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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)Add)Mod)Mul)
EulerGamma)FloatIInteger)Pow)S)Abssign)sqrt)Integral)AndOr)simplifyWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  T/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rules/trinomial_products.py
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}xt|xtE}yttttdtd tdtd ttt tdtd  ttdtd tdtd   t||||4|2|,||>	}zt|ztF}{ttttd	 ttttd tdtd  ttd	 tdtd   t||||$|%}|t||tG}}ttttd	 ttttd tdtd  ttd	 tdtd   t||||$|&|'}~t|~tH}ttttd	 ttttd tdtd  ttd	 tdtd   t||||$|(|)}t|tI}ttttd	 ttttd tdtd  ttd	 tdtd   t||||$ttJ}t|tK}ttttd	 ttttd tdtd  ttd	 tdtd   t||||$ttL}t|tM}ttttd	 ttttd tdtd  ttd	 tdtd   t||||$ttN}t|tO}ttttd	 ttttd tdtd  ttd	 tdtd   t||||$ttP}t|tQ}ttttd	 ttttd tdtd  ttd	 tdtd   t|||||*}t|tR}ttttd	 ttttd tdtd  ttd	 tdtd   t|||||+}t|tS}ttttdtd ttt tdtd  ttdtd tdtd  t  t|||||,|||A	}t|tT}ttttdtd tdtd ttt tdtd  ttdtd tdtd  t  t||||4||,|||M
}t|tU}ttttdtd t. ttt tdtd  ttdtd tdtd  t  t||||4|2||,|||N}t|tV}ttttdtd ttt tdtd  ttdtd tdtd  t  t||||2||,||	}t|tW}ttt2t t. ttt tdtd  ttdtd tdtd  t  t||||4|2||,||
}t|tX}ttttdtd ttt tdtd  ttdtd tdtd  t  t||||2|||,||Z|[}t|tY}ttt2t t. ttt tdtd  ttdtd tdtd  t  t||||4|2|||,||Z|[}t|tZ}ttttdtd tdtd ttt tdtd  ttdtd tdtd   t||||4|2||,|	}t|t[}ttttdtd tdtd ttt tdtd  ttdtd tdtd  t  t||||4|2||,||\
}t|t\}ttttdtd tdtd ttt tdtd  ttdtd tdtd  t  t||||4|2|||,	}t|t]}ttttdtd ttt tdtd  ttd
td tdtd  tdtd  t||||2||-||.	}t|t^}ttttdtd ttt tdtd  ttd
td tdtd  tdtd  t||||2|||-|
|.
}t|t_}ttt2t tdtd ttt tdtd  ttd
td tdtd  tdtd  t||||4|2|||-	}t|t`}ttttdtd tat tdtd tatdtd tdtd  tdtd tdtd  t||||||,|]|A|^
}t|tb}ttttdtd tat tdtd tatdtd tdtd  tdtd tdtd  t||||2|||,|_	}t|tc}ttt2tt tdtd  tdtd ttt tdtd  ttdtd tdtd  tdtd  t||||4|a|| |`|6
}t|td}tttttdtd tdtd  tdtd t2tt tdtd  tdtd  t|||4|a|| |`|6	}t|te}ttt2tt tdtd  tdtd tt tdtd tt tdtd  tdtd t  t||||4|a||b| |
}t|tf}ttttt tdtd  t t2tt tdtd  tdtd  t|||4|a||b| |	}t|tg}ttt2tt tdtd  tdtd tt tdtd ttdtd tdtd  tdtd tdtd  t||||4|a||b| |
}t|th}tttttdtd tdtd  tdtd t2tt tdtd  tdtd  t|||4|a||b| |	}t|ti}ttt2tt tdtd  tt tdtd tt tdtd  t  t|||4|a||| |
|
}t|tj}ttt2tt tdtd  tt tdtd tt tdtd  t  t|||4|a||| |
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}t|tm}ttt2tt tdtd  tdtd ttt tdtd  tt tdtd  t  t||||4|a|||b| |	|
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}t|Đtp}ttt2tt tdtd  tq ttt tdtd  tt tdtd  t  t||||4|a|||b| ||e|
}t|Ɛtr}ttttt tdtd  t t2tt tdtd  tq  t|||4|a|||b| |f|
}t|Ȑts}ttt2tt tdtd  tdtd ttt tdtd  tt tdtd   t||||4|a|| ||g|h}t|ʐtt}ttttt tdtd  t2tt tdtd  tdtd  t|||4|a|| |i|h	}t|̐tu}ttt2tt tdtd  tq ttt tdtd  tt tdtd   t||||4|a|| ||g|j|k}t|ΐtv}ttttt tdtd  t2tt tdtd  tq  t|||4|a|| |i|j|k
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}t|t}ttt2tt tdtd  ttt tdtd  tt tdtd  t  t||||4|a|| ||x|||y| |!}t|t}ttttt tdtd  t t2tt tdtd   t|||4|a|| |x|||y| |!}t|t}ttt2tt tdtd  ttt tdtd  tt tdtd  t  t||||4|a|| |||| |!}t|t}ttttt tdtd  t t2tt tdtd   t|||4|a|| ||| |!} t| t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$|%}t|t}ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|z|%}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$|&|'tt
}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$|&|'tt
}t|t}	ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$|(|)tt
}
t|
t}ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|(|)tt}t|t}ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|(|)tt}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$|(|)tt
}t|t}ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|(|)tt}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$tt}t|t}ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|{}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$tt}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$tt}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$tt}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a|$tt}t|t}ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a||*tt	} t| t}!ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|*tt}"t|"t}#ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a||*tt	}$t|$t}%ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|*tt}&t|&t}'ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|+|f|z}(t|(t})ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|+|f||}*t|*t}+ttt2ttd	 tdtd  ttttd tdtd   t|||4|a|+|i},t|,t}-ttt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd   t||||4|a||+}.t|.t}/ttt2tt tdtd  ttt tdtd  tt tdtd  t  t||||4|a|| |	}0t|0t}1ttttt tdtd  t t2tt tdtd   t|||4|a|| }2t|2t}3ttt2tt tdtd  tq ttt tdtd  tt tdtd  t  t||||4|a||b| |||}|>|~}4t|4t}5ttttt tdtd  t t2tt tdtd  tq  t|||4|a||b| ||}|>|~}6t|6t}7ttttttd tdtd  ttd	 tdtd  t2ttd	 tdtd   t||||4|a||g}8t|8t}9ttttttd tdtd  t2ttd	 tdtd   t|||4|a|i}:t|:t};tttttd tdtd  ttd	 tdtd  tdd	  t2ttd	 tdtd   t||||4|a||g|$	}<t|<t}=tttttd tdtd  tdd	  t2ttd	 tdtd   t|||4|a|i|{}>t|>t}?tttttd tdtd  ttd	 tdtd  t t2ttd	 tdtd   t||||4|a||g|	}@t|@t}Atttttd tdtd  t t2ttd	 tdtd   t|||4|a|i|}Bt|Bt}Ctttdt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a|$|%}Dt|Dt}Etttdttttd tdtd  t2ttd	 tdtd    t|||4|a|z|%}Ft|Ft}Gtttdt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a|$|}Ht|HtÃ}Itttdttttd tdtd  t2ttd	 tdtd    t|||4|a|{|}Jt|Jtă}Ktttdt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a||g|*ttŃ
}Lt|Ltƃ}Mtttdttttd tdtd  t2ttd	 tdtd    t|||4|a|i|*ttǃ}Nt|Ntȃ}Otttdttttd tdtd  t2ttd	 tdtd    t|||4|a|+|z}Pt|PtɃ}Qtttdttttd tdtd  t2ttd	 tdtd    t|||4|a|+||}Rt|Rtʃ}Stttdt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a||+}Tt|Tt˃}Utttttd tdtd  ttd	 tdtd  t t2ttd	 tdtd   t||||4|a||g|	}Vt|Vt̃}Wtttttd tdtd  t t2ttd	 tdtd   t|||4|a|i|}Xt|Xt̓}Ytttdt2ttd	 tdtd  td	 ttttd tdtd  ttd	 tdtd    t||||4|a||g}Zt|Zt΃}[tttdttttd tdtd  t2ttd	 tdtd  td	   t|||4|a|i}\t|\tσ}]ttt2ttd	 tdtd  tq tttd tdtd  ttd	 tdtd  t  t||||4|a|b||g||}^t|^tЃ}_tttttd tdtd  t t2ttd	 tdtd  tq  t|||4|a|b|i||	}`t|`tу}atttdtt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a||z|	}bt|bt҃}ctttdtt2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a||}dt|dtӃ}ettttttd tdtd  ttd	 tdtd  tt2ttd	 tdtd   t||||4|a||z|	}ft|ftԃ}gttttttd tdtd  ttd	 tdtd  tt2ttd	 tdtd   t||||4|a||}ht|htՃ}ittt2tt tdtd  tq ttt tdtd  tt tdtd  t  t||||4|a|||b| ||g|}jt|jtփ}kttttt tdtd  t t2tt tdtd  tq  t|||4|a|||b| |i|}lt|lt׃}mttttt tdtd  t t2tt tdtd  tq  t|||4|a||| |i||}nt|nt؃}ottt2tt tdtd  tq ttt tdtd  tt tdtd  t  t||||4|a|||b| |}pt|ptك}qttttt tdtd  t t2tt tdtd  tq  t|||4|a|||b| |
}rt|rtڃ}sttt2tt tdtd  tdtd ttt tdtd  tt tdtd  tdtd  t||||4|a|||b| |/|0}tt|ttۃ}uttttt tdtd  tdtd t2tt tdtd  tdtd  t|||4|a|||b| |/|0}vt|vt܃}wttt2ttdtd tdtd  tdtd ttd
td tdtd ttdtd tdtd  tdtd tdtd  t||||4|a|||,|-|v}xt|xt݃}ytttttdtd tdtd  tdtd t2ttdtd tdtd  tdtd  t|||4|a||||v	}zt|ztރ}{ttt2ttdtd tdtd  tq ttd
td tdtd ttdtd tdtd  tdtd tdtd  t||||4|a||b|,|-|w|}|t||t߃}}tttttdtd tdtd  tdtd t2ttdtd tdtd  tq  t|||4|a||b||w|
}~t|~t}ttt2ttdtd tdtd  tq ttd
td tdtd ttdtd tdtd  tdtd t  t||||4|a|||b|,|-|w|
|.}t|t}tttttdtd tdtd  t t2ttdtd tdtd  tq  t|||4|a|||b||w|
|}t|t}ttt2ttdtd tdtd  tq ttd
td tdtd ttdtd tdtd  tdtd t  t||||4|a||b|,|-|w|
|6}t|t}tttttdtd tdtd  t t2ttdtd tdtd  tq  t|||4|a||b||w|
|}t|t}ttt2tt tdtd  tdtd ttt tdtd  ttd
td tdtd  tdtd  t||||4|a||b|-|
}t|t}ttt2tt tdtd  tdtd ttt tdtd  ttd
td tdtd  tdtd  t||||4|a|||b|-|
}t|t}ttt2tt tdtd  tdtd ttt tdtd  tdtd  ttt tdtd  tt tdtd  t  t||||4|a|||||b|| |	|
}t|t}ttt2tt tdtd  tdtd ttt tdtd  tdtd  ttt tdtd  tt tdtd  tdtd  t||||4|a||||b|| ||e|}t|t}ttttt tdtd  tdtd t2tt tdtd  tdtd  ttt tdtd  tdtd  t|||4|a||||b|| |f|}t|t}ttt2tt tdtd  tdtd ttt tdtd  tdtd  ttt tdtd  tt tdtd  t  t||||4|a|||||b|| ||e|
}t|t}ttttt tdtd  t t2tt tdtd  tdtd  ttt tdtd  tdtd  t|||4|a|||||b|| |f|
}t|t}ttttd	 tdtd tdtd t2ttd	 tdtd  ttttd tdtd  ttd	 tdtd    t||||4|a|||$|g|tt}t|t}tttttd	 tdtd  ttttd tdtd  t2ttd	 tdtd    t|||4|a|||{|i|tt}t|t}tttttdtd tdtd  tdtd tttdtd tdtd  tdtd  tt tdtd tt tdtd  tdtd tdtd  t||||||||||b| |||}t|t}tttttdtd tdtd  tdtd tttdtd tdtd  tdtd  tt tdtd tt tdtd  tdtd tdtd  t||||||||||b| ||}t|t}tttttdtd tdtd  t2tt tdtd  tdtd  ttt tdtd  tt tdtd  tdtd  t||||4|a|||2|||b| |1}t|t}tttttdtd tdtd  ttt tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a|||2|||b| |1}t|t}ttttdtd tdtd tt tdtd tq  ttt tdtd  ttdtd tdtd  tdtd  t||||a||2|||b| ||O}t|t}ttttdtd tdtd tt tdtd tq  tttdtd tdtd  tdtd  t|||a||2|||b| ||O}t|t}ttttdtd tdtd tt tdtd tq  ttt tdtd  ttdtd tdtd  tdtd  t||||a||2|||b| ||3}t|t}ttttdtd tdtd tt tdtd tq  tttdtd tdtd  tdtd  t|||a||2|||b| ||3}t|t}tttt tdtd tt tdtd tq  ttt tdtd  ttdtd tdtd  tdtd  t||||a||2|||b| |}t|t}tttt tdtd tt tdtd tq  tttdtd tdtd  tdtd  t|||a||2|||b| |}t|t}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a|2|||b| |1}t|t}ttttdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a|2|||b| |1}t|t}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a|2|| |`|6}t|t }ttttdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a|2|| |`|6
}t|t}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||b| |	|
|}t|t}ttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||2|||b| |	|
}t|t}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a|2|||b| |O}t|t}ttttdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a|2|||b| |O}t|t}tttt tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a||2|||b| |O}t|t}tttt tdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||2|||b| |O}t|t}ttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  tt tdtd  tdtd  t||||4|a||2||b| ||e|}t|t}ttttdtd tdtd ttt tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||b|2||b| |f|}t|Đt	}ttttdtd tdtd t2tt tdtd  tq  ttt tdtd  tt tdtd  t  t||||4|a||2|||b| ||e|
}t|Ɛt
}ttttdtd tdtd ttt tdtd  t  t2tt tdtd  tq  t|||4|a||2|||b| |f|
}t|Ȑt}ttttdtd t2tt tdtd  tq  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a| ||||k|}t|ʐt}ttttdtd tttdtd tdtd  tdtd  t2tt tdtd  tq  t|||4|a| |||k|
}t|̐t}tttt. t2tt tdtd  tq  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a| ||||k|}t|ΐt}tttt. tttdtd tdtd  tdtd  t2tt tdtd  tq  t|||4|a| |||k|
}t|Аt}ttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a||2|b| ||||w|}t|Ґt}ttttdtd tdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||2|b| |||w|}t|Ԑt}ttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a||2|b| |}t|֐t}ttttdtd tdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||2|b| | |}t|ؐt}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||b| ||>|Att}t|ڐt}ttttdtd tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a||b| |>|Att}t|ܐt}ttttdtd t. t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a|||b| ||>|M|}t|ސt}ttttdtd t. tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a|||b| |>|M|}t|t}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  tdtd  t||||4|a|| ||>|?||L||R}t|t}ttttdtd tdtd ttt tdtd  tdtd  t2tt tdtd   t|||4|a|| |>|?||L||R}t|t}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  tdtd  t||||4|a||2| ||>|||D||R}t|t}ttttdtd tdtd ttt tdtd  tdtd  t2tt tdtd   t|||4|a||2| |>|||D||R}t|t}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  tdtd  t||||4|a|| ||>|?||J|R}t|t}ttttdtd tdtd ttt tdtd  tdtd  t2tt tdtd   t|||4|a|| |>|?||J|R}t|t}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  t  t||||4|a||2| ||>|||R}t|t }ttttdtd tdtd ttt tdtd  t  t2tt tdtd   t|||4|a||2| |>|||R}t|t!}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  t  t||||4|a||| ||>|I|J||R}t|t"}ttttdtd tdtd ttt tdtd  t  t2tt tdtd   t|||4|a||| |>|I|J||R}t|t#}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  t  t||||4|a||| ||>|I|L|R}t|t$}ttttdtd tdtd ttt tdtd  t  t2tt tdtd   t|||4|a||| |>|I|L|R}t|t%}ttttdtd t. t2tt tdtd   ttt tdtd  tt tdtd   t||||4|a|| |T|||Utt&}t|t'}ttttdtd t. t2tt tdtd   ttt tdtd   t|||4|a|| |||tt(}t|t)}ttttdtd tdtd t2ttd	 tdtd   tttd tdtd  ttd	 tdtd   t||||4|a||2||l||}t|t*}ttttdtd tdtd t2ttd	 tdtd   tttd tdtd   t|||4|a||2|l|	} t| t+}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd   t||||4|a||2| |T|||Utt,}t|t-}ttttdtd tdtd t2tt tdtd   ttt tdtd   t|||4|a||2| |||tt.}t|t/}ttttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd   t||||4|a||2| ||>}t|t0}ttttdtd tdtd t2tt tdtd   ttt tdtd   t|||4|a||2| |>	}t|t1}	ttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd   t||||4|a||2| ||>|v|A}
t|
t2}ttttdtd tdtd t2tt tdtd  tdtd  tttdtd tdtd   t|||4|a||2| |>|v|A}t|t3}ttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd   t||||4|a||2| ||>|v|}t|t4}ttttdtd tdtd t2tt tdtd  tdtd  tttdtd tdtd   t|||4|a||2| |>|v|}t|t5}ttttdtd tdtd tt tdtd tdtd tq  ttt tdtd  ttdtd tdtd   t||||4|a|| ||>|w|||H}t|t6}ttttdtd tdtd tt tdtd tdtd tq  tttdtd tdtd   t|||4|a||b| |>|w|I|H}t|t7}ttttdtd tdtd tt tdtd tdtd tq  ttt tdtd  ttdtd tdtd   t||||4|a|| ||>|w|||G}t|t8}ttttdtd tdtd tt tdtd tdtd tq  tttdtd tdtd   t|||4|a|| |>|w|||G}t|t9}ttttdtd t. tt tdtd tdtd tq  ttt tdtd  ttdtd tdtd   t||||4|a|| ||>|w|||}t|t:}ttttdtd t. tt tdtd tdtd tq  tttdtd tdtd   t|||4|a|| |>|w|||}t|t;}ttttdtd tdtd tt tdtd tdtd tq  ttt tdtd  ttdtd tdtd   t||||4|a|| ||>|w||k|H}t|t<}ttttdtd tdtd tt tdtd tdtd tq  tttdtd tdtd   t|||4|a|| |>|w||k|H} t| t=}!ttttdtd tdtd tt tdtd tdtd tq  ttt tdtd  ttdtd tdtd   t||||4|a|| ||>|w||k|G}"t|"t>}#ttttdtd tdtd tt tdtd tdtd tq  tttdtd tdtd   t|||4|a|| |>|w||k|G}$t|$t?}%ttttdtd tdtd t2tt tdtd  tq  ttt tdtd  tt tdtd   t||||4|a||2| ||>|w|j|k}&t|&t@}'ttttdtd tdtd t2tt tdtd  tq  ttt tdtd   t|||4|a||2| |>|w|j|k}(t|(tA})ttttdtd tdtd t2tt tdtd  tq  ttt tdtd  ttdtd tdtd   t||||4|a||b|| ||>|w|A}*t|*tB}+ttttdtd tdtd t2tt tdtd  tq  tttdtd tdtd   t|||4|a||b|| |>|w|A},t|,tC}-ttttdtd tdtd t2tt tdtd  tq  ttt tdtd  ttdtd tdtd   t||||4|a||2|b|| ||>|w|}.t|.tD}/ttttdtd tdtd t2tt tdtd  tq  tttdtd tdtd   t|||4|a||2|b|| |>|w|}0t|0tE}1ttttdtd t. tt tdtd ttdtd tdtd  tdtd tdtd  tt tdtd tdtd  t||||4|a|| ||>|?||}2t|2tF}3ttttdtd t. tttdtd tdtd  tdtd  tt tdtd tdtd  t|||4|a|| |>|?||}4t|4tG}5ttttdtd t. tt tdtd ttdtd tdtd  tdtd tdtd  tt tdtd tdtd  t||||4|a|| ||>|?||}6t|6tH}7ttttdtd t. tttdtd tdtd  tdtd  tt tdtd tdtd  t|||4|a|| |>|?||}8t|8tI}9ttttdtd tdtd tt tdtd ttdtd tdtd  tdtd t  tt tdtd tdtd  t||||4|a|| ||>|?||}:t|:tJ};ttttdtd tdtd tttdtd tdtd  t  tt tdtd tdtd  t|||4|a|| |>|?||}<t|<tK}=ttttdtd tdtd tt tdtd ttdtd tdtd  tdtd t  tt tdtd tdtd  t||||4|a|| ||>|?||}>t|>tL}?ttttdtd tdtd tttdtd tdtd  t  tt tdtd tdtd  t|||4|a|| |>|?||}@t|@tM}Attttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a||2|b| ||>|}Bt|BtN}Cttttdtd tdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||2|b| |>|}Dt|DtO}Ettttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||b| |||A}Ft|FtP}Gttttdtd tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a||b| ||A
}Ht|HtQ}Ittttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a|||b| |||M}Jt|JtR}Kttttdtd tdtd tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a|||b| ||M}Lt|LtS}Mttttdtd t. t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||2||b| |||N}Nt|NtT}Ottttdtd t. tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a||2||b| ||N}Pt|PtU}Qttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a|2||b| ||}Rt|RtV}Sttttdtd tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a|2||b| |
}Tt|TtW}Utttt t. t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||2||b| ||}Vt|VtX}Wtttt t. tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a||2||b| |}Xt|XtY}Yttttdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a|2|||b| ||Z|[}Zt|ZtZ}[ttttdtd tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a|2|||b| |Z|[}\t|\t[}]tttt t. t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  t  t||||4|a||2||b| ||Z|[}^t|^t\}_tttt t. tttdtd tdtd  t  t2tt tdtd  tdtd  t|||4|a||2||b| |Z|[}`t|`t]}attttdtd tdtd t2tt tdtd  tq  ttt tdtd  ttdtd tdtd   t||||4|a||2||b| |}bt|bt^}cttttdtd tdtd t2tt tdtd  tq  tttdtd tdtd   t|||4|a||2||b| 
}dt|dt_}ettttdtd tdtd t2tt tdtd   ttt tdtd  tt tdtd  t  t||||4|a||2|| ||\}ft|ft`}gttttdtd tdtd ttt tdtd  t  t2tt tdtd   t|||4|a||2|| |\
}ht|hta}ittttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a||2|||b| ||}jt|jtb}kttttdtd tdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||2|||b| |}lt|ltc}mttttdtd tdtd ttt tdtd  t  t2tt tdtd  tq  t|||4|a||2|||b| ||}nt|ntd}ottttdtd t. ttt tdtd  t  t2tt tdtd  tq  t|||4|a||2|||b| ||}pt|pte}qttttdtd tdtd t2tt tdtd  tdtd  ttt tdtd  ttdtd tdtd  tdtd  t||||4|a||2|||b| }rt|rtf}sttttdtd tdtd tttdtd tdtd  tdtd  t2tt tdtd  tdtd  t|||4|a||2|||b| }tt|ttg}uttttdtd t2tat tdtd  tdtd  ttat tdtd  tatdtd tdtd  tdtd  t||||4|a|2|||b| |_}vt|vth}wttttdtd ttatdtd tdtd  tdtd  t2tat tdtd  tdtd  t|||4|a|2||| |_
}xt|xti}yttttdtd t2ttdtd tdtd  tdtd  ttd
td tdtd ttdtd tdtd  tdtd tdtd  t||||4|a|2|||,|-|v}zt|ztj}{ttttdtd tttdtd tdtd  tdtd  t2ttdtd tdtd  tdtd  t|||4|a|2||||v
}|t||tk}}ttttdtd t2ttdtd tdtd  tq  ttd
td tdtd ttdtd tdtd  tdtd tdtd  t||||4|a|2||b|,|-|w|}~t|~tl}ttttdtd tttdtd tdtd  tdtd  t2ttdtd tdtd  tq  t|||4|a|2||b||w|}t|tm}ttttdtd t2ttdtd tdtd  tq  ttd
td tdtd ttdtd tdtd  tdtd t  t||||4|a|2|||b|,|-|w|
}t|tn}ttttdtd tttdtd tdtd  t  t2ttdtd tdtd  tq  t|||4|a|2|||b||w|
}t|to}tttt t. t2ttdtd tdtd  tdtd  ttd
td tdtd ttdtd tdtd  tdtd tdtd  t||||4|a||2|||b|,|-}t|tp}tttt t. tttdtd tdtd  t  t2ttdtd tdtd  tdtd  t|||4|a||2|||b|}t|tq}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttd
td tdtd  tdtd  t||||4|a|2||b|-|}t|tr}ttttdtd t2tt tdtd  tdtd  ttt tdtd  ttd
td tdtd  tdtd  t||||4|a|2|||b|-|
}t|ts}tttt tdtd t2tt tdtd  tdtd  ttt tdtd  ttd
td tdtd  tdtd  t||||4|a||2|||b|-}t|tt}ttttdtd tdtd tttdtd tdtd  tdtd  tttdtd tdtd  tdtd  tt tdtd tt tdtd  tdtd tdtd  t|||||||||||b| |||}t|tu}ttttdtd tdtd tttdtd tdtd  tdtd  tttdtd tdtd  tdtd  tt tdtd tt tdtd  tdtd tdtd  t|||||||||||b| ||}t|tv}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t|||||||}t|tw}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t|||||b|||	}t|tx}tttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t|||||b||}t|ty}tttdtttd
td tdtd ttdtd tdtd  ttdtd tdtd   t|||||b||}t|tz}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t|||||b|||
||||}t|t{}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t|||||b|||
|||}t|t|}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t||||||b|||

