
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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     d     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 } 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 d t d   t t 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  | | | | |  }   f d
   } t | |  } t t t d t d   t d t d   t t 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 t  | | | | |  }   f d   } t | |  } t t t d t d   t d t d   t t 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 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 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 t  | | | |	  }   f d   } t | |  } t 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  | | | | | |	 |
  }   f d   } t | |  } t 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  | | | | | |	 |
  }   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 t  | | | | | |  }   f d   } t | |  } t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | | |  }   f d   } t | |  } t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | | |  }   f d   } t | |  }t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | | |  }  f d   }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | | |  }  f d   }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | | |  }  f d   }	t ||	 }
t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | |  }  f d   }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | |  }  f d   }t || }t 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  | | | | | | |  }  f d   }t || }t 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  | | | | | | |  }  f d   }t || }t t t d  t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t  | | | | | | |  }  f d!   }t || }t t t d  t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t  | | | | | | |  }  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 t 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 t t t d  t d  t d    t  | | | | | | | | | 
 }   f d$   }!t | |! }"t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | | | | 	 }#  f d%   }$t |#|$ }%t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | | | | 	 }&  f d&   }'t |&|' }(  f d'   })t t 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  | | | | | | |  }*t |*|) }+  f d)   },t t 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  | | | | | | |  }-t |-|, }.t t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | | 	 }/  f d*   }0t |/|0 }1t t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | | 	 }2  f d+   }3t |2|3 }4t t 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  | | | | | | | | | 
 }5  f d,   }6t |5|6 }7t t 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  | | | | | | | | | 
 }8  f d-   }9t |8|9 }:t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t d.  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 t t d  t d  t d   t d.  d t  | | | | | | | | | 
 }>  f d0   }?t |>|? }@t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t d.  d t  | | | | | | | | 	 }A  f d1   }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 t d  t d  t d   t d.  d t  | | | | | | | | 	 }D  f d2   }Et |D|E }Ft t t t 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  | | | | | | | | | |  }G  f d3   }Ht |G|H }It t t t 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  | | | | | | | | | |  }J  f d4   }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 t t d  t d  t d   t  | | | | | | |	  }M  f d5   }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 t t d  t d  t d   t  | | | | | | |	  }P  f d6   }Qt |P|Q }Rt t 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 t  | | | | | | | | | 
 }S  f d7   }Tt |S|T }Ut t 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 t  | | | | | | | | | 
 }V  f d8   }Wt |V|W }Xt t 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  | | | | | | | | | 
 }Y  f d9   }Zt |Y|Z }[t t 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  | | | | | | | | | 
 }\  f d:   }]t |\|] }^t t 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  | | | | | | | | | 
 }_  f d;   }`t |_|` }at t 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  | | | | | | | | | 
 }b  f d<   }ct |b|c }d  f d=   }et t 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  | | | | | | |   }ft |f|e }g  f d>   }ht t 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  | | | | | | |   }it |i|h }jt t 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  | | | | | | | |! |" 
 }k  f d?   }lt |k|l }mt t 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  | | | | | | | |! |" 
 }n  f d@   }ot |n|o }pt t 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  | | | | | | | |# 	 }q  f dA   }rt |q|r }st t 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  | | | | | | | |# 	 }t  f dB   }ut |t|u }vt t t t t d  t d   t t t t dC t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' |( | | |$ |% |&  }w  f dD   }xt |w|x }yt t t t t d  t d   t t t t dC t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' |( | | |$ |% |&  }z  f dE   }{t |z|{ }|t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | | |	  }}  f dF   }~t |}|~ }t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | | |	  }  f dG   }t || }t t t 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  | | | | | | | | | |)  }  f dH   }t || }t t t 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  | | | | | | | | | |)  }  f dI   }t || }t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d   t  | | | | | | |	  }  f dJ   }t || }t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d   t  | | | | | | |	  }  f dK   }t || }t t t t dL t d   t t t 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  | | | | | |' | | | | | |* |
  }  f dM   }t || }t t t t dL t d   t t t 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  | | | | | |' | | | | | |* |
  }  f dN   }t || }t t 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 t  | | | | | | |  }  f dO   }t || }t t 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 t  | | | | | | |  }  f dP   }t || }t t t t dL t d   t 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  | | | | | |' | | |+ 
 }  f dQ   }t || }t t t t dL t d   t 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  | | | | | |' | | |+ 
 }  f dR   }t || }  f dS   }t t t t dL t d   t 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  | | | | | |' | | | 
 }t || }  f dT   }t t t t dL t d   t 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  | | | | | |' | | | 
 }t || }  f dU   }t t t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t  | | | | | | |, |- |. |  }t || }  f dV   }t t t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t  | | | | | | |, |- |. |  }t || }  f dW   }t t t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t  | | | | | | |/ |- 	 }t || }  f dX   }t t t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t  | | | | | | |/ |- 	 }t || }t t t t dL t d   t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' | |0 | |1  }  f dY   }t || }t t t t dL t d   t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' | |0 | |1  }  f dZ   }t || }t t t t dL t d   t 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  | | | | | |' | |2 | | |1  }  f d[   }t || }t t t t dL t d   t 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  | | | | | |' | |2 | | |1  }  f d\   }t || }t t t t dL t d   t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' | | | | |3 |4  }  f d]   }t || }t t t t dL t d   t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' | | | | |3 |4  }  f d^   }t || }t t t t dL t d   t 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  | | | | | |' | | | | | |3 |4  }  f d_   }t || }t t t t dL t d   t 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  | | | | | |' | | | | | |3 |4  }  f d`   }t || }t t t t dL t d   t t t 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  | | | | | |' | | |0 | |1 |5  }  f da   }t || }t t t t dL t d   t t t 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  | | | | | |' | | |0 | |1 |5  }  f db   }t || }t t t t dL t d   t t t 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  | | | | | |' | |2 | | |6  }  f dc   }t || }t t t t dL t d   t t t 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  | | | | | |' | |2 | | |6  }  f dd   }t || }t t t t dL t d   t t t 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  | | | | | |' | | | | | |7 |8  }  f de   }t || }t t t t dL t d   t t t 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  | | | | | |' | | | | | |7 |8  }  f df   }t || }t t t t dL t d   t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | |' | |0 | |6 |5  }  f dg   }t || }t t t t dL t d   t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | |' | |0 | |6 |5  }  f dh   }t || }t t t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | | | |	 |5 
 }  f di   }t || }t t t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | | | |	 |5 
 }  f dj   }t || }t t t t dL t d   t t d t d   t d t d   t t t d t d    t t t t d  t d  t d    t  | | | | | |' | | | |9  }  f dk   }t || }t t t t dL t d   t t d t d   t d t d   t t t d t d    t t t t d  t d  t d    t  | | | | | |' | | | |9  }  f dl   }t || }t t t t dL t d   t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | |' | | | | | |:  }  f dm   }t || }t t t t dL t d   t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | |' | | | | | |:  }  f dn   }t || }t t t t dL t d   t t t 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  | | | | | |' | | |0 | |6 |; |5  }  f do   }t || }t t t t dL t d   t t t 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  | | | | | |' | | |0 | |6 |; |5  }  f dp   }t || }t t t t dL 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 t  | | | | | |' | | | | | |<  }  f dq   }t || }t t t t dL 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 t  | | | | | |' | | | | | |<  }  f dr   }t || } t t t t dL t d   t d t d   t d t d   t d t d   t t t d t d    t t t t t d  t d  t d    t  | | | | | |' | | | | |  }  f ds   }t || }t t t t dL t d   t d t d   t d t d   t d t d   t t t d t d    t t t t t d  t d  t d    t  | | | | | |' | | | | |  }  f dt   }t || }t t t t dL 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 t  | | | | | |' | | | |5 |= |  }  f du   }t || }	t t t t dL 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 t  | | | | | |' | | | |5 |= |  }
  f dv   }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 t t d t d    t d t d   t  | | | | | | | |> |? | |  }  f dw   }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 t t d t d    t d t d   t  | | | | | | | |> |? | |  }  f dx   }t || }t t t t d t d   t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t t  | | | | | | | |> |? | |  }  f dy   }t || }t t t t d t d   t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t t  | | | | | | | |> |? | |  }  f dz   }t || }t t t t dL t d   t t t 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  | | | | | |' | | | | |/ |@ |5 |A  }  f d{   }t || }t t t t dL t d   t t t 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  | | | | | |' | | | | |/ |@ |5 |A  }  f d|   }t || }t t t 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  | | | | | | | |) 	 }  f d}   } t ||  }!t t t 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  | | | | | | | |) 	 }"  f d~   }#t |"|# }$  f d   }%t t t t dL 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  | | | | | |' | | |! |B  }&t |&|% }'  f d   }(t t t t dL 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  | | | | | |' | | |! |B  })t |)|( }*t t t t dL 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  | | | | | |' | |	 |! |5  }+  f d   },t |+|, }-t t t t dL 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  | | | | | |' | |	 |! |5  }.  f d   }/t |.|/ }0t t t t dL 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  | | | | | |' | | | |C  }1  f d   }2t |1|2 }3t t t t dL 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  | | | | | |' | | | |C  }4  f d   }5t |4|5 }6t t t t d t d   t d t d   t t t d  t d   t t t t dC t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' |( |D | | | |$ |% |&  }7  f d   }8t |7|8 }9t t t t d t d   t d t d   t t t d  t d   t t t t dC t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' |( |D | | | |$ |% |&  }:  f d   };t |:|; }<t t t d t d   t d t d   t t t d t d    t d t d   t 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 d t d   t t t d  t d   t  | | | | | |	  }@  f d   }At |@|A }Bt t 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  | | | | | | |	 |
 	 }C  f d   }Dt |C|D }Et t 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  | | | | | | |	 |
 	 }F  f d   }Gt |F|G }Ht t 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 t  | | | | | | | | 	 }I  f d   }Jt |I|J }Kt t 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 t  | | | | | | | | 	 }L  f d   }Mt |L|M }Nt 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 t  | | | | | | |  }O  f d   }Pt |O|P }Qt 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 t  | | | | | | |  }R  f d   }St |R|S }T  f d   }Ut t t t d t d   t d t d   t t t d t d    t  | | | |E  }Vt |V|U }W  f d   }Xt t t t d t d   t d t d   t t t d t d    t  | | | |E  }Yt |Y|X }Zt t t t d t d   t d t d   t t t d t d    t t  | | | | |E  }[  f d   }\t |[|\ }]t t t t d t d   t d t d   t t t d t d    t t  | | | | |E  }^  f d   }_t |^|_ }`  f d   }at t 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  | | | | | | |E  }bt |b|a }c  f d   }dt t 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  | | | | | | |E  }et |e|d }f  f d   }gt t t t t d  t d   t t t dC t d   t dL t d   t d( t d   t d t d   t d t d   t t t d t d    t t  | | | | | |' |( |F |G |H  }ht |h|g }i  f d   }jt t t t t d  t d   t t t dC t d   t dL t d   t d( t d   t d t d   t d t d   t t t d t d    t t  | | | | | |' |( |F |G |H  }kt |k|j }l  f d   }m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 t dC t d   t dL t d   t d( t d   t t t d  t d   t d  t  | | | | | |' |( |D |F |I  }nt |n|m }o  f d   }p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 t dC t d   t dL t d   t d( t d   t t t d  t d   t d  t  | | | | | |' |( |D |F |I  }qt |q|p }rt t t 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 t  | | | | | |E |	 |5 	 }s  f d   }tt |s|t }ut t t 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 t  | | | | | |E |	 |5 	 }v  f d   }wt |v|w }x  f d   }yt t t t t d  t d  t d   t t t t dC t d   t d t d   t d t d   t d t d   t t t d t d    t  | | | | | |' |( | |5 |J | |K |L  }zt |z|y }{  f d   }|t t t t t d  t d  t d   t t t t dC t d   t d t d   t d t d   t d t d   t t t d t d    t  | | | | | |' |( | |5 |J | |K |L  }}t |}|| }~t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |M | |	 |K |N  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |M | |	 |K |N  }  f d   }t || }t t t t t t d  t d  t d    t t t dC t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' |( | |5 | |	 |O  }  f d   }t || }t t t t t t d  t d  t d    t t t dC t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |' |( | |5 | |	 |O  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |/ | |	  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |/ | |	  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |P | |	 |O  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |P | |	 |O  }  f d   }t || }t t t t t dC t d   t d t d   t d t d   t d t d   t t t d t d    t t t t t d  t d  t d    t  | | | | | |' |( | |5 | |K | |  }  f d   }t || }t t t t t dC t d   t d t d   t d t d   t d t d   t t t d t d    t t t t t d  t d  t d    t  | | | | | |' |( | |5 | |K | |  }  f d   }t || }t t t t t dC 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 d  t d  t d    t  | | | | | |' |( | | |5 | |Q  }  f d   }t || }t t t t t dC 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 d  t d  t d    t  | | | | | |' |( | | |5 | |Q  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |J | |	  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | |5 |J | |	  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | | |5 |, |  }  f d   }t || }t t t t t d  t d  t d   t t t t dC 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  | | | | | |' |( | | |5 |, |  }  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 t dC t d   t dL t d   t d t d   t d t d    t t t t d  t d  t d    t  | | | | | |' |( |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 t t dC t d   t dL t d   t d t d   t d t d    t t t t d  t d  t d    t  | | | | | |' |( |D | | | |	  }  f d   }t || }t t t t 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 t dC t d   t dL t d   t d t d   t d t d    t  | | | | | |' |( |D | | | |, |  }  f d   }t || }t t t t 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 t dC t d   t dL t d   t d t d   t d t d    t  | | | | | |' |( |D | | | |, |  }  f d   }t || }  f d   }t t t t t d  t d   t t t t dC t d   t t d t d   t d t d   t t t d t d    t  | | | | | |' |( |R 	 }t || }  f d   }t t t t t d  t d   t t t t dC t d   t t d t d   t d t d   t t t d t d    t  | | | | | |' |( |R 	 }t || }t t t t t d  t d   t d t d   t t t dC 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  | | | | | |' |( | |5 
 }  f d   }t || }t t t t t d  t d   t d t d   t t t dC 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  | | | | | |' |( | |5 
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 }  f d   }t || }t t t t t d t d   t t t d t d    t d t d   t t t d  t d  t d   t 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 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  | | | | |  }  f d   }t || } t t t d t d   t d t d   t t t t d t d    t d t d   t  | | | | | |V  }  f d   }t || }t t t d t d   t d t d   t t t t d t d    t d t d   t  | | | | | |V  }  f d   }t || }t t t t dL t d   t d  t d   t d t d   t d t d   t d t d   t t t t d t d    t d t d   t  | | | | | |' | | |W 
 }  f d   }t || }	t t t t dL t d   t d  t d   t d t d   t d t d   t d t d   t 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 t d t d    t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | |Z |[ |\ | | |X |Y  }  f d   }t || }t t t d t d   t d t d   t t t t d t d    t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | |Z |[ |\ | | |X |Y  }  f d   }t || }t t t t dL t d   t d  t d   t d t d   t d t d   t d t d   t t t t d t d    t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | | |' |Z |[ |\ | | | |X |Y  }  f d   }t || }t t t t dL t d   t d  t d   t d t d   t d t d   t d t d   t t t t d t d    t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | | |' |Z |[ |\ | | | |X |Y  }  f d   }t || }t t t t d t d   t d t d   t t t t d  t d t d     t  | | | | |]  }  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  | | | |^  }  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  | | | |^  }  f d   } t ||  }!t t t d t d   t d t d   t t t t d  t d t d    t t  | | | | |] | |_  }"  f d   }#t |"|# }$t t t d t d   t d t d   t t t t d  t d t d    t t  | | | | |] | |_  }%  f d   }&t |%|& }'t t t d  t d t d   t d t d   t t t t d  t d t d    t  | | | | |]  }(  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  | | | |^  }+  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  | | | |^  }.  f d   }/t |.|/ }0t t t d  t t d t d   t d t d   t t t t d  t d t d     t  | | | | |]  }1  f d   }2t |1|2 }3t t t d  t t d t d   t d t d   t t t d  t d t d   t d    t  | | | |^  }4  f d   }5t |4|5 }6t t t d  t t d t d   t d t d   t t t d  t d t d   t d    t  | | | |^  }7  f d   }8t |7|8 }9t t t d t d   t d t d   t t t t d  t d t d    t d  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  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  d t  | | | |^  }@  f d   }At |@|A }Bt t t d t d   t d t d   t t t t d  t d t d    t d  t  | | | | |]  }C  f d   }Dt |C|D }Et t t d t d   t d t d   t t t d  t d t d   t d   t d  t  | | | |^  }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 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 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 d    t t  | | | | |] | | |` 	 }O  f d   }Pt |O|P }Qt t t t t t d t d    t d t d   t t  | | |	  }R  f d   }St |R|S }Tt t t t t t d t d    t d t d   t t  | | |	  }U  f d   }Vt |U|V }Wt t t d t d   t t d t d   t t d t d   t d t d   t d t d    t d t d   t  | | | | | |a  }X  f d   }Yt |X|Y }Zt t t d t d   t t d t d   t t d t d   t d t d   t d t d    t d t d   t  | | | | | |a  }[  f d   }\t |[|\ }]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  | | |b  }^  f d   }_t |^|_ }`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  | | |b  }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 d t d   t  | | | |' |	  }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 d t d   t  | | | |' |	  }g  f d   }ht |g|h }it t t t t d  t d t d   t t t t d  t d t d    t d t d    t  | | | | |c  }j  f d   }kt |j|k }lt t t t t d  t d t d   t t t t d  t d t d    t d t d    t  | | | | |c  }m  f d   }nt |m|n }ot t t t  t  |d |e  }p  f d   }qt |p|q }rt t t t  t  |d |e  }s  f d   }tt |s|t }ut 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 |f |e 
 }v  f d   }wt |v|w }xt 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 |f |e 
 }y  f d   }zt |y|z }{d   }|t t t t d t d   t d t d   t t  t  | | |d |g t ||  }}  f d  }~t |}|~ }d  }t t t t d t d   t d t d   t t  t  | | |d |h t |  }  f d  }t || }t t t t t d t d    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  | | | |	  }  f d  }t || }t t t t t d t d    t d t d   t d t d   t t  | | | | |i  }  f d  }t || }t t t d t d   t d t d   t t t d t d    t t  | | | | |i  }  f d  }t || }t t 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  | | | | | |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 t d  t d   t  | | | | | |j |	  }  f d	  }t || }t t t t t d t d    t t t d  t d   t  | | | |k |l  }  f d
  }t || }t t t t t d t d    t t d  t d   t d t d   t  | | | |m  }  f d  }t || }t t t t t d t d    t t d  t d   t d t d   t  | | | |m  }  f d  }t || }t t t t t t d t d    t d t d   t t d  t d   t d t d   t  | | | | | |n  }  f d  }t || }t t t t d t d   t t t d t d    t t d  t d   t d t d   t  | | | | | |n  }  f d  }t || }t t t t d  t d   t d t d   t d( t d   t t t d t d    t d t d   t d t d   t  | | | | | | |)  }  f d  }t || }t t t t d  t d   t d t d   t d( t d   t 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  | | | |o |_  }  f d  }t || }t t t d t d   t d t d   t t t d t d    t t t  | | | |o |_  }  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  | | | | |o |_ |
  }  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 t  | | | | |o |_ |
  }  f d  }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 d t d   t  | | | | | |F  }  f d  }t || }t t 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  | | | | | |F  }  f d  }t || }t t t t d  t d   t d t d   t d( t d   t t t d t d    t d t d   t 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 d   t d t d   t t t d t d    t d t d   t  | | | | | | | |# 	 }  f d  }t || }t t t t d t d   t t t d t d    t d t d   t d t d   t d t d   t t t d  t d   t  | | | | | |j |	 |p |K 
 }  f d  }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t d t d   t t t d  t d   t  | | | | | |j |	 |p |K 
 }  f d  }t || }t t t t t d t d    t d t d   t d t d   t d t d   t t t t d  t d   t  | | | | | |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 t t d  t d   t  | | | | | |j |	  }  f d  }t || }t t t t 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  | | | | | |j |	 |p |1 
 }  f d  }t || }t t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d   t  | | | | | |j |	 |p |1 
 }  f d  }t || }t t t t d t d   t t t d  t d   t d( t d   t t t d t d    t d t d   t d t d   t 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 d t d   t t t d t d    t d t d   t  | | | | | | |! |	 |q 
 }  f d   }t || }t t t 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 d t d   t  | | | | | | | | |r 
 }  f d!  }t || }t t t t d t d   t t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | | |r 
 }  f d"  }t || }t t 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  | | | | | |s |t | 	 }  f d#  }t || }t t 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  | | | | | |s |t | 	 }  f d$  }t || }t t 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 t  | | | | | |s | | |_ 
 }  f d%  }t || }t t 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 t  | | | | | |s | | |_ 
 }  f d&  }t || }t t t d  t t t d  t d  t d   t t t d t d    t d t d   t d t d   t  | | | | | |s  }  f d'  }t || }t t 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  | | | | | |s  }  f d(  }t || }t t 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  | | | | | | |s | 	 }  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 t d  t d  t d   t  | | | | | | |s | 	 }  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 d    t  | | | | | |s |  }  f d+  }t || }t t t d t d   t d t d   t t t d t d    t t t t d  t d  t d    t  | | | | | |s |  }  f d,  }t || }t t t t t d t d    t d t d   t d t d   t d t d   t t t t d  t d  t d    t  | | | | | |s |	 | 	 }  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 t t d  t d  t d    t  | | | | | |s |	 | 	 }  f d.  }t || }t t t t t d t d    t d t d   t d t d   t d t d   t t t t d  t d  t d    t  | | | | | |s |	 | 	 }  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 t t d  t d  t d    t  | | | | | |s |	 | 	 }  f d0  }	t ||	 }
t t 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  | | | | | |s | | 	 }  f d1  }t || }t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t d  t  | | | | | |s | | 	 }  f d2  }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.  d t  | | | | | |s  }  f d3  }t || }t t t d t d   t d t d   t t t d t d    t t t d  t d  t d   t d.  d t  | | | | | |s  }  f d4  }t || }t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t  | | | | | |s |t | | 
 }  f d5  }t || }t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t  | | | | | |s |t | | 
 }  f d6  }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 d   t d.  d t  | | | | | |s | |_ 	 }  f d7  }t || }t t t d t d   t d t d   t t t d t d    t t t t d  t d  t d   t d.  d t  | | | | | |s | |_ 	 }   f d8  }!t | |! }"t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t t  | | | | | |s | | |_ |  }#  f d9  }$t |#|$ }%t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t t  | | | | | |s | | |_ |  }&  f d:  }'t |&|' }(t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t t  | | | | | |s | | | 
 })  f d;  }*t |)|* }+t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t t  | | | | | |s | | | 
 },  f d<  }-t |,|- }.t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s |u | 
 }/  f d=  }0t |/|0 }1t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s |u | 
 }2  f d>  }3t |2|3 }4t t t t 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  | | | | | | |s |u |! 
 }5  f d?  }6t |5|6 }7t t t t 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  | | | | | | |s |u |& 
 }8  f d@  }9t |8|9 }:t t t t t d t d    t t d  t d  t d   t d t d   t  | | | |m  };  f dA  }<t |;|< }=t t t t t d t d    t t d  t d  t d   t d t d   t  | | | |m  }>  f dB  }?t |>|? }@t t t t t t d t d    t d t d   t t d  t d  t d   t d t d   t  | | | | | |n  }A  f dC  }Bt |A|B }Ct t t t d t d   t t t d t d    t t d  t d  t d   t d t d   t  | | | | | |n  }D  f dD  }Et |D|E }F  f dE  }Gt t t t d  t d  t d   t d t d   t d( t d   t t t d t d    t d t d   t d t d   t  | | | | | |v  }Ht |H|G }I  f dF  }Jt t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | |v  }Kt |K|J }Lt t t t t d  t d  t d   t d( t d   t t t d t d    t d t d   t d t d   t d t d   t  | | | | | |! |	  }M  f dG  }Nt |M|N }Ot t 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  | | | | | |! |	  }P  f dH  }Qt |P|Q }Rt t t t d  t d  t d   t d t d   t d( t d   t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | | |# 	 }S  f dI  }Tt |S|T }Ut t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |# 	 }V  f dJ  }Wt |V|W }Xt t t t 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  | | | | | |0 | |6 	 }Y  f dK  }Zt |Y|Z }[t t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |0 | |6 	 }\  f dL  }]t |\|] }^t t t t 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  | | | | | |0 | |1 	 }_  f dM  }`t |_|` }at t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |0 | |1 	 }b  f dN  }ct |b|c }dt t t 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  | | | | | |s |	  }e  f dO  }ft |e|f }gt t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |s |	  }h  f dP  }it |h|i }j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 d   t  | | | | | |s |i | 	 }k  f dQ  }lt |k|l }mt t t t d t d   t d t d   t t t d t d    t t t t d  t d  t d   t  | | | | | |s |i | 	 }n  f dR  }ot |n|o }pt t t t 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  | | | | | |s |0 | |6 
 }q  f dS  }rt |q|r }st t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |s |0 | |6 
 }t  f dT  }ut |t|u }vt t t t t d t d    t d t d   t d t d   t d t d   t t t t d  t d  t d   t  | | | | | |s | | 	 }w  f dU  }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 t t t d  t d  t d   t  | | | | | |s | | 	 }z  f dV  }{t |z|{ }|t t t t 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  | | | | | |s |0 | |1 
 }}  f dW  }~t |}|~ }t t t t t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |s |0 | |1 
 }  f dX  }t || }t 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 d   t  | | | | | | |s | | 
 }  f dY  }t || }t t t t t d t d   t d t d   t t t d t d    t t t t d  t d  t d   t  | | | | | | |s | | 
 }  f dZ  }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  | | | | | |5 |w  }  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 t t d  t d  t d   t  | | | | | |5 |w  }  f d\  }t || }t t t t t t d  t d  t d   t d( t d   t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s | | |)  }  f d]  }t || }t t t 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  | | | | | | |s | | |)  }  f d^  }t || }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 d   t d  t  | | | | | |s | | |` 
 }  f d_  }t || }t t t t d t d   t d t d   t t t d t d    t t t t d  t d  t d   t d  t  | | | | | |s | | |` 
 }  f d`  }t || }t t t t d  t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t  | | | | | |s |t | |x 
 }  f da  }t || }t 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 d    t  | | | | | |s |t | |x 
 }  f db  }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 t t d  t d  t d   t d  t  | | | | | |s | | 	 }  f dc  }t || }t t t t d  t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t d  t  | | | | | |s | | 	 }  f dd  }t || }t t t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t  | | | | | |s |y |t | 
 }  f de  }t || }t t t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t  | | | | | |s |y |t | 
 }  f df  }t || }t t t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t t  | | | | | | |s |y | | |_  }  f dg  }t || }t t t t t t t d  t d  t d   t t d t d   t d t d   t t t d t d    t t  | | | | | | |s |y | | |_  }  f dh  }t || }t t t t d t d   t t t d  t d  t d   t d( t d   t t t d t d    t d t d   t d t d   t t  | | | | | | | |s |y | |  }  f di  }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 t t d t d    t t  | | | | | | | |s |y | |  }  f dj  }t || }t t t t d t d   t t t d  t d  t d   t d( t d   t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | | |s |* | | |
  }  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 d   t d t d   t t t d t d    t d t d   t  | | | | | | | |s |* | | |
  }  f dl  }t || }t t t 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  | | | | | | |s |z 	 }  f dm  }t || }t t t t t t t t d  t d  t d    t d t d   t d t d   t t t d t d    t  | | | | | | |s |z 	 }  f dn  }t || }t t t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s |	 |! |{  }  f do  }t || }t t t t t t 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  | | | | | | |s |	 |! |{  }  f dp  }t || }t t t t t t t d  t d  t d   t d( t d   t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s |t | |	 ||  }  f dq  }t || }t t t t 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  | | | | | | |s |t | |	 ||  }  f dr  }t || }t t t t t t t d t d    t d t d   t d t d   t d t d   t t t t d  t d  t d    t  | | | | | |s |0 | |6 
 }  f ds  }t || }t t t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | |s |0 | |6 
 }  f dt  }t || }t t t t t d t d    t d t d   t d t d   t t t t t d  t d  t d    t  | | | | | |s |  }  f du  }t || }t t t d t d   t d t d   t t t d t d    t t t t t d  t d  t d    t  | | | | | |s |  }  f dv  }t || }t t t t t d t d    t d t d   t d t d   t t t t t t d  t d  t d    t  | | | | | |s |	 | 	 }  f dw  }t || }t t t d t d   t d t d   t t t d t d    t t t t t t d  t d  t d    t  | | | | | |s |	 | 	 }  f dx  }t || }t t 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  t d    t  | | | | | |s |	 | 	 }  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 t t t d  t d  t d    t  | | | | | |s |	 | 	 }  f dz  }t || }t t t t t d t d    t d t d   t d t d   t d t d   t t d  t t t t d  t d  t d    t  | | | | | |s | | 	 }  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 d  t t t t d  t d  t d    t  | | | | | |s | | 	 }  f d|  }t || }t t t t t t t d t d    t d t d   t d t d   t d t d   t t t t d  t d  t d    t  | | | | | |s |0 | |1 |}  }  f d}  }t || }t t t t t d t d   t d t d   t t t d t d    t d t d   t t t t d  t d  t d    t  | | | | | |s |0 | |1 |}  }  f d~  }t || }t t t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | |s |~ | |6 |  }  f d  }t || }t t t t t t 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  | | | | | |s |~ | |6 |  }  f d  }t || }t t t t t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | |s |~ | |O |  }  f d  }t || }t t t t t t 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  | | | | | |s |~ | |O |  }  f d  }t || } t t t t d t d   t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | |s |2 | | |  }  f d  }t || }t t t t d t d   t t 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  | | | | | |s |2 | | |  }  f d  }t || }t t t t d t d   t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s | | |  }  f d  }t || }	t t t t d t d   t t t d  t d  t d   t t t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |s | | |  }
  f d  }t |
| }t t t t d t d   t t 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  | | | | | | |s | | |!  }  f d  }t || }t t t t d t d   t t 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  | | | | | | |s | | |&  }  f d  }t || }t t t t t d  t d  t d   t d t d   t d( t d   t t t d t d    t d 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 d   t d t d   t d t d   t t t d t d    t  | | | | | | |)  }  f d  }t || }  f d  }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t t t d t d    t d t d   t d t d   t  | | | | | | | | 	 }t || }  f d  }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t 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 t t d t d    t d t d   t d t d   t d t d   t  | | | | | | |! |	 | 
 }  f d  } t ||  }!t t t t d t d   t t t d  t d  t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | |! |	 | 
