





from math import factorial







class      lowerCamelCase:
     '''simple docstring'''


     def __init__(    self				,     snake_case_				,     snake_case_							):
         _A     =							real
         if isinstance(snake_case_				,     snake_case_							):
             _A     =							[1] * rank
         else:
             _A     =							rank




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




     def        lowerCAmelCase__		(    self							):
         _A     =							self.duals.copy()
         while cur[-1] == 0:
             cur.pop(-1							)
         return Dual(self.real				,     snake_case_							)




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

     __magic_name__   =			__add__




     def __sub__(    self				,     snake_case_							):
         return self + other * -1




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

     __magic_name__   =			__mul__




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




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




     def __pow__(    self				,     snake_case_							):
         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
         _A     =							self
         for _ in range(n - 1							):
             x *= self
         return x





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> str:




    """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     =							Dual(_SCREAMING_SNAKE_CASE							,     1				)
    _A     =							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:




     """simple docstring"""




     return y**2 * y**4



 print(differentiate(f, 9, 2))












from ... import PretrainedConfig


__A							:			Optional[Any]         =			{
    "sijunhe/nezha-cn-base": "https://huggingface.co/sijunhe/nezha-cn-base/resolve/main/config.json",
}







class      lowerCamelCase(						__snake_case	):
     '''simple docstring'''


     __magic_name__   =			NEZHA_PRETRAINED_CONFIG_ARCHIVE_MAP
     __magic_name__   =			'nezha'




     def __init__(    self				,     snake_case_=2_1128				,     snake_case_=768				,     snake_case_=12				,     snake_case_=12				,     snake_case_=3072				,     snake_case_="gelu"				,     snake_case_=0.1				,     snake_case_=0.1				,     snake_case_=512				,     snake_case_=64				,     snake_case_=2				,     snake_case_=0.02				,     snake_case_=1E-12				,     snake_case_=0.1				,     snake_case_=0				,     snake_case_=2				,     snake_case_=3				,     snake_case_=True				,     **snake_case_				,     ):
         super().__init__(pad_token_id=snake_case_				,     bos_token_id=snake_case_				,     eos_token_id=snake_case_				,     **snake_case_							)

         _A     =							vocab_size
         _A     =							hidden_size
         _A     =							num_hidden_layers
         _A     =							num_attention_heads
         _A     =							hidden_act
         _A     =							intermediate_size
         _A     =							hidden_dropout_prob
         _A     =							attention_probs_dropout_prob
         _A     =							max_position_embeddings
         _A     =							max_relative_position
         _A     =							type_vocab_size
         _A     =							initializer_range
         _A     =							layer_norm_eps
         _A     =							classifier_dropout
         _A     =							use_cache





