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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`.
é    )Úimport_moduleÚmatchpy)ÚPatternÚReplacementRuleÚCustomConstraintÚis_match(Ú  ÚIntÚSumÚSetÚWithÚModuleÚScanÚMapAndÚFalseQÚZeroQÚ	NegativeQÚNonzeroQÚFreeQÚNFreeQÚListÚLogÚ	PositiveQÚPositiveIntegerQÚNegativeIntegerQÚIntegerQÚ	IntegersQÚComplexNumberQÚPureComplexNumberQÚRealNumericQÚPositiveOrZeroQÚNegativeOrZeroQÚFractionOrNegativeQÚNegQÚEqualÚUnequalÚIntPartÚFracPartÚ	RationalQÚProductQÚSumQÚNonsumQÚSubstÚFirstÚRestÚSqrtNumberQÚSqrtNumberSumQÚLinearQÚSqrtÚArcCoshÚCoefficientÚDenominatorÚHypergeometric2F1ÚNotÚSimplifyÚFractionalPartÚIntegerPartÚAppellF1Ú
EllipticPiÚ	EllipticEÚ	EllipticFÚArcTanÚArcCotÚArcCothÚArcTanhÚArcSinÚArcSinhÚArcCosÚArcCscÚArcSecÚArcCschÚArcSechÚSinhÚTanhÚCoshÚSechÚCschÚCothÚ	LessEqualÚLessÚGreaterÚGreaterEqualÚ	FractionQÚIntLinearcQÚExpandÚIndependentQÚPowerQÚIntegerPowerQÚPositiveIntegerPowerQÚFractionalPowerQÚAtomQÚExpQÚLogQÚHeadÚMemberQÚTrigQÚSinQÚCosQÚTanQÚCotQÚSecQÚCscQÚSinÚCosÚTanÚCotÚSecÚCscÚHyperbolicQÚSinhQÚCoshQÚTanhQÚCothQÚSechQÚCschQÚInverseTrigQÚSinCosQÚ	SinhCoshQÚ	LeafCountÚ	NumeratorÚNumberQÚNumericQÚLengthÚListQÚImÚReÚInverseHyperbolicQÚInverseFunctionQÚTrigHyperbolicFreeQÚInverseFunctionFreeQÚRealQÚEqQÚFractionalPowerFreeQÚComplexFreeQÚPolynomialQÚFactorSquareFreeÚPowerOfLinearQÚExponentÚ
QuadraticQÚLinearPairQÚBinomialPartsÚTrinomialPartsÚPolyQÚEvenQÚOddQÚPerfectSquareQÚNiceSqrtAuxQÚ	NiceSqrtQÚTogetherÚPosAuxÚPosQÚCoefficientListÚ
ReplaceAllÚExpandLinearProductÚGCDÚContentFactorÚNumericFactorÚNonnumericFactorsÚMakeAssocListÚGensymSubstÚKernelSubstÚExpandExpressionÚApartÚ
SmartApartÚMatchQÚPolynomialQuotientRemainderÚFreeFactorsÚNonfreeFactorsÚRemoveContentAuxÚRemoveContentÚ	FreeTermsÚNonfreeTermsÚExpandAlgebraicFunctionÚCollectReciprocalsÚExpandCleanupÚAlgebraicFunctionQÚCoeffÚLeadTermÚRemainingTermsÚ
LeadFactorÚRemainingFactorsÚLeadBaseÚ
LeadDegreeÚNumerÚDenomÚ	hypergeomÚExponÚMergeMonomialsÚPolynomialDivideÚ	BinomialQÚ
TrinomialQÚGeneralizedBinomialQÚGeneralizedTrinomialQÚFactorSquareFreeListÚPerfectPowerTestÚSquareFreeFactorTestÚRationalFunctionQÚRationalFunctionFactorsÚNonrationalFunctionFactorsÚReverseÚRationalFunctionExponentsÚRationalFunctionExpandÚExpandIntegrandÚSimplerQÚSimplerSqrtQÚSumSimplerQÚBinomialDegreeÚTrinomialDegreeÚCancelCommonFactorsÚSimplerIntegrandQÚGeneralizedBinomialDegreeÚGeneralizedBinomialPartsÚGeneralizedTrinomialDegreeÚGeneralizedTrinomialPartsÚ	MonomialQÚMonomialSumQÚMinimumMonomialExponentÚMonomialExponentÚLinearMatchQÚPowerOfLinearMatchQÚQuadraticMatchQÚCubicMatchQÚBinomialMatchQÚTrinomialMatchQÚGeneralizedBinomialMatchQÚGeneralizedTrinomialMatchQÚQuotientOfLinearsMatchQÚPolynomialTermQÚPolynomialTermsÚNonpolynomialTermsÚPseudoBinomialPartsÚNormalizePseudoBinomialÚPseudoBinomialPairQÚPseudoBinomialQÚPolynomialGCDÚPolyGCDÚAlgebraicFunctionFactorsÚNonalgebraicFunctionFactorsÚQuotientOfLinearsPÚQuotientOfLinearsPartsÚQuotientOfLinearsQÚFlattenÚSortÚAbsurdNumberQÚAbsurdNumberFactorsÚNonabsurdNumberFactorsÚSumSimplerAuxQÚPrependÚDropÚCombineExponentsÚFactorIntegerÚFactorAbsurdNumberÚSubstForInverseFunctionÚSubstForFractionalPowerÚ*SubstForFractionalPowerOfQuotientOfLinearsÚ"FractionalPowerOfQuotientOfLinearsÚSubstForFractionalPowerQÚSubstForFractionalPowerAuxQÚFractionalPowerOfSquareQÚFractionalPowerSubexpressionQÚApplyÚFactorNumericGcdÚMergeableFactorQÚMergeFactorÚMergeFactorsÚTrigSimplifyQÚTrigSimplifyÚTrigSimplifyRecurÚOrderÚFactorOrderÚSmallestÚOrderedQÚMinimumDegreeÚPositiveFactorsÚSignÚNonpositiveFactorsÚPolynomialInAuxQÚPolynomialInQÚExponentInAuxÚ
ExponentInÚPolynomialInSubstAuxÚPolynomialInSubstÚDistribÚDistributeDegreeÚFunctionOfPowerÚDivideDegreesOfFactorsÚMonomialFactorÚFullSimplifyÚFunctionOfLinearSubstÚFunctionOfLinearÚNormalizeIntegrandÚNormalizeIntegrandAuxÚNormalizeIntegrandFactorÚNormalizeIntegrandFactorBaseÚNormalizeTogetherÚNormalizeLeadTermSignsÚAbsorbMinusSignÚNormalizeSumFactorsÚSignOfFactorÚNormalizePowerOfLinearÚSimplifyIntegrandÚSimplifyTermÚTogetherSimplifyÚSmartSimplifyÚSubstForExpnÚExpandToSumÚUnifySumÚ
UnifyTermsÚ	UnifyTermÚ	CalculusQÚFunctionOfInverseLinearÚPureFunctionOfSinhQÚPureFunctionOfTanhQÚPureFunctionOfCoshQÚIntegerQuotientQÚOddQuotientQÚEvenQuotientQÚFindTrigFactorÚFunctionOfSinhQÚFunctionOfCoshQÚOddHyperbolicPowerQÚFunctionOfTanhQÚFunctionOfTanhWeightÚFunctionOfHyperbolicQÚSmartNumeratorÚSmartDenominatorÚSubstForAuxÚActivateTrigÚ
ExpandTrigÚ
TrigExpandÚSubstForTrigÚSubstForHyperbolicÚInertTrigFreeQÚLCMÚSubstForFractionalPowerOfLinearÚFractionalPowerOfLinearÚInverseFunctionOfLinearÚ
InertTrigQÚInertReciprocalQÚDeactivateTrigÚFixInertTrigFunctionÚDeactivateTrigAuxÚPowerOfInertTrigSumQÚPiecewiseLinearQÚKnownTrigIntegrandQÚKnownSineIntegrandQÚKnownTangentIntegrandQÚKnownCotangentIntegrandQÚKnownSecantIntegrandQÚTryPureTanSubstÚTryTanhSubstÚTryPureTanhSubstÚAbsurdNumberGCDÚAbsurdNumberGCDListÚExpandTrigExpandÚExpandTrigReduceÚExpandTrigReduceAuxÚNormalizeTrigÚ	TrigToExpÚExpandTrigToExpÚ
TrigReduceÚFunctionOfTrigÚAlgebraicTrigFunctionQÚFunctionOfHyperbolicÚFunctionOfQÚFunctionOfExpnQÚPureFunctionOfSinQÚPureFunctionOfCosQÚPureFunctionOfTanQÚPureFunctionOfCotQÚFunctionOfCosQÚFunctionOfSinQÚOddTrigPowerQÚFunctionOfTanQÚFunctionOfTanWeightÚFunctionOfTrigQÚFunctionOfDensePolynomialsQÚFunctionOfLogÚPowerVariableExpnÚPowerVariableDegreeÚPowerVariableSubstÚEulerIntegrandQÚFunctionOfSquareRootOfQuadraticÚSquareRootOfQuadraticSubstÚDividesÚEasyDQÚProductOfLinearPowersQÚRtÚNthRootÚ	AtomBaseQÚSumBaseQÚNegSumBaseQÚAllNegTermQÚSomeNegTermQÚTrigSquareQÚRtAuxÚ
TrigSquareÚIntSumÚIntTermÚMap2ÚConstantFactorÚSameQÚReplacePartÚCommonFactorsÚMostMainFactorPositionÚFunctionOfExponentialQÚFunctionOfExponentialÚFunctionOfExponentialFunctionÚ FunctionOfExponentialFunctionAuxÚFunctionOfExponentialTestÚFunctionOfExponentialTestAuxÚstdevÚ	rubi_testÚIfÚIntQuadraticQÚIntBinomialQÚRectifyTangentÚRectifyCotangentÚ
InequalityÚ	ConditionÚSimpÚSimpHelpÚSplitProductÚSplitSumÚSubstForrG  ÚFresnelSÚFresnelCÚErfcÚErfiÚGammaÚFunctionOfTrigOfLinearQÚElementaryFunctionQÚComplexÚUnsameQÚ_SimpFixFactorÚSimpFixFactorÚ_FixSimplifyÚFixSimplifyÚ_SimplifyAntiderivativeSumÚSimplifyAntiderivativeSumÚ_SimplifyAntiderivativeÚSimplifyAntiderivativeÚ_TrigSimplifyAuxÚTrigSimplifyAuxÚCancelÚPartÚPolyLogÚDÚDistÚSum_doitÚPolynomialQuotientÚFloorÚPolynomialRemainderÚFactorr¿  ÚCosIntegralÚSinIntegralÚLogIntegralÚSinhIntegralÚCoshIntegralÚRuleÚErfÚ	PolyGammaÚExpIntegralEiÚExpIntegralEÚLogGammaÚUtilityOperatorÚ	FactorialÚZetaÚ
ProductLogÚDerivativeDividesÚHypergeometricPFQÚIntHideÚOneQÚNullÚrubi_expÚrubi_logÚDiscriminantÚNegativeÚQuotient)ÚAdd)ÚMod)ÚMul)Ú
EulerGamma)ÚFloatÚIÚInteger)ÚPow)ÚS)ÚAbsÚsign)Úsqrt)ÚIntegral)ÚAndÚOr)Úsimplify©ÚWC)ÚsymbolsÚSymbol)ÚsinÚcosÚtanÚcotÚcscÚsecrë  Úerf)ÚacoshÚasinhÚatanhÚacothÚacschÚasechÚcoshÚsinhÚtanhÚcothÚsechÚcsch)ÚatanÚacscÚasinÚacotÚacosÚasecÚatan2)Úpic                 C   ó   g | ]}t |ƒ‘qS © rð  ©Ú.0Úir  r  úS/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rules/binomial_products.pyÚ
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ƒ tdtdƒƒ  ƒ tƒ|||%ƒ}Jt|Jt7ƒ}Ktttdƒt2tttdƒ tdtdƒƒ  ƒ tƒ|||ƒ}Lt|Lt8ƒ}Mtttdƒt2tttdƒ tdtdƒƒ  ƒ tƒ|||&|ƒ}Nt|Nt9ƒ}Otttdƒt2tttdƒ tdtdƒƒ  ƒ tƒ|||'|(t:t;ƒƒ}Pt|Pt<ƒ}Qtttdƒt2tttdƒ tdtdƒƒ  ƒ tƒ|||'|(ƒ}Rt|Rt=ƒ}Stttdƒt2tttdƒ tdtdƒƒ  ƒ tƒ|||&|ƒ}Tt|Tt>ƒ}Utttdƒt2tttd	ƒ tdtdƒƒ  ƒ tƒ|||ƒ}Vt|Vt?ƒ}Wtttdƒt2tttdƒ tdtdƒƒ  ƒ tƒ|||ƒ}Xt|Xt@ƒ}Ytttttdƒ tdtdƒƒ  tdƒd  tƒ|||ƒ}Zt|ZtAƒ}[tttttdƒ tdtdƒƒ  tdƒd  tƒ|||&|ƒ}\t|\tBƒ}]tttttdƒ tdtdƒƒ  tdƒd  tƒ|||&|ƒ}^t|^tCƒ}_tttttdƒ tdtdƒƒ  tdƒd  tƒ||||ƒ}`t|`tDƒ}atttttdƒ tdtdƒƒ  tdƒd  tƒ||||&ƒ}bt|btEƒ}ctttttdƒ tdtdƒƒ  tdƒd  tƒ|||ƒ}dt|dtFƒ}etttttdƒ tdtdƒƒ  tdƒd
  tƒ|||ƒ}ft|ftGƒ}gtttttdƒ tdtdƒƒ  tdƒd
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}€t|€tWƒ}tttUttdtdƒƒ tdtdƒƒ  t tVttdtdƒƒ tdtdƒƒ  t  tƒ|9|:|;|<|7|=|||>ƒ
}‚t|‚tXƒ}ƒtttUtt tdtdƒƒ  t tVtt tdtdƒƒ  t  tƒ|9|:|;|<||7|?ƒ}„t|„tYƒ}…tttUtt tdtdƒƒ  t tVtt tdtdƒƒ  t  tƒ|9|:|;|<||7|@ƒ}†t|†tZƒ}‡tttt tdtdƒƒ tdtdƒƒ t tt tdtdƒƒ tdtdƒƒ t  tƒ|9|:|;|<|||7|Aƒ	}ˆt|ˆt[ƒ}‰ttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|||7|8ƒ}Št|Št\ƒ}‹ttttdtdƒƒ tdtdƒƒ tt tdtdƒƒ t  tƒ||B|C|||D|Eƒ}Œt|Œt]ƒ}ttttdtdƒƒ tdtdƒƒ ttdtdƒƒ tdtdƒƒ t  tƒ||B|C|||D|Fƒ}Žt|Žt^ƒ}ttt_t t` ttdtdƒƒ tdtdƒƒ t  tƒ||B|C|||Gƒ}t|taƒ}‘ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||C|||Hƒ}’t|’tbƒ}“ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C|||I|Jƒ	}”t|”tcƒ}•ttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|||7|K|Jƒ}–t|–tdƒ}—ttttdtdƒƒ tt tdtdƒƒ tdtdƒƒ t  tƒ|||C|||Eƒ}˜t|˜teƒ}™ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|C|||7|Lƒ
}št|štfƒ}›ttt_t t` ttt tdtdƒƒ  t  tƒ|||B|C|||Eƒ}œt|œtgƒ}ttt_t t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|||7|Lƒ}žt|žthƒ}Ÿttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  tƒ|||B|C||/ƒ} t| tiƒ}¡tttt` ttt tdtdƒƒ  t  tƒ|||C|||M|Jƒ}¢t|¢tjƒ}£tttt` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|C|||7|N|Jƒ}¤t|¤tkƒ}¥ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C|||M|ƒ	}¦t|¦tlƒ}§ttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|||7|N|ƒ}¨t|¨tmƒ}©ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||||Ot:tnƒƒ}ªt|ªtoƒ}«ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<||7|=|Ot:tpƒƒ
}¬t|¬tqƒ}­ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B||P||Q|R|Sƒ
}®t|®trƒ}¯ttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|7|=|P||T|Uƒ}°t|°tsƒ}±ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C||P||V|Sƒ
}²t|²ttƒ}³ttttdƒ tttdƒ tdtdƒƒ  tdƒd   tƒ|||ƒ}´t|´tuƒ}µtttt` tttdƒ tdtdƒƒ  tdƒd   tƒ||||Wƒ}¶t|¶tvƒ}·tttt` tttdƒ tdtdƒƒ  tdƒd   tƒ||||Xƒ}¸t|¸twƒ}¹ttt2ttdtdƒƒ ƒtttdƒ tdtdƒƒ  tdƒd   tƒ|||B|ƒ}ºt|ºtxƒ}»ttttdtdƒƒ t` tttdƒ tdtdƒƒ  tdƒd   tƒ|||B||Y|Zƒ}¼t|¼tyƒ}½ttttdtdƒƒ t` tttdƒ tdtdƒƒ  tdƒd   tƒ|||B||Y|Qƒ}¾t|¾tzƒ}¿ttttdƒ tttdƒ tdtdƒƒ  tdƒd   tƒ|||&ƒ}Àt|Àt{ƒ}Áttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B||P||[|\|Sƒ
}Ât|Ât|ƒ}Ãttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|7|=|P||]|^|Uƒ}Ät|Ät}ƒ}Åttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C||P||Sƒ	}Æt|Æt~ƒ}Çttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|7|=|P||Uƒ}Èt|Ètƒ}Éttttttd
ƒ tdtdƒƒ   tƒ|||ƒ}Êt|Êt€ƒ}Ëttttdtdƒƒ ttt tdtdƒƒ   tƒ|||_|`|a|ƒ}Ìt|Ìtƒ}Íttttdtdƒƒ ttt tdtdƒƒ   tƒ|||b|`|a|ƒ}Ît|Ît‚ƒ}Ïttttdtdƒƒ ttt tdtdƒƒ   tƒ|||c|`|a|ƒ}Ðt|Ðtƒƒ}Ñttttdtdƒƒ ttt tdtdƒƒ   tƒ|||c|`|a|ƒ}Òt|Òt„ƒ}Óttttdƒ tttdƒ tdtdƒƒ   tƒ|||ƒ}Ôt|Ôt…ƒ}Õttttdƒ tttdƒ tdtdƒƒ   tƒ|||ƒ}Öt|Öt†ƒ}×ttttdtdƒƒ ttt tdtdƒƒ   tƒ|||d|`|a|!ƒ}Øt|Øt‡ƒ}Ùtttt` ttt tdtdƒƒ   tƒ|||d|`|e|ƒ}Út|Útˆƒ}Ûtttt` ttt tdtdƒƒ   tƒ|||d|`|f|ƒ}Üt|Üt‰ƒ}Ýtttt` ttt tdtdƒƒ   tƒ|||g|hƒ}Þt|ÞtŠƒ}ßtttt2tttd
ƒ tdtdƒƒ  ƒ tƒ|||$ƒ}àt|àt‹ƒ}átttt2tttd
ƒ tdtdƒƒ  ƒ tƒ|||%ƒ}ât|âtŒƒ}ãttttdƒ t2tttdƒ tdtdƒƒ  ƒ tƒ|||ƒ}ät|ätƒ}åttttdƒ t2tttdƒ tdtdƒƒ  ƒ tƒ|||'|(ƒ}æt|ætŽƒ}çttttdƒ t2tttdƒ tdtdƒƒ  ƒ tƒ|||&ƒ}èt|ètƒ}éttttdƒ t2tttd	ƒ tdtdƒƒ  ƒ tƒ|||ƒ}êt|êtƒ}ëttttdƒ t2tttdƒ tdtdƒƒ  ƒ tƒ|||ƒ}ìt|ìt‘ƒ}íttttdƒ tttdƒ tdtdƒƒ  tdƒd   tƒ|||ƒ}ît|ît’ƒ}ïttttdƒ tttdƒ tdtdƒƒ  tdƒd   tƒ|||&ƒ}ðt|ðt“ƒ}ñtttdƒttdƒ tttdƒ tdtdƒƒ  tdƒd    tƒ|||ƒ}òt|òt”ƒ}ótttdƒttdƒ tttdƒ tdtdƒƒ  tdƒd    tƒ|||&ƒ}ôt|ôt•ƒ}õttt2t_t ƒtttdƒ tdtdƒƒ  tdƒd   tƒ|||B|ƒ}öt|öt–ƒ}÷ttt2t_t ƒtttdƒ tdtdƒƒ  tdƒd   tƒ|||B|&ƒ}øt|øt—ƒ}ùtttdƒttdtdƒƒ td
ƒd  tttdƒ tdtdƒƒ  tdƒd    tƒ|||B|ƒ}út|út˜ƒ}ûtttdƒttdtdƒƒ td
ƒd  tttdƒ tdtdƒƒ  tdƒd    tƒ|||B|&ƒ}üt|üt™ƒ}ýttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B|||i|j|V|Sƒ
}þt|þtšƒ}ÿttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B|C|||k|V|lƒ
} t| t›ƒ}ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B||7|=|i|h|T|Uƒ}t|tœƒ}ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|=|m|T|nƒ}t|tƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B|||i|Q|Sƒ	}t|tžƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B|C|||o|lƒ	}t|tŸƒ}	ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B||7|=|i|Q|Uƒ}
t|
t ƒ}ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|=|p|nƒ}t|t¡ƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B|||q|Sƒ}t|t¢ƒ}ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B||7|=|q|Uƒ}t|t£ƒ}ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||||)|*|rƒ}t|t¤ƒ}ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|7|=||)|*|sƒ}t|t¥ƒ}ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||||)|*|O|tƒ	}t|t¦ƒ}ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|7|=||)|*|O|uƒ}t|t§ƒ}ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ||||-|Oƒ}t|t¨ƒ}ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<||7|?|Oƒ	}t|t©ƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B||-|qƒ}t|tªƒ}ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B||7|?|qƒ
} t| t«ƒ}!ttttdtdƒƒ t` ttt tdtdƒƒ  t  tƒ|||B|C||-|vƒ}"t|"t¬ƒ}#ttttdtdƒƒ t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|?|vƒ}$t|$t­ƒ}%ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||C||.ƒ}&t|&t®ƒ}'ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|C||7|@ƒ	}(t|(t¯ƒ})ttt_t t` ttt tdtdƒƒ  t  tƒ|||B|C||.ƒ}*t|*t°ƒ}+ttt_t t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|@ƒ
},t|,t±ƒ}-ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||C|||w|xƒ}.t|.t²ƒ}/ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|C|||7|y|zƒ}0t|0t³ƒ}1ttt_t t` ttt tdtdƒƒ  t  tƒ|||B|C|||w|xƒ	}2t|2t´ƒ}3ttt_t t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|||7|y|zƒ}4t|4tµƒ}5ttttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||C||{||ƒ}6t|6t¶ƒ}7ttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|C||7||||ƒ}8t|8t·ƒ}9ttt_t t` ttt tdtdƒƒ  t  tƒ|||B|C||{||ƒ	}:t|:t¸ƒ};ttt_t t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7||||ƒ}<t|<t¹ƒ}=ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C||}|||Vƒ
}>t|>tºƒ}?ttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|~|||Tƒ}@t|@t»ƒ}Attttdtdƒƒ ttt tdtdƒƒ  t  tƒ|||C||}||)ƒ}Bt|Bt¼ƒ}Cttttdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|C||7|~||)ƒ}Dt|Dt½ƒ}Ettt_t t` ttt tdtdƒƒ  t  tƒ|||B|C||}||)ƒ	}Ft|Ft¾ƒ}Gttt_t t` tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|~||)ƒ}Ht|Ht¿ƒ}Ittttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C||}||ƒ	}Jt|JtÀƒ}Kttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C||7|}||ƒ}Lt|LtÁƒ}Mttttdtdƒƒ ttt tdtdƒƒ   tƒ|||C|||kƒ}Nt|NtÂƒ}Otttt` ttt tdtdƒƒ   tƒ|||C|||oƒ}Pt|PtÃƒ}Qttt_t t` ttt tdtdƒƒ   tƒ|||B|C|||€ƒ}Rt|RtÄƒ}Sttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C|||0|ƒ	}Tt|TtÅƒ}Uttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  tƒ|||B|C|||0|‚ƒ	}Vt|VtÆƒ}Wttttdtdƒƒ ttÇt tdtdƒƒ  tdtdƒƒ  tƒ|||||ƒ|O|„ƒ}Xt|XtÈƒ}YtttRtdtdƒƒ ttÇt tdtdƒƒ  tdtdƒƒ  tƒ|||C|||…ƒ}Zt|ZtÉƒ}[ttttdtdƒƒ tdtdƒƒ tUtt tdtdƒƒ  t  tVtt tdtdƒƒ  t  tƒ|9|:|;|<|B|C|||7|Aƒ}\t|\tÊƒ}]ttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ||†|‡ƒ}^t|^tËƒ}_ttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ||†|‰|Hƒ	}`t|`tÌƒ}attttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ||Š|†|-ƒ	}bt|btÍƒ}cttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ||Š|†|.ƒ	}dt|dtÎƒ}ettttt tdtdƒƒ  t t_tt tdtdƒƒ   tƒ|||B|ˆ|†|‹|Œƒ}ft|ftÏƒ}gttttt tdtdƒƒ  t t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|||†||Ž||ƒ}ht|htÐƒ}ittttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||Š|†||ƒ
}jt|jtÒƒ}kttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|||Š|†|ƒ
}lt|ltÓƒ}mttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|||Š|†|‘|’ƒ}nt|ntÔƒ}ottttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||Š|†|‘|“|ƒ}pt|ptÕƒ}qttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ   tƒ|||B|ˆ|||†|”ƒ	}rt|rtÖƒ}sttttt tdtdƒƒ  t t_tt tdtdƒƒ   tƒ|||B|ˆ|||†|•ƒ	}tt|tt×ƒ}uttt_tt tdtdƒƒ  ttt tdtdƒƒ   tƒ|||B|ˆ||†|	|
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  t_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|†|™|ƒ}~t|~tÜƒ}tttdƒtttdƒ tdtdƒƒ  tdƒd
  t_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|†|™|&ƒ}€t|€tÝƒ}tttttdƒ tdtdƒƒ  tdƒd
  t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†|™ƒ}‚t|‚tÞƒ}ƒtttdƒtttdƒ tdtdƒƒ  tdƒd  t_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|†ƒ}„t|„tßƒ}…tttdƒtttdƒ tdtdƒƒ  td
ƒd  t_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|†ƒ}†t|†tàƒ}‡tttttdƒ tdtdƒƒ  tdtdƒƒ t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†|||šƒ	}ˆt|ˆtáƒ}‰tttttdƒ tdtdƒƒ  t t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†|||›|œƒ
}Št|Štâƒ}‹ttt2tttdƒ tdtdƒƒ  ƒt_ttdƒ tdtdƒƒ   tƒ|||B|ˆ||žƒ}Œt|Œtãƒ}ttt2tttdƒ tdtdƒƒ  ƒt_ttdƒ tdtdƒƒ   tƒ|||B|ˆ||Ÿƒ}Žt|Žtäƒ}ttt2tttdƒ tdtdƒƒ  ƒt_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†ƒ}t|tåƒ}‘tttttdƒ tdtdƒƒ  tdƒd  t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†ƒ}’t|’tæƒ}“tttttdƒ tdtdƒƒ  t t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†|| ƒ}”t|”tçƒ}•tttdƒt2tttdƒ tdtdƒƒ  ƒt_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|†ƒ}–t|–tèƒ}—tttdƒtttdƒ tdtdƒƒ  td
ƒd  t_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|†ƒ}˜t|˜téƒ}™ttt2tttdƒ tdtdƒƒ  ƒt_ttdƒ tdtdƒƒ  td
ƒd   tƒ|||B|ˆ||¡ƒ}št|štêƒ}›ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||†|¢||£|¤ƒ}œt|œtëƒ}ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||†|¢||¥|¤ƒ}žt|žtìƒ}Ÿttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||Š|†|||¦|¤ƒ} t| tíƒ}¡ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|†||‰|§ƒ	}¢t|¢tîƒ}£ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|||†|Ž|¥|¨|©|¤ƒ}¤t|¤tïƒ}¥ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||†|¢|||¤ƒ}¦t|¦tðƒ}§tttdƒt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|¡||ªƒ}¨t|¨tñƒ}©tttdƒt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|«|¬||­ƒ	}ªt|ªtòƒ}«tttdƒt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|«|¬|®ƒ}¬t|¬tóƒ}­tttdƒt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|¯ƒ}®t|®tôƒ}¯ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tƒ|||B|ˆ|¡|ƒ}°t|°tõƒ}±ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tƒ|||B|ˆ|¡|&ƒ}²t|²töƒ}³ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tƒ|||B|ˆ|«|¬|ƒ}´t|´t÷ƒ}µttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tƒ|||B|ˆ|«|¬|®ƒ}¶t|¶tøƒ}·ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tƒ|||B|ˆ|«|¬|ƒ}¸t|¸tùƒ}¹ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tƒ|||B|ˆ|«|¯ƒ}ºt|ºtúƒ}»ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||Š|†|/ƒ	}¼t|¼tûƒ}½ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|||Š|†|°||¬ƒ}¾t|¾tüƒ}¿ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|||Š|†|°|ƒ}Àt|Àtýƒ}Átttttdtdƒƒ tdtdƒƒ  tdtdƒƒ t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|||±|²|³ƒ
}Ât|Âtþƒ}Ãtttttdtdƒƒ tdtdƒƒ  t t_ttdtdƒƒ tdtdƒƒ  tÑ  tƒ|||B|ˆ|||Š|±|´|Aƒ}Ät|Ätÿƒ}ÅtttRt tdtdƒƒ tdtdƒƒ tdtdƒƒ tRt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|||Š|5|6ƒ
}Æt|Æt ƒ}ÇtttRtdtdƒƒ tÇtdtdƒƒ  tƒ||Š|µƒ}Èt|Ètƒ}ÉtttRtdtdƒƒ tÇtdtdƒƒ  ttdtdƒƒ  tƒ||Š|¶|·ƒ}Êt|Êtƒ}Ëttttdtdƒƒ tdtdƒƒ tt tdtdƒƒ t  t_tt tdtdƒƒ  tdtdƒƒ  tƒ||B|ˆ|¹|C|||Š|¸|Eƒ}Ìt|Ìtƒ}Íttttdtdƒƒ tdtdƒƒ ttdtdƒƒ tdtdƒƒ t  t_tt tdtdƒƒ  tdtdƒƒ  tƒ||B|ˆ|¹|C|||Š|¸|Fƒ}Ît|Îtƒ}Ïtttt t` ttdtdƒƒ tdtdƒƒ t  t_tt tdtdƒƒ  tdtdƒƒ  tƒ||B|ˆ|¹|C|||Š|Gƒ
}Ðt|Ðtƒ}Ñttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|C|||Š|†|ºƒ}Òt|Òtƒ}Óttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|C||†|‰|Hƒ
}Ôt|Ôtƒ}Õttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|C|||Š|†|Eƒ}Öt|Öt	ƒ}×tttt tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|¹|C|||Š|†|Eƒ}Øt|Øt
ƒ}Ùttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|¹|C||†|‡ƒ
}Út|Útƒ}Ûttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|C|||†|»|Jƒ}Üt|Ütƒ}Ýttttdtdƒƒ tdtdƒƒ tUttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|9|:|;|<|B|ˆ|¹|C|||¼|7|½|Jƒ}Þt|Þtƒ}ßttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹||†|¾|¿|À|Áƒ}àt|àtƒ}áttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|C|||†|¾|Jƒ}ât|âtƒ}ãttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹||†|¿|À|Á|Âƒ}ät|ätƒ}åttttdtdƒƒ tdtdƒƒ tUttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|9|:|;|<|B|ˆ|¹||¼|7|¿|À|Á|Âƒ}æt|ætƒ}çtttt` tttdƒ tdtdƒƒ  t  t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†|||Ã|Äƒ
}èt|ètƒ}étttt` tttdƒ tdtdƒƒ  t  t_ttdƒ tdtdƒƒ   tƒ|||B|ˆ|†|||Å|Äƒ
}êt|êtƒ}ëttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|C||†|||Æƒ}ìt|ìtƒ}íttttdtdƒƒ tdtdƒƒ tUttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|9|:|;|<|B|ˆ|¹|C||¼|7|||Æƒ}ît|îtƒ}ïttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|C|||†|Çƒ}ðt|ðtƒ}ñttttdtdƒƒ tdtdƒƒ tUttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ   tƒ|9|:|;|<|B|ˆ|¹|C|||¼|7|Çƒ}òt|òtƒ}óttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|C|†||/|Èƒ}ôt|ôtƒ}õttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tdƒ  tƒ|||B|ˆ|¹||†||À|Q|Éƒ}öt|ötƒ}÷ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tdƒ  tƒ|||B|ˆ|¹|C||†|||ƒ}øt|øtƒ}ùttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tdƒ  tƒ|||B|ˆ|¹|C|||†||Êƒ}út|útƒ}ûttttdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||Š|†||Ot:tƒƒ}üt|ütƒ}ýttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||Š|†||q|ƒ}þt|þtƒ}ÿttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|†||Ë|||Ì|Íƒ} t| tƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|†||¢||¥|Íƒ}t|t ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|†||¢||£|Íƒ}t|t!ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|Š|†||P||Î|Íƒ}t|t"ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|Š|†||P||Ï|Íƒ}t|t#ƒ}	ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|Š|†||||Íƒ}
t|
t$ƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|†||Ë||Q||Íƒ}t|t%ƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||†||Ð|¥|Q|Íƒ}t|t&ƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||†||Ð|£|Q|Íƒ}t|t'ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|†||¢|||Íƒ}t|t(ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||†||Ž|¥|Íƒ}t|t)ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||†||Ð||Ì|Íƒ}t|t*ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||Š|†||i|Î|Íƒ}t|t+ƒ}ttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||Š|†||i|Q|Íƒ}t|t,ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t_tt tdtdƒƒ    tƒ|||B|ˆ|C||†||i|Ñƒ}t|t-ƒ}ttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t_tt tdtdƒƒ    tƒ|||B|ˆ|¹|C|†|ƒ	}t|t.ƒ}tttt` ttt tdtdƒƒ  t2t_tt tdtdƒƒ  ƒ  tƒ|||B|ˆ|†|Ò|Ó|Ôƒ	} t| t/ƒ}!ttttdƒ tttdƒ tdtdƒƒ  t2t_ttdƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|†ƒ}"t|"t0ƒ}#ttttttd
ƒ tdtdƒƒ  t2t_ttd
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ƒ tdtdƒƒ  t2t_ttd
ƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|†|Õ|Öƒ}&t|&t2ƒ}'tttt` tttd
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ƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|†|Õ|×ƒ}(t|(t3ƒ})ttttdƒ t2t_ttdƒ tdtdƒƒ  ƒ tttdƒ tdtdƒƒ   tƒ|||B|ˆ|†ƒ}*t|*t4ƒ}+ttttdtdƒƒ t2t_ttd
ƒ tdtdƒƒ  ƒ tttd
ƒ tdtdƒƒ   tƒ|||B|ˆ|†|Õ|Øƒ},t|,t5ƒ}-ttttdƒ t2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ  tƒ|||B|ˆ|†||¡|ªƒ	}.t|.t6ƒ}/tttt t2ttt tdtdƒƒ  ƒt2t_tt tdtdƒƒ  ƒ  tƒ|||B|ˆ|†|Ù|Úƒ}0t|0t7ƒ}1ttttdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ||P|Û|)ƒ	}2t|2t8ƒ}3ttttdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ||Š|†|-|Oƒ
}4t|4t9ƒ}5ttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹||Š|-|qƒ
}6t|6t:ƒ}7ttttdtdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||Š|†|-|vƒ}8t|8t;ƒ}9ttttdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|C||Š|†|.ƒ
}:t|:t<ƒ};tttt t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||Š|†|.ƒ}<t|<t=ƒ}=ttttdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|C|||Š|†|w|xƒ}>t|>t>ƒ}?tttt tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|||Š|†|w|xƒ}@t|@t?ƒ}Attttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||†|¢||¥|Íƒ}Bt|Bt@ƒ}Cttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||†|¢||£|Íƒ}Dt|DtAƒ}Ettttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||Š|†|||Íƒ}Ft|FtBƒ}Gttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||†|¢|||Íƒ}Ht|HtCƒ}Ittttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|||†|Ž|¥|Íƒ}Jt|JtDƒ}Ktttt` ttt tdtdƒƒ  t_tt tdtdƒƒ    tƒ|||B|ˆ|C||†|Üƒ	}Lt|LtEƒ}Mttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t_tt tdtdƒƒ    tƒ|||B|ˆ|¹||C|†ƒ	}Nt|NtFƒ}Ottttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C||†|Ý|Þ|ßƒ}Pt|PtGƒ}Qttttdtdƒƒ tttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tƒ|||B|ˆ|C|||±|²|³ƒ}Rt|RtHƒ}Sttttdtdƒƒ tttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  tÑ  tƒ|||B|ˆ|C|||Š|±|´|Aƒ}Tt|TtIƒ}Utttt t` t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  ttdtdƒƒ tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|C|||Š|±ƒ}Vt|VtJƒ}Wttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|||Š|†|J|à||¬ƒ}Xt|XtKƒ}Yttttdtdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  tƒ|||B|ˆ|¹|C|||Š|†|J|à|ƒ}Zt|ZtLƒ}[ttttdtdƒƒ tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|||Š|ƒ|O|„ƒ}\t|\tMƒ}]tttRtdtdƒƒ tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|C|||Š|…ƒ