 }"  f d  }#t |"|# }$t t t t d t d   t t t t d t d    t d t d   t t t d  t d  t d   t d( t d   t  | | | | | | | | 	 }%  f d  }&t |%|& }'t t t t d t d   t t d t d   t t t d t d    t t t d  t d  t d   t d( t d   t  | | | | | | | | 	 }(  f d  })t |(|) }*t t t t d t d   t t 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  | | | | | | | | |r 
 }+  f d  },t |+|, }-t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | | |r 
 }.  f d  }/t |.|/ }0t t 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  t d   t  | | | | | |s | | | 
 }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 t  t t t d  t d  t d   t  | | | | | |s | | | 
 }4  f d  }5t |4|5 }6t t 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  t d   t  | | | | | |s | | | 
 }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 t  t t t d  t d  t d   t  | | | | | |s | | | 
 }:  f d  };t |:|; }<t t 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  t d   t  | | | | | |s | | | 
 }=  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  t t t d  t d  t d   t  | | | | | |s | | | 
 }@  f d  }At |@|A }Bt t 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  t d   t  | | | | | |s | | | 
 }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 t  t t t d  t d  t d   t  | | | | | |s | | | 
 }F  f d  }Gt |F|G }Ht t t t t d t d    t d t d   t d t d   t d t d   t t t  t t t d  t d  t d   t  | | | | | | |s | | |  }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 t t  t t t d  t d  t d   t  | | | | | | |s | | |  }L  f d  }Mt |L|M }Nt t t t t d t d    t d t d   t d t d   t d t d   t t t  t t t d  t d  t d   t  | | | | | | |s | | |  }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 t t  t t t d  t d  t d   t  | | | | | | |s | | |  }R  f d  }St |R|S }Tt t t d  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 d   t t t d t d    t  | | | | | |s  }U  f d  }Vt |U|V }Wt t t t t d t d    t d t d   t d t d   t d t d   t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |s |T | 	 }X  f d  }Yt |X|Y }Zt t t t t d t d    t d t d   t d t d   t d t d   t d t d   t d t d   t t t d t d    t d t d   t t t d  t d  t d   t  | | | | | |s |T | 	 }[  f d  }\t |[|\ }]t t t t t d t d    t t t d t d   t d t d   t  | | | |o |  }^  f d  }_t |^|_ }`t t t t t d t d    t t t d t d   t d t d   t  | | | |o |  }a  f d  }bt |a|b }ct t 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 dC t d   t dL t d    t  | | | | | |' |( | 	 }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 d  t d   t t t d  t dC t d   t dL t d    t  | | | | | |' |( | 	 }g  f d  }ht |g|h }i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 dC t d   t dL t d    t  | | | | | |' |( | 	 }j  f d  }kt |j|k }l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 t t d  t dC t d   t dL t d    t  | | | | | |' |( | 	 }m  f d  }nt |m|n }o  f d  }p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 dC t d   t dL t d    t  | | | | | |' |( | 	 }qt |q|p }r  f d  }s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 t t d  t dC t d   t dL t d    t  | | | | | |' |( | 	 }tt |t|s }u  f d  }v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 dC t d   t dL t d    t  | | | | | |' |( |5 | 
 }wt |w|v }x  f d  }yt t t t d t d   t d t d   t d t d   t t t d t d    t d t d   t d  t d   t t t d  t dC t d   t dL t d    t  | | | | | |' |( |5 | 
 }zt |z|y }{t t t t t t d t d    t d t d   t d t d   t d  t d t d   t d  t d   t t t t d  t dC t d    t  | | | | | |' |( | 	 }|  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 d   t d  t d   t t t t d  t dC t d    t  | | | | | |' |( | 	 }  f d  }t || }t t t t t t t d t d     t  | |  }  f d  }t || }t t t t d t d   t t t t t d t d     t  | | |  }  f d  }t || }t t t t t t d t d    t d t d    t  | | |  }  f d  }t || }t t t t d t d   t t t t d t d    t d t d    t  | | | |  }  f d  }t || }t t t t t d t d   t d( t d   t d t d   t t t t d t d    t d t d    t  | | | | | | |  }  f d  }t || }t t t t t d t d   t d( t d   t d t d   t t t t d t d    t d t d    t  | | | | | | |  }  f d  }t || }t t t t d t d   t t d( t d   t d t d   t t t t d t d    t d t d    t  | | | | | |!  }  f d  }t || }t t t t d t d   t t t d t d   t t t t t d t d     t  | | | | | |& | | 	 }  f d  }t || }t t t t d t d   t t t d t d   t t t t t d t d     t  | | | | | |& | | 	 }  f d  }t || }t t t t d t d   t t t d t d   t t t t d t d    t d t d    t  | | | | | | |&  }  f 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.  d t  | | | | | |  }  f d  }t || }t t t t t d  t d t d   t t t t t d t d    t d t d    t  | | | | | |t | | | |>  }  f d  }t || }t t t t t t d t d    t d t d    t t 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 t 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 t t t d t d    t d t d    t  | | | | | | |  }  f d  }t || }t t t t t d  t d t d   t t t t t t d t d     t  | | | | | | |  }  f d  }t || }t t t t t d  t d t d   t t t t t t d t d     t  | | | | | | |  }  f d  }t || }t t t t t d  t d t d   t t t t t d t d    t d t d    t  | | | | | | |  }  f d  }t || }t t t t t t t d t d    t d t d    t t t d  t d t d   t d.  d t  | | | | | |  }  f d  }t || }t t t t t t d  t d t d   t t t t 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 t t t d t d    t d t d    t  | | | | | | |  }  f d  }t || }t t t t d  t t t d  t d t d   t 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 t t t 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 t t t d t d    t d t d    t  | | | | | | | | 	 }  f d  }t || }t t t t d t d   t t t d  t d t d   t t t t t t d t d     t  | | | | | | | | 	 }  f d  }t || }t t t t d t d   t t t d  t d t d   t t t t t t d t d     t  | | | | | | | | 	 }  f d  }t || }t t t t d t d   t t t d  t d t d   t t t t t d t d    t d t d    t  | | | | | | | | 	 }  f d  }t || }t t t t t t d  t d t d   t d( t d   t t t t d t d    t d t d    t  | | | | | | |  }  f d  }t || }t t t t t t d  t d t d   t d( t d   t t t t t d t d     t  | | | | | | | | 	 }  f d  }t || }t t t t t t d  t d t d   t t t t t d t d    t d t d    t  | | | | | | | | 	 }  f d  }t || }t t t t d t d   t t d  t d( t d   t d t d   t t t t d t d    t d t d    t  | | | | | |!  }  f d  }t || }t t t t d t d   t t d  t t d t d   t t t t t d t d     t  | | | | | |& | | 	 }  f d  }t || }t t t t d t d   t t d  t t d t d   t t t t t d t d     t  | | | | | | |& | | 
 }  f d  }t || }t t t t d t d   t t d  t t d t d   t t t t d t d    t d t d    t  | | | | | | |& | 	 }  f d  }t || }t t t t t t t d t d   t d t d    t d t d    t  | | | | |  }  f d  }t || }t t t t t t t t t t d t d   t d t d     t  | | | |G | |  }  f d  }t || }t t t t d  t d   t d t d   t d t d   t t t 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 d   t t d t d   t d( t d   t d t d   t t t t t d t d    t d t d    t  | | | | | | | | | |  }  f d  }t || }t t t t t d  t d  t d   t t d t d   t d( t d   t d t d   t t t t t d t d    t d t d    t  | | | | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   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 t t d t d     t  | |  }  f d  }t || }t t t t t t t d t d     t  | |  }  f d  }t || }t t t t d t d   t t t t t d t d     t  | | |5  }   f d  }t | | }t t t t d t d   t t t d t d     t  | | |  }  f d  }t || }t t t t d t d   t t d t d   t t t d t d     t  | | | |5  }  f d  }t || }t t t t t t t t t d t d     t  | | | |9  }	  f d  }
t |	|
 }t t t t t t d t d   t t t d t d     t  | | | | |9  }  f d  }t || }t t t t t d t d   t d( t d   t d t d   t t d t d   t t t d t d     t  | | | | | | |!  }  f d  }t || }t t t t t d t d   t t d t d   t t d t d   t t t d t d     t  | | | | | | | |& 	 }  f d  }t || }t t t t d t d   t t d( t d   t t d t d   t t t d t d     t  | | | | | | | | 	 }  f d  }t || }t t t t d t d   t t d t d   t t d( t d   t t d t d   t t t d t d     t  | | | | | | | | | |5  }  f d  }t || }t t t t d t d   t t t t d t d   t t t d t d     t  | | | | | | | | 	 }  f d  }t || }t t t t t t d t d   t t d( t d   t t d t d   t t t d t d     t  | | | | | | | | | |9  }  f d  }t || } t t t t d t d   t t t d t d   t t d t d   t t t d t d     t  | | | | | | | | 	 }!  f d  }"t |!|" }#t t t t d t d   t t t d t d     t t t d  t d t d   t  | | | | |  }$  f d  }%t |$|% }&t t t t d t d   t t t d t d     t t t d  t d t d   t d.  d t  | | | | | |  }'  f d  }(t |'|( })t t t t t d  t d t d   t t t d t d   t t t d t d     t  | | | | | |t | | | | |  }*  f d  }+t |*|+ },t t t t t d t d   t t t d t d     t t t d  t d t d   t d.  d t  | | | | | |  }-  f d  }.t |-|. }/t t t t t t d  t d t d   t t t d t d   t t t d t d     t  | | | | | |t | | | | |  }0  f d  }1t |0|1 }2t 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 d     t  | | | | | | |  }3  f d  }4t |3|4 }5t t t t d  t t t d  t d t d   t t t d t d   t t t d t d     t  | | | | | |t | | | | |  }6  f d  }7t |6|7 }8t t t t d t d   t t t d  t d t d   t t t d t d   t t t d t d     t  | | | | | |5 | |! 	 }9  f d  }:t |9|: };t t t t t d  t d t d   t d( t d   t d t d   t 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 t d t d   t t d t d   t t t d t d     t  | | | | | | | |& 	 }?  f d  }@t |?|@ }At t t t d t d   t t d  t d( t d   t d t d   t t d t d   t t t d t d     t  | | | | | | | | | 
 }B  f d  }Ct |B|C }Dt t t t d t d   t t d  t d( t d   t t d t d   t t t d t d     t  | | | | | | | | | 
 }E  f d  }Ft |E|F }Gt t t t d t d   t t d t d   t t d  t d( t d   t t d t d   t t t d t d     t  | | | | | | | | | |5  }H  f d  }It |H|I }Jt t t t t t d t d   t t d  t d( t d   t t d t d   t t t d t d     t  | | | | | | | | | | |9  }K  f d  }Lt |K|L }Mt t t t d t d   t t d  t t d t d   t t d t d   t t t d t d     t  | | | | | | | | 	 }N  f d  }Ot |N|O }Pt t t d t d   t t t t t t d t d   t d t d     t  | | | |  }Q  f d  }Rt |Q|R }St t t t d t d   t t t t d t d   t d t d     t  | | | | |  }T  f d  }Ut |T|U }Vt t t t t t t t t t d t d   t d t d     t  | | | |G | |  }W  f d  }Xt |W|X }Yt t t t d  t d   t d t d   t d t d   t t d t d   t t t t d t d   t d t d     t  | | | | | | | | 	 }Z  f d  }[t |Z|[ }\t t t t t d  t d  t d   t t d t d   t d( t d   t d t d   t t d t d   t t t t d t d     t  | | | | | | | | | | |  }]  f d  }^t |]|^ }_t t t t t d  t d  t d   t t d t d   t d( t d   t d t d   t t d t d   t t t t d t d     t  | | | | | | | | | | |  }`  f d  }at |`|a }bt t t d t d   t t d t d   t t d t d   t t d t d   t d t d     t  | | | | |  }c  f d  }dt |c|d }et t t t t t d t d    t d t d   t d t d   t d t d   t  | | | | |	  }f  f d  }gt |f|g }ht t t d t d   t d t d   t t t t d t d    t d t d   t  | | | | |	  }i  f d  }jt |i|j }kt t t t t t d t d    t d t d   t d t d   t t  | | | | | |i  }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 t  | | | | | |i  }o  f d  }pt |o|p }qt t t t dL 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 d t d   t  | | | | | |' | | |	 
 }r  f d  }st |r|s }tt t t t dL t d   t d  t d   t d t d   t d t d   t d t d   t t t t d t d    t d t d   t  | | | | | |' | | |	 
 }u  f d  }vt |u|v }wt t t t dL t d   t d  t d   t t t t t d t d    t d t d   t d t d   t t  | | | | | |' | | |i 
 }x  f d   }yt |x|y }zt t t t dL t d   t d  t d   t t d t d   t d t d   t t t t d t d    t t  | | | | | |' | | |i 
 }{  f d  }|t |{|| }}t t t t t t d t d    t d t d   t d t d   t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | |Z |[ |\ | | | |Y  }~  f d  }t |~| }t t t d t d   t d t d   t t t t d t d    t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | |Z |[ |\ | | | |Y  }  f d  }t || }t t t t dL 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 d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | | |' |Z |[ |\ | | | | |Y  }  f d  }t || }t t t t dL t d   t d  t d   t d t d   t d t d   t d t d   t t t t d t d    t d t d   t t d  t d t d   t t d t d   t d t d   t d( t d   t  | | | | | |' |Z |[ |\ | | | | |Y  }  f d  }t || }t t t t t t d t d    t t t d t d   t d t d   t  | | | | |  }  f d  }t || }t t t t t t d t d    t t t d t d   t d t d   t  | | | | |  }  f d  }t || }t t t t t t d t d    t t t t d t d   t  | | | | | |  }  f d  }t || }t t t t t t d t d    t t t t d t d   t  | | | | | |  }  f d	  }t || }t t t t t t t d t d    t  | | | |  }  f d
  }t || }t t t t t t t d t d    t  | | | |  }  f d  }t || }t t t t t t d t d   t d t d    t t  | | | |  }  f d  }t || }t t 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 t t d t d    t  | | |0 | |  }  f d  }t || }t t t t d t d   t t t t t d t d    t  | | |0 | |  }  f d  }t || }t t t t t t d t d   t d t d   t d t d   t d t d    t  | | | | |' |  }  f d  }t || }t t t t t t d t d   t d t d   t d t d   t d t d    t  | | | | |' |  }  f d  }t || }t t t t d t d   t t t t d t d   t d t d   t d t d   t d t d    t  | | | | |' |5 |K  }  f d  }t || }t t t t d t d   t t t t d t d   t d t d   t d t d   t d t d    t  | | | | |' |5 |K  }  f d  }t || }t t t t d t d   t t d t d   t d t d   t d t d    t d t d   t d t d   t  | | | | | |a  }  f d  }t || }t t t d t d   t t d t d   t t d t d   t d t d   t d t d    t d t d   t  | | | | | |a  }  f d  }t || }t t t d  t t t d  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  | | | |  }  f d  }t || }t t t d  t t t d  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  | | | |  }  f 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 t 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 d  t d t d   t d t d     t d t d   t t t d  t d t d   t d t d    t  | | | | | |
  }  f d  }t || }t t t t t d t d   t t t d  t d t d   t d t d     t d t d   t t t d  t d  t d   t d t d    t  | | | | | | | | 	 }  f d  }t || }t t t t t d t d   t t t d  t d t d   t d t d     t d t d   t t t d  t d  t d   t d t d    t  | | | | | | | | 	 }  f d  }t || }t t t t t t  t dt d    t d t d   t  | |  }  f d  }t || }t t t d t d   t t t t  t dt d    t  | |  }  f d  }t || }d  }t t t t t d t d   t  | |o | | | t |  }  f d   }t || }d!  }t t t t t d t d   t  | |o | | | t |  }  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  | | | | |  }  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  | | | | |  }  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  | | | | |  }  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  | | | | |  }  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  | | | | |  }  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  | | | | |  }  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  | | | | |  }  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  | | | | |  }  f d*  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d+  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d,  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d-  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d.  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d/  }t || } t t t t dL t d   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  | | | | | |' | | 	 }  f d0  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d1  }t || }t t t t dL t d   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  | | | | | |' | | 	 }  f d2  }t || }	t t t t t t d t d   t d t d     t  | | |  }
  f d3  }t |
| }t t t t t t d t d   t d t d     t  | | |  }  f d4  }t || }t t t t d  t t t d t d   t d t d     t  | | |  }  f d5  }t || }t t t t d  t t t d t d   t d t d     t  | | |  }  f d6  }t || }t t t t dL t d   t d  t d   t d t d   t t t t d t d   t d t d     t  | | | |' |  }  f d7  }t || }t t t t dL t d   t d  t d   t d t d   t t t t d t d   t d t d     t  | | | |' |  }  f d8  }t || }t t t t dL t d   t d  t d   t d t d   t t d  t t t d t d   t d t d     t  | | | |' |  }  f d9  }t || }t t t t dL t d   t d  t d   t d t d   t t d  t t t d t d   t d t d     t  | | | |' |  }  f d:  } t ||  }!t t t t d t d   t d t d   t t t 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 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 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 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 d t d   t d t d     t  | | | | |  }.  f d?  }/t |.|/ }0t t t t d t d   t d t d   t t t d t d   t d t d     t  | | | | |  }1  f d@  }2t |1|2 }3t t t t d t d   t d t d   t t t d t d   t d t d     t  | | | | |  }4  f dA  }5t |4|5 }6t t t t d t d   t d t d   t t t d t d   t d t d     t  | | | | |  }7  f dB  }8t |7|8 }9t t t t dL t d   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  | | | | | |' | | 	 }:  f dC  };t |:|; }<t t t t dL t d   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  | | | | | |' | | 	 }=  f dD  }>t |=|> }?t t t t dL t d   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  | | | | | |' | | 	 }@  f dE  }At |@|A }Bt t t t dL t d   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  | | | | | |' | | 	 }C  f dF  }Dt |C|D }Et t t t dL t d   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  | | | | | |' | | 	 }F  f dG  }Gt |F|G }Ht t t t dL t d   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  | | | | | |' | | 	 }I  f dH  }Jt |I|J }Kt t t t dL t d   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  | | | | | |' | | 	 }L  f dI  }Mt |L|M }Nt t t t dL t d   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  | | | | | |' | | 	 }O  f dJ  }Pt |O|P }Qt t t t  t  |d  }R  f dK  }St |R|S }Tt t t t  t  |d  }U  f dL  }Vt |U|V }W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 |f | 
 }X  f dM  }Yt |X|Y }Zt 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 |f | 
 }[  f dN  }\t |[|\ }]dO  }^t t t t t  t d t d   t d t d   t  | | |d | | t |^  }_  f dP  }`t |_|` }adQ  }bt t t t d t d   t d t d   t t  t  | | |d | | t |b  }c  f dR  }dt |c|d }et t t t  t t  t t d t d   t d t d   t  | | | | | |  }f  f dS  }gt |f|g }ht t t t  t t  t  | |  }i  f dT  }jt |i|j }kt t t t  t t  t  | |  }l  f dU  }mt |l|m }ndV  }ot t t t t  t t  t  | | t |o  }p  f dW  }qt |p|q }rdX  }st t t t t  t t  t  | | t |s  }t  f dY  }ut |t|u }vt t t t t d t d    t  | |  }w  f dZ  }xt |w|x }yt t t t t d t d    t  | |  }z  f d[  }{t |z|{ }|t t t d t d   t d t d   t t 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 t  | | | | |  }  f d]  }t || }t t t d t d   t d t d   t t t d t d    t t  | | | |S  }  f d^  }t || }t t t d t d   t d t d   t t t d t d    t t  | | | |S  }  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`  }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t  | | | | |
  }  f da  }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | |5  }  f db  }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t t  | | | | |5  }  f dc  }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |  }  f dd  }t || }t t t t d t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | |  }  f de  }t || }  f df  }t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | |   }t || }  f dg  }t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | |   }t || }t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | |!  }  f dh  }t || }t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | |!  }  f di  }t || }t t t t d  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  | | | | | | | |M | |  }  f dj  }t || }t t t t d  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  | | | | | | | |M | |  }  f dk  }t || }t t t t d  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  | | | | | | | |M | 
 }  f dl  }t || }t t t t d  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  | | | | | | | |M | 
 }  f dm  }t || }t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |# 	 }  f dn  }t || }t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |# 	 }  f do  }t || }t t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | | |)  }  f dp  }t || }t t t t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | | |)  }  f dq  }t || }  f dr  }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | | | | 	 }t || }  f ds  }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t  | | | | | | | | 	 }t || }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | |  }  f dt  }t || }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | |  }  f du  }t || }t t t t d t d   t t d  t d  t d   t d t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |5 |M | |  }  f dv  }t || }t t t t d t d   t t d  t d  t d   t d t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |5 |M | |  }  f dw  }t || }t t t t d t d   t t d  t d  t d   t d t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |5 |M |  }  f dx  }t || }t t t t d t d   t t d  t d  t d   t d t d   t t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | |5 |M |  }  f dy  }t || }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | | |r 
 }  f dz  }t || }t t t t d t d   t t d  t d  t d   t d t d   t d( t d   t d t d   t d t d   t t t d t d    t d t d   t  | | | | | | | | |r 
 }  f d{  }t || }t t t t t t d t d    t  | | |  }  f d|  }t || }t t t t t t d t d    t  | | |  }  f d}  }t || }t t t t t t d t d    t t  | | | |  }  f d~  }t || }t t t t t t d t d    t t  | | | |  }  f d  }t || }t t t t t t d t d    t t  | | |  }  f d  }t || }t t t t t t d t d    t t  | | |  }  f d  }t || }t t t t d t d   t t t t d t d    t  | | | |5 |
  }  f d  }t || }t t t t d t d   t t t t d t d    t  | | | |5 |
  }  f d  }t || }t t t t d t d   t t t t d t d    t t  | | | |  }  f d  }t || }t t t t d t d   t t t t d t d    t t  | | | |  }  f d  }t || }t t t d t d   t t d t d   t t d t d   t d t d   t d t d    t d t d   t  | | | | | |a  }  f d  }t || }t t t d t d   t t d t d   t t d t d   t d t d   t d t d    t d t d   t  | | | | | |a  }  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  | | | |' |	  }  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  | | | |' |	  }  f d  }t || }t t t t  t  |d |e  }  f d  }t || }	t t t t  t  |d |e  }
  f d  }t |
| }t 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 |f |e 
 }  f d  }t || }t 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 |f |e 
 }  f d  }t || }d  }t t t t d t d   t d t d   t t  t  | | |d | t |  }  f d  }t || }d  }t t t t d t d   t d t d   t t  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|{|~|||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|||||||||||||||||||||||||||||||||||||||||||||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|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|}||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|a|e|h|k|n|r|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	|||||gdS(  Ni(   t   cons87t   cons88t   cons2t   cons3t   cons7t   cons89t   cons1579t   cons4t   cons148t   cons66t   cons27t   cons21t   cons62t   cons1734t   cons1735t   cons1736t   cons1737t   cons268t   cons48t   cons584t   cons1738t   cons128t   cons338t   cons163t   cons137t   cons230t   cons5t   cons1739t   cons1740t   cons1741t   cons1742t   cons1743t   cons38t   cons1744t   cons1570t   cons336t   cons1745t   cons147t   cons125t   cons208t   cons54t   cons242t   cons1746t   cons347t   cons1747t   cons486t   cons961t   cons93t   cons94t   cons162t   cons272t   cons1748t   cons17t   cons166t   cons274t   cons1749t   cons18t   cons1750t   cons238t   cons237t   cons1751t   cons246t   cons1752t   cons1753t   cons1754t   cons1755t   cons1756t   cons209t   cons925t   cons464t   cons84t   cons1757t   cons1758t   cons719t   cons168t   cons1759t   cons667t   cons1760t   cons267t   cons717t   cons1761t   cons1608t   cons14t   cons150t   cons1198t   cons1273t   cons1360t   cons1762t   cons1763t   cons34t   cons35t   cons36t   cons1764t   cons1765t   cons165t   cons1442t   cons1766t   cons1767t   cons1768t   cons1230t   cons1769t   cons1770t   cons1771t   cons1772t   cons340t   cons1773t   cons1774t   cons1775t   cons1776t   cons1043t   cons85t   cons31t   cons1777t   cons1497t   cons1778t   cons13t   cons1779t   cons1780t   cons1781t   cons1782t   cons240t   cons241t   cons146t   cons1783t   cons1510t   cons1784t   cons1152t   cons319t   cons1785t   cons1786t   cons1787t   cons1788t   cons1789t   cons1790t   cons1791t   cons1792t   cons1793t   cons1794t   cons1795t   cons1796t   cons601t   cons1797t   cons261t   cons1798t   cons1799t   cons1800t   cons1801t   cons1802t   cons1803t   cons1804t   cons1805t   cons177t   cons117t   cons1806t   cons1807t   cons1808t   cons1809t   cons1810t   cons1811t   cons1812t   cons1813t   cons1814t   cons1815t   cons1816t   cons1817t   cons1580t   cons1818t   cons1819t   cons1820t   cons1821t   cons1822t   cons1823t   cons1824t   cons1825t   cons1826t   cons1827t   cons1828t   cons1829t   cons1830t   cons1094t   cons1831t   cons1832t   cons1833t   cons1834t   cons1835t   cons383t   cons1836t   cons1837t   cons818t   cons463t   cons1838t   cons1839t   cons1840t   cons1841t   cons1842t   cons1843t   cons1844t   cons67t   cons1845t   cons1846t   cons1847t   cons1848t   cons1849t   cons1850t   cons1851t   cons552t   cons1146t   cons1852t   cons1853t   cons1242t   cons1243t   cons1854t   cons178t   cons1855t   cons1856t   cons1299t   cons1857t   cons1858t   ai    t   bi   t   ct   nc      	      s     j  d  t |  | | t | | |  t | |  | t d  t | t d  | t d  t d   |  |  t | | |  t | |  | |  S(   Ni  ii   i   (   t   appendR  R   R  R  R  R  (   R  R  R  R  t   x(   t   rubi(    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5031   s    c      	      s     j  d  t |  | | t | | |  t | |  | t d  t | t d  | t d  t d   |  |  t | | |  t | |  | |  S(   Ni  ii   i   (   R  R  R   R	  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5032   s    c      	      s     j  d  t | |  | t d  t | | |  t | |  | t d  t | t d  | t d  t d   |  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5033   s    c      	      s     j  d  t | |  | t d  t | | |  t | |  | t d  t | t d  | t d  t d   |  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5034   s    c      
      sl     j  d  t t d  |  | t t | | t | |  | |   |  | | |  t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5035   s    c      
      sl     j  d  t t d  |  | t t | | t | |  | |   |  | | |  t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R	  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5036   s    c            sF     j  d  t t | |  | | t |  |  | t | |   S(   Ni  (   R  R*   R   R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5037   s    c            sG     j  d  t t | |  | | t |  |  | t | |   S(   Ni  (   R  R*   R   R  R	  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5038   s    t   dt   mc      	      s     j  d  t | | | | |  t d  t | | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | | |  t d  | | t | |  | | |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5039   s    c      	      s     j  d  t | | | | |  t d  t | | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | | |  t d  | | t | |  | | |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R	  R  R  (   R  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5040   s    c      	      s     j  d  t | | | |  t d  t | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | |  t d  | | t | |  | |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5041   s    c      	      s     j  d  t | | | |  t d  t | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | |  t d  | | t | |  | |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R	  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5042   s    c            s2    j  d  t | |  t d  | | t d  t t t | | | | t d  |  |  t d  t |  t d  t |  |  t d  |  |  | t | |   |  t | |  | | t | |  | t d  t	 | t d  | t d  t d   | | | t d  |  S(   Ni  ii   i   (
   R  R  R  R*   R   Rc  R  R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5043   s    c            s2    j  d  t | |  t d  | | t d  t t t | | | | t d  |  |  t d  t |  t d  t |  |  t d  |  |  | t | |   |  t | |  | | t | |  | t d  t	 | t d  | t d  t d   | | | t d  |  S(   Ni  ii   i   (
   R  R  R  R*   R   Rc  R  R	  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5044   s    c      
      s    j  d  t |  | | | t d  t | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | |  t d  | | t d  t | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | |  | | t | |  | t d  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5045   s    c      
      s    j  d  t |  | | | t d  t | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | |  t d  | | t d  t | |  t d  | | t | |  | t d  t | t d  | t d  t d   |  |  t | |  | | t | |  | t d  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R	  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5046   s    c            so     j  d  t | |  t d  t t | | | | t |  |  t |  |  | t | |   |  S(   Ni  i(   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5047   s    c            sp     j  d  t | |  t d  t t | | | | t |  t |  |  |  | t | |   |  S(   Ni  i(   R  R  R  R*   R   R  R  R	  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5048   s    c            s<     j  d  t | | |  | | t | |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5049   s    c            s<     j  d  t | | |  | | t | |  | |  S(   Ni  (   R  R   R	  (   R  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5050   s    i   t   ec            sD     j  d  t t | |  t | |   |  | t |  |  S(   Ni  (   R  R  t   logR  R  (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5051   s    c            sE     j  d  t t | |  t | |   |  | t |  |  S(   Ni  (   R  R  R"  R	  R  (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5052   s    c            sZ     j  d  t | |  t | |  | t d  |  | t |  | t d  |  S(   Ni  i   (   R  R  R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5053   s    c            s[     j  d  t | |  t | |  | t d  |  | t |  | t d  |  S(   Ni  i   (   R  R  R	  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5054  s    c      	      s     j  d  t t | t d  | t d  t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5055  s    c      	      s     j  d  t t | t d  | t d  t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5056  s    c      
      s   t  | | | t d  |  |  }   j d  t | | t t | t | t d  | t d  t d   |  |  |  t | | t | |  | |  S(   Ni   i  i   (   R  R  R  R  R   R,  R  R  (   t   pR  R  R  R  R	  R!  t   u(   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5057  s    %R)  c      
      s   t  | | | t d  |  |  }   j d  t | | t 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5058  s    %c      
      s    j  d  t t | | | t d   t d  t | t d  | t d  t d   t | |  t | |  | t | t d  | t d  t d   |  |  t |  | | t | | | t d   t d  t | t d  | t d  t d   t | | |  t | |  | t d  |  |  t | | |  t | |  | t | | | t d   t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5059  s    c      
      s    j  d  t t | | | t d   t d  t | t d  | t d  t d   t | |  t | |  | t | t d  | t d  t d   |  |  t |  | | t | | | t d   t d  t | t d  | t d  t d   t | | |  t | |  | t d  |  |  t | | |  t | |  | t | | | t d   t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R	  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5060"  s    c      
      s    j  d  t t d  | |  t d  |  t d  t | | t | |  | | | | t d  |  t d  |  |  t | | | t |   | | | | t d  t |   | t d  | t d  t d  t |   t d  |  t d  t | | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5061'  s    c      
      s    j  d  t t d  | |  t d  |  t d  t | | t | |  | | | | t d  |  t d  |  |  t | | | t |   | | | | t d  t |   | t d  | t d  t d  t |   t d  |  t d  t | | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5062,  s    i   c      
      s     j  d  t |  | | t |  t | | |  t | |  | t d  | | | t d  |  |  t | | |  t | |  | | t | | | t d   |  S(   Ni  ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement50631  s    c      
      s     j  d  t |  | | t |  t | | |  t | |  | t d  | | | t d  |  |  t | | |  t | |  | | t | | | t d   |  S(   Ni  ii   (   R  R  R  R   R	  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement50646  s    c      
      s    j  d  t |  | | t | t d  | t d  t d   | t | | | t d   t | | |  t | |  | t d  | t d  | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5065;  s    c      
      s    j  d  t |  | | t | t d  | t d  t d   | t | | | t d   t | | |  t | |  | t d  | t d  | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5066@  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 |   | t d  | t d  t d  t |   t d  |  t d  t | | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t | |  | | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R  R$   R%   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5067E  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 |   | t d  | t d  t d  t |   t d  |  t d  t | | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t | |  | | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R	  R$   R%   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5068J  s    c            s`     j  d  t t d  | | t t | |  | | t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5069O  s    c            sa     j  d  t t d  | | t t | |  | | t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R	  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5070T  s    c      	      s    j  d  t | | t |   | | | t d  t |   t d  |  t d  | t d  | t d  t d  t |   | | t d  t | | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | t | |  | t d  | | | t d  |  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   i   i(	   R  R  R$   R  R%   R   R  R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5071Y  s    c      	      s    j  d  t | | t |   | | | t d  t |   t d  |  t d  | t d  | t d  t d  t |   | | t d  t | | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | t | |  | t d  | | | t d  |  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   i   i(	   R  R  R$   R  R%   R   R	  R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5072^  s    c      	      sr     j  d  t | |  | t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5073c  s    c      	      ss     j  d  t | |  | t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5074h  s    c            s     j  d  t | |  t d  d t | | | t d   t | t d  | t d  t d   t | | t | |  | | t d  | t d  t d  |  |  |  S(   Ni  ii   i   (   R  R  R  R  R   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5075m  s    c            s     j  d  t | |  t d  d t | | | t d   t | t d  | t d  t d   t | | t | |  | | t d  | t d  t d  |  |  |  S(   Ni  ii   i   (   R  R  R  R  R   R	  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5076r  s    c      
      s   t  | | | t d  |  |  }   j d  t | | t 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5077v  s    %c      
      s   t  | | | t d  |  |  }   j d  t | | t 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5078|  s    %c            sR     j  d  t t | | t | |  | | | | t d  |  |  |  S(   Ni  i   (   R  R   R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5079  s    c            sR     j  d  t t | | t | |  | | | | t d  |  |  |  S(   Ni  i   (   R  R   R   R	  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5080  s    c            sJ     j  d  t | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5081  s    c            sJ     j  d  t | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R	  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5082  s    t   gc
   