}t|t}}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t||||||b|}t|t~}ttttd
td tdtd ttdtd tdtd  ttdtd tdtd  t t||||||b||/|0
}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  tdtd  t||||2||||	}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  tdtd  t||||2||b|||
}t|t}ttttdtd tttd
td tdtd ttdtd tdtd  ttdtd tdtd   t||||2||b|||
}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  tdd	   t||||||||	}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  tdd	   t||||||||	}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>||}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||||Ã}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>||||Ń}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>||||}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||ǃ}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||ȃ}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||Ƀ}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||ʃ}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||̃}t|t}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||̓}t|Đt}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||ȃ}t|Ɛt}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||||
||>|||΃}t|Ȑt}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  t  t||||2|||b||
|}t|ʐt}ttttdtd ttd
td tdtd ttdtd tdtd  ttdtd tdtd  tdtd  t||||2|||b||/|0}t|̐t}tttttdtd tdtd  ttdtd tdtd ttd
td tdtd  ttdtd tdtd  tdtd  t|||||||b||||}t|ΐt}tttttdtd tdtd  tttd
td tdtd ttdtd tdtd  ttdtd tdtd   t|||||||b|||||Ӄ}t|Аt}tttttdtd tdtd  ttdtd tdtd ttd
td tdtd  ttdtd tdtd  t  t|||||||b|||
|||||ԃ}t|Ґt}tttttdtd tdtd  ttdtd tdtd ttdtd tdtd  t  t|||||b|
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}t|Ԑt}tttttdtd tdtd  ttdtd tdtd ttd
td tdtd  ttdtd tdtd  t  t|||||||b|||
|||}t|֐t}tttttdtd tdtd  ttdtd tdtd ttdtd tdtd  t  t|||||b|
||tt
}t|ؐt}tttttdtd tdtd  ttd
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td tdtd ttdtd tdtd  ttdtd tdtd  tdtd  t||||||||b|||/|0}t|ܐt}ttttdtd tttdtd tdtd   ttdtd tdtd ttd
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td tdtd  ttdtd tdtd  tdtd  t||||||||
||>|||||׃}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttdtd tdtd  tdtd  t|||||
||tt	}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttd
td tdtd  ttdtd tdtd  tdtd  t||||||||
||>|||؃}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttdtd tdtd  tdtd  t|||||
||tt	}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttd
td tdtd  ttdtd tdtd  tdtd  t||||||||
||>|||||׃}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttdtd tdtd  tdtd  t|||||
||tt	}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttd
td tdtd  ttdtd tdtd  tdtd  t||||||||
||>|||ڃ}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttdtd tdtd  tdtd  t|||||
||tt	}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttd
td tdtd  ttdtd tdtd  tdtd  t||||||||
||>||||׃}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttdtd tdtd  tdtd  t|||||
||ːtt	}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttd
td tdtd  ttdtd tdtd  tdtd  t||||||||
||>||||փ}t|t}ttttdtd tttdtd tdtd   ttdtd tdtd ttdtd tdtd  tdtd  t|||||
|tt}t|t}ttttdtd tttdtd tdtd   tttd
td tdtd ttdtd tdtd  ttdtd tdtd   t||||||2||b||||||ރ}t|t}ttttdtd tttq tdtd   ttdtd tdtd ttdtd tdtd  ttd
td tdtd  t  t||||||||2||||
|}t|t}ttttdtd tttdtd tdtd   ttd
td tdtd ttdtd tdtd  ttdtd tdtd  tdtd  t||||||2|||b|||/|0}t|t}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|{|}|||||||||||||||||||||||||||||||||||Ñ|ő|Ǒ|ɑ|ˑ|͑|ϑ|ё|ӑ|Ց|ב|ّ|ۑ|ݑ|ߑ|||||||||||||||||||||	||||||||||||!|#|%|'|)|+|-|/|1|3|5|7|9|;|=|?|A|C|E|G|I|K|M|O|Q|S|U|W|Y|[|]|_|a|c|e|g|i|k|m|o|q|s|u|w|y|{|}|||||||||||||||||||||||||||||||||||Ñ|ő|Ǒ|ɑ|ˑ|͑|ϑ|ё|ӑ|Ց|ב|ّ|ۑ|ݑ|ߑ|||||||||||||||||||||	||||||||||||!|#|%|'|)|+|-|/|1|3|5|7|9|;|=|?|A|C|E|G|I|K|M|O|Q|S|U|W|Y|[|]|_|a|c|e|g|i|k|m|o|q|s|u|w|y|{|}|||||||||||||||||||||||||||||||||||Ñ|ő|Ǒ|ɑ|ˑ|͑|ϑ|ё|ӑ|Ց|ב|ّ|ۑ|ݑ|ߑ|||||||||||||||S )Nr   )cons48cons89cons465cons40cons2cons3cons8cons491cons5cons47cons149cons666cons4cons667cons586cons668cons13cons165cons669cons316cons670cons464cons198cons671cons672cons148cons673cons674cons340cons139cons228cons130cons248cons675cons676cons415cons677cons295cons678cons679cons486cons179cons680cons681cons682cons587cons683cons70cons71cons55cons19cons503cons29cons65cons504cons684cons157cons685cons686cons227cons58cons245cons150cons246cons687cons20cons688cons689cons512cons690cons691cons692cons531cons33cons532cons693cons96cons369cons358cons502cons694cons695cons696cons697cons698cons699cons700cons701cons702cons703cons543cons25cons704cons554cons555cons556cons222cons50cons52cons705cons706cons258cons259cons281cons223cons282cons397cons398cons707cons708cons709cons710cons711cons87cons712cons713cons714cons715cons588cons388cons151cons716cons45cons717cons450cons718cons402cons719cons720cons721cons349cons566cons722cons270cons723cons724cons725cons726cons727cons728cons729cons730cons127cons210cons54cons595cons731cons732cons733cons654cons734cons656cons36cons37cons735cons21cons736cons466cons737cons170cons269cons738cons739cons740cons741cons742cons83cons436cons743cons744cons745cons746cons613cons405cons747cons748cons749cons750cons751cons752cons753cons754cons755cons756cons757cons758cons759cons760cons761cons762cons608cons763cons764cons765cons766cons767cons768cons769cons770cons771cons772cons773cons774cons775cons776cons777cons778cons779cons780cons781cons782cons783cons784cons785cons786cons787cons788cons789cons790cons791cons792cons793cons794cons795cons796cons797cons798cons799b   r!  cp      nmdaeq      r0  grfr1  r"  r#  Bjk(   sympy.integrals.rubi.constraintsr4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  a_x_n_r  r  r   replacement1079p_With1080replacement1081replacement1082replacement1083replacement1084r  n2_replacement1085replacement1086replacement1087replacement1088replacement1089replacement1090replacement1091replacement1092replacement1093With1094With1095With1096With1097r   With1098replacement1098With1099With1100replacement1100With1101replacement1101With1102replacement1102With1103replacement1103With1104With1105replacement1106mn_replacement1107replacement1108u_replacement1109replacement1110replacement1111replacement1112replacement1113replacement1114replacement1115replacement1116replacement1117replacement1118replacement1119replacement1120replacement1121replacement1122replacement1123replacement1124replacement1125replacement1126replacement1127replacement1128replacement1129replacement1130replacement1131With1132m_replacement1133replacement1134replacement1135d_replacement1136With1137replacement1137With1138replacement1139replacement1140replacement1141replacement1142replacement1143replacement1144replacement1145replacement1146replacement1147replacement1148replacement1149With1150With1151With1152With1153With1154With1155With1156With1157With1158replacement1158With1159replacement1159With1160replacement1160With1161replacement1161With1162With1163replacement1164With1165replacement1166With1167replacement1168replacement1169replacement1170With1171replacement1172replacement1173replacement1174replacement1175replacement1176v_replacement1177replacement1178replacement1179replacement1180replacement1181replacement1182With1183With1184replacement1185replacement1186replacement1187replacement1188replacement1189replacement1190replacement1191q_replacement1192replacement1193replacement1194replacement1195replacement1196replacement1197replacement1198replacement1199With1200With1201With1202With1203With1204With1205replacement1206With1207With1208With1209With1210With1211replacement1212replacement1213replacement1214replacement1215With1216With1217replacement1218replacement1219replacement1220replacement1221With1222With1223With1224replacement1224With1225replacement1225With1226replacement1226With1227replacement1227With1228replacement1228With1229replacement1229With1230replacement1230With1231replacement1231replacement1232With1233replacement1233With1234replacement1234With1235replacement1235With1236replacement1236With1237replacement1237With1238replacement1238With1239replacement1239With1240replacement1240replacement1241replacement1242With1243With1244replacement1245replacement1246replacement1247replacement1248replacement1249replacement1250With1251With1252replacement1253replacement1254With1255With1256With1257With1258With1259replacement1259With1260replacement1260With1261replacement1262With1263replacement1264replacement1265replacement1266replacement1267With1268With1269replacement1270replacement1271replacement1272replacement1273replacement1274replacement1275replacement1276replacement1277replacement1278replacement1279replacement1280replacement1281replacement1282replacement1283replacement1284replacement1285replacement1286replacement1287replacement1288replacement1289replacement1290f_replacement1291replacement1292replacement1293replacement1294replacement1295With1296replacement1296With1297replacement1297d1_d2_replacement1298replacement1299A_replacement1300replacement1301replacement1302replacement1303replacement1304replacement1305replacement1306replacement1307replacement1308replacement1309replacement1310replacement1311replacement1312replacement1313replacement1314replacement1315replacement1316replacement1317replacement1318replacement1319replacement1320replacement1321replacement1322replacement1323replacement1324replacement1325replacement1326replacement1327replacement1328replacement1329With1330replacement1330With1331replacement1331With1332With1333replacement1334replacement1335replacement1336replacement1337replacement1338replacement1339replacement1340replacement1341replacement1342replacement1343replacement1344replacement1345With1346replacement1346With1347replacement1347With1348With1349With1350replacement1350With1351replacement1351With1352With1353replacement1354replacement1355replacement1356replacement1357replacement1358replacement1359replacement1360replacement1361replacement1362replacement1363replacement1364replacement1365replacement1366replacement1367replacement1368replacement1369replacement1370replacement1371replacement1372replacement1373replacement1374replacement1375replacement1376replacement1377replacement1378replacement1379replacement1380replacement1381replacement1382replacement1383replacement1384replacement1385With1386With1387replacement1388replacement1389With1390With1391replacement1392replacement1393replacement1394replacement1395replacement1396replacement1397With1398With1399replacement1400replacement1401replacement1402replacement1403replacement1404replacement1405replacement1406replacement1407replacement1408replacement1409replacement1410replacement1411replacement1412replacement1413replacement1414replacement1415replacement1416replacement1417replacement1418replacement1419replacement1420replacement1421replacement1422replacement1423replacement1424replacement1425replacement1426replacement1427replacement1428replacement1429replacement1430replacement1431replacement1432replacement1433replacement1434replacement1435replacement1436replacement1437replacement1438replacement1439replacement1440replacement1441replacement1442replacement1443replacement1444replacement1445replacement1446replacement1447replacement1448replacement1449replacement1450replacement1451replacement1452replacement1453replacement1454With1455replacement1455replacement1456With1457replacement1457replacement1458replacement1459replacement1460replacement1461With1462replacement1462replacement1463With1464replacement1464replacement1465With1466replacement1466replacement1467With1468replacement1468replacement1469With1470replacement1470replacement1471With1472replacement1472replacement1473replacement1474replacement1475(  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  pattern1079rule1079pattern1080rule1080pattern1081rule1081pattern1082rule1082pattern1083rule1083pattern1084rule1084pattern1085rule1085pattern1086rule1086pattern1087rule1087pattern1088rule1088pattern1089rule1089pattern1090rule1090pattern1091rule1091pattern1092rule1092pattern1093rule1093pattern1094rule1094pattern1095rule1095pattern1096rule1096pattern1097rule1097pattern1098rule1098pattern1099rule1099pattern1100rule1100pattern1101rule1101pattern1102rule1102pattern1103rule1103pattern1104rule1104pattern1105rule1105pattern1106rule1106pattern1107rule1107pattern1108rule1108pattern1109rule1109pattern1110rule1110pattern1111rule1111pattern1112rule1112pattern1113rule1113pattern1114rule1114pattern1115rule1115pattern1116rule1116pattern1117rule1117pattern1118rule1118pattern1119rule1119pattern1120rule1120pattern1121rule1121pattern1122rule1122pattern1123rule1123pattern1124rule1124pattern1125rule1125pattern1126rule1126pattern1127rule1127pattern1128rule1128pattern1129rule1129pattern1130rule1130pattern1131rule1131pattern1132rule1132pattern1133rule1133pattern1134rule1134pattern1135rule1135pattern1136rule1136pattern1137rule1137pattern1138rule1138pattern1139rule1139pattern1140rule1140pattern1141rule1141pattern1142rule1142pattern1143rule1143pattern1144rule1144pattern1145rule1145pattern1146rule1146pattern1147rule1147pattern1148rule1148pattern1149rule1149pattern1150rule1150pattern1151rule1151pattern1152rule1152pattern1153rule1153pattern1154rule1154pattern1155rule1155pattern1156rule1156pattern1157rule1157pattern1158rule1158pattern1159rule1159pattern1160rule1160pattern1161rule1161pattern1162rule1162pattern1163rule1163pattern1164rule1164pattern1165rule1165pattern1166rule1166pattern1167rule1167pattern1168rule1168pattern1169rule1169pattern1170rule1170pattern1171rule1171pattern1172rule1172pattern1173rule1173pattern1174rule1174pattern1175rule1175pattern1176rule1176pattern1177rule1177pattern1178rule1178pattern1179rule1179pattern1180rule1180pattern1181rule1181pattern1182rule1182pattern1183rule1183pattern1184rule1184pattern1185rule1185pattern1186rule1186pattern1187rule1187pattern1188rule1188pattern1189rule1189pattern1190rule1190pattern1191rule1191pattern1192rule1192pattern1193rule1193pattern1194rule1194pattern1195rule1195pattern1196rule1196pattern1197rule1197pattern1198rule1198pattern1199rule1199pattern1200rule1200pattern1201rule1201pattern1202rule1202pattern1203rule1203pattern1204rule1204pattern1205rule1205pattern1206rule1206pattern1207rule1207pattern1208rule1208pattern1209rule1209pattern1210rule1210pattern1211rule1211pattern1212rule1212pattern1213rule1213pattern1214rule1214pattern1215rule1215pattern1216rule1216pattern1217rule1217pattern1218rule1218pattern1219rule1219pattern1220rule1220pattern1221rule1221pattern1222rule1222pattern1223rule1223pattern1224rule1224pattern1225rule1225pattern1226rule1226pattern1227rule1227pattern1228rule1228pattern1229rule1229pattern1230rule1230pattern1231rule1231pattern1232rule1232pattern1233rule1233pattern1234rule1234pattern1235rule1235pattern1236rule1236pattern1237rule1237pattern1238rule1238pattern1239rule1239pattern1240rule1240pattern1241rule1241pattern1242rule1242pattern1243rule1243pattern1244rule1244pattern1245rule1245pattern1246rule1246pattern1247rule1247pattern1248rule1248pattern1249rule1249pattern1250rule1250pattern1251rule1251pattern1252rule1252pattern1253rule1253pattern1254rule1254pattern1255rule1255pattern1256rule1256pattern1257rule1257pattern1258rule1258pattern1259rule1259pattern1260rule1260pattern1261rule1261pattern1262rule1262pattern1263rule1263pattern1264rule1264pattern1265rule1265pattern1266rule1266pattern1267rule1267pattern1268rule1268pattern1269rule1269pattern1270rule1270pattern1271rule1271pattern1272rule1272pattern1273rule1273pattern1274rule1274pattern1275rule1275pattern1276rule1276pattern1277rule1277pattern1278rule1278pattern1279rule1279pattern1280rule1280pattern1281rule1281pattern1282rule1282pattern1283rule1283pattern1284rule1284pattern1285rule1285pattern1286rule1286pattern1287rule1287pattern1288rule1288pattern1289rule1289pattern1290rule1290pattern1291rule1291pattern1292rule1292pattern1293rule1293pattern1294rule1294pattern1295rule1295pattern1296rule1296pattern1297rule1297pattern1298rule1298pattern1299rule1299pattern1300rule1300pattern1301rule1301pattern1302rule1302pattern1303rule1303pattern1304rule1304pattern1305rule1305pattern1306rule1306pattern1307rule1307pattern1308rule1308pattern1309rule1309pattern1310rule1310pattern1311rule1311pattern1312rule1312pattern1313rule1313pattern1314rule1314pattern1315rule1315pattern1316rule1316pattern1317rule1317pattern1318rule1318pattern1319rule1319pattern1320rule1320pattern1321rule1321pattern1322rule1322pattern1323rule1323pattern1324rule1324pattern1325rule1325pattern1326rule1326pattern1327rule1327pattern1328rule1328pattern1329rule1329pattern1330rule1330pattern1331rule1331pattern1332rule1332pattern1333rule1333pattern1334rule1334pattern1335rule1335pattern1336rule1336pattern1337rule1337pattern1338rule1338pattern1339rule1339pattern1340rule1340pattern1341rule1341pattern1342rule1342pattern1343rule1343pattern1344rule1344pattern1345rule1345pattern1346rule1346pattern1347rule1347pattern1348rule1348pattern1349rule1349pattern1350rule1350pattern1351rule1351pattern1352rule1352pattern1353rule1353pattern1354rule1354pattern1355rule1355pattern1356rule1356pattern1357rule1357pattern1358rule1358pattern1359rule1359pattern1360rule1360pattern1361rule1361pattern1362rule1362pattern1363rule1363pattern1364rule1364pattern1365rule1365pattern1366rule1366pattern1367rule1367pattern1368rule1368pattern1369rule1369pattern1370rule1370pattern1371rule1371pattern1372rule1372pattern1373rule1373pattern1374rule1374pattern1375rule1375pattern1376rule1376pattern1377rule1377pattern1378rule1378pattern1379rule1379pattern1380rule1380pattern1381rule1381pattern1382rule1382pattern1383rule1383pattern1384rule1384pattern1385rule1385pattern1386rule1386pattern1387rule1387pattern1388rule1388pattern1389rule1389pattern1390rule1390pattern1391rule1391pattern1392rule1392pattern1393rule1393pattern1394rule1394pattern1395rule1395pattern1396rule1396pattern1397rule1397pattern1398rule1398pattern1399rule1399pattern1400rule1400pattern1401rule1401pattern1402rule1402pattern1403rule1403pattern1404rule1404pattern1405rule1405pattern1406rule1406pattern1407rule1407pattern1408rule1408pattern1409rule1409pattern1410rule1410pattern1411rule1411pattern1412rule1412pattern1413rule1413pattern1414rule1414pattern1415rule1415pattern1416rule1416pattern1417rule1417pattern1418rule1418pattern1419rule1419pattern1420rule1420pattern1421rule1421pattern1422rule1422pattern1423rule1423pattern1424rule1424pattern1425rule1425pattern1426rule1426pattern1427rule1427pattern1428rule1428pattern1429rule1429pattern1430rule1430pattern1431rule1431pattern1432rule1432pattern1433rule1433pattern1434rule1434pattern1435rule1435pattern1436rule1436pattern1437rule1437pattern1438rule1438pattern1439rule1439pattern1440rule1440pattern1441rule1441pattern1442rule1442pattern1443rule1443pattern1444rule1444pattern1445rule1445pattern1446rule1446pattern1447rule1447pattern1448rule1448pattern1449rule1449pattern1450rule1450pattern1451rule1451pattern1452rule1452pattern1453rule1453pattern1454rule1454pattern1455rule1455pattern1456rule1456pattern1457rule1457pattern1458rule1458pattern1459rule1459pattern1460rule1460pattern1461rule1461pattern1462rule1462pattern1463rule1463pattern1464rule1464pattern1465rule1465pattern1466rule1466pattern1467rule1467pattern1468rule1468pattern1469rule1469pattern1470rule1470pattern1471rule1471pattern1472rule1472pattern1473rule1473pattern1474rule1474pattern1475rule1475r  r  r  trinomial_products   sP     `
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   C   sj   t |}t|tt||td  | ||||    ||td| |    |  |||td|  |S Nr  r  r4   r  r+   r   r  )r!  r  r  r  r!  r  r  r+  r  r  r  r2  H  s   br2  c                 C   sV   t |td|  |||    | |||   ||td|    |  td|   |S r  r  r  r  r  r  r  r3  M     Vr3  c                 C   s   t || |||   ||td|    |td   | td| td   | t |td|  |||    | |||   ||td|    |  td|  |td   | S Nr  r  r  r  r  r  r  r4  Q  s   r4  c              	   C   s   t t| |||   ||td|    |td| ||    t|td| ||   | |||   ||td|    |tdd    ||S Nr  r  r  r  r  r   r  r  r  r  r5  U     r5  c                 C   s   t td| t|  |td| ||   td t|   | |||   ||td|    t|  t|td| ||   td|  ||S Nr  r  r  r  r%   r&   r   r  r  r  r  r6  Y     r6  c              	   C   s   t |t| |||   ||td|     |td  |t || | t| |||   ||td|     |td| ||   |td   | S r  )r  r  r  r!  r  r  r  r!  r  r  r  r  r8  ]     r8  c                 C   P   t t| |||    ||td |    | |td  ||td|  S r  r+   r   r  r  r  r  r  r9  a     Pr9  c                 C   s~  t td|  |td  | td| td  td| | td |td| td  td   t| |||   ||td|    |td  ||t|| |||   ||td|    |  td| | td  | t|| | td|  |||    | |||   ||td|    |td   td| | td |td| td  td   | S Nr  r  r  r  r  r   r  r  r  r  r  r:  e      r:  c                 C   s  t td| |td  td |td| td  td  td|  |td  |td  td| td   t| |||   ||td|    |td  ||t|td|  |||    | |||   ||td|    |  td|  | td| td   | t||td| td  td  | |||   ||td|    |td   td|  |td  |td  td| td   | S r  r'  r  r  r  r  r;  i      r;  c                 C   s   t |t|  |td |||   td t|   | |||   ||td|    t|  t|td |||   td|  ||S r  r  r%   r  r&   r   r  r  r  r  r<  m     r<  c                 C   r#  r  r$  r  r  r  r  r=  q  r%  r=  c                 C   s4   t t| |||   ||td|    | ||S r  r   r   r  r  r  r  r  r>  u  s   4r>  c              	   C   s   t || td| | td  ttd|  |||   | |||   ||td|    |td   ||t|| |||   ||td|    |  td| | td  | S Nr  r  r  r'  r  r  r  r  r?  y     r?  c              
   C   s  t td| | |td  td |  | |td    t| |||   ||td|    |td  td |  | |td  || ||  |td| td  td   ||td  td |  | |td     ||t|| |||   ||td|    |td   td |  | |td  || ||    | | |td  td |  | |td    | S Nr  r  r  r$  r'  r  r  r  r  r@  }      r@  c              
   C   s   t | | td}t | | td|  td}tdd| | |  t|||d   ||||d    ||   ||tdd| | |  t|||d   ||||d    ||   || S r  r  r  r  r   )r!  r  r  r  r!  r  r#  r'  r  r  r  rA    s    rA  c              	   C   s   t td |  | |td  td}t|| ttd|td |||   |td   ||t|| ttd|td |||   |td   || S Nr  r  r  r1  )r!  r  r  r  r!  r  r#  r  r  r  rB    s   (|rB  c                 C   s   t td |  | |td  td}ttdt|  ttdt| td| |td   | t|td| |td   |   ||S r2  r  r  r  r  r   r!  r  r  r  r#  r  r  r  rC    s   (nrC  c              	   C      t ||  td}tt| ||td   ||td   | |td |td  td td   |td |td  td  ttdt||  | |td  td|  tdd   td| t| ||td   ||td     |S r2  r  r  r  r  r=   r>   r4  r  r  r  rD       rD  c                 C   sN   t |ttttfrdS ttd |  | |td  td}t|r%dS dS NFr  r  T)
isinstanceintr  floatr  r  r  r   r4  r  r  r  rE    s   (rE  c              
   C   s  t td |  | |td  td}tttd|  |td ||   | ttd |  |td ||    ttttd| ttd|  |td ||   |  || td|   tdt|   t| ||td   ||td     |S r  r  r  r  r  r=   r	  r4  r  r  r  rF       (rF  c              
   C   sD  t td |  | |td  td}tttd|  |td ||   | ttd|  |td ||   td|  |td ||     ttttd| ttd|  |td ||   |  || td|   tdt| td|  |td ||     t| ||td   ||td     |S r  r<  r4  r  r  r  rG    s   ( rG  c              
   C      t |ttttfrdS ttd |  | |td  td}tt|| |  t	tt|| |  t
|| td|   || td|   rJdS dS r8  r9  r:  r  r;  r  r  r  r  r   r6   r   r4  r  r  r  rH       (RrH  c              	   C   s   t td |  | |td  td}tttd|  |td ||   td|  |td ||    td|  |td ||    tt|t || td|   td td| ||   td|  t| ||td   ||td    t || td|   td  |S r  r6  r4  r  r  r  rI    s   (rI  c                 C   V   t |ttttfrdS ttd |  | |td  td}t|| |  r)dS dS r8  r9  r:  r  r;  r  r  r  r   r4  r  r  r  rJ       (rJ  c              	   C   s"  t td |  | |td  td}tttd|  |td ||   td|  |td ||    td|  |td ||    tt|t || td|   td td | ||   td|  t| ||td   ||td    t || td|   td  |S r  r6  r4  r  r  r  rK    s   (rK  c              
   C      t |ttttfrdS ttd |  | |td  td}tt|| |  t	tt|| |  t
||  td|   ||  td|   rLdS dS r8  r9  r:  r  r;  r  r  r  r  r"   r6   r   r4  r  r  r  rL       (VrL  c              	   C   s  t td |  | |td  td}tttd|td ||  td|    ttd|td ||  td|     tt|t ||  td|   td || ||   t| ||td   ||td   t ||  td|   td  |S r2  r<  r4  r  r  r  rM    r=  rM  c                 C   rA  r8  r9  r:  r  r;  r  r  r  r"   r4  r  r  r  rN    rC  rN  c              	   C   s  t td |  | |td  td}tttd|td ||  td|    ttd|td ||  td|     tt|t ||  td|   td || ||   t| ||td   ||td   t ||  td|   td  |S r2  r<  r4  r  r  r  rO    r=  rO  c              	   C   r5  r2  r6  r4  r  r  r  rP    r7  rP  c              
   C   s  t td |  | |td  td}tttd| |td  ||  td ttd| |td  ||  td  t| ||td   ||td    ttdttd| |td  ||  td ttd| |td  ||  td   ||S r2  r3  r4  r  r  r  rQ    s   (rQ  c                 C   sr  t | t| td| ||  |ttd |  | |td  td  td t|   td| ||  |ttd |  | |td  td  td t|   | |||   ||td|    t|  ttd| ||  |ttd |  | |td    td | td| ||  |ttd |  | |td    td |  ||S Nr  r  r  r  r%   r  r  r&   r   r  r  r  r  r  rR       t rR  c                 C   s<   t || |  | ||  | ||td|    |  |S r  r  r!  r  r  r0  r  r  r  r  r  r  rT       <rT  c              	   C   s   t ||t|  | |||    |||   t|  | ||  | ||td|    t|   t|| |  | ||  | ||td|    |  ||S r  r  r&   r  r   rK  r  r  r  rU    s   rU  c              	   C   sR   t tdt||td tt| |||   ||td|    | ||||S Nr  r  r  r  r3   r+   r   )r!  r  r  r  r!  r  ur  r  r  r  rW       RrW  c              	   C   sB   t td| tt| ||  ||td   | |||| |S rN  r  r  r+   r   r!  r  r  r  r  r!  r  r  r  r  r  rX        BrX  c	           	      C   s@   t t|| | | |||   ||td|    |  ||S r  r,  	r!  r  r  r   r  r  r!  r  r  r  r  r  rY       @rY  c                 C   sJ   t ||td| |   | |td |   |||    | |  |S r  r  rS  r  r  r  rZ       JrZ  c              	   C   s   t t| |||   ||td|    | |t |t| |||   ||td|     t| |td| ||    | S r  )r  r  r  logr!  r  r  r  r[       r[  c                 C   s   t | t| |||   ||td|    |td  | ||t| |||   ||td|    | td| |  | ttd|  |||   | |||   ||td|    |td   td| td| td   | S r  r  r   r  r  r  r  r  r  r\       r\  c                 C   s  t td|  t| |||   ||td|    |td  | ||t| |||   ||td|    |td  td|  | |td   | ttd|  |||   | |||   ||td|    |  td|  | td| td   | S rN  r'  r  r  r  r  r]        r]  c                 C   s   t |t|  |td |||   td t|   | |||   ||td|    t|  t|td |||   td|  | ||S r  r*  r  r  r  r  r^    r  r^  c	           	      C   sn   t || |td  |td| ||    | |||   ||td|    |  || |td   |S rN  r  rU  r  r  r  r_       nr_  c                 C   sn   t t| |||   ||td|    |td| ||    t|| | |td| ||    ||S r  r  r!  r  r  r   r  r  r!  r  r  r  r  r`     r]  r`  c              	   C   s   t || |td  t| |||   ||td|     ||| td   |t || || |td   t| |||   ||td|     ||td| ||    |td  || td   | S rN  r  r  r  r^  r  r  r  ra  $     ra  c                 C   s   t |td|   ttd|t| |||   ||td|      || t||td  t| |||   ||td|     | |  | S r  r  r  r   r  r  r!  r  r  r  r  r!  r  r  r  r  rb  (  r  rb  c	           	      C   s  t || |td  td|  |||    | |||   ||td|    |  td|  | | td| td   | t || |td  | |||   ||td|    |td   td|  | | |td  td| td   | S rN  r  rU  r  r  r  rc  ,  s    rc  c              	   C   s   t |td|  t||td  | |||   ||td|    |  || t| |||   ||td|    |td  td| | |td   | S r&  r'  rS  r  r  r  rd  0     rd  c	           	   	   C   s  t |||   |td  | td| td  |td |td| |  td   t|| ||  | |||   ||td|    |td   || t|| |td  | |||   ||td|    |  ||td| |  td   | t|| || |td   td|  |||    | |||   ||td|    |td   ||td  |td| |  td   | S r&  r'  rU  r  r  r  re  4  s    re  c	           	   	   C   s  t td| |td |   |td  | td| td  |td || td   t|| |td|   | |||   ||td|    |td   ||t|| |td  | |||   ||td|    |  ||td| td   td  ||td  || td   | t|| || |td   td|  |||    | |||   ||td|    |td   ||td  || td   | S r&  r'  rU  r  r  r  rf  8      rf  c	           	   	   C   s  t td|  |td  | td| td  |td| |  td ||td| td   td   t|| | | |||   ||td|    |td   ||t|| |td  | |||   ||td|    |  ||td| |  td   | t|| || |td   td|  |||    | |||   ||td|    |td   ||td| |  td  ||td| td   td   | S r&  r'  rU  r  r  r  rg  <  s    rg  c	           	   	   C   s  t || || td  ||td| td   td  ||td  |td  td| td   t|| ||  | |||   ||td|    |td   || t|| |td  |td| ||    | |||   ||td|    |  || | td| td   | t||td  || || td   | |||   ||td|    |td   ||td| td   td  ||td  |td  td| td   | S Nr  r  r  r'  rU  r  r  r  rh  @      rh  c	           	   	   C   s2  t |td|  |td|  td  || td  td| |td  |td  td| td   t|| |td|   | |||   ||td|    |td   ||t|td| td  || |td|  td   td|  |||    | |||   ||td|    |  td| | td| td   | t|td| td  || |td|  td   | |||   ||td|    |td   |td| |  td|  td  td| |td  |td  td| td   | S )Nr  r  r  r$  r'  rU  r  r  r  ri  D  s    6 ri  c	           	   	   C   s  t |td| |td   td ||td| td   td  td|  |td  |td  td| td   t|| | | |||   ||td|    |td   ||t|| |td  td|  |||    | |||   ||td|    |  td|  | | td| td   | t|| |td  | |||   ||td|    |td   ||td| td   td  td|  | |td  |td  td| td   | S r  r'  rU  r  r  r  rj  H      rj  c	           	   	   C   s  t |||  || td  td| |td| |  td   t|| ||  | |||   ||td|    |  || t||td  || || td   |td| ||    | |||   ||td|    |  td| |td| |  td   | S re  r'  rU  r  r  r  rk  L  s    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   
   C      t |}	t|	| tt||	 |td  td  | |||   ||	 |    ||td |   |td |	 |    |  |||| td |	  | S Nr  r  r  r  
r!  r  r  r   r  r  r!  r  r  r+  r  r  r  rn  X     rn  c	           	   
   C      t |t| || t|  td| t|  tt|| td  | |||    ||td |    |  ||td| | S Nr  rj  r  r  r%   r&   r  r+   r   rU  r  r  r  rp  ]     rp  c	           	      C   s   t |t|  |td |||   td t|   | |||   ||td|    t|  t|| | |td |||   td|   ||S r  r*  rU  r  r  r  rq  a  s   rq  c              
   C   s^   t td| tt|td|td |   | ||  ||td   |  |||| |S rl  rR  rS  r  r  r  rr  e     ^rr  c	           	   	   C   d   t |t| |t|   || t|  t|| | |||   ||td|    |  ||S r  r  r%   r&   r   r  rU  r  r  r  rt  i     drt  c           	      C   s>   t |ttttfrdS t|td |}t|tdrdS dS NFr  Tr9  r:  r  r;  r  r   r  r$   	r!  r  r  r  r  r!  r  r  r+  r  r  r  ru  m     ru  c           	   
   C   s   t |td |}ttd| tt|td|td |   | ||||    ||td| |    |  |||| |S rl  r   r  r  r+   r   ry  r  r  r  rv  v  s   nrv  c	           
   
