022replacement4023replacement4024replacement4025replacement4026replacement4027replacement4028replacement4029replacement4030replacement4031replacement4032replacement4033replacement4034replacement4035replacement4036replacement4037replacement4038replacement4039replacement4040replacement4041replacement4042replacement4043replacement4044replacement4045replacement4046replacement4047replacement4048replacement4049replacement4050replacement4051replacement4052replacement4053replacement4054replacement4055replacement4056replacement4057replacement4058replacement4059replacement4060replacement4061replacement4062replacement4063replacement4064replacement4065replacement4066replacement4067replacement4068replacement4069replacement4070replacement4071replacement4072replacement4073replacement4074replacement4075replacement4076replacement4077replacement4078replacement4079replacement4080replacement4081replacement4082replacement4083replacement4084replacement4085replacement4086replacement4087replacement4088replacement4089replacement4090replacement4091replacement4092replacement4093replacement4094replacement4095replacement4096replacement4097replacement4098replacement4099replacement4100replacement4101replacement4102replacement4103replacement4104replacement4105replacement4106replacement4107replacement4108replacement4109replacement4110replacement4111replacement4112replacement4113replacement4114replacement4115replacement4116replacement4117replacement4118replacement4119replacement4120replacement4121replacement4122replacement4123replacement4124replacement4125replacement4126replacement4127replacement4128replacement4129replacement4130replacement4131replacement4132replacement4133replacement4134replacement4135replacement4136replacement4137replacement4138replacement4139replacement4140replacement4141replacement4142replacement4143replacement4144replacement4145replacement4146replacement4147replacement4148replacement4149replacement4150replacement4151p_replacement4152replacement4153r  replacement4154replacement4155replacement4156replacement4157replacement4158replacement4159replacement4160replacement4161replacement4162replacement4163replacement4164replacement4165replacement4166replacement4167replacement4168replacement4169replacement4170replacement4171replacement4172replacement4173replacemen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486replacement4487replacement4488replacement4489replacement4490replacement4491replacement4492replacement4493replacement4494replacement4495replacement4496replacement4497replacement4498replacement4499replacement4500replacement4501replacement4502replacement4503replacement4504replacement4505replacement4506replacement4507replacement4508replacement4509replacement4510replacement4511replacement4512replacement4513replacement4514replacement4515replacement4516replacement4517replacement4518replacement4519replacement4520replacement4521replacement4522replacement4523replacement4524replacement4525replacement4526replacement4527replacement4528replacement4529replacement4530replacement4531replacement4532replacement4533replacement4534replacement4535replacement4536replacement4537replacement4538replacement4539replacement4540replacement4541replacement4542replacement4543replacement4544replacement4545replacement4546replacement4547replacement4548replacement4549replacement4550replacement4551replacement4552replacement4553replacement4554replacement4555replacement4556replacement4557replacement4558replacement4559replacement4560replacement4561replacement4562replacement4563replacement4564replacement4565replacement4566replacement4567replacement4568replacement4569replacement4570replacement4571replacement4572replacement4573replacement4574replacement4575replacement4576replacement4577replacement4578replacement4579replacement4580replacement4581replacement4582replacement4583replacement4584replacement4585replacement4586replacement4587replacement4588replacement4589replacement4590replacement4591replacement4592replacement4593replacement4594replacement4595replacement4596replacement4597replacement4598replacement4599replacement4600replacement4601replacement4602replacement4603replacement4604replacement4605With4606With4607With4608With4609With4610With4611With4612With4613replacement4614replacement4615With4616With4617With4618With4619replacement4620replacement4621replacement4622replacement4623With4624With4625n2_With4626With4627With4628With4629replacement4630replacement4631replacement4632replacement4633replacement4634replacement4635With4636With4637With4638With4639replacement4640replacement4641replacement4642replacement4643With4644With4645replacement4646replacement4647replacement4648replacement4649replacement4650replacement4651replacement4652replacement4653replacement4654replacement4655replacement4656replacement4657replacement4658replacement4659replacement4660replacement4661replacement4662replacement4663replacement4664replacement4665u_v_replacement4666replacement4667replacement4668replacement4669replacement4670replacement4671replacement4672replacement4673replacement4674replacement4675replacement4676replacement4677replacement4678replacement4679replacement4680replacement4681e_replacement4682replacement4683replacement4684replacement4685replacement4686replacement4687(  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  pattern3920rule3920pattern3921rule3921pattern3922rule3922pattern3923rule3923pattern3924rule3924pattern3925rule3925pattern3926rule3926pattern3927rule3927pattern3928rule3928pattern3929rule3929pattern3930rule3930pattern3931rule3931pattern3932rule3932pattern3933rule3933pattern3934rule3934pattern3935rule3935pattern3936rule3936pattern3937rule3937pattern3938rule3938pattern3939rule3939pattern3940rule3940pattern3941rule3941pattern3942rule3942pattern3943rule3943pattern3944rule3944pattern3945rule3945pattern3946rule3946pattern3947rule3947pattern3948rule3948pattern3949rule3949pattern3950rule3950pattern3951rule3951pattern3952rule3952pattern3953rule3953pattern3954rule3954pattern3955rule3955pattern3956rule3956pattern3957rule3957pattern3958rule3958pattern3959rule3959pattern3960rule3960pattern3961rule3961pattern3962rule3962pattern3963rule3963pattern3964rule3964pattern3965rule3965pattern3966rule3966pattern3967rule3967pattern3968rule3968pattern3969rule3969pattern3970rule3970pattern3971rule3971pattern3972rule3972pattern3973rule3973pattern3974rule3974pattern3975rule3975pattern3976rule3976pattern3977rule3977pattern3978rule3978pattern3979rule3979pattern3980rule3980pattern3981rule3981pattern3982rule3982pattern3983rule3983pattern3984rule3984pattern3985rule3985pattern3986rule3986pattern3987rule3987pattern3988rule3988pattern3989rule3989pattern3990rule3990pattern3991rule3991pattern3992rule3992pattern3993rule3993pattern3994rule3994pattern3995rule3995pattern3996rule3996pattern3997rule3997pattern3998rule3998pattern3999rule3999pattern4000rule4000pattern4001rule4001pattern4002rule4002pattern4003rule4003pattern4004rule4004pattern4005rule4005pattern4006rule4006pattern4007rule4007pattern4008rule4008pattern4009rule4009pattern4010rule4010pattern4011rule4011pattern4012rule4012pattern4013rule4013pattern4014rule4014pattern4015rule4015pattern4016rule4016pattern4017rule4017pattern4018rule4018pattern4019rule4019pattern4020rule4020pattern4021rule4021pattern4022rule4022pattern4023rule4023pattern4024rule4024pattern4025rule4025pattern4026rule4026pattern4027rule4027pattern4028rule4028pattern4029rule4029pattern4030rule4030pattern4031rule4031pattern4032rule4032pattern4033rule4033pattern4034rule4034pattern4035rule4035pattern4036rule4036pattern4037rule4037pattern4038rule4038pattern4039rule4039pattern4040rule4040pattern4041rule4041pattern4042rule4042pattern4043rule4043pattern4044rule4044pattern4045rule4045pattern4046rule4046pattern4047rule4047pattern4048rule4048pattern4049rule4049pattern4050rule4050pattern4051rule4051pattern4052rule4052pattern4053rule4053pattern4054rule4054pattern4055rule4055pattern4056rule4056pattern4057rule4057pattern4058rule4058pattern4059rule4059pattern4060rule4060pattern4061rule4061pattern4062rule4062pattern4063rule4063pattern4064rule4064pattern4065rule4065pattern4066rule4066pattern4067rule4067pattern4068rule4068pattern4069rule4069pattern4070rule4070pattern4071rule4071pattern4072rule4072pattern4073rule4073pattern4074rule4074pattern4075rule4075pattern4076rule4076pattern4077rule4077pattern4078rule4078pattern4079rule4079pattern4080rule4080pattern4081rule4081pattern4082rule4082pattern4083rule4083pattern4084rule4084pattern4085rule4085pattern4086rule4086pattern4087rule4087pattern4088rule4088pattern4089rule4089pattern4090rule4090pattern4091rule4091pattern4092rule4092pattern4093rule4093pattern4094rule4094pattern4095rule4095pattern4096rule4096pattern4097rule4097pattern4098rule4098pattern4099rule4099pattern4100rule4100pattern4101rule4101pattern4102rule4102pattern4103rule4103pattern4104rule4104pattern4105rule4105pattern4106rule4106pattern4107rule4107pattern4108rule4108pattern4109rule4109pattern4110rule4110pattern4111rule4111pattern4112rule4112pattern4113rule4113pattern4114rule4114pattern4115rule4115pattern4116rule4116pattern4117rule4117pattern4118rule4118pattern4119rule4119pattern4120rule4120pattern4121rule4121pattern4122rule4122pattern4123rule4123pattern4124rule4124pattern4125rule4125pattern4126rule4126pattern4127rule4127pattern4128rule4128pattern4129rule4129pattern4130rule4130pattern4131rule4131pattern4132rule4132pattern4133rule4133pattern4134rule4134pattern4135rule4135pattern4136rule4136pattern4137rule4137pattern4138rule4138pattern4139rule4139pattern4140rule4140pattern4141rule4141pattern4142rule4142pattern4143rule4143pattern4144rule4144pattern4145rule4145pattern4146rule4146pattern4147rule4147pattern4148rule4148pattern4149rule4149pattern4150rule4150pattern4151rule4151pattern4152rule4152pattern4153rule4153pattern4154rule4154pattern4155rule4155pattern4156rule4156pattern4157rule4157pattern4158rule4158pattern4159rule4159pattern4160rule4160pattern4161rule4161pattern4162rule4162pattern4163rule4163pattern4164rule4164pattern4165rule4165pattern4166rule4166pattern4167rule4167pattern4168