   	      s     j  d  t | |	 | t |   | | | t |   | | |	 | | t d  t |   t | | t | |  | | | |	 | | t d  |  |  |  S(   Ni  i   (   R  R  R%   R  R   R  (
   R)  RE  R  t   fR  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5083  s    c
   
   	      s     j  d  t | |	 | t |   | | | t |   | | |	 | | t d  t |   t | | t | |  | | | |	 | | t d  |  |  |  S(   Ni  i   (   R  R  R%   R  R   R	  (
   R)  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5084  s    c            s]     j  d  t t d  | t t | |  | | t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5085  s    c            s\     j  d  t t d  | t t | |  | | t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R	  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5086  s    c            sb    j  d  t | | t |   | | | | t d  t |   | t d  | t d  t d  t |   t d  | |  t d  t | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | t | |  | | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i(   R  R  R$   R  R%   R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5087  s    c            sc    j  d  t | | t |   | | | | t d  t |   | t d  | t d  t d  t |   t d  | |  t d  t | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | t | |  | | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i(   R  R  R$   R  R%   R   R	  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5088  s    c            sf     j  d  t t d  | t t | |  | | t |  t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5089  s    c            sg     j  d  t t d  | t t | |  | | t |  t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  R	  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5090  s    RF  c
   
   	      s    j  d  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  t d  | | | t d  |  S(   Ni  i   i   i(   R  R  R$   R  R%   R   R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5091  s    c
   
   	      s    j  d  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  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  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5092  s    c      	      s    j  d  t | t | | t | |  | | | t d  |  t d  | |  |  t | | | |  t d  |  t | t d  | t d  t d  |  t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5093  s    c      	      s    j  d  t | t | | t | |  | | | t d  |  t d  | |  |  t | | | |  t d  |  t | t d  | t d  t d  |  t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5094  s    c	   	   	      s    j  d  t t d  | |  | t d  | t d  t | | | t d  | | t | |  | | | t d  |  t d  |  |  t | | | |  | | t d  t | | | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | | t d  |  | | t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (	   R)  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5095  s    c	   	   	      s    j  d  t t d  | |  | t d  | t d  t | | | t d  | | t | |  | | | t d  |  t d  |  |  t | | | |  | | t d  t | | | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | | t d  |  | | t d  |  S(   Ni  i   i   i(   R  R  R  R   R	  R  (	   R)  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5096  s    c	   
   
      s   t  | | | | | | t d  |  |  }	   j d  t | | t t |	 t | t d  | t d  t d   |  |  |  t | | t | |  |	 |  S(   Ni   i  i   (   R  R  R  R  R   R,  R  R  (
   R)  R  RF  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5097  s    1c	   
   
      s   t  | | | | | | t d  |  |  }	   j d  t | | t t |	 t | t d  | t d  t d   |  |  |  t | | t | |  |	 |  S(   Ni   i  i   (   R  R  R  R  R   R,  R  R	  (
   R)  R  RF  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5098  s    1c   	         s   t  | | | t d  | t d  t d  |  |  }   j d  t | |  | | t | |  | |  t | | | |  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!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5099  s    >c   	         s   t  | | | t d  | t d  t d  |  |  }   j d  t | |  | | t | |  | |  t | | | |  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!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5100  s    >c   	   
      sG  t  | | | t d  | t d  t d  |  |  }   j d  t | | | |  t d  d t | | | t d   t | t d  | t d  t d   t t | t | t d  | t d  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!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5101  s    >c   	   
      sF  t  | | | t d  | t d  t d  |  |  }   j d  t | | | |  t d  d t | | | t d   t | t d  | t d  t d   t t | t | t d  | t d  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!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5102  s    >c	   	   
      s    j  d  t | t d  t | | | t d   | t d  |  t d  t | t d  | t d  t d   t | | |  t d  | | t | |  | t | t d  | t d  t d   |  |  t | | | t | | | t d   | |  t d  t | t d  | t d  t d   t | | |  t d  | | t | |  | t d  |  |  t | | |  t d  | | t | |  | t | | | t d   | |  t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R  R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5103  s    c	   	   
      s    j  d  t | t d  t | | | t d   | t d  |  t d  t | t d  | t d  t d   t | | |  t d  | | t | |  | t | t d  | t d  t d   |  |  t | | | t | | | t d   | |  t d  t | t d  | t d  t d   t | | |  t d  | | t | |  | t d  |  |  t | | |  t d  | | t | |  | t | | | t d   | |  t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R	  R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5104  s    c
   
   
      s    j  d  t t d  |	 |  | t d  | t d  t | | | t d  | | t | |  | | |	 | t d  |  t d  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  | | t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5105  s    c
   
   
      s    j  d  t t d  |	 |  | t d  | t d  t | | | t d  | | t | |  | | |	 | t d  |  t d  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  | | t d  |  S(   Ni  i   i   i(   R  R  R  R   R	  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5106  s    c	   	   
      s    j  d  t t | | | t d   |  t d  t | t d  | t d  t d   t | | |  | | t | |  | t | t d  | t d  t d   |  |  t | | | t | | | t d   | |  t d  t | t d  | t d  t d   t | | |  t d  | | t | |  | t d  |  |  t | | |  t d  | | t | |  | t | | | t d   | |  t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R  R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5107  s    c	   	   
      s    j  d  t t | | | t d   |  t d  t | t d  | t d  t d   t | | |  | | t | |  | t | t d  | t d  t d   |  |  t | | | t | | | t d   | |  t d  t | t d  | t d  t d   t | | |  t d  | | t | |  | t d  |  |  t | | |  t d  | | t | |  | t | | | t d   | |  t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R	  R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5108  s    c
   
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      s    j  d  t t d  | |  | t d  |  t d  t | | | | | t | |  | | |	 | t d  |  t d  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  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  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5109  s    c
   
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      s    j  d  t t d  | |  | t d  |  t d  t | | | | | t | |  | | |	 | t d  |  t d  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  | | t d  |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R	  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5110$  s    c
   
   
      s#    j  d  t | t d  | t d  |  t d  | t d  | t d  t | | | t d  | | t | |  | | |	 | t d  |  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  t d  | | | t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5111)  s    c
   
   
      s#    j  d  t | t d  | t d  |  t d  | t d  | t d  t | | | t d  | | t | |  | | |	 | t d  |  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  t d  | | | t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R	  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5112.  s    c
   
   
      s4    j  d  t | t d  | t d  t d  |	 |  t d  t | | | t d  | | t | |  | | |	 | t d  |  t d  |  |  t | | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   t d  | |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | t d  | | t | |  | | |	 | t d  |  t d  t d  |	 |  t d  |  S(   Ni  i   ii   i(   R  R  R  R   R  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement51133  s    c
   
   
      s4    j  d  t | t d  | t d  t d  |	 |  t d  t | | | t d  | | t | |  | | |	 | t d  |  t d  |  |  t | | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   t d  | |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | t d  | | t | |  | | |	 | t d  |  t d  t d  |	 |  t d  |  S(   Ni  i   ii   i(   R  R  R  R   R	  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement51148  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 |   | t d  | t d  t d  t |   t d  | |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  t d  t d  | | |  t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5115=  s    c
   
   
      s)    j  d  t | t d  |  t d  t d  | |  t d  t | | | | | t | |  | | |	 | t d  |  t d  |  |  t | | | t |   | | |	 | t d  t |   | t d  | t d  t d  t |   t d  | |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | t d  | | t | |  | | |	 | t d  |  t d  t d  | | |  t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R	  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5116B  s    c	   	   
      s    j  d  t | t d  |  t d  | t d  |  t | | |  t d  | | t | |  | t | | | t d   |  |  t | | | t | t d  | t d  t d   | |  t | | | t d   t | | |  t d  | | t | |  | t d  |  |  t | | | |  t d  | | t | |  | t | | | t d   | |  |  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5117G  s    c	   	   
      s    j  d  t | t d  |  t d  | t d  |  t | | |  t d  | | t | |  | t | | | t d   |  |  t | | | t | t d  | t d  t d   | |  t | | | t d   t | | |  t d  | | t | |  | t d  |  |  t | | | |  t d  | | t | |  | t | | | t d   | |  |  S(   Ni  i   iii   (   R  R  R  R   R	  R  R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5118L  s    c            so     j  d  t | |  t d  t |  t t | | | | t |  |  |  | t | |   |  S(   Ni  i(   R  R  R  R  R*   R   R  R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5119Q  s    c            sp     j  d  t | |  t d  t |  t t | | | | t |  |  |  | t | |   |  S(   Ni   i(   R  R  R  R  R*   R   R  R	  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5120V  s    c      
      s    j  d  t | | |  t d  | | t | |  t t d  d |  t d  t d  d |  t d  t d  d | t d  | t d   t |  | |  t d  |  t | | | | |  t d  t t t d  |  t d  t d  |  t d  t d   t |  t d  t d  d |  t d  t d   | t d  | t d   t |  | t d  |  t d  |  t d  |  S(   Ni  i   i   i   (   R  R  R  R  R4   R  R  R   (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5121[  s    c      
      s    j  d  t | | |  t d  | | t | |  t t d  d |  t d  t d  d |  t d  t d  d | t d  | t d   t |  | |  t d  |  t | | | | |  t d  t t t d  |  t d  t d  |  t d  t d   t |  t d  t d  d |  t d  t d   | t d  | t d   t |  | t d  |  t d  |  t d  |  S(   Ni  i   i   i   (   R  R  R  R	  R4   R  R  R   (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5122`  s    c	   	   	      s     j  d  t t | t d  | t d  t d   t | | | t d   t | | |  | | t | |  | t | t d  | t d  t d   |  |  S(   Ni  i   i   (   R  R  R  R  R   R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5123e  s    c	   	   	      s     j  d  t t | t d  | t d  t d   t | | | t d   t | | |  | | t | |  | t | t d  | t d  t d   |  |  S(   Ni  i   i   (   R  R  R  R  R   R	  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5124j  s    c
   