   C   s   t |}	t|	| tt||	|td  td  | |||   ||	|    ||td |   |td|	 |    |  |||| td|	  |S rl  r  rm  r  r  r  rw  |  s   rw  c	           	      C   s  t || | | ||td| |  td  ||td| td   td   t|| ||  | |||   ||td|    |td   t| | || td  || td|  | ||td| td   td  |td |||td   td     | || t||td  || || td   || | |||  ||td| td   td    | |||   ||td|    |  ||td| |  td  ||td| td   td   | S r-  r'  rU  r  r  r  rx    s    rx  c	           	   	   C   s   t ||  | | |td  t|| ||  |td| ||    | |||   ||td|    |td   || t|| |td  | |||   ||td|    |  ||td   | S re  r'  rU  r  r  r  ry       ry  c	           	   	   C   s   t || |td| |  td  t|| | td|  |||    | |||   ||td|    |td   ||t|| |td  | |||   ||td|    |  ||td| |  td   | S r-  r'  rU  r  r  r  rz       rz  c	           	      C   sr  t || ||td  td |  | |td    t|| ||  ||| td  td| ||  |td| |td   td    | |||   ||td|    |td   || t||td  || || td   |td| ||    | |||   ||td|    |td   ||td  td |  | |td    | S Nr  r  r  r  r'  rU  r  r  r  r{    rJ  r{  c	           	      C   s  t |td|  ||td  td |  | |td    t|| |td|   td|  |td|  td  |||  ||td| td   td    | |||   ||td|    |td   ||t|td| td  || |td|  td   td|  |||    | |||   ||td|    |td   ||td  td |  | |td    | S )Nr  r  r  r  r'  rU  r  r  r  r|    s    r|  c	           	      C     t td| | |td  td |  | |td    t|| | | |||   ||td|    |td   ttd |  | |td| |td   td  |td |||td   td   || ||  |td| |  td|  td   | ||t|| |td  | |||   ||td|    |td   td |  | |td  || ||    | | | |td  td |  | |td    | S r/  r'  rU  r  r  r  r}        r}  c	           	      C   sT  t |td|  ||td| |  td   t|| |td|   | |||   ||td|    |  t| |td|  td  |||  |||td   td   | || t|td| td  || |td|  td   | |||   ||td|    |td   ||td| |  td   | S r-  r'  rU  r  r  r  r~       V r~  c	           	      C   s  t ||  | |td   t|| ||  ||||td   td  |||  |td| |td   td    | |||   ||td|    |  || t|| |td  | |||   ||td|    |td   | | |td   | S rN  r'  rU  r  r  r  r    s    r  c              	   C   s   t ||  |  t|| ||  ||||    | |||   ||td|     || t|| |td  | | |td   | S r  rZ  r^  r  r  r  r       r  c                 C   s6   t t|| | |||   ||td|    ||S r  )r   r   r  rb  r  r  r  r       6r  c              	   C   s   t |td|  | t|| |td|   | |||    | |||   ||td|     || t|td| td  || |td|  td   ||td|  td   | S r&  r'  r^  r  r  r  r    s   r  c              
   C   s   t | | td}ttdd t||td  | ||td   ||td    || ttdd t||td  | ||td   ||td    || S Nr  r  r  r1  r4  r  r  r  r    s   r  c           	   
   C   s   t | | td}t | | td|  td}tdd| |  t||d| d   ||||d     ||||d    ||   || tdd| |  t||d| d   ||||d     ||||d    ||   || S )Nr  r  r$  r1  	r!  r  r  r  r  r!  r  r#  r'  r  r  r  r    s    r  c           	   
   C   s   t | | td}t | | td|  td}tdd| |  t|||d   ||||d    ||   ||tdd| |  t|||d   ||||d    ||   || S r  r1  r  r  r  r  r    s    r  c           	   	   C   s   t td |  | |td  td}t|| || td  td t|| ||  |td |||   |td   || t|| || td  td t|| ||  |td |||   |td   || S )Nr  r  r  r  r1  	r!  r  r  r   r  r  r!  r  r#  r  r  r  r    s   (r  c           	   	   C   s   t td |  | |td  td}t|| t|| | |td |||   |td   ||t|| t|| | |td |||   |td   || S r  r1  r  r  r  r  r       (r  c                 C   s   t td |  | |td  td}ttdt|  t|td t| td| |td   | t|td| |td   |   ||S r  r3  r4  r  r  r  r    s   (rr  c                 C      t ||  td}ttd| t| |td  td t| ||td   ||td    || ttd| ttdt| ||td   ||td    || S r  r  r  r  r   r  r4  r  r  r  r       r  c                 C      t td |  | |td  td}ttdtd|  t|td| |td   | t| ||td   ||td    ||t|| td|  ttdt| ||td   ||td    || S r2  r  r4  r  r  r  r    s   (r  c              
   C   r>  r8  r?  r4  r  r  r  r    r@  r  c              
   C   s~  t td |  | |td  td}t||td| |td   |  td| t| ||td   ||td     |tttd|  |td ||   td|  |td ||    td|  |td ||    tt|t || td|   td td| ||   t || td|   td td| t| ||td   ||td     | S r  r  r  r  r  r<   r>   r4  r  r  r  r    s   (X r  c                 C   rA  r8  rB  r4  r  r  r  r    rC  r  c              
   C   s  t td |  | |td  td}t||td| |td   |  td| t| ||td   ||td     |tttd|  |td ||   td|  |td ||    td|  |td ||    tt|t || td|   td td | ||   t || td|   td td| t| ||td   ||td     | S r  r  r4  r  r  r  r    s   (Z r  c              
   C   rD  r8  rE  r4  r  r  r  r    rF  r  c                 C   s   t td |  | |td  td}ttdtd|  t|td| |td   | t| ||td   ||td    ||t|| td|  ttdt| ||td   ||td    || S r2  r  r4  r  r  r  r       (r  c                 C   rA  r8  rG  r4  r  r  r  r    rC  r  c                 C   r  r2  r  r4  r  r  r  r    r  r  c                 C   r  r  r  r4  r  r  r  r    r  r  c              
   C   s  t td |  | |td  td}tttd| |td  ||  td ttd| |td  ||  td  t| ||td   ||td    t|td ttd| |td  ||  td ttd| |td  ||  td   ||S r2  r3  r4  r  r  r  r    s   (r  c                 C   rh  ri  r$  rS  r  r  r  r    r  r  c	           
   