rule4168pattern4169rule4169pattern4170rule4170pattern4171rule4171pattern4172rule4172pattern4173rule4173pattern4174rule4174pattern4175rule4175pattern4176rule4176pattern4177rule4177pattern4178rule4178pattern4179rule4179pattern4180rule4180pattern4181rule4181pattern4182rule4182pattern4183rule4183pattern4184rule4184pattern4185rule4185pattern4186rule4186pattern4187rule4187pattern4188rule4188pattern4189rule4189pattern4190rule4190pattern4191rule4191pattern4192rule4192pattern4193rule4193pattern4194rule4194pattern4195rule4195pattern4196rule4196pattern4197rule4197pattern4198rule4198pattern4199rule4199pattern4200rule4200pattern4201rule4201pattern4202rule4202pattern4203rule4203pattern4204rule4204pattern4205rule4205pattern4206rule4206pattern4207rule4207pattern4208rule4208pattern4209rule4209pattern4210rule4210pattern4211rule4211pattern4212rule4212pattern4213rule4213pattern4214rule4214pattern4215rule4215pattern4216rule4216pattern4217rule4217pattern4218rule4218pattern4219rule4219pattern4220rule4220pattern4221rule4221pattern4222rule4222pattern4223rule4223pattern4224rule4224pattern4225rule4225pattern4226rule4226pattern4227rule4227pattern4228rule4228pattern4229rule4229pattern4230rule4230pattern4231rule4231pattern4232rule4232pattern4233rule4233pattern4234rule4234pattern4235rule4235pattern4236rule4236pattern4237rule4237pattern4238rule4238pattern4239rule4239pattern4240rule4240pattern4241rule4241pattern4242rule4242pattern4243rule4243pattern4244rule4244pattern4245rule4245pattern4246rule4246pattern4247rule4247pattern4248rule4248pattern4249rule4249pattern4250rule4250pattern4251rule4251pattern4252rule4252pattern4253rule4253pattern4254rule4254pattern4255rule4255pattern4256rule4256pattern4257rule4257pattern4258rule4258pattern4259rule4259pattern4260rule4260pattern4261rule4261pattern4262rule4262pattern4263rule4263pattern4264rule4264pattern4265rule4265pattern4266rule4266pattern4267rule4267pattern4268rule4268pattern4269rule4269pattern4270rule4270pattern4271rule4271pattern4272rule4272pattern4273rule4273pattern4274rule4274pattern4275rule4275pattern4276rule4276pattern4277rule4277pattern4278rule4278pattern4279rule4279pattern4280rule4280pattern4281rule4281pattern4282rule4282pattern4283rule4283pattern4284rule4284pattern4285rule4285pattern4286rule4286pattern4287rule4287pattern4288rule4288pattern4289rule4289pattern4290rule4290pattern4291rule4291pattern4292rule4292pattern4293rule4293pattern4294rule4294pattern4295rule4295pattern4296rule4296pattern4297rule4297pattern4298rule4298pattern4299rule4299pattern4300rule4300pattern4301rule4301pattern4302rule4302pattern4303rule4303pattern4304rule4304pattern4305rule4305pattern4306rule4306pattern4307rule4307pattern4308rule4308pattern4309rule4309pattern4310rule4310pattern4311rule4311pattern4312rule4312pattern4313rule4313pattern4314rule4314pattern4315rule4315pattern4316rule4316pattern4317rule4317pattern4318rule4318pattern4319rule4319pattern4320rule4320pattern4321rule4321pattern4322rule4322pattern4323rule4323pattern4324rule4324pattern4325rule4325pattern4326rule4326pattern4327rule4327pattern4328rule4328pattern4329rule4329pattern4330rule4330pattern4331rule4331pattern4332rule4332pattern4333rule4333pattern4334rule4334pattern4335rule4335pattern4336rule4336pattern4337rule4337pattern4338rule4338pattern4339rule4339pattern4340rule4340pattern4341rule4341pattern4342rule4342pattern4343rule4343pattern4344rule4344pattern4345rule4345pattern4346rule4346pattern4347rule4347pattern4348rule4348pattern4349rule4349pattern4350rule4350pattern4351rule4351pattern4352rule4352pattern4353rule4353pattern4354rule4354pattern4355rule4355pattern4356rule4356pattern4357rule4357pattern4358rule4358pattern4359rule4359pattern4360rule4360pattern4361rule4361pattern4362rule4362pattern4363rule4363pattern4364rule4364pattern4365rule4365pattern4366rule4366pattern4367rule4367pattern4368rule4368pattern4369rule4369pattern4370rule4370pattern4371rule4371pattern4372rule4372pattern4373rule4373pattern4374rule4374pattern4375rule4375pattern4376rule4376pattern4377rule4377pattern4378rule4378pattern4379rule4379pattern4380rule4380pattern4381rule4381pattern4382rule4382pattern4383rule4383pattern4384rule4384pattern4385rule4385pattern4386rule4386pattern4387rule4387pattern4388rule4388pattern4389rule4389pattern4390rule4390pattern4391rule4391pattern4392rule4392pattern4393rule4393pattern4394rule4394pattern4395rule4395pattern4396rule4396pattern4397rule4397pattern4398rule4398pattern4399rule4399pattern4400rule4400pattern4401rule4401pattern4402rule4402pattern4403rule4403pattern4404rule4404pattern4405rule4405pattern4406rule4406pattern4407rule4407pattern4408rule4408pattern4409rule4409pattern4410rule4410pattern4411rule4411pattern4412rule4412pattern4413rule4413pattern4414rule4414pattern4415rule4415pattern4416rule4416pattern4417rule4417pattern4418rule4418pattern4419rule4419pattern4420rule4420pattern4421rule4421pattern4422rule4422pattern4423rule4423pattern4424rule4424pattern4425rule4425pattern4426rule4426pattern4427rule4427pattern4428rule4428pattern4429rule4429pattern4430rule4430pattern4431rule4431pattern4432rule4432pattern4433rule4433pattern4434rule4434pattern4435rule4435pattern4436rule4436pattern4437rule4437pattern4438rule4438pattern4439rule4439pattern4440rule4440pattern4441rule4441pattern4442rule4442pattern4443rule4443pattern4444rule4444pattern4445rule4445pattern4446rule4446pattern4447rule4447pattern4448rule4448pattern4449rule4449pattern4450rule4450pattern4451rule4451pattern4452rule4452pattern4453rule4453pattern4454rule4454pattern4455rule4455pattern4456rule4456pattern4457rule4457pattern4458rule4458pattern4459rule4459pattern4460rule4460pattern4461rule4461pattern4462rule4462pattern4463rule4463pattern4464rule4464pattern4465rule4465pattern4466rule4466pattern4467rule4467pattern4468rule4468pattern4469rule4469pattern4470rule4470pattern4471rule4471pattern4472rule4472pattern4473rule4473pattern4474rule4474pattern4475rule4475pattern4476rule4476pattern4477rule4477pattern4478rule4478pattern4479rule4479pattern4480rule4480pattern4481rule4481pattern4482rule4482pattern4483rule4483pattern4484rule4484pattern4485rule4485pattern4486rule4486pattern4487rule4487pattern4488rule4488pattern4489rule4489pattern4490rule4490pattern4491rule4491pattern4492rule4492pattern4493rule4493pattern4494rule4494pattern4495rule4495pattern4496rule4496pattern4497rule4497pattern4498rule4498pattern4499rule4499pattern4500rule4500pattern4501rule4501pattern4502rule4502pattern4503rule4503pattern4504rule4504pattern4505rule4505pattern4506rule4506pattern4507rule4507pattern4508rule4508pattern4509rule4509pattern4510rule4510pattern4511rule4511pattern4512rule4512pattern4513rule4513pattern4514rule4514pattern4515rule4515pattern4516rule4516pattern4517rule4517pattern4518rule4518pattern4519rule4519pattern4520rule4520pattern4521rule4521pattern4522rule4522pattern4523rule4523pattern4524rule4524pattern4525rule4525pattern4526rule4526pattern4527rule4527pattern4528rule4528pattern4529rule4529pattern4530rule4530pattern4531rule4531pattern4532rule4532pattern4533rule4533pattern4534rule4534pattern4535rule4535pattern4536rule4536pattern4537rule4537pattern4538rule4538pattern4539rule4539pattern4540rule4540pattern4541rule4541pattern4542rule4542pattern4543rule4543pattern4544rule4544pattern4545rule4545pattern4546rule4546pattern4547rule4547pattern4548rule4548pattern4549rule4549pattern4550rule4550pattern4551rule4551pattern4552rule4552pattern4553rule4553pattern4554rule4554pattern4555rule4555pattern4556rule4556pattern4557rule4557pattern4558rule4558pattern4559rule4559pattern4560rule4560pattern4561rule4561pattern4562rule4562pattern4563rule4563pattern4564rule4564pattern4565rule4565pattern4566rule4566pattern4567rule4567pattern4568rule4568pattern4569rule4569pattern4570rule4570pattern4571rule4571pattern4572rule4572pattern4573rule4573pattern4574rule4574pattern4575rule4575pattern4576rule4576pattern4577rule4577pattern4578rule4578pattern4579rule4579pattern4580rule4580pattern4581rule4581pattern4582rule4582pattern4583rule4583pattern4584rule4584pattern4585rule4585pattern4586rule4586pattern4587rule4587pattern4588rule4588pattern4589rule4589pattern4590rule4590pattern4591rule4591pattern4592rule4592pattern4593rule4593pattern4594rule4594pattern4595rule4595pattern4596rule4596pattern4597rule4597pattern4598rule4598pattern4599rule4599pattern4600rule4600pattern4601rule4601pattern4602rule4602pattern4603rule4603pattern4604rule4604pattern4605rule4605pattern4606rule4606pattern4607rule4607pattern4608rule4608pattern4609rule4609pattern4610rule4610pattern4611rule4611pattern4612rule4612pattern4613rule4613pattern4614rule4614pattern4615rule4615pattern4616rule4616pattern4617rule4617pattern4618rule4618pattern4619rule4619pattern4620rule4620pattern4621rule4621pattern4622rule4622pattern4623rule4623pattern4624rule4624pattern4625rule4625pattern4626rule4626pattern4627rule4627pattern4628rule4628pattern4629rule4629pattern4630rule4630pattern4631rule4631pattern4632rule4632pattern4633rule4633pattern4634rule4634pattern4635rule4635pattern4636rule4636pattern4637rule4637pattern4638rule4638pattern4639rule4639pattern4640rule4640pattern4641rule4641pattern4642rule4642pattern4643rule4643pattern4644rule4644pattern4645rule4645pattern4646rule4646pattern4647rule4647pattern4648rule4648pattern4649rule4649pattern4650rule4650pattern4651rule4651pattern4652rule4652pattern4653rule4653pattern4654rule4654pattern4655rule4655pattern4656rule4656pattern4657rule4657pattern4658rule4658pattern4659rule4659pattern4660rule4660pattern4661rule4661pattern4662rule4662pattern4663rule4663pattern4664rule4664pattern4665rule4665pattern4666rule4666pattern4667rule4667pattern4668rule4668pattern4669rule4669pattern4670rule4670pattern4671rule4671pattern4672rule4672pattern4673rule4673pattern4674rule4674pattern4675rule4675pattern4676rule4676pattern4677rule4677pattern4678rule4678pattern4679rule4679pattern4680rule4680pattern4681rule4681pattern4682rule4682pattern4683rule4683pattern4684rule4684pattern4685rule4685patte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TVVVVVPPXXVVTTXXVVTTttzzxx||zzttzzxx||zzxx~~tt~~rr~~                            
 
