
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Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmJZJmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZd d	 lmZmZd d
 lmZmZmZmZm Z mZmZmZd d lmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZd d lmZmZmZmZmZmZmZd d lmZg  d D] Zee ^ q\ ZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6Z7Z8Z9g  d d d d d d d d d d d d d d d d d d d d  d! d" d# d$ d% d& d' d( d) d* g D] Zee ^ q\ Z:Z;Z<Z=Z>Z?Z@ZAZBZCZDZEZFZGZHZIZBZCZJZKZLZMZNZOZPZQZRZSZTZUed+  \	 ZZVZWZXZYZZZ[Z\Z]e^Z_e^Z`eaZbn  d,   Zcd- S(.   s   
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
i(   t   import_modulet   matchpy(   t   doctest_depends_on(   t   Patternt   ReplacementRulet   CustomConstraintt   is_match(  t   Intt   Sumt   Sett   Witht   Modulet   Scant   MapAndt   FalseQt   ZeroQt	   NegativeQt   NonzeroQt   FreeQt   NFreeQt   Listt   Logt	   PositiveQt   PositiveIntegerQt   NegativeIntegerQt   IntegerQt	   IntegersQt   ComplexNumberQt   PureComplexNumberQt   RealNumericQt   PositiveOrZeroQt   NegativeOrZeroQt   FractionOrNegativeQt   NegQt   Equalt   Unequalt   IntPartt   FracPartt	   RationalQt   ProductQt   SumQt   NonsumQt   Substt   Firstt   Restt   SqrtNumberQt   SqrtNumberSumQt   LinearQt   Sqrtt   ArcCosht   Coefficientt   Denominatort   Hypergeometric2F1t   Nott   Simplifyt   FractionalPartt   IntegerPartt   AppellF1t
   EllipticPit	   EllipticEt	   EllipticFt   ArcTant   ArcCott   ArcCotht   ArcTanht   ArcSint   ArcSinht   ArcCost   ArcCsct   ArcSect   ArcCscht   ArcSecht   Sinht   Tanht   Cosht   Secht   Cscht   Cotht	   LessEqualt   Lesst   Greatert   GreaterEqualt	   FractionQt   IntLinearcQt   Expandt   IndependentQt   PowerQt   IntegerPowerQt   PositiveIntegerPowerQt   FractionalPowerQt   AtomQt   ExpQt   LogQt   Headt   MemberQt   TrigQt   SinQt   CosQt   TanQt   CotQt   SecQt   CscQt   Sint   Cost   Tant   Cott   Sect   Csct   HyperbolicQt   SinhQt   CoshQt   TanhQt   CothQt   SechQt   CschQt   InverseTrigQt   SinCosQt	   SinhCoshQt	   LeafCountt	   Numeratort   NumberQt   NumericQt   Lengtht   ListQt   Imt   Ret   InverseHyperbolicQt   InverseFunctionQt   TrigHyperbolicFreeQt   InverseFunctionFreeQt   RealQt   EqQt   FractionalPowerFreeQt   ComplexFreeQt   PolynomialQt   FactorSquareFreet   PowerOfLinearQt   Exponentt
   QuadraticQt   LinearPairQt   BinomialPartst   TrinomialPartst   PolyQt   EvenQt   OddQt   PerfectSquareQt   NiceSqrtAuxQt	   NiceSqrtQt   Togethert   PosAuxt   PosQt   CoefficientListt
   ReplaceAllt   ExpandLinearProductt   GCDt   ContentFactort   NumericFactort   NonnumericFactorst   MakeAssocListt   GensymSubstt   KernelSubstt   ExpandExpressiont   Apartt
   SmartApartt   MatchQt   PolynomialQuotientRemaindert   FreeFactorst   NonfreeFactorst   RemoveContentAuxt   RemoveContentt	   FreeTermst   NonfreeTermst   ExpandAlgebraicFunctiont   CollectReciprocalst   ExpandCleanupt   AlgebraicFunctionQt   Coefft   LeadTermt   RemainingTermst
   LeadFactort   RemainingFactorst   LeadBaset
   LeadDegreet   Numert   Denomt	   hypergeomt   Expont   MergeMonomialst   PolynomialDividet	   BinomialQt
   TrinomialQt   GeneralizedBinomialQt   GeneralizedTrinomialQt   FactorSquareFreeListt   PerfectPowerTestt   SquareFreeFactorTestt   RationalFunctionQt   RationalFunctionFactorst   NonrationalFunctionFactorst   Reverset   RationalFunctionExponentst   RationalFunctionExpandt   ExpandIntegrandt   SimplerQt   SimplerSqrtQt   SumSimplerQt   BinomialDegreet   TrinomialDegreet   CancelCommonFactorst   SimplerIntegrandQt   GeneralizedBinomialDegreet   GeneralizedBinomialPartst   GeneralizedTrinomialDegreet   GeneralizedTrinomialPartst	   MonomialQt   MonomialSumQt   MinimumMonomialExponentt   MonomialExponentt   LinearMatchQt   PowerOfLinearMatchQt   QuadraticMatchQt   CubicMatchQt   BinomialMatchQt   TrinomialMatchQt   GeneralizedBinomialMatchQt   GeneralizedTrinomialMatchQt   QuotientOfLinearsMatchQt   PolynomialTermQt   PolynomialTermst   NonpolynomialTermst   PseudoBinomialPartst   NormalizePseudoBinomialt   PseudoBinomialPairQt   PseudoBinomialQt   PolynomialGCDt   PolyGCDt   AlgebraicFunctionFactorst   NonalgebraicFunctionFactorst   QuotientOfLinearsPt   QuotientOfLinearsPartst   QuotientOfLinearsQt   Flattent   Sortt   AbsurdNumberQt   AbsurdNumberFactorst   NonabsurdNumberFactorst   SumSimplerAuxQt   Prependt   Dropt   CombineExponentst   FactorIntegert   FactorAbsurdNumbert   SubstForInverseFunctiont   SubstForFractionalPowert*   SubstForFractionalPowerOfQuotientOfLinearst"   FractionalPowerOfQuotientOfLinearst   SubstForFractionalPowerQt   SubstForFractionalPowerAuxQt   FractionalPowerOfSquareQt   FractionalPowerSubexpressionQt   Applyt   FactorNumericGcdt   MergeableFactorQt   MergeFactort   MergeFactorst   TrigSimplifyQt   TrigSimplifyt   TrigSimplifyRecurt   Ordert   FactorOrdert   Smallestt   OrderedQt   MinimumDegreet   PositiveFactorst   Signt   NonpositiveFactorst   PolynomialInAuxQt   PolynomialInQt   ExponentInAuxt
   ExponentInt   PolynomialInSubstAuxt   PolynomialInSubstt   Distribt   DistributeDegreet   FunctionOfPowert   DivideDegreesOfFactorst   MonomialFactort   FullSimplifyt   FunctionOfLinearSubstt   FunctionOfLineart   NormalizeIntegrandt   NormalizeIntegrandAuxt   NormalizeIntegrandFactort   NormalizeIntegrandFactorBaset   NormalizeTogethert   NormalizeLeadTermSignst   AbsorbMinusSignt   NormalizeSumFactorst   SignOfFactort   NormalizePowerOfLineart   SimplifyIntegrandt   SimplifyTermt   TogetherSimplifyt   SmartSimplifyt   SubstForExpnt   ExpandToSumt   UnifySumt
   UnifyTermst	   UnifyTermt	   CalculusQt   FunctionOfInverseLineart   PureFunctionOfSinhQt   PureFunctionOfTanhQt   PureFunctionOfCoshQt   IntegerQuotientQt   OddQuotientQt   EvenQuotientQt   FindTrigFactort   FunctionOfSinhQt   FunctionOfCoshQt   OddHyperbolicPowerQt   FunctionOfTanhQt   FunctionOfTanhWeightt   FunctionOfHyperbolicQt   SmartNumeratort   SmartDenominatort   SubstForAuxt   ActivateTrigt
   ExpandTrigt
   TrigExpandt   SubstForTrigt   SubstForHyperbolict   InertTrigFreeQt   LCMt   SubstForFractionalPowerOfLineart   FractionalPowerOfLineart   InverseFunctionOfLineart
   InertTrigQt   InertReciprocalQt   DeactivateTrigt   FixInertTrigFunctiont   DeactivateTrigAuxt   PowerOfInertTrigSumQt   PiecewiseLinearQt   KnownTrigIntegrandQt   KnownSineIntegrandQt   KnownTangentIntegrandQt   KnownCotangentIntegrandQt   KnownSecantIntegrandQt   TryPureTanSubstt   TryTanhSubstt   TryPureTanhSubstt   AbsurdNumberGCDt   AbsurdNumberGCDListt   ExpandTrigExpandt   ExpandTrigReducet   ExpandTrigReduceAuxt   NormalizeTrigt	   TrigToExpt   ExpandTrigToExpt
   TrigReducet   FunctionOfTrigt   AlgebraicTrigFunctionQt   FunctionOfHyperbolict   FunctionOfQt   FunctionOfExpnQt   PureFunctionOfSinQt   PureFunctionOfCosQt   PureFunctionOfTanQt   PureFunctionOfCotQt   FunctionOfCosQt   FunctionOfSinQt   OddTrigPowerQt   FunctionOfTanQt   FunctionOfTanWeightt   FunctionOfTrigQt   FunctionOfDensePolynomialsQt   FunctionOfLogt   PowerVariableExpnt   PowerVariableDegreet   PowerVariableSubstt   EulerIntegrandQt   FunctionOfSquareRootOfQuadratict   SquareRootOfQuadraticSubstt   Dividest   EasyDQt   ProductOfLinearPowersQt   Rtt   NthRoott	   AtomBaseQt   SumBaseQt   NegSumBaseQt   AllNegTermQt   SomeNegTermQt   TrigSquareQt   RtAuxt
   TrigSquaret   IntSumt   IntTermt   Map2t   ConstantFactort   SameQt   ReplacePartt   CommonFactorst   MostMainFactorPositiont   FunctionOfExponentialQt   FunctionOfExponentialt   FunctionOfExponentialFunctiont    FunctionOfExponentialFunctionAuxt   FunctionOfExponentialTestt   FunctionOfExponentialTestAuxt   stdevt	   rubi_testt   Ift   IntQuadraticQt   IntBinomialQt   RectifyTangentt   RectifyCotangentt
   Inequalityt	   Conditiont   Simpt   SimpHelpt   SplitProductt   SplitSumt   SubstForRF  t   FresnelSt   FresnelCt   Erfct   Erfit   Gammat   FunctionOfTrigOfLinearQt   ElementaryFunctionQt   Complext   UnsameQt   _SimpFixFactort   SimpFixFactort   _FixSimplifyt   FixSimplifyt   _SimplifyAntiderivativeSumt   SimplifyAntiderivativeSumt   _SimplifyAntiderivativet   SimplifyAntiderivativet   _TrigSimplifyAuxt   TrigSimplifyAuxt   Cancelt   Partt   PolyLogt   Dt   Distt   Sum_doitt   PolynomialQuotientt   Floort   PolynomialRemaindert   FactorR  t   CosIntegralt   SinIntegralt   LogIntegralt   SinhIntegralt   CoshIntegralt   Rulet   Erft	   PolyGammat   ExpIntegralEit   ExpIntegralEt   LogGammat   UtilityOperatort	   Factorialt   Zetat
   ProductLogt   DerivativeDividest   HypergeometricPFQt   IntHidet   OneQt   Nullt   rubi_expt   rubi_logt   Discriminantt   Negativet   Quotient(   t   Integralt   St   sqrtt   Andt   Ort   Integert   Floatt   Modt   It   Abst   simplifyt   Mult   Addt   Powt   signt
   EulerGamma(   t   WC(   t   symbolst   Symbol(   t   sint   cost   tant   cott   csct   secR  t   erf(   t   acosht   asinht   atanht   acotht   acscht   asecht   cosht   sinht   tanht   cotht   secht   csch(   t   atant   acsct   asint   acott   acost   asect   atan2(   t   pit   ABCFGHabcdefghijklmnpqrtuvswxyzt   a1t   a2t   b1t   b2t   c1t   c2t   d1t   d2t   n1t   n2t   e1t   e2t   f1t   f2t   g1t   g2t   n3t   Pqt   Pmt   Pxt   Qmt   Qrt   Qxt   jnt   mnt   non2t   RFxt   RGxs   i ii Pqq Q R r C k uc   	        s d d l  m } m } m } m } m } m } m } m } m	 }	 m
 }
 m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m  }  m! }! m" }" m# }# m$ }$ m% }% m& }& m' }' m( }( m) }) m* }* m+ }+ m, }, m- }- m. }. m/ }/ m0 }0 m1 }1 m2 }2 m3 }3 m4 }4 m5 }5 m6 }6 m7 }7 m8 }8 m9 }9 m: }: m; }; m< }< m= }= m> }> m? }? m@ }@ mA }A mB }B mC }C mD }D mE }E mF }F mG }G mH }H mI }I mJ }J mK }K mL }L mM }M mN }N mO }O mP }P mQ }Q mR }R mS }S mT }T mU }U mV }V mW }W mX }X mY }Y mZ }Z m[ }[ m\ }\ m] }] m^ }^ m_ }_ m` }` ma }a mb }b mc }c md }d me }e mf }f mg }g mh }h mi }i mj }j mk }k ml }l mm }m mn }n mo }o mp }p mq }q mr }r ms }s mt }t mu }u mv }v mw }w mx }x my }y mz }z m{ }{ m| }| m} }} m~ }~ m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | 	 }   f d	   } t | |  } t t t d  t t t d t d   t d t d    t d
 t d   t d  t t t d t d   t d t d    t d t d   t  | | |	  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d  t t t d t d   t d t d    t d t d   t  | | | | |
 | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d  t t t d t d   t d t d    t d t d   t  | | | | |
 | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | | 
 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t t t d t d   t d t d    t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | | 
 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t t t d t d   t d t d    t t  | | | | | | | | | 
 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | |  }   f d   } t | |  } t t t d  t t t d t d   t d t d    t t  | | |  }   f d   } t | |  } t t t d  t t t d t d   t d t d    t t  | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t  | | | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t  | | | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t  | | | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t t  | | | | |  }   f d   } t | |  } t t t d  t t 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  | | |  }   f d    } t | |  } t t t d t d   t t t d t d   t d t d    t t  | | | |  }   f d!   } t | |  } t t t d t d   t t t d t d   t d t d    t t  | | | |  }   f d"   } t | |  }t t t d t d   t t t d t d   t d t d    t t  | | | | |  }  f d#   }t || }t t t d t d   t t t d t d   t d t d    t t  | | | | |  }  f d$   }t || }t t t t d t d   t t t d t d   t d t d    t d%  t  | | | | |   }  f d&   }	t ||	 }
t t t t d t d   t t t d t d   t d t d    t d%  t  | | | | |   }  f d'   }t || }t t t t t d t d   t t t d t d   t d t d     t  | | | | |!  }  f d(   }t || }t t t t t d t d   t t t d t d   t d t d     t  | | | | |!  }  f d)   }t || }t t t t d t d   t t t d t d   t d t d    t t  | | | | |! | | | 	 }  f d*   }t || }t t t t d t d   t t t d t d   t d t d    t t  | | | | |! | | | 	 }  f d+   }t || }t t t d  t t t d t d   t t t d t d   t d t d     t  | | | | |!  }  f d,   }t || }t t t d  t t t d t d   t t t d t d   t d t d     t  | | | | |!  }  f d-   }t || }t t t t d t d   t t t d t d   t d t d    t t  | | | | |! | |" | 	 }   f d.   }!t | |! }"t t t t d t d   t t t d t d   t d t d    t t  | | | | |! | |" | 	 }#  f d/   }$t |#|$ }%t t t t d t d   t t t d t d   t d t d    t t  | | | | | |! |# |$ 	 }&  f d0   }'t |&|' }(t t t t d t d   t t t d t d   t d t d    t t  | | | | | |! |# |$ 	 })  f d1   }*t |)|* }+t t t t d t d   t t t d t d   t d t d    t t  | | | | | |! |# |% 	 },  f d2   }-t |,|- }.t t t t d t d   t t t d t d   t d t d    t t  | | | | | |! |# |% 	 }/  f d3   }0t |/|0 }1t t t t t d t d   t t t d t d   t d t d     t  | | | | |&  }2  f d4   }3t |2|3 }4t t t t t d t d   t t t d t d   t d t d     t  | | | | |&  }5  f d5   }6t |5|6 }7t t t t d t d   t t t d t d   t d t d    t d6  d% t  | | | | |&  }8  f d7   }9t |8|9 }:t t t t d t d   t t t d t d   t d t d    t d6  d% t  | | | | |&  };  f d8   }<t |;|< }=t t t t d t d   t t t d t d   t d t d    t t  | | | | |& | |' | 	 }>  f d9   }?t |>|? }@t t t t d t d   t t t d t d   t d t d    t t  | | | | |& | |' | 	 }A  f d:   }Bt |A|B }Ct t t d  t t d t d   t t t d t d   t d t d    t  | | | | |&  }D  f d;   }Et |D|E }Ft t t d  t t d t d   t t t d t d   t d t d    t  | | | | |&  }G  f d<   }Ht |G|H }It t t d  t t t d t d   t t t d t d   t d t d     t  | | | | |&  }J  f d=   }Kt |J|K }Lt t t d  t t t d t d   t t t d t d   t d t d     t  | | | | |&  }M  f d>   }Nt |M|N }Ot t t t d t d   t t t d t d   t d t d    t t  | | | | |& | | | 	 }P  f d?   }Qt |P|Q }Rt t t t d t d   t t t d t d   t d t d    t t  | | | | |& | | | 	 }S  f d@   }Tt |S|T }Ut t t t d t d   t t t d t d   t d t d    t t  | | | | | |& |#  }V  f dA   }Wt |V|W }Xt t t t d t d   t t t d t d   t d t d    t t  | | | | | |& |#  }Y  f dB   }Zt |Y|Z }[t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t  | | | | | | |(  }\  f dC   }]t |\|] }^t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t  | | | | | | |(  }_  f dD   }`t |_|` }at t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d%  t  | | | | | | |(  }b  f dE   }ct |b|c }dt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d%  t  | | | | | | |(  }e  f dF   }ft |e|f }gt t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d%  t  | | | | |)  }h  f dG   }it |h|i }jt t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d%  t  | | | | |)  }k  f dH   }lt |k|l }mt t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d6  t  | | | | |)  }n  f dI   }ot |n|o }pt t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d6  t  | | | | |)  }q  f dJ   }rt |q|r }st t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! |* |  }t  f dK   }ut |t|u }vt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! |* |  }w  f dL   }xt |w|x }y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  | | | | |!  }z  f dM   }{t |z|{ }|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  | | | | |!  }}  f dN   }~t |}|~ }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |! | |+ |, 	 }  f dO   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |! | |+ |, 	 }  f dP   }t || }t t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | |!  }  f dQ   }t || }t t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | |!  }  f dR   }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | |!  }  f dS   }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | |!  }  f dT   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |! | |- |, 	 }  f dU   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |! | |- |, 	 }  f dV   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |! | |-  }  f dW   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |! | |-  }  f dX   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | |! |.  }  f dY   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | |! |.  }  f dZ   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | |! | |-  }  f d[   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | |! | |-  }  f d\   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | | |! |.  }  f d]   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | | |! |.  }  f d^   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |! |/  }  f d_   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |! |/  }  f d`   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |! |0  }  f da   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |! |0  }  f db   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | | | 
 }  f dc   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | | | 
 }  f dd   }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d     t  | | | | | |!  }  f de   }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d     t  | | | | | |!  }  f df   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | |1 | 
 }  f dg   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | |1 | 
 }  f dh   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | | |!  }  f di   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | | |!  }  f dj   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |! |2 |$ 	 }  f dk   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |! |2 |$ 	 }  f dl   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |!  }  f dm   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |!  }  f dn   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | | |+ |,  }  f do   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | | |+ |,  }  f dp   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | | |- |,  }  f dq   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | | |- |,  }  f dr   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | |3 |- 
 }  f ds   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | |3 |- 
 }  f dt   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! |4 |.  }  f du   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! |4 |.  }  f dv   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | | |5 |,  }  f dw   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | | |5 |,  }  f dx   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! | | |6 |,  }  f dy   }t || } t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! | | |6 |,  }  f dz   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | | |7 |8  }  f d{   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | | |7 |8  }  f d|   }t || }	t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | | |' |8  }
  f d}   }t |
| }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |! | | |' |8  }  f d~   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! | | |8  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! | | |8  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |! | | 	 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |! | | 	 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |! | |9 	 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |! | |9 	 }  f d   } t ||  }!t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |!  }"  f d   }#t |"|# }$t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |!  }%  f d   }&t |%|& }'t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t  | | | | | |!  }(  f d   })t |(|) }*t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t  | | | | | |!  }+  f d   },t |+|, }-t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | |' | 
 }.  f d   }/t |.|/ }0t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | |' | 
 }1  f d   }2t |1|2 }3t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | |9 | 
 }4  f d   }5t |4|5 }6t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |! | |9 | 
 }7  f d   }8t |7|8 }9t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! | |' |6 |:  }:  f d   };t |:|; }<t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! | |' |6 |:  }=  f d   }>t |=|> }?t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |$ | |/  }@  f d   }At |@|A }Bt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |$ | |/  }C  f d   }Dt |C|D }Et t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |$ | |;  }F  f d   }Gt |F|G }Ht t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |$ | |;  }I  f d   }Jt |I|J }Kt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |$  }L  f d   }Mt |L|M }Nt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |$  }O  f d   }Pt |O|P }Qt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |%  }R  f d   }St |R|S }Tt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | |%  }U  f d   }Vt |U|V }W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  | | | | |&  }X  f d   }Yt |X|Y }Z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  | | | | |&  }[  f d   }\t |[|\ }]t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |& | | |, 	 }^  f d   }_t |^|_ }`t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |& | | |, 	 }a  f d   }bt |a|b }ct t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | |&  }d  f d   }et |d|e }ft t t d  t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | |&  }g  f d   }ht |g|h }it t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | |&  }j  f d   }kt |j|k }lt t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | |&  }m  f d   }nt |m|n }ot t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |& | | |, 	 }p  f d   }qt |p|q }rt t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | |& | | |, 	 }s  f d   }tt |s|t }ut t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | |& |<  }v  f d   }wt |v|w }xt t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | |& |<  }y  f d   }zt |y|z }{t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |& | |=  }|  f d   }}t |||} }~t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |& | |=  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |& | |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t 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 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 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  | | | | |&  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | |&  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | |&  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | |& | |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | |& | |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | | |& |>  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d6  t  | | | | | |& |>  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | |? |@ 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | |? |@ 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& | |? |A |B  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& | |? |A |B  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | | |C |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | | |C |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | | |7 |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | | |7 |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | | |D 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | | |D 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& |E  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& |E  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& | | |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& | | |  }  f d   }t || }t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t d  d% t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t d  d% t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& | |F 	 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& | |F 	 }  f d   }t || }t t t d  t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d  t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& | |" | 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& | |" | 
 }  f d   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |& | | | 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t 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 t t d t d   t d t d     t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |& | |" | 
 }   f d   }t | | }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |& | |" | 
 }  f d   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }	  f d   }
t |	|
 }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |& | |' | 
 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t 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 t 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 t t d t d   t t t d t d   t d t d     t  | | | | |&  }  f d   }t || }t t t d  t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }  f d   }t || } t t t d  t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | |&  }!  f d   }"t |!|" }#t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |& | | | 
 }$  f d   }%t |$|% }&t t t d t d   t t t d t d   t d t d    t t t t d t d   t t t d t d   t d t d     t  | | | | | |& | | | 
 }'  f d   }(t |'|( })t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d6  d% t  | | | | | |& | |" |G 
 }*  f d   }+t |*|+ },t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d6  d% t  | | | | | |& | |" |G 
 }-  f d   }.t |-|. }/t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& | |F |H |I  }0  f d   }1t |0|1 }2t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& | |F |H |I  }3  f d   }4t |3|4 }5t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | |J |K |6 |A  }6  f d   }7t |6|7 }8t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | |J |K |6 |A  }9  f d   }:t |9|: };t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | |L |M |6 |H  }<  f d   }=t |<|= }>t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | |& | |L |M |6 |H  }?  f d   }@t |?|@ }At t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d     t  | | | | | |&  }B  f d   }Ct |B|C }Dt t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d     t  | | | | | |&  }E  f d   }Ft |E|F }Gt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |*  }H  f d   }It |H|I }Jt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |*  }K  f d   }Lt |K|L }Mt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | |N 	 }N  f d   }Ot |N|O }Pt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | |N 	 }Q  f d   }Rt |Q|R }St t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |P |Q |O  }T  f d   }Ut |T|U }Vt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |P |Q |O  }W  f d   }Xt |W|X }Yt t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d t d   t  | | | | | |R |!  }Z  f d   }[t |Z|[ }\t t t t d t d   t t t d t d   t d t d    t t t 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 t d t d   t d t d    t t t t d t d   t d t d    t d t d   t  | | | | | |R |&  }`  f d   }at |`|a }bt t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d t d   t  | | | | | |R |&  }c  f d   }dt |c|d }et t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | |S  }f  f d   }gt |f|g }ht t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | |S  }i  f d   }jt |i|j }kt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | |P | |Q |T 	 }l  f d   }mt |l|m }nt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t  | | | | |P | |Q |T 	 }o  f d   }pt |o|p }qt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |P | |Q |U 	 }r  f d   }st |r|s }tt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |P | |Q |U 	 }u  f d   }vt |u|v }wt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |P | |Q |V 	 }x  f d   }yt |x|y }zt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |P | |Q |V 	 }{  f d   }|t |{|| }}t t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |W |! |:  }~  f d   }t |~| }t t t t d t d   t t t d t d   t d t d    t d t d   t d  t t t d t d   t d t d    t d
 t d   t  | | | | |W |! |:  }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d
 t d   t  | | | | | |W |! | 	 }  f d   }t || }t t t t d t d   t t t d t d   t d t d    t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | |W |! | 	 }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | |   }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | |   }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | | | | |X  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | | | | |X  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d
 t d   t  | | | | | |W |&  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | |W |&  }  f d	  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |Y  }  f d
  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |Y  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | |! |Z |[  }  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 t t d t d   t d t d    t d
 t d   t  | | | | |! |Z |[  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! |\ 	 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |! |\ 	 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |! | 
 }  f d  }t || }t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d  }t || }t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& |]  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& |]  }  f d  }t || }t t t d  t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d  }t || }t t t d  t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | |&  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& |^  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | |& |^  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |&  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | |&  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& |Y 	 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |& |Y 	 }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d
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 }  f d"  }t || }t t t d  t t t d t d   t d t d    t t d t d   t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | |Q | 
 }  f d#  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |a |! |* |\ |b  }  f d$  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t t  | | | | | | | |a |! |* |\ |b  }  f d%  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | |a |! |O | |c  }  f d&  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | |a |! |O | |c  }  f d'  } t ||  }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |a |! |d  }  f d(  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | |a |! |d  }  f d)  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |a |! | |e  }  f d*  }	t ||	 }
t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |a |! | |e  }  f d+  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t  | | | | | | |a |! | |1  }  f d,  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t  | | | | | | |a |! | |1  }  f d-  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |a |! | |1  }  f d.  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |a |! | |1  }  f d/  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | |a |! |f  }  f d0  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | |a |! |f  }  f d1  }t || }t t t t d t d   t t t d t d   t d t d    t d  d% t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |a |! | |1  }   f d2  }!t | |! }"t t t t d t d   t t t d t d   t d t d    t d  d% t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |a |! | |1  }#  f d3  }$t |#|$ }%t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |a |! |g |  }&  f d4  }'t |&|' }(t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |a |! |g |  })  f d5  }*t |)|* }+t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | |a |!  },  f d6  }-t |,|- }.t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | |a |!  }/  f d7  }0t |/|0 }1t t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | |a  }2  f d8  }3t |2|3 }4t t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | |a  }5  f d9  }6t |5|6 }7t t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | |h |i 	 }8  f d:  }9t |8|9 }:t t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | |h |i 	 };  f d;  }<t |;|< }=t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |! 	 }>  f d<  }?t |>|? }@t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |! 	 }A  f d=  }Bt |A|B }Ct t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& 	 }D  f d>  }Et |D|E }Ft t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& 	 }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 t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |! |,  }J  f d@  }Kt |J|K }Lt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |! |,  }M  f dA  }Nt |M|N }Ot t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |& |,  }P  f dB  }Qt |P|Q }Rt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |& |,  }S  f dC  }Tt |S|T }Ut t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | |h  }V  f dD  }Wt |V|W }Xt t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | |h  }Y  f dE  }Zt |Y|Z }[t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t  | | | | | | |h |! 	 }\  f dF  }]t |\|] }^t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t  | | | | | | |h |! 	 }_  f dG  }`t |_|` }at t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t  | | | | | | |h |& 	 }b  f dH  }ct |b|c }dt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t  | | | | | | |h |& 	 }e  f dI  }ft |e|f }gt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |! |,  }h  f dJ  }it |h|i }jt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |! |,  }k  f dK  }lt |k|l }mt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |& |,  }n  f dL  }ot |n|o }pt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | |h | | |& |,  }q  f dM  }rt |q|r }st t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | | |h |< 
 }t  f dN  }ut |t|u }vt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t  | | | | | | | |h |< 
 }w  f dO  }xt |w|x }yt t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |j 	 }z  f dP  }{t |z|{ }|t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |j 	 }}  f dQ  }~t |}|~ }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f dR  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f dS  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t  | | | | | | |h |j 	 }  f dT  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t  | | | | | | |h |j 	 }  f dU  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f dV  }t || }t t t t d t d   t t t d t d   t d t d    t d6  d% t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f dW  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |j 	 }  f dX  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |j 	 }  f dY  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& 	 }  f dZ  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |h |& 	 }  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 t t d t d   t d t d     t  | | | | | | |h |! |l 
 }  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 t t d t d   t d t d     t  | | | | | | |h |! |l 
 }  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 t t d t d   t d t d     t  | | | | | | |h  }  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 t t d t d   t d t d     t  | | | | | | |h  }  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 t t d t d   t d t d     t  | | | | | | |h |! |l 
 }  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 t t d t d   t d t d     t  | | | | | | |h |! |l 
 }  f da  }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 t t d t d   t d t d     t  | | | | | | |h |! |k 
 }  f db  }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 t t d t d   t d t d     t  | | | | | | |h |! |k 
 }  f dc  }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 t t d t d   t d t d     t  | | | | | | |h |& |l 
 }  f dd  }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 t t d t d   t d t d     t  | | | | | | |h |& |l 
 }  f de  }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 t t d t d   t d t d     t  | | | | | | |h |& |k 
 }  f df  }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 t t d t d   t d t d     t  | | | | | | |h |& |k 
 }  f dg  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | |h |! |l 
 }  f dh  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | |h |! |l 
 }  f di  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | |h  }  f dj  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | |h  }  f dk  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d6  d% t  | | | | | | |h |k 	 }  f dl  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d6  d% t  | | | | | | |h |k 	 }  f dm  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | |h |! |k |g  }  f dn  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | |h |! |k |g  }  f do  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |h |O |: |m  }  f dp  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |h |O |: |m  }  f dq  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |h |d |n |m  }  f dr  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |h |d |n |m  }  f ds  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |h | |<  }  f dt  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |h | |<  }  f du  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |Y 
 }  f dv  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |Y 
 }  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 t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | |o 
 }  f dx  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | | | |o 
 }  f dy  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | |O 	 }  f dz  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | |O 	 }  f d{  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | |Q |  }  f d|  }t || } t t t d t d   t t t d t d   t d t d    t t d t d   t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | |Q |  }  f d}  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | | | |a |! |4 |p  }  f d~  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | | | |a |! |4 |p  }  f d  }t || }	t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | | | |a |! |q |p |r |s  }
  f d  }t |
| }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | | | |a |! |q |p |r |s  }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |a |! 	 }  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 t t d t d   t d t d     t t 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 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  | | | | | | | |a |! |t  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | | |a |! |t  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | |a |! |u | |-  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | |a |! |u | |-  }  f d  } t ||  }!t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |a |! |u |. |v  }"  f d  }#t |"|# }$t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |a |! |u |. |v  }%  f d  }&t |%|& }'t t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |a |! |Y 
 }(  f d  })t |(|) }*t t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |a |! |Y 
 }+  f d  },t |+|, }-t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | |a |! |Y |- |,  }.  f d  }/t |.|/ }0t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | |a |! |Y |- |,  }1  f d  }2t |1|2 }3t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | | |a |! |w |x |y  }4  f d  }5t |4|5 }6t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | | | | | | |a |! |w |x |y  }7  f d  }8t |7|8 }9t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | |a |! |d 
 }:  f d  };t |:|; }<t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | |a |! |d 
 }=  f d  }>t |=|> }?t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |a |! |z  }@  f d  }At |@|A }Bt t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |a |! |z  }C  f d  }Dt |C|D }Et t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |a |!  }F  f d  }Gt |F|G }Ht t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |a |!  }I  f d  }Jt |I|J }Kt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |P | |Q |a |! |w |x |y  }L  f d  }Mt |L|M }Nt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | | |P | |Q |a |! |w |x |y  }O  f d  }Pt |O|P }Qt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P |Q |a |! |d  }R  f d  }St |R|S }Tt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P |Q |a |! |d  }U  f d  }Vt |U|V }Wt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |a |!  }X  f d  }Yt |X|Y }Zt t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |a |!  }[  f d  }\t |[|\ }]t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }^  f d  }_t |^|_ }`t t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }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 t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }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 t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }g  f d  }ht |g|h }it t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |! 	 }j  f d  }kt |j|k }lt t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |! 	 }m  f d  }nt |m|n }ot t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |& |l 
 }p  f d  }qt |p|q }rt t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |& |l 
 }s  f d  }tt |s|t }ut t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }v  f d  }wt |v|w }xt t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }y  f d  }zt |y|z }{t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }|  f d  }}t |||} }~t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |j 	 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |j 	 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d%  t  | | | | | | |h |j 	 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d%  t  | | | | | | |h |j 	 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d%  t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d%  t  | | | | | | |h |& |k 
 }  f d  }t || }t 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 t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }  f d  }t || }t 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 t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |! 
 }  f d  }t || }t 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 t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }  f d  }t || }t 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 t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | |P |h |& 
 }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |! |k 
 }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |! |k 
 }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |& |l 
 }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |& |l 
 }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  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 t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |! |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |! |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t d%  t  | | | | | | |h  }  f d  }t || }t t t d  t t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t d%  t  | | | | | | |h  }  f d  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t d t d    t  | | | | | | |h |& |k 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |h |! |k |{  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |h |! |k |{  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P |Q |h |O |:  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P |Q |h |O |:  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | |Q |h || |O  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | |Q |h || |O  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |h || |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |h || |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d  t t t d t d   t d t d    t d t d   t  | | | | | | | | |h |g |[ |} |~  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d  t t t d t d   t d t d    t d t d   t  | | | | | | | | |h |g |[ |} |~  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |h |  }   f d  }t | | }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |h |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t d t d   t d t d   t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t d t d   t d t d   t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t t  | | | | | | |P | | |Q |  }	  f d  }
t |	|
 }t t t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t d t d    t  | | | | | | | | |h |& |k |  }  f d  }t || }t t t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d    t d6  d% t t t d t d   t d t d    t  | | | | | | | | |h |& |k |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | | | | |"  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | | | | |"  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | | | | 
 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | | | | 
 }  f d  }t || }t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t  | | | | | | |  }  f d  }t || } t t t t dt d   t t t d t d   t d t d    t t d t d   t 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 t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |! |  }$  f d  }%t |$|% }&t t t t dt d   t t t d t d   t d t d    t t d t d   t 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 d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |! | | |-  }*  f d  }+t |*|+ },t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |! | | |-  }-  f d  }.t |-|. }/t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |! | |.  }0  f d  }1t |0|1 }2t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |! | |.  }3  f d  }4t |3|4 }5t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |& | |=  }6  f d  }7t |6|7 }8t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |& | |=  }9  f d  }:t |9|: };t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |& | |  }<  f d  }=t |<|= }>t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |& | |  }?  f d  }@t |?|@ }At t t t dt d   t t t d t d   t d t d    t t t d t d   t t 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t t t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |& | 	 }E  f d  }Ft |E|F }Gt t t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t t t d t d   t d t d    t  | | | | | | |& | 	 }H  f d  }It |H|I }Jt t t t dt d   t t t d t d   t d t d    t t t d t d   t t 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 dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |& | |<  }N  f d  }Ot |N|O }Pt t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | |& | |<  }Q  f d  }Rt |Q|R }St t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |& 
 }T  f d  }Ut |T|U }Vt t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |& 
 }W  f d  }Xt |W|X }Yt t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | | | |! | |-  }Z  f d  }[t |Z|[ }\t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | | | |! | |-  }]  f d  }^t |]|^ }_t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | | | |& | |  }`  f d  }at |`|a }bt t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | | | |& | |  }c  f d  }dt |c|d }et t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | | | | |> 
 }f  f d  }gt |f|g }ht t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t d%  t  | | | | | | | | |> 
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  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |! | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |! | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |! | |9  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |! | |9  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |!  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |!  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |"  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |"  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |C  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |C  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |"  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | |& | | |"  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | | | |  }  f d   }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | |"  }  f d!  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | |& | |"  }  f d"  }t || }t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d#  }t || }t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d$  }t || }t t t t d t d   t t t d t d   t d t d     t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d%  }t || }t t t t d t d   t t t d t d   t d t d     t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d&  }t || }t t t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d'  }t || }t t t t dt d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d     t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d(  } t ||  }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | | | | |&  }  f d)  }t || }t t t d t d   t t t d t d   t d t d    t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t  | | | | | | | | | |&  }  f d*  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | | |&  }  f d+  }	t ||	 }
