





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_A :   List[Any]  			=  {
    'configuration_lilt': ['LILT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'LiltConfig'],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _A :   Optional[Any]  			=  [
           'LILT_PRETRAINED_MODEL_ARCHIVE_LIST',
           'LiltForQuestionAnswering',
           'LiltForSequenceClassification',
           'LiltForTokenClassification',
           'LiltModel',
           'LiltPreTrainedModel',
       ]

if TYPE_CHECKING:
       from .configuration_lilt import LILT_PRETRAINED_CONFIG_ARCHIVE_MAP, LiltConfig

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_lilt import (
                  LILT_PRETRAINED_MODEL_ARCHIVE_LIST,
                  LiltForQuestionAnswering,
                  LiltForSequenceClassification,
                  LiltForTokenClassification,
                  LiltModel,
                  LiltPreTrainedModel,
              )

else:
       import sys

       _A :   Optional[int]  			=  _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)











from math import factorial


class        __SCREAMING_SNAKE_CASE      :







       def __init__(				self					:     List[Any]		, A					:     Dict		, A					:     Any      )       ->Optional[Any]:
          lowerCamelCase__       :						Tuple        =							real
          if isinstance(A		, A      ):
             lowerCamelCase__       :						Optional[int]        =							[1] * rank
          else:
             lowerCamelCase__       :						List[Any]        =							rank







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







       def 						__lowerCamelCase   (				self					:     List[Any]      )       ->List[Any]:
          lowerCamelCase__       :						Tuple        =							self.duals.copy()
          while cur[-1] == 0:
             cur.pop(-1      )
          return Dual(self.real		, A      )







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

       _UpperCAmelCase				:  List[Any]			   =   __add__







       def __sub__(				self					:     Any		, A					:     Dict      )       ->int:
          return self + other * -1







       def __mul__(				self					:     Optional[Any]		, A					:     List[Any]      )       ->Union[str, Any]:
          if not isinstance(A		, A      ):
             lowerCamelCase__       :						Optional[int]        =							[]
             for i in self.duals:
                new_duals.append(i * other      )
             return Dual(self.real * other		, A      )
          lowerCamelCase__       :						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		, A      )

       _UpperCAmelCase				:  Optional[Any]			   =   __mul__







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







       def __floordiv__(				self					:     Dict		, A					:     Union[str, Any]      )       ->Union[str, Any]:
          if not isinstance(A		, A      ):
             lowerCamelCase__       :						Tuple        =							[]
             for i in self.duals:
                new_duals.append(i // other      )
             return Dual(self.real // other		, A      )
          raise ValueError







       def __pow__(				self					:     Any		, A					:     List[Any]      )       ->Tuple:
          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
          lowerCamelCase__       :						Union[str, Any]        =							self
          for _ in range(n - 1      ):
             x *= self
          return x



def 	_a						(   UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase					)    ->    Dict:







   """simple docstring"""
   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'''					)
   lowerCamelCase__       :						List[str]        =							Dual(UpperCAmelCase      ,  1					)
   lowerCamelCase__       :						Any        =							func(UpperCAmelCase					)
   if order == 0:
      return result.real
   return result.duals[order - 1] * factorial(UpperCAmelCase					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()



       def 	_a						(   UpperCAmelCase					)    ->    int:







          """simple docstring"""
          return y**2 * y**4




       print(differentiate(f, 9, 2))



