
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Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmJZJmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZd d	 lmZmZd d
 lmZmZmZmZm Z mZmZmZd d lmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZd d lmZmZmZmZmZmZmZd d lmZg  d D] Zee ^ q\ ZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6Z7Z8Z9g  d d d d d d d d d d d d d d d d d d d d  d! d" d# d$ d% d& d' d( d) d* g D] Zee ^ q\ Z:Z;Z<Z=Z>Z?Z@ZAZBZCZDZEZFZGZHZIZBZCZJZKZLZMZNZOZPZQZRZSZTZUed+  \	 ZZVZWZXZYZZZ[Z\Z]e^Z_e^Z`eaZbn  d,   Zcd- S(.   s   
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
i(   t   import_modulet   matchpy(   t   doctest_depends_on(   t   Patternt   ReplacementRulet   CustomConstraintt   is_match(  t   Intt   Sumt   Sett   Witht   Modulet   Scant   MapAndt   FalseQt   ZeroQt	   NegativeQt   NonzeroQt   FreeQt   NFreeQt   Listt   Logt	   PositiveQt   PositiveIntegerQt   NegativeIntegerQt   IntegerQt	   IntegersQt   ComplexNumberQt   PureComplexNumberQt   RealNumericQt   PositiveOrZeroQt   NegativeOrZeroQt   FractionOrNegativeQt   NegQt   Equalt   Unequalt   IntPartt   FracPartt	   RationalQt   ProductQt   SumQt   NonsumQt   Substt   Firstt   Restt   SqrtNumberQt   SqrtNumberSumQt   LinearQt   Sqrtt   ArcCosht   Coefficientt   Denominatort   Hypergeometric2F1t   Nott   Simplifyt   FractionalPartt   IntegerPartt   AppellF1t
   EllipticPit	   EllipticEt	   EllipticFt   ArcTant   ArcCott   ArcCotht   ArcTanht   ArcSint   ArcSinht   ArcCost   ArcCsct   ArcSect   ArcCscht   ArcSecht   Sinht   Tanht   Cosht   Secht   Cscht   Cotht	   LessEqualt   Lesst   Greatert   GreaterEqualt	   FractionQt   IntLinearcQt   Expandt   IndependentQt   PowerQt   IntegerPowerQt   PositiveIntegerPowerQt   FractionalPowerQt   AtomQt   ExpQt   LogQt   Headt   MemberQt   TrigQt   SinQt   CosQt   TanQt   CotQt   SecQt   CscQt   Sint   Cost   Tant   Cott   Sect   Csct   HyperbolicQt   SinhQt   CoshQt   TanhQt   CothQt   SechQt   CschQt   InverseTrigQt   SinCosQt	   SinhCoshQt	   LeafCountt	   Numeratort   NumberQt   NumericQt   Lengtht   ListQt   Imt   Ret   InverseHyperbolicQt   InverseFunctionQt   TrigHyperbolicFreeQt   InverseFunctionFreeQt   RealQt   EqQt   FractionalPowerFreeQt   ComplexFreeQt   PolynomialQt   FactorSquareFreet   PowerOfLinearQt   Exponentt
   QuadraticQt   LinearPairQt   BinomialPartst   TrinomialPartst   PolyQt   EvenQt   OddQt   PerfectSquareQt   NiceSqrtAuxQt	   NiceSqrtQt   Togethert   PosAuxt   PosQt   CoefficientListt
   ReplaceAllt   ExpandLinearProductt   GCDt   ContentFactort   NumericFactort   NonnumericFactorst   MakeAssocListt   GensymSubstt   KernelSubstt   ExpandExpressiont   Apartt
   SmartApartt   MatchQt   PolynomialQuotientRemaindert   FreeFactorst   NonfreeFactorst   RemoveContentAuxt   RemoveContentt	   FreeTermst   NonfreeTermst   ExpandAlgebraicFunctiont   CollectReciprocalst   ExpandCleanupt   AlgebraicFunctionQt   Coefft   LeadTermt   RemainingTermst
   LeadFactort   RemainingFactorst   LeadBaset
   LeadDegreet   Numert   Denomt	   hypergeomt   Expont   MergeMonomialst   PolynomialDividet	   BinomialQt
   TrinomialQt   GeneralizedBinomialQt   GeneralizedTrinomialQt   FactorSquareFreeListt   PerfectPowerTestt   SquareFreeFactorTestt   RationalFunctionQt   RationalFunctionFactorst   NonrationalFunctionFactorst   Reverset   RationalFunctionExponentst   RationalFunctionExpandt   ExpandIntegrandt   SimplerQt   SimplerSqrtQt   SumSimplerQt   BinomialDegreet   TrinomialDegreet   CancelCommonFactorst   SimplerIntegrandQt   GeneralizedBinomialDegreet   GeneralizedBinomialPartst   GeneralizedTrinomialDegreet   GeneralizedTrinomialPartst	   MonomialQt   MonomialSumQt   MinimumMonomialExponentt   MonomialExponentt   LinearMatchQt   PowerOfLinearMatchQt   QuadraticMatchQt   CubicMatchQt   BinomialMatchQt   TrinomialMatchQt   GeneralizedBinomialMatchQt   GeneralizedTrinomialMatchQt   QuotientOfLinearsMatchQt   PolynomialTermQt   PolynomialTermst   NonpolynomialTermst   PseudoBinomialPartst   NormalizePseudoBinomialt   PseudoBinomialPairQt   PseudoBinomialQt   PolynomialGCDt   PolyGCDt   AlgebraicFunctionFactorst   NonalgebraicFunctionFactorst   QuotientOfLinearsPt   QuotientOfLinearsPartst   QuotientOfLinearsQt   Flattent   Sortt   AbsurdNumberQt   AbsurdNumberFactorst   NonabsurdNumberFactorst   SumSimplerAuxQt   Prependt   Dropt   CombineExponentst   FactorIntegert   FactorAbsurdNumbert   SubstForInverseFunctiont   SubstForFractionalPowert*   SubstForFractionalPowerOfQuotientOfLinearst"   FractionalPowerOfQuotientOfLinearst   SubstForFractionalPowerQt   SubstForFractionalPowerAuxQt   FractionalPowerOfSquareQt   FractionalPowerSubexpressionQt   Applyt   FactorNumericGcdt   MergeableFactorQt   MergeFactort   MergeFactorst   TrigSimplifyQt   TrigSimplifyt   TrigSimplifyRecurt   Ordert   FactorOrdert   Smallestt   OrderedQt   MinimumDegreet   PositiveFactorst   Signt   NonpositiveFactorst   PolynomialInAuxQt   PolynomialInQt   ExponentInAuxt
   ExponentInt   PolynomialInSubstAuxt   PolynomialInSubstt   Distribt   DistributeDegreet   FunctionOfPowert   DivideDegreesOfFactorst   MonomialFactort   FullSimplifyt   FunctionOfLinearSubstt   FunctionOfLineart   NormalizeIntegrandt   NormalizeIntegrandAuxt   NormalizeIntegrandFactort   NormalizeIntegrandFactorBaset   NormalizeTogethert   NormalizeLeadTermSignst   AbsorbMinusSignt   NormalizeSumFactorst   SignOfFactort   NormalizePowerOfLineart   SimplifyIntegrandt   SimplifyTermt   TogetherSimplifyt   SmartSimplifyt   SubstForExpnt   ExpandToSumt   UnifySumt
   UnifyTermst	   UnifyTermt	   CalculusQt   FunctionOfInverseLineart   PureFunctionOfSinhQt   PureFunctionOfTanhQt   PureFunctionOfCoshQt   IntegerQuotientQt   OddQuotientQt   EvenQuotientQt   FindTrigFactort   FunctionOfSinhQt   FunctionOfCoshQt   OddHyperbolicPowerQt   FunctionOfTanhQt   FunctionOfTanhWeightt   FunctionOfHyperbolicQt   SmartNumeratort   SmartDenominatort   SubstForAuxt   ActivateTrigt
   ExpandTrigt
   TrigExpandt   SubstForTrigt   SubstForHyperbolict   InertTrigFreeQt   LCMt   SubstForFractionalPowerOfLineart   FractionalPowerOfLineart   InverseFunctionOfLineart
   InertTrigQt   InertReciprocalQt   DeactivateTrigt   FixInertTrigFunctiont   DeactivateTrigAuxt   PowerOfInertTrigSumQt   PiecewiseLinearQt   KnownTrigIntegrandQt   KnownSineIntegrandQt   KnownTangentIntegrandQt   KnownCotangentIntegrandQt   KnownSecantIntegrandQt   TryPureTanSubstt   TryTanhSubstt   TryPureTanhSubstt   AbsurdNumberGCDt   AbsurdNumberGCDListt   ExpandTrigExpandt   ExpandTrigReducet   ExpandTrigReduceAuxt   NormalizeTrigt	   TrigToExpt   ExpandTrigToExpt
   TrigReducet   FunctionOfTrigt   AlgebraicTrigFunctionQt   FunctionOfHyperbolict   FunctionOfQt   FunctionOfExpnQt   PureFunctionOfSinQt   PureFunctionOfCosQt   PureFunctionOfTanQt   PureFunctionOfCotQt   FunctionOfCosQt   FunctionOfSinQt   OddTrigPowerQt   FunctionOfTanQt   FunctionOfTanWeightt   FunctionOfTrigQt   FunctionOfDensePolynomialsQt   FunctionOfLogt   PowerVariableExpnt   PowerVariableDegreet   PowerVariableSubstt   EulerIntegrandQt   FunctionOfSquareRootOfQuadratict   SquareRootOfQuadraticSubstt   Dividest   EasyDQt   ProductOfLinearPowersQt   Rtt   NthRoott	   AtomBaseQt   SumBaseQt   NegSumBaseQt   AllNegTermQt   SomeNegTermQt   TrigSquareQt   RtAuxt
   TrigSquaret   IntSumt   IntTermt   Map2t   ConstantFactort   SameQt   ReplacePartt   CommonFactorst   MostMainFactorPositiont   FunctionOfExponentialQt   FunctionOfExponentialt   FunctionOfExponentialFunctiont    FunctionOfExponentialFunctionAuxt   FunctionOfExponentialTestt   FunctionOfExponentialTestAuxt   stdevt	   rubi_testt   Ift   IntQuadraticQt   IntBinomialQt   RectifyTangentt   RectifyCotangentt
   Inequalityt	   Conditiont   Simpt   SimpHelpt   SplitProductt   SplitSumt   SubstForRF  t   FresnelSt   FresnelCt   Erfct   Erfit   Gammat   FunctionOfTrigOfLinearQt   ElementaryFunctionQt   Complext   UnsameQt   _SimpFixFactort   SimpFixFactort   _FixSimplifyt   FixSimplifyt   _SimplifyAntiderivativeSumt   SimplifyAntiderivativeSumt   _SimplifyAntiderivativet   SimplifyAntiderivativet   _TrigSimplifyAuxt   TrigSimplifyAuxt   Cancelt   Partt   PolyLogt   Dt   Distt   Sum_doitt   PolynomialQuotientt   Floort   PolynomialRemaindert   FactorR  t   CosIntegralt   SinIntegralt   LogIntegralt   SinhIntegralt   CoshIntegralt   Rulet   Erft	   PolyGammat   ExpIntegralEit   ExpIntegralEt   LogGammat   UtilityOperatort	   Factorialt   Zetat
   ProductLogt   DerivativeDividest   HypergeometricPFQt   IntHidet   OneQt   Nullt   rubi_expt   rubi_logt   Discriminantt   Negativet   Quotient(   t   Integralt   St   sqrtt   Andt   Ort   Integert   Floatt   Modt   It   Abst   simplifyt   Mult   Addt   Powt   signt
   EulerGamma(   t   WC(   t   symbolst   Symbol(   t   sint   cost   tant   cott   csct   secR  t   erf(   t   acosht   asinht   atanht   acotht   acscht   asecht   cosht   sinht   tanht   cotht   secht   csch(   t   atant   acsct   asint   acott   acost   asect   atan2(   t   pit   ABCFGHabcdefghijklmnpqrtuvswxyzt   a1t   a2t   b1t   b2t   c1t   c2t   d1t   d2t   n1t   n2t   e1t   e2t   f1t   f2t   g1t   g2t   n3t   Pqt   Pmt   Pxt   Qmt   Qrt   Qxt   jnt   mnt   non2t   RFxt   RGxs   i ii Pqq Q R r C k uc          sLQ d d l  m } m } m } m } m } m } m } m } m	 }	 m
 }
 m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m  }  m! }! m" }" m# }# m$ }$ m% }% m& }& m' }' m( }( m) }) m* }* m+ }+ m, }, m- }- m. }. m/ }/ m0 }0 m1 }1 m2 }2 m3 }3 m4 }4 m5 }5 m6 }6 m7 }7 m8 }8 m9 }9 m: }: m; }; m< }< m= }= m> }> m? }? m@ }@ mA }A mB }B mC }C mD }D mE }E mF }F mG }G mH }H mI }I mJ }J mK }K mL }L mM }M mN }N mO }O mP }P mQ }Q mR }R mS }S mT }T mU }U mV }V mW }W mX }X mY }Y mZ }Z m[ }[ m\ }\ m] }] m^ }^ m_ }_ m` }` ma }a mb }b mc }c md }d me }e mf }f mg }g mh }h mi }i mj }j mk }k ml }l mm }m mn }n mo }o mp }p mq }q mr }r ms }s mt }t mu }u mv }v mw }w mx }x my }y mz }z m{ }{ m| }| m} }} m~ }~ m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } t t t t d t d   t d t d   t d t d   t t t d t d   t d	 t d    t  | | | | | |  }   f d
   } t | |  } t t t t d t d   t d t d   t d t d   t t t d t d   t d	 t d    t  | | | | | |  }   f d   } t | |  } t t t t d t d   t d t d   t t t t d t d   t d	 t d    t  | | | | | |  }   f d   } t | |  } t t t t d t d   t d t d   t t t t d t d   t d	 t d    t  | | | | | |  }   f d   } t | |  } t t t t t d t d   t d	 t d    t t d t d   t d t d   t  | | | | |  }   f d   } t | |  } t t t t t d t d   t d	 t d    t t d t d   t d t d   t  | | | | |  }   f d   } t | |  } t t t t t d t d   t d	 t d    t t d t d   t d t d   t  | | | | |	  }   f d   } t | |  } t t t t t d t d   t d	 t d    t t d t d   t d t d   t  | | | | |	  }   f d   } t | |  } t t t t d t d   t d t d   t d t d   t t t d t d   t d	 t d    t  | | | | | |
  }   f d   } t | |  } t t t t d t d   t d t d   t d t d   t t t d t d   t d	 t d    t  | | | | | |
  }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t  | | | | | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t  | | | | | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t d t d   t t t t d t d   t d	 t d    t t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t d t d   t t t t d t d   t d	 t d    t t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t d t d   t t t t d t d   t d	 t d    t t  | | | | | | | | | 
 }   f d   } t | |  } t t t t d t d   t d t d   t t t t d t d   t d	 t d    t t  | | | | | | | | | 
 }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t  | | | | | | | | 	 }   f d    } t | |  } t t t d 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  | | | | | | | | | 
 }   f d!   } t | |  } t t t d 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  | | | | | | | | | 
 }  f d"   }t || }t t t t d t d   t 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  | | | | | | | | | 
 }  f d$   }t || }t t t t d t d   t t t d t d   t d	 t d    t d# t d   t t d t d   t d t d   t d t d   t  | | | | | | | | | 
 }  f d%   }t || }	t t t t d t d   t t t d t d   t d	 t d    t d# t d   t t d t d   t d t d   t d t d   t  | | | | | | | | | 
 }
  f d&   }t |
| }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t d t d   t  | | | | | | | | | |  }  f d'   }t || }t t t t d t d   t t t d t d   t d	 t d    t d# t d   t t d t d   t d t d   t d t d   t  | | | | | | | | | 
 }  f d(   }t || }t t t t d t d   t t t d t d   t d	 t d    t d# t d   t t d t d   t d t d   t d t d   t  | | | | | | | | | 
 }  f d)   }t || }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t d t d   t  | | | | | | | | | |  }  f d*   }t || }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t d t d   t  | | | | | | | | | |  }  f d+   }t || }t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t  | | | | | | |  |! 	 }  f d,   }t || }t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t  | | | | | | |" |! 	 }  f d-   } t ||  }!t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t d.  t  | | | | | | |  |! 	 }"  f d/   }#t |"|# }$t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t d.  t  | | | | | | |" |! 	 }%  f d0   }&t |%|& }'t t t t d 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  | | | | | | |  |# |! 
 }(  f d1   })t |(|) }*t t t t d 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  | | | | | | |" |# |! 
