





from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase_         =						{
    'configuration_informer': [
        'INFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'InformerConfig',
    ],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase_         =						[
          'INFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
          'InformerForPrediction',
          'InformerModel',
          'InformerPreTrainedModel',
      ]


if TYPE_CHECKING:
      from .configuration_informer import INFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, InformerConfig

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_informer import (
                INFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
                InformerForPrediction,
                InformerModel,
                InformerPreTrainedModel,
            )

else:
      import sys

      lowercase_         =						_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)







"""simple docstring"""






from math import factorial



class      A__  :




	'''simple docstring'''





	def __init__(	self:						str			,     _SCREAMING_SNAKE_CASE:						Tuple			,     _SCREAMING_SNAKE_CASE:						Any)							->			str:

				"""simple docstring"""

				__lowerCAmelCase :    str				=			real
				if isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    Optional[int]				=			[1] * rank
				else:
							__lowerCAmelCase :    Optional[Any]				=			rank

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

				"""simple docstring"""

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

	def 				_SCREAMING_SNAKE_CASE  (	self:						List[str])							->			Union[str, Any]:

				"""simple docstring"""

				__lowerCAmelCase :    List[str]				=			self.duals.copy()
				while cur[-1] == 0:
							cur.pop(-1)
				return Dual(self.real			,     _SCREAMING_SNAKE_CASE)

	def __add__(	self:						Optional[int]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			Union[str, Any]:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							return Dual(self.real + other			,     self.duals)
				__lowerCAmelCase :    int				=			self.duals.copy()
				__lowerCAmelCase :    List[Any]				=			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)))
				__lowerCAmelCase :    Tuple				=			[]
				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)

	SCREAMING_SNAKE_CASE        =      __add__

	def __sub__(	self:						Dict			,     _SCREAMING_SNAKE_CASE:						str)							->			Optional[Any]:

				"""simple docstring"""

				return self + other * -1

	def __mul__(	self:						str			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			Optional[int]:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    List[Any]				=			[]
							for i in self.duals:
										new_duals.append(i * other)
							return Dual(self.real * other			,     _SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    List[str]				=			[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)

	SCREAMING_SNAKE_CASE        =      __mul__

	def __truediv__(	self:						Any			,     _SCREAMING_SNAKE_CASE:						str)							->			Dict:

				"""simple docstring"""

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

	def __floordiv__(	self:						List[Any]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			str:

				"""simple docstring"""

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







	def __pow__(	self:						Optional[Any]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			List[Any]:

				"""simple docstring"""

				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
				__lowerCAmelCase :    List[Any]				=			self
				for _ in range(n - 1):
							x *= self
				return x






def      _lowercase							(    __snake_case   ,__snake_case   ,__snake_case      )		->  Any:
			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"      )
			__lowerCAmelCase :    Any				=			Dual(__snake_case   ,1      )
			__lowerCAmelCase :    Tuple				=			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      _lowercase							(    __snake_case      )		->  Tuple:
				return y**2 * y**4





	print(differentiate(f, 9, 2))