






from math import factorial




class 							_lowerCAmelCase:





       """simple docstring"""







       def __init__(   self    ,     _lowerCamelCase    ,     _lowerCamelCase				):
         UpperCamelCase_:   List[Any]        =							real
         if isinstance(_lowerCamelCase    ,     _lowerCamelCase				):
           UpperCamelCase_:   Optional[int]        =							[1] * rank
         else:
           UpperCamelCase_:   List[str]        =							rank





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





       def      _a       (   self				):
         UpperCamelCase_:   Union[str, Any]        =							self.duals.copy()
         while cur[-1] == 0:
           cur.pop(-1				)
         return Dual(self.real    ,     _lowerCamelCase				)





       def __add__(   self    ,     _lowerCamelCase				):
         if not isinstance(_lowerCamelCase    ,     _lowerCamelCase				):
           return Dual(self.real + other    ,     self.duals				)
         UpperCamelCase_:   List[Any]        =							self.duals.copy()
         UpperCamelCase_:   Optional[int]        =							other.duals.copy()
         if len(_lowerCamelCase				) > len(_lowerCamelCase				):
           o_dual.extend([1] * (len(_lowerCamelCase				) - len(_lowerCamelCase				))				)
         elif len(_lowerCamelCase				) < len(_lowerCamelCase				):
           s_dual.extend([1] * (len(_lowerCamelCase				) - len(_lowerCamelCase				))				)
         UpperCamelCase_:   List[str]        =							[]
         for i in range(len(_lowerCamelCase				)				):
           new_duals.append(s_dual[i] + o_dual[i]				)
         return Dual(self.real + other.real    ,     _lowerCamelCase				)

       a							:						Union[str, Any]										=__add__





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





       def __mul__(   self    ,     _lowerCamelCase				):
         if not isinstance(_lowerCamelCase    ,     _lowerCamelCase				):
           UpperCamelCase_:   Union[str, Any]        =							[]
           for i in self.duals:
             new_duals.append(i * other				)
           return Dual(self.real * other    ,     _lowerCamelCase				)
         UpperCamelCase_:   List[Any]        =							[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    ,     _lowerCamelCase				)

       a							:						Optional[int]										=__mul__





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





       def __floordiv__(   self    ,     _lowerCamelCase				):
         if not isinstance(_lowerCamelCase    ,     