 }+  f d2   },t |+|, }-t t t t d t d   t d3 t d   t d t d   t t  t d# t d   t  | | | |& |$ |%  }.  f d4   }/t |.|/ }0t t t t d t d   t d3 t d   t d t d   t t  t d# t d   t  | | | |& |$ |%  }1  f d5   }2t |1|2 }3t t t t d t d   t d t d   t d t d   t d3 t d   t d t d   t t t d t d   t d	 t d    t d# t d   t  | | | | | | | |& |' 
 }4  f d6   }5t |4|5 }6t t t t d t d   t d t d   t d t d   t d3 t d   t d t d   t t t d t d   t d	 t d    t d# t d   t  | | | | | | | |& |' 
 }7  f d7   }8t |7|8 }9t t t t t t d t d   t d8 t d   t t t d t d   t d t d    t  | | | | |& |(  }:  f d9   };t |:|; }<t t t t t t d t d   t d8 t d   t t t d t d   t d t d    t  | | | | |& |(  }=  f d:   }>t |=|> }?t t t t t t d t d   t t t t d t d   t d t d    t  | | | | |) | |* |+ 	 }@  f d;   }At |@|A }Bt t t t t t d t d   t t t t d t d   t d t d    t  | | | | |) | |* |+ 	 }C  f d<   }Dt |C|D }Et t t t t t d t d   t t t t d t d   t d t d    t  | | | | |, | |-  }F  f d=   }Gt |F|G }Ht t t t t t d t d   t t t t d t d   t d t d    t  | | | | |, | |-  }I  f d>   }Jt |I|J }Kt t t t t t d t d   t t t t d t d   t d t d    t  | | | | |, |.  }L  f d?   }Mt |L|M }Nt t t t t t d t d   t t t t d t d   t d t d    t  | | | | |, |.  }O  f d@   }Pt |O|P }Qt t t t t t d t d   t t t t d t d   t d t d    t  | | | | |& |0 |/  }R  f dA   }St |R|S }Tt t t t t t d t d   t t t t d t d   t d t d    t  | | | | |& |0 |/  }U  f dB   }Vt |U|V }Wt t t t d	 t d   t d t d   t t t t d t d   t d8 t d   t t t d t d   t d t d    t  | | | | | | |& |( 	 }X  f dC   }Yt |X|Y }Zt t t t d	 t d   t d t d   t t t t d t d   t d8 t d   t t t d t d   t d t d    t  | | | | | | |& |( 	 }[  f dD   }\t |[|\ }]t t t t d	 t d   t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | | | |& |) |1 |2 |* |3  }^  f dE   }_t |^|_ }`t t t t d	 t d   t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | | | |& |) |1 |2 |* |3  }a  f dF   }bt |a|b }ct t t t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | |) | | |* |4 
 }d  f dG   }et |d|e }ft t t t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | |) | | |* |4 
 }g  f dH   }ht |g|h }it t t t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | |, |5 | |- 	 }j  f dI   }kt |j|k }lt t t t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | |, |5 | |- 	 }m  f dJ   }nt |m|n }ot t t t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | | |, |.  }p  f dK   }qt |p|q }rt t t t d t d   t t t t d t d   t t t t d t d   t d t d    t  | | | | | |, |.  }s  f dL   }tt |s|t }ut t t t d	 t d   t d t d   t t t t d t d   t d8 t d   t t t d t d   t d t d    t  | | | | | | |& |0 |6 
 }v  f dM   }wt |v|w }xt t t t d	 t d   t d t d   t t t t d t d   t d8 t d   t t t d t d   t d t d    t  | | | | | | |& |0 |6 
 }y  f dN   }zt |y|z }{t t t t t t d t d   t d t d    t  | | | |  }|  f dO   }}t |||} }~t t t t t t d t d   t d t d    t  | | | |  }  f dP   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | |7 | |8  }  f dQ   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | |7 | |8  }  f dR   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |) |.  }  f dS   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |) |.  }  f dT   }t || }  f dU   }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |) |9  }t || }  f dV   }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |) |9  }t || }t t t t t t d t d   t d t d    t  | | |& |:  }  f dW   }t || }t t t t t t d t d   t d t d    t  | | |& |:  }  f dX   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | |& |(  }  f dY   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | |& |(  }  f dZ   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |) |; |< 	 }  f d[   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |) |; |< 	 }  f d\   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | |& |0 |;  }  f d]   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | |& |0 |;  }  f d^   }t || }t t t d3 t d   t d t d   t t  t d8 t d   t  | | |0 |= |>  }  f d_   }t || }t t t d3 t d   t d t d   t t  t d8 t d   t  | | |0 |= |>  }  f d`   }t || }t t t t t t d t d    t t  | |& |?  }  f da   }t || }t t t t t t d t d    t t  | |& |?  }  f db   }t || }t t t t t t t d t d    t t  | | |& |:  }  f dc   }t || }t t t t t t t d t d    t t  | | |& |:  }  f dd   }t || }de   }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |) t | 	 }  f df   }t || }dg   }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |) t | 	 }  f dh   }t || }di   }t t t t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |) t | 
 }  f dj   }t || }dk   }t t t t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |) t | 
 }  f dl   }t || }t t t t d	 t d   t d t d   t t t t d t d   t d t d    t  | | | | | |@  }  f dm   }t || }t t t t d	 t d   t d t d   t t t t d t d   t d t d    t  | | | | | |@  }  f dn   }t || }t t t t d	 t d   t t t t t d t d   t d t d    t  | | | | | |  }  f do   }t || }t t t t d	 t d   t t t t t d t d   t d t d    t  | | | | | |  }  f dp   }t || }t t t t d	 t d   t d t d   t t t t d t d   t d t d    t  | | | | |  }  f dq   }t || }t t t t d	 t d   t d t d   t t t t d t d   t d t d    t  | | | | |  }  f dr   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |7 |A |8 |B  }  f ds   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |7 |A |8 |B  }  f dt   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | | |& |C |2 |8  }  f du   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | | |& |C |2 |8  }  f dv   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |D |2 |8 |E  }  f dw   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |D |2 |8 |E  }  f dx   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |D |2 |8 |F |G  }  f dy   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |D |2 |8 |F |G  }  f dz   }t || }  f d{   }t t t t d	 t d   t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |) | |H 	 }t || }  f d|   }t t t t d	 t d   t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |) | |H 	 }t || }t t t t d	 t d   t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | | | |) | |8 
 }  f d}   }t || } t t t t d	 t d   t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | | | |) | |8 
 }  f d~   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | | |& |C |2 |* |I 	 }  f d   }t || }t t t t d t d   t t t t d t d   t d3 t d    t t  | | | |& |C |2 |* |I 	 }  f d   }t || }	t t t t d t d   t t t t d t d   t d3 t d    t t  | | |D |2 |* |I |E  }
  f d   }t |
| }t t t t d t d   t t t t d t d   t d3 t d    t t  | | |D |2 |* |I |E  }  f d   }t || }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |) |. |5  }  f d   }t || }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |) |. |5  }  f d   }t || }  f d   }t t t t d	 t d   t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |) |. |H 	 }t || }  f d   }t t t t d	 t d   t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |) |. |H 	 }t || }t t t t d	 t d   t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |) |. |J 
 }  f d   }t || }t t t t d	 t d   t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |) |. |J 
 }  f d   } t ||  }!  f d   }"t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |) |9  }#t |#|" }$  f d   }%t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |) |9  }&t |&|% }'t t t t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |) |9 	 }(  f d   })t |(|) }*t t t t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |) |9 	 }+  f d   },t |+|, }-t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |) |K |L |M  }.  f d   }/t |.|/ }0t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |) |K |L |M  }1  f d   }2t |1|2 }3t t t t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |) |K |L |M  }4  f d   }5t |4|5 }6t t t t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |) |K |L |M  }7  f d   }8t |7|8 }9t t t t d	 t d   t d t d   t t t t d t d   t d t d    t  | | | | |& |N  }:  f d   };t |:|; }<t t t t d	 t d   t d t d   t t t t d t d   t d t d    t  | | | | |& |N  }=  f d   }>t |=|> }?t t t t d	 t d   t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | | | |& |( 	 }@  f d   }At |@|A }Bt t t t d	 t d   t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t t  | | | | | | |& |( 	 }C  f d   }Dt |C|D }Et t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |; |< |5 
 }F  f d   }Gt |F|G }Ht t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |; |< |5 
 }I  f d   }Jt |I|J }Kt t t t d	 t d   t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |0 |; 
 }L  f d   }Mt |L|M }Nt t t t d	 t d   t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |0 |; 
 }O  f d   }Pt |O|P }Qt t t t t d t d   t d3 t d   t d t d   t t  t d8 t d   t  | | | | |0 |= |>  }R  f d   }St |R|S }Tt t t t t d t d   t d3 t d   t d t d   t t  t d8 t d   t  | | | | |0 |= |>  }U  f d   }Vt |U|V }Wt t t t d t d   t t t d# t d   t d t d   t d3 t d    t d8 t d   t t t d# t d   t d t d   t d3 t d    t  | | | |& |0 |1 |O  }X  f d   }Yt |X|Y }Zt t t t d t d   t t t d# t d   t d t d   t d3 t d    t t t d# t d   t d t d   t d3 t d    t d8 t d   t  | | | |& |0 |1 |O  }[  f d   }\t |[|\ }]t t t t d t d   t t t d# t d   t d t d   t d3 t d    t d8 t d   t t t d# t d   t d t d   t d3 t d    t  | | |0 | |@ |O  }^  f d   }_t |^|_ }`t t t t d t d   t t t d# t d   t d t d   t d3 t d    t t t d# t d   t d t d   t d3 t d    t d8 t d   t  | | |0 | |@ |O  }a  f d   }bt |a|b }ct t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | |P  }d  f d   }et |d|e }ft t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | |P  }g  f d   }ht |g|h }it t t t t d.  t d t d   t t d t d   t d3 t d    t t  | | | | |  }j  f d   }kt |j|k }lt t t t t d.  t d t d   t t d t d   t d3 t d    t t  | | | | |  }m  f d   }nt |m|n }ot t t t  t d# t d   t  | |Q |R  }p  f d   }qt |p|q }rt t t t  t d# t d   t  | |Q |R  }s  f d   }tt |s|t }ut t t t d	 t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | |S  }v  f d   }wt |v|w }xt t t t d	 t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | |S  }y  f d   }zt |y|z }{t t t t d	 t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | |T  }|  f d   }}t |||} }~t t t t d	 t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | |T  }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |S 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |S 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |T 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |T 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |S 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |S 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |T 	 }  f d   }t || }t t t t d	 t d   t d t d   t t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | | |T 	 }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | |U  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | | |U  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t t  | | | | | | | | 	 }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t t  | | | | | | | | 	 }  f d   }t || }t t t t d t d   t t  t d# t d   t  | | |; |Q |V  }  f d   }t || }t t t t d t d   t t  t d# t d   t  | | |; |Q |V  }  f d   }t || }t t t t d t d   t d3 t d   t d t d   t t t d t d   t d	 t d    t  | | | | |!  }  f d   }t || }t t t t d t d   t d3 t d   t d t d   t t t d t d   t d	 t d    t  | | | | |!  }  f d   }t || }t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d3 t d   t d t d   t  | | | | | | | | 	 }  f d   }t || }t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d3 t d   t d t d   t  | | | | | | | | 	 }  f d   }t || }t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d3 t d   t d t d   t  | | | | | | | | 	 }  f d   }t || }t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d3 t d   t d t d   t  | | | | | | | | 	 }  f d   }t || }t t t t d t d   t 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  | | | | | | | |W 	 }  f d   }t || }t t t t d t d   t 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  | | | | | | | |W 	 }  f d   }t || }t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t  | | | | | | |X | | 
 }  f d   }t || }t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t  | | | | | | |X | | 
 }  f d   }t || }t t t d  t t d t d   t t t d t d   t d	 t d    t t d t d   t d t d   t d.  t  | | | | | | |X  }  f d   }t || }t t t d  t t d t d   t t t d t d   t d	 t d    t t d t d   t d t d   t d.  t  | | | | | | |X  }  f d   }t || }t t t t d t d   t d t d   t t t d t d   t t t d t d   t d	 t d    t  | | | | | | |X | | |Y  }  f d   }t || }t t t t d t d   t d t d   t t t d t d   t t t d t d   t d	 t d    t  | | | | | | |X | | |Y  }  f d   }t || }t t t d  t t d t d   t t t d t d   t d	 t d    t t d t d   t d t d   t  | | | | | | |X  }  f d   }t || }t t t d  t t d t d   t t t d t d   t d	 t d    t t d t d   t d t d   t  | | | | | | |X  }  f d   }t || }t t t t d t d   t d t d   t t t d t d   t t t d t d   t d	 t d    t  | | | | | | | |X |Z 
 }  f d   }t || }t t t t d t d   t d t d   t t t d t d   t t t d t d   t d	 t d    t  | | | | | | | |X |Z 
 }  f d   }t || }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | |X |[ 	 }  f d   }t || }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | |X |[ 	 }  f d   }t || }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | | |X |. 
 }  f d   }t || }t t t t d t d   t t t d t d   t d	 t d    t t t d t d   t d t d   t t  | | | | | | | |X |. 
 }  f d   }t || }  f d   }t t t t d 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  | | | | | | |X |\ | |  }t || }  f d   }t t t t d 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  | | | | | | |X |\ | |  }t || }t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t  | | | | | | |" |! 	 }  f d   }t || }t t t t d t d   t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t  | | | | | | |" |! 	 }  f d   }t || }t t t t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t d.  t  | | | | | | |"  }  f d   }t || }t t t t d t d   t d t d   t t d t d   t t t d t d   t d	 t d    t d.  t  | | | | | | |"  }  f d   }t || }t t t t d 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  | | | | | | |" |. |! 
 }   f d   }t | | }t t t t d 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  | | | | | | |" |. |! 
 }  f d   }t || }t t t t d t d   t d3 t d   t d t d   t t  t d# t d   t  | | | |& |$ |%  }  f d   }t || }t t t t d t d   t d3 t d   t d t d   t t  t d# t d   t  | | | |& |$ |%  }	  f d   }
t |	|
 }t t t t d t d   t d t d   t d t d   t d3 t d   t d t d   t t t d t d   t d	 t d    t d# t d   t  | | | | | | | |& |' 
 }  f d   }t || }t t t t d t d   t d t d   t d t d   t d3 t d   t d t d   t t t d t d   t d	 t d    t d# t d   t  | | | | | | | |& |' 
 }  f d   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |0 |] |)  }  f d   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |0 |] |)  }  f d   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |/  }  f d   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |/  }  f d   }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |; |< 	 }  f d   }t || } t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |; |< 	 }!  f d   }"t |!|" }#t t t d3 t d   t d t d   t t  t d8 t d   t  | | |0 |= |>  }$  f d   }%t |$|% }&t t t d3 t d   t d t d   t t  t d8 t d   t  | | |0 |= |>  }'  f d   }(t |'|( })t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |^ |) 
 }*  f d   }+t |*|+ },t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |^ |) 
 }-  f d   }.t |-|. }/t t t t d t d   t t t t d t d   t d t d    t d.  t  | | | |& |_  }0  f d   }1t |0|1 }2t t t t d t d   t t t t d t d   t d t d    t d.  t  | | | |& |_  }3  f d   }4t |3|4 }5t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |` 	 }6  f d   }7t |6|7 }8t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |` 	 }9  f d   }:t |9|: };t t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |0 |6 
 }<  f d   }=t |<|= }>t t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |0 |6 
 }?  f d   }@t |?|@ }At t t t t d t d   t d3 t d   t d t d   t t  t d8 t d   t  | | | | |0 |= |>  }B  f d   }Ct |B|C }Dt t t t t d t d   t d3 t d   t d t d   t t  t d8 t d   t  | | | | |0 |= |>  }E  f d   }Ft |E|F }Gt t t t d t d   t d  t t t d# t d   t d t d   t d3 t d    t d8 t d   t t t d# t d   t d t d   t d3 t d    t d t d   t  | | |0 | | |a |b  }H  f d   }It |H|I }Jt t t t d t d   t d  t t t d# t d   t d t d   t d3 t d    t d8 t d   t d  t t t d# t d   t d t d   t d3 t d    t d t d   t  | | |0 | | |a |b  }K  f d   }Lt |K|L }Mt t t t t d.  t d t d   t t d t d   t d3 t d    t d# t d   t  | | | |& |c  }N  f d   }Ot |N|O }Pt t t d  t t t d.  t d t d   t t d t d   t d3 t d    t d# t d   t  | | | |& |c  }Q  f d   }Rt |Q|R }St t t t d	 t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | |d  }T  f d   }Ut |T|U }Vt t t t d	 t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t  | | | | | |d  }W  f d   }Xt |W|X }Yt t t t d	 t d   t d t d   t d t d   t t t d.  t d t d   t t d t d   t d3 t d    t d# t d   t  | | | | | | |& |e 	 }Z  f d   }[t |Z|[ }\t t t t d	 t d   t d t d   t d t d   t d  t t t d.  t d t d   t t d t d   t d3 t d    t d# t d   t  | | | | | | |& |e 	 }]  f d   }^t |]|^ }_t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t  | | | | |!  }`  f d   }at |`|a }bt t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t  | | | | |!  }c  f d   }dt |c|d }et t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t d.  t  | | | | | |  }f  f d   }gt |f|g }ht t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t d.  t  | | | | | |  }i  f d   }jt |i|j }kt t t t d t d   t d t d   t d  t t t d t d   t d3 t d    t t  | | | | | | |f  }l  f d   }mt |l|m }nt t t t d t d   t d t d   t d  t t t d t d   t d3 t d    t t  | | | | | | |f  }o  f d   }pt |o|p }qt t t t d t d   t d t d   t t d  t t t d t d   t d3 t d    t t  | | | | | | |f | 	 }r  f d   }st |r|s }tt t t t d t d   t d t d   t t d  t t t d t d   t d3 t d    t t  | | | | | | |f | 	 }u  f d   }vt |u|v }wt t t t d t d   t d t d   t d  t t t d t d   t d3 t d    t t  | | | | | |  }x  f d   }yt |x|y }zt t t t d t d   t d t d   t d  t t t d t d   t d3 t d    t t  | | | | | |  }{  f d   }|t |{|| }}t t t t d t d   t d t d   t t d  t t t d t d   t d3 t d    t t  | | | | | | |  }~  f d   }t |~| }t t t t d t d   t d t d   t t d  t t t d t d   t d3 t d    t t  | | | | | | |  }  f d   }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t t  | | | | | |& |M  }  f d   }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t t  | | | | | |& |M  }  f d  }t || }t t t t d t d   t 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  | | | | | | | |W 	 }  f d  }t || }t t t t d t d   t 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  | | | | | | | |W 	 }  f d  }t || }t t t t d t d   t 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  | | | | | | |. |! 	 }  f d  }t || }t t t t d t d   t 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  | | | | | | |. |! 	 }  f d  }t || }t t t t d t d   t d  t t  t d# t d   t  | |& |$ |%  }  f d  }t || }t t t t d t d   t d  t t  t d# t d   t  | |& |$ |%  }  f d  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t  | | | | | |& |g  }  f d  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t  | | | | | |& |g  }  f d	  }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |0 |] |)  }  f d
  }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |0 |] |)  }  f d  }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |/  }  f d  }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |/  }  f d  }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |; |< 	 }  f d  }t || }t t t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | |& |0 |; |< 	 }  f d  }t || }t t t d3 t d   t d t d   t t  t d8 t d   t  | | |0 |= |>  }  f d  }t || }t t t d3 t d   t d t d   t t  t d8 t d   t  | | |0 |= |>  }  f d  }t || }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |^ |) 
 }  f d  }t || }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |^ |) 