   
      s?    j  d  t | t d  | t d  | t d  | t d  |  t d  t | | | t d  | | t | |  | | |	 | t d  |  |  |  t | | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | t d  | | t | |  | | |	 | t d  |  t d  |	 | t d  |  t d  |  S(   Ni  i   ii   i(   R  R  R  R   R  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5125o  s    c
   
   
      s?    j  d  t | t d  | t d  | t d  | t d  |  t d  t | | | t d  | | t | |  | | |	 | t d  |  |  |  t | | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   | | t d  |  t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | t d  | | t | |  | | |	 | t d  |  t d  |	 | t d  |  t d  |  S(   Ni  i   ii   i(   R  R  R  R   R	  R$   R%   R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5126t  s    c
   
   	      s    j  d  t | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   | | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | | t | |  | t d  | |	 | t d  |  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   i   i(	   R  R  R$   R  R%   R   R  R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5127y  s    c
   
   	      s    j  d  t | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   | | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | | t | |  | t d  | |	 | t d  |  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   i   i(	   R  R  R$   R  R%   R   R	  R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5128~  s    c	   	   	      s     j  d  t | |  | | t |  | 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  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5129  s    c	   	   	      s     j  d  t | |  | | t |  | 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  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5130  s    c
   
   
      s    j  d  t | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   | | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | t |   | |	 | t d  t |   | t d  | t d  t d  t |   | t d  |  t d  | | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | | t | |  | t d  | |	 | t d  |  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   i   i(	   R  R  R$   R  R%   R   R  R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5131  s    c
   
   
      s    j  d  t | t |   | | | |	 | t d  t |   | t d  | t d  t d  t |   | | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | t |   | |	 | t d  t |   | t d  | t d  t d  t |   | t d  |  t d  | | | t d  t | | | t d  | | t | |  | t d  | t d  | t d  t d  |  t d  d |  |  t | | | | | t | |  | t d  | |	 | t d  |  t | t d  | t d  t d   | | | t d  |  S(   Ni  i   i   i(	   R  R  R$   R  R%   R   R	  R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5132  s    c	   	   	      s     j  d  t | | t d  | |  t t | | | | t |  | t |  t d  |  t d  |  | t | |   |  S(   Ni  ii   i   (   R  R  R  R*   R   R  R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5133  s    c	   	   	      s     j  d  t | | t d  | |  t t | | | | t |  t d  |  t d  t |  | |  | t | |   |  S(   Ni  ii   i   (   R  R  R  R*   R   R  R  R	  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5134  s    c	   	   	      s     j  d  t | t |   | | | t d  t |   | t d  | t d  t d  t |   t | | | | t | |  | | t d  | t d  t d  |  |  |  S(   Ni  i   i   (   R  R  R$   R  R%   R   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5135  s    c	   	   	      s     j  d  t | t |   | | | t d  t |   | t d  | t d  t d  t |   t | | | | t | |  | | t d  | t d  t d  |  |  |  S(   Ni  i   i   (   R  R  R$   R  R%   R   R	  (	   R)  R  R  R  R  R  R  R	  R!  (   R
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   	      s     j  d  t t | | t | |  | t | |	 | t d   | | | | |	 | t d  |  t d  d |  |  S(   Ni  i   i   (   R  R   R   R  R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
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   
   	      s     j  d  t t | | t | |  | t | |	 | t d   | | | | |	 | t d  |  t d  d |  |  S(   Ni  i   i   (   R  R   R   R	  R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5138  s    c      	      s     j  d  t | | t d  | |  t d  t | | | t d  |  t d  t | t d  | t d  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5139  s    c      	      s     j  d  t | | t d  | |  t d  t | | | t d  |  t d  t | t d  | t d  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5140  s    c	   
   
      s   t  | | | | | | t d  |  |  }	   j d  t | | t t |	 t | t d  | t d  t d   |  |  |  t | | t | |  |	 |  S(   Ni   i  i   (   R  R  R  R  R   R,  R  R  (
   R)  R  RF  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5141  s    1c	   
   
      s   t  | | | | | | t d  |  |  }	   j d  t | | t t |	 t | t d  | t d  t d   |  |  |  t | | t | |  |	 |  S(   Ni   i  i   (   R  R  R  R  R   R,  R  R	  (
   R)  R  RF  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5142  s    1c
   
   	      s^     j  d  t t | | t | |  | | | | | |	 | t d  |  |  |  S(   Ni  i   (   R  R   R   R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5143  s    c
   
   	      s^     j  d  t t | | t | |  | | | | | |	 | t d  |  |  |  S(   Ni  i   (   R  R   R   R	  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5144  s    c
   
         sV     j  d  t | | | | | t | |  | | |	 | t d  |  |  S(   Ni  i   (   R  R   R  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5145  s    c
   
         sV     j  d  t | | | | | t | |  | | |	 | t d  |  |  S(   Ni  i   (   R  R   R	  R  (
   R)  R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5146  s    t   hc      	      s     j  d  t | | |	 t |   | | |	 t |   | | | | |	 t d  t |   t |
 |	 | | | t | |	  | | | | | |	 t d  |  |	  |	  S(   Ni  i   (   R  R  R%   R  R   R  (   R)  R  RE  R  RF  R  R  R  R  R	  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5147  s    c      	      s     j  d  t | | |	 t |   | | |	 t |   | | | | |	 t d  t |   t |
 |	 | | | t | |	  | | | | | |	 t d  |  |	  |	  S(   Ni  i   (   R  R  R%   R  R   R	  (   R)  R  RE  R  RF  R  R  R  R  R	  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5148  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5149  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5150  s    c      	      s     j  d  t | | | | |  t d  t | | t | |  | t d  | | | |  t d  t | t d  | 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5151  s    c      	      s     j  d  t | | | | |  t d  t | | t | |  | t d  | | | |  t d  t | t d  | 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5152  s    c            sI     j  d  t t | | t | |  | | | | |  |  |  S(   Ni!  (   R  R   R   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5153  s    c            sI     j  d  t t | | t | |  | | | | |  |  |  S(   Ni"  (   R  R   R   R	  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5154  s    c      	      s{     j  d  t | |  t d  t t | | | | | | | t |  |  t |  |  | t | |   |  S(   Ni#  i(   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5155  s    c      	      s|     j  d  t | |  t d  t t | | | | | | | t |  |  t |  |  | t | |   |  S(   Ni$  i(   R  R  R  R*   R   R  R  R	  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5156  s    c      
      s   t  | |  }   j d  t |  | t 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*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5157  s    c      
      s   t  | |  }   j d  t |  | t 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*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5158  s    c            s=     j  d  t t | | |  t | |  | |  |  S(   Ni'  (   R  R   R   R  (   R  R!  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5159  s    c            s=     j  d  t t | | |  t | |  | |  |  S(   Ni(  (   R  R   R   R	  (   R  R!  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5160"  s    c   	   
      s   t  | | | | |  |  }   j d  t | | t 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  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5161&  s    c   	   
      s   t  | | | | |  |  }   j d  t | | t 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  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5162,  s    c      
      s   t  | |
 |	 | | | |	 |  |	  }   j d  t | | | t t | | | t | |	  | t d  t | t d  |	 t d  t d   |	  |	  |	  t | | t | |	  | | |	  S(   Ni+  ii   i   (   R  R  R  R   R,  R  R  R  (   R)  R  RF  R  RE  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With51632  s    +c      
      s   t  | |
 |	 | | | |	 |  |	  }   j d  t | | | t t | | | t | |	  | t d  t | t d  |	 t d  t d   |	  |	  |	  t | | t | |	  | | |	  S(   Ni,  ii   i   (   R  R  R  R   R,  R	  R  R  (   R)  R  RF  R  RE  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With51648  s    +c      
      s   t  | | | |	 | t d  |  | |
 | t d  |  }   j d  t | | | t t | | | t | |  | t d  t | t d  | t d  t d   |  |  |  t | | t | |  | | |  S(   Ni   i-  ii   (   R  R  R  R  R   R,  R  R  (   R)  RF  R  RE  R  R  R  R  R	  R  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5165>  s    Cc      
      s   t  | | | |	 | t d  |  | |
 | t d  |  }   j d  t | | | t t | | | t | |  | t d  t | t d  | t d  t d   |  |  |  t | | t | |  | | |  S(   Ni   i.  ii   (   R  R  R  R  R   R,  R	  R  (   R)  RF  R  RE  R  R  R  R  R	  R  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5166D  s    Cc	   	         sM     j  d  t t | | | t | |  | | | | |  |  |  S(   Ni/  (   R  R   R   R  (	   R  R  R!  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5167K  s    c	   	         sM     j  d  t t | | | t | |  | | | | |  |  |  S(   Ni0  (   R  R   R   R	  (	   R  R  R!  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5168P  s    c
      
      s   t  | |	 | t d  |  | | | | |  }
   j d  t | | t t t d  t | t d  | t d  t d   |
 |  |  |  t | | t | |  |
 |  S(   Ni   i1  i   (   R  R  R  R  R   R  R  (   R)  R  RE  R  RF  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5169T  s    5c
      
      s   t  | |	 | t d  |  | | | | |  }
   j d  t | | t t t d  t | t d  | t d  t d   |
 |  |  |  t | | t | |  |
 |  S(   Ni   i2  i   (   R  R  R  R  R   R  R	  (   R)  R  RE  R  RF  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5170Z  s    5c            sb     j  d  t t | | t | |	  | | |
 |	 t d  |  | | |	 | |	  |	  S(   Ni3  i   (   R  R   R   R  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5171a  s    c            sb     j  d  t t | | t | |	  | | |
 |	 t d  |  | | |	 | |	  |	  S(   Ni4  i   (   R  R   R   R	  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5172f  s    c
   
   	      s@    j  d  t t d  | | t |  | t d  t | | t | |  | t d  | | | |  t d  | | |  t d  |	 | | |	 | | t d  |  t d  |  |  t | | t | |  | t d  | |	 | t d  | | | |  | | t |  | t d  |  S(   Ni5  i   ii   (   R  R  R  R  R   R  R  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5173k  s    c
   
   	      s?    j  d  t t d  | | t |  | t d  t | | t | |  | t d  | | | |  t d  | | |  t d  |	 | | |	 | | t d  |  t d  |  |  t | | t | |  | t d  | |	 | t d  | | | |  | | t |  | t d  |  S(   Ni6  i   ii   (   R  R  R  R  R   R	  R  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5174p  s    c      	      s     j  d  t t | | t | |	  | t | |
 |	 t d   | |
 |	 t d  |  t d  d | | |	 | |	  |	  S(   Ni7  i   i(   R  R   R   R  R  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5175u  s    c      	      s     j  d  t t | | t | |	  | t | |
 |	 t d   | |
 |	 t d  |  t d  d | | |	 | |	  |	  S(   Ni8  i   i(   R  R   R   R	  R  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5176z  s    c            s    j  d  t t d  | | t |  | t d  t t | | t | |	  | t d  | | |	 | t d  | |
 |	 t d  |  t d  d | | | |
 | |	 t d  |  t d  |
 | |	 t d  | t d  |  t d  |	  |	  |	  t | | t | |	  | t d  | |
 |	 t d  |  t d  d | | |	 | | | t |  | t d  |	  S(   Ni9  i   ii   (   R  R  R  R  R   R   R  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5177  s    c            s    j  d  t t d  | | t |  | t d  t t | | t | |	  | t d  | | |	 | t d  | |
 |	 t d  |  t d  d | | | |
 | |	 t d  |  t d  |
 | |	 t d  | t d  |  t d  |	  |	  |	  t | | t | |	  | t d  | |
 |	 t d  |  t d  d | | |	 | | | t |  | t d  |	  S(   Ni:  i   ii   (   R  R  R  R  R   R   R	  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5178  s    c
   
         s     j  d  t | |  | | t |  | t d  t | | t | |  | t d  | | | |  t d  |  |  t | | t | |  | t d  | | | |  | | t |  | t d  |  S(   Ni;  i   i(   R  R  R  R  R   R  R  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5179  s    c
   
         s     j  d  t | |  | | t |  | t d  t | | t | |  | t d  | | | |  t d  |  |  t | | t | |  | t d  | | | |  | | t |  | t d  |  S(   Ni<  i   i(   R  R  R  R  R   R	  R  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5180  s    c
   
   	      s{     j  d  t | |  t d  t |  t t | | | | | | | t |  |  |  | t | |   |  S(   Ni=  i(   R  R  R  R  R*   R   R  R  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5181  s    c
   
   	      s|     j  d  t | |  t d  t |  t t | | | | | | | t |  |  |  | t | |   |  S(   Ni>  i(   R  R  R  R  R*   R   R  R	  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5182  s    c      	      s     j  d  t t | | t | |	  | t | |
 |	 t d   | |
 |	 t d  |  t d  d | | |	 | |	  |	  S(   Ni?  i   i   (   R  R   R   R  R  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5183  s    c      	      s     j  d  t t | | t | |	  | t | |
 |	 t d   | |
 |	 t d  |  t d  d | | |	 | |	  |	  S(   Ni@  i   i   (   R  R   R   R	  R  R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5184  s    c            s     j  d  t | t |   | |
 |	 t d  t |   | t d  |	 t d  t d  t |   t | | t | |	  | | | |	 | | t d  |	 t d  t d  |  |	  |	  S(   NiA  i   i   (   R  R  R$   R  R%   R   R  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5185  s    c            s     j  d  t | t |   | |
 |	 t d  t |   | t d  |	 t d  t d  t |   t | | t | |	  | | | |	 | | t d  |	 t d  t d  |  |	  |	  S(   NiB  i   i   (   R  R  R$   R  R%   R   R	  (   R)  R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5186  s    c            s     j  d  t | |  | | t |  | t d  t | | t | |  | t d  | | | |  |  t | | t | |  | t d  t |	 | | | |   | | t |  | t d  |  S(   NiC  i   (   R  R  R  R  R   R  R  R"  (   R  RF  RE  R  R  R  R  R  R	  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5187  s    c            s     j  d  t | |  | | t |  | t d  t | | t | |  | t d  | | | |  |  t | | t | |  | t d  t |	 | | | |   | | t |  | t d  |  S(   NiD  i   (   R  R  R  R  R   R	  R  R"  (   R  RF  RE  R  R  R  R  R  R	  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5188  s    c      	      s     j  d  t | t |   | | |	 t d  t |   | t d  |	 t d  t d  t |   t | | t | |	  | | t d  |	 t d  t d  |  t |
 | | |	 |  |	  |	  S(   NiE  i   i   (   R  R  R$   R  R%   R   R  R"  (   R)  R  RF  RE  R  R  R  R  R  R	  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5189  s    c      	      s     j  d  t | t |   | | |	 t d  t |   | t d  |	 t d  t d  t |   t | | t | |	  | | t d  |	 t d  t d  |  t |
 | | |	 |  |	  |	  S(   NiF  i   i   (   R  R  R$   R  R%   R   R	  R"  (   R)  R  RF  RE  R  R  R  R  R  R	  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5190  s    c	   
   
      s   t  | | | |  | | | |  |  }	   j d  t | | t t t d  t | t d  | t d  t d   |	 |  |  |  t | | t | |  |	 |  S(   NiG  i   i   (   R  R  R  R   R  R  R  (
   R  RE  R  RF  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5191  s    +c	   
   
      s   t  | | | |  | | | |  |  }	   j d  t | | t t t d  t | t d  | t d  t d   |	 |  |  |  t | | t | |  |	 |  S(   NiH  i   i   (   R  R  R  R   R  R  R	  (
   R  RE  R  RF  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5192  s    +c
   
         sY     j  d  t t | | t | |  | | |	 | |  | | | |  |  |  S(   NiI  (   R  R   R   R  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5193  s    c
   
         sY     j  d  t t | | t | |  | | |	 | |  | | | |  |  |  S(   NiJ  (   R  R   R   R	  (
   R  RE  R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5194  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   t
   isinstancet   intR  t   floatR  t   FalseR  R   t   True(   R*  R  R  R  R	  t   v(    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5195  s    c      
      s   t  |  |  }   j d  t | | t t | t | t d  | t d  t d   |  |  |  t | | t | |  | |  S(   NiK  i   i   (   R  R  R  R   R,  R  R  R  (   R*  R  R  R  R	  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5195  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R*  R  R  R  R	  R  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5196  s    c      
      s   t  |  |  }   j d  t | | t t | t | t d  | t d  t d   |  |  |  t | | t | |  | |  S(   NiL  i   i   (   R  R  R  R   R,  R  R  R	  (   R*  R  R  R  R	  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5196  s    c	   
      S   sv   t  | t t t t f  r t St | | | t | |  | | | | t d  |  |  }	 t	 |	  rr t
 St S(   Ni   (   R  R  R  R  R  R  R   R  R  R(   R  (
   R)  R  R!  R  R  R  R  R	  R!  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5197  s    Cc	   
         s]   t  | | | t | |  | | | | t d  |  |  }	   j d  t |	 |  S(   Ni   iM  (   R   R  R  R  R   (
   R)  R  R!  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5197  s    Cc	   
      S   sv   t  | t t t t f  r t St | | | t | |  | | | | t d  |  |  }	 t	 |	  rr t
 St S(   Ni   (   R  R  R  R  R  R  R   R	  R  R(   R  (
   R)  R  R!  R  R  R  R  R	  R!  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5198  s    Cc	   
         s]   t  | | | t | |  | | | | t d  |  |  }	   j d  t |	 |  S(   Ni   iN  (   R   R	  R  R  R   (
   R)  R  R!  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5198  s    Cc      	   S   s   t  |
 t t t t f  r t St | | | t |	 |
  | | | | | |
 t d  |  | |
  } t	 |  r~ t
 St S(   Ni   (   R  R  R  R  R  R  R   R  R  R(   R  (   R)  R  RE  R  RF  R!  R  R  R  R  R	  R!  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5199  s    OR!  c      	      si   t  | | | t |	 |
  | | | | | |
 t d  |  | |
  }   j d  t | |
  S(   Ni   iO  (   R   R  R  R  R   (   R)  R  RE  R  RF  R!  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5199  s    Oc      	   S   s   t  |
 t t t t f  r t St | | | t |	 |
  | | | | | |
 t d  |  | |
  } t	 |  r~ t
 St S(   Ni   (   R  R  R  R  R  R  R   R	  R  R(   R  (   R)  R  RE  R  RF  R!  R  R  R  R  R	  R!  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5200   s    Oc      	      si   t  | | | t |	 |
  | | | | | |
 t d  |  | |
  }   j d  t | |
  S(   Ni   iP  (   R   R	  R  R  R   (   R)  R  RE  R  RF  R!  R  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5200(  s    Oc         S   sS   t  |  t t t t f  r t St t | |   | | |   } t |  rO t	 St S(   N(
   R  R  R  R  R  R  R   R  R(   R  (   R	  R  R  R(  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5201.  s     c            s:   t  t | |   | | |   }   j d  t | |   S(   NiQ  (   R   R  R  R   (   R	  R  R  R(  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement52016  s     c         S   sS   t  |  t t t t f  r t St t | |   | | |   } t |  rO t	 St S(   N(
   R  R  R  R  R  R  R   R	  R(   R  (   R	  R  R  R(  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5202<  s     c            s:   t  t | |   | | |   }   j d  t | |   S(   NiR  (   R   R	  R  R   (   R	  R  R  R(  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5202D  s     c            s=     j  d  t t |  | | t | |  | |  |  S(   NiS  (   R  R   R   R  (   R(  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5203K  s    c            s=     j  d  t t |  | | t | |  | |  |  S(   NiT  (   R  R   R   R	  (   R(  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5204P  s    c         S   sm   t  | t t t t f  r t St | | | t d  |  t | |  | | |  } t	 |  ri t
 St S(   Ni   (   R  R  R  R  R  R  R   R  R  R(   R  (   R)  R(  R  R  R  R	  R!  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5205T  s    :c            sT   t  | | | t d  |  t | |  | | |  }   j d  t | |  S(   Ni   iU  (   R   R  R  R  R   (   R)  R(  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5205\  s    :c         S   sm   t  | t t t t f  r t St | | | t d  |  t | |  | | |  } t	 |  ri t
 St S(   Ni   (   R  R  R  R  R  R  R   R  R	  R(   R  (   R)  R(  R  R  R  R	  R!  R*  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5206b  s    :c            sT   t  | | | t d  |  t | |  | | |  }   j d  t | |  S(   Ni   iV  (   R   R  R	  R  R   (   R)  R(  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5206j  s    :c	   	   	      sV     j  d  t t | | | t d  |  | | | t | |  | |  |  S(   NiW  i   (   R  R   R   R  R  (	   R)  R(  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5207q  s    c	   	   	      sV     j  d  t t | | | t d  |  | | | t | |  | |  |  S(   NiX  i   (   R  R   R   R  R	  (	   R)  R(  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5208v  s    R*  c            s4     j  d  t |  | | t | |  | |  S(   NiY  (   R  R   R  (   R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5209{  s    c            s4     j  d  t |  | | t | |  | |  S(   NiZ  (   R  R   R	  (   R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5210  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5211  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5212  s    c	   	   	      s{     j  d  t t d  | t t | | t |  | | | | | | | | | |  |  | | | |  |  S(   Ni]  i   (   R  R  R  R*   R   R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5213  s    c	   	   	      s{     j  d  t t d  | t t | | t |  | | | | | | | | | |  |  | | | |  |  S(   Ni^  i   (   R  R  R  R*   R   R	  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5214  s    t   Ct   Bt   Ac
   
   
      s     j  d  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  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5215  s    c
   
