


'''simple docstring'''



from math import factorial





class 							__UpperCamelCase    :




 def __init__(       self						,    __a						,    __a							):

      '''simple docstring'''





      __a      :	List[str]    =  real
      if isinstance(__a						,    __a							):
           __a      :	int    =  [1] * rank
      else:
           __a      :	Optional[int]    =  rank




 def __repr__(       self							):

      '''simple docstring'''





      return (
          f"""{self.real}+"""
          f"""{"+".join(str(__a							)+"E"+str(n+1							)for n,dual in enumerate(self.duals							)							)}"""
      )




 def 				__UpperCAmelCase							(       self							):

      '''simple docstring'''





      __a      :	List[str]    =  self.duals.copy()
      while cur[-1] == 0:
           cur.pop(-1							)
      return Dual(self.real						,    __a							)




 def __add__(       self						,    __a							):

      '''simple docstring'''





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

 A_           =   __add__




 def __sub__(       self						,    __a							):

      '''simple docstring'''





      return self + other * -1




 def __mul__(       self						,    __a							):

      '''simple docstring'''





      if not isinstance(__a						,    __a							):
           __a      :	Dict    =  []
           for i in self.duals:
                new_duals.append(i * other							)
           return Dual(self.real * other						,    __a							)
      __a      :	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						,    __a							)

 A_           =   __mul__




 def __truediv__(       self						,    __a							):

      '''simple docstring'''





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




 def __floordiv__(       self						,    __a							):

      '''simple docstring'''





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





 def __pow__(       self						,    __a							):

      '''simple docstring'''





      if n < 0 or isinstance(__a						,    __a							):
           raise ValueError('power must be a positive integer'							)
      if n == 0:
           return 1
      if n == 1:
           return self
      __a      :	List[str]    =  self
      for _ in range(n - 1							):
           x *= self
      return x






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Dict						,				_SCREAMING_SNAKE_CASE				:       Optional[int]						,				_SCREAMING_SNAKE_CASE				:       Union[str, Any]       ):
     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      :	str    =  Dual(_SCREAMING_SNAKE_CASE						,				1       )
     __a      :	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   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Dict       ):
      return y**2 * y**4




 print(differentiate(f, 9, 2))







'''simple docstring'''



import re

from filelock import FileLock


try:
	import nltk

	__lowercase     :						Optional[Any]	=     True
except (ImportError, ModuleNotFoundError):
	__lowercase     :						Dict	=     False

if NLTK_AVAILABLE:
	with FileLock('.lock') as lock:
		nltk.download('punkt', quiet=True)






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       str       ):
					re.sub('<n>'						,				''						,				_SCREAMING_SNAKE_CASE       )  # remove pegasus newline char
					assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
					return "\n".join(nltk.sent_tokenize(_SCREAMING_SNAKE_CASE       )       )