 " "   0 0 TT\\\\^^  hhrrrrxxppvv``llllppJJff                 r  c                 C   s^   t | | | t|||   |td   |t|||   |td   ||td   |S N)r  r  r  r  r  r  r  r  r  r  xr  r  r  r  	     ^r  c              
   C   sh   t td| t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	  	     hr	  c              
   C   s   t | td|  | tt| | || td  |td td | td tdd    ||tdt|||   | S Nr  r  r  r  r  r+   r   r  r  r  r  r  r  r  r  r  r  r
  	     r
  c              
   C   s   t | td|  | tt| | || td  |td td | td tdd    ||tdt|||   |S r  r  r  r+   r   r  r  r  r  r  r  	     r  c              	   C   s   t | td |td  |td |td   t| t|||   |td  |t|||   |td   ||t| | t|||   |td   |t|||   |td   || |td   | S Nr  r  r  r  r  r   r  r  r  r  r  r  r  r  	     r  c              	   C   s   t |td |td  | td |td   t| t|||   |td  |t|||   |td   ||t|| 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d  |td  t| t|||   |td  |t|||   |  ||t| | | t|||   |td   |t|||   |td   ||td   | S Nr  r   r  r!  r  r  r  r  r  	     r  c              	   C   s   t |td || td  |td  t| t|||   | |t|||   |td   ||t| | | t|||   |td   |t|||   |td   ||td   | S r#  r!  r  r  r  r  r  	  r$  r  c              	   C   s   t |td | td ||   t| t|||   |td  |t|||   |  ||t|| t|||   |td   |t|||   |td   | | ||   | S r  r!  r  r  r  r  r  	     r  c              	   C   s   t |td |td ||   t| t|||   | |t|||   |td   ||t| | t|||   |td   |t|||   |td   || ||   | S r  r!  r  r  r  r  r  	  r%  r  c                 C   sd   t | t|||   | |t|||   |  t|||  |   tt|||  | ||S N)r  r  r  r  r   r  r  r  r  r  	     dr  c              	   C   s   t | t|||   | | t|||   |  |t|||   |  |t|||   |  t| t|||   |  |t|||   |   ||S r&  )r  r  r  r   r  r  r  r  r  	     r  c              	   C   sX   t td| ttt|td td |td td  |||t| ||  |S r  r  r  r+   r   r   r  r  r  r  r  r  r  r  r  	     Xr  c              
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  r?  r"  c                 C   sf   t td| | tttd| |td   |||t|||   t| |t|||     |S Nr  r  r  r  r+   r   r  r  r  r>  r  r  r  r#  
  r:  r#  c                 C   sh   t td | | tttd| |td   |||t| |t|||    t|||    |S rA  r  r  r+   r   r  r  r  r>  r  r  r  r$  	
  r  r$  c              
   C   s   t | |td  t| |t|||    |td  | |td  |td| 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%  c              
   C   s   t | |td  t| |t|||    |td  | |td  |td| td  t|||     ||t|td | |t|||    |td   ||td  t|||    | S rD  r  r  r   r  r  r  rG  r  r  r  r&  
  rH  r&  c                 C   x   t td|  tt| |t|||    ||t ||  ttdt| |t|||    t|||    || S Nr  r  r  r   r  r  r>  r  r  r  r'  
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   C   s   t td| td td| td   t| |t|||    |td  | td| td  ||td  t|||     ||t| |t|||    | t|||   |td| td   | S r1  rF  rG  r  r  r  r)  
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   C   s   t | | t|||   |ttdtdt|||     ttdtdt|||      tttd|| |   |tdd   |ttd|| |     ||tdt|||   | S r  r  r  r  r  r  r+   r   rG  r  r  r  r+  %
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   C   s   t | | |ttdtdt|||     ttdtdt|||     t|||    tttd|| |   |tdd   |ttd|| |     ||tdt|||   |S r  )r  r  r  r  r  r+   r   rG  r  r  r  r,  )
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   C      t | t| td|| t|||     t|   | |t|||    t|  ttd|| t|||     | ||S rK  r  r%   r  r  r&   r   rG  r  r  r  r-  -
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     r7  c                 C   s   t tdt|tdtdt|||     | |   t| tdtdt|||     | |   t| | |  tt| |t|||    t| | td | | | |   t| | td t|||   | |  |S rA  rV  r>  r  r  r  r8  Y
     r8  c                 C   sP  t td| | td |td   |td   t| |t|||    |td  t|  | |td  t|||   |td |td  t|||  td   | td |td  |td   | ||t|td | |t|||    |td   t|||   | | | td |td   |td   | S r1  rF  rG  r  r  r  r9  ]
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   C   sj   t | | ttd| |t|||    t|||  td   || tt|||  ||  | S r1  )r  r   r  r  r  r  rq  r  r  r  rC  
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   C   sr   t | | ttd| |t|||    t|||  td   || ttd|| t|||    | S r1  )r  r   r  r  r  r  rq  r  r  r  rD  
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   C   s\   t td |  |t|t|||    t| |t|||     t|||    |S rz  r}  r  r  r  r  r`  
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   C   s   t td| tt|| td  | ||  |  |td |td tdd    |td |td tdd    ||tdt|||   |S r  r  r  r  r  r  r    r  r  c              
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   C   p   t |t|||   | |t|||   |  t|t|||   |  | |t|||    |  ||S r&  )r  r  r   r  r  r  r  r  r  =  rr  r  c              
   C   r  r&  )r  r  r   r  r  r  r  r  r  A  rr  r  c              	   C   s   t | | | td  ||   | tt|| |  | ||  |td tdd    | ||  |td | tdd    ||t|||  | S r  r  r  r  r  r  r  r  r  r  r  r  r  E  r(  r  c              	   C   s   t | | | td  ||   | tt|| |  | ||  |td tdd    | ||  |td | tdd    ||t|||  |S r  r  r  r  r  r  r  I  r  r  c              
   C   s   t |td|  | tt|  ||  |td tdd   | ||  |td | tdd    | ||tdt|||   |S r  r  r  r  r  r  r  M  rn  r  c              
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   C   s   t |td | t|t|||   |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  r  U  rP  r  c              
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   C   s   t td|td tdd   |td|   | tt| | | |td |td  |td tdd    | |||t|||   | S r  r  r  r  r  r  r  y  r/  r  c              	   C   >   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   >   t t|t|||   | | |t|||    | ||S r&  r   r   r  r  r  r  r  r  r    r  r  c                 C   s   t td| |td | tdd    | tt|| | |td  td |td | tdd    | |td  td  ||t|||  t| |t|||     |S r  rB  r  r  r  r  r    r  r  c                 C   s   t td | |td | tdd    | tt|| | |td  td |td | tdd    | |td  td  ||tdt| |t|||    t|||    |S r  rC  r  r  r  r  r    r  r  c              
   C   sp   t | td|  |td |   t|t|||   |td|   |  |t|||    |   ||S rz  r  r  r   r  r  r  r  r  r  r    rr  r  c              
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   C   sp   t td|  tt|t|||   ||t ||  tt|t|||   | t|||   |  || S rK  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r
    rr  r
  c              
   C   sp   t td|  tt|t|||   ||t ||  tt|t|||   | t|||   |  || S rK  r  r  r   r  r  r  r  r  r  r  r    rr  r  c                 C   s   t |td |td  t|t|||   |td  | |t|||     || t |td | td |td   |td  t|t|||   |td  | |t|||     || S Nr  r   r  r  r  r  r  r    r  r  c                 C   s   t |td |td  t|t|||   |td  | |t|||     || t |td | td |td   |td  t|t|||   |td  | |t|||     || S r  r  r  r  r  r  r    r  r  c                 C   s   t td|  ttdt|t|||    ||t ||  ttdt|t|||   | t|||   |   || S rK  r  r  r  r  r  r    r  r  c                 C   s   t td|  ttdt|t|||    ||t ||  ttdt|t|||   | t|||   |   || S rK  r  r  r  r  r  r    r  r  c                 C   s   t |td |td | td |td    t|t|||   |td  | |t|||     ||t td| td |td   t|t|||   | | |t|||     || S rA  r  r  r  r  r  r    rH  r  c                 C   s   t |td |td | td |td    t|t|||   |td  | |t|||     ||t td| td |td   t|t|||   | | |t|||     || S rA  r  r  r  r  r  r    rH  r  c                 C   B   t tdt|||  td  | |t|||    |  |S Nr  r   )r   r  r  rG  r  r  r  r    r|  r  c                 C   r  r  )r   r  r  rG  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   sP   t | t|||   | | t|||  |  t|||  | |   |S r&  r  r  r  r  r  r    r  r  c                 C   sP   t | t|||   | | t|||  | |   t|||  |  |S r&  r  r  r  r  r  r    r  r  c                 C   s:   t |t|||   | | |t|||    |  |S r&  )r   r  r  r  r  r  r  r    r  r  c                 C   s:   t |t|||   | | |t|||    |  |S r&  )r   r  r  r  r  r  r  r    r  r  c	           	   
   C   s|   t |t|||   | |  |t|||  |  |  t|t|||   ||  | |t|||    |  ||S r&  )r  r  r   r  	r  r  r  r  r  r  r  r   r  r  r  r  r    r  r  c	           	   
   C   s   t |tdt|||   |  | |t|||   | |   t|t|||   ||  | |t|||    |  ||S rK  )r  r  r  r   r  r  r  r  r  r    rS  r  c	           	      C   V   t || tttd||t|||     | | |t|||    | |||S rK  )r  r   rI  r  r  	r  r  r  r  r  r  r  r  r  r  r  r  r       Vr  c	           	      C   r  rK  )r  r   rI  r  r  r  r  r  r  r    r  r  c	           	   	   C   sV   t |  | | t||t|||    | |  t|||  td|   ||S rz  )r  r   r  r  r  r  r  r  r  r    r  r  c	           	   	   C   s^   t |  | | t||t|||    | |  tdt|||   td|   ||S r1  )r  r   r  r  r  r  r  r  r  r     r  r   c              
   C   s   t |  | |tdd   t|||   t| |t|||    t||t|||      tt|||  td|  ||S r1  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r!    r2  r!  c              
   C   s   t |  | |tdd   t| |t|||    t||t|||     t|||    ttdt|||   td|  ||S r1  r  r  r  r  r  r   r  r  r  r  r"    r  r"  c                 C   s   t |tt| |t|||    ||t|||    |td   ||ttd |  | ||t|||    |td   t|||   |t| |t|||     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t| |t|||    ||t|||    |td   ||ttd|  | ||t|||    |td   |t| |t|||     td| td  t|||    | S r  r  r   r  r  r  r  r  r!  r  r  r  r$    rH  r$  c                 C   s   t td| tt| |t|||    ||t|||    |td   ||ttd|  ||t|||    |  t|||   |t| |t|||     td| td   | S r1  r  r  r   r  r  r  r  r!  r  r  r  r%    r$  r%  c                 C   s   t td| tt| |t|||    ||t|||    |td   ||ttd |  ||t|||    |  |t| |t|||     td| td  t|||    | S r1  r  r  r   r  r  r  r  r!  r  r  r  r&  	  rP  r&  c                 C   s   t | | tt| |t|||    ||t|||    |td   ||ttd| td  ||t|||    |  t|||   |t| |t|||     td| td   | S Nr     r  r   r!  r  r  r  r'    rH  r'  c                 C   s   t | | tt| |t|||    ||t|||    |td   ||ttd | td  ||t|||    |  |t| |t|||     td| td  t|||    | S r%  r"  r!  r  r  r  r(    r  r(  c                 C   s   t | tt| |t|||    ||t|||    |  ||ttd| td  ||t|||    |  t|||   |t| |t|||     td| td   | S rA  )r  r   r  r  r  r  r  r!  r  r  r  r)       r)  c                 C   s   t | tt| |t|||    ||t|||    |  ||ttd | td  ||t|||    |  |t| |t|||     td| td  t|||    | S rA  )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d   ||ttd| td  ||t|||    |  t|||   |t| |t|||     td| td   | S Nr     r  r  r#  r!  r  r  r  r+       r+  c                 C   s   t | td |td  tt| |t|||    ||t|||    |td   ||ttd | td  ||t|||    |  |t| |t|||     td| td  t|||    | S r(  r$  r!  r  r  r  r,  !  r  r,  c	           	   
   C   s   t | | t|||   |t| |t|||     t||t|||      tt|| |  | | | |tdd    || | |tdd    ||t|||  |S r  r  r  r  r  r+   r   r  r  r  r  r  r-  %  r  r-  c	           	   
   C   s   t | | |t| |t|||     t||t|||     t|||    tt|| |  | | | |tdd    || | |tdd    ||t|||  | S r  r  r  r  r  r+   r   r  r  r  r  r  r.  )  r  r.  c	           	   
   C   s   t | | t|||   |t| |t|||     t||t|||      tt| ||  |tdd   |||  |tdd    | ||tdt|||   | S r  r+  r  r  r  r  r/  -  r  r/  c	           	   
   C   s   t | | |t| |t|||     t||t|||     t|||    tt| ||  |tdd   |||  |tdd    | ||tdt|||   |S r  r,  r  r  r  r  r0  1  s   r0  c                 C   <   t || tt|||  td ||t| | | | S Nr   r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r1  5  r  r1  c                 C   r-  r.  r  r   r  r  r  r0  r  r  r  r2  9  r  r2  c              	   C   n   t || tt|||  td ||t | | ||  ttdt|||   || t| | | | S Nr   r  r/  r0  r  r  r  r3  =  r  r3  c              	   C   r2  r3  r1  r0  r  r  r  r4  A  r  r4  c                 C   d   t |tt| |t|||    ||t |tt| |t|||    t|||   || S r&  r  r0  r  r  r  r5  E  r'  r5  c                 C   r4  r&  r  r0  r  r  r  r6  I  r'  r6  c                 C      t | | ttdt| |t|||     ||t| | ||  || t|||    t| |t|||    t|||    | S rK  r  r   r  r  r  r0  r  r  r  r7  M  r  r7  c                 C   r5  rK  r  r   r  r  r  r0  r  r  r  r8  Q  r  r8  c                 C   s   t td| t| |t|||    |td  t| | | | | td| td  || |  t|||    | ||t|| | |t|||    |td   t|||   ||  | S r  rF  r  r  r  r  r9  U  r  r9  c                 C   s   t td| t| |t|||    |td  t| | | | | td| td  || |  t|||    | ||t|| | |t|||    |td   || t|||    | S r  rI  r  r  r  r  r:  Y  r  r:  c                 C   s:  t td| t| |t|||    |td  t| td | | || | td| td  || |   t|||  td   | td | | td|  | | |  |td | |td   t|||    | ||t|| | |t|||    |td   t|||   ||  | S r  rF  r  r  r  r  r;  ]  r  r;  c                 C   s:  t td| t| |t|||    |td  t| td | | || | td| td  || |   t|||  td   | td | | td|  | | |  |td | |td   t|||    | ||t|| | |t|||    |td   || t|||    | S r  rI  r  r  r  r  r<  a  r  r<  c              
   C   d   t |  | ||  |  ttd| |t|||    t|||    || t|| |  | S rK  r  r   r  r  r  r0  r  r  r  r=  e  r'  r=  c              
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   C   d   t |t| |t|||    | ||t |t| |t|||    | t|||   || S r&  r  r   r  r  r  r  r  rG    r'  rG  c              
   C   r@  r&  r  r   r  r  r  r  r  rH    r'  rH  c                 C      t td| tt| |t|||    ||t || tt| |t|||    ||t|||    t|||    || S rK  rL  r0  r  r  r  rI    r2  rI  c                 C   rC  rK  rN  r0  r  r  r  rJ    r2  rJ  c                 C      t | | ttdt| |t|||     ||t |  | ||  | ttdt| |t|||    ||t|||     t|||    || S rK  r6  r0  r  r  r  rK    r  rK  c                 C   rD  rK  r7  r0  r  r  r  rL    r  rL  c                 C      t | | tt| |t|||    ||t |  | ||  | tt| |t|||    ||t|||    t|||    || S r&  r  r0  r  r  r  rM    r  rM  c                 C   rE  r&  r  r0  r  r  r  rN    r  rN  c                 C      t td||  t| td | |td | t|||    t| |t|||     ||t |  | ||  td ||  ttdt| |t|||    ||t|||     t|||    || S r1  rY  r0  r  r  r  rO    r  rO  c                 C   rF  r1  r[  r0  r  r  r  rP    r  rP  c                 C      t td||  | ||    t|  | ||  || t|||    t| |t|||     ||t |td ||  | ||    tt| |t|||    ||t|||    t|||    || S r1  rY  r0  r  r  r  rQ    r  rQ  c                 C   rG  r1  r[  r0  r  r  r  rR    r  rR  c                 C      t td| ttdt| |t|||     ||t || ttdt| |t|||    ||t|||     t|||    || S rK  rL  r0  r  r  r  rS    r/  rS  c                 C   rH  rK  rN  r0  r  r  r  rT    r/  rT  c              	   C   sb   t t| |t|||    t||t|||     t|||   tt|||  ||S r&  )r  r  r  r  r   r0  r  r  r  rU    r,  rU  c              	   C   sj   t t| |t|||    t||t|||     t|||   ttdt|||   ||S rK  )r  r  r  r  r   r  r0  r  r  r  rV    rs  rV  c                 C      t |tt| |t|||    t||t|||     ||t |tt| |t|||    t||t|||    t|||    || S r&  r  r0  r  r  r  rW    r  rW  c                 C   rI  r&  r  r0  r  r  r  rX    r  rX  c                 C      t td| tt| |t|||    t||t|||     ||t || tt| |t|||    t||t|||    t|||    || S rK  rL  r0  r  r  r  rY    r  rY  c                 C   rJ  rK  rN  r0  r  r  r  rZ    r  rZ  c                 C   s   t td|  | tttd| | |td  td  ||t|||  t| |t|||    t||t|||      |S rA  rB  r0  r  r  r  r[    s   r[  c                 C   s   t td |  | tttd| | |td  td  ||tdt| |t|||    t||t|||     t|||    |S rA  rC  r0  r  r  r  r\    r  r\  c                 C      t | | tt||t|||    t| |t|||     ||t |  | ||  | ttdt| |t|||    t||t|||     t|||    || S rK  r  r0  r  r  r  r]    r  r]  c                 C   rK  rK  r  r0  r  r  r  r^    r  r^  c                 C   s  t td ttdtdt|||    |  | ||   | |t|||    ||    ttdtdt|||     |  | ||   | |t|||    ||    | |t|||     t| ||  || |   tt||t|||    t| | ||  td t| |t|||     | | ||  | | ||    || t| | ||  td t|||    |S rA  rU  r0  r  r  r  r_    s    r_  c                 C   s  t tdttdtdt|||    |  | ||   | |t|||    ||    ttdtdt|||     |  | ||   | |t|||    ||    | |t|||     t| ||  || |   tt||t|||    t| | ||  td t| |t|||     | | ||  | | ||    t|||   || t| | ||  td  |S rA  rV  r0  r  r  r  r`    s    r`  c              
   C   sj   t t|||  t| |t|||    t||t|||      ttdt|||   ||S rK  )r  r  r  r  r   r  r0  r  r  r  ra    rs  ra  c              
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   C   s   t | td t|||   |t| |t|||     t| |t|||      tt| ||  |tdd   |||  |  |t| ||    ||tdt|||   | S r  r  r  r  r  r  rg    r'  rg  c	           	   
   C   s   t | td t|||   |t| |t|||     t| |t|||      tt| ||  |tdd   |||  |  |t| ||    ||tdt|||   |S r  )r  r  r  r  r  r+   r   r  r  r  r  rh       rh  c	           	      C   X   t | t|||   | | |t|||   | |  t|||  | |   |S r&  re  r  r  r  r  ri    r+  ri  c	           	      C   rQ  r&  rg  r  r  r  r  rj    r+  rj  c	           	   	   C      t t| |t|||    t|t|||   |  t||t|||    t| t|||   |   t| t|||   | | |t|||   | |  t|||  | |   ||S r&  r  r  r  r  r  rk    rH  rk  c	           	   	   C   rR  r&  r  r  r  r  r  rl  !  rH  rl  c	           	   	   C      t | |t|||    | ||t|||    |  | t|||   | |   |t|||   | |   t|||  ||   t| t|||   | | |t|||   | |  t|||  | |   ||S r&  r6  r  r  r  r  rm  %  rb  rm  c	           	   	   C   rS  r&  r8  r  r  r  r  rn  )  rb  rn  c	           	   	   C   B   t t| |t|||    | ||t|||    | ||S r&  rv  r  r  r  r  ro  -  r|  ro  c	           	   	   C   rT  r&  ry  r  r  r  r  rp  1  r|  rp  c	           	      C   >   t | |t|||    | ||t|||    |  |S r&  re  r  r  r  r  rq  5  r  rq  c	           	      C   rU  r&  rg  r  r  r  r  rr  9  r  rr  c              	   C   L   t || t|t|||   | |  | t|||   | |  ||S r&  rA  rw  r  r  r  rs  =  r7  rs  c              	   C   rV  r&  rB  rw  r  r  r  rt  A  r7  rt  c
           