}^t|^tNƒ}_tttUttdtdƒƒ tdtdƒƒ  tdtdƒƒ tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tdtdƒƒ tƒ|9|:|;|<|B|ˆ|||Š|¼|7|8ƒ}`t|`tOƒ}atttUttdtdƒƒ tdtdƒƒ  tdtdƒƒ tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tdtdƒƒ tƒ|9|:|;|<|B|ˆ|¹|||Š|¼|á|7|8ƒ}bt|btPƒ}ctttUttdtdƒƒ tdtdƒƒ  t tVttdtdƒƒ tdtdƒƒ  t  t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tdtdƒƒ tƒ|9|:|;|<|B|ˆ|||Š|¼|7ƒ}dt|dtQƒ}etttUttdtdƒƒ tdtdƒƒ  tdtdƒƒ tVttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tdtdƒƒ tƒ|9|:|;|<|B|ˆ|¹|||Š|¼|á|7ƒ}ft|ftRƒ}gttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||âƒ	}ht|htSƒ}ittttt td tdƒƒ  ttt tdtdƒƒ  t_tt tdtdƒƒ    tƒ|||B|ˆ|¹|ã||äƒ	}jt|jtTƒ}kttttt td tdƒƒ  ttt tdtdƒƒ  t2t_tt tdtdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã||äƒ	}lt|ltUƒ}mttttt td tdƒƒ  t2ttt tdtdƒƒ  ƒt2t_tt tdtdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã||åƒ	}nt|ntVƒ}otttttdƒ td tdƒƒ  t2tttdƒ tdtdƒƒ  ƒt_ttdƒ tdtdƒƒ  td
ƒd    tƒ|||B|ˆ|¹|ã||¡ƒ	}pt|ptWƒ}qttttt tdtdƒƒ  t t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||¢||ƒ}rt|rtXƒ}sttttt tdtdƒƒ  t t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||Š||ƒ}tt|ttYƒ}uttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã|||Ž||æƒ}vt|vtZƒ}wtttttdƒ td tdƒƒ  tttdƒ tdtdƒƒ  td
ƒd  t_ttdƒ tdtdƒƒ    tƒ|||B|ˆ|¹|ã|çƒ}xt|xt[ƒ}yttttt tdtdƒƒ  t ttt td tdƒƒ   t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|ã|||èƒ
}zt|zt\ƒ}{ttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã|||Š|éƒ}|t||t]ƒ}}tttdƒtttdƒ tdtdƒƒ  t_ttdƒ tdtdƒƒ   t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|çƒ}~t|~t^ƒ}tttdƒttdƒ t_ttdƒ tdtdƒƒ   t2tttdƒ td tdƒƒ  ƒ  tƒ|B|ˆ|¹|ã|êƒ}€t|€t_ƒ}ttt2t_ttdƒ tdtdƒƒ  ƒt2tttdƒ td tdƒƒ  ƒ tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|ë|ì|íƒ
}‚t|‚t`ƒ}ƒttt2t_ttdƒ tdtdƒƒ  ƒt2tttdƒ td tdƒƒ  ƒ tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|îƒ}„t|„taƒ}…tttdƒtttdƒ tdtdƒƒ  t2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|¡|ï|íƒ
}†t|†tbƒ}‡tttdƒtttdƒ tdtdƒƒ  t2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|«|¬|ð|ñƒ}ˆt|ˆtcƒ}‰tttdƒtttdƒ tdtdƒƒ  t2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|¯ƒ}Št|Štdƒ}‹ttt2t_ttdƒ tdtdƒƒ  ƒtttdƒ tdtdƒƒ  t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|¡ƒ}Œt|Œteƒ}ttt2t_ttdƒ tdtdƒƒ  ƒtttdƒ tdtdƒƒ  t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|«ƒ}Žt|Žtfƒ}ttt2tttdƒ td tdƒƒ  ƒtttdƒ tdtdƒƒ  t_ttdƒ tdtdƒƒ  td
ƒd    tƒ|||B|ˆ|¹|ã|¡|ïƒ	}t|tgƒ}‘tttttdƒ td tdƒƒ  td
ƒd  tttdƒ tdtdƒƒ  t_ttdƒ tdtdƒƒ  td
ƒd    tƒ|||B|ˆ|¹|ã|¡|ïƒ	}’t|’thƒ}“ttt_ttdƒ tdtdƒƒ  td
ƒd  t2tttdƒ td tdƒƒ  ƒ tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|¡|ïƒ	}”t|”tiƒ}•ttt_ttdƒ tdtdƒƒ  tÑ tttdƒ td tdƒƒ  tj  tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|ò|ó|ôƒ
}–t|–tkƒ}—ttt_ttdƒ tdtdƒƒ  tÑ tttdƒ td tdƒƒ  tj  tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|õ|Ž|¥ƒ
}˜t|˜tlƒ}™ttt_ttdƒ tdtdƒƒ  tÑ tttdƒ td tdƒƒ  tj  tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|õ|Ž|óƒ
}št|štmƒ}›ttt_ttdƒ tdtdƒƒ  tÑ tttdƒ td tdƒƒ  tj  tttdƒ tdtdƒƒ   tƒ|||B|ˆ|¹|ã|õ|Ž|öƒ
}œt|œtnƒ}ttt2t_ttdƒ tdtdƒƒ  ƒt2tttdƒ td tdƒƒ  ƒ tttdƒ tdtdƒƒ  tdƒ  tƒ|||B|ˆ|¹|ã|çƒ}žt|žtoƒ}Ÿtttdƒtttdƒ tdtdƒƒ  tdƒ t2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|çƒ} t| tpƒ}¡ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ  tj  tƒ|||B|ˆ|¹|ã||õ||Ž|ƒ}¢t|¢tqƒ}£ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ  tj  tƒ|||B|ˆ|¹|ã||Š||Ž|öƒ}¤t|¤trƒ}¥tttdƒt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|çƒ}¦t|¦tsƒ}§ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒt2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|çƒ}¨t|¨ttƒ}©ttt2t_ttdƒ tdtdƒƒ  ƒtttdƒ tdtdƒƒ  td
ƒd  t2tttdƒ td tdƒƒ  ƒ  tƒ|||B|ˆ|¹|ã|çƒ}ªt|ªtuƒ}«ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ tƒ|||B|ˆ|¹|ã|÷ƒ}¬t|¬tvƒ}­ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ t2tttdƒ td tdƒƒ  ƒ tƒ|||B|ˆ|¹|ã|øƒ}®t|®twƒ}¯ttt2tttdƒ tdtdƒƒ  ƒt2t_ttdƒ tdtdƒƒ  ƒ tttdƒ td tdƒƒ  td
ƒd   tƒ|||B|ˆ|¹|ã|çƒ}°t|°txƒ}±ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ  tj  tƒ|||B|ˆ|¹|ã||Š|õ|t:tyƒƒ}²t|²tzƒ}³ttttt tdtdƒƒ  t t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ  tj  tƒ|||B|ˆ|¹|ã||Š|õ|-ƒ}´t|´t{ƒ}µttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|||Š|õ|ùƒ}¶t|¶t|ƒ}·tttRt tdtdƒƒ tdtdƒƒ tdtdƒƒ tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  t}t td tdƒƒ tdtdƒƒ td!tdƒƒ  tƒ|||B|ˆ|¹|ã|||Š|õ|ú|û|5|6ƒ}¸t|¸t~ƒ}¹ttt_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ tttdtdƒƒ td tdƒƒ  td!tdƒƒ  ttdtdƒƒ tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|ã|||õ|±|²ƒ}ºt|ºtƒ}»ttt_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ tttdtdƒƒ td tdƒƒ  td!tdƒƒ  ttdtdƒƒ tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|ã||Š|±||üƒ}¼t|¼t€ƒ}½ttt_ttdtdƒƒ tdtdƒƒ  tÑ tttdtdƒƒ td tdƒƒ  td!tdƒƒ  ttdtdƒƒ tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|ã|||Š|õ|±|´ƒ}¾t|¾tƒ}¿ttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  t‚ttdtdƒƒ td"tdƒƒ  td!tdƒƒ  tƒttdtdƒƒ td#tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ| ||||||Š|õ|ý|þ|ÿƒ}Àt|Àt„ƒ}Áttttt tdtdƒƒ  tdtdƒƒ t_tt tdtdƒƒ  tdtdƒƒ  t‚ttdtdƒƒ td"tdƒƒ  td!tdƒƒ  tƒttdtdƒƒ td#tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ| ||||||Š|õ|ý|þƒ}Ât|Ât…ƒ}Ãttttd$tdƒƒ tdtdƒƒ tt tdtdƒƒ t  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ||B|ˆ|¹|ã||C|||Š|õ||Eƒ}Ät|Ät†ƒ}Åttttd$tdƒƒ tdtdƒƒ ttdtdƒƒ tdtdƒƒ t  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ||B|ˆ|¹|ã||C|||Š|õ||Fƒ}Æt|Æt‡ƒ}Çtttˆt t` ttdtdƒƒ tdtdƒƒ t  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ||B|ˆ|¹|ã||C|||Š|õ|Gƒ}Èt|Èt‰ƒ}Éttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C||ƒ}Êt|ÊtŠƒ}Ëttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|C|||Š|õ|ºƒ}Ìt|Ìt‹ƒ}Íttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|C|||Hƒ}Ît|ÎtŒƒ}Ïttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|C|||Š|õ|Eƒ}Ðt|Ðtƒ}Ñtttˆt tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C|||Š|õ|Eƒ}Òt|ÒtŽƒ}Óttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||Š|õ||Ot:tƒƒ}Ôt|Ôtƒ}Õttttd$tdƒƒ t` ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ  tj  tƒ|||B|ˆ|¹|ã|||Š|õ||qƒ}Öt|Öt‘ƒ}×ttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C||¢|||ƒ}Øt|Øt’ƒ}Ùttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||Š||P||Ìƒ}Út|Út“ƒ}Ûttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C|Š|||ƒ}Üt|Üt”ƒ}Ýttttd$tdƒƒ t` ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||||Ð||Q|	ƒ}Þt|Þt•ƒ}ßttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C|||Ž||	ƒ}àt|àt–ƒ}áttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã|||Š||i|jƒ}ât|ât—ƒ}ãttttd$tdƒƒ t` ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã|||Š||i|Qƒ}ät|ät˜ƒ}åttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  ttt td tdƒƒ   t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|ã||C||ƒ}æt|æt™ƒ}çttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C||Š|ƒ}èt|ètšƒ}éttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C||Š||
ƒ}êt|êt›ƒ}ëttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||Š|õ|-|Oƒ}ìt|ìtœƒ}íttttd$tdƒƒ t` ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|||Š|õ|-|qƒ}ît|îtƒ}ïttttd$tdƒƒ t` ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C||Š|õ|-|vƒ}ðt|ðtžƒ}ñttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|C||Š|õ|.ƒ}òt|òtŸƒ}ótttˆt t` ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C||Š|õ|.ƒ}ôt|ôt ƒ}õttttdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|C|||Š|õ|wƒ}öt|öt¡ƒ}÷tttˆt tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C|||Š|õ|wƒ}øt|øt¢ƒ}ùttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C||¢|||ƒ}út|út£ƒ}ûttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C||Š||ƒ}üt|üt¤ƒ}ýttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C|||Ž||	ƒ}þt|þt¥ƒ}ÿttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  ttt td tdƒƒ   t_tt tdtdƒƒ   tƒ|||B|ˆ|¹|ã||C|||ƒ} t| t¦ƒ}ttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  t  t_tt tdtdƒƒ  tÑ  ttt td tdƒƒ   tƒ|||B|ˆ|¹|ã||C|||Š|ƒ}t|t§ƒ}ttttdtdƒƒ tttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tttdtdƒƒ td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã|C|||õ|±|²ƒ}t|t¨ƒ}ttttdtdƒƒ t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tttdtdƒƒ td tdƒƒ  td!tdƒƒ  ttdtdƒƒ tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|ã|C||Š|±||üƒ}t|t©ƒ}ttttdtdƒƒ t_ttdtdƒƒ tdtdƒƒ  tÑ  tttdtdƒƒ td tdƒƒ  td!tdƒƒ  ttdtdƒƒ tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|ã|C|||Š|õ|±|´ƒ}t|tªƒ}	tttˆt t` tttdtdƒƒ tdtdƒƒ  tdtdƒƒ  t_ttdtdƒƒ tdtdƒƒ  tdtdƒƒ  tttdtdƒƒ td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C|||Š|õ|±ƒ}
t|
t«ƒ}ttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  ttt td tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ|¹|ã||C|||Š|õ|ƒ}t|t¬ƒ}tttRtdtdƒƒ ttÇt td tdƒƒ  td!tdƒƒ  tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tÇt tdtdƒƒ tdtdƒƒ tdtdƒƒ  tƒ|||B|ˆ|¹|ã|C|||Š|õ|…ƒ}t|t­ƒ}ttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  t‚ttdtdƒƒ td"tdƒƒ  td!tdƒƒ  tƒttdtdƒƒ td#tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ| |||||C|||Š|õ|ý|þ|ÿƒ}t|t®ƒ}ttttd$tdƒƒ tdtdƒƒ ttt tdtdƒƒ  tdtdƒƒ  t_tt tdtdƒƒ  tdtdƒƒ  t‚ttdtdƒƒ td"tdƒƒ  td!tdƒƒ  tƒttdtdƒƒ td#tdƒƒ  td!tdƒƒ  tƒ|||B|ˆ| |||||C|||Š|õ|ý|þƒ}t|t¯ƒ}g |‘|‘|‘|‘|‘|‘|‘|‘|‘|!‘|#‘|%‘|'‘|)‘|+‘|-‘|/‘|1‘|3‘|5‘|7‘|9‘|;‘|=‘|?‘|A‘|C‘|E‘|G‘|I‘|K‘|M‘|O‘|Q‘|S‘|U‘|W‘|Y‘|[‘|]‘|_‘|a‘|c‘|e‘|g‘|i‘|k‘|m‘|o‘|q‘|s‘|u‘|w‘|y‘|{‘|}‘|‘|‘|ƒ‘|…‘|‡‘|‰‘|‹‘|‘|‘|‘‘|“‘|•‘|—‘|™‘|›‘|‘|Ÿ‘|¡‘|£‘|¥‘|§‘|©‘|«‘|­‘|¯‘|±‘|³‘|µ‘|·‘|¹‘|»‘|½‘|¿‘|Á‘|Ã‘|Å‘|Ç‘|É‘|Ë‘|Í‘|Ï‘|Ñ‘|Ó‘|Õ‘|×‘|Ù‘|Û‘|Ý‘|ß‘|á‘|ã‘|å‘|ç‘|é‘|ë‘|í‘|ï‘|ñ‘|ó‘|õ‘|÷‘|ù‘|û‘|ý‘|ÿ‘|‘|‘|‘|‘|	‘|‘|‘|‘|‘|‘|‘|‘|‘|‘|‘|‘|!‘|#‘|%‘|'‘|)‘|+‘|-‘|/‘|1‘|3‘|5‘|7‘|9‘|;‘|=‘|?‘|A‘|C‘|E‘|G‘|I‘|K‘|M‘|O‘|Q‘|S‘|U‘|W‘|Y‘|[‘|]‘|_‘|a‘|c‘|e‘|g‘|i‘|k‘|m‘|o‘|q‘|s‘|u‘|w‘|y‘|{‘|}‘|‘|‘|ƒ‘|…‘|‡‘|‰‘|‹‘|‘|‘|‘‘|“‘|•‘|—‘|™‘|›‘|‘|Ÿ‘|¡‘|£‘|¥‘|§‘|©‘|«‘|­‘|¯‘|±‘|³‘|µ‘|·‘|¹‘|»‘|½‘|¿‘|Á‘|Ã‘|Å‘|Ç‘|É‘|Ë‘|Í‘|Ï‘|Ñ‘|Ó‘|Õ‘|×‘|Ù‘|Û‘|Ý‘|ß‘|á‘|ã‘|å‘|ç‘|é‘|ë‘|í‘|ï‘|ñ‘|ó‘|õ‘|÷‘|ù‘|û‘|ý‘|ÿ‘|‘|‘|‘|‘|	‘|‘|‘|‘|‘|‘|‘|‘|‘|‘|‘|‘|!‘|#‘|%‘|'‘|)‘|+‘|-‘|/‘|1‘|3‘|5‘|7‘|9‘|;‘|=‘|?‘|A‘|C‘|E‘|G‘|I‘|K‘|M‘|O‘|Q‘|S‘|U‘|W‘|Y‘|[‘|]‘|_‘|a‘|c‘|e‘|g‘|i‘|k‘|m‘|o‘|q‘|s‘|u‘|w‘|y‘|{‘|}‘|‘|‘|ƒ‘|…‘|‡‘|‰‘|‹‘|‘|‘|‘‘|“‘|•‘|—‘|™‘|›‘|‘|Ÿ‘|¡‘|£‘|¥‘|§‘|©‘|«‘|­‘|¯‘|±‘|³‘|µ‘|·‘|¹‘|»‘|½‘|¿‘|Á‘|Ã‘|Å‘|Ç‘|É‘|Ë‘|Í‘|Ï‘|Ñ‘|Ó‘|Õ‘|×‘|Ù‘|Û‘|Ý‘|ß‘|á‘|ã‘|å‘|ç‘|é‘|ë‘|í‘|ï‘|ñ‘|ó‘|õ‘|÷‘|ù‘|û‘|ý‘|ÿ‘|‘|‘|‘|‘|	‘|‘|‘|‘|‘|‘S )%Nr   (  Úcons461Úcons3Úcons4Úcons5Úcons462Úcons2Úcons463Úcons56Úcons464Úcons89Úcons465Úcons40Úcons466Úcons150Úcons13Úcons165Úcons467Úcons468Úcons45Úcons450Úcons69Úcons139Úcons469Úcons470Úcons471Úcons472Úcons473Úcons474Úcons475Úcons476Úcons477Úcons478Úcons479Úcons480Úcons481Úcons482Úcons483Úcons484Úcons485Úcons486Úcons107Úcons487Úcons488Úcons489Úcons490Úcons198Úcons491Úcons130Úcons359Úcons492Úcons493Úcons494Úcons495Úcons70Úcons71Úcons57Úcons496Úcons59Úcons60Úcons61Úcons62Úcons497Úcons498Úcons499Úcons500Úcons149Úcons8Úcons19Úcons501Úcons502Úcons503Úcons21Úcons504Úcons505Úcons68Úcons506Úcons507Úcons508Úcons509Úcons20Úcons246Úcons96Úcons510Úcons511Úcons512Úcons513Úcons514Úcons515Úcons516Úcons517Úcons518Úcons519Úcons520Úcons521Úcons522Úcons523Úcons64Úcons524Úcons525Úcons526Úcons527Úcons528Úcons529Úcons530Úcons531Úcons33Úcons532Úcons533Úcons534Úcons535Úcons536Úcons537Úcons538Úcons369Úcons539Úcons540Úcons541Úcons542Úcons358Úcons543Úcons25Úcons544Úcons545Úcons546Úcons547Úcons548Úcons549Úcons550Úcons551Úcons552Úcons553Úcons554Úcons555Úcons556Úcons73Úcons557Úcons29Úcons222Úcons52Úcons558Úcons87Úcons559Úcons397Úcons405Úcons65Úcons560Úcons561Úcons562Úcons563Úcons564Úcons565Úcons566Úcons567Úcons568Úcons569Úcons570Úcons571Úcons72Úcons572Úcons573Úcons574Úcons575Úcons404Úcons576Úcons577Úcons578Úcons407Úcons579Úcons580Úcons581Úcons582Úcons583Úcons179Úcons584Úcons585Úcons119Úcons586Úcons587Úcons588Úcons589Úcons388Úcons590Úcons591Úcons592Úcons593Úcons50Úcons55Úcons594Úcons595Úcons596Úcons597Úcons598Úcons95Úcons599Úcons600Úcons601Úcons602Úcons603Úcons604Úcons605Úcons606Úcons90Úcons607Úcons608Úcons609Úcons610Úcons611Úcons612Úcons613Úcons614Úcons615Úcons616Úcons617Úcons618Úcons619Úcons620Úcons621Úcons622Úcons623Úcons624Úcons625Úcons626Úcons627Úcons628Úcons629Úcons48Úcons630Úcons127Úcons631Úcons632Úcons633Úcons155Úcons634Úcons635Úcons178Úcons636Úcons637Úcons638Úcons639Úcons640Úcons180Úcons641Úcons642Úcons398Úcons643Úcons54Úcons644Úcons645Úcons646Úcons647Úcons648Úcons649Úcons650Úcon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sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r  rŽ  r  r  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  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  r   rì  Úx_Ún_rñ  rè  Úp_r   Úreplacement692Úa_Úreplacement693Úreplacement694Úreplacement695Úreplacement696Úreplacement697Úreplacement698Úreplacement699Úreplacement700Úreplacement701Úreplacement702Úreplacement703ÚWith704ÚWith705Úreplacement706Úreplacement707Úreplacement708Úreplacement709Úreplacement710Úreplacement711ÚWith712ÚWith713ÚWith714ÚWith715ÚWith716ÚWith717rë  Úreplacement718Úreplacement719Úreplacement720ÚWith721ÚWith722ÚWith723Úreplacement724r   ÚWith725Úreplacement725ÚWith726Úreplacement727ÚWith728Úreplacement729Úreplacement730Úreplacement731Úreplacement732Úreplacement733Úreplacement734Úreplacement735Úreplacement736Úreplacement737Úreplacement738Úreplacement739Úreplacement740Úreplacement741Úreplacement742ÚWith743Úreplacement744Úreplacement745Úreplacement746Úu_Úreplacement747Úreplacement748Úa1_Úa2_Úreplacement749Úreplacement750Úreplacement751ÚWith752Úreplacement753Úreplacement754Úreplacement755Úreplacement756Úc_Úm_Úreplacement757Úreplacement758Úreplacement759Úreplacement760Úreplacement761Úreplacement762Úreplacement763Úreplacement764Úreplacement765Úreplacement766Úreplacement767Úreplacement768Úreplacement769ÚWith770Úreplacement770ÚWith771Úreplacement771Úreplacement772Úreplacement773Úreplacement774Úreplacement775Úreplacement776Úreplacement777Úreplacement778Úreplacement779Úreplacement780Úreplacement781Úreplacement782Úreplacement783Úreplacement784Úreplacement785Úreplacement786ÚWith787ÚWith788ÚWith789ÚWith790ÚWith791ÚWith792ÚWith793ÚWith794ÚWith795Úreplacement796ÚWith797ÚWith798ÚWith799ÚWith800ÚWith801ÚWith802Úreplacement803Úreplacement804Úreplacement805Úreplacement806Úreplacement807Úreplacement808Úreplacement809Úreplacement810Úreplacement811Úreplacement812Úreplacement813Úreplacement814Úreplacement815Úreplacement816Úreplacement817Úreplacement818Úreplacement819ÚWith820ÚWith821Úreplacement822Úreplacement823Úreplacement824Úreplacement825Úreplacement826Úreplacement827ÚWith828ÚWith829Úreplacement830Úreplacement831ÚWith832ÚWith833Úreplacement834Úreplacement835Úreplacement836Úreplacement837Úreplacement838Úreplacement839Úreplacement840Úreplacement841Úreplacement842Úreplacement843Úreplacement844Úreplacement845ÚWith846ÚWith847Úreplacement848Úreplacement849Úreplacement850Úreplacement851ÚWith852Úreplacement853Úreplacement854Úreplacement855Úreplacement856Úv_Úreplacement857Úreplacement858Úreplacement859Úreplacement860Úreplacement861Úreplacement862ÚWith863Úreplacement864Úreplacement865Úq_Úreplacement866Úreplacement867Úreplacement868Úreplacement869Úreplacement870Úreplacement871Úreplacement872Úreplacement873Úreplacement874Úreplacement875Úreplacement876Úreplacement877Úreplacement878Úreplacement879Úreplacement880Úreplacement881Úreplacement882Úreplacement883ÚWith884Úreplacement885Úreplacement886Úreplacement887Úreplacement888Úreplacement889Úreplacement890Úreplacement891Úreplacement892Úreplacement893Úreplacement894Úreplacement895Úreplacement896Úreplacement897Úreplacement898Úreplacement899Úreplacement900Úreplacement901Úreplacement902Úreplacement903Úreplacement904Úreplacement905Úreplacement906Úreplacement907Úreplacement908Úreplacement909Úreplacement910Úreplacement911Úreplacement912Úreplacement913Úreplacement914Úreplacement915Úreplacement916Úe_Úreplacement917Úreplacement918Úreplacement919Úreplacement920Úreplacement921Úreplacement922Úreplacement923Úreplacement924Úreplacement925Úreplacement926Úreplacement927Úreplacement928Úreplacement929Úreplacement930Úreplacement931Úreplacement932Úreplacement933Úreplacement934Úreplacement935Úreplacement936Úreplacement937Úreplacement938ÚWith939Úreplacement939ÚWith940Úreplacement941Úreplacement942Úreplacement943Úreplacement944Úreplacement945Úreplacement946Úreplacement947Úreplacement948Úreplacement949Úreplacement950Úreplacement951Úreplacement952Úreplacement953Úreplacement954Úreplacement955Úreplacement956Úreplacement957ÚWith958ÚWith959Úreplacement960Úreplacement961Úreplacement962Úreplacement963Úreplacement964Úreplacement965ÚWith966Úreplacement967ÚWith968Úreplacement969ÚWith970Úreplacement971Úreplacement972Úreplacement973Úreplacement974Úreplacement975Úreplacement976Úreplacement977Úreplacement978Úreplacement979Úreplacement980Úreplacement981Úreplacement982Úreplacement983Úreplacement984Úreplacement985Úreplacement986Úreplacement987Úreplacement988Úreplacement989Úreplacement990Úreplacement991Úreplacement992Úreplacement993Úreplacement994Úreplacement995Úreplacement996Úreplacement997Úreplacement998Úreplacement999Úreplacement1000Úreplacement1001Úreplacement1002Úreplacement1003Úreplacement1004Úreplacement1005Úreplacement1006Úreplacement1007Úreplacement1008Úreplacement1009Úreplacement1010Úreplacement1011Úreplacement1012Úreplacement1013Úreplacement1014Úreplacement1015Úr_Úreplacement1016Úreplacement1017Úreplacement1018Úreplacement1019Úreplacement1020Úreplacement1021Úreplacement1022Úreplacement1023Úreplacement1024Úreplacement1025Úreplacement1026Úreplacement1027Úreplacement1028Úreplacement1029ÚWith1030Úreplacement1030Úreplacement1031Úreplacement1032Úw_Úreplacement1033Úreplacement1034Úreplacement1035Úreplacement1036Úe1_Úe2_Úreplacement1037Úreplacement1038Úreplacement1039Úreplacement1040Úg_Úreplacement1041Úreplacement1042Úreplacement1043Úreplacement1044Úreplacement1045Úreplacement1046ÚWith1047Úreplacement1047ÚWith1048Úreplacement1049Úreplacement1050Úreplacement1051Úreplacement1052Úreplacement1053Úreplacement1054Úreplacement1055Úreplacement1056Úreplacement1057Úreplacement1058Úreplacement1059ÚWith1060Úreplacement1061ÚWith1062Úreplacement1063Úreplacement1064Úreplacement1065Úreplacement1066Úreplacement1067Úreplacement1068Úreplacement1069Úreplacement1070Úreplacement1071Úreplacement1072Úreplacement1073Úreplacement1074Úreplacement1075Úreplacement1076Úreplacement1077Úreplacement1078(  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‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r  rŽ  r  r  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  r  r  r	  r
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pattern692Úrule692Ú
pattern693Úrule693Ú
pattern694Úrule694Ú
pattern695Úrule695Ú
pattern696Úrule696Ú
pattern697Úrule697Ú
pattern698Úrule698Ú
pattern699Úrule699Ú
pattern700Úrule700Ú
pattern701Úrule701Ú
pattern702Úrule702Ú
pattern703Úrule703Ú
pattern704Úrule704Ú
pattern705Úrule705Ú
pattern706Úrule706Ú
pattern707Úrule707Ú
pattern708Úrule708Ú
pattern709Úrule709Ú
pattern710Úrule710Ú
pattern711Úrule711Ú
pattern712Úrule712Ú
pattern713Úrule713Ú
pattern714Úrule714Ú
pattern715Úrule715Ú
pattern716Úrule716Ú
pattern717Úrule717Ú
pattern718Úrule718Ú
pattern719Úrule719Ú
pattern720Úrule720Ú
pattern721Úrule721Ú
pattern722Úrule722Ú
pattern723Úrule723Ú
pattern724Úrule724Ú
pattern725Úrule725Ú
pattern726Úrule726Ú
pattern727Úrule727Ú
pattern728Úrule728Ú
pattern729Úrule729Ú
pattern730Úrule730Ú
pattern731Úrule731Ú
pattern732Úrule732Ú
pattern733Úrule733Ú
pattern734Úrule734Ú
pattern735Úrule735Ú
pattern736Úrule736Ú
pattern737Úrule737Ú
pattern738Úrule738Ú
pattern739Úrule739Ú
pattern740Úrule740Ú
pattern741Úrule741Ú
pattern742Úrule742Ú
pattern743Úrule743Ú
pattern744Úrule744Ú
pattern745Úrule745Ú
pattern746Úrule746Ú
pattern747Úrule747Ú
pattern748Úrule748Ú
pattern749Úrule749Ú
pattern750Úrule750Ú
pattern751Úrule751Ú
pattern752Úrule752Ú
pattern753Úrule753Ú
pattern754Úrule754Ú
pattern755Úrule755Ú
pattern756Úrule756Ú
pattern757Úrule757Ú
pattern758Úrule758Ú
pattern759Úrule759Ú
pattern760Úrule760Ú
pattern761Úrule761Ú
pattern762Úrule762Ú
pattern763Úrule763Ú
pattern764Úrule764Ú
pattern765Úrule765Ú
pattern766Úrule766Ú
pattern767Úrule767Ú
pattern768Úrule768Ú
pattern769Úrule769Ú
pattern770Úrule770Ú
pattern771Úrule771Ú
pattern772Úrule772Ú
pattern773Úrule773Ú
pattern774Úrule774Ú
pattern775Úrule775Ú
pattern776Úrule776Ú
pattern777Úrule777Ú
pattern778Úrule778Ú
pattern779Úrule779Ú
pattern780Úrule780Ú
pattern781Úrule781Ú
pattern782Úrule782Ú
pattern783Úrule783Ú
pattern784Úrule784Ú
pattern785Úrule785Ú
pattern786Úrule786Ú
pattern787Úrule787Ú
pattern788Úrule788Ú
pattern789Úrule789Ú
pattern790Úrule790Ú
pattern791Úrule791Ú
pattern792Úrule792Ú
pattern793Úrule793Ú
pattern794Úrule794Ú
pattern795Úrule795Ú
pattern796Úrule796Ú
pattern797Úrule797Ú
pattern798Úrule798Ú
pattern799Úrule799Ú
pattern800Úrule800Ú
pattern801Úrule801Ú
pattern802Úrule802Ú
pattern803Úrule803Ú
pattern804Úrule804Ú
pattern805Úrule805Ú
pattern806Úrule806Ú
pattern807Úrule807Ú
pattern808Úrule808Ú
pattern809Úrule809Ú
pattern810Úrule810Ú
pattern811Úrule811Ú
pattern812Úrule812Ú
pattern813Úrule813Ú
pattern814Úrule814Ú
pattern815Úrule815Ú
pattern816Úrule816Ú
pattern817Úrule817Ú
pattern818Úrule818Ú
pattern819Úrule819Ú
pattern820Úrule820Ú
pattern821Úrule821Ú
pattern822Úrule822Ú
pattern823Úrule823Ú
pattern824Úrule824Ú
pattern825Úrule825Ú
pattern826Úrule826Ú
pattern827Úrule827Ú
pattern828Úrule828Ú
pattern829Úrule829Ú
pattern830Úrule830Ú
pattern831Úrule831Ú
pattern832Úrule832Ú
pattern833Úrule833Ú
pattern834Úrule834Ú
pattern835Úrule835Ú
pattern836Úrule836Ú
pattern837Úrule837Ú
pattern838Úrule838Ú
pattern839Úrule839Ú
pattern840Úrule840Ú
pattern841Úrule841Ú
pattern842Úrule842Ú
pattern843Úrule843Ú
pattern844Úrule844Ú
pattern845Úrule845Ú
pattern846Úrule846Ú
pattern847Úrule847Ú
pattern848Úrule848Ú
pattern849Úrule849Ú
pattern850Úrule850Ú
pattern851Úrule851Ú
pattern852Úrule852Ú
pattern853Úrule853Ú
pattern854Úrule854Ú
pattern855Úrule855Ú
pattern856Úrule856Ú
pattern857Úrule857Ú
pattern858Úrule858Ú
pattern859Úrule859Ú
pattern860Úrule860Ú
pattern861Úrule861Ú
pattern862Úrule862Ú
pattern863Úrule863Ú
pattern864Úrule864Ú
pattern865Úrule865Ú
pattern866Úrule866Ú
pattern867Úrule867Ú
pattern868Úrule868Ú
pattern869Úrule869Ú
pattern870Úrule870Ú
pattern871Úrule871Ú
pattern872Úrule872Ú
pattern873Úrule873Ú
pattern874Úrule874Ú
pattern875Úrule875Ú
pattern876Úrule876Ú
pattern877Úrule877Ú
pattern878Úrule878Ú
pattern879Úrule879Ú
pattern880Úrule880Ú
pattern881Úrule881Ú
pattern882Úrule882Ú
pattern883Úrule883Ú
pattern884Úrule884Ú
pattern885Úrule885Ú
pattern886Úrule886Ú
pattern887Úrule887Ú
pattern888Úrule888Ú
pattern889Úrule889Ú
pattern890Úrule890Ú
pattern891Úrule891Ú
pattern892Úrule892Ú
pattern893Úrule893Ú
pattern894Úrule894Ú
pattern895Úrule895Ú
pattern896Úrule896Ú
pattern897Úrule897Ú
pattern898Úrule898Ú
pattern899Úrule899Ú
pattern900Úrule900Ú
pattern901Úrule901Ú
pattern902Úrule902Ú
pattern903Úrule903Ú
pattern904Úrule904Ú
pattern905Úrule905Ú
pattern906Úrule906Ú
pattern907Úrule907Ú
pattern908Úrule908Ú
pattern909Úrule909Ú
pattern910Úrule910Ú
pattern911Úrule911Ú
pattern912Úrule912Ú
pattern913Úrule913Ú
pattern914Úrule914Ú
pattern915Úrule915Ú
pattern916Úrule916Ú
pattern917Úrule917Ú
pattern918Úrule918Ú
pattern919Úrule919Ú
pattern920Úrule920Ú
pattern921Úrule921Ú
pattern922Úrule922Ú
pattern923Úrule923Ú
pattern924Úrule924Ú
pattern925Úrule925Ú
pattern926Úrule926Ú
pattern927Úrule927Ú
pattern928Úrule928Ú
pattern929Úrule929Ú
pattern930Úrule930Ú
pattern931Úrule931Ú
pattern932Úrule932Ú
pattern933Úrule933Ú
pattern934Úrule934Ú
pattern935Úrule935Ú
pattern936Úrule936Ú
pattern937Úrule937Ú
pattern938Úrule938Ú
pattern939Úrule939Ú
pattern940Úrule940Ú
pattern941Úrule941Ú
pattern942Úrule942Ú
pattern943Úrule943Ú
pattern944Úrule944Ú
pattern945Úrule945Ú
pattern946Úrule946Ú
pattern947Úrule947Ú
pattern948Úrule948Ú
pattern949Úrule949Ú
pattern950Úrule950Ú
pattern951Úrule951Ú
pattern952Úrule952Ú
pattern953Úrule953Ú
pattern954Úrule954Ú
pattern955Úrule955Ú
pattern956Úrule956Ú
pattern957Úrule957Ú
pattern958Úrule958Ú
pattern959Úrule959Ú
pattern960Úrule960Ú
pattern961Úrule961Ú
pattern962Úrule962Ú
pattern963Úrule963Ú
pattern964Úrule964Ú
pattern965Úrule965Ú
pattern966Úrule966Ú
pattern967Úrule967Ú
pattern968Úrule968Ú
pattern969Úrule969Ú
pattern970Úrule970Ú
pattern971Úrule971Ú
pattern972Úrule972Ú
pattern973Úrule973Ú
pattern974Úrule974Ú
pattern975Úrule975Ú
