
'''simple docstring'''
from math import factorial







class  __A				:
 def __init__(   self			:    Dict				,   lowerCamelCase			:    List[Any]				,   lowerCamelCase			:    Tuple       ):



   """simple docstring"""





   __A		:     Dict												=		real
   if isinstance(lowerCamelCase				,   lowerCamelCase       ):
     __A		:     List[str]												=		[1] * rank
   else:
     __A		:     str												=		rank
 def __repr__(   self			:    Optional[Any]       ):



   """simple docstring"""





   return (
       f"{self.real}+"
       f"{'+'.join(str(lowerCamelCase       )+'E'+str(n+1       )for n,dual in enumerate(self.duals       )       )}"
   )
 def 		lowercase_(   self			:    Dict       ):



   """simple docstring"""





   __A		:     int												=		self.duals.copy()
   while cur[-1] == 0:
     cur.pop(-1       )
   return Dual(self.real				,   lowerCamelCase       )
 def __add__(   self			:    List[str]				,   lowerCamelCase			:    List[str]       ):



   """simple docstring"""





   if not isinstance(lowerCamelCase				,   lowerCamelCase       ):
     return Dual(self.real + other				,   self.duals       )
   __A		:     Dict												=		self.duals.copy()
   __A		:     Optional[int]												=		other.duals.copy()
   if len(lowerCamelCase       ) > len(lowerCamelCase       ):
     o_dual.extend([1] * (len(lowerCamelCase       ) - len(lowerCamelCase       ))       )
   elif len(lowerCamelCase       ) < len(lowerCamelCase       ):
     s_dual.extend([1] * (len(lowerCamelCase       ) - len(lowerCamelCase       ))       )
   __A		:     Any												=		[]
   for i in range(len(lowerCamelCase       )       ):
     new_duals.append(s_dual[i] + o_dual[i]       )
   return Dual(self.real + other.real				,   lowerCamelCase       )

 lowerCamelCase				       =__add__
 def __sub__(   self			:    Optional[int]				,   lowerCamelCase			:    str       ):



   """simple docstring"""





   return self + other * -1
 def __mul__(   self			:    int				,   lowerCamelCase			:    Any       ):



   """simple docstring"""





   if not isinstance(lowerCamelCase				,   lowerCamelCase       ):
     __A		:     List[str]												=		[]
     for i in self.duals:
       new_duals.append(i * other       )
     return Dual(self.real * other				,   lowerCamelCase       )
   __A		:     Optional[int]												=		[0] * (len(self.duals       ) + len(other.duals       ) + 1)
   for i, item in enumerate(self.duals       ):
     for j, jtem in enumerate(other.duals       ):
       new_duals[i + j + 1] += item * jtem
   for k in range(len(self.duals       )       ):
     new_duals[k] += self.duals[k] * other.real
   for index in range(len(other.duals       )       ):
     new_duals[index] += other.duals[index] * self.real
   return Dual(self.real * other.real				,   lowerCamelCase       )

 lowerCamelCase				       =__mul__
 def __truediv__(   self			:    int				,   lowerCamelCase			:    int       ):



   """simple docstring"""





   if not isinstance(lowerCamelCase				,   lowerCamelCase       ):
     __A		:     Union[str, Any]												=		[]
     for i in self.duals:
       new_duals.append(i / other       )
     return Dual(self.real / other				,   lowerCamelCase       )
   raise ValueError
 def __floordiv__(   self			:    Union[str, Any]				,   lowerCamelCase			:    Union[str, Any]       ):



   """simple docstring"""





   if not isinstance(lowerCamelCase				,   lowerCamelCase       ):
     __A		:     List[Any]												=		[]
     for i in self.duals:
       new_duals.append(i // other       )
     return Dual(self.real // other				,   lowerCamelCase       )
   raise ValueError






 def __pow__(   self			:    Any				,   lowerCamelCase			:    Optional[int]       ):



   """simple docstring"""





   if n < 0 or isinstance(lowerCamelCase				,   lowerCamelCase       ):
     raise ValueError("""power must be a positive integer"""       )
   if n == 0:
     return 1
   if n == 1:
     return self
   __A		:     Optional[Any]												=		self
   for _ in range(n - 1       ):
     x *= self
   return x







def        A_     (						__SCREAMING_SNAKE_CASE						:  Union[str, Any]			,     __SCREAMING_SNAKE_CASE						:  Dict			,     __SCREAMING_SNAKE_CASE						:  Optional[Any] )				->       Optional[int]:





  """simple docstring"""

  if not callable(__SCREAMING_SNAKE_CASE ):
    raise ValueError("""differentiate() requires a function as input for func""" )
  if not isinstance(__SCREAMING_SNAKE_CASE			,     (float, int) ):
    raise ValueError("""differentiate() requires a float as input for position""" )
  if not isinstance(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):
    raise ValueError("""differentiate() requires an int as input for order""" )
  __A		:     int												=		Dual(__SCREAMING_SNAKE_CASE			,     1 )
  __A		:     Optional[Any]												=		func(__SCREAMING_SNAKE_CASE )
  if order == 0:
    return result.real
  return result.duals[order - 1] * factorial(__SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
     import doctest

     doctest.testmod()







     def        A_     (						__SCREAMING_SNAKE_CASE						:  str )				->       Union[str, Any]:





       """simple docstring"""

       return y**2 * y**4

     print(differentiate(f, 9, 2))





'''simple docstring'''
def        A_     (						__SCREAMING_SNAKE_CASE						:  list			,     __SCREAMING_SNAKE_CASE						:  list			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int )				->       int:





  """simple docstring"""

  if index == number_of_items:
    return 0
  __A		:     List[Any]												=		0
  __A		:     Union[str, Any]												=		0
  __A		:     List[Any]												=		knapsack(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     index + 1 )
  if weights[index] <= max_weight:
    __A		:     Tuple												=		values[index] + knapsack(
        __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     max_weight - weights[index]			,     index + 1 )
  return max(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
     import doctest

     doctest.testmod()



