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 ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd  Zdd!d" Zed#d$ Zfd%d& Zgd'd( Zhd)d* Zid+d, Zjd-d. Zkd/d0 Zld1d2 Zmd3d4 Znd5d6 Zod7d8 Zpd9d: Zqd;d< Zrd=d> Zsd?d@ ZtdAdB ZudCdD ZvdEdF ZwdGdH ZxdIdJ ZydKdL ZzdMdN Z{dOdP Z|dQdR Z}dSdT Z~dUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdÐdĄ ZdŐdƄ ZdǐdȄ Zdɐdʄ Zdːd̄ Zd͐d΄ ZdϐdЄ Zdѐd҄ ZdӐdԄ ZdՐdք Zdאd؄ Zdِdڄ Zdېd܄ Zdݐdބ ZÐdߐd ZĐdd ZŐdd ZƐdd Zǐdd ZȐdd Zɐdd Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd  ZԐdd ZՐdd Z֐dd Zאdd Zؐd	d
 Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX Z dYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Z	dkdl Z
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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)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGammaWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  C/usr/lib/python3/dist-packages/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|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
tdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    tŃ|||||| }tɐ|tD}tttd
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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}/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
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}Atɐ|At}Bttttd
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tdtttdtd tdtd  tdd  tttdtdtttdtd tdtd    tŃ||||||%}Itɐ|It}Jtttd
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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
}tɐ|tj}tttdtdtttdtd tdtd  tdd  tttdtdtttdtd tdtd   ttd
tdtttdtd tdtd     tŃ|||||||O|g| 
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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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8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(  r  r  r  r  r  r 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 " "   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              
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   C   sb   t td| ttt|td td |td td  |||tdt| ||   | S r  r  r  r  r  r  r  	     br  c                 C   s   t | td |td  |td  t| t|||   |td  ||t| | t|||   |td   t|||   ||td   | S r	  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  	     r  c                 C   s   t | td |td  |td  t| t|||   |td  ||t| | t|||   |td   t|||   ||td   | S r	  r  r  r   r  r  r  r  r  r  r  r  	  r  r  c                 C   s   t |td | td |  t| t|||   |td  ||t| t|||   |td  t|||   | | |  | S Nr  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|||   | | |  | 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   	  s   r   c                 C   s    t tt| ||  | | S r  )r  r  r  r  r  r  r  r  	      r  c                 C   L   t | t|||   | t|||  |  tt|||  |  ||S r  r  r  r   r  r  r  r  r  	     Lr  c                 C   r  r  r  r  r   r  r  r  r  r  	  r  r  c                 C   f   t t|||  |  |td  | t|||   |td   tt|||  |  |  | |S r  )r  r  r  r   r  r  r  r  r  	     fr  c                 C   r  r  )r  r  r  r   r  r  r  r  r  	  r   r  c              	   C   v   t |td tt|||  td ||t td|  | ttdt|||   || t| td | | S Nr  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  	     vr  c              	   C   r!  r"  r  r  r   r  r  r$  r  r  r  r  	  r%  r  c                 C   sf   t td| | tttd| |td   |||t|||   t| |t|||     |S Nr  r  r  r  r+   r   r  r  r  r$  r  r  r  r	  	  r   r	  c                 C   sh   t td | | tttd| |td   |||t| |t|||    t|||    |S r'  r  r  r+   r   r  r  r  r$  r  r  r  r
  	  r  r
  c              
   C   s   t | |td  t| |t|||    |td  | |td  |td| td  t|||     ||t|td | |t|||    |td   t|||   ||td   | S Nr  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  
     r  c              
   C   s   t | |td  t| |t|||    |td  | |td  |td| td  t|||     ||t|td | |t|||    |td   ||td  t|||    | S r*  r  r  r   r  r  r  r-  r  r  r  r  
  r.  r  c                 C   x   t td|  tt| |t|||    ||t ||  ttdt| |t|||    t|||    || S Nr  r  r  r   r  r  r$  r  r  r  r  
     xr  c                 C   r0  r1  r  r  r   r  r  r$  r  r  r  r  
  r3  r  c              
   C   s   t td| td td| td   t| |t|||    |td  | td| td  ||td  t|||     ||t| |t|||    | t|||   |td| td   | S r  r,  r-  r  r  r  r  
  r  r  c              
   C   s   t td| td td| td   t| |t|||    |td  | td| td  ||td  t|||     ||t| |t|||    | |td| td  t|||    | S r  r/  r-  r  r  r  r  
  r  r  c              
   C   s   t | | t|||   |ttdtdt|||     ttdtdt|||      tttd|| |   |tdd   |ttd|| |     ||tdt|||   | S r  r  r  r  r  r  r+   r   r-  r  r  r  r  
  r.  r  c              
   C   s   t | | |ttdtdt|||     ttdtdt|||     t|||    tttd|| |   |tdd   |ttd|| |     ||tdt|||   |S r  )r  r  r  r  r  r+   r   r-  r  r  r  r  
     r  c              
   C      t | t| td|| t|||     t|   | |t|||    t|  ttd|| t|||     | ||S r1  r  r%   r  r  r&   r   r-  r  r  r  r  #
     r  c              
   C   r7  r1  r  r%   r  r  r&   r   r-  r  r  r  r  '
  r9  r  c                 C   s  t td t|tdtdt|||     | |t|||      t| tdtdt|||     | |t|||      | |t|||     t| | |  tt| | tdt| |t|||     | | | |   |t| | td t|||    |S r'  r  r  r  r  r;   r	  r  r  r$  r  r  r  r  +
  s     r  c                 C   s  t tdt|tdtdt|||     | |t|||      t| tdtdt|||     | |t|||      | |t|||     t| | |  tt| | tdt| |t|||     | | | |   t|||   |t| | td  |S r'  r  r  r  r  r;   r	  r  r  r$  r  r  r  r  /
      r  c                 C      t |td ttdtdt|||    t| |t|||    t|||    ||t| td |td|  |  t|||    t| |t|||     | S r'  r  r  r   r  r  r$  r  r  r  r  3
     r  c                 C   r>  r'  r  r  r   r  r  r$  r  r  r  r  7
  r@  r  c                 C   s>  t td|td  t| |t|||    |td  t| td |td  | |td  td| td  t|||  td   |td| td  |td  |td |td    t|||    | ||t|td | |t|||    |td   t|||   ||td   | S Nr  r  r  r  r+  r  r,  r-  r  r  r  r  ;
     @ r  c                 C   s>  t td|td  t| |t|||    |td  t| td |td  | |td  td| td  t|||  td   |td| td  |td  |td |td    t|||    | ||t|td | |t|||    |td   ||td  t|||    | S rB  r/  r-  r  r  r  r  ?
  rD  r  c              	   C   N   t td|  ttd| t|||   | td  || t||  | S r1  r#  r$  r  r  r  r  C
     Nr  c              	   C   rE  r1  r&  r$  r  r  r  r  G
  rF  r  c                 C   s   t td t|tdtdt|||     | |   t| tdtdt|||     | |   t| | |  tt| |t|||    t| | td | | | |   t| | td | | t|||    |S r'  r;  r$  r  r  r  r  K
     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d t|||   | |  |S r'  r<  r$  r  r  r  r  O
     r  c                 C   sP  t td| | td |td   |td   t| |t|||    |td  t|  | |td  t|||   |td |td  t|||  td   | td |td  |td   | ||t|td | |t|||    |td   t|||   | | | td |td   |td   | S r  r,  r-  r  r  r  r  S
     R r  c                 C   sP  t td| | td |td   |td   t| |t|||    |td  t|  | |td  t|||   |td |td  t|||  td   | td |td  |td   | ||t|td | |t|||    |td   | | | td |td   |td  t|||    | S r  r/  r-  r  r  r  r   W
  rI  r   c                 C   "   t | |t|||    | |S r  r   r  r-  r  r  r  r!  [
     "r!  c                 C   rJ  r  r   r  r-  r  r  r  r"  _
