from math import factorial



class 				a							:







 """simple docstring"""






 def __init__(					self		,				lowerCAmelCase_		,				lowerCAmelCase_							)  ->					List[str]:
        _A        =  real
        if isinstance(lowerCAmelCase_		,				lowerCAmelCase_							):
               _A        =  [1] * rank
        else:
               _A        =  rank



 def __repr__(					self							)  ->					Tuple:
        return (
            F'''{self.real}+'''
            F'''{'+'.join(str(lowerCAmelCase_							)+'E'+str(n+1							)for n,dual in enumerate(self.duals							)							)}'''
        )



 def      UpperCAmelCase							(					self							)  ->					Any:
        _A        =  self.duals.copy()
        while cur[-1] == 0:
               cur.pop(-1							)
        return Dual(self.real		,				lowerCAmelCase_							)



 def __add__(					self		,				lowerCAmelCase_							)  ->					Optional[int]:
        if not isinstance(lowerCAmelCase_		,				lowerCAmelCase_							):
               return Dual(self.real + other		,				self.duals							)
        _A        =  self.duals.copy()
        _A        =  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        =  []
        for i in range(len(lowerCAmelCase_							)							):
               new_duals.append(s_dual[i] + o_dual[i]							)
        return Dual(self.real + other.real		,				lowerCAmelCase_							)

 lowerCamelCase	:Dict    			=		__add__



 def __sub__(					self		,				lowerCAmelCase_							)  ->					Union[str, Any]:
        return self + other * -1



 def __mul__(					self		,				lowerCAmelCase_							)  ->					int:
        if not isinstance(lowerCAmelCase_		,				lowerCAmelCase_							):
               _A        =  []
               for i in self.duals:
                      new_duals.append(i * other							)
               return Dual(self.real * other		,				lowerCAmelCase_							)
        _A        =  [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	:Tuple    			=		__mul__



 def __truediv__(					self		,				lowerCAmelCase_							)  ->					int:
        if not isinstance(lowerCAmelCase_		,				lowerCAmelCase_							):
               _A        =  []
               for i in self.duals:
                      new_duals.append(i / other							)
               return Dual(self.real / other		,				lowerCAmelCase_							)
        raise ValueError



 def __floordiv__(					self		,				lowerCAmelCase_							)  ->					str:
        if not isinstance(lowerCAmelCase_		,				lowerCAmelCase_							):
               _A        =  []
               for i in self.duals:
                      new_duals.append(i // other							)
               return Dual(self.real // other		,				lowerCAmelCase_							)
        raise ValueError



 def __pow__(					self		,				lowerCAmelCase_							)  ->					Optional[int]:
        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        =  self
        for _ in range(n - 1							):
               x *= self
        return x






def  snake_case  (       snake_case__			:List[str]   ,	snake_case__			:Optional[Any]   ,	snake_case__			:Union[str, Any])						->   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""")
       _A        =  Dual(snake_case__   ,	1)
       _A        =  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  snake_case  (       snake_case__			:List[str])						->   List[Any]:
           return y**2 * y**4







    print(differentiate(f, 9, 2))





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


_SCREAMING_SNAKE_CASE										=						logging.get_logger(__name__)

_SCREAMING_SNAKE_CASE										=						{
    'microsoft/biogpt': 'https://huggingface.co/microsoft/biogpt/resolve/main/config.json',
    # See all BioGPT models at https://huggingface.co/models?filter=biogpt
}



class 				a							(			__lowerCAmelCase       ):







 """simple docstring"""






 lowerCamelCase	:Any    			=		'''biogpt'''



 def __init__(					self		,				lowerCAmelCase_=4_23_84		,				lowerCAmelCase_=10_24		,				lowerCAmelCase_=24		,				lowerCAmelCase_=16		,				lowerCAmelCase_=40_96		,				lowerCAmelCase_="gelu"		,				lowerCAmelCase_=0.1		,				lowerCAmelCase_=0.1		,				lowerCAmelCase_=10_24		,				lowerCAmelCase_=0.02		,				lowerCAmelCase_=1E-12		,				lowerCAmelCase_=True		,				lowerCAmelCase_=True		,				lowerCAmelCase_=0.0		,				lowerCAmelCase_=0.0		,				lowerCAmelCase_=1		,				lowerCAmelCase_=0		,				lowerCAmelCase_=2		,				**lowerCAmelCase_		,				)  ->					Tuple:
        _A        =  vocab_size
        _A        =  max_position_embeddings
        _A        =  hidden_size
        _A        =  num_hidden_layers
        _A        =  num_attention_heads
        _A        =  intermediate_size
        _A        =  hidden_act
        _A        =  hidden_dropout_prob
        _A        =  attention_probs_dropout_prob
        _A        =  initializer_range
        _A        =  layer_norm_eps
        _A        =  scale_embedding
        _A        =  use_cache
        _A        =  layerdrop
        _A        =  activation_dropout
        super().__init__(pad_token_id=lowerCAmelCase_		,				bos_token_id=lowerCAmelCase_		,				eos_token_id=lowerCAmelCase_		,				**lowerCAmelCase_							)