 }  f d  }t || }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |` 	 }  f d  }t || }t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | |& |0 |` 	 }  f d  }t || }t t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |0 |6 
 }  f d  }t || }t t t t t d t d   t d3 t d   t d t d   t t t t d t d   t d t d    t d8 t d   t  | | | | | | |& |0 |6 
 }  f d  }t || }t t t t t d t d   t d3 t d   t d t d   t t  t d8 t d   t  | | | | |0 |= |>  }  f d  }t || }t t t t t d t d   t d3 t d   t d t d   t t  t d8 t d   t  | | | | |0 |= |>  }  f d  }t || }t t t t d t d   t d  t t t d# t d   t d t d   t d3 t d    t t t t d# t d   t d t d   t d3 t d    t  | | |0 | | |a |h  }  f d  }t || }t t t t d t d   t d  t t t d# t d   t d t d   t d3 t d    t t t t d# t d   t d t d   t d3 t d    t  | | |0 | | |a |h  }  f d  }t || }t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t  | | | | |& |! |i  }  f d  }t || }t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t t t d t d   t d3 t d    t d# t d   t  | | | | |& |! |i  }  f d  }t || }t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t d8 t d   t  | | | | | |j  }  f d  }t || }t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t d8 t d   t  | | | | | |j  }  f d  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d8 t d   t t t d t d   t d3 t d    t d# t d   t  | | | | | |j  }  f d   }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t d8 t d   t  | | | | |& |k | | 	 }  f d!  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t d  t t t d t d   t d3 t d    t d8 t d   t  | | | | |& |k | | 	 }  f d"  }t || }t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t d.  t  | | | | |& |! |i  }  f d#  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t d.  t  | | | | |& |! |i  }  f d$  }t || }t t t t d t d   t d t d   t d t d   t t t d t d   t d3 t d    t t t t d t d   t d3 t d    t  | | | | | |l  }  f d%  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t t  | | | | | |& |l  }  f d&  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t t t t d t d   t d3 t d    t  | | | | | |l  }  f d'  }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t d  t t t d t d   t d3 t d    t t  | | | | | |& |l  }  f d(  }t || }  f d)  }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t t t d t d   t d3 t d    t d8 t d   t  | | | | |& |0 |! |m 	 } t | | }  f d*  }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t d  t t t d t d   t d3 t d    t d8 t d   t  | | | | |& |0 |! |m 	 }t || }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t d  t t t d t d   t d3 t d    t d# t d   t  | | | | | |  }  f d+  }t || }  f d,  }t t t t d t d   t d t d   t d t d   t d  t t t d t d   t d3 t d    t d# t d   t d  t t t d t d   t d3 t d    t d8 t d   t  | | | | |7 | | |n 	 }	t |	| }
t t t t t t t t d t d   t  | |& |0 |o |p |q |r |s 	 }  f d-  }t || }t t t t d t d   t 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 t t d t d   t d t d    t  | | | | | | |& |! |i 
 }  f d.  }t || }t t t t d t d   t 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 t t d t d   t d t d    t  | | | | | | |& |! |i 
 }  f d/  }t || }t t t t d t d   t 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 t t d t d   t d t d    t d.  t  | | | | | | |& |! |i 
 }  f d0  }t || }t t t t d t d   t 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 t t d t d   t d t d    t d.  t  | | | | | | |& |! |i 
 }  f d1  }t || }t t t t d t d   t 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 t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |& |! |i 
 }  f d2  }t || }t t t t d t d   t 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 t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |& |! |i 
 }  f d3  }t || }t t t t d t d   t d	 t d   t d t d   t t t d t d   t d3 t d    t d8 t d   t t t d t d   t d t d    t d t d   t  | | | | | | |t |5 	 }   f d4  }!t | |! }"t t t t d t d   t d	 t d   t d t d   t t t d t d   t d3 t d    t d8 t d   t t t d t d   t d t d    t d t d   t  | | | | | | |t |5 	 }#  f d5  }$t |#|$ }%t t t t d t d   t d	 t d   t d t d   t t t d t d   t d3 t d    t d8 t d   t t t d t d   t d t d    t d t d   t  | | | | | | | |t 	 }&  f d6  }'t |&|' }(t t t t t d t d   t d3 t d   t t t d t d   t d t d   t t d t d   t d	 t d   t d t d   t  | | | | | | | |u |v |t |w |x  })  f d7  }*t |)|* }+t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t  |z | | | | | |y  },  f d8  }-t |,|- }.t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t  |z | | | | | |y  }/  f d9  }0t |/|0 }1t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |{ | | 
 }2  f d:  }3t |2|3 }4t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |{ | | 
 }5  f d;  }6t |5|6 }7t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |& || |i |}  }8  f d<  }9t |8|9 }:t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |& || |i |}  };  f d=  }<t |;|< }=t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |~ | | |  }>  f d>  }?t |>|? }@t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |~ | | |  }A  f d?  }Bt |A|B }Ct t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |& |M 	 }D  f d@  }Et |D|E }Ft t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t t  |z | | | | | |& |M 	 }G  f dA  }Ht |G|H }It t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t d# t d   t  |z | | | | | |  }J  f dB  }Kt |J|K }Lt t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t d# t d   t  |z | | | | | |  }M  f dC  }Nt |M|N }Ot t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t t  |z | | | | | | | | 
 }P  f dD  }Qt |P|Q }Rt t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t t  |z | | | | | | | | 
 }S  f dE  }Tt |S|T }Ut t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t t  |z | | | | | |& | |B |  }V  f dF  }Wt |V|W }Xt t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t t  |z | | | | | |& | |B |  }Y  f dG  }Zt |Y|Z }[t t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t t  |z | | | | | | | | |f  }\  f dH  }]t |\|] }^t t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t t  |z | | | | | | | | |f  }_  f dI  }`t |_|` }at t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t d# t d   t  |z | | | | | |  }b  f dJ  }ct |b|c }dt t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t d# t d   t  |z | | | | | |  }e  f dK  }ft |e|f }gt t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t d# t d   t  |z | | | | | |M  }h  f dL  }it |h|i }jt t t t t d t d   t d3 t d   t d t d   t d  t t t d	 t d   t d t d    t d# t d   t  |z | | | | | |M  }k  f dM  }lt |k|l }mt t t t t d t d   t d3 t d   t d t d   t t dNt d   t t t d	 t d   t d t d    t d# t d   t  |z | | | | | | | | |.  }n  f dO  }ot |n|o }pt t t t t d t d   t d3 t d   t d t d   t t dNt d   t t t d	 t d   t d t d    t d# t d   t  |z | | | | | | | | |.  }q  f dP  }rt |q|r }st t t t t d t d   t d3 t d   t d t d   t t dNt d   t t t d	 t d   t d t d    t d# t d   t  |z | | | | | | | | |.  }t  f dQ  }ut |t|u }vt t t t t d t d   t d3 t d   t d t d   t t dNt d   t t t d	 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  |z | | | | | | | | |D |  }w  f dR  }xt |w|x }yt t t t t d t d   t d3 t d   t d t d   t t dNt d   t t t d	 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  |z | | | | | | | | |D |  }z  f dS  }{t |z|{ }|t t t t t d t d   t d3 t d   t d t d   t t dNt d   t t t d	 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  |z | | | | | | | | |D |  }}  f dT  }~t |}|~ }t t t t t d t d   t d3 t d   t d t d   t t dUt d   t t t d	 t d   t d t d    t t dNt d   t t t d	 t d   t d t d    t  |z | | | | | | | | | | | |  }  f dV  }t || }t t t t t d t d   t d3 t d   t d t d   t t dUt d   t t t d	 t d   t d t d    t t dNt d   t t t d	 t d   t d t d    t  |z | | | | | | | | | | | |  }  f dW  }t || }t t t t t d t d   t t t  |z | |& |p |$ |%  }  f dX  }t || }  f dY  }t t t t t d t d   t d3 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  |z | | | | | | | | 
 }t || }  f dZ  }t t t t t d t d   t d3 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  |z | | | | | | | | 
 }t || }t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t d t d   t t t dNt d   t d t d    t d# t d   t  |z | | | | | | | |W 
 }  f d[  }t || }t t t t t d t d   t d3 t d   t d t d   t t d8 t d   t t t d	 t d   t d t d    t d t d   t t t dNt d   t d t d    t d# t d   t  |z | | | | | | | | 
 }  f d\  }t || }t t t t t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d   t t t d	 t d   t d t d   t  |z | | | | | |W |p | 
 }  f d]  }t || }t t t t t t  t d# t d   t  |z | | |  }  f d^  }t || }t t t t t t  t d# t d   t  |z | | |  }  f d_  }t || }t t t t t t  t d t d   t t  t d# t d   t  |z | | |W  }  f d`  }t || }t t t t d t d   t t t d# t d   t d t d     t d8 t d   t  | |  }  f da  }t || }t t t t d t d   t t t d# t d   t d t d     t d8 t d   t  | |  }  f db  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |0 | |O  }  f dc  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |0 | |O  }  f dd  }t || }t t t t t d3 t d   t d t d   t t t d# t d   t d t d      t  | | | |& |  }  f de  }t || }t t t t t d3 t d   t d t d   t t t d# t d   t d t d      t  | | | |& |  }  f df  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | |& |( |  }  f dg  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | |& |( |  }  f dh  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | |& |  }  f di  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | |& |  }  f dj  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |8 |  }  f dk  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |8 |  }  f dl  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |* |I | 	 }  f dm  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |* |I | 	 }  f dn  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |0 |  }  f do  }t || }t t t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |0 |  }  f dp  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |0 | |O |K 
 }  f dq  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |0 | |O |K 
 }  f dr  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | | |& |( |  }  f ds  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | | |& |( |  }  f dt  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | | |& | |K  }  f du  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | | |& | |K  }  f dv  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& | |2 |8 |K 
 }  f dw  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& | |2 |8 |K 
 }  f dx  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& | |2 |* |I |K  }  f dy  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& | |2 |* |I |K  }  f dz  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |0 |  }  f d{  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |0 |  }  f d|  }t || }t t t d  t t d t d   t t t d# t d   t d t d     t d8 t d   t  | |  }  f d}  }t || }t t t d  t t d t d   t t t d# t d   t d t d     t d8 t d   t  | |  }  f d~  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | |& |  }  f d  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | |& |  }  f d  }t || } t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |0 | |h  }  f d  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |0 | |h  }  f d  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |8 | | 	 }  f d  }t || }	t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |8 | | 	 }
  f d  }t |
| }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |* |  }  f d  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | |& |2 |* |  }  f d  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | |& |0 |  }  f d  }t || }t t t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | |& |0 |  }  f d  }t || }t t t t d t d   t d  t t d t d   t t t d# t d   t d t d     t d8 t d   t  | |  }  f d  }t || }t t t t d t d   t d  t t d t d   t t t d# t d   t d t d     t d8 t d   t  | |  }  f d  }t || }t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | | |& |  }  f d  } t ||  }!t t t t d t d   t t d3 t d   t d t d   t t t d# t d   t d t d     t  | | | | |& |  }"  f d  }#t |"|# }$t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |0 | |K |h 
 }%  f d  }&t |%|& }'t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |0 | |K |h 
 }(  f d  })t |(|) }*t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |2 |8 | | 
 }+  f d  },t |+|, }-t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |2 |8 | | 
 }.  f d  }/t |.|/ }0t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |2 |* | 	 }1  f d  }2t |1|2 }3t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t t  | | | | |& |2 |* | 	 }4  f d  }5t |4|5 }6t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | | |& |0 |  }7  f d  }8t |7|8 }9t t t t d t d   t d  t t d3 t d   t d t d   t t t d# t d   t d t d     t d8 t d   t  | | | | |& |0 |  }:  f d  };t |:|; }<t t t t t d t d    t d8 t d   t t t d3 t d   t t t d t d    t d8 t d    t  | | |2 |  }=  f d  }>t |=|> }?t t t t t d t d    t d8 t d   t t t d3 t d   t t t d t d    t d8 t d    t  | | |2 |  }@  f d  }At |@|A }Bt t t t t d t d    t d8 t d   t t t t d3 t d   t t t d t d    t d8 t d    t  | | | |  }C  f d  }Dt |C|D }Et t t t t d t d    t d8 t d   t t t t d3 t d   t t t d t d    t d8 t d    t  | | | |  }F  f d  }Gt |F|G }Ht t t t d t d   t t t d t d    t d8 t d   t t t d# t d   t d3 t d   t t t d t d    t d8 t d    t  | | | |& |1 |2 |  }I  f d  }Jt |I|J }Kt t t t d t d   t t t d t d    t d8 t d   t t t d# t d   t d3 t d   t t t d t d    t d8 t d    t  | | | |& |1 |2 |  }L  f d  }Mt |L|M }Nt t t t t t t d t d    t d8 t d   t t t d# t d   t d3 t d   t t t d t d    t d8 t d    t  | | | | |  }O  f d  }Pt |O|P }Qt t t t t t t d t d    t d8 t d   t t t d# t d   t d3 t d   t t t d t d    t d8 t d    t  | | | | |  }R  f d  }St |R|S }Tt t t t d3 t d   t t d t d   t d t d    t d# t d   t  | | | |  }U  f d  }Vt |U|V }Wt t t t d3 t d   t t d t d   t d t d    t d# t d   t  | | | |  }X  f d  }Yt |X|Y }Zt t t t t d t d   t d3 t d   t d	 t d   t t d t d   t d t d    t d# t d   t  | | | | | |  }[  f d  }\t |[|\ }]t t t t t d t d   t d3 t d   t d	 t d   t t d t d   t d t d    t d# t d   t  | | | | | |  }^  f d  }_t |^|_ }`  f d  }at t t t  t d# t d   t  | |  }bt |b|a }c  f d  }dt t t t  t d# t d   t  | |  }et |e|d }ft t t dt d   t t  t d8 t d   t t  t d t d   t  |q  }g  f d  }ht |g|h }it t t dt d   t t  t d8 t d   t t  t d t d   t  |q  }j  f d  }kt |j|k }lt t t t  t d8 t d   t t  t d t d   t  |t |  }m  f d  }nt |m|n }ot t t t  t d8 t d   t t  t d t d   t  |t |  }p  f d  }qt |p|q }rt t t t d t d   t t  t d8 t d   t t  t d t d   t  | |  }s  f d  }tt |s|t }ut t t t d t d   t t  t d8 t d   t t  t d t d   t  | |  }v  f d  }wt |v|w }xt t t dt d   t t  t d8 t d   t t  t d8 t d   t  |q |)  }y  f d  }zt |y|z }{t t t t  t d8 t d   t t  t d t d   t  |t |  }|  f d  }}t |||} }~t t t t d t d   t t  t d8 t d   t t  t d t d   t  | |  }  f d  }t || }t t t t  t t  t d# t d   t  | | |  }  f d  }t || }t t t d  t t  t d# t d   t t  t  | | |  }  f d  }t || }t t t d  t t  t d# t d   t t  t  | | |  }  f d  }t || }t t t t  t t  t d# t d   t  | | |  }  f d  }t || }t t t d  t t  t d# t d   t t  t  | | |  }  f d  }t || }t t t d  t t  t d# t d   t t  t  | | |  }  f d  }t || }t t t d  t t  t d# t d   t t  t  | | |  }  f d  }t || }t t t d  t t  t d# t d   t t  t  | | |  }  f d  }t || }t t t t d 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 t d t d   t d	 t d   t d t d   t  | | | | | | | |& |' 
 }  f d  }t || }t t t t d t d   t t d t d   t t t d t d   t d t d    t d.  t t  | | | | | |D | | | 
 }  f d  }t || }t t t t d t d   t t d t d   t t t d t d   t d t d    t d.  t t  | | | | | |D | | | 
 }  f d  }t || }t t t t d t d   t d	 t d   t d t d   t t t t d t d   t t d t d   t d3 t d    t d8 t d   t  | | | | | | |& |! |2 
 }  f d  }t || }t t t t d t d   t d	 t d   t d t d   t t t t d t d   t t d t d   t d3 t d    t d8 t d   t  | | | | | | |& |! |2 
 }  f d  }t || }t t t t dNt d   t d t d   t d t d   t d3 t d   t d t d   t t t d	 t d   t d t d    t d.  t d t d   t t t d	 t d   t d t d    t d.  t  | | | | | | | |! | |  }  f d  }t || }t t t t dNt d   t d t d   t d t d   t 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.  t  | | | | | | |!  }  f d  }t || }t t t t dNt d   t d t d   t d t d   t d3 t d   t t t d	 t d   t d t d    t d.  t d t d   t d t d   t t t d	 t d   t d t d    t d.  t t t d	 t d   t d t d    t d.  t  | | | | | | | |! | |  }  f d  }t || }t t t t dNt d   t d t d   t d t d   t 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.  t  | | | | | | |!  }  f d  }t || }t t t t dNt d   t d t d   t d t d   t d3 t d   t t t d	 t d   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 t t d	 t d   t d t d    t d.  t  | | | | | | | |! | |  }  f d  }t || }t t t t d t d   t d	 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 d    t  | | | | | | |!  }  f d  }t || }t t t t d t d   t d	 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 d    t  | | | | | | |!  }  f d  }t || }t t t t d t d   t d	 t d   t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |! | | |  }  f d  }t || }t t t t d t d   t d	 t d   t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |! | | |X  }  f d  }t || }t t t t d t d   t d	 t d   t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |! | | |   }  f d  }t || }t t t t d t d   t d	 t d   t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |! | | |"  }  f d  }t || }t t t t dt d   t t t d t d   t d t d    t t d t d   t d	 t d   t t d t d   t t t d t d   t d t d    t d.  t  | | | | | | | | | 
 }  f d  }t || }t t t t dt d   t t t d t d   t d t d    t t d t d   t d	 t d   t t d t d   t t t d t d   t d t d    t d.  t  | | | | | | | | | 