   
      s     j  d  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  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5216  s    c      
      s     j  d  t t d  | t t | | t |  | | | t d  | t d  | | t d  | | | | |	 | | | | | |  | |	 | |  |  S(   Nia  i   i   (   R  R  R  R*   R   R  (   R  R  R)  R  RF  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5217  s    c      
      s     j  d  t t d  | t t | | t |  | | | t d  | t d  | | t d  | | | | |	 | | | | | |  | |	 | |  |  S(   Nib  i   i   (   R  R  R  R*   R   R	  (   R  R  R)  R  RF  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5218  s    c            s5    j  d  t | t | |  t | | | t d    |  t t t  | | t | t d  |   t | t d  |   t t | t |   t | |  t | | | t d     t | |   | t t | | | t d   t d   t t | | | t d   t d   |  t t t  | | t | t d  |   t | t d  |   t	 t | t |   t | |  t | | | t d     t | |   | t t | | | t d   t d   t t | | | t d   t d   |  S(   Nic  i   (
   R  R  R  R  R  t   PiR  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5219  s    c            s7    j  d  t t d  t | | t |  | t d  t d    t t |  | t d  t d   t d   t d  |  | |  t t d  t t  t t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | t t d  |  |  t t d  t t  t t t d  t |  t | | t |  | t d  t d     t t |  | t d  t d   t d   t	 | t d  |  |  | t t d  |  |  S(   Nid  i   i   (
   R  R  R  R  R	  R  R  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5220  s    c            s6    j  d  t t d  t | | t |  | t d  t d    t t |  | t d  t d   t d   t d  |  | |  t t d  t t  t t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | t t d  |  |  t t d  t t  t t t d  t |  t | | t |  | t d  t d     t	 | t d  |  t t |  | t d  t d   t d   |  | t t d  |  |  S(   Nie  i   ii   (
   R  R  R  R  R	  R  R  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5221  s    c            sH    j  d  t t d  |  t d  | | t d  t | |  t | | | t d   | t d  |  |  t | | |  t | | | t d   | |  t t d  |  | | |  t | | | t d   | t d  t t d  | | | t d  | t d  | t d   | | |  S(   Nif  i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5222  s    c            sH    j  d  t t d  |  t d  | | t d  t | |  t | | | t d   | t d  |  |  t | | |  t | | | t d   | |  t t d  |  | | |  t | | | t d   | t d  t t d  | | | t d  | t d  | t d   | | |  S(   Nig  i   i   ii(   R  R  R  R   R	  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5223  s    c            s    j  d  t | | t | t d  |   t | t d  |   t | | |  t | | | t d   t d  |   t d  |  | t t | | | t d   t d   t t | | | t d   t d   |  t | | t | t d  |   t | t d  |   t | | |  t | | | t d   t d  |   t d  |  | t t | | | t d   t d   t t | | | t d   t d   |  S(   Nih  i   (   R  R  R  R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5224  s    c            sA    j  d  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t |  | t d   |  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t |  | t d   |  S(   Nii  i   i   (	   R  R  R  R  R  R	  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5225  s    c            s?    j  d  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t |  | t d   |  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t |  | t d   |  S(   Nij  i   i(	   R  R  R  R  R  R	  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5226  s    c            s    j  d  t t t  | | t | t d  |   t | t d  |   t t | |  t | | | t d    t t  t |  |   t |  |  | t t | | | t d   t d   t t | | | t d   t d   |  t t t  | | t | t d  |   t | t d  |   t	 t | |  t | | | t d    t t  t |  |   t |  |  | t t | | | t d   t d   t t | | | t d   t d   |  S(   Nik  i   (
   R  R  R  R  R  R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5227  s    c            s    j  d  t t d  t t |  t t t d  t |  t | | t |  | t d  t d     t t |  | t d  t d   t d   t | t d  |  |  | |  t t d  t t |  t	 t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | |  S(   Nil  i   i   (
   R  R  R  R  R  R  R	  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5228  s    c            s    j  d  t t d  t t |  t t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | |  t t d  t t |  t	 t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | |  S(   Nim  i   i   i(
   R  R  R  R  R  R  R	  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5229  s    ic            s    j  d  t t t d  | | | t d  | t d  | t d   |  | | t | |  t | | | t d    |  t t t  | | |  t d  d | t | t d  |   t | t d  |   t t | t |   t | |  t | | | t d     | t t | | | t d   t d   t t | | | t d   t d   |  t t t  | | |  t d  d | t | t d  |   t | t d  |   t	 t | t |   t | |  t | | | t d     | t t | | | t d   t d   t t | | | t d   t d   |  S(   Nin  i   i   i   (
   R  R  R  R  R  R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5230  s    c            sC    j  d  t t |  t d  | t d  t d  |  | t d   | |  | t | | t |  | t d  t d    |  t t d  t t  t d  | t d  d t t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | |  t t d  t t  t d  | t d  d t t t d  t |  t | | t |  | t d  t d     t t |  | t d  t d   t d   t	 | t d  |  |  | |  S(   Nio  i   i   i   i   (
   R  R  R  R  R	  R  R  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5231  s    c            sC    j  d  t t |  t d  | t d  t d  |  | t d   | |  | t | | t |  | t d  t d    |  t t d  t t  t d  | t d  d t t t d  t |  t | | t |  | t d  t d     t | t d  |  t t |  | t d  t d   t d   |  | |  t t d  t t  t d  | t d  d t t t d  t |  t | | t |  | t d  t d     t	 | t d  |  t t |  | t d  t d   t d   |  | |  S(   Nip  i   i   ii   i   (
   R  R  R  R  R	  R  R  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5232  s    ic            sx    j  d  t | | t | t d  |   t | 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 | | t | t d  |   t | 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 t t d  | | | t d  | t d  | t d   t d  |  | | | |  t | | | t d   |  S(   Niq  i   i   (	   R  R  R  R  R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5233  s    c            s    j  d  t t |  t d  | t d  t d  |  | t d   t d  | |  | | | t |  | t d  t d   |  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t d  t |  | t d   |  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t d  t |  | t d   |  S(   Nir  i   i   i   (	   R  R  R  R  R	  R  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5234  s    c            s    j  d  t t |  t d  | t d  t d  |  | t d   t d  | |  | | | t |  | t d  t d   |  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t d  t |  | t d   |  t t t d   | t | | t |  | t d  t d   t d  |  t | t d  |  t d  | t d  t |  | t d   |  S(   Nis  i   i   i(	   R  R  R  R  R	  R  R  R  R  (   R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5235  s    c            s    j  d  t t d  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 | | | t d   | t d  t t d  | | | t d  | t d  | t d   t d  |  | | | t d  |  S(   Nit  i   i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5236  s    c            s    j  d  t t d  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 | | | t d   | t d  t t d  | | | t d  | t d  | t d   t d  |  | | | t d  |  S(   Niu  i   i   i   (   R  R  R  R   R	  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5237  s    c      	      sX     j  d  t t d  | t t |  | t |   |   |  t | |  |   |   S(   Niv  i   (   R  R  R  R*   R   R  R  (   R	  R  R  R)  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5238  s    c      	      sY     j  d  t t d  | t t |  | t |   |   |  t | |  |   |   S(   Niw  i   (   R  R  R  R*   R   R  R	  (   R	  R  R  R)  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5239  s    c            s<     j  d  t |  t | | | | | |  | |  S(   Nix  (   R  R   R  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5240  s    c            s<     j  d  t |  t | | | | | |  | |  S(   Niy  (   R  R   R
  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5241  s    c      
      s     j  d  t t | |  t d   | |  t t t |   | t |  t d  t d   |   |  t | |  t d  t d    |   S(   Niz  i   i   (   R  R  R  R  R*   R   R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5242   s    c      
      s     j  d  t t | |  t d   | |  t t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5243%  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*  RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5244*  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*  RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5245/  s    c            s    j  d  t | t | t d  | t d  t d  | |  t | | | t d   |  t d  |  t | t d  | t d  | t d  t d  | |  t | | | t d   |  t d  |  t | t d  | t | | | t d   |  | t | | | t d   t | t d  | t d  t d  | |  t | | | t d   |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement52464  s    c            s    j  d  t | t | t d  | t d  t d  | |  t | | | t d   |  t d  |  t | t d  | t d  | t d  t d  | |  t | | | t d   |  t d  |  t | t d  | t | | | t d   |  | t | | | t d   t | t d  | t d  t d  | |  t | | | t d   |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement52479  s    c            sg     j  d  t t |  t | |   t | t d  t d   |   |   t |  t |  |   S(   Ni  i   i   (   R  R   R,  R  R  R  R  R  (   R	  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5248>  s    c            sf     j  d  t t |  t | |   t | t d  t d   |   |   t |  t |  |   S(   Ni  i   i   (   R  R   R,  R  R  R  R  R	  (   R	  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5249C  s    c      	      s     j  d  t | | | t d  t t | | | | t d  t |  |  t |  t d  t d   |  |  |  t | | t |   | | | | t d  | | t d  |  S(   Ni  i   i   (	   R  R  R  R   R,  R  R  R  R  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5250H  s    c      	      s     j  d  t | | | t d  t t | | | | t d  t |  |  t |  t d  t d   |  |  |  t | | t |   | | | | t d  | | t d  |  S(   Ni  i   i   (	   R  R  R  R   R,  R  R  R  R	  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5251M  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R*  R  R  R	  t   w(    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5252Q  s    c      	      s   t  |  |  }   j d  t | t t | 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	  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5252Y  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R*  R  R  R	  R  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5253_  s    c      	      s   t  |  |  }   j d  t | t t | 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	  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5253g  s    c      	      s     j  d  t |  | | t | | |  t | |  | t d  | t d  | t d  t d  |  |  t | | |  t | |  | |  S(   Ni  ii   i   (   R  R  R   R=   R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5254n  s    c      	      s     j  d  t |  | | t | | |  t | |  | t d  | t d  | t d  t d  |  |  t | | |  t | |  | |  S(   Ni  ii   i   (   R  R  R   R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5255s  s    c            s0     j  d  t | |  t | |  | |  S(   Ni  (   R  R   R=   (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5256x  s    c            s0     j  d  t | |  t | |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5257}  s    c      	      s     j  d  t |  | | | t | |  t | |  | t d  t t d  | | | |  | t d  | t d  t d  |  |  t | |  t | |  | t t d  | | | |  | |  S(   Ni  ii   i   (   R  R  R   R=   R  R"  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5258  s    c      	      s     j  d  t |  | | | t | |  t | |  | t d  t t d  | | | |  | t d  | t d  t d  |  |  t | |  t | |  | t t d  | | | |  | |  S(   Ni  ii   i   (   R  R  R   R  R  R"  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5259  s    c      
      s     j  d  t t t t d  t t | | | |  t | | | |    t d  | |   t t t t d  t t | | | |  t | | | |    t d  | |   t t | | |  t | | |   | |   S(   Ni  i   (   R  R  R  R  R  R=   R"  (   R	  R  R  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5260  s    c            s     j  d  t t t d  t t t | | t d   |  | | |  |  t t t d  t t t | | t d   |  | | |  |  S(   Ni  i   i   (   R  R  R  R  R   R"  (   R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5261  s    c      	      s     j  d  t t t d  t t t d  t | |  |  | | |  |  t t t d  t t t d  t | |  |  | | |  |  S(   Ni  i   i   (   R  R  R  R  R   R"  (   R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5262  s    c            sh     j  d  t |  t t | |  | | | |  |  t | t t | | | |   | |  S(   Ni  (   R  R  R   R=   R  R"  R   (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5263  s    c            sh     j  d  t |  t t | |  | | | |  |  t | t t | | | |   | |  S(   Ni  (   R  R  R   R  R  R"  R   (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5264  s    c            s     j  d  t | | | |  t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5265  s    c            s     j  d  t | | | |  t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5266  s    c      	      s    j  d  t t d  |  | | t | |  t | |  | t d  t t d  t d  t | | t  | t d  | t d  t d  |  |  t t d  | |  t | |  | t t d  t d  t | | t  |  S(   Ni  i   ii   (   R  R  R  R   R=   R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5267  s    c      	      s    j  d  t t d  |  | | t | |  t | |  | t d  t t d  t d  t | | t  | t d  | t d  t d  |  |  t t d  | |  t | |  | t t d  t d  t | | t  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5268  s    c      	      s     j  d  t | | | |  t d  t | |  t d  | | t | |  | t d  | t d  | t d  t d  |  |  t | |  t d  | | t | |  | |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R=   R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5269  s    c      	      s     j  d  t | | | |  t d  t | |  t d  | | t | |  | t d  | t d  | t d  t d  |  |  t | |  t d  | | t | |  | |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5270  s    c            sI     j  d  t t | | t | |  | | | | |  |  |  S(   Ni  (   R  R   R   R=   (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5271  s    c            sI     j  d  t t | | t | |  | | | | |  |  |  S(   Ni  (   R  R   R   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5272  s    c            s@     j  d  t | | t | |  | | | | |  |  S(   Ni  (   R  R   R=   (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5273  s    c            s@     j  d  t | | t | |  | | | | |  |  S(   Ni  (   R  R   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5274  s    c      
      s     j  d  t t d  | t | |  t d  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | |  |  S(   Ni  i   i(   R  R  R  R   R=   (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5275  s    c      
      s     j  d  t t d  | t | |  t d  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | |  |  S(   Ni  i   i(   R  R  R  R   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5276  s    c      	      s     j  d  t |  | | | t | |  t | |  | t d  t t d  | | | | |  | t d  | t d  t d  |  |  t | |  t | |  | t t d  | | | | |  | |  S(   Ni  ii   i   (   R  R  R   R=   R  R"  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5277  s    c      	      s     j  d  t |  | | | t | |  t | |  | t d  t t d  | | | | |  | t d  | t d  t d  |  |  t | |  t | |  | t t d  | | | | |  | |  S(   Ni  ii   i   (   R  R  R   R  R  R"  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5278  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5279  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5280  s    c	   	         sQ     j  d  t t | | | | t | |  | | | | |  |  |  S(   Ni  (   R  R   R   R=   (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5281  s    c	   	         sQ     j  d  t t | | | | t | |  | | | | |  |  |  S(   Ni  (   R  R   R   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5282  s    c	   	         sH     j  d  t | | | | t | |  | | | | |  |  S(   Ni  (   R  R   R=   (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5283  s    c	   	         sH     j  d  t | | | | t | |  | | | | |  |  S(   Ni  (   R  R   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5284  s    c      	      s(    j  d  t t d  | |  t d  |  t d  t | | t | |  | | | t d  |  t d  |  |  t | | | t | |  | | | t d  |  t d  |  t d  |  t | | | | t d  |  t d  | |  t d  |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R=   R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5285	  s    c      	      s(    j  d  t t d  | |  t d  |  t d  t | | t | |  | | | t d  |  t d  |  |  t | | | t | |  | | | t d  |  t d  |  t d  |  t | | | | t d  |  t d  | |  t d  |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5286  s    c      
      s    j  d  t t d  | |  t d  |  t d  t | | t | |  | | | | t d  |  t d  |  |  t | t d  | | | t d  t d  |  t d  |  t d  t | | t | |  | t d  | | | t d  |  t d  |  |  t | | | t | |  | | | | t d  |  t d  |  t d  |  t | | | | t | |  | t d  | | | t d  |  t d  | |  t d  |  t d  |  S(   Ni  i   i   ii(   R  R  R  R   R=   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5287  s    c      
      s    j  d  t t d  | |  t d  |  t d  t | | t | |  | | | | t d  |  t d  |  |  t | t d  | | | t d  t d  |  t d  |  t d  t | | t | |  | t d  | | | t d  |  t d  |  |  t | | | t | |  | | | | t d  |  t d  |  t d  |  t | | | | t | |  | t d  | | | t d  |  t d  | |  t d  |  t d  |  S(   Ni  i   i   ii(   R  R  R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5288  s    c            sG     j  d  t t t | |  t | |  |   |  | | |  S(   Ni  (   R  R  R"  R   R=   (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5289  s    c            sH     j  d  t t t | |  t | |  |   |  | | |  S(   Ni  (   R  R  R"  R   R  (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5290"  s    c            sT     j  d  t | |  t | |  | t d  |  | | | t d  |  S(   Ni  i   (   R  R  R=   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5291'  s    c            sU     j  d  t | |  t | |  | t d  |  | | | t d  |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5292,  s    c      
      s_    j  d  t t |  t t d  t t t | | t d   t t | | t d    | t |  |  t t |  t t d  t t t | | t d   t t | | t d    | t |  |  t t d  t | |  t | |  t t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement52931  s    c      
      s`    j  d  t t |  t t d  t t t | | t d   t t | | t d    | t |  |  t t |  t t d  t t t | | t d   t t | | t d    | t |  |  t t d  t | |  t | |  t t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement52946  s    c            sf     j  d  t t d  | t |  t t | |  | | t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R  R*   R   R  R=   (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5295;  s    c      	      s     j  d  t | t t d  t d  | t d  | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5296@  s    c      	      s     j  d  t t | t d  | t d  t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5297E  s    c      	      s     j  d  t t | t d  | t d  t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5298J  s    c      	      s#    j  d  t |  | | t d  t | | |  t | |  | t d  | | | t d  t d  |  |  t | | |  t | |  | t d  | | | | t d  |  t | |  t | |  | t d  t d  |  | | t d  | t d  |  S(   Ni  i   ii   (   R  R  R  R   R=   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5299O  s    c      	      s"    j  d  t |  | | t d  t | | |  t | |  | t d  | | | t d  t d  |  |  t | | |  t | |  | t d  | | | | t d  |  t | |  t | |  | t d  t d  |  | | t d  | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5300T  s    c      
      s     j  d  t |  | | t | | | t d   |  t | | |  t | |  | t | | | t d   |  S(   Ni  i   (   R  R  R  R  R=   (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5301Y  s    c      
      s     j  d  t |  | | t | | | t d   |  t | | |  t | |  | t | | | t d   |  S(   Ni  i   (   R  R  R  R  R  (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5302^  s    c      	      sJ    j  d  t t d  |  t d  t d  | |  t d  t | | t | |  | | | t d  |  t d  |  |  t | | | | t d  |  t d  t d  | | |  t d  t d  |  t | | | t | |  | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i   i   (   R  R  R  R   R=   R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5303c  s    c      	      sJ    j  d  t t d  |  t d  t d  | |  t d  t | | t | |  | | | t d  |  t d  |  |  t | | | | t d  |  t d  t d  | | |  t d  t d  |  t | | | t | |  | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i   i   (   R  R  R  R   R  R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5304h  s    c      
      s'    j  d  t |  t d  | | t d  t | |  t | |  | t d  | | | t d  t d  d |  |  t | | |  t | |  | | t | | | t d   |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5305m  s    c      
      s'    j  d  t |  t d  | | t d  t | |  t | |  | t d  | | | t d  t d  d |  |  t | | |  t | |  | | t | | | t d   |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5306r  s    c      
      s    j  d  t t d  |  t d  t d  | |  t d  t | | t | |  | | | | t d  |  t d  |  |  t | t d  | | 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 | |  | t d  | | | t d  |  t d  t d  | | |  t d  t d  |  S(   Ni  i   i   i   ii   i(   R  R  R  R   R=   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5307w  s    c      
      s    j  d  t t d  |  t d  t d  | |  t d  t | | t | |  | | | | t d  |  t d  |  |  t | t d  | | 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 | |  | t d  | | | t d  |  t d  t d  | | |  t d  t d  |  S(   Ni  i   i   i   ii   i(   R  R  R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5308|  s    c      	      s     j  d  t t d  | |  t d  | | t d  t | | | t | |  | t d  | | | 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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5309  s    c      	      s     j  d  t t d  | |  t d  | | t d  t | | | t | |  | t d  | | | 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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5310  s    c      	      ss     j  d  t | |  | t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5311  s    c            s     j  d  t | |  t d  d t | t d  | t d  t d   t | | | t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5312  s    c      	      st     j  d  t | |  | t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5313  s    c      	      s     j  d  t | |  t d  d | t | t d  | t d  t d  | t d  | t d   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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5314  s    c      
      s     j  d  t t t d  t t t | | t d   |  | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5315  s    c      
      s     j  d  t t t d  t t t d  t | |  |  | | t d  |  |  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5316  s    c      
      s{     j  d  t | t t d  | | | t d  |  |  t |  t t | |  | | | t d  |  |  S(   Ni  i   i   (   R  R  R   R  R=   (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5317  s    c      
      s{     j  d  t | t t d  | | | t d  |  |  t |  t t | |  | | | t d  |  |  S(   Ni  i   i   (   R  R  R   R  R  (   R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5318  s    c      	      s   t  | | | t d  |  |  }   j d  t | | 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!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5319  s    %c      	      s   t  | | | t d  |  |  }   j d  t | | 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!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5320  s    %c            sS     j  d  t t | | t | |  | | | | t d  |  |  |  S(   Ni  i   (   R  R   R   R=   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5321  s    c            sS     j  d  t t | | t | |  | | | | t d  |  |  |  S(   Ni  i   (   R  R   R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5322  s    c            sJ     j  d  t | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R=   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5323  s    c            sJ     j  d  t | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5324  s    c      
      s     j  d  t t d  | t | |  t d  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   ii   (   R  R  R  R   R=   (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5325  s    c      
      s     j  d  t t d  | t | |  t d  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   ii   (   R  R  R  R   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5326  s    c      
      s     j  d  t t d  | t | |  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   i   (   R  R  R  R   R=   (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5327  s    c      
      s     j  d  t t d  | t | |  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5328  s    c            s     j  d  t t d  | | t | |  t | |  | | | 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5329  s    c            s     j  d  t t d  | | t | |  t | |  | | | 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5330  s    c            s     j  d  t t d  |  | | | t d  t | |  t | |  | t d  |  |  t | | |  t | |  | t d  |  | | | t d  |  S(   Ni  i   (   R  R  R  R   R=   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5331  s    c            s     j  d  t t d  |  | | | t d  t | |  t | |  | t d  |  |  t | | |  t | |  | t d  |  | | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5332  s    c      
      s     j  d  t t d  | t | |  t d  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   ii   (   R  R  R  R   R=   (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5333  s    c      
      s     j  d  t t d  | t | |  t d  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   ii   (   R  R  R  R   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5334   s    c            s     j  d  t t | t | |  t | |  | | | | 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5335  s    c            s     j  d  t t | t | |  t | |  | | | | 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5336
  s    c      
      s     j  d  t t d  | t | |  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   i   (   R  R  R  R   R=   (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5337  s    c      
      s     j  d  t t d  | t | |  | | t | |  | |  |  t | | t | |  t d  | | t | |  | | | | t d  |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5338  s    c      	      s     j  d  t |  | | | | t d  t | |  t d  | | t | |  | t d  |  |  t | |  | | t | |  | t d  | | | | t d  |  S(   Ni  i   i(   R  R  R  R   R=   R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5339  s    c      	      s     j  d  t |  | | | | t d  t | |  t d  | | t | |  | t d  |  |  t | |  | | t | |  | t d  | | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5340  s    c      	      sR     j  d  t t | | t | |  | |  | | | t d  |  |  S(   Ni  i   (   R  R   R   R=   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5341#  s    c      	      sR     j  d  t t | | t | |  | |  | | | t d  |  |  S(   Ni  i   (   R  R   R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5342(  s    c      	      s     j  d  t | | t d  | |  t d  t | | t | |  | t d  | | | t d  |  |  |  t | | t | |  | | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R=   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5343-  s    c      	      s     j  d  t | | t d  | |  t d  t | | t | |  | t d  | | | t d  |  |  |  t | | t | |  | | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement53442  s    c      	      s    j  d  t t d  |  t d  | t d  | t d  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  |  S(   Ni  i   i   i   (   R  R  R  R   R=   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement53457  s    c      	      s    j  d  t t d  |  t d  | t d  | t d  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  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5346<  s    c      	      sc    j  d  t t d  t d  | t d  | |  t d  t | | t | |  | | | 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  |  S(   Ni  i   i   i   i   (   R  R  R  R   R=   R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5347A  s    c      	      sc    j  d  t t d  t d  | t d  | |  t d  t | | t | |  | | | 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  |  S(   Ni  i   i   i   i   (   R  R  R  R   R  R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5348F  s    c      	      s:    j  d  t |  | t d  | t | | |  t | |  | t d  | | | t d  t d  |  |  t | |  t | |  | t d  t d  |  | t d  | t d  | t d  |  t | | |  t | |  | t d  | t d  | | | | t d  |  S(   Ni  i   ii   i   (   R  R  R  R   R=   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5349K  s    c      	      s;    j  d  t |  | t d  | t | | |  t | |  | t d  | | | t d  t d  |  |  t | |  t | |  | t d  t d  |  | t d  | t d  | t d  |  t | | |  t | |  | t d  | t d  | | | | t d  |  S(   Ni  i   ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5350P  s    c      	      sH    j  d  t | t d  | t d  | | t | | t d  | | t | |  | | | t d  |  t d  |  |  t | | | | | | t d  |  t d  | | | t d  |  t | | t d  | | t | |  | | | t d  |  t d  | t d  | | |  S(   Ni  ii   ii   (   R  R  R  R   R=   R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5351U  s    c      	      sH    j  d  t | t d  | t d  | | t | | t d  | | t | |  | | | t d  |  t d  |  |  t | | | | | | t d  |  t d  | | | t d  |  t | | t d  | | t | |  | | | t d  |  t d  | t d  | | |  S(   Ni  ii   ii   (   R  R  R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5352Z  s    c	   	   
      s    j  d  t | t d  | | t d  | t d  t | | | | t | |  | t d  | | | t d  |  |  |  t | t d  | t d  | | t | | t d  | | t | |  | | | | t d  |  t d  |  |  t | | t d  | | t | |  | | | | t d  |  t d  | t d  | | |  t | | | | | | t | |  | t d  | | | t d  |  t d  | | | t d  |  S(   Ni  i   iii   (   R  R  R  R   R=   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5353_  s    c	   	   
      s    j  d  t | t d  | | t d  | t d  t | | | | t | |  | t d  | | | t d  |  |  |  t | t d  | t d  | | t | | t d  | | t | |  | | | | t d  |  t d  |  |  t | | t d  | | t | |  | | | | t d  |  t d  | t d  | | |  t | | | | | | t | |  | t d  | | | t d  |  t d  | | | t d  |  S(   Ni  i   iii   (   R  R  R  R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5354d  s    c	   	   	      s     j  d  t | | | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | | | t | |  | t d  | | | t d  |  t d  | | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R=   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5355i  s    c	   	   	      s     j  d  t | | | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | | | t | |  | t d  | | | t d  |  t d  | | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5356n  s    c	   	   	      s     j  d  t | | | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | t d  | | t | |  | | | | t d  |  t d  | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R=   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5357s  s    c	   	   	      s     j  d  t | | | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | t d  | | t | |  | | | | t d  |  t d  | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5358x  s    c            s    j  d  t | |  t d  t | |  | | t | |  t | | | t d   |  |  t | | | |  t d  t | |  t d  t | | | t d   |  |  t | |  t d  | | t | |  t | | | t d   |  t d  |  S(   Ni  i   i   (   R  R  R  R   R=   R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5359}  s    c            s    j  d  t | |  t d  t | |  | | t | |  t | | | t d   |  |  t | | | |  t d  t | |  t d  t | | | t d   |  |  t | |  t d  | | t | |  t | | | t d   |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5360  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5361  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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5362  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5363  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5364  s    c            sa    j  d  t |  t d  | t d  |  t | |  t d  | | t | |  | t | | | t d   |  |  t | | | |  t | |  t d  | | t | |  | t d  t | | | 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  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5365  s    c            sa    j  d  t |  t d  | t d  |  t | |  t d  | | t | |  | t | | | t d   |  |  t | | | |  t | |  t d  | | t | |  | t d  t | | | 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  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5366  s    c      
      sG    j  d  t t d  | |  t | |  t t t | | t d   t t | | t d    t |  |  t t |  t t d  t t | | t d   t t | | t d    t |  |  t t |  t t d  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5367  s    c      
      sG    j  d  t t d  | |  t | |  t t t | | t d   t t | | t d    t |  |  t t |  t t d  t t | | t d   t t | | t d    t |  |  t t |  t t d  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5368  s    c            sb     j  d  t t d  t |  t t | |  | | t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R  R*   R   R  R=   (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5369  s    c      	      s     j  d  t | | t t d  t d  | t d  | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5370  s    c      
      s     j  d  t t | t d  | t d  t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5371  s    c      
      s     j  d  t t | t d  | t d  t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5372  s    c            s     j  d  t |  | | t | |  t | |  | t d  | t | | | t d   |  |  t | |  t | |  | t | | | t d   | | |  S(   Ni  ii   (   R  R  R   R=   R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5373  s    c            s     j  d  t |  | | t | |  t | |  | t d  | t | | | t d   |  |  t | |  t | |  | t | | | t d   | | |  S(   Ni  ii   (   R  R  R   R  R  R  R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5374  s    c            sq    j  d  t | t d  |  t d  |  t d  t | |  t d  | | t | |  | t | | | t d   |  |  t | | | |  t d  t | |  t d  | | t | |  | 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  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5375  s    c            sq    j  d  t | t d  |  t d  |  t d  t | |  t d  | | t | |  | t | | | t d   |  |  t | | | |  t d  t | |  t d  | | t | |  | 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  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5376  s    c	   	   
      s     j  d  t t d  | t | | t d  | | t | |  | | | | t d  |  t d  |  |  t | | t | | t d  | | t | |  | | | | t d  |  |  |  S(   Ni  i   ii   (   R  R  R  R   R=   (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5377  s    c	   	   
      s     j  d  t t d  | t | | t d  | | t | |  | | | | t d  |  t d  |  |  t | | t | | t d  | | t | |  | | | | t d  |  |  |  S(   Ni  i   ii   (   R  R  R  R   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5378  s    c	   	   
      s     j  d  t t d  | t | | | | t | |  | | | | t d  |  t d  |  |  t | | t | | t d  | | t | |  | | | | t d  |  |  |  S(   Ni  i   i   (   R  R  R  R   R=   (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5379  s    c	   	   
      s     j  d  t t d  | t | | | | t | |  | | | | t d  |  t d  |  |  t | | t | | t d  | | t | |  | | | | t d  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5380  s    c	   	   
      s    j  d  t | | | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | t d  |  t d  | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | | | t | |  | t d  | | | t d  |  t d  | | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R=   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5381  s    c	   	   
      s    j  d  t | | | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | t d  |  t d  | | t d  t | | t d  | | t | |  | t d  | | | t d  |  |  |  t | | | | t | |  | t d  | | | t d  |  t d  | | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5382  s    c	   	   	      s     j  d  t | | t d  | |  t t | | | | t |  | t |  | t d  |  t d  |  | t | |   |  S(   Ni  ii   i(   R  R  R  R*   R   R  R  R=   (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5383  s    c	   	   	      s     j  d  t | |  t d  d t | t d  | t d  t d   t | | | t d   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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5384  s    c	   	   	      s     j  d  t | | t d  | |  t t | | | | t |  | t d  |  t d  t |  | |  | t | |   |  S(   Ni	  ii   i(   R  R  R  R*   R   R  R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5385  s    c	   	   	      s    j  d  t | | | |  t d  d | t | t d  | t d  t d  | t d  | t d   t | | | t d   t t | | | | t |  | t d  |  t d  t |  | |  | t | |   |  S(   Ni
  i   i   i(	   R  R  R  R  R*   R   R  R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5386  s    c            s     j  d  t | | t d  | |  t d  t | | | t d  |  t d  | t d  | t d  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5387	  s    c            s     j  d  t | | t d  | |  t d  t | | | t d  |  t d  | t d  | t d  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5388  s    c   	   	      s   t  | | | | | t d  |  |  }   j d  t | | 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5389  s    -c   	   	      s   t  | | | | | t d  |  |  }   j d  t | | 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5390  s    -c	   	   	      sZ     j  d  t t | | t | |  | | | | | | t d  |  |  |  S(   Ni  i   (   R  R   R   R=   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5391  s    c	   	   	      sZ     j  d  t t | | t | |  | | | | | | t d  |  |  |  S(   Ni  i   (   R  R   R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5392$  s    c      
      s     j  d  t | t | | | | | t d  |  |  |  t | t | | | | | t d  |  t | |  |  |  S(   Ni  i   (   R  R  R   R  R=   (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5393)  s    c      
      s     j  d  t | t | | | | | t d  |  |  |  t | t | | | | | t d  |  t | |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5394.  s    c	   	         sR     j  d  t | | | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R=   R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement53953  s    c	   	         sR     j  d  t | | | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement53968  s    c      
      s     j  d  t t d  d t | | t | |  | t |  t d   | | | t d  |  |  t t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5397=  s    c      
      s     j  d  t t d  d t | | t | |  | t t t d  t d  |  |   | | | t d  |  |  t t d  d t | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5398B  s    c      
      s     j  d  t t d  d t | | t | |  | t |  t d   | | | t d  |  |  t t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5399G  s    c      
      s     j  d  t t d  d t | | t | |  | t t t d  t d  |  |   | | | t d  |  |  t t d  d t | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5400L  s    c      
      s     j  d  t t | | t d  t | | t | |  | t d  t t d  t |  t d    | | | t d  |  |  t t | | 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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5401Q  s    c      
      s     j  d  t t | | t d  t | | t | |  | t d  t t d  t |  t d    | | | t d  |  |  t t | | 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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5402V  s    c      
      s     j  d  t t | | t d  t | | t | |  | t d  t t d  t |  t d    | | | t d  |  |  t t | | 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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5403[  s    c      
      s     j  d  t t | | t d  t | | t | |  | t d  t t d  t |  t d    | | | t d  |  |  t t | | 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	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5404`  s    c	   	   	      s     j  d  t t | | t d  t | | t | |  | t d  t |  t d  |  | | | t d  |  |  t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5405e  s    c	   	   	      s     j  d  t t | | t d  t | | t | |  | t d  t |  t d  |  | | | t d  |  |  t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5406j  s    c	   	   	      s     j  d  t t | | t d  t | | t | |  | t d  t |  t d  |  | | | t d  |  |  t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5407o  s    c	   	   	      s     j  d  t t | | t d  t | | t | |  | t d  t |  t d  |  | | | t d  |  |  t 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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5408t  s    c            s     j  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5409y  s    c      	      s     j  d  t | |  t d  t | | t | |  | t d  | | t | |  |  t d  | | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5410~  s    c      	      s     j  d  t | |  t d  t | | t | |  |  t d  | | t | |  | t d  | | | t d  |  |  t | | t | |  |  t d  | | t | |  | | | | |  t d  |  S(   Ni#  i   ii   (   R  R  R  R   R=   R  R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5411  s    c      	      s     j  d  t t t d  t t t | | t d   | |  | | |  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5412  s    c      	      s     j  d  t t t d  t t t d  t | |  | |  | | |  |  t t t d  t t t d  t | |  | |  | | |  |  S(   Ni%  i   i   (   R  R  R  R  R   R"  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5413  s    c            s    j  d  t | | t | | | t |  | | t d   | t d  | t d  t d  |  |  t t d  | | t | t d  | | t | |  |  | | t d  |  |  t | | | t | |  | | t |  | | t d   |  S(   Ni&  i   i   (   R  R  R   R"  R  R=   R  (   RF  R  RE  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5414  s    c            s    j  d  t | | t | | | t |  | | t d   | t d  | t d  t d  |  |  t t d  | | t | t d  | | t | |  |  | | t d  |  |  t | | | t | |  | | t |  | | t d   |  S(   Ni'  i   i   (   R  R  R   R"  R  R  R  (   RF  R  RE  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5415  s    c	   	         sc    j  d  t | | |  t d  t | |  t d  | | t | | | t d   | t d  | t d  t d  |  |  t t d  | | |  t d  t | |  t d  | | t | |  | | | t d  |  |  t | |  t d  | | t | |  | | t | | | t d   |  t d  |  S(   Ni(  i   i   (   R  R  R  R   R"  R=   R  (	   R  RF  R  RE  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5416  s    c	   	         sb    j  d  t | | |  t d  t | |  t d  | | t | | | t d   | t d  | t d  t d  |  |  t t d  | | |  t d  t | |  t d  | | t | |  | | | t d  |  |  t | |  t d  | | t | |  | | t | | | t d   |  t d  |  S(   Ni)  i   i   (   R  R  R  R   R"  R  R  (	   R  RF  R  RE  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5417  s    c	   
   
