
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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          s 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 } t t 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 t  | | | | | | |  }   f d	   } t | |  } t t 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 t  | | | | | | |  }   f d
   } t | |  } 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 d t d   t  | | |  }   f d   } t | |  } t t 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  | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 d t d   t d t d   t t t d t d   t d t d    t t  | | | | | | | |" | 
 }  f d0   }t || }t t t d t d   t t 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 t  | | | | | | | |" | 
 }  f d1   }t || }t t 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 t  | | | | | | |# | 	 }   f d2   }!t | |! }"t t 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 t  | | | | | | |# | 	 }#  f d3   }$t |#|$ }%t t t d t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t  | | | | | | |$ |" | 
 }&  f d4   }'t |&|' }(t t t d t d   t t 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 t  | | | | | | |$ |" | 
 })  f d5   }*t |)|* }+t t t d  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 d6   }-t |,|- }.t t t d  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 d7   }0t |/|0 }1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  | | | |%  }2  f d8   }3t |2|3 }4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  | | | |%  }5  f d9   }6t |5|6 }7t t 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 t  | | | | | | |& |' 	 }8  f d:   }9t |8|9 }:t t 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 t  | | | | | | |& |' 	 };  f d;   }<t |;|< }=t t t d t d   t t 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 t  | | | | | | |( |) 	 }>  f d<   }?t |>|? }@t t t d t d   t t 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 t  | | | | | | |( |) 	 }A  f d=   }Bt |A|B }Ct t 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 t  | | | | | | | |
 	 }D  f d>   }Et |D|E }Ft t 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 t  | | | | | | | |
 	 }G  f d?   }Ht |G|H }I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 d t d   t t t d t d   t d t d    t t  | | |, | | | |- | | |* |+  }J  f dA   }Kt |J|K }L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 d t d   t t t d t d   t d t d    t t  | | |, | | | |- | | |* |+  }M  f dB   }Nt |M|N }O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 d t d   t t t d t d   t d t d    t t  | | |, | | | |- | | |. |+  }P  f dC   }Qt |P|Q }R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 d t d   t t t d t d   t d t d    t t  | | |, | | | |- | | |. |+  }S  f dD   }Tt |S|T }Ut t t d t d   t t t d@ t d   t dE t d    t t  | |/ |, | |  }V  f dF   }Wt |V|W }Xt t t d t d   t t t d@ t d   t dE t d    t t  | |/ |, | |  }Y  f dG   }Zt |Y|Z }[t t t d t d   t t t d@ t d   t dE t d    t t  | |/ |, | |  }\  f dH   }]t |\|] }^t t t d t d   t t t d@ t d   t dE t d    t t  | |/ |, | |  }_  f dI   }`t |_|` }at t t t t d@ t d   t dE t d    t  |/ |, |0  }b  f dJ   }ct |b|c }dt t t d  t t t d@ t d   t dE t d    t  |/ |, |0  }e  f dK   }ft |e|f }gt t t d t d   t t t d@ t d   t dE t d    t t  | |/ |, | |
  }h  f dL   }it |h|i }jt t t d t d   t t t d@ t d   t dE t d    t t  | |/ |, | |
  }k  f dM   }lt |k|l }mt t t t d t d   t t t d@ t d   t dE t d    t dN  t  | | |/ |, |1  }n  f dO   }ot |n|o }pt t t t d t d   t t t d@ t d   t dE t d    t dN  t  | | |/ |, |1  }q  f dP   }rt |q|r }st t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |2 | |  }t  f dQ   }ut |t|u }vt t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |2 | |  }w  f dR   }xt |w|x }yt t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |2 | |3  }z  f dS   }{t |z|{ }|t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |2 | |3  }}  f dT   }~t |}|~ }t t t t t d t d   t t t d@ t d   t dE t d     t  | | |/ |, |2  }  f dU   }t || }t t t t t d t d   t t t d@ t d   t dE t d     t  | | |/ |, |2  }  f dV   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, | |2  }  f dW   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, | |2  }  f dX   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |4 | |  }  f dY   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |4 | |  }  f dZ   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |4 | |  }  f d[   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, |4 | |  }  f d\   }t || }t t t d  t t d t d   t t t d@ t d   t dE t d    t  | | |/ |, |4  }  f d]   }t || }t t t d  t t d t d   t t t d@ t d   t dE t d    t  | | |/ |, |4  }  f d^   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, | |4  }  f d_   }t || }t t t t d t d   t t t d@ t d   t dE t d    t t  | | |/ |, | |4  }  f d`   }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 t t d t d   t d t d    t  | | |, | | | |5  }  f da   }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 t t d t d   t d t d    t  | | |, | | | |5  }  f db   }t || }t t 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    t t  | | | | | |2 |  }  f dc   }t || }t t 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    t t  | | | | | |2 |  }  f dd   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |6 
 }  f de   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |6 
 }  f df   }t || }t t t d  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  | | | | |2  }  f dg   }t || }t t t d  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  | | | | |2  }  f dh   }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 t t d t d   t d t d    t t  | | |, | | |2 |7 | |8 
 }  f di   }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 t t d t d   t d t d    t t  | | |, | | |2 |7 | |8 
 }  f dj   }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 t t d t d   t d t d    t t  | | |, | | |2 |7 | | 
 }  f dk   }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 t t d t d   t d t d    t t  | | |, | | |2 |7 | | 
 }  f dl   }t || }t t 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 t  | | |, | | | | |2 |7 
 }  f dm   }t || }t t 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 t  | | |, | | | | |2 |7 
 }  f dn   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |9 
 }  f do   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |9 
 }  f dp   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |: |
  }  f dq   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |: |
  }  f dr   }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 t t d t d   t d t d     t  | | |, | | |2  }  f ds   }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 t t d t d   t d t d     t  | | |, | | |2  }  f dt   }t || }t t 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 t  | | |, | | |2 | | |; |<  }  f du   }t || }t t 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 t  | | |, | | |2 | | |= |<  }  f dv   }t || }t t 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 t  | | |, | | |2 | |8 | |  }  f dw   }t || }t t 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 t  | | |, | | |2 | |8 | |  }  f dx   }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 t t d t d   t d t d    t t  | | |, | | | |2 | |8 |" |  }  f dy   }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 t t d t d   t d t d    t t  | | |, | | | |2 | |8 |" |  }  f dz   }t || }t t t d@ t d   t t t d t d   t d t d    t d{  dN t t t d t d   t t t d t d   t d t d     t  | | |, | | |2  }  f d|   }t || }t t t d@ t d   t t t d t d   t d t d    t d{  dN t t t d t d   t t t d t d   t d t d     t  | | |, | | |2  }  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 t t d t d   t d t d    t t  | | |, | | | |2 | | |> |<  }  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 t t d t d   t d t d    t t  | | |, | | | |2 | | |> |<  }  f d   }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 t t d t d   t d t d    t t  | | |, | | |2 | |3 | |? |" |  }  f d   }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 t t d t d   t d t d    t t  | | |, | | |2 | |3 | |? |" |  }  f d   }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 t t d t d   t d t d    t t  | | |, | | | |2 | |3 |@ |  }  f d   }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 t t d t d   t d t d    t t  | | |, | | | |2 | |3 |@ |  }  f d   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |A |  }
  f d   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |A |  }  f d   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |B |@  }  f d   }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 t t d t d   t d t d    t t  | | |, | | | | |2 |B |@  }  f d   }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 t t d t d   t d t d    t d t d   t  | | |, | | | | |2 	 }  f d   }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 t t d t d   t d t d    t d t d   t  | | |, | | | | |2 	 }  f d   }t || }t t 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    t t  | | | | | |4 |  }  f d   }t || }t t 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    t t  | | | | | |4 |  }  f d   } t ||  }!t t t t d t d   t t t d t d   t d t d    t dN  t t t d t d   t d t d    t  | | | | |4  }"  f d   }#t |"|# }$t t t t d t d   t t t d t d   t d t d    t dN  t t t d t d   t d t d    t  | | | | |4  }%  f d   }&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 t t d t d   t d t d    t dN  t  | | |, | | | |4 |C 	 }(  f d   })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 t t d t d   t d t d    t dN  t  | | |, | | | |4 |C 	 }+  f d   },t |+|, }-t t t d  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  | | | | |4  }.  f d   }/t |.|/ }0t t t d  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  | | | | |4  }1  f d   }2t |1|2 }3t t 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  | | |, | | |4 |D  }4  f d   }5t |4|5 }6t t 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  | | |, | | |4 |D  }7  f d   }8t |7|8 }9t t 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  | | |, | | |4 |E  }:  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 t t d t d   t d t d    t  | | |, | | |4 |E  }=  f d   }>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 t t d t d   t d t d    t t  | | |, | | | | |4 |) 
 }@  f d   }At |@|A }B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 t t d t d   t d t d    t t  | | |, | | | | |4 |) 
 }C  f d   }Dt |C|D }Et t t t 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  | | |, | | |2  }F  f d   }Gt |F|G }Ht t t t 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  | | |, | | |2  }I  f d   }Jt |I|J }Kt t t d  t d@ t d   t t t d t d   t d t d    t d{  dN t t t d t d   t t t d t d   t d t d     t  | | |, | | |2  }L  f d   }Mt |L|M }Nt t t d  t d@ t d   t t t d t d   t d t d    t d{  dN t t t d t d   t t t d t d   t d t d     t  | | |, | | |2  }O  f d   }Pt |O|P }Qt t 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 d t d   t  | | |, | | | | | 	 }R  f d   }St |R|S }Tt t 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 d t d   t  | | |, | | | | | 	 }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 t t t d t d   t d t d    t t  | | | | | |  }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 t t t d t d   t d t d    t 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 t d t d   t d t d    t d t d   t  | | | | |F |G  }^  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 t d t d   t d t d    t d t d   t  | | | | |F |G  }a  f d   }bt |a|b }ct t t t d 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  | | | | |F |H |I  }d  f d   }et |d|e }ft t t t d 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  | | | | |F |H |I  }g  f d   }ht |g|h }i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 t d t d   t d t d    t d t d   t  | | |, | | | | | 	 }j  f d   }kt |j|k }l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 t d t d   t d t d    t d t d   t  | | |, | | | | | 	 }m  f d   }nt |m|n }ot t t t d 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 t t d t d   t d t d    t d t d   t  | | | | | |- |J  }p  f d   }qt |p|q }rt t t t d 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 t t d t d   t d t d    t d t d   t  | | | | | |- |J  }s  f d   }tt |s|t }u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 t t d t d   t d t d    t d t d   t  | | |/ |, | | | |K |2 |	 |L  }v  f d   }wt |v|w }x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 t t d t d   t d t d    t d t d   t  | | |/ |, | | | |K |2 |	 |L  }y  f d   }zt |y|z }{t t t 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 t  | | |/ |, | | | | |K |2  }|  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 t t d t d   t d t d    t t  | | |/ |, | | | | |K |2  }  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 t t d t d   t d t d    t  | | |/ |, | | |M |K 	 }  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 t t d t d   t d t d    t  | | |/ |, | | |M |K 	 }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |N 	 }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |N 	 }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |2 | |O  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |2 | |O  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |2 |P  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |2 |P  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 | |Q  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 | |Q  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 | |  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 | |  }  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 t t d t d   t d t d    t  | | |/ |, | | |M |4 |R 
 }  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 t t d t d   t d t d    t  | | |/ |, | | |M |4 |R 
 }  f d   }t || }t t t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 |S 
 }  f d   }t || }t t t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 |S 
 }  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 t t d t d   t d t d     t  | |/ |, | | |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 t t d t d   t d t d     t  | |/ |, | | |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 t t d t d   t d t d     t  | |/ |, | | |U  }  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 t t d t d   t d t d     t  | |/ |, | | |U  }  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 t t d t d   t d t d     t  | |/ |, | | |V |W  }  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 t t d t d   t d t d     t  | |/ |, | | |V |W  }  f d   }t || }t t t dE 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  | | |/ |, | | |M |4 |W |X  }  f d   }t || }t t t dE 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  | | |/ |, | | |M |4 |W |X  }  f d   }t || }  f d   }t t t dE 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  | | |/ |, | | |M |4 |W |Y |Z  }t || }  f d   }t t t dE 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  | | |/ |, | | |M |4 |W |Y |Z  }t || }t t t t d@ t d   t t 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 t  | | |/ |, | | | |M |4 |U  }  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 d t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |4 |U  }  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 t 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 d t d    t t t d@ t d   t t t d t d   t d t d    t  | |/ |, | | | |W |[ 	 }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |4 |W |  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |4 |W |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |M | | |2  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |M | | |2  }  f d   }t || }t t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 	 }  f d   }t || }t t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 	 }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |M | | |4  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |M | | |4  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | | |M |\ |]  }  f d   }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | | |M |\ |]  }  f d   }t || }t t t t t d t d   t t t d t d   t d t d     t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W 
 }  f d   }t || }t t t t t d t d   t t t d t d   t d t d     t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W 
 }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |^ |_  }   f d   }t | | }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |^ |_  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |^ |`  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |^ |`  }	  f d   }
t |	|
 }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |a |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |a |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | | |M |2 |W | |b  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | | |M |2 |W | |b  }  f d   }t || }t t t dE 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  | | |/ |, | | |M |2 |W | |c  }  f d   }t || }t t t dE 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  | | |/ |, | | |M |2 |W | |c  }  f d   }t || }t t t dE 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  | | |/ |, | | |M |2 |W | |  }  f d   }t || } t t t dE 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  | | |/ |, | | |M |2 |W | |  }!  f d   }"t |!|" }#t t t d  t d t d   t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |2 |W 
 }$  f d   }%t |$|% }&t t t d  t d t d   t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |2 |W 
 }'  f d   }(t |'|( })t t t dE 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  | | |/ |, | | | |M |2 |W |d  }*  f d   }+t |*|+ },t t t dE 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  | | |/ |, | | | |M |2 |W |d  }-  f d   }.t |-|. }/t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | | | |e  }0  f d   }1t |0|1 }2t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | | | |e  }3  f d   }4t |3|4 }5t t t t d t d   t t t d t d   t d t d    t d{  dN t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |2 |W 
 }6  f d   }7t |6|7 }8t t t t d t d   t t t d t d   t d t d    t d{  dN t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |2 |W 
 }9  f d   }:t |9|: };t t t t d t d   t t t d t d   t d t d    t d{  dN t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W 
 }<  f d   }=t |<|= }>t t t t d t d   t t t d t d   t d t d    t d{  dN t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W 
 }?  f d   }@t |?|@ }At t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W |< | |" |e  }B  f d   }Ct |B|C }Dt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W |< | |" |e  }E  f d   }Ft |E|F }Gt t t t d t d   t t t d t d   t d t d    t t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W | |O |f  }H  f d   }It |H|I }Jt t t t d t d   t t t d t d   t d t d    t t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W | |O |f  }K  f d   }Lt |K|L }Mt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |O | |e  }N  f d   }Ot |N|O }Pt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |2 |W | |O | |e  }Q  f d   }Rt |Q|R }St t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W | |O |e  }T  f d   }Ut |T|U }Vt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W | |O |e  }W  f d   }Xt |W|X }Yt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W | | |" |g  }Z  f d   }[t |Z|[ }\t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W | | |" |g  }]  f d   }^t |]|^ }_t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W | | |g  }`  f d   }at |`|a }bt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |2 |W | | |g  }c  f d   }dt |c|d }et t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |2 |W  }f  f d   }gt |f|g }ht t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |2 |W  }i  f d   }jt |i|j }kt t t t t d t d   t t t d t d   t d t d     t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W 
 }l  f d   }mt |l|m }nt t t t t d t d   t t t d t d   t d t d     t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |M |2 |W 
 }o  f d   }pt |o|p }qt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | | |M |2 |W  }r  f d   }st |r|s }tt t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | | |M |2 |W  }u  f d   }vt |u|v }wt t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | |h | |<  }x  f d   }yt |x|y }zt t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | |h | |<  }{  f d   }|t |{|| }}t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |4 |W |< |h |i |j  }~  f d  }t |~| }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |4 |W |< |h |i |j  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | | |k |<  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | | |k |<  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | | |8 |<  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | | |8 |<  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |4 |W |< | |l |m  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | | |M |4 |W |< | |l |m  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | | |8 |n  }  f d	  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |M |4 |W | | |8 |n  }  f d
  }t || }t t t d  t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 |W 
 }  f d  }t || }t t t d  t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 |W 
 }  f d  }t || }t t t t d t d   t d t d   t t t d t d   t d t d     t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, |M |4 |W  }  f d  }t || }t t t t d t d   t d t d   t t t d t d   t d t d     t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, |M |4 |W  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d{  dN t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 |W 
 }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d{  dN t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |M |4 |W 
 }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |4 |W |  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | | |M |4 |W |  }  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 t d t d   t d t d    t t  | | |/ |, | | | | |M |4 |W  }  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 t d t d   t d t d    t t  | | |/ |, | | | | |M |4 |W  }  f d  }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 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 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 dE t d   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 dE t d   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 d t d   t 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 t  | | |/ |, | | |p | | |- |o  }  f d  }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 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 t  | | |/ |, | | |p | | |- |o  }  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 t t d 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 d   t  | | |/ |, | | |p |- |q |	 |J  }  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 t t d 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 d   t  | | |/ |, | | |p |- |q |	 |J  }  f d  }t || }t t t dt d   t t t d t d   t d t d    t t t t d@ t d   t t t d t d   t d t d    t d t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |p | | |- |s |q |r  }  f d  }t || }t t t d  t t t d t d   t d t d    t t dt d   t t t d@ t d   t t t d t d   t d t d    t d t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |p | | |- |s |q |r  }  f d  }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 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 d   t  | | |/ |, | | |p | |- |J  }  f d   }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 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 d   t  | | |/ |, | | |p | |- |J  }  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 t t d t d   t d t d    t t t t d t d   t d t d    t d t d   t  | | |/ |, | | | |
 |	 |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 t t d t d   t d t d    t t d  t t t d t d   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 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 t  | | |/ |, | | |p | |- |
 |	 |q  }  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 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 t  | | |/ |, | | |p | |- |
 |	 |q  }  f d%  }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 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 t  | | |/ |, | | |p | | |- |
 |  }  f d&  }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 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 t  | | |/ |, | | |p | | |- |
 |  }  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 t t d 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  | | |/ |, | | |u |v | | |K |2  }  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 t t d 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  | | |/ |, | | |u |v | | |K |2  }  f d+  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M 
 }  f d,  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M 
 }  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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M | | |2  }  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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M | | |2  }  f d/  } t ||  }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M | | |4  }  f d0  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M | | |4  }  f d1  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t d t d   t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | |M |\  }  f d2  }	t ||	 }
t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t d t d   t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | |M |\  }  f d3  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |2 | | |  }  f d4  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |2 | | |  }  f d5  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | | |w  }  f d6  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | | |w  }  f d7  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |2 | |O |8  }  f d8  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |2 | |O |8  }  f d9  }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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | |O |d  }   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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | |O |d  }#  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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | |8  }&  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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | |8  })  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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | |  },  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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |2 | |  }/  f d?  }0t |/|0 }1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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |2 |x  }2  f d@  }3t |2|3 }4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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |2 |x  }5  f dA  }6t |5|6 }7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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | |M |2 |y  }8  f dB  }9t |8|9 }: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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | |M |2 |y  };  f dC  }<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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |2 |y  }>  f dD  }?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 t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |2 |y  }A  f dE  }Bt |A|B }Ct t t t d)t d   t t 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 t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 | |
 | |z  }D  f dF  }Et |D|E }Ft t t t d)t d   t t 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 t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 | |
 | |z  }G  f dG  }Ht |G|H }It t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 | |
 | |{  }J  f dH  }Kt |J|K }Lt t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 | |
 | |{  }M  f dI  }Nt |M|N }Ot t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |4 |W | | | |e  }P  f dJ  }Qt |P|Q }Rt t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |4 |W | | | |e  }S  f dK  }Tt |S|T }Ut t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |4 |W | | |e ||  }V  f dL  }Wt |V|W }Xt t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |4 |W | | |e ||  }Y  f dM  }Zt |Y|Z }[t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |4 |W | | |c |e  }\  f dN  }]t |\|] }^t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |4 |W | | |c |e  }_  f dO  }`t |_|` }at t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |4 |W | | |e |m  }b  f dP  }ct |b|c }dt t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | |M |4 |W | | |e |m  }e  f dQ  }ft |e|f }gt t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |4 |W | |} |c  }h  f dR  }it |h|i }jt t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v |M |4 |W | |} |c  }k  f dS  }lt |k|l }mt t 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 dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M |4 |W  }n  f dT  }ot |n|o }pt t 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 dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M |4 |W  }q  f dU  }rt |q|r }st t t d(t d   t d)t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d     t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M |4 |W  }t  f dV  }ut |t|u }vt t t d(t d   t d)t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d     t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v |M |4 |W  }w  f dW  }xt |w|x }yt t t d(t d   t d)t d   t t t d t d   t d t d    t dE t d   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 t d t d   t d t d    t  | | |/ |, | | |u |v | |M |4 |W  }z  f dX  }{t |z|{ }|t t t d(t d   t d)t d   t t t d t d   t d t d    t dE t d   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 t d t d   t d t d    t  | | |/ |, | | |u |v | |M |4 |W  }}  f dY  }~t |}|~ }t t t d(t d   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 t d t d   t d t d     t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |u |v |M |4 |W  }  f dZ  }t || }t t t d(t d   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 t d t d   t d t d     t t dE t d   t d@ t d   t t t d t d   t d t d     t  | | |/ |, | | |u |v |M |4 |W  }  f d[  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 |z  }  f d\  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 |z  }  f d]  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 |{  }  f d^  }t || }t t t d(t d   t d)t d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u |v | | |M |4 |{  }  f d_  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | |~ 	 }  f da  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | |~ 	 }  f db  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t d(t d   t d)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 dN  t  | | | | |u |v | | | 
 }  f dc  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t d(t d   t d)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 dN  t  | | | | |u |v | | | 
 }  f dd  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | | 	 }  f de  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | | 	 }  f df  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t d(t d   t d)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 dN  t  | | | | |u |v | | | | |2  }  f dg  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t d(t d   t d)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 dN  t  | | | | |u |v | | | | |2  }  f dh  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | | | |2  }  f di  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | | | |2  }  f dj  }t || }t t t t d)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 dN  t d t d   t d t d   t t t d t d   t d t d    t  | | | | |u |v | |4 | 
 }  f dk  }t || }t t t t d)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 dN  t d t d   t d t d   t t t d t d   t d t d    t  | | | | |u |v | |4 | 
 }  f dl  }t || }t t t t d)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 dN  t t t d t d   t d t d    t  | | |u |v | |  }  f dm  }t || }t t t t d)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 dN  t t t d t d   t d t d    t  | | |u |v | |  }  f dn  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t t t d t d   t d t d    t  | | |u | |  }  f do  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t t t d t d   t d t d    t  | | |u | |  }  f dp  }t || }t t t t d)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 dN  t d t d   t d t d   t t t d t d   t d t d    t  | | | | |u |v | | |4 |  }  f dq  }t || }t t t t d)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 dN  t d t d   t d t d   t t t d t d   t d t d    t  | | | | |u |v | | |4 |  }  f dr  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t t d t d   t t t d t d   t d t d    t  | | | | |u | | |4 | 
 }  f ds  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t t d t d   t t t d t d   t d t d    t  | | | | |u | | |4 | 
 }  f dt  }t || }t t t d t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | | | |u |v | | | | |4  }  f du  }t || }t t t d t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | | | |u |v | | | | |4  }  f dv  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t  | | | | |u | | | | |4  }  f dw  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t  | | | | |u | | | | |4  }  f dx  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t d(t d   t d)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 dN  t  | | | | |u |v | | | |\  }  f dy  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t d(t d   t d)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 dN  t  | | | | |u |v | | | |\  }  f dz  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | | |\ 
 }  f d{  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t  | | | | |u | | | |\ 
 }  f d|  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | | |~  }  f d}  }t || }t t t t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | | |~  }  f d~  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | |M |W | |  }  f d  }t || }t t t d t d   t d t d   t t t d t d   t d t d    t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | |M |W | |  }  f d  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | |M |W | |  }  f d  }t || }t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | |M |W | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d(t d   t d)t 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 dN  t  | | |/ |, | | |u |v | | |M |W |w  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d(t d   t d)t 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 dN  t  | | |/ |, | | |u |v | | |M |W |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 d`t d   t t t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | |M |W |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 d`t d   t t t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | |M |W |w  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d(t d   t d)t 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 dN  t  | | |/ |, | | |u |v | | |M |2 |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d(t d   t d)t 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 dN  t  | | |/ |, | | |u |v | | |M |2 |  }  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 t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | |M |2 |  }
  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 t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | |M |2 |  }  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 dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | |M |2 |P | | |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 dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | |M |2 |P | | |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 d(t d   t d`t d   t t t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | |M |2 |P | | |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 d(t d   t d`t d   t t t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | |M |2 |P | | |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 dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d(t d   t d)t 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 dN  t  | | |/ |, | | |u |v | | | |M |2 |P |  }  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 dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t d(t d   t d)t 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 dN  t  | | |/ |, | | |u |v | | | |M |2 |P |  }  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 d(t d   t d`t d   t t t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | | |M |2 |P |  }"  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 d(t d   t d`t d   t t t d t d   t d t d    t dN  t dE t d   t d@ t d   t t t d t d   t d t d    t d t d   t  | | |/ |, | | |u | | | |M |2 |P |  }%  f d  }&t |%|& }'t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | |M |4 |W | |Q |  }(  f d  })t |(|) }*t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | |M |4 |W | |Q |  }+  f d  },t |+|, }-t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | |M |4 |W | |Q |  }.  f d  }/t |.|/ }0t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | |M |4 |W | |Q |  }1  f d  }2t |1|2 }3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 dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | |M |4 |W | |Q |  }4  f d  }5t |4|5 }6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 dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | |M |4 |W | |Q |  }7  f d  }8t |7|8 }9t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | |M |4 |W | |Q |  }:  f d  };t |:|; }<t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t d t d   t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | |M |4 |W | |Q |  }=  f d  }>t |=|> }?t t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | |M |4 |W | | |m  }@  f d  }At |@|A }Bt t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | |M |4 |W | | |m  }C  f d  }Dt |C|D }Et t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | |M |4 |W | | |m  }F  f d  }Gt |F|G }Ht t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | |M |4 |W | | |m  }I  f d  }Jt |I|J }K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 t d t d   t d t d    t dN  t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | |M |4 |W  }L  f d  }Mt |L|M }N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 t d t d   t d t d    t dN  t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | |M |4 |W  }O  f d  }Pt |O|P }Qt t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u | |M |4 |W  }R  f d  }St |R|S }Tt t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t t d t d   t t t d t d   t d t d    t dE t d   t d@ t d   t t t d t d   t d t d    t  | | |/ |, | | |u | |M |4 |W  }U  f d  }Vt |U|V }Wt t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | | |M |4 |W |d |  }X  f d  }Yt |X|Y }Zt t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t  | | |/ |, | | |u |v | | |M |4 |W |d |  }[  f d  }\t |[|\ }]t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t dE t d   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 t d t d   t d t d    t  | | |/ |, | | |u | | |M |4 |W |d |  }^  f d  }_t |^|_ }`t t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t dE t d   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 t d t d   t d t d    t  | | |/ |, | | |u | | |M |4 |W |d |  }a  f d  }bt |a|b }ct t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | | |M |4 |W  }d  f d  }et |d|e }ft t t d t d   t d t d   t t t d t d   t d t d    t t dE t d   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 t d t d   t d t d    t d`t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |u |v | | | |M |4 |W  }g  f d  }ht |g|h }it t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | | |M |4 |W  }j  f d  }kt |j|k }lt t t d(t d   t d`t d   t t t d t d   t d t d    t dN  t d t d   t d t d   t t t d t d   t d t d    t t dE t d   t d@ t d   t t t d t d   t d t d    t t  | | |/ |, | | |u | | | |M |4 |W  }m  f d  }nt |m|n }ot t t d  t t d t d   t t t d@ t d   t dE t d    t dN  t  | | |/ |, |  }p  f d  }qt |p|q }rt t t d  t t d t d   t t t d@ t d   t dE t d    t dN  t  | | |/ |, |  }s  f d  }tt |s|t }ut t t d  t t d t d   t t t d@ t d   t dE t d    t dN  t  | | |/ |, |  }v  f d  }wt |v|w }xt t t d  t t d t d   t t t d@ t d   t dE t d    t dN  t  | | |/ |, |  }y  f d  }zt |y|z }{t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t  | | |/ |, | | |- | 	 }|  f d  }}t |||} }~t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t  | | |/ |, | | |- | 	 }  f d  }t || }  f d  }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t t t d@ t d   t dE t d    t t  | | |/ |, | | |- | 	 }t || }  f d  }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t t t d@ t d   t dE t d    t t  | | |/ |, | | |- | 	 }t || }  f d  }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | | |t  }t || }  f d  }t t t t d  t t t d@ t d   t dE t d    t t d t d   t d t d   t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | | |t  }t || }  f d  }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t d t d   t d  t t t d@ t d   t dE t d    t t  | | |/ |, | | |- | 	 }t || }  f d  }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t d t d   t d  t t t d@ t d   t dE t d    t t  | | |/ |, | | |- | 	 }t || }  f d  }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t d  t t t d@ t d   t dE t d    t d t d   t  | | |/ |, |F | |t  }t || }  f d  }t t t t d  t t t d@ t d   t dE t d    t t d t d   t d t d   t d  t t t d@ t d   t dE t d    t d t d   t  | | |/ |, |F | |t  }t || }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | | | |- | 
 }  f d  }t || }t t t t d t d   t t t d@ t d   t dE t d    t t d t d   t t d  t t t d@ t d   t dE 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 dE t d   t t t d t d   t d@ t d    t dt d   t d t d   t  | | |/ |, | | | | |t 
 }  f d  }t || }t t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t  | | |/ |, | | | | |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 dE t d   t t t d t d   t d@ t d    t dt d   t t  | | |/ |, | | | | |q 
 }  f d  }t || }t t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t t  | | |/ |, | | | | |q 
 }  f d  }t || }  f d  }t t t d  t d t d   t d t d   t t t d t d   t d@ t d    t d t d   t dE t d   t t t d t d   t d@ t d    t dt d   t  | | |/ |, | | | | 	 }t || }  f d  }t t t d  t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t  | | |/ |, | | | | 	 }t || }t t t d t d   t t t d t d   t d@ t d    t d t d   t d t d   t d t d   t t t d t d   t d@ t d    t dt d   t dE 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 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 dE t d   t d t d   t t t t d t d   t d@ t d    t t  | | |/ |, | | | |- | |  }  f d  }t || }  f 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 dE t d   t t 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 d   t  | | |/ |, | | | | |t 
 }t || }  f d  }t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d t d   t dE t d   t t 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 d   t  | | |/ |, | | | | |t 
 }t || }t t t d t d   t t t d t d   t d@ t d    t d t d   t d t d   t d t d   t t t d t d   t d@ t d    t dt d   t dE t d   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 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 dE t d   t d t d   t d t d   t t t d t d   t d@ t d    t t  | | |/ |, | | | |- | |  }  f d  }t || }  f 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 dE t d   t t 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 t  | | |/ |, | | | | |t 
 }t || }  f d  }t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t d t d   t t t d t d   t d@ t d    t t  | | |/ |, | | | | |t 
 }t || }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 dE t d   t t t d t d   t d@ t d    t dt d   t t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | | | | |t  }  f d  }t || }t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t t d  t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | | | | |t  }  f d  }t || }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 dE t d   t t t d t d   t d@ t d    t dt d   t t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | | |- | | |q  }  f d  }t || }t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t t d  t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | | |- | | |q  }  f d  }t || }t t t d t d   t t t d t d   t d@ t d    t d t d   t d t d   t d t d   t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t 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 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 dE t d   t d t d   t 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 d t d   t t t d t d   t d@ t d    t d t d   t dE 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 d   t  | | |/ |, | | | | | |t  }  f d  }t || }t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE 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  | | |/ |, | | | | | |t  }  f d  }t || }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 dE t d   t 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 d    t d t d   t  | | |/ |, | | | |- | | |q  }  f d  }t || }t t t d  t t t d t d   t d@ t d    t d t d   t d t d   t d  t t t d t d   t d@ t d    t dt d   t dE t d   t d t d   t t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | | |- | | |q  }  f d  }t || }  f d  }t t t d t d   t d t d   t t t d t d   t d@ t d    t t dE t d   t t t d t d   t d@ t d    t t d t d   t d  t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | |- | | |  }t || }  f d  }t t t d  t t t d t d   t d@ t d    t t dE 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 d   t t t d t d   t d@ t d    t d t d   t  | | |/ |, | | |- | | |  }t || }t t t 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 dE t d   t t t d t d   t d@ t d    t dN  t t  | | |/ |, | |u |v | |J 
 }  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 t t d t d   t d@ t d    t dE t d   t t t d t d   t d@ t d    t dN  t t  | | |/ |, | |u |v | |J 
 }  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 t t d t d   t d@ t d    t dE t d   t t t d t d   t d@ t d    t dN  t t  | | |/ |, | |u |v | |
 