  rL  r"  c              	   C   X   t | t|t|||   | ||t || t|t|||   |td  || S r1  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r#  c
  r  r#  c              	   C   rN  r1  r  r   r  r  rP  r  r  r  r$  g
  r  r$  c              	   C      t td|  | | t|t|||   |td  ||t|t|||   | | td |td t|||  td    | S r'  r  r  r   r  rP  r  r  r  r%  k
     r%  c              	   C   rR  r'  r  r  r   r  rP  r  r  r  r&  o
  rT  r&  c                 C   p   t td| ttdt|||   ||t | | ttd| |t|||    t|||    || S r1  rS  r  r  r  r  r  r  r  r  r'  s
     pr'  c                 C   rV  r1  rU  rW  r  r  r  r(  w
  rX  r(  c              
   C   sj   t | | ttd| |t|||    t|||  td   || tt|||  ||  | S r  )r  r   r  r  r  r  rW  r  r  r  r)  {
     jr)  c              
   C   sr   t | | ttd| |t|||    t|||  td   || ttd|| t|||    | S r  )r  r   r  r  r  r  rW  r  r  r  r*  
     rr*  c              	   C   @   t t|t|||   | | |t|||    |  ||S r  r   rI  r  r  r  r  r  r  r  r  r  r  r  r  r+  
     @r+  c              	   C   r[  r  r   rI  r  r]  r  r  r  r,  
  r^  r,  c              
   C   sB   t td| t|||   |t| |t|||      |S Nr  r  r  r  r  r  rW  r  r  r  r-  
     Br-  c              
   C   sD   t td | |t| |t|||     t|||    |S r`  r  r  r  r  r  rW  r  r  r  r.  
  s   Dr.  c              	   C   s   t | td| td  | t| |t|||    |td  t|||   ||t|| |t|||    |td   t|||   ||  | S Nr  r  r,  r  r  r  r  r  r  r  r  r  r/  
     r/  c              	   C   s   t | td| td  | t| |t|||    |td  t|||   ||t|| |t|||    |td   || t|||    | S rd  r/  re  r  r  r  r0  
  rf  r0  c                 C   s2   t t|||  || t|||   |   |S r  )r  r  r  rW  r  r  r  r1  
     2r1  c                 C   s<   t td|| t|||   |  t|||    | S r1  )r  r  r  r  rW  r  r  r  r2  
     <r2  c                 C   sj   t td| tttdtd|  |td   |||t|||   t| |t|||     |S r'  r(  rW  r  r  r  r3  
  rY  r3  c                 C   sl   t td | tttdtd|  |td   |||t| |t|||    t|||    |S r'  r)  rW  r  r  r  r4  
     lr4  c              	   C   s   t |td | td| td   t| |t|||    |td  t|||   ||t|| |t|||    |  t|||   | | td| td   | S r  r,  re  r  r  r  r5  
  r@  r5  c              	   C   s   t |td | td| td   t| |t|||    |td  t|||   ||t|| |t|||    |  | | td| td  t|||    | S r  r/  re  r  r  r  r6  
  r@  r6  c              	   C   s   t ||td| td   t| |t|||    |td  t|||   ||t| |t|||    | t|||   |td| td   | S r'  r,  re  r  r  r  r7  
     r7  c              	   C   s   t ||td| td   t| |t|||    |td  t|||   ||t| |t|||    | |td| td  t|||    | S r'  r/  re  r  r  r  r8  
  rj  r8  c              	   C   s   t | | ||td   t| |t|||    | t|||   ||t| |t|||    | t|||   ||td   | S r1  r,  re  r  r  r  r9  
     r9  c              	   C   s   t | | ||td   t| |t|||    | t|||   ||t| |t|||    | ||td  t|||    | S r1  r/  re  r  r  r  r:  
  rk  r:  c              
   C   s   t td| td td| td   t| |t|||    |td  | | |td| td  t|||     t|||   || t|| |t|||    |  t|||   | | td| td   | S r  r,  re  r  r  r  r;  
  rG  r;  c              
   C   s   t td| td td| td   t| |t|||    |td  | | |td| td  t|||     t|||   || t|| |t|||    |  | | td| td  t|||    | S r  r/  re  r  r  r  r<  
  rG  r<  c              	   C      t td||td   t| |t|||    | |  t|||   ||td    t|||   ||t| |t|||    |td  t|||   || |td   | S r  r,  re  r  r  r  r=  
     r=  c              	   C      t td||td   t| |t|||    | |  t|||   ||td    t|||   ||t| |t|||    |td  || |td  t|||    | S r  r/  re  r  r  r  r>  
  rm  r>  c                 C   s   t td|  t| | |  ||  tttdttd|td |    |||t|||   t| |t|||     |S r'  )r  r  r  r+   r   r  r  r  r  r  r  r  r  r  r  r  r?  
     r?  c                 C   s   t td |  t| | |  ||  tttdttd|td |    |||t| |t|||    t|||    |S r'  )r  r  r  r+   r   r  r  ro  r  r  r  r@  
  r  r@  c                 C   s   t td| | | tttd|||td    |||t|||   t|t|||   t| |t|||      |S r'  r(  ro  r  r  r  rA  
  rp  rA  c                 C   s   t td | | | tttd|||td    |||t|t|||   t| |t|||     t|||    |S r'  r)  ro  r  r  r  rB  
  r  rB  c                 C   s   t td|  | |td  |td| td   t|t|||   |td  t| |t|||     ||ttd| | |t|||   |td   t|||   |t| |t|||     td| td   | S rd  r  r  r   r  r  r  r  rP  r  r  r  rC  
     rC  c                 C   s   t td|  | |td  |td| td   t|t|||   |td  t| |t|||     ||ttd | | |t|||   |td   |t| |t|||     td| td  t|||    | S rd  r  r  r   r  r  r  r  rP  r  r  r  rD  
     rD  c              
   C   sZ   t td|  t|||   |t|t|||    t| |t|||      |S r`  ra  ro  r  r  r  rE  
     ZrE  c              
   C   s\   t td |  |t|t|||    t| |t|||     t|||    |S r`  rc  ro  r  r  r  rF  
     \rF  c                 C   s   t | td| td  td| | |  t|t|||   |td  t| |t|||     ||t| |t|||   |  t|||   || t| |t|||      | S r'  rq  rP  r  r  r  rG  
  r
  rG  c                 C   s   t | td| td  td| | |  t|t|||   |td  t| |t|||     ||t| |t|||   |  || t| |t|||     t|||    | S r'  rs  rP  r  r  r  rH  
  r
  rH  c              
   C   s   t | td | t|||   |t| |t|||     t| |t|||      tt|| |td  t| ||   ||tdt|||   | S Nr  r  r  r  r  r  r  r  r+   r   rP  r  r  r  rI  
     rI  c              
   C   s   t | td | |t| |t|||     t| |t|||     t|||    tt|| |td  t| ||   ||tdt|||   |S rw  r  r  r  r  r  r+   r   rP  r  r  r  rJ  
  s   rJ  c                 C   sv   t ttdt|  ||  tttdt|td td  |||t|||   | |t|||     |S r'  )r  r  r  r+   r   r  r  ro  r  r  r  rK    r%  rK  c                 C   sx   t ttdt|  ||  tttdt|td td  |||| |t|||    t|||    | S r'  )r  r  r  r+   r   r  r  ro  r  r  r  rL    r3  rL  c                 C   s   t td| | | |  tttdtd| ||td    |||t|||   t|t|||   t| |t|||      |S r'  r(  ro  r  r  r  rM       rM  c                 C   s   t td | | | |  tttdtd| ||td    |||t|t|||   t| |t|||     t|||    |S r'  r)  ro  r  r  r  rN       rN  c              
   C   s   t |td| td  ||  t|t|||   |td  | |t|||    |td   ||t| |t|||   |  | |t|||    |td   t|||   ||  | S rw  r,  r]  r  r  r  rO    r.  rO  c              
   C   s   t |td| td  ||  t|t|||   |td  | |t|||    |td   ||t| |t|||   |  | |t|||    |td   || t|||    | S rw  r/  r]  r  r  r  rP    r.  rP  c              
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   C   s   t | td t|t|||   | | |td  || t|||     || t|t|||   | || |t|||     t|||    | S r  r/  rP  r  r  r  rd  g  r  rd  c              
   C   s   t ||td  | |  t|t|||   |td  | |t|||     ||t|| |t|||   |td   t|||   | | | |t|||      | S r  r,  rP  r  r  r  re  k     re  c              
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   C   s   t td| t| |t|||    |td  | td | | | td| td  t|||    |td |td    t|||   ||t|| |t|||    |td   || t|||    | S r  r/  re  r  r  r  rz    r  rz  c              	   C   >   t td| ttd| t|||   | td  ||S r1  rS  rW  r  r  r  r{       >r{  c              	   C   r  r1  rU  rW  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d || t|||    |S r'  r  r  r  r  r=   r	  r  r  rW  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d t|||   ||  |S r'  r  r  r  r  r=   r	  r  r  rW  r  r  r  r~    r  r~  c              
   C   s   t td| td |td  |td   t| |t|||    |td  | |td  ||td  t|||     t|||   ||t|| |t|||    |td   t|||   || td |td   |td   | S r  r,  re  r  r  r  r    r  r  c              