pattern976Úrule976Ú
pattern977Úrule977Ú
pattern978Úrule978Ú
pattern979Úrule979Ú
pattern980Úrule980Ú
pattern981Úrule981Ú
pattern982Úrule982Ú
pattern983Úrule983Ú
pattern984Úrule984Ú
pattern985Úrule985Ú
pattern986Úrule986Ú
pattern987Úrule987Ú
pattern988Úrule988Ú
pattern989Úrule989Ú
pattern990Úrule990Ú
pattern991Úrule991Ú
pattern992Úrule992Ú
pattern993Úrule993Ú
pattern994Úrule994Ú
pattern995Úrule995Ú
pattern996Úrule996Ú
pattern997Úrule997Ú
pattern998Úrule998Ú
pattern999Úrule999Úpattern1000Úrule1000Úpattern1001Úrule1001Úpattern1002Úrule1002Úpattern1003Úrule1003Úpattern1004Úrule1004Úpattern1005Úrule1005Úpattern1006Úrule1006Úpattern1007Úrule1007Úpattern1008Úrule1008Úpattern1009Úrule1009Úpattern1010Úrule1010Úpattern1011Úrule1011Úpattern1012Úrule1012Úpattern1013Úrule1013Úpattern1014Úrule1014Úpattern1015Úrule1015Úpattern1016Úrule1016Úpattern1017Úrule1017Úpattern1018Úrule1018Úpattern1019Úrule1019Úpattern1020Úrule1020Úpattern1021Úrule1021Úpattern1022Úrule1022Úpattern1023Úrule1023Úpattern1024Úrule1024Úpattern1025Úrule1025Úpattern1026Úrule1026Úpattern1027Úrule1027Úpattern1028Úrule1028Úpattern1029Úrule1029Úpattern1030Úrule1030Úpattern1031Úrule1031Úpattern1032Úrule1032Úpattern1033Úrule1033Úpattern1034Úrule1034Úpattern1035Úrule1035Úpattern1036Úrule1036Úpattern1037Úrule1037Úpattern1038Úrule1038Úpattern1039Úrule1039Úpattern1040Úrule1040Úpattern1041Úrule1041Úpattern1042Úrule1042Úpattern1043Úrule1043Úpattern1044Úrule1044Úpattern1045Úrule1045Úpattern1046Úrule1046Úpattern1047Úrule1047Úpattern1048Úrule1048Úpattern1049Úrule1049Úpattern1050Úrule1050Úpattern1051Úrule1051Úpattern1052Úrule1052Úpattern1053Úrule1053Úpattern1054Úrule1054Úpattern1055Úrule1055Úpattern1056Úrule1056Úpattern1057Úrule1057Úpattern1058Úrule1058Úpattern1059Úrule1059Úpattern1060Úrule1060Úpattern1061Úrule1061Úpattern1062Úrule1062Úpattern1063Úrule1063Úpattern1064Úrule1064Úpattern1065Úrule1065Úpattern1066Úrule1066Úpattern1067Úrule1067Úpattern1068Úrule1068Úpattern1069Úrule1069Úpattern1070Úrule1070Úpattern1071Úrule1071Úpattern1072Úrule1072Úpattern1073Úrule1073Úpattern1074Úrule1074Úpattern1075Úrule1075Úpattern1076Úrule1076Úpattern1077Úrule1077Úpattern1078Úrule1078r  r  r  Úbinomial_products”   sF  þþ þ þ ‚ >FHHFBHPPNHJHHLLJLLJHHJJHHRRPPPPR\RRPPNPPPPNNNNNJJDDDLLT¦¨ttŽ¤nz``v¦l\Œ~V†v¦h˜x¨x^\\nrr^x¨v¦FZZZZPPZNNJLLVXVVV^^hhbb€€llœœjjššh˜b’d”^Žf–h˜^ŽZŠb’^Žb’^Žx¨b’^Žv¦ZNVvvnl¤ŒŽŽŽnˆxxzz|pjnvpˆˆ|„„„zttrzv|„‚zz|v~z†ˆ†‚zz|||zv|z¨’¨Hbª¶œª¨ª²º¬þ ¬¬¬þ ††¬þ ªþžžªªšš¨¨¨¨¨¨œœœ¨¨¨¨œ˜”|‚z‚‚‚ŽŽ€š–šŒ”œ¨¨¨¨¨v”¦Â¸È¬ªÂÀþ þ2 èþ0 ÄŽ”š®ªª¸¦–¶¨Œ¨¤²´®¤¤®¶®¨¨¨¨®¸¦¦´ª²ªª²®¤Êôúúðþ* þ( êöÚöäâäîìÈÞÎÎÞêæÚÄäúâìîâàäîÞÎêÈÐþ
 þ þ þ üüþZ þX þþ þ þ þ þ þ þ þ ( rü  c                 C   sH   t | t|ƒ || t|ƒ   | ||  t|ƒ  t|||  |ƒ|ƒS ©N©rÁ  r%   r&   r   )rB  rP  rO  Úxr  r  r  r_  &  ó   Hr_  c                 C   s*   t || |||   |tdƒ   |  |ƒS ©NrC  ©r¥  rè  ©rN  rB  rP  rO  rÿ  r  r  r  ra  *  ó   *ra  c                 C   óŒ   t ||tdƒ  tdƒ | | |tdƒ   t| |||   |tdƒ  |ƒ|ƒt|| |||   |tdƒ   | | |tdƒ   |ƒ S r  ©rÁ  rè  r   r¥  r  r  r  r  rb  .  ó   Œrb  c                 C   sF   t | tdƒ tdƒ|  | ||   |tdƒ |tdƒ|    |ƒS ©NrD  ©r   rè  )rN  rB  rP  rÿ  r  r  r  rc  2  ó   Frc  c                 C   s(   t |||  | ||   | |  |ƒS rý  ©r   r  r  r  r  rd  6  s   (rd  c                 C   ó    t t| |||   | |ƒ|ƒS rý  ©r   rË   r  r  r  r  re  :  ó    re  c                 C   sp   t | | | || tdƒ  t| |||   |tdƒ  |ƒ|ƒt|| |||   |  || tdƒ  |ƒ S ©NrC  rK  r  r  r  r  r  rf  >  ó   prf  c              	   C   ó\   t tdƒtt|t||  tdƒƒ ƒtdƒ tdƒƒ | tdƒd  t||  tdƒƒ  |ƒS )NrD  rS  rF  )r¥  rè  r<   r>   r„  ©rN  rB  rÿ  r  r  r  rg  B  ó   \rg  c                 C   s~   t tdƒ||tdƒ  |   tdƒd  | | ||tdƒ   tdƒd    ttdƒ||tdƒ  |   tdƒd  |ƒ|ƒS )NrC  rD  rF  rE  ©rÁ  rè  r   r  r  r  r  rh  F  ó   ~rh  c                 C   sœ   t tdƒ| | ||tdƒ    tdƒd  | ||tdƒ   tdƒd    tt| |tdƒ  tdƒ tdƒd  |ƒ||t| ||tdƒ   ƒ ƒ|ƒS )NrC  rD  rI  rK  )rÁ  rè  r+   r   rë  r  r  r  r  ri  J  ó   œri  c                 C   r  r  r  r  r  r  r  rj  N  r  rj  c              
   C   s
  t tdƒtdƒt| tdƒƒtdƒ   t| t|tdƒƒ tdƒt| tdƒƒ  |tdƒ t|tdƒƒtdƒ  |t| tdƒƒ t|tdƒƒ  t| tdƒƒtdƒ   |ƒ|ƒt tdƒtdƒt| tdƒƒtdƒ   ttdƒ|t|tdƒƒ t| tdƒƒ  |ƒ|ƒ S ©NrC  rI  rD  ©rÁ  rè  r„  r   r  r  r  r  rk  R  s   þ rk  c              
   C   s~  t t| | |ƒƒ}tt| | |ƒƒ}tdƒ}tdƒ}t||| tttdƒ| tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒ}t||| ttd| d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒ}tt	d| | |  t
|t|d|d d ƒƒ|ƒ|td|||   |ƒ | |   |ƒS ©NÚkrW  rD  rK  rC  ç      à?©rx   r„  r4   ró  r   rõ  ÚPirè  r¥  rÁ  rÂ  r   ©rN  rB  rP  rÿ  rY  Úsr  rW  r  r  r  rl  V  s   ŠjVrl  c              
   C   s‚  t t|  | |ƒƒ}tt|  | |ƒƒ}tdƒ}tdƒ}t||| tttdƒ| tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒ}t||| ttd| d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒ}tt	d| | |  t
|t|d|d d ƒƒ|ƒ|td|||   |ƒ | |   |ƒS r  r  r  r  r  r  rm  `  s   ŠjVrm  c                 C   sF   t t|t|tdƒƒ t| tdƒƒ ƒt| tdƒƒt|tdƒƒ  |ƒS r  ©r¥  r>   r„  rè  r  r  r  r  rn  j  r
  rn  c                 C   sP   t t|t| tdƒƒ t|  tdƒƒ ƒt|  tdƒƒt| tdƒƒ  |ƒ S r  r   r  r  r  r  ro  n  ó   Pro  c                 C   s6   t t|t| | tdƒƒ ƒt| | tdƒƒ |  |ƒS r  r   r  r  r  r  rp  r  ó   6rp  c                 C   sJ   t t|t| tdƒƒ t| tdƒƒ ƒt| tdƒƒt| tdƒƒ  |ƒS r  ©r¥  rý  r„  rè  r  r  r  r  rq  v  ó   Jrq  c                 C   sL   t t|t|tdƒƒ t|  tdƒƒ ƒt|  tdƒƒt|tdƒƒ  |ƒ S r  r#  r  r  r  r  rr  z  ó   Lrr  c                 C   s:   t t|  | tdƒƒt|t|  | tdƒƒ ƒ |  |ƒS r  )r¥  r„  rè  rý  r  r  r  r  rs  ~  ó   :rs  c           	   
   C   sŽ  t t| | |ƒƒ}tt| | |ƒƒ}tdƒ}tdƒ}tdƒ}t||| tttdƒ| tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒt||| tttdƒ| tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒ }t||| ttd| d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒt||| ttd| d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒ }tt	d| | |  t
|t|d|d d ƒƒ|ƒd|d  td|d |d |d    |ƒ | |   |ƒS )	Nr  rW  ÚvrD  rK  rC  rF  r  r  )	rN  rB  rP  rÿ  rY  r  r  rW  r'  r  r  r  rt  ‚  s   þ Ôjrt  c              
   C   sZ  t t|  | |ƒƒ}tt|  | |ƒƒ}tdƒ}tdƒ}t||| ttdƒt | | ƒ  |tdƒ tdƒ| | | ttdƒt | | ƒ  |tdƒ |tdƒ    |ƒt||| ttdƒt | | ƒ  |tdƒ tdƒ| | | ttdƒt | | ƒ  |tdƒ |tdƒ    |ƒ }t||| tdt | | ƒ  |d d| | | tdt | | ƒ  |d |d    |ƒt||| tdt | | ƒ  |d d| | | tdt | | ƒ  |d |d    |ƒ }tt	d| | |  t
|t|d|d d ƒƒ|ƒd|d  td|d |d |d    |ƒ | |   |ƒS ©Nr  rW  rD  rC  rF  r  ©rx   r„  r4   ró  r   rõ  rè  r  r¥  rÁ  rÂ  r   r  r  r  r  ru    s   ôÄjru  c              
   C   s¸   t t| | tdƒƒƒ}tt| | tdƒƒƒ}ttdƒtdƒ|  t|||tdƒ   | ||tdƒ    |ƒ|ƒttdƒtdƒ|  t|||tdƒ   | ||tdƒ    |ƒ|ƒ S ©NrD  rC  rF  ©rx   r„  rè  r4   rÁ  r   ©rN  rB  rÿ  rY  r  r  r  r  rv  —  s   Œrv  c              
   C   sœ   t t|  | tdƒƒƒ}tt|  | tdƒƒƒ}t|tdƒ|   ttdƒ|||tdƒ    |ƒ|ƒt|tdƒ|   ttdƒ|||tdƒ    |ƒ|ƒ S ©NrD  rC  r+  r,  r  r  r  rw    s   lrw  c                 C   sX  t t| | tdƒƒƒ}tt| | tdƒƒƒ}tttdƒƒ| tdƒ|   tttdƒƒ| |||tdƒ    |tdƒ ttdƒƒ| | ||tdƒ    |tdƒ ||tdƒ     |ƒ|ƒtttdƒƒ| tdƒ|   tttdƒƒ| |||tdƒ    |tdƒ ttdƒƒ| | ||tdƒ    |tdƒ ||tdƒ     |ƒ|ƒ S ©NrF  rD  ©rx   r„  rè  r4   rÁ  rë  r   ©rN  rB  rP  rÿ  rY  r  r  r  r  rx  £  s   þ. rx  c                 C   s¤   t t|  | tdƒƒƒ}tt|  | tdƒƒƒ}t|tdƒ|   ttdƒ||||tdƒ     |ƒ|ƒt|tdƒ|   ttdƒ||||tdƒ     |ƒ|ƒ S r-  r+  r0  r  r  r  ry  ©  ó   try  c                 C   s2   t t|t|tdƒƒ t| ƒ ƒt|tdƒƒ |ƒS r  )r¥  rü  r„  rè  rë  r  r  r  r  rz  ¯  s   2rz  c                 C   s6   t t|t| tdƒƒ t| ƒ ƒt| tdƒƒ |ƒS r  )r¥  r	  r„  rè  rë  r  r  r  r  r{  ³  r"  r{  c              
   C   sH   t ttdƒ| |tdƒ  tdƒ  |ƒ||t| ||tdƒ   ƒ ƒS ©NrC  rD  )r+   r   rè  rë  r  r  r  r  r|  ·  r   r|  c                 C   s  t t||  tdƒƒƒ}tt||  tdƒƒƒ}ttdƒtdƒtdƒd   t|tdƒ |tdƒ  || |  |tdƒ  || |tdƒttdƒƒ   tdƒ  ƒ tttdƒƒtdƒ ƒ || |  tt|| |tdƒttdƒƒ   || |tdƒttdƒƒ    ƒtdƒtdƒttdƒƒ  ƒ tdƒ| t||| |  || |tdƒttdƒƒ   tdƒ  ƒ t| ||tdƒ   ƒ  |ƒS ©NrI  rD  rF  rC  rG  ©r¸   r„  rè  r¹   r¥  rë  r=   r	  r,  r  r  r  r}  »  s   þf r}  c                 C   s’  t t||  tdƒƒƒ}tt||  tdƒƒƒ}ttdƒtdƒtdƒd   t|tdƒ |tdƒ  || |  |tdƒ  || |tdƒttdƒƒ   tdƒ  ƒ ttdƒttdƒƒ ƒ || |  tt|| |tdƒttdƒƒ   || |tdƒttdƒƒ    ƒtdƒtdƒttdƒƒ  ƒ tdƒ| t| || |  || |tdƒttdƒƒ   tdƒ  ƒ t| ||tdƒ   ƒ  |ƒS r3  r4  r,  r  r  r  r~  Á  s   þh r~  c              	   C   sÂ   t ||  tdƒƒ}tt| ||tdƒ   | |tdƒ |tdƒ  tdƒ tdƒ   ƒ|tdƒ |tdƒ  tdƒ  ttdƒt|| ƒ tdƒd ƒ tdƒ| t| ||tdƒ   ƒ  |ƒS )NrF  rD  rC  )r„  rè  r¥  rë  r=   r>   ©rN  rB  rÿ  rU  r  r  r  r  Ç  s   °r  c                 C   sT   t tt|t| tdƒƒ t| tdƒƒ ƒtdƒƒt| tdƒƒt| tdƒƒ  |ƒS ©NrF  rK  )r¥  r=   r	  r„  rè  r  r  r  r  r€  Ì  ó   Tr€  c                 C   s:   t |ttttfƒrdS t|  | tdƒƒ}t|ƒrdS dS )NFrD  T)Ú
isinstanceÚintræ  Úfloaträ  r„  rè  r   r5  r  r  r  r  Ð  s   r  c                 C   sÄ   t |  | tdƒƒ}tttdƒƒt| ||tdƒ   | ƒ t|  ||tdƒ   ƒ ttttdƒƒ| t| ||tdƒ   | ƒ ƒtdƒd ƒ tdƒt|  ƒ t| ||tdƒ   ƒ  |ƒS r*  ©r„  rè  r¥  rë  r=   r	  r5  r  r  r  r‚  Ù  s   °r‚  c                 C   sè   t |  | tdƒƒ}tttdƒƒt| ||tdƒ   | ƒ t| ||tdƒ   | ||tdƒ    ƒ ttttdƒƒ| t| ||tdƒ   | ƒ ƒtdƒd ƒ tdƒt| | ||tdƒ    ƒ t| ||tdƒ   ƒ  |ƒS r*  r;  r5  r  r  r  rƒ  ß  s   Ôrƒ  c              
   C   sj   t ttdƒ||tdƒ  |   ƒt| ||tdƒ   ƒ ttdƒttdƒ||tdƒ  |   ƒ |ƒ|ƒS ©NrC  rF  ©rÁ  rë  rè  r   r  r  r  r  r„  ä  ó   jr„  c              
   C   s¼  t t||  tdƒƒƒ}tt||  tdƒƒƒ}ttdƒtdƒd  | t|tdƒ |tdƒ  || |tdƒ   |tdƒ  ||tdƒ  tdƒttdƒƒ  | tdƒ  ƒ ||tdƒ  |  tt||tdƒ  tdƒttdƒƒ  | ||tdƒ  tdƒttdƒƒ  |  ƒttdƒƒtdƒ tdƒd  ƒ tdƒ| t||tdƒ  ||tdƒ  |  ||tdƒ  tdƒttdƒƒ  | tdƒ  ƒ t| ||tdƒ   ƒ  |ƒS )NrI  rF  rD  rC  rH  )r¸   r„  rè  r¹   r¥  rë  r=   r  r,  r  r  r  r…  è  s   þ’ r…  c                 C   sª   t tdƒd t|tdƒ  t||  tdƒƒ tdƒ t| ||tdƒ   ƒ |ƒ|ƒt tdƒd t|tdƒ t||  tdƒƒ tdƒ t| ||tdƒ   ƒ |ƒ|ƒ S ©NrC  rD  rF  rJ  )rÁ  rè  r   r„  rë  r  r  r  r  r†  î  ó   ªr†  c                 C   sb   t | t| ||tdƒ   tdƒd  |ƒ|ƒ ttdƒ| | ||tdƒ   tdƒd   |ƒ S )NrD  rE  rF  rC  ©rÁ  r   rè  r¥  r  r  r  r  r‡  ò  ó   br‡  c              	   C   ó`   t tdƒtt|t| |  tdƒƒ ƒtdƒ tdƒƒ | tdƒd  t| |  tdƒƒ  |ƒS r*  )r¥  rè  r<   r	  r„  r  r  r  r  rˆ  ö  ó   `rˆ  c                 C   sz   t tdƒ||tdƒ  |   tdƒd  | ||tdƒ   tdƒd   ttdƒ||tdƒ  |   tdƒd  |ƒ|ƒS )NrC  rD  rF  rK  r  r  r  r  r  r‰  ú  ó   zr‰  c              	   C   r  ©NrD  rI  rF  )r¥  rè  r=   r>   r„  r  r  r  r  rŠ  þ  r  rŠ  c              	   C   rC  rF  )r¥  rè  r=   r	  r„  r  r  r  r  r‹    rD  r‹  c                 C   sz   t tdƒ||tdƒ  |   tdƒd  | ||tdƒ   tdƒd   ttdƒ||tdƒ  |   tdƒd  |ƒ|ƒS )NrC  rD  rI  rF  rL  r  r  r  r  r  rŒ    rE  rŒ  c              
   C   st   t tdƒt||tdƒ  ƒ tdƒ| |  tt|t|  |tdƒ  ƒ |ƒ|| ||tdƒ   tdƒd  ƒ|ƒS ©NrI  rD  rC  ©rÁ  rè  rë  r+   r   r  r  r  r  r  
  ó   tr  c              
   C   sx   t tdƒt||tdƒ  ƒ tdƒ| |  tttdƒt|  |tdƒ  ƒ |ƒ|| ||tdƒ   tdƒd  ƒ|ƒS rG  rH  r  r  r  r  rŽ    ó   xrŽ  c              
   C   sš   t |tdƒ | ||tdƒ   tdƒ tdƒd   | ||tdƒ   tdƒd   ttdƒ|tdƒ | ||tdƒ   tdƒ tdƒd    |ƒ|ƒS )NrI  rF  rC  r  r  r  r  r  r    ó   šr  c              	   C   sr   t | tdƒ t| ||tdƒ   tdƒd  |ƒ|ƒ ttdƒ| tdƒ| ||tdƒ   tdƒd    |ƒ S )NrD  rG  rH  rI  rC  r  r  r  r  r  r    ó   rr  c              
   C   st   t | |tdƒ|   tt| ||  tdƒ | tdƒ tdƒ|   |ƒ||| |||   tdƒ |   ƒ|ƒS r  ©rÁ  rè  r+   r   r  r  r  r  r‘    rI  r‘  c              
   C   s¤   t | | |||    |tdƒ|   | |||   |tdƒ|    tt| ||  tdƒ | tdƒ tdƒ|   |ƒ||| |||   tdƒ |   ƒ|ƒS r  rM  r  r  r  r  r’    s   ¤r’  c                 C   s:   t t| |||    | |tdƒ  |ƒ|tdƒ| ƒ S r-  ©r+   r   rè  r  r  r  r  r“  "  r&  r“  c              
   C   sR   t |ƒ}t|tt||tdƒ  | ||||    |  |ƒ||tdƒ|  ƒ|ƒS ©NrK  rC  ©r4   rÁ  r+   r   rè  )rN  rB  rP  rO  rÿ  r  r  r  r  r”  &  s   Jr”  c                 C   r  rý  r  r  r  r  r  r•  +  r  r•  c              	   C   sH   t | | | t| tdƒ| tdƒtdƒ|  | ||  |  ƒ |ƒS r  )r¥  r5   rè  r  r  r  r  r–  /  r   r–  c                 C   sl   t | t|ƒ tdƒ|||  |   t|ƒ   | |||   t|ƒ  ttdƒ|||  |   | |ƒ|ƒS r  ©rÁ  r%   rè  r&   r   r  r  r  r  r—  3  ó   lr—  c                 C   s>   t tdƒt||tdƒƒ tt| |||   | |ƒ||ƒ|ƒS r  ©rÁ  rè  r3   r+   r   )rN  rB  rP  rO  rW  rÿ  r  r  r  r™  7  ó   >r™  c                 C   s*   t | | || |tdƒ|    | |ƒS r  r	  ©r  r  r  r  rP  rO  rÿ  r  r  r  rš  ;  r  rš  c                 C   s¼   t tdƒ|  | | | tdƒ| | tdƒ  t| |||   |tdƒ  ||||   |tdƒ   |ƒ|ƒt|| |||   |  ||||   |  tdƒ| | tdƒ  |ƒ S ©NrD  rC  rK  r  rU  r  r  r  r  ?  ó   ¼r  c                 C   sä   t tdƒ| |tdƒ  tdƒ tdƒ|  | | |tdƒ   t| |||   |tdƒ  ||||   |tdƒ   |ƒ|ƒt|| |||   |tdƒ   ||||   |tdƒ   tdƒ|  | | |tdƒ   |ƒ S r-  r  rU  r  r  r  rž  C  ó   ärž  c                 C   sP   t t| |||    | ||||    |  |tdƒ  |ƒ|tdƒ| ƒ S r-  rN  rU  r  r  r  rŸ  G  r!  rŸ  c              
   C   sr   t tdƒ| ƒ}t|tt||tdƒ  | ||||    |  |||||    |  |ƒ||tdƒ|  ƒ|ƒS ©NrD  rK  rC  ©r4   rè  rÁ  r+   r   )r  r  r  r  rP  rO  rÿ  r  r  r  r  r   K  s   br   c                 C   sˆ   t | |||   t|ƒ ||||   t|ƒ  | | || |tdƒ|    t|ƒ   t| | || |tdƒ|    | |ƒ|ƒS r  ©rÁ  r&   rè  r   rU  r  r  r  r¡  P  ó   ˆr¡  c	           	      C   s6   t || | | | || |tdƒ|    |  |ƒS r  r	  ©	r  r  r  r  rQ  rR  rP  rO  rÿ  r  r  r  r¢  T  r"  r¢  c              	   C   sb   t | tdƒ|tdƒ |   ||  | tt| | |tdƒ |tdƒ |   |ƒ||| ƒ|ƒS r  rM  ©rB  rQ  rR  rP  rO  rÿ  r  r  r  r£  X  rB  r£  c                 C   sT   t | t|ƒ ||  || t|ƒ   | ||  t|ƒ  t||||   |ƒ|ƒS rý  rþ  r^  r  r  r  r¤  \  r7  r¤  c                 C   sL   t |t|ƒ |t|ƒ   || t|ƒ  t|| | ||  |  |ƒ|ƒS rý  rþ  r^  r  r  r  r§  `  r%  r§  c                 C   s,   t ||||   | ||   | |  |ƒS rý  r  ©rN  rB  rR  rP  rO  rÿ  r  r  r  r¨  d  ó   ,r¨  c                 C   sJ   t || |tdƒ  | |||   |tdƒ   | | |tdƒ   |ƒS r  r  ©rN  rB  rQ  rR  rP  rO  rÿ  r  r  r  r©  h  r$  r©  c	           	      C   sj   t || |tdƒ  | |||   |tdƒ   ||||   |tdƒ   | | | |tdƒ   |ƒS r  r  r]  r  r  r  rª  l  r>  rª  c              	   C   sN   t tdƒ| tt|tdƒ|tdƒ |   | ||  |  |ƒ||| ƒ|ƒS r  rM  r_  r  r  r  r«  p  ó   Nr«  c              	   C   s^   t tdƒ| tt|tdƒ|tdƒ |   | ||  |  |||  |  |ƒ||| ƒ|ƒS r  rM  ©r  r  r  r  rR  rP  rO  rÿ  r  r  r  r¬  t  ó   ^r¬  c                 C   óP   t |t|ƒ |t|ƒ   || t|ƒ  t|| | |||   |  |ƒ|ƒS rý  rþ  ra  r  r  r  r­  x  r!  r­  c	           	      C   ód   t |t|ƒ |t|ƒ   || t|ƒ  t|| | |||   |  ||||   |  |ƒ|ƒS rý  rþ  r]  r  r  r  r®  |  ó   dr®  c                 C   s,   t t|| | | |||   |  |ƒ|ƒS rý  r  ra  r  r  r  r¯  €  r`  r¯  c                 C   sž   t ||||tdƒ   tdƒ  | |tdƒ   t|||  | |||   |  |ƒ|ƒ t||tdƒ  | |||   |tdƒ   | |tdƒ   |ƒ S r  r  r_  r  r  r  r°  „  ó   žr°  c                 C   sê   t || |tdƒ| |tdƒ   tdƒ  | | |tdƒ   t||tdƒ|   | |||   |  ||||   |  |ƒ|ƒ t||tdƒ  | |||   |tdƒ   ||||   |tdƒ   | | |tdƒ   |ƒ S r-  r  rc  r  r  r  r±  ˆ  s   êr±  c                 C   ó°   t |||tdƒ   tdƒ | | |tdƒ   t|| | | |||   |tdƒ   |ƒ|ƒt|| |tdƒ  | |||   |tdƒ   | | | |tdƒ   |ƒ S r  r  ra  r  r  r  r²  Œ  ó   °r²  c	           	      C   ó  t |tdƒ| |tdƒ   tdƒ tdƒ|  | | |tdƒ   t|| | | |||   |tdƒ   ||||   |tdƒ   |ƒ|ƒt|| |tdƒ  | |||   |tdƒ   ||||   |tdƒ   tdƒ|  | | | |tdƒ   |ƒ S r-  r  r]  r  r  r  r³    ó   þ
 r³  c                 C   s>   t |ttttfƒrdS t|tdƒ |ƒ}t|tdƒƒrdS dS ©NFrC  T©r8  r9  ræ  r:  rä  r›   rè  r$   ©rN  rB  rR  rP  rO  rÿ  r  r  r  r  r´  ”  ó   r´  c              
   C   sh   t |tdƒ |ƒ}ttdƒ| tt|tdƒ|tdƒ |   | ||||    |  |ƒ||| ƒ|ƒS r  ©r›   rè  rÁ  r+   r   ro  r  r  r  rµ    s   Vrµ  c           	      C   sF   t |ttttfƒrdS t|tdƒ tdƒ| ƒ}t|tdƒƒr!dS dS )NFrC  rD  Trn  ©	r  r  r  r  rR  rP  rO  rÿ  r  r  r  r  r¶  £  s   r¶  c           	   
   C   sˆ   t |tdƒ tdƒ| ƒ}ttdƒ| tt|tdƒ|tdƒ |   | ||||    |  |||||    |  |ƒ||| ƒ|ƒS ©NrC  rD  rK  rq  rr  r  r  r  r·  ¬  s   nr·  c                 C   s˜   t |||   | | |tdƒ  t|| ||  | |||   |tdƒ   |ƒ|ƒ t|| |tdƒ  | |||   |  ||tdƒ   |ƒ S r  r  ra  r  r  r  r¸  ²  ó   ˜r¸  c	           	      C   óä   t tdƒ|  | | | |tdƒ| |  tdƒ  t|| | | |||   |tdƒ   ||||   |tdƒ   |ƒ|ƒt|| |tdƒ  | |||   |  ||||   |  ||tdƒ| |  tdƒ   |ƒ S rV  r  r]  r  r  r  r¹  ¶  rX  r¹  c                 C   ó˜   t | | | |||  tdƒ  t|| | | |||   |tdƒ   |ƒ|ƒt|| |tdƒ  | |||   |  ||||  tdƒ   |ƒ S r  r  ra  r  r  r  rº  º  rt  rº  c              
   C   s–   t || ||tdƒ   tdƒ tdƒd   || ||tdƒ   tdƒd    ttdƒ|tdƒ | ||tdƒ   tdƒ tdƒd    |ƒ|ƒS )NrF  rC  rI  rS  r  r  r  r  r  r»  ¾  ó   –r»  c              	   C   s¢   t | |tdƒ  ||tdƒ   t||tdƒ  | ||tdƒ   tdƒd   |ƒ|ƒ t||tdƒ  || ||tdƒ   tdƒd   |tdƒ   |ƒ S )NrL  éüÿÿÿrF  rS  rC  r  ©rN  rB  rR  rÿ  r  r  r  r¼  Â  s   ¢r¼  c              	   C   sš   t || | |tdƒ   t||tdƒ  | ||tdƒ   tdƒd   |ƒ|ƒ t||tdƒ  | | ||tdƒ   tdƒd   |tdƒ   |ƒ S )NrC  rF  rS  r  ry  r  r  r  r½  Æ  rK  r½  c              
   C   sž   t t|| ƒ| ||tdƒ   tdƒ tdƒd   || ||tdƒ   tdƒd    ttdƒ|tdƒ | ||tdƒ   tdƒ tdƒd    |ƒ|ƒS )NrD  rC  rF  rS  r=  ©rN  rB  rQ  rÿ  r  r  r  r¾  Ê  rh  r¾  c              	   C   sÚ   t tdƒ|  |tdƒ  |tdƒ  |tdƒ| tdƒ   t|| |tdƒ  | ||tdƒ   tdƒd   |ƒ|ƒ ttdƒ| || |tdƒ   || ||tdƒ   tdƒd   tdƒ| tdƒ   |ƒ S )NrD  rK  rL  rM  rS  rF  rC  r  ©rN  rB  rQ  rR  rÿ  r  r  r  r¿  Î  ó   Úr¿  c              	   C   sÊ   t |tdƒ| tdƒ  tdƒ|  |tdƒ  |tdƒ   t|| |tdƒ  | ||tdƒ   tdƒd   |ƒ|ƒ t|| |tdƒ  | | | ||tdƒ   tdƒd   |tdƒ   |ƒ S )NrD  rC  rS  rF  r  r{  r  r  r  rÀ  Ò  ó   ÊrÀ  c              
   C   s‚   t tdƒ| ttdƒ|tdƒ | ||tdƒ   tdƒd    |ƒ|ƒ ttdƒ|| | ||tdƒ   tdƒd    |ƒ S ©NrC  rD  rF  r  r  r  r  r  rÁ  Ö  ó   ‚rÁ  c                 C   sÂ   t || || tdƒ  || |tdƒ   t|| ||  | |||   |tdƒ   |ƒ|ƒ t||tdƒ  || || tdƒ   | |||   |tdƒ   || |tdƒ   |ƒ S r  r  ra  r  r  r  rÂ  Ú  ó   ÂrÂ  c	           	      C   s:  t |tdƒ|  |tdƒ|  tdƒ  tdƒ| | | |tdƒ   t|| |tdƒ|   | |||   |tdƒ   ||||   |tdƒ   |ƒ|ƒ t|tdƒ| tdƒ  || |tdƒ|  tdƒ   | |||   |tdƒ   ||||   |tdƒ   tdƒ| | | |tdƒ   |ƒ S rV  r  r]  r  r  r  rÃ  Þ  ó   þ< rÃ  c                 C   ri  r  r  ra  r  r  r  rÄ  â  rj  rÄ  c	           	      C   rk  r-  r  r]  r  r  r  rÅ  æ  rl  rÅ  c              
   C   s  t tdƒtdƒt| tdƒƒ t|tdƒƒ  t|t|tdƒƒ t| tdƒƒ |tdƒ t|tdƒƒtdƒ  |t| tdƒƒ t|tdƒƒ  t| tdƒƒtdƒ   |ƒ|ƒt tdƒtdƒt| tdƒƒ t|tdƒƒ  ttdƒ|t|tdƒƒ t| tdƒƒ  |ƒ|ƒ S r  r  r  r  r  r  rÆ  ê  ó   þ rÆ  c           	   
   C   sø  t t| | |ƒƒ}tt| | |ƒƒ}tdƒ}tdƒ}t|tt| tdƒ| tdƒ  | ƒ || tttdƒ| tdƒ  |tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒ}t|tt| d| d  | ƒ || ttd| d  |d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒ}tt	d||d   ||   | |  t
|t|d|d d ƒƒ|ƒ||  | |d   td|||   |ƒ | |   |ƒS r  r  ©	rN  rB  rR  rP  rÿ  rY  r  r  rW  r  r  r  rÇ  î  s   ºŽ|rÇ  c           	   
   C   sþ  t t|  | |ƒƒ}tt|  | |ƒƒ}tdƒ}tdƒ}t|tt| tdƒ| tdƒ  | ƒ || tttdƒ| tdƒ  |tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒ}t|tt| d| d  | ƒ || ttd| d  |d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒ}tt	d||   | |d   | |  t
|t|d|d d ƒƒ|ƒ ||d  ||   td|||   |ƒ | |   |ƒS r  r  rƒ  r  r  r  rÈ  ø  s   ºŽ~rÈ  c           	      C   sZ  t t| | |ƒƒ}tt| | |ƒƒ}tdƒ}tdƒ}t|tt| tdƒ| tdƒ  | ƒ || tttdƒ| tdƒ  |tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒt|tt| tdƒ| tdƒ  | ƒ || tttdƒ| tdƒ  |tdƒ  | ƒ  |tdƒ tdƒ| | | tttdƒ| tdƒ  | ƒ  |tdƒ |tdƒ    |ƒ }t|tt| d| d  | ƒ || ttd| d  |d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒt|tt| d| d  | ƒ || ttd| d  |d  | ƒ  |d d| | | ttd| d  | ƒ  |d |d    |ƒ }tdd|d   ||d   ||   td|d |d |d    |ƒ | |  t	d||d   ||   | |  t
|t|d|d d ƒƒ|ƒ |ƒS )Nr  rW  rD  rK  rC  rF  r  r  rƒ  r  r  r  rÉ    s   þv þ –rÉ  c           	   
   C   s
  t t|  | |ƒƒ}tt|  | |ƒƒ}tdƒ}tdƒ}t|ttdƒt | | | ƒ || ttdƒt | |tdƒ  | ƒ  |tdƒ tdƒ| | | ttdƒt | | ƒ  |tdƒ |tdƒ    |ƒt|ttdƒt | | | ƒ || ttdƒt | |tdƒ  | ƒ  |tdƒ tdƒ| | | ttdƒt | | ƒ  |tdƒ |tdƒ    |ƒ }t|tdt | | | ƒ || tdt | |d  | ƒ  |d d| | | tdt | | ƒ  |d |d    |ƒt|tdt | | | ƒ || tdt | |d  | ƒ  |d d| | | tdt | | ƒ  |d |d    |ƒ }tt	d||d   ||   | |  t
|t|d|d d ƒƒ|ƒd||d   ||   td|d |d |d    |ƒ | |   |ƒS r(  r)  rƒ  r  r  r  rÊ    s   þF þ ŠrÊ  c              
   C   sº   t t| | tdƒƒƒ}tt| | tdƒƒƒ}ttdƒtdƒ|  t|||tdƒ   | ||tdƒ    |ƒ|ƒ ttdƒtdƒ|  t|||tdƒ   | ||tdƒ    |ƒ|ƒ S r*  r+  r,  r  r  r  rË    s   ŽrË  c              
   C   sž   t t|  | tdƒƒƒ}tt|  | tdƒƒƒ}t|tdƒ|  ttdƒ|||tdƒ    |ƒ|ƒ t|tdƒ|  ttdƒ|||tdƒ    |ƒ|ƒ S r-  r+  r,  r  r  r  rÌ    s   nrÌ  c                 C   sP  t t| | tdƒƒƒ}tt| | tdƒƒƒ}tttdƒƒ|tdƒ  tdƒ| |  t|||tdƒ   |tdƒ ttdƒƒ| | ||tdƒ    |tdƒ ||tdƒ     |ƒ|ƒtttdƒƒ|tdƒ  tdƒ| |  t|||tdƒ   |tdƒ ttdƒƒ| | ||tdƒ    |tdƒ ||tdƒ     |ƒ|ƒ S )NrF  rD  rI  r/  ©rN  rB  rR  rP  rÿ  rY  r  r  r  r  rÍ  "  s   þ& rÍ  c                 C   s¤   t t|  | tdƒƒƒ}tt|  | tdƒƒƒ}t|tdƒ|   t|| ||||tdƒ     |ƒ|ƒt|tdƒ|   t|| ||||tdƒ     |ƒ|ƒ S r  r+  r„  r  r  r  rÎ  (  r1  rÎ  c                 C   s¾   t t|  | tdƒƒƒ}tt|  | tdƒƒƒ}t|tdƒ|  t|||tdƒ   ||||tdƒ     |ƒ|ƒ t|tdƒ|  t|||tdƒ   ||||tdƒ     |ƒ|ƒ S r  r+  r„  r  r  r  rÏ  .  s   ŽrÏ  c                 C   s"   t t|| | |||   |ƒ|ƒS rý  ©r   r½   ©rN  rB  rR  rP  rÿ  r  r  r  rÐ  4  ó   "rÐ  c                 C   sÐ   t t||  tdƒƒƒ}tt||  tdƒƒƒ}ttdƒ| t|| |tdƒttdƒƒ   t| ||tdƒ   ƒ |ƒ|ƒtttdƒƒ| |tttdƒƒtdƒ ƒ  ttdƒt| ||tdƒ   ƒ |ƒ|ƒ S ©NrI  rC  rD  ©r¸   r„  rè  r¹   rÁ  r   rë  r,  r  r  r  rÑ  8  ó   ¤rÑ  c                 C   sÐ   t t||  tdƒƒƒ}tt||  tdƒƒƒ}ttdƒ| t|| |tdƒttdƒƒ   t| ||tdƒ   ƒ |ƒ|ƒtttdƒƒ| |ttdƒttdƒƒ ƒ  ttdƒt| ||tdƒ   ƒ |ƒ|ƒ S rˆ  r‰  r,  r  r  r  rÒ  >  rŠ  rÒ  c                 C   s’   t ||  tdƒƒ}ttdƒ| t| |tdƒ  tdƒ t| ||tdƒ   ƒ |ƒ|ƒ ttdƒ| ttdƒt| ||tdƒ   ƒ |ƒ|ƒ S r*  ©r„  rè  rÁ  r   rë  r5  r  r  r  rÓ  D  s   €rÓ  c                 C   s”   t | |  tdƒƒ}ttdƒ| t| |tdƒ  tdƒ t| ||tdƒ   ƒ |ƒ|ƒ ttdƒ| ttdƒt| ||tdƒ   ƒ |ƒ|ƒ S r*  r‹  r5  r  r  r  rÔ  I  s   €rÔ  c                 C   s   t | |  tdƒƒ}ttdƒ| t||tdƒ  tdƒ t| ||tdƒ   ƒ |ƒ|ƒttdƒ| ttdƒt| ||tdƒ   ƒ |ƒ|ƒ S r*  r‹  r5  r  r  r  rÕ  N  s   |rÕ  c                 C   s  t t||  tdƒƒƒ}tt||  tdƒƒƒ}ttdƒtdƒ|tdƒ   ttdƒ |tdƒ  |tdƒ  |tdƒ tdƒttdƒƒ   t| ||tdƒ   ƒ |ƒ|ƒ t|tdƒ tdƒttdƒƒ  tdƒ|tdƒ   ttdƒt| ||tdƒ   ƒ |ƒ|ƒ S )NrI  rC  rD  rF  rK  rH  r‰  r,  r  r  r  rÖ  S  s   àrÖ  c                 C   sØ   t tdƒtdƒt||  tdƒƒ  t|tdƒ  t||  tdƒƒ tdƒ t| ||tdƒ   ƒ |ƒ|ƒ t tdƒtdƒt||  tdƒƒ  t|tdƒ t||  tdƒƒ tdƒ t| ||tdƒ   ƒ |ƒ|ƒ S r?  )rÁ  rè  r„  r   rë  r  r  r  r  r×  Y  ó   Ør×  c              	   C   s~   t | tdƒ t|tdƒ | ||tdƒ   tdƒd   |ƒ|ƒ t|tdƒ tdƒ| ||tdƒ   tdƒd    |ƒ S )NrD  rF  rS  rI  rC  r  r  r  r  r  rØ  ]  r  rØ  c              
   C   s„   t | tdƒ|  ttdƒ|tdƒ | ||tdƒ   tdƒd    |ƒ|ƒt| ||tdƒ   tdƒd  tdƒ| |  |ƒ S )NrD  rC  rF  rI  r  r  r  r  r  rÙ  a  ó   „rÙ  c              	   C   sn   t |t|tdƒ | ||tdƒ   tdƒd   |ƒ|ƒ ttdƒ|| ||tdƒ   tdƒd    |ƒ S )NrD  rF  rS  rC  rA  r  r  r  r  rÚ  e  ó   nrÚ  c              
   C   s’   t || ||tdƒ   tdƒ tdƒd   | ||tdƒ   tdƒd   ttdƒ|tdƒ | ||tdƒ   tdƒ tdƒd    |ƒ|ƒS )NrF  rC  rI  r  r  r  r  r  rÛ  i  ó   ’rÛ  c              	   C   sz   t | tdƒ tt|| ƒ| ||tdƒ   tdƒd   |ƒ|ƒ t|t|| ƒ | ||tdƒ   tdƒd   |ƒ S ©NrD  rS  rF  rC  ©rÁ  rè  r   rë  r¥  rz  r  r  r  rÜ  m  rE  rÜ  c              
   C   sœ   t | |tdƒ  tdƒ|  ttdƒ|| tdƒd  | ||tdƒ   tdƒd    |ƒ|ƒt|| ||tdƒ   tdƒd   |t|| ƒ  |ƒ S ©NrD  rC  rI  rF  )rÁ  rè  r   r¥  rë  rz  r  r  r  rÝ  q  r  rÝ  c              	   C   sˆ   t ||tdƒ  tt|| ƒ| ||tdƒ   tdƒd   |ƒ|ƒ ttdƒ |t|| ƒ | ||tdƒ   tdƒd    |ƒ S r  r‘  rz  r  r  r  rÞ  u  r\  rÞ  c              
   C   s¦   t t|| ƒ| ||tdƒ   tdƒ tdƒd   |tdƒ | ||tdƒ   tdƒd    ttdƒ|tdƒ | ||tdƒ   tdƒ tdƒd    |ƒ|ƒS r*  r=  rz  r  r  r  rß  y  ó   ¦rß  c                 C   óÆ   t | ||  || tdƒ  ||||  tdƒ   t|| ||  | |||   |  |ƒ|ƒ t||tdƒ  || || tdƒ   | |||   |tdƒ   ||||  tdƒ   |ƒ S r  r  ra  r  r  r  rà  }  ó   Ærà  c                 C   r”  r  r  ra  r  r  r  rá    r•  rá  c	           	      C   ó:  t | | |tdƒ|   |tdƒ|  tdƒ  || |tdƒ| |  tdƒ   t|| |tdƒ|   | |||   |  ||||   |  |ƒ|ƒ t|tdƒ| tdƒ  || |tdƒ|  tdƒ   | |||   |tdƒ   ||||   |tdƒ   || |tdƒ| |  tdƒ   |ƒ S rV  r  r]  r  r  r  râ  …  r  râ  c	           	      C   r–  rV  r  r]  r  r  r  rã  ‰  r  rã  c                 C   ó´   t |||   |||tdƒ   tdƒ  | |tdƒ   t|| ||  | |||   |  |ƒ|ƒ t|| |tdƒ  | |||   |tdƒ   | | |tdƒ   |ƒ S r  r  ra  r  r  r  rä    ó   ´rä  c                 C   r—  r  r  ra  r  r  r  rå  ‘  r˜  rå  c	           	      C   ó  t || |tdƒ |   |tdƒ| |tdƒ   tdƒ  | | |tdƒ   t|| |tdƒ|   | |||   |  ||||   |  |ƒ|ƒ t|| |tdƒ  | |||   |tdƒ   ||||   |tdƒ   | | | |tdƒ   |ƒ S r-  r  r]  r  r  r  ræ  •  rl  ræ  c	           	      C   r™  r-  r  r]  r  r  r  rç  ™  rl  rç  c              
   C   sp   t |ƒ}t|| tt|||tdƒ  tdƒ  | |||   |||    |  |ƒ||| tdƒ|  ƒ|ƒS r  rP  ©rN  rB  rQ  rR  rP  rO  rÿ  r  r  r  r  rè    s   hrè  c	           
   