   C   rk  rl  r  rm  r  r  r  r  !  rn  r  c	           	   
   C   ro  rp  rq  rU  r  r  r  r  &  rr  r  c           	   
   C   sv   t |}t|tt|||td  td  | ||||    ||td| |    |  |||td|  |S rl  r  ry  r  r  r  r  *  s   nr  c	           	   	   C   rt  r  ru  rU  r  r  r  r  /  rv  r  c                 C   sr   t td|td  tt| ||||td     ||td| |td     | ||||td  |S rN  rR  rS  r  r  r  r  3     rr  c	           	   	   C   rt  r  ru  rU  r  r  r  r  7  rv  r  c           	   	   C   s   t td |  | |td  td}ttd| | t|| | |td| ||   |  ||ttd| | t|| | |td| ||   |  || S r  r1  r  r  r  r  r  ;  r  r  c	           	      C   r  r/  r'  rU  r  r  r  r  @  r  r  c	           	      C   s~  t | t| td| ||  |ttd |  | |td  td  td t|   td| ||  |ttd |  | |td  td  td t|   | |||   ||td|    t|  t|| | td| ||  |ttd |  | |td    td |  td| ||  |ttd |  | |td    td |  ||S rH  rI  rU  r  r  r  r  D  r(  r  c                 C   s>   t ||||   | ||  | ||td|    |  |S r  r  r!  r  r  r  r0  r  r  r  r  r  r  r  H  s   >r  c              	   C   s   t ||t|  | |||    |||   t|  | ||  | ||td|    t|   t||||   | ||  | ||td|    |  ||S r  rM  r  r  r  r  r  L  rc  r  c	           	      C   s^   t |t| |t|   || t|  t|| | |||    |||   |  ||S Nr  r%   r&   r   )	r!  r  r  r   r  r0  r  r  r  r  r  r  r  P  rs  r  c	           	      C   sv   t t||td| td  ttt|t||td | | |||   ||td|    |  |||||S )Nr  r  r   r  )r  r3   r  r+   r   r-  )	r!  r  r  r  r  r!  r  vr  r  r  r  r  T     vr  c
           
   
   C   sd   t || ||   t||	td tt|	| | ||	|   ||	td|    |  |	|	||	S rN  r  r3   r  r+   r   )
r!  r  r  r  r  r!  r  rP  r  r  r  r  r  r  X  rv  r  c
           
      C   s`   t |	|td| |   ||	|   | |  | |	td |   ||	|    | |  |	S r  r  
r!  r  r  r   r"  r  r!  r  r#  r  r  r  r  r  \     `r  c	           	      C   sR   t ||td| |   | |td |   | |  |||   | |  |S r  r  	r!  r  r   r"  r  r!  r  r#  r  r  r  r  r  `  rQ  r  c
           
      C   sf   t t|||	|    | | ||	|    ||	td |    |  |	td  |	|	td|	  S r  r$  r  r  r  r  r  d     fr  c	           	      C   sX   t t| ||td |    | ||||    |  |td  ||td|  S r  r$  r  r  r  r  r  h     Xr  c
              
   C   s   t |}
t|
tt|	|
td  |||	|
|    |  | ||	|
|    ||	td|
 |    |  |	|	|	td|
  |	S r  r  )r!  r  r  r   r"  r  r!  r  r#  r  r&  r  r  r  r  l  s   zr  c	           
   
   C   sr   t |}	t|	tt||	td  | ||td|	 |    |  ||||	|    |  |||td|	  |S r  r  )
r!  r  r   r"  r  r!  r  r#  r  r&  r  r  r  r  q  s   jr  c              	   C   s   t || t||  | ||  ||td|    |td   ||t|td | |td   | | ||   | ||  ||td|    |td   | | | |td   | S r  rZ  r  r  r   r"  r  r!  r  r  r  r  r  r  v     r  c                 C   sj   t ||td|   | ||  ||td|    |td   ||td| td  td   |S rN  r  r  r  r  r  r  z  s   jr  c                 C   s   t | | || td  || |td| td  td   ||td| td  td   t| ||  ||td|    | || t||td|   | ||  ||td|    |td   ||td| td  td   | S rN  r'  r  r  r  r  r  ~  s   r  c	           	      C   s   t || t|  | |||   t|   | ||  ||td|    t|  t|||  | |||   |  ||||   |  ||S r  rM  )	r  r  r   r"  r  r!  r  r#  r  r  r  r  r    r+  r  c
           
      C   s   t td| t|  |td| |	|   td t|   | ||	|   ||	td|    t|  t|td| |	|   td|  |||	|   |  |	|	S r  r  r  r  r  r  r       r  c
           
      C   s:   t |||	|   ||  | | ||	|  |  |  |	S r  r   r  r  r  r  r       :r  c	           	      C   s:   t ||||   ||  | | |||  |  |  |S r  r  r  r  r  r  r    r  r  c
           
      C   s   t |||	|   t|  | | ||	|  |  t|   | ||	|   ||	td|    t|  t|||	|   ||  | | ||	|  |  |  |	|	S r  rM  r  r  r  r  r    rc  r  c	           	      C   s   t | ||td|    t| ||||   t|   | | |||  |  t|   t||||   ||  | | |||  |  |  ||S r  r  r  r&   r   r  r  r  r  r    r   r  c	           	      C   sD   t t||||   | | |||   ||td|     ||S r  r,  	r!  r  r  r   r"  r  r!  r#  r  r  r  r  r       Dr  c                 C   s8   t t| ||td|    ||||   |  ||S r  r,  r!  r  r   r"  r  r!  r#  r  r  r  r  r       8r  c	           	   
   C   s.  t td||td  | |td   t||||   |td  t| |td  ||td  td  || |  ||td   || | | ||  |td   | ||t|||||   |td   | |td  || |  ||td    ||td  | |td   | S rN  r'  r  r  r  r  r    s   0 r  c              
   C   s  t td||td  | |td   t||||   |td  t| |td  ||td  td  ||td   || | | ||  |td   | ||t|||||   |td   | |td  ||td    ||td  | |td   | S rN  r'  r  r  r  r  r        r  c	           	      C   s   t td|||td  td   t||||   | | | ||td  td  || | | ||td  td  || |td      ||t|||td   ||||   |td   |||td  td   | S rN  r'  r  r  r  r  r       r  c              	   C   s   t td|||td  td   t||||   | | | ||td  td  || ||  |td    ||t|||td   ||||   |td   |||td  td   | S rN  r'  r  r  r  r  r       r  c                 C   s   t td| | td}t|td td|  ttd||||   |||td     ||t|td td|  ttd||||   |||td     || S r  r1  r!  r  r   r"  r  r!  r  r#  r  r  r  r    s   r  c                 C   s   t td | | td}t|td|   t||||td    ||||   |||td     ||t|td|   t||||td    ||||   |||td     || S r  r1  r  r  r  r  r    s   r  c              
   C   s   t | | td}t|  | ||  td|  |  t| |td  | | ||td    ||t| | ||  td|  |  t||td  | | ||td    || S Nr  r  r1  r!  r  r   r"  r  r#  r  r  r  r    s   r  c                 C   sF  t | | td}tttdtd| |td   tttd| | ||td  |||td     |td ttd| ||td    ||   ||tttdtd| |td   tttd| | ||td  |||td     |td ttd| ||td    ||   || S )Nr  r  r$  r3  r  r  r  r  r    s   6 r  c              
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   C   s\   t |ttd| ||td|     ||t |t|| | ||td|     || S rN  r  r   r  )r!  r  r   r"  r  r!  r  r  r  r  r       \r  c           	      C   s   t | | td| |  td}t|td td|  ttd||| ||td    |||    ||t|td td|  ttd||| ||td    |||    || S r  r1  	r!  r  r  r   r"  r  r!  r  r#  r  r  r  r    s   $r  c           	   	   C      t td |  | |td  td}t|td | | td| |  td|   ttd|td |||   |td   ||t|td | | td| |  td|   ttd|td |||   |td   || S r2  r1  r  r  r  r  r       (r  c           
   