t t t d t d   t t t d t d   t d t d    t d t d   t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | | | | | | | | | |&  }  f d,  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d t d   t d-t d   t dt d   t t t d t d   t d t d    t d t d   t  | | | | | | | | | |Q |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 t d t d   t t t d t d   t d t d    t d t d   t d-t d   t dt d   t t t d t d   t d t d    t d t d   t  | | | | | | | | | |Q |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 dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | 
 }  f d1  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | 
 }  f d2  }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }  f d3  }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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }  f d4  }t || }t t t d t d   t t t d t d   t d t d    t d
 t d   t t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }   f d5  }!t | |! }"t t t d t d   t t t d t d   t d t d    t d
 t d   t t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }#  f d6  }$t |#|$ }%t t t d t d   t t t d t d   t d t d    t d
 t d   t t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }&  f d7  }'t |&|' }(t t t d t d   t t t d t d   t d t d    t d
 t d   t t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 })  f d8  }*t |)|* }+t t t d t d   t t t d t d   t d t d    t d
 t d   t t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 },  f d9  }-t |,|- }.t t t d t d   t t t d t d   t d t d    t d
 t d   t t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }/  f d:  }0t |/|0 }1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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }2  f d;  }3t |2|3 }4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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }5  f d<  }6t |5|6 }7t t t d t d   t t t d t d   t d t d    t d
 t d   t t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }8  f d=  }9t |8|9 }:t t t d t d   t t t d t d   t d t d    t d
 t d   t t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 };  f d>  }<t |;|< }=t t t t d t d   t t t d t d   t d t d    t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }>  f d?  }?t |>|? }@t t t t d t d   t t t d t d   t d t d    t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }D  f dA  }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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }G  f dB  }Ht |G|H }It t t d-t d   t dt d   t t t d t d   t d t d    t d0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 d t d    t  | | | | | | | | 	 }J  f dC  }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 d0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 d t d    t  | | | | | | | | 	 }M  f dD  }Nt |M|N }Ot t t d-t d   t d0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 d t d    t  | | | | | | |  }P  f dE  }Qt |P|Q }Rt t t d-t d   t d0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 d t d    t  | | | | | | |  }S  f dF  }Tt |S|T }Ut t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |! | |-  }V  f dG  }Wt |V|W }Xt t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |! | |-  }Y  f dH  }Zt |Y|Z }[t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |! | |- 
 }\  f dI  }]t |\|] }^t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |! | |- 
 }_  f dJ  }`t |_|` }at t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |! |.  }b  f dK  }ct |b|c }dt t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |! |.  }e  f dL  }ft |e|f }g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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |! |. 
 }h  f dM  }it |h|i }j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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |! |. 
 }k  f dN  }lt |k|l }mt t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& | 
 }n  f dO  }ot |n|o }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 d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& | 
 }q  f dP  }rt |q|r }s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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |& | 	 }t  f dQ  }ut |t|u }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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |& | 	 }w  f dR  }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 d0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  | | | | | | | |& 	 }z  f dS  }{t |z|{ }|t t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | |& 	 }}  f dT  }~t |}|~ }t t t d-t d   t d0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  | | | | | | |&  }  f dU  }t || }t t t d-t d   t d0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  | | | | | | |&  }  f dV  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d 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 t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d 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 d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |& |, | 
 }  f dY  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |& |, | 
 }  f dZ  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& |<  }  f d[  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& |<  }  f d\  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& |< 
 }  f d]  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& |< 
 }  f d^  }t || }t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }  f d_  }t || }t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }  f d`  }t || }t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }  f da  }t || }t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | |  }  f db  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |Q |  }  f dc  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |Q |  }  f dd  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |Q | 
 }  f de  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |Q | 
 }  f df  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |  }  f dg  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |  }  f dh  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | 
 }  f di  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | 
 }  f dj  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |  }  f dk  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |  }  f dl  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | 
 }  f dm  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | 
 }  f dn  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | | | |!  }  f do  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | | | |!  }  f dp  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0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  | | | | | | | | |! 
 }  f dq  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0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  | | | | | | | | |! 
 }  f dr  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | | | |&  }  f ds  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | | | |&  }  f dt  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0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  | | | | | | | | |& 
 }  f du  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0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  | | | | | | | | |& 
 }  f dv  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | | |> 
 }  f dw  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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  | | | | | | | | |> 
 }  f dx  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0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  | | | | | | | |> 	 }  f dy  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0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  | | | | | | | |> 	 }  f dz  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |! | |-  }  f d{  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |! | |-  }  f d|  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |! | |-  }  f d}  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |! | |-  }  f d~  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |! |. |  }  f d  }t || } t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |! |. |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |! |. |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |! |. |  }  f d  }t || }	t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |! |. | |  }
  f d  }t |
| }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |! |. | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |! |. | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |! |. | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | | |& | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | | |& | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | |& | | 
 }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | |& | | 
 }  f d  } t ||  }!t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | | | |& |>  }"  f d  }#t |"|# }$t t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | | | |& |>  }%  f d  }&t |%|& }'t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | | |& |> 
 }(  f d  })t |(|) }*t t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t t t d t d   t d t d    t d%  t  | | | | | | | |& |> 
 }+  f d  },t |+|, }-t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |= |"  }.  f d  }/t |.|/ }0t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |= |"  }1  f d  }2t |1|2 }3t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& | |= |"  }4  f d  }5t |4|5 }6t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& | |= |"  }7  f d  }8t |7|8 }9t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | |= |  }:  f d  };t |:|; }<t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | |= |  }=  f d  }>t |=|> }?t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |= |  }@  f d  }At |@|A }Bt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |= |  }C  f d  }Dt |C|D }Et t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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 t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0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 t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& | | |  }L  f d  }Mt |L|M }Nt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | |& | | |  }O  f d  }Pt |O|P }Qt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | | |  }R  f d  }St |R|S }Tt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | | |  }U  f d  }Vt |U|V }Wt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | | |  }X  f d  }Yt |X|Y }Zt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | | |  }[  f d  }\t |[|\ }]t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | |  }^  f d  }_t |^|_ }`t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | |  }a  f d  }bt |a|b }ct t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |  }d  f d  }et |d|e }ft t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |  }g  f d  }ht |g|h }it t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | |"  }j  f d  }kt |j|k }lt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |& | |"  }m  f d  }nt |m|n }ot t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |"  }p  f d  }qt |p|q }rt t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | |& | |"  }s  f d  }tt |s|t }ut t t d-t d   t dt d   t t t d t d   t d t d    t d0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 d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | | | |& 
 }v  f d  }wt |v|w }xt t t d-t d   t dt d   t t t d t d   t d t d    t d0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 d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | | | |& 
 }y  f d  }zt |y|z }{t t t d-t d   t d0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 d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | | |& 	 }|  f d  }}t |||} }~t t t d-t d   t d0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 d t d     t t d t d   t t t d t d   t d t d    t  | | | | | | | |& 	 }  f d  }t || }t t t d-t d   t dt d   t t t d t d   t d t d    t d0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 d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d  }t || }t t t d-t d   t dt d   t t t d t d   t d t d    t d0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 d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | | | |& 
 }  f d  }t || }t t t d-t d   t d0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 d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | | |& 	 }  f d  }t || }t t t d-t d   t d0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 d t d     t t t d t d   t t t d t d   t d t d     t  | | | | | | | |& 	 }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t 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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |O  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |O  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |O  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | |O  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t 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 d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | | |Q |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t dt d   t t t d t d   t d t d    t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | | |Q |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |Q |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t t t d t d   t d t d    t d
 t d   t d-t d   t d0t d   t t t d t d   t d t d    t d%  t  | | | | | | | | | | |Q |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d%  t t  | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d%  t t  | | | | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t d%  t 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 t  | | | | |Q |  }  f d  }t || }t t t d  t t d t d   t t t d t d   t d t d    t d%  t  | | | | |  }  f d  }t || }t t t d  t t d t d   t t t d t d   t d t d    t d%  t  | | | | |  }  f d  }t || }t t t t d t d   t t t d t d   t d t d    t d%  t 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 t  | | | | |Q | |  }  f d  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t t t t d t d   t d t d    t t  | | | | |Q | |  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t t t t d t d   t d t d    t t  | | | | |Q | |  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | |  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | |  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t t d  t t t d t d   t d t d    t t  | | | | |Q | |  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t t d  t t t d t d   t d t d    t t  | | | | |Q | |  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | |}  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | |}  }t || }t t t t d  t t t d t d   t d t d    t t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | |  }  f d  }t || }t t t t d  t t t d t d   t d t d    t t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | |  }  f d  }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | |: |} 	 }t || }  f d  }t t t t d  t t t d t d   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    t d
 t d   t  | | | | | | |: |} 	 }t || }  f d  }t t t t d  t t t d t d   t d t d    t t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | |  }t || }  f d  }t t t t d  t t t d t d   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    t d
 t d   t  | | | | | |  }t || }t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t d t d   t  | | | | | | | | |} 
 }  f d  }t || }t t t d  t t t d t d   t d t d    t d t d   t 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 d t d   t  | | | | | | | | |} 
 }  f d  }t || }t t t d  t t t d t d   t d t d    t d t d   t 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  | | | | | | |Q | | |V  }  f d  }t || }t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t  | | | | | | |Q | | |V  }  f d  }t || }  f d  } 	t t t d  t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t  | | | | | | | | 	 }	t |	| 	 }	  f d  }	t t t d  t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t  | | | | | | | | 	 }	t |	|	 }	  f d  }	t t t d  t t t d t d   t d t d    t t 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 d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }	t |	|	 }	  f d  }		t t t d  t t t d t d   t d t d    t t 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 d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }
	t |
	|		 }	  f d  }	t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t t d t d   t d t d   t d t d   t t t d t d   t d t d    t t  | | | | | |Q | | | 
 }	t |	|	 }	  f d  }	t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t t d t d   t d t d   t d t d   t t t d t d   t d t d    t t  | | | | | |Q | | | 
 }	t |	|	 }	t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | | | | |}  }	  f d  }	t |	|	 }	t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | | | | |}  }	  f d  }	t |	|	 }	t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | | |Q | | |V  }	  f d  }	t |	|	 }	t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | | |Q | | |V  }	  f d  }	t |	|	 }	t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }	  f d  }	t |	|	 } 	t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }!	  f d  }"	t |!	|"	 }#	  f d  }$	t t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | |: |}  }%	t |%	|$	 }&	  f d  }'	t t t t d  t t t d t d   t d t d    t d t d   t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | | | |: |}  }(	t |(	|'	 })	  f d  }*	t t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }+	t |+	|*	 },	  f d  }-	t t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t dt d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }.	t |.	|-	 }/	t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t t  | | | | | | | | |: 
 }0	  f d  }1	t |0	|1	 }2	t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t t  | | | | | | | | |: 
 }3	  f d  }4	t |3	|4	 }5	t t t t dt d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t 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 d    t t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t t  | | | | | | | | | 
 }9	  f d  }:	t |9	|:	 };	  f d  }<	t t t t dt d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }=	t |=	|<	 }>	  f d  }?	t t t t dt d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t  | | | | | | | | 	 }@	t |@	|?	 }A	t t t t dt d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t t  | | | | | | | | |: 
 }B	  f d  }C	t |B	|C	 }D	t t t t dt d   t t t d t d   t d t d    t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d%  t t  | | | | | | | | |: 
 }E	  f d  }F	t |E	|F	 }G	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  | | | | |*  }H	  f d  }I	t |H	|I	 }J	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  | | | | |*  }K	  f d  }L	t |K	|L	 }M	t t t t d t d   t d t d   t d
 t d   t t t d t d   t d t d    t d%  t  | | | | | |=  }N	  f d  }O	t |N	|O	 }P	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  | | | | | |=  }Q	  f d  }R	t |Q	|R	 }S	t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d   t  | | | | | | | | 	 }T	  f d  }U	t |T	|U	 }V	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  | | | | | | | | 	 }W	  f d  }X	t |W	|X	 }Y	t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d   t t  | | | | | | | | | 
 }Z	  f d  }[	t |Z	|[	 }\	t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d   t t  | | | | | | | | | 
 }]	  f d  }^	t |]	|^	 }_	t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d   t  | | | | | | |  }`	  f d  }a	t |`	|a	 }b	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  | | | | | | |  }c	  f d  }d	t |c	|d	 }e	t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d   t t  | | | | | | | | 	 }f	  f d  }g	t |f	|g	 }h	t t t d t d   t t t d t d   t d t d    t t t d t d   t d t d   t t  | | | | | | | | 	 }i	  f d  }j	t |i	|j	 }k	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  | | | | | | | | 	 }l	  f d  }m	t |l	|m	 }n	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  | | | | | | | | 	 }o	  f d  }p	t |o	|p	 }q	t t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t d t d   t d
 t d   t  | | | | | | | | 	 }r	  f d  }s	t |r	|s	 }t	t t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t d t d   t d
 t d   t  | | | | | | | | 	 }u	  f d  }v	t |u	|v	 }w	t t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t d t d   t d
 t d   t  | | | | | | |\ |* 	 }x	  f d  }y	t |x	|y	 }z	t t t t d t d   t t t d t d   t d t d    t d t d   t t d t d   t d t d   t d
 t d   t  | | | | | | |\ |* 	 }{	  f d  }|	t |{	||	 }}	t t t t d
 t d   t d t 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 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 d t d   t  | | | | | | | | |o 
 }	  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 d t d   t  | | | | | | | | |o 
 }	  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 d t d   t  | | | | |Q | |}  }	  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 d t d   t  | | | | |Q | |}  }	  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 d t d   t  | | | | | |Q |  }	  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 d t d   t  | | | | | |Q |  }	  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 d t d   t  | | | | | |Q | | 	 }	  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 d t d   t  | | | | | |Q | | 	 }	  f d	  }	t |	|	 }	t t t d t d   t d t d   t t  t d t d   t  | | |Q | |  }	  f d
  }	t |	|	 }	t t t d t d   t d t d   t t  t d t d   t  | | |Q | |  }	  f d  }	t |	|	 }	t t t t d
 t d   t d t d   t d t d   t t t t d t d   t d t d    t d t d   t  | | | | | | |Q | |} 
 }	  f d  }	t |	|	 }	t t t t d
 t d   t d t d   t d t d   t t t t d t d   t d t d    t d t d   t  | | | | | | |Q | |} 
 }	  f d  }	t |	|	 }	t t t t d
 t d   t d t d   t d t d   t t t t d t d   t d t d    t d t d   t  | | | | | | |Q | 	 }	  f d  }	t |	|	 }	t t t t d
 t d   t d t d   t d t d   t t t t d t d   t d t d    t d t d   t  | | | | | | |Q | 	 }	  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 d t d   t  | | | | | | | |Q | 
 }	  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 d t d   t  | | | | | | | |Q | 
 }	  f d  }	t |	|	 }	t t t t t d
 t d   t d t d   t d t d   t t  t d t d   t  | | | | |Q | |  }	  f d  }	t |	|	 }	t t t t t d
 t d   t d t d   t d t d   t t  t d t d   t  | | | | |Q | |  }	  f d  }	t |	|	 }	t t t t d
 t d   t d  t t t d t d   t d t d   t d t d    t t t 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 d  t t t d t d   t d t d   t d t d    t t t t d t d   t d t d   t d t d    t  | | |Q | |: | |  }	  f d  }	t |	|	 }	| | | | | | | | | | | | | | | | | | | | | ||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||||||||||||||||||||||||||||||||||||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}|||||||||||||||||||||||||||||||||||||||||||||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||||||||||||||||||||||||||||||||||||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}|||||||||||||||||||||||||||||||||||||||||||||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~||||||||||||||||||||||||||||||||||||||||||||	|	|	|	|	|	|	|	|	|	| 	|#	|&	|)	|,	|/	|2	|5	|8	|;	|>	|A	|D	|G	|J	|M	|P	|S	|V	|Y	|\	|_	|b	|e	|h	|k	|n	|q	|t	|w	|z	|}	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	|	g S(  Ni(   t   cons1581t   cons1502t   cons2t   cons3t   cons48t   cons125t   cons21t   cons4t   cons1582t   cons1512t   cons1583t   cons18t   cons93t   cons166t   cons89t   cons1170t   cons94t   cons165t   cons31t   cons1584t   cons87t   cons1359t   cons23t   cons1255t   cons1258t   cons674t   cons7t   cons27t   cons808t   cons1261t   cons1585t   cons1264t   cons1265t   cons1586t   cons543t   cons43t   cons448t   cons1267t   cons744t   cons1587t   cons1254t   cons62t   cons1423t   cons515t   cons1320t   cons1321t   cons1588t   cons1589t   cons1590t   cons1330t   cons111t   cons155t   cons1591t   cons1519t   cons1336t   cons1592t   cons463t   cons85t   cons1593t   cons77t   cons168t   cons272t   cons1333t   cons1594t   cons1334t   cons1595t   cons1325t   cons1596t   cons1597t   cons1598t   cons1599t   cons1553t   cons1600t   cons1357t   cons1601t   cons1602t   cons1603t   cons1604t   cons17t   cons208t   cons5t   cons1274t   cons1605t   cons1606t   cons1308t   cons147t   cons1228t   cons1507t   cons148t   cons1515t   cons1607t   cons196t   cons1311t   cons1608t   cons1609t   cons1580t   cons70t   cons1610t   cons1611t   cons79t   cons1612t   cons1613t   cons1304t   cons71t   cons1412t   cons1409t   cons1323t   cons1322t   cons1614t   cons80t   cons1360t   cons1421t   cons1315t   cons1231t   cons1615t   cons1314t   cons1266t   cons1616t   cons150t   cons1617t   cons1618t   cons1619t   cons1620t   cons1621t   cons38t   cons1622t   cons1415t   cons380t   cons1428t   cons34t   cons35t   cons1245t   cons1569t   cons1623t   cons1624t   cons1625t   cons1626t   cons1627t   cons32t   cons1549t   cons1628t   cons1629t   cons346t   cons88t   cons1327t   cons1630t   cons1631t   cons1256t   cons1632t   cons375t   cons33t   cons36t   cons1433t   cons1633t   cons1634t   cons1431t   cons1635t   cons1636t   cons1637t   cons1638t   cons1639t   cons1640t   cons683t   cons1641t   cons1642t   cons1643t   cons1454t   cons1478t   cons54t   cons1480t   cons1479t   cons1481t   cons376t   cons46t   cons45t   cons226t   cons1644t   cons528t   cons810t   cons811t   cons1573t   cons1495t   cons68t   cons69t   cons823t   cons824t   cons1574t   cons1576t   cons1497t   cons1577t   cons1645t   ai   t   ft   ei    t   bc            sx     j  d  t | | | t | | |  |  t d  | t | | |  | t d  | | t d  |  S(   NiM  i(   t   appendR  R  R  R  (   t   mR  R  R  t   nt   xR  (   t   rubi(    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3917   s    R  R  c      
      s     j  d  t t d  | t t | |  | t d  t d  |  t d  | t d  t d  |  | t | | |   |  S(   NiN  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3918   s    c      
      s     j  d  t | | t d  | t t | | |  | t d  | t d  t d  | t d  t d  d |  | t d  t | | |   |  S(   NiO  i   ii   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3919   s    c      
      s     j  d  t | | t d  | t t | | |  | t d  | t d  t d  | t d  t d  d |  | t d  t | | |   |  S(   NiP  i   ii   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3920   s    c      	      s	    j  d  t | t d  | t d  | t d  |  t d  t | t | | |  |  t d  | t | | |  | t d  |  |  t | | t | | |  |  t d  | t | | |  | t d  | | |  t d  |  S(   NiQ  i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3921   s    c      	      s	    j  d  t | t d  |  t d  | t d  | t d  t | t | | |  |  t d  | t | | |  | t d  |  |  t | | t | | |  |  t d  | t | | |  | t d  | | | t d  |  S(   NiR  i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3922   s    c      	      s     j  d  t | t d  |  | t d  |  t d  t | t | | |  |  t d  | t | | |  | |  |  t | | | t | | |  |  t d  | t | | |  | t d  | |  t d  |  S(   NiS  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3923   s    c      	      s     j  d  t | t d  |  | t d  | t d  t | t | | |  |  | t | | |  | t d  |  |  t | | | t | | |  |  t d  | t | | |  | t d  | | t d  |  S(   NiT  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3924   s    c      	      s     j  d  t |  t d  | t d  |  | t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  t d  | t | | |  | t d  | | |  | |  S(   NiU  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3925   s    c      	      s     j  d  t | t d  | t d  |  | t | t | | |  |  | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3926   s    c            s     j  d  t | t | | |  |  | t | | |  | t | | |  | t t | | |  | |  |  S(   NiW  (   R  R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3927   s    c      	      s     j  d  t | t | | |  |  | t | | |  |  | t | | |  | | t | | |  | t | t | | |  |  | t | | |  | |  |  S(   NiX  (   R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3928   s    t   dt   cc      	      s     j  d  t t d  |  t t t | t d  t d  | t d  t d  |  |  | t | |  |   |  S(   NiY  i   i   i(   R  R  R  R*   R   R   R  (   R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3929   s    c      
      s     j  d  t t d  |  t t t | t d  t d  | t d  t d  |  |  | t d  t | |  |   |  S(   NiZ  i   i   i(   R  R  R  R*   R   R   R  (   R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3930   s    c            s     j  d  t |  t d  | t d  | t d  t |  t | | |  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3931   s    c            s     j  d  t |  t d  | t d  | t d  t |  t | | |  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3932   s    c            s     j  d  t | t d  |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3933   s    c            s     j  d  t | t d  |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3934   s    c            s2     j  d  t t t | |  |   |  |  S(   Ni_  (   R  R  R  R  (   R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3935   s    c            s3     j  d  t t t | |  |   |  |  S(   Ni`  (   R  R  R  R  (   R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3936   s    c            se     j  d  t |  t | | |  | t | | |  | t t | | |  | |  |  S(   Nia  (   R  R  R  R   (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3937   s    c            se     j  d  t |  t | | |  | t | | |  | t t | | |  | |  |  S(   Nib  (   R  R  R  R   (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3938   s    c            s     j  d  t t | | |  |  | t d  |  t | | |  | t d  t t | | |  |  | |  |  S(   Nic  i(   R  R  R  R  R   (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3939   s    c            s     j  d  t t | | |  |  | t d  |  t | | |  | t d  t t | | |  |  | |  |  S(   Nid  i(   R  R  R  R  R   (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3940  s    i   c      	      s     j  d  t |  t d  t t | | |  t d  |  |  t t d  | |  t t d  t | | |  |  |  t | t d  | |  S(   Nie  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3941  s    c      	      s     j  d  t |  t d  t t | | |  t d  |  |  t t d  | |  t t d  t | | |  |  |  t | t d  | |  S(   Nif  i   ii   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3942  s    c            s     j  d  t t d  |  | t t t d  | | t d  |  | |  t | | |  t | |  t | | |    |  S(   Nig  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3943  s    c            s     j  d  t t d  |  | t t t d  | | t d  |  | |  t | |  t | | |   t | | |   |  S(   Nih  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3944  s    c      
      s     j  d  t | | t d  t | |  t | | |  | t d  | | t d  |  t d  | t d  t | | |  |  |  t |  t d  | |  t | | |  | t d  t | | |  | | t d  |  S(   Nii  iii   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3945  s    c      
      s     j  d  t | | t d  t | |  t | | |  | t d  | | t d  |  t d  | t d  t | | |  |  |  t |  t d  | |  t | | |  | t d  | | t d  t | | |  |  S(   Nij  iii   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3946   s    c            s     j  d  t t d  | t t | |  t | | |   |  |  t |  | t t d  t | |  t | | |   t | | |  |  |  S(   Nik  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3947%  s    c            s     j  d  t t d  | t t | |  t | | |   |  |  t |  | t t d  t | |  t | | |   t | | |  |  |  S(   Nil  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3948*  s    c      
      s    j  d  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  |  S(   Nim  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3949/  s    c      
      s    j  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 | | |  |  S(   Nin  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement39504  s    c      
      s    j  d  t | | t | | |  | t t d  t d  t | | |   t t d  t d  t | | |   t t t d  |  | | | t d  d | t t d  |  | |  |  | t d  t | | |   |  S(   Nio  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement39519  s    c      
      s     j  d  t | | | t t d  t d  t | | |   t t d  t d  t | | |   t | | |  t t t d  |  | | | t d  d | t t d  |  | |  |  | t d  t | | |   |  S(   Nip  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3952>  s    c      
      s     j  d  t | t |  t d  |  | t | | |  t |  | |  t | | |  t |  t t d  |  | t | | |  | |  |  S(   Niq  i   (   R  R  R$   R  R  R%   R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3953C  s    c      
      s     j  d  t | t |  t d  |  | t | | |  t |  | |  t | | |  t |  t t d  |  | t | | |  | |  |  S(   Nir  i   (   R  R  R$   R  R  R%   R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3954H  s    c            sZ    j  d  t t d  t |  t d  t d  t | | |  | |  t | | |   t |  t d  t d  t | | |  | |  t | | |   | |  t | | |  t | | |  t t | |  t d   t | |  t | | |    | |  | |   | t | |  t d   t | | |  |  S(   Nis  i   i   (	   R  R  R  R  R  R:   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3955M  s    c            sY    j  d  t t d  t |  t d  t d  t | | |  | |  t | | |   t |  t d  t d  t | | |  | |  t | | |   | |  t | | |  t | | |  t t | |  t d   t | |  t | | |    | |  | |   t | | |  | t | |  t d   |  S(   Nit  i   i   (	   R  R  R  R  R  R:   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3956R  s    i   c            s     j  d  t |  t d  t t d  t d  t | | |  t | |  t | | |   t | | |  |  |  t | t d  |  t d  | |  t | | |  t | |  t | | |   |  S(   Niu  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3957W  s    c            s     j  d  t |  t d  t t d  t d  t | | |  t | |  t | | |   t | | |  |  |  t | t d  |  t d  | |  t | | |  t | |  t | | |   |  S(   Niv  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3958\  s    c            s    j  d  t t d  | t d  t | |  t | | |  | t d  t | t d  | t d  | |  t d  t d  | t d  t | | |  t d  |  t d  | t d  | t d  |  t d  | t d  t | | |  |  |  |  t |  t d  | |  t | | |  | t d  t | | |  | | t d  |  S(	   Niw  i   iii   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3959a  s    c            s    j  d  t t d  | t d  t | |  t | | |  | t d  t | t d  | t d  | |  t d  t d  | t d  t | | |  t d  |  t d  | t d  | t d  |  t d  | t d  t | | |  |  |  |  t |  t d  | |  t | | |  | t d  | | t d  t | | |  |  S(	   Nix  i   iii   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3960f  s    c      	      sl     j  d  t t d  | t t d  | t | | |  |  t d  |  |  t | | |  S(   Niy  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3961k  s    c      	      sl     j  d  t t d  | t t d  | t | | |  |  t d  |  |  t | | |  S(   Niz  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3962p  s    c            s     j  d  t t d  t |  t d  t d  t | | |  | |   t |  t d  t d  t | | |  | |   t | |  | t t | |  t | | |   t | |  t d    | |  | |   t | |  t d   | | t | | |  |  S(   Ni{  i   i   (	   R  R  R  R  R  R:   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3963u  s    c            s    j  d  t t d  t |  t d  t d  t | | |  | |   t |  t d  t d  t | | |  | |   t | |  | t t | |  t | | |   t | |  t d    | |  | |   t | |  t d   t | | |  | | |  S(   Ni|  i   i   (	   R  R  R  R  R  R:   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3964z  s    c            s    j  d  t t d  | | t d  |  t d  | t d  t | |  t | | |  | t d  t | |  | t d  t | | |  |  t d  | t d  t | | |  t d  | t d  |  t d  | t d  |  |  |  t |  t d  | |  t | | |  | t d  t | | |  | | | t d  |  t d  | t d  |  S(   Ni}  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3965  s    c            s    j  d  t t d  | | t d  |  t d  | t d  t | |  t | | |  | t d  t | |  | t d  t | | |  |  t d  | t d  t | | |  t d  | t d  |  t d  | t d  |  |  |  t |  t d  | |  t | | |  | t d  | | | t d  |  t d  | t d  t | | |  |  S(   Ni~  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3966  s    c            s4     j  d  t | |  t | | |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3967  s    c            s4     j  d  t | |  t | | |  | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3968  s    c      	      sy     j  d  t | t | t | |  |  | |  |  t | | t | t | |  |  | t d  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3969  s    c      	      sy     j  d  t | t | t | |  |  | |  |  t | | t | t | |  |  | t d  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3970  s    c      	      s     j  d  t t d  | | | t | t | |  |  | t d  |  |  t | t | |  |  | | t d  | t d  t | |  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3971  s    c      	      s     j  d  t t d  | | | t | t | |  |  | t d  |  |  t | t | |  |  | | t d  | t d  t | |  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3972  s    c            s     j  d  t t d  | t t d  t | |  |  |  |  t | | t t d  | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3973  s    c            s     j  d  t t d  | t t d  t | |  |  |  |  t | | t t d  | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3974  s    c      
      s     j  d  t | | t t d  | | t | |  |  t | |  |  t d  |  |  t t | |  |  | |  |  S(   Ni  i   i   (   R  R  R   R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3975  s    c      
      s     j  d  t | | t t d  | | t | |  |  t | |  |  t d  |  |  t t d  | |  t | |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3976  s    c      	      sW     j  d  t t | t | | |  | | | t | | |  |  |  |  S(   Ni  (   R  R   RH  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3977  s    c      	      sW     j  d  t t | t | | |  | | | t | | |  |  |  |  S(   Ni  (   R  R   RH  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3978  s    c      
      sZ     j  d  t t d  | t | |  |  |  t | | t | |  |   |  S(   Ni  i   (   R  R  R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3979  s    c      
      s[     j  d  t t d  | |  t | | t | |  |   t | |  |  |  S(   Ni  i   (   R  R  R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3980  s    c      	      s     j  d  t | t d  |  t d  |  t | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3981  s    c      	      s     j  d  t | t d  |  t d  |  t | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3982  s    c            sF     j  d  t t | |  |  |  | t | |  |  | |  S(   Ni  (   R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3983  s    c            sQ     j  d  t t d  |  | t | |  |  | t | |  |  |  S(   Ni  i   (   R  R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3984  s    c            s     j  d  t t d  |  t t t d  t d  | | t d  |  | | t | |  |  t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3985  s    c            s     j  d  t t d  |  t t t d  t d  | | t d  |  | | t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3986  s    c      	      s     j  d  t |  t d  | t d  |  t d  t | | t | | |  |  t d  t | | |  |  |  t | | | t | | |  |  t | | |  | | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3987  s    c      	      s     j  d  t |  t d  | t d  |  t d  t | | t | | |  |  t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3988  s    c      	      s     j  d  t |  | t d  |  t d  t | | t | | |  |  t d  t | | |  |  |  t | | t | | |  |  t | | |  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3989  s    c      	      s     j  d  t |  | t d  |  t d  t | | t | | |  |  t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3990  s    c      	      s     j  d  t | |  | |  t d  t | | t | | |  |  t | | |  |  |  t | | t | | |  |  t | | |  | |  t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3991  s    c      	      s     j  d  t | |  | |  t d  t | | t | | |  |  t | | |  |  |  t | | t | | |  |  | |  t d  t | | |  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3992  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 | | | t | | |  |  t | | |  | | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3993  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 | | | t | | |  |  | | t d  |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3994  s    c      	      s     j  d  t t d  | |  t d  t | | t | | |  |  | t | | |  | |  t d  t | | |  |  |  t | | t | | |  |  t d  t | | |  | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3995  s    c      	      s     j  d  t t d  | |  t d  t | | t | | |  |  | t | | |  | |  t d  t | | |  |  |  t | | t | | |  |  t d  | | |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3996  s    c            s     j  d  t t d  | t | | |  | |  t t t d  t t d  | t d  |  |  | | t | |  |  t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3997  s    c            s     j  d  t t d  | t | | |  | |  t t t d  t t d  | t d  |  |  | | t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3998$  s    c            s     j  d  t t d  | | |  t t t d  | | | t d  |  | | t | |  |  t | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement3999)  s    c            s     j  d  t t d  | | |  t t t d  | | | t d  |  | | t | t | |  |   t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4000.  s    c            s+    j  d  t t d  | | | t d  | t d  | t d  t | t | |  |  | t d  t | | t | |  |   |  |  t t d  | | | t | |  |  | t d  t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement40013  s    c            s,    j  d  t t d  | | | t d  | t d  | t d  t | t | |  |  | t d  t | | t | |  |   |  |  t t d  | | | t | |  |  | t d  |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement40028  s    c      
      sv     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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4003=  s    c      
      sw     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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4004B  s    c            s     j  d  t | t d  | t d  t d  | | | t | t | |  |  | t d  t | | t | |  |   |  |  t | | t | |  |  | t | |  |  |  | t | | t | |  |   |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4005G  s    c            s     j  d  t | t d  | t d  t d  | | | t | t | |  |  | t d  t | | t | |  |   |  |  t | | t | |  |  | |  | t | | t | |  |   t | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4006L  s    c      
      s     j  d  t | t d  | t | |  |  |  t | | t | |  |   t | | t | |  |   t t | | | t d  t | | |  |  | t d  t | |  |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4007Q  s    c      
      s     j  d  t | t d  | |  t | | t | |  |   t | | t | |  |   t | |  |  t t | | | t d  t | | |  |  | t d  t | |  |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4008V  s    c            s     j  d  t t t d   t |  | |  t t t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4009[  s    c            s     j  d  t t t d   t |  | |  t t t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4010`  s    c            s     j  d  t t d  | | | |  t t t d  t d  | | | t d  |  | | t | |  |  t | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4011e  s    c            s     j  d  t t d  | | | |  t t t d  t d  | | | t d  |  | | t | t | |  |   t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4012j  s    c      
      s     j  d  t | t d  |  t d  | |  t | t | | |  | t d  | | t | | |  |  t d  |  |  t | | t | | |  | | | t | | |  |  t d  t | | |  | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4013o  s    c      
      s     j  d  t | t d  |  t d  | |  t | t | | |  | t d  | | t | | |  |  t d  |  |  t | | t | | |  | | | t | | |  |  t d  | |  t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4014t  s    c      
      s    j  d  t | |  t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  |  |  t | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4015y  s    c      
      s    j  d  t | |  t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  |  |  t | | | t | | |  | t d  | | t | | |  |  | | t d  |  t d  t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4016~  s    c      
      s     j  d  t |  | t d  |  t d  t | t | | |  | | | t | | |  |  t d  |  |  t | t | | |  | | | t | | |  |  t | | |  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4017  s    c      
      s     j  d  t |  | t d  |  t d  t | t | | |  | | | t | | |  |  t d  |  |  t | t | | |  | | | t | | |  |  | t d  |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4018  s    c      
      s     j  d  t | |  | | |  t d  t | t | | |  | t d  | | t | | |  |  |  |  t | t | | |  | | | t | | |  |  t | | |  | |  t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4019  s    c      
      s     j  d  t | |  | | |  t d  t | 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4020  s    c      
      s=    j  d  t | | | t | t | | |  | t d  | | t | | |  |  t d  | |  t d  | t d  t | | |  | |  t d  | t d  |  |  t | t d  | t | | |  | | | t | | |  |  t d  t | | |  | | |  S(   Ni  i   ii   i(   R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4021  s    c      
      s=    j  d  t | | | t | t | | |  | t d  | | t | | |  |  t d  | |  t d  | t d  t | | |  | |  t d  | t d  |  |  t | t d  | t | | |  | | | t | | |  |  t d  | | t | | |  |  S(   Ni  i   ii   i(   R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4022  s    c      
      sS    j  d  t | |  | t d  t | t | | |  | | | t | | |  |  t d  | t d  |  t d  | t d  t | | |  | |  t d  | t d  |  |  t | t d  | t | | |  | | | t | | |  |  t d  t | | |  | |  | t d  |  S(   Ni  iii   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4023  s    c      
      sS    j  d  t | |  | t d  t | t | | |  | | | t | | |  |  t d  | t d  |  t d  | t d  t | | |  | |  t d  | t d  |  |  t | t d  | t | | |  | | | t | | |  |  t d  | |  | t d  t | | |  |  S(   Ni  iii   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4024  s    c      
      sD    j  d  t | | | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  | | t d  | |  | t | | |  |  |  t | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4025  s    c      
      sD    j  d  t | | | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  | | t d  | |  | t | | |  |  |  t | | | t | | |  | t d  | | t | | |  |  | | t d  |  t d  t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4026  s    c      
      sY    j  d  t | t d  | | t d  |  t d  t | t | | |  | 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   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4027  s    c      
      sY    j  d  t | t d  | | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  | |  | t d  t | | |  | | t d  |  |  t | t d  | t | | |  | t d  | | t | | |  |  | t d  |  t d  t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4028  s    c      
      sG    j  d  t t d  | t d  t d  |  t d  t | t | | |  | | | t | | |  |  t d  | t d  |  | t d  | |  | t d  t | | |  |  |  t | t | | |  | | | t | | |  |  t | | |  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4029  s    c      
      sG    j  d  t t d  | t d  t d  |  t d  t | t | | |  | | | t | | |  |  t d  | t d  |  | t d  | |  | t 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4030  s    c      
      s     j  d  t | t d  | | t | t | |  |  | t d  | | t d  t | |  |  | | t d  |  |  t | t d  | t | |  |  | t d  t | |  |  |  | | t | |  |  |  S(   Ni  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4031  s    c      
      s     j  d  t | t d  | | t | t | |  |  | t d  | | t d  t | |  |  | | t d  |  |  t | t d  | t | |  |  | t d  |  | | t | |  |  t | |  |  |  S(   Ni  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4032  s    c      
      s     j  d  t | t d  t | t | |  |  | | | t d  | | t | |  |  |  |  t | t | |  |  | t | |  |  |  | | t | |  |  |  S(   Ni  ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4033  s    c      
      s     j  d  t | t d  t | t | |  |  | | | t d  | | t | |  |  |  |  t | t | |  |  | |  | | t | |  |  t | |  |  |  S(   Ni  ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4034  s    c      
      s     j  d  t | | t d  | | t | t | |  |  | t d  | | t | |  |  |  |  t | | | t | |  |  | t d  t | |  |  | |  | | t | |  |  |  S(   Ni  i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4035  s    c      