 }  f d  }t || }t t t t d t d   t t  t d# t d   t d  t t  t d t d   t  | | |D | |  }  f d  }t || }t t t t d t d   t t  t d# t d   t d  t t  t d t d   t  | | |D | |  }  f d  }t || }t t t dt d   t t t d t d   t d3 t d    t d t d   t t t d t d   t d t d    t d# t d   t  | | | | |W  }  f d  }t || }t t t dt d   t t t d t d   t d3 t d    t d t d   t t t d t d   t d t d    t d# t d   t  | | | | |W  }  f d  }t || }t t t d  t t t t d t d    t t t d t d   t d3 t d    t  | | | | | |  }  f d  }t || }t t t d  t t t t d t d    t t t d t d   t d3 t d    t  | | | | | |  }  f d  }t || }t t t t t t d t d    t t t d t d   t d3 t d    t  | | | | | |  }  f d  }t || }t t t d  t t t t d t d    t t t d t d   t d3 t d    t  | | | | | |  }  f d  }t || }t t t d3 t d   t t  t d t d   t t  t d# t d   t dt d   t  | | |& |X  }  f d  }t || }| | | | | | | | | | | | | | | | | | | | | | | |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||||||||||||||||||||||||||||||||||||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}|||||||||||||||||||||||||||||||||||||||||||||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~||||||||||||||||||||||||||||||||||||gS(  Ni(   t   cons31t   cons168t   cons7t   cons27t   cons48t   cons125t   cons94t   cons1116t   cons176t   cons1488t   cons21t   cons87t   cons165t   cons3t   cons93t   cons166t   cons85t   cons1489t   cons245t   cons247t   cons89t   cons1442t   cons148t   cons1859t   cons2t   cons1490t   cons1439t   cons808t   cons1491t   cons1492t   cons1454t   cons1440t   cons62t   cons1267t   cons1493t   cons810t   cons811t   cons4t   cons1360t   cons128t   cons38t   cons137t   cons744t   cons63t   cons1494t   cons196t   cons1495t   cons5t   cons53t   cons13t   cons596t   cons1496t   cons17t   cons1497t   cons376t   cons146t   cons489t   cons1498t   cons68t   cons69t   cons823t   cons824t   cons1499t   cons1501t   cons1255t   cons1502t   cons56t   cons150t   cons1503t   cons1504t   cons683t   cons367t   cons1505t   cons356t   cons66t   cons854t   cons23t   cons1506t   cons54t   cons14t   cons818t   cons1131t   cons1132t   cons1133t   cons1507t   cons819t   cons528t   cons1265t   cons1510t   cons18t   cons1571t   cons1572t   cons1573t   cons1574t   cons1575t   cons1576t   cons1577t   cons1578t   cons1579t   cons1043t   cons1580t   cons1644t   cons1736t   cons1645t   cons584t   cons464t   cons1683t   cons1408t   cons1684t   cons1685t   cons1860t   cons1861t   cons1688t   cons812t   cons813t   cons555t   cons1862t   cons1863t   cons25t   cons1691t   cons1864t   cons1099t   cons1865t   cons1866t   cons1395t   cons1867t   cons1693t   cons1868t   cons963t   cons1869t   cons1870t   cons208t   cons1700t   cons1011t   cons1551t   cons1701t   cons1702t   cons209t   cons224t   cons1699t   cons1871t   cons1703t   cons1704t   cons1872t   cons1706t   cons1707t   cons1873t   cons1874t   cons1875t   cons1876t   cons1877t   cons1878t   cons1879t   cons1880t   cons1881t   cons1882t   cons1883t   cons1884t   cons1885t   cons1886t   cons1720t   cons1887t   cons1888t   cons1889t   cons1723t   cons1890t   cons163t   cons338t   cons162t   cons627t   cons71t   cons1725t   cons1726t   cons1727t   cons88t   cons1728t   cons1456t   cons463t   cons1729t   cons1478t   cons1730t   cons1891t   cons34t   cons35t   cons1474t   cons1481t   cons1733t   di   t   ci    t   mt   ft   ec            s     j  d  t | |  | t | | | |  t d  t | | |  |  |  t | | | |  t | | |  | |  S(   Ni  i(   t   appendR  R   R  R  R  (   R  R  R  R  t   xR  (   t   rubi(    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5643   s    c            s     j  d  t | |  | t | | | |  t d  t | | |  |  |  t | | | |  t | | |  | |  S(   Ni  i(   R  R  R   R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5644   s    c            s     j  d  t | | |  t d  t | | | |  t d  t | | |  |  |  t | | | |  t d  t | | |  | |  t d  |  S(   Ni  i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5645   s    c            s     j  d  t | | |  t d  t | | | |  t d  t | | |  |  |  t | | | |  t d  t | | |  | |  t d  |  S(   Ni  i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5646   s    c            s,     j  d  t t | |  |  | |  S(   Ni  (   R  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5647   s    c            s,     j  d  t t | |  |  | |  S(   Ni  (   R  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5648   s    c            s     j  d  t t | |  | | |  t t | |  | |  |  | | | |  |  t t | |  | | |  t t | |  | |  |  | | | |  |  S(   Ni  (   R  R  R   R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5649   s    c            s     j  d  t t | |  | | |  t t | |  | |  |  | | | |  |  t t | |  | | |  t t | |  | |  |  | | | |  |  S(   Ni  (   R  R  R   R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5650   s    c      	      s     j  d  t t d  d t | | | |  t | | |  |  |  t t d  d t | | | |  t | | |  |  |  S(   Ni  i   i   (   R  R  R  R   t   exp(   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5651   s    c      	      s     j  d  t t d  d t | | | |  t | | |  |  |  t t d  d t | | | |  t | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5652   s    t   bc            s	    j  d  t | t d  | t d  | t | t | |  |  | t d  | | | |  |  t | | t | |  |  | |  t d  | t d  |  t | | t | |  |  | t d  | | | t | |  |  |  | |  S(   Ni  i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  t   nR  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5653   s    c            s    j  d  t | t d  | t d  | t | t | |  |  | t d  | | | |  |  t | | t | |  |  | |  t d  | t d  |  t | | t | |  |  | t d  | | | t | |  |  |  | |  S(   Ni  i   ii(   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5654   s    c      	      s    j  d  t | t d  | t d  | t | t | | |  | t d  | | | |  |  |  t | t d  |  |  t d  | t d  | t d  t | t | | |  | | | | |  t d  |  |  t | | t | | |  | t d  | | | |  t | | |  | | |  t | |  | t | | |  | | | | |  t d  | t d  | t d  |  S(   Ni  i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5655   s    c      	      s    j  d  t | t d  | t d  | t | t | | |  | t d  | | | |  |  |  t | t d  |  |  t d  | t d  | t d  t | t | | |  | | | | |  t d  |  |  t | | t | | |  | t d  | | | |  t | | |  | | |  t | |  | t | | |  | | | | |  t d  | t d  | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5656   s    c            sD     j  d  t t | | | |  t | | |  | |  |  S(   Ni  (   R  R   Rc  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5657   s    c            sD     j  d  t t | | | |  t | | |  | |  |  S(   Ni  (   R  R   Rc  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5658   s    c      
      s     j  d  t | | | |  t d  t t | | | |  t d  t | | |  | t d  t | | |  |  |  |  t | | | |  t d  t | | |  | | |  t d  |  S(   Ni  i   i(   R  R  R  R   Rc  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5659   s    c      
      s     j  d  t | | | |  t d  t t | | | |  t d  t | | |  t | | |  | t d  |  |  |  t | | | |  t d  t | | |  | | |  t d  |  S(   Ni  i   i(   R  R  R  R   Rc  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5660   s    c      	      s    j  d  t | t d  | t d  | t d  |  t d  |  t d  t | t | | |  | | | | |  t d  |  |  t | t d  | t d  | | t d  | t d  |  t d  |  t d  t | t | | |  | t d  | | | |  t d  |  |  t | t | | |  | | | | |  t d  | |  t d  |  t | | | | t | | |  | t d  | | | |  t d  t | | |  | t d  |  t d  |  t d  |  S(   Ni  i   i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5661   s    c      	      s    j  d  t | t d  | t d  | t d  |  t d  |  t d  t | t | | |  | | | | |  t d  |  |  t | t d  | t d  | | t d  | t d  |  t d  |  t d  t | t | | |  | t d  | | | |  t d  |  |  t | t | | |  | | | | |  t d  | |  t d  |  t | | | | t | | |  | t d  | | | |  t d  t | | |  | t d  |  t d  |  t d  |  S(   Ni  i   i   ii(   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5662   s    c            sC    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  | | | |  |  t | | t | |  |  | t d  | t d  |  t d  | t d  | t d  |  t | t | |  |  | t d  | | | t | |  |  | |  | t d  |  S(   Ni  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5663   s    c            sB    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  | | | |  |  t | | t | |  |  | t d  | t d  |  t d  | t d  | t d  |  t | t | |  |  | t d  | | | t | |  |  | |  | t d  |  S(   Ni   i   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5664   s    c      	      s    j  d  t | t d  | t d  | t d  t | t | | |  | t d  | | | |  |  |  t | t d  |  |  t d  | t d  | t d  | t d  | t d  t | t | | |  | t d  | | | |  t d  |  |  t | t | | |  | t d  | | | |  t | | |  | | | t d  |  t | |  | t | | |  | t d  | | | |  t d  | t d  | t d  | t d  | t d  |  S(   Ni!  i   i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5665   s    c      	      s    j  d  t | t d  | t d  | t d  t | t | | |  | t d  | | | |  |  |  t | t d  |  |  t d  | t d  | t d  | t d  | t d  t | t | | |  | t d  | | | |  t d  |  |  t | t | | |  | t d  | | | |  t | | |  | | | t d  |  t | |  | t | | |  | t d  | | | |  t d  | t d  | t d  | t d  | t d  |  S(   Ni"  i   i   ii(   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5666  s    R  c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni#  (   R  R   R   R   (	   R  R  R  R  R  R  t   aR  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5667  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni$  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5668  s    c	   	   	      s     j  d  t t d  | | t | | | |  t t | t d  | | t d  | | t d   t d  | |  |  S(   Ni%  i   i   (   R  R  R  R   R  t   Pi(	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5669  s    c	   	   	      s    j  d  t t d  | t |  | | t | | |  t |  t t | t d  | | t d  | | t d   t d  t |  t | | | |  t t | t d  | | t d  | | t d   t d  | |  |  S(   Ni&  i   i   (	   R  R  R  R$   R   R%   R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5670  s    c	   	   	      st     j  d  t t d  | | t | | | |  t | t d  | | t d   t d  | |  |  S(   Ni'  i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5671  s    c	   	   	      su     j  d  t t d  | | t | | | |  t | t d  | | t d   t d  | |  |  S(   Ni(  i   (   R  R  R  R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5672   s    c	   	   	      s     j  d  t t d  | t |  | | t | | |  t |  t | t d  | | t d   t d  t |  t | | | |  t | t d  | | t d   t d  | |  |  S(   Ni)  i   (   R  R  R  R$   R  R%   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5673%  s    c	   	   	      s     j  d  t t d  | t |  | | t | | |  t |  t | t d  | | t d   t d  t |  t | | | |  t | t d  | | t d   t d  | |  |  S(   Ni*  i   (   R  R  R  R$   R  R%   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5674*  s    c      
      s     j  d  t t d  t | | | |  t | | |  t d  | t | | |  | t t d  | t d  | |  | |  |  S(   Ni+  ii   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5675/  s    c      
      s     j  d  t t d  t | | | |  t | | |  t d  | t | | |  | t t d  | t d  | |  | |  |  S(   Ni,  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement56764  s    i   c            sT    j  d  t | | t d  | t d  t | | | |  | | t | | |  |  |  t | | |  | | t d  | t d  t | | | |  t d  t | | |  | | t | | |  |  |  t | | | | |  t | | |  | | | t | | |  | t d  | t d  |  S(   Ni-  i   i(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement56779  s    c            sT    j  d  t | | t d  | t d  t | | | |  | | t | | |  |  |  t | | |  | | t d  | t d  t | | | |  t d  t | | |  | | t | | |  |  |  t | | | | |  t | | |  | | | t | | |  | t d  | t d  |  S(   Ni.  i   i(   R  R  R  R   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5678>  s    c	   	   
      s1    j  d  t | | t d  | t d  t | | t | | |  | t d  | | | |  |  |  t | | t d  | t d  | t d  | t d  t | | t | | |  | t d  | | | |  t | | |  |  |  t | | |  | | t d  | t d  | t d  t | | t | | |  | t d  | | | |  t d  t | | |  |  |  t | | | t | | |  | t d  | | | |  t | | |  | | t d  | t d  | t d  |  S(   Ni/  i   i   i(   R  R  R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5679C  s    c	   	   
      s1    j  d  t | | t d  | t d  t | | t | | |  | t d  | | | |  |  |  t | | t d  | t d  | t d  | t d  t | | t | | |  | t d  | | | |  t | | |  |  |  t | | |  | | t d  | t d  | t d  t | | t | | |  | t d  | | | |  t d  t | | |  |  |  t | | | t | | |  | t d  | | | |  t | | |  | | t d  | t d  | t d  |  S(   Ni0  i   i   i(   R  R  R  R   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5680H  s    R  c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni1  (   R  R   R   R1  (   t   vt   uR  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5681M  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni2  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5682R  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni3  (   R  R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5683W  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni4  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5684\  s    t   pc            sD     j  d  t t t | | |  | | | | |  |  |  S(   Ni5  (   R  R   R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5685a  s    c            sD     j  d  t t t | | |  | | | | |  |  |  S(   Ni6  (   R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5686f  s    c      	      sM    j  d  t | | | |  t d  t | | t d  | | | | |  t d  t | | |  |  |  t | t d  | | |  t d  t | | | | | | |  t d  t | | |  |  |  t | | t d  | | | | |  t d  t | | |  | | |  t d  |  S(   Ni7  i   (   R  R  R  R   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5687k  s    c      	      sM    j  d  t | | | |  t d  t | | t d  | | | | |  t d  t | | |  |  |  t | t d  | | |  t d  t | | | | | | |  t d  t | | |  |  |  t | | t d  | | | | |  t d  t | | |  | | |  t d  |  S(   Ni8  i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5688p  s    c            sD     j  d  t t t | | |  | | | | |  |  |  S(   Ni9  (   R  R   R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5689u  s    c            sD     j  d  t t t | | |  | | | | |  |  |  S(   Ni:  (   R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5690z  s    c            sI     j  d  t | | |  | | | | |  t | | |  |  S(   Ni;  (   R  R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5691  s    c            sI     j  d  t | | |  | | | | |  t | | |  |  S(   Ni<  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5692  s    c            s<     j  d  t | | | | |  t | | |  |  S(   Ni=  (   R  R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5693  s    c            s<     j  d  t | | | | |  t | | |  |  S(   Ni>  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5694  s    c	   	         sP     j  d  t t t | | |  | | | | | | | |  |  |  S(   Ni?  (   R  R   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5695  s    c	   	         sP     j  d  t t t | | |  | | | | | | | |  |  |  S(   Ni@  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5696  s    c	   	         s     j  d  t | | | | | |  t d  t | | | | |  t d  t | | |  |  |  t | | | | | | |  t d  t | | |  | | |  t d  |  S(   NiA  i   (   R  R  R  R   R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5697  s    c	   	         s     j  d  t | | | | | |  t d  t | | | | |  t d  t | | |  |  |  t | | | | | | |  t d  t | | |  | | |  t d  |  S(   NiB  i   (   R  R  R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5698  s    c      	      sY    j  d  t | | | |  t d  t | | | t d  | | | | |  t d  t | | |  |  |  t | | t d  | | |  t d  t | | | | | | | |  t d  t | | |  |  |  t | | | t d  | | | | |  t d  t | | |  | | |  t d  |  S(   NiC  i   (   R  R  R  R   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5699  s    c      	      sY    j  d  t | | | |  t d  t | | | t d  | | | | |  t d  t | | |  |  |  t | | t d  | | |  t d  t | | | | | | | |  t d  t | | |  |  |  t | | | t d  | | | | |  t d  t | | |  | | |  t d  |  S(   NiD  i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5700  s    c            sL     j  d  t t t | | |  | | | | | | |  |  |  S(   NiE  (   R  R   R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5701  s    c            sL     j  d  t t t | | |  | | | | | | |  |  |  S(   NiF  (   R  R   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5702  s    c            sM     j  d  t | | | |  | | | | |  t | | |  |  S(   NiG  (   R  R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5703  s    c            sM     j  d  t | | | |  | | | | |  t | | |  |  S(   NiH  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5704  s    c	   	         sH     j  d  t | | | | | | | |  t | | |  |  S(   NiI  (   R  R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5705  s    c	   	         sH     j  d  t | | | | | | | |  t | | |  |  S(   NiJ  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5706  s    c      	      sy     j  d  t t d  d t t | |  | |  |  |  t t d  d t t | |  | |  |  |  S(   NiK  i   i   (   R  R  R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5707  s    c      	      sx     j  d  t t d  d t t | |  | |  |  |  t t d  d t t | |  | |  |  |  S(   NiL  i   i   (   R  R  R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5708  s    c      	      sA     j  d  t t | | t | | | |  |  |  |  S(   NiM  (   R  R   Rc  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5709  s    c      	      sA     j  d  t t | | t | | | |  |  |  |  S(   NiN  (   R  R   Rc  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5710  s    c      	      s^     j  d  t t | | t | | | |  |  | t d  |  | t d  |  S(   NiO  i   i   (   R  R*   R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5711  s    c      	      s^     j  d  t t | | t | | | |  |  | t d  |  | t d  |  S(   NiP  i   i   (   R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5712  s    c            s   t  |  }   j d  t | t t | | t d  | | t | | | | |  |  |  | | t d  |  |  S(   NiQ  ii   (   R3   R  R  R*   R   R  R   (   R  R  R  R  R  R  R  t   k(   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5713  s    c            s   t  |  }   j d  t | t t | | t d  | | t | | | | |  |  |  | | t d  |  |  S(   NiR  ii   (   R3   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5714  s    c      	      sy     j  d  t t d  d t t | |  | |  |  |  t t d  d t t | |  | |  |  |  S(   NiS  i   i   (   R  R  R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5715  s    c      	      sx     j  d  t t d  d t t | |  | |  |  |  t t d  d t t | |  | |  |  |  S(   NiT  i   i   (   R  R  R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5716  s    c      	      sA     j  d  t t | | t | | | |  |  |  |  S(   NiU  (   R  R   Rc  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5717  s    c      	      sA     j  d  t t | | t | | | |  |  |  |  S(   NiV  (   R  R   Rc  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5718  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   NiW  i   (   R  R  R  R2   R*   R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5719  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   NiX  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5720  s    c            s8     j  d  t | | t | | | |  |  |  S(   NiY  (   R  R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5721  s    c            s8     j  d  t | | t | | | |  |  |  S(   NiZ  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5722  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni[  (   R  R   R   R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5723!  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni\  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5724&  s    c            s,     j  d  t t |  | |  | |  S(   Ni]  (   R  R  R  (   R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5725+  s    c            s,     j  d  t t |  | |  | |  S(   Ni^  (   R  R  R  (   R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement57260  s    c            so     j  d  t t |  t t |  | |  | |  |  t t |  t t |  | |  | |  |  S(   Ni_  (   R  R  R   R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement57275  s    c            so     j  d  t t |  t t |  | |  | |  |  t t |  t t |  | |  | |  |  S(   Ni`  (   R  R  R   R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5728:  s    c   	      S   sw   t  | t t t t f  r t S| t d  | } t t |  t	 t
 |  t d   t | t d     rs t St S(   Ni   i    (   t
   isinstancet   intR  t   floatR  t   FalseR  R  R   R  R"   RP   t   True(	   R  R  R  R  R  R  R  R  R&  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5729>  s    <c   	         s   | t  d  | }   j d  t t  d  | t t | | t  d  | | t | | |  |  |  | | |  |  S(   Ni   ia  i(   R  R  R  R*   R   R   (	   R  R  R  R  R  R  R  R  R&  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5729F  s    c   	      S   sw   t  | t t t t f  r t S| t d  | } t t |  t	 t
 |  t d   t | t d     rs t St S(   Ni   i    (   RL  RM  R  RN  R  RO  R  R  R   R  R"   RP   RP  (	   R  R  R  R  R  R  R  R  R&  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5730L  s    <c   	         s   | t  d  | }   j d  t t  d  | t t | | t  d  | | t | | |  |  |  | | |  |  S(   Ni   ib  i(   R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R&  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5730T  s    c	   
      S   sw   t  | t t t t f  r t S| t d  | }	 t t |	  t	 t
 |  t d   t |	 t d     rs t St S(   Ni   i    (   RL  RM  R  RN  R  RO  R  R  R   R  R"   RP   RP  (
   R  R  R  R  R  R  R  R  R  R&  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5731Z  s    <c	   
         s   | t  d  | }	   j d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni   ic  (   R  R  R  R$   R%   R   R   (
   R  R  R  R  R  R  R  R  R  R&  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5731b  s    c	   
      S   sw   t  | t t t t f  r t S| t d  | }	 t t |	  t	 t
 |  t d   t |	 t d     rs t St S(   Ni   i    (   RL  RM  R  RN  R  RO  R  R  R   R  R"   RP   RP  (
   R  R  R  R  R  R  R  R  R  R&  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5732h  s    <c	   
         s   | t  d  | }	   j d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni   id  (   R  R  R  R$   R%   R   R  (