   C      t | | td}t | | td|  td}	tdd| | |	  t||	 ||d  |||    ||	||d    ||   ||tdd| | |	  t||	 ||d  |||    ||	||d    ||   || S r  r1  
r!  r  r  r   r"  r  r!  r  r#  r'  r  r  r  r        r  c           	   	   C   r  r2  r1  r  r  r  r  r    r  r  c           
   
   C   r  r  r1  r  r  r  r  r    r  r  c	           	      C   sD   t t||||   | | |||   ||td|     ||S r  r,  r  r  r  r  r    r  r  c                 C   s8   t t||||   | | ||td|     ||S r  r,  r  r  r  r  r    r  r  c	           	   
   C   s   t |td | |td  || |  ||td    t||||   | ||t td| |td  || |  ||td    t||||   |td  | | ||  || ||    | |||   ||td|     || S r  r  r  r   r  r  r  r  r    s   r  c              	   C   s   t || |td  ||td    t||||   ||||   |td   | ||td|     ||t |td | |td  ||td    t||||   | || S r  r  r  r  r  r  r    r.  r  c	           
   	   C   s   t td |  | |td  td}	ttd| |	 t||||   | |td| ||   |	  ||ttd| |	 t||||   | |td| ||   |	  || S r  r1  )
r!  r  r  r   r"  r  r!  r#  r  r'  r  r  r  r    s   (r  c           	      C   s   t |  | td}t|td|  t||||   | | ||  |  || t|td|  t||||   | |||  |  || S r  r1  )	r!  r  r   r"  r  r!  r#  r  r'  r  r  r  r    s   r  c	           	      C   s   t || |td| | td  td| | | td   t| |||   ||td|    |td  t|  | | td|  | | td| | | td   || td|  | | td| | td  |td | || td   || | td| | | td     | ||t|| |||   ||td|    |  || | | || td| | | td   || ||  td| | td    |td| | td  td| | | td   | S r-  r'  	r!  r  r  r   r"  r  r!  r  r  r  r  r  r  	  s     r  c              	   C   sX  t td|  | | td| | td td| | | td   t| ||td|    |td  |td| | | td  |||  td| | td    ||t|| ||td|    |  |td| | | td  |||  td| | td    td| | td td| | | td   | S r-  r'  r!  r  r   r"  r  r!  r  r  r  r  r  r    s   Z r  c	           	   
   C   s  t td| | |td  td |  | |td    t| |||   ||td|    |td  t|  | | td|  | | td| | td|  td   |td | || | td   |||  td |  | ||   td| | td|  td   | ||t|| |||   ||td|    |td   |  | | td|  | |  |td |  |||  td |  | ||     | | |td  td |  | |td    | S r/  r'  r  r  r  r  r    rg  r  c              	   C   s  t tdtd|  | |td   t| ||td|    |td  |td| | td|  td  |||  td| | td|  td    ||t|| ||td|    |td   ||||    td|  | |td   | S Nr  r  r$  r'  r  r  r  r  r        r  c                 C   s   t td |  | |td  td}ttdt|  t|||td   t| td| |td   | t|td| |td   |   ||S r  r3  r!  r  r  r   r"  r  r#  r  r  r  r    s   (zr  c              
   C   sn   t |  | td}tt| t|||td   t| |td  | t||td  |   ||S r  r3  r  r  r  r  r    s   Zr  c                 C   H   t |ttttfrdS t||  td}t||td  | r"dS dS r8  r9  r:  r  r;  r  r  r  r   r  r  r  r  r  #     r  c              
   C   X  t ||  td}t|| t| ||td   ||td    | |td |td  td   | t|t| ||td   ||td   | |td |td  td td    |td |td  td  ttdt||  | |td  td|  tdd   |t| ||td   ||td     | S r2  r  r  r  r  r  r  ,     H r  c                 C   @   t |ttttfrdS t||  td}t|| | rdS dS NFr  Tr9  r:  r  r;  r  r  r  r   r  r  r  r  r  2     r  c                 C      t ||  td}t|| t| |td  td t| ||td   ||td    || t|| | | ttdt| ||td   ||td    || S r  r  r  r  r  r  r  ;     r  c                 C   f   t |ttttfrdS ttd |  | |td  td}ttd| | |||   r1dS dS r8  r  r  r  r  r  r  A     ( r  c                 C   s  t td |  | |td  td}t|| |td| |td   |  td| t| ||td   ||td     |t|| ttd|  |td ||   |  ttd|  |td ||   td|  |td ||     ttttd| ttd|  |td ||   |  || td|   td| t| td|  |td ||     t| ||td   ||td     | S r  r  r  r  r  r<   r	  r  r  r  r  r  J  s   ( r  c                 C   sP   t |ttttfrdS t|  | td}tt|| ||  t	|r&dS dS r  )
r9  r:  r  r;  r  r  r  r  r   r   r  r  r  r  r  P  s   r  c                 C   s  t |  | td}t|| ||td  |  |t| ||td     |tttd| | t| ||td   |  t|  ||td    ttttd| t| ||td   |  tdd  |t|   t| ||td     | S rH  r  r  r  r  r  r  Y  s   r  c                 C   F   t |ttttfrdS t|  | td}t|| ||  r!dS dS r  r  r  r  r  r  r  _     r  c                 C   s*  t |  | td}t|| ||td  |  |t| ||td     |tttd| | t| ||td   |  t| ||td   | ||td     ttttd| t| ||td   |  tdd  |t| | ||td     t| ||td     | S rH  r  r  r  r  r  r  h  s    r  c                 C   r  r8  r  r  r  r  r  r  n  r  r  c                 C      t td |  | |td  td}t|td|  t|td| |td   | t| ||td   ||td    ||ttd| | |||   td|  ttdt| ||td   ||td    || S r2  r  r  r  r  r  r  w     (r  c                 C   r  r  r  r  r  r  r  r  }  r  r  c                 C   s   t |  | td}t|| t| |td  | t| ||td    || t|| ||  | ttdt| ||td    || S rH  r  r  r  r  r  r    s   r  c                 C   sh   t |ttttfrdS ttd |  | |td  td}tt|| |  t|| |  r2dS dS r8  )	r9  r:  r  r;  r  r  r  r  r   r  r  r  r  r    s   ("r  c                 C   s   t td |  | |td  td}t|ttdt| ||td   ||td    ||t|t|td t| ||td   ||td    || S r2  r  r  r  r  r  r    s   (r  c                 C   s`   t |ttdt| ||td    ||t |t|td t| ||td    || S Nr  r  r  )r  r   r  r  r!  r  r   r"  r  r  r  r  r    r  r  c              	   C      t |ttttfrdS ttd |  | |td  td}tt|| |  t	td| | |||   t
t||  td|   ||  td|   rRdS dS r8  )r9  r:  r  r;  r  r  r  r  r"   r   r6   r   r  r  r  r  r       (br  c              	   C   s  t td |  | |td  td}t| | ttd|td ||  td|     ttd|td ||  td|     tt|t ||  td|   td || ||   t ||  td|   td |t| ||td   ||td     | S r2  r  r  r  r  r  r       (r  c              	   C   r  r8  )r9  r:  r  r;  r  r  r  r  r"   r   r6   r   r  r  r  r  r    r  r  c                 C   s   t td |  | |td  td}t|td|  t|td| |td   | t| ||td   ||td    ||ttd| | |||   td|  ttdt| ||td   ||td    || S r2  r  r  r  r  r  r    r  r  c                 C   x   t |ttttfrdS ttd |  | |td  td}tt|| |  t	td| | |||   r:dS dS r8  )
r9  r:  r  r;  r  r  r  r  r"   r   r  r  r  r  r       (2r  c              	   C   s  t td |  | |td  td}t| | ttd|td ||  td|     ttd|td ||  td|     tt|t ||  td|   td || ||   t ||  td|   td |t| ||td   ||td     | S r2  r  r  r  r  r  r    r  r  c                 C   r  r8  )
r9  r:  r  r;  r  r  r  r  r"   r   r  r  r  r  r    r  r  c                 C   r  r2  r  r  r  r  r  r    r  r  c                 C   r  r8  r  r  r  r  r  r    r  r  c              
   C   r  r2  r  r  r  r  r  r    r  r  c                 C   sH   t |ttttfrdS t||  td}t||td  | r"dS dS r8  r  r  r  r  r  r    r  r  c              
   C   s
  t ||  td}t|| t| ||td    | |td |td  td   | t|t| ||td   | |td |td  td td    |td |td  td  ttdt||  tdd  |t| ||td     | S r2  r  r  r  r  r  r    s   r  c                 C   r  r  r  r  r  r  r  r    r  r  c                 C   r  r  r  r  r  r  r  r  	  r  r  c                 C   s@   t |ttttfrdS t||  td}t|| | rdS dS r  r  r  r  r  r  r  	  r  r  c                 C   s   t ||  td}t|| t| |td  td t| ||td    || t|| | | ttdt| ||td    || S r  r  r  r  r  r  r  	  s   r  c              
   C   sV   t |t|  tttd||td  |  ttd||td  |   ||S rN  )r  r  r   r  r  r  r  r  r  	  r  r  c              
   C   sv   t ttd||td  |   t| ||td    t|||td   ttd||td  |    ||S r  r  r  r  r  r  r  	  r  r  c                 C   s   t | |  td}t|| t||td  td t| ||td    ||t|| | | ttdt| ||td    || S r  r  r  r  r  r  r  	  s   |r  c              
   C   s  t td |  | |td  td}tttd| |td  ||  td ttd| |td  ||  td  t| ||td   ||td    t|||td   ttd| |td  ||  td ttd| |td  ||  td   ||S r2  r3  r  r  r  r  r  $	  s   (r  c	           	      C   sD   t t||||   | |||   ||td|    |  ||S r  r,  r  r  r  r  r  )	  r  r  c                 C   s8   t t| ||td|    | ||||    ||S r  r,  r  r  r  r  r  -	  r  r  c
           
   	   C   s8  t |||	|   | t||  | |	td| | |   td| | | td  |td| | ||  td   || |	td| |    | ||	|   ||	td|    |  |	 |	t|| |	td| | | td   |||	|   |td   |td| | ||  td   |	 S r  r   r2  r  r  r  r  r  r  r  1	  s   : r  c	           	   	   C   s,  t ||||   | t||  | |td| | |   td| | | td  |td| | ||  td   || |td| |    | ||td|    |  | |t|| |td| | | td   ||||   |td   |td| | ||  td   | S r  r  r  r  r  r  r  5	     . r  c                 C   s   t |td t| | ||  || |td   t| ||td   ||td    || t | |td  || |  ||td   |td  ttd|||td   t| ||td   ||td     || S )Nrj  r  r  r  r  r  r   r  r!  r  r  r   r"  r  r  r  r  r  9	     r  c                 C   s   t ||td  t|||td   t| ||td    || t | |td  ||td   |td  ttdt| ||td   |||td     || S rH  r  r  r  r  r  r  =	     r  c                 C   s  t td |  | |td  td}t|td tt|td  |td  |td  ||td  |td  td | | ||    td| | |td  || |  ||td   td  td| | |||     ||td  |td |td  |td |td   td| | |  | ||      | | ||  td|  |td  || |  ||td     |t| ||td   ||td    || t| |td  || |  ||td   td |td td| | |||     t|td| |td   | |||td   t| ||td   ||td     || S )Nr  r  r$  r%  r  r  r  r   r  r  r  r  r  r  r  A	  s   ( l r  c                 C   s  t |  | td}t||td  tt|| |td  |td  ||td  |td   |td|  |td  ||td     ||td  td|  |td  ||td     | |td  ||td   td || ||    |t| ||td    || t| |td  ||td   td |td || ||    t||td  | t| ||td   |||td     || S )Nr  r  r$  r%  r  r  r  r  r  r  F	  s    r  c              
   C   s  t | t| ||td   ||td   |td  |||td    ||t |t|td | ||td   ||td   |td   |||td    || t |t|td | ||td   ||td   |td   |||td    || S )Nr  r  r  r  r!  r  r  r   r"  r  r  r  r  r  r   K	      r   c              
   C   s   t | t| ||td   |td  |||td    ||t |t|td | ||td   |td   |||td    || S )Nr  r  r  r  r!  r  r   r"  r  r  r  r  r  r  O	  s   r  c                 C   s   t td |  | |td  td}ttdt|  ttd|||td   t| td| |td   |  t|td| |td   |   ||S r2  r3  r  r  r  r  r  S	  s   (r  c              
   C   sv   t |  | td}tt| ttd|||td   t| |td  |  t||td  |   ||S r  r3  r  r  r  r  r  X	  s   br  c                 C   s  t td |  | |td  td}ttd| td| | |||    ttdt| ||td   ||td    ||t|td| | |||    t|td| |td   | |||td   t| ||td   ||td     || S r2  r  r  r  r  r  r  ]	  s   (r  c                 C   s   t |  | td}t||| ||   ttdt| ||td    ||t||| ||   t| |td  | t| ||td   |||td     || S r  r  r  r  r  r  r  b	  s   r  c                 C   sJ   t |ttttfrdS t||  td}t| |td  | r#dS dS r8  r  r  r  r  r  r  g	     r  c              
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  	  s   @r
  c              
   C   s~   t ttd||td  |   t| ||td    ttdttd||td  |   |||td     ||S r  r  r  r  r  r  r  	  s   ~r  c              
   C   s&  t td |  | |td  td}tttd| |td  ||  td ttd| |td  ||  td  t| ||td   ||td    ttd|||td   ttd| |td  ||  td  ttd| |td  ||  td   ||S r2  r3  r  r  r  r  r  	  s   (r  c                 C   s  t tdtd|  |td  td |  | |td   | |td  || |  ||td     t| ||td   ||td   |td  t|  | | | | td| td  td|  | td|  |td  |td  ||td  td| td     |td | | td| td   |td td|  |td  |td  ||td  td| td     || |td  td| td  td|  | | |td |  || |    |td td|  |td  | | |td |td  td| td   td|td  | | | |td   || | |td  td| td  ||td  td| td       | |||td    || t|| ||td   ||td   |td   td|  | | | td|  |td  |  |td |  |td | |  ||td  td|  | | |td |  || |     td|  |td  td |  | |td   | |td  || |  ||td     | S )	Nr  r  r           r$     r'  r  r  r  r  r  	  s
      & r  c                 C   s  t td td| td  | |td  | |td  ||td     t| ||td   |td  ttd |  |td  | | |td  td|  |td  |td  |td  td| td   td|  | td|  |td  |td  ||td  td| td     | |||td    || t| | ||td   |td   td |  |td  | td|  |td  | |td    td| td  | |td  | |td  ||td     | S )Nr  r  r  r  r  r  r'  r  r  r  r  r  	  s     r  c                 C   s  t |td| | |td  || |  ||td     t|||td   t| ||td   ||td    || t | |td  td| | |  td| |td   td| | |td  || |  ||td     ttd|||td   t| ||td   ||td     || t|td | t| ||td   ||td    td| |||td    | |td  || |  ||td     | S Nr  r  r$  r  ra  r  r  r  r  r  	  s    r  c                 C   sh  t |td| | |td  ||td     t|||td   t| ||td    || t | |td  td| |td   td| | |td  ||td     ttdt| ||td   |||td     || t|td | t| ||td    td| |||td    | |td  ||td     | S r  ra  r  r  r  r  r  	  s   j r  c           	      C   s>  t td |  | |td  td}t| t| td| |td  ||  td t|   td| |td  ||  td t|   | ||td   ||td   t|  t|||td   | td| |td  ||  td |  td| |td  ||  td |  ||S r2  r  r  r  r%   r&   r   )	r!  r  r  r   r"  r  r#  r  r'  r  r  r  r  	  s   ( r  c                 C   s   t |  | td}t| t| | ||td   t|  | |td  | td t|   ||td  | td t|   t|||td   | | |td  | td |  ||td  | td |  ||S rH  r  )r!  r  r   r"  r  r#  r  r'  r  r  r  r  	  s   r  c              	   C   sp   t ttdt|t| | td  || td|  |  tdt|  t| t| | td  |S r  )r  r=   r  r	  r  r  r  r  r  r  r  	     pr  c                 C   s   t t| ||td   ||td   |  t|||td   |  t|||td   t| ||td   ||td     ttdttd||td  |  ttd||td  |   ||td  |     ||S rH  r  r  r  r  r  r  	  r[  r  c              
   C   sp   t t| ttdt|t| | td  || td|  |   tdt| t| | td  |S r  )r  r  r<   r  r	  r  r  r  r  r  r  	  r  r  c              
   C   s   t t|||td   | t| ||td   ||td    t| ||td   ||td   |  t|||td     tttd||td  |   ||td  |   ttd||td  |   ||S rH  r  r  r  r  r  r  	     r  c
           
      C   sH   t t|||	|   | | ||	|   ||	td|    |  |	|	S r  r,  r  r  r  r  r  	     Hr  c	           	      C   s<   t t| ||td|    | ||||   |  ||S r  r,  r  r  r  r  r  	  rL  r  c	           	   
   C   s   t t| ||td|    | ||td |td |td|     |||  |td |td |td|      |  ||S r  r,  r  r  r  r  r  	  r  r  c
           