      s     j  d  t | | t d  | | t | t | |  |  | t d  | | t | |  |  |  |  t | | | t | |  |  | t d  | |  | | t | |  |  t | |  |  |  S(   Ni  i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4036  s    c            s     j  d  t | | t t | t | |  |   t | | t | |  |   |  |  t | | | t t | t | |  |   t | | t | |  |   |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4037  s    c            s     j  d  t | | t t | t | |  |   t | | t | |  |   |  |  t | | | t t | t | |  |   t | | t | |  |   |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4038  s    c            sR    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  | t | |  |  t d  | | t d  t | | t | |  |   |  |  t t d  | t d  | t | |  |  | t d  t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4039  s    c            sS    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  | t | |  |  t d  | | t d  t | | t | |  |   |  |  t t d  | t d  | t | |  |  | t d  |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Ni  i   ii(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4040  s    c            s    j  d  t t d  t d  | | | t | t | |  |  | t d  | | t d  | t d  t | |  |  t | | t | |  |   |  |  t | t | |  |  | t | |  |  |  | t | | t | |  |   |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4041  s    c            s    j  d  t t d  t d  | | | t | t | |  |  | t d  | | t d  | t d  t | |  |  t | | t | |  |   |  |  t | t | |  |  | |  | t | | t | |  |   t | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4042   s    c      
      s1    j  d  t | t d  | |  | t d  t | t | | |  | t d  | | t | | |  |  | |  t | | |  | | t d  |  |  t | t d  | t | | |  | t d  | | t | | |  |  t | | |  | |  | t d  |  S(   Ni  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4043  s    c      
      s1    j  d  t | t d  | |  | t d  t | t | | |  | t d  | | t | | |  |  | |  t | | |  | | t d  |  |  t | t d  | t | | |  | t d  | | t | | |  |  | |  | t d  t | | |  |  S(   Ni  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4044
  s    c            s     j  d  t | | t d  | | | | t | | |  | t | | t | | |   t | | t | | |   t t | | | t d  t d  | | |  t d  d t |  |  | | | t | | |   |  S(   Ni  i   i(   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4045  s    c            s     j  d  t | | t d  | | | | | t | | t | | |   t | | t | | |   t | | |  t t | | | t d  t d  | | |  t d  d t |  |  | | | t | | |   |  S(   Ni  i   i(   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4046  s    c            s     j  d  t | | t d  | | | | t | | |  | t | | t | | |   t | | t | | |   t t | |  t d  d | | | t d  t t d  | |  |  | | | t | | |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4047  s    c            s     j  d  t | | t d  | | | | | t | | t | | |   t | | t | | |   t | | |  t t | |  t d  d | | | t d  t t d  | |  |  | | | t | | |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4048  s    c      
      s     j  d  t | t d  | t | | |  | t | | t | | |   t | | t | | |   t t | | | t d  | | | |  t d  d t | | |  |  | t d  t | | |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4049#  s    c      
      s     j  d  t | t d  | | t | | t | | |   t | | t | | |   t | | |  t t | | | t d  | | | |  t d  d t | | |  |  | t d  t | | |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4050(  s    c            s     j  d  t | t |   t d  | | t | | |  t |   | | t | | |  t |   t | t | | |  | t d  | | t | | |  |  |  |  S(   Ni  i   (   R  R  R$   R  R  R%   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4051-  s    c            s     j  d  t | t |   t d  | | t | | |  t |   | | t | | |  t |   t | t | | |  | t d  | | t | | |  |  |  |  S(   Ni  i   (   R  R  R$   R  R  R%   R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement40522  s    c            s     j  d  t | t t d  t d  t | |  |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement40537  s    c            s     j  d  t | t t d  t d  t | |  |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4054<  s    c      
      s    j  d  t t d  |  t | | t | | |  |  t d  | t d  |  | | t d  |  t d  t | | |  | t d  |  t d  t | | |  |  |  t | | | t | | |  |  t d  t | | |  | |  |  S(   Ni  i   ii   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4055A  s    c      
      s    j  d  t t d  |  t | | t | | |  |  t d  | t d  |  | | t d  |  t d  t | | |  | t d  |  t d  t | | |  |  |  t | | | t | | |  |  t d  | |  t | | |  |  S(   Ni  i   ii   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4056F  s    c      	      sZ     j  d  t t d  | t t d  | t | |  |  | t d  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4057K  s    c      	      sZ     j  d  t t d  | t t d  | t | |  |  | t d  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4058P  s    c            s    j  d  t t d  t | t d  t d  t | |  |  | |  t | t d  t d  t | |  |  | |  t t t | | t | |  |   t | | t d    | | | |  t | | t d   | |  t | |  |  |  S(   Ni  i   i   (	   R  R  R  R  R  R<   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4059U  s    c            s    j  d  t t d  t | t d  t d  t | |  |  | |  t | t d  t d  t | |  |  | |  t t t | | t | |  |   t | | t d    | | | |  t | | t d   t | |  |  | |  |  S(   Ni  i   i   (	   R  R  R  R  R  R<   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4060Z  s    c      
      s7    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | |  t d  | |  t d  t | | |  t | | |  |  |  t | | | t | | |  |  t d  t | | |  | | t d  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4061_  s    c      
      s7    j  d  t t d  | t d  | 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 | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4062d  s    c      
      s     j  d  t t | | |  | t t d  t d  t | | |   t t d  t d  t | | |   t t | | | |  t | t d   t | t d   |  | t d  t | | |   |  S(   Ni  i   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4063i  s    c      
      s     j  d  t t d  | t t d  t d  t | | |   t t d  t d  t | | |   t | | |  t t | | | |  t | t d   t | t d   |  | t d  t | | |   |  S(   Ni  i   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4064n  s    c      	      s     j  d  t |  |  t d  t | | t | | |  |  t d  | t | | |  | t | | |  |  |  t | | t | | |  |  t | | |  | |  t d  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4065s  s    c      	      s     j  d  t |  |  t d  t | | t | | |  |  t d  | t | | |  | t | | |  |  |  t | | t | | |  |  | |  t d  t | | |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4066x  s    c      	      s9    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | |  t d  t | | |  | |  t d  t | | |  |  |  t | | | t | | |  |  t d  t | | |  | | t d  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4067}  s    c      	      s9    j  d  t t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | |  t d  t | | |  | |  t d  t | | |  |  |  t | | | t | | |  |  t d  | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4068  s    c      
      s     j  d  t t d  t | | t | |  |   t | |  |  |  t t d  t d  t | |  |  t | | t | |  |   t | |  |  |  S(   Ni  i   (   R  R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4069  s    c      
      s     j  d  t t d  t | | t | |  |   t | |  |  |  t t d  t d  t | |  |  t | | t | |  |   t | |  |  |  S(   Ni  i   (   R  R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4070  s    c      
      s     j  d  t t d  | t | | t | | |  |  t d  t | | |  |  |  t | | t | | t | | |  |  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4071  s    c      
      s     j  d  t t d  | t | | t | | |  |  t d  t | | |  |  |  t | | t | | t | | |  |  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4072  s    c            sn    j  d  t t d  | | t d  | t d  |  t d  t | | t | | |  |  t d  t | | |  t d  | t d  | t d  |  t d  t | | |  |  t | | |  |  |  t | t d  | | t | | |  |  t d  t | | |  | | | t d  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4073  s    c            sn    j  d  t t d  | | t d  | t d  |  t d  t | | t | | |  |  t d  t | | |  t d  | t d  | t d  |  t d  t | | |  |  t | | |  |  |  t | t d  | | t | | |  |  t d  | | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4074  s    c      	      s     j  d  t t d  | |  t d  t | | t | | |  |  | t | | |  | |  t d  t | | |  |  |  t | | t | | |  |  t d  t | | |  | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4075  s    c      	      s     j  d  t t d  | |  t d  t | | t | | |  |  | t | | |  | |  t d  t | | |  |  |  t | | t | | |  |  t d  | | |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4076  s    c            s    j  d  t t d  | | t | t | | |  | t d  | | t | | |  |  t d  t | t d  | |  t d  | t d  | | t d  | t d  t d  | t d  | t | | |  | | t d  |  | t d  | t d  | t | | |  t d  |  |  |  t | t d  | t | | |  | | | t | | |  |  t d  t | | |  | | |  S(   Ni  i   ii   ii   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4077  s    c            s    j  d  t t d  | | t | t | | |  | t d  | | t | | |  |  t d  t | t d  | |  t d  | t d  | | t d  | t d  t d  | t d  | t | | |  | | t d  |  | t d  | t d  | t | | |  t d  |  |  |  t | t d  | t | | |  | | | t | | |  |  t d  | | t | | |  |  S(   Ni  i   ii   ii   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4078  s    c            s    j  d  t t d  | |  | t d  t | t | | |  | | | t | | |  |  t d  t | t d  | |  | t d  | | t d  | | | | t d  | t d  |  t d  | t d  t | | |  t d  | t d  | t d  | |  | t d  | t d  | |  | t d  t | | |  |  |  |  t | t d  | t | | |  | | | t | | |  |  t d  t | | |  | |  | t d  |  S(	   Ni  i   iii   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4079  s    c            s    j  d  t t d  | |  | t d  t | t | | |  | | | t | | |  |  t d  t | t d  | |  | t d  | | t d  | | | | t d  | t d  |  t d  | t d  t | | |  t d  | t d  | t d  | |  | t d  | t d  | |  | t d  t | | |  |  |  |  t | t d  | t | | |  | | | t | | |  |  t d  | |  | t d  t | | |  |  S(	   Ni  i   iii   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4080  s    c            s    j  d  t t d  | t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  t | | |  t d  t | | |  | | | t d  | | |  | t d  t | | |  t d  |  |  |  t | | | t | | |  | t 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  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4081  s    c            s    j  d  t t d  | t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  t | | |  t d  t | | |  | | | t d  | | |  | t d  t | | |  t d  |  |  |  t | | | t | | |  | t d  | | t | | |  |  t d  | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4082  s    c      
      s    j  d  t | t d  | t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  | |  | t | | |  t d  | | t d  | |  t d  t | | |  |  |  t | | t d  | t | | |  | t 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  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4083  s    c      
      s    j  d  t | t d  | t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  | |  | t | | |  t d  | | t d  | |  t d  t | | |  |  |  t | | t d  | t | | |  | t d  | | t | | |  |  t d  | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4084  s    c            s    j  d  t | t d  | | t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  t | t d  | t d  | | |  t d  t | | |  | t d  | t d  | t d  |  t d  t | | |  t d  |  |  |  t | t d  | t d  | t | | |  | t d  | | t | | |  |  t d  t | | |  | | | t d  | t d  |  t d  |  S(   Ni  i   i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4085  s    c            s    j  d  t | t d  | | t d  | t d  |  t d  t | t | | |  | t d  | | t | | |  |  t d  t | t d  | t d  | | |  t d  t | | |  | t d  | t d  | t d  |  t d  t | | |  t d  |  |  |  t | t d  | t d  | t | | |  | t d  | | t | | |  |  t d  | | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4086  s    c            sV    j  d  t t d  | | | t | t | | |  | t d  | | t | | |  |  t | | t d  t | | |  | |  | t d  | |  | 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4087  s    c            sV    j  d  t t d  | | | t | t | | |  | t d  | | t | | |  |  t | | t d  t | | |  | |  | t d  | |  | 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4088  s    c      
      s    j  d  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 d  t | | |  t d  |  |  t | t d  | t | | |  | | | t | | |  |  t d  t | | |  | | | t d  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4089  s    c      
      s    j  d  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 d  t | | |  t d  |  |  t | t d  | t | | |  | | | t | | |  |  t d  | | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4090  s    c      	      s     j  d  t t | t | |  |   t | t | |  |   | t t | t | |  |   | t | |  |  | |  |  S(   Ni  (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4091  s    c      	      s     j  d  t t | t | |  |   t | t | |  |   | t t | t | |  |   | t | |  |  | |  |  S(   Ni  (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4092  s    c      
      s     j  d  t | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4093  s    c      
      s     j  d  t | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4094  s    i   c            s     j  d  t | | t | t | |  |  t d  d |  |  t | | | t | t | |  |  t d  d | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4095	  s    c            s     j  d  t | | t | t | |  |  t d  d |  |  t | | | t | t | |  |  t d  d | | t | |  |  |  |  S(   Ni   i   i   (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4096  s    c            sL    j  d  t | t d  | | t d  t | t | |  |  | t d  t | | t d  | | t d  t | |  |  t d  | | t d  t | |  |  |  | | t | |  |  |  |  t | t d  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4097  s    c            sL    j  d  t | t d  | | t d  t | t | |  |  | t d  t | | t d  | | t d  t | |  |  t d  | | t d  t | |  |  |  | | t | |  |  |  |  t | t d  | t | |  |  | t d  | |  | t d  t | |  |  |  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4098  s    c            s     j  d  t | t d  t | | t | |  |  t | t | |  |   |  |  t | t d  | t d  | t d  t | t | |  |  t d  d | | t | |  |  |  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4099  s    c            s     j  d  t | t d  t | | t | |  |  t | t | |  |   |  |  t | t d  | t d  | t d  t | t | |  |  t d  d | | t | |  |  |  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4100"  s    c            s    j  d  t t d  | | | t | t | |  |  | t d  t | | t d  t | |  |  | | | | t d  t | |  |  t d  |  | | t | |  |  |  |  t | t | |  |  | t | |  |  | |  | |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4101'  s    c            s    j  d  t t d  | | | t | t | |  |  | t d  t | | t d  t | |  |  | | | | t d  t | |  |  t d  |  | | t | |  |  |  |  t | t | |  |  | | |  | t | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4102,  s    c            s     j  d  t | t t | t | |  |   t | | t | |  |   |  |  t | | t | t | |  |  t d  d t | | t | |  |   |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement41031  s    c            s     j  d  t | t t | t | |  |   t | | t | |  |   |  |  t | | t | t | |  |  t d  d t | | t | |  |   |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement41046  s    c            s    j  d  t | t d  t d  | t d  t | t | |  |  | t d  t t d  | | t d  | t | |  |  t d  | t d  | t d  t | |  |  |  t | | t | |  |   |  |  t t d  | | t | |  |  | t d  t | | t | |  |   t | |  |  |  t d  | t d  |  S(   Ni	  i   iii(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4105;  s    c            s    j  d  t | t d  t d  | t d  t | t | |  |  | t d  t t d  | | t d  | t | |  |  t d  | t d  | t d  t | |  |  |  t | | t | |  |   |  |  t t d  | | t | |  |  | t d  t | | t | |  |   t | |  |  |  t d  | t d  |  S(   Ni
  i   iii(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4106@  s    c      	      s     j  d  t t | | t | |  |   t | t | |  |   t | t | |  |  |  t t | t | |  |  |  |  |  S(   Ni  (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4107E  s    c      	      s     j  d  t t | | t | |  |   t | t | |  |   t | t | |  |  |  t t | t | |  |  |  |  |  S(   Ni  (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4108J  s    c            sP    j  d  t t d  t d  | | t | t | |  |  | t d  t t d  | | t d  t | |  |  | t d  | t d  t | |  |  t d  | |  t | | t | |  |   |  |  t | t | |  |  | t | | t | |  |   t | |  |  |  | |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4109O  s    c            sP    j  d  t t d  t d  | | t | t | |  |  | t d  t t d  | | t d  t | |  |  | t d  | t d  t | |  |  t d  | |  t | | t | |  |   |  |  t | t | |  |  | t | | t | |  |   |  | t | |  |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4110T  s    c      
      s     j  d  t t | t | |  |   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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4111Y  s    c      
      s     j  d  t t | t | |  |   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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4112^  s    c      
      s     j  d  t | t | t | |  |   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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4113c  s    c      
      s     j  d  t | t | t | |  |   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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4114h  s    c            s    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  t t d  | | t d  t d  | | t d  t | |  |  t d  | t d  | t d  t | |  |  |  t | | t | |  |   |  |  t t d  | t d  | t | |  |  | t d  t | | t | |  |   t | |  |  | |  t d  | t d  |  S(   Ni  i   i   iii(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4115m  s    c            s    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  t t d  | | t d  t d  | | t d  t | |  |  t d  | t d  | t d  t | |  |  |  t | | t | |  |   |  |  t t d  | t d  | t | |  |  | t d  t | | t | |  |   t | |  |  | |  t d  | t d  |  S(   Ni  i   i   iii(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4116r  s    c            s     j  d  t | t d  | t t d  t | |  |  t d  t | | t | |  |   |  |  t t | | t | |  |   t | |  |  | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4117w  s    c            s     j  d  t | t d  | t t d  t | |  |  t d  t | | t | |  |   |  |  t t | | t | |  |   t | |  |  | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4118|  s    c            s     j  d  t t d  | t t | | t | |  |   t | t | |  |   |  |  t | | | t t | t | |  |   t | | t | |  |   |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4119  s    c            s     j  d  t t d  | t t | | t | |  |   t | t | |  |   |  |  t | | | t t | t | |  |   t | | t | |  |   |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4120  s    c            s|    j  d  t t d  t d  | | | t | t | |  |  | t d  t t d  | | t d  t | |  |  | t d  | t d  | t d  | t d  t | |  |  t d  |  t | | t | |  |   |  |  t | t | |  |  | t d  t | | t | |  |   t | |  |  | | |  | |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4121  s    c            s|    j  d  t t d  t d  | | | t | t | |  |  | t d  t t d  | | t d  t | |  |  | t d  | t d  | t d  | t d  t | |  |  t d  |  t | | t | |  |   |  |  t | t | |  |  | t d  t | | t | |  |   t | |  |  | | |  | |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4122  s    c            s    j  d  t t d  t d  | | t | t | |  |  | t d  t | | t d  | t d  | | t d  | t d  t | |  |  t d  t d  | t d  | t d  | t d  | t | |  |  |  t | | t | |  |   |  |  t | | t | |  |  | t | | t | |  |   t | |  |  |  | |  S(   Ni  i   i   ii   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4123  s    c            s    j  d  t t d  t d  | | t | t | |  |  | t d  t | | t d  | t d  | | t d  | t d  t | |  |  t d  t d  | t d  | t d  | t d  | t | |  |  |  t | | t | |  |   |  |  t | | t | |  |  | t | | t | |  |   |  | t | |  |  |  S(   Ni  i   i   ii   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4124  s    c            s    j  d  t | t d  | |  | t d  t | t | | |  | t d  | | t | | |  |  t | | t d  | | t d  t | | |  t d  | |  | t d  t | | |  |  |  |  t | t d  | t | | |  | t d  | | t | | |  |  t d  t | | |  | | |  | t d  |  S(   Ni  i   iiii   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4125  s    c            s    j  d  t | t d  | |  | t d  t | t | | |  | t d  | | t | | |  |  t | | t d  | | t d  t | | |  t d  | |  | t d  t | | |  |  |  |  t | t d  | t | | |  | t d  | | t | | |  |  t d  | | |  | t d  t | | |  |  S(   Ni  i   iiii   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4126  s    c            s    j  d  t | |  | t d  t | t | | |  | t d  | | t | | |  |  t d  t | | | t d  | | t d  |  | t d  t | | |  t d  | t d  |  | t d  | t d  |  | t d  t | | |  |  |  |  t | | | t | | |  | t d  | | t | | |  |  t d  t | | |  | |  | t d  |  S(   Ni  iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4127  s    c            s    j  d  t | |  | t d  t | t | | |  | t d  | | t | | |  |  t d  t | | | t d  | | t d  |  | t d  t | | |  t d  | t d  |  | t d  | t d  |  | t d  t | | |  |  |  |  t | | | t | | |  | t d  | | t | | |  |  t d  | |  | t d  t | | |  |  S(   Ni   iii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4128  s    c            s    j  d  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 | | |  | t d  | | t | | |  |  t | | |  | |  | t d  |  S(   Ni!  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4129  s    c            s    j  d  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 | | |  | t d  | | t | | |  |  | |  | t d  t | | |  |  S(   Ni"  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4130  s    c            s     j  d  t | t t | | t | |  |   t | t | |  |   |  |  t | | t t | t | |  |   t | | t | |  |   |  |  S(   Ni#  (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4131  s    c            s     j  d  t | t t | | t | |  |   t | t | |  |   |  |  t | | t t | t | |  |   t | | t | |  |   |  |  S(   Ni$  (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4132  s    c            s     j  d  t | t | t | | |  | | | t | | |  |  t d  |  |  t | | t | t | | |  | t d  | | t | | |  |  t d  |  |  S(   Ni%  ii   (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4133  s    c            s     j  d  t | t | t | | |  | | | t | | |  |  t d  |  |  t | | t | t | | |  | t d  | | t | | |  |  t d  |  |  S(   Ni&  ii   (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4134  s    c            sN     j  d  t | t | | |  | | | t | | |  |  |  S(   Ni'  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4135  s    c            sN     j  d  t | t | | |  | | | t | | |  |  |  S(   Ni(  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4136  s    t   gt   pc            se     j  d  t | t | | |  |  | t | | |  | | t | | |  | |  S(   Ni)  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4137  s    c            se     j  d  t | t | | |  |  | t | | |  | | t | | |  | |  S(   Ni*  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4138  s    c      
      s     j  d  t | |  t d  | t t | |  t d  | | | |  t d  t d  d | | | | |  t d  t d  d |  | t d  t | | |   |  S(   Ni+  i   ii   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4139  s    c      
      s     j  d  t | |  t d  | t t | |  t d  | | | |  t d  t d  d | | | | |  t d  t d  d |  | t d  t | | |   |  S(   Ni,  i   ii   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4140  s    c      
      s     j  d  t t d  | t t | |  t d  | | | | | t d  |  t d  t d  d | t d  |  t d  t d  d |  | t d  t | | |   |  S(   Ni-  i   ii   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4141  s    c      
      s     j  d  t t d  | t t | |  t d  | | | | | t d  |  t d  t d  d | t d  |  t d  t d  d |  | t d  t | | |   |  S(   Ni.  i   ii   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4142  s    c      	      s     j  d  t | |  t | | t | | |  |  t d  t | | |  |  |  t | | t | | |  |  | t | | |  |  S(   Ni/  i(   R  R  R   R  R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4143  s    c      	      s     j  d  t | |  t | | t | | |  |  t d  t | | |  |  |  t | | t | | |  |  t | | |  | |  S(   Ni0  i(   R  R  R   R  R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4144  s    c      	      s     j  d  t | | t | | |  t |  | t | | |  | t |  t | | |  t |  t | t | | |  |  | t | | |  | | t | | |  | |  |  S(   Ni1  (   R  R  R  R%   R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4145  s    c      	      s     j  d  t | | t | | |  t |  | t | | |  | t |  t | | |  t |  t | t | | |  |  | t | | |  | | t | | |  | |  |  S(   Ni2  (   R  R  R  R%   R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4146  s    c            sN     j  d  t | t | | |  |  | | t | | |  | |  S(   Ni3  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4147  s    c            sN     j  d  t | t | | |  |  | | t | | |  | |  S(   Ni4  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4148  s    c      
      s     j  d  t | t | | |  |  | t | | |  |  t | t | | |  |  | | t | | |  | |  |  S(   Ni5  (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4149  s    c      
      s     j  d  t | t | | |  |  | t | | |  |  t | t | | |  |  | | t | | |  | |  |  S(   Ni6  (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4150  s    c      	      s     j  d  t | |  | t d  | | | t t | |  | | | | |  t d  t d  d | | | |  t d  | t d  d |  | t | | |   |  S(   Ni7  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4151!  s    c      	      s     j  d  t | |  | t d  | | | t t | |  | | | | |  t d  t d  d | | | |  t d  | t d  d |  | t | | |   |  S(   Ni8  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4152&  s    c      
      s     j  d  t | |  t d  | t t | | | |  t d  t d  d | | | |  t d  | t d  d | |  | t d  t | | |   |  S(   Ni9  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4153+  s    c      
      s     j  d  t | |  t d  | t t | | | |  t d  t d  d | | | |  t d  | t d  d | |  | t d  t | | |   |  S(   Ni:  i   i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement41540  s    c      
      s     j  d  t | t d  |  t | t | | |  |  t d  | |  | |  t d  t | | |  |  |  t | | t | | |  |  t d  | |  | |  t d  t | | |  | |  |  t d  |  S(   Ni;  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement41555  s    c      
      s     j  d  t | t d  |  t | t | | |  |  t d  | |  | |  t d  t | | |  |  |  t | | t | | |  |  t d  | |  | |  t d  t | | |  | |  |  t d  |  S(   Ni<  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4156:  s    c      
      s     j  d  t t d  | t d  |  t d  t | t | | |  |  t d  | |  t d  | |  t d  t | | |  |  |  t | t | | |  |  t d  | | t | | |  | | |  t d  |  S(   Ni=  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4157?  s    c      
      s     j  d  t t d  | t d  |  t d  t | t | | |  |  t d  | |  t d  | |  t d  t | | |  |  |  t | t | | |  |  t d  | | t | | |  | | |  t d  |  S(   Ni>  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4158D  s    c            sB     j  d  t | t | | |  |  t | | |  |  S(   Ni?  (   R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4159I  s    c            sB     j  d  t | t | | |  |  t | | |  |  S(   Ni@  (   R  R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4160N  s    c      	      s}     j  d  t | t | t | | |  |  |  |  t | t | t | | |  |  t | | |  |  |  S(   NiA  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4161S  s    c      	      s}     j  d  t | t | t | | |  |  |  |  t | t | t | | |  |  t | | |  |  |  S(   NiB  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4162X  s    c      
      s     j  d  t t d  |  t d  t d  d | |  t d  | t t | | | | t d  | t d  |  t d  t d  d | |  | | t | | |   |  S(   NiC  ii   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4163]  s    c      
      s     j  d  t t d  |  t d  t d  d | |  t d  | t t | | | | t d  | t d  |  t d  t d  d | |  | | t | | |   |  S(   NiD  ii   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4164b  s    c      	      sV     j  d  t t | t | | |  |  | | t | | |  | |  |  S(   NiE  (   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4165g  s    c      	      sV     j  d  t t | t | | |  |  | | t | | |  | |  |  S(   NiF  (   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4166l  s    c            s     j  d  t t d  | |  t d  | t d  d | t t | |  | | t d  t d  |  t d  | t d  d | | t d  t d  |  | t | | |  t | | t | | |    |  S(   NiG  i   i   i(   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4167q  s    c            s     j  d  t t d  | |  t d  | t d  d | t t | |  | | t d  t d  |  t d  | t d  d | | t d  t d  |  | t d  t | | t | | |   t | | |   |  S(   NiH  i   i   i(   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4168v  s    c      
      s     j  d  t | t d  | | t d  | t | t | | |  |  t d  | | | t | | |  | |  |  S(   NiI  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4169{  s    c      
      s     j  d  t | t d  | | t d  | t | t | | |  |  t d  | | | t | | |  | |  |  S(   NiJ  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4170  s    c            sn    j  d  t t d  |  | t d  | | | t | | |  |  | t d  | t | | |  |  t d  | | t | | |  | t |  t d  t d  d |  | t d  |  t d  t d  d | | t | | |  | | t | | |  | | t | | |  | | t | | |   | | |  t d  |  S(   NiK  i   i   i   (   R  R  R  R  R  R9   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4171  s    c            so    j  d  t t d  |  | t d  | | | t | | |  |  | t d  | t | | |  |  t d  | | t | | |  | t |  t d  t d  d |  | t d  |  t d  t d  d | | t | | |  | | t | | |  | | t | | |  | | t | | |   | | |  t d  |  S(   NiL  i   i   i   (   R  R  R  R  R  R9   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4172  s    c      
      s     j  d  t t d  | t t | t | | |   |  |  t |  | t t | t | | |   | t | | |  |  |  |  S(   NiM  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4173  s    c      
      s     j  d  t t d  | t t | t | | |   |  |  t |  | t t | t | | |   | t | | |  |  |  |  S(   NiN  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4174  s    c            s     j  d  t | t d  | t d  t | t | | |  |  t d  | | t | | |  |  |  t | t d  | t d  | t d  | t d  t | t | | |  |  t d  | | t | | |  |  |  S(   NiO  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4175  s    c            s     j  d  t | t d  | t d  t | t | | |  |  t d  | | t | | |  |  |  t | t d  | t d  | t d  | t d  t | t | | |  |  t d  | | t | | |  |  |  S(   NiP  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4176  s    c            s     j  d  t t d  | t t d  t | t | | |   |  |  t |  | t t d  t | t | | |   | t | | |  |  |  |  S(   NiQ  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4177  s    c            s     j  d  t t d  | t t d  t | t | | |   |  |  t |  | t t d  t | t | | |   | t | | |  |  |  |  S(   NiR  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4178  s    c            s     j  d  t | t d  | t d  | t d  | t d  t | t | | |  |  t d  | | t | | |  |  |  t t d  | t d  | t d  t | t | | |  |  | | t | | |  |  |  S(   NiS  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4179  s    c            s     j  d  t | t d  | t d  | t d  | t d  t | t | | |  |  t d  | | t | | |  |  |  t t d  | t d  | t d  t | t | | |  |  | | t | | |  |  |  S(   NiT  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4180  s    c            sZ     j  d  t t d  t | | |  t d  | |  t | | |  | |  S(   NiU  ii(   R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4181  s    c            sZ     j  d  t t d  t | | |  t d  | |  t | | |  | |  S(   NiV  ii(   R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4182  s    c      	      sV     j  d  t t | t | | |  |  | | t | | |  | |  |  S(   NiW  (   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4183  s    c      	      sV     j  d  t t | t | | |  |  | | t | | |  | |  |  S(   NiX  (   R  R   R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4184  s    c            se     j  d  t | t | | |  | | t | | |  |  t | | |  |  | |  S(   NiY  (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4185  s    c            se     j  d  t | t | | |  | | t | | |  |  | t | | |  |  |  S(   NiZ  (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4186  s    c            sN     j  d  t | t | | |  |  | | t | | |  | |  S(   Ni[  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4187  s    c            sN     j  d  t | t | | |  |  | | t | | |  | |  S(   Ni\  (   R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4188  s    c	   	   
      s     j  d  t | t | | |  | |  | t | | |  |  | t | t | | |  | |  | | t | | |  | |  |  S(   Ni]  (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4189  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4190  s    c	   	         st     j  d  t | | t t t d  | | t | | |  | | | t | | |  |  |  |  |  S(   Ni_  i   (   R  R  R   RH  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4191  s    c	   	         st     j  d  t | | t t t d  | | t | | |  | | | t | | |  |  |  |  |  S(   Ni`  i   (   R  R  R   RH  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4192  s    c	   	   	      sn     j  d  t | | |  t | | t | | |  |  | t | | |  t d  |  |  |  S(   Nia  i   (   R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4193  s    c	   	   	      sx     j  d  t | | |  t | | t | | |  |  | t d  t | | |  t d  |  |  |  S(   Nib  i   i   (   R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4194  s    c      
      s     j  d  t | | |  t d  d t | | |  t | | t | | |   t | | t | | |   t t | | |  t d  |  |  |  S(   Nic  i   i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4195  s    c      
      s     j  d  t | | |  t d  d t | | t | | |   t | | t | | |   t | | |  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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4196  s    c            s     j  d  t | t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | | | | t | |  |  | t d  t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Nie  ii   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4197  s    c            s     j  d  t | t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | | | | t | |  |  | t d  |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Nif  ii   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4198  s    c            s     j  d  t t d  | t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | | | t | |  |  | t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Nig  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4199  s    c            s     j  d  t t d  | t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | | | t | |  |  | |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Nih  i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4200  s    c            s     j  d  t | | t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | t d  | | t | |  |  | t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Nii  i   i   i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4201  s    c            s     j  d  t | | t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | t d  | | t | |  |  | |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Nij  i   i   i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4202   s    c            s     j  d  t | t t | | t | |  |   | | t | |  |  | |  |  t t d  | t d  | | t | |  |  | t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Nik  i   i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4203%  s    c            s     j  d  t | t t | | t | |  |   | | t | |  |  | |  |  t t d  | t d  | | t | |  |  | |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Nil  i   i   (   R  R  R   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4204*  s    c            s    j  d  t | t d  | t d  t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | t d  | | t | |  |  | t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Nim  i   i   i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4205/  s    c            s    j  d  t | t d  | t d  t t | | t | |  |   | | t | |  |  | t d  |  |  t t d  | t d  | | t | |  |  | |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Nin  i   i   i   i   (   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement42064  s    c	   	   
      s     j  d  t | | t | | |  | t | | t | | |   t | | t | | |   t t | |  | | | | |  t d  d | | | | t d  d |  | t | | |   |  S(   Nio  ii   (   R  R  R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement42079  s    c	   	   
      s     j  d  t | | | t | | t | | |   t | | t | | |   t | | |  t t | |  | | | | |  t d  d | | | | t d  d |  | t | | |   |  S(   Nip  ii   (   R  R  R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4208>  s    c	   	   
      s     j  d  t | | t | | |  | t | | t | | |   t | | t | | |   t t | | | |  t d  d | | | | t d  d | |  | t d  t | | |   |  S(   Niq  ii   i   (   R  R  R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4209C  s    c	   	   
      s     j  d  t | | | t | | t | | |   t | | t | | |   t | | |  t t | | | |  t d  d | | | | t d  d | |  | t d  t | | |   |  S(   Nir  ii   i   (   R  R  R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4210H  s    c            sW     j  d  t | | t t | |  |  t d  |  |  t | | | |  S(   Nis  i(   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4211M  s    c            sW     j  d  t | | t t | |  |  t d  |  |  t | | | |  S(   Nit  i(   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4212R  s    c      	      s     j  d  t | | t t | |  |  t d  |  |  t | | | | t t d  t | |  |  |  |  t | | | |  S(   Niu  ii   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4213W  s    c      	      s     j  d  t | | t t | |  |  t d  |  |  t | | | | t t d  t | |  |  |  |  t | | | |  S(   Niv  ii   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4214\  s    c            s     j  d  t | t t | | t | |  |   |  |  t | t t | | t | |  |   t | |  |  |  |  S(   Niw  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4215a  s    c            s     j  d  t | t t | | t | |  |   |  |  t | t t | | t | |  |   t | |  |  |  |  S(   Nix  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4216f  s    c            s     j  d  t | | t t d  t | | t | |  |   |  |  t | | | | | | t | |  |  t | | t | |  |   t | |  |  |  S(   Niy  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4217k  s    c            s     j  d  t | | t t d  t | | t | |  |   |  |  t | | | | | | t | |  |  t | | t | |  |   t | |  |  |  S(   Niz  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4218p  s    c            s     j  d  t t d  |  t | | t | | |  |  t d  t | | |  | | t d  |  t d  | | |  t | | |  |  |  |  t | | | | t | | |  |  t d  t | | |  | |  |  S(   Ni{  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4219u  s    c            s     j  d  t t d  |  t | | t | | |  |  t d  t | | |  | | t d  |  t d  | | |  t | | |  |  |  |  t | | | | t | | |  |  t d  | |  t | | |  |  S(   Ni|  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4220z  s    c            st    j  d  t t d  |  t | | t | | |  |  t d  t | t d  | |  | | | t d  |  t d  | | |  t | | |  t d  | t d  | |  t d  | | | |  | t d  | |  t d  t | | |  |  |  |  t | | | | t | | |  |  t d  t | | |  | |  |  S(   Ni}  i   ii   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4221  s    c            st    j  d  t t d  |  t | | t | | |  |  t d  t | t d  | |  | | | t d  |  t d  | | |  t | | |  t d  | t d  | |  t d  | | | |  | t d  | |  t d  t | | |  |  |  |  t | | | | t | | |  |  t d  | |  t | | |  |  S(   Ni~  i   ii   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4222  s    c      
      s     j  d  t | | | | | t t d  | | t | |  |  t | |  |  |  |  t | | | |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4223  s    c      
      s     j  d  t | | | | | t t d  | | t | |  |  t | |  |  |  |  t | | | |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4224  s    c            s     j  d  t | | 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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4225  s    c            s     j  d  t | | 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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4226  s    c            s     j  d  t | t t d  t | | t | |  |   |  |  t | t t d  t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4227  s    c            s     j  d  t | t t d  t | | t | |  |   |  |  t | t t d  t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4228  s    c            s:    j  d  t t d  | t d  t d  |  t d  t | | t | | |  |  t d  t | | t d  |  t d  |  t d  | | | | t | | |  |  |  |  t | | t | | |  |  | | | | t | | |  | | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4229  s    c            s:    j  d  t t d  | t d  t d  |  t d  t | | t | | |  |  t d  t | | t d  |  t d  |  t d  | | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4230  s    c            s    j  d  t t d  | | t d  | t d  |  t d  t | | t | | |  |  t d  t | |  t d  | | | | t | | |  | |  t d  | | | | t | | |  t d  | | t d  | t d  |  t d  |  |  |  t | | | t | | |  |  t d  | | | | t | | |  | | | t d  | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4231  s    c            s    j  d  t t d  | | t d  | t d  |  t d  t | | t | | |  |  t d  t | |  t d  | | | | t | | |  | |  t d  | | | | t | | |  t d  | | t d  | t d  |  t d  |  |  |  t | | | t | | |  |  t d  | | | | | | | t d  | t d  |  t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4232  s    c      
      s     j  d  t | t | | t | | |  |  |  |  t | t | | t | | |  |  t | | |  |  |  S(   Ni  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4233  s    c      
      s     j  d  t | t | | t | | |  |  |  |  t | t | | t | | |  |  t | | |  |  |  S(   Ni  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4234  s    c            s     j  d  t t d  | t t | | t | |  |   |  |  t | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4235  s    c            s     j  d  t t d  | t t | | t | |  |   |  |  t | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4236  s    c            s     j  d  t | | 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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4237  s    c            s     j  d  t | | 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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4238  s    c            s     j  d  t | | t t | | t | |  |   |  |  t | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4239  s    c            s     j  d  t | | t t | | t | |  |   |  |  t | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4240  s    c            s    j  d  t t d  | | t | t d  | | t d  | t | |  |  t | | t | |  |   |  |  t | | | | t d  | | t t d  t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4241  s    c            s    j  d  t t d  | | t | t d  | | t d  | t | |  |  t | | t | |  |   |  |  t | | | | t d  | | t t d  t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4242  s    c            s    j  d  t t d  | | | | | t | | | | | | t | |  |  t | | t | |  |   |  |  t | t d  | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4243  s    c            s    j  d  t t d  | | | | | t | | | | | | t | |  |  t | | t | |  |   |  |  t | t d  | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4244  s    c            s     j  d  t t 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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4245  s    c            s     j  d  t t 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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4246  s    c      	      s     j  d  t t | | t | |  |   t | | t | |  |   t | |  |  t t | |  |  |  |  S(   Ni  (   R  R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4247  s    c      	      s     j  d  t t | | t | |  |   t | | t | |  |   t | |  |  t t d  t | |  |  |  |  S(   Ni  i   (   R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4248  s    c            s     j  d  t | t t | | t | |  |   t | | t | |  |   |  |  t | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4249  s    c            s     j  d  t | t t | | t | |  |   t | | t | |  |   |  |  t | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4250  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4251  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4252  s    c            s     j  d  t t d  | |  t t t d  | | | t d  t d  |  | t | |  |  t | | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4253  s    c            s     j  d  t t d  | |  t t t d  | | | t d  t d  |  | t d  t | | t | |  |   t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4254$  s    c            s     j  d  t | | t t | | t | |  |   t | | t | |  |   |  |  t | | | | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4255)  s    c            s     j  d  t | | t t | | t | |  |   t | | t | |  |   |  |  t | | | | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4256.  s    c            s    j  d  t t d  t t d  t d  t | |  |  | | | | | | t | |  |  | |  t t d  t d  t | |  |  | | | | | | t | |  |  | |  | | t | |  |  t | | | | | | t t | | t | |  |   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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement42573  s    c            s    j  d  t t d  t t d  t d  t | |  |  | | | | | | t | |  |  | |  t t d  t d  t | |  |  | | | | | | t | |  |  | |  | | t | |  |  t | | | | | | t t | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement42588  s    c      
      s     j  d  t t | |  |  t | | t | |  |   t | | t | |  |   t t d  t | |  |  |  |  S(   Ni  i   (   R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4259=  s    c      
      s     j  d  t t d  t | | t | |  |   t | | t | |  |   t | |  |  t t | |  |  |  |  S(   Ni  i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4260B  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4261G  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4262L  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t | | t | |  |   | | t | |  |  t d  d t | |  |  |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4263Q  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   |  |  t | | t t | | t | |  |   | | t | |  |  t d  d t | |  |  |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4264V  s    c	   	   
      s     j  d  t | t d  t | | |  | t | | t | | |   t | | t | | |   t t | | | |  t d  d | | | | | t | | |  |  | t d  t | | |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4265[  s    c	   	   
      s     j  d  t | t d  t | | |  | t | | t | | |   t | | t | | |   t t | | | |  t d  d | | | | | t | | |  |  | t d  t | | |   |  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4266`  s    c	   	         sm     j  d  t | t | | |  | |  | t | | |  | | t | | |  |  | |  S(   Ni  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4267e  s    c	   	         sm     j  d  t | t | | |  | |  | t | | |  | | t | | |  |  | |  S(   Ni  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4268j  s    c	   	   	      s     j  d  t t | | t | | |   t | t | | |  |  t | | t | | |   t | t | | |  |  t | t | | |  | |  | t | | |  | | t | | |  |  | |  |  S(   Ni  (   R  R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4269o  s    c	   	   	      s     j  d  t t | | t | | |   t | t | | |  |  t | | t | | |   t | t | | |  |  t | t | | |  | |  | t | | |  | | t | | |  |  | |  |  S(   Ni  (   R  R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4270t  s    c	   	   	      s	    j  d  t | | t | | |  |  | | t | | |  | | t | | |  | |  | t | | |  | | t | | |  |  | t | t | | |  | |  | t | | |  | | t | | |  |  | |  |  S(   Ni  (   R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4271y  s    c	   	   	      s	    j  d  t | | t | | |  |  | | t | | |  | | t | | |  | |  | t | | |  | | t | | |  |  | t | t | | |  | |  | t | | |  | | t | | |  |  | |  |  S(   Ni  (   R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4272~  s    c	   	   	      sZ     j  d  t t | | t | | |  |  | | t | | |  | |  |  S(   Ni  (   R  R   RH  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4273  s    c	   	   	      sZ     j  d  t t | | t | | |  |  | | t | | |  | |  |  S(   Ni  (   R  R   RH  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4274  s    c	   	         sR     j  d  t | | t | | |  |  | | t | | |  | |  S(   Ni  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4275  s    c	   	         sR     j  d  t | | t | | |  |  | | t | | |  | |  S(   Ni  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4276  s    c      	      sc     j  d  t | |  t | t | | |  |  | | t | | |  | |  |  |  S(   Ni  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4277  s    c      	      sc     j  d  t | |  t | t | | |  |  | | t | | |  | |  |  |  S(   Ni  (   R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4278  s    c
   