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   C   s   t t|||  |ttdtdt|||     ttdtdt|||      tt| ||  | ttd| t|td   ||tdt|||   | S r1  r5  re  r  r  r  r    r@  r  c              
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   C   ~   t t|t|||   t| t|||   |  t| |t|||     ttdt| t|||   |  ||S r1  r  ro  r  r  r  r       ~r  c              
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   C   sp   t | td|  |td |   t|t|||   |td|   |  |t|||    |   ||S r`  r  r  r   r  r  r  r  r  r  r    rX  r  c              
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   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 r1  )r  r  r  r   r  r  r  r  r  r    r9  r  c	           	      C   V   t || tttd||t|||     | | |t|||    | |||S r1  )r  r   rI  r  r  	r  r  r  r  r  r  r  r  r  r  r  r  r       Vr  c	           	      C   r  r1  )r  r   rI  r  r  r   r  r  r  r    r  r  c	           	   	   C   sV   t |  | | t||t|||    | |  t|||  td|   ||S r`  )r  r   r  r  r  r   r  r  r  r    r  r  c	           	   	   C   s^   t |  | | t||t|||    | |  tdt|||   td|   ||S r  )r  r   r  r  r  r   r  r  r  r    r  r  c              
   C   s   t |  | |tdd   t|||   t| |t|||    t||t|||      tt|||  td|  ||S r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r    r  r  c              
   C   s   t |  | |tdd   t| |t|||    t||t|||     t|||    ttdt|||   td|  ||S r  r  r  r  r  r  r   r  r  r  r  r    rk  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
    r.  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 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d   ||ttd |  ||t|||    |  |t| |t|||     td| td  t|||    | S r  r  r  r   r  r  r  r  r  r  r  r  r    r6  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    r.  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 r'  )r  r   r  r  r  r  r  r  r  r  r  r       r  c                 C   s   t | tt| |t|||    ||t|||    |  ||ttd | td  ||t|||    |  |t| |t|||     td| td  t|||    | S r'  )r  r   r  r  r  r  r  r  r  r  r  r    rm  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	           	   
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   C   d   t |  | ||  |  ttd| |t|||    t|||    || t|| |  | S r1  r  r   r  r  r  r  r  r  r  r#  [  r  r#  c              
   C   r  r1  r  r   r  r  r  r  r  r  r  r$  _  r  r$  c                 C      t ||  tt| |t|||    ||t |  | ||  |  ttdt| |t|||    t|||    || S r1  r  r  r  r  r  r%  c  r  r%  c                 C   r!  r1  r  r  r  r  r  r&  g  r  r&  c                 C   t   t |ttdt| |t|||     ||t |ttdt| |t|||    t|||    || S r1  r  r  r  r  r  r'  k     tr'  c                 C   r"  r1  r  r  r  r  r  r(  o  r#  r(  c                 C   s  t td| td td| td   t| |t|||    |td  t| | td| td  |td |  | ||   t|||    | ||t| |t|||    | |  | ||   t|||   || td| td   | S r  r,  r  r  r  r  r)  s      r)  c                 C   s  t td| td td| td   t| |t|||    |td  t| | td| td  |td |  | ||   t|||    | ||t| |t|||    | |  | ||   || td| td  t|||    | S r  r/  r  r  r  r  r*  w  r$  r*  c                 C   sv  t td| | td |td   |td   t| |t|||    |td  t|  |td  |  | ||   t|||   ||td  |  | ||   t|||  td   || td |td   |td   | ||t|| |t|||    |td   |  | ||   t|||   | | | td |td   |td   | S r  r,  r  r  r  r  r+  {     x r+  c                 C   sv  t td| | td |td   |td   t| |t|||    |td  t|  |td  |  | ||   t|||   ||td  |  | ||   t|||  td   || td |td   |td   | ||t|| |t|||    |td   |  | ||   | | | td |td   |td  t|||    | S r  r/  r  r  r  r  r,    r%  r,  c              
   C   d   t |t| |t|||    | ||t |t| |t|||    | t|||   || S r  r  r   r  r  r  r  r  r-    r  r-  c              
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   C   sj   t t|||  t| |t|||    t||t|||      ttdt|||   ||S r1  )r  r  r  r  r   r  r  r  r  r  rG    rY  rG  c              
   C   sj   t tdt| |t|||    t||t|||     t|||    tt|||  ||S r1  r  r  r  r  r  rH    rY  rH  c                 C      t td|  tt| |t|||    t||t|||     ||t ||  ttdt| |t|||    t||t|||     t|||    || S r1  r2  r  r  r  r  rI       rI  c                 C   r2  r1  r4  r  r  r  r  rJ    r3  rJ  c                 C      t td| tt| |t|||    t||t|||     ||t || tt| |t|||    ||t|||    tdd  t|||    || S Nr  r  r  r2  r  r  r  r  rK    r3  rK  c                 C   r4  r5  r4  r  r  r  r  rL    r3  rL  c	           	   
   C   s   t | td t|||   |t| |t|||     t| |t|||      tt| ||  |tdd   |||  |  |t| ||    ||tdt|||   | S rw  rx  r   r  r  r  rM    r  rM  c	           	   
   C   s   t | td t|||   |t| |t|||     t| |t|||      tt| ||  |tdd   |||  |  |t| ||    ||tdt|||   |S rw  )r  r  r  r  r  r+   r   r   r  r  r  rN       rN  c	           	      C   X   t | t|||   | | |t|||   | |  t|||  | |   |S r  rK  r   r  r  r  rO    r  rO  c	           	      C   r7  r  rM  r   r  r  r  rP    r  rP  c	           	   	   C      t t| |t|||    t|t|||   |  t||t|||    t| t|||   |   t| t|||   | | |t|||   | |  t|||  | |   ||S r  r  r   r  r  r  rQ    r.  rQ  c	           	   	   C   r8  r  r  r   r  r  r  rR    r.  rR  c	           	   	   C      t | |t|||    | ||t|||    |  | t|||   | |   |t|||   | |   t|||  ||   t| t|||   | | |t|||   | |  t|||  | |   ||S r  r  r   r  r  r  rS    rH  rS  c	           	   	   C   r9  r  r  r   r  r  r  rT    rH  rT  c	           	   	   C   B   t t| |t|||    | ||t|||    | ||S r  r\  r   r  r  r  rU  #  rb  rU  c	           	   	   C   r:  r  r_  r   r  r  r  rV  '  rb  rV  c	           	      C   >   t | |t|||    | ||t|||    |  |S r  rK  r   r  r  r  rW  +  r  rW  c	           	      C   r;  r  rM  r   r  r  r  rX  /  r  rX  c              	   C   L   t || t|t|||   | |  | t|||   | |  ||S r  r'  r]  r  r  r  rY  3  r  rY  c              	   C   r<  r  r(  r]  r  r  r  rZ  7  r  rZ  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  r[  ;  r|  r[  c
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   
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   C   rG  rw  r,  r   r  r  r  rk  {  r  rk  c	           	   
   C   rH  rw  r/  r   r  r  r  rl    r  rl  c	           	      C   sj   t |  | | ttt|||  td|  t|||   ||t|||    | |  |||S r`  )r  r   rI  r  r  r  r   r  r  r  rm    rY  rm  c	           	      C   sr   t |  | | tttdt|||   td|  t|||   ||t|||    | |  |||S r  )r  r   rI  r  r  r  r   r  r  r  rn    rZ  rn  c              
   C   s   t |  | |tdd   t|||   t| |t|||    t||t|||      tt|||  td|  t|||   ||S r  r  r  r  r  r  ro    r  ro  c              
   C   s   t |  | |tdd   t| |t|||    t||t|||     t|||    ttdt|||   td|  t|||   ||S r  r  r  r  r  r  rp    rf  rp  c	           	   
   C   r@  r  r,  r   r  r  r  rq    rA  rq  c	           	   
   C   rB  r  r/  r   r  r  r  rr    rA  rr  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  rs    r@  rs  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  rt       rt  c                 C   sr   t |  | | tt|t|||
   |	 t|||
  td|   ||t|||
    | |  |
|
|
S r`  )r  r   rI  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  ru    rZ  ru  c                 C   sz   t |  | | tt|t|||
   |	 tdt|||
   td|   ||t|||
    | |  |
|
|
S r  )r  r   rI  r  r  r  rJ  r  r  r  rv    rF  rv  c
           