      C   sB   t |||	|   | | ||	|   ||	td|    |  |	S r  r  r  r  r  r  r  	  rT  r  c	           	      C   s6   t | ||td|    | ||||   |  |S r  r  r  r  r  r  r  	  r  r  c              
   C   sf   t tdt|	|
td tt|||
|   | | ||
|   ||
td|    |  |
|
|	|
S rN  rO  )r!  r  r  r   r"  r  r!  r  r#  rP  r  r  r  r  r  	  r  r  c
           
   	   C   sZ   t tdt||	td tt| ||	td|    | |||	|   |  |	|	||	S rN  rO  )
r!  r  r   r"  r  r!  r  r#  rP  r  r  r  r  r  	  s   Zr  c                 C   sP   t |
| |	  ||
|  | |	  | ||
|   ||
td|    |  |
S r  r  r!  r  r  r   r"  r0  r  r!  r  r#  r  r  r  r  r  	  r%  r  c	           	      C   s<   t |||  | |||   |  |||   | |  |S r  r  	r!  r  r   r"  r0  r!  r  r#  r  r  r  r  r  	  rL  r  c                 C   s\   t |
td| |  |||
|    |	  | |
td |   ||
|    | |  |
S r  r  r  r  r  r  r   	  r  r   c	           	      C   sL   t |td | |  ||||   |  | |td|   | |  |S r  r  r  r  r  r  r!  	  s   Lr!  c              	   C   s   t |
|t|	  |||
|    t|	  ||
|  | t|	   t|
| |	  ||
|  | |	  | ||
|   ||
td|    |  |
|
S r  r  r&   r   r  r  r  r  r  r"  	  s   r"  c	           	      C   s   t || t|  ||||   t|  |||   | t|   t|||  | |||   |  |||   | |  ||S r  r  r&   r   r  r  r  r  r#  	  s   r#  c                 C   s   t |
td | t|  | ||
|   ||
td|    t|  | |
td |   ||
|    | t|   t|
td| |  |||
|    |	  | |
td |   ||
|    | |  |
|
S r  r  r  r  r  r  r$  	  r`  r$  c	           	      C   s   t || t|  | |||   t|  | |td|   | t|   t|||  ||||   |  | |td|   | |  ||S r  rM  r  r  r  r  r%  	  r+  r%  c
           
      C   sP   t |	| |  |||	|   |  | |	|  | ||	td|    |  |	S r  r  
r!  r  r  r   r"  r0  r  r  r#  r  r  r  r  r&  	  r%  r&  c
           
   	   C   s   t |	|t|  | ||	|    ||	|   t|  | |	|  | ||	td|    t|   t|	| |  |||	|   |  | |	|  | ||	td|    |  |	|	S r  rM  r  r  r  r  r'  	  s   r'  c                 C   s   t td| t|	  |td| ||   td t|	   | |||   ||td|    t|	  t|td| ||   td|	  ||||   |
  ||||   |  ||S r  r  r!  r  r  r   r"  r(  r&  r  r!  r  r#  r'  r  r  r  r  r)  
  s   r)  c                 C   sN   t ||||   |	|
  ||||   |  | | |||  |  |	  |S r  r  r  r  r  r  r*  
     Nr*  c                 C   sN   t ||||   ||	  ||||   |
  | | |||  |  |  |S r  r  r!  r  r   r"  r(  r&  r  r!  r  r#  r'  r  r  r  r  r+  	
  r  r+  c                 C   s   t ||||   t|	  | | |||  |  t|	   | |||   ||td|    t|	  t||||   |	|
  ||||   |  | | |||  |  |	  ||S r  rM  r  r  r  r  r,  
     r,  c                 C   s   t | ||td|    t| ||||   t|   | | |||  |  t|   t||||   ||	  ||||   |
  | | |||  |  |  ||S r  r  r  r  r  r  r-  
  r  r-  c           	      C   sf   t |ttttfrdS ttd |  | |td  td}ttd| | |||   r1dS dS r8  r  	r!  r  r  r   r"  r(  r&  r  r#  r  r  r  r.  
  r  r.  c           	      C   s.  t td |  | |td  td}ttd| | |||   td| | |||    ttdt| ||td   ||td    ||t| | ||  td| | |||    t|td| |td   | |||td   t| ||td   ||td     || S r2  r  r  r  r  r  r/  
  s   ( r/  c                 C   sF   t |ttttfrdS t|  | td}t|| ||  r!dS dS r  r  r!  r  r   r"  r(  r&  r  r#  r  r  r  r0  $
  r  r0  c                 C   s   t |  | td}t|| ||  || ||   ttdt| ||td    ||t| | ||  || ||   t| |td  | t| ||td   |||td     || S r  r  r  r  r  r  r1  -
  s   r1  c                 C   sJ   t || || ||   | | |||   ||td|    |
  |S r  r  r!  r  r  r  r  r"  r#  r  r!  r1  r  r#  r  r  r  r  r4  3
  rW  r4  c              	   C   s   t ||||td    t| ||||td    t|  || || ||   t|   t|| || ||   | | |||   ||td|    |
  ||S r  r  r  r  r  r  r5  7
     r5  c              
   C   s   t | t||||   | ||||   ||td|    |
  ||t |t|| ||||   |  ||||   ||td|    |
  || S r  r  )Ar)  r!  r  r  r   r"  r  r  r!  r  r#  r  r  r  r  r7  ;
  r"  r7  c              
   C   s   t | t|||td|    |	 ||||   |
  ||t |t|| |||td|    |	  ||||   |
  || S r  r  )r  r)  r!  r  r   r"  r  r  r!  r  r#  r  r  r  r  r8  ?
  rY  r8  c              
   C   s   t |td|td |   ||  | tt||
 |	td |td |   | ||
  ||
td   |  |
|
|
| |
S rl  rR  r!  r  r  r"  r(  r  r  r!  r  r#  r  r  r  r  r9  C
  s   r9  c
           
   
   C   sz   t |td|td |   ||  | tt||	 |td |td |   | ||	td   |  |	|	|	| |	S rl  rR  
r!  r  r"  r(  r  r  r!  r  r#  r  r  r  r  r:  G
     zr:  c              	   C   s|   t |t|	 ||  |
| t|	   ||
|  t|	  t|
|||	   | ||
|   ||
td|    |  |
|
S r  ru  r  r  r  r  r;  K
  s   |r;  c
           
   	   C   sp   t |t| ||  |	| t|   ||	|  t|  t|	|||   | ||	td|    |  |	|	S r  ru  r  r  r  r  r<  O
  r  r<  c              	   C   st   t |t| |
t|   ||
 t|  t|
| ||
|  |	  | ||
|   ||
td|    |  |
|
S r  ru  r  r  r  r  r=  S
  s   tr=  c
           
   	   C   sh   t |t| |	t|   ||	 t|  t|	| ||	|  |  | ||	td|    |  |	|	S r  ru  r  r  r  r  r>  W
  s   hr>  c              
   C   sR   t td| tt|||
  |	 | ||
  ||
td   |  |
|
|
| |
S rN  rR  r!  r  r  r   r"  r  r  r!  r  r#  r  r  r  r  r?  [
  rQ  r?  c
           
   	   C   sJ   t td| tt| ||	td   | |||	  |  |	|	|	| |	S rN  rR  
r!  r  r   r"  r  r  r!  r  r#  r  r  r  r  r@  _
  rW  r@  c                 C   sd   t |
||td| |	    ||
|   | |	  | |
td |   ||
|    | |  |
S r  r  r  r  r  r  rA  c
  rv  rA  c
           
      C   sV   t |	||td| |    | |	td |   | |  ||	|   | |  |	S r  r  r  r  r  r  rB  g
  r  rB  c              
   C   n   t td| tt|
td|td |   |||
  |	  | ||
  ||
td   |  |
|
|
| |
S rl  rR  r  r  r  r  rC  k
  r]  rC  c                 C   s   t |t|	  |td |||   td t|	   | |||   ||td|    t|	  t|| | |td |||   td|	   ||||   |
  ||S r  r*  r!  r  r  r   r"  r(  r  r  r!  r  r#  r  r  r  r  rD  o
  r  rD  c              
   C   r  rl  rR  r  r  r  r  rE  s
  r]  rE  c
           
   
   C   sf   t td| tt|	td|td |   | ||	td   |  |||	  |  |	|	|	| |	S rl  rR  r  r  r  r  rF  w
  r  rF  c              	   C   x   t |t| |t|   || t|  t|| ||||   |
  | |||   ||td|    |	  ||S r  ru  r  r  r  r  rG  {
     xrG  c              	   C   l   t |t| |
t|   ||
 t|  t|
| | ||
td|    |  |||
|   |	  |
|
S r  ru  r!  r  r   r"  r(  r  r  r!  r  r#  r  r  r  r  rH  
     lrH  c                 C   sF   t || | ||||   |	|
   | | |||  |  |	  |S r  r  r  r  r  r  rI  
  r  rI  c                 C   sF   t ||
 | |||
|   ||	   | | ||
|  |  |  |
S r  r  r  r  r  r  rJ  
  r  rJ  c                 C   s   t ||||   t|	  | | |||  |  t|	   | |||   ||td|    t|	  t|| | ||||   |	|
   | | |||  |  |	  ||S r  rM  r  r  r  r  rK  
  r  rK  c                 C   s   t | ||
td|    t| |||
|   t|   | | ||
|  |  t|   t||
 | |||
|   ||	   | | ||
|  |  |  |
|
S r  r  r  r  r  r  rL  
  rc  rL  c                 C   s>  t |td | |t|| |   ||	td   t|
t|| |||
|   |	td   tt|td| |t|| |   | |
|t||   |	td  | ||
|   ||
td|    |  | td|t|| |   |t||td  ||
|  ||	td  t|| td    | |td  || |  ||td   |   |||
|    |
 |
|
t|td | |t|| |   |
t||td   | td|t|| |    |||
|   |	td   | |td  || |  ||td   |  ||	td   |
 S r-  r  r  r  r   r2  r   r  r  r  r  r  rM  
  s    B rM  c
           
      C   s  t |td | |t|| |   ||td   t|	t|| |||	|   |td   tt|td| |t|| |   | |	|t||   | ||	td|    |  |td  | td|t|| |   | |td  ||td   |  |t||td  ||	|  ||td  t|| td     |||	|    |	 |	|	t|td | |t|| |   |	t||td   | td|t|| |    |||	|   |td   | |td  ||td   |  ||td   |	 S r-  r	  r  r  r  r  rN  
  s     rN  c                 C   sN  t |td |  | td|t|| |    ||	td   t|
| |||
|   |	td   tt|td|  | | td|t|| |    |	td  | ||
|   ||
td|    |  ||t||  |  |
| t||   |t||td  ||
|  ||	td  t|| td    | |td  || |  ||td   |   |||
|    |
 |
|
t|td | |t|| |   |
t||td   | td|t|| |    |||
|   |	td   | |td  || |  ||td   |  ||	td   |
 S r&  r	  r  r  r  r  rO  
  s    R rO  c
           
      C   s*  t |td |  | td|t|| |    ||td   t|	| |||	|   |td   tt|td|  | | td|t|| |    | ||	td|    |  |td  ||t||  |  |	| t||   | |td  ||td   |  |t||td  ||	|  ||td  t|| td     |||	|    |	 |	|	t|td | |t|| |   |	t||td   | td|t|| |    |||	|   |td   | |td  ||td   |  ||td   |	 S r&  r	  r  r  r  r  rP  
  s    . rP  c                 C   s  t td||td| |	  ||
  td   t|| | ||||   |
  t||	  | |td| |	 |   |td| |	  | td  |||	  |td| |	   | |||   ||td|    |	   |td| |	  ||
  td   | ||t||	 |td | |	 | td   || |td| |	  | td   ||||   |
td   ||td| |	  ||
  td   | S re  r  r  r   r2  r  r  r  r  r  rQ  
  s    rQ  c                 C   s  t td||td| |  ||	  td   t||
 | |||
|   |	  t||  | |
td| | |   |td| |  | td  |||  |
td| |   | ||
td|    |   |td| |  ||	  td   |
 |
|
t|| |td | | | td   ||
 |td| |  | td   |||
|   |	td   ||td| |  ||	  td   |
 S re  r	  r  r  r  r  rR  
  s    rR  c                 C   T   t t|| | ||||   |
  | |||   ||td|    |	  ||S r  r,  r  r  r  r  rS  
     TrS  c                 C   H   t t||
 | | ||
td|    |  |||
|   |	  |
|
S r  r,  r  r  r  r  rT  
  r  rT  c                 C   s>   t |
ttttfrdS t|td |}t|tdrdS dS rw  rx  r!  r  r  r   r"  r  r  r!  r  r#  r  r+  r  r  r  rU  
  rz  rU  c              
   C   s   t |td |}ttd| tt|
td|td |   |||
||    |	  | ||
||    ||
td| |    |  |
|
|
| |
S rl  r{  r	  r  r  r  rV  
  s   rV  c
                 C   s>   t |	ttttfrdS t|td |}
t|
tdrdS dS rw  rx  r!  r  r   r"  r  r  r!  r  r#  r  r+  r  r  r  rW  
  rz  rW  c
              
   C   s   t |td |}
ttd|
 tt|	td|td |
   | ||	td| |
    |  |||	||
    |  |	|	|	|
 |	S rl  r{  r	  r  r  r  rX  
  s   vrX  c              
   C   s   t |}t|| tt|||td  td  ||||   |||    |
  | |||   |||    ||td |   |td| |    |	  |||| td|  |S rl  r  )r!  r  r  r   r"  r(  r  r  r!  r  r#  r  r+  r  r  r  rY  
  s   rY  c              
   C   s   t |}t|| tt|
||td  td  | ||
td| |   |  |  |||
||   |  |	  |
|
||
 td|  |
S rl  r  )r!  r  r   r"  r(  r  r  r!  r  r#  r  r+  r  r  r  rZ  
     rZ  c                 C   s  t ||  | |	 |td ||td|	 td   td   t||
 ||  | ||
|   ||
td|    |	td   ttd|  | |td  || ||td|	 td   td   |
| || |td  td| | ||td|	 td   td     |
 |
|
t||
 |td  |||td|	 td   td  ||
|  |td    | ||
|   ||
td|    |	  ||td  ||td|	 td   td   |
 S re  r'  r!  r  r  r   r"  r(  r  r  r!  r  r  r  r  r  r[  
  s    r[  c
           
      C   sz  t td||   | | |td ||td| td   td   t||	 ||  | ||	td|    |td   | | |td  || |	|  ||td| td   td    |	|	t||	 |td  | ||	td|    |  |||td| td   td  ||	|  |td    ||td  ||td| td   td   |	 S r-  r'  
r!  r  r   r"  r(  r  r  r!  r  r  r  r  r  r\  
  s   | r\  c                 C   sh  t ||	 ||td| |	  td  ||td|	 td   td   t||
 | | ||
|   ||
td|    |	td   t|  | | |td  td|  | | ||td|	 td   td   |
| td|  | | |td| |	  td  |td | |||	  td   || | ||td|	 td   td     |
 |
|
t||
 |td  | ||
|   ||
td|    |	  || | |	 || ||td|	 td   td   || |
|  |td| |	  td    || |td| |	  td  ||td|	 td   td   |
 S r-  r'  r		  r  r  r  r]  
  s    l r]  c
           
      C   s  t td|  | | |td| |  td ||td| td   td   t||	 | | ||	td|    |td   t|||td| td   td  ||	|  |td| |  td   |	 |	|	t||	 |td  | ||	td|    |  || ||td| td   td  || |	|  |td| |  td    || |td| |  td  ||td| td   td   |	 S r-  r'  r
	  r  r  r  r^  
  s    r^  c              
   C   s  t || ||	td  td |  | |td    t||
 ||  | ||
|   ||
td|    |	td   t|
| || td| |   |td| |	  td|  td  td |  | ||  | | td   |
 |
|
t||td  ||
 || td   | ||
|   ||
td|    |	td   td |  | ||  |
| || td| |     ||	td  td |  | |td    |
 S r~  r'  r		  r  r  r  r_  
  rd  r_  c
           
   	   C   sB  t || td|  | | |td   t||	 ||  | ||	td|    |td   | | | | td  || |	|  |td| |  td|  td    |	|	t||td  ||	 || td   | ||	td|    |td   | | || |	|    td|  | | |td   |	 S r-  r'  r
	  r  r  r  r`  
  s   D r`  c                 C   "  t td| | |	td  td |  | |td    t||
 | | ||
|   ||
td|    |	td   t|  | | |td  ||
|  td |  | ||   ||td|	 td   td   |td |  | |td| |	td   td  |td |||	td   td     |
 |
|
t||
 |td  | ||
|   ||
td|    |	td   |  | | ||
|  td |  | ||    |td |  | |td     | | | |	td  td |  | |td    |
 S r/  r'  r		  r  r  r  ra  
      & ra  c
           
      C   *  t tdtd|  | |td   t||	 | | ||	td|    |td   t||td| |td   td  ||	|  ||td| td   td   |	 |	|	t||	 |td  | ||	td|    |td   |||	|    td|  | | |td   |	 S r  r'  r
	  r  r  r  rb  
     , rb  c                 C   sl  t || |||td|	 td   td   t||
 ||  | ||
|   ||
td|    |	  t| | || td  |
| || |||	  td  || ||td|	 td   td     |
 |
|
 t|||td   ||
 || td   | ||
|   ||
td|    |	td   |||td|	 td   td   |
 S r-  r'  r		  r  r  r  rc  
  s   n rc  c
           
      C   s2  t || |||td| td   td   t||	 ||  | ||	td|    |  | | || td  || |	|  ||td| td   td    |	|	 t|||td   ||	 || td   | ||	td|    |td   |||td| td   td   |	 S r-  r'  r
	  r  r  r  rd  
  s   4 rd  c                 C   s0  t ||  | |td   t||
 ||  | ||
|   ||
td|    |	  t| | |td  || |||	td   td   || |
|  |td| |	td   td   |
 |
|
t|||
 |td   | ||
|   ||
td|    |	td   | | |td   |
 S rN  r'  r		  r  r  r  re    s   2 re  c
           