   
      s     j  d  t | t |  | | t |	 | |  |  t |  | t |	 | |  |  t |  t | t |	 | |  | |  | | t |	 | |  | |  |  S(   Ni  (   R  R  R$   R  R%   R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4279  s    c
   
   
      s     j  d  t | t |  | | t |	 | |  |  t |  | t |	 | |  |  t |  t | t |	 | |  | |  | | t |	 | |  | |  |  S(   Ni  (   R  R  R$   R  R%   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4280  s    c	   	         s     j  d  t | | | t | | |  |  | | t | | |  | t | | |  | | t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4281  s    c	   	         s     j  d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4282  s    c	   	   
      s    j  d  t |  | t d  | t d  |  t d  t | | t | | |  |  t d  | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4283  s    c	   	   
      s    j  d  t |  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | 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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4284  s    c      
      s     j  d  t | | t t d  | | t | |  |   t | |  |  | |  t | | t | |  |   t | | t | |  |   |  S(   Ni  i   (   R  R  t   logR  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4285  s    c      
      s     j  d  t | | t t d  | | t | |  |   | |  t | | t | |  |   t | | t | |  |   t | |  |  |  S(   Ni  i   (   R  R  Rf  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4286  s    c      
      s     j  d  t t d  | | | | t | | |  |  t | | |  | | t | | t | | |   t d  |  t d  |  S(   Ni  i   i   (   R  R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4287  s    c      
      s     j  d  t t d  | | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4288  s    c	   	   
      sM    j  d  t | t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | |  |  |  t t d  | | | | t | | |  |  | | t | | |  | t d  t | | |  | | t d  |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4289  s    c	   	   
      sL    j  d  t | t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | |  |  |  t t d  | | | | t | | |  |  | | t | | |  | t d  | | t d  |  t d  t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4290  s    c	   	   
      s    j  d  t | t d  | t d  |  | t | | t | | |  |  | | t | | |  | t d  t | | |  |  |  t | | | t | | |  |  | | t | | |  | t d  t | | |  | |  | |  S(   Ni  i   i(   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4291  s    c	   	   
      s    j  d  t | t d  | t d  |  | t | | t | | |  |  | | t | | |  | t d  t | | |  |  |  t | | | t | | |  |  | | t | | |  | t d  | |  | t | | |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4292  s    c            s    j  d  t t d  | t | | t | |  |  | t d  t | | t | |  |   t | |  |  |  |  t t d  | | | t | |  |  | t d  t | |  |  |  t | | t | |  |   t d  | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4293  s    c            s    j  d  t t d  | t | | t | |  |  | t d  t | | t | |  |   t | |  |  |  |  t t d  | | | t | |  |  | t d  |  t | | t | |  |   t d  | t d  t | |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4294  s    c	   	   
      sM    j  d  t | t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | |  |  |  t t d  | | | | t | | |  |  | | t | | |  | t d  t | | |  | | t d  |  t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4295  s    c	   	   
      sL    j  d  t | t d  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | t d  t | | |  |  |  t t d  | | | | t | | |  |  | | t | | |  | t d  | | t d  |  t d  t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4296  s    c	   	         s     j  d  t | | |  t t t | | |  t d  |  t | | |  | | t | | |  |  | |  |  |  S(   Ni  i   (   R  R  R   RH  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4297  s    c	   	         s     j  d  t | | |  t t t d  t | | |  t d  |  t | | |  | | t | | |  |  | |  |  |  S(   Ni  i   i   (   R  R  R   RH  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4298   s    c      
      s     j  d  t | | |  t d  d t | | |  t | | t | | |   t | | t | | |   t t | | |  t d  |  t | | |  |  |  S(   Ni  i   i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4299  s    c      
      s     j  d  t | | |  t d  d t | | t | | |   t | | t | | |   t | | |  t t d  t | | |  t d  |  t | | |  |  |  S(   Ni  i   i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4300
  s    c	   	   
      s    j  d  t |  | t d  | t d  |  t d  t | | t | | |  |  t d  | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4301  s    c	   	   
      s    j  d  t |  | t d  | t d  |  t d  t | | t | | |  |  t d  | | t | | |  | 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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4302  s    c	   	   
      s     j  d  t | | t | | |  | t | | t | | |   t | | t | | |   t t | | | |  t d  d | | | | t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4303  s    c	   	   
      s     j  d  t | | | t | | t | | |   t | | t | | |   t | | |  t t | | | |  t d  d | | | | t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4304  s    c            s     j  d  t | | | t t | t |
 | |	  |  t |
 | |	  t d  | | | t |
 | |	  | | |	  |	  |	  S(   Ni  i   (   R  R  R   RH  R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4305#  s    c            s     j  d  t | | | t t | t |
 | |	  |  t d  t |
 | |	  t d  | | | t |
 | |	  | | |	  |	  |	  S(   Ni  i   i   (   R  R  R   RH  R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4306(  s    c
   