   R  R  R  R  R  R  R  R  R  R&  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5732p  s    c      	      s     j  d  t | | |  | t d  | | t | | |  | t | | | |  |  |  t | | t d  | | |  | t d  t | | | |  | | |  S(   Nie  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5733w  s    c      	      s     j  d  t | | |  | t d  | | t | | |  | t | | | |  |  |  t | | t d  | | |  | t d  t | | | |  | | |  S(   Nif  i   i(   R  R  R  R   R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5734|  s    c      	      s     j  d  t | | | | |  t d  t | | |  | t | | | |  |  |  t | | |  t d  t | | | |  | |  t d  |  S(   Nig  i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5735  s    c      	      s     j  d  t | | | | |  t d  t | | |  | t | | | |  |  |  t | | |  t d  t | | | |  | |  t d  |  S(   Nih  i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5736  s    c      
      s     j  d  t t d  d t | | |  t | | | |  |  |  t t d  d t | | |  t | | | |  |  |  S(   Nii  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5737  s    c      
      s     j  d  t t d  d t | | |  t | | | |  |  |  t t d  d t | | |  t | | | |  |  |  S(   Nij  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5738  s    c      	      s     j  d  t | | |  | t d  t t | | | |  |  t d  t | | | |  |  |  t | | t d  t | | | |  |  | t d  |  S(   Nik  ii   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5739  s    c      	      s     j  d  t | | |  | t d  t t | | | |  t | | | |  |  t d  |  |  t | | t d  t | | | |  |  | t d  |  S(   Nil  ii   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5740  s    c      	      s     j  d  t |  t d  |  t | | t | | | |  |  t d  |  |  t t | | | |  |  | t d  | |  t d  |  t | | t | | | |  |  t d  t | | | |  | | |  |  S(   Nim  iii   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5741  s    c      	      s     j  d  t |  t d  |  t | | t | | | |  |  t d  |  |  t t | | | |  |  | t d  | |  t d  |  t | | t | | | |  t | | | |  |  t d  | | |  |  S(   Nin  iii   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5742  s    c      
      s    j  d  t |  t d  |  t | | t | | | |  |  t d  |  |  t | t d  | t d  | | t d  | t d  | t d  |  t d  t | | t d  | t | | | |  |  |  |  t | | t d  | t d  | | t d  t | | | |  |  | t d  | t d  |  t d  |  t | | | t d  t | | | |  |  t d  t | | | |  | | |  |  S(   Nio  iii   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5743  s    c      
      s    j  d  t |  t d  |  t | | t | | | |  |  t d  |  |  t | t d  | t d  | | t d  | t d  | t d  |  t d  t | | t d  | t | | | |  |  |  |  t | | t d  | t d  | | t d  t | | | |  |  | t d  | t d  |  t d  |  t | | | t d  t | | | |  t | | | |  |  t d  | | |  |  S(   Nip  iii   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5744  s    c      
      s    j  d  t | t d  | t d  |  t d  | t d  | | t d  t | | t d  | t | | | |  |  |  |  t | t d  | t d  |  |  t d  | t d  | | t d  t | | t d  | t | | | |  |  t d  |  |  t | | t d  t | | | |  |  | t d  |  t | | |  | | | t d  t | | | |  |  t d  t | | | |  | t d  | | t d  |  S(   Niq  i   i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5745  s    c      
      s    j  d  t | t d  | t d  |  t d  | t d  | | t d  t | | t d  | t | | | |  |  |  |  t | t d  | t d  |  |  t d  | t d  | | t d  t | | t d  | t | | | |  |  t d  |  |  t | | t d  t | | | |  |  | t d  |  t | | |  | | | t d  t | | | |  t | | | |  |  t d  | t d  | | t d  |  S(   Nir  i   i   ii(   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5746  s    c	   
         s   t  |  }	   j d  t |	 | t t | |	 | t d  t d  | | t | | | | | |	 |  |  |  | | | t d  |	  |  S(   Nis  i   i(   R3   R  R  R*   R   R  R   (
   R  R  R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5747  s    c	   
         s   t  |  }	   j d  t |	 | t t | |	 | t d  t d  | | t | | | | | |	 |  |  |  | | | t d  |	  |  S(   Nit  i   i(   R3   R  R  R*   R   R  R  (
   R  R  R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5748  s    c	   	   
      sL     j  d  t t | | | | | t | | | |  |  |  |  S(   Niu  (   R  R   Rc  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5749  s    c	   	   
      sL     j  d  t t | | | | | t | | | |  |  |  |  S(   Niv  (   R  R   Rc  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5750  s    c      	      s#    j  d  t |  t d  |  t d  t | | t | | | |  |  t d  |  |  t t | | | |  |  t d  | t d  | |  t d  |  t d  |  t | | t | | | |  |  t d  t | | | |  | | |  t d  |  S(   Niw  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5751  s    c      	      s"    j  d  t |  t d  |  t d  t | | t | | | |  |  t d  |  |  t t | | | |  |  t d  | t d  | |  t d  |  t d  |  t | | t | | | |  t | | | |  |  t d  | | |  t d  |  S(   Nix  i   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5752  s    c      
      s    j  d  t |  t d  |  t d  t | | t | | | |  |  t d  |  |  t | t d  | t d  | | t d  | t d  | t d  |  t d  |  t d  t | | t d  | t | | | |  |  t d  |  |  t | | | t d  t | | | |  |  t d  t | | | |  | | |  t d  |  t | | t d  | t d  | | t d  t | | | |  |  t d  | t d  | t d  |  t d  |  t d  |  S(   Niy  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5753  s    c      
      s    j  d  t |  t d  |  t d  t | | t | | | |  |  t d  |  |  t | t d  | t d  | | t d  | t d  | t d  |  t d  |  t d  t | | t d  | t | | | |  |  t d  |  |  t | | | t d  t | | | |  t | | | |  |  t d  | | |  t d  |  t | | t d  | t d  | | t d  t | | | |  |  t d  | t d  | t d  |  t d  |  t d  |  S(   Niz  i   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5754  s    c      
      sc     j  d  t t | | t d  | | t | | | |  |  |  | t d  |  S(   Ni{  ii   (   R  R*   R   R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5755  s    c      
      sc     j  d  t t | | t d  | | t | | | |  |  |  | t d  |  S(   Ni|  ii   (   R  R*   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5756  s    c	   
         s   t  |  }	   j d  t |	 | t t | |	 | t d  t d  | | t | | | | | |	 |  |  |  | | | t d  |	  |  S(   Ni}  i   i(   R3   R  R  R*   R   R  R   (
   R  R  R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5757  s    c	   
         s   t  |  }	   j d  t |	 | t t | |	 | t d  t d  | | t | | | | | |	 |  |  |  | | | t d  |	  |  S(   Ni~  i   i(   R3   R  R  R*   R   R  R  (
   R  R  R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5758  s    c	   	         s     j  d  t | | | t d  | | t t | | t d  | | t | | | |  |  |  | t d  |  |  S(   Ni  i   i(   R  R  R  R*   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5759  s    c	   	         s     j  d  t | | | t d  | | t t | | t d  | | t | | | |  |  |  | t d  |  |  S(   Ni  i   i(   R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5760  s    c   	         s   t  |  }   j d  t | t t | | | t d  t d  | | t | | | | |  |  |  | | t d  |  |  S(   Ni  i   i(   R3   R  R  R*   R   R  R   (	   R  R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5761  s    c   	         s   t  |  }   j d  t | t t | | | t d  t d  | | t | | | | |  |  |  | | t d  |  |  S(   Ni  i   i(   R3   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R;  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5762  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5763  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5764  s    c            s     j  d  t t d  | t d  t t | | t | | | | | t d   |  |  | | | t d   |  S(   Ni  i   (   R  R  R  R*   R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5765  s    c            s     j  d  t t d  | t d  t t | | t | | | | | t d   |  |  | | | t d   |  S(   Ni  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5766"  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5767'  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5768,  s    c      
      s     j  d  t t d  d t | | |  t | | | |  |  |  t t d  d t | | |  t | | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement57691  s    c      
      s     j  d  t t d  d t | | |  t | | | |  |  |  t t d  d t | | |  t | | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement57706  s    c	   	   
      sL     j  d  t t | | | | | t | | | |  |  |  |  S(   Ni  (   R  R   Rc  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5771;  s    c	   	   
      sL     j  d  t t | | | | | t | | | |  |  |  |  S(   Ni  (   R  R   Rc  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5772@  s    c	   	         s     j  d  t t | | t d   | t d  t t | | t | | | |  |  | t | | t d   | |  | |  |  S(   Ni  i   ii    (   R  R  R2   R  R*   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5773E  s    c	   	         s     j  d  t t | | t d   | t d  t t | | t | | | |  |  | t | | t d   | |  | |  |  S(   Ni  i   ii    (   R  R  R2   R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5774J  s    c
   
   	      sD     j  d  t |	 | | | | t | | | |  |  |  S(   Ni  (   R  R   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5775O  s    c
   
   	      sD     j  d  t |	 | | | | t | | | |  |  |  S(   Ni  (   R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5776T  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   Ni  (   R  R   R   R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5777Y  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5778^  s    c            sP     j  d  t t | | | |  |  t d  | | |  t d  |  S(   Ni  i   (   R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5779c  s    c            sP     j  d  t t | | | |  |  t d  | | |  t d  |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5780h  s    c      	      s     j  d  t | | t d  | | |  t d  t | | | t | | | |  |  t d  |  |  t | | | t d  t | | | |  |  t d  | | |  t d  |  S(   Ni  i   (   R  R  R  R   R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5781m  s    c      	      s     j  d  t | | t d  | | |  t d  t | | | t | | | |  |  t d  |  |  t | | | t d  t | | | |  |  t d  | | |  t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5782r  s    c      
      s     j  d  t t d  d t t | | |  | |  t d   |   |   t t d  d t t | | |  | |  t d   |   |   S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5783w  s    c      
      s     j  d  t t d  d t t | | |  | |  t d   |   |   t t d  d t t | | |  | |  t d   |   |   S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5784|  s    c            sG     j  d  t t t | |  | | | t d   | |  |  S(   Ni  i   (   R  R   Rc  R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5785  s    c            sG     j  d  t t t | |  | | | t d   | |  |  S(   Ni  i   (   R  R   Rc  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5786  s    c            s-     j  d  t t t |  |   | |  S(   Ni  (   R  R   R   R1  (   R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5787  s    c            s-     j  d  t t t |  |   | |  S(   Ni  (   R  R   R  R1  (   R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5788  s    c            sL     j  d  t | t | |  | | | t d   t d  | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5789  s    c            sL     j  d  t | t | |  | | | t d   t d  | |  S(   Ni  i   (   R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5790  s    c      	      s     j  d  t |  | t d  | | t d  | t t | |  | | | t d   |  |  t | t | |  | | | t d   t d  | |  S(   Ni  i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5791  s    c      	      s     j  d  t |  | t d  | | t d  | t t | |  | | | t d   |  |  t | t | |  | | | t d   t d  | |  S(   Ni  i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5792  s    c      
      s     j  d  t | t d  |  t d  t d  | t | | | |  t d  t | | | | | t d   |  |  t | | | | |  t d  t | | | | | t d   t d  | |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5793  s    c      
      s     j  d  t | t d  |  t d  t d  | t | | | |  t d  t | | | | | t d   |  |  t | | | | |  t d  t | | | | | t d   t d  | |  S(   Ni  i   ii(   R  R  R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5794  s    c            sW    j  d  t | | t d  | | t d  | t | | | |  t d  t | | | | | t d   |  |  t | t d  |  t d  t d  | t | | | |  t d  t | | | | | t d   |  |  t | | | | |  t d  t | | | | | t d   t d  | |  S(   Ni  i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5795  s    c            sW    j  d  t | | t d  | | t d  | t | | | |  t d  t | | | | | t d   |  |  t | t d  |  t d  t d  | t | | | |  t d  t | | | | | t d   |  |  t | | | | |  t d  t | | | | | t d   t d  | |  S(   Ni  i   ii(   R  R  R  R   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5796  s    c      
      s     j  d  t t d  | | t d  |  t d  t | | | |  t d  t | | | | | t d   |  |  t | | | |  t d  t | | | | | t d   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5797  s    c      
      s     j  d  t t d  | | t d  |  t d  t | | | |  t d  t | | | | | t d   |  |  t | | | |  t d  t | | | | | t d   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5798  s    c            se    j  d  t t d  | | t d  |  t d  t | | | |  t d  t | | | | | t d   |  |  t | | t d  | | | t d  |  t d  t | | | |  t d  t | | | | | t d   |  |  t | | | |  t d  t | | | | | t d   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5799  s    c            se    j  d  t t d  | | t d  |  t d  t | | | |  t d  t | | | | | t d   |  |  t | | t d  | | | t d  |  t d  t | | | |  t d  t | | | | | t d   |  |  t | | | |  t d  t | | | | | t d   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5800  s    c            sJ     j  d  t | | | |  t | | | | | t d   |  S(   Ni  i   (   R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5801  s    c            sJ     j  d  t | | | |  t | | | | | t d   |  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5802  s    c      	      sV     j  d  t t | | | |  t | | | | | t d   | |  |  S(   Ni  i   (   R  R   Rc  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5803  s    c      	      sV     j  d  t t | | | |  t | | | | | t d   | |  |  S(   Ni  i   (   R  R   Rc  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5804  s    c            s>     j  d  t t | |  | t t |  |   | |  S(   Ni  (   R  R   R1  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5805  s    c            s>     j  d  t t | |  | t t |  |   | |  S(   Ni  (   R  R   R1  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5806  s    c            s     j  d  t t d  t | | | |  t t d  | t d  | |  t t d  | t d  | |  t d  |  |  t | | | |  t d  | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5807  s    c            s     j  d  t t d  t | | | |  t t d  | t d  | |  t t d  | t d  | |  t d  |  |  t | | | |  t d  | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5808  s    c      	      s     j  d  t | t d  t | t | | |  | t d  | | | |  |  |  t | | |  | | t d  t | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5809  s    c      	      s     j  d  t | t d  t | t | | |  | t d  | | | |  |  |  t | | |  | | t d  t | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5810  s    c      	      s     j  d  t | t d  t | t | | |  | t d  | | | |  |  |  t | |  | | | t d  t | t | | |  | t d  | | | |  t d  |  |  t | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  ii   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5811  s    c      	      s     j  d  t | t d  t | t | | |  | t d  | | | |  |  |  t | |  | | | t d  t | t | | |  | t d  | | | |  t d  |  |  t | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  ii   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5812  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5813  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5814  s    c      
      s     j  d  t | | |  t d  | | t | | | |  t d  | | t | | |  |  |  t | | | |  t d  t d  | | |  t d  |  t | | | | |  t d  | | | | t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5815  s    c      
      s     j  d  t | | |  t d  | | t | | | |  t d  | | t | | |  |  |  t | | | |  t d  t d  | | |  t d  |  t | | | | |  t d  | | | | t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5816  s    c      
      s     j  d  t |  | | t t t d  | t d  |  |  | | | |  |  t |  | | t t t d  | t d  |  |  | | | |  |  t t d  | | | t | |  |  | | | |  S(   Ni  i   i   (   R  R  R   R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5817!  s    c      
      s     j  d  t |  | | t t t d  | t d  |  |  | | | |  |  t |  | | t t t d  | t d  |  |  | | | |  |  t t d  | | | t | |  |  | | | |  S(   Ni  i   i   (   R  R  R   R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5818&  s    c      
      s    j  d  t t d  | | | | |  t d  t | | | |  t d  | | t | | |  |  |  t | | | |  t d  | | | t | | |  |  t d  |  t | | | | |  t d  | | t d  |  t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5819+  s    c      
      s    j  d  t t d  | | | | |  t d  t | | | |  t d  | | t | | |  |  |  t | | | |  t d  | | | t | | |  |  t d  |  t | | | | |  t d  | | t d  |  t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement58200  s    c            s     j  d  t t d  t d  | t t t d  | t d  |  |  | | | |  |  t t d  t d  | t t t d  | t d  |  |  | | | |  |  t t | | |  t d  | | |  S(   Ni  i   i   (   R  R  R  R   R  R   R  t   log(   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement58215  s    c            s     j  d  t t d  t d  | t t t d  | t d  |  |  | | | |  |  t t d  t d  | t t t d  | t d  |  |  | | | |  |  t t | | |  t d  | | |  S(   Ni  i   i   (   R  R  R  R   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5822:  s    c      	      s     j  d  t t d  t d  | t | | | |  t t d  | | | | |  |  |  t | | | |  t d  t d  | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5823?  s    c      	      s     j  d  t t d  t d  | t | | | |  t t d  | | | | |  |  |  t | | | |  t d  t d  | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5824D  s    c	   	         s     j  d  t t | | | |  t t d  | t d  | |  t d  | t t d  | t d  | |  t d  | t d  t d  | | |  |  S(   Ni  i   i   (   R  R   R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5825I  s    c	   	         s     j  d  t t | | | |  t t d  | t d  | |  t d  | t t d  | t d  | |  t d  | t d  t d  | | |  |  S(   Ni  i   i   (   R  R   R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5826N  s    c	   	   	      s~     j  d  t t | | | |  t d  t d  | t t d  | | | | |  t d  | | |  |  S(   Ni  i   i   (   R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5827S  s    c	   	   	      s~     j  d  t t | | | |  t d  t d  | t t d  | | | | |  t d  | | |  |  S(   Ni  i   i   (   R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5828X  s    c	   
         s   t  | | t | | |  | |  }	   j d  t | |  t t | | | |  t d  |	 |  |  |  t | | | |  |	 |  S(   Ni  i(   R  R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5829\  s    )c	   
         s   t  | | t | | |  | |  }	   j d  t | |  t t | | | |  t d  |	 |  |  |  t | | | |  |	 |  S(   Ni  i(   R  R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5830b  s    )c      
      s     j  d  t t d  | t | | | |  | t d  | t d  | | t d  t t d  | t d  | |  |  |  t | | | |  t d  | | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5831i  s    c      
      s     j  d  t t d  | t | | | |  | t d  | t d  | | t d  t t d  | t d  | |  |  |  t | | | |  t d  | | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5832n  s    c      
      s8    j  d  t t d  |  | t d  | t d  t t d  | | |  t d  | | |  | | | | | t | |  |  |  |  t | | | t d  t d  | | t d  | t d  |  t | | | | |  | | t | |  |  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5833s  s    c      
      s8    j  d  t t d  |  | t d  | t d  t t d  | | |  t d  | | |  | | | | | t | |  |  |  |  t | | | t d  t d  | | t d  | t d  |  t | | | | |  | | t | |  |  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5834x  s    c	   	   
      s     j  d  t t | | | |  t d  | | t d  | t d  | | t d  t t d  | t d  | |  t d  | | | |  |  S(   Ni  i   i   (   R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5835}  s    c	   	   