 }  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 t t d t d   t d@ t d    t dE t d   t t t d t d   t d@ t d    t dN  t t  | | |/ |, | |u |v | |
 
 }  f d  }t || }  f d  }t t t t d)t d   t t 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 dE t d   t t t d t d   t d@ t d    t dN  t  | | |/ |, | |u |v | 	 }t || }  f d  }t t t t d)t d   t t 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 dE t d   t t t d t d   t d@ t d    t dN  t  | | |/ |, | |u |v | 	 }t || }t t t t d)t d   t t 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 dE t d   t t t d t d   t d@ t d    t dN  t t  | | |/ |, | |u |v | |J 
 }   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 d t d   t t t d t d   t d@ t d    t dE t d   t t t d t d   t d@ t d    t dN  t t  | | |/ |, | |u |v | |J 
 }  f d  }t || }t t t t d@ t d   t dE 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 dE 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 dE t d   t d t d   t  | |/ |, | | | | |Q 	 }  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 dE t d   t d t d   t  | |/ |, | | | | |Q 	 }  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 dE t d   t d t d   t  | |/ |, | | | | |Q 	 }  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 dE t d   t d t d   t  | |/ |, | | | | |Q 	 }  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 dE 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 dE t d   t d t d   t  | | |/ |, | | | | 	 }  f d  }t || }t t t t d@ t d   t dE t d   t d t d   t t d t d   t t t d t d   t d t d    t  | | |/ |, | | |2 | |Q 
 }  f d  }t || } t t t t d@ t d   t dE t d   t d t d   t t d t d   t t t d t d   t d t d    t  | | |/ |, | | |2 | |Q 
 }!  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 dE t d   t dN  t  | | |/ |, | | |2  }$  f d  }%t |$|% }&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 dE t d   t dN  t  | | |/ |, | | |2  }'  f d  }(t |'|( })t t t t d@ t d   t dE t d   t t t d t d   t t t d t d   t d t d    t  | | |/ |, | | |2 | | |  }*  f d  }+t |*|+ },t t t t d@ t d   t dE t d   t t t d t d   t t t d t d   t d t d    t  | | |/ |, | | |2 | | |  }-  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 dE t d   t  | | |/ |, | | |2  }0  f d  }1t |0|1 }2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 dE t d   t  | | |/ |, | | |2  }3  f d  }4t |3|4 }5t t t t d@ t d   t dE t d   t t t d t d   t t t d t d   t d t d    t  | | |/ |, | | | |2 | 
 }6  f d  }7t |6|7 }8t t t t d@ t d   t dE t d   t t t d t d   t t t d t d   t d t d    t  | | |/ |, | | | |2 | 
 }9  f d  }:t |9|: };t t t t d t d   t t t d t d   t d t d    t t t d@ t d   t dE t d   t t  | | |/ |, | | |2 | 	 }<  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 dE t d   t t  | | |/ |, | | |2 | 	 }?  f d  }@t |?|@ }At t t t d t d   t t t d t d   t d t d    t t t d@ t d   t dE t d   t t  | | |/ |, | | | |2 |H 
 }B  f d  }Ct |B|C }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 dE t d   t t  | | |/ |, | | | |2 |H 
 }E  f d  }Ft |E|F }G  f d  }Ht t t t d t d   t t t d t d   t d t d    t t t d@ t d   t dE t d   t d t d   t  | | |/ |, | | |2 | | |Q  }It |I|H }J  f d  }Kt t t t d t d   t t t d t d   t d t d    t t t d@ t d   t dE t d   t d t d   t  | | |/ |, | | |2 | | |Q  }Lt |L|K }Mt t t t d@ t d   t dE t d   t d t d   t t d t d   t t t d t d   t d t d    t  | | |/ |, | | |4 | 	 }N  f d  }Ot |N|O }Pt t t t d@ t d   t dE t d   t d t d   t t d t d   t t t d t d   t d t d    t  | | |/ |, | | |4 | 	 }Q  f d  }Rt |Q|R }St t t t d@ t d   t dE t d   t t d t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |4  }T  f d  }Ut |T|U }Vt t t t d@ t d   t dE t d   t t d t d   t t t d t d   t d t d    t dN  t  | | |/ |, | | |4  }W  f d  }Xt |W|X }Yt t t t d t d   t t t d t d   t d t d    t t t d@ t d   t dE t d   t d t d   t  | | |/ |, | | |4 |H | 
 }Z  f d  }[t |Z|[ }\t t t t d t d   t t t d t d   t d t d    t t t d@ t d   t dE t d   t d t d   t  | | |/ |, | | |4 |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  | | | | | |  }`  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  | | | | | |  }c  f d  }dt |c|d }et t t t d@ t d   t dE 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  | | |/ |, | | | | | 
 }f  f d  }gt |f|g }ht t t t d@ t d   t dE 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  | | |/ |, | | | | | 
 }i  f d  }jt |i|j }kt t t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, |- | |t  }l  f d   }mt |l|m }nt t t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, |- | |t  }o  f d  }pt |o|p }qt t t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | |- |  }r  f d  }st |r|s }tt t t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | |- |  }u  f d  }vt |u|v }wt t t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | |- | | 	 }x  f d  }yt |x|y }zt t t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | |- | | 	 }{  f d  }|t |{|| }}t t t d t d   t d t d   t t  t d t d   t  | | |- | |  }~  f d  }t |~| }t t t d 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 t t t d@ t d   t dE t d    t d 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 t d@ t d   t dE t d    t d t d   t  | | |/ |, | | |- | |t 
 }  f d	  }t || }t t t t d t d   t t t t d@ t d   t dE t d    t dN  t  |/ |, | | |  }  f d
  }t || }t t t t d t d   t t t t d@ t d   t dE t d    t dN  t  |/ |, | | |  }  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 dE 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 t d@ t d   t dE t d    t d t d   t  | | |/ |, | | |- | 	 }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | | | |- | 
 }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t t t d@ t d   t dE t d    t d t d   t  | | |/ |, | | | |- | 
 }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t  t d t d   t  | | | | |- | |  }  f d  }t || }t t t t t d t d   t d 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 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 d   t  | | |- | |J | |  }  f d  }t || }t t t t d t d   t d  t t t d t d   t d t d   t d t d    t d t d   t d  t t t d t d   t d t d   t d t d    t dt d   t  | | |- | |J | |  }  f d  }t || }t t t t t dN  t dE t d   t t d t d   t d t d    t d t d   t  | | |/ | |  }  f d  }t || }t t t d  t t t dN  t dE 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 t t dN  t dE t d   t t d t d   t d t d    t  | | |/ |, | |  }  f d  }t || }t t t t t d t d   t t t dN  t dE 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 t t dN  t dE 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 t t dN  t dE 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 dN  t dE 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 d   t d t d   t d  t t t dN  t dE t d   t t d t d   t d t d    t d t d   t  | | |/ |, | | | | 	 }  f d  }t || }| | | | | | | | | | | | | | | | | | | | | | | | | | | | ||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||||||||||||||||||||||||||||||||||||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}|||||||||||||||||||||||||||||||||||||||||||||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||||||||||||||||||||||||||||||||||||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}||||||||||||||||||||||gS(  Ni(   t   cons1508t   cons2t   cons3t   cons48t   cons125t   cons21t   cons4t   cons1509t   cons17t   cons23t   cons93t   cons165t   cons94t   cons1510t   cons1170t   cons87t   cons1511t   cons89t   cons166t   cons683t   cons31t   cons266t   cons32t   cons1512t   cons1513t   cons18t   cons155t   cons1250t   cons1514t   cons1515t   cons1516t   cons1517t   cons1518t   cons1519t   cons1520t   cons1521t   cons1522t   cons80t   cons79t   cons1523t   cons1524t   cons1525t   cons1526t   cons27t   cons5t   cons1527t   cons7t   cons1261t   cons1264t   cons1439t   cons463t   cons1440t   cons1528t   cons1255t   cons1529t   cons88t   cons1530t   cons1531t   cons1532t   cons515t   cons1533t   cons1534t   cons1535t   cons1536t   cons1537t   cons1538t   cons66t   cons1539t   cons84t   cons1228t   cons148t   cons196t   cons1540t   cons85t   cons70t   cons1541t   cons71t   cons1412t   cons267t   cons1303t   cons168t   cons1542t   cons1543t   cons1322t   cons1544t   cons1323t   cons1545t   cons1546t   cons1547t   cons1548t   cons77t   cons1549t   cons1550t   cons1551t   cons1423t   cons1385t   cons111t   cons272t   cons1325t   cons1327t   cons1334t   cons1552t   cons1553t   cons1333t   cons1554t   cons1555t   cons1336t   cons1556t   cons1557t   cons808t   cons380t   cons208t   cons147t   cons1417t   cons50t   cons38t   cons34t   cons35t   cons346t   cons1418t   cons1426t   cons1558t   cons1559t   cons1560t   cons1256t   cons1561t   cons36t   cons33t   cons1433t   cons1562t   cons1563t   cons1564t   cons1565t   cons1566t   cons1567t   cons1568t   cons1569t   cons1492t   cons1456t   cons1570t   cons1481t   cons1479t   cons743t   cons1497t   cons46t   cons45t   cons226t   cons1480t   cons62t   cons528t   cons1571t   cons1572t   cons810t   cons811t   cons1360t   cons1573t   cons1495t   cons68t   cons69t   cons823t   cons824t   cons1574t   cons1575t   cons1576t   cons1577t   cons1578t   cons1579t   cons47t   cons239t   cons1580t   ai   t   ft   ei    t   bc            sa     j  d  t | | t | | |  |  | t | | |  | t d  | |  |  S(   NiF  i(   t   appendR  R  R  R  (   t   mR  R  R  t   nt   xR  (   t   rubi(    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3398   s    c            s`     j  d  t | | t | | |  |  | t | | |  | t d  | |  |  S(   NiG  i(   R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3399   s    R  R  c      
      s     j  d  t t d  | t t | | | t d  t d  |  t d  | t d  t d  d |  | t | | |   |  S(   NiH  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3400   s    c      
      s     j  d  t t d  | t t | | | t d  t d  |  t d  | t d  t d  d |  | t | | |   |  S(   NiI  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3401   s    c      	      sf     j  d  t | |  t | t | | |  |  | t d  t | | |  |  |  |  S(   NiJ  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3402   s    c      	      sf     j  d  t | |  t | t | | |  |  | t d  t | | |  |  |  |  S(   NiK  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3403   s    c      	      s    j  d  t | t d  |  t d  | t d  | t d  t | t | | |  |  t d  | t | | |  | t d  |  |  t | | t | | |  |  t d  | t | | |  | t d  | t d  | | t d  |  S(   NiL  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3404   s    c      	      s    j  d  t | t d  |  t d  | t d  | t d  t | t | | |  |  t d  | t | | |  | t d  |  |  t | | t | | |  |  t d  | t | | |  | t d  | t d  | | t d  |  S(   NiM  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3405   s    c      	      s     j  d  t | t d  |  | t d  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | | t | | |  |  | t | | |  | t d  | | t d  |  S(   NiN  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3406   s    c      	      s     j  d  t | t d  |  | t d  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | | t | | |  |  | t | | |  | t d  | | t d  |  S(   NiO  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3407   s    c      	      s     j  d  t | t d  | t d  | t d  |  t | t | | |  |  t d  | t | | |  | t d  |  |  t | t | | |  |  | t | | |  | t d  | | |  |  S(   NiP  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3408   s    c      	      s     j  d  t | t d  | t d  | t d  |  t | t | | |  |  t d  | t | | |  | t d  |  |  t | t | | |  |  | t | | |  | t d  | | |  |  S(   NiQ  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3409   s    c      	      s     j  d  t | t d  | t d  |  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | t | | |  |  | t | | |  | t d  | | |  | t d  |  S(   NiR  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3410   s    c      	      s     j  d  t | t d  | t d  |  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | t | | |  |  | t | | |  | t d  | | |  | t d  |  S(   NiS  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3411   s    c      	      s     j  d  t | t d  |  | t d  |  t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  | t | | |  | t d  | |  |  S(   NiT  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3412   s    c      	      s     j  d  t | t d  |  | t d  |  t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  | t | | |  | t d  | |  |  S(   NiU  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3413   s    c      	      s    j  d  t |  t d  | t d  |  | t d  t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  t d  | t | | |  | t d  | t d  | |  | t d  |  S(   NiV  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3414   s    c      	      s    j  d  t |  t d  | t d  |  | t d  t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  t d  | t | | |  | t d  | t d  | |  | t d  |  S(   NiW  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3415   s    c      
      s     j  d  t t d  | t t | |  | | t d  | t d  | t d  t d  d |  | | t | | |   |  S(   NiX  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3416   s    c      
      s     j  d  t t d  | t t | |  | | t d  | t d  | t d  t d  d |  | | t | | |   |  S(   NiY  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3417   s    c      	      s    j  d  t | t d  t | t d  t d  d  t d  | t d  t | t d  t d  d  t d  | t | | |  t d  t | t d  t d  d  | t | | |  t d  t | t d  t d  d  t | | |  t d  t | t d  t d  d  | t t	 | | |  | | t d  t d  | t d  t d  d |  | t | | |   |  S(   NiZ  i   i   i(
   R  R  R  R$   R  R%   R  R  R*   R   (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3418   s    c      	      s    j  d  t | t d  t | t d  t d  d  t d  | t d  t | t d  t d  d  t d  | t | | |  t d  t | t d  t d  d  | t | | |  t d  t | t d  t d  d  t | | |  t d  t | t d  t d  d  | t t	 | | |  | | t d  t d  | t d  t d  d |  | t | | |   |  S(   Ni[  i   i   i(
   R  R  R  R$   R  R%   R  R  R*   R   (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3419   s    c      	      s     j  d  t t d  | t | | |  t |   | t | | |  t |   t t d  | t | | |  |  | t | | |  | |  |  S(   Ni\  i   (   R  R  R  R  R%   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3420   s    c      	      s     j  d  t t d  | t | | |  t |   | t | | |  t |   t t d  | t | | |  |  | t | | |  | |  |  S(   Ni]  i   (   R  R  R  R  R%   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3421  s    c            sq     j  d  t | t | | |  |  | t | | |  |  t | t | | |  |  | |  |  S(   Ni^  (   R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3422  s    c            sa     j  d  t | t | | |  |  | t | | |  | t d  | | |  |  S(   Ni_  i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3423  s    c            s`     j  d  t | t | | |  |  | t | | |  | t d  | | |  |  S(   Ni`  i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3424  s    c      
      s     j  d  t | | t t | | |  t d  | t d  t d  | t d  t d  d |  | t d  t | | |   |  S(   Nia  ii   i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3425  s    c      
      s     j  d  t | | t t | | |  t d  | t d  t d  | t d  t d  d |  | t d  t | | |   |  S(   Nib  ii   i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3426  s    c      	      s     j  d  t t d  | t t | | | | t d  t d  |  t d  t d  |  | t | | |   |  S(   Nic  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3427   s    c      
      s     j  d  t t d  | t t | | | | t d  t d  |  t d  t d  |  | t d  t | | |   |  S(   Nid  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3428%  s    c      	      s    j  d  t | t d  |  t d  | t d  | t d  t | t | | |  |  t d  | t | | |  | t d  |  |  t | t d  | t | | |  |  t d  | t | | |  | t d  | | | t d  |  S(   Nie  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3429*  s    c      	      s    j  d  t | t d  |  t d  | t d  | t d  t | t | | |  |  t d  | t | | |  | t d  |  |  t | t d  | t | | |  |  t d  | t | | |  | t d  | | | t d  |  S(   Nif  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3430/  s    c      	      s     j  d  t |  | t d  | t d  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | t | | |  |  | t | | |  | t d  | | | t d  |  S(   Nig  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement34314  s    c      	      s     j  d  t |  | t d  | t d  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | t | | |  |  | t | | |  | t d  | | | t d  |  S(   Nih  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement34329  s    c      	      s     j  d  t | t d  | t d  | t d  |  t | t | | |  |  t d  | t | | |  | t d  |  |  t | | t | | |  |  | t | | |  | t d  | |  |  S(   Nii  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3433>  s    c      	      s     j  d  t | t d  | t d  | t d  |  t | t | | |  |  t d  | t | | |  | t d  |  |  t | | t | | |  |  | t | | |  | t d  | |  |  S(   Nij  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3434C  s    c      	      s     j  d  t | t d  | t d  |  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | | t | | |  |  | t | | |  | t d  | |  | t d  |  S(   Nik  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3435H  s    c      	      s     j  d  t | t d  | t d  |  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | | t | | |  |  | t | | |  | t d  | |  | t d  |  S(   Nil  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3436M  s    c      	      s     j  d  t |  | t d  | t d  |  t | t | | |  |  t d  | t | | |  | |  |  t | t | | |  |  | t | | |  | t d  | | |  |  S(   Nim  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3437R  s    c      	      s     j  d  t |  | t d  | t d  |  t | t | | |  |  t d  | t | | |  | |  |  t | t | | |  |  | t | | |  | t d  | | |  |  S(   Nin  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3438W  s    c      	      s    j  d  t | t d  |  t d  |  | t d  t | t | | |  |  t d  | t | | |  | |  |  t | t d  | t | | |  |  t d  | t | | |  | t d  | | |  | t d  |  S(   Nio  i   iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3439\  s    c      	      s    j  d  t | t d  |  t d  |  | t d  t | t | | |  |  t d  | t | | |  | |  |  t | t d  | t | | |  |  t d  | t | | |  | t d  | | |  | t d  |  S(   Nip  i   iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3440a  s    c      
      s     j  d  t t t | | |    t | t | | |    t t | | |    t t d  t t | | |    t t | | |    |   |   S(   Niq  i   (   R  R  R  R  R  R  R   R  (   R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3441f  s    c      
      s     j  d  t t t | | |    t | t | | |    t t | | |    t t d  t t | | |    t t | | |    |   |   S(   Nir  i   (   R  R  R  R  R  R  R   R  (   R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3442k  s    c      	      s     j  d  t t | t | | |    t t | | |    t t | | |    t t t | | |    t t | | |    |   |   S(   Nis  (   R  R  R  R  R  R  R   (   R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3443p  s    c      	      s     j  d  t t | t | | |    t t | | |    t t | | |    t t t | | |    t t | | |    |   |   S(   Nit  (   R  R  R  R  R  R  R   (   R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3444u  s    c            s     j  d  t | |  | | t | | |  | | t | | |  | | t | | |  | t | t | | |  | t | | |  |  | |  |  S(   Niu  (   R  R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3445z  s    c            s     j  d  t | |  | | t | | |  | | t | | |  | | t | | |  | t | t | | |  | t | | |  |  | |  |  S(   Niv  (   R  R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3446  s    c      
      s1    j  d  t | t | | |  |  | t | | |  | t d  t | | |  t d  |  t d  | t d  t d  d t | t d  t d  d |  t d  | t d  t d  d | t d  t d  d t | | |  t d   | | | t d  |  S(   Niw  i   i   i   (   R  R  R  R  R  R4   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3447  s    c      