   
      s     j  d  t | | | t d  d t |	 | |  t | | t |	 | |   t | | t |	 | |   t | t |	 | |  |  t |	 | |  t d  | |  |  S(   Ni  i   i   (   R  R  R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4307-  s    c
   
   
      s     j  d  t | | | t d  d t | | t |	 | |   t | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement43082  s    c      
      s     j  d  t | | | t |
 | |	  | t | | t |
 | |	   t | | t |
 | |	   t t | |	 |  t d  | | |	 | t d  d | | |	 | t d  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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement43097  s    c      
      s     j  d  t | | | | t | | t |
 | |	   t | | t |
 | |	   t |
 | |	  t t | |	 |  t d  | | |	 | t d  d | | |	 | t d  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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4310<  s    c            s     j  d  t t d  | | |  t t t d  | | | | | | | t d  |  | | t | |  |  t | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4311A  s    c            s     j  d  t t d  | | |  t t t d  | | | | | | | t d  |  | | t | t | |  |   t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4312F  s    c            s     j  d  t | | t t | t | |  |   t | | t | |  |   |  |  t | | | | | | t | t | |  |  t d  d t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4313K  s    c            s     j  d  t | | t t | t | |  |   t | | t | |  |   |  |  t | | | | | | t | t | |  |  t d  d t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4314P  s    c            s     j  d  t t d  | |  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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4315U  s    c            s     j  d  t t d  | |  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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4316Z  s    c            s    j  d  t t | | | t | |  |   t | | t | |  |   t t | t | |  |  | | t | |  |   | | | | | | | |  | |  t | | | | t | |  |  | | t | |  |  | | | |  |  S(   Ni  (   R  R  R  R  R;   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4317_  s    c            s    j  d  t t | | | t | |  |   t | | t | |  |   t t | | | t | |  |  t | |  |   | | | | | | | |  | |  t | | | | t | |  |  | | t | |  |  | | | |  |  S(   Ni  (   R  R  R  R  R;   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4318d  s    c            s     j  d  t | | t t d  t | | t | |  |   t | |  |  |  |  t | | | | | t t d  t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4319i  s    c            s     j  d  t | | t t d  t | | t | |  |   t | |  |  |  |  t | | | | | t t d  t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4320n  s    c            s     j  d  t | | t t | t | |  |   t | | t | |  |   |  |  t | | | t t | t | |  |   t | | t | |  |   | | t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4321s  s    c            s     j  d  t | | t t | t | |  |   t | | t | |  |   |  |  t | | | t t | t | |  |   t | | t | |  |   | | t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4322x  s    c            s     j  d  t | | t | t | |  |  t d  d t | | t | |  |   |  |  t | | | | | t | t | |  |  t d  d t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4323}  s    c            s     j  d  t | | t | t | |  |  t d  d t | | t | |  |   |  |  t | | | | | t | t | |  |  t d  d t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4324  s    c            s     j  d  t | | | | | t t d  t | | t | |  |   t | |  |  |  |  t | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4325  s    c            s     j  d  t | | | | | t t d  t | | t | |  |   t | |  |  |  |  t | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4326  s    c            s%    j  d  t t d  t | | t | |  |  | |  t t d  | | | t t t d   t t d  t d  t | |  |   t d   t d  | | |  t | |  |  |  t t | |  |  t d   t | | t | |  |   | | |  S(   Ni  i   i   (   R  R  R  R  R  R:   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4327  s    c            s0    j  d  t t d  t | | t | |  |  | |  t t d  | | | t t t d   t t d  t d  t | |  |   t d   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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4328  s    c            s     j  d  t | | | | | | t t | t | |  |   t | | t | |  |   |  |  t | | | | | | t t | t | |  |   t | | t | |  |   | | t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4329  s    c            s     j  d  t | | | | | | t t | t | |  |   t | | t | |  |   |  |  t | | | | | | t t | t | |  |   t | | t | |  |   | | t | |  |  |  |  S(   Ni  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4330  s    c      
      s     j  d  t | t | t | |  |   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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4331  s    c      
      s     j  d  t | t | t | |  |   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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4332  s    c            s     j  d  t | | | | | t t d  t | | t | |  |   t | |  |  |  |  t | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4333  s    c            s     j  d  t | | | | | t t d  t | | t | |  |   t | |  |  |  |  t | | | | | t t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4334  s    c            s     j  d  t t d  | t t d  t | | t | |  |   t | |  |  |  |  t | | t t d  t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4335  s    c            s     j  d  t t d  | t t d  t | | t | |  |   t | |  |  |  |  t | | t t d  t | | t | |  |   | | t | |  |  t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4336  s    c            s@    j  d  t | t d  | | | | | t t | t | |  |   | | | | | | t | |  |  t | | t | |  |   |  |  t | t d  | t d  | | | | | t t | t | |  |   t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4337  s    c            s@    j  d  t | t d  | | | | | t t | t | |  |   | | | | | | t | |  |  t | | t | |  |   |  |  t | t d  | t d  | | | | | t t | t | |  |   t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4338  s    c            s     j  d  t | | t | t | |  |  t d  d t | | t | |  |   |  |  t | | | t | t | |  |  t d  d t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4339  s    c            s     j  d  t | | t | t | |  |  t d  d t | | t | |  |   |  |  t | | | t | t | |  |  t d  d t | | t | |  |   | | t | |  |  |  |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4340  s    c            s     j  d  t t d  | |  t t t d  | | | t d  t d  |  | t | |  |  t | | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4341  s    c            s     j  d  t t d  | |  t t t d  | | | t d  t d  |  | t d  t | | t | |  |   t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4342  s    c            s     j  d  t | | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  t | | | | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4343  s    c            s     j  d  t | | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  t | | | | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4344  s    c            s    j  d  t t d  t t d  t d  t | |  |  | | | | | | t | |  |  | |  t t d  t d  t | |  |  | | | | | | t | |  |  | |  | | t | |  |  t | | | | | | t t | | | |  t | | t | |  |   t | | t | |  |    | | | | | | | |  | |  t | | | |  t | |  |  |  S(   Ni  i   i   (   R  R  R  R  R  R:   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4345  s    c            s    j  d  t t d  t t d  t d  t | |  |  | | | | | | t | |  |  | |  t t d  t d  t | |  |  | | | | | | t | |  |  | |  | | t | |  |  t | | | | | | t t | | | |  t | | t | |  |   t | | t | |  |    | | | | | | | |  t | |  |  | |  t | | | |  |  S(   Ni  i   i   (   R  R  R  R  R  R:   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4346  s    c            s     j  d  t t d  | | |  t t t d  | t d  | | | | t d  |  | t | |  |  t | | t | |  |   t | | t | |  |    |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4347  s    c            s     j  d  t t d  | | |  t t t d  | t d  | | | | t d  |  | t d  t | | t | |  |   t | | t | |  |   t | |  |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4348  s    c            s    j  d  t t d  t t d  t d  t | |  |  | | | | | | | | t | |  |   t t d  t d  t | |  |  | | | | | | | | t | |  |   | | t | |  |  t t t | | t | |  |   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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4349  s    c            s    j  d  t t d  t t d  t d  t | |  |  | | | | | | | | t | |  |   t t d  t d  t | |  |  | | | | | | | | t | |  |   | | t | |  |  t t t | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4350	  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  t | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4351		  s    c            s     j  d  t t d  | t t | | t | |  |   t | | t | |  |   t | |  |  |  |  t | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  S(   Ni   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4352	  s    c            s4    j  d  t | | | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  t | | | | | | t t d  t d  t | |  |  t | | t | |  |   | | t | |  |  t d  d t | |  |  |  |  S(   Ni  i   i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4353	  s    c            s4    j  d  t | | | | t t d  t | | t | |  |   t | | t | |  |   t | |  |  |  |  t | | | | | | t t d  t d  t | |  |  t | | t | |  |   | | t | |  |  t d  d t | |  |  |  |  S(   Ni  i   i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4354	  s    c      
      s    j  d  t | t d  | t |
 | |	  | t | | t |
 | |	   t | | t |
 | |	   t t | |	 |  t d  | | |	 | t d  d | | |	 | t | | |	  |	  |	 t d  t |
 | |	   |	  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4355	  s    c      
      s     j  d  t | t d  | | t | | t |
 | |	   t | | t |
 | |	   t |
 | |	  t t | |	 |  t d  | | |	 | t d  d | | |	 | t | | |	  |	  |	 t d  t |
 | |	   |	  S(   Ni  i   ii   (   R  R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4356"	  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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4357'	  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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4358,	  s    c      	      s     j  d  t | | | t |
 | |	  | |  | | t |
 | |	  | | t |
 | |	  | | t | t |
 | |	  | | | t |
 | |	  | | |	  |	  S(   Ni  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement43591	  s    c      	      s     j  d  t | | | t |
 | |	  | |  | | t |
 | |	  | | t |
 | |	  | | t | t |
 | |	  | | | t |
 | |	  | | |	  |	  S(   Ni  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement43606	  s    c      	      s     j  d  t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | | t |
 | |	  | | | t |
 | |	  | | t | t |
 | |	  | | | t |
 | |	  | | |	  |	  S(   Ni	  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4361;	  s    c      	      s     j  d  t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | | t |
 | |	  | | | t |
 | |	  | | t | t |
 | |	  | | | t |
 | |	  | | |	  |	  S(   Ni
  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4362@	  s    c
   
   	      s     j  d  t t | | t |	 | |   t | t |	 | |  |  t | | t |	 | |   t | t |	 | |  |  t | t |	 | |  | | | t |	 | |  | | t |	 | |  | | |  |  |  S(   Ni  (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4363E	  s    c
   
   	      s     j  d  t t | | t |	 | |   t | t |	 | |  |  t | | t |	 | |   t | t |	 | |  |  t | t |	 | |  | | | t |	 | |  | | t |	 | |  | | |  |  |  S(   Ni  (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4364J	  s    c      	      su     j  d  t t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | |	  |	  S(   Ni  (   R  R   RH  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4365O	  s    c      	      su     j  d  t t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | |	  |	  S(   Ni  (   R  R   RH  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4366T	  s    c            sl     j  d  t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | |	  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4367Y	  s    c            sl     j  d  t | t |
 | |	  |  | | t |
 | |	  | | | t |
 | |	  | |	  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4368^	  s    t   Bc	   	         s    j  d  t t d  | t t d  t d  t | | |  | | | | | | | | t | | |   t d  t d  t | | |  t t t | | t | | |   t | | | | t d   t | | t | | |    | | | | | | | |  | t t d  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  R  t   AR  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4369c	  s    c	   	         s    j  d  t t d  | t t d  t d  t | | |  | | | | | | | | t | | |   t d  t d  t | | |  t t t | | t | | |   t | | | | t d   t | | t | | |    | | | | | | | |  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  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4370h	  s    c	   	         s     j  d  t t d  | | t | t | | |  | t 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4371m	  s    c	   	         s     j  d  t t d  | | t | t | | |  | t 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4372r	  s    c	   	         s     j  d  t t d  | t d  t | t | | |  | t | | | t d  |  | | | t d  | | |  | t | | |  |  |  |  t |  | | t | | |  | t | | |  | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4373w	  s    c	   	         s     j  d  t t d  | t d  t | t | | |  | t | | | t d  |  | | | t d  | | |  | t | | |  |  |  |  t |  | | t | | |  | | | t d  t | | |  |  S(   Ni  i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4374|	  s    c            s     j  d  t |  | t t d  t | | |  |  |  t | | |  | | t t d  | | t | | |  t | | |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4375	  s    c            s     j  d  t |  | t t d  t | | |  |  |  t | | |  | | t t d  | | t | | |  t | | |  |  |  S(   Ni  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4376	  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4377	  s    c            s]     j  d  t |  | | t | | |  | | | t d  t | | |  |  S(   Ni  i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4378	  s    c      	      s    j  d  t | | | t d  |  | | | | t d  | t d  t | | t | | |  | t d  t | | |  |  |  t | | t | | |  | | | |  | t | | |  | | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4379	  s    c      	      s    j  d  t | | | t d  |  | | | | t d  | t d  t | | t | | |  | t d  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4380	  s    c      	      s     j  d  t | | | t d  |  | | | | t d  t | | t | | |  | t | | |  |  |  t |  | | t | | |  | t | | |  | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4381	  s    c      	      s     j  d  t | | | t d  |  | | | | t d  t | | t | | |  | t | | |  |  |  t |  | | t | | |  | | | t d  t | | |  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4382	  s    c            s    j  d  t t d  | t d  t | | t | | |  | t d  t | | | t d  |  | | | | | t d  |  | | t | | |  |  t | | |  |  |  t |  | | t | | |  | t | | |  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4383	  s    c            s    j  d  t t d  | t d  t | | t | | |  | t d  t | | | t d  |  | | | | | t d  |  | | t | | |  |  t | | |  |  |  t |  | | t | | |  | | | t d  t | | |  |  S(   Ni   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4384	  s    c            sd    j  d  t t d  | t d  | t d  | t d  t | | t | | |  | t d  t | t d  | | |  | | t d  | | |  | t | | |  |  t | | |  |  |  t | | t | | |  | t d  | | |  | t | | |  | | t d  | t d  | t d  |  S(   Ni!  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4385	  s    c            sd    j  d  t t d  | t d  | t d  | t d  t | | t | | |  | t d  t | t d  | | |  | | t d  | | |  | t | | |  |  t | | |  |  |  t | | t | | |  | t d  | | |  | | | t d  | t d  | t d  t | | |  |  S(   Ni"  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4386	  s    c            sN    j  d  t t d  t | t d  t d  t | | |  | |  t | t d  t d  t | | |  | |  | | |  | t t t | | t | | |   t | |  | | t d    | | |  | | | |  |  t | |  | | t d   | t d  | t | | |  |  S(   Ni#  i   i   (	   R  R  R  R  R  R;   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4387	  s    c            sO    j  d  t t d  t | t d  t d  t | | |  | |  t | t d  t d  t | | |  | |  | | |  | t t t | | t | | |   t | |  | | t d    | | |  | | | |  |  t | |  | | t d   t | | |  | t d  | |  S(   Ni$  i   i   (	   R  R  R  R  R  R;   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4388	  s    c            s     j  d  t |  t t d  t d  t | | |  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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4389	  s    c            s     j  d  t |  t t d  t d  t | | |  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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4390	  s    c            sd    j  d  t t d  t t d   | t | |  t | | |  |  | | | t | | |  | | |  | | | |  t | | |  | | t | | |  | t t d  d t d  d | t d  d | |  t | | |  t d  | | | |  t | | |  | | |  |  |  | t | | |  |  S(   Ni'  i   i   ii   (   R  R  R  R  R  R9   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4391	  s    c            sc    j  d  t t d  t t d   | t | |  t | | |  |  | | | t | | |  | | |  | | | |  t | | |  | | t | | |  | t t d  d t d  d | t d  d | |  t | | |  t d  | | | |  t | | |  | | |  |  t | | |  |  | |  S(   Ni(  i   i   ii   (   R  R  R  R  R  R9   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4392	  s    c      
      s     j  d  t |  | t | | t | | |  | t d  t | | |  |  |  t | | |  | | t | | t | | |  | t | | |  |  |  S(   Ni)  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4393	  s    c      
      s     j  d  t |  | t | | t | | |  | t d  t | | |  |  |  t | | |  | | t | | t | | |  | t | | |  |  |  S(   Ni*  i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4394	  s    c            sD    j  d  t t d  | t d  t d  | t d  t | | t | | |  | t d  t | | | |  | | |  | t d  | t d  t | | |  |  t | | |  |  |  t | | t | | |  | | | |  | t | | |  | | t d  | t d  |  S(   Ni+  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4395	  s    c            sD    j  d  t t d  | t d  t d  | t d  t | | t | | |  | t d  t | | | |  | | |  | t d  | t 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4396	  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | | |  | | | | | t d  |  | t d  | t d  | t d  t | | |  |  t | | |  |  |  t | | | t | | |  | t d  | | |  | t | | |  | | | t d  | t d  | t d  |  S(   Ni-  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4397	  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | | |  | | | | | t d  |  | t d  | t d  | t d  t | | |  |  t | | |  |  |  t | | | t | | |  | t d  | | |  | | | | t d  | t d  | t d  t | | |  |  S(   Ni.  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4398	  s    c            s    j  d  t t d  | | t d  t | | t | | |  | t |  | | t d  | | | 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4399	  s    c            s    j  d  t t d  | | t d  t | | t | | |  | t |  | | t d  | | | t d  |  | t | | |  |  t | | |  |  |  t |  | | t | | |  | t d  | | | t d  t | | |  |  S(   Ni0  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4400	  s    c
   
         sm     j  d  t | | t |	 | |  | | | t |	 | |  | t |	 | |  | | |  S(   Ni1  (   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4401
  s    c
   
         sl     j  d  t | | t |	 | |  | | | t |	 | |  | | | t |	 | |  |  S(   Ni2  (   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4402
  s    c
   
   
      s+    j  d  t | | | |  | | t d  | t d  t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  |  |  t | t |	 | |  | | | t |	 | |  | | | |  | t |	 | |  | | t d  | t d  |  S(   Ni3  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4403
  s    c
   
   
      s+    j  d  t | | | |  | | t d  | t d  t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  |  |  t | t |	 | |  | | | t |	 | |  | | | |  | | | t d  | t d  t |	 | |  |  S(   Ni4  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4404
  s    c
   
   
      s     j  d  t | | | |  | | | | | t | t |	 | |  | t d  | | t |	 | |  | |  |  t | | t |	 | |  | | | t |	 | |  | t |	 | |  | | |  S(   Ni5  i   (   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4405
  s    c
   
   
      s     j  d  t | | | |  | | | | | t | t |	 | |  | t d  | | t |	 | |  | |  |  t | | t |	 | |  | | | t |	 | |  | | | t |	 | |  |  S(   Ni6  i   (   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4406
  s    c	   	   
      s     j  d  t t d  |  | | t | | |  | t | | |  | t | | t | | |   t d  | t d  |  S(   Ni7  i   i   (   R  R  R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4407!
  s    c	   	   
      s     j  d  t t d  |  | | t | | |  | | t | | t | | |   t d  | t d  t | | |  |  S(   Ni8  i   i   (   R  R  R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4408&
  s    c	   	         s!    j  d  t | | t d  | t d  t d  |  | | t d  | | | t | t | | |  | t d  t | | t | | |   |  |  t | | t d  | t | | |  | t | | |  | | | t | | t | | |   |  S(   Ni9  i   i   (   R  R  R  R   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4409+
  s    c	   	         s!    j  d  t | | t d  | t d  t d  |  | | t d  | | | t | t | | |  | t d  t | | t | | |   |  |  t | | t d  | t | | |  | | | | t | | t | | |   t | | |  |  S(   Ni:  i   i   (   R  R  R  R   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement44100
  s    c	   	         s-    j  d  t | | t d  | t d  t d  |  | | | t d  | t d  t | t | | |  | t | | t | | |   |  |  t t d  |  | | t | | |  | t | | |  | t | | t | | |   t d  | t d  |  S(   Ni;  i   i   (   R  R  R  R   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement44115
  s    c	   	         s.    j  d  t | | t d  | t d  t d  |  | | | t d  | t d  t | t | | |  | t | | t | | |   |  |  t t d  |  | | 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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4412:
  s    c
   
         sE    j  d  t | | | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | t d  |  | | | | | | |  | | t |	 | |  |  |  |  t | | | t |	 | |  | | | t |	 | |  | t d  t |	 | |  | | |  S(   Ni=  i   i(   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4413?
  s    c
   
         sE    j  d  t | | | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | t d  |  | | | | | | |  | | t |	 | |  |  |  |  t | | | t |	 | |  | | | t |	 | |  | t d  | | t |	 | |  |  S(   Ni>  i   i(   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4414D
  s    c
   
         sb    j  d  t t d  | | | t | t |	 | |  | | | t |	 | |  | t d  t | | | | | |  | | | | | | | | |  | | t d  | | t d  t |	 | |  |  |  |  t |  | | t |	 | |  | | | t |	 | |  | t d  t |	 | |  | | | |  S(   Ni?  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4415I
  s    c
   
         sb    j  d  t t d  | | | t | t |	 | |  | | | t |	 | |  | t d  t | | | | | |  | | | | | | | | |  | | t d  | | t d  t |	 | |  |  |  |  t |  | | t |	 | |  | | | t |	 | |  | t d  | | | t |	 | |  |  S(   Ni@  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4416N
  s    c
   