   C   s’   t |ƒ}	t|	| tt||	|tdƒ  tdƒ  | |||   ||	|    |  ||||   ||	|    |  |ƒ||| tdƒ|	  ƒ|ƒS r  rP  ©
r  r  r  r  rQ  rR  rP  rO  rÿ  r  r  r  r  ré  ¢  ó   Šré  c              
   C   s„   t | ||tdƒ |   tt|| | ||  tdƒ | tdƒ |tdƒ |    |ƒ||| |||   tdƒ |   ƒ|ƒS r  rM  r_  r  r  r  rê  §  r  rê  c              
   C   s  t | | ||tdƒ tdƒ|    tt|| | ||  tdƒ | tdƒ |tdƒ tdƒ|     | ||  tdƒ | tdƒ |tdƒ tdƒ|     |ƒ||| |||   tdƒ tdƒ|    ||||   tdƒ tdƒ|    ƒ|ƒS rs  rM  rc  r  r  r  rë  «  ó   þ rë  c              
   C   s¸   t | | |||    ||tdƒ |   | |||   ||tdƒ |    tt|| | ||  tdƒ | tdƒ |tdƒ |    |ƒ||| |||   tdƒ |   ƒ|ƒS r  rM  r_  r  r  r  rì  ¯  ó   ¸rì  c              
   C   s–  t | | |||    ||tdƒ tdƒ|    |||||    ||tdƒ tdƒ|     | |||   ||tdƒ tdƒ|     ||||   ||tdƒ tdƒ|     tt|| | ||  tdƒ | tdƒ |tdƒ tdƒ|     | ||  tdƒ | tdƒ |tdƒ tdƒ|     |ƒ||| |||   tdƒ tdƒ|    ||||   tdƒ tdƒ|    ƒ|ƒS rs  rM  rc  r  r  r  rí  ³  s   þ˜ rí  c                 C   s@   t t|| tdƒ  | |||    |  |ƒ|tdƒ| ƒ S ©NrM  rC  rN  r_  r  r  r  rî  ·  ó   @rî  c                 C   sV   t t|| tdƒ  | |||    |  ||||    |  |ƒ|tdƒ| ƒ S rŸ  rN  rc  r  r  r  rï  »  ó   Vrï  c              
   C   sx   t |ƒ}t|| tt|| |tdƒ  tdƒ  | |||   || |    |  |ƒ||| tdƒ |  ƒ|ƒ S r  rP  rš  r  r  r  rð  ¿  s   prð  c	           
   