      s2    j  d  t | t | | |  |  | t | | |  | t d  t | | |  t d  |  t d  | t d  t d  d t | t d  t d  d |  t d  | t d  t d  d | t d  t d  d t | | |  t d   | | | t d  |  S(   Nix  i   i   i   (   R  R  R  R  R  R4   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3448  s    c      	      s     j  d  t t | | |  | t |   | t | | |  t |   t t | | |  | |  | t | | |  | |  |  S(   Niy  (   R  R  R  R%   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3449  s    c      	      s     j  d  t t | | |  | t |   | t | | |  t |   t t | | |  | |  | t | | |  | |  |  S(   Niz  (   R  R  R  R%   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3450  s    t   dc	   	   	      s    j  d  t | t d  | t d  | |  | t d  t | | t | | |  |  | | t | | |  | t d  |  |  t | | | t | | |  |  | | t | | |  | t d  | | |  | t d  |  S(   Ni{  i   ii(   R  R  R  R   R  R  R  (	   t   pR  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3451  s    c	   	   	      s    j  d  t | t d  | t d  | |  | t d  t | | t | | |  |  | | t | | |  | t d  |  |  t | | | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3452  s    c	   	   	      s     j  d  t | |  | t d  | t d  | t d  t | | t | | |  |  | | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3453  s    c	   	   	      s     j  d  t | |  | t d  | t d  | t d  t | | t | | |  |  | | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3454  s    t   cc            s     j  d  t |  t d  t |  t | | |  | t d  |  |  t |  |  t | | |  | t d  | | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3455  s    c            s     j  d  t |  t d  t |  t | | |  | t d  |  |  t |  |  t | | |  | t d  | | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3456  s    c            s     j  d  t |  t d  t |  t | | |  | t d  |  |  t |  t | | |  | t d  |  | | t d  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3457  s    c            s     j  d  t |  t d  t |  t | | |  | t d  |  |  t |  t | | |  | t d  |  | | t d  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3458  s    c            s<     j  d  t t t t | |  |  |   |  |  S(   Ni  (   R  R  t   logR   R  (   R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3459  s    c            s;     j  d  t t t t | |  |  |   |  |  S(   Ni  (   R  R  R  R   R  (   R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3460  s    c      
      sh     j  d  t |  | t t | | |  t d  | t d  |  | |  t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3461  s    c      
      si     j  d  t |  | t t | | |  t d  | t d  |  | |  t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3462  s    i   c            s     j  d  t t d  | |  t t | | |  |  |  t | | t d  |  t d  |  t |  t d  t | | |  | |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3463  s    c            s     j  d  t t d  | |  t t d  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3464  s    c      	      s     j  d  t t d  | t | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3465  s    c      	      s     j  d  t t d  | t | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3466  s    c      	      s     j  d  t t d  t d  | t | |  t | | |  | t d  |  |  t | | |  t | | |  | t d  |  | | |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3467  s    c      	      s     j  d  t t d  t d  | t | |  t | | |  | t d  |  |  t | | |  t | | |  | t d  |  | | |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3468  s    c            s     j  d  t t d  |  | t t t d  t d  | | t d  |  | t | |  t | | |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3469  s    c            s~     j  d  t t d  |  | t t t d  t d  | | t d  |  | t | |  t | | |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3470  s    c      
      sc     j  d  t |  | t t | | | t d  | | |  | |  t | | |   |  S(   Ni  i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3471  s    c      
      sb     j  d  t |  | t t | | | t d  | | |  | |  t | | |   |  S(   Ni  i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3472  s    c      	      s     j  d  t | |  t | | |  | t d  | t d  t d  | |  t | | |  |  t d  |  t |  | |  t | | |  | t d  | | t d  |  S(   Ni  ii   i(   R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3473  s    c      	      s     j  d  t | |  t | | |  | t d  | t d  t d  | |  t | | |  |  t d  |  t |  | |  t | | |  | t d  | | t d  |  S(   Ni  ii   i(   R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3474  s    c      
      s     j  d  t t d  | t d  |  t d  t | |  t | | |  | |  t | | |  | t d  |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3475  s    c      
      s     j  d  t t d  | t d  |  t d  t | |  t | | |  | |  t | | |  | t d  |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3476  s    c      
      s     j  d  t |  | t d  |  t d  t | t | | |  |  | |  t | | |  |  |  t | | | t d  |  t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3477  s    c      
      s     j  d  t |  | t d  |  t d  t | t | | |  |  | |  t | | |  |  |  t | | | t d  |  t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3478  s    c      
      sl     j  d  t |  | t t | | | |  t d  | t d  |  | |  t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3479$  s    c      
      sm     j  d  t |  | t t | | | |  t d  | t d  |  | |  t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3480)  s    c            sk     j  d  t | t | t | | |  |  |  |  t | | t | | |  |  | |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3481.  s    c            sk     j  d  t | t | t | | |  |  |  |  t | | t | | |  |  | |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement34823  s    c      
      s     j  d  t | |  t d  | | t t | | |  t d  t d  | | |  t d  | t d  |  | | t | | |   |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement34838  s    c      
      s     j  d  t | |  t d  | | t t | | |  t d  t d  | | |  t d  | t d  |  | | t | | |   |  S(   Ni  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3484=  s    c            s^     j  d  t | | t | | |  |  | | t | | |  | | | |  |  S(   Ni  (   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3485B  s    c            s_     j  d  t | | t | | |  |  | | t | | |  | | | |  |  S(   Ni  (   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3486G  s    c            s     j  d  t t d  | | |  t t t d  | | t d  t d  |  | t d  t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3487L  s    c            s     j  d  t t d  | | |  t t t d  | | t d  t d  |  | t d  t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3488Q  s    c      
      s     j  d  t | t d  | t d  t | t | | |  |  t d  | | t | | |  | t d  |  |  t | | t | | |  |  | | t | | |  | | | |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3489V  s    c      
      s     j  d  t | t d  | t d  t | t | | |  |  t d  | | t | | |  | t d  |  |  t | | t | | |  |  | | t | | |  | | | |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3490[  s    c      
      s	    j  d  t t d  | t d  | t | t | | |  |  t d  | | t | | |  | t d  |  |  t t d  | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3491`  s    c      
      s
    j  d  t t d  | t d  | t | t | | |  |  t d  | | t | | |  | t d  |  |  t t d  | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3492e  s    c      	      s     j  d  t | | t d  t |  | t | | |  t d  t |  | | t | | |  t |  | | t | | |  t |  t | | t | | |  | |  |  S(   Ni  i   (   R  R  R  R$   R  R%   R  R   (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3493j  s    c      	      s     j  d  t | | t d  t |  | t | | |  t d  t |  | | t | | |  t |  | | t | | |  t |  t | | t | | |  | |  |  S(   Ni  i   (   R  R  R  R$   R  R%   R  R   (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3494o  s    c            sn     j  d  t t d  | | t | | |  |  | | t | | |  | t d  | |  |  S(   Ni  i   i(   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3495t  s    c            so     j  d  t t d  | | t | | |  |  | | t | | |  | t d  | |  |  S(   Ni  i   i(   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3496y  s    c      
      s     j  d  t | |  t d  | t d  |  | t d  t | t | | |  |  | | t | | |  | t d  |  |  t | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3497~  s    c      
      s     j  d  t | |  t d  | t d  |  | t d  t | t | | |  |  | | t | | |  | t d  |  |  t | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3498  s    c            s     j  d  t t d  | | t d  |  t t | t d  | t d  | t d  | t d  |  | t | | t | |  |   t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3499  s    c            s     j  d  t t d  | | t d  |  t t | t d  | t d  | t d  | t d  |  | t | | t | |  |   t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3500  s    c      
      s    j  d  t | t d  |  t d  | t d  | t d  |  t | t | | |  |  t d  | | t | | |  | t d  |  |  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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3501  s    c      
      s	    j  d  t | t d  |  t d  | t d  | t d  |  t | t | | |  |  t d  | | t | | |  | t d  |  |  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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3502  s    c      
      s     j  d  t | |  | | t d  |  t | t | | |  |  t d  | | t | | |  | t d  |  |  t | | t | | |  |  | | t | | |  | | | |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3503  s    c      
      s     j  d  t | |  | | t d  |  t | t | | |  |  t d  | | t | | |  | t d  |  |  t | | t | | |  |  | | t | | |  | | | |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3504  s    c      
      s     j  d  t | |  t d  | t d  |  | t d  t | t | | |  |  | | t | | |  | t d  |  |  t | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3505  s    c      
      s     j  d  t | |  t d  | t d  |  | t d  t | t | | |  |  | | t | | |  | t d  |  |  t | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3506  s    i   c            s     j  d  t | t | | t | |  |   t | | t | |  |   t | |  |  t t | t | |  |   t | | t | |  |   |  |  S(   Ni  (   R  R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3507  s    c            s     j  d  t | t | | t | |  |   t | | t | |  |   t | |  |  t t | t | |  |   t | | t | |  |   |  |  S(   Ni  (   R  R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3508  s    c      
      s.    j  d  t | t d  |  t d  | t d  |  t d  | t | t | | |  |  t d  | | t | | |  | t d  |  |  t t d  | t d  | t | | |  |  t d  | | t | | |  | t d  | | |  t d  | |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3509  s    c      
      s/    j  d  t | t d  |  t d  | t d  |  t d  | t | t | | |  |  t d  | | t | | |  | t d  |  |  t t d  | t d  | t | | |  |  t d  | | t | | |  | t d  | | |  t d  | |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3510  s    c      
      s    j  d  t | t d  |  t d  | |  | t d  t | t | | |  |  t d  | | t | | |  | t d  |  |  t | t d  | t | | |  |  t d  | | t | | |  | t d  | | |  | t d  |  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3511  s    c      
      s    j  d  t | t d  |  t d  | |  | t d  t | t | | |  |  t d  | | t | | |  | t d  |  |  t | t d  | t | | |  |  t d  | | t | | |  | t d  | | |  | t d  |  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3512  s    c      
      s     j  d  t |  | | |  t d  | t | t | | |  |  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3513  s    c      
      s     j  d  t |  | | |  t d  | t | t | | |  |  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3514  s    c      
      s     j  d  t | |  t d  | t d  |  | t d  t | t | | |  |  | | t | | |  | t d  |  |  t | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3515  s    c      
      s     j  d  t | |  t d  | t d  |  | t d  t | t | | |  |  | | t | | |  | t d  |  |  t | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3516  s    c      
      s     j  d  t |  | | |  t d  | t | t | | |  |  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3517  s    c      
      s     j  d  t |  | | |  t d  | t | t | | |  |  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3518  s    c      
      s     j  d  t | t | | |  |  | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3519  s    c      
      s     j  d  t | t | | |  |  | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3520  s    c      
      s     j  d  t t d  | | t t t d  | t d  | t d  |  t d  t d  | | | |  | | t | | |   |  S(   Ni  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3521  s    c      
      s     j  d  t t d  | | t t t d  | t d  | t d  |  t d  t d  | | | |  | | t | | |   |  S(   Ni  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3522  s    c            s     j  d  t | t d  t t | |  |   |  |  t | t d  | t d  t | |  |  |  |  t t d  | | t | |  |  |  |  S(   Ni  i   (   R  R  R  R  R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3523   s    c            s     j  d  t | t d  t t | |  |   |  |  t | t d  | t d  t | |  |  |  |  t t d  | | t | |  |  |  |  S(   Ni  i   (   R  R  R  R  R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3524  s    c      
      s     j  d  t t d  |  t d  t | t | | |  |  | t d  |  t d  | | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3525
  s    c      
      s     j  d  t t d  |  t d  t | t | | |  |  | t d  |  t d  | | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3526  s    c      
      s     j  d  t t d  |  t t t d  | t d  | t d  | t d  |  | | t | |  |  | t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3527  s    c      
      s     j  d  t t d  |  t t t d  | t d  | t d  | t d  |  | | t | |  |  | t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3528  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 | | |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3529  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 | | |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3530#  s    c            s     j  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 | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3531(  s    c            s     j  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 | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3532-  s    c      
      s    j  d  t | 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  |  t d  t d  | | | |  | | t | | |   |  S(   Ni  i   ii   i(	   R  R  R  R$   R  R%   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement35332  s    c      
      s    j  d  t | 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  |  t d  t d  | | | |  | | t | | |   |  S(   Ni  i   ii   i(	   R  R  R  R$   R  R%   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement35347  s    c            s     j  d  t t d  | |  t t | t d  | t d  | t d  | t d  |  | t | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3535<  s    c            s     j  d  t t d  | |  t t | t d  | t d  | t d  | t d  |  | t | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3536A  s    c      
      s     j  d  t t d  | t | | t | |  |   t | | t | |  |   t | |  |  t t | | t | |  |   t | t | |  |   |  |  S(   Ni  i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3537F  s    c      
      s     j  d  t t d  | t | | t | |  |   t | | t | |  |   t | |  |  t t | | t | |  |   t | t | |  |   |  |  S(   Ni  i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3538K  s    c      
      s     j  d  t | t | | |  |  | t | | |  |  t | t | | |  |  | | t | | |  | |  |  S(   Ni  (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3539P  s    c      
      s     j  d  t | t | | |  |  | t | | |  |  t | t | | |  |  | | t | | |  | |  |  S(   Ni  (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3540U  s    c      
      s     j  d  t | | t t | |  | | | | t d  | t d  |  t d  t d  |  | | t | | |   |  S(   Ni  i   i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3541Z  s    c      
      s     j  d  t | | t t | |  | | | | t d  | t d  |  t d  t d  |  | | t | | |   |  S(   Ni  i   i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3542_  s    c            sJ     j  d  t | | t | | |  | t | | |  |  |  S(   Ni  (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3543d  s    c            sJ     j  d  t | | t | | |  | t | | |  |  |  S(   Ni  (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3544i  s    c            ss     j  d  t | t | | |  | t | | |  | t | | |  |  t | | |  | |  S(   Ni  (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3545n  s    c            ss     j  d  t | t | | |  | t | | |  | t | | |  | t | | |  |  |  S(   Ni  (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3546s  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  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3547x  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  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3548}  s    R  c            sv     j  d  t | t | | |  | t | | |  | t | | |  |  t | | |  | | |  S(   Ni  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3549  s    c            sv     j  d  t | t | | |  | t | | |  | t | | |  | | t | | |  |  |  S(   Ni  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3550  s    c	   	   	      s{     j  d  t | |  | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3551  s    c	   	   	      s{     j  d  t | |  | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3552  s    c	   	   	      sx     j  d  t | | | t t | | | |  t d  | | | | t d  |  | t | | |   |  S(   Ni  i(   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3553  s    c	   	   
      s     j  d  t | | | t t | | | |  t d  | | | | t d  |  | t d  t | | |   |  S(   Ni  ii   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3554  s    c            sQ     j  d  t | | | | | |  t | | t | |  |  |  |  S(   Ni  (   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3555  s    c            sQ     j  d  t | | | | | |  t | | |  t | |  |  |  S(   Ni  (   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3556  s    c            s     j  d  t | | | | t t | |  |  |  |  t | | | | | |  t | | t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3557  s    c            s     j  d  t | | | | t t d  t | |  |  |  |  t | | | | | |  t | | |  t | |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3558  s    c      	      s     j  d  t | | | | t d  | | t | | t | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3559  s    c      	      s     j  d  t | | | | t d  | | t | | t | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3560  s    c      	      s     j  d  t | | | | | t | | t | | |  |  |  |  t | | | t | | |  |  | |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3561  s    c      	      s     j  d  t | | | | | t | | t | | |  |  |  |  t | | | t | | |  |  | |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3562  s    c      	      s     j  d  t | | t | | |  |  t d  t | | | | | | | | t | | |  |  |  t | | | t | | |  |  | |  |  S(   Ni  i(   R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3563  s    c      	      s     j  d  t | | t | | |  |  t d  t | | | | | | | | t | | |  |  |  t | | | t | | |  |  | |  |  S(   Ni  i(   R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3564  s    c            s    j  d  t t d  | t d  | t d  t | | t | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3565  s    c            s    j  d  t t d  | t d  | t d  t | | t | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3566  s    c      
      s]     j  d  t | t t | t | |  |  | t | |  |  |   | |  |  S(   Ni  (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3567  s    c      
      s^     j  d  t | t t | t | |  |  | t | |  |  |   | |  |  S(   Ni  (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3568  s    c      
      s     j  d  t | | | | | t d  | t d  t | t | |  |  | | | t | |  |  |  |  t | | | | | | t d  | t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3569  s    c      