   
   C   s   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  ru  E  r  ru  c
           
   
   C   s   t |t| ||t|||	   |  t|  |t|||	   | t|   t|t|||	   ||  | |t|||	    |  |	|	S r&  )r  r%   r  r&   r   r  rW  r  r  r  rv  I  r  rv  c	           	      C   sp   t || |t|||    |  ||t|||    |  t|||   | | td| td   | S rA  r  r  r  r  r  r  r  r  rw  M  rr  rw  c	           	      C   sn   t || |t|||    |  ||t|||    |  | | td| td  t|||    |S rA  r  r  r  r  r  r  r  r  rx  Q  r  rx  c	           	   
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   C   s   t | | ttd|| t|||      t|||   || t| |t|||     t||t|||      | S rK  )r  logr  r  r  r  r0  r  r  r  r{  ]  rS  r{  c              
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   C   ra  r  rF  r  r  r  r  r    r  r  c	           	   
   C   rb  r  rI  r  r  r  r  r    r  r  c	           	      C   sj   t |  | | ttt|||  td|  t|||   ||t|||    | |  |||S rz  )r  r   rI  r  r  r  r  r  r  r  r    rs  r  c	           	      C   sr   t |  | | tttdt|||   td|  t|||   ||t|||    | |  |||S r1  )r  r   rI  r  r  r  r  r  r  r  r    rt  r  c              
   C   s   t |  | |tdd   t|||   t| |t|||    t||t|||      tt|||  td|  t|||   ||S r1  r  r  r  r  r  r    r/  r  c              
   C   s   t |  | |tdd   t| |t|||    t||t|||     t|||    ttdt|||   td|  t|||   ||S r1  r  r  r  r  r  r    r  r  c	           	   
   C   rZ  r1  rF  r  r  r  r  r    r[  r  c	           	   
   C   r\  r1  rI  r  r  r  r  r    r[  r  c	           	   
   C   s   t | | t|||   |t| |t|||     t||t|||      tt| ||  |tdd   |||  |tdd    ||tdt|||   | S r  r+  r  r  r  r  r    rZ  r  c	           	   
   C   s   t | | |t| |t|||     t||t|||     t|||    tt| ||  |tdd   |||  |tdd    ||tdt|||   |S r  r,  r  r  r  r  r       r  c                 C   sr   t |  | | tt|t|||
   |	 t|||
  td|   ||t|||
    | |  |
|
|
S rz  )r  r   rI  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r    rt  r  c                 C   sz   t |  | | tt|t|||
   |	 tdt|||
   td|   ||t|||
    | |  |
|
|
S r1  )r  r   rI  r  r  r  rd  r  r  r  r    r`  r  c
           
   
   C   s   t |  | |tdd   t|||	   t| |t|||	    t||t|||	      t|t|||	   | t|||	  td|   |	|	S r1  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|||	    t||t|||	     t|||	    t|t|||	   | tdt|||	   td|   |	|	S r1  r  re  r  r  r  r    r  r  c              
   C   s   t | | | t|||
   |t| |t|||
     t||t|||
      tt||
 |	td  | ||
  |tdd    |||
  |tdd    |
|
tdt|||
   |
 S r  r+  rd  r  r  r  r    rH  r  c              
   C   s   t | | | |t| |t|||
     t||t|||
     t|||
    tt||
 |	td  | ||
  |tdd    |||
  |tdd    |
|
tdt|||
   |
S r  r,  rd  r  r  r  r    rP  r  c                 C   s   t td| | | tttd| | ||  || |td    |||t|||   t|t|||   t| |t|||      |S rA  rB  r  r  r  r  r  r  r  r  r  r  r  r    r	  r  c                 C   s   t td | | | tttd| | ||  || |td    |||t|t|||   t| |t|||     t|||    |S rA  rC  rf  r  r  r  r    r/  r  c                 C      t | | tt|t|||   t| |t|||     ||t |  | ||  ||  t|t|||   tdd  t| |t|||    ||t|||      || S r  r  rf  r  r  r  r    rP  r  c                 C   rg  r  r  rf  r  r  r  r    rP  r  c                 C   sv   t td| | tttd| | ||  ||td    |||t|||   t| |t|||     |S rA  rB  r0  r  r  r  r    r?  r  c                 C   sx   t td | | tttd| | ||  ||td    |||t| |t|||    t|||    |S rA  rC  r0  r  r  r  r    rM  r  c                 C   s   t t|||t|||     t| |t|||     tt|t|||   ||t|||     |  | ||   | | ||    || t|| | |t|||     ||t|||    | | ||      |S r&  )r  r  r  r<   r	  r  r0  r  r  r  r    r  r  c                 C   s   t t|||t|||     t| |t|||     tt|||t|||    t|||    |  | ||   | | ||    || t|| | |t|||     ||t|||    | | ||      | S r&  )r  r  r  r<   r	  r  r0  r  r  r  r       r  c                 C      t || ttdt| |t|||    t|||    ||t |  | ||  | ttdt| |t|||    ||t|||     t|||    || S rK  r6  r0  r  r  r  r    rc  r  c                 C   ri  rK  r7  r0  r  r  r  r    rc  r  c                 C      t || tt|t|||   t| |t|||     ||t || | tt|t|||   t| |t|||     ||t|||     || S r&  r  rf  r  r  r  r    r  r  c                 C   rj  r&  r  rf  r  r  r  r    r  r  c                 C      t || t|t|||   tdd  t| |t|||     ||t |  | ||  | t|t|||   tdd  t| |t|||    ||t|||      || S r  r  r   r  r  r  rf  r  r  r  r    r  r  c                 C   rk  r  r  r   r  r  r  rf  r  r  r  r    r  r  c                 C      t ||  | ||   ttdt| |t|||    t|||    ||t ||  | ||   tt| |t|||    ||t|||    t|||    || S rK  r6  r0  r  r  r  r    r  r  c                 C   rn  rK  r7  r0  r  r  r  r    r  r  c                 C   s   t tdt| |t|||    | |   ttd| ||  tttdttdtdt|||     td td| | |   t|||   |tt|||  td   t| |t|||     ||   |S rA  r  r  r  r  r;   r	  r  r0  r  r  r  r    r  r  c                 C   s   t td t| |t|||    | |   ttd| ||  tttdttdtdt|||     td td| | |   |ttd t|||  td   t| |t|||     ||  t|||    |S rA  r  r  r  r  r;   r	  r  r0  r  r  r  r  	  r  r  c                 C      t | | |  | ||   tt|t|||   t| |t|||     || t || |  | ||   tt|t|||   t| |t|||     ||t|||     || S r&  r  rf  r  r  r  r    rP  r  c                 C   rq  r&  r  rf  r  r  r  r    rP  r  c              
   C      t |t|t|||    t| t|||   |  t| |t|||     ttdt| t|||   | |t|||   |   ||S rK  r  rf  r  r  r  r    r  r  c              
   C   rr  rK  r  rf  r  r  r  r    r  r  c                 C      t | |  | ||   ttdt| |t|||    t|||    || t ||  | ||   tt| |t|||    ||t|||    t|||    || S rK  r6  r0  r  r  r  r    r  r  c                 C   rs  rK  r7  r0  r  r  r  r  !  r  r  c                 C      t td| ttdt| |t|||    t|||    ||t || ttdt| |t|||    ||t|||     t|||    || S rK  rL  r0  r  r  r  r  %  r  r  c                 C   rt  rK  rN  r0  r  r  r  r  )  r  r  c                 C     t |td ||  | ||    tt|t|||   | | |  | ||  t|||     t| |t|||     ||t |td |td  ||  | ||    tt|t|||   t| |t|||     ||t|||     || S rz  rL  rf  r  r  r  r  -      r  c                 C   ru  rz  rN  rf  r  r  r  r  1  rv  r  c                 C      t || t|t|||   tdd  t| |t|||     ||t || | t|t|||   tdd  t| |t|||    ||t|||      || S r  rl  rf  r  r  r  r  5  r  r  c                 C   rw  r  rm  rf  r  r  r  r  9  r  r  c                 C   s   t td| | tttd| | |td  td  ||t|||  t| |t|||    t||t|||      |S rA  rB  r0  r  r  r  r  =  rn  r  c                 C   s   t td | | tttd| | |td  td  ||tdt| |t|||    t||t|||     t|||    |S rA  rC  r0  r  r  r  r  A  r	  r  c                 C      t || tt||t|||    t| |t|||    t|||    ||t |  | ||  | ttdt| |t|||    t||t|||     t|||    || S rK  r  r0  r  r  r  r  E  rP  r  c                 C   rx  rK  r  r0  r  r  r  r  I  rP  r  c                 C   s  t tdttdtdt|||    |  | ||   | |t|||    ||    ttdtdt|||     |  | ||   | |t|||    ||    | |t|||     t|||  || |   tt| | ||  t||t|||     t| |t|||     | | ||  | | ||    || t| | ||   t|||    |S rA  ro  r0  r  r  r  r  M  s    r  c                 C   s  t td ttdtdt|||    |  | ||   | |t|||    ||    ttdtdt|||     |  | ||   | |t|||    ||    | |t|||     t|||  || |   tt| | ||  t||t|||     t| |t|||     | | ||  | | ||    t|||   || t| | ||    |S rA  rp  r0  r  r  r  r  Q      r  c                 C   s   t td|  ||  tttd|td | | ||   td  ||t|||  t| |t|||    t||t|||      |S rA  rB  r0  r  r  r  r  U  r	  r  c                 C   s   t td |  ||  tttd|td | | ||   td  ||tdt| |t|||    t||t|||     t|||    |S rA  rC  r0  r  r  r  r  Y  r  r  c                 C   s  t tdttdtdt|||    |  | ||   | | ||t|||       ttdtdt|||     |  | ||   | | ||t|||       ||t|||     ttt| |t|||    t|| | |  td t||t|||     | | ||  | | ||    ||  | ||   t|| | |  td t|||    |S rA  r  r0  r  r  r  r  ]  r  r  c                 C   s  t td ttdtdt|||    |  | ||   | | ||t|||       ttdtdt|||     |  | ||   | | ||t|||       ||t|||     ttt| |t|||    t|| | |  td t||t|||     | | ||  | | ||    t|||   ||  | ||   t|| | |  td  |S rA  r  r0  r  r  r  r  a  s    r  c                 C      t td| tt| |t|||    t||t|||    t|||    ||t | | ttdt| |t|||    t||t|||     t|||    || S rK  rL  r0  r  r  r  r  e  r'  r  c                 C   rz  rK  rN  r0  r  r  r  r  i  r'  r  c                 C      t | | ||  ttdt| |t|||    t||t|||     t|||    ||t |  | ||  ||  ttdtdt|||    t| |t|||    ||t|||    tdd   t|||    || S rO  r6  r0  r  r  r  r  m     r  c                 C   r{  rO  r7  r0  r  r  r  r  q  r|  r  c              
   C   s   t | td | t|||
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|
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   |
 S r  r  rd  r  r  r  r  u  s   r  c              
   C   s   t | td | |t| |t|||
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S r  r  rd  r  r  r  r  y  r  r  c              	   C   p   t || |  t|t|||
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|
S r&  rA  rd  r  r  r  r  }  rr  r  c              	   C   r}  r&  rB  rd  r  r  r  r    rr  r  c              	   C      t ||  |t|||
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|
S r&  r6  rd  r  r  r  r    r  r  c              	   C   r~  r&  r8  rd  r  r  r  r    r  r  c              	   C      t |t|||
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    |  | t|||
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   | |  |
|
S r&  r6  rd  r  r  r  r    r  r  c              	   C   r  r&  r8  rd  r  r  r  r    r  r  c
           