   
   C   s   t |  | |tdd   t|||	   t| |t|||	    t||t|||	      t|t|||	   | t|||	  td|   |	|	S r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  rw    rf  rw  c
           
   
   C   s   t |  | |tdd   t| |t|||	    t||t|||	     t|||	    t|t|||	   | tdt|||	   td|   |	|	S r  r  rK  r  r  r  rx    ry  rx  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  rJ  r  r  r  ry    r.  ry  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  rJ  r  r  r  rz    r6  rz  c                 C   s   t td| | | tttd| | ||  || |td    |||t|||   t|t|||   t| |t|||      |S r'  r(  r  r  r  r  r  r  r  r  r  r  r  r{    r  r{  c                 C   s   t td | | | tttd| | ||  || |td    |||t|t|||   t| |t|||     t|||    |S r'  r)  rL  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  rL  r  r  r  r}    r6  r}  c                 C   rM  r  r  rL  r  r  r  r~    r6  r~  c                 C   sv   t td| | tttd| | ||  ||td    |||t|||   t| |t|||     |S r'  r(  r  r  r  r  r    r%  r  c                 C   sx   t td | | tttd| | ||  ||td    |||t| |t|||    t|||    |S r'  r)  r  r  r  r  r    r3  r  c                 C   s   t t|||t|||     t| |t|||     tt|t|||   ||t|||     |  | ||   | | ||    || t|| | |t|||     ||t|||    | | ||      |S r  )r  r  r  r<   r	  r  r  r  r  r  r    r}  r  c                 C   s   t t|||t|||     t| |t|||     tt|||t|||    t|||    |  | ||   | | ||    || t|| | |t|||     ||t|||    | | ||      | S r  )r  r  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|||     t|||    || S r1  r  r  r  r  r  r    rI  r  c                 C   rO  r1  r  r  r  r  r  r    rI  r  c                 C      t || tt|t|||   t| |t|||     ||t || | tt|t|||   t| |t|||     ||t|||     || S r  r  rL  r  r  r  r    ry  r  c                 C   rP  r  r  rL  r  r  r  r    ry  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  rL  r  r  r  r    rm  r  c                 C   rQ  r  r  r   r  r  r  rL  r  r  r  r    rm  r  c                 C      t ||  | ||   ttdt| |t|||    t|||    ||t ||  | ||   tt| |t|||    ||t|||    t|||    || S r1  r  r  r  r  r  r    r  r  c                 C   rT  r1  r  r  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 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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 r'  r  r  r  r  r;   r	  r  r  r  r  r  r    rt  r  c                 C      t | | |  | ||   tt|t|||   t| |t|||     || t || |  | ||   tt|t|||   t| |t|||     ||t|||     || S r  r  rL  r  r  r  r    r6  r  c                 C   rW  r  r  rL  r  r  r  r    r6  r  c              
   C      t |t|t|||    t| t|||   |  t| |t|||     ttdt| t|||   | |t|||   |   ||S r1  r  rL  r  r  r  r    r  r  c              
   C   rX  r1  r  rL  r  r  r  r    r  r  c                 C      t | |  | ||   ttdt| |t|||    t|||    || t ||  | ||   tt| |t|||    ||t|||    t|||    || S r1  r  r  r  r  r  r    r  r  c                 C   rY  r1  r  r  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 r1  r2  r  r  r  r  r    ry  r  c                 C   rZ  r1  r4  r  r  r  r  r    ry  r  c                 C     t |td ||  | ||    tt|t|||   | | |  | ||  t|||     t| |t|||     ||t |td |td  ||  | ||    tt|t|||   t| |t|||     ||t|||     || S r`  r2  rL  r  r  r  r  #      r  c                 C   r[  r`  r4  rL  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  rR  rL  r  r  r  r  +  r  r  c                 C   r]  r  rS  rL  r  r  r  r  /  r  r  c                 C   s   t td| | tttd| | |td  td  ||t|||  t| |t|||    t||t|||      |S r'  r(  r  r  r  r  r  3  rT  r  c                 C   s   t td | | tttd| | |td  td  ||tdt| |t|||    t||t|||     t|||    |S r'  r)  r  r  r  r  r  7  r  r  c                 C      t || tt||t|||    t| |t|||    t|||    ||t |  | ||  | ttdt| |t|||    t||t|||     t|||    || S r1  r  r  r  r  r  r  ;  r6  r  c                 C   r^  r1  r  r  r  r  r  r  ?  r6  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 r'  rU  r  r  r  r  r  C  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 r'  rV  r  r  r  r  r  G      r  c                 C   s   t td|  ||  tttd|td | | ||   td  ||t|||  t| |t|||    t||t|||      |S r'  r(  r  r  r  r  r  K  r  r  c                 C   s   t td |  ||  tttd|td | | ||   td  ||tdt| |t|||    t||t|||     t|||    |S r'  r)  r  r  r  r  r  O  rf  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 r'  r  r  r  r  r  r  S  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 r'  r  r  r  r  r  r  W  s    r  c                 C      t td| tt| |t|||    t||t|||    t|||    ||t | | ttdt| |t|||    t||t|||     t|||    || S r1  r2  r  r  r  r  r  [  r  r  c                 C   r`  r1  r4  r  r  r  r  r  _  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 r5  r  r  r  r  r  r  c     r  c                 C   ra  r5  r  r  r  r  r  r  g  rb  r  c              
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|
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           
   	   C      t t| |t|||	    t|t|||	   |  t||t|||	    t| t|||	   |   t| t|||	   | | |t|||	   | |  t|||	  | | |   |	|	S r  r  r=  r  r  r  r    r  r  c
           