      s     j  d  t | | | | | t d  | t d  t | t | |  |  | | | t | |  |  |  |  t | | | | | | t d  | t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3570  s    c            s     j  d  t t d  | t d  |  t t t d  | | t d  t d  | | |  | | | t | |  |  t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3571  s    c            s     j  d  t t d  | t d  |  t t t d  | | t d  t d  | | |  | | | t | |  |  t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3572  s    c            s     j  d  t t d  | t d  |  t t t d  | | | | t d  |  | t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3573  s    c            s     j  d  t t d  | t d  |  t t t d  | | | | t d  |  | t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3574  s    c            s     j  d  t t d  |  t t | | | | t d  | t d  | t d  |  | t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3575  s    c            s     j  d  t t d  |  t t | | | | t d  | t d  | t d  |  | t | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3576	  s    c            s     j  d  t t d  | t d  |  t t t d  t d  | | t d  t d  | | | | t d  |  | t d  | | | | | | t | |  |  t | | t | |  |    |  S(   Ni  i   i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3577  s    c            s     j  d  t t d  | t d  |  t t t d  t d  | | t d  t d  | | | | t d  |  | t d  | | | | | | t | |  |  t | | t | |  |    |  S(   Ni  i   i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3578  s    c            sS  t  | t d  | t d  t d   }   j d  t t d  t d  | t | | | | | | | | | | | | t | |  |  t | | t | |  |   |  |  t t d  t d  | t | | | | | | | | | | | | t | |  |  t | | t | |  |   |  |  S(   Ni   i  i   (   R  R  R  R  R   R  R  (   R  R  R  R  R  R  R  t   q(   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3579  s    -c            sS  t  | t d  | t d  t d   }   j d  t t d  t d  | t | | | | | | | | | | | | t | |  |  t | | t | |  |   |  |  t t d  t d  | t | | | | | | | | | | | | t | |  |  t | | t | |  |   |  |  S(   Ni   i  i   (   R  R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3580  s    -c      
      sr     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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3581$  s    c      
      ss     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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3582)  s    c      	      sy     j  d  t | t | t | | |  |  |  |  t | | t | t | | |  |  t d  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3583.  s    c      	      sy     j  d  t | t | t | | |  |  |  |  t | | t | t | | |  |  t d  |  |  S(   Ni   i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement35843  s    c      
      s     j  d  t | t d  t | t d  t | | t | | |  |  t t | | |  t d  |  |  t | t d  t | t d  t | | t | | |  |  t t | | |  t d  |  |  S(   Ni  i   i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement35858  s    c            s     j  d  t | t d  t | t d  t t d  t t | | |  | | t | | |  |  |  |  t | t d  t | t d  t t d  t t | | |  | | t | | |  |  |  |  S(   Ni  i   i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3586=  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 | | |  |  |  |  t | | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3587B  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 | | |  |  |  |  t | | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3588G  s    c      
      s     j  d  t | | | | t d  | t d  t t d  | | t | |  |  |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3589L  s    c      
      s     j  d  t | | | | t d  | t d  t t d  | | t | |  |  |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3590Q  s    c            sz    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 | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3591V  s    c            sz    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 | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3592[  s    c      	      s     j  d  t | | t | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3593`  s    c      	      s     j  d  t | | t | | |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3594e  s    c            s     j  d  t t d  | | |  t t t d  t d  | t d  | t d  | | | | |  | t | | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3595j  s    c            s     j  d  t t d  | | |  t t t d  t d  | t d  | t d  | | | | |  | t | | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3596o  s    c	   	   
      s    j  d  t t d  | t d  | | | | t | | t | | |  |  t d  | | t | | |  | t d  |  |  t | | | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3597t  s    c	   	   
      s    j  d  t t d  | t d  | | | | t | | t | | |  |  t d  | | t | | |  | t d  |  |  t | | | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3598y  s    c	   	   
      s     j  d  t | | | | t d  | t d  t | | t | | |  |  t d  | | t | | |  | t d  |  |  t | | | t | | |  |  | | t | | |  | t d  | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3599~  s    c	   	   
      s     j  d  t | | | | t d  | t d  t | | t | | |  |  t d  | | t | | |  | t d  |  |  t | | | t | | |  |  | | t | | |  | t d  | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3600  s    c	   	   
      s     j  d  t t d  t d  | t | | t | | |  |  t d  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3601  s    c	   	   
      s     j  d  t t d  t d  | t | | t | | |  |  t d  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3602  s    c	   	   
      s     j  d  t | | | | | t | | t | | |  |  | | t | | |  | 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  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3603  s    c	   	   
      s     j  d  t | | | | | t | | t | | |  |  | | t | | |  | 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  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3604  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 | |  |  | | | | | t d  |  | | t | |  |  | | | | |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3605  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 | |  |  | | | | | t d  |  | | t | |  |  | | | | |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3606  s    c            sY    j  d  t t d  t d  | t d  t | | t | |  |  | t d  t | | t d  | | t d  | t d  | | | | | | | | t d  | | | t | |  |  |  |  |  t | | t | |  |  | t d  | | | | t d  | |  | | t | |  |  |  S(   Ni  i   i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3607  s    c            sY    j  d  t t d  t d  | t d  t | | t | |  |  | t d  t | | t d  | | t d  | t d  | | | | | | | | t d  | | | t | |  |  |  |  |  t | | t | |  |  | t d  | | | | t d  | |  | | t | |  |  |  S(   Ni  i   i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3608  s    c            s     j  d  t | | | | | t t d  | | t | |  |  |  |  t | | | | | t t d  | | t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3609  s    c            s     j  d  t | | | | | t t d  | | t | |  |  |  |  t | | | | | t t d  | | t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3610  s    c            s    j  d  t t d  t d  | | | | | t | | t | |  |  | t | | | t d  | | | | | t | |  |  |  |  |  t | | | t | |  |  | t d  t d  |  | | t | |  |  | | | | |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3611  s    c            s    j  d  t t d  t d  | | | | | t | | t | |  |  | t | | | t d  | | | | | t | |  |  |  |  |  t | | | t | |  |  | t d  t d  |  | | t | |  |  | | | | |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3612  s    c	   	         s    j  d  t | | | t d  | | | | t | | t | | |  |  t d  | | t | | |  | t d  t | | | |  t d  | t d  | | |  t d  | t d  | |  | t d  | | | |  t d  | t d  | | t d  t | | |  |  |  |  t | t d  | | t | | |  |  t d  | | t | | |  | t d  | | | | | | | t d  | | | | |  S(   Ni  i   ii   ii(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3613  s    c	   	         s    j  d  t | | | t d  | | | | t | | t | | |  |  t d  | | t | | |  | t d  t | | | |  t d  | t d  | | |  t d  | t d  | |  | t d  | | | |  t d  | t d  | | t d  t | | |  |  |  |  t | t d  | | t | | |  |  t d  | | t | | |  | t d  | | | | | | | t d  | | | | |  S(   Ni  i   ii   ii(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3614  s    c            s!    j  d  t t d  | t d  | | | | t t | | t | |  |   |  |  t | | t d  | t d  t d  | | | | | t d  | t d  t | | t | |  |  t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3615  s    c            s!    j  d  t t d  | t d  | | | | t t | | t | |  |   |  |  t | | t d  | t d  t d  | | | | | t d  | t d  t | | t | |  |  t | | t | |  |   | | t | |  |  |  |  S(   Ni   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3616  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t | | t | |  |   | t | |  |  | t | | t | |  |   |  |  S(   Ni!  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3617  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t | | t | |  |   | t | |  |  | t | | t | |  |   |  |  S(   Ni"  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3618  s    c	   	         s    j  d  t | | |  | t d  t | | t | | |  |  t d  | | t | | |  | t | | |  t d  | | | |  t d  | | |  t d  | | t d  |  t d  | t d  t | | |  |  |  |  t | t d  | | t | | |  |  t d  | | t | | |  | t d  | | |  | t d  |  S(   Ni#  iii   i   ii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3619  s    c	   	         s    j  d  t | | |  | t d  t | | t | | |  |  t d  | | t | | |  | t | | |  t d  | | | |  t d  | | |  t d  | | t d  |  t d  | t d  t | | |  |  |  |  t | t d  | | t | | |  |  t d  | | t | | |  | t d  | | |  | t d  |  S(   Ni$  iii   i   ii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3620  s    c            sF    j  d  t t d  t d  | t d  |  t | | t | | |  |  t d  t t d  | | |  | | t d  |  t d  t | | |  | | |  t | | t | | |   |  |  t | | | t | | |  |  t | | t | | |   t d  | | |  |  S(   Ni%  i   i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3621  s    c            sF    j  d  t t d  t d  | t d  |  t | | t | | |  |  t d  t t d  | | |  | | t d  |  t d  t | | |  | | |  t | | t | | |   |  |  t | | | t | | |  |  t | | t | | |   t d  | | |  |  S(   Ni&  i   i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3622  s    c	   	         s    j  d  t t d  t d  | t d  |  t | | t | | |  |  t d  | | t | | |  | t d  t | | | |  | | | t d  | | | |  | t d  | | |  | t d  t | | |  | | | | t d  | | |  |  |  |  t | | t | | |  |  | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3623  s    c	   	         s    j  d  t t d  t d  | t d  |  t | | t | | |  |  t d  | | t | | |  | t d  t | | | |  | | | t d  | | | |  | t d  | | |  | t d  t | | |  | | | | t d  | | |  |  |  |  t | | t | | |  |  | | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3624  s    c	   	         sm    j  d  t t d  t d  | |  | | | | t | | t | | |  |  t d  | | t | | |  | t | | t d  |  | t d  | | |  | | |  | t d  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3625   s    c	   	         sm    j  d  t t d  t d  | |  | | | | t | | t | | |  |  t d  | | t | | |  | t | | t d  |  | t d  | | |  | | |  | t d  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3626  s    c	   	         s    j  d  t t d  | |  | t d  t | | t | | |  |  | | t | | |  | t d  t | | t d  |  | t d  | | | |  t d  | t d  | | |  t | | |  | | | | t d  | | |  |  |  |  t | | | t | | |  |  | | t | | |  | t d  | |  | t d  |  S(   Ni+  i   iii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3627
  s    c	   	         s    j  d  t t d  | |  | t d  t | | t | | |  |  | | t | | |  | t d  t | | t d  |  | t d  | | | |  t d  | t d  | | |  t | | |  | | | | t d  | | |  |  |  |  t | | | t | | |  |  | | t | | |  | t d  | |  | t d  |  S(   Ni,  i   iii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3628  s    c	   	         sv    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  |  | | t | | |  | t d  t | | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3629  s    c	   	         sv    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  |  | | t | | |  | t d  t | | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3630  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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3631  s    c            s     j  d  t | | | | | t | | t | | |  |  |  |  t | | | | | t | | t | | |  |  | t | | |  | | | t | | |  |  |  S(   Ni0  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3632#  s    c            s     j  d  t | | t t | | t | |  |   | t | |  |  | t | | t | |  |   |  |  t | | | | | t t | | t | |  |   t | | t | |  |   |  |  S(   Ni1  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3633(  s    c            s     j  d  t | | t t | | t | |  |   | t | |  |  | t | | t | |  |   |  |  t | | | | | t t | | t | |  |   t | | t | |  |   |  |  S(   Ni2  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3634-  s    c	   	   
      s     j  d  t | | | t t | | |  t d  | | | | | | | | t d  |  | | t | | |   |  S(   Ni3  ii   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement36352  s    c	   	   
      s     j  d  t | | | t t | | |  t d  | | | | | | | | t d  |  | | t | | |   |  S(   Ni4  ii   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement36367  s    c	   	         s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  |  t d  | | t | | |  | t d  t | t d  | | | | t d  | | |  t d  | t d  | | | | | | | t d  | | |  t d  | | | | | t d  | | |  | t d  | t d  | t d  |  t d  | t d  | t d  t | | |  t d  | | t d  | t d  | t d  | t d  | | t d  | | t d  | | t d  | t | | |  |  |  |  t | | t | | |  |  t d  | | t | | |  | t d  | | | | t d  | | | t d  | t d  | t d  |  S(   Ni5  i   i   iiii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3637<  s    c	   	         s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  |  t d  | | t | | |  | t d  t | t d  | | | | t d  | | |  t d  | t d  | | | | | | | t d  | | |  t d  | | | | | t d  | | |  | t d  | t d  | t d  |  t d  | t d  | t d  t | | |  t d  | | t d  | t d  | t d  | t d  | | t d  | | t d  | | t d  | t | | |  |  |  |  t | | t | | |  |  t d  | | t | | |  | t d  | | | | t d  | | | t d  | t d  | t d  |  S(   Ni6  i   i   iiii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3638A  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 d  | t d  | | t d  |  t d  | t d  | | |  t d  t | | |  t d  | | t d  | t d  | t d  |  | t d  t | | |  |  |  |  t | t d  | | t | | |  |  t d  | | t | | |  | t d  | | |  | t d  |  S(	   Ni7  i   iii   i   ii(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3639F  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 d  | t d  | | t d  |  t d  | t d  | | |  t d  t | | |  t d  | | t d  | t d  | t d  |  | t d  t | | |  |  |  |  t | t d  | | t | | |  |  t d  | | t | | |  | t d  | | |  | t d  |  S(	   Ni8  i   iii   i   ii(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3640K  s    c	   	         s5    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | t d  |  t d  | | t d  | t d  | | | |  | t d  | |  | | | | | t | | |  t d  |  t d  t d  | | | | | t d  | | t d  t | | |  |  |  |  t | | t | | |  |  t d  | | t | | |  | t d  | | | | | | t d  | t d  |  t d  |  S(   Ni9  i   i   ii(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3641P  s    c	   	         s5    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | t d  |  t d  | | t d  | t d  | | | |  | t d  | |  | | | | | t | | |  t d  |  t d  t d  | | | | | t d  | | t d  t | | |  |  |  |  t | | t | | |  |  t d  | | t | | |  | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3642U  s    c	   	         s    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | |  t d  | | | | | |  | t d  t | | |  t d  |  t d  | | | | t | | |  |  |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3643Z  s    c	   	         s    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | |  t d  | | | | | |  | t d  t | | |  t d  |  t d  | | | | t | | |  |  |  |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3644_  s    c	   	         s    j  d  t t d  | t d  | t d  |  t d  | | | | t | | t | | |  |  t d  | | t | | |  | t | |  t d  | | | | | t d  | |  | t d  t | | |  t d  | t d  | |  | t d  | |  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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3645d  s    c	   	         s    j  d  t t d  | t d  | t d  |  t d  | | | | t | | t | | |  |  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 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3646i  s    c	   	         s    j  d  t t d  |  | t d  t | | t | | |  |  t d  | | t | | |  | t d  t | t d  | |  | t d  | | | | | | |  t d  | | | t d  |  | t d  | | | t | | |  t d  |  | t d  | t d  | t d  | | | | t d  | t | | |  |  |  |  t | | | t | | |  |  t d  | | t | | |  | | |  | t d  |  S(   Ni?  i   iii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3647n  s    c	   	         s    j  d  t t d  |  | t d  t | | t | | |  |  t d  | | t | | |  | t d  t | t d  | |  | t d  | | | | | | |  t d  | | | t d  |  | t d  | | | t | | |  t d  |  | t d  | t d  | t d  | | | | t d  | t | | |  |  |  |  t | | | t | | |  |  t d  | | t | | |  | | |  | t d  |  S(   Ni@  i   iii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3648s  s    c            sd    j  d  t | t d  | t d  | t d  | | | | t | t | |  |  | | | t | |  |  |  |  t | t d  | t d  | t d  | | | | t | t | |  |  | | | t | |  |  |  |  t | | | | | | t d  | t d  | t d  | t d  |  S(   NiA  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3649x  s    c            sd    j  d  t | t d  | t d  | t d  | | | | t | t | |  |  | | | t | |  |  |  |  t | t d  | t d  | t d  | | | | t | t | |  |  | | | t | |  |  |  |  t | | | | | | t d  | t d  | t d  | t d  |  S(   NiB  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3650}  s    c            sC    j  d  t | | | | | | t d  | t d  t t | |  |  t d  t d  t | | t | |  |   | | t | |  |  |  |  t t d  | t d  | t d  t t | | | | | | | | t | |  |  |  t | | t | |  |   |  |  S(   NiC  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3651  s    c            sC    j  d  t | | | | | | t d  | t d  t t d  t | |  |  t d  t | | t | |  |   | | t | |  |  |  |  t t d  | t d  | t d  t t | | | | | | | | t | |  |  |  t | | t | |  |   |  |  S(   NiD  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3652  s    c            s    j  d  t | | | | t d  | t d  | t d  t t | |  |  t d  t d  t | | t | |  |   | | t | |  |  |  |  t t d  | t d  | t d  t t | t d  | t d  | | | | t d  | | t d  | t d  | | | | t d  | t | |  |  |  t | | t | |  |   |  |  S(   NiE  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3653  s    c            s    j  d  t | | | | t d  | t d  | t d  t t d  t | |  |  t d  t | | t | |  |   | | t | |  |  |  |  t t d  | t d  | t d  t t | t d  | t d  | | | | t d  | | t d  | t d  | | | | t d  | t | |  |  |  t | | t | |  |   |  |  S(   NiF  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3654  s    c            s    j  d  t | t d  | t d  | t d  t | | t | | |  |  t | | |  t d  t d  | | t | | |  |  |  t t d  | t d  | t d  t | | t | | |  |  | | t | | |  |  |  S(   NiG  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3655  s    c            s    j  d  t | t d  | t d  | t d  t t d  t | | |  t d  | | t | | |  |  | | t | | |  |  |  t t d  | t d  | t d  t | | t | | |  |  | | t | | |  |  |  S(   NiH  i   i   i(   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3656  s    c	   	   
      s     j  d  t | | t t | | |  | | | | | | t d  | t d  |  | | t | | |   |  S(   NiI  i   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3657  s    c	   	   
      s     j  d  t | | t t | | |  | | | | | | t d  | t d  |  | | t | | |   |  S(   NiJ  i   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3658  s    c      	      sc     j  d  t | |  t | t | | |  |  | | t | | |  | |  |  |  S(   NiK  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3659  s    c      	      sc     j  d  t | |  t | t | | |  |  | | t | | |  | |  |  |  S(   NiL  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3660  s    c
   