   	   C      t t| |t|||	    t|t|||	   |  t||t|||	    t| t|||	   |   t| t|||	   | | |t|||	   | |  t|||	  | | |   |	|	S r&  r  rW  r  r  r  r    r  r  c
           
   	   C   r  r&  r  rW  r  r  r  r    r  r  c              	   C   \   t t|t|||
   |	 | |t|||
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    |  |
|
S r&  rv  rd  r  r  r  r    r  r  c              	   C   r  r&  ry  rd  r  r  r  r    r  r  c                 C   V   t |t|||
   |	 | |t|||
    |  ||t|||
    |  |
S r&  re  rd  r  r  r  r    r  r  c                 C   r  r&  rg  rd  r  r  r  r    r  r  c	           	      C   s  t td|  ttdtdt|||    | | ||   || ||t|||       tdtdt|||     ttt||t|||    t|| ||  td t||t|||     || ||  || ||    |ttdtdt|||     | | ||   || ||t|||       | | ||   t|| ||  td t|||    |S rA  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dtdt|||    | | ||   || ||t|||       tdtdt|||     ttt||t|||    t|| ||  td t||t|||     || ||  || ||    t|||   |ttdtdt|||     | | ||   || ||t|||       | | ||   t|| ||  td  |S rA  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d  || |  t|||    | ||t| | |t|||   |  t|||   ||  | S rK  rF  	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|||    | ||t| | |t|||   |  || t|||    | S rK  rI  r  r  r  r  r    r  r  c	           	      C   s   t td|td  t|t|||   | t| | |td  || |  |td | | ||   t|||    | ||t|| |t|||   |  t|||   ||td   | S rK  rF  r  r  r  r  r    r  r  c	           	      C   s   t td|td  t|t|||   | t| | |td  || |  |td | | ||   t|||    | ||t|| |t|||   |  ||td  t|||    | S rK  rI  r  r  r  r  r    r  r  c                 C   x   t || ttdt|||   ||t | | ||  | ttd||t|||    t|||    || S rK  )r  r   r  r  r  r  r  r  r  r  r  r  r  r  r    rM  r  c                 C   r  rK  )r  r   r  r  r  r  r  r  r    rM  r  c                 C   sF   t |||t|||    |  t|||   ||td   |S rK  rX  r  r  r  r  r  r  r  r  r  r  r  r       Fr  c                 C   sH   t |||t|||    |  ||td  t|||    | S rK  rY  r  r  r  r  r    s   Hr  c              	   C   s   t | | |td  || |  || td| td   t||t|||    |td  t|||   ||t||t|||    | | | ||   t|||   || td| td   | S r1  rF  r  r  r  r  r    r"  r  c              	   C   s   t | | |td  || |  || td| td   t||t|||    |td  t|||   ||t||t|||    | | | ||   || td| td  t|||    | S r1  rI  r  r  r  r  r    r"  r  c              	   C   s   t | | |td  || |  ||td   t||t|||    | t|||   ||t|||t|||    |  t|||   ||td   | S rK  rF  r  r  r  r  r    r  r  c              	   C   s   t | | |td  || |  ||td   t||t|||    | t|||   ||t|||t|||    |  ||td  t|||    | S rK  rI  r  r  r  r  r    r  r  c                 C   s   t td|td  t||t|||    |td  t| | |td  || |  | | |td  || |  t|||    | t|||   ||t|||t|||    |  t|||   ||td   | S r  rF  r  r  r  r  r    rh  r  c                 C   s   t td|td  t||t|||    |td  t| | |td  || |  | | |td  || |  t|||    | t|||   ||t|||t|||    |  ||td  t|||    | S r  rI  r  r  r  r  r    rh  r  c                 C   s*  t td|td |td  |td   t||t|||    |td  t|td | | ||   |td | | ||   t|||    | t|||   ||t||t|||    |td  | | ||   t|||   ||td |td   |td   | S r1  rF  r  r  r  r  r       , r  c                 C   s*  t td|td |td  |td   t||t|||    |td  t|td | | ||   |td | | ||   t|||    |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   C      t || t||t|||    |td  t|||   ||t | | ||  | t||t|||    | t|||   || S rK  ri  r  r  r  r  r    r  r  c              
   C   r  rK  rk  r  r  r  r  r    r  r  c                 C   s  t td|td td| td   t||t|||    |td  t| | | || |  || td| td  t|||    | t|||   ||t||t|||    | | | ||   t|||   || td| td   | S r1  rF  r  r  r  r  r    rv  r  c                 C   s  t td|td td| td   t||t|||    |td  t| | | || |  || td| td  t|||    | t|||   ||t||t|||    | | | ||   || td| td  t|||    | S r1  rI  r  r  r  r  r    rv  r  c                 C   s`  t td||td |td   |td   t||t|||    |td  t||td  | | ||   | | | |td  ||td |td |td     t|||    | t|||   || t|||t|||    |td   | | ||   t|||   || |td |td   |td   | S r1  rF  r  r  r  r  r       b r  c                 C   s`  t td||td |td   |td   t||t|||    |td  t||td  | | ||   | | | |td  ||td |td |td     t|||    | t|||   || t|||t|||    |td   | | ||   || |td |td   |td  t|||    | S r1  rI  r  r  r  r  r  !  r  r  c                 C   s   t td||td   t||t|||    | t|| |td  | | |td  ||  t|||    | t|||   ||t|||t|||    |td   t|||   || |td   | S r1  rF  r  r  r  r  r  %     r  c                 C   s   t td||td   t||t|||    | t|| |td  | | |td  ||  t|||    | t|||   ||t|||t|||    |td   || |td  t|||    | S r1  rI  r  r  r  r  r  )  r  r  c
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      C   sX   t | |t|||	   |  ||t|||	    |  t|||	   ||  |	 S r&  r  r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r  -  r+  r  c
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      C   s  t td||td |td   |td   t|t|||	   | ||t|||	    |td   t| |td |td  |td || td    || | |  ||td  | | ||   t|||	    || | ||   || td  t|||	  td   |	 |	|	t||t|||	   |  ||t|||	    |td   | | ||   t|||	   || |td |td   |td   |	 S r1  rF  r  r  r  r  r        r  c
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      C   sF  t |||  t|t|||	   |td  ||t|||	    |td   t|| |td  | | ||  || || td   t|||	    | | ||  || |  t|||	  td   |	 |	|	t|| |t|||	   |td   ||t|||	    |  t|||	   |||   |	 S r  r  r  r  r  r  r    r  r  c
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           
      C   R   t |t|||	   | | |t|||	     ||t|||	    |  |	S r&  re  r  r  r  r  r$       Rr$  c
           
      C   r  r&  rg  r  r  r  r  r%    r  r%  c              	   C   s   t | | | t| t|||   | |
 |t|||   | | |	   t|||  td|   t|||  | |	 |
   ||S rz  )r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r&    r  r&  c              	   C   s   t | | | t| t|||   | |
 |t|||   | | |	   t|||  | |	 |
   t|||  td|   ||S rz  )r  r   r  r  r  r  r  r  r  r'  	  r  r'  c	           	      C   h   t |td t||t|||    |td  t|| ||  || t|||    | ||S r3  r=  	r  r  r  r  r  r  r  r  r  r  r  r  r(    r  r(  c	           	      C   r  r3  r@  r  r  r  r  r)    r  r)  c                 C   ^   t ||td  t||t|||    |td  t| |t|||    | ||S rA  r=  r  r  r  r  r  r  r  r  r  r  r  r*    r  r*  c                 C   r  rA  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,    r  r,  c                 C   s:   t | |t|||   |  || t|||    |S r&  r  r  r  r  r  r-  !  r  r-  c                 C   s   t | |td  ||  |td |  t|t|||   |td  ||t| |t|||   |  t|||   ||  | S r1  rF  r  r  r  r  r.  %  rn  r.  c                 C   s   t | |td  ||  |td |  t|t|||   |td  ||t| |t|||   |  || t|||    | S r1  rI  r  r  r  r  r/  )  rn  r/  c                 C   s   t | |td  ||  |td  t|t|||   | ||t||t|||   |  t|||   ||td   | S rK  rF  r  r  r  r  r0  -  r2  r0  c                 C   s   t | |td  ||  |td  t|t|||   | ||t||t|||   |  ||td  t|||    | S rK  rI  r  r  r  r  r1  1  r2  r1  c              	   C   l   t | | t|t|||   |td  ||t ||td  t|t|||   |td  || S r1  ri  r  r  r  r  r  r  r  r  r  r  r2  5  r  r2  c              	   C   r  r1  rk  r  r  r  r  r3  9  r  r3  c              	   C   p   t || t|t|||   |td  ||t|t|||   | | |t|||  td    | S r1  ri  r  r  r  r  r  r  r  r  r  r  r  r4  =  rr  r4  c              	   C   r  r1  rk  r  r  r  r  r5  A  rr  r5  c              
   C   s   t tdd tttd|  | td| | |td|  |   t|||    td|| ||   t|||  td   |||t|| t|||   td| t|||    | S r1  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r6  E  rP  r6  c              
   C   s   t tdd tttd|  | td| | |td|  |   t|||    td|| ||   t|||  td   |||t|| td| t|||   t|||    | S r1  r  r  r   r  r  r  r  r  r  r  r7  I  rP  r7  c              
   C   s   t tdd tttd|  | td| | t|||  td   |td|  |  t|||    |||t|| t|||   td| t|||    | S r1  r  r  r  r  r  r  r  r  r  r  r  r8  M  rc  r8  c              
   C   s   t tdd tttd|  | td| | t|||  td   |td|  |  t|||    |||t|| td| t|||   t|||    | S r1  r  r  r  r  r  r9  Q  rc  r9  c              
   C      t td| t| | || ||  t|||    ||t|||     ||t || ttdt|||   || S rK  rm  r  r  r  r  r:  U  r  r:  c              
   C   r  rK  ro  r  r  r  r  r;  Y  r  r;  c              
   C   x   t td| t| | || t|||    ||t|||     ||t || ttdt|||   || S rK  rm  r  r  r  r  r<  ]  rM  r<  c              
   C   r  rK  ro  r  r  r  r  r=  a  rM  r=  c	           	      C   s  t td|| td| td   t||t|||    |td  t| | td| td  || |td  || |td  ||    t|||    | ||t||t|||    | | | ||  ||   t|||   || td| td   | S r1  rF  r  r  r  r  r>  e      r>  c	           	      C   s  t td|| td| td   t||t|||    |td  t| | td| td  || |td  || |td  ||    t|||    | ||t||t|||    | | | ||  ||   || td| td  t|||    | S r1  rI  r  r  r  r  r?  i  r  r?  c                 C   s   t td|| td| td   t||t|||    |td  t| | td| td  || |td  ||   t|||    | ||t| | ||t|||    |  t|||   |td| td   | S r1  rF  r  r  r  r  r@  m     r@  c                 C   s   t td|| td| td   t||t|||    |td  t| | td| td  || |td  ||   t|||    | ||t| | ||t|||    |  |td| td  t|||    | S r1  rI  r  r  r  r  rA  q  r  rA  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td  || |  t|||    | ||t|||t|||    |  t|||   ||td   | S rK  rF  r  r  r  r  rB  u  r  rB  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td  || |  t|||    | ||t|||t|||    |  ||td  t|||    | S rK  rI  r  r  r  r  rC  y  r  rC  c                 C   s   t td||td   t||t|||    | t| | |td  || | t|||    | ||t|||t|||    |  t|||   ||td   | S rK  rF  r  r  r  r  rD  }  r  rD  c                 C   s   t td||td   t||t|||    | t| | |td  || | t|||    | ||t|||t|||    |  ||td  t|||    | S rK  rI  r  r  r  r  rE    r  rE  c	           	      C   s  t td|td  t||t|||    |td  t| | |td  || |td  || |  t|||  td   || | |td | | ||    t|||    | ||t|||t|||    |  t|||   ||td   | S r  rF  r  r  r  r  rF    r  rF  c	           	      C   s  t td|td  t||t|||    |td  t| | |td  || |td  || |  t|||  td   || | |td | | ||    t|||    | ||t|||t|||    |  ||td  t|||    | S r  rI  r  r  r  r  rG    r  rG  c                 C   s   t td|td  t||t|||    |td  t| | |td  || | t|||  td   | | |td  || |  t|||    | ||t|||t|||    |  t|||   ||td   | S r  rF  r  r  r  r  rH    r  rH  c                 C   s   t td|td  t||t|||    |td  t| | |td  || | t|||  td   | | |td  || |  t|||    | ||t|||t|||    |  ||td  t|||    | S r  rI  r  r  r  r  rI    r  rI  c                 C      t |ttdtdt|||    t||t|||    t|||    ||t| || t|||    t||t|||     | S rK  r  r  r  r  r  rJ    r/  rJ  c                 C   r  rK  r  r  r  r  r  rK    r/  rK  c                 C      t |ttdtdt|||    t||t|||    t|||    ||t| |t|||    t||t|||     | S rK  r  r  r  r  r  rL    r  rL  c                 C   r  rK  r  r  r  r  r  rM    r  rM  c	           	      C   s  t td||td |td   |td   t||t|||    |td  t| |td |td   |td  ||td  | | ||  ||   t|||    |td | |td  || |  ||td    t|||  td   | ||t||t|||    |td  | |td  || |  ||td    t|||   || |td |td   |td   | S r1  rF  r  r  r  r  rN        rN  c	           	      C   s  t td||td |td   |td   t||t|||    |td  t| |td |td   |td  ||td  | | ||  ||   t|||    |td | |td  || |  ||td    t|||  td   | ||t||t|||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   C      t td| t||t|||    | | | || ||  t|||     ||t || t||t|||    |td  t|||   || S rK  rm  r  r  r  r  rR    r  rR  c	           	   
   C   r  rK  ro  r  r  r  r  rS    r  rS  c              
   C      t td| t||t|||    | | | || t|||     ||t || t||t|||    |td  t|||   || S rK  rm  r  r  r  r  rT    r/  rT  c              
   C   r  rK  ro  r  r  r  r  rU    r/  rU  c              
   C   j   t |td t|t|||   |td  | t|||  td  |t|||    |  ||S r  rm  r  r  r  r  rV    rs  rV  c              
   C   r  r  ro  r  r  r  r  rW    rs  rW  c              	   C   V   t |td t|t|||   |td  | t|||  td  |  ||S r  rm  r  r  r  r  rX    r  rX  c              	   C   r  r  ro  r  r  r  r  rY    r  rY  c
           