      s   t  | |  | | t | | | t d   |  }	   j d  t | | t t |	 | t d  | t d  t d  |  |  |  t | | t | |  |	 |  S(   Ni   i*  i   (   R  R"  R  R  R  R   R   R=   (
   R  RF  R  RE  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5418  s    7c	   
   
      s   t  | |  | | t | | | t d   |  }	   j d  t | | t t |	 | t d  | t d  t d  |  |  |  t | | t | |  |	 |  S(   Ni   i+  i   (   R  R"  R  R  R  R   R   R  (
   R  RF  R  RE  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5419  s    7c	   
   
      s   t  | |  | | t | |  |  }	   j d  t t d  | | t t |	 | | | | t d  |  |  |  t | | t | | | t d   |	 |  S(   Ni,  i   (   R  R=   R  R  R  R   R   R"  (
   R  RF  R  RE  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5420  s    )c	   
   
      s   t  | |  | | t | |  |  }	   j d  t t d  | | t t |	 | | | | t d  |  |  |  t | | t | | | t d   |	 |  S(   Ni-  i   (   R  R  R  R  R  R   R   R"  (
   R  RF  R  RE  R  R  R  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5421  s    )c            s~    j  d  t | | t | | t | |  | | t | |  | t d   |  |  t | | | t | t d  | | t | |  | t d  | t d  t d  |  |  t | | t d  | | t | |  t d  t d  |  t | | t | |  t d  | | t | |  | t d   | |  | t d  t d  |  |  S(   Ni.  i   i   (   R  R  R   R=   R"  R  R  (   RE  R  RF  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5422  s    c            s}    j  d  t | | t | | t | |  | | t | |  | t d   |  |  t | | | t | t d  | | t | |  | t d  | t d  t d  |  |  t | | t d  | | t | |  t d  t d  |  t | | t | |  t d  | | t | |  | t d   | |  | t d  t d  |  |  S(   Ni/  i   i   (   R  R  R   R  R"  R  R  (   RE  R  RF  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5423  s    c            s     j  d  t t | |  t d  t | t d  t d  d t | |  t d  t | t d  t d  d t | t d  |  t d  t d   |   S(   Ni0  i   i   (   R  R   R  R  R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5424  s    c            s     j  d  t |  | t | |  t d  t | t d  t d  d t | |  t d  t | t d  t d  d t | t d  |  t d  t d   |   S(   Ni1  i   i   (   R  R   R  R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5425  s    c            sh     j  d  t t | |  t d  t | t d  t | |  t d  t | t d  |   S(   Ni2  i   i   (   R  R   R  R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5426  s    c            sp     j  d  t |  | t | |  t d  t | t d  t | |  t d  t | t d  |   S(   Ni3  i   i   (   R  R   R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5427  s    c            s     j  d  t | |  t | t d  | | | |  t | | t d  t | t d  t | | t d  t | t d  |  |  S(   Ni4  i   i   (   R  R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5428  s    c            s|     j  d  t | | | | |  t | | t d  t | t d  t | | t d  t | t d  |  S(   Ni5  i   i   (   R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5429  s    c      	      se     j  d  t | |  t | | |  | | | t d  |  t | t | |   |  |  S(   Ni6  i   (   R  R  R   R  t   expR=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5430  s    c            s     j  d  t t d  | t d  | |  t | t d  t | | t | t d  t d  t | | t | t d  t d  | | | |  |  |  S(   Ni7  ii   i   (   R  R  R  R   R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5431  s    c            s|     j  d  t | | | | |  t | | t d  t | t d  t | | t d  t | t d  |  S(   Ni8  i   i   (   R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5432  s    c      	      s     j  d  t | |  | | | |  | | | t d  |  t | | |  | | | t d  |  t | t | |   |  |  S(   Ni9  i   (   R  R  R  R   R  R=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5433  s    c      	      sv     j  d  t | | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5434  s    c      	      s`    j  d  t t d  |  t d  t d  |  t d  | | t d  t d  |  t d  t d  t | | | t d  |  t d  t | t | |   |  |  t | | | t d  |  t d  t d  | | |  t d  | t | t | |   | | | t d  t d  |  t d  t d  |  S(   Ni;  i   i   i   i   (   R  R  R  R   R  R=   R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5435  s    c            s:     j  d  t t | t | |   | | | |  S(   Ni<  (   R  R  R  R=   (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5436	  s    c            s     j  d  t | |  t | t d  | t d  t d  t | t d  |  t | | t d  t | |  |  S(   Ni=  i   i   (   R  R  R   R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5437		  s    c            s     j  d  t | |  t t | | t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5438	  s    c            s     j  d  t | t | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5439	  s    c            s     j  d  t | t | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5440	  s    c      	      s     j  d  t | t |   | | | t d  t |   | t d  | t d  t d  t |   t | t d  | t d  t d  |  t | t | |   |  |  S(   NiA  i   i   (   R  R  R$   R  R%   R   R  R=   (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5441	  s    c      	      s~     j  d  t | | | t d  t | t | |   |  t | |  | t d   | t d  t d  |  S(   NiB  i   i   (   R  R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5442"	  s    c      	      s     j  d  t | | | t d  | |  t d  t | | | t d  |  t | t | |   |  |  t | | | t d  |  t d  t | t | |   t d  | |  t d  |  S(   NiC  i   i   (   R  R  R  R   R  R=   R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5443'	  s    c            s     j  d  t | | | t d  |  t d  | | | t d  t | t | |   | | | | t d  t d  |  S(   NiD  i   i   (   R  R  R  R  R=   (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5444,	  s    c      	      sV    j  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 d  |  t d  t d  | | |  t d  | t | t | |   | | | t d  t d  |  t d  t d  |  S(   NiE  i   ii   i   (   R  R  R  R   R  R=   R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement54451	  s    c            s     j  d  t | |  t | | | t d  | t d  t d  t | t d  |  t | | t d  t | |  |  S(   NiF  i   i   (   R  R  R   R  R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement54466	  s    c            s     j  d  t | |  t | | t | | t d  t | t d  |  t | | t d  t | t d  |  |  |  S(   NiG  i   i   (   R  R  R   R  R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5447;	  s    c      	      s     j  d  t | t | t d  t | | | | | t d  t | t d  |  t | | t d  t | |  |  S(   NiH  i   i   (   R  R  R  R  R   (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5448@	  s    c      	      s     j  d  t | t | t d  t | | | | | t d  t | t d  |  t | | t d  t | |  |  S(   NiI  i   i   (   R  R  R  R  R   (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5449E	  s    c      	      s     j  d  t | t |   | | | t d  t |   | t d  | t d  t d  t |   t | | | t d  | t d  t d  |  t | t | |   |  |  S(   NiJ  i   i   (   R  R  R$   R  R%   R   R  R=   (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5450J	  s    c            s     j  d  t | |  t | t | | t d  t | t d  |  t | | t d  t | t d  |  |  |  S(   NiK  i   i   (   R  R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5451O	  s    c            s     j  d  t | t |   | | | t d  t |   t | | t d  t |   t | | t d  t |   t | t | | t d  t | t d  |  t | | t d  t | t d  |  |  |  S(   NiL  i   i   (   R  R  R$   R  R%   R  R   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5452T	  s    c      	      s     j  d  t | t |   | | | t d  t |   | t d  | t d  t d  t |   t | | t d  | t d  t d  |  t | t | |   |  |  S(   NiM  i   i   (   R  R  R$   R  R%   R   R  R=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5453Y	  s    c      	      s     j  d  t | |  t | | t d  |  | t d  | t d  t d  |  t | t | |   |  |  S(   NiN  i   i   (   R  R  R   R  R  R=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5454^	  s    c      	      sv     j  d  t | |  t | t d  t | | |  t d  t | | |  t | t | |   |  |  S(   NiO  i   (   R  R  R   R  R  R  R=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5455c	  s    c      	      s     j  d  t | t d  |  | | | t d  |  t | | t d  |  t | | t d  |  t | | t d  |  t | | t d  |  t | | t d  |  t | t | |   |  |  S(   NiP  i   i   (   R  R  R  R  R   R  R=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5456h	  s    c      	      s     j  d  t | t d  |  | | | t d  |  | t d  | t d  t d  |  t | | t d  |  | t d  | t d  t d  |  t | t | |   |  |  S(   NiQ  i   i   (   R  R  R  R   R  R=   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5457m	  s    c            s     j  d  t t | | t |  | | t d  t | t d  t | | t |  | | t d  t | t d  |  S(   NiR  i   i   (   R  R   R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5458r	  s    c      
      sT    j  d  t t d  t |  | |  t d  | |  t d  | t t | t d  t | t d  | t d  t | |  t d  t | | t d  | t d  t | t | | t d  |  |  | t | | | | t d  t | t d  t | | | | t d  t | t d   |  S(   NiS  i   ii   i   i(   R  R  R  R  R*   R   (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5459w	  s    c            s     j  d  t | | | |  t | | t | | | t d  t | t d  t | | t | | | t d  t | t d  |  S(   NiT  i   i   (   R  R   R  R  (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5460|	  s    c	   	         s     j  d  t | | t d  t d  |  t | t | t | | t d  t | t d  |  t | t | | t d  t | t d  |  |  |  S(   NiU  i   i   (   R  R  R  R   R  (	   R)  R*  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5461	  s    c	   	   	      s     j  d  t | | | | | t d  |  | t d  t d  | | | | t d  | t d  t d  |  t | | t d  t d  | | | | t d  | t d  t d  |  t | t | |   |  |  S(   NiV  i   i   (   R  R  R  R   R  R=   (	   R)  R*  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5462	  s    c            s>     j  d  t |  t | t | | | | |   |  S(   NiW  (   R  R   R  R  (   R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5463	  s    c      	      sW     j  d  t t d  t | t d  t | t | t | |    |   |   S(   NiX  ii   (   R  R  R  R  R   R  R=   (   R	  R  R  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5464	  s    c      
      s     j  d  t t t d  t |  | t | t d  t d  d t d  t |  | t | t d  t d  d |  t d  t t d  |  t d  | t d   |   |  t d  |   S(   NiY  i   i   (   R  R*   R   R  R  R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5465	  s    c      	      s     j  d  t t |  | t d  t d  t |  | t | t d  t d  d t d  t |  | t | t d  t d  d t t d  |  t d  | t d   |   |  t d  |   S(   NiZ  ii   i   (   R  R*   R   R  R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5466	  s    c            s     j  d  t t t d  t |  | t | t d  t d  t |  | t | t d  |  t d  |   |  t d  |   S(   Ni[  i   i   (   R  R*   R   R  R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5467	  s    c            s     j  d  t t |  | t d  t d  t |  | | t d  t d  t |  | | t d  |   |  t d  |   S(   Ni\  ii   i   (   R  R*   R   R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5468	  s    c            s     j  d  t |  | t d  |  | t t |  | t d  t d  t |  | t | t d  t d  d t d  t |  | t | t d  t d  d t t d  |  t d  | t d   |   |  t d  |   |   S(   Ni]  i   ii   (   R  R  R  R*   R   R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5469	  s    c            s     j  d  t t |  | t d  t d  t |  | | t d  t d  t |  | | t d  |   |  t d  |   S(   Ni^  ii   i   (   R  R*   R   R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5470	  s    c      	      sd     j  d  t | |  t | | |  | | | t d  |  t | t | |   |  |  S(   Ni_  i   (   R  R  R   R  R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5471	  s    c      	      s     j  d  t | |  | | | |  | | | t d  |  t | | |  | | | t d  |  t | t | |   |  |  S(   Ni`  i   (   R  R  R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5472	  s    c      	      s     j  d  t | |  t t t d  t | | t | t d  t d  t | | t | t d  t d  | | | |  | t d  |  | t d  |  |  S(   Nia  i   i   (   R  R  R*   R   R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5473	  s    c      	      s     j  d  t | |  t t | | t d  t d  t | | t | t d  t d  t | | t | t d  t d  | | | |  |  | t d  |  |  S(   Nib  ii   i   (   R  R  R*   R   R  R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5474	  s    c      	      s{     j  d  t t d  | | | |  | | | |  t t d  | | | |  t | t | |   |  |  S(   Nic  i   (   R  R  R  R   R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5475	  s    c      	      s     j  d  t | |  | | t d  | | t t | | t d  t d  t | | t | t d  t d  t | | t | t d  t d  | | | |  |  | t d  |  |  S(   Nid  i   ii   (   R  R  R  R*   R   R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5476	  s    c      	      s     j  d  t t d  | | | |  | | | |  t | t d  | | | |  t | t | |   |  |  S(   Nie  i   (   R  R  R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5477	  s    c            s;     j  d  t t | t | |   | | | |  S(   Nif  (   R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5478	  s    c      	      sx     j  d  t | | | t | t | |   | | t | |  | t d   | t d  t d  |  S(   Nig  i   i   (   R  R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5479	  s    c      	      s_    j  d  t t d  |  t d  t d  |  t d  | | t d  t d  |  t d  t d  t | | | t d  |  t d  t | t | |   |  |  t | | | t d  |  t d  t d  | | |  t d  | t | t | |   | | | t d  t d  |  t d  t d  |  S(   Nih  i   i   i   i   (   R  R  R  R   R  R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5480	  s    c      	      s     j  d  t | | | t d  t | t | |   | t d  | t | |  | t d   | t d  t d  |  S(   Nii  i   i   (   R  R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5481	  s    c      	      sZ    j  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 | t | |   | t d  | | t d  t d  |  t d  t d  |  S(   Nij  i   i   i   i   (   R  R  R  R   R  R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5482	  s    c            s     j  d  t | | | t d  |  t d  t d  | | |  t d  | t | t | |   | t d  | | t d  | t d  t d  |  S(   Nik  i   i   i   (   R  R  R  R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5483	  s    c      	      sm    j  d  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 d  t d  | | |  t d  | t | t | |   | t d  | | t d  t d  |  t d  t d  |  S(   Nil  i   ii   i   i   (   R  R  R  R   R  R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5484	  s    c      	      s     j  d  t | | t d  | |  t t t d  t |  | t d  |  t d  t | |  t |  t d  |  t d  |  | t | |   |  S(   Nim  ii   i   i(	   R  R  R  R*   R   R  R  R  R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5485	  s    c      
      s     j  d  t | |  t | | t d  |  t d  t d  | t d  | t d  |  t | t | |   |  |  S(   Nin  i   i   (   R  R  R   R  R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5486	  s    c      
      s     j  d  t | t d  |  t d  t d  | t d  | t d  |  | | | t d  |  t | | t d  |  t d  t d  | t d  | t d  |  t | t | |   |  |  S(   Nio  i   i   (   R  R  R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5487
  s    c            s     j  d  t | |  t | t d  |  t | | t d  |  t | | t d  t | t d  |  t | | t d  t | t d  |  |  |  S(   Nip  i   ii   (   R  R  R  R  R   (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5488
  s    c      	      s     j  d  t | |  t t t d  t | | t | t d  |  t d  t | | t | t d  |  | t d  |  | t d  |  |  S(   Niq  i   i   (   R  R  R*   R   R  R  (   R)  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5489
  s    c      	      s     j  d  t | |  t t | | t d  t d  t | | t | t d  |  t d  t | | t | t d  |  |  | t d  |  |  S(   Nir  ii   i   (   R  R  R*   R   R  R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5490
  s    c      	      s     j  d  t | |  | | t d  | | t t | | t d  t d  t | | t | t d  |  t d  t | | t | t d  |  |  | t d  |  |  S(   Nis  i   ii   (   R  R  R  R*   R   R  (   R)  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5491
  s    c      
      s     j  d  t t d  t d  | t d  | t d  |  | | | t d  |  t | t d  t d  | t d  | t d  |  t | t | |   |  |  S(   Nit  i   i   (   R  R  R  R   R  R  (   R)  R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5492
  s    c            s_     j  d  t t d  t | t d  t |  t | t | | | |   |  |  S(   Niu  ii   (   R  R  R  R  R   R  R=   (   R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5493!
  s    c            s    j  d  t t | | |  | t | t d  t d  t | | |  | t | t d  t | | t |  | | t d  t | t d  t t | | t |  | | t d  t | t d  t | | t |  | | t d  t | t d  |  |  S(   Niv  i   i   i(   R  R  R  R  R   (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5494&
  s    c            sS    j  d  t t d  t |  | |  t d  | |  t d  | t t | t d  t | t d  | t d  t | |  t d  t | | t d  | t d  t | t | | t d  |  |  | t d  t | | | | t | t d  t d  t | | | | t | t d   |  S(   Niw  i   ii   ii   (   R  R  R  R  R*   R   (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5495+
  s    c            s.    j  d  t t | | | | t | t d  t d  t | | | | t | t d  t | | t | | | t d  t | t d  t | | | |  t | | t | | | t d  t | t d  t | | t | | | t d  t | t d  |  |  S(   Nix  i   i   i(   R  R  R  R  R   (   R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement54960
  s    c	   	         s    j  d  t | | t d  t d  |  t | t | | t d  t | t | | t | t d  t | t | | t | t | | t d  t | t d  t | t | | t d  t | t d  t | t | | t d  t | t d  t | t | t | | t d  t | t d  |  t | t | | t d  t | t d  |  |  |  S(   Niy  i   i   i(   R  R  R  R  R   (	   R)  R*  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement54975
  s    c	   	   	      s     j  d  t | | | | | t d  |  | t d  t d  | | | | t d  | t d  t d  |  t | | t d  t d  | | | | t d  | t d  t d  |  t | t | |   |  |  S(   Niz  i   i   (   R  R  R  R   R  R  (	   R)  R*  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5498:
  s    c            s>     j  d  t |  t | t | | | | |   |  S(   Ni{  (   R  R   R  R=   (   R*  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5499?
  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5500D
  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5501I
  s    c            s4     j  d  t | |  t | | |  | |  S(   Ni~  (   R  R   R=   (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5502N
  s    c            s4     j  d  t | |  t | | |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5503S
  s    c	   	   	      s{     j  d  t t d  | t t | | t |  | | | | | | | | | |  |  | | | |  |  S(   Ni  i   (   R  R  R  R*   R   R=   (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5504X
  s    c	   	   	      s{     j  d  t t d  | t t | | t |  | | | | | | | | | |  |  | | | |  |  S(   Ni  i   (   R  R  R  R*   R   R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5505]
  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni  (   R  R   R=   (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5506b
  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni  (   R  R   R  (	   R  RF  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5507g
  s    c
   