   
      s     j  d  t | t |  | | t |	 | |  |  t |  | t |	 | |  |  t |  t | t |	 | |  | |  | | t |	 | |  | |  |  S(   NiM  (   R  R  R$   R  R%   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3661  s    c
   
   
      s     j  d  t | t |  | | t |	 | |  |  t |  | t |	 | |  |  t |  t | t |	 | |  | |  | | t |	 | |  | |  |  S(   NiN  (   R  R  R$   R  R%   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3662  s    t   gc            sl     j  d  t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | |	  S(   NiO  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3663  s    c            sl     j  d  t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | |	  S(   NiP  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3664  s    c      	      s     j  d  t | | | t | t |
 | |	  | | |  | t |
 | |	  | | | t |
 | |	  | | |	  |	  S(   NiQ  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3665  s    c      	      s     j  d  t | | | t | t |
 | |	  | | |  | t |
 | |	  | | | t |
 | |	  | | |	  |	  S(   NiR  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3666  s    c      
      s     j  d  t | t | | |	  |  |
 | t | | |	  |
 |  t | t | | |	  |  |
 | | t | | |	  | | | t | | |	  | |	  |	  S(   NiS  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3667  s    c      
      s     j  d  t | t d  t | | |	  |
 |  | t | | |	  |  |
 t | t | | |	  |  |
 | | t | | |	  | | | t | | |	  | |	  |	  S(   NiT  i   (   R  R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3668  s    c      
      s     j  d  t | | t | t |
 | |	  | |  | | t |
 | |	  | | t |
 | |	  | | |	  |	  S(   NiU  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3669  s    c      
      s     j  d  t | | t | t |
 | |	  | |  | | t |
 | |	  | | t |
 | |	  | | |	  |	  S(   NiV  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3670  s    c
   
         sw     j  d  t | | t |	 | |  | | t |	 | |  | | t d  t |	 | |  | |  |  S(   NiW  i   (   R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3671  s    c
   
         sm     j  d  t | | t |	 | |  | | t |	 | |  | | t |	 | |  | |  |  S(   NiX  (   R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3672  s    c      	      s     j  d  t | t |
 | |	  |  t d  t |
 | |	  |  t | | t |
 | |	  | | t |
 | |	  | | t d  t |
 | |	  | |  |	  |	  S(   NiY  i   (   R  R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3673  s    c      	      s     j  d  t | t |
 | |	  |  t |
 | |	  |  t | | t |
 | |	  | | t |
 | |	  | | t |
 | |	  | |  |	  |	  S(   NiZ  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3674  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  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3675  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  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3676  s    t   At   Bc      	      s     j  d  t | | | t t |
 |  |	 | | |	 | t d  | | |	 | t d  |	  |	 t | | |	   |	  S(   Ni]  i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3677  s    c      
      s     j  d  t | | | t t | |  |	 | | |	 | t d  | | |	 | t d  |	  |	 t d  t |
 | |	   |	  S(   Ni^  ii   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3678	  s    c	   	   
      s     j  d  t t d  | t t | | | | | | |  | | | | t | | |  |  | | t | | |  |  |  t |  | | t t | | |  |  |  S(   Ni_  i   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3679  s    c	   	   
      s     j  d  t t d  | t t | | | | | | |  | | | | t | | |  |  | | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3680  s    c
   
         s*    j  d  t t d  t d  | | t | | t | | |  | t d  t |	 | | |	 | | |  | | t d  |  | | t | | |  |  | | |  |  |  t | | t | | |  | |	 | |  | | | | | t d  | t d  | | |  S(   Nia  i   i   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3681  s    c
   
         s*    j  d  t t d  t d  | | t | | t |	 | |  | t d  t | | | | | | |  | | t d  |  | | t |	 | |  |  | | |  |  |  t | | t |	 | |  | | | |  | | | | | t d  | t d  | | |  S(   Nib  i   i   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3682  s    c
   
         sl    j  d  t t d  | t d  | t d  t | | t | | |  | t d  t |	 | | |	 | | |  | | |  | | |	 | | |	 | | |  | | |  | | t | | |  |  |  |  t | | t | | |  | t d  |	 | |  | | | | | | | | t d  | t d  | t d  |  S(   Nic  i   i   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3683"  s    c
   
         sl    j  d  t t d  | t d  | t d  t | | t | | |  | t d  t |	 | | |	 | | |  | | |  | | |	 | | |	 | | |  | | |  | | t | | |  |  |  |  t | | t | | |  | t d  |	 | |  | | | | | | | | t d  | t d  | t d  |  S(   Nid  i   i   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3684'  s    c
   
   	      s     j  d  t | | t |	 | |  | t | | |  | | | |  | t |	 | |  |  |  t |  | | | t |	 | |  | t d  | | | t d  |  S(   Nie  i   (   R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3685,  s    c
   
   	      s     j  d  t | | t |	 | |  | t | | |  | | | |  | t |	 | |  |  |  t |  | | | t |	 | |  | t d  | | | t d  |  S(   Nif  i   (   R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement36861  s    c            s    j  d  t | | | t d  | | | | t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | t d  |  | | | t d  | | | t d  |
 | | | | |  | | | t d  | | | t d  t | | |	  |	  |	  |	  t | t d  | | t | | |	  | t d  | | t | | |	  | t d  |
 | |  | | | | t d  | | | | |	  S(   Nig  i   iii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement36876  s    c            s    j  d  t | | | t d  | | | | t | | t |
 | |	  | t d  | | t |
 | |	  | t d  t | | | | | t d  |  | | | t d  | | | t d  | | | | | |  | | | t d  | | | t d  t |
 | |	  |	  |	  |	  t | t d  | | t |
 | |	  | t d  | | t |
 | |	  | t d  | | |  | | | | t d  | | | | |	  S(   Nih  i   iii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3688;  s    c            s    j  d  t t d  | | | t | | t | | |	  | t d  | | t | | |	  | t |
 | | | | |  | | | t d  | | | t d  |  | t d  | | | | | | | |
 | |  | t | | |	  |	  |	  |	  t |  | | | t | | |	  | t d  | | t | | |	  | t d  | | | | |	  S(   Nii  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3689@  s    c            s    j  d  t t d  | | | t | | t |
 | |	  | t d  | | t |
 | |	  | t | | | | | |  | | | t d  | | | t d  |  | t d  | | | | | | | | | |  | t |
 | |	  |	  |	  |	  t |  | | | t |
 | |	  | t d  | | t |
 | |	  | t d  | | | | |	  S(   Nij  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3690E  s    c            sw    j  d  t t d  t d  | t d  | t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | | | |  | | | | | | | |
 | | | |  | | | t | | |	  |	  |	  |	  t | | t | | |	  | | | t | | |	  | |
 | |  | t d  | | | |	  S(   Nik  i   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3691J  s    c            sw    j  d  t t d  t d  | t d  | t | | t |
 | |	  | t d  | | t |
 | |	  | t d  t | | | | | | | |  | | | | | | | | | | | |  | | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | | | |  | t d  | | | |	  S(   Nil  i   i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3692O  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 | | |	  | t d  |
 | |  | t d  | | | | | | |	  S(   Nim  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3693T  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 |
 | |	  | t d  | | |  | t d  | | | | | | |	  S(   Nin  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3694Y  s    c            sK    j  d  t t d  | | | t | | t | | |	  | | | t | | |	  | t d  t |
 | | | | |  | | | | | | |
 | | | | |  | | | | | | t | | |	  |	  |	  |	  t |  | | t | | |	  | | | t | | |	  | | | | |	  S(   Nio  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3695^  s    c            sK    j  d  t t d  | | | t | | t |
 | |	  | | | t |
 | |	  | t d  t | | | | | |  | | | | | | | | | | | |  | | | | | | t |
 | |	  |	  |	  |	  t |  | | t |
 | |	  | | | t |
 | |	  | | | | |	  S(   Nip  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3696c  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |	  | | | t | | |	  | t d  t |
 | | | t d  | | | |  | | | t d  | | | | |
 | |  | | | t d  t | | |	  |	  |	  |	  t | | t | | |	  | | | t | | |	  | t d  |
 | |  | | | t d  | t d  | t d  |	  S(   Niq  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3697h  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t |
 | |	  | | | t |
 | |	  | t d  t | | | | t d  | | | |  | | | t d  | | | | | | |  | | | t d  t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | t d  | | |  | | | t d  | t d  | t d  |	  S(   Nir  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3698m  s    c      	      sn     j  d  t |  | | t t | | |	 | t d  | | |	 | |	  |	 t | | |	   |	  S(   Nis  i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3699r  s    c      
      sy     j  d  t |  | | t t | | |	 | t d  | | |	 | |	  |	 t d  t |
 | |	   |	  S(   Nit  ii   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3700w  s    c
   
         s     j  d  t |	 | |  | | | | | t | | t | | |  | |  |  t |	 | |  | | | | | t | | t | | |  | | t | | |  | | | t | | |  |  |  S(   Niu  (   R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3701|  s    c
   