   
   C      t |t| ||t|||	   |  t|  |t|||	   | t|   t|t|||	   ||  | |t|||	    |t|||	  td    |	|	S rz  r  r%   r  r&   r   r  
r  r  r  r  r  r  r  r  r   r  r  r  r  rZ    r  rZ  c
           
   
   C   r  rz  r  r%   r  r&   r   r  r  r  r  r  r[    r  r[  c	           	   
   C      t |t| ||t|||   |  t|  |t|||   | t|   t|t|||   ||  | |t|||  td    ||S rz  r  	r  r  r  r  r  r  r  r   r  r  r  r  r\    r/  r\  c	           	   
   C   r  rz  r  r  r  r  r  r]    r/  r]  c
           
      C   s   t td||  t|t|||	   |td  t|| | t|||	  td  || | ||    | | |td  ||| ||    t|||	    |	 |	|	t| | |t|||	   |  t|||	   ||  |	 S r1  rF  
r  r  r  r  r  r  r  r  r  r  r  r  r  r^    rh  r^  c
           
      C   s   t td||  t|t|||	   |td  t|| | t|||	  td  || | ||    | | |td  ||| ||    t|||	    |	 |	|	t| | |t|||	   |  || t|||	    |	 S r1  rI  r  r  r  r  r_    rh  r_  c	           	      C   s   t td||  t|t|||   |td  t| | | || | t|||  td   || |td  ||   t|||    | ||t| | |t|||   |  t|||   ||  | S r1  rF  	r  r  r  r  r  r  r  r  r  r  r  r  r`       r`  c	           	      C   s   t td||  t|t|||   |td  t| | | || | t|||  td   || |td  ||   t|||    | ||t| | |t|||   |  || t|||    | S r1  rI  r  r  r  r  ra    r  ra  c
           
      C   s"  t td|td  t|t|||	   | t| | |td  |td || ||   t|||	  td   || |td  || |td  ||td     t|||	    |	 |	|	t|| |t|||	   |  t|||	   ||td  t|||	    |	 S r1  rF  r  r  r  r  rb    r  rb  c
           
      C   s"  t td|td  t|t|||	   | t| | |td  |td || ||   t|||	  td   || |td  || |td  ||td     t|||	    |	 |	|	t|| |t|||	   |  ||td  t|||	   t|||	    |	 S r1  rI  r  r  r  r  rc    r  rc  c	           	      C   s  t td|td  t|t|||   | t| | |td  || |td  t|||  td   || |td  ||td    t|||    | ||t|| |t|||   |  t|||   ||td  t|||    | S r1  rF  r  r  r  r  rd    r>  rd  c	           	      C   s  t td|td  t|t|||   | t| | |td  || |td  t|||  td   || |td  ||td    t|||    | ||t|| |t|||   |  ||td  t|||   t|||    | S r1  rI  r  r  r  r  re    r>  re  c	           	      C   sV  t td|| td| td   t||t|||    |td  ttd |  | |td  ||  ||  || |td  || |td  ||td     t|||    | t|||   || t||t|||    | | | ||  ||   t|||   || td| td  t|||    | S r  rF  r  r  r  r  rf    r  rf  c	           	      C   sV  t td|| td| td   t||t|||    |td  ttd |  | |td  ||  ||  || |td  || |td  ||td     t|||    | t|||   || t||t|||    | | | ||  ||   || td| td  t|||   t|||    | S r  rI  r  r  r  r  rg  	  r  rg  c                 C   s&  t td|| td| td   t||t|||    |td  ttd |  | |td  ||  || |td  ||td    t|||    | t|||   || t| | ||t|||    |  t|||   |td| td  t|||    | S r  rF  r  r  r  r  rh       ( rh  c                 C   s&  t td|| td| td   t||t|||    |td  ttd |  | |td  ||  || |td  ||td    t|||    | t|||   || t| | ||t|||    |  |td| td  t|||   t|||    | S r  rI  r  r  r  r  ri    r  ri  c	           	      C   s  t td||td |td   |td   t||t|||    |td  t||td  | | ||  ||   | |td  || |  ||td   ||td  | | ||  ||    t|||    | t|||   ||t||t|||    |td  | |td  || |  ||td    t|||   || |td |td   |td   | S r1  rF  r  r  r  r  rj        rj  c	           	      C   s  t td||td |td   |td   t||t|||    |td  t||td  | | ||  ||   | |td  || |  ||td   ||td  | | ||  ||    t|||    | t|||   ||t||t|||    |td  | |td  || |  ||td    || |td |td   |td  t|||    | S r1  rI  r  r  r  r  rk    r  rk  c                 C   sf  t td||td |td   |td   t||t|||    |td  t|| | |  |td  | |td  ||td   ||td  | | ||    t|||    | t|||   ||t||t|||    |td  | |td  ||td    t|||   || |td |td   |td   | S r1  rF  r  r  r  r  rl       h rl  c                 C   sf  t td||td |td   |td   t||t|||    |td  t|| | |  |td  | |td  ||td   ||td  | | ||    t|||    | t|||   ||t||t|||    |td  | |td  ||td    || |td |td   |td  t|||    | S r1  rI  r  r  r  r  rm  !  r  rm  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td   || |td  ||  t|||    | t|||   ||t|||t|||    |td   t|||   || |td   | S r1  rF  r  r  r  r  rn  %  r  rn  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td   || |td  ||  t|||    | t|||   ||t|||t|||    |td   || |td  t|||    | S r1  rI  r  r  r  r  ro  )  r  ro  c                 C   s   t td||td   t||t|||    | t| | |td  || t|||    || |td   | t|||   ||t|||t|||    |td   t|||   || |td   | S r1  rF  r  r  r  r  rp  -  r  rp  c                 C   s   t td||td   t||t|||    | t| | |td  || t|||    || |td   | t|||   ||t|||t|||    |td   || |td  t|||    | S r1  rI  r  r  r  r  rq  1  r  rq  c                 C   sv  t td|| td| td   t|t|||
   |	 ||t|||
    |td   t|  | td| |	 td  || |	  || |	  || ||	 td  || ||	 td  |||	     t|||
    |
 |
|
 t|t|||
   |	 ||t|||
    |  | | ||  ||   t|||
   || td| td   |
 S r1  rF  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rr  5  r?  rr  c                 C   sv  t td|| td| td   t|t|||
   |	 ||t|||
    |td   t|  | td| |	 td  || |	  || |	  || ||	 td  || ||	 td  |||	     t|||
    |
 |
|
 t|t|||
   |	 ||t|||
    |  | | ||  ||   || td| td  t|||
    |
 S r1  rI  r  r  r  r  rs  9  r?  rs  c
           
      C   s:  t td|| td| td   t|t|||	   | ||t|||	    |td   t| | td| | td  || |  || || td  |||    t|||	    |	 |	|	t|t|||	   | | |  ||t|||	    |  t|||	   |td| td   |	 S r1  rF  
r  r  r  r  r  r  r  r  r  r  r  r  r  rt  =  r  rt  c
           
      C   s:  t td|| td| td   t|t|||	   | ||t|||	    |td   t| | td| | td  || |  || || td  |||    t|||	    |	 |	|	t|t|||	   | | |  ||t|||	    |  |td| td  t|||	    |	 S r1  rI  r  r  r  r  ru  A  r  ru  c                 C   s   t td|| |	  t|t|||
   |	td  ||t|||
    |  t| | | || |	  || ||	 td  ||	   t|||
    |
 |
|
 t| |t|||
   |	  ||t|||
    |  t|||
   ||	  |
 S rK  rF  r  r  r  r  rv  E  r  rv  c                 C   s   t td|| |	  t|t|||
   |	td  ||t|||
    |  t| | | || |	  || ||	 td  ||	   t|||
    |
 |
|
 t| |t|||
   |	  ||t|||
    |  ||	 t|||
    |
 S rK  rI  r  r  r  r  rw  I  r  rw  c
           
      C   s   t td|| |  t|t|||	   |td  ||t|||	    |  t| | | || || td  ||   t|||	    |	 |	|	 t| |t|||	   |  ||t|||	    |  t|||	   ||  |	 S rK  rF  r  r  r  r  rx  M  r  rx  c
           
      C   s   t td|| |  t|t|||	   |td  ||t|||	    |  t| | | || || td  ||   t|||	    |	 |	|	 t| |t|||	   |  ||t|||	    |  || t|||	    |	 S rK  rI  r  r  r  r  ry  Q  r  ry  c                 C   s  t td|||	 td   t|t|||
   |	 ||t|||
    |  t| | ||	 td  || |	  || ||	 td  || |  t|||
    |
 |
|
t||t|||
   |	  ||t|||
    |  t|||
   |||	 td   |
 S rK  rF  r  r  r  r  rz  U  r  rz  c                 C   s  t td|||	 td   t|t|||
   |	 ||t|||
    |  t| | ||	 td  || |	  || ||	 td  || |  t|||
    |
 |
|
t||t|||
   |	  ||t|||
    |  |||	 td  t|||
    |
 S rK  rI  r  r  r  r  r{  Y  r  r{  c
           
      C   s  t td||| td   t|t|||	   | ||t|||	    |  t| | || td  || | t|||	    || |  |	 |	|	t||t|||	   |  ||t|||	    |  t|||	   ||| td   |	 S rK  rF  r  r  r  r  r|  ]  r  r|  c
           