   C   sœ   t |ƒ}	t|	| tt||	 |tdƒ  tdƒ  | |||   ||	 |    |  ||||   ||	 |    |  |ƒ||| tdƒ |	  ƒ|ƒ S r  rP  r›  r  r  r  rñ  Ä  ó   ”rñ  c              	   C   s`   t || | tdƒ| |  tt|| tdƒ  | |||    |  |ƒ|tdƒ| ƒ|ƒ S ©NrC  rM  rM  ra  r  r  r  rò  É  rD  rò  c	           	   	   C   sv   t || | tdƒ| |  tt|| tdƒ  | |||    |  ||||    |  |ƒ|tdƒ| ƒ|ƒ S r£  rM  r]  r  r  r  ró  Í  ó   vró  c              
   C   s^   t |ƒ}t|tt|||tdƒ  tdƒ  | ||||    |  |ƒ||tdƒ|  ƒ|ƒS r  rP  ro  r  r  r  rô  Ñ  s   Vrô  c           	   
   C   s~   t tdƒ| ƒ}t|tt|||tdƒ  tdƒ  | ||||    |  |||||    |  |ƒ||tdƒ|  ƒ|ƒS rV  rZ  rr  r  r  r  rõ  Ö  s   nrõ  c                 C   re  rý  rþ  ra  r  r  r  rö  Û  r!  rö  c	           	      C   rf  rý  rþ  r]  r  r  r  r÷  ß  rg  r÷  c                 C   sR   t tdƒ|tdƒ  tt| ||||tdƒ     | |ƒ|||tdƒ  ƒ|ƒS r  rM  r_  r  r  r  rø  ã  ó   Rrø  c                 C   sr   t tdƒ|tdƒ  tt| ||||tdƒ     | |||||tdƒ     |  |ƒ|||tdƒ  ƒ|ƒS r  rM  rc  r  r  r  rù  ç  rL  rù  c                 C   re  rý  rþ  ra  r  r  r  rú  ë  r!  rú  c	           	      C   rf  rý  rþ  r]  r  r  r  rû  ï  rg  rû  c                 C   s‚   t || | |tdƒ  t|||  | |||   |tdƒ   |ƒ|ƒ t||tdƒ  | |||   |  |tdƒ  |ƒ S r  r  r_  r  r  r  rü  ó  r  rü  c                 C   s¾   t tdƒ| | | | |tdƒ  t|||  | |||   |tdƒ   ||||   |tdƒ   |ƒ|ƒ t||tdƒ  | |||   |  ||||   |  |tdƒ  |ƒ S rV  r  rc  r  r  r  rý  ÷  s   ¾rý  c                 C   re  rý  rþ  ra  r  r  r  rþ  û  r!  rþ  c	           	      C   rf  rý  rþ  r]  r  r  r  rÿ  ÿ  rg  rÿ  c                 C   rv  r  r  ra  r  r  r  r     rt  r   c	           	      C   ru  rV  r  r]  r  r  r  r    rX  r  c              
   C   s´   t |ƒ}t| ||tdƒ |   | | tt|||tdƒ  | tdƒ  | ||  tdƒ | tdƒ |tdƒ |    |ƒ||||  | |||   tdƒ |   ƒ|ƒS r  ©r4   rÁ  rè  r+   r   ro  r  r  r  r    ó   ¬r  c           	   
   C   s:  t |ƒ}t|| | ||tdƒ tdƒ|     tdƒ|  tt|||tdƒ  tdƒ|  tdƒ  | ||  tdƒ | tdƒ |tdƒ tdƒ|     | ||  tdƒ | tdƒ |tdƒ tdƒ|     |ƒ||tdƒ| |  | |||   tdƒ |   ||||   tdƒ |   ƒ|ƒS rs  r¦  rr  r  r  r  r    s   þ4 r  c                 C   re  rý  rþ  ra  r  r  r  r    r!  r  c	           	      C   rf  rý  rþ  r]  r  r  r  r    rg  r  c                 C   ri  r  r  ra  r  r  r  r    rj  r  c	           	      C   rk  r-  r  r]  r  r  r  r  !  rl  r  c                 C   sZ   || }t | | t|| | |||    |ƒ|ƒ t||tdƒ  ||tdƒ   |ƒ S r  ©rÁ  r   r¥  rè  )rN  rB  rR  rP  rÿ  r0  r  r  r  r  %  s   Rr  c                 C   sV   t ||  t|||  | |||    |ƒ|ƒ t||tdƒ  | |tdƒ   |ƒ S r  r¨  r†  r  r  r  r	  *  r¡  r	  c                 C   sL   t |t|ƒ |t|ƒ   || t|ƒ  t|| | |||    |ƒ|ƒS rý  rþ  )rN  rB  rQ  rR  rP  rÿ  r  r  r  r
  .  r%  r
  c              	   C   sp   t | | || |tdƒ   t| |tdƒ | tdƒ|tdƒ |  | ||  |  ƒ ||tdƒ   |ƒS r  ©r¥  rè  r5   ra  r  r  r  r  2  r  r  c                 C   sx   t | t|ƒ tdƒ|||  |   t|ƒ   | |||   t|ƒ  t|| | tdƒ|||  |   |  |ƒ|ƒS r  rQ  ra  r  r  r  r  6  rJ  r  c                 C   sb   t t||tdƒƒ| tdƒ  ttt| |||   | |t||tdƒƒ |  |ƒ|ƒ||ƒ|ƒS ©NrC  rK  r   ©rÁ  r3   rè  r+   r   r-  )rN  rB  rR  rP  rO  r'  rÿ  r  r  r  r  :  rB  r  c              	   C   sP   t || ||   t||tdƒƒ tt|| | |||   |  |ƒ||ƒ|ƒS r  ©rÁ  r3   rè  r+   r   )rN  rB  rR  rP  rO  rW  r'  rÿ  r  r  r  r  >  r!  r  c	           	   	   C   s”   t | |||   t|ƒ ||||   t|ƒ  | | || |tdƒ|    t|ƒ   t|| | | | || |tdƒ|    |  |ƒ|ƒS r  r[  r]  r  r  r  r  B  ó   ”r  c                 C   ó4   t t| |||   | ||||   |  |ƒ|ƒS rý  r  ©rN  rB  rQ  rT  rP  rO  rU  rÿ  r  r  r  r  F  ó   4r  c                 C   sB   t ||||   | ||   | |  |||   | |  |ƒS rý  r  r¯  r  r  r  r  J  ó   Br  c                 C   sP   t t| |||    | ||||    |  |tdƒ  |ƒ|tdƒ| ƒ S r-  rN  r¯  r  r  r  r  N  r!  r  c           	   
   C   sj   t |ƒ}t|tt||tdƒ  | ||||    |  |||||    |  |ƒ||tdƒ|  ƒ|ƒS rO  rP  )	rN  rB  rQ  rT  rP  rO  rU  rÿ  rZ  r  r  r  r  R  s   br  c                 C   sR   t ttdƒ||| |  | ||     |ƒ||| |||   tdƒ |   ƒS r  rN  ©rN  rB  rQ  rT  rP  rO  rÿ  r  r  r  r  W  r¥  r  c                 C   sª   t || | |tdƒ   t| |||   |tdƒ  ||||   |tdƒ   |ƒ|ƒ t|| |||   |tdƒ   ||||   |  | | |tdƒ   |ƒ S r  r  r¯  r  r  r  r  [  r@  r  c                 C   s–   t | | || tdƒ   | ||||   tdƒ |   ttdƒ| | tdƒtdƒ|  ||  |  | ||   | ||||     ƒ |ƒS rO  r©  r¯  r  r  r  r  _  rw  r  c                 C   sÆ   t ||| |||    | ||||     |   | |||   |  ||||   | tdƒ|    ttdƒ| | tdƒtdƒ|  ||  |  | ||   | ||||     ƒ | |ƒS r  r©  r¯  r  r  r  r  c  r•  r  c                 C   sJ   t || |||   |tdƒ   ||||   |tdƒ   | |  |ƒS r  r  r¯  r  r  r  r  g  r$  r  c                 C   sö   t || ||tdƒ  |  | ||    | | |tdƒ  |  | ||    t| |||   |tdƒ  ||||   |  |ƒ|ƒt|| | |||   |tdƒ   ||||   |tdƒ   | | |tdƒ  |  | ||    |ƒ S r  r  r¯  r  r  r  r  k  ó   ör  c                 C   s.   t || | |||   |tdƒ   |  |ƒS r  r  r²  r  r  r  r  o  ó   .r  c                 C   s¸   t | | || ||tdƒ  tdƒ   | | | |tdƒ   t| |||   |tdƒ  |ƒ|ƒ t|| |||   |tdƒ   |  | ||   | | | |tdƒ   |ƒ S r  r  r²  r  r  r  r  s  rž  r  c                 C   sN   t |  | ||  |  ttdƒ| ||   |  |ƒ|ƒ t|| |  |ƒ S r  rA  ©rN  rB  rQ  rT  rP  rÿ  r  r  r  r  w  rb  r  c                 C   sª   t | | || ||tdƒ  tdƒ   |||tdƒ  tdƒ   t| |||   | |ƒ|ƒ t|| | |||   |tdƒ   |||tdƒ  tdƒ   |ƒ S r  r  r²  r  r  r  r  {  r@  r  c                 C   s4   t t| |||   | ||||   |  |ƒ|ƒS rý  r…  r¯  r  r  r  r     r°  r   c              	   C   sp   t ||  | ||   ttdƒ| |||    |ƒ|ƒt ||  | ||   ttdƒ||||    |ƒ|ƒ S r  ©rÁ  r   rè  rµ  r  r  r  r!  ƒ  r  r!  c                 C   sÚ   t ttdƒƒtdƒ|  ttdƒ| ||tdƒ   tdƒd  | t||  tdƒƒ ttdƒƒ   |ƒ|ƒt ttdƒƒtdƒ|  ttdƒ| ||tdƒ   tdƒd  |t||  tdƒƒ ttdƒƒ   |ƒ|ƒ S rG  )rÁ  rë  rè  r   r„  ©rN  rB  rQ  rT  rÿ  r  r  r  r"  ‡  r|  r"  c                 C   sÖ   t tdƒd t| t| |  tdƒƒ tdƒ | ||tdƒ   tdƒd  |||tdƒ     |ƒ|ƒt tdƒd t|t| |  tdƒƒ tdƒ | ||tdƒ   tdƒd  |||tdƒ     |ƒ|ƒ S )NrC  rH  rD  rI  )rÁ  rè  r   r„  r·  r  r  r  r#  ‹  s   Ör#  c                 C   sŽ   t || t| ||tdƒ   tdƒd  |ƒ|ƒt |  | ||  | ttdƒ| ||tdƒ   tdƒd  |||tdƒ     |ƒ|ƒ S )NrD  rK  rI  rC  r¶  r·  r  r  r  r$    ó   Žr$  c              	   C   s~   t t| |tdƒ  |  ƒtdƒ|  tttdƒt| | |  ƒ| ||  tdƒd   |||    |ƒ||tdƒ ƒ|ƒS r*  ©rÁ  rë  rè  r+   r   r·  r  r  r  r%  “  r  r%  c              	   C   s~   t t| |tdƒ  |  ƒtdƒ|  tttdƒt| | |  ƒ| ||  tdƒd   |||    |ƒ||tdƒ ƒ|ƒS r’  r¹  r·  r  r  r  r&  —  r  r&  c              
   C   ó†   t || t| ||tdƒ   |tdƒ  |ƒ|ƒt |  | ||  | t| ||tdƒ   |tdƒ  |||tdƒ    |ƒ|ƒ S ©NrD  rK  r¶  ©rN  rB  rQ  rT  rO  rÿ  r  r  r  r'  ›  ó   †r'  c              
   C   sŒ   t ||  | ||   t| ||tdƒ   | |ƒ|ƒt ||  | ||   t| ||tdƒ   |tdƒ  |||tdƒ    |ƒ|ƒ S r-  r¶  r¼  r  r  r  r(  Ÿ  r  r(  c                 C   s`   t | | tttdƒtdƒ |  | |tdƒ  tdƒ  |ƒ||t| ||tdƒ   ƒ ƒ|ƒS r<  )rÁ  r+   r   rè  rë  r·  r  r  r  r)  £  rD  r)  c                 C   sÐ   t |  | tdƒƒ}t| t|| | |tdƒ |tdƒ    | t| ||tdƒ   ƒ  ƒ tdƒ| |  |ƒt| t|| | |tdƒ |tdƒ    | t| ||tdƒ   ƒ  ƒ tdƒ| |  |ƒ S r.  )r„  rè  r¥  r>   rë  rý  ©rN  rB  rQ  rT  rÿ  rU  r  r  r  r*  §  s   ¼r*  c                 C   s†   t || ttdƒt| ||tdƒ   ƒ |ƒ|ƒt |  | ||  | ttdƒt| ||tdƒ   ƒ|||tdƒ     |ƒ|ƒ S r<  ©rÁ  r   rè  rë  r·  r  r  r  r+  ¬  r½  r+  c                 C   s®   t t| | ||tdƒ    ƒt| ||tdƒ   ƒ tttdƒ||tdƒ |  | ||    t| |tdƒ  tdƒ ƒ  |ƒ||| ||tdƒ   tdƒd   ƒ|ƒS )NrF  rC  r¹  r·  r  r  r  r,  °  s   ®r,  c              
   C   rº  r6  r¶  r¼  r  r  r  r-  ´  r½  r-  c                 C   sÎ   t tdƒtdƒ|  ttdƒt| ||tdƒ   ƒ|tdƒ  t| | tdƒƒ tdƒ   |ƒ|ƒt tdƒtdƒ|  ttdƒt| ||tdƒ   ƒ|tdƒ t| | tdƒƒ tdƒ   |ƒ|ƒ S r~  )rÁ  rè  r   rë  r„  r·  r  r  r  r.  ¸  ó   Îr.  c              
   C   s”   t ||  | ||   t| ||tdƒ   tdƒd  |ƒ|ƒt ||  | ||   t| ||tdƒ   tdƒd  |||tdƒ    |ƒ|ƒ S ©NrF  rL  rC  r¶  r·  r  r  r  r/  ¼  r­  r/  c                 C   s´   t t| ||tdƒ   ƒtt|t|| tdƒƒ ƒtdƒ|| | |   ƒ |t|| ||tdƒ    | |||tdƒ     ƒ t|||tdƒ   ƒ t|| tdƒƒ  |ƒS r-  )r¥  rë  rè  r<   r>   r„  r·  r  r  r  r0  À  r˜  r0  c                 C   sö   t tdƒ| | |tdƒ   t| |||   |tdƒ  ||||   |tdƒ   t|||tdƒ  tdƒ  |||  ||| tdƒ  tdƒ   |ƒ |ƒ|ƒt|| |||   |tdƒ   ||||   |  | | |tdƒ   |ƒ S r  r  r¯  r  r  r  r1  Ä  r³  r1  c                 C   sH  t tdƒ| | | |tdƒ   t| |||   |tdƒ  ||||   |tdƒ   t|| | || ||tdƒ  tdƒ    |||  | | ||tdƒ  tdƒ  || |||  tdƒ     |ƒ |ƒ|ƒ t|| |||   |tdƒ   ||||   |tdƒ   | | ||   | | | |tdƒ   |ƒ S ©NrC  rM  rK  r  r¯  r  r  r  r2  È  ó   þJ r2  c                 C   s0  t tdƒ| | |tdƒ  |  | ||    t| |||   |tdƒ  ||||   |  t|| || ||  ||| tdƒ  tdƒ   ||tdƒ  |  | ||    |ƒ |ƒ|ƒt|| | |||   |tdƒ   ||||   |tdƒ   | | |tdƒ  |  | ||    |ƒ S r2  r  r¯  r  r  r  r3  Ì  s   þ2 r3  c                 C   r®  rý  r  r¯  r  r  r  r4  Ð  r°  r4  c                 C   sB  t tdƒ||||  tdƒ   t| |||   | ||||   |tdƒ   t||  | || |||  tdƒ    |||  |  | ||tdƒ  tdƒ  || ||tdƒ|  tdƒ  tdƒ     |ƒ |ƒ|ƒt|| | |||   |tdƒ   ||||   |tdƒ   ||||  tdƒ   |ƒ S )NrC  rM  rK  rD  r  r¯  r  r  r  r5  Ô  ó   þD r5  c                 C   sä   t ||||  tdƒ  t| |||   |tdƒ  ||||   |tdƒ   t| | ||  || | | ||  ||  | ||      |ƒ |ƒ|ƒt|| |||   |  ||||   |  |||  tdƒ  |ƒ S r  r  r¯  r  r  r  r6  Ø  rX  r6  c                 C   s´   t t| ||tdƒ   ƒtt|t|| tdƒƒ ƒtdƒ|| | |   ƒ | t|| ||tdƒ    | |||tdƒ     ƒ t|||tdƒ   ƒ t|| tdƒƒ  |ƒS r-  )r¥  rë  rè  r=   r>   r„  r·  r  r  r  r7  Ü  r˜  r7  c                 C   sX   t tt|t| | tdƒƒ ƒ|| | |  ƒt| ƒt|ƒ t| | tdƒƒ  |ƒS r  )r¥  r=   r	  r„  rè  rë  r·  r  r  r  r8  à  ó   Xr8  c                 C   sp   t tt|t| | tdƒƒ ƒ|| |  | ||   ƒt|ƒt| || |  ƒ t| | tdƒƒ  |ƒ S r  )r¥  r=   r  r„  rè  rë  r·  r  r  r  r9  ä  r  r9  c                 C   s‚   t ttdƒ||tdƒ  |  ƒt|||tdƒ   ƒ ttdƒttdƒ||tdƒ  |  ƒt| ||tdƒ   ƒ  |ƒ|ƒS r2  r=  r·  r  r  r  r:  è  r  r:  c                 C   s   t | ttdƒt| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒt |t|tdƒ t| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ S r2  r¿  r·  r  r  r  r;  ì  s   r;  c                 C   sš   t || tt|||tdƒ   ƒt| ||tdƒ   ƒ |ƒ|ƒt |  | ||  | ttdƒt| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ S r-  ©rÁ  r   rë  rè  r·  r  r  r  r<  ð  rK  r<  c              	   C   sX   t t| ƒtt|t| | tdƒƒ ƒ|| | |  ƒ t|ƒt| | tdƒƒ  |ƒS r  )r¥  rë  r<   r	  r„  rè  r·  r  r  r  r=  ô  rÅ  r=  c              	   C   sp   t t| || |  ƒtt|t| | tdƒƒ ƒ|| |  | ||   ƒ t|ƒt| | tdƒƒ  |ƒ S r  )r¥  rë  r<   r  r„  rè  r·  r  r  r  r>  ø  r  r>  c              
   C   sz   t t| ||tdƒ   ƒttdƒ||tdƒ  |   ƒ tttdƒ||tdƒ  |   ƒt|||tdƒ   ƒ |ƒ|ƒS r-  r=  r·  r  r  r  r?  ü  rE  r?  c              
   C   sz   t ttdƒ||tdƒ  |  ƒt|||tdƒ   ƒ tt| ||tdƒ   ƒttdƒ||tdƒ  |  ƒ |ƒ|ƒS r2  r=  r·  r  r  r  r@   	  rE  r@  c                 C   r®  rý  r  r¯  r  r  r  rA  	  r°  rA  c                 C   sd   t | | ||  | ttdƒ| | | tdƒtdƒ|  | ||  |  | ||  | ƒ |ƒS r  )r¥  r:   rè  r¯  r  r  r  rB  	  rg  rB  c                 C   s€   t | t|ƒ tdƒ|||  |   t|ƒ   | |||   t|ƒ  ttdƒ|||  |   | ||||   |  |ƒ|ƒS r  rQ  r¯  r  r  r  rC  	  ó   €rC  c	           	      C   s<   t || |  | |||   |  |||  | |  |ƒS rý  r  ©	rN  rB  rQ  rT  r0  rP  rO  rU  rÿ  r  r  r  rD  	  ó   <rD  c	           	      C   s„   t ||t|ƒ  ||||    t|ƒ  |||  | t|ƒ   t|| |  | |||   |  |||  | |  |ƒ|ƒS rý  ©rÁ  r&   r   rÈ  r  r  r  rE  	  r  rE  c	           	   	   C   sR   t tdƒt||tdƒƒ tt| |||   | ||||   |  |ƒ||ƒ|ƒS r  rS  )	rN  rB  rQ  rT  rP  rO  rU  rW  rÿ  r  r  r  rF  	  r¥  rF  c                 C   s"   t t||ƒ|  t||ƒ|  |ƒS rý  ©r   rè   )rO  rU  rW  r'  rÿ  r  r  r  rG  	  r‡  rG  c                 C   s.   t t||ƒ| t||| |   |ƒ|  |ƒS rý  rË  )rR  rO  rU  rW  r'  rÿ  r  r  r  rH   	  r´  rH  c	           	   	   C   sr   t | tdƒ|tdƒ |   ||  | tt| | |tdƒ |tdƒ |   |||  |  |ƒ||| ƒ|ƒS r  rM  ©	rB  rQ  rT  rV  rR  rP  rO  rU  rÿ  r  r  r  rI  $	  rL  rI  c	           	      C   sh   t | t|ƒ ||  || t|ƒ   | ||  t|ƒ  t||||   ||||   |  |ƒ|ƒS rý  rþ  rÌ  r  r  r  rJ  (	  s   hrJ  c	           	      C   s`   t |t|ƒ |t|ƒ   || t|ƒ  t|| | ||  |  ||||   |  |ƒ|ƒS rý  rþ  rÌ  r  r  r  rL  ,	  rD  rL  c	           	      C   sB   t tdƒ| tt| ||  | |||  |  |ƒ||| ƒ|ƒS r  rM  ©	rN  rB  rQ  rT  rR  rP  rO  rU  rÿ  r  r  r  rM  0	  r±  rM  c	           	      C   sF   t |||||    | ||   | |  |||   | |  |ƒS rý  r  rÍ  r  r  r  rN  4	  r
  rN  c	           	   	   C   s^   t tdƒ| tt|tdƒ|tdƒ |   | ||  |  |||  |  |ƒ||| ƒ|ƒS r  rM  rÍ  r  r  r  rO  8	  rd  rO  c
           