         s    j  d  t t d  | | t d  | t d  t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | t d  |  | | | t d  | | | | | |  | | | t d  t |	 | |  |  |  |  t | | t |	 | |  | t d  | | t |	 | |  | | | |  | t |	 | |  | | t d  | t d  |  S(   NiA  i   i   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4417S
  s    c
   
         s    j  d  t t d  | | t d  | t d  t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | t d  |  | | | t d  | | | | | |  | | | t d  t |	 | |  |  |  |  t | | t |	 | |  | t d  | | t |	 | |  | | | |  | | | t d  | t d  t |	 | |  |  S(   NiB  i   i   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4418X
  s    c
   
         s    j  d  t t d  | t d  t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | | t d  |  | | | | |  | | | t d  t |	 | |  |  |  |  t | t |	 | |  | | | t |	 | |  | | | |  | t |	 | |  | | t d  | t d  |  S(   NiC  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4419]
  s    c
   
         s    j  d  t t d  | t d  t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | | t d  |  | | | | |  | | | t d  t |	 | |  |  |  |  t | t |	 | |  | | | t |	 | |  | | | |  | | | t d  | t d  t |	 | |  |  S(   NiD  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4420b
  s    c
   
         s.    j  d  t | | | | t | t |	 | |  | t d  | | t |	 | |  | t |  | | t d  | | | | |  | | t |	 | |  |  |  |  t |  | | t |	 | |  | t d  | | t |	 | |  | t |	 | |  | | | |  S(   NiE  i(   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4421g
  s    c
   
         s.    j  d  t | | | | t | t |	 | |  | t d  | | t |	 | |  | t |  | | t d  | | | | |  | | t |	 | |  |  |  |  t |  | | t |	 | |  | t d  | | t |	 | |  | | | | t |	 | |  |  S(   NiF  i(   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4422l
  s    c
   
         s#    j  d  t t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t | | | | | | | t d  t |	 | |  |  | | |  |  |  t | | t |	 | |  | | | t |	 | |  | t |	 | |  | | |  S(   NiG  i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4423q
  s    c
   
         s#    j  d  t t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t | | | | | | | t d  t |	 | |  |  | | |  |  |  t | | t |	 | |  | | | t |	 | |  | | | t |	 | |  |  S(   NiH  i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4424v
  s    c
   
         s     j  d  t |  | t | t |	 | |  | | | t |	 | |  | t d  |  |  t | | |  | | t | t |	 | |  | | | t |	 | |  | |  |  S(   NiI  i   (   R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4425{
  s    c
   
         s     j  d  t |  | t | t |	 | |  | | | t |	 | |  | t d  |  |  t | | |  | | t | t |	 | |  | | | t |	 | |  | |  |  S(   NiJ  i   (   R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4426
  s    c
   
         s    j  d  t t d  | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | | t d  |  | | | | | | | |  | | t |	 | |  t d  | | t d  | t d  | t d  | t d  |  | | | t |	 | |  |  |  |  t | | | t |	 | |  | | | t |	 | |  | t d  t |	 | |  | | |  S(   NiK  i   iii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4427
  s    c
   
         s    j  d  t t d  | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | | t d  |  | | | | | | | |  | | t |	 | |  t d  | | t d  | t d  | t d  | t d  |  | | | t |	 | |  |  |  |  t | | | t |	 | |  | | | t |	 | |  | t d  | | t |	 | |  |  S(   NiL  i   iii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4428
  s    c
   
         s    j  d  t t d  | | t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | | |  | | | | | | | | |  | t d  | | t d  t |	 | |  t d  |  | t d  | | t d  | | | t d  | | |  | t |	 | |  |  |  |  t |  | | t |	 | |  | | | t |	 | |  | t d  t |	 | |  | | | |  S(   NiM  i   ii   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4429
  s    c
   
         s    j  d  t t d  | | t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | | |  | | | | | | | | |  | t d  | | t d  t |	 | |  t d  |  | t d  | | t d  | | | t d  | | |  | t |	 | |  |  |  |  t |  | | t |	 | |  | | | t |	 | |  | t d  | | | t |	 | |  |  S(   NiN  i   ii   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4430
  s    c
   
         s    j  d  t t d  | t d  | t d  | t d  t | t |	 | |  | t d  | | t |	 | |  | t d  t | | t d  | | |  | t |	 | |  | | t d  | | |  | | | | |  | | | t d  t |	 | |  t d  |  |  |  t | | t |	 | |  | t d  | | t |	 | |  | t d  | | |  | t |	 | |  | | t d  | t d  | t d  |  S(   NiO  i   i   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4431
  s    c
   
         s    j  d  t t d  | t d  | t d  | t d  t | t |	 | |  | t d  | | t |	 | |  | t d  t | | t d  | | |  | t |	 | |  | | t d  | | |  | | | | |  | | | t d  t |	 | |  t d  |  |  |  t | | t |	 | |  | t d  | | t |	 | |  | t d  | | |  | | | t d  | t d  | t d  t |	 | |  |  S(   NiP  i   i   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4432
  s    c
   
         s3    j  d  t | | | t d  | 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  t |	 | |  t d  |  |  |  t | | t d  | t |	 | |  | t d  | | t |	 | |  | t d  | | |  | t |	 | |  | | | t d  | t d  | t d  |  S(   NiQ  i   i   ii(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4433
  s    c
   
         s3    j  d  t | | | t d  | 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  t |	 | |  t d  |  |  |  t | | t d  | t |	 | |  | t d  | | t |	 | |  | t d  | | |  | | | | t d  | t d  | t d  t |	 | |  |  S(   NiR  i   i   ii(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4434
  s    c
   
         s
    j  d  t t d  | | t d  | t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | t d  | t d  | | t d  |  | | | | | t d  | | |  | t |	 | |  | | | |  | | | t d  t |	 | |  t d  |  |  |  t | | t |	 | |  | | | t |	 | |  | t d  | | |  | t |	 | |  | | | t d  | t d  | t d  |  S(   NiS  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4435
  s    c
   
         s
    j  d  t t d  | | t d  | t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | t d  | t d  | | t d  |  | | | | | t d  | | |  | t |	 | |  | | | |  | | | t d  t |	 | |  t d  |  |  |  t | | t |	 | |  | | | t |	 | |  | t d  | | |  | | | | t d  | t d  | t d  t |	 | |  |  S(   NiT  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4436
  s    c
   
         sz    j  d  t | | | t | t |	 | |  | t d  | | t |	 | |  | t d  t |  | | t d  | | | | |  | | | t d  t |	 | |  | | | | |  | | t |	 | |  t d  |  |  |  t |  | | t |	 | |  | t d  | | t |	 | |  | t |	 | |  | | | |  S(   NiU  ii   (   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4437
  s    c
   
         sz    j  d  t | | | t | t |	 | |  | t d  | | t |	 | |  | t d  t |  | | t d  | | | | |  | | | t d  t |	 | |  | | | | |  | | t |	 | |  t d  |  |  |  t |  | | t |	 | |  | t d  | | t |	 | |  | | | | t |	 | |  |  S(   NiV  ii   (   R  R  R   R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4438
  s    c
   
         sg    j  d  t t d  | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | | | | t d  t |	 | |  t d  |  | | | | | t d  |  | | t |	 | |  |  |  |  t | | t |	 | |  | | | t |	 | |  | t |	 | |  | | |  S(   NiW  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4439
  s    c
   
         sg    j  d  t t d  | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | | | | t d  t |	 | |  t d  |  | | | | | t d  |  | | t |	 | |  |  |  |  t | | t |	 | |  | | | t |	 | |  | | | t |	 | |  |  S(   NiX  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4440
  s    c
   
         s    j  d  t | t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t |  | | t d  |  | | | t d  t |	 | |  | | | | |  | | t d  t |	 | |  t d  |  |  |  t |  | t d  | t |	 | |  | t d  | | t |	 | |  | t d  t |	 | |  | | | | |  S(   NiY  i   iii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4441
  s    c
   
         s    j  d  t | t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t |  | | t d  |  | | | t d  t |	 | |  | | | | |  | | t d  t |	 | |  t d  |  |  |  t |  | t d  | t |	 | |  | t d  | | t |	 | |  | t d  | | | | t |	 | |  |  S(   NiZ  i   iii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4442
  s    c
   
         sp    j  d  t t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t | | | t d  t |	 | |  | | | | t d  | | | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4443
  s    c
   
         sp    j  d  t t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t | | | t d  t |	 | |  | | | | t d  | | | | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4444
  s    c            s     j  d  t | | t t | | t | | |   t | t | | |   |  |  t | | |  | | | t t | t | | |   t | | t | | |   |  |  S(   Ni]  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4445
  s    c            s     j  d  t | | t t | | t | | |   t | t | | |   |  |  t | | |  | | | t t | t | | |   t | | t | | |   |  |  S(   Ni^  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4446
  s    c            s     j  d  t | t t | t | | |   t | | t | | |   |  |  t |  | t | t | | |  t d  d t | | t | | |   |  |  S(   Ni_  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4447
  s    c            s     j  d  t | t t | t | | |   t | | t | | |   |  |  t |  | t | t | | |  t d  d t | | t | | |   |  |  S(   Ni`  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4448
  s    c            s     j  d  t | t t | | t | | |   t | t | | |   |  |  t |  | t t | t | | |   t | | t | | |   |  |  S(   Nia  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4449
  s    c            s     j  d  t | t t | | t | | |   t | t | | |   |  |  t |  | t t | t | | |   t | | t | | |   |  |  S(   Nib  (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4450
  s    c	   	         s     j  d  t | | t | t | | |  | |  |  t | | |  | | | t | t | | |  | t d  | | t | | |  |  |  S(   Nic  i   (   R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4451
  s    c	   	         s     j  d  t | | t | t | | |  | |  |  t | | |  | | | t | t | | |  | t d  | | t | | |  |  |  S(   Nid  i   (   R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4452  s    c
   
         sh     j  d  t | t |	 | |  | | |  t |	 | |  | | t |	 | |  | |  S(   Nie  (   R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4453  s    c
   
         sh     j  d  t | t |	 | |  | | |  t |	 | |  | | t |	 | |  | |  S(   Nif  (   R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4454  s    R  c      	      s     j  d  t | |	 | t | t | | |
  |  | |	 t | | |
  | | | t | | |
  t d  | t | | |
  | | | |
  |
  S(   Nig  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4455  s    c      	      s     j  d  t | | | t |	 t | | |
  |  | | t | | |
  | | | t | | |
  | | | t | | |
  t d  | |
  |
  S(   Nih  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4456  s    t   Cc	   	         s     j  d  t | t d  t | | t | | |  | t d  t |  | | | | | t | | |  |  |  |  S(   Nii  ii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4457  s    c	   	         s     j  d  t | t d  t | | t | | |  | t d  t |  | | | | | t | | |  |  |  |  S(   Nij  ii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4458   s    c            s|     j  d  t |  | t d  t | | t | | |  | t d  t | | t | | |  |  |  |  S(   Nik  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4459%  s    c            s|     j  d  t |  | t d  t | | t | | |  | t d  t | | t | | |  |  |  |  S(   Nil  i   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4460*  s    c            sO     j  d  t | | t | | |  | t | | |  | | |  S(   Nim  (   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4461/  s    c            sN     j  d  t | | t | | |  | | | t | | |  |  S(   Nin  (   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement44624  s    c            s     j  d  t | | t d  |  | | t d  | t | t | | |  | t d  |  |  t | | t | | |  | t | | |  | | |  S(   Nio  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement44639  s    c            s     j  d  t | | t d  |  | | t d  | t | t | | |  | t d  |  |  t | | t | | |  | | | t | | |  |  S(   Nip  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4464>  s    c            s     j  d  t | | t d  |  | | t d  t | t | | |  | |  |  t |  | t | | |  | t | | |  | | t d  |  S(   Niq  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4465C  s    c            s     j  d  t | | t d  |  | | t d  t | t | | |  | |  |  t |  | t | | |  | | | t d  t | | |  |  S(   Nir  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4466H  s    c      	      s     j  d  t |  | t | t | | |  | t d  |  |  t | | t d  t | t | | |  | t d  |  |  S(   Nis  i   i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4467M  s    c      	      s     j  d  t |  | t | t | | |  | t d  |  |  t | | t d  t | t | | |  | t d  |  |  S(   Nit  i   i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4468R  s    c      	      s     j  d  t |  | t | t | | |  | t d  |  |  t | t | | |  | | | t | | |  t d  |  S(   Niu  i   i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4469W  s    c      	      s     j  d  t |  | t | t | | |  | t d  |  |  t | t | | |  | | | t | | |  t d  |  S(   Niv  i   i   (   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4470\  s    c      
      s     j  d  t t d  d t t t d  | | t d  |  | | t d  | | t | | |  t d  |  | | | t | | |  t d  |  |  |  t | | t | | |  t d  | t | | |  |  S(   Niw  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4471a  s    c      
      s     j  d  t t d  d t t t d  | | t d  |  | | t d  | | t | | |  t d  |  | | | t | | |  t d  |  |  |  t | | t d  | t | | |  t | | |  |  S(   Nix  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4472f  s    c      
      s     j  d  t t d  d t t t d  | | t d  |  | t | | |  t d  | t d  | |  t | | |  |  |  |  t |  | t | | |  t d  | t | | |  |  S(   Niy  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4473k  s    c      
      s     j  d  t t d  d t t t d  | | t d  |  | t | | |  t d  | t d  | |  t | | |  |  |  |  t |  | t d  | t | | |  t | | |  |  S(   Niz  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4474p  s    c      
      s     j  d  t t d  | t | | |  | | | t | | |  | | t | | |  |  |  t | | t t d  t | | |  |  |  S(   Ni{  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4475u  s    c      
      s     j  d  t t d  | t | | |  | | | t | | |  | | t | | |  |  |  t | | t t d  t | | |  |  |  S(   Ni|  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4476z  s    c      
      s     j  d  t t d  | t | | |  | t | | |  | | t | | |  |  |  t |  | t t d  t | | |  |  |  S(   Ni}  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4477  s    c      
      s     j  d  t t d  | t | | |  | t | | |  | | t | | |  |  |  t |  | t t d  t | | |  |  |  S(   Ni~  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4478  s    c	   	         sP    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t | | t d  | t d  |  | | t d  | | | t d  | | t | | |  |  |  |  t | | t | | |  | | | |  | | | t | | |  | | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4479  s    c	   	         sP    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t | | t d  | t d  |  | | t d  | | | t d  | | t | | |  |  |  |  t | | t | | |  | | | |  | | | | | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4480  s    c            s&    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t | | t d  | t d  | | | t d  |  | t | | |  |  |  |  t | |  | | t | | |  | t | | |  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4481  s    c            s&    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t | | t d  | t d  | | | t d  |  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4482  s    c	   	         s     j  d  t t d  | | t d  t | | t | | |  | t | | | t d  |  | | t d  | | | t | | |  |  |  |  t | | | t | | |  | t | | |  | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4483  s    c	   	         s     j  d  t t d  | | t d  t | | t | | |  | t | | | t d  |  | | t d  | | | t | | |  |  |  |  t | | | t | | |  | | | t d  t | | |  |  S(   Ni  i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4484  s    c            s     j  d  t t d  | | t d  t | | t | | |  | t | | | t d  |  | | t | | |  |  |  |  t |  | | t | | |  | t | | |  | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4485  s    c            s     j  d  t t d  | | t d  t | | t | | |  | t | | | t d  |  | | t | | |  |  |  |  t |  | | t | | |  | | | t d  t | | |  |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4486  s    c	   	         sF    j  d  t t d  | t d  t | | t | | |  | t d  t | | | t d  |  | | t d  | | | t | | |  t d  | | | | t d  | | |  | t | | |  |  |  |  t | | | t | | |  | t | | |  | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4487  s    c	   	         sF    j  d  t t d  | t d  t | | t | | |  | t d  t | | | t d  |  | | t d  | | | t | | |  t d  | | | | t d  | | |  | t | | |  |  |  |  t | | | t | | |  | | | t d  t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4488  s    c            s(    j  d  t t d  | t d  t | | t | | |  | t d  t | | | t d  |  | | t | | |  t d  | | | t d  |  | | t | | |  |  |  |  t |  | | t | | |  | t | | |  | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4489  s    c            s(    j  d  t t d  | t d  t | | t | | |  | t d  t | | | t d  |  | | t | | |  t d  | | | t d  |  | | t | | |  |  |  |  t |  | | t | | |  | | | t d  t | | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4490  s    c            s     j  d  t | t t d  t d  t | | |  t | | t | | |   t | | |  |  |  t | |  | t | | |  t | | t | | |   |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4491  s    c            s     j  d  t | t t d  t d  t | | |  t | | t | | |   t | | |  |  |  t | |  | t | | |  t | | t | | |   |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4492  s    c            s     j  d  t |  t t d  t d  t | | |  t | | t | | |   t | | |  |  |  t | |  t | | |  t | | t | | |   |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4493  s    c            s     j  d  t |  t t d  t d  t | | |  t | | t | | |   t | | |  |  |  t | |  t | | |  t | | t | | |   |  S(   Ni  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4494  s    c	   	         s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | 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 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4495  s    c	   	         s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | 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 d  | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4496  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | 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 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4497  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | 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 d  | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4498  s    c	   	   
      s     j  d  t t d  | t | | t | | |  | | | |  | | | t | | |  |  |  t | | t | | t | | |  | t d  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4499  s    c	   	   
      s     j  d  t t d  | t | | t | | |  | | | |  | | | t | | |  |  |  t | | t | | t | | |  | t d  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4500  s    c      
      s     j  d  t t d  | t | | t | | |  | | | |  | t | | |  |  |  t |  | t | | t | | |  | t d  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4501  s    c      
      s     j  d  t t d  | t | | t | | |  | | | |  | t | | |  |  |  t |  | t | | t | | |  | t d  t | | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4502  s    c      
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | |  |  S(   Ni  i   i(   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4503  s    c      
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | |  |  S(   Ni  i   i(   R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4504  s    c      	      st     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  |  |  S(   Ni  i   i(   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4505  s    c      	      st     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  |  |  S(   Ni  i   i(   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4506  s    c
   
   
      s     j  d  t | t |  | | t | | |  | t |  | t | | |  | t |  t | t | | |  | | |	 |  t | | |  | t | | |  t d  |  |  S(   Ni  i   (   R  R  R$   R  R%   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4507  s    c
   
   
      s     j  d  t | t |  | | t | | |  | t |  | t | | |  | t |  t | t | | |  | | |	 |  t | | |  | t | | |  t d  |  |  S(   Ni  i   (   R  R  R$   R  R%   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4508  s    c	   	   
      s     j  d  t | t |  | | t | | |  | t |  | t | | |  | t |  t | t | | |  | | | |  t | | |  t d  |  |  S(   Ni  i   (   R  R  R$   R  R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4509  s    c	   	   
      s     j  d  t | t |  | | t | | |  | t |  | t | | |  | t |  t | t | | |  | | | |  t | | |  t d  |  |  S(   Ni  i   (   R  R  R$   R  R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4510$  s    c
   
         s    j  d  t t d  | | t | t | | |  | t d  t | | | t | | |  t d  | |	 | |  | |	 | | t d  | |  | | | t | | |  |  |  |  t |	 | | t | | |  | t | | |  | | |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4511)  s    c
   
         s    j  d  t t d  | | t | t |	 | |  | t d  t | | | t |	 | |  t d  | | | |  | | | | t d  | |  | | | t |	 | |  |  |  |  t | | | t |	 | |  | | | t |	 | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4512.  s    c	   	         s    j  d  t t d  | | t | t | | |  | t d  t | | | |  | | t | | |  t d  | | | t d  |  | t | | |  |  |  |  t | | | t | | |  | t | | |  | | |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement45133  s    c	   	         s    j  d  t t d  | | t | t | | |  | t d  t | | | |  | | t | | |  t d  | | | t d  |  | t | | |  |  |  |  t | | | t | | |  | | | t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement45148  s    c
   
         sZ    j  d  t t d  | t d  t | t |	 | |  | t | | | t d  | t d  |  | | | t |	 | |  t d  |  | | t d  | | | t d  | | t d  t |	 | |  |  |  |  t | | | t |	 | |  | t |	 | |  | | t d  t |	 | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4515=  s    c
   
         sZ    j  d  t t d  | t d  t | t |	 | |  | t | | | t d  | t d  |  | | | t |	 | |  t d  |  | | t d  | | | t d  | | t d  t |	 | |  |  |  |  t | | | t |	 | |  | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4516B  s    c	   	         s<    j  d  t t d  | t d  t | t | | |  | t | | | t d  |  | | t d  t | | |  t d  | | | t d  |  | t d  t | | |  |  |  |  t |  | | t | | |  | t | | |  | | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4517G  s    c	   	         s<    j  d  t t d  | t d  t | t | | |  | t | | | t d  |  | | t d  t | | |  t d  | | | t d  |  | t d  t | | |  |  |  |  t |  | | t | | |  | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4518L  s    c	   	         s    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t t d  | | | t d  |  | | | |  | | t d  | | | t d  | | t d  t | | |  |  t | | |  |  |  t | | t | | |  | | | |  | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4519Q  s    c	   	         s    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t t d  | | | t d  |  | | | |  | | t d  | | | t d  | | t d  t | | |  |  t | | |  |  |  t | | t | | |  | | | |  | | | | | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4520V  s    c            s^    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t t d  | | | t d  |  | | | | t d  |  | t d  t | | |  |  t | | |  |  |  t | |  | | t | | |  | t | | |  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4521[  s    c            s^    j  d  t t d  | | t d  | t d  t | | t | | |  | t d  t t d  | | | t d  |  | | | | t d  |  | t d  t | | |  |  t | | |  |  |  t | |  | | t | | |  | | t d  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4522`  s    c	   	         s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | | |  | | | | | t d  |  | | | | t d  | | t d  | | |  | | | t | | |  |  t | | |  |  |  t | | t | | |  | t d  | | t d  |  | | | | t d  t | | |  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4523e  s    c	   	         s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | t d  | | |  | | | | | t d  |  | | | | t d  | | t d  | | |  | | | t | | |  |  t | | |  |  |  t | | t | | |  | t d  | | t d  |  | | | | t d  | | | t d  | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4524j  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | | |  | t d  | | t d  |  | t d  | | t d  | | |  | t | | |  |  t | | |  |  |  t | | t | | |  | t d  | | t d  |  | t d  t | | |  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4525o  s    c            s    j  d  t t d  | | t d  | t d  | t d  t | | t | | |  | t d  t | | | |  | t d  | | t d  |  | t d  | | t d  | | |  | t | | |  |  t | | |  |  |  t | | t | | |  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4526t  s    c	   	         s,    j  d  t t d  | | t d  t | | t | | |  | t | | | t d  | | | t d  |  | | 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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4527y  s    c	   	         s,    j  d  t t d  | | t d  t | | t | | |  | t | | | t d  | | | t d  |  | | t 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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4528~  s    c            s    j  d  t t d  | | t d  t | | t | | |  | t | | | t d  |  | t | | |  |  | | t d  |  t | | |  |  |  t |  | | t | | |  | t d  t | | |  | | | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4529  s    c            s    j  d  t t d  | | t d  t | | t | | |  | t | | | t d  |  | t | | |  |  | | t d  |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4530  s    c            s    j  d  t t d  | | t d  | t d  t | t | | |	  | | | t | | |	  | t d  t |
 | t d  | | t d  |  | | | | | |  | | | t d  | |
 | | t d  | | | t | | |	  |	  |	  |	  t | t | | |	  | | | t | | |	  | |
 | |  | | | t | | |	  | | t d  | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4531  s    c            s    j  d  t t d  | | t d  | t d  t | t |
 | |	  | | | t |
 | |	  | t d  t | | t d  | | t d  |  | | | | | |  | | | t d  | | | | t 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  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4532  s    c
   
         sr    j  d  t t d  | | t d  | t d  t | t | | |  | | | t | | |  | t d  t |	 | t d  | | t d  |  | | | |	 | | t d  |  | | t | | |  |  |  |  t | t | | |  | |	 |  | | t | | |  | t | | |  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4533  s    c
   
         sr    j  d  t t d  | | t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  t | | t d  | | t d  |  | | | | | | t d  |  | | t |	 | |  |  |  |  t | t |	 | |  | | |  | | t |	 | |  | | t d  | t d  t |	 | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4534  s    c            s+    j  d  t t d  | | | t | t | | |	  | t d  | | t | | |	  | t |
 | | |  | | | |
 | | t d  | | t | | |	  |	  |	  |	  t |
 | t | | |	  | | | t | | |	  | t | | |	  | | |	  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4535  s    c            s+    j  d  t t d  | | | t | t |
 | |	  | t d  | | t |
 | |	  | t | | | |  | | | | | | t d  | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | | | t |
 | |	  |	  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4536  s    c
   
         s    j  d  t t d  | | | t | t | | |  | t d  | | t | | |  | t |	 | | | |	 | | t d  |  | t | | |  |  |  |  t |	 | t | | |  | | | t | | |  | t | | |  | | |  S(   Ni  i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4537  s    c
   
         s    j  d  t t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t | | | | | | | t d  |  | t |	 | |  |  |  |  t | | t |	 | |  | | | t |	 | |  | | | t |	 | |  |  S(   Ni  i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4538  s    c            sJ    j  d  t t d  | | | t d  t | t | | |	  | | | t | | |	  | t |
 | | | t d  | | | |  | | | t d  | | | t | | |	  |	  |	  |	  t | | t | | |	  | | | t | | |	  | t | | |	  | | | t d  |	  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4539  s    c            sJ    j  d  t t d  | | | t d  t | t |
 | |	  | | | t |
 | |	  | t | | | | t d  | | | |  | | | 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  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4540  s    c
   
         s0    j  d  t t d  | | | t d  t | t | | |  | | | t | | |  | t |	 | | | t d  |  | | t | | |  |  | | |  |  |  t |  | t | | |  | | | t | | |  | t | | |  | | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4541  s    c
   
         s0    j  d  t t d  | | | t d  t | t |	 | |  | | | t |	 | |  | 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  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4542  s    c	   	         st    j  d  t t d  | t d  | t d  | t d  | t d  t | | t | | |  | t d  t | | | t d  | t d  | t d  t | | |  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 | | |  | t d  | | t d  |  | | | | t d  t | | |  | t d  | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4543  s    c	   	         st    j  d  t t d  | t d  | t d  | t d  | t d  t | | t | | |  | t d  t | | | t d  | t d  | t d  t | | |  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 | | |  | t d  | | t d  |  | | | | t d  | t d  | | t d  | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4544  s    c            s4    j  d  t t d  | t d  | t d  | t d  | t d  t | | t | | |  | t d  t |  | | t d  | t d  | t d  t | | |  t d  | | | t d  | t d  |  | t d  | t d  | t d  t | | |  | | t d  | | t d  |  | t d  |  t | | |  |  |  t | | | t | | |  | t d  | | t d  |  | t d  t | | |  | t d  | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4545  s    c            s4    j  d  t t d  | t d  | t d  | t d  | t d  t | | t | | |  | t d  t |  | | t d  | t d  | t d  t | | |  t d  | | | t d  | t d  |  | t d  | t d  | t d  t | | |  | | t d  | | t d  |  | t d  |  t | | |  |  |  t | | | t | | |  | t d  | | t d  |  | t d  | t d  | | t d  | t d  | t d  t | | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4546  s    c	   	         si    j  d  t t d  | | t d  t | | t | | |  | t | | | | | t d  | | t d  t | | |  |  | | t d  t d  | | t | | |  t d  |  t | | |  |  |  t | | | t | | |  | t d  t | | |  | | | t d  t | | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4547  s    c	   	         si    j  d  t t d  | | t d  t | | t | | |  | t | | | | | t d  | | t d  t | | |  |  | | t d  t d  | | t | | |  t d  |  t | | |  |  |  t | | | t | | |  | 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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4548  s    c            sR    j  d  t t d  | | t d  t | | t | | |  | t |  | t d  |  | t | | |  t d  | | | t d  |  | t d  t | | |  |  t | | |  |  |  t |  | | t | | |  | t d  t | | |  | | | t d  t | | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4549  s    c            sR    j  d  t t d  | | t d  t | | t | | |  | t |  | t d  |  | t | | |  t d  | | | t d  |  | t d  t | | |  |  t | | |  |  |  t |  | | t | | |  | t d  | | | t d  t | | |  t | | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4550  s    c            sw    j  d  t t d  | | t | t | | |	  | t d  | | t | | |	  | t d  t |
 | | |  | | | |
 | | t d  | | t | | |	  t d  |  | | | |
 | t d  | | t | | |	  |	  |	  |	  t |
 | t | | |	  | | | t | | |	  | t | | |	  | | |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4551  s    c            sw    j  d  t t d  | | t | t |
 | |	  | t d  | | t |
 | |	  | t d  t | | | |  | | | | | | t d  | | t |
 | |	  t d  |  | | | | | t d  | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | | | t |
 | |	  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4552  s    c
   