      C   s  t td||| td   t|t|||	   | ||t|||	    |  t| | || td  || | t|||	    || |  |	 |	|	t||t|||	   |  ||t|||	    |  ||| td  t|||	    |	 S rK  rI  r  r  r  r  r}  a  r  r}  c	           	      C   s  t td|td |td |td   |td   t||t|||    |td  t| | |td |td   |td  t|||  td  ||td  | |td  ||| ||      || |td |td |td    || |td  |td  ||td |td |td       t|||    | t|||   || t|||t|||    |td   | |td  || |  ||td    t|||   |td | |td |td   |td   | S r1  rF  r  r  r  r  r~  e       r~  c	           	      C   s  t td|td |td |td   |td   t||t|||    |td  t| | |td |td   |td  t|||  td  ||td  | |td  ||| ||      || |td |td |td    || |td  |td  ||td |td |td       t|||    | t|||   || t|||t|||    |td   | |td  || |  ||td    |td | |td |td   |td  t|||    | S r1  rI  r  r  r  r  r  i  r  r  c                 C   s  t td|td |td |td   |td   t||t|||    |td  t| | |td |td   |td  t|||  td  || |td  |td  ||td |td |td      t|||    ||td  | |td  ||td     | t|||   || t|||t|||    |td   | |td  ||td    t|||   |td | |td |td   |td   | S r1  rF  r  r  r  r  r  m      r  c                 C   s  t td|td |td |td   |td   t||t|||    |td  t| | |td |td   |td  t|||  td  || |td  |td  ||td |td |td      t|||    ||td  | |td  ||td     | t|||   || t|||t|||    |td   | |td  ||td    |td | |td |td   |td  t|||    | S r1  rI  r  r  r  r  r  q  r  r  c	           	      C   s0  t td||td   t||t|||    | t|| || |td  ||td    t|||    | | |td  td| |  t|||  td   | t|||   ||t|||t|||    |td   t|||   || |td  t|||    | S rO  rF  r  r  r  r  r  u  r  r  c	           	      C   s0  t td||td   t||t|||    | t|| || |td  ||td    t|||    | | |td  td| |  t|||  td   | t|||   ||t|||t|||    |td   || |td  t|||   t|||    | S rO  rI  r  r  r  r  r  y  r  r  c                 C   s  t td||td   t||t|||    | t|| td| | t|||  td   || |td  ||td    t|||    | t|||   ||t|||t|||    |td   t|||   || |td  t|||    | S rO  rF  r  r  r  r  r  }  r  r  c                 C   s  t td||td   t||t|||    | t|| td| | t|||  td   || |td  ||td    t|||    | t|||   ||t|||t|||    |td   || |td  t|||   t|||    | S rO  rI  r  r  r  r  r    r  r  c                 C   sD  t td||	  t|t|||
   |	td  ||t|||
    |td   t| | | || |	  || ||	 td  ||	   t|||
  td   || |	 || |	td  ||	    t|||
    |
 |
|
 t| |t|||
   |	  ||t|||
    |  t|||
   ||	  |
 S r  rF  r  r  r  r  r       F r  c                 C   sD  t td||	  t|t|||
   |	td  ||t|||
    |td   t| | | || |	  || ||	 td  ||	   t|||
  td   || |	 || |	td  ||	    t|||
    |
 |
|
 t| |t|||
   |	  ||t|||
    |  ||	 t|||
    |
 S r  rI  r  r  r  r  r    r  r  c
           
      C   s,  t td||  t|t|||	   |td  ||t|||	    |td   t| | | || |td  ||   t|||	    || || td  ||   t|||	  td   |	 |	|	 t| |t|||	   |  ||t|||	    |  t|||	   ||  |	 S r  rF  r  r  r  r  r       . r  c
           
      C   s,  t td||  t|t|||	   |td  ||t|||	    |td   t| | | || |td  ||   t|||	    || || td  ||   t|||	  td   |	 |	|	 t| |t|||	   |  ||t|||	    |  || t|||	    |	 S r  rI  r  r  r  r  r    r  r  c                 C   sf  t td||	 td  t|t|||
   |	 ||t|||
    |td   t| | ||	 td  || |	  || ||	 td  || |  t|||
  td   || ||	  | | ||  ||	 td   t|||
    |
 |
|
t||t|||
   |	  ||t|||
    |  t|||
   |||	 td   |
 S r  rF  r  r  r  r  r    r  r  c                 C   sf  t td||	 td  t|t|||
   |	 ||t|||
    |td   t| | ||	 td  || |	  || ||	 td  || |  t|||
  td   || ||	  | | ||  ||	 td   t|||
    |
 |
|
t||t|||
   |	  ||t|||
    |  |||	 td  t|||
    |
 S r  rI  r  r  r  r  r    r  r  c
           
      C   sB  t td|| td  t|t|||	   | ||t|||	    |td   t| | || td  || | t|||	  td   || |  || || td  |||    t|||	    |	 |	|	t||t|||	   |  ||t|||	    |  t|||	   ||| td   |	 S r  rF  r  r  r  r  r       D r  c
           
      C   sB  t td|| td  t|t|||	   | ||t|||	    |td   t| | || td  || | t|||	  td   || |  || || td  |||    t|||	    |	 |	|	t||t|||	   |  ||t|||	    |  ||| td  t|||	    |	 S r  rI  r  r  r  r  r    r  r  c                 C   s  t |||td |td   |td   t|t|||
   |	td  ||t|||
    |td   t| |td  |	td  ||	td  || ||    ||td  | | ||  ||   t|||
    ||td |	 |td |td    || | ||   ||	 td   t|||
  td   |
 |
|
t||t|||
   |	td   ||t|||
    |td   | |td  || |  ||td    t|||
   || |td |td   |td   |
 S r  rF  r  r  r  r  r         r  c                 C   s  t |||td |td   |td   t|t|||
   |	td  ||t|||
    |td   t| |td  |	td  ||	td  || ||    ||td  | | ||  ||   t|||
    ||td |	 |td |td    || | ||   ||	 td   t|||
  td   |
 |
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t||t|||
   |	td   ||t|||
    |td   | |td  || |  ||td    || |td |td   |td  t|||
    |
 S r  rI  r  r  r  r  r    r  r  c
           
      C   s  t |||td |td   |td   t|t|||	   |td  ||t|||	    |td   t| |td  |td  ||td  |td   || | |  |td  t|||	    | |td  || td  ||td | |td |td     t|||	  td   |	 |	|	t||t|||	   |td   ||t|||	    |td   | |td  ||td    t|||	   || |td |td   |td   |	 S r  rF  r  r  r  r  r        r  c
           
      C   s  t |||td |td   |td   t|t|||	   |td  ||t|||	    |td   t| |td  |td  ||td  |td   || | |  |td  t|||	    | |td  || td  ||td | |td |td     t|||	  td   |	 |	|	t||t|||	   |td   ||t|||	    |td   | |td  ||td    || |td |td   |td  t|||	    |	 S r  rI  r  r  r  r  r    r  r  c                 C   s  t td||td |td   |td   t|t|||
   |	 ||t|||
    |td   t||td  | | ||  ||   ||td  | | ||  ||   t|||
    ||	 td | |td  || |  ||td     ||	 td | |td  || |  ||td    t|||
  td   |
 |
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   || |td |td   |td   |
 S r1  rF  r  r  r  r  r         r  c                 C   s  t td||td |td   |td   t|t|||
   |	 ||t|||
    |td   t||td  | | ||  ||   ||td  | | ||  ||   t|||
    ||	 td | |td  || |  ||td     ||	 td | |td  || |  ||td    t|||
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 |
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   |	 ||t|||
    |td   | |td  || |  ||td    || |td |td   |td  t|||
    |
 S r1  rI  r  r  r  r  r    r  r  c
           
      C   s  t td||td |td   |td   t|t|||	   | ||t|||	    |td   t|td | |  |td  || | |  |td  t|||	    | |td  ||td   || td   | |td  ||td   || td  t|||	  td   |	 |	|	t|t|||	   | ||t|||	    |td   | |td  ||td    t|||	   || |td |td   |td   |	 S r1  rF  r  r  r  r  r    r  r  c
           
      C   s  t td||td |td   |td   t|t|||	   | ||t|||	    |td   t|td | |  |td  || | |  |td  t|||	    | |td  ||td   || td   | |td  ||td   || td  t|||	  td   |	 |	|	t|t|||	   | ||t|||	    |td   | |td  ||td    || |td |td   |td  t|||	    |	 S r1  rI  r  r  r  r  r    r  r  c                 C   sf  t ||||	 td   t|t|||
   |	td  ||t|||
    |  t|| |	td  | | ||	 td  || ||	   t|||
    || ||	 td  || |	  t|||
  td   |
 |
|
t|| |t|||
   |	td   ||t|||
    |td   t|||
   || ||	 td   |
 S r  rF  r  r  r  r  r    r  r  c                 C   sf  t ||||	 td   t|t|||
   |	td  ||t|||
    |  t|| |	td  | | ||	 td  || ||	   t|||
    || ||	 td  || |	  t|||
  td   |
 |
|
t|| |t|||
   |	td   ||t|||
    |td   || ||	 td  t|||
    |
 S r  rI  r  r  r  r  r    r  r  c
           
      C   sP  t |||| td   t|t|||	   |td  ||t|||	    |  t| | | t|||	  td  || |td   | | || td  || ||   t|||	    |	 |	|	t|| |t|||	   |td   ||t|||	    |td   t|||	   || || td   |	 S r  rF  r  r  r  r  r    rc  r  c
           
      C   sP  t |||| td   t|t|||	   |td  ||t|||	    |  t| | | t|||	  td  || |td   | | || td  || ||   t|||	    |	 |	|	t|| |t|||	   |td   ||t|||	    |td   || || td  t|||	    |	 S r  rI  r  r  r  r  r    rc  r  c                 C   s@  t td|| |	  t|t|||
   |	td  ||t|||
    |  t|  | ||	 td  | | ||	 td  t|||
  td   || |	  || |	 |  ||	   t|||
    |
 |
|
t| |t|||
   |	  ||t|||
    |td   t|||
   || |	  |
 S r1  rF  r  r  r  r  r    r  r  c                 C   s@  t td|| |	  t|t|||
   |	td  ||t|||
    |  t|  | ||	 td  | | ||	 td  t|||
  td   || |	  || |	 |  ||	   t|||
    |
 |
|
t| |t|||
   |	  ||t|||
    |td   || |	 t|||
    |
 S r1  rI  r  r  r  r  r    r  r  c
           
      C   s4  t td|| |  t|t|||	   |td  ||t|||	    |  t|  | || td  | | || td  t|||	  td   || | |  ||   t|||	    |	 |	|	t| |t|||	   |  ||t|||	    |td   t|||	   || |  |	 S r1  rF  r  r  r  r  r    r  r  c
           
      C   s4  t td|| |  t|t|||	   |td  ||t|||	    |  t|  | || td  | | || td  t|||	  td   || | |  ||   t|||	    |	 |	|	t| |t|||	   |  ||t|||	    |td   || | t|||	    |	 S r1  rI  r  r  r  r  r    r  r  c	           	      C      t |td t| | | | ||  t|||    t|t|||    ||t | |td  || |  ||td   |td |td   t|t|||   tdd  ||t|||     || S r  rY  	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d t| | | | t|||    t|t|||    ||t | |td  ||td   |td |td   t|t|||   tdd  ||t|||     || S r  rY  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d  t|t|||   tdd  t||t|||     ||t| |t|||    t|t|||   t||t|||      | S Nr  r  rY  r  r  r  r  r    r  r  c	           	      C   r  r  r[  r  r  r  r  r    r  r  c                 C      t | ttdt|t|||   t||t|||      ||t ||td  t|t|||   tdd  t||t|||     || S r  r6  r  r  r  r  r    r  r  c                 C   r  r  r7  r  r  r  r  r    r  r  c                 C   n   t |t|||
   |	 ||t|||
    |  | |t|||
    |t|||
  td    |
S rz  r   r  r  r  r  r  r  r    r  r  c                 C   r  rz  r   r  r  r  r  r  r  r  	  r  r  c
           
      C   Z   t |t|||	   | | |t|||	  td    ||t|||	    |  |	S rz  r  r  r  r  r  r    r  r  c
           
      C   r  rz  r  r  r  r  r  r    r  r  c              
   C      t ||td  t|t|||
   | |	 td  |t|||
   | |  | t|||
  td  |t|||
    |  |
|
S r  rm  r  r  r  r  r    r  r  c              
   C   r  r  ro  r  r  r  r  r    r  r  c
           
   	   C   |   t ||td  t|t|||	   | | td  | t|||	  td  |  |t|||	   | |  |	|	S r  rm  r  r  r  r  r    r  r  c
           