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S r  r\  rJ  r  r  r  r    rv  r  c              	   C   rg  r  r_  rJ  r  r  r  r    rv  r  c                 C   V   t |t|||
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   C      t || t||t|||    |td  t|||   ||t | | ||  | t||t|||    | t|||   || S r1  rO  ro  r  r  r  r    rk  r  c              
   C   rv  r1  rQ  ro  r  r  r  r    rk  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 r  r,  ro  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d| td  t|||    | S r  r/  ro  r  r  r  r    r\  r  c                 C   s`  t td||td |td   |td   t||t|||    |td  t||td  | | ||   | | | |td  ||td |td |td     t|||    | t|||   || t|||t|||    |td   | | ||   t|||   || |td |td   |td   | S r  r,  ro  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 r  r/  ro  r  r  r  r    rw  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 r  r,  ro  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 r  r/  ro  r  r  r  r    rx  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 r  r,  rz  r  r  r  r        r  c
           
      C   s  t td||td |td   |td   t|t|||	   | ||t|||	    |td   t| |td |td  |td || td    || | |  ||td  | | ||   t|||	    || | ||   || td  t|||	  td   |	 |	|	t||t|||	   |  ||t|||	    |td   | | ||   || |td |td   |td  t|||	    |	 S r  r/  rz  r  r  r  r    r  r  c
           
      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  rz  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  rz  r  r  r  r    r  r  c
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      C   s4  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  r,  rz  r  r  r  r       6 r  c
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      C   s4  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  r/  rz  r  r  r  r    r  r  c
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      C   s:  t td|| |  t|t|||	   |td  ||t|||	    |  t| | |td  t|||	   | | || td   | | || td  t|||	  td   || |  |	 |	|	t| |t|||	   |  ||t|||	    |td   || | t|||	    |	 S r  r/  rz  r  r  r  r    r  r  c                 C      t | | tt||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  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C      t | tt|t|||   t||t|||     ||t || t|t|||   tdd  t||t|||     || S r  r  r  r  r  r  r    rk  r  c                 C   r  r  r  r  r  r  r  r    rk  r  c                 C      t | tt||t|||    t|t|||    ||t || tt|t|||   t||t|||     || S r  r  r  r  r  r  r    r  r  c                 C   r  r  r  r  r  r  r  r    r  r  c	           	      C      t | | t|t|||   | ||t | | ||  ||  t|t|||   |td  ||t|||     || S r1  rO  rl  r  r  r  r    r9  r  c	           	      C   r  r1  rQ  rl  r  r  r  r	    r9  r	  c
           
      C   R   t |t|||	   | | |t|||	     ||t|||	    |  |	S r  rK  rz  r  r  r  r
       Rr
  c
           