      C   ód   t |t|ƒ |	t|ƒ   ||	 t|ƒ  t|	| | ||	|   |  |||	|   |  |	ƒ|	ƒS rý  rþ  ©
rN  rB  rQ  rT  rV  rR  rP  rO  rU  rÿ  r  r  r  rP  <	  rg  rP  c
           
      C   ó@   t t||	 | | ||	|   |  |||	|   |  |	ƒ|	ƒS rý  r  rÏ  r  r  r  rQ  @	  r   rQ  c	           	      C   sN   t ||| |tdƒ   | |||   |tdƒ   | | |tdƒ   |ƒS r  r  ©	rN  rB  rQ  rT  rV  rR  rP  rO  rÿ  r  r  r  rR  D	  rb  rR  c                 C   s~   t ||| |tdƒ   | |||tdƒ    |
tdƒ   ||||tdƒ    |
tdƒ   | | | |tdƒ   |ƒS r2  r  ©r  r  r  r  rQ  rT  rV  rR  rP  r1  rO  rÿ  r  r  r  rS  H	  r  rS  c	           	      C   sŠ   t |||   t|| ||  | |||   |  |ƒ|ƒt||| |tdƒ   | |||   |tdƒ   | | |tdƒ   |ƒ S r  r¨  rÑ  r  r  r  rT  L	  ó   ŠrT  c	           	      C   sš   t || t|| | | |||   |tdƒ   |ƒ|ƒt|| |tdƒ  | |||   |tdƒ   |  | ||   | | | |tdƒ   |ƒ S r  rA  rÑ  r  r  r  rU  P	  rK  rU  c	           	   	   C   sÎ   t ||  | | |tdƒ  || |||tdƒ   tdƒ    | |tdƒ   t|| ||  | |||   |  |ƒ|ƒt||| |tdƒ   | |||   |tdƒ   | | |tdƒ   |ƒ S r  r  rÑ  r  r  r  rV  T	  rÀ  rV  c              
   C   s.  t ||  | | | |tdƒ  || | |||
tdƒ   tdƒ    | | |tdƒ   t|| ||  | |||tdƒ    |
  ||||tdƒ    |
  |ƒ|ƒt||| |tdƒ   | |||tdƒ    |
tdƒ   ||||tdƒ    |
tdƒ   | | | |tdƒ   |ƒ S r2  r  rÒ  r  r  r  rW  X	  s   þ0 rW  c                 C   sª  t || tdƒ tdƒ  tdƒ|tdƒ   t| ||tdƒ   |tdƒ  ttdƒ| |tdƒ  |tdƒ  t||tdƒ  ||tdƒ   |||tdƒ    |  |tdƒ tdƒ  |  | ||    | ||tdƒ    ƒ |  |tdƒ tdƒ  |  | ||    |ƒ |ƒ|ƒt|| tdƒ tdƒ  | |  |tdƒ tdƒ   | ||tdƒ   |tdƒ   |  | ||   tdƒ|tdƒ   |ƒ S )NrD  rK  rC  rM  ©rÁ  rè  r   r2  r•   r¥  ©rN  rB  rQ  rT  rR  rO  rÿ  r  r  r  rX  \	  s   þ¬ rX  c                 C   s°  t || tdƒ tdƒ  tdƒ|tdƒ   t|| | ||tdƒ   |tdƒ   ttdƒ| |tdƒ  t||tdƒ  |||tdƒ    |tdƒ|  |  |tdƒ tdƒ   |  | ||    | ||tdƒ    ƒ ||  |  |tdƒ tdƒ   |  | ||    |ƒ |ƒ|ƒt|| tdƒ tdƒ  | |  |tdƒ tdƒ   | ||tdƒ   |tdƒ   |  | ||   tdƒ|tdƒ   |ƒ S rY  rÔ  rÕ  r  r  r  rY  `	  s   þ² rY  c	           	      C   sè   t | | |tdƒ  || |||tdƒ   tdƒ   | | | |tdƒ   t|| | | |||   |tdƒ   |ƒ|ƒ t|| |tdƒ  | |||   |tdƒ   |  | ||   | | | | |tdƒ   |ƒ S r  r  rÑ  r  r  r  rZ  d	  s   èrZ  c              
   C   s`  t | | | |tdƒ  || | |||
tdƒ   tdƒ   | | | | | |
tdƒ   t|| | | |||tdƒ    |
tdƒ   ||||tdƒ    |
tdƒ   |ƒ|ƒ t|| |tdƒ  | |||tdƒ    |
tdƒ   ||||tdƒ    |
tdƒ   |  | | || |   | | | | | | |
tdƒ   |ƒ S r2  r  rÒ  r  r  r  r[  h	  ó   þb r[  c	           	   	   C   sâ   t | | |tdƒ  || |||tdƒ   tdƒ   ||||tdƒ   tdƒ   t|| | | |||   |  |ƒ|ƒ t||| |tdƒ   | |||   |tdƒ   || |||tdƒ   tdƒ   |ƒ S r  r  rÑ  r  r  r  r\  l	  s   âr\  c              
   C   sB  t | | | |tdƒ  || | |||
tdƒ   tdƒ   || |||
tdƒ   tdƒ   t|| | | |||tdƒ    |
  ||||tdƒ    |
  |ƒ|ƒ t||| |tdƒ   | |||tdƒ    |
tdƒ   ||||tdƒ    |
tdƒ   || | |||
tdƒ   tdƒ   |ƒ S r2  r  rÒ  r  r  r  r]  p	  rÄ  r]  c	           	      C   s<   t t|| | | |||   |  ||||    |ƒ|ƒS rý  r  rÑ  r  r  r  r^  t	  rÉ  r^  c	           	   
   C   s  t ||  | |tdƒ   t|| ||  | |||   |  t|  |tdƒ  ||  |tdƒ  ||tdƒ  | |tdƒ   ||tdƒ  tdƒ |  | ||    |ƒ |ƒ|ƒ t|tdƒ || |tdƒ   | |||   |tdƒ   | | |tdƒ   |ƒ S r2  r  rÑ  r  r  r  r_  x	  s   þ r_  c	           	   
   C   sN  t tdƒ| |tdƒ  | |tdƒ   t|| | | |||   |tdƒ   t| | |tdƒ  | ||  |tdƒ  |tdƒ |tdƒ  | |tdƒ   |tdƒ |  | ||  tdƒ   |ƒ |ƒ|ƒt|| |tdƒ  | |||   |tdƒ   |  | ||  tdƒ  | |tdƒ  | | |tdƒ   |ƒ S r2  r  rÑ  r  r  r  r`  |	  s   þP r`  c	           	      C   sR  t tdƒ||||tdƒ   tdƒ   t|| | | |||   |  t||tdƒ  |||tdƒ   tdƒ  |||  tdƒ| | | |tdƒ  |  | tdƒ| |  || tdƒ     |ƒ |ƒ|ƒt|tdƒ || tdƒ   || || tdƒ   | |||   |tdƒ   ||||tdƒ   tdƒ   |ƒ S rs  r  rÑ  r  r  r  ra  €	  s   þT ra  c	           
      C   s>   t |ttttfƒrdS t|tdƒ |ƒ}	t|	tdƒƒrdS dS rm  rn  ©
rN  rB  rQ  rT  rR  rP  rO  rU  rÿ  r  r  r  r  rb  „	  rp  rb  c	           
   
