





from math import factorial




class   UpperCamelCase_       :


							def __init__(							self    :Optional[Any]							,				__A    :Any							,				__A    :str		)   ->   Tuple:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__			=      real
									if isinstance(__A							,				__A		):
											SCREAMING_SNAKE_CASE__			=      [1] * rank
									else:
											SCREAMING_SNAKE_CASE__			=      rank


							def __repr__(							self    :Tuple		)   ->   List[str]:



									"""simple docstring"""



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


							def      _snake_case  (							self    :int		)   ->   Dict:



									"""simple docstring"""



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


							def __add__(							self    :Optional[int]							,				__A    :Tuple		)   ->   Optional[int]:



									"""simple docstring"""



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

							lowerCamelCase_           =					__add__


							def __sub__(							self    :Tuple							,				__A    :Tuple		)   ->   Dict:



									"""simple docstring"""



									return self + other * -1


							def __mul__(							self    :str							,				__A    :Optional[int]		)   ->   List[str]:



									"""simple docstring"""



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

							lowerCamelCase_           =					__mul__


							def __truediv__(							self    :str							,				__A    :Any		)   ->   Optional[Any]:



									"""simple docstring"""



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


							def __floordiv__(							self    :Union[str, Any]							,				__A    :Union[str, Any]		)   ->   Optional[int]:



									"""simple docstring"""



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


							def __pow__(							self    :str							,				__A    :List[Any]		)   ->   str:



									"""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
									SCREAMING_SNAKE_CASE__			=      self
									for _ in range(n - 1		):
											x *= self
									return x






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


if __name__ == "__main__":
	import doctest

	doctest.testmod()






	def 				SCREAMING_SNAKE_CASE__							(       UpperCamelCase__:							Optional[int]    ):
			return y**2 * y**4

	print(differentiate(f, 9, 2))






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


_lowerCamelCase   				=			logging.get_logger(__name__)




class   UpperCamelCase_       (     UpperCamelCase__    ):
							lowerCamelCase_           =					"timm_backbone"


							def __init__(							self    :Union[str, Any]							,				__A    :str=None							,				__A    :Union[str, Any]=3							,				__A    :str=True							,				__A    :Any=True							,				__A    :Optional[Any]=None							,				**__A    :List[str]							,				)   ->   Tuple:



									"""simple docstring"""



									super().__init__(**__A		)
									SCREAMING_SNAKE_CASE__			=      backbone
									SCREAMING_SNAKE_CASE__			=      num_channels
									SCREAMING_SNAKE_CASE__			=      features_only
									SCREAMING_SNAKE_CASE__			=      use_pretrained_backbone
									SCREAMING_SNAKE_CASE__			=      True
									SCREAMING_SNAKE_CASE__			=      out_indices if out_indices is not None else (-1,)