         s_    j  d  t t d  | | t | t | | |  | t d  | | t | | |  | t d  t |	 | | | |	 | t d  |  | t | | |  | |	 | | t d  |  | t | | |  t d  |  |  |  t |	 | t | | |  | | | t | | |  | t | | |  | | |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4553  s    c
   
         s_    j  d  t t d  | | t | t |	 | |  | t d  | | t |	 | |  | t d  t | | | | | | t d  |  | t |	 | |  | | | | t d  |  | t |	 | |  t d  |  |  |  t | | t |	 | |  | | | t |	 | |  | | | t |	 | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4554   s    c            s    j  d  t t d  | | t d  t | t | | |	  | | | t | | |	  | t d  t |
 | | | t d  | | | |  | | | t d  | | | t | | |	  t d  | | | | |
 | |  | | | t d  t | | |	  |	  |	  |	  t | | t | | |	  | | | t | | |	  | t | | |	  | | | t d  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4555  s    c            s    j  d  t t d  | | t d  t | t |
 | |	  | | | t |
 | |	  | t d  t | | | | t d  | | | |  | | | t d  | | | t |
 | |	  t d  | | | | | | |  | | | t d  t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | | | | t d  t |
 | |	  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4556
  s    c
   
         sx    j  d  t t d  | | t d  t | t | | |  | | | t | | |  | t d  t |	 | | | t d  |  | | t | | |  t d  |  | | | |	 | | t d  |  | | t | | |  |  |  |  t |  | t | | |  | | | t | | |  | t | | |  | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4557  s    c
   
         sx    j  d  t t d  | | t d  t | t |	 | |  | | | t |	 | |  | t d  t | | | | t d  |  | | t |	 | |  t d  |  | | | | | | t d  |  | | t |	 | |  |  |  |  t |  | t |	 | |  | | | t |	 | |  | | | | t d  t |	 | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4558  s    c            sd    j  d  t | | | t d  | t d  | t d  t | t | | |	  | t d  | | t | | |	  | t d  t |
 | t d  | t d  | | t d  |  | | | | | t d  |
 | |  | | | t | | |	  | | t d  | | t d  | t d  | |
 | |  | | | t d  t | | |	  t d  |	  |	  |	  t | | t | | |	  | t d  | | t | | |	  | t d  |
 | t d  |  | | | | t d  t | | |	  | | | 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  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4559  s    c            sd    j  d  t | | | t d  | t d  | t d  t | t |
 | |	  | t d  | | t |
 | |	  | t d  t | | t d  | t d  | | t d  |  | | | | | t d  | | |  | | | t |
 | |	  | | t d  | | t d  | t d  | | | |  | | | t d  t |
 | |	  t d  |	  |	  |	  t | | t |
 | |	  | t d  | | t |
 | |	  | t d  | | t d  |  | | | | t d  | | | t d  | t d  | t d  t |
 | |	  |	  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4560  s    c
   
         sH    j  d  t | | | t d  | t d  | t d  t | t | | |  | t d  | | t | | |  | t d  t |	 | t d  | t d  |  | t d  | t d  | | |	 |  | t d  t | | |  |	 | t d  | | t d  |  | t d  | | t d  | t d  t | | |  t d  |  |  |  t | | t | | |  | t d  | | t | | |  | t d  |	 | t d  |  | t d  t | | |  | | | t d  | t d  | t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4561#  s    c
   
         sH    j  d  t | | | t d  | t d  | t d  t | t |	 | |  | t d  | | t |	 | |  | t d  t | | t d  | t d  |  | t d  | t d  | | | |  | t d  t |	 | |  | | t d  | | t d  |  | t d  | | t d  | t d  t |	 | |  t d  |  |  |  t | | t |	 | |  | t d  | | t |	 | |  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  t |	 | |  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4562(  s    c            sf    j  d  t t d  | | t d  | t d  | t d  t | t | | |	  | | | t | | |	  | t d  t | | t d  |
 | |  | | | | | t d  |
 | |  | | | t | | |	  | | 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 | | |	  | | | t d  | t d  | t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4563-  s    c            sf    j  d  t t d  | | t d  | t d  | t d  t | t |
 | |	  | | | t |
 | |	  | t d  t | | t d  | | |  | | | | | t d  | | |  | | | t |
 | |	  | | 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 d  | t d  | t d  t |
 | |	  |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement45642  s    c
   
         s0    j  d  t t d  | | t d  | t d  | t d  t | t | | |  | | | t | | |  | t d  t | t d  |	 |  | t d  | | |	 |  | t d  t | | |  |	 | t d  |  | t d  | | t d  |	 | t d  |  | t d  | | t d  t | | |  t d  |  |  |  t | t | | |  | | | t | | |  | t d  |	 | t d  |  | t d  t | | |  | | | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement45657  s    c
   
         s0    j  d  t t d  | | t d  | t d  | t d  t | t |	 | |  | | | t |	 | |  | t d  t | t d  | |  | t d  | | | |  | t d  t |	 | |  | | t d  |  | t d  | | t d  | | t d  |  | t d  | | t d  t |	 | |  t d  |  |  |  t | t |	 | |  | | | t |	 | |  | t d  | | t d  |  | t d  | | | t d  | t d  | t d  t |	 | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4566<  s    c            s    j  d  t | | | | t d  t | t | | |	  | t d  | | t | | |	  | t | | | t d  |
 | | | t d  | | | | t | | |	  |  | | | t d  | | | t | | |	  t d  |	  |	  |	  t | | | t | | |	  | t d  | | t | | |	  | t d  t | | |	  | | | | t d  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4567A  s    c            s    j  d  t | | | | t d  t | t |
 | |	  | t d  | | t |
 | |	  | t | | | t d  | | | | t d  | | | | t |
 | |	  |  | | | t d  | | | t |
 | |	  t d  |	  |	  |	  t | | | t |
 | |	  | t d  | | t |
 | |	  | t d  | | | | t d  t |
 | |	  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4568F  s    c
   
         s    j  d  t | | | | t d  t | t | | |  | t d  | | t | | |  | t |  | | t | | |  t d  |  | | t d  |	 | | | t d  |  | | | t | | |  |  |  |  t |  | | t | | |  | t d  | | t | | |  | t d  t | | |  | | | | t d  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4569K  s    c
   
         s    j  d  t | | | | t d  t | t |	 | |  | t d  | | t |	 | |  | t |  | | t |	 | |  t d  |  | | t d  | | | | t d  |  | | | t |	 | |  |  |  |  t |  | | t |	 | |  | t d  | | t |	 | |  | t d  | | | | t d  t |	 | |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4570P  s    c            ss    j  d  t t d  | | | t | t | | |	  | t d  | | t | | |	  | t |
 | | | t d  |
 | | | t d  t | | |	  t d  |  | | | |
 | |
 | | t | | |	  |	  |	  |	  t |
 | t | | |	  | | | t | | |	  | t d  t | | |	  | | | |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4571U  s    c            ss    j  d  t t d  | | | t | t |
 | |	  | t d  | | t |
 | |	  | t | | | | t d  | | | | t d  t |
 | |	  t d  |  | | | | | | | | t |
 | |	  |	  |	  |	  t | | t |
 | |	  | | | t |
 | |	  | t d  | | | t |
 | |	  |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4572Z  s    c
   
         sg    j  d  t t d  | | | t | t | | |  | t d  | | t | | |  | t |	 | | | t d  |	 | | | t d  t | | |  t d  | |	 | |	 |  | t | | |  |  |  |  t |	 | t | | |  | | | t | | |  | t d  t | | |  | | | |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4573_  s    c
   
         sg    j  d  t t d  | | | t | t |	 | |  | t d  | | t |	 | |  | t | | | | t d  | | | | t d  t |	 | |  t d  | | | | |  | t |	 | |  |  |  |  t | | t |	 | |  | | | t |	 | |  | t d  | | | t |	 | |  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4574d  s    c	   	         s    j  d  t | t d  t | | | | |  | t | | |  t | t | | |   |  |  t | | t d  |  | | | | t d  | t d  | t d  t | t | | |  t d  d | | t | | |  |  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4575i  s    c	   	         s    j  d  t | t d  t | | | | |  | t | | |  t | t | | |   |  |  t | | t d  |  | | | | t d  | t d  | t d  t | t | | |  t d  d | | t | | |  |  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4576n  s    c            s     j  d  t | t d  t | | | | t | | |  t | t | | |   |  |  t | | t d  |  | t d  | t d  | t d  t | t | | |  t d  d | | t | | |  |  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4577s  s    c            s     j  d  t | t d  t | | | | t | | |  t | t | | |   |  |  t | | t d  |  | t d  | t d  | t d  t | t | | |  t d  d | | t | | |  |  |  S(   Ni  ii   i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4578x  s    c	   	         s     j  d  t | | t d  t | t | | |  t d  d t | | t | | |   |  |  t | |  t | | |  t | t | | |   t | | t | | |   |  S(   Ni  i   i   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4579}  s    c	   	         s     j  d  t | | t d  t | t | | |  t d  d t | | t | | |   |  |  t | |  t | | |  t | t | | |   t | | t | | |   |  S(   Ni  i   i   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4580  s    c            s     j  d  t | t t d  t | t | | |   t | | t | | |   |  |  t |  | t d  t | t | | |  t d  d t | | t | | |   |  |  S(   Ni  i   i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4581  s    c            s     j  d  t | t t d  t | t | | |   t | | t | | |   |  |  t |  | t d  t | t | | |  t d  d t | | t | | |   |  |  S(   Ni  i   i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4582  s    c            s     j  d  t | t |
 | |	  | | | t |
 | |	  | | |  t |
 | |	  | t |
 | |	  t d  |	  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4583  s    c            s     j  d  t | t |
 | |	  | | | t |
 | |	  | | |  t |
 | |	  | t |
 | |	  t d  |	  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4584  s    c
   
         sr     j  d  t | t |	 | |  | | |  t |	 | |  t d  | | t |	 | |  | |  S(   Ni  i   (   R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4585  s    c
   
         sr     j  d  t | t |	 | |  | | |  t |	 | |  t d  | | t |	 | |  | |  S(   Ni  i   (   R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4586  s    c      
      s     j  d  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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4587  s    c      
      s     j  d  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  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4588  s    c
   
   	      s     j  d  t | | t d  t | t |	 | |  | | t d  | t |	 | |  t d  |  | t |	 | |  | | |  |  S(   Ni  i   i(   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4589  s    c
   
   	      s     j  d  t | | t d  t | t |	 | |  | | t d  | t |	 | |  t d  |  | t |	 | |  | | |  |  S(   Ni  i   i(   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4590  s    c      
      s     j  d  t | t |  | | t | | |  | t |  | t | | |  | t |  t | t | | |  | | |	 | t | | |  | |
 |  t | | |  | t | | |  t d  |  |  S(   Ni  i   (   R  R  R$   R  R%   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4591  s    c      
      s     j  d  t | t |  | | t | | |  | t |  | t | | |  | t |  t | t | | |  | | |	 | t | | |  | |
 |  t | | |  | t | | |  t d  |  |  S(   Ni  i   (   R  R  R$   R  R%   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4592  s    c      
      s     j  d  t | t |  | | t | | |
  | t |  | t | | |
  | t |  t | t | | |
  | | |	 |  t | | |
  t d  | | t | | |
  | |
  |
  S(   Ni  i   (   R  R  R$   R  R%   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4593  s    c      
      s     j  d  t | t |  | | t | | |
  | t |  | t | | |
  | t |  t | t | | |
  | | |	 |  t | | |
  t d  | | t | | |
  | |
  |
  S(   Ni  i   (   R  R  R$   R  R%   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4594  s    c      	      sd     j  d  t |  | t t |  | t d  |  | t d  |  | t | | |   |  S(   Ni  i   i(   R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4595  s    c      
      so     j  d  t |  | t t |  | t d  |  | t d  |  | t d  t | | |   |  S(   Ni  i   ii   (   R  R  R*   R   R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4596  s    c            s;     j  d  t | t | | |  t d  |  |  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4597  s    c            s;     j  d  t | t | | |  t d  |  |  S(   Ni  i   (   R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4598  s    c      	      sf     j  d  t |  | t t d  | t | | |  t d  |  |  |  t | | |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4599  s    c      	      sf     j  d  t |  | t t d  | t | | |  t d  |  |  |  t | | |  S(   Ni  i   i   (   R  R  R   R  R  R  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4600  s    c      	      s|     j  d  t t d  | t t | | | t d  | |  | t d  t d  |  | t | | |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4601  s    c      
      s     j  d  t t d  | t t | | | t d  | |  | t d  t d  |  | t d  t | | |   |  S(   Ni  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4602  s    c   	         s   t  t | | |  |  }   j d  t | | t d  | t t | | | t d  | t d  t d  | t d  t d  t | | | t d  | t d  t d  | t d  |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4603  s    c   	         s  t  t d  t | | |  |  }   j d  t | | t d  | t t | | | t d  | t d  t d  | t d  t d  t | | | t d  | t d  t d  | t d  |  |  |  | t d  | t | | |   |  S(   Ni   i  i   i(   R   R  R  R  R  R*   R   R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4604  s    'c   	   	      s   t  t | | |  |  }   j d  t | | t t | | | |  | | | | | |  | t d  | t d  t d  | t d  t d  d |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4605   s    c   	   	      s   t  t | | |  |  }   j d  t | | t t | | | |  | | | | | |  | t d  | t d  t d  | t d  t d  d |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4606  s    c   	         s   t  t | | |  |  }   j d  t | | t t | t d  | t d  t d  | t d  t d  t | | | t d  | t d  t d  | t d  |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4607  s    c   	         s   t  t d  t | | |  |  }   j d  t | | t t | t d  | t d  t d  | t d  t d  t | | | t d  | t d  t d  | t d  |  |  |  | t d  | t | | |   |  S(   Ni   i   i   i(   R   R  R  R  R  R*   R   R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4608  s    'c   	         s  t  t | | |  |  }   j d  t | | t t | t d  | t d  t d  | t d  | |  t d  t d  d t | | t d  | t d  t d  | t d  | |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4609  s    c   	         s  t  t | | |  |  }   j d  t | | t t | t d  | t d  t d  | t d  | |  t d  t d  d t | | t d  | t d  t d  | t d  | |  |  |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4610  s    c      	      sk     j  d  t t | | t d  t | | |  | |  t d  t | | |  | |  |  S(   Ni  i   (   R  R   RH  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4611%  s    c      	      sk     j  d  t t | | t d  t | | |  | |  t d  t | | |  | |  |  S(   Ni  i   (   R  R   RH  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4612*  s    c   	   	      s   t  t | | |  |  }   j d  t | | | |  t d  | t t | | | |  | | | | | |  | t d  | t d  t d  | t d  t d  d |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4613.  s    c   	   	      s   t  t | | |  |  }   j d  t | | | |  t d  | t t | | | |  | | | | | |  | t d  | t d  t d  | t d  t d  d |  | t | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With46144  s    c   	         s   t  t | | |  |  }   j d  t | | t d  | t t | | t | | | t d  | t d  t d  | t d  |  |  | t d  | t d  t d  |  | t | | |  |  |  S(   Ni  i   i   (   R   R  R  R  R  R*   R   R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4615:  s    c   	         s   t  t d  t | | |  |  }   j d  t | | t d  | t t | | t | | | t d  | t d  t d  | t d  |  |  | t d  | t d  t d  |  | t d  | t | | |   |  S(   Ni   i  i   (   R   R  R  R  R  R*   R   R1  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4616@  s    'R  c	   	   
      sv     j  d  t t d  |  | |  t | t d  | t d  t | | |  | t d  |  |  |  S(   Ni	  i   i   i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4617G  s    c	   	   
      sv     j  d  t t d  |  | |  t | t d  | t d  t | | |  | t d  |  |  |  S(   Ni
  i   i   i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4618L  s    c	   	         s     j  d  t | t d  | t d  t | | |  | t d  |  | | t d  t | | |  | | t d  t | | |  t d  | |  t t | t d  | t d  t | | |  | t d  |  |  |  S(   Ni  i   i   (   R  R  R  R  R   t   u(	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4619Q  s    c	   	         s     j  d  t | t d  | t d  t | | |  | t d  |  | | t d  t | | |  | | t d  t | | |  t d  | |  t t | t d  | t d  t | | |  | t d  |  |  |  S(   Ni  i   i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4620V  s    c   	         s  t  t d  | | |  t d  t d   }   j d  t t d  | | t t d  |  t d  | t d  t | | |  | | |  |  t t d  | | t t d  |  t d  | t d  t | | |  | | |  |  S(   Ni   i   i  i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  t   q(   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4621Z  s    2c   	         s  t  t d  | | |  t d  t d   }   j d  t t d  | | t t d  |  t d  | t d  t | | |  | | |  |  t t d  | | t t d  |  t d  | t d  t | | |  | | |  |  S(   Ni   i   i  i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4622`  s    2c
      	      s   t  t | |	 |  |  }
   j d  t |
 |	 t t |
 | | |  | |
 | | | |  |
 t d  | t d  t d  | t d  t d  d |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4623f  s    c
      	      s   t  t | |	 |  |  }
   j d  t |
 |	 t t |
 | | |  | |
 | | | |  |
 t d  | t d  t d  | t d  t d  d |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4624l  s    c
            s-  t  t | |	 |  |  }
   j d  t |
 | t d  |	 t t | | |
 t d  | t d  t d  | t d  t d  t | | |
 t d  | t d  t d  | t d  | |
 t d  | t d  t d  | |  |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4625r  s    c
            sB  t  t d  t | |	 |  |  }
   j d  t |
 | t d  |	 t t | | |
 t d  | t d  t d  | t d  t d  t | | |
 t d  | t d  t d  | t d  | |
 t d  | t d  t d  | |  |  |  | t d  |
 t | |	 |   |  S(   Ni   i  i   i(   R   R  R  R  R  R*   R   R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4626x  s    'c
   
   
      s     j  d  t t d  |  | |  t | t d  | t d  t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4627  s    c
   
   
      s     j  d  t t d  |  | |  t | t d  | t d  t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   i   (   R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4628  s    c
   
   
      s    j  d  t | t d  | t d  t | |	 |  | t d  |  | | t d  t | |	 |  | | t d  t | |	 |  t d  | |  t | t d  | t d  t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4629  s    c
   
   
      s    j  d  t | t d  | t d  t | |	 |  | t d  |  | | t d  t | |	 |  | | t d  t | |	 |  t d  | |  t | t d  | t d  t | |	 |  | t d  |  t d  t | |	 |  | |  |  S(   Ni  i   i   (   R  R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4630  s    c
   
   	      s     j  d  t t | | t d  t | |	 |  | | t d  t | |	 |  t d  | |  t d  t | |	 |  | |  |  S(   Ni  i   i   (   R  R   RH  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4631  s    c
   
   	      s     j  d  t t | | t d  t | |	 |  | | t d  t | |	 |  t d  | |  t d  t | |	 |  | |  |  S(   Ni  i   i   (   R  R   RH  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4632  s    c
      
      s	  t  t | |	 |  |  }
   j d  t |
 | | |  t d  |	 t t | | t d  | |  |
 t d  | t d  t d  | t d  t d  d | |
 | | | |
 | t d  | | |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4633  s    c
      