         s     j  d  t | | |  | | | | | t | | t |	 | |  | |  |  t | | |  | | | | | t | | t |	 | |  | | t |	 | |  | | | t |	 | |  |  |  S(   Niv  (   R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3702  s    c            s     j  d  t |  | t | | t | | |	  | | t | | |	  | | | t | | |	  | |	  |	  t |
 | |  | | t | | t | | |	  | | | t | | |	  | |	  |	  S(   Niw  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3703  s    c            s     j  d  t |  | t | | t |
 | |	  | | t |
 | |	  | | | t |
 | |	  | |	  |	  t | | |  | | t | | t |
 | |	  | | | t |
 | |	  | |	  |	  S(   Nix  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3704  s    c      	      sv     j  d  t | t d  | t t | | |	 | | | |	 | | |  |	 |	  |	 t |
 | |	   |	  S(   Niy  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3705  s    c      
      s     j  d  t | t d  | t t | | |	 | | | |	 | | |  |	 |	  |	 t d  t |
 | |	   |	  S(   Niz  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3706  s    c            s(    j  d  t |
 t d  t |  t d  t | | t | | |	  | | | t | | |	  | t t | | |	  t d  |	  |	  t |
 t d  t |  t d  t | | t | | |	  | | | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3707  s    c            s'    j  d  t |
 t d  t |  t d  t t d  t t | | |	  | | t | | |	  | | | t | | |	  | |	  |	  t |
 t d  t |  t d  t t d  t t | | |	  | | t | | |	  | | | t | | |	  | |	  |	  S(   Ni|  i   i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3708  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | | t d  | | | t d  | |  | | t d  | t d  | t d  | t d  | | | |
 | | |
 | | |  | | t | | |	  t d  | | t d  |
 | |  | | | | | |
 | |  | | | | | t | | |	  |  | | | |
 | |  | | | | t d  | | | t d  |	  |	  |	  t | | t | | |	  | t d  | | t | | |	  | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3709  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | | t d  | | | t d  | |  | | t d  | t d  | t d  | t d  | | | |
 | | |
 | | |  | | t | | |	  t d  | | t d  |
 | |  | | | | | |
 | |  | | | | | t | | |	  |  | | | |
 | |  | | | | t d  | | | t d  |	  |	  |	  t | | t | | |	  | t d  | | t | | |	  | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3710  s    c            s    j  d  t t d  | | | t | | t | | |	  | t d  | | t | | |	  | t |
 | t d  | | | |  | | | | t d  | | | t d  | | | t d  |
 | | |  | t d  | t d  t | | |	  |  | | t d  | | | | | | | | |
 | |  | t | | |	  t d  |	  |	  |	  t |  | | | t | | |	  | t d  | | t | | |	  | t d  | | | | |	  S(   Ni  i   ii   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3711  s    c            s    j  d  t t d  | | | t | | t | | |	  | t d  | | t | | |	  | t |
 | t d  | | | |  | | | | t d  | | | t d  | | | t d  |
 | | |  | t d  | t d  t | | |	  |  | | t d  | | | | | | | | |
 | |  | t | | |	  t d  |	  |	  |	  t |  | | | t | | |	  | t d  | | t | | |	  | t d  | | | | |	  S(   Ni  i   ii   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3712  s    c            s#    j  d  t t d  | | t d  | t d  | t d  t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | t d  | | | |  | | | | | | | t d  | | |
 | |  | | | t d  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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3713  s    c            s#    j  d  t t d  | | t d  | t d  | t d  t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | t d  | | | |  | | | | | | | t d  | | |
 | |  | | | t d  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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3714  s    c            sd    j  d  t t d  | t d  | t d  | t d  | | | | t | | t | | |	  | t d  | | t | | |	  | t |
 | | t d  | | | | | t d  | | | t d  |  | | | | t d  | | | t d  | | |
 | |  | | | t d  t | | |	  t d  | t d  |
 | |  | | | | | t | | |	  |	  |	  |	  t | | | 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  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3715  s    c            sd    j  d  t t d  | t d  | t d  | t d  | | | | t | | t | | |	  | t d  | | t | | |	  | t |
 | | t d  | | | | | t d  | | | t d  |  | | | | t d  | | | t d  | | |
 | |  | | | t d  t | | |	  t d  | t d  |
 | |  | | | | | t | | |	  |	  |	  |	  t | | | 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  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3716  s    c            s    j  d  t t d  | | t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | |  | | | | | | | | |
 | | |
 | | |  | | |  | | t | | |	  |
 | | | | |  | | | | | | t | | |	  t d  |	  |	  |	  t |  | | t | | |	  | | | t | | |	  | | | | |	  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3717  s    c            s    j  d  t t d  | | t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | |  | | | | | | | | |
 | | |
 | | |  | | |  | | t | | |	  |
 | | | | |  | | | | | | t | | |	  t d  |	  |	  |	  t |  | | t | | |	  | | | t | | |	  | | | | |	  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3718  s    c	   	         s    j  d  t | | | |  | | t d  | t d  | | | | t | t | | |  | | | t | | |  |  |  t | | | |  | | t d  | t d  | | | | t | t | | |  | | | t | | |  |  |  t | | | | | | |  | | | | | t d  | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3719  s    c	   	         s    j  d  t | | | |  | | t d  | t d  | | | | t | t | | |  | | | t | | |  |  |  t | | | |  | | t d  | t d  | | | | t | t | | |  | | | t | | |  |  |  t | | | | | | |  | | | | | t d  | 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3720  s    c	   	         s    j  d  t | | |  | | | | | | t d  | t d  t t | | |  t d  t d  | | t | | |  t | | t | | |   |  |  t t d  | t d  | t d  t t | | | | | |  | | | | | | | | | |  | | | | t | | |  |  t | | t | | |   |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3721  s    c	   	         s    j  d  t | | |  | | | | | | t d  | t d  t t d  t | | |  t d  | | t | | |  t | | t | | |   |  |  t t d  | t d  | t d  t t | | | | | |  | | | | | | | | | |  | | | | t | | |  |  t | | t | | |   |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3722  s    c
   
         s<    j  d  t | |	 | |  | | t d  | t d  t | | t | | |  | t | | |  t d  t d  | | t | | |  |  |  t t d  | t d  | t d  t | | t | | |  | t |	 | |  | |	 | |  | t | | |  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3723  s    c
   
         s<    j  d  t | |	 | |  | | t d  | t d  t t d  t | | |  t d  | | t | | |  | | | t | | |  |  |  t t d  | t d  | t d  t | | t | | |  | t |	 | |  | |	 | |  | t | | |  |  |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3724  s    c	   	         s    j  d  t |  | t t | | |  t d  t d  t | | t | | |   t | | t | | |   |  |  t t | | |  | | | |  | t | | |  |  t | | t | | |   t | | t | | |   |  S(   Ni  i   i   (   R  R  R   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3725  s    c	   	         s    j  d  t |  | t t d  t | | |  t d  t | | t | | |   t | | t | | |   |  |  t t | | |  | | | |  | t | | |  |  t | | t | | |   t | | t | | |   |  S(   Ni  i   i(   R  R  R   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3726  s    c      	      sv     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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3727  s    c      
      s     j  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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3728  s    c            s(    j  d  t |
 t d  t |  t d  t | | t | | |	  | | | t | | |	  | t t | | |	  t d  |	  |	  t |
 t d  t |  t d  t | | t | | |	  | | | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3729  s    c            s'    j  d  t |
 t d  t |  t d  t t d  t t | | |	  | | t | | |	  | | | t | | |	  | |	  |	  t |
 t d  t |  t d  t t d  t t | | |	  | | t | | |	  | | | t | | |	  | |	  |	  S(   Ni  i   i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3730  s    t   Cc      
      sT     j  d  t | | | t t | | | |  | | t | | |   |  S(   Ni  (   R  R  R*   R   R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3731  s    c      
      sU     j  d  t | | | t t | | | |  | | t | | |   |  S(   Ni  (   R  R  R*   R   R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3732  s    c	   	         s     j  d  t | t d  t | | t | | |  | t d  t |  | | | | | t | | |  |  |  |  S(   Ni  ii   (   R  R  R  R   R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3733  s    c	   	         s     j  d  t | t d  t | | t | | |  | t d  t |  | | | | | t | | |  |  |  |  S(   Ni  ii   (   R  R  R  R   R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3734!  s    c      
      ss     j  d  t |  | t d  t | | t | | |  | | t | | |  | t d  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3735&  s    c      
      ss     j  d  t |  | t d  t | | t | | |  | | t | | |  | t d  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3736+  s    c	   	         sR    j  d  t t d  t d  | t d  | t | | t | | |  | t d  t | | t d  | t d  |  | | | | | | t d  | t d  | | |  | t | | |  |  |  |  t | | t | | |  | | | |  | | | t | | |  t d  | | | |  S(   Ni  i   i   i(   R  R  R  R   R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement37370  s    c	   	         sR    j  d  t t d  t d  | t d  | t | | t | | |  | t d  t | | t d  | t d  |  | | | | | | t d  | t d  | | |  | t | | |  |  |  |  t | | t | | |  | | | |  | | | t d  | | | t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement37385  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 | | |  |  |  |  t | | t | | |  | | | |  | t | | |  t d  | | | |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3739:  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 | | |  |  |  |  t | | t | | |  | | | |  | t d  | | | t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3740?  s    c      
      s     j  d  t | | t d  |  | | | | t d  | t d  | 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  R2  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3741D  s    c      
      s     j  d  t | | t d  |  | | | | t d  | t d  | t d  t t d  t | | |  t d  | | t | | |  |  |  t | | | |  | | | | t d  | t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3742I  s    c            sv     j  d  t | t t d  t | | |  |  |  t | t t | | |  |  |  t |  | |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R2  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3743N  s    c      	      sv     j  d  t | t t | | |  |  |  t | t t d  t | | |  |  |  t |  | |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R2  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3744S  s    c            se     j  d  t | t t d  t | | |  |  |  t |  t t | | |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R2  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3745X  s    c      	      se     j  d  t | t t | | |  |  |  t |  t t d  t | | |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R2  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3746]  s    c            sC    j  d  t | | |  | | | | t d  | t d  t t | | |  |  |  t | | t d  |  | | | | t d  | t d  | 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  R2  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3747b  s    c            sM    j  d  t | | |  | | | | t d  | t d  t t d  t | | |  |  |  t | | t d  |  | | | | t d  | t d  | t d  t t d  t | | |  t d  | | t | | |  |  |  t | | | |  | | | | t d  | t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3748g  s    c      
      s    j  d  t | | t d  |  | t d  | t d  | t d  t t | | |  t d  t d  | | t | | |  |  |  t | | |  | t d  | t d  t t | | |  |  |  t | | | |  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3749l  s    c      
      s(    j  d  t | | t d  |  | t d  | t d  | t d  t t d  t | | |  t d  | | t | | |  |  |  t | | |  | t d  | t d  t t d  t | | |  |  |  t | | | |  | t d  | t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3750q  s    c	   	         sF    j  d  t t d  | t d  | t d  t | | t | | |  | t d  t |  | | | | | | |  | | | t | | |  |  |  |  t | | t | | |  | t d  | | t d  |  | | | | t d  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3751v  s    c	   	         sF    j  d  t t d  | t d  | t d  t | | t | | |  | t d  t |  | | | | | | |  | | | t | | |  |  |  |  t | | t | | |  | t d  | | t d  |  | | | | t d  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3752{  s    c            s*    j  d  t t d  | t d  | t d  t | | t | | |  | t d  t | | |  | | |  | t | | |  |  |  |  t | | t | | |  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3753  s    c            s*    j  d  t t d  | t d  | t d  t | | t | | |  | t d  t | | |  | | |  | t | | |  |  |  |  t | | t | | |  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3754  s    c	   	   	      s     j  d  t | | t | | |  | t | |  t | | |  | |  |  t | | | t | | |  | t d  | | | t d  |  S(   Ni  i   (   R  R   R  R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3755  s    c	   	   	      s     j  d  t | | t | | |  | t | |  t | | |  | |  |  t | | | t | | |  | t d  | | | t d  |  S(   Ni  i   (   R  R   R  R  R  (	   R  R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3756  s    c      	      s     j  d  t | |  t | | t | | |  | |  |  t |  | | t | | |  | t d  | | | t d  |  S(   Ni  i   (   R  R  R   R  R  R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3757  s    c      	      s     j  d  t | |  t | | t | | |  | |  |  t |  | | t | | |  | t d  | | | t d  |  S(   Ni  i   (   R  R  R   R  R  R  (   R2  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3758  s    c      	      s`     j  d  t | | t t | | |	 | | | |	 | |	  |	 t |
 | |	   |	  S(   Ni  (   R  R  R*   R   R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3759  s    c      
      sk     j  d  t | | t t | | |	 | | | |	 | |	  |	 t d  t |
 | |	   |	  S(   Ni  i   (   R  R  R*   R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3760  s    c            s    j  d  t t d  | | t d  | t d  t | | t |
 | |	  | t d  t | | | t d  | t d  t |
 | |	  t d  | | | | |  | | | | | | t d  |  | | | | t d  | | | | | | | |  | | |  | | | | | | | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | t d  | | | | | | t d  |  | | | | t d  | t d  | | t d  | t d  | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3761  s    c            s    j  d  t t d  | | t d  | t d  t | | t | | |	  | t d  t | | | t d  | t d  t | | |	  t d  | | |
 | |  | | | | |
 | t d  |  | | | | t d  | |
 | | |
 | | |  | | |  | | | | | | | | t | | |	  |	  |	  |	  t | | t | | |	  | t d  | | | | |
 | t d  |  | | | | t d  | t d  | | t d  | t d  | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3762  s    c
   
         s    j  d  t t d  | | t d  | t d  t | | t |	 | |  | t d  t |  | | t d  | t d  t |	 | |  t d  | | | | |  | | | | t d  |  | t d  | | | | | | | |  | | |  | | t |	 | |  |  |  |  t | | t |	 | |  | t d  | | t d  |  | t d  | | | | | t d  | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (
   R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3763  s    c
   
         s    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t |  | | t d  | t d  t | | |  t d  | | |	 | |  | | |	 | t d  |  | t d  | |	 | | |	 | | |  | | |  | | t | | |  |  |  |  t | | t | | |  | t d  |	 | t d  |  | t d  | | | | | t d  | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (
   R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3764  s    c            s    j  d  t t d  | | t d  t | | t |
 | |	  | t | | | | t d  | | | | | t d  | | |  | | | t |
 | |	  | | | | t d  | |  | | t d  | | t |
 | |	  t d  |	  |	  |	  t | | | | t |
 | |	  | t d  t |
 | |	  | | | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3765  s    c            s    j  d  t t d  | | t d  t | | t |
 | |	  | t | | | | t d  | | | | | t d  | | |  | | | t |
 | |	  | | | | t d  | |  | | t d  | | t |
 | |	  t d  |	  |	  |	  t | | | | t |
 | |	  | t d  | | | t d  t |
 | |	  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3766  s    c
   
         s`    j  d  t t d  | | t d  t | | t |	 | |  | t | | | | t d  |  | | | | t d  | | |  | t |	 | |  |  | | | t d  |  | | t |	 | |  t d  |  |  |  t |  | | | t |	 | |  | t d  t |	 | |  | | | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (
   R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3767  s    c
   
         s`    j  d  t t d  | | t d  t | | t |	 | |  | t | | | | t d  |  | | | | t d  | | |  | t |	 | |  |  | | | t d  |  | | t |	 | |  t d  |  |  |  t |  | | | t |	 | |  | t d  | | | t d  t |	 | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (
   R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3768  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 d  | | | | | t d  | |  | | | t d  t d  | | | t | | |
  |
  |
  |
  t | | t | | |
  | | | t | | |
  | t d  |	 | |  | | | t d  | | | | | | |
  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3769  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 d  | | | | | t d  | |  | | | t d  t d  | | | t | | |
  |
  |
  |
  t | | t | | |
  | | | t | | |
  | t d  |	 | |  | | | t d  | | | | | | |
  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3770  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 d  |  | | | |  | | | | t d  t |
 | |	  |	  |	  |	  t | | |  | | t |
 | |	  | | | t |
 | |	  | t d  t d  | | | | | | |	  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3771  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 d  |  | | | |  | | | | t d  t |
 | |	  |	  |	  |	  t | | |  | | t |
 | |	  | | | t |
 | |	  | t d  t d  | | | | | | |	  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3772  s    c            s2    j  d  t t d  | | | t d  | t d  | t d  t | | t | | |
  | | | t | | |
  | t d  t | | | t d  |	 | |  | | | | | | t d  | | t d  | t d  | |	 | |  | | | t d  t | | |
  | | |	 | t d  |  | | | | t d  |
  |
  |
  t | | t | | |
  | | | t | | |
  | t d  |	 | t d  |  | | | | t d  | | | t d  | t d  | t d  |
  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3773  s    c            s2    j  d  t t d  | | | t d  | t d  | t d  t | | t | | |
  | | | t | | |
  | t d  t | | | t d  |	 | |  | | | | | | t d  | | t d  | t d  | |	 | |  | | | t d  t | | |
  | | |	 | t d  |  | | | | t d  |
  |
  |
  t | | t | | |
  | | | t | | |
  | t d  |	 | t d  |  | | | | t d  | | | t d  | t d  | t d  |
  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3774  s    c            s    j  d  t t d  | | | t d  | t d  | t d  t | | t |
 | |	  | | | t |
 | |	  | t d  t | | | t d  | | |  | | | | t d  | | t d  |  | t d  | | t d  | t d  t |
 | |	  | | | | t d  |  | t d  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3775  s    c            s    j  d  t t d  | | | t d  | t d  | t d  t | | t |
 | |	  | | | t |
 | |	  | t d  t | | | t d  | | |  | | | | t d  | | t d  |  | t d  | | t d  | t d  t |
 | |	  | | | | t d  |  | t d  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3776  s    c            s    j  d  t t d  | | | | t d  t | | t | | |
  | | | t | | |
  | t |	 | | | | t d  | | | | | | | t d  |  | | | | t d  | | | | | | t | | |
  |
  |
  |
  t | | | t | | |
  | | | t | | |
  | t d  | | | | t d  |
  S(   Ni  i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3777  s    c            s    j  d  t t d  | | | | t d  t | | t | | |
  | | | t | | |
  | t |	 | | | | t d  | | | | | | | t d  |  | | | | t d  | | | | | | t | | |
  |
  |
  |
  t | | | t | | |
  | | | t | | |
  | t d  | | | | t d  |
  S(   Ni  i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3778  s    c            sc    j  d  t t d  | | | | t d  t | | t |
 | |	  | | | t |
 | |	  | t | | | | | t d  |  | | | | | t |
 | |	  |  | | | | | | t d  |	  |	  |	  t |  | | t |
 | |	  | | | t |
 | |	  | t d  | | | | t d  |	  S(   Ni  i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3779  s    c            sc    j  d  t t d  | | | | t d  t | | t |
 | |	  | | | t |
 | |	  | t | | | | | t d  |  | | | | | t |
 | |	  |  | | | | | | t d  |	  |	  |	  t |  | | t |
 | |	  | | | t |
 | |	  | t d  | | | | t d  |	  S(   Ni  i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3780  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |
  | t d  | | t | | |
  | t d  t |	 | | | | t d  | | | | | | t d  | | t d  | t d  | |	 | |  | | | t d  t | | |
  t d  | | t d  |  | | | | |	 | | | | | t | | |
  |  | | | | | | t d  | | | |
  |
  |
  t | | t | | |
  | | | t | | |
  | t d  |	 | t d  | |  | | | | | | t d  | t d  | t d  |
  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3781  s    c            s    j  d  t t d  | | t d  | t d  |	 t d  t | | t | | |
  | t d  | | t | | |
  |	 t d  t | | | | |	 t d  | | | | | | t d  | | t d  |	 t d  | | | |  | | |	 t d  t | | |
  t d  | |	 t d  |  | | | | | | | | | | t | | |
  |  | | | | | |	 t d  | | | |
  |
  |
  t | | t | | |
  | | | t | | |
  |	 t d  | | t d  | |  | | | | | | t d  | t d  |	 t d  |
  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3782  s    c            s]    j  d  t t d  | | t d  | t d  | t d  t | | t |
 | |	  | t d  | | t |
 | |	  | t d  t | | | | | t d  | | | |  | | | | t d  | | | | | | t d  | | t d  |  | t d  | | t d  | t d  t |
 | |	  t d  | | |  | t d  | | | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  |	  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3783  s    c            s]    j  d  t t d  | | t d  | t d  | t d  t | | t | | |	  | t d  | | t | | |	  | t d  t |
 | | | | t d  | | | |  | | | | t d  | | | | |
 | t d  | | t d  |  | t d  | | t d  | t d  t | | |	  t d  | |
 |  | t d  | | | | t | | |	  |	  |	  |	  t | | t | | |	  | | | t | | |	  | t d  |
 | t d  |  | t d  | | | t d  | t d  | t d  |	  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3784  s    c            s    j  d  t t d  | | | t d  t | | t | | |
  | t d  | | t | | |
  | t |	 | | | | t d  | | | | t d  | | | | | | t d  |	 | |  | | | t | | |
  |  | | | | t d  | | | | | | t | | |
  t d  |
  |
  |
  t | | | t | | |
  | | | t | | |
  | t d  | | | | t d  |
  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3785   s    c            s    j  d  t t d  | | | t d  t | | t | | |
  | t d  | | t | | |
  | t |	 | | | | t d  | | | | t d  | | | | | | t d  |	 | |  | | | t | | |
  |  | | | | t d  | | | | | | t | | |
  t d  |
  |
  |
  t | | | t | | |
  | | | t | | |
  | t d  | | | | t d  |
  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3786%  s    c            s    j  d  t t d  | | | t d  t | | t |
 | |	  | t d  | | t |
 | |	  | t | | | | | t d  |  | | | | | t |
 | |	  t d  |  | | | t d  | | | | | | |  | | | t d  t |
 | |	  |	  |	  |	  t |  | | t |
 | |	  | | | t |
 | |	  | t d  | | | | t d  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3787*  s    c            s    j  d  t t d  | | | t d  t | | t |
 | |	  | t d  | | t |
 | |	  | t | | | | | t d  |  | | | | | t |
 | |	  t d  |  | | | t d  | | | | | | |  | | | t d  t |
 | |	  |	  |	  |	  t |  | | t |
 | |	  | | | t |
 | |	  | t d  | | | | t d  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3788/  s    c            s    j  d  t t d  | t d  | t d  | t d  | | | | t | | t | | |
  | t d  | | t | | |
  | t |	 | | t d  | | | | | t d  | | | t d  | |	 | t d  | |  | | | | | t d  t | | |
  t d  | t d  | | | | |	 | |  | | | t | | |
  |  | | | | | | t d  | | | t d  |
  |
  |
  t | | t | | |
  | t d  | | t | | |
  | t d  |	 | t d  | |  | | | | | t d  | t d  | t d  | | | | |
  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement37894  s    c            s    j  d  t t d  | t d  | t d  | t d  | | | | t | | t | | |
  | t d  | | t | | |
  |	 t | | | t d  | | | | | t d  | | |	 t d  | | | t d  | |  | | | | |	 t d  t | | |
  t d  | t d  | | | | | | |  | | | t | | |
  |  | | | | | |	 t d  | | | t d  |
  |
  |
  t | | t | | |
  | t d  | | t | | |
  |	 t d  | | t d  | |  | | | | | t d  | t d  | t d  | | | | |
  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement37909  s    c            s    j  d  t t d  | t d  | t d  | t d  | | | | t | | t |
 | |	  | t d  | | t |
 | |	  | t | | | t d  | | | | | t d  | | | t d  |  | | | | t d  | | | t d  | | | t d  |  | t d  | | t d  t |
 | |	  t d  | t d  | | |  | | | | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | t d  | | t |
 | |	  | t d  | | t d  |  | t d  | | t d  | t d  | t d  | | | | |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3791>  s    c            s    j  d  t t d  | t d  | t d  | t d  | | | | t | | t | | |	  | t d  | | t | | |	  | t |
 | | t d  | | | | | t d  | | | t d  |  | | | | t d  | | | t d  | |
 | t d  |  | t d  | | t d  t | | |	  t d  | t d  |
 | |  | | | | | t | | |	  |	  |	  |	  t | | t | | |	  | t d  | | t | | |	  | t d  |
 | t d  |  | t d  | | t d  | t d  | t d  | | | | |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3792C  s    c
   