      s     j  d  t t | | | |  t d  | | t d  | t d  | | t d  t t d  | t d  | |  t d  | | | |  |  S(   Ni  i   i   (   R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5836  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5837  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5838  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5839  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5840  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5841  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5842  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5843  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5844  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5845  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5846  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5847  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5848  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5849  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5850  s    c      	      s     j  d  t |  | t d  | | t | |  | t | | | |  |  |  t | |  |  t | |  | t d  t | | | |  | | |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5851  s    c      	      s     j  d  t |  | t d  | | t | |  | t | | | |  |  |  t | |  |  t | |  | t d  | | t | | | |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5852  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5853  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5854  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5855  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5856  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5857  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5858  s    t   qc      
      s     j  d  t | | t d  | | |  t | | | t d  t | | | |  |  |  |  t | | | t d  t d  t | | | |  |  | | |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5859  s    c      
      s     j  d  t | | t d  | | |  t | | | t d  t | | | |  |  |  |  t | | | t d  t d  t | | | |  |  | | |  |  S(   Ni  i   (   R  R  R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5860  s    c            s>     j  d  t t | |  | | | t d   | |  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5861  s    c            sH     j  d  t t d  t | |  | | | t d   | |  S(   Ni  i   i   (   R  R   R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5862  s    c      
      s     j  d  t |  | t d  | | t d  | t t | |  | | | t d   |  |  t | t t | |  | | | t d    t d  | |  S(   Ni  i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5863	  s    c      
      s     j  d  t |  | t d  | | t d  | t t d  t | |  | | | t d   |  |  t | t t | |  | | | t d    t d  | |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5864  s    c            sN     j  d  t | | | |  t | | | | | t d   | |  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5865  s    c      	      sX     j  d  t | | | |  t d  t | | | | | t d   | |  S(   Ni  i   i   (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5866  s    c            s    j  d  t t | |  | t | | | |  t d  t t t | | |  t d   |  |  t t | |  | t | | | |  t d  t t t | | |  t d   |  |  t t d  | | | |  t t | | |   | |  S(   Ni  ii   i   (	   R  R  R  R   R  R  R  R  R=   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5867  s    c      
      s    j  d  t | |  | t | | | |  t d  t t | | |  t d   |  |  t | |  | t | | | |  t d  t t | | |  t d   |  |  t t d  | | | |  t t | | |   | |  S(   Ni  ii   i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5868"  s    c            s     j  d  t | |  | t | | | |  t d  t | | |  |  |  t | | | |  t | | |  | |  S(   Ni  i(   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5869'  s    c            s     j  d  t | |  | t | | | |  t d  t | | |  |  |  t | | | |  | t | | |  |  S(   Ni  i(   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5870,  s    c      	      s4    j  d  t | t d  | t d  t | | | t d  t | |  |  | t d  |  |  t | t d  t | |  |  | t d  |  t d  | t d  | t d  |  t | | | t d  t | |  |  | t d  t | |  |  |  | t d  |  S(   Ni  iii   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement58711  s    c      	      s5    j  d  t | t d  | t d  t | | | t d  t | |  |  | t d  |  |  t | t d  t | |  |  | t d  |  t d  | t d  | t d  |  t | | | t d  t | |  |  | t d  |  | t d  t | |  |  |  S(   Ni  iii   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement58726  s    c      
      s    j  d  t | t d  | t d  t | | | |  t d  t | | |  | t d  |  |  t | t d  |  |  t d  | t d  | t d  | t d  t | | | |  t d  t d  t | | |  | t d  |  |  t | | | |  t d  t | | |  | t d  t | | |  | | t d  |  t | |  | | | |  t d  t d  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni  iii   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5873;  s    c      
      s    j  d  t | t d  | t d  t | | | |  t d  t | | |  | t d  |  |  t | t d  |  |  t d  | t d  | t d  | t d  t | | | |  t d  t d  t | | |  | t d  |  |  t | | | |  t d  t | | |  | t d  | | t d  t | | |  |  t | |  | | | |  t d  t d  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni  iii   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5874@  s    c      	      s    j  d  t | t d  | t | | | t d  t | |  |  | t d  |  |  t | t d  t | |  |  | |  t d  | t d  |  t | | | t d  t | |  |  | t d  t | |  |  |  | |  S(   Ni  i   i   (   R  R  R  R   R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5875E  s    c      	      s	    j  d  t | t d  | t | | | t d  t | |  |  | t d  |  |  t | t d  t | |  |  | |  t d  | t d  |  t | | | t d  t | |  |  | t d  t | |  |  |  | |  S(   Ni  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5876J  s    c      
      s    j  d  t | t d  | t | | | |  t d  t | | |  | t d  |  |  t | t d  |  |  t d  | t d  | t d  t | | | |  t d  t d  t | | |  | |  |  t | | | |  t d  t | | |  | t d  t | | |  | | |  t | |  | | | |  t d  t d  t | | |  | | t d  | t d  |  S(   Ni  i   i   ii(   R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5877O  s    c      
      s    j  d  t | t d  | t | | | |  t d  t | | |  | t d  |  |  t | t d  |  |  t d  | t d  | t d  t | | | |  t d  t d  t | | |  | |  |  t | | | |  t d  t | | |  | t d  t | | |  | | |  t | |  | | | |  t d  t d  t | | |  | | t d  | t d  |  S(   Ni  i   i   ii(   R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5878T  s    c            s{     j  d  t t d  t | | |  | t | | |  | t | | | |  t | | |  | |  |  S(   Ni  i   (   R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5879Y  s    c            s{     j  d  t t d  t | | |  | t | | |  | t | | | |  t | | |  | |  |  S(   Ni  i   (   R  R  R  R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5880^  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5881c  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5882h  s    c	   	         sc     j  d  t t | | | |  | t | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5883m  s    c	   	         sc     j  d  t t | | | |  | t | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5884r  s    c            sH     j  d  t t d  t t |  |   | t | |  | |  S(   Ni  i   (   R  R   R  R  R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5885w  s    c            sH     j  d  t t d  t t |  |   | t | |  | |  S(   Ni  i   (   R  R   R  R   R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5886|  s    c            sF     j  d  t | | | |  t d  t | | |  | |  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5887  s    c            sF     j  d  t | | | |  t d  t | | |  | |  S(   Ni   i   (   R  R   R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5888  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5889  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni  i   i(   R  R  R  R*   R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5890  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5891  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni  (   R  R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5892  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5893  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni  i   (   R  R  R  R2   R*   R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5894  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5895  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni  (   R  R   R   R1  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5896  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   Ni	  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5897  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   Ni
  i   i(   R  R  R  R*   R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5898  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5899  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   Ni  (   R  R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5900  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5901  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni  (   R  R  R$   R%   R   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5902  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   Ni  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5903  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   Ni  (   R  R   R   R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5904  s    c      
      s     j  d  t | | t d  | | |  t d  t | | | t d  t | | | |  |  t d  |  |  t | | | t d  t d  t | | | |  |  t d  | | |  t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5905  s    c      
      s     j  d  t | | t d  | | |  t d  t | | | t d  t | | | |  |  t d  |  |  t | | | t d  t d  t | | | |  |  t d  | | |  t d  |  S(   Ni  i   i(   R  R  R  R   R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5906  s    c            s     j  d  t | |  | | t d  t | | | |  t d  t | | |  | t d  |  |  t | | | |  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5907  s    c            s     j  d  t | |  | | t d  t | | | |  t d  t | | |  | t d  |  |  t | | | |  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5908  s    c            sZ     j  d  t t | | | | t | | |  | t | | |  |  |  |  S(   Ni  (   R  R   Rc  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5909  s    c            s     j  d  t | | | | t | | |  | t | | |  |  t d  |  t | | | | t | | |  | t d  t | | |  |  |  S(   Ni  i(   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5910  s    c            s     j  d  t | | | | t d  t | | |  |  t | | |  | t d  |  t | | | | t d  t | | |  |  t d  t | | |  | |  S(   Ni  i   i(   R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5911  s    c      	      s     j  d  t | | | | t | | | | t d  t d  t | | |  | |  |  t | | | | t d  t | | |  | | | |  S(   Ni  ii   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5912  s    c      	      s     j  d  t | | | | t | | | | t d  t d  t | | |  | |  |  t | | | | t d  t | | |  | | | |  S(   Ni  ii   (   R  R  R   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5913  s    c            s     j  d  t | |  | | t d  t | | | |  t d  t | | |  | t d  |  |  t | | | |  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5914  s    c      	      s     j  d  t | |  | | t d  t | | | |  t d  t d  t | | |  | t d  |  |  t | | | |  t d  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5915  s    c            s     j  d  t | | | | t | | |  |  t d  t | | |  t d  |  t | | | | t | | |  |  t d  t | | |  |  S(   Ni  ii   (   R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5916  s    c            s     j  d  t | | | | t d  t | | |  | t | | |  |  t d  |  t | | | | t d  t | | |  | t d  t | | |  |  t d  |  S(   Ni  i   ii   (   R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5917  s    c            s     j  d  t | | | | t d  t | | |  |  t d  t | | |  t d  |  t | | | | t d  t | | |  |  t d  t | | |  |  S(   Ni  i   ii   (   R  R   R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5918  s    c            s     j  d  t | | | | t d  t | | |  | t d  t | | |  |  t d  |  t | | | | t d  t | | |  | t d  t d  t | | |  |  t d  |  S(   Ni  i   ii   (   R  R   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5919!  s    c   	         s   t  t d  t | | |  | t | | |  |  |  }   j d  t | | t | | | | | t d  |  |  t | | | | | |  S(   Ni   i   i(   R  R  R  R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5920%  s    Ac   	         s   t  t d  t | | |  | t d  t | | |  |  |  }   j d  t | | t | | | | | t d  |  |  t | | | | | |  S(   Ni   i!  i(   R  R  R   R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5921+  s    Kc      	      sp     j  d  t t d  | t | | | |  t d  t t d  | t d  | |  | |  |  S(   Ni"  i   i   (   R  R  R  R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement59222  s    c   	         s   t  t d  t | | |  | t d  t | | |  |  |  }   j d  t | | t | | | | | t d  |  |  t | | | | | |  S(   Ni   i#  i(   R  R  R   R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With59236  s    Kc	   	         sU     j  d  t t | |  | | t |  |   | | t |  |   | |  S(   Ni$  (   R  R   R1  (	   R  t   wR  R  R  t   GR  R  t   F(   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5924=  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni%  i   i(   R  R  R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5925B  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni&  i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5926G  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni'  i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5927L  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni(  i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5928Q  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni)  i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5929V  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni*  i   i(   R  R  R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5930[  s    c
   
         sZ     j  d  t t |	 | | | t | | |  |  t | | |  | |  |  S(   Ni+  (   R  R   Rc  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5931`  s    c
   
         sZ     j  d  t t |	 | | | t | | |  |  t | | |  | |  |  S(   Ni,  (   R  R   Rc  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5932e  s    c
   
         sZ     j  d  t t |	 | | | t | | |  |  t | | |  | |  |  S(   Ni-  (   R  R   Rc  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5933j  s    c            s]     j  d  t t |
 | | | | | | |  |	 | | | | |  | | |  |  S(   Ni.  (   R  R   Rb  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5934o  s    c            s     j  d  t | | | |  | | t | | |  |  t d  | t d  t |  t d  | t d  |  t | | | |  | |  | t |  t | | |  |  t d  | t d  t |  t d  | t d  |  S(   Ni/  i   (   R  R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5935t  s    c            s     j  d  t | | | |  | | t | | |  |  t d  | t d  t |  t d  | t d  |  t | | | |  | |  | t |  t | | |  |  t d  | t d  t |  t d  | t d  |  S(   Ni0  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5936y  s    c            s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | |  | t |  t | | |  | |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t | | |  | t d  t | | |  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni1  i   ii(   R  R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5937~  s    c            s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | |  | t |  t | | |  | |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t | | |  t | | |  | t d  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni2  i   ii(   R  R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5938  s    c            s     j  d  t | | | |  | t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni3  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5939  s    c            s     j  d  t | | | |  | t | | |  t | | |  | t d  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni4  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5940  s    c            s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni5  i   i   (   R  R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5941  s    c            s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | t | | |  t | | |  | t d  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni6  i   i   (   R  R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5942  s    c      	      s     j  d  t t t d  | t d  | |  t d  | t | | | |  t | | |  | t | | | |  | t t d  | t d  | |  t d  | t | | | |  |  |  S(   Ni7  i   i(   R  R  R  R  R   R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5943  s    c      	      s     j  d  t t t d  | t d  | |  t d  | t | | | |  t | | |  | t | | | |  | t t d  | t d  | |  t d  | t | | | |  |  |  S(   Ni8  i   i   (   R  R  R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5944  s    c            s     j  d  t t | | | |  | t t d  | t d  | |  t d  | t t d  | t d  | |  t d  | |  |  S(   Ni9  i   ii   (   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5945  s    c            s     j  d  t t | | | |  | t t d  | t d  | |  t d  | t t d  | t d  | |  t d  | |  |  S(   Ni:  i   ii   (   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5946  s    c      	      s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | |  | t d  t | | |  | t |  |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t d  t | | |  | t d  t | | |  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni;  i   i   (   R  R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5947  s    c      	      s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | |  | t d  t | | |  | t |  |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t d  t | | |  | t d  t | | |  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni<  i   i   (   R  R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5948  s    c            s     j  d  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni=  i   iii   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5949  s    c            s     j  d  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni>  i   iii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5950  s    c      	      s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni?  i   iii   (   R  R  R  R  R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5951  s    c      	      s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni@  i   iii   (   R  R  R  R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5952  s    c      
      s     j  d  t t d  | | | | |  | t | |  | t |  t d  | | t d  |  | t |  t d  | | t d  t d  t t d  | t d  | |   t | | | |  |  | t |  | | |  S(   NiA  i   i   (   R  R  R  R4   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5953  s    c      
      s     j  d  t t d  | | | | |  | t | |  | t |  t d  | | t d  |  | t |  t d  | | t d  t d  t t d  | t d  | |   t | | | |  |  | t |  | | |  S(   NiB  ii   i   (   R  R  R  R4   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5954  s    c      
      s     j  d  t t t d  | t d  | |  t d  | t d  t | | |  | t | | | |  t t | | | |  | t t d  | t d  | |  t d  | t | | | |  |  |  |  S(   NiC  i   i   (   R  R  R  R  R  R   R,  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5955  s    c      
      s     j  d  t t t d  | t d  | |  t d  | t d  t | | |  | t | | | |  t t | | | |  | t t d  | t d  | |  t d  | t | | | |  |  |  |  S(   NiD  i   i   (   R  R  R  R  R   R   R,  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5956  s    t   gc
   
   	      s     j  d  t t d  | | | t | | | | | t t | t d  |  | t d  |	 | t d   t d  | |  |  S(   NiE  i   i   (   R  R  R  R   R  R  (
   R>  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5957  s    c
   
   	      s|     j  d  t t d  | |  | t | | | | | t | t d  |	 | t d   t d  | |  |  S(   NiF  i   (   R  R  R  R   R  (
   R>  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5958  s    c
   
   	      s|     j  d  t t d  | |  | t | | | | | t | t d  |	 | t d   t d  | |  |  S(   NiG  i   (   R  R  R  R   R   (
   R>  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5959  s    c      	      s{     j  d  t | | t |	 | | | | t t | t d  | | t d  |