      C   r  r  rM  rz  r  r  r  r    r  r  c              	   C   s   t | | | t| t|||   | |
 |t|||   | | |	   t|||  td|   t|||  | |	 |
   ||S r`  )r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    rk  r  c              	   C   s   t | | | t| t|||   | |
 |t|||   | | |	   t|||  | |	 |
   t|||  td|   ||S r`  )r  r   r  r  r  r  r  r  r  r    rk  r  c	           	      C   h   t |td t||t|||    |td  t|| ||  || t|||    | ||S r  r#  	r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c	           	      C   r  r  r&  r  r  r  r  r    r  r  c                 C   ^   t ||td  t||t|||    |td  t| |t|||    | ||S r'  r#  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   r  r'  r&  r  r  r  r  r    r  r  c                 C   s<   t | |t|||   |  t|||   ||  | S r  ry  r  r  r  r  r  r  r  r  r  r  r    rh  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 r  r,  r  r  r  r  r    rT  r  c                 C   s   t | |td  ||  |td |  t|t|||   |td  ||t| |t|||   |  || t|||    | S r  r/  r  r  r  r  r    rT  r  c                 C   s   t | |td  ||  |td  t|t|||   | ||t||t|||   |  t|||   ||td   | S r1  r,  r  r  r  r  r  #  r  r  c                 C   s   t | |td  ||  |td  t|t|||   | ||t||t|||   |  ||td  t|||    | S r1  r/  r  r  r  r  r  '  r  r  c              	   C   l   t | | t|t|||   |td  ||t ||td  t|t|||   |td  || S r  rO  r  r  r  r  r  r  r  r  r  r  r  +  ri  r  c              	   C   r  r  rQ  r  r  r  r  r  /  ri  r  c              	   C   p   t || t|t|||   |td  ||t|t|||   | | |t|||  td    | S r  rO  r  r  r  r  r  r  r  r  r  r  r  r  3  rX  r  c              	   C   r  r  rQ  r  r  r  r  r  7  rX  r  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 r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  ;  r6  r  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 r  r  r  r   r  r  r  r  r  r  r  r  ?  r6  r  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 r  r  r  r  r  r  r  r  r  r  r  r  r  C  rI  r  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 r  r  r  r  r  r  r  G  rI  r  c              
   C      t td| t| | || ||  t|||    ||t|||     ||t || ttdt|||   || S r1  rS  r  r  r  r  r   K  r  r   c              
   C   r  r1  rU  r  r  r  r  r!  O  r  r!  c              
   C   x   t td| t| | || t|||    ||t|||     ||t || ttdt|||   || S r1  rS  r  r  r  r  r"  S  r3  r"  c              
   C   r  r1  rU  r  r  r  r  r#  W  r3  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 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|||    | ||t||t|||    | | | ||  ||   || td| td  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d  || |td  ||   t|||    | ||t| | ||t|||    |  t|||   |td| td   | S r  r,  r  r  r  r  r&  c     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 r  r/  r  r  r  r  r'  g  r  r'  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td  || |  t|||    | ||t|||t|||    |  t|||   ||td   | S r1  r,  r  r  r  r  r(  k  r  r(  c	           	      C   s   t td||td   t||t|||    | t| | |td  || |td  || |  t|||    | ||t|||t|||    |  ||td  t|||    | S r1  r/  r  r  r  r  r)  o  r  r)  c                 C   s   t td||td   t||t|||    | t| | |td  || | t|||    | ||t|||t|||    |  t|||   ||td   | S r1  r,  r  r  r  r  r*  s  r  r*  c                 C   s   t td||td   t||t|||    | t| | |td  || | t|||    | ||t|||t|||    |  ||td  t|||    | S r1  r/  r  r  r  r  r+  w  r  r+  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  r,  r  r  r  r  r,  {  r  r,  c	           	      C   s  t td|td  t||t|||    |td  t| | |td  || |td  || |  t|||  td   || | |td | | ||    t|||    | ||t|||t|||    |  ||td  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d  || | t|||  td   | | |td  || |  t|||    | ||t|||t|||    |  t|||   ||td   | S r  r,  r  r  r  r  r.    rt  r.  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  r/  r  r  r  r  r/    rt  r/  c                 C      t |ttdtdt|||    t||t|||    t|||    ||t| || t|||    t||t|||     | S r1  r  r  r  r  r  r0    r  r0  c                 C   r  r1  r  r  r  r  r  r1    r  r1  c                 C      t |ttdtdt|||    t||t|||    t|||    ||t| |t|||    t||t|||     | S r1  r  r  r  r  r  r2    r|  r2  c                 C   r  r1  r  r  r  r  r  r3    r|  r3  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 r  r,  r  r  r  r  r4        r4  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 r1  rS  r  r  r  r  r8    rf  r8  c	           	   
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   C      t td| t||t|||    | | | || t|||     ||t || t||t|||    |td  t|||   || S r1  rS  r  r  r  r  r:    r  r:  c              
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   C   j   t |td t|t|||   |td  | t|||  td  |t|||    |  ||S r  rS  r  r  r  r  r<    rY  r<  c              
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   
   C      t |t| ||t|||	   |  t|  |t|||	   | t|   t|t|||	   ||  | |t|||	    |t|||	  td    |	|	S r`  r  r%   r  r&   r   r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r@    r  r@  c
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   C   r  r`  r  r%   r  r&   r   r  r  r  r  r  rA    r  rA  c	           	   
   C      t |t| ||t|||   |  t|  |t|||   | t|   t|t|||   ||  | |t|||  td    ||S r`  r  	r  r  r  r  r  r  r  r  r  r  r  r  rB    r  rB  c	           	   
   C   r  r`  r  r  r  r  r  rC    r  rC  c
           
      C   s   t td||  t|t|||	   |td  t|| | t|||	  td  || | ||    | | |td  ||| ||    t|||	    |	 |	|	t| | |t|||	   |  t|||	   ||  |	 S r  r,  
r  r  r  r  r  r  r  r  r  r  r  r  r  rD    rN  rD  c
           
      C   s   t td||  t|t|||	   |td  t|| | t|||	  td  || | ||    | | |td  ||| ||    t|||	    |	 |	|	t| | |t|||	   |  || t|||	    |	 S r  r/  r  r  r  r  rE    rN  rE  c	           	      C   s   t td||  t|t|||   |td  t| | | || | t|||  td   || |td  ||   t|||    | ||t| | |t|||   |  t|||   ||  | S r  r,  	r  r  r  r  r  r  r  r  r  r  r  r  rF       rF  c	           	      C   s   t td||  t|t|||   |td  t| | | || | t|||  td   || |td  ||   t|||    | ||t| | |t|||   |  || t|||    | S r  r/  r  r  r  r  rG    r  rG  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 r  r,  r  r  r  r  rH    r  rH  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 r  r/  r  r  r  r  rI    r  rI  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 r  r,  r  r  r  r  rJ    r$  rJ  c	           	      C   s  t td|td  t|t|||   | t| | |td  || |td  t|||  td   || |td  ||td    t|||    | ||t|| |t|||   |  ||td  t|||   t|||    | S r  r/  r  r  r  r  rK    r$  rK  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  r,  r  r  r  r  rL    r  rL  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  r/  r  r  r  r  rM    r  rM  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  r,  r  r  r  r  rN       ( rN  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  r/  r  r  r  r  rO    r  rO  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 r  r,  r  r  r  r  rP        rP  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 r  r/  r  r  r  r  rQ    r  rQ  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 r  r,  r  r  r  r  rR       h rR  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 r  r/  r  r  r  r  rS    r  rS  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 r  r,  r  r  r  r  rT    r~  rT  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 r  r/  r  r  r  r  rU    r~  rU  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 r  r,  r  r  r  r  rV  #  rx  rV  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 r  r/  r  r  r  r  rW  '  rx  rW  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 r  r,  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rX  +  r%  rX  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 r  r/  r  r  r  r  rY  /  r%  rY  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 r  r,  
r  r  r  r  r  r  r  r  r  r  r  r  r  rZ  3  r  rZ  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 r  r/  r  r  r  r  r[  7  r  r[  c                 C   s   t td|| |	  t|t|||
   |	td  ||t|||
    |  t| | | || |	  || ||	 td  ||	   t|||
    |
 |
|
 t| |t|||
   |	  ||t|||
    |  t|||
   ||	  |
 S r1  r,  r  r  r  r  r\  ;  r  r\  c                 C   s   t td|| |	  t|t|||
   |	td  ||t|||
    |  t| | | || |	  || ||	 td  ||	   t|||
    |
 |
|
 t| |t|||
   |	  ||t|||
    |  ||	 t|||
    |
 S r1  r/  r  r  r  r  r]  ?  r  r]  c
           