         s    j  d  t | | t d  |  | | | | t d  | t d  | t d  | | | | 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   (   R  R  R  R   R  R  (
   R  R2  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3793H  s    c
   
         s    j  d  t | | t d  |  | | | | t d  | t d  | t d  | | | | 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   (   R  R  R  R   R  R  (
   R  R2  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3794M  s    c	   	         s    j  d  t | | t d  |  | t d  | t d  | t d  | | | | 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   (   R  R  R  R   R  R  (	   R2  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3795R  s    c	   	         s    j  d  t | | t d  |  | t d  | t d  | t d  | | | | 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   (   R  R  R  R   R  R  (	   R2  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3796W  s    c            s`    j  d  t | | t d  |  | | | | t d  | t d  | t d  t | | t |
 | |	  | t |
 | |	  t d  t d  | | t |
 | |	  |	  |	  t t d  | t d  | t d  t | | t |
 | |	  | t |  | | | | |  | | | | t |
 | |	  |	  |	  |	  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3797\  s    c            s`    j  d  t |
 | t d  |  | | | | t d  | t d  | t d  t t d  t | | |	  t d  | | t | | |	  | | | t | | |	  |	  |	  t t d  | t d  | t d  t | | t | | |	  | t |  | | |
 | |  | | |
 | t | | |	  |	  |	  |	  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R  R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3798a  s    c
   
         sH    j  d  t | | t d  |  | t d  | t d  | t d  t | | t |	 | |  | t |	 | |  t d  t d  | | t |	 | |  |  |  t t d  | t d  | t d  t | | t |	 | |  | t | | |  | | |  | t |	 | |  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (
   R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3799f  s    c
   
         sH    j  d  t |	 | t d  |  | t d  | t d  | t d  t t d  t | | |  t d  | | t | | |  | | | t | | |  |  |  t t d  | t d  | t d  t | | t | | |  | t | |	 |  |	 | |  | t | | |  |  |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (
   R2  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3800k  s    c      
      s     j  d  t t d  | | t t | |
 | | | |
 | | |	 | t d  |  | |
 | |
 t d  | t d  |
 t d  |
  |
 | t | | |
   |
  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3801p  s    c      
      s     j  d  t t d  | | t t | |
 | | | |
 | |	 | | t d  |  | |
 | |
 t d  | t d  |
 t d  |
  |
 | t | | |
   |
  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R  R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3802u  s    c      
      s     j  d  t t d  | | t t | |	 | | | |	 | | | | t d  |  |	 t d  | t d  |	 t d  |	  |	 | t |
 | |	   |	  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3803z  s    c      
      s     j  d  t t d  | | t t | |	 | | | |	 | | |
 | t d  |  |	 t d  | t d  |	 t d  |	  |	 | t | | |	   |	  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R2  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3804  s    c            sH     j  d  t t d  | t t | | |  t d  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3805  s    c            sH     j  d  t t d  | t t | | |  t d  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3806  s    c      
      s     j  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3807  s    c      
      s     j  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3808  s    c      
      st     j  d  t | | t t | | | | |  | t d  | t d  |  | | t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3809  s    c      
      su     j  d  t | | t t | | | | |  | t d  | t d  |  | | t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3810  s    c	   
   	      s   t  t | | |  |  }	   j d  t |	 | t d  | t t | | | | | |	 | | |  |	 t d  | t d  t d  | t d  t d  |  | t | | |  |	  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3811  s    c	   
         s   t  t d  t | | |  |  }	   j d  t |	 | t d  | t t | | | | | |	 | | |  |	 t d  | t d  t d  | t d  t d  |  | t d  |	 t | | |   |  S(   Ni   i  i   i(   R   R  R  R  R  R*   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3812  s    'c   	         s  t  t | | |  |  }   j d  t | | t t | | | |  | t d  | t d  t d  | t d  t d  d t | | | | | | t d  | t d  t d  | t d  |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3813  s    c   	         s  t  t | | |  |  }   j d  t | | t t | | | |  | t d  | t d  t d  | t d  t d  d t | | | | | | t d  | t d  t d  | t d  |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3814  s    c	   
   	      s   t  t | | |  |  }	   j d  t |	 | t t | | | |	 | | |  |	 t d  | t d  t d  | t d  t d  |  | t | | |  |	  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3815  s    c	   
         s   t  t d  t | | |  |  }	   j d  t |	 | t t | | | |	 | | |  |	 t d  | t d  t d  | t d  t d  |  | t d  |	 t | | |   |  S(   Ni   i  i   i(   R   R  R  R  R  R*   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3816  s    'c   	         s  t  t | | |  |  }   j d  t | | t t | t d  | t d  t d  | t d  | |  t d  t d  d t | | t d  | t d  t d  | t d  | | | | |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3817  s    c   	         s  t  t | | |  |  }   j d  t | | t t | t d  | t d  t d  | t d  | |  t d  t d  d t | | t d  | t d  t d  | t d  | | | | |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3818  s    c	   	   
      s     j  d  t | | t t | | | | | | | |  | t d  | t d  |  | | t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3819  s    c	   	   
      s     j  d  t | | t t | | | | | | | |  | t d  | t d  |  | | t | | |   |  S(   Ni  i   (   R  R  R*   R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3820  s    R  c	   	   	      sl     j  d  t t d  |  | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3821  s    c	   	   
      sv     j  d  t t d  |  | |  t | t d  | t d  t | | |  | t d  |  |  |  S(   Ni  i   i   i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3822  s    c	   	   	      s     j  d  t | t d  | t | | |  | t d  |  | | t | | |  | | t | | |  t d  | |  t | t d  | t | | |  | t d  |  |  |  S(   Ni  i   (   R  R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3823  s    c	   	   
      s     j  d  t | t d  | t d  t | | |  | t d  |  | | t d  t | | |  | | t d  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  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3824  s    c   	         s   t  t d  | | |  t d  t d   }   j d  t t d  | | t t d  |  t d  | t | | |  | | |  |  t t d  | | t t d  |  t d  | t | | |  | | |  |  S(   Ni   i   i  i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3825  s    2c   	         s  t  t d  | | |  t d  t d   }   j d  t t d  | | t t d  |  t d  | t d  t | | |  | | |  |  t t d  | | t t d  |  t d  | t d  t | | |  | | |  |  S(   Ni   i   i  i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3826  s    2c      
      s     j  d  t | |
 t t |	 | | t d  |	 t d  | t d  t d  | | |	 | | |	 t d  | |  |	  |	 | t | |
 |	   |	  S(   Ni  i   i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3827  s    c      
      s     j  d  t | |
 t t |	 | | t d  |	 t d  | t d  t d  | | |	 | | |	 t d  | |  |	  |	 | t | |
 |	   |	  S(   Ni  i   i(   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3828	  s    c
            s[  t  t | |	 |  |  }
   j d  t |
 |	 t t |
 | t d  | |  |
 t d  | t d  t d  | t d  t d  d t | |
 | t d  | | |
 | | |
 t d  | t d  t d  | t d  | |
 t d  | t d  t d  | |  |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3829	  s    c
            sZ  t  t | |	 |  |  }
   j d  t |
 |	 t t |
 | t d  | |  |
 t d  | t d  t d  | t d  t d  d t | |
 | t d  | | |
 | | |
 t d  | t d  t d  | t d  | |
 t d  | t d  t d  | |  |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3830	  s    c      
      s     j  d  t | | t d  |
 t t | t d  |	 t d  | t d  t d  | | |	 | | |	 t d  | |  |	  |	 | t | |
 |	   |	  S(   Ni  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3831	  s    c      
      s     j  d  t | | t d  |
 t t | t d  |	 t d  | t d  t d  | | |	 | | |	 t d  | |  |	  |	 | t | |
 |	   |	  S(   Ni  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3832	  s    c
            s#  t  t | |	 |  |  }
   j d  t |
 |	 t t |
 t d  | t d  t d  | t d  | |  t d  d t | | t d  t d  | | | | | t d  t d  | t d  | | t d  | |  |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3833	  s    c
            s$  t  t | |	 |  |  }
   j d  t |
 |	 t t |
 t d  | t d  t d  | t d  | |  t d  d t | | t d  t d  | | | | | t d  t d  | t d  | | t d  | |  |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3834!	  s    c
   
   	      s     j  d  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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3835(	  s    c
   
   
      s     j  d  t t d  |  | |  t | t d  | t d  t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3836-	  s    c
   
   	      s     j  d  t | t d  | t | |	 |  | t d  |  | | t | |	 |  | | t | |	 |  t d  | |  t | t d  | t | |	 |  | t d  |  t | |	 |  | |  |  S(   Ni  i   (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement38372	  s    c
   
   
      s    j  d  t | t d  | t d  t | |	 |  | t d  |  | | t d  t | |	 |  | | t d  t | |	 |  t d  | |  t | t d  | t d  t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement38387	  s    c      
      s     j  d  t | |
 t t |	 | | | | |	 | | |	 t d  | |  | t d  |	 t d  |	  |	 | t | |
 |	   |	  S(   Ni  i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3839<	  s    c      
      s     j  d  t | |
 t t |	 | | | | |	 | | |	 t d  | |  | t d  |	 t d  |	  |	 | t | |
 |	   |	  S(   Ni   i   (   R  R  R*   R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3840A	  s    c
   
   	      s     j  d  t t d  |  | |  t | t d  | t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3841F	  s    c
   
   
      s     j  d  t t d  |  | |  t | t d  | t d  t | |	 |  | t d  |  t | |	 |  | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3842K	  s    c
   
   	      s     j  d  t | t d  | t | |	 |  | t d  |  | | t | |	 |  | | t | |	 |  t d  | |  t | t d  | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3843P	  s    c
   
   
      s    j  d  t | t d  | t d  t | |	 |  | t d  |  | | t d  t | |	 |  | | t d  t | |	 |  t d  | |  t | t d  | t d  t | |	 |  | t d  |  t | |	 |  | |  |  S(   Ni  i   i   (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3844U	  s    c
            s   t  t d  t | |	 |  |  }
   j d  t |
 |	 t t |
 | | t d  | |  | |
 | t d  | | |
 | | | |  |
 t d  | t d  t d  |  | t d  |
 t | |	 |   |  S(   Ni   i  i   (   R   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3845Y	  s    'c
      	      s   t  t | |	 |  |  }
   j d  t |
 |	 t t |
 | | t d  | |  | |
 | t d  | | |
 | | | |  |
 t d  | t d  t d  |  | t | |	 |  |
  |  S(   Ni  i   i   (   R   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3846_	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3847f	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3848k	  s    c	   	   
      s     j  d  t | t d  | t | | |  t d  | | | t | | |  | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3849p	  s    c	   	   
      s     j  d  t | t d  | t | | |  t d  | | | t | | |  | 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  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3850u	  s    c   	         s  t  t d  | | | t d  t d   }   j d  t |  t d  | | |  | | t t d  t | t d  | t | | |  | |  |  |  t |  t d  | | |  | | t t d  t | t d  | t | | |  | |  |  |  S(   Ni   i   i  i   (   R  R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3851y	  s    2c   	         s  t  t d  | | | t d  t d   }   j d  t |  t d  | | |  | | t t d  t | t d  | t | | |  | |  |  |  t |  t d  | | |  | | t t d  t | t d  | t | | |  | |  |  |  S(   Ni   i   i  i   (   R  R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3852	  s    2c	   	   	      sw     j  d  t t | |  t | | |  | | t | | |  | t | | |  t d  | |  |  S(   Ni  i   (   R  R   RH  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3853	  s    c	   	   	      sw     j  d  t t | |  t | | |  | | t | | |  | t | | |  t d  | |  |  S(   Ni  i   (   R  R   RH  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3854	  s    c      	      s     j  d  t t d  t t | | | |  t t d  t | | |  t t d  t | | |  t d  |  |  t t | | | |  t d  | |  t d  |  S(   Ni  i   i   (   R  R  R  R  R   t   expR  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3855	  s    c      	      s     j  d  t t d  t t | | | |  t t d  t | | |  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3856	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3857	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3858	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3859	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3860	  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3861	  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3862	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3863	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3864	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3865	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3866	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3867	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3868	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3869	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3870	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3871	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3872	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3873	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3874	  s    c	   	         s}     j  d  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3875	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3876	  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  t   u(   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3877	  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   With3878
  s    )c            s     j  d  t t d  t | t | | | |  | t d  | t d  | t | t 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3879