      s  t  t | |	 |  |  }
   j d  t |
 | | |  t d  |	 t t | | t d  | |  |
 t d  | t d  t d  | t d  t d  d | |
 | | | |
 | t d  | | |  |  | t | |	 |  |
  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4634  s    c
            s  t  t | |	 |  |  }
   j d  t |
 | t d  |	 t t | | t | | |
 t d  | t d  t d  | t d  | |
 t d  | t d  t d  | |  |  |
 t d  | t d  t d  |  | t | |	 |  |
  |  S(   Ni  i   i   (   R   R  R  R  R  R*   R   R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4635  s    c
            s)  t  t d  t | |	 |  |  }
   j d  t |
 | t d  |	 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 | |	 |   |  S(   Ni   i  i   (   R   R  R  R  R  R*   R   R1  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4636  s    'c	   	   
      s     j  d  t t d  | | | t | |  t | | |  | t d  | t | | |  t d  | |  |  S(   Ni  i   i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4637  s    c	   	   
      s     j  d  t t d  | | | t | |  t | | |  | t d  | t | | |  t d  | |  |  S(   Ni  i   i   (   R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4638  s    c	   	   
      s     j  d  t | t d  | t | | |  t d  | | | t | | |  | t | | |  t d  | t | |  t | | |  | t d  | t | | |  t d  | |  |  S(   Ni  i   (   R  R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4639  s    c	   	   
      s     j  d  t | t d  | t | | |  t d  | | | t | | |  | t | | |  t d  | t | |  t | | |  | t d  | t | | |  t d  | |  |  S(   Ni   i   (   R  R  R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4640  s    c   	         s  t  t d  | | | t d  t d   }   j d  t |  t d  | | |  | | t t d  | t d  | t | | |  | |  |  t |  t d  | | |  | | t t d  | t d  | t | | |  | |  |  S(   Ni   i   i!  i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4641  s    2c   	         s  t  t d  | | | t d  t d   }   j d  t |  t d  | | |  | | t t d  | t d  | t | | |  | |  |  t |  t d  | | |  | | t t d  | t d  | t | | |  | |  |  S(   Ni   i   i"  i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   With4642  s    2c	   	   	      sw     j  d  t t | |  t | | |  | | t | | |  | t | | |  t d  | |  |  S(   Ni#  i   (   R  R   RH  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4643  s    c	   	   	      sw     j  d  t t | |  t | | |  | | t | | |  | t | | |  t d  | |  |  S(   Ni$  i   (   R  R   RH  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4644  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   |  |  t t d  t | | | |  t t t | t | |   | |  S(   Ni%  ii   i   (	   R  R  R   R  Rf  R  t   expR  R=   (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4645  s    c            s    j  d  t | |  | t | | | |  t d  t t t | | |  t d   |  |  t | |  | t | | | |  t d  t t t | | |  t d   |  |  t t d  | | | |  t t t | t | |   | |  S(   Ni&  ii   i   (	   R  R  R   R  Rf  R  R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4646  s    c            s     j  d  t | |  | t | | | |  t d  t | | |  |  |  t | | | |  t | | |  | |  S(   Ni'  i(   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4647  s    c            s     j  d  t | |  | t | | | |  t d  t | | |  |  |  t | | | |  | t | | |  |  S(   Ni(  i(   R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4648  s    c            sL    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  | | | |  |  t | t d  | | t | |  |  | t d  |  t d  | t d  | t d  |  t | t d  | t | |  |  | t d  | | | t | |  |  |  | t d  |  S(   Ni)  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4649  s    c            sL    j  d  t | t d  | t d  | t d  t | t | |  |  | t d  | | | |  |  t | t d  | | t | |  |  | t d  |  t d  | t d  | t d  |  t | t d  | t | |  |  | t d  | | | |  | t d  t | |  |  |  S(   Ni*  i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4650  s    c      	      s    j  d  t | t d  | t d  | t d  t | t | | |  | t d  | | | |  |  |  t | t d  | t d  |  |  t d  | t d  | t d  | t d  t | t | | |  | t d  | | | |  t d  |  |  t | t d  | t | | |  | t d  | | | |  t | | |  | | t d  |  t | t d  | |  | t | | |  | t d  | | | |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4651  s    c      	      s    j  d  t | t d  | t d  | t d  t | t | | |  | t d  | | | |  |  |  t | t d  | t d  |  |  t d  | t d  | t d  | t d  t | t | | |  | t d  | | | |  t d  |  |  t | t d  | t | | |  | t d  | | | |  | | t d  t | | |  |  t | t d  | |  | t | | |  | t d  | | | |  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  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4652  s    c            s    j  d  t | t d  | t d  | t | t | |  |  | t d  | | | |  |  t | | t | |  |  | |  t d  | t d  |  t | t | |  |  | t d  | | | t | |  |  | |  | |  S(   Ni-  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4653  s    c            s    j  d  t | t d  | t d  | t | t | |  |  | t d  | | | |  |  t | | t | |  |  | |  t d  | t d  |  t | t | |  |  | t d  | | | t | |  |  | |  | |  S(   Ni.  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4654  s    c      	      s    j  d  t | t d  | t d  | t | t | | |  | t d  | | | |  |  |  t | t d  |  |  t d  | t d  | t d  t | t | | |  | | | | |  t d  |  |  t | t | | |  | t d  | | | |  t | | |  | | | |  t | |  | t | | |  | | | | |  t d  | t d  | t d  |  S(   Ni/  i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4655  s    c      	      s    j  d  t | t d  | t d  | t | t | | |  | t d  | | | |  |  |  t | t d  |  |  t d  | t d  | t d  t | t | | |  | | | | |  t d  |  |  t | t | | |  | t d  | | | |  t | | |  | | | |  t | |  | t | | |  | | | | |  t d  | t d  | t d  |  S(   Ni0  i   i   ii(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4656  s    c            s}     j  d  t | t | | |  | | t | | |  | t | t | | |  | | | | |  |  |  S(   Ni1  (   R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4657  s    c            s}     j  d  t | t | | |  | | t | | |  | t | t | | |  | | | | |  |  |  S(   Ni2  (   R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4658   s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni3  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4659%  s    c	   	   	      sL     j  d  t t | | | |  | | t | | |  | |  |  S(   Ni4  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4660*  s    c	   	         sc     j  d  t t | | | |  | t | | |  | | t | | |  | |  |  S(   Ni5  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4661/  s    c	   	         sc     j  d  t t | | | |  | t | | |  | | t | | |  | |  |  S(   Ni6  (   R  R   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement46624  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni7  (   R  R   R  R1  (   t   vR  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement46639  s    c            sF     j  d  t | | t t |  |   | t | |  | |  S(   Ni8  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4664>  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni9  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4665C  s    c	   	         sD     j  d  t | | t | | |  | | | | |  |  S(   Ni:  (   R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4666H  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni;  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4667M  s    c            sv     j  d  t t d  | t t | t d  t d  | | | t | | |  |  |  | | |  |  S(   Ni<  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4668R  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni=  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4669W  s    c            s8     j  d  t | | t | | | |  |  |  S(   Ni>  (   R  R   R  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4670\  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni?  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4671a  s    c            sl     j  d  t t d  t | | t d   t t | | t | | | |  |  |  | |  |  S(   Ni@  i   (   R  R  R  R2   R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4672f  s    c            s5     j  d  t | | t t | |   |  |  S(   NiA  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4673k  s    c            s5     j  d  t | | t t | |   |  |  S(   NiB  (   R  R   R  R1  (   R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4674p  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   NiC  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4675u  s    c            sz     j  d  t t d  | t t | t d  | t d  | | | t | | |  |  |  | | |  |  S(   NiD  i   i(   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4676z  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   NiE  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4677  s    c      	      s@     j  d  t | | | | t | | | |  |  |  S(   NiF  (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4678  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   NiG  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4679  s    c	   	         sw     j  d  t | t |  | t |  | | t |  t | | | | t | | | |  |  |  |  S(   NiH  (   R  R  R$   R%   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4680  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   NiI  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4681  s    c            sA     j  d  t | | | | | t t | |   |  |  S(   NiJ  (   R  R   R  R1  (   R  R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4682  s    c      
      s     j  d  t | | t d  | | |  t d  t | | | t d  t | | | |  |  t d  |  |  t | | | t d  t d  t | | | |  |  t d  | | |  t d  |  S(   NiK  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4683  s    c      
      s     j  d  t | | t d  | | |  t d  t | | | t d  t | | | |  |  t d  |  |  t | | | t d  t d  t | | | |  |  t d  | | |  t d  |  S(   NiL  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   replacement4684  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  t   x_t   m_R  t   n_R   t   a_R  t   p_R  t   c_t   A_t   n2_t   u_t   v_t   e_(	  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  t   pattern3917R  t   rule3917t   pattern3918R  t   rule3918t   pattern3919R  t   rule3919t   pattern3920R  t   rule3920t   pattern3921R  t   rule3921t   pattern3922R  t   rule3922t   pattern3923R  t   rule3923t   pattern3924R  t   rule3924t   pattern3925R  t   rule3925t   pattern3926R  t   rule3926t   pattern3927R  t   rule3927t   pattern3928R  t   rule3928t   pattern3929R   t   rule3929t   pattern3930R  t   rule3930t   pattern3931R  t   rule3931t   pattern3932R  t   rule3932t   pattern3933R  t   rule3933t   pattern3934R  t   rule3934t   pattern3935R  t   rule3935t   pattern3936R  t   rule3936t   pattern3937R  t   rule3937t   pattern3938R	  t   rule3938t   pattern3939R
  t   rule3939t   pattern3940R  t   rule3940t   pattern3941R  t   rule3941t   pattern3942R  t   rule3942t   pattern3943R  t   rule3943t   pattern3944R  t   rule3944t   pattern3945R  t   rule3945t   pattern3946R  t   rule3946t   pattern3947R  t   rule3947t   pattern3948R  t   rule3948t   pattern3949R  t   rule3949t   pattern3950R  t   rule3950t   pattern3951R  t   rule3951t   pattern3952R  t   rule3952t   pattern3953R  t   rule3953t   pattern3954R  t   rule3954t   pattern3955R  t   rule3955t   pattern3956R  t   rule3956t   pattern3957R  t   rule3957t   pattern3958R  t   rule3958t   pattern3959R  t   rule3959t   pattern3960R  t   rule3960t   pattern3961R   t   rule3961t   pattern3962R!  t   rule3962t   pattern3963R"  t   rule3963t   pattern3964R#  t   rule3964t   pattern3965R$  t   rule3965t   pattern3966R%  t   rule3966t   pattern3967R&  t   rule3967t   pattern3968R'  t   rule3968t   pattern3969R(  t   rule3969t   pattern3970R)  t   rule3970t   pattern3971R*  t   rule3971t   pattern3972R+  t   rule3972t   pattern3973R,  t   rule3973t   pattern3974R-  t   rule3974t   pattern3975R.  t   rule3975t   pattern3976R/  t   rule3976t   pattern3977R0  t   rule3977t   pattern3978R1  t   rule3978t   pattern3979R2  t   rule3979t   pattern3980R3  t   rule3980t   pattern3981R4  t   rule3981t   pattern3982R5  t   rule3982t   pattern3983R6  t   rule3983t   pattern3984R7  t   rule3984t   pattern3985R8  t   rule3985t   pattern3986R9  t   rule3986t   pattern3987R:  t   rule3987t   pattern3988R;  t   rule3988t   pattern3989R<  t   rule3989t   pattern3990R=  t   rule3990t   pattern3991R>  t   rule3991t   pattern3992R?  t   rule3992t   pattern3993R@  t   rule3993t   pattern3994RA  t   rule3994t   pattern3995RB  t   rule3995t   pattern3996RC  t   rule3996t   pattern3997RD  t   rule3997t   pattern3998RE  t   rule3998t   pattern3999RF  t   rule3999t   pattern4000RG  t   rule4000t   pattern4001RH  t   rule4001t   pattern4002RI  t   rule4002t   pattern4003RJ  t   rule4003t   pattern4004RK  t   rule4004t   pattern4005RL  t   rule4005t   pattern4006RM  t   rule4006t   pattern4007RN  t   rule4007t   pattern4008RO  t   rule4008t   pattern4009RP  t   rule4009t   pattern4010RQ  t   rule4010t   pattern4011RR  t   rule4011t   pattern4012RS  t   rule4012t   pattern4013RT  t   rule4013t   pattern4014RU  t   rule4014t   pattern4015RV  t   rule4015t   pattern4016RW  t   rule4016t   pattern4017RX  t   rule4017t   pattern4018RY  t   rule4018t   pattern4019RZ  t   rule4019t   pattern4020R[  t   rule4020t   pattern4021R\  t   rule4021t   pattern4022R]  t   rule4022t   pattern4023R^  t   rule4023t   pattern4024R_  t   rule4024t   pattern4025R`  t   rule4025t   pattern4026Ra  t   rule4026t   pattern4027Rb  t   rule4027t   pattern4028Rc  t   rule4028t   pattern4029Rd  t   rule4029t   pattern4030Re  t   rule4030t   pattern4031Rf  t   rule4031t   pattern4032Rg  t   rule4032t   pattern4033Rh  t   rule4033t   pattern4034Ri  t   rule4034t   pattern4035Rj  t   rule4035t   pattern4036Rk  t   rule4036t   pattern4037Rl  t   rule4037t   pattern4038Rm  t   rule4038t   pattern4039Rn  t   rule4039t   pattern4040Ro  t   rule4040t   pattern4041Rp  t   rule4041t   pattern4042Rq  t   rule4042t   pattern4043Rr  t   rule4043t   pattern4044Rs  t   rule4044t   pattern4045Rt  t   rule4045t   pattern4046Ru  t   rule4046t   pattern4047Rv  t   rule4047t   pattern4048Rw  t   rule4048t   pattern4049Rx  t   rule4049t   pattern4050Ry  t   rule4050t   pattern4051Rz  t   rule4051t   pattern4052R{  t   rule4052t   pattern4053R|  t   rule4053t   pattern4054R}  t   rule4054t   pattern4055R~  t   rule4055t   pattern4056R  t   rule4056t   pattern4057R  t   rule4057t   pattern4058R  t   rule4058t   pattern4059R  t   rule4059t   pattern4060R  t   rule4060t   pattern4061R  t   rule4061t   pattern4062R  t   rule4062t   pattern4063R  t   rule4063t   pattern4064R  t   rule4064t   pattern4065R  t   rule4065t   pattern4066R  t   rule4066t   pattern4067R  t   rule4067t   pattern4068R  t   rule4068t   pattern4069R  t   rule4069t   pattern4070R  t   rule4070t   pattern4071R  t   rule4071t   pattern4072R  t   rule4072t   pattern4073R  t   rule4073t   pattern4074R  t   rule4074t   pattern4075R  t   rule4075t   pattern4076R  t   rule4076t   pattern4077R  t   rule4077t   pattern4078R  t   rule4078t   pattern4079R  t   rule4079t   pattern4080R  t   rule4080t   pattern4081R  t   rule4081t   pattern4082R  t   rule4082t   pattern4083R  t   rule4083t   pattern4084R  t   rule4084t   pattern4085R  t   rule4085t   pattern4086R  t   rule4086t   pattern4087R  t   rule4087t   pattern4088R  t   rule4088t   pattern4089R  t   rule4089t   pattern4090R  t   rule4090t   pattern4091R  t   rule4091t   pattern4092R  t   rule4092t   pattern4093R  t   rule4093t   pattern4094R  t   rule4094t   pattern4095R  t   rule4095t   pattern4096R  t   rule4096t   pattern4097R  t   rule4097t   pattern4098R  t   rule4098t   pattern4099R  t   rule4099t   pattern4100R  t   rule4100t   pattern4101R  t   rule4101t   pattern4102R  t   rule4102t   pattern4103R  t   rule4103t   pattern4104R  t   rule4104t   pattern4105R  t   rule4105t   pattern4106R  t   rule4106t   pattern4107R  t   rule4107t   pattern4108R  t   rule4108t   pattern4109R  t   rule4109t   pattern4110R  t   rule4110t   pattern4111R  t   rule4111t   pattern4112R  t   rule4112t   pattern4113R  t   rule4113t   pattern4114R  t   rule4114t   pattern4115R  t   rule4115t   pattern4116R  t   rule4116t   pattern4117R  t   rule4117t   pattern4118R  t   rule4118t   pattern4119R  t   rule4119t   pattern4120R  t   rule4120t   pattern4121R  t   rule4121t   pattern4122R  t   rule4122t   pattern4123R  t   rule4123t   pattern4124R  t   rule4124t   pattern4125R  t   rule4125t   pattern4126R  t   rule4126t   pattern4127R  t   rule4127t   pattern4128R  t   rule4128t   pattern4129R  t   rule4129t   pattern4130R  t   rule4130t   pattern4131R  t   rule4131t   pattern4132R  t   rule4132t   pattern4133R  t   rule4133t   pattern4134R  t   rule4134t   pattern4135R  t   rule4135t   pattern4136R  t   rule4136t   pattern4137R  t   rule4137t   pattern4138R  t   rule4138t   pattern4139R  t   rule4139t   pattern4140R  t   rule4140t   pattern4141R  t   rule4141t   pattern4142R  t   rule4142t   pattern4143R  t   rule4143t   pattern4144R  t   rule4144t   pattern4145R  t   rule4145t   pattern4146R  t   rule4146t   pattern4147R  t   rule4147t   pattern4148R  t   rule4148t   pattern4149R  t   rule4149t   pattern4150R  t   rule4150t   pattern4151R  t   rule4151t   pattern4152R  t   rule4152t   pattern4153R  t   rule4153t   pattern4154R  t   rule4154t   pattern4155R  t   rule4155t   pattern4156R  t   rule4156t   pattern4157R  t   rule4157t   pattern4158R  t   rule4158t   pattern4159R  t   rule4159t   pattern4160R  t   rule4160t   pattern4161R  t   rule4161t   pattern4162R  t   rule4162t   pattern4163R  t   rule4163t   pattern4164R  t   rule4164t   pattern4165R  t   rule4165t   pattern4166R  t   rule4166t   pattern4167R  t   rule4167t   pattern4168R  t   rule4168t   pattern4169R  t   rule4169t   pattern4170R  t   rule4170t   pattern4171R  t   rule4171t   pattern4172R  t   rule4172t   pattern4173R  t   rule4173t   pattern4174R  t   rule4174t   pattern4175R  t   rule4175t   pattern4176R  t   rule4176t   pattern4177R  t   rule4177t   pattern4178R  t   rule4178t   pattern4179R  t   rule4179t   pattern4180R  t   rule4180t   pattern4181R  t   rule4181t   pattern4182R  t   rule4182t   pattern4183R   t   rule4183t   pattern4184R  t   rule4184t   pattern4185R  t   rule4185t   pattern4186R  t   rule4186t   pattern4187R  t   rule4187t   pattern4188R  t   rule4188t   pattern4189R  t   rule4189t   pattern4190R  t   rule4190t   pattern4191R  t   rule4191t   pattern4192R	  t   rule4192t   pattern4193R
  t   rule4193t   pattern4194R  t   rule4194t   pattern4195R  t   rule4195t   pattern4196R  t   rule4196t   pattern4197R  t   rule4197t   pattern4198R  t   rule4198t   pattern4199R  t   rule4199t   pattern4200R  t   rule4200t   pattern4201R  t   rule4201t   pattern4202R  t   rule4202t   pattern4203R  t   rule4203t   pattern4204R  t   rule4204t   pattern4205R  t   rule4205t   pattern4206R  t   rule4206t   pattern4207R  t   rule4207t   pattern4208R  t   rule4208t   pattern4209R  t   rule4209t   pattern4210R  t   rule4210t   pattern4211R  t   rule4211t   pattern4212R  t   rule4212t   pattern4213R  t   rule4213t   pattern4214R  t   rule4214t   pattern4215R   t   rule4215t   pattern4216R!  t   rule4216t   pattern4217R"  t   rule4217t   pattern4218R#  t   rule4218t   pattern4219R$  t   rule4219t   pattern4220R%  t   rule4220t   pattern4221R&  t   rule4221t   pattern4222R'  t   rule4222t   pattern4223R(  t   rule4223t   pattern4224R)  t   rule4224t   pattern4225R*  t   rule4225t   pattern4226R+  t   rule4226t   pattern4227R,  t   rule4227t   pattern4228R-  t   rule4228t   pattern4229R.  t   rule4229t   pattern4230R/  t   rule4230t   pattern4231R0  t   rule4231t   pattern4232R1  t   rule4232t   pattern4233R2  t   rule4233t   pattern4234R3  t   rule4234t   pattern4235R4  t   rule4235t   pattern4236R5  t   rule4236t   pattern4237R6  t   rule4237t   pattern4238R7  t   rule4238t   pattern4239R8  t   rule4239t   pattern4240R9  t   rule4240t   pattern4241R:  t   rule4241t   pattern4242R;  t   rule4242t   pattern4243R<  t   rule4243t   pattern4244R=  t   rule4244t   pattern4245R>  t   rule4245t   pattern4246R?  t   rule4246t   pattern4247R@  t   rule4247t   pattern4248RA  t   rule4248t   pattern4249RB  t   rule4249t   pattern4250RC  t   rule4250t   pattern4251RD  t   rule4251t   pattern4252RE  t   rule4252t   pattern4253RF  t   rule4253t   pattern4254RG  t   rule4254t   pattern4255RH  t   rule4255t   pattern4256RI  t   rule4256t   pattern4257RJ  t   rule4257t   pattern4258RK  t   rule4258t   pattern4259RL  t   rule4259t   pattern4260RM  t   rule4260t   pattern4261RN  t   rule4261t   pattern4262RO  t   rule4262t   pattern4263RP  t   rule4263t   pattern4264RQ  t   rule4264t   pattern4265RR  t   rule4265t   pattern4266RS  t   rule4266t   pattern4267RT  t   rule4267t   pattern4268RU  t   rule4268t   pattern4269RV  t   rule4269t   pattern4270RW  t   rule4270t   pattern4271RX  t   rule4271t   pattern4272RY  t   rule4272t   pattern4273RZ  t   rule4273t   pattern4274R[  t   rule4274t   pattern4275R\  t   rule4275t   pattern4276R]  t   rule4276t   pattern4277R^  t   rule4277t   pattern4278R_  t   rule4278t   pattern4279R`  t   rule4279t   pattern4280Ra  t   rule4280t   pattern4281Rb  t   rule4281t   pattern4282Rc  t   rule4282t   pattern4283Rd  t   rule4283t   pattern4284Re  t   rule4284t   pattern4285Rg  t   rule4285t   pattern4286Rh  t   rule4286t   pattern4287Ri  t   rule4287t   pattern4288Rj  t   rule4288t   pattern4289Rk  t   rule4289t   pattern4290Rl  t   rule4290t   pattern4291Rm  t   rule4291t   pattern4292Rn  t   rule4292t   pattern4293Ro  t   rule4293t   pattern4294Rp  t   rule4294t   pattern4295Rq  t   rule4295t   pattern4296Rr  t   rule4296t   pattern4297Rs  t   rule4297t   pattern4298Rt  t   rule4298t   pattern4299Ru  t   rule4299t   pattern4300Rv  t   rule4300t   pattern4301Rw  t   rule4301t   pattern4302Rx  t   rule4302t   pattern4303Ry  t   rule4303t   pattern4304Rz  t   rule4304t   pattern4305R{  t   rule4305t   pattern4306R|  t   rule4306t   pattern4307R}  t   rule4307t   pattern4308R~  t   rule4308t   pattern4309R  t   rule4309t   pattern4310R  t   rule4310t   pattern4311R  t   rule4311t   pattern4312R  t   rule4312t   pattern4313R  t   rule4313t   pattern4314R  t   rule4314t   pattern4315R  t   rule4315t   pattern4316R  t   rule4316t   pattern4317R  t   rule4317t   pattern4318R  t   rule4318t   pattern4319R  t   rule4319t   pattern4320R  t   rule4320t   pattern4321R  t   rule4321t   pattern4322R  t   rule4322t   pattern4323R  t   rule4323t   pattern4324R  t   rule4324t   pattern4325R  t   rule4325t   pattern4326R  t   rule4326t   pattern4327R  t   rule4327t   pattern4328R  t   rule4328t   pattern4329R  t   rule4329t   pattern4330R  t   rule4330t   pattern4331R  t   rule4331t   pattern4332R  t   rule4332t   pattern4333R  t   rule4333t   pattern4334R  t   rule4334t   pattern4335R  t   rule4335t   pattern4336R  t   rule4336t   pattern4337R  t   rule4337t   pattern4338R  t   rule4338t   pattern4339R  t   rule4339t   pattern4340R  t   rule4340t   pattern4341R  t   rule4341t   pattern4342R  t   rule4342t   pattern4343R  t   rule4343t   pattern4344R  t   rule4344t   pattern4345R  t   rule4345t   pattern4346R  t   rule4346t   pattern4347R  t   rule4347t   pattern4348R  t   rule4348t   pattern4349R  t   rule4349t   pattern4350R  t   rule4350t   pattern4351R  t   rule4351t   pattern4352R  t   rule4352t   pattern4353R  t   rule4353t   pattern4354R  t   rule4354t   pattern4355R  t   rule4355t   pattern4356R  t   rule4356t   pattern4357R  t   rule4357t   pattern4358R  t   rule4358t   pattern4359R  t   rule4359t   pattern4360R  t   rule4360t   pattern4361R  t   rule4361t   pattern4362R  t   rule4362t   pattern4363R  t   rule4363t   pattern4364R  t   rule4364t   pattern4365R  t   rule4365t   pattern4366R  t   rule4366t   pattern4367R  t   rule4367t   pattern4368R  t   rule4368t   pattern4369R  t   rule4369t   pattern4370R  t   rule4370t   pattern4371R  t   rule4371t   pattern4372R  t   rule4372t   pattern4373R  t   rule4373t   pattern4374R  t   rule4374t   pattern4375R  t   rule4375t   pattern4376R  t   rule4376t   pattern4377R  t   rule4377t   pattern4378R  t   rule4378t   pattern4379R  t   rule4379t   pattern4380R  t   rule4380t   pattern4381R  t   rule4381t   pattern4382R  t   rule4382t   pattern4383R  t   rule4383t   pattern4384R  t   rule4384t   pattern4385R  t   rule4385t   pattern4386R  t   rule4386t   pattern4387R  t   rule4387t   pattern4388R  t   rule4388t   pattern4389R  t   rule4389t   pattern4390R  t   rule4390t   pattern4391R  t   rule4391t   pattern4392R  t   rule4392t   pattern4393R  t   rule4393t   pattern4394R  t   rule4394t   pattern4395R  t   rule4395t   pattern4396R  t   rule4396t   pattern4397R  t   rule4397t   pattern4398R  t   rule4398t   pattern4399R  t   rule4399t   pattern4400R  t   rule4400t   pattern4401R  t   rule4401t   pattern4402R  t   rule4402t   pattern4403R  t   rule4403t   pattern4404R  t   rule4404t   pattern4405R  t   rule4405t   pattern4406R  t   rule4406t   pattern4407R  t   rule4407t   pattern4408R  t   rule4408t   pattern4409R  t   rule4409t   pattern4410R  t   rule4410t   pattern4411R  t   rule4411t   pattern4412R  t   rule4412t   pattern4413R  t   rule4413t   pattern4414R  t   rule4414t   pattern4415R  t   rule4415t   pattern4416R  t   rule4416t   pattern4417R  t   rule4417t   pattern4418R  t   rule4418t   pattern4419R  t   rule4419t   pattern4420R  t   rule4420t   pattern4421R  t   rule4421t   pattern4422R  t   rule4422t   pattern4423R  t   rule4423t   pattern4424R  t   rule4424t   pattern4425R  t   rule4425t   pattern4426R  t   rule4426t   pattern4427R  t   rule4427t   pattern4428R  t   rule4428t   pattern4429R  t   rule4429t   pattern4430R  t   rule4430t   pattern4431R  t   rule4431t   pattern4432R  t   rule4432t   pattern4433R  t   rule4433t   pattern4434R  t   rule4434t   pattern4435R  t   rule4435t   pattern4436R   t   rule4436t   pattern4437R  t   rule4437t   pattern4438R  t   rule4438t   pattern4439R  t   rule4439t   pattern4440R  t   rule4440t   pattern4441R  t   rule4441t   pattern4442R  t   rule4442t   pattern4443R  t   rule4443t   pattern4444R  t   rule4444t   pattern4445R	  t   rule4445t   pattern4446R
  t   rule4446t   pattern4447R  t   rule4447t   pattern4448R  t   rule4448t   pattern4449R  t   rule4449t   pattern4450R  t   rule4450t   pattern4451R  t   rule4451t   pattern4452R  t   rule4452t   pattern4453R  t   rule4453t   pattern4454R  t   rule4454t   pattern4455R  t   rule4455t   pattern4456R  t   rule4456t   pattern4457R  t   rule4457t   pattern4458R  t   rule4458t   pattern4459R  t   rule4459t   pattern4460R  t   rule4460t   pattern4461R  t   rule4461t   pattern4462R  t   rule4462t   pattern4463R  t   rule4463t   pattern4464R  t   rule4464t   pattern4465R  t   rule4465t   pattern4466R  t   rule4466t   pattern4467R   t   rule4467t   pattern4468R!  t   rule4468t   pattern4469R"  t   rule4469t   pattern4470R#  t   rule4470t   pattern4471R$  t   rule4471t   pattern4472R%  t   rule4472t   pattern4473R&  t   rule4473t   pattern4474R'  t   rule4474t   pattern4475R(  t   rule4475t   pattern4476R)  t   rule4476t   pattern4477R*  t   rule4477t   pattern4478R+  t   rule4478t   pattern4479R,  t   rule4479t   pattern4480R-  t   rule4480t   pattern4481R.  t   rule4481t   pattern4482R/  t   rule4482t   pattern4483R0  t   rule4483t   pattern4484R1  t   rule4484t   pattern4485R2  t   rule4485t   pattern4486R3  t   rule4486t   pattern4487R4  t   rule4487t   pattern4488R5  t   rule4488t   pattern4489R6  t   rule4489t   pattern4490R7  t   rule4490t   pattern4491R8  t   rule4491t   pattern4492R9  t   rule4492t   pattern4493R:  t   rule4493t   pattern4494R;  t   rule4494t   pattern4495R<  t   rule4495t   pattern4496R=  t   rule4496t   pattern4497R>  t   rule4497t   pattern4498R?  t   rule4498t   pattern4499R@  t   rule4499t   pattern4500RA  t   rule4500t   pattern4501RB  t   rule4501t   pattern4502RC  t   rule4502t   pattern4503RD  t   rule4503t   pattern4504RE  t   rule4504t   pattern4505RF  t   rule4505t   pattern4506RG  t   rule4506t   pattern4507RH  t   rule4507t   pattern4508RI  t   rule4508t   pattern4509RJ  t   rule4509t   pattern4510RK  t   rule4510t   pattern4511RL  t   rule4511t   pattern4512RM  t   rule4512t   pattern4513RN  t   rule4513t   pattern4514RO  t   rule4514t   pattern4515RP  t   rule4515t   pattern4516RQ  t   rule4516t   pattern4517RR  t   rule4517t   pattern4518RS  t   rule4518t   pattern4519RT  t   rule4519t   pattern4520RU  t   rule4520t   pattern4521RV  t   rule4521t   pattern4522RW  t   rule4522t   pattern4523RX  t   rule4523t   pattern4524RY  t   rule4524t   pattern4525RZ  t   rule4525t   pattern4526R[  t   rule4526t   pattern4527R\  t   rule4527t   pattern4528R]  t   rule4528t   pattern4529R^  t   rule4529t   pattern4530R_  t   rule4530t   pattern4531R`  t   rule4531t   pattern4532Ra  t   rule4532t   pattern4533Rb  t   rule4533t   pattern4534Rc  t   rule4534t   pattern4535Rd  t   rule4535t   pattern4536Re  t   rule4536t   pattern4537Rf  t   rule4537t   pattern4538Rg  t   rule4538t   pattern4539Rh  t   rule4539t   pattern4540Ri  t   rule4540t   pattern4541Rj  t   rule4541t   pattern4542Rk  t   rule4542t   pattern4543Rl  t   rule4543t   pattern4544Rm  t   rule4544t   pattern4545Rn  t   rule4545t   pattern4546Ro  t   rule4546t   pattern4547Rp  t   rule4547t   pattern4548Rq  t   rule4548t   pattern4549Rr  t   rule4549t   pattern4550Rs  t   rule4550t   pattern4551Rt  t   rule4551t   pattern4552Ru  t   rule4552t   pattern4553Rv  t   rule4553t   pattern4554Rw  t   rule4554t   pattern4555Rx  t   rule4555t   pattern4556Ry  t   rule4556t   pattern4557Rz  t   rule4557t   pattern4558R{  t   rule4558t   pattern4559R|  t   rule4559t   pattern4560R}  t   rule4560t   pattern4561R~  t   rule4561t   pattern4562R  t   rule4562t   pattern4563R  t   rule4563t   pattern4564R  t   rule4564t   pattern4565R  t   rule4565t   pattern4566R  t   rule4566t   pattern4567R  t   rule4567t   pattern4568R  t   rule4568t   pattern4569R  t   rule4569t   pattern4570R  t   rule4570t   pattern4571R  t   rule4571t   pattern4572R  t   rule4572t   pattern4573R  t   rule4573t   pattern4574R  t   rule4574t   pattern4575R  t   rule4575t   pattern4576R  t   rule4576t   pattern4577R  t   rule4577t   pattern4578R  t   rule4578t   pattern4579R  t   rule4579t   pattern4580R  t   rule4580t   pattern4581R  t   rule4581t   pattern4582R  t   rule4582t   pattern4583R  t   rule4583t   pattern4584R  t   rule4584t   pattern4585R  t   rule4585t   pattern4586R  t   rule4586t   pattern4587R  t   rule4587t   pattern4588R  t   rule4588t   pattern4589R  t   rule4589t   pattern4590R  t   rule4590t   pattern4591R  t   rule4591t   pattern4592R  t   rule4592t   pattern4593R  t   rule4593t   pattern4594R  t   rule4594t   pattern4595R  t   rule4595t   pattern4596R  t   rule4596t   pattern4597R  t   rule4597t   pattern4598R  t   rule4598t   pattern4599R  t   rule4599t   pattern4600R  t   rule4600t   pattern4601R  t   rule4601t   pattern4602R  t   rule4602R  t   pattern4603t   rule4603R  t   pattern4604t   rule4604R  t   pattern4605t   rule4605R  t   pattern4606t   rule4606R  t   pattern4607t   rule4607R  t   pattern4608t   rule4608R  t   pattern4609t   rule4609R  t   pattern4610t   rule4610t   pattern4611R  t   rule4611t   pattern4612R  t   rule4612R  t   pattern4613t   rule4613R  t   pattern4614t   rule4614R  t   pattern4615t   rule4615R  t   pattern4616t   rule4616t   pattern4617R  t   rule4617t   pattern4618R  t   rule4618t   pattern4619R  t   rule4619t   pattern4620R  t   rule4620R  t   pattern4621t   rule4621R  t   pattern4622t   rule4622R  t   pattern4623t   rule4623R  t   pattern4624t   rule4624R  t   pattern4625t   rule4625R  t   pattern4626t   rule4626t   pattern4627R  t   rule4627t   pattern4628R  t   rule4628t   pattern4629R  t   rule4629t   pattern4630R  t   rule4630t   pattern4631R  t   rule4631t   pattern4632R  t   rule4632R  t   pattern4633t   rule4633R  t   pattern4634t   rule4634R  t   pattern4635t   rule4635R  t   pattern4636t   rule4636t   pattern4637R  t   rule4637t   pattern4638R  t   rule4638t   pattern4639R  t   rule4639t   pattern4640R  t   rule4640R  t   pattern4641t   rule4641R  t   pattern4642t   rule4642t   pattern4643R  t   rule4643t   pattern4644R  t   rule4644t   pattern4645R  t   rule4645t   pattern4646R  t   rule4646t   pattern4647R  t   rule4647t   pattern4648R  t   rule4648t   pattern4649R  t   rule4649t   pattern4650R  t   rule4650t   pattern4651R  t   rule4651t   pattern4652R  t   rule4652t   pattern4653R  t   rule4653t   pattern4654R  t   rule4654t   pattern4655R  t   rule4655t   pattern4656R  t   rule4656t   pattern4657R  t   rule4657t   pattern4658R  t   rule4658t   pattern4659R  t   rule4659t   pattern4660R  t   rule4660t   pattern4661R  t   rule4661t   pattern4662R  t   rule4662t   pattern4663R  t   rule4663t   pattern4664R  t   rule4664t   pattern4665R  t   rule4665t   pattern4666R  t   rule4666t   pattern4667R  t   rule4667t   pattern4668R  t   rule4668t   pattern4669R  t   rule4669t   pattern4670R  t   rule4670t   pattern4671R  t   rule4671t   pattern4672R  t   rule4672t   pattern4673R  t   rule4673t   pattern4674R  t   rule4674t   pattern4675R  t   rule4675t   pattern4676R  t   rule4676t   pattern4677R  t   rule4677t   pattern4678R  t   rule4678t   pattern4679R  t   rule4679t   pattern4680R  t   rule4680t   pattern4681R  t   rule4681t   pattern4682R  t   rule4682t   pattern4683R  t   rule4683t   pattern4684R  t   rule4684(    (   R  s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   secant   s       XXggggTTddggqqmmttwwttttttmmuuttqqwwttqq                   F F   " " 
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                       ( (   " " % %   " " = = O O                             	 	                   
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     V V * *           - - * *         1 1 a a   p p * * N N   N N   K K   k k % % k k % % q q + + X X   X X   k k % % n n ( ( k k % % n n ( ( k k % % k k % % ` `   f f       @ @ w w 1 1   N Nqqxx{{{{       D D ) ) T T W W K K J T 5 ?        }}cc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  Rf  R  R  R  t   sympyR  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   sympy.integrals.rubi.symbolR  t   sympy.core.symbolR  R  t   sympy.functionsR  R  R  R  R  R  R  t%   sympy.functions.elementary.hyperbolicR  R  R  R  R  R  R  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  t   Pit   iR  t   B_t   C_t   F_t   G_t   H_R  t   b_R  t   d_R	  t   f_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_t   w_R  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_R  t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_t   n3_t   Pq_t   Pm_t   Px_t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_t   iit   Pqqt   Qt   Rt   rR  t   kR  t   Falset	   _UseGammat	   ShowStepst   Nonet   StepCounterR
  (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/rubi/rules/secant.pyt   <module>   s>   "           1nj:R4|'	