      C   s   t ||  | |td   t||	 ||  | ||	td|    |  | | |td  || |	|  |td| |td   td    |	|	t|||	 |td   | ||	td|    |td   | | |td   |	 S rN  r'  r
	  r  r  r  rf    r[  rf  c
                 C   v   t |	ttttfrdS t| | td}
t| | td| |
  td}tt| | td| |
  r9dS dS r  	r9  r:  r  r;  r  r  r  r6   r   r!  r  r  r   r"  r(  r  r  r!  r  r#  r'  r  r  r  rg       $"rg  c
                 C   s  t | | td}
t | | td| |
  td}t|d|
 |  t||	 | t|| |	|d  || ||
    |	 ||	|  |
 ||	|d     |	|	t|d|
 |  t||	 | t|| |	|d  || ||
    |	 ||	|  |
 ||	|d     |	|	 S r  r  r  r  r   r  r	  r  r  r  rh    s   $rh  c	                 C   b   t |ttttfrdS t| | td}	ttd| |	 td}
tttd| |	 r/dS dS r  r	  r!  r  r   r"  r(  r  r  r!  r  r#  r'  r  r  r  ri       ri  c	                 C   s  t | | td}	t td| |	 td}
t|d|	 |
  t|| | t||
 ||d  || ||	    | |||  |	 |
||d     ||t|d|	 |
  t|| | t||
 ||d  || ||	    | |||  |	 |
||d     || S r  r	  r	  r  r  r  rj  &  s   rj  c           	   
   C   s   t || | td| |   | td}t|td t|| | || | ||td   ||   ||t|td t|| | || | ||td   ||   || S r  r1  )	r!  r  r  r   r"  r(  r  r  r'  r  r  r  rk  -  s   ,rk  c              
   C   s   t td|td  | | td}t|td t|| | || | ||td   ||   ||t|td t|| | || | ||td   ||   || S r  r1  )r!  r  r   r"  r(  r  r  r'  r  r  r  rl  2  s   &rl  c
                 C   r	  r  r	  r	  r  r  r  rm  7  r	  rm  c
              
   C   s
  t | | td}
t | | td| |
  td}t|d|
 |  t||	 | || |	|d  || ||
     ||	|  |
 ||	|d     |	|	t|d|
 |  t||	 | || |	|d  || ||
     ||	|  |
 ||	|d     |	|	 S r  r1  r	  r  r  r  rn  A  s   $rn  c	                 C   r	  r  r	  r	  r  r  r  ro  H  r	  ro  c	              
   C   s   t | | td}	t td| |	 td}
t|d|	 |
  t|| | ||
 ||d  || ||	     |||  |	 |
||d     ||t|d|	 |
  t|| | ||
 ||d  || ||	     |||  |	 |
||d     || S r  r1  r	  r  r  r  rp  R  s   rp  c
              	   C   s   t td |  | |td  td}
t|td | | td| |  td|
   t||	 | |td ||	|   |
td   |	|	t|td | | td| |  td|
   t||	 | |td ||	|   |
td   |	|	 S r  r1  )r!  r  r  r   r"  r(  r  r  r!  r  r#  r  r  r  rq  Y  s   (rq  c	           
      C   s   t |  | td}	t| | td|	  |td  t|| | |||  |	  ||t|| td|	  |td  t|| | | ||  |	  || S r  r1  )
r!  r  r   r"  r(  r  r  r!  r  r#  r  r  r  rr  ^  s   rr  c                 C   sP   t t||
 | |||
|   |	  | ||
|   ||
td|     |
|
S r  r,  r!  r  r  r   r"  r(  r  r  r!  r#  r  r  r  r  rs  c  r%  rs  c
           
      C   sD   t t||	 | |||	|   |  | ||	td|     |	|	S r  r,  
r!  r  r   r"  r(  r  r  r!  r#  r  r  r  r  rt  g  r  rt  c              	   C   sN   t t||
 | |||
|   |	 | ||
|   ||
td|     |
|
S r  r,  r	  r  r  r  ru  k  r  ru  c
           
   	   C   sB   t t||	 | |||	|   | | ||	td|     |	|	S r  r,  r	  r  r  r  rv  o  rT  rv  c                 C   sF  t |td|  |td  t||
 |td|   |||
|   |	td   | | ||  || |
|    |
|
t |td|  |td  t||
 |td|   |||
|   |	td   t| | | ||   |
| | | | |td |  || |    |
 | ||
|   ||
td|     |
|
 S r  r'  r	  r  r  r  rw  s     H rw  c
           
   
   C   s   t |td|  | t||	 |td|   |||	|   |  |	|	t | |td|   | t||	 |td|   |||	|   |  | ||	td|     |	|	 S r  r  r	  r  r  r  rx  w  r  rx  c              
   C   s   t || | t||
 ||  |||
|   |	td   t| | |
| | | ||    |
 | ||
|   ||
td|     |
|
 t |||  | t||
 ||  |||
|   |	td   |
|
 S Nr  r  rZ  r	  r  r  r  ry  {     ry  c
           
   	   C   s   t || | t||	 ||  |||	|   |td   t| | || |	|   |	 | ||	td|     |	|	 t |||  | t||	 ||  |||	|   |td   |	|	 S r	  rZ  r	  r  r  r  rz    r  rz  c              
   C   s   t ||  t||
 | |||
|   |	td   |
|
t ||  |  t||
 ||  |||
|   |	td   t|  | ||  || |
|   |
 | ||
|   ||
td|     |
|
 S r	  rZ  r	  r  r  r  r{       r{  c
           
   
   C   s   t ||  t||	 | |||	|   |td   |	|	t ||  |  t||	 ||  |||	|   |td   t| | || |	|   |	 | ||	td|     |	|	 S r	  rZ  r	  r  r  r  r|    s   r|  c              
   C   sF  t |td|  | |td  || |  ||td    t||
 |td|   |||
|   |	td   t| | |
| |  | ||    |
 | ||
|   ||
td|     |
|
 t |td |td|   | |td  || |  ||td    t||
 |td|   |||
|   |	  |
|
 S r  r'  r	  r  r  r  r}    r	  r}  c
           
   	   C   s  t | |td|   | |td  ||td    t||	 |td|   |||	|    |||	|   |td   | ||	td|     |	|	 t |td |td|   | |td  ||td    t||	 |td|   |||	|   |  |	|	 S r  r  r	  r  r  r  r~    r  r~  c              	   C   s  t || | |td  || |  ||td    t||
 ||  |||
|   |	td   t| | || |
|   |
 | ||
|   ||
td|     |
|
t || ||  | |td  || |  ||td    t||
 ||  |||
|   |	  |
|
 S r  r'  r	  r  r  r  r    r  r  c
           
   	   C   s   t || | |td  ||td    t||	 ||  |||	|   |td   t| | || |	|   |	 | ||	td|     |	|	t || ||  | |td  ||td    t||	 ||  |||	|   |  |	|	 S r  r'  r	  r  r  r  r    r  r  c              
   C   s  t |td | |td  || |  ||td    t||
 | |||
|   |	  |
|
t td| |td  || |  ||td    t||
 | |||
|   |	td   t| | ||  || |
|   |
 | ||
|   ||
td|     |
|
 S r  r'  r	  r  r  r  r    s    r  c
           
   	   C   s   t || |td  ||td    t||	 | |||	|    |||	|   |td   | ||	td|     |	|	t |td | |td  ||td    t||	 | |||	|   |  |	|	 S r  r  r	  r  r  r  r    r|  r  c              	   C   sN   t t|||
|   |	 ||
 | | ||
|   ||
td|     |
|
S r  r,  r	  r  r  r  r    r  r  c
           
   	   C   sB   t t|||	|   | ||	 | | ||	td|     |	|	S r  r,  r	  r  r  r  r    rT  r  c              	   C   sV   t t||
 | |||
|   |	  td| ||
|   ||
td|     |
|
S rN  r,  r	  r  r  r  r    r  r  c
           
   	   C   sJ   t t||	 | |||	|   |  td| ||	td|     |	|	S rN  r,  r	  r  r  r  r    rW  r  c              
   C   s   t |td t||
 | | | |
| |  | ||     | ||
|   ||
td|    |	td   |
|
t |td |  | |td  || |  ||td    |td  t||
 |td|   | ||
|   ||
td|    |	td   |||
|    |
|
 S )Nrj  r  r  r  r		  r  r  r  r    s   " r  c
           
   
   C   s   t | |td  t||	 | | ||	td|    |td   |||	|    |	|	t |td |  | |td  ||td    |td  t||	 |td|   | ||	td|    |td   |||	|    |	|	 S r  r  r
	  r  r  r  r    r[  r  c              
   C   s  t td||  t||
 | | | || |
|    | ||
|   ||
td|    |	td   |
|
t ||  | |td  || |  ||td    ||  t||
 ||  | ||
|   ||
td|    |	td   |||
|    |
|
 S re  r  r		  r  r  r  r    r\  r  c
           
   
   C   s   t td||  t||	 | | ||	td|    |td   | | || |	|    |	|	t ||  | |td  ||td    ||  t||	 ||  | ||	td|    |td   |||	|    |	|	 S re  r  r
	  r  r  r  r       r  c              
   C   sT  t |td|  | |td  || |  ||td    t||
 |td|   | | |
| |  | ||     | ||
|   ||
td|    |	  |
|
 t |td |td|   | |td  || |  ||td    t||
 |td|   | ||
|   ||
td|    |	td   |||
|    |
|
 S r  r  r		  r  r  r  r    r  r  c
           
   
   C   s  t | |td|   | |td  ||td    t||	 |td|   | ||	td|    |  |||	|    |	|	 t |td |td|   | |td  ||td    t||	 |td|   | ||	td|    |td   |||	|    |	|	 S r  r  r
	  r  r  r  r    r  r  c              
   C   s$  t || | |td  || |  ||td    t||
 ||  | | || |
|    | ||
|   ||
td|    |	  |
|
t || ||  | |td  || |  ||td    t||
 ||  | ||
|   ||
td|    |	td   |||
|    |
|
 S r  r  r		  r  r  r  r    s   & r  c
           
   
   C   s   t || | |td  ||td    t||	 ||  | ||	td|    |  | | || |	|    |	|	t || ||  | |td  ||td    t||	 ||  | ||	td|    |td   |||	|    |	|	 S r  r  r
	  r  r  r  r    s   r  c                 C   sR   t t| |||   ||td|    |	 || | ||||   |
  ||S r  r,  r  r  r  r  r    rQ  r  c                 C   sF   t t| ||
td|    | ||
 | |||
|   |	  |
|
S r  r,  r  r  r  r  r    r  r  c                 C   sl   t t|
| td  |||
|    |	  | ||
|    ||
td |    |  |
|
td|
  S ri  r$  r  r  r  r  r    r 	  r  c
           
      C   s^   t t|	| td  | ||	td |    |  |||	|    |  |	|	td|	  S ri  r$  r  r  r  r  r    rs  r  c              
   C   s   t |}t|| tt|| |td  td  ||||   || |    |
  | |||   || |    ||td |   |td | |    |	  |||| td |  | S rl  r  )r!  r  r  r   r"  r(  r  r  r!  r  r#  r  r&  r  r  r  r    s   r  c              
   C   s   t |}t|| tt|
| |td  td  | ||td |   |
td | |    |  ||||   |
| |    |	  |
|
||
 td |  |
 S rl  r  )r!  r  r   r"  r(  r  r  r!  r  r#  r  r&  r  r  r  r    s   r  c              
   C   s   t |t| || t|  td| t|  tt|| td  ||||    |
  | |||    ||td |    |	  ||td| | S rp  rq  r  r  r  r  r       r  c              
   C   s   t |t| ||
 t|  td|
 t|  tt|
| td  | ||
td |    |  |||
|    |	  |
|
td|
 |
 S rp  rq  r  r  r  r  r    r+  r  c              
   C   s   t |}t|tt|
||td  td  |||
||    |	  | ||
||    ||
td| |    |  |
|
|
td|  |
S rl  r  )r!  r  r  r   r"  r  r  r!  r  r#  r  r&  r  r  r  r    r	  r  c
              
   C   s~   t |}
t|
tt|	|
|td  td  | ||	td|
 |    |  |||	|
|    |  |	|	|	td|
  |	S rl  r  )r!  r  r   r"  r  r  r!  r  r#  r  r&  r  r  r  r    s   vr  c              	   C   r  r  ru  r  r  r  r  r    r  r  c              	   C   r  r  ru  r  r  r  r  r    r 	  r  c                 C   s   t td|td  tt|||
||td     |	 | ||
||td     ||
td| |td     |  |
|
|
|td  |
S rN  rR  r  r  r  r  r    r+  r  c
           
      C   sz   t td|td  tt| ||	td| |td     | |||	||td     |  |	|	|	|td  |	S rN  rR  r  r  r  r  r    r  r  c              	   C   r  r  ru  r  r  r  r  r    r  r  c              	   C   r  r  ru  r  r  r  r  r    r 	  r  c              	   C   s   t td |  | |td  td}ttd| | t||
 | |||
|   |	  |td| |
|   |  |
|
ttd| | t||
 | |||
|   |	  |td| |
|   |  |
|
 S r  r1  )r!  r  r  r   r"  r(  r  r  r!  r#  r  r'  r  r  r  r    s   (r  c
              	   C   s   t |  | td}
t|td|
  t||	 | |||	|   |  | |	|  |
  |	|	 t|td|
  t||	 | |||	|   |  ||	|  |
  |	|	 S r  r1  )r!  r  r   r"  r(  r  r  r!  r#  r  r'  r  r  r  r    s   r  c                 C   r	  r/  r'  r		  r  r  r  r  !  r	  r  c
           
      C   r	  r  r'  r
	  r  r  r  r  %  r	  r  c                 C   r	  r  r,  r  r  r  r  r  )  r	  r  c                 C   r	  r  r,  r  r  r  r  r  -  r  r  c                 C   s   t || tt|
| | ||
td|    |  ||td |td |
td|     ||
|  |td |td |
td|      |	  |
|
|
S r  )r  r   r   r  r  r  r  r  r  1  r	  r  c              	   C   sX   t |
|  ||
 |  t|
| | ||
td|    |  |||
|   |	  |
|
S r  r  r  r  r  r  r  5  r  r  c                 C   sN   t || | ||||   |
  | |||   ||td|    |	  |S r  r  r  r  r  r  r  9  r  r  c                 C   sB   t ||
 | | ||
td|    |  |||
|   |	  |
S r  r  r  r  r  r  r  =  rT  r  c              
   C   sx   t |
| ||   t||td tt|| ||||   |	  | |||   ||td|    |  ||||S rN  r  )r!  r  r  r   r"  r  r  r!  r  r#  rP  r  r  r  r  r  r  A  r  r  c              
   C   sl   t |	| |
|   t|
|td tt|| | ||td|    |  ||||   |  |||
|S rN  r  )r!  r  r   r"  r  r  r!  r  r#  rP  r  r  r  r  r  r  E  r 	  r  c                 C   sR   t ||||
   |||  | |
  | |||   ||td|    |	  |S r  r  r!  r  r  r   r"  r  r0  r  r!  r  r#  r  r  r  r  r  I  rQ  r  c
           
      C   s@   t |	|||   | ||	|   |  ||	|   | |  |	S r  r  
r!  r  r   r"  r  r0  r!  r  r#  r  r  r  r  r  M  rV  r  c                 C   s`   t ||td| |	   ||||    |
  | |td |   |||    | |	  |S r  r  r	  r  r  r  r  Q  r  r  c
           
      C   sN   t |	|td| |   |||	|   |  | |	td|   | |  |	S r  r  r 	  r  r  r  r  U  r  r  c              	   C   s   t ||t|
  ||||    t|
  |||  | t|
   t||||
   |||  | |
  | |||   ||td|    |	  ||S r  r  r	  r  r  r  r  Y  r   r  c
           