   C   s€   t |tdƒ |ƒ}	ttdƒ|	 tt|tdƒ|tdƒ |	   | ||||	    |  |||||	    |  |ƒ|||	 ƒ|ƒS r  rq  r×  r  r  r  rc  	  s   nrc  c
              
   C   s’   t |ƒ}
t|
| tt|	|
|tdƒ  tdƒ  | |||   |	|
|    |  ||||   |	|
|    |  |	ƒ|	||	 tdƒ|
  ƒ|	ƒS r  rP  )rN  rB  rQ  rT  rV  rR  rP  rO  rU  rÿ  r  r  r  r  rd  “	  rœ  rd  c
           
      C   s$  t || || |tdƒ   t||	 ||  | ||	|   |tdƒ   |||	|   |tdƒ   t||| tdƒ  ||	|  |||tdƒ   tdƒ   |	ƒ |	ƒ|	ƒ t||tdƒ  ||	 || tdƒ   | ||	|   |tdƒ   |||	|   |  || |tdƒ   |	ƒ S r  r  rÏ  r  r  r  re  ˜	  s   þ& re  c
           
      C   ó€  t tdƒ| | | |tdƒ   t||	 | | ||	|   |tdƒ   |||	|   |tdƒ   t||| | |tdƒ  |tdƒ |  | ||     ||	|  || | |tdƒ  |  | ||  |||tdƒ   tdƒ     |	ƒ |	ƒ|	ƒt||	 |tdƒ  | ||	|   |tdƒ   |||	|   |tdƒ   |  | ||   | | | | |tdƒ   |	ƒ S rÂ  r  rÏ  r  r  r  rf  œ	  ó   þ‚ rf  c
           
      C   ó  t tdƒ| | |tdƒ   t||	 | | ||	|   |tdƒ   |||	|   |tdƒ   t||||tdƒ   tdƒ  ||	|  |||| tdƒ   tdƒ   |	ƒ |	ƒ|	ƒt||	 |tdƒ  | ||	|   |tdƒ   |||	|   |  | | | |tdƒ   |	ƒ S r  r  rÏ  r  r  r  rg   	  ó   þ  rg  c
           
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      C   s>  t ||  | | |tdƒ   t||	 ||  | ||	|   |  |||	|   |  t|| |	|  |||| tdƒ   tdƒ  || | | || |    | | ||  || tdƒ   |	ƒ |	ƒ|	ƒ t||	 |tdƒ  | ||	|   |tdƒ   |||	|   |tdƒ   | | | |tdƒ   |	ƒ S r2  r  rÏ  r  r  r  rr  Ì	  s   þ@ rr  c              	   C   s’   t | ||  |  | ||   t|| ||  | |||    |ƒ|ƒ t |||  |  | ||   t|| ||  ||||    |ƒ|ƒ S rý  ©rÁ  r   ©rN  rB  rQ  rT  rV  rR  rP  rÿ  r  r  r  rs  Ð	  r  rs  c              	   C   óx   t ||  | ||   t|| | | |||    |ƒ|ƒt ||  | ||   t|| | ||||    |ƒ|ƒ S rý  rá  râ  r  r  r  rt  Ô	  rJ  rt  c                 C   sx   t tdƒ| t|||  t||||   ƒ |ƒ|ƒt | | t|||  | |||   t||||   ƒ  |ƒ|ƒ S r  ©rÁ  rè  r   rë  ©rN  rB  rQ  rT  rR  rP  rÿ  r  r  r  ru  Ø	  rJ  ru  c                 C   sÎ   t t|  | tdƒƒƒ}tt|  | tdƒƒƒ}t|tdƒ|  ttdƒt|||tdƒ   ƒ|||tdƒ     |ƒ|ƒ t|tdƒ|  ttdƒt|||tdƒ   ƒ|||tdƒ     |ƒ|ƒ S r*  )rx   r„  rè  r4   rÁ  r   rë  )rN  rB  rQ  rT  rÿ  rY  r  r  r  r  rv  Ü	  s   žrv  c                 C   s¼  t || tdƒƒ}ttdƒtdƒd  | ttdƒtdƒd   | | tdƒ t|||tdƒ   ƒt|ƒ  ƒ tdƒ| t|ƒ  |ƒttdƒtdƒd  | ttdƒtdƒd   | | tdƒ t|||tdƒ   ƒt|ƒ  ƒ tdƒ| t|ƒ  |ƒ ttdƒtdƒd  | tt|||tdƒ   ƒt|ƒ ƒ tdƒ| t|ƒ  |ƒ ttdƒtdƒd  ttdƒƒ | tttdƒƒtdƒ tdƒtdƒd  ttdƒƒ t|ƒt|||tdƒ   ƒ  tdƒt|ƒ | |   ƒ tdƒ| t|ƒ  |ƒ ttdƒtdƒd  ttdƒƒ | tttdƒƒtdƒ tdƒtdƒd  ttdƒƒ t|ƒt|||tdƒ   ƒ  tdƒt|ƒ | |   ƒ tdƒ| t|ƒ  |ƒ S )NrI  rD  rC  é   é   )r„  rè  r¥  Úlogrë  rý  r>   r¾  r  r  r  rw  â	  s   þþ ® rw  c                 C   sŒ   t tdƒ| t||tdƒ  t|||tdƒ   ƒ |ƒ|ƒt | | t||tdƒ  | ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S )NrC  rL  rI  rä  ©rN  rB  rQ  rT  rR  rÿ  r  r  r  rx  ç	  r  rx  c                 C   s„   t tdƒ|  t|| t|||tdƒ   ƒ |ƒ|ƒt ||  t||tdƒ  | ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S )NrC  rI  rä  ré  r  r  r  ry  ë	  r  ry  c                 C   sŽ   t || t|tdƒ t|||tdƒ   ƒ |ƒ|ƒt |  | ||  | t|tdƒ | ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S )NrD  rF  r¿  r·  r  r  r  rz  ï	  r¸  rz  c                 C   s†   t || t|| t|||tdƒ   ƒ |ƒ|ƒt |  | ||  | t|| | ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S )NrI  rÆ  ré  r  r  r  r{  ó	  r½  r{  c              
   C   sŠ   t || tt| ||tdƒ   ƒ|||tdƒ   tdƒd   |ƒ|ƒ t|t| ||tdƒ   ƒ |t|||tdƒ   ƒ  |ƒ S ©NrD  rI  )rÁ  r   rë  rè  r¥  r·  r  r  r  r|  ÷	  rÓ  r|  c                 C   s€   t tdƒ| tt| |||   ƒt||||   ƒ |ƒ|ƒt | | ttdƒt| |||   ƒt||||   ƒ  |ƒ|ƒ S r  rä  rµ  r  r  r  r}  û	  rÇ  r}  c	           
   
   C   sÚ   t |ƒ}	t| ||tdƒ |   |	 | tt||	|tdƒ  | tdƒ  |||	 |  | ||    |  | ||	  tdƒ | | tdƒ |tdƒ |    |ƒ||||	  | |||   tdƒ |	   ƒ|ƒS r  r¦  r×  r  r  r  r~  ÿ	  s   Òr~  c	           	      C   sV   t t|| tdƒ  | |||    |  ||||    |  |ƒ|tdƒ| ƒ S rŸ  rN  rÍ  r  r  r  r  
  r¡  r  c
              
   C   sœ   t |ƒ}
t|
| tt|	|
 |tdƒ  tdƒ  | |||   |	|
 |    |  ||||   |	|
 |    |  |	ƒ|	||	 tdƒ |
  ƒ|	ƒ S r  rP  )rN  rB  rQ  rT  rV  rR  rP  rO  rU  rÿ  rZ  r  r  r  r€  
  r¢  r€  c
           
   	   C   sv   t ||	 | tdƒ|	 |  tt|	| tdƒ  | ||	|    |  |||	|    |  |	ƒ|	tdƒ|	 ƒ|	ƒ S r£  rM  rÏ  r  r  r  r  
  r¤  r  c	           
   
   C   sv   t |ƒ}	t|	tt||	|tdƒ  tdƒ  | |||	|    |  ||||	|    |  |ƒ||tdƒ|	  ƒ|ƒS r  rP  )
rN  rB  rQ  rT  rR  rP  rO  rU  rÿ  rZ  r  r  r  r‚  
  s   nr‚  c
           
      C   rÎ  rý  rþ  rÏ  r  r  r  rƒ  
  rg  rƒ  c	           	      C   sr   t tdƒ|tdƒ  tt| ||||tdƒ     | |||||tdƒ     |  |ƒ|||tdƒ  ƒ|ƒS r  rM  rÍ  r  r  r  r„  
  rL  r„  c
           
      C   rÎ  rý  rþ  rÏ  r  r  r  r…  
  rg  r…  c
           
      C   rØ  rÂ  r  rÏ  r  r  r  r†  "
  rÙ  r†  c
           
      C   rÚ  r  r  rÏ  r  r  r  r‡  &
  rÛ  r‡  c
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      C   rÝ  r2  r  rÏ  r  r  r  rˆ  *
  rÖ  rˆ  c
           
      C   rÞ  r  r  rÏ  r  r  r  r‰  .
  r‚  r‰  c
           
      C   rß  rÂ  r  rÏ  r  r  r  rŠ  2
  rà  rŠ  c              	   C   sz   t | |  | ||   t|||  | |||    |ƒ|ƒ t ||  | ||   t|||  ||||    |ƒ|ƒ S rý  rá  rå  r  r  r  r‹  6
  rE  r‹  c              	   C   rã  rý  rá  râ  r  r  r  rŒ  :
  rJ  rŒ  c
           
      C   rÐ  rý  r  rÏ  r  r  r  r  >
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           
      C   s>   t |	|||   | ||	|   |  ||	|  | |  |	ƒS rý  r  ©
rN  rB  rQ  rT  rR  r0  rP  rO  rU  rÿ  r  r  r  rŽ  B
  rT  rŽ  c
           
      C   s†   t |	|t|ƒ  |||	|    t|ƒ  ||	|  | t|ƒ   t|	|||   | ||	|   |  ||	|  | |  |	ƒ|	ƒS rý  rÊ  rë  r  r  r  r  F
  r½  r  c                 C   sf   t |t|ƒ |
t|ƒ   ||
 t|ƒ  t|
| | ||
|   |  |||
|    |	  |
ƒ|
ƒS rý  rþ  )rN  rB  rQ  rT  rV  rR  r0  rP  rO  rU  rÿ  r  r  r  r  J
  ó   fr  c
           
      C   sŒ   t | | ||  ||	 |tdƒ   t|tdƒ | | | tdƒ|tdƒ |  | |	|  |  | |	|  | ƒ ||tdƒ   |	ƒS r  )r¥  rè  r:   rÏ  r  r  r  r‘  N
  r  r‘  c
           
      C   sŒ   t | t|ƒ tdƒ||	|  |   t|ƒ   | ||	|   t|ƒ  t||	 | tdƒ||	|  |   |  |||	|   |  |	ƒ|	ƒS r  rQ  rÏ  r  r  r  r’  R
  r  r’  c
           
      C   sv   t t||	tdƒƒ| tdƒ  ttt| ||	|   | |||	|   |  |	t||	tdƒƒ |  |	ƒ|	ƒ|	|ƒ|	ƒS rª  r«  )
rN  rB  rQ  rT  rR  rP  rO  rU  r'  rÿ  r  r  r  r“  V
  r¤  r“  c              	   C   sd   t || |	|   t|	|
tdƒƒ tt|
| | ||
|   |  |||
|   |  |
ƒ|
|	ƒ|
ƒS r  r¬  )rN  rB  rQ  rT  rR  rP  rO  rU  rW  r'  rÿ  r  r  r  r”  Z
  rg  r”  c                 C   s:   t |
||||   |	  | | || ||   |  |ƒS rý  r  ©r  r  r  r  rQ  rT  rP  r1  rO  rU  rW  rÿ  r  r  r  r•  ^
  r&  r•  c                 C   sN   t || | || ||   |
  ||||   ||tdƒ|    |  |ƒS r  r	  ©r  r  r  r  rQ  rT  rV  rP  r!  r1  rO  rU  rW  rÿ  r  r  r  r–  b
  rb  r–  c                 C   s    t | |||tdƒ    t|ƒ ||||tdƒ    t|ƒ  | | || ||   t|ƒ   t|
||||   |	  | | || ||   |  |ƒ|ƒS r  ©rÁ  rè  r&   r   rí  r  r  r  r—  f
  s    r—  c              	   C   s´   t | |||tdƒ    t|
ƒ ||||tdƒ    t|
ƒ  | | || ||   t|
ƒ   t|| | || ||   |
  ||||   ||tdƒ|    |  |ƒ|ƒS r  rï  rî  r  r  r  r˜  j
  r˜  r˜  c                 C   sH   t t| ||
|   | |||
|   |  |||
|   |	  |
ƒ|
ƒS rý  r  ©rN  rB  rQ  rT  rV  rX  rP  rO  rU  rY  rÿ  r  r  r  r™  n
  r   r™  c              	   C   sŒ   t |  | ||  |  | ||   ttdƒ| |||    |ƒ|ƒt | | ||  |  | ||   ttdƒ||||    |ƒ|ƒ S r  r¶  ©rN  rB  rQ  rT  rV  rX  rP  rÿ  r  r  r  rš  r
  r  rš  c                 C   sz   t || ttdƒt||||   ƒ |ƒ|ƒt |  | ||  | ttdƒ| |||   t||||   ƒ  |ƒ|ƒ S r  r¿  rñ  r  r  r  r›  v
  rE  r›  c                 C   sŠ   t || tt| |||   ƒt||||   ƒ |ƒ|ƒt |  | ||  | ttdƒt| |||   ƒt||||   ƒ  |ƒ|ƒ S r  rÆ  rñ  r  r  r  rœ  z
  rÓ  rœ  c                 C   sÌ   t |  | ||  |  | ||   ttdƒt| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒt | | ||  |  | ||   tt| ||tdƒ   ƒ|||tdƒ   tdƒd   |ƒ|ƒ S )NrC  rD  rI  r¿  ©rN  rB  rQ  rT  rV  rX  rÿ  r  r  r  r  ~
  s   Ìr  c
           
      C   s@  t tdƒ| | | |tdƒ   t| ||	|   |tdƒ  |||	|   |tdƒ   t||  | || | |tdƒ   ||   ||	|  || | |tdƒ  |  | ||  || tdƒ     |	ƒ |	ƒ|	ƒt|	| ||	|   |tdƒ   |||	|   |  |  | ||   | | | |tdƒ   |	ƒ S r  r  ©
rN  rB  rQ  rT  rV  rX  rP  rO  rU  rÿ  r  r  r  rž  ‚
  s   þB rž  c
           
      C   s^  t tdƒ| | |tdƒ  |  | ||    t| ||	|   |tdƒ  |||	|   |  t||  | ||   ||	|  |  | ||   ||| tdƒ  tdƒ   || |tdƒ  |  | ||    |	ƒ |	ƒ|	ƒt|	| ||	|   |tdƒ   |||	|   |tdƒ   |  | ||   | | |tdƒ  |  | ||    |	ƒ S r2  r  ró  r  r  r  rŸ  †
  ó   þ` rŸ  c
           
      C   sT  t tdƒ|||| tdƒ  tdƒ   t| ||	|   | |||	|   |tdƒ   t||  | || | || tdƒ   ||   |	| || | | || tdƒ  ||  | ||    || | |  | ||      |	ƒ |	ƒ|	ƒt||	 | ||	|   |tdƒ   |||	|   |  |||| tdƒ  tdƒ   |	ƒ S r  r  ró  r  r  r  r   Š
  s   þV r   c              
   C   s°   t |  | ||  |  | ||   t| ||tdƒ   tdƒd  |ƒ|ƒt | | ||  |  | ||   t| ||tdƒ   tdƒd  |||tdƒ    |ƒ|ƒ S rÁ  r¶  rò  r  r  r  r¡  Ž
  rj  r¡  c	           	   	   C   sj   t || t| |||   | |ƒ|ƒt | | ||  | t| |||   | ||||    |ƒ|ƒ S rý  rá  )	rN  rB  rQ  rT  rV  rX  rP  rO  rÿ  r  r  r  r¢  ’
  r>  r¢  c
           