   
      s     j  d  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  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5508l
  s    c
   
   
      s     j  d  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  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5509q
  s    c      
      s     j  d  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  RF  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5510v
  s    c      
      s     j  d  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  RF  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5511{
  s    c      	      s     j  d  t t t d  t t t | t |  | t d   | | | | |  |  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5512
  s    c      	      s     j  d  t t t d  t t | |  | t | |  |  | | | | |  |  t t t d  t t | |  | t | |  |  | | | | |  |  S(   Ni  i   (   R  R  R  R  R   R"  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5513
  s    c            s8     j  d  t t | |  |  | | | | |  S(   Ni  (   R  R   R=   (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5514
  s    c            s8     j  d  t t | |  |  | | | | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5515
  s    c      	      s     j  d  t | | t |  | | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5516
  s    c      	      s     j  d  t | | t |  | | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5517
  s    c      	      s     j  d  t t t d  t t t | t | |  | t d   |  |   |   t t t d  t t t | t | |  | t d   |  |   |   S(   Ni  i   i   (   R  R  R  R  R   R"  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5518
  s    c            s     j  d  t t t d  t t t d  t | | |  |  |  |   |   t t t d  t t t d  t | | |  |  |  |   |   S(   Ni  i   i   (   R  R  R  R  R   R"  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5519
  s    c      	      s     j  d  t | | |  t d  t | |  | | t d  t d  | | | | | t d  | t d  | t d  |  |  t | |  t d  t | | | |  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R=   (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5520
  s    c      	      s     j  d  t | | |  t d  t | |  | | t d  t d  | | | | | t d  | t d  | t d  |  |  t | |  t d  t | | | |  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5521
  s    c            s     j  d  t t t d  t t t | t | |  | | | t d   |  |  t t t d  t t t | t | |  | | | t d   |  |  S(   Ni  i   i   (   R  R  R  R  R   R"  (   RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5522
  s    c            s     j  d  t t t d  t t t d  t | | |  | | |  |  |  t t t d  t t t d  t | | |  | | |  |  |  S(   Ni  i   i   (   R  R  R  R  R   R"  (   RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5523
  s    c            s     j  d  t t t d  t | |  t t | t | | | | | t d   |  |  t t t d  t | |  t t | t | | | | | t d   |  |  S(   Ni  i   i   (   R  R  R  R  R   R"  (   R  RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5524
  s    c            s     j  d  t t t d  t | |  t t d  t | | | | | |  |  |  t t t d  t | |  t t d  t | | | | | |  |  |  S(   Ni  i   i   (   R  R  R  R  R   R"  (   R  RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5525
  s    c            s<     j  d  t |  t | | | | | |  | |  S(   Ni  (   R  R   R  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5526
  s    c            s<     j  d  t |  t | | | | | |  | |  S(   Ni  (   R  R   R=   (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5527
  s    c      
      sJ     j  d  t t t | |  t | | |  t d     | |   S(   Ni  i   (   R  R  R"  R=   R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5528
  s    c      
      sK     j  d  t t t | |  t | | |  t d     | |   S(   Ni  i   (   R  R  R"  R  R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5529
  s    c      	      s`     j  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5530
  s    c      	      sa     j  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5531
  s    c            s     j  d  t t | | | t d   t | | | t d   t t | | t | | | t d    |  t | | | t d   |  |  S(   Ni  i   (   R  R  R  R  R   R=   (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5532
  s    c            s     j  d  t t | | | t d   t | | | t d   t t | | t | | | t d    |  t | | | t d   |  |  S(   Ni  i   (   R  R  R  R  R   R  (   R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5533
  s    t   sc            sa     j  d  t t d  d t | t |   |  |  t t | t d  t | |  |  S(   Ni  i   i   i   (   R  R  R  R   R=   R  (   R  R  R*  R	  R#  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5534
  s    c            sb     j  d  t t d  d t | t |   |  |  t t | t d  t | |  |  S(   Ni  i   i   i   (   R  R  R  R   R=   R  (   R  R  R*  R	  R#  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5535
  s    c      
   S   s   t  | t t t t f  r t Sy t | |  } t t t	 |   t
 t |  t  t t |  |  t d  t |  |  t | t d   t d    } Wn t t f k
 r t SX| r t St S(   Ni   i   (   R  R  R  R  R  R  RP  R  R5   R   R  R]   R=   R   R  R  R  R  t	   TypeErrort   AttributeErrorR  (   R  R	  R  R*  t   tmpt   res(    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5536
  s    tc      
      s   t  | |  }   j d  t t |  |  t d  t |  | t d   | t t | t d   | t d   t t t	 t d  t
 |  t d  | t d  t | | |  |  |  | |  |  S(   Ni  i   i   i   (   RP  R  R  R  R  R2   R  R*   R   R,  R  R   (   R  R	  R  R*  R(  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5536  s    c      
   S   s   t  | t t t t f  r t Sy t | |  } t t t	 |   t
 t |  t  t t |  |  t d  t |  |  t | t d   t d    } Wn t t f k
 r t SX| r t St S(   Ni   i   (   R  R  R  R  R  R  RP  R  R5   R   R  R]   R>   R   R  R  R  R  R&  R'  R  (   R  R	  R  R*  R(  R)  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5537	  s    tc      
      s   t  | |  }   j d  t t |  |  t d  t |  | t d   | t t | t d   | t d   t t t	 t d  t
 |  t d  | t d  t | | |  |  |  | |  |  S(   Ni  i   i   i   (   RP  R  R  R  R  R2   R  R*   R   R,  R  R   (   R  R	  R  R*  R(  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5537  s    c      
      s     j  d  t t |  t | | t t d  t | t d  t |  |  | t | |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5538  s    c      
      s     j  d  t t |  t | | t t d  t | t d  t |  |  | t | |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5539!  s    c      
      s     j  d  t t |  t | | t t d  t | t d  t |  |  | t | |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5540&  s    c      
      s     j  d  t t |  t | | t t d  t | t d  t |  |  | t | |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5541+  s    c            s    j  d  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  t t d  t | t d  t |  |  t d  |  |  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement55420  s    c            s    j  d  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  t t d  t | t d  t |  |  t d  |  |  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement55435  s    c            s    j  d  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  t t d  t | t d  t |  |  t d  |  |  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5544:  s    c            s    j  d  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  t t d  t | t d  t |  |  t d  |  |  t |  t | | t d  t | t t d  t | t d  t |  |  t | | t | | t d  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5545?  s    c      
      s     j  d  t t | | |  t d  t | | | |  t d  | t t d  t | t d  t | |  | t | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R=   R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5546D  s    c      
      s     j  d  t t | | |  t d  t | | | |  t d  | t t d  t | t d  t | |  | t | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R  R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5547I  s    c      
      s     j  d  t t | | |  t d  t | | | |  t d  | t t d  t | t d  t | |  | t | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R=   R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5548N  s    c      
      s     j  d  t t | | |  t d  t | | | |  t d  | t t d  t | t d  t | |  | t | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R  R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5549S  s    c            s#    j  d  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R=   R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5550X  s    c            s$    j  d  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R  R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5551]  s    c            s$    j  d  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R=   R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5552b  s    c            s#    j  d  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | t | | t d  | |  t d  t | | | |  t d  t t d  t | t d  t | |  t | | t | | t d  t t d  t | t d  t | |  t d  |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (	   R  R  R  R  R   R  R  R  R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5553g  s    c            sr     j  d  t | t |  t t d  | t d  | |   |   |   t |  t t | | |    |   S(   Ni  i   (   R  R  R   R  R  R  R=   R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5554l  s    c            sq     j  d  t | t |  t t d  | t d  | |   |   |   t |  t t | | |    |   S(   Ni  i   (   R  R  R   R  R  R  R  R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5555q  s    c      	      s{     j  d  t | t |  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5556v  s    c      	      s|     j  d  t | t |  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5557{  s    c            s     j  d  t | | |  t d  t | | | |  t d  t t d  | t d  | |  |  |  t | | | |  t d  t t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R=   R  (   R  RF  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5558  s    c            s     j  d  t | | |  t d  t | | | |  t d  t t d  | t d  | |  |  |  t | | | |  t d  t t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  RF  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5559  s    c      	      s     j  d  t | | |  t d  t | | | |  t d  t t d  | t d  | |  |  |  t | | | |  t d  t t d  t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R=   R  (   R  RF  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5560  s    c      	      s     j  d  t | | |  t d  t | | | |  t d  t t d  | t d  | |  |  |  t | | | |  t d  t t d  t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  RF  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5561  s    c      
      s     j  d  t |  t | | t t d  | t d  |  |  | | |  |  t | t | | t | |  |   |  S(   Ni  i   (   R  R  R   R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5562  s    c      
      s     j  d  t |  t | | t t d  | t d  |  |  | | |  |  t | t | | t | |  |   |  S(   Ni  i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5563  s    c      
      s     j  d  t |  t | | t t d  | t d  |  |  | | |  |  t | t | | t | |  |   |  S(   Ni  i   (   R  R  R   R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5564  s    c      
      s     j  d  t |  t | | t t d  | t d  |  |  | | |  |  t | t | | t | |  |   |  S(   Ni  i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5565  s    c            sW    j  d  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5566  s    c            sX    j  d  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5567  s    c            sX    j  d  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R=   R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5568  s    c            sW    j  d  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t t |  | | t t | t t d  | t d  |  |  | | | | t t t d  | t d  |  |  t |  |  t | t | | t | |  |   |  S(   Ni  i   (	   R  R  R  R   R  R  R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5569  s    c      
      s     j  d  t | | |  t d  t | | | |  t d  | t t d  | t d  | |  | | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R=   R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5570  s    c      
      s     j  d  t | | |  t d  t | | | |  t d  | t t d  | t d  | |  | | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5571  s    c      
      s     j  d  t | | |  t d  t | | | |  t d  | t t d  | t d  | |  | | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R=   R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5572  s    c      
      s     j  d  t | | |  t d  t | | | |  t d  | t t d  | t d  | |  | | |  |  t | | | |  t d  t | | t | | |   | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5573  s    c            s    j  d  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t t t d  | t d  | |  t |  |  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t 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  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5574  s    c            s    j  d  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t t t d  | t d  | |  t |  |  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t 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  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5575  s    c            s    j  d  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t t t d  | t d  | |  t |  |  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t 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  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5576  s    c            s    j  d  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t t t d  | t d  | |  t |  |  t t | | | t | |  t d  t | | | |  t d  t t d  | t d  | |  | | | | t 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  RF  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5577  s    c            s`     j  d  t t |  t | |   | t d  t d  |   |   t |  t |  |   S(   Ni  i   i   (   R  R   R,  R  R  R  R=   (   R	  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5578  s    c            s_     j  d  t t |  t | |   | t d  t d  |   |   t |  t |  |   S(   Ni  i   i   (   R  R   R,  R  R  R  R  (   R	  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5579  s    c            s     j  d  t | | | t d  t t | | | | t d  t |  |  |  t d  t d  |  |  |  t | | t |   | | | | t d  | | t d  |  S(   Ni  i   i   (   R  R  R  R   R,  R  R  R=   (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5580  s    c            s     j  d  t | | | t d  t t | | | | t d  t |  |  |  t d  t d  |  |  |  t | | t |   | | | | t d  | | t d  |  S(   Ni  i   i   (   R  R  R  R   R,  R  R  R  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5581  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R*  R  R  R	  R  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5582  s    c            s   t  |  |  }   j d  t | t 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  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5582  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R*  R  R  R	  R  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5583  s    c            s   t  |  |  }   j d  t | t 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  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5583  s    c      	      s     j  d  t t t d  t t |  t t |  t d   | | | |  |  t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5584  s    c            s     j  d  t t | t |   t | |  | |  |  t t | t |  |  t |  |  t d  t d  |  |  t | t |   t |  |  S(   Ni  i   i   (   R  R   R,  R=   R  R"  R  R  (   R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5585  s    c            s     j  d  t t | t | |  t |   | |  |  t t | t |  |  t |  |  t d  t d  |  |  t | t |  t |   |  S(   Ni  i   i   (   R  R   R,  R  R  R"  R  R  (   R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5586  s    c         S   sE   t  | t t t t f  r t St | |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R*  R	  t   z(    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5587"  s    c            s   t  | |  }   j d  t t |   t |  | |  t t | t |   t | |  | |  |  t t | t |  |  t |  |  t d  t d  |  |  S(   Ni  i   i   (	   R  R  R  R=   R"  R   R,  R  R  (   R  R  R*  R	  Ra  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5587*  s    c         S   sE   t  | t t t t f  r t St | |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R*  R	  Ra  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With55880  s    c            s   t  | |  }   j d  t t |  t |   | |  t t | t | |  t |   | |  |  t t | t |  |  t |  |  t d  t d  |  |  S(   Ni  i   i   (	   R  R  R  R"  R  R   R,  R  R  (   R  R  R*  R	  Ra  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement55888  s    c            s     j  d  t t d  | t t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5589?  s    c            s     j  d  t t d  | t t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5590D  s    c            sf     j  d  t t d  | t t | |  | | t |  t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  R
  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5591I  s    c            sg     j  d  t t d  | t t | |  | | t |  t |  |  | t | |   |  S(   Ni  i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5592N  s    c            sG     j  d  t t | | t |  |  |  |   |  t d  |   S(   Ni  i   (   R  R*   R   R	  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5593S  s    c            sG     j  d  t t | | t |  |  |  |   |  t d  |   S(   Ni  i   (   R  R*   R   R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5594X  s    c            s     j  d  t | | |  t d  t | |  t d  t t d  t d  | t d  | t d   |  |  t | |  t d  | | t | |  |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R
  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5595]  s    c            s     j  d  t | | |  t d  t | |  t d  t t d  t d  | t d  | t d   |  |  t | |  t d  | | t | |  |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5596b  s    c      	      s     j  d  t | |  t d  t t | | | | t d  t |  |  t d  t |  |  | t | |   |  S(   Ni  ii   (   R  R  R  R*   R   R  R  R
  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5597g  s    c      	      s     j  d  t | |  t d  t t | | | | t d  t |  |  t d  t |  |  | t | |   |  S(   Ni  ii   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5598l  s    c            s8     j  d  t | |  | | t | |  | |  S(   Ni  (   R  R   R
  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5599q  s    c            s8     j  d  t | |  | | t | |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5600v  s    c            s   t  | | | t d  |  |  }   j d  t | | | t | t d  | t d   t 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5601z  s    %c            s   t  | | | t d  |  |  }   j d  t | | | t | t d  | t d   t 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	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5602  s    %c            s~     j  d  t t | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5603  s    c            s~     j  d  t t | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5604  s    c      
      s     j  d  t t | t d   | t t | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5605  s    c      
      s     j  d  t t | t d   | t t | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5606  s    c      
      s     j  d  t t | | | t d   | t | | t d  |  t t | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5607  s    c      
      s     j  d  t t | | | t d   | t | | t d  |  t t | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5608  s    c            sJ     j  d  t | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R
  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5609  s    c            sJ     j  d  t | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R  R  (   R)  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5610  s    c      
      s    j  d  t | | | t d  | t | t d  | t d   |  t d  t | | | t d  |  t d  | t | t d  | t d  t d   |  |  t | | t | |  | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R  R
  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5611  s    c      
      s    j  d  t | | | t d  | t | t d  | t d   |  t d  t | | | t d  |  t d  | t | t d  | t d  t d   |  |  t | | t | |  | | | t d  |  t d  t d  | |  t d  |  S(   Ni  i   i   i(   R  R  R  R  R   R  R  (   R)  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5612  s    c   	         s   t  | | | | | t d  |  |  }   j d  t | | | t | t d  | t d   t 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  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5613  s    -c   	         s   t  | | | | | t d  |  |  }   j d  t | | | t | t d  | t d   t 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  R	  R!  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5614  s    -c	   	         s     j  d  t t | | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5615  s    c	   	         s     j  d  t t | | t d  |  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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5616  s    c	   	   
      s     j  d  t t | t d   | t t | | t d  |  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5617  s    c	   	   
      s     j  d  t t | t d   | t t | | t d  |  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5618  s    c	   	   
      s     j  d  t t | | | t d   | t | | t d  |  t t | | t d  |  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5619  s    c	   	   
      s     j  d  t t | | | t d   | t | | t d  |  t t | | t d  |  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!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5620  s    c	   	         sR     j  d  t | | | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R
  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5621  s    c	   	         sR     j  d  t | | | | t | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R  R  (	   R)  R  R  R  R  R  R  R	  R!  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5622  s    c            s     j  d  t t d  t t d  t d  | | |  t d   | | |  |   t | | |  t | | |   | |   S(   Ni  i   i   (   R  R   R  R  R  R
  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5623  s    c            s     j  d  t t d  t t d  t d  | | |  t d   | | |  |   t | | |  t | | |   | |   S(   Ni  i   i   (   R  R   R  R  R  R  (   R	  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5624  s    c      	      sb     j  d  t t d  | t t |  | t |   t |   |   |  t | | |    |   S(   Ni  i   (   R  R  R  R*   R   R  R  R
  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5625  s    c      	      sc     j  d  t t d  | t t |  | t |   t |   |   |  t | | |    |   S(   Ni  i   (   R  R  R  R*   R   R  R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5626  s    c            s`    j  d  t t t t d  t | t d  t d   t d  t t t | | |    |  |   t t t t d  t | t d  t d   t d  t t t | | |    |  |   t t t t d  t t d  t t | | |     t d  |   t t t d  t | t d  t d   t d  t t t | | |    |  t | | |   |   t t t d  t | t d  t d   t d  t t t | | |    |  t | | |   |   t t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5627  s    c            s    j  d  t t t t d  t t | t d  t d   t d  t t t | | |    |  |   t t t t d  t t | t d  t d   t d  t t t | | |    |  |   t t t t d  t t d  t t | | |     t d  |   t t t | | |   t d  |   t t t d  t t | t d  t d   t d  t t t | | |    |  t | | |   |   t t t d  t t | t d  t d   t d  t t t | | |    |  t | | |   |   t t 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5628  s    c      
      s<    j  d  t | | t d  | t d  t t |  | t d  | |  | t d  | |  t d  | t d  t |  t d  t d   |   |  t d  | | |   |   t | | t d  | | t d  |  | t d  | | t d  t | | |   | t d  |   S(   Ni  ii   i   (   R  R  R  R*   R   R  R  R
  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5629  s    c      
