



from math import factorial



class 							lowerCAmelCase_						:
       def __init__(     self,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			)	->						Tuple:
          UpperCamelCase       :    Tuple		      =      real
          if isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
             UpperCamelCase       :    int		      =      [1] * rank
          else:
             UpperCamelCase       :    List[Any]		      =      rank
       def __repr__(     self			)	->						Any:
          return (
              F"""{self.real}+"""
              F"""{"+".join(str(SCREAMING_SNAKE_CASE_			)+"E"+str(n+1			)for n,dual in enumerate(self.duals			)			)}"""
          )
       def    snake_case_			(     self			)	->						str:
          UpperCamelCase       :    Optional[Any]		      =      self.duals.copy()
          while cur[-1] == 0:
             cur.pop(-1			)
          return Dual(self.real,     SCREAMING_SNAKE_CASE_			)
       def __add__(     self,     SCREAMING_SNAKE_CASE_			)	->						Union[str, Any]:
          if not isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
             return Dual(self.real + other,     self.duals			)
          UpperCamelCase       :    List[str]		      =      self.duals.copy()
          UpperCamelCase       :    Optional[int]		      =      other.duals.copy()
          if len(SCREAMING_SNAKE_CASE_			) > len(SCREAMING_SNAKE_CASE_			):
             o_dual.extend([1] * (len(SCREAMING_SNAKE_CASE_			) - len(SCREAMING_SNAKE_CASE_			))			)
          elif len(SCREAMING_SNAKE_CASE_			) < len(SCREAMING_SNAKE_CASE_			):
             s_dual.extend([1] * (len(SCREAMING_SNAKE_CASE_			) - len(SCREAMING_SNAKE_CASE_			))			)
          UpperCamelCase       :    Optional[Any]		      =      []
          for i in range(len(SCREAMING_SNAKE_CASE_			)			):
             new_duals.append(s_dual[i] + o_dual[i]			)
          return Dual(self.real + other.real,     SCREAMING_SNAKE_CASE_			)

       UpperCAmelCase__							:   List[Any]  	=    __add__
       def __sub__(     self,     SCREAMING_SNAKE_CASE_			)	->						List[str]:
          return self + other * -1
       def __mul__(     self,     SCREAMING_SNAKE_CASE_			)	->						List[Any]:
          if not isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
             UpperCamelCase       :    List[str]		      =      []
             for i in self.duals:
                new_duals.append(i * other			)
             return Dual(self.real * other,     SCREAMING_SNAKE_CASE_			)
          UpperCamelCase       :    Tuple		      =      [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,     SCREAMING_SNAKE_CASE_			)

       UpperCAmelCase__							:   int  	=    __mul__
       def __truediv__(     self,     SCREAMING_SNAKE_CASE_			)	->						Tuple:
          if not isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
             UpperCamelCase       :    Dict		      =      []
             for i in self.duals:
                new_duals.append(i / other			)
             return Dual(self.real / other,     SCREAMING_SNAKE_CASE_			)
          raise ValueError
       def __floordiv__(     self,     SCREAMING_SNAKE_CASE_			)	->						int:
          if not isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
             UpperCamelCase       :    Any		      =      []
             for i in self.duals:
                new_duals.append(i // other			)
             return Dual(self.real // other,     SCREAMING_SNAKE_CASE_			)
          raise ValueError






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






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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    def 						UpperCamelCase      (  snake_case__			:       str      )      ->	Optional[Any]:
       return y**2 * y**4


    print(differentiate(f, 9, 2))






'''simple docstring'''





from ...configuration_utils import PretrainedConfig
from ...utils import logging


UpperCamelCase_    						=       logging.get_logger(__name__)

UpperCamelCase_    						=       {
    """facebook/s2t-wav2vec2-large-en-de""": (
        """https://huggingface.co/facebook/s2t-wav2vec2-large-en-de/resolve/main/config.json"""
    ),
    # See all Speech2Text models at https://huggingface.co/models?filter=speech2text2
}





class 		__SCREAMING_SNAKE_CASE							(			lowercase__      ):
				lowerCamelCase_		       =    'speech_to_text_2'
				lowerCamelCase_		       =    ['past_key_values']
				lowerCamelCase_		       =    {'num_attention_heads': 'decoder_attention_heads', 'hidden_size': 'd_model'}







				def __init__(       self     :		int		,					UpperCAmelCase__     :		Dict=10000		,					UpperCAmelCase__     :		Optional[int]=6		,					UpperCAmelCase__     :		str=2048		,					UpperCAmelCase__     :		Optional[Any]=4		,					UpperCAmelCase__     :		Union[str, Any]=0.0		,					UpperCAmelCase__     :		Optional[Any]=True		,					UpperCAmelCase__     :		Optional[Any]="relu"		,					UpperCAmelCase__     :		List[str]=256		,					UpperCAmelCase__     :		Union[str, Any]=0.1		,					UpperCAmelCase__     :		List[Any]=0.0		,					UpperCAmelCase__     :		Optional[Any]=0.0		,					UpperCAmelCase__     :		Tuple=0.02		,					UpperCAmelCase__     :		int=2		,					UpperCAmelCase__     :		str=True		,					UpperCAmelCase__     :		str=1		,					UpperCAmelCase__     :		Optional[Any]=0		,					UpperCAmelCase__     :		Optional[int]=2		,					UpperCAmelCase__     :		List[Any]=1024		,					**UpperCAmelCase__     :		Dict		,					):
										'''simple docstring'''
										lowercase :							List[str]    		=vocab_size
										lowercase :							Optional[int]    		=d_model
										lowercase :							Optional[Any]    		=decoder_ffn_dim
										lowercase :							Any    		=decoder_layers
										lowercase :							Dict    		=decoder_attention_heads
										lowercase :							List[Any]    		=dropout
										lowercase :							List[Any]    		=attention_dropout
										lowercase :							Any    		=activation_dropout
										lowercase :							Optional[Any]    		=activation_function
										lowercase :							Optional[int]    		=init_std
										lowercase :							Dict    		=decoder_layerdrop
										lowercase :							Optional[int]    		=use_cache
										lowercase :							Optional[Any]    		=decoder_layers
										lowercase :							List[str]    		=scale_embedding  # scale factor will be sqrt(d_model) if True
										lowercase :							str    		=max_target_positions

										super().__init__(
										    pad_token_id=UpperCAmelCase__		,					bos_token_id=UpperCAmelCase__		,					eos_token_id=UpperCAmelCase__		,					decoder_start_token_id=UpperCAmelCase__		,					**UpperCAmelCase__		,					)