   	   C   r  r  ro  r  r  r  r  r  !  r  r  c              
   C      t |t|
 ||t|||   |  t|
  |t|||   | t|
   t|t|||   |
|  ||t|||    |	  | |t|||    |t|||  td    ||S rz  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  %  r$  r  c              
   C   r  rz  r  r  r  r  r  r  )  r$  r  c              
   C      t |t|	 ||t|||   |
  t|	  |t|||   |
 t|	   t|t|||   |	|
  | |t|||  td    ||t|||    |  ||S rz  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  -  rZ  r  c              
   C   r  rz  r  r  r  r  r  r  1  rZ  r  c              	   C   sF   t | | tt| |td  |  |td  ||t|||  |S r~  r  r+   r   r  r  r.  r  r  r  r  5  r  r  c              
   C   sP   t | | tt| |td  |  |td  ||tdt|||   | S r  r  r.  r  r  r  r  9  r  r  c                 C   s(   t |  t|||  td  | |S rz  r   r  r  r  r  r  r  r   r  r  r  r  r  =     (r  c                 C   s(   t |  t|||  td  | |S rz  r  r  r  r  r  r  A  r  r  c              	   C   J   t ||  ttd| t|||  td  |  || t||  | S r1  r9  r>  r  r  r  r  E     Jr  c              	   C   r  r1  r:  r>  r  r  r  r  I  r  r  c              	   C   sZ   t td| tt| ||td   | | |td td  ||t|||  |S r1  r  r  r  r  r  r  M  r  r  c              
   C   sd   t td| tt| ||td   | | |td td  ||tdt|||   | S r1  r  r  r  r  r  r  Q  r'  r  c           	      C   s   t t|||  |}t||td  | tt|| |td |td  td | td td   t| ||td |td  td |td    ||  ||t|||  | |S r  r   r  r  r  r+   r   r2  	r  r  r  r  r  r  r   r  r  r  r  r  r  U  s   r  c           	      C   s   t tdt|||   |}t||td  | tt|| |td |td  td | td td   t| ||td |td  td |td    ||  ||td|t|||    | S r  r   r  r  r  r+   r   r2  r  r  r  r  r  Z  s   r  c           	   	   C   s   t t|||  |}t|| tt|| | |  | || |  | |  |td  |td  td |td tdd    ||t|||  | | S r  r   r  r  r+   r   r  r  r  r  r  r  _     r  c           	   	   C   s   t t|||  |}t|| tt|| | |  | || |  | |  |td  |td  td |td tdd    ||t|||  | |S r  r   r  r  r+   r   r  r  r  r  r  r  d     r  c           	      C   s   t t|||  |}t|| tt|td |td  td |td td  t| ||td |td  td |td    ||  ||t|||  | |S r  )r   r  r  r+   r   r  r2  r  r  r  r  r  i     r  c           	      C   s   t tdt|||   |}t|| tt|td |td  td |td td  t| ||td |td  td |td    ||  ||td|t|||    | S r  r  r  r  r  r  r  n     r  c           	      C   s   t t|||  |}t|| tt|td  |td  td | td || td  tdd   t| |td  |td  td |td   | ||  ||t|||  | |S r  )r   r  r  r+   r   r  r2  r  r  r  r  r  s  s   r  c           	      C   s   t t|||  |}t|| tt|td  |td  td | td || td  tdd   t| |td  |td  td |td   | ||  ||t|||  | | S r  )r   r  r  r+   r   r  r2  r  r  r  r  r  x  s   r  c              	   C   P   t t| |tdt|||   |   | tdt|||   |  ||S rK  r   rI  r  r  r  r  r  r  r  r  r   r  r  r  r  r  }  r  r  c              	   C   r  rK  r   rI  r  r  r  r  r  r  r    r  r  c           	   	   C   s   t t|||  |}t|| ||  td  | tt|| ||   | || |  | |  |td  |td  td |td tdd    ||t|||  | | S r  r   r  r  r  r+   r   r  r  r  r  r    s   r  c           	   	   C   s   t t|||  |}t|| ||  td  | tt|| ||   | || |  | |  |td  |td  td |td tdd    ||t|||  | |S r  r   r  r  r  r+   r   r  r  r  r  r    s   r  c           	      C   s   t t|||  |}t||td  | tt|| t| ||td |td  td |td    ||  |td |td  td  ||t|||  | |S r1  r  r  r  r  r  r    r  r  c           	      C   s   t tdt|||   |}t||td  | tt|| t| ||td |td  td |td    ||  |td |td  td  ||td|t|||    | S r1  r  r  r  r  r  r    r  r  c	           	   
   C   Z   t td|  ||   t|td| tdt|||   |   td|  ||S Nr&  r  r  rm  	r  r  r  r  r  r  r!  r   r  r  r  r  r    r  r  c	           	   
   C   r  r  ro  r  r  r  r  r    r  r  c	           	      C      t |td| tdt|||   |   td |  | |tdt|||   |   |tdt|||   td|    |  tt|td| tdt|||   |   td|   ||S rA  )r  r  r  r   ur  r  r  r  r    r  r  c	           	      C   r  rA  )r  r  r  r   r  r  r  r  r  r    r  r  c           	      C      t td |  | |td  td}ttd| | ttd|td| tdt|||   |   |  ||ttd| | ttd|td| tdt|||   |   |  || S r  r  r  r  r   r  	r  r  r  r  r  r  r!  r  qr  r  r  r       (r  c           	      C   r  r  r  r  r  r   r  r  r  r  r  r    r
  r  c
              	   C   s   t t|||	  |	}
t|
| tt|
|	 | |  | |
|	 |  | |  |
td  |	td  td |td tdd    |	|	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d  td |td tdd    |	|	t|||	  |
 |	S r  r  r  r  r  r  r    r  r  c
                 C   s   t t|||	  |	}
t|
|td  | tt|	| |
td |	td  td | td td   t| ||
td |	td  td |td    ||
td |	td  td |   |	|  |	|	t|||	  |
 |	S r  r  r  r  r  r  r    s   r  c
                 C   s  t tdt|||	   |	}
t|
|td  | tt|	| |
td |	td  td | td td   t| ||
td |	td  td |td    ||
td |	td  td |   |	|  |	|	td|
t|||	    |	 S r  r  r  r  r  r  r    s   r  c
           
   
   C   v   t td|  ||   t|td| tdt|||	   |   td|  tdt|||	   |  |	|	S r  rm  
r  r  r  r  r  r  r  r!  r   r  r  r  r  r    r?  r  c
           
   
   C   r  r  ro  r  r  r  r  r    r?  r  c
           
   
   C      t |td| tdt|||	   |   td |  | |tdt|||	   |   |tdt|||	   td|    |  t|td| tdt|||	   |   td|  tdt|||	   |  |	|	S rA  r  r  r  r   r  r  r  r  r    rb  r  c
           
   
   C   r  rA  r  r  r  r   r  r  r  r  r    rb  r  c
           
   	   C   x   t t| |tdt|||	   |   |tdt|||	   td|    | tdt|||	   |  |	|	S r1  r  r  r  r  r  r    rM  r  c
           
   	   C   r  r1  r  r  r  r  r  r    rM  r  c
              
   C   s   t t|||	  |	}
t|
| ||  td  | tt|	| td| |   |
td  |	td  td |td tdd    ||
|	 |  ||
|	 td|    | |  |	|	t|||	  |
 |	 S r  r  r  r  r  r  r    s   r  c
              
   C   s   t t|||	  |	}
t|
| ||  td  | tt|	| td| |   |
td  |	td  td |td tdd    ||
|	 |  ||
|	 td|    | |  |	|	t|||	  |
 |	S r  r   r  r  r  r  r       r  c
                 C   s   t t|||	  |	}
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  |	|	t|||	  |
 |	S r1  r  r  r  r  r  r    r  r  c
                 C   s   t tdt|||	   |	}
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  |	|	td|
t|||	    |	 S r1  r  r  r  r  r  r    s   r  c	           	   
   C   f   t td|  ||   t| |t|||    |td| t|||    td|   ||S Nr&  r  rm  	r  r  r  r  r  r  r  r  r  r  r  r  r    r:  r  c	           	   
   C   r  r  ro  r  r  r  r  r    r:  r  c	           	   
   C      t |td| t|||    td |  ||t|||    |t|||  td   |  t| |t|||    |td| t|||    td|   ||S rz  r  r  r  r  r  r    rZ  r  c	           	   
   C   r  rz  r  r  r  r  r  r    rZ  r  c           	      C      t td | | |td  td}t|td |  | ||  |  ttd|td| t|||    |  ||t|td |  | ||  |  ttd|td| t|||    |  || S r  r  	r  r  r  r  r  r  r  r  r	  r  r  r  r       (r  c           	      C   r  r  r  r  r  r  r  r    r  r  c	           	   	   C   \   t t| |t|||    ||t|||    |t|||  td   |  ||S rz  )r   rI  r  r  r  r  r  r  r    r  r  c	           	   	   C   r  rz  )r   rI  r  r  r  r  r  r  r    r  r  c                 C   s   t || | t| ||  |td  tt tt|||    td  || t || | t| ||  |td  tttt|||    td  || ttd t | ||  |  ttt| t| |   | | S Nr  r  r  )r  r   r  r]  r  expr  r>   r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t || | t| ||  |td  ttdtt|||     || t || | t| ||  |td  ttt|||   td  || ttd | ||  |  ttt| t| |   | | S r  )r  r   r  r]  r  r  r  r  r  r  r  r  r    r  r  c                 C   sj   t || | t| ||  |td  t|||   || t| ||  | t|||   | | S r  r  r   r  r  r  r  r  r  r  r    rs  r  c                 C   sh   t || | t| ||  |td  t|||   ||t| ||  | |t|||    | S r  r  r  r  r  r  r  !  r  r  c                 C   s  t | td |td  |td  t| t|||   |td  |||   ||t| td | | t|||   |td   |td |td  |td   | t| td | t|||   |td   |||   t|||   ||td   | S r#  rF  r  r  r  r  r  r  r  r  r  r  r  %  r  r  c                 C   s  t | td |td  |td  t| t|||   |td  |||   ||t| td | | t|||   |td   |td |td  |td   | t| td | t|||   |td   |||   ||td  t|||    | S r#  rI  r   r  r  r  r  )  r  r  c              	   C   s  t | td |td  |td  t| t|||   |td  |||  |  ||t | td |td  | |td  |td |td  |td   t| t|||   |td  |||  |td   || t| td | t|||   |td   |||  |  t|||   ||td   | t| td | | | t|||   |td   |||  |td   |td |td  |td   | S r#  rF  r  r  r  r  r  r  r  r  r  r  r  r  -      r  c              	   C   s  t | td |td  |td  t| t|||   |td  |||  |  ||t | td |td  | |td  |td |td  |td   t| t|||   |td  |||  |td   || t| td | t|||   |td   |||  |  ||td  t|||    | t| td | | | t|||   |td   |||  |td   |td |td  |td   | S r#  rI  r!  r  r  r  r  1  r"  r  c                 C   s   t |td | td |  t| t|||   |td  |||   ||t|| t|||   |  |td |td   | t| t|||   |td  |||   t|||   | | |  | S r1  r-  r   r  r  r  r  5  r  r  c                 C   s   t |td | td |  t| t|||   |td  |||   ||t|| t|||   |  |td |td   | t| t|||   |td  |||   t|||   | | |  | S r1  r0  r   r  r  r  r  9  r  r  c              	   C   sl  t |td | td |  t| t|||   |td  |||  |  ||t |td | |td  |td |td   t| t|||   | |||  |td   || t| t|||   |td  |||  |  t|||   | | |  | t|| | t|||   |  |||  |td   |td |td   | S Nr  r  r  r   r-  r!  r  r  r  r  =     n r  c              	   C   sl  t |td | td |  t| t|||   |td  |||  |  ||t |td | |td  |td |td   t| t|||   | |||  |td   || t| t|||   |td  |||  |  t|||   | | |  | t|| | t|||   |  |||  |td   |td |td   | S r#  r0  r!  r  r  r  r  A  r$  r  c                 C   d   t | t|||   | | t|||   |  t| t|||   |  |||  |  ||S r&  r6  r!  r  r  r  r  E  r'  r  c                 C   r%  r&  r8  r!  r  r  r  r  I  r'  r  c	           	   	   C   6   t t|||  | | |t|||    | ||S r&  r   r   r  r  r  r  r  r  M     6r  c	           	   	   C   r&  r&  r   r   r  r  r  r  r  r  Q  r(  r  c	           	      C   L   t t|||  | | t|||   | | t|||  |   ||S r&  r'  r  r  r  r  r  U  r7  r  c	           	      C   r*  r&  r)  r  r  r  r  r  Y  r7  r  c                 C   .   t | |tt||  | t|||  |S r&  r   r  r2  r  r  r  r  r  vr  r  r  r  r  ]  r  r  c                 C   r+  r&  r   r  r2  r-  r  r  r  r  a  r  r  c	           	      C   2   t | |t|||    | |||  |  |S r&  re  r  r  r  r  r  e  r  r  c	           	      C   r0  r&  rg  r  r  r  r  r  i  r  r  c                 C   V   t td| tt|tdtd|   | |t|||    |  |||| |S r  r  r  r  r  r  r  r   r  r  r  r  r  m  r  r  c                 C   r1  r  r  r2  r  r  r  r  q  r  r  c                 C   &   t | |t||||     | |S r&  re  r2  r  r  r  r  u     &r  c                 C   r3  r&  rg  r2  r  r  r  r   y  r4  r   c                 C   J   t tdt||td tt| |t||||     | ||||S rK  )r  r  r3   r+   r   r  r  r  r  r  r  r   r  r  r  r  r  r  }  r  r  c                 C   r5  rK  )r  r  r3   r+   r   r  r6  r  r  r  r    r  r  c                 C       t | |tt||  | |S r&  r,  r  r  r   r  r  r  r  r  r    r4  r  c                 C   r7  r&  r/  r8  r  r  r  r    r4  r  c                 C   Z   t td| tt|td|td |   | |t|||    |  |||| |S r  r  r  r  r  r  r    r  r  c                 C   r9  r  r  r  r  r  r  r    r  r  c              	   C   .   t || | |t||||     |  |S r&  re  r  r  r  r  r    r  r  c              	   C   r:  r&  rg  r  r  r  r  r    r  r  c	           	      C   \   t |t| |t|   || t|  t|| | |t||||     |  ||S r&  )r  r%   r&   r   r  r  r  r  r  r
    r  r
  c	           	      C   r;  r&  )r  r%   r&   r   r  r  r  r  r  r    r  r  c                 C   ,   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   s   t || td || |td   t|||  tdt| |||    |td   || 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  c              
   C   s   t || td || |td   t|||  tdt| |||    |td   ||t||| td  tdt| |||    |td   || |td   | S r  r@  r?  r  r  r  r    r  r  (k  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r]  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  Pir  B_C_F_G_H_r   b_r  d_r	  f_g_h_i_j_k_l_r  r  r  q_r_t_r  r  s_w_r  y_z_a1_a2_b1_b2_c1_c2_d1_d2_n1_r  e1_e2_f1_f2_g1_g2_n3_Pq_Pm_Px_Qm_Qr_Qx_jn_mn_non2_RFx_RGx_r  iiPqqQRrr  kr  	_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$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r
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