      s;    j  d  t | | t d  | t d  t t |  | t d  | |  | t d  | |  t d  | t d  t |  t d  t d   |   |  t d  | | |   |   t | | t d  | | t d  |  | t d  | | t d  t | | |   | t d  |   S(   Ni  ii   i   (   R  R  R  R*   R   R  R  R  (   R	  R  R  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5630  s    c      	      s     j  d  t | |  t d  t t | | | t d  t |  |  t |  t |  |  | t | | |   |  S(   Ni  ii   (   R  R  R  R*   R   R  R  R
  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5631  s    c      	      s     j  d  t | |  t d  t t | | | t d  t |  |  t |  t |  |  | t | | |   |  S(   Ni   ii   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5632  s    c            s<     j  d  t |  t | | | | | |  | |  S(   Ni  (   R  R   R	  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5633  s    c            s<     j  d  t |  t | | | | | |  | |  S(   Ni  (   R  R   R  (   R*  R  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5634$  s    c            s     j  d  t t d  | t t | | | | t |  t | | | t d  | t |    t |  t |  |  | t	 | | |   |  S(   Ni  i   (
   R  R  R  R*   R   R   R  R  R  R
  (   R*  RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5635)  s    c            s     j  d  t t d  | t t | | | | t |  t | | | t d  | t |    t |  t |  |  | t	 | | |   |  S(   Ni  i   (
   R  R  R  R*   R   R   R  R  R  R  (   R*  RF  R  R  R  R  R	  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5636.  s    c      
      s     j  d  t | t | t d   t t |  t | |   | t | t d  t d   |   |   |   t |  t |  |   S(   Ni  i   i(	   R  R  R  R  R   R,  R  R  R
  (   R	  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement56373  s    c      
      s     j  d  t | t | t d   t t |  t | |   | t | t d  t d   |   |   |   t |  t |  |   S(   Ni  i   i(	   R  R  R  R  R   R,  R  R  R  (   R	  R*  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement56388  s    c      
      s     j  d  t | |  | | t d  t |  t d   t t | | | | t d  t |  |  |  t |  t d  t d   |  |  |  t | | t |   | | | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5639=  s    c      
      s     j  d  t | |  | | t d  t |  t d   t t | | | | t d  t |  |  |  t |  t d  t d   |  |  |  t | | t |   | | | | 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
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5640B  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R*  R  R  R	  R  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5641F  s    c      
      s   t  |  |  }   j d  t | | t | t d   t t | 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	  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5641N  s    c         S   sE   t  | t t t t f  r t St |  |  } t | |  rA t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R*  R  R  R	  R  (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   With5642T  s    c      
      s   t  |  |  }   j d  t | | t | t d   t t | 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	  R  (   R
  (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   replacement5642\  s    (   t    sympy.integrals.rubi.constraintsR*  R+  R,  R-  R.  R/  R0  R1  R2  R3  R4  R5  R6  R7  R8  R9  R:  R;  R<  R=  R>  R?  R@  RA  RB  RC  RD  RE  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  R{  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R  R  R  R   R  R  R  R  t   x_R   R	  t   n_R  t   d_t   p_t   f_t   m_t   Px_R"  t   u_R   t   RFx_t   a_t   c_t   v_R=   R  R  R  R  R  t   w_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  t   pattern5031R  t   rule5031t   pattern5032R  t   rule5032t   pattern5033R  t   rule5033t   pattern5034R  t   rule5034t   pattern5035R  t   rule5035t   pattern5036R  t   rule5036t   pattern5037R  t   rule5037t   pattern5038R  t   rule5038t   pattern5039R  t   rule5039t   pattern5040R  t   rule5040t   pattern5041R  t   rule5041t   pattern5042R  t   rule5042t   pattern5043R  t   rule5043t   pattern5044R  t   rule5044t   pattern5045R  t   rule5045t   pattern5046R  t   rule5046t   pattern5047R  t   rule5047t   pattern5048R  t   rule5048t   pattern5049R  t   rule5049t   pattern5050R   t   rule5050t   pattern5051R#  t   rule5051t   pattern5052R$  t   rule5052t   pattern5053R%  t   rule5053t   pattern5054R&  t   rule5054t   pattern5055R'  t   rule5055t   pattern5056R(  t   rule5056R+  t   pattern5057t   rule5057R,  t   pattern5058t   rule5058t   pattern5059R-  t   rule5059t   pattern5060R.  t   rule5060t   pattern5061R/  t   rule5061t   pattern5062R0  t   rule5062t   pattern5063R1  t   rule5063t   pattern5064R2  t   rule5064t   pattern5065R3  t   rule5065t   pattern5066R4  t   rule5066t   pattern5067R5  t   rule5067t   pattern5068R6  t   rule5068t   pattern5069R7  t   rule5069t   pattern5070R8  t   rule5070t   pattern5071R9  t   rule5071t   pattern5072R:  t   rule5072t   pattern5073R;  t   rule5073t   pattern5074R<  t   rule5074t   pattern5075R=  t   rule5075t   pattern5076R>  t   rule5076R?  t   pattern5077t   rule5077R@  t   pattern5078t   rule5078t   pattern5079RA  t   rule5079t   pattern5080RB  t   rule5080t   pattern5081RC  t   rule5081t   pattern5082RD  t   rule5082t   pattern5083RG  t   rule5083t   pattern5084RH  t   rule5084t   pattern5085RI  t   rule5085t   pattern5086RJ  t   rule5086t   pattern5087RK  t   rule5087t   pattern5088RL  t   rule5088t   pattern5089RM  t   rule5089t   pattern5090RN  t   rule5090t   pattern5091RO  t   rule5091t   pattern5092RP  t   rule5092t   pattern5093RQ  t   rule5093t   pattern5094RR  t   rule5094t   pattern5095RS  t   rule5095t   pattern5096RT  t   rule5096RU  t   pattern5097t   rule5097RV  t   pattern5098t   rule5098RW  t   pattern5099t   rule5099RX  t   pattern5100t   rule5100RY  t   pattern5101t   rule5101RZ  t   pattern5102t   rule5102t   pattern5103R[  t   rule5103t   pattern5104R\  t   rule5104t   pattern5105R]  t   rule5105t   pattern5106R^  t   rule5106t   pattern5107R_  t   rule5107t   pattern5108R`  t   rule5108t   pattern5109Ra  t   rule5109t   pattern5110Rb  t   rule5110t   pattern5111Rc  t   rule5111t   pattern5112Rd  t   rule5112t   pattern5113Re  t   rule5113t   pattern5114Rf  t   rule5114t   pattern5115Rg  t   rule5115t   pattern5116Rh  t   rule5116t   pattern5117Ri  t   rule5117t   pattern5118Rj  t   rule5118t   pattern5119Rk  t   rule5119t   pattern5120Rl  t   rule5120t   pattern5121Rm  t   rule5121t   pattern5122Rn  t   rule5122t   pattern5123Ro  t   rule5123t   pattern5124Rp  t   rule5124t   pattern5125Rq  t   rule5125t   pattern5126Rr  t   rule5126t   pattern5127Rs  t   rule5127t   pattern5128Rt  t   rule5128t   pattern5129Ru  t   rule5129t   pattern5130Rv  t   rule5130t   pattern5131Rw  t   rule5131t   pattern5132Rx  t   rule5132t   pattern5133Ry  t   rule5133t   pattern5134Rz  t   rule5134t   pattern5135R{  t   rule5135t   pattern5136R|  t   rule5136t   pattern5137R}  t   rule5137t   pattern5138R~  t   rule5138t   pattern5139R  t   rule5139t   pattern5140R  t   rule5140R  t   pattern5141t   rule5141R  t   pattern5142t   rule5142t   pattern5143R  t   rule5143t   pattern5144R  t   rule5144t   pattern5145R  t   rule5145t   pattern5146R  t   rule5146t   pattern5147R  t   rule5147t   pattern5148R  t   rule5148t   pattern5149R  t   rule5149t   pattern5150R  t   rule5150t   pattern5151R  t   rule5151t   pattern5152R  t   rule5152t   pattern5153R  t   rule5153t   pattern5154R  t   rule5154t   pattern5155R  t   rule5155t   pattern5156R  t   rule5156R  t   pattern5157t   rule5157R  t   pattern5158t   rule5158t   pattern5159R  t   rule5159t   pattern5160R  t   rule5160R  t   pattern5161t   rule5161R  t   pattern5162t   rule5162R  t   pattern5163t   rule5163R  t   pattern5164t   rule5164R  t   pattern5165t   rule5165R  t   pattern5166t   rule5166t   pattern5167R  t   rule5167t   pattern5168R  t   rule5168R  t   pattern5169t   rule5169R  t   pattern5170t   rule5170t   pattern5171R  t   rule5171t   pattern5172R  t   rule5172t   pattern5173R  t   rule5173t   pattern5174R  t   rule5174t   pattern5175R  t   rule5175t   pattern5176R  t   rule5176t   pattern5177R  t   rule5177t   pattern5178R  t   rule5178t   pattern5179R  t   rule5179t   pattern5180R  t   rule5180t   pattern5181R  t   rule5181t   pattern5182R  t   rule5182t   pattern5183R  t   rule5183t   pattern5184R  t   rule5184t   pattern5185R  t   rule5185t   pattern5186R  t   rule5186t   pattern5187R  t   rule5187t   pattern5188R  t   rule5188t   pattern5189R  t   rule5189t   pattern5190R  t   rule5190R  t   pattern5191t   rule5191R  t   pattern5192t   rule5192t   pattern5193R  t   rule5193t   pattern5194R  t   rule5194R  t   pattern5195R  t   rule5195R  t   pattern5196R  t   rule5196R  t   pattern5197R  t   rule5197R  t   pattern5198R  t   rule5198R  t   pattern5199R  t   rule5199R  t   pattern5200R  t   rule5200R  t   pattern5201R  t   rule5201R  t   pattern5202R  t   rule5202t   pattern5203R  t   rule5203t   pattern5204R  t   rule5204R  t   pattern5205R  t   rule5205R  t   pattern5206R  t   rule5206t   pattern5207R  t   rule5207t   pattern5208R  t   rule5208t   pattern5209R  t   rule5209t   pattern5210R  t   rule5210t   pattern5211R  t   rule5211t   pattern5212R  t   rule5212t   pattern5213R  t   rule5213t   pattern5214R  t   rule5214t   pattern5215R  t   rule5215t   pattern5216R  t   rule5216t   pattern5217R  t   rule5217t   pattern5218R  t   rule5218t   pattern5219R  t   rule5219t   pattern5220R  t   rule5220t   pattern5221R  t   rule5221t   pattern5222R  t   rule5222t   pattern5223R  t   rule5223t   pattern5224R  t   rule5224t   pattern5225R  t   rule5225t   pattern5226R  t   rule5226t   pattern5227R  t   rule5227t   pattern5228R  t   rule5228t   pattern5229R  t   rule5229t   pattern5230R  t   rule5230t   pattern5231R  t   rule5231t   pattern5232R  t   rule5232t   pattern5233R  t   rule5233t   pattern5234R  t   rule5234t   pattern5235R  t   rule5235t   pattern5236R  t   rule5236t   pattern5237R  t   rule5237t   pattern5238R  t   rule5238t   pattern5239R  t   rule5239t   pattern5240R  t   rule5240t   pattern5241R  t   rule5241t   pattern5242R  t   rule5242t   pattern5243R  t   rule5243t   pattern5244R  t   rule5244t   pattern5245R  t   rule5245t   pattern5246R  t   rule5246t   pattern5247R   t   rule5247t   pattern5248R  t   rule5248t   pattern5249R  t   rule5249t   pattern5250R  t   rule5250t   pattern5251R  t   rule5251R  t   pattern5252R  t   rule5252R  t   pattern5253R	  t   rule5253t   pattern5254R
  t   rule5254t   pattern5255R  t   rule5255t   pattern5256R  t   rule5256t   pattern5257R  t   rule5257t   pattern5258R  t   rule5258t   pattern5259R  t   rule5259t   pattern5260R  t   rule5260t   pattern5261R  t   rule5261t   pattern5262R  t   rule5262t   pattern5263R  t   rule5263t   pattern5264R  t   rule5264t   pattern5265R  t   rule5265t   pattern5266R  t   rule5266t   pattern5267R  t   rule5267t   pattern5268R  t   rule5268t   pattern5269R  t   rule5269t   pattern5270R  t   rule5270t   pattern5271R  t   rule5271t   pattern5272R  t   rule5272t   pattern5273R  t   rule5273t   pattern5274R  t   rule5274t   pattern5275R  t   rule5275t   pattern5276R   t   rule5276t   pattern5277R!  t   rule5277t   pattern5278R"  t   rule5278t   pattern5279R#  t   rule5279t   pattern5280R$  t   rule5280t   pattern5281R%  t   rule5281t   pattern5282R&  t   rule5282t   pattern5283R'  t   rule5283t   pattern5284R(  t   rule5284t   pattern5285R)  t   rule5285t   pattern5286R*  t   rule5286t   pattern5287R+  t   rule5287t   pattern5288R,  t   rule5288t   pattern5289R-  t   rule5289t   pattern5290R.  t   rule5290t   pattern5291R/  t   rule5291t   pattern5292R0  t   rule5292t   pattern5293R1  t   rule5293t   pattern5294R2  t   rule5294t   pattern5295R3  t   rule5295t   pattern5296R4  t   rule5296t   pattern5297R5  t   rule5297t   pattern5298R6  t   rule5298t   pattern5299R7  t   rule5299t   pattern5300R8  t   rule5300t   pattern5301R9  t   rule5301t   pattern5302R:  t   rule5302t   pattern5303R;  t   rule5303t   pattern5304R<  t   rule5304t   pattern5305R=  t   rule5305t   pattern5306R>  t   rule5306t   pattern5307R?  t   rule5307t   pattern5308R@  t   rule5308t   pattern5309RA  t   rule5309t   pattern5310RB  t   rule5310t   pattern5311RC  t   rule5311t   pattern5312RD  t   rule5312t   pattern5313RE  t   rule5313t   pattern5314RF  t   rule5314t   pattern5315RG  t   rule5315t   pattern5316RH  t   rule5316t   pattern5317RI  t   rule5317t   pattern5318RJ  t   rule5318RK  t   pattern5319t   rule5319RL  t   pattern5320t   rule5320t   pattern5321RM  t   rule5321t   pattern5322RN  t   rule5322t   pattern5323RO  t   rule5323t   pattern5324RP  t   rule5324t   pattern5325RQ  t   rule5325t   pattern5326RR  t   rule5326t   pattern5327RS  t   rule5327t   pattern5328RT  t   rule5328t   pattern5329RU  t   rule5329t   pattern5330RV  t   rule5330t   pattern5331RW  t   rule5331t   pattern5332RX  t   rule5332t   pattern5333RY  t   rule5333t   pattern5334RZ  t   rule5334t   pattern5335R[  t   rule5335t   pattern5336R\  t   rule5336t   pattern5337R]  t   rule5337t   pattern5338R^  t   rule5338t   pattern5339R_  t   rule5339t   pattern5340R`  t   rule5340t   pattern5341Ra  t   rule5341t   pattern5342Rb  t   rule5342t   pattern5343Rc  t   rule5343t   pattern5344Rd  t   rule5344t   pattern5345Re  t   rule5345t   pattern5346Rf  t   rule5346t   pattern5347Rg  t   rule5347t   pattern5348Rh  t   rule5348t   pattern5349Ri  t   rule5349t   pattern5350Rj  t   rule5350t   pattern5351Rk  t   rule5351t   pattern5352Rl  t   rule5352t   pattern5353Rm  t   rule5353t   pattern5354Rn  t   rule5354t   pattern5355Ro  t   rule5355t   pattern5356Rp  t   rule5356t   pattern5357Rq  t   rule5357t   pattern5358Rr  t   rule5358t   pattern5359Rs  t   rule5359t   pattern5360Rt  t   rule5360t   pattern5361Ru  t   rule5361t   pattern5362Rv  t   rule5362t   pattern5363Rw  t   rule5363t   pattern5364Rx  t   rule5364t   pattern5365Ry  t   rule5365t   pattern5366Rz  t   rule5366t   pattern5367R{  t   rule5367t   pattern5368R|  t   rule5368t   pattern5369R}  t   rule5369t   pattern5370R~  t   rule5370t   pattern5371R  t   rule5371t   pattern5372R  t   rule5372t   pattern5373R  t   rule5373t   pattern5374R  t   rule5374t   pattern5375R  t   rule5375t   pattern5376R  t   rule5376t   pattern5377R  t   rule5377t   pattern5378R  t   rule5378t   pattern5379R  t   rule5379t   pattern5380R  t   rule5380t   pattern5381R  t   rule5381t   pattern5382R  t   rule5382t   pattern5383R  t   rule5383t   pattern5384R  t   rule5384t   pattern5385R  t   rule5385t   pattern5386R  t   rule5386t   pattern5387R  t   rule5387t   pattern5388R  t   rule5388R  t   pattern5389t   rule5389R  t   pattern5390t   rule5390t   pattern5391R  t   rule5391t   pattern5392R  t   rule5392t   pattern5393R  t   rule5393t   pattern5394R  t   rule5394t   pattern5395R  t   rule5395t   pattern5396R  t   rule5396t   pattern5397R  t   rule5397t   pattern5398R  t   rule5398t   pattern5399R  t   rule5399t   pattern5400R  t   rule5400t   pattern5401R  t   rule5401t   pattern5402R  t   rule5402t   pattern5403R  t   rule5403t   pattern5404R  t   rule5404t   pattern5405R  t   rule5405t   pattern5406R  t   rule5406t   pattern5407R  t   rule5407t   pattern5408R  t   rule5408t   pattern5409R  t   rule5409t   pattern5410R  t   rule5410t   pattern5411R  t   rule5411t   pattern5412R  t   rule5412t   pattern5413R  t   rule5413t   pattern5414R  t   rule5414t   pattern5415R  t   rule5415t   pattern5416R  t   rule5416t   pattern5417R  t   rule5417R  t   pattern5418t   rule5418R  t   pattern5419t   rule5419R  t   pattern5420t   rule5420R  t   pattern5421t   rule5421t   pattern5422R  t   rule5422t   pattern5423R  t   rule5423t   pattern5424R  t   rule5424t   pattern5425R  t   rule5425t   pattern5426R  t   rule5426t   pattern5427R  t   rule5427t   pattern5428R  t   rule5428t   pattern5429R  t   rule5429t   pattern5430R  t   rule5430t   pattern5431R  t   rule5431t   pattern5432R  t   rule5432t   pattern5433R  t   rule5433t   pattern5434R  t   rule5434t   pattern5435R  t   rule5435t   pattern5436R  t   rule5436t   pattern5437R  t   rule5437t   pattern5438R  t   rule5438t   pattern5439R  t   rule5439t   pattern5440R  t   rule5440t   pattern5441R  t   rule5441t   pattern5442R  t   rule5442t   pattern5443R  t   rule5443t   pattern5444R  t   rule5444t   pattern5445R  t   rule5445t   pattern5446R  t   rule5446t   pattern5447R  t   rule5447t   pattern5448R  t   rule5448t   pattern5449R  t   rule5449t   pattern5450R  t   rule5450t   pattern5451R  t   rule5451t   pattern5452R  t   rule5452t   pattern5453R  t   rule5453t   pattern5454R  t   rule5454t   pattern5455R  t   rule5455t   pattern5456R  t   rule5456t   pattern5457R  t   rule5457t   pattern5458R  t   rule5458t   pattern5459R  t   rule5459t   pattern5460R  t   rule5460t   pattern5461R  t   rule5461t   pattern5462R  t   rule5462t   pattern5463R  t   rule5463t   pattern5464R  t   rule5464t   pattern5465R  t   rule5465t   pattern5466R  t   rule5466t   pattern5467R  t   rule5467t   pattern5468R  t   rule5468t   pattern5469R  t   rule5469t   pattern5470R  t   rule5470t   pattern5471R  t   rule5471t   pattern5472R  t   rule5472t   pattern5473R  t   rule5473t   pattern5474R  t   rule5474t   pattern5475R  t   rule5475t   pattern5476R  t   rule5476t   pattern5477R  t   rule5477t   pattern5478R  t   rule5478t   pattern5479R  t   rule5479t   pattern5480R  t   rule5480t   pattern5481R  t   rule5481t   pattern5482R  t   rule5482t   pattern5483R  t   rule5483t   pattern5484R  t   rule5484t   pattern5485R  t   rule5485t   pattern5486R  t   rule5486t   pattern5487R  t   rule5487t   pattern5488R  t   rule5488t   pattern5489R  t   rule5489t   pattern5490R  t   rule5490t   pattern5491R  t   rule5491t   pattern5492R  t   rule5492t   pattern5493R  t   rule5493t   pattern5494R  t   rule5494t   pattern5495R  t   rule5495t   pattern5496R  t   rule5496t   pattern5497R  t   rule5497t   pattern5498R  t   rule5498t   pattern5499R   t   rule5499t   pattern5500R  t   rule5500t   pattern5501R  t   rule5501t   pattern5502R  t   rule5502t   pattern5503R  t   rule5503t   pattern5504R  t   rule5504t   pattern5505R  t   rule5505t   pattern5506R  t   rule5506t   pattern5507R  t   rule5507t   pattern5508R	  t   rule5508t   pattern5509R
  t   rule5509t   pattern5510R  t   rule5510t   pattern5511R  t   rule5511t   pattern5512R  t   rule5512t   pattern5513R  t   rule5513t   pattern5514R  t   rule5514t   pattern5515R  t   rule5515t   pattern5516R  t   rule5516t   pattern5517R  t   rule5517t   pattern5518R  t   rule5518t   pattern5519R  t   rule5519t   pattern5520R  t   rule5520t   pattern5521R  t   rule5521t   pattern5522R  t   rule5522t   pattern5523R  t   rule5523t   pattern5524R  t   rule5524t   pattern5525R  t   rule5525t   pattern5526R  t   rule5526t   pattern5527R  t   rule5527t   pattern5528R  t   rule5528t   pattern5529R  t   rule5529t   pattern5530R  t   rule5530t   pattern5531R   t   rule5531t   pattern5532R!  t   rule5532t   pattern5533R"  t   rule5533t   pattern5534R$  t   rule5534t   pattern5535R%  t   rule5535R*  t   pattern5536R+  t   rule5536R,  t   pattern5537R-  t   rule5537t   pattern5538R.  t   rule5538t   pattern5539R/  t   rule5539t   pattern5540R0  t   rule5540t   pattern5541R1  t   rule5541t   pattern5542R2  t   rule5542t   pattern5543R3  t   rule5543t   pattern5544R4  t   rule5544t   pattern5545R5  t   rule5545t   pattern5546R6  t   rule5546t   pattern5547R7  t   rule5547t   pattern5548R8  t   rule5548t   pattern5549R9  t   rule5549t   pattern5550R:  t   rule5550t   pattern5551R;  t   rule5551t   pattern5552R<  t   rule5552t   pattern5553R=  t   rule5553t   pattern5554R>  t   rule5554t   pattern5555R?  t   rule5555t   pattern5556R@  t   rule5556t   pattern5557RA  t   rule5557t   pattern5558RB  t   rule5558t   pattern5559RC  t   rule5559t   pattern5560RD  t   rule5560t   pattern5561RE  t   rule5561t   pattern5562RF  t   rule5562t   pattern5563RG  t   rule5563t   pattern5564RH  t   rule5564t   pattern5565RI  t   rule5565t   pattern5566RJ  t   rule5566t   pattern5567RK  t   rule5567t   pattern5568RL  t   rule5568t   pattern5569RM  t   rule5569t   pattern5570RN  t   rule5570t   pattern5571RO  t   rule5571t   pattern5572RP  t   rule5572t   pattern5573RQ  t   rule5573t   pattern5574RR  t   rule5574t   pattern5575RS  t   rule5575t   pattern5576RT  t   rule5576t   pattern5577RU  t   rule5577t   pattern5578RV  t   rule5578t   pattern5579RW  t   rule5579t   pattern5580RX  t   rule5580t   pattern5581RY  t   rule5581RZ  t   pattern5582R[  t   rule5582R\  t   pattern5583R]  t   rule5583t   pattern5584R^  t   rule5584t   pattern5585R_  t   rule5585t   pattern5586R`  t   rule5586Rb  t   pattern5587Rc  t   rule5587Rd  t   pattern5588Re  t   rule5588t   pattern5589Rf  t   rule5589t   pattern5590Rg  t   rule5590t   pattern5591Rh  t   rule5591t   pattern5592Ri  t   rule5592t   pattern5593Rj  t   rule5593t   pattern5594Rk  t   rule5594t   pattern5595Rl  t   rule5595t   pattern5596Rm  t   rule5596t   pattern5597Rn  t   rule5597t   pattern5598Ro  t   rule5598t   pattern5599Rp  t   rule5599t   pattern5600Rq  t   rule5600Rr  t   pattern5601t   rule5601Rs  t   pattern5602t   rule5602t   pattern5603Rt  t   rule5603t   pattern5604Ru  t   rule5604t   pattern5605Rv  t   rule5605t   pattern5606Rw  t   rule5606t   pattern5607Rx  t   rule5607t   pattern5608Ry  t   rule5608t   pattern5609Rz  t   rule5609t   pattern5610R{  t   rule5610t   pattern5611R|  t   rule5611t   pattern5612R}  t   rule5612R~  t   pattern5613t   rule5613R  t   pattern5614t   rule5614t   pattern5615R  t   rule5615t   pattern5616R  t   rule5616t   pattern5617R  t   rule5617t   pattern5618R  t   rule5618t   pattern5619R  t   rule5619t   pattern5620R  t   rule5620t   pattern5621R  t   rule5621t   pattern5622R  t   rule5622t   pattern5623R  t   rule5623t   pattern5624R  t   rule5624t   pattern5625R  t   rule5625t   pattern5626R  t   rule5626t   pattern5627R  t   rule5627t   pattern5628R  t   rule5628t   pattern5629R  t   rule5629t   pattern5630R  t   rule5630t   pattern5631R  t   rule5631t   pattern5632R  t   rule5632t   pattern5633R  t   rule5633t   pattern5634R  t   rule5634t   pattern5635R  t   rule5635t   pattern5636R  t   rule5636t   pattern5637R  t   rule5637t   pattern5638R  t   rule5638t   pattern5639R  t   rule5639t   pattern5640R  t   rule5640R  t   pattern5641R  t   rule5641R  t   pattern5642R  t   rule5642(    (   R
  sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   inverse_trig   s        +vvggggww~~ddkk    	m	m					W	Wkk		}} 1 1wzz{{{~~{~~~~RR!!	Z	ZssggXddkknnkk>XPj{vvmiQ>XPjL^~{nmizznn 1 1ooccBBUU\\}}QQ	D	D||||||||PPZZ||||||||	]	]a++	8	844ggddzz~~;;BB??XXYY!!	Z	ZN(d  t   __doc__t   sympy.externalR    R   t   sympy.utilities.decoratorR   R   R   R   R   t%   sympy.integrals.rubi.utility_functionR   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Re   Rf   Rg   Rh   Ri   Rj   Rk   Rl   Rm   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R}   R~   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R!  R"  R#  R$  R%  R&  R'  R(  R)  R*  R+  R,  R-  R.  R/  R0  R1  R2  R3  R4  R5  R6  R7  R8  R9  R:  R;  R<  R=  R>  R?  R@  RA  RB  RC  RD  RE  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  R{  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R"  R  R  R  t   sympyR  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   sympy.integrals.rubi.symbolR  t   sympy.core.symbolR  R  t   sympy.functionsR  R  R  R  R  R  R  t%   sympy.functions.elementary.hyperbolicR  R  R  R  R  R  R  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  R  t   it   A_t   B_t   C_t   F_t   G_t   H_R  t   b_R  R  t   e_R  t   g_t   h_t   i_t   j_t   k_t   l_R  R  R  t   q_t   r_t   t_R  R  t   s_R  R  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_t   n2_t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_t   n3_t   Pq_t   Pm_R  t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_R  t   RGx_t   iit   Pqqt   Qt   Rt   rR  t   kR*  R  t	   _UseGammat	   ShowStepst   Nonet   StepCounterRt
  (    (    (    sF   lib/python2.7/site-packages/sympy/integrals/rubi/rules/inverse_trig.pyt   <module>   s>   "           1nj:R4|'	