  s    c            s     j  d  t t d  t | t | | | |  | t d  | t d  | t | t 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3880
  s    c      
      s6    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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3881
  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3882
  s    c	   	         s     j  d  t t | | | |  t d  t | | t d  | t d  | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3883
  s    c	   	         s     j  d  t t | | | |  t d  t | | t d  | t d  | 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  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3884#
  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni-  (   R  R   R  R1  (   t   vR  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3885(
  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni.  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3886-
  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni/  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement38872
  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni0  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement38887
  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni1  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3889<
  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni2  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3890A
  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni3  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3891F
  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni4  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3892K
  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni5  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3893P
  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni6  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3894U
  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni7  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3895Z
  s    c            s5     j  d  t | | t t | |   |  |  S(   Ni8  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3896_
  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   Ni9  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3897d
  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3898i
  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3899n
  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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3900s
  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   Ni=  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3901x
  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   Ni>  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3902}
  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni?  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3903
  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   Ni@  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3904
  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   NiA  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3905
  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   NiB  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3906
  s    R  c      
      s     j  d  t | | t d  | | |  t | | | t d  t | | | |  |  |  |  t | | | t d  t d  t | | | |  |  | | |  |  S(   NiC  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3907
  s    c      
      s     j  d  t | | t d  | | |  t | | | t d  t | | | |  |  |  |  t | | | t d  t d  t | | | |  |  | | |  |  S(   NiD  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3908
  s    c            s>     j  d  t t | |  | | | t d   | |  S(   NiE  i   (   R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3909
  s    c            sH     j  d  t t d  t | |  | | | t d   | |  S(   NiF  i   i   (   R  R   R  R  (   R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3910
  s    c      	      sS     j  d  t | t t | |  | | | t d    t d  | |  S(   NiG  i   (   R  R  R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3911
  s    c      	      sR     j  d  t | t t | |  | | | t d    t d  | |  S(   NiH  i   (   R  R  R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3912
  s    c      
      s     j  d  t |  | t d  | | t d  | t t | |  | | | t 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  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3913
  s    c      
      s     j  d  t |  | t d  | | t d  | t t d  t | |  | | | t d   |  |  t | t t | |  | | | t d    t d  | |  S(   NiJ  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3914
  s    c            sN     j  d  t | | | |  t | | | | | t d   | |  S(   NiK  i   (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3915
  s    c      	      sX     j  d  t | | | |  t d  t | | | | | t d   | |  S(   NiL  i   i   (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   replacement3916
  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  t   x_t   m_R  t   n_R   R  R  t   p_t   a_t   c_t   q_t   A_t   n2_t   u_t   v_t   e_t   d_(  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  t   pattern3398R  t   rule3398t   pattern3399R  t   rule3399t   pattern3400R  t   rule3400t   pattern3401R  t   rule3401t   pattern3402R  t   rule3402t   pattern3403R  t   rule3403t   pattern3404R  t   rule3404t   pattern3405R  t   rule3405t   pattern3406R  t   rule3406t   pattern3407R  t   rule3407t   pattern3408R  t   rule3408t   pattern3409R  t   rule3409t   pattern3410R  t   rule3410t   pattern3411R  t   rule3411t   pattern3412R  t   rule3412t   pattern3413R  t   rule3413t   pattern3414R  t   rule3414t   pattern3415R  t   rule3415t   pattern3416R  t   rule3416t   pattern3417R  t   rule3417t   pattern3418R  t   rule3418t   pattern3419R  t   rule3419t   pattern3420R  t   rule3420t   pattern3421R  t   rule3421t   pattern3422R  t   rule3422t   pattern3423R  t   rule3423t   pattern3424R  t   rule3424t   pattern3425R  t   rule3425t   pattern3426R  t   rule3426t   pattern3427R  t   rule3427t   pattern3428R  t   rule3428t   pattern3429R  t   rule3429t   pattern3430R  t   rule3430t   pattern3431R  t   rule3431t   pattern3432R  t   rule3432t   pattern3433R   t   rule3433t   pattern3434R  t   rule3434t   pattern3435R  t   rule3435t   pattern3436R  t   rule3436t   pattern3437R  t   rule3437t   pattern3438R  t   rule3438t   pattern3439R  t   rule3439t   pattern3440R  t   rule3440t   pattern3441R  t   rule3441t   pattern3442R	  t   rule3442t   pattern3443R
  t   rule3443t   pattern3444R  t   rule3444t   pattern3445R  t   rule3445t   pattern3446R  t   rule3446t   pattern3447R  t   rule3447t   pattern3448R  t   rule3448t   pattern3449R  t   rule3449t   pattern3450R  t   rule3450t   pattern3451R  t   rule3451t   pattern3452R  t   rule3452t   pattern3453R  t   rule3453t   pattern3454R  t   rule3454t   pattern3455R  t   rule3455t   pattern3456R  t   rule3456t   pattern3457R  t   rule3457t   pattern3458R  t   rule3458t   pattern3459R  t   rule3459t   pattern3460R  t   rule3460t   pattern3461R   t   rule3461t   pattern3462R!  t   rule3462t   pattern3463R"  t   rule3463t   pattern3464R#  t   rule3464t   pattern3465R$  t   rule3465t   pattern3466R%  t   rule3466t   pattern3467R&  t   rule3467t   pattern3468R'  t   rule3468t   pattern3469R(  t   rule3469t   pattern3470R)  t   rule3470t   pattern3471R*  t   rule3471t   pattern3472R+  t   rule3472t   pattern3473R,  t   rule3473t   pattern3474R-  t   rule3474t   pattern3475R.  t   rule3475t   pattern3476R/  t   rule3476t   pattern3477R0  t   rule3477t   pattern3478R1  t   rule3478t   pattern3479R2  t   rule3479t   pattern3480R3  t   rule3480t   pattern3481R4  t   rule3481t   pattern3482R5  t   rule3482t   pattern3483R6  t   rule3483t   pattern3484R7  t   rule3484t   pattern3485R8  t   rule3485t   pattern3486R9  t   rule3486t   pattern3487R:  t   rule3487t   pattern3488R;  t   rule3488t   pattern3489R<  t   rule3489t   pattern3490R=  t   rule3490t   pattern3491R>  t   rule3491t   pattern3492R?  t   rule3492t   pattern3493R@  t   rule3493t   pattern3494RA  t   rule3494t   pattern3495RB  t   rule3495t   pattern3496RC  t   rule3496t   pattern3497RD  t   rule3497t   pattern3498RE  t   rule3498t   pattern3499RF  t   rule3499t   pattern3500RG  t   rule3500t   pattern3501RH  t   rule3501t   pattern3502RI  t   rule3502t   pattern3503RJ  t   rule3503t   pattern3504RK  t   rule3504t   pattern3505RL  t   rule3505t   pattern3506RM  t   rule3506t   pattern3507RN  t   rule3507t   pattern3508RO  t   rule3508t   pattern3509RP  t   rule3509t   pattern3510RQ  t   rule3510t   pattern3511RR  t   rule3511t   pattern3512RS  t   rule3512t   pattern3513RT  t   rule3513t   pattern3514RU  t   rule3514t   pattern3515RV  t   rule3515t   pattern3516RW  t   rule3516t   pattern3517RX  t   rule3517t   pattern3518RY  t   rule3518t   pattern3519RZ  t   rule3519t   pattern3520R[  t   rule3520t   pattern3521R\  t   rule3521t   pattern3522R]  t   rule3522t   pattern3523R^  t   rule3523t   pattern3524R_  t   rule3524t   pattern3525R`  t   rule3525t   pattern3526Ra  t   rule3526t   pattern3527Rb  t   rule3527t   pattern3528Rc  t   rule3528t   pattern3529Rd  t   rule3529t   pattern3530Re  t   rule3530t   pattern3531Rf  t   rule3531t   pattern3532Rg  t   rule3532t   pattern3533Rh  t   rule3533t   pattern3534Ri  t   rule3534t   pattern3535Rj  t   rule3535t   pattern3536Rk  t   rule3536t   pattern3537Rl  t   rule3537t   pattern3538Rm  t   rule3538t   pattern3539Rn  t   rule3539t   pattern3540Ro  t   rule3540t   pattern3541Rp  t   rule3541t   pattern3542Rq  t   rule3542t   pattern3543Rr  t   rule3543t   pattern3544Rs  t   rule3544t   pattern3545Rt  t   rule3545t   pattern3546Ru  t   rule3546t   pattern3547Rv  t   rule3547t   pattern3548Rw  t   rule3548t   pattern3549Rx  t   rule3549t   pattern3550Ry  t   rule3550t   pattern3551Rz  t   rule3551t   pattern3552R{  t   rule3552t   pattern3553R|  t   rule3553t   pattern3554R}  t   rule3554t   pattern3555R~  t   rule3555t   pattern3556R  t   rule3556t   pattern3557R  t   rule3557t   pattern3558R  t   rule3558t   pattern3559R  t   rule3559t   pattern3560R  t   rule3560t   pattern3561R  t   rule3561t   pattern3562R  t   rule3562t   pattern3563R  t   rule3563t   pattern3564R  t   rule3564t   pattern3565R  t   rule3565t   pattern3566R  t   rule3566t   pattern3567R  t   rule3567t   pattern3568R  t   rule3568t   pattern3569R  t   rule3569t   pattern3570R  t   rule3570t   pattern3571R  t   rule3571t   pattern3572R  t   rule3572t   pattern3573R  t   rule3573t   pattern3574R  t   rule3574t   pattern3575R  t   rule3575t   pattern3576R  t   rule3576t   pattern3577R  t   rule3577t   pattern3578R  t   rule3578R  t   pattern3579t   rule3579R  t   pattern3580t   rule3580t   pattern3581R  t   rule3581t   pattern3582R  t   rule3582t   pattern3583R  t   rule3583t   pattern3584R  t   rule3584t   pattern3585R  t   rule3585t   pattern3586R  t   rule3586t   pattern3587R  t   rule3587t   pattern3588R  t   rule3588t   pattern3589R  t   rule3589t   pattern3590R  t   rule3590t   pattern3591R  t   rule3591t   pattern3592R  t   rule3592t   pattern3593R  t   rule3593t   pattern3594R  t   rule3594t   pattern3595R  t   rule3595t   pattern3596R  t   rule3596t   pattern3597R  t   rule3597t   pattern3598R  t   rule3598t   pattern3599R  t   rule3599t   pattern3600R  t   rule3600t   pattern3601R  t   rule3601t   pattern3602R  t   rule3602t   pattern3603R  t   rule3603t   pattern3604R  t   rule3604t   pattern3605R  t   rule3605t   pattern3606R  t   rule3606t   pattern3607R  t   rule3607t   pattern3608R  t   rule3608t   pattern3609R  t   rule3609t   pattern3610R  t   rule3610t   pattern3611R  t   rule3611t   pattern3612R  t   rule3612t   pattern3613R  t   rule3613t   pattern3614R  t   rule3614t   pattern3615R  t   rule3615t   pattern3616R  t   rule3616t   pattern3617R  t   rule3617t   pattern3618R  t   rule3618t   pattern3619R  t   rule3619t   pattern3620R  t   rule3620t   pattern3621R  t   rule3621t   pattern3622R  t   rule3622t   pattern3623R  t   rule3623t   pattern3624R  t   rule3624t   pattern3625R  t   rule3625t   pattern3626R  t   rule3626t   pattern3627R  t   rule3627t   pattern3628R  t   rule3628t   pattern3629R  t   rule3629t   pattern3630R  t   rule3630t   pattern3631R  t   rule3631t   pattern3632R  t   rule3632t   pattern3633R  t   rule3633t   pattern3634R  t   rule3634t   pattern3635R  t   rule3635t   pattern3636R  t   rule3636t   pattern3637R  t   rule3637t   pattern3638R  t   rule3638t   pattern3639R  t   rule3639t   pattern3640R  t   rule3640t   pattern3641R  t   rule3641t   pattern3642R  t   rule3642t   pattern3643R  t   rule3643t   pattern3644R  t   rule3644t   pattern3645R  t   rule3645t   pattern3646R  t   rule3646t   pattern3647R  t   rule3647t   pattern3648R  t   rule3648t   pattern3649R  t   rule3649t   pattern3650R  t   rule3650t   pattern3651R  t   rule3651t   pattern3652R  t   rule3652t   pattern3653R  t   rule3653t   pattern3654R  t   rule3654t   pattern3655R  t   rule3655t   pattern3656R  t   rule3656t   pattern3657R  t   rule3657t   pattern3658R  t   rule3658t   pattern3659R  t   rule3659t   pattern3660R  t   rule3660t   pattern3661R  t   rule3661t   pattern3662R  t   rule3662t   pattern3663R  t   rule3663t   pattern3664R  t   rule3664t   pattern3665R  t   rule3665t   pattern3666R  t   rule3666t   pattern3667R  t   rule3667t   pattern3668R  t   rule3668t   pattern3669R  t   rule3669t   pattern3670R  t   rule3670t   pattern3671R  t   rule3671t   pattern3672R  t   rule3672t   pattern3673R  t   rule3673t   pattern3674R  t   rule3674t   pattern3675R  t   rule3675t   pattern3676R  t   rule3676t   pattern3677R  t   rule3677t   pattern3678R  t   rule3678t   pattern3679R  t   rule3679t   pattern3680R  t   rule3680t   pattern3681R   t   rule3681t   pattern3682R  t   rule3682t   pattern3683R  t   rule3683t   pattern3684R  t   rule3684t   pattern3685R  t   rule3685t   pattern3686R  t   rule3686t   pattern3687R  t   rule3687t   pattern3688R  t   rule3688t   pattern3689R  t   rule3689t   pattern3690R	  t   rule3690t   pattern3691R
  t   rule3691t   pattern3692R  t   rule3692t   pattern3693R  t   rule3693t   pattern3694R  t   rule3694t   pattern3695R  t   rule3695t   pattern3696R  t   rule3696t   pattern3697R  t   rule3697t   pattern3698R  t   rule3698t   pattern3699R  t   rule3699t   pattern3700R  t   rule3700t   pattern3701R  t   rule3701t   pattern3702R  t   rule3702t   pattern3703R  t   rule3703t   pattern3704R  t   rule3704t   pattern3705R  t   rule3705t   pattern3706R  t   rule3706t   pattern3707R  t   rule3707t   pattern3708R  t   rule3708t   pattern3709R  t   rule3709t   pattern3710R  t   rule3710t   pattern3711R  t   rule3711t   pattern3712R  t   rule3712t   pattern3713R   t   rule3713t   pattern3714R!  t   rule3714t   pattern3715R"  t   rule3715t   pattern3716R#  t   rule3716t   pattern3717R$  t   rule3717t   pattern3718R%  t   rule3718t   pattern3719R&  t   rule3719t   pattern3720R'  t   rule3720t   pattern3721R(  t   rule3721t   pattern3722R)  t   rule3722t   pattern3723R*  t   rule3723t   pattern3724R+  t   rule3724t   pattern3725R,  t   rule3725t   pattern3726R-  t   rule3726t   pattern3727R.  t   rule3727t   pattern3728R/  t   rule3728t   pattern3729R0  t   rule3729t   pattern3730R1  t   rule3730t   pattern3731R3  t   rule3731t   pattern3732R4  t   rule3732t   pattern3733R5  t   rule3733t   pattern3734R6  t   rule3734t   pattern3735R7  t   rule3735t   pattern3736R8  t   rule3736t   pattern3737R9  t   rule3737t   pattern3738R:  t   rule3738t   pattern3739R;  t   rule3739t   pattern3740R<  t   rule3740t   pattern3741R=  t   rule3741t   pattern3742R>  t   rule3742t   pattern3743R?  t   rule3743t   pattern3744R@  t   rule3744t   pattern3745RA  t   rule3745t   pattern3746RB  t   rule3746t   pattern3747RC  t   rule3747t   pattern3748RD  t   rule3748t   pattern3749RE  t   rule3749t   pattern3750RF  t   rule3750t   pattern3751RG  t   rule3751t   pattern3752RH  t   rule3752t   pattern3753RI  t   rule3753t   pattern3754RJ  t   rule3754t   pattern3755RK  t   rule3755t   pattern3756RL  t   rule3756t   pattern3757RM  t   rule3757t   pattern3758RN  t   rule3758t   pattern3759RO  t   rule3759t   pattern3760RP  t   rule3760t   pattern3761RQ  t   rule3761t   pattern3762RR  t   rule3762t   pattern3763RS  t   rule3763t   pattern3764RT  t   rule3764t   pattern3765RU  t   rule3765t   pattern3766RV  t   rule3766t   pattern3767RW  t   rule3767t   pattern3768RX  t   rule3768t   pattern3769RY  t   rule3769t   pattern3770RZ  t   rule3770t   pattern3771R[  t   rule3771t   pattern3772R\  t   rule3772t   pattern3773R]  t   rule3773t   pattern3774R^  t   rule3774t   pattern3775R_  t   rule3775t   pattern3776R`  t   rule3776t   pattern3777Ra  t   rule3777t   pattern3778Rb  t   rule3778t   pattern3779Rc  t   rule3779t   pattern3780Rd  t   rule3780t   pattern3781Re  t   rule3781t   pattern3782Rf  t   rule3782t   pattern3783Rg  t   rule3783t   pattern3784Rh  t   rule3784t   pattern3785Ri  t   rule3785t   pattern3786Rj  t   rule3786t   pattern3787Rk  t   rule3787t   pattern3788Rl  t   rule3788t   pattern3789Rm  t   rule3789t   pattern3790Rn  t   rule3790t   pattern3791Ro  t   rule3791t   pattern3792Rp  t   rule3792t   pattern3793Rq  t   rule3793t   pattern3794Rr  t   rule3794t   pattern3795Rs  t   rule3795t   pattern3796Rt  t   rule3796t   pattern3797Ru  t   rule3797t   pattern3798Rv  t   rule3798t   pattern3799Rw  t   rule3799t   pattern3800Rx  t   rule3800t   pattern3801Ry  t   rule3801t   pattern3802Rz  t   rule3802t   pattern3803R{  t   rule3803t   pattern3804R|  t   rule3804t   pattern3805R}  t   rule3805t   pattern3806R~  t   rule3806t   pattern3807R  t   rule3807t   pattern3808R  t   rule3808t   pattern3809R  t   rule3809t   pattern3810R  t   rule3810R  t   pattern3811t   rule3811R  t   pattern3812t   rule3812R  t   pattern3813t   rule3813R  t   pattern3814t   rule3814R  t   pattern3815t   rule3815R  t   pattern3816t   rule3816R  t   pattern3817t   rule3817R  t   pattern3818t   rule3818t   pattern3819R  t   rule3819t   pattern3820R  t   rule3820t   pattern3821R  t   rule3821t   pattern3822R  t   rule3822t   pattern3823R  t   rule3823t   pattern3824R  t   rule3824R  t   pattern3825t   rule3825R  t   pattern3826t   rule3826t   pattern3827R  t   rule3827t   pattern3828R  t   rule3828R  t   pattern3829t   rule3829R  t   pattern3830t   rule3830t   pattern3831R  t   rule3831t   pattern3832R  t   rule3832R  t   pattern3833t   rule3833R  t   pattern3834t   rule3834t   pattern3835R  t   rule3835t   pattern3836R  t   rule3836t   pattern3837R  t   rule3837t   pattern3838R  t   rule3838t   pattern3839R  t   rule3839t   pattern3840R  t   rule3840t   pattern3841R  t   rule3841t   pattern3842R  t   rule3842t   pattern3843R  t   rule3843t   pattern3844R  t   rule3844R  t   pattern3845t   rule3845R  t   pattern3846t   rule3846t   pattern3847R  t   rule3847t   pattern3848R  t   rule3848t   pattern3849R  t   rule3849t   pattern3850R  t   rule3850R  t   pattern3851t   rule3851R  t   pattern3852t   rule3852t   pattern3853R  t   rule3853t   pattern3854R  t   rule3854t   pattern3855R  t   rule3855t   pattern3856R  t   rule3856t   pattern3857R  t   rule3857t   pattern3858R  t   rule3858t   pattern3859R  t   rule3859t   pattern3860R  t   rule3860t   pattern3861R  t   rule3861t   pattern3862R  t   rule3862t   pattern3863R  t   rule3863t   pattern3864R  t   rule3864t   pattern3865R  t   rule3865t   pattern3866R  t   rule3866t   pattern3867R  t   rule3867t   pattern3868R  t   rule3868t   pattern3869R  t   rule3869t   pattern3870R  t   rule3870t   pattern3871R  t   rule3871t   pattern3872R  t   rule3872t   pattern3873R  t   rule3873t   pattern3874R  t   rule3874t   pattern3875R  t   rule3875t   pattern3876R  t   rule3876R  t   pattern3877t   rule3877R  t   pattern3878t   rule3878t   pattern3879R  t   rule3879t   pattern3880R  t   rule3880t   pattern3881R  t   rule3881t   pattern3882R  t   rule3882t   pattern3883R  t   rule3883t   pattern3884R  t   rule3884t   pattern3885R  t   rule3885t   pattern3886R  t   rule3886t   pattern3887R  t   rule3887t   pattern3888R  t   rule3888t   pattern3889R  t   rule3889t   pattern3890R  t   rule3890t   pattern3891R  t   rule3891t   pattern3892R  t   rule3892t   pattern3893R  t   rule3893t   pattern3894R  t   rule3894t   pattern3895R  t   rule3895t   pattern3896R  t   rule3896t   pattern3897R  t   rule3897t   pattern3898R  t   rule3898t   pattern3899R  t   rule3899t   pattern3900R  t   rule3900t   pattern3901R  t   rule3901t   pattern3902R  t   rule3902t   pattern3903R  t   rule3903t   pattern3904R  t   rule3904t   pattern3905R  t   rule3905t   pattern3906R  t   rule3906t   pattern3907R  t   rule3907t   pattern3908R  t   rule3908t   pattern3909R  t   rule3909t   pattern3910R  t   rule3910t   pattern3911R  t   rule3911t   pattern3912R  t   rule3912t   pattern3913R  t   rule3913t   pattern3914R  t   rule3914t   pattern3915R  t   rule3915t   pattern3916R  t   rule3916(    (   R  sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   tangent   sr       
ggggJTggqqqqqqmmnnqqqqqqnn     = = G Q : :  " " " " " @ @ / / - - < < H H 4 4 7 7 4 4 7 7 4 4 4 4 4 4 - - 4 4 = = L L I I L L I I L L F F & & ; ; < < A A C C C C 9 9 ? ?     0 0 < < V V   F F   F F   J J   S S   _ _   P P   b b   S S v v 0 0   L L   M M{{{{   M M B L \ \ 3 G 6 T 9 W _ i O Y C M 1 ;        }}ccuu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  t   Pit   iR  t   B_t   C_t   F_t   G_t   H_R  t   b_R  R  R  t   f_t   g_t   h_t   i_t   j_t   k_t   l_R  R  R  R  t   r_t   t_R  R  t   s_t   w_R  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_R  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   rR2  t   kR  t   Falset	   _UseGammat	   ShowStepst   Nonet   StepCounterR	  (    (    (    sA   lib/python2.7/site-packages/sympy/integrals/rubi/rules/tangent.pyt   <module>   s>   "           1nj:R4|'	