




from math import factorial





class     lowerCamelCase__:
      def __init__(				self: List[str]    ,       UpperCamelCase_: str    ,       UpperCamelCase_: int   ):
             __lowerCamelCase   =						real
             if isinstance(UpperCamelCase_    ,       UpperCamelCase_   ):
                    __lowerCamelCase   =						[1] * rank
             else:
                    __lowerCamelCase   =						rank
      def __repr__(				self: List[Any]   ):
             return (
                 F'{self.real}+'
                 F'{"+".join(str(UpperCamelCase_   )+"E"+str(n+1   )for n,dual in enumerate(self.duals   )   )}'
             )
      def 			lowerCAmelCase__						(				self: Tuple   ):
             __lowerCamelCase   =						self.duals.copy()
             while cur[-1] == 0:
                    cur.pop(-1   )
             return Dual(self.real    ,       UpperCamelCase_   )
      def __add__(				self: int    ,       UpperCamelCase_: Tuple   ):
             if not isinstance(UpperCamelCase_    ,       UpperCamelCase_   ):
                    return Dual(self.real + other    ,       self.duals   )
             __lowerCamelCase   =						self.duals.copy()
             __lowerCamelCase   =						other.duals.copy()
             if len(UpperCamelCase_   ) > len(UpperCamelCase_   ):
                    o_dual.extend([1] * (len(UpperCamelCase_   ) - len(UpperCamelCase_   ))   )
             elif len(UpperCamelCase_   ) < len(UpperCamelCase_   ):
                    s_dual.extend([1] * (len(UpperCamelCase_   ) - len(UpperCamelCase_   ))   )
             __lowerCamelCase   =						[]
             for i in range(len(UpperCamelCase_   )   ):
                    new_duals.append(s_dual[i] + o_dual[i]   )
             return Dual(self.real + other.real    ,       UpperCamelCase_   )

      UpperCAmelCase__      :	Dict    		=   __add__
      def __sub__(				self: List[str]    ,       UpperCamelCase_: Dict   ):
             return self + other * -1
      def __mul__(				self: Any    ,       UpperCamelCase_: Optional[Any]   ):
             if not isinstance(UpperCamelCase_    ,       UpperCamelCase_   ):
                    __lowerCamelCase   =						[]
                    for i in self.duals:
                           new_duals.append(i * other   )
                    return Dual(self.real * other    ,       UpperCamelCase_   )
             __lowerCamelCase   =						[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    ,       UpperCamelCase_   )

      UpperCAmelCase__      :	Optional[int]    		=   __mul__
      def __truediv__(				self: Dict    ,       UpperCamelCase_: Tuple   ):
             if not isinstance(UpperCamelCase_    ,       UpperCamelCase_   ):
                    __lowerCamelCase   =						[]
                    for i in self.duals:
                           new_duals.append(i / other   )
                    return Dual(self.real / other    ,       UpperCamelCase_   )
             raise ValueError
      def __floordiv__(				self: int    ,       UpperCamelCase_: int   ):
             if not isinstance(UpperCamelCase_    ,       UpperCamelCase_   ):
                    __lowerCamelCase   =						[]
                    for i in self.duals:
                           new_duals.append(i // other   )
                    return Dual(self.real // other    ,       UpperCamelCase_   )
             raise ValueError




      def __pow__(				self: Tuple    ,       UpperCamelCase_: str   ):
             if n < 0 or isinstance(UpperCamelCase_    ,       UpperCamelCase_   ):
                    raise ValueError("""power must be a positive integer"""   )
             if n == 0:
                    return 1
             if n == 1:
                    return self
             __lowerCamelCase   =						self
             for _ in range(n - 1   ):
                    x *= self
             return x




def 					lowerCamelCase__       (						A__       :					List[str]  ,			A__       :					str  ,			A__       :					str	):





       '''simple docstring'''



       if not callable(A__	):
              raise ValueError("""differentiate() requires a function as input for func"""	)
       if not isinstance(A__  ,			(float, int)	):
              raise ValueError("""differentiate() requires a float as input for position"""	)
       if not isinstance(A__  ,			A__	):
              raise ValueError("""differentiate() requires an int as input for order"""	)
       __lowerCamelCase   =						Dual(A__  ,			1	)
       __lowerCamelCase   =						func(A__	)
       if order == 0:
              return result.real
       return result.duals[order - 1] * factorial(A__	)


if __name__ == "__main__":
       import doctest

       doctest.testmod()




       def 					lowerCamelCase__       (						A__       :					int	):





              '''simple docstring'''



              return y**2 * y**4




       print(differentiate(f, 9, 2))






'''simple docstring'''




from __future__ import annotations


def 				lowerCAmelCase_   (	_lowerCamelCase:   list[int]					):
		if not nums:
				return 0
		__SCREAMING_SNAKE_CASE       :		Optional[int]           =		nums[0]
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0
		for num in nums[1:]:
				__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       :		Any           =		(
				    max_excluding + num,
				    max(_lowerCamelCase       ,      _lowerCamelCase					),
				)
		return max(_lowerCamelCase       ,      _lowerCamelCase					)


if __name__ == "__main__":
						import doctest

						doctest.testmod()