      C   s   t |	| t|  |||	|   t|  ||	|   | t|   t|	|||   | ||	|   |  ||	|   | |  |	|	S r  r  r 	  r  r  r  r  ]  rr  r  c              	   C   sx   t |t| |t|   || t|  t|| ||||   |  | |||   ||td|    |
  ||S r  ru  )r!  r  r  r   r"  r(  r  r0  r  r!  r  r#  r  r  r  r  r  a  r  r  c              	   C   sl   t |t| |
t|   ||
 t|  t|
| | ||
tdt    |  |||
|   |	  |
|
S r  )r  r%   r&   r   r  r  )r!  r  r   r"  r(  r  r0  r!  r  r#  r  r  r  r  r  e  r 	  r  c                 C   sR   t |
|||   |||
|   |	  | |
|  | ||
td|    |  |
S r  r  r!  r  r  r   r"  r  r0  r  r  r#  r  r  r  r  r  i  rQ  r  c              	   C   s   t |
|t|  | ||
|    ||
|   t|  | |
|  | ||
td|    t|   t|
|||   |||
|   |	  | |
|  | ||
td|    |  |
|
S r  rM  r!	  r  r  r  r  m  r  r  c                 C   sr   t |t| |t|   || t|  t|| ||||   |
  | |||    |||   |	  ||S r  r  )r!  r  r  r   r"  r(  r  r0  r  r  r#  r  r  r  r  r  q  r  r  c                 C   sV   t || | || || ||	   |  | |||	   ||td|	    |  |S r  r  r!  r  r  r  r  r"  r#  r(  r  r  r!  r1  r  r#  r  r  r  r  r  u  r  r  c              	   C   s   t ||||	td    t| ||||	td    t|  || || ||	   t|   t|| | || || ||	   |  | |||	   ||td|	    |  ||S r  r  r"	  r  r  r  r  y  r.  r  c                 C   s   t || | | |  | |S r  r  r!  r  r  r  r  r#  r'  r  r  r  r  r  }  s   r  c                 C   sJ   t |||  | ||||    ||td| td|     |  |S r  r  r#	  r  r  r  r    rW  r  c                 C   s   t || td  t| ||  |||   ||td| |     t| ||||    ||td| td|      t||td  t| ||||    ||td| td|      ||S r  r  r  r  r   r!  r  r  r  r#  r'  r  r  r  r  r    r  r  c                 C   s   t ||td  t| ||||    ||td| td|      t| ||  |||   ||td| |     t|| td  t| ||||    ||td| td|      ||S r  r$	  r%	  r  r  r  r    r  r  c              	   C   s   t |||  |td| |  td  t|| td|  ||||     | ||  |||   ||td| |    |td   ||t|| ||  |||   ||td| |    |  |td| |  td  | S r-  r'  r#	  r  r  r  r    r  r  c              
   C   s  t td| ||  |td  td |  | |td    t||  | ||  |||   ||td| |    |td   || |||   || || td| td   td  || |td  td |  | |td    td |  | |td  || td    ||t|td|  td |  | |td  || |||     | ||  |||   ||td| |    |td   | ||  |td  td |  | |td    | S r/  r'  r#	  r  r  r  r    s    r  c              
   C   s   t || |  | ||||    ||td| td|     |   | ||  |||   ||td| |    |  t|||  | ||||    ||td| td|     |  ||S r  r  r#	  r  r  r  r    r	  r  c                 C   s:   t | ||  |||   ||td| |    | |S r  r  r#	  r  r  r  r    r  r  c	           	   	   C   s^   t tdt||td tt| ||  |||   ||td| |    | ||||S rN  rO  )	r!  r  r  r  r  r#  r'  rP  r  r  r  r  r    rs  r  c	           	      C   s&   t || || | | |  |  |S r  r  	r!  r  r  r  r  r  r#  r'  r  r  r  r  r    s   &r  c	           	      C   sN   t ||||   | ||||    ||td| td|     |  |S r  r  r&	  r  r  r  r    r  r  c                 C   s   t ||td  t| ||||    ||td| td|      t| ||  |||   ||td| |     t|||td   t| ||||    ||td| td|      ||S r  r$	  r!  r  r  r  r  r#  r'  r  r  r  r  r    s   r  c              
   C   s   t td ||td tdd    |td| |   td |  | |td  t| ||td   |||   |||td      |S Nr  r  r  r  r_  r'	  r  r  r  r    r  r  c              
   C   s   t ||td tdd   td|  td| |   td |  | |td  t| ||td   |||   |||td      |S r(	  r_  r'	  r  r  r  r    s   r  c	           	   
   C   s   t |td|  t||td  | ||td   |||   |||td    |  || t|||  | ||td   |||   |||td    |td   td| |td   | S r&  r'  r&	  r  r  r  r       r  c	           	   	   C   s,  t |td |  | |td   td| td| td   t|||  | ||  |||   ||td| |    |td   || t||| | td  |td| |||     | ||  |||   ||td| |    |  td| ||  td| td   | S )Nr  r  r  r  r'  r&	  r  r  r  r    r  r  c	           	      C   s`  t |||  |||td| |   td  |||  || td| td   td   t||| td|   | ||  |||   ||td| |    |td   t|  | || ||  | td  |||  td|  | |||  || td| td   td  |td |||  || |td   td     | ||t||| | td  || ||  ||||   |||  || td| td   td    | ||  |||   ||td| |    |  |||td| |   td  |||  || td| td   td   | S r-  r'  r&	  r  r  r  r    s    d r  c	           	   	   C   s   t |||  |||  td  t|||  |td| |||     | ||  |||   ||td| |    |td   || t||td  | ||  |||   ||td| |    |  |||  td  | S re  r'  r&	  r  r  r  r    r[  r  c	           	   	   C   s  t |||  ||td| |   td  t|||  td|  ||||     | ||  |||   ||td| |    |td   ||t||td  | ||  |||   ||td| |    |  ||td| |   td  | S r-  r'  r&	  r  r  r  r    r  r  c	           	   	   C   sf  t td|  | |td |td   | |td  td |  | |td    t|||  | ||  |||   ||td| |    |td   ||t||| td  td |  | |td  || |||     | ||  |||   ||td| |    |td   | ||  |td  td |  | |td    | S r  r'  r&	  r  r  r  r    s   h r  c	           	      C   s  t td|| |td  td |  | |td    t||td|  |  td|  |td|  ||  td|  td  ||||   |||  || td| td   td    | ||  |||   ||td| |    |td   ||t||td|  | td  td|  ||||     | ||  |||   ||td| |    |td   || |td  td |  | |td    | S r  r'  r&	  r  r  r  r    rd  r  c	           	      C   s  t td| ||  |td  td |  | |td    t|||  | ||  |||   ||td| |    |td   td |  | |||  td||  |td   td  |td |||  || |td   td   || |||   |||  || td| td   td    ||t||| td  td |  | |td  || |||     | ||  |||   ||td| |    |td   | ||  |td  td |  | |td    | S r/  r'  r&	  r  r  r  r    s     r  c	           	      C   s  t td|| |td  td |  | |td    t|||  ||| ||  | td  td| |||   |||  td||  |td   td    | ||  |||   ||td| |    |td   || t||| td  |td| |||     | ||  |||   ||td| |    |td   || |td  td |  | |td    | S r  r'  r&	  r  r  r  r    s    r  c	           	   	   C   s   t |td|  t||| |  | ||  |||   ||td| |    |  || t||td|  | td  | ||  |||   ||td| |    |td   td| ||  |td   | S r  r'  r&	  r  r  r  r    r	  r  c	           	   	   C   s   t |td|   t||| |  | ||  |||   ||td| |    |  || t||| td  | ||  |||   ||td| |    |td   td|  ||  |td   | S r  r'  r&	  r  r  r  r    r	  r  c	           	      C   s  t td||||  td| ||   td   t||td|  td|   | |td|  ||  td|  td  ||||   |||  || |td   td    | ||  |||   ||td| |    |  || t||td|  | td  | ||  |||   ||td| |    |td   ||||  td| ||   td   | S re  r'  r&	  r  r  r  r    r0  r  c	           	      C   sJ  t td| |||  td   t||| |  ||||  || |td   td  ||||   |||  td||  |td   td    | ||  |||   ||td| |    |  || t||| td  | ||  |||   ||td| |    |td   | |||  td   | S rN  r'  r&	  r  r  r  r    s   L r  c	           	   
   C   s   t || |  | ||||    ||td| td|     |   | ||  |||   ||td| |    |  t||||   | ||||    ||td| td|     |  ||S r  r  r&	  r  r  r  r    r)	  r  c
           
   
   C   sf   t tdt||	td tt|	| | |	|  ||	|   ||	td| |    |  |	|	||	S rN  rO  )
r!  r  r  r  r  r  r#  r'  rP  r  r  r  r  r    r  r  c                 C   s^   t |
||  | ||
||     |||
||    ||
td| td|     |  |
S r  r  r  r)  r!  r  r  r*  r  r  r#  r'  r  r  r  r  r    rs  r  c
           
      C   s   t |	|td  t|||	||    ||	td| td|      t||	|  ||	|   ||	td| |     t|	| td  | ||	||     t|||	||    ||	td| td|      |	|	S r  r$	  )
r  r)  r!  r  r  r*  r  r#  r'  r  r  r  r  r    r}  r  c                 C   s  t |||  ||td| |  td  || || td| td   td   t|
| ||
|  ||
|   ||
td| |    |td   td|  | | || || td| td   td  || | || td   |
||  | | | || || td| td   td  td| | | |td| |  td   ||td  || |||   td      |
|
t|
||
|  ||
|   ||
td| |    |  | | || || td| td   td  || | ||   || |
||   |td| |  td    ||td| |  td  || || td| td   td   |
 S r-  r'  r*	  r  r  r  r    s     r  c	           
   	   C   s   t |ttttfrdS || }	tt|td|	  | t|td|	 |  td t|| |	| td| td   td rEdS dS )NFr  r  T)	r9  r:  r  r;  r  r  r   r  r   
r  r)  r!  r  r*  r  r#  r'  r  r  r  r  r  r    s   hr  c	           
   
   C   s  || }	t ||	|  |td|	 |  td || |	| td| td   td   t|| |||  ||td|	 |    |td   td|  | || |	| td| td   td  td| | ||	|   |td|	 |  td    ||t|| || |	| td| td   td  |||	|   |td|	 |  td    |||  ||td|	 |    |  |td|	 |  td || |	| td| td   td   | S r-  r'  r+	  r  r  r  r        r  c                 C   sV  t td|||  |td  td | | |td    t|
|  ||
|  ||
|   ||
td| |    |td   td |  | | || td||  |td   td  | |td  || || |td   td   || | || td   ||
||   | | td| |   || || td| td   td    |
|
t|
td|  ||
|  ||
|   ||
td| |    |td   td |  | | | |td   || |  ||
||   | | td| |     |||  |td  td | | |td    |
 S r/  r'  r*	  r  r  r  r        Z r  c	           
      C   s>   t |ttttfrdS || }	t|td|	  | rdS dS r  )r9  r:  r  r;  r  r   r  r+	  r  r  r  r    s   r  c	           
      C   s  || }	t tdtd|td  | |	|  |td   t||  |||  ||td|	 |    |td   | | | || td|	|  |td   td  || | ||	|   || |	| td| td   td    ||t|td|  |||  ||td|	 |    |td   | | | || | ||	|     td|td  | |	|  |td   | S r  r'  r+	  r  r  r  r    s    r  c                 C   sN   t | ||
||    ||
|  ||
|   ||
td| |    |  |
S r  r  r*	  r  r  r  r    r  r  c              
   C   sr   t tdt|
|td tt| ||||    |||  |||   ||td| |    |  |||
|S rN  rO  )r  r)  r!  r  r  r*  r  r  r#  r'  rP  r  r  r  r  r  #  r  r  c                 C   sb   t ||||	   | ||||	     |||||	    ||td| td|	     |  |S r  r  r  r)  r!  r  r  r*  r  r  r  r#  r'  r  r  r  r  r  '  s   br  c                 C   sV  t |||	  |||	  td |||	  ||	 td| td   td   t|||  |||	  |||   ||td| |	    |td   t|  | |||	  ||	 td| td   td  td| | |||	  td   |||	  td |  | |||	  ||	 td| td   td  || |||	  td     | ||t||td  | |||	  ||	 td| td   td  ||||	   |||	  td    |||	  |||   ||td| |	    |  |||	  td |||	  ||	 td| td   td   | S re  r'  r.	  r  r  r  r  +  r-	  r  c
                 C   s   t |	ttttfrdS || }
tt|td|
  | t|
t	|||  |
 | t
|||  td tdt
|||  |
| td| td   td tdrWdS dS NFr  r  r   T)r9  r:  r  r;  r  r  r   r  r   rO   r$   r  r)  r!  r  r*  r  r  r#  r'  r  r  r  r  r  r  /  s   r  c
                 C   s  || }
t td| |
|  |||  td |||  |
| td| td   td   t|	||
  ||	|  ||	td|
 |    |td   t|  | |	|
|   |||  |
| td| td   td  || |||  td   |	 |	|	t|	|td  | |||  |
| td| td   td  ||	|
|   |||  td    ||	|  ||	td|
 |    |  |||  td |||  |
| td| td   td   |	 S r-  r'  r0	  r  r  r  r  8  r,	  r  c                 C   s  t td||	 |td  td | | |td    t|||  |||	  |||   ||td| |	    |td   t|||	  td |  | ||   |||	  td||	  |td   td  |  | td| |  || ||	  |	 td   | ||t||| td  | | td| |  |||	  td |  | ||     |||	  |||   ||td| |	    |td   ||	 |td  td | | |td    | S r  r'  r.	  r  r  r  r  >  rf  r  c
                 C   d   t |	ttttfrdS || }
tt|td|
  | t|
t	|||  |
| td r0dS dS NFr  r  T)
r9  r:  r  r;  r  r  r   r  r   rQ   r0	  r  r  r  r  B     >r  c
                 C   sx  || }
t tdtd| | |
|  |td   t|	||
  ||	|  ||	td|
 |    |td   t|  | |	|
|   |||  td|
|  |td   td  || ||
 ||  | td   |	 |	|	 t|	||
 td  ||	|  ||	td|
 |    |td   |  | |	|
|   ||   td| | |
|  |td   |	 S rN  r'  r0	  r  r  r  r  K  s   r r  c                 C   s  t |||	  |||td| |	   td  |||	  ||	 td| td   td   t|||	  |||	  |||   ||td| |	    |td   ttd|  | | |||	  ||	 td| td   td  || | |||	  td   |||	  | | | |||	  ||	 td| td   td  td| | | |||	  td| ||	   td   ||td  |||	  |||	   td     | ||t||td  |||	  |||   ||td| |	    |  | | |||	  ||	 td| td   td  || | ||	   || |||	   |||	  td| ||	   td    |||td| |	   td  |||	  ||	 td| td   td   | S r-  r'  r.	  r  r  r  r  Q  s     r  c
                 C   s   t |	ttttfrdS || }
tt|td|
  | t|
t	|||  |
 | t
|||  td| |
|   td tdt
|||  |
| td| td   td tdt
|td |
ridS dS r/	  )r9  r:  r  r;  r  r  r   r  r   rQ   r$   r0	  r  r  r  r  U  s   r  c
                 C   s.  || }
t ||
|  ||td|
 |   td |||  |
| td| td   td   t|	||  ||	|  ||	td|
 |    |td   ttd|  | |||  |
| td| td   td  td| | |	|
|   |||  td| |
|   td   |	 |	|	t|	|td  | |||  |
| td| td   td  ||	|
|   |||  td| |
|   td    ||	|  ||	td|
 |    |  ||td|
 |   td |||  |
| td| td   td   |	 S r-  r'  r0	  r  r  r  r  ^  s    * r  c                 C   sr  t td|||	  |td  td | | |td    t|||	  |||	  |||   ||td| |	    |td   ttd |  | | |||	  td||	  |td   td  | |td  |||	  ||	 |td   td   || | |||	  td   ||||	   | | td| |   |||	  ||	 td| td   td   | ||t|||	 td  |||	  |||   ||td| |	    |td   td |  | | | |td   || |  ||||	   | | td| |     |||	  |td  td | | |td    | S r/  r'  r.	  r  r  r  r  d  s    v r  c
                 C   r1	  r2	  )
r9  r:  r  r;  r  r  r   r  r   rP   r0	  r  r  r  r  h  r3	  r  c
                 C   s  || }
t tdtd| | |
|  |td   t|	||  ||	|  ||	td|
 |    |td   t| | |||  td|
|  |td   td  || |	|
|   |||  |
| td| td   td   |	 |	|	t|	|| td  | | || |	|
|     ||	|  ||	td|
 |    |td   td| | |
|  |td   |	 S r  r'  r0	  r  r  r  r  q  s    r  c                 C   s  t td||||	  ||	 td| td   td   t||| |	  |||	  |||   ||td| |	    |  t|| || ||	  |	 td  |||	  |  | |||	  ||	 td| td   td  || |||	  |||	   td     | || t|||| td   |||	  |||   ||td| |	    |td   ||||	  ||	 td| td   td   | S rN  r'  r.	  r  r  r  r  w  r)  r  c
              
   C   s   t |	ttttfrdS || }
tt|td|
  | t|
t	|||  |
| td t
|||  |
| td| td   td tdrLdS dS )NFr  r  r  r   T)r9  r:  r  r;  r  r  r   r  r   rR   r$   r0	  r  r  r  r  {  s   vr  c
                 C   sz  || }
t td||||  |
| td| td   td   t|	||
 |  ||	|  ||	td|
 |    |  t|  | |	|
|   |||  |
| td| td   td  || ||
 ||  | td   |	 |	|	 t||	||
 td   ||	|  ||	td|
 |    |td   ||||  |
| td| td   td   |	 S rN  r'  r0	  r  r  r  r    s   t r  c                 C   sx  t td||||	  td   t||| |	  |||	  |||   ||td| |	    |  t|  | |||	  ||	 |td   td  | | |||	   |||	  td||	  |td   td   || |||	  td   | ||t| |||	 td   |||	  |||   ||td| |	    |td   ||||	  td   | S rN  r'  r.	  r  r  r  r    s   z r  c
                 C   s   t |	ttttfrdS || }
tt|td|
  | t|
t	t
tdt|ttdt|||  |
| td| td   td tdt|||  |
 | t|||  td tdrddS dS )NFr  r  r   r  T)r9  r:  r  r;  r  r  r   r  r   r  r  rO   rP   r#   r$   r0	  r  r  r  r    s   r  c
                 C   s8  || }
t td||||  td   t|	||
 |  ||	|  ||	td|
 |    |  t|  | |	|
|   |||  td|
|  |td   td  || |||  td   |	 |	|	t| |	|| td   ||	|  ||	td|
 |    |td   ||||  td   |	 S rN  r'  r0	  r  r  r  r    s   2 r  c                 C   s   t |
|td  t|||
||    ||
td| td|      t||
|  ||
|   ||
td| |     t|
||td   | ||
||     t|||
||    ||
td| td|      |
|
S r  r$	  )r  r)  r!  r  r  r*  r  r  r#  r'  r  r  r  r  r    r  r  c              
   C   s   t || |	  |||| |    ||td | td|     |	   |||  |||   |||   |	  t|||	 |  | ||| |     |||| |    ||td | td|     |	  ||S r  r  )r  r)  r!  r  r  r*  r+  r  r  r  r#  r  r  r  r  r    s   r  c              
   C   sz   t tdt||td tt|| | ||||	     |||	  |||   ||td| |	    |  ||||S rN  rO  )r  r)  r!  r  r  r*  r  r  r  r#  r'  rP  r  r  r  r  r    r  r  ($  __doc__sympy.externalr   r   r   r   r   r   %sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  expr  rX  r  r  r  sympy.core.addr  sympy.core.modr  sympy.core.mulr  
sympy.corer  sympy.core.numbersr  r  r  sympy.core.powerr  sympy.core.singletonr  $sympy.functions.elementary.complexesr  r  (sympy.functions.elementary.miscellaneousr  sympy.integrals.integralsr  sympy.logic.boolalgr  r  sympy.simplify.simplifyr  sympy.integrals.rubi.symbolr  sympy.core.symbolr  r  sympy.functionsr  r  r  r  r  r  r  %sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  (sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  Pir6  B_C_F_G_H_r-  b_c_rs  e_r(  g_h_i_j_k_l_ro  r/  r1  r  r_t_rV  r  s_w_r.  y_z_a1_a2_b1_b2_c1_c2_r2  r3  n1_r7  e1_e2_f1_f2_g1_g2_n3_Pq_Pm_Px_Qm_Qr_Qx_jn_rS  non2_RFx_RGx_r  iiPqqQRr'  Cr+  rP  	_UseGamma	ShowStepsStepCounterr  r0  r2  r3  r4  r5  r6  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  rT  rU  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  rp  rq  rr  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r)  r*  r+  r,  r-  r.  r/  r0  r1  r4  r5  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  <module>   s              n"JjB.
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