 | t d   |  |  |  S(   NiH  i   i   (   R  R  R   R  R  R  (   R  R>  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5960  s    c      	      sd     j  d  t | | t |	 | | | | t | t d  |
 | t d   |  |  |  S(   NiI  i   (   R  R  R   R  R  (   R  R>  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5961  s    c      
      sn     j  d  t | | t |	 | | | | t d  t | t d  |
 | t d   |  |  |  S(   NiJ  i   i   (   R  R  R   R  R  (   R  R>  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5962  s    t   ic      
      s     j  d  t t d  | t |	 | | | | t | |
 |  | |  t | |
 |  |  |  t |	 | | | | | | t | |
 |  | |  t | |
 |  |  S(   NiK  i   (   R  R  R  R   R  R   (   R>  R  R  RE  R  R  R  R  t   hR  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5963   s    c      
      s     j  d  t t d  | t |	 | | | | t | |
 |  | |  t | |
 |  |  |  t |	 | | | | | | t | |
 |  | |  t | |
 |  |  S(   NiL  i   (   R  R  R  R   R   R  (   R>  R  R  RE  R  R  R  R  RF  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5964  s    c            sB     j  d  t | | t | |  | t |  |   | |  S(   NiM  (   R  R   R1  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5965
  s    c	   
         s   t  | | | | | t | | |  | |  }	   j d  t |  t |	 | |  t d  |  |  t |	 | |  |  S(   NiN  i(   R  R   R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5966  s    5c	   
         s   t  | | | | | t | | |  | |  }	   j d  t |  t |	 | |  t d  |  |  t |	 | |  |  S(   NiO  i(   R  R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With5967  s    5c            s^     j  d  t t |	 | | | | t | |
 |  |  t | | |  | |  |  S(   NiP  (   R  R   Rc  R   R  (   R  R  R>  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5968  s    c            sf     j  d  t t |
 | | | |	 |	 |  t | | |	  | t | | |	  | |	  |	  S(   NiQ  (   R  R   Rc  R   R  (   R  R  R  R>  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5969   s    c            s^     j  d  t t |	 | | | | | | |
 |  |  | | |
 |  | |  |  S(   NiR  (   R  R   Rg  (   R  R  R  R  R  R  R  t   HR  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5970%  s    c            s4     j  d  t t | | t |   | |  |  S(   NiS  (   R  R   Rg  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5971*  s    c            s4     j  d  t t | | t |   | |  |  S(   NiT  (   R  R   Rg  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5972/  s    c            sB     j  d  t t | | t |   | t |   | |  |  S(   NiU  (   R  R   Rg  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement59734  s    c            sO     j  d  t | | | | t d  | | | | t d  |  |  S(   NiV  i   (   R  R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement59749  s    c            sO     j  d  t | | | | t d  | | | | t d  |  |  S(   NiW  i   (   R  R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5975>  s    c            s     j  d  t | |  t d  t | | t | | |   |  t d  |  t d  |  t | t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   NiX  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5976C  s    c      
      s     j  d  t | |  t d  t | | t | | |   |  t d  |  t d  |  t | t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   NiY  i   i   (   R  R  R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5977H  s    c      
      s     j  d  t | t t | |  t | | |    t | | | t d  | t t d  |  t d   t t | | | t d  | t t d  |  t d   | |  |  S(   NiZ  i   i   i(   R  R  R  R   R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5978M  s    c      
      s     j  d  t | t t | |  t | | |    t | | | t d  | t t d  |  t d   t t | | | t d  | t t d  |  t d   | |  |  S(   Ni[  i   i   i   (   R  R  R  R  R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5979R  s    c            s     j  d  t t | | | t d  | |  t | | | |   t d  | | |  | | | t d  | |  t | | | |   t d  | | |  |  |  |  S(   Ni\  i   i   (   R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5980W  s    c            s     j  d  t t | | | t d  | |  t | | | |   t d  | | | t d  | |  t | | | |   t d  |  |  |  S(   Ni]  i   i   (   R  R   R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5981\  s    c      
      s     j  d  t | t | |  t | | |   |  t d  | t d  t d  |  t |  | | t | |  t | | |   |  t d  | t d  t d  |  S(   Ni^  i   i(   R  R  R   R  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5982a  s    c      
      s     j  d  t | t | |  t | | |   |  t d  | t d  t d  |  t |  | | t | |  t | | |   |  t d  | t d  t d  |  S(   Ni_  i   i(   R  R  R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5983f  s    c      
      s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Ni`  i   ii(   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5984k  s    c      
      s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t | | t | | |   t | | t | | |   |  t d  | t d  | t d  |  t d  t d  |  S(   Nia  i   ii(   R  R  R  R   R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5985p  s    c            s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Nib  i   ii   (   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5986u  s    c      
      s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Nic  i   ii   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5987z  s    c      
      sF    j  d  t | t d  t d  | | | t d  | t t d  |  |  | | | | t |  | | | | t |  |  t |  | | |  t d  t d  | | t d  | | |  t d  t d  | | | | | t d  | t t d  |   | | |  t d  |  S(   Nid  i   i   (   R  R  R  R  R4   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5988  s    c      
      sG    j  d  t | t d  t d  | | | t d  | t t d  |  |  | | | | t |  | | | | t |  |  t |  | | |  t d  t d  | | t d  | | |  t d  t d  | | | | | t d  | t t d  |   | | |  t d  |  S(   Nie  i   i   (   R  R  R  R  R4   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5989  s    c            s     j  d  t | | t d  |  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Nif  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5990  s    c      
      s     j  d  t | | t d  |  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Nig  i   i   (   R  R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5991  s    c            s    j  d  t t d  |  t t | | | | | | t d  | |  | t d  t | | | |  | t d   | | |  | | | | t d  | |  | t d  t | | | |  | t d   | | |  |  |  |  |  S(   Nih  i   i   (   R  R  R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5992  s    c            s     j  d  t t d  |  t t | | | | | | t d  | |  t | | | |  | t d   | | | | t d  | |  t | | | |  | t d   |  |  |  |  S(   Nii  i   i   (   R  R  R  R   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5993  s    c      
      s    j  d  t | |  t d  |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  t | | | |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Nij  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5994  s    c      
      s    j  d  t | |  t d  |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  t | | | |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Nik  i   i   (   R  R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5995  s    c            s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  | t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  | t d  t d  |  S(   Nil  i   ii   i(   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5996  s    c            s
    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  | t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t | | t | | |   t | | t | | |   |  t d  | t d  | t d  |  t d  | t d  t d  |  S(   Nim  i   ii   i(   R  R  R  R   R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5997  s    c            s    j  d  t | t d  | t d  |  t d  t d  | t d  t d  | t d  | t d  |  t d  |  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  t | | t d  | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   Nin  i   i   (   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5998  s    c            s    j  d  t | t d  | t d  |  t d  t d  | t d  t d  | t d  | t d  |  t d  |  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  t | | t d  | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   Nio  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement5999  s    c      
      s`    j  d  t | | t d  t d  t d  | | | t d  | t t d  |  |  | | | | t |  | | | | t |  |  t |  | | |  | t d  t d  | | t d  | | |  | t d  t d  | | | | | t d  | t t d  |   | | |  | t d  |  S(   Nip  i   i   (   R  R  R  R  R4   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6000  s    c      
      sa    j  d  t | | t d  t d  t d  | | | t d  | t t d  |  |  | | | | t |  | | | | t |  |  t |  | | |  | t d  t d  | | t d  | | |  | t d  t d  | | | | | t d  | t t d  |   | | |  | t d  |  S(   Niq  i   i   (   R  R  R  R  R4   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6001  s    c            sd     j  d  t t d  |  t | | | | | | | t d  | t d  |  |  |  S(   Nir  i   i   (   R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6002  s    c            sd     j  d  t t d  |  t | | | | | | | t d  | t d  |  |  |  S(   Nis  i   i(   R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6003  s    c            s     j  d  t t d  t | |  |  t | | | t d  | | | | t d  | t t d  | |  |  |  |  S(   Nit  i   i   (   R  R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6004  s    c            s     j  d  t t d  |  | t | |  |  t | | | t d  | | | | t d  | t t d  | |  |  |  |  S(   Niu  i   i   (   R  R  R  R  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6005  s    c            s     j  d  t | |  t d  t d  t | | t | | |   |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Niv  ii   i(   R  R  R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6006  s    c            s     j  d  t | |  t d  t d  t | | t | | |   |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Niw  ii   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6007  s    c            s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Nix  i   iii   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6008  s    c            s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Niy  i   iii   (   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6009  s    c            s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Niz  i   i   i(   R  R  R  R   R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6010  s    c            s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Ni{  i   i   i(   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6011  s    c      
      s`    j  d  t t d  |  | | | | | t |  | | | t d  | t t d  |  t d  |  | | | t d  | t t d  |  t d  |  t |  | | |  t d  t d  | | t d  | | |  t d  t d  | | | | | t d  | t t d  |   | | |  t d  |  S(   Ni|  i   i   (   R  R  R  R  R4   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6012  s    c      
      s\    j  d  t | | | | | t |  | | | t d  | 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  |  S(   Ni}  i   ii   (   R  R  R  R  R4   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6013  s    c            sl     j  d  t t d  |  t | | | | | | | | | t d  | t d  |  |  |  S(   Ni~  i   i   (   R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6014  s    c            sl     j  d  t t d  |  t | | | | | | | | | t d  | t d  |  |  |  S(   Ni  i   i(   R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6015  s    c      
      s     j  d  t t d  t | | | |  t d   t | |  | | | |  t d  | | | | t d  |  t d  | t t d  | | | |  t d   |  |  S(   Ni  i   i   (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6016  s    c      
      s     j  d  t t d  | | t | | | |  t d   |  t d  t | |  | | | |  t d  | | | | t d  |  t d  | t t d  | | | |  t d   |  |  S(   Ni  i   i   (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6017  s    c            s    j  d  t | | t d  |  t d  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Ni  i   ii(   R  R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6018  s    c            s    j  d  t | | t d  |  t d  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6019  s    c            s    j  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 | | t | | |   |  t d  |  |  t | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  t | | t d  | t d  t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   Ni  i   ii   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6020  s    c            s    j  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 | | t | | |   |  t d  |  |  t | | t d  t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  t | | t d  | t d  t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   Ni  i   ii   i(   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6021$  s    c            s(    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t d  t | | t | | |   |  t d  |  |  t | | t d  | t d  t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  | t d  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6022)  s    c            s)    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t d  t | | t | | |   |  t d  |  |  t | | t d  | t d  t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  | t d  t d  |  S(   Ni  i   i   (   R  R  R  R   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6023.  s    c      
      sz    j  d  t t d  |  | | t d  | | | | t |  | | | t d  | t t d  |  t d  |  | | | t d  | t t d  |  t d  |  t |  | | |  | t d  t d  | | t d  | | |  | t d  t d  | | | | | t d  | t t d  |   | | |  | t d  |  S(   Ni  i   i   (   R  R  R  R  R4   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement60243  s    c      
      sz    j  d  t t d  |  | | t d  | | | | t |  | | | t d  | t t d  |  t d  |  | | | t d  | t t d  |  t d  |  t |  | | |  | t d  t d  | | t d  | | |  | t d  t d  | | | | | t d  | t t d  |   | | |  | t d  |  S(   Ni  i   i   i(   R  R  R  R  R4   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement60258  s    c      	      s     j  d  t | t t | |   | t d  t | |  t | |   |  |   |   t t | |  t | |   |  | |   S(   Ni  i(   R  R  R   R  R  R   R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6026=  s    c      	      s     j  d  t | t t | |   | t d  t | |  t | |   |  |   |   t t | |  t | |   |  | |   S(   Ni  i(   R  R  R   R  R  R  R  R   (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6027B  s    c      
      s    j  d  t |  | t t | |  |  t d  t | | | t | |  |   |  |  t | t d  | | t | | t | | | t | |  |   |  |  t | | t d  t | | | t | |  |   | | |  S(   Ni  ii   (   R  R  R   R  R  R   R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6028G  s    c      
      s    j  d  t |  | t t | |  |  t d  t | | | t | |  |   |  |  t | t d  | | t | | t | | | t | |  |   |  |  t | | t d  t | | | t | |  |   | | |  S(   Ni  ii   (   R  R  R   R  R  R  R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6029L  s    c      	      s     j  d  t |  | t | | t d  t | |  |  t d  t | | | t | |  |   |  |  t t | | | t | |  |   | | |  S(   Ni  i(   R  R  R   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6030Q  s    c      	      s     j  d  t |  | t | | t d  t | |  |  t d  t | | | t | |  |   |  |  t t | | | t | |  |   | | |  S(   Ni  i(   R  R  R   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6031V  s    c      
      s    j  d  t |  | t | | t | |  |  t d  t | | | t | |  |   |  |  t | | t d  | | t | | | t | | | t | |  |   |  |  t | | | t d  t | | | t | |  |   | | |  S(   Ni  ii   (   R  R  R   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6032[  s    c      
      s    j  d  t |  | t | | t | |  |  t d  t | | | t | |  |   |  |  t | | t d  | | t | | | t | | | t | |  |   |  |  t | | | t d  t | | | t | |  |   | | |  S(   Ni  ii   (   R  R  R   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6033`  s    c      	      sk     j  d  t t d  |  t t t | |  | | t d  |  | t d  | |  |  |  S(   Ni  i   i   (   R  R  R  R*   R   R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6034e  s    c      	      sk     j  d  t t d  |  t t t | |  | | t d  |  | t d  | |  |  |  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6035j  s    c      
      s     j  d  t t d  | t t t |  | | | | | | |  | |  | | t d  |  | t d  | | |  |  S(   Ni  i   i   (   R  R  R  R*   R   R   (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6036o  s    c      
      s     j  d  t t d  | t t t |  | | | | | | |  | |  | | t d  |  | t d  | | |  |  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6037t  s    c            s   t  | |   }   j d  t t |  t | t d   t | t d   |  t | t d   t | t d    | |   S(   Ni  i   i   i   i   (   R   R  R   R   R  R  (   R  R  R  t   lst(   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With6038x  s    c            s   t  | |   }   j d  t t |  t | t d   t | t d   |  t | t d   t | t d    | |   S(   Ni  i   i   i   i   (   R   R  R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   With6039~  s    R  c            s,     j  d  t | t |   | | |  S(   Ni  (   R  R   R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6040  s    c            s,     j  d  t | t |   | | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6041  s    c            s;     j  d  t t t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6042  s    c            s;     j  d  t t t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6043  s    c            sB     j  d  t t | | t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6044  s    c            sB     j  d  t t | | t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6045  s    c            sI     j  d  t t d  | t | t t d  |   | |  |  S(   Ni  i   (   R  R  R  R   R   (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6046  s    c            s;     j  d  t t t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6047  s    c            sB     j  d  t t | | t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6048  s    c            sz     j  d  t t |  |  t t |  | t d  t |  |  |  t t |   t |  | t d  |  S(   Ni  i(   R  R  R  R   R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6049  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t d  t |  | t d  t |   |  S(   Ni  i   i(   R  R  R  R   R  R  R   (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6050  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t d  t |  | t d  t |   |  S(   Ni  i   i(   R  R  R   R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6051  s    c            sz     j  d  t t |  |  t t |  | t d  t |  |  |  t t |   t |  | t d  |  S(   Ni  i(   R  R  R   R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6052  s    c            s     j  d  t t |  |  t t d  t |  | t d  |  |  t t |  |  t t d  t |  | t d  t |  |  |  S(   Ni  i   i(   R  R  R   R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6053  s    c            s     j  d  t t |  |  t t d  t |  | t d  |  |  t t |  |  t t d  t |  | t d  t |  |  |  S(   Ni  i   i(   R  R  R   R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6054  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t |  |  t t d  t |  | t d  |  |  S(   Ni  i   i(   R  R  R   R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6055  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t |  |  t t d  t |  | t d  |  |  S(   Ni  i   i(   R  R  R   R   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6056  s    c	   	         sb     j  d  t | | t t d  | t d  | |  t d  | | | | |  |  S(   Ni  i   (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6057  s    c      
      su     j  d  t t d  | t | |  t d  | | t t d  | t d  | |  | | |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6058  s    c      
      su     j  d  t t d  | t | |  t d  | | t t d  | t d  | |  | | |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6059  s    c
   
   
      s|     j  d  t | | t d  t t | | | |	 | | | t | | | |  |  |  | | | |  |  S(   Ni  i(   R  R  R  R*   R   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6060  s    c
   