   	   C   st   t |t| ||	|   | |||	|   |  |	ƒ|	ƒt |t|	| | ||	|   |  |||	|   |  |	ƒ|	ƒ S rý  rá  ró  r  r  r  r£  –
  rI  r£  c                 C   s¨   t ||  | ||   ttdƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒt ||  | ||   ttdƒ|||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S r2  r¿  rò  r  r  r  r¤  š
  s   ¨r¤  c                 C   sˆ   t tdƒ|  ttdƒ|tdƒ t|||tdƒ   ƒ  |ƒ|ƒt ||  ttdƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S r2  rä  )rQ  rT  rV  rX  rÿ  r  r  r  r¥  ž
  r\  r¥  c                 C   ó¦   t || tt|||tdƒ   ƒt|||tdƒ   ƒ |ƒ|ƒt |  | ||  | tt|||tdƒ   ƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S r  rÆ  rò  r  r  r  r¦  ¢
  r“  r¦  c                 C   rõ  r  rÆ  rò  r  r  r  r§  ¦
  r“  r§  c                 C   s¼   t ||  | ||   tt|||tdƒ   ƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒt ||  | ||   ttdƒt|||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ S r-  rÆ  rò  r  r  r  r¨  ª
  rW  r¨  c              	   C   sj   t t|| | |  t|t| | tdƒƒ ƒ|| ||  ƒ| t|ƒ t|ƒ t| | tdƒƒ  |ƒS r  )r¥  r;   r	  r„  rè  rë  rò  r  r  r  r©  ®
  r>  r©  c                 C   s–   t ttdƒ||tdƒ  |  ƒt|||tdƒ   ƒ ttdƒttdƒ||tdƒ  |  ƒ| ||tdƒ    t|||tdƒ   ƒ  |ƒ|ƒS r2  r=  rò  r  r  r  rª  ²
  rw  rª  c                 C   sÔ   t |t|||tdƒ   ƒ ttdƒ|| | |   t|t|| tdƒƒ ƒ| | ||  tdƒ ƒ | | t||||tdƒ    ||||tdƒ     ƒ t|||tdƒ   ƒ t|| tdƒƒ  |ƒS r-  )r¥  rë  rè  r;   r>   r„  rò  r  r  r  r«  ¶
  s   Ôr«  c                 C   s¶   t || ttdƒt|||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒt |  | ||  | ttdƒ| ||tdƒ   t|||tdƒ   ƒ t|||tdƒ   ƒ  |ƒ|ƒ S r2  r¿  rò  r  r  r  r¬  º
  ó   ¶r¬  c                 C   s¼   t ||  | ||   tt|||tdƒ   ƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒt ||  | ||   tt|||tdƒ   ƒ|||tdƒ   tdƒd   |ƒ|ƒ S rê  rÆ  rò  r  r  r  r­  ¾
  rW  r­  c                 C   sØ   t |  | ||  |  | ||   tt|||tdƒ   ƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒt | | ||  |  | ||   tt|||tdƒ   ƒ|||tdƒ   tdƒd   |ƒ|ƒ S rê  rÆ  rò  r  r  r  r®  Â
  rŒ  r®  c                 C   sì   t ||tdƒ  tt|||tdƒ   ƒ|  | tdƒ| |  || |tdƒ    t|||tdƒ   ƒ |ƒ|ƒt |  | ||  tdƒ |tdƒ  tt|||tdƒ   ƒ| ||tdƒ   t|||tdƒ   ƒ  |ƒ|ƒ S r  rä  rò  r  r  r  r¯  Æ
  s   ìr¯  c	           	   
   C   sV  t ||  | ||   |  | ||  tdƒ  t|||tdƒ   |tdƒ  |||tdƒ   |tdƒ   | ||tdƒ    |ƒ|ƒt |  | ||  tdƒ t|||tdƒ   | |||tdƒ   |tdƒ   |  |tdƒ  | ||tdƒ  |  tdƒ| | | |  |tdƒ |tdƒ  |  | ||     |ƒ|ƒ S )NrD  rK  rM  r  ©	rN  rB  rQ  rT  rV  rX  rU  rY  rÿ  r  r  r  r±  Ê
  s   þX r±  c	           	   
   C   s¶   t || t|||tdƒ   |tdƒ  |||tdƒ   |  |ƒ|ƒt |  | ||  | t|||tdƒ   |tdƒ  |||tdƒ   |  | ||tdƒ    |ƒ|ƒ S r»  r¶  r÷  r  r  r  r²  Î
  rö  r²  c	           	   
   C   s  t |tdƒ |  | ||  tdƒ  t|||tdƒ   |tdƒ  |||tdƒ   |  | ||tdƒ    |ƒ|ƒt ||  | ||  tdƒ  t|||tdƒ   | |||tdƒ   |  |  | tdƒ| |  || |tdƒ    |ƒ|ƒ S r  r  r÷  r  r  r  r³  Ò
  r  r³  c	           	   
   C   s¼   t ||  | ||   t|||tdƒ   |tdƒ  |||tdƒ   |  | ||tdƒ    |ƒ|ƒt ||  | ||   t|||tdƒ   | |||tdƒ   |  |ƒ|ƒ S r-  r¶  r÷  r  r  r  r´  Ö
  rW  r´  c                 C   s`  t | tdƒ  | | |tdƒ | |  tdƒ|  |tdƒ   ttdƒ| ||tdƒ   t|||tdƒ   ƒ t|||tdƒ   ƒ  |ƒ|ƒt || tdƒ|  |tdƒ   t| ||tdƒ   t|||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ t|t|||tdƒ   ƒ t|||tdƒ   ƒ tdƒ|  | ||tdƒ     |ƒ S r-  r‘  rò  r  r  r  rµ  Ú
  rÖ  rµ  c                 C   sæ  t tdƒ| tdƒ  | | tdƒ|  | || ||    |tdƒ | |  tdƒ|  |  | ||   |  | ||    ttdƒ| ||tdƒ   t|||tdƒ   ƒ t|||tdƒ   ƒ  |ƒ|ƒt || tdƒ|  |  | ||   |  | ||    t| ||tdƒ   t|||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ t|tdƒ | t|||tdƒ   ƒ t|||tdƒ   ƒ tdƒ|  | ||tdƒ    |  | ||   |  | ||    |ƒ S rG  r‘  rò  r  r  r  r¶  Þ
  s   þè r¶  c              	   C   sÂ   t || t| ||
|   |tdƒ  |||
|   |tdƒ   |||
|   |	  |
ƒ|
ƒt |  | ||  | t| ||
|   | |||
|   |tdƒ   |||
|   |	  |
ƒ|
ƒ S r  r¶  rð  r  r  r  r·  â
  r€  r·  c              	   C   sÈ   t ||  | ||   t| ||
|   | |||
|   |tdƒ   |||
|   |	  |
ƒ|
ƒt ||  | ||   t| ||
|   |tdƒ  |||
|   |  |||
|   |	  |
ƒ|
ƒ S r  r¶  rð  r  r  r  r¸  æ
  s   Èr¸  c                 C   s*  t t| |||tdƒ    || ||tdƒ     ƒt|||tdƒ   ƒ |t| |||tdƒ    || ||tdƒ     ƒ t|||tdƒ   ƒ  tttdƒttdƒ|tdƒ |  | ||   |  ƒttdƒ|tdƒ |  | ||   |  ƒ  |ƒ||t| ||tdƒ   ƒ ƒ|ƒS r-  r¹  rò  r  r  r  r¹  ê
  s   þ, r¹  c                 C   sH  t | t| |||tdƒ    || ||tdƒ     ƒ t|||tdƒ   ƒ |t| |||tdƒ    || ||tdƒ     ƒ t|||tdƒ   ƒ  tttdƒttdƒ|tdƒ |  | ||   |  ƒttdƒ|tdƒ |  | ||   |  ƒ | |tdƒ  tdƒ   |ƒ||t| ||tdƒ   ƒ ƒ|ƒS r-  r¹  rò  r  r  r  rº  î
  rÃ  rº  c                 C   s"  t t| |||tdƒ    || ||tdƒ     ƒt|||tdƒ   ƒ | t| |||tdƒ    || ||tdƒ     ƒ t|||tdƒ   ƒ  ttttdƒ|tdƒ |  | ||   |  ƒttdƒ|tdƒ |  | ||   |  ƒ |ƒ||t| ||tdƒ   ƒ ƒ|ƒS r-  r¹  rò  r  r  r  r»  ò
  s   þ$ r»  c                 C   sì  t || | ||   tdƒ|  tt| ||tdƒ   ƒ|||tdƒ   tdƒd  t|||tdƒ   ƒ  |ƒ|ƒ t |  | | || |  || |  tdƒ| |  tt|||tdƒ   ƒt| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ t || | | ||   tdƒ| |  ttdƒt| ||tdƒ   ƒt|||tdƒ   ƒ t|||tdƒ   ƒ  |ƒ|ƒ t|| t| ||tdƒ   ƒ t|||tdƒ   ƒ tdƒ| t|||tdƒ   ƒ  |ƒ S ©NrD  rI  rC  r‘  rò  r  r  r  r¼  ö
  s   þî r¼  c                 C   sþ  t |  | | || |  || |  tdƒ|tdƒ   tt|||tdƒ   ƒt| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒ t ||  | ||   tdƒ|  tt|||tdƒ   ƒt| ||tdƒ   ƒ|||tdƒ   tdƒd    |ƒ|ƒ t |  | ||  tdƒ | | ||   tdƒ|tdƒ   ttdƒt| ||tdƒ   ƒt|||tdƒ   ƒ t|||tdƒ   ƒ  |ƒ|ƒ t|t| ||tdƒ   ƒ t|||tdƒ   ƒ tdƒt|||tdƒ   ƒ  |ƒ S rø  r‘  rò  r  r  r  r½  ú
  s   þþ  r½  c                 C   sÊ   t || tt|||tdƒ   ƒt| ||tdƒ   ƒt|||tdƒ   ƒ  |ƒ|ƒt |  | ||  | tt|||tdƒ   ƒt| ||tdƒ   ƒ|||tdƒ   tdƒd    |ƒ|ƒ S rê  rÆ  rò  r  r  r  r¾  þ
  r}  r¾  c                 C   sh   t |
ttttfƒrdS t| ||
|   | |||
|   |  |||
|   |	  |
ƒ}t|ƒr2dS dS )NFT)r8  r9  ræ  r:  rä  rË   r)   ©rN  rB  rQ  rT  rV  rX  rP  rO  rU  rY  rÿ  rW  r  r  r  r¿    s   Br¿  c                 C   sL   t | ||
|   | |||
|   |  |||
|   |	  |
ƒ}t||
ƒS rý  )rË   r   rù  r  r  r  rÀ    s   B
rÀ  c                 C   sf   t t| ||
|    | |||
|    |  |||
|    |	  |
tdƒ  |
ƒ|
tdƒ|
 ƒ S r-  rN  rð  r  r  r  rÁ    rì  rÁ  c                 C   sB   t | ||
|   | |||
|   |  |||
|   |	  |
ƒS rý  r  rð  r  r  r  rÂ    r±  rÂ  c              	   C   sf   t tdƒt|
|tdƒƒ tt| |||   | ||||   |  ||||   |	  |ƒ||
ƒ|ƒS r  rS  )rN  rB  rQ  rT  rV  rX  rP  rO  rU  rY  rW  r'  Úwrÿ  r  r  r  rÄ    rì  rÄ  c                 C   sP   t || |	  | |||   |  ||||   |
  |||  | |	  |ƒS rý  r  ©rN  rB  rQ  rT  rV  rX  r0  rP  rO  rU  rY  rÿ  r  r  r  rÅ    r!  rÅ  c                 C   sX   t ||||
   ||||    |	  | ||   | |  |||   | |
  |ƒS rý  r  rû  r  r  r  rÆ  !  rÅ  rÆ  c                 C   s˜   t ||t|	ƒ  ||||    t|	ƒ  |||  | t|	ƒ   t|| |	  | |||   |  ||||   |
  |||  | |	  |ƒ|ƒS rý  rÊ  rû  r  r  r  rÇ  %  rt  rÇ  c                 C   sJ   t | |||   |
 ||||   |  || || ||   |  |ƒS rý  r  ©rN  rB  rQ  rT  r"  r#  r$  r%  rP  r!  rO  rU  rY  rÿ  r  r  r  rÊ  )  r$  rÊ  c                 C   s°   t ||||tdƒ    t|ƒ ||||tdƒ    t|ƒ  || || ||   t|ƒ   t| |||   |
 ||||   |  || || ||   |  |ƒ|ƒS r  rï  rü  r  r  r  rË  -  rj  rË  c              	   C   s‚   t | tdƒ|tdƒ |   ||  | tt| | |tdƒ |tdƒ |   |||  |	  |||  |
  |ƒ||| ƒ|ƒS r  rM  ©rB  rQ  rT  rV  rX  rZ  rR  rP  rO  rU  rY  rÿ  r  r  r  rÌ  1  r  rÌ  c                 C   s|   t | t|ƒ ||  || t|ƒ   | ||  t|ƒ  t||||   ||||   |	  ||||   |
  |ƒ|ƒS rý  rþ  rý  r  r  r  rÍ  5  s   |rÍ  c                 C   st   t |t|ƒ |t|ƒ   || t|ƒ  t|| | ||  |  ||||   |	  ||||   |
  |ƒ|ƒS rý  rþ  rý  r  r  r  rÏ  9  rI  rÏ  c                 C   sT   t t|| | | |||   |	  ||||   |
  ||||   |  |ƒ|ƒS rý  r  ©rN  rB  rQ  rT  rV  rX  rZ  rR  rP  rO  rU  rY  rÿ  r  r  r  rÐ  =  r7  rÐ  c                 C   sR   t tdƒ| tt| ||  | |||  |	  |||  |
  |ƒ||| ƒ|ƒS r  rM  ©rN  rB  rQ  rT  rV  rX  rR  rP  rO  rU  rY  rÿ  r  r  r  rÑ  A  r¥  rÑ  c                 C   s`   t |||||	 |
    | ||   | |  |||   | |	  |||   | |
  |ƒS rý  r  rÿ  r  r  r  rÒ  E  rD  rÒ  c              	   C   sn   t tdƒ| tt|tdƒ|tdƒ |   | ||  |  |||  |	  |||  |
  |ƒ||| ƒ|ƒS r  rM  rÿ  r  r  r  rÓ  I  rŽ  rÓ  c                 C   óx   t |t|ƒ |t|ƒ   || t|ƒ  t|| | |||   |	  ||||   |
  ||||   |  |ƒ|ƒS rý  rþ  rþ  r  r  r  rÔ  M  rJ  rÔ  c                 C   s>   t |ttttfƒrdS t|tdƒ |ƒ}t|tdƒƒrdS dS rm  rn  ©rN  rB  rQ  rT  rV  rX  rR  rP  rO  rU  rY  rÿ  r  r  r  r  rÕ  Q  rp  rÕ  c              
   C   s˜   t |tdƒ |ƒ}ttdƒ| tt|tdƒ|tdƒ |   | ||||    |  |||||    |	  |||||    |
  |ƒ||| ƒ|ƒS r  rq  r	  r  r  r  rÖ  Z  s   †rÖ  c              
   C   s´   t |ƒ}t|| tt|||tdƒ  tdƒ  | |||   |||    |	  ||||   |||    |
  ||||   |||    |  |ƒ||| tdƒ|  ƒ|ƒS r  rP  ©rN  rB  rQ  rT  rV  rX  rZ  rR  rP  rO  rU  rY  rÿ  r  r  r  r  r×  `  r§  r×  c                 C   óp  t tdƒ| | | |	tdƒ   t|| | | |||   |	tdƒ   ||||   |
tdƒ   t||| | |	tdƒ  |tdƒ |  | ||     |||  || | |	tdƒ  |  | ||  |||
  tdƒ     |ƒ |ƒ|ƒt|| |tdƒ  | |||   |	tdƒ   ||||   |
  |  | ||   | | | | |	tdƒ   |ƒ S r  r  ©rN  rB  rQ  rT  rV  rX  rZ  rR  rP  rO  rU  rÿ  r  r  r  rØ  e  ó   þr rØ  c                 C   sœ  t || || |	tdƒ  |  | ||    t|| ||  | |||   |	tdƒ   ||||   |
  t||  | ||   || tdƒ  || | | |	tdƒ  || ||   ||  | ||   |||
  tdƒ     |ƒ |ƒ|ƒ t||tdƒ  || || tdƒ   | |||   |	tdƒ   ||||   |
tdƒ   |  | ||   || |	tdƒ  |  | ||    |ƒ S r  r  r	  r  r  r  rÙ  i  s   þž rÙ  c                 C   óŽ  t tdƒ| | |	tdƒ  |  | ||    t|| | | |||   |	tdƒ   ||||   |
  t||tdƒ  |  | ||   |||  |  | ||   |||	|
 tdƒ   tdƒ   || |	tdƒ  |  | ||    |ƒ |ƒ|ƒt|| |tdƒ  | |||   |	tdƒ   ||||   |
tdƒ   |  | ||   | | | |	tdƒ  |  | ||    |ƒ S r2  r  r	  r  r  r  rÚ  m  rÜ  rÚ  c                 C   s^  t ||  | |tdƒ   t|| ||  | |||   |	  ||||   |
tdƒ   t||tdƒ  |  | ||   |||  || | |	|
 tdƒ  |tdƒ |  | ||      || | | |
 || |	tdƒ     |ƒ |ƒ|ƒ t||| |tdƒ   | |||   |	tdƒ   ||||   |
  | | |tdƒ   |ƒ S r  r  r	  r  r  r  rÛ  q  rô  rÛ  c                 C   ó”  t tdƒ||||	|
 tdƒ   tdƒ   t|| | | |||   |	  ||||   |
tdƒ   t||| | |	|
 tdƒ  |tdƒ |  | ||     || || | | |	|
 tdƒ  ||tdƒ  |  | ||    || |
 |  | ||      |ƒ |ƒ|ƒt||| |tdƒ   | |||   |	tdƒ   ||||   |
  || |||	|
 tdƒ   tdƒ   |ƒ S r  r  r	  r  r  r  rÜ  u  ó   þ– rÜ  c                 C   s˜  t || || |||	|
 tdƒ   tdƒ   t|| ||  | |||   |	  ||||   |
  t| | | || tdƒ  || | | | |||
  tdƒ  ||| |||	  tdƒ  || |||	|
 tdƒ   tdƒ       |ƒ |ƒ|ƒ t|||tdƒ   || || tdƒ   | |||   |	tdƒ   ||||   |
tdƒ   || |||	|
 tdƒ   tdƒ   |ƒ S r  r  r	  r  r  r  rÝ  y  s   þš rÝ  c                 C   sd  t ||  | | |tdƒ   t|| ||  | |||   |	  ||||   |
  t| | | |tdƒ  || | ||  |||	|
 tdƒ   tdƒ   || | | |
 || |	    || | ||   || tdƒ   |ƒ |ƒ|ƒt||| |tdƒ   | |||   |	tdƒ   ||||   |
tdƒ   | | | |tdƒ   |ƒ S r2  r  r	  r  r  r  rÞ  }  s   þf rÞ  c                 C   óL   t t||
 | | ||
|   |	  |||
|    |||
|    |
ƒ|
ƒS rý  r  ©rN  rB  rQ  rT  rV  rX  rZ  rR  rP  rO  rÿ  r  r  r  rß    r%  rß  c              	   C   s’   t |t|| | | |||   |	  ||||   |
  |ƒ|ƒt ||  | t|| ||  | |||   |	  ||||   |
  |ƒ|ƒ S rý  rá  r	  r  r  r  rà  …  r  rà  c              	   C   sÊ   t |t|| | | |||   |	  ||||   |
  ||||   |tdƒ   |ƒ|ƒt ||  | t|| ||  | |||   |	  ||||   |
  ||||   |tdƒ   |ƒ|ƒ S )NrK  r¶  rþ  r  r  r  rá  ‰  r}  rá  c                 C   sl   t t|| tdƒ  | |||    |  ||||    |	  ||||    |
  |ƒ|tdƒ| ƒ S rŸ  rN  rÿ  r  r  r  râ    rR  râ  c              
   C   sÀ   t |ƒ}t|| tt|| |tdƒ  tdƒ  | |||   || |    |	  ||||   || |    |
  ||||   || |    |  |ƒ||| tdƒ |  ƒ|ƒ S r  rP  r	  r  r  r  rã  ‘  s   ¸rã  c              	   C   sŒ   t || | tdƒ| |  tt|| tdƒ  | |||    |	  ||||    |
  ||||    |  |ƒ|tdƒ| ƒ|ƒ S r£  rM  rþ  r  r  r  rä  –  r  rä  c              
   C   sŽ   t |ƒ}t|tt|||tdƒ  tdƒ  | ||||    |  |||||    |	  |||||    |
  |ƒ||tdƒ|  ƒ|ƒS r  rP  r	  r  r  r  rå  š  s   †rå  c                 C   r 	  rý  rþ  rþ  r  r  r  ræ  Ÿ  rJ  ræ  c                 C   s’   t tdƒ|tdƒ  tt| ||||tdƒ     | |||||tdƒ     |	  |||||tdƒ     |
  |ƒ|||tdƒ  ƒ|ƒS r  rM  rÿ  r  r  r  rç  £  r  rç  c                 C   r 	  rý  rþ  rþ  r  r  r  rè  §  rJ  rè  c                 C   r	  r  r  r	  r  r  r  ré  «  r	  ré  c                 C   r	  r2  r  r	  r  r  r  rê  ¯  rÜ  rê  c                 C   r	  r  r  r	  r  r  r  rë  ³  r	  rë  c                 C   r		  rý  r  r
	  r  r  r  rì  ·  r%  rì  c              	   C   sš   t |t|| | | |||   |	  ||||   |
  |ƒ|ƒt |||   || |  t|||  | |||   |	  ||||   |
  |ƒ|ƒ S rý  rá  r	  r  r  r  rí  »  rK  rí  c                 C   sR   t ||||
   | |||   |	  ||||   |  |||  | |
  |ƒS rý  r  ©rN  rB  rQ  rT  rV  rX  rR  r0  rP  rO  rU  rY  rÿ  r  r  r  rî  ¿  r¥  rî  c                 C   s\   t ||||	|    ||||    |
  | ||   | |	  |||   | |  |ƒS rý  r  r	  r  r  r  rï  Ã  r  rï  c                 C   sš   t ||t|
ƒ  ||||    t|
ƒ  |||  | t|
ƒ   t||||
   | |||   |	  ||||   |  |||  | |
  |ƒ|ƒS rý  rÊ  r	  r  r  r  rð  Ç  rK  rð  c                 C   sz   t |t|ƒ |t|ƒ   || t|ƒ  t|| | |||	   |
  ||||	    |  ||||	   |  |ƒ|ƒS rý  rþ  )rN  rB  rQ  rT  rV  rX  rZ  rR  r0  rP  rO  rU  rY  rÿ  r  r  r  rñ  Ë  rE  rñ  c                 C   sN   t || | | |||   |	  ||||   |
  ||||   |  |ƒS rý  r  rþ  r  r  r  rò  Ï  rb  rò  c              	   C   sx   t || ||   t||tdƒƒ tt|| | |||   |  ||||   |	  ||||   |
  |ƒ||ƒ|ƒS r  r¬  )rN  rB  rQ  rT  rV  rX  rR  rP  rO  rU  rY  rW  r'  rÿ  r  r  r  ró  Ó  rJ  ró  c                 C   sV   t || |	 | |||
   |  ||||
   |  || || ||
   |  |ƒS rý  r  ©rN  rB  rQ  rT  r"  r#  r$  r%  rZ  rR  rP  r!  rO  rU  rY  rÿ  r  r  r  rô  ×  r¡  rô  c                 C   s¼   t ||||
tdƒ    t|ƒ ||||
tdƒ    t|ƒ  || || ||
   t|ƒ   t|| |	 | |||
   |  ||||
   |  || || ||
   |  |ƒ|ƒS r  rï  r	  r  r  r  rõ  Û  rW  rõ  (ô  Ú__doc__Úsympy.externalr   r   r   r   r   r   Ú%sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   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‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r   rŽ   r   r   r‘   r’   r“   r”   r•   r–   r—   r˜   r™   rš   r›   rœ   r   rž   rŸ   r    r¡   r¢   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   r³   r´   rµ   r¶   r·   r¸   r¹   rº   r»   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rØ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   ré   rê   rë   rì   rí   rî   rï   rð   rñ   rò   ró   rô   rõ   rö   r÷   rø   rù   rú   rû   rü   rý   rþ   rÿ   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r  rŽ  r  r  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  ÚexprÜ  rè  rÝ  rÞ  rß  Úsympy.core.addrà  Úsympy.core.modrá  Úsympy.core.mulrâ  Ú
sympy.corerã  Úsympy.core.numbersrä  rå  ræ  Úsympy.core.powerrç  Úsympy.core.singletonrè  Ú$sympy.functions.elementary.complexesré  rê  Ú(sympy.functions.elementary.miscellaneousrë  Úsympy.integrals.integralsrì  Úsympy.logic.boolalgrí  rî  Úsympy.simplify.simplifyrï  Úsympy.integrals.rubi.symbolrñ  Úsympy.core.symbolrò  ró  Úsympy.functionsrô  rõ  rö  r÷  rø  rù  rú  Ú%sympy.functions.elementary.hyperbolicrû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  Ú(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r  ÚA_ÚB_ÚC_ÚF_ÚG_ÚH_r`  Úb_r¥  Úd_rK  Úf_rÎ  Úh_Úi_Új_Úk_Úl_r¦  r]  r^  r  r°  Út_r˜  r  Ús_rÃ  r\  Úy_Úz_r›  rœ  Úb1_Úb2_Úc1_Úc2_Úd1_Úd2_Ún1_Ún2_rÈ  rÉ  Úf1_Úf2_Úg1_Úg2_Ún3_ÚPq_ÚPm_ÚPx_ÚQm_ÚQr_ÚQx_Újn_Úmn_Únon2_ÚRFx_ÚRGx_r  ÚiiÚPqqÚQÚRrY  ÚCr  rW  Ú	_UseGammaÚ	ShowStepsÚStepCounterrü  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‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r  rŽ  r  r  r‘  r’  r“  r”  r•  r–  r—  r™  rš  r  rž  rŸ  r   r¡  r¢  r£  r¤  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  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  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‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r  rŽ  r  r  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÄ  rÅ  rÆ  rÇ  rÊ  rË  rÌ  rÍ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  r  r  r  r  Ú<module>   sx   þþ þ þ þ þ þ þ þ þ þ  n"JjBŠ†.
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