      C   s   t td|| |  t|t|||	   |td  ||t|||	    |  t| | | || || td  ||   t|||	    |	 |	|	 t| |t|||	   |  ||t|||	    |  t|||	   ||  |	 S r1  r,  r  r  r  r  r^  C  rr  r^  c
           
      C   s   t td|| |  t|t|||	   |td  ||t|||	    |  t| | | || || td  ||   t|||	    |	 |	|	 t| |t|||	   |  ||t|||	    |  || t|||	    |	 S r1  r/  r  r  r  r  r_  G  rr  r_  c                 C   s  t td|||	 td   t|t|||
   |	 ||t|||
    |  t| | ||	 td  || |	  || ||	 td  || |  t|||
    |
 |
|
t||t|||
   |	  ||t|||
    |  t|||
   |||	 td   |
 S r1  r,  r  r  r  r  r`  K  r  r`  c                 C   s  t td|||	 td   t|t|||
   |	 ||t|||
    |  t| | ||	 td  || |	  || ||	 td  || |  t|||
    |
 |
|
t||t|||
   |	  ||t|||
    |  |||	 td  t|||
    |
 S r1  r/  r  r  r  r  ra  O  r  ra  c
           
      C   s  t td||| td   t|t|||	   | ||t|||	    |  t| | || td  || | t|||	    || |  |	 |	|	t||t|||	   |  ||t|||	    |  t|||	   ||| td   |	 S r1  r,  r  r  r  r  rb  S  r  rb  c
           
      C   s  t td||| td   t|t|||	   | ||t|||	    |  t| | || td  || | t|||	    || |  |	 |	|	t||t|||	   |  ||t|||	    |  ||| td  t|||	    |	 S r1  r/  r  r  r  r  rc  W  r  rc  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 r  r,  r  r  r  r  rd  [       rd  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 r  r/  r  r  r  r  re  _  r  re  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 r  r,  r  r  r  r  rf  c      rf  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 r  r/  r  r  r  r  rg  g  r  rg  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 r5  r,  r  r  r  r  rh  k  ru  rh  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 r5  r/  r  r  r  r  ri  o  ru  ri  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 r5  r,  r  r  r  r  rj  s  r  rj  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 r5  r/  r  r  r  r  rk  w  r  rk  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  r,  r  r  r  r  rl  {     F rl  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  r/  r  r  r  r  rm    r  rm  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  r,  r  r  r  r  rn       . rn  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  r/  r  r  r  r  ro    r  ro  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|||
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    |  t|||
   |||	 td   |
 S r  r,  r  r  r  r  rp    r  rp  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  r/  r  r  r  r  rq    r  rq  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  r,  r  r  r  r  rr       D rr  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  r/  r  r  r  r  rs    r  rs  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  r,  r  r  r  r  rt         rt  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d |td   |td  t|||
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           
      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  r,  r  r  r  r  rv        rv  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  r/  r  r  r  r  rw    r  rw  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 r  r,  r  r  r  r  rx         rx  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|||
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 S r  r/  r  r  r  r  ry    r  ry  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 r  r,  r  r  r  r  rz    r  rz  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 r  r/  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  r,  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  r/  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  r,  r  r  r  r  r~    rI  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  r/  r  r  r  r  r    rI  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 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d   || |	  || |	 |  ||	   t|||
    |
 |
|
t| |t|||
   |	  ||t|||
    |td   || |	 t|||
    |
 S r  r/  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 r  r,  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 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  r?  	r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c	           	      C   r  r  rA  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  r?  r  r  r  r  r  r  r  r  r  r  r  r    r
  r  c                 C   r  r  rA  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  r?  r  r  r  r  r    ry  r  c	           	      C   r  r  rA  r  r  r  r  r    ry  r  c                 C      t | ttdt|t|||   t||t|||      ||t ||td  t|t|||   tdd  t||t|||     || S r  r  r  r  r  r  r    rf  r  c                 C   r  r  r  r  r  r  r  r    rf  r  c                 C   n   t |t|||
   |	 ||t|||
    |  | |t|||
    |t|||
  td    |
S r`  r   r  r  r  r  r  r  r    r  r  c                 C   r  r`  r   r  r  r  r  r  r  r    r  r  c
           
      C   Z   t |t|||	   | | |t|||	  td    ||t|||	    |  |	S r`  r  r  r  r  r  r    ru  r  c
           
      C   r  r`  r  r  r  r  r  r    ru  r  c              
   C      t ||td  t|t|||
   | |	 td  |t|||
   | |  | t|||
  td  |t|||
    |  |
|
S r  rS  r  r  r  r  r    rk  r  c              
   C   r  r  rU  r  r  r  r  r    rk  r  c
           
   	   C   |   t ||td  t|t|||	   | | td  | t|||	  td  |  |t|||	   | |  |	|	S r  rS  r  r  r  r  r    r  r  c
           
   	   C   r  r  rU  r  r  r  r  r    r  r  c              
   C      t |t|
 ||t|||   |  t|
  |t|||   | t|
   t|t|||   |
|  ||t|||    |	  | |t|||    |t|||  td    ||S r`  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r
  r  c              
   C   r  r`  r  r  r  r  r  r    r
  r  c              
   C      t |t|	 ||t|||   |
  t|	  |t|||   |
 t|	   t|t|||   |	|
  | |t|||  td    ||t|||    |  ||S r`  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  #  r@  r  c              
   C   r  r`  r  r  r  r  r  r  '  r@  r  c              	   C   sF   t | | tt| |td  |  |td  ||t|||  |S rd  r  r+   r   r  r  r  r  r  r  r  +  rp  r  c              
   C   sP   t | | tt| |td  |  |td  ||tdt|||   | S rw  r  r  r  r  r  r  /  r  r  c                 C   s(   t |  t|||  td  | |S r`  r   r  r  r  r  r  r  r  r  r  r  r  r  3     (r  c                 C   s(   t |  t|||  td  | |S r`  r  r  r  r  r  r  7  r  r  c              	   C   J   t ||  ttd| t|||  td  |  || t||  | S r  r  r$  r  r  r  r  ;     Jr  c              	   C   r  r  r   r$  r  r  r  r  ?  r  r  c              	   C   sZ   t td| tt| ||td   | | |td td  ||t|||  |S r  r  r  r  r  r  r  C  ru  r  c              
   C   sd   t td| tt| ||td   | | |td td  ||tdt|||   | S r  r  r  r  r  r  r  G  r  r  c           	      C   s   t t|||  |}t||td  | tt|| |td |td  t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  K  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  P  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  U     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  Z     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  _     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  d     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  i  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  n  s   r  c              	   C   P   t t| |tdt|||   |   | tdt|||   |  ||S r1  r   rI  r  r  r  r  r  r  r  r  r  r  r  r  r  r  s  r  r  c              	   C   r  r1  r   rI  r  r  r  r  r  r  r  w  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 r  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 r  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  rS  	r  r  r  r  r  r  r  r  r  r  r  r  r    ru  r  c	           	   
   C   r  r  rU  r  r  r  r  r    ru  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 r'  )r  r  r  r   ur  r  r  r  r    r  r  c	           	      C   r  r'  )r  r  r  r   r  r  r  r  r  r    r  r  c           	      C      t td |  | |t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  rS  
r  r  r  r  r  r  r  r  r  r  r  r  r  r    r%  r  c
           
   
   C   r  r  rU  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 r'  r  r  r  r   r  r  r  r  r    rH  r  c
           
   
   C   r  r'  r  r  r  r   r  r  r  r  r    rH  r  c
           
   	   C   x   t t| |tdt|||	   |   |tdt|||	   td|    | tdt|||	   |  |	|	S r  r  r  r  r  r  r    r3  r  c
           
   	   C   r  r  r  r  r  r  r  r    r3  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 r  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 r  r  r  r  r  r  r    s   r  c	           	   
   C   f   t td|  ||   t| |t|||    |td| t|||    td|   ||S Nr  r  rS  	r  r  r  r  r  r  r  r  r  r  r  r  r    r   r  c	           	   
   C   r  r  rU  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 r`  r  r  r  r  r  r    r@  r  c	           	   
   C   r  r`  r  r  r  r  r  r    r@  r  c           	      C      t td | | |td  td}t|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 r`  )r   rI  r  r  r  r  r  r  r    rv  r  c	           	   	   C   r  r`  )r   rI  r  r  r  r  r  r  r    rv  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  rC  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  rC  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    rY  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	  r,  r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s  t | td |td  |td  t| t|||   |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	  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|||   ||td   | t| td | | | t|||   |td   |||  |td   |td |td  |td   | S r	  r,  r  r  r  r  r  r  r  r  r  r  r  r  #      r  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	  r/  r  r  r  r  r  '  r  r  c                 C   s   t |td | td |  t| t|||   |td  |||   ||t|| t|||   |  |td |td   | t| t|||   |td  |||   t|||   | | |  | S r  r  r  r  r  r  r  +  r  r  c                 C   s   t |td | td |  t| t|||   |td  |||   ||t|| t|||   |  |td |td   | t| t|||   |td  |||   t|||   | | |  | S r  r  r  r  r  r  r  /  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  3     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	  r  r  r  r  r  r  7  r
  r  c                 C   d   t | t|||   | | t|||   |  t| t|||   |  |||  |  ||S r  r  r  r  r  r  r  ;  r  r  c                 C   r  r  r  r  r  r  r  r  ?  r  r  c	           	   	   C   6   t t|||  | | |t|||    | ||S r  r   r   r  r   r  r  r  r  C     6r  c	           	   	   C   r  r  r   r   r  r   r  r  r  r  G  r  r  c	           	      C   L   t t|||  | | t|||   | | t|||  |   ||S r  r  r   r  r  r  r  K  r  r  c	           	      C   r  r  r  r   r  r  r  r  O  r  r  c                 C   .   t | |tt||  | t|||  |S r  r   r  r2  r  r  r  r  r  vr  r  r  r  r  S  r  r  c                 C   r  r  r   r  r2  r  r  r  r  r  W  r  r  c	           	      C   2   t | |t|||    | |||  |  |S r  rK  r   r  r  r  r  [  rg  r  c	           	      C   r  r  rM  r   r  r  r  r  _  rg  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  c  r  r  c                 C   r  r  r   r  r  r  r  r  g  r  r  c                 C   &   t | |t||||     | |S r  rK  r  r  r  r  r  k     &r  c                 C   r  r  rM  r  r  r  r  r  o  r  r  c                 C   J   t tdt||td tt| |t||||     | ||||S r1  )r  r  r3   r+   r   r  r  r  r  r  r  r  r  r  r  r  r  r  s  r  r  c                 C   r  r1  )r  r  r3   r+   r   r  r  r  r  r  r  w  r  r  c                 C       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  c                 C   Z   t td| tt|td|td |   | |t|||    |  |||| |S r  r  r  r  r  r  r    ru  r  c                 C   r  r  r   r  r  r  r  r    ru  r  c              	   C   .   t || | |t||||     |  |S r  rK  r  r  r  r  r    r  r  c              	   C   r   r  rM  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    rv  r  c	           	      C   r!  r  )r  r%   r&   r   r  r  r  r  r  r    rv  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$  r  c              
   C   s   t || td || |td   t|||  tdt| |||    |td   || t||| td  tdt| |||    |td   || |td   | S r  r#  r  r  r  r  r  r  r  r  r  r    r  r  c              
   C   s   t || td || |td   t|||  tdt| |||    |td   ||t||| td  tdt| |||    |td   || |td   | S r  r&  r%  r  r  r  r    r  r  (`  __doc__Zsympy.externalr   r   r   r   r   r   Z%sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rC  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  ZPir  ZB_ZC_ZF_ZG_ZH_r  Zb_r  Zd_r  Zf_Zg_Zh_Zi_Zj_Zk_Zl_r  r  r  Zq_Zr_Zt_r  r  Zs_Zw_r  Zy_Zz_Za1_Za2_Zb1_Zb2_Zc1_Zc2_Zd1_Zd2_Zn1_r  Ze1_Ze2_Zf1_Zf2_Zg1_Zg2_Zn3_ZPq_ZPm_ZPx_ZQm_ZQr_ZQx_Zjn_Zmn_Znon2_ZRFx_ZRGx_r  iiZPqqQRrr  kr  Z	_UseGammaZ	ShowStepsZStepCounterr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r	  r
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