





'''simple docstring'''




from math import factorial







class     A_      :




 def __init__(   self			:       Dict      ,     snake_case_			:       Optional[int]      ,     snake_case_			:       Dict       ):
      _UpperCAmelCase					=  real
      if isinstance(snake_case_      ,     snake_case_       ):
           _UpperCAmelCase					=  [1] * rank
      else:
           _UpperCAmelCase					=  rank




 def __repr__(   self			:       List[Any]       ):
      return (
          f'{self.real}+'
          f'{"+".join(str(snake_case_       )+"E"+str(n+1       )for n,dual in enumerate(self.duals       )       )}'
      )




 def 	lowercase      (   self			:       List[Any]       ):
      _UpperCAmelCase					=  self.duals.copy()
      while cur[-1] == 0:
           cur.pop(-1       )
      return Dual(self.real      ,     snake_case_       )




 def __add__(   self			:       Tuple      ,     snake_case_			:       List[str]       ):

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

 _lowerCamelCase    :					Any       			=				__add__




 def __sub__(   self			:       Optional[int]      ,     snake_case_			:       int       ):
      return self + other * -1




 def __mul__(   self			:       Union[str, Any]      ,     snake_case_			:       int       ):

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

 _lowerCamelCase    :					Tuple       			=				__mul__




 def __truediv__(   self			:       int      ,     snake_case_			:       int       ):

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




 def __floordiv__(   self			:       List[Any]      ,     snake_case_			:       Optional[int]       ):

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




 def __pow__(   self			:       Optional[Any]      ,     snake_case_			:       Dict       ):

      if n < 0 or isinstance(snake_case_      ,     snake_case_       ):
           raise ValueError("power must be a positive integer"       )
      if n == 0:
           return 1
      if n == 1:
           return self
      _UpperCAmelCase					=  self
      for _ in range(n - 1       ):
           x *= self
      return x





def       UpperCAmelCase_				(   __lowercase				: Optional[Any]     ,	__lowercase				: str     ,	__lowercase				: List[str]			)						->			Union[str, Any]:


     '''simple docstring'''



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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  def       UpperCAmelCase_				(   __lowercase				: int			)						->			Tuple:


       '''simple docstring'''



       return y**2 * y**4






  print(differentiate(f, 9, 2))







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


a_      =     {'configuration_plbart': ['PLBART_PRETRAINED_CONFIG_ARCHIVE_MAP', 'PLBartConfig']}

try:
			if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			a_      =     ['PLBartTokenizer']

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			a_      =     [
			    'PLBART_PRETRAINED_MODEL_ARCHIVE_LIST',
			    'PLBartForCausalLM',
			    'PLBartForConditionalGeneration',
			    'PLBartForSequenceClassification',
			    'PLBartModel',
			    'PLBartPreTrainedModel',
			]


if TYPE_CHECKING:
			from .configuration_plbart import PLBART_PRETRAINED_CONFIG_ARCHIVE_MAP, PLBartConfig

			try:
						if not is_sentencepiece_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_plbart import PLBartTokenizer

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_plbart import (
						    PLBART_PRETRAINED_MODEL_ARCHIVE_LIST,
						    PLBartForCausalLM,
						    PLBartForConditionalGeneration,
						    PLBartForSequenceClassification,
						    PLBartModel,
						    PLBartPreTrainedModel,
						)


else:
			import sys

			a_      =     _LazyModule(__name__, globals()['__file__'], _import_structure)