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      s|     j  d  t | | t d  t t | | | |	 | | | t | | | |  |  |  | | | |  |  S(   Ni  i(   R  R  R  R*   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6061  s    c	   	   
      s|     j  d  t t d  t | | | |  t d  | | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R  R>  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6062  s    c      
      sn     j  d  t t d  t | | | |  | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R>  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6063  s    c	   	   
      s|     j  d  t t d  t | | | |  t d  | | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R  R>  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6064  s    c      
      sn     j  d  t t d  t | | | |  | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R>  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6065	  s    c	   	   
      s|     j  d  t t d  t | | | |  t d  | | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R  R  R>  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6066	  s    c      	      s&    j  d  t | | | |  t | | |  | | t | | |  t | t d  | t d  t d   |  t | | | |  t | | |  | | t | | |  t | t d  | t d  t d   |  t | | | |  t d  | | |  t d  |  S(   Ni  i   i   (   R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6067	  s    c      	      s&    j  d  t | | | |  t | | |  | | t | | |  t | t d  | t d  t d   |  t | | | |  t | | |  | | t | | |  t | t d  | t d  t d   |  t | | | |  t d  | | |  t d  |  S(   Ni  i   i   (   R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6068	  s    c	   	   	      s     j  d  t t d  | t | | | |  t | | |  | t d  |  |  t t d  | t | | | |  t | | |  t | | |  | t d  |  |  S(   Ni  i   i(   R  R  R  R   R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6069	  s    c	   	   	      s     j  d  t t d  | t | | | |  t | | |  | t d  |  |  t t d  | t | | | |  t | | |  | t d  t | | |  |  |  S(   Ni  i   i(   R  R  R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6070	  s    c	   	         sF    j  d  t t d  | t | | | |  t | | |  t | | |  | t d  |  |  t | | t d  t | | | |  t | | |  | t d  |  |  t | t d  | t d  | t d  t | | | |  t | | |  | t d  | | t | | |  |  |  S(   Ni  i   ii   (   R  R  R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6071 	  s    c	   	         sF    j  d  t t d  | t | | | |  t | | |  | t d  t | | |  |  |  t | | t d  t | | | |  t | | |  | t d  |  |  t | t d  | t d  | t d  t | | | |  t | | |  | t d  | | t | | |  |  |  S(   Ni  i   ii   (   R  R  R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6072%	  s    t   Bc	   	   
      s     j  d  t |  | | | t t | | |  | | t | | |  |  |  t |  | | | t | | |  | | | | t | | |  |  S(   Ni  (   R  R  R   R  R   R  (	   R  R  R  R  R  R  t   AR  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6073*	  s    c	   	   
      s     j  d  t |  | | | t t | | |  | | t | | |  |  |  t |  | | | t | | |  | | | | t | | |  |  S(   Ni  (   R  R  R   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6074/	  s    c            s6     j  d  t | t |   | t |   | |  S(   Ni  (   R  R   R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement60754	  s    c            s6     j  d  t | t |   | t |   | |  S(   Ni  (   R  R   R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement60769	  s    c            sN     j  d  t t |  t | | |  | t | | |  | |  |  S(   Ni  (   R  R   Rc  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6077>	  s    c            sN     j  d  t t |  t | | |  | t | | |  | |  |  S(   Ni  (   R  R   Rc  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6078C	  s    c            s     j  d  t t d  t | | |  | |   t t | | |  |  |  t t d  t | | |  | |  t t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6079H	  s    c      	      s     j  d  t t d  t | | |  | |   t t d  t | |  |  |  |  t t d  t | | |  | |  t t d  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6080M	  s    c      	      s     j  d  t |  t | | |  | |  | t t d  t | |  |  t | | |  |  |  t |  | | |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6081R	  s    c      	      s|     j  d  t t | | |  | |  t t d  t | |  |  t | | |  |  |  t |  | | |  S(   Ni  i   (   R  R  R  R   R  R   R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6082W	  s    c            s4     j  d  t | | t | |  |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   replacement6083\	  s    (   t    sympy.integrals.rubi.constraintsR*  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  t   x_R  R  R   R   R  t   m_t   n_t   a_t   u_t   v_t   p_t   c_R   t   e_R  t   F_t   G_t   w_t   f_t   h_t   H_R  R  R  R  t   b_t   A_(  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  t   pattern5643R  t   rule5643t   pattern5644R  t   rule5644t   pattern5645R  t   rule5645t   pattern5646R  t   rule5646t   pattern5647R  t   rule5647t   pattern5648R  t   rule5648t   pattern5649R  t   rule5649t   pattern5650R  t   rule5650t   pattern5651R  t   rule5651t   pattern5652R  t   rule5652t   pattern5653R  t   rule5653t   pattern5654R  t   rule5654t   pattern5655R  t   rule5655t   pattern5656R  t   rule5656t   pattern5657R  t   rule5657t   pattern5658R  t   rule5658t   pattern5659R   t   rule5659t   pattern5660R  t   rule5660t   pattern5661R  t   rule5661t   pattern5662R  t   rule5662t   pattern5663R  t   rule5663t   pattern5664R  t   rule5664t   pattern5665R  t   rule5665t   pattern5666R  t   rule5666t   pattern5667R	  t   rule5667t   pattern5668R
  t   rule5668t   pattern5669R  t   rule5669t   pattern5670R  t   rule5670t   pattern5671R  t   rule5671t   pattern5672R  t   rule5672t   pattern5673R  t   rule5673t   pattern5674R  t   rule5674t   pattern5675R  t   rule5675t   pattern5676R  t   rule5676t   pattern5677R  t   rule5677t   pattern5678R  t   rule5678t   pattern5679R  t   rule5679t   pattern5680R  t   rule5680t   pattern5681R  t   rule5681t   pattern5682R  t   rule5682t   pattern5683R  t   rule5683t   pattern5684R  t   rule5684t   pattern5685R  t   rule5685t   pattern5686R   t   rule5686t   pattern5687R!  t   rule5687t   pattern5688R"  t   rule5688t   pattern5689R#  t   rule5689t   pattern5690R$  t   rule5690t   pattern5691R%  t   rule5691t   pattern5692R&  t   rule5692t   pattern5693R'  t   rule5693t   pattern5694R(  t   rule5694t   pattern5695R)  t   rule5695t   pattern5696R*  t   rule5696t   pattern5697R+  t   rule5697t   pattern5698R,  t   rule5698t   pattern5699R-  t   rule5699t   pattern5700R.  t   rule5700t   pattern5701R/  t   rule5701t   pattern5702R0  t   rule5702t   pattern5703R1  t   rule5703t   pattern5704R2  t   rule5704t   pattern5705R3  t   rule5705t   pattern5706R4  t   rule5706t   pattern5707R5  t   rule5707t   pattern5708R6  t   rule5708t   pattern5709R7  t   rule5709t   pattern5710R8  t   rule5710t   pattern5711R9  t   rule5711t   pattern5712R:  t   rule5712R<  t   pattern5713t   rule5713R=  t   pattern5714t   rule5714t   pattern5715R>  t   rule5715t   pattern5716R?  t   rule5716t   pattern5717R@  t   rule5717t   pattern5718RA  t   rule5718t   pattern5719RB  t   rule5719t   pattern5720RC  t   rule5720t   pattern5721RD  t   rule5721t   pattern5722RE  t   rule5722t   pattern5723RF  t   rule5723t   pattern5724RG  t   rule5724t   pattern5725RH  t   rule5725t   pattern5726RI  t   rule5726t   pattern5727RJ  t   rule5727t   pattern5728RK  t   rule5728RQ  t   pattern5729RR  t   rule5729RS  t   pattern5730RT  t   rule5730RU  t   pattern5731RV  t   rule5731RW  t   pattern5732RX  t   rule5732t   pattern5733RY  t   rule5733t   pattern5734RZ  t   rule5734t   pattern5735R[  t   rule5735t   pattern5736R\  t   rule5736t   pattern5737R]  t   rule5737t   pattern5738R^  t   rule5738t   pattern5739R_  t   rule5739t   pattern5740R`  t   rule5740t   pattern5741Ra  t   rule5741t   pattern5742Rb  t   rule5742t   pattern5743Rc  t   rule5743t   pattern5744Rd  t   rule5744t   pattern5745Re  t   rule5745t   pattern5746Rf  t   rule5746Rg  t   pattern5747t   rule5747Rh  t   pattern5748t   rule5748t   pattern5749Ri  t   rule5749t   pattern5750Rj  t   rule5750t   pattern5751Rk  t   rule5751t   pattern5752Rl  t   rule5752t   pattern5753Rm  t   rule5753t   pattern5754Rn  t   rule5754t   pattern5755Ro  t   rule5755t   pattern5756Rp  t   rule5756Rq  t   pattern5757t   rule5757Rr  t   pattern5758t   rule5758t   pattern5759Rs  t   rule5759t   pattern5760Rt  t   rule5760Ru  t   pattern5761t   rule5761Rv  t   pattern5762t   rule5762t   pattern5763Rw  t   rule5763t   pattern5764Rx  t   rule5764t   pattern5765Ry  t   rule5765t   pattern5766Rz  t   rule5766t   pattern5767R{  t   rule5767t   pattern5768R|  t   rule5768t   pattern5769R}  t   rule5769t   pattern5770R~  t   rule5770t   pattern5771R  t   rule5771t   pattern5772R  t   rule5772t   pattern5773R  t   rule5773t   pattern5774R  t   rule5774t   pattern5775R  t   rule5775t   pattern5776R  t   rule5776t   pattern5777R  t   rule5777t   pattern5778R  t   rule5778t   pattern5779R  t   rule5779t   pattern5780R  t   rule5780t   pattern5781R  t   rule5781t   pattern5782R  t   rule5782t   pattern5783R  t   rule5783t   pattern5784R  t   rule5784t   pattern5785R  t   rule5785t   pattern5786R  t   rule5786t   pattern5787R  t   rule5787t   pattern5788R  t   rule5788t   pattern5789R  t   rule5789t   pattern5790R  t   rule5790t   pattern5791R  t   rule5791t   pattern5792R  t   rule5792t   pattern5793R  t   rule5793t   pattern5794R  t   rule5794t   pattern5795R  t   rule5795t   pattern5796R  t   rule5796t   pattern5797R  t   rule5797t   pattern5798R  t   rule5798t   pattern5799R  t   rule5799t   pattern5800R  t   rule5800t   pattern5801R  t   rule5801t   pattern5802R  t   rule5802t   pattern5803R  t   rule5803t   pattern5804R  t   rule5804t   pattern5805R  t   rule5805t   pattern5806R  t   rule5806t   pattern5807R  t   rule5807t   pattern5808R  t   rule5808t   pattern5809R  t   rule5809t   pattern5810R  t   rule5810t   pattern5811R  t   rule5811t   pattern5812R  t   rule5812t   pattern5813R  t   rule5813t   pattern5814R  t   rule5814t   pattern5815R  t   rule5815t   pattern5816R  t   rule5816t   pattern5817R  t   rule5817t   pattern5818R  t   rule5818t   pattern5819R  t   rule5819t   pattern5820R  t   rule5820t   pattern5821R  t   rule5821t   pattern5822R  t   rule5822t   pattern5823R  t   rule5823t   pattern5824R  t   rule5824t   pattern5825R  t   rule5825t   pattern5826R  t   rule5826t   pattern5827R  t   rule5827t   pattern5828R  t   rule5828R  t   pattern5829t   rule5829R  t   pattern5830t   rule5830t   pattern5831R  t   rule5831t   pattern5832R  t   rule5832t   pattern5833R  t   rule5833t   pattern5834R  t   rule5834t   pattern5835R  t   rule5835t   pattern5836R  t   rule5836t   pattern5837R  t   rule5837t   pattern5838R  t   rule5838t   pattern5839R  t   rule5839t   pattern5840R  t   rule5840t   pattern5841R  t   rule5841t   pattern5842R  t   rule5842t   pattern5843R  t   rule5843t   pattern5844R  t   rule5844t   pattern5845R  t   rule5845t   pattern5846R  t   rule5846t   pattern5847R  t   rule5847t   pattern5848R  t   rule5848t   pattern5849R  t   rule5849t   pattern5850R  t   rule5850t   pattern5851R  t   rule5851t   pattern5852R  t   rule5852t   pattern5853R  t   rule5853t   pattern5854R  t   rule5854t   pattern5855R  t   rule5855t   pattern5856R  t   rule5856t   pattern5857R  t   rule5857t   pattern5858R  t   rule5858t   pattern5859R  t   rule5859t   pattern5860R  t   rule5860t   pattern5861R  t   rule5861t   pattern5862R  t   rule5862t   pattern5863R  t   rule5863t   pattern5864R  t   rule5864t   pattern5865R  t   rule5865t   pattern5866R  t   rule5866t   pattern5867R  t   rule5867t   pattern5868R  t   rule5868t   pattern5869R  t   rule5869t   pattern5870R  t   rule5870t   pattern5871R  t   rule5871t   pattern5872R  t   rule5872t   pattern5873R  t   rule5873t   pattern5874R  t   rule5874t   pattern5875R  t   rule5875t   pattern5876R  t   rule5876t   pattern5877R  t   rule5877t   pattern5878R  t   rule5878t   pattern5879R  t   rule5879t   pattern5880R  t   rule5880t   pattern5881R  t   rule5881t   pattern5882R  t   rule5882t   pattern5883R  t   rule5883t   pattern5884R  t   rule5884t   pattern5885R  t   rule5885t   pattern5886R  t   rule5886t   pattern5887R  t   rule5887t   pattern5888R  t   rule5888t   pattern5889R  t   rule5889t   pattern5890R  t   rule5890t   pattern5891R  t   rule5891t   pattern5892R  t   rule5892t   pattern5893R  t   rule5893t   pattern5894R  t   rule5894t   pattern5895R  t   rule5895t   pattern5896R  t   rule5896t   pattern5897R  t   rule5897t   pattern5898R   t   rule5898t   pattern5899R  t   rule5899t   pattern5900R  t   rule5900t   pattern5901R  t   rule5901t   pattern5902R  t   rule5902t   pattern5903R  t   rule5903t   pattern5904R  t   rule5904t   pattern5905R  t   rule5905t   pattern5906R  t   rule5906t   pattern5907R	  t   rule5907t   pattern5908R
  t   rule5908t   pattern5909R  t   rule5909t   pattern5910R  t   rule5910t   pattern5911R  t   rule5911t   pattern5912R  t   rule5912t   pattern5913R  t   rule5913t   pattern5914R  t   rule5914t   pattern5915R  t   rule5915t   pattern5916R  t   rule5916t   pattern5917R  t   rule5917t   pattern5918R  t   rule5918t   pattern5919R  t   rule5919R  t   pattern5920t   rule5920R  t   pattern5921t   rule5921t   pattern5922R  t   rule5922R  t   pattern5923t   rule5923t   pattern5924R  t   rule5924t   pattern5925R  t   rule5925t   pattern5926R  t   rule5926t   pattern5927R   t   rule5927t   pattern5928R!  t   rule5928t   pattern5929R"  t   rule5929t   pattern5930R#  t   rule5930t   pattern5931R$  t   rule5931t   pattern5932R%  t   rule5932t   pattern5933R&  t   rule5933t   pattern5934R'  t   rule5934t   pattern5935R(  t   rule5935t   pattern5936R)  t   rule5936t   pattern5937R*  t   rule5937t   pattern5938R+  t   rule5938t   pattern5939R,  t   rule5939t   pattern5940R-  t   rule5940t   pattern5941R.  t   rule5941t   pattern5942R/  t   rule5942t   pattern5943R0  t   rule5943t   pattern5944R1  t   rule5944t   pattern5945R2  t   rule5945t   pattern5946R3  t   rule5946t   pattern5947R4  t   rule5947t   pattern5948R5  t   rule5948t   pattern5949R6  t   rule5949t   pattern5950R7  t   rule5950t   pattern5951R8  t   rule5951t   pattern5952R9  t   rule5952t   pattern5953R:  t   rule5953t   pattern5954R;  t   rule5954t   pattern5955R<  t   rule5955t   pattern5956R=  t   rule5956t   pattern5957R?  t   rule5957t   pattern5958R@  t   rule5958t   pattern5959RA  t   rule5959t   pattern5960RB  t   rule5960t   pattern5961RC  t   rule5961t   pattern5962RD  t   rule5962t   pattern5963RG  t   rule5963t   pattern5964RH  t   rule5964t   pattern5965RI  t   rule5965RJ  t   pattern5966t   rule5966RK  t   pattern5967t   rule5967t   pattern5968RL  t   rule5968t   pattern5969RM  t   rule5969t   pattern5970RO  t   rule5970t   pattern5971RP  t   rule5971t   pattern5972RQ  t   rule5972t   pattern5973RR  t   rule5973t   pattern5974RS  t   rule5974t   pattern5975RT  t   rule5975t   pattern5976RU  t   rule5976t   pattern5977RV  t   rule5977t   pattern5978RW  t   rule5978t   pattern5979RX  t   rule5979t   pattern5980RY  t   rule5980t   pattern5981RZ  t   rule5981t   pattern5982R[  t   rule5982t   pattern5983R\  t   rule5983t   pattern5984R]  t   rule5984t   pattern5985R^  t   rule5985t   pattern5986R_  t   rule5986t   pattern5987R`  t   rule5987t   pattern5988Ra  t   rule5988t   pattern5989Rb  t   rule5989t   pattern5990Rc  t   rule5990t   pattern5991Rd  t   rule5991t   pattern5992Re  t   rule5992t   pattern5993Rf  t   rule5993t   pattern5994Rg  t   rule5994t   pattern5995Rh  t   rule5995t   pattern5996Ri  t   rule5996t   pattern5997Rj  t   rule5997t   pattern5998Rk  t   rule5998t   pattern5999Rl  t   rule5999t   pattern6000Rm  t   rule6000t   pattern6001Rn  t   rule6001t   pattern6002Ro  t   rule6002t   pattern6003Rp  t   rule6003t   pattern6004Rq  t   rule6004t   pattern6005Rr  t   rule6005t   pattern6006Rs  t   rule6006t   pattern6007Rt  t   rule6007t   pattern6008Ru  t   rule6008t   pattern6009Rv  t   rule6009t   pattern6010Rw  t   rule6010t   pattern6011Rx  t   rule6011t   pattern6012Ry  t   rule6012t   pattern6013Rz  t   rule6013t   pattern6014R{  t   rule6014t   pattern6015R|  t   rule6015t   pattern6016R}  t   rule6016t   pattern6017R~  t   rule6017t   pattern6018R  t   rule6018t   pattern6019R  t   rule6019t   pattern6020R  t   rule6020t   pattern6021R  t   rule6021t   pattern6022R  t   rule6022t   pattern6023R  t   rule6023t   pattern6024R  t   rule6024t   pattern6025R  t   rule6025t   pattern6026R  t   rule6026t   pattern6027R  t   rule6027t   pattern6028R  t   rule6028t   pattern6029R  t   rule6029t   pattern6030R  t   rule6030t   pattern6031R  t   rule6031t   pattern6032R  t   rule6032t   pattern6033R  t   rule6033t   pattern6034R  t   rule6034t   pattern6035R  t   rule6035t   pattern6036R  t   rule6036t   pattern6037R  t   rule6037R  t   pattern6038t   rule6038R  t   pattern6039t   rule6039t   pattern6040R  t   rule6040t   pattern6041R  t   rule6041t   pattern6042R  t   rule6042t   pattern6043R  t   rule6043t   pattern6044R  t   rule6044t   pattern6045R  t   rule6045t   pattern6046R  t   rule6046t   pattern6047R  t   rule6047t   pattern6048R  t   rule6048t   pattern6049R  t   rule6049t   pattern6050R  t   rule6050t   pattern6051R  t   rule6051t   pattern6052R  t   rule6052t   pattern6053R  t   rule6053t   pattern6054R  t   rule6054t   pattern6055R  t   rule6055t   pattern6056R  t   rule6056t   pattern6057R  t   rule6057t   pattern6058R  t   rule6058t   pattern6059R  t   rule6059t   pattern6060R  t   rule6060t   pattern6061R  t   rule6061t   pattern6062R  t   rule6062t   pattern6063R  t   rule6063t   pattern6064R  t   rule6064t   pattern6065R  t   rule6065t   pattern6066R  t   rule6066t   pattern6067R  t   rule6067t   pattern6068R  t   rule6068t   pattern6069R  t   rule6069t   pattern6070R  t   rule6070t   pattern6071R  t   rule6071t   pattern6072R  t   rule6072t   pattern6073R  t   rule6073t   pattern6074R  t   rule6074t   pattern6075R  t   rule6075t   pattern6076R  t   rule6076t   pattern6077R  t   rule6077t   pattern6078R  t   rule6078t   pattern6079R  t   rule6079t   pattern6080R  t   rule6080t   pattern6081R  t   rule6081t   pattern6082R  t   rule6082t   pattern6083R  t   rule6083(    (   R  sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt
   hyperbolic   s
       pzzzz}}||yyvvyyQQQQcc??FF				rr~~rruurruuxxuunnuu77TT}}ccuu[[cc   P $ $     F BB_ss||}}ss44aaQQhhdQhAKKAKKKK  T T{{~~t~}N(d  t   __doc__t   sympy.externalR    R   t   sympy.utilities.decoratorR   R   R   R   R   t%   sympy.integrals.rubi.utility_functionR   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Re   Rf   Rg   Rh   Ri   Rj   Rk   Rl   Rm   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R}   R~   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R!  R"  R#  R$  R%  R&  R'  R(  R)  R*  R+  R,  R-  R.  R/  R0  R1  R2  R3  R4  R5  R6  R7  R8  R9  R:  R;  R<  R=  R>  R?  R@  RA  RB  RC  RD  RE  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  R{  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   sympyR  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   sympy.integrals.rubi.symbolR  t   sympy.core.symbolR  R  t   sympy.functionsR  R  R  R  R  R  R  t%   sympy.functions.elementary.hyperbolicR  R  R  R  R  R  R  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  R  RE  R  t   B_t   C_R  R  R  R  R  R  t   d_R  R  t   g_R  t   i_t   j_t   k_t   l_R  R  R  t   q_t   r_t   t_R  R  t   s_R  R  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_t   n2_t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_t   n3_t   Pq_t   Pm_t   Px_t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_t   iit   Pqqt   Qt   Rt   rt   CR;  R  RO  t	   _UseGammat	   ShowStepst   Nonet   StepCounterRH  (    (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/hyperbolic.pyt   <module>   s>   "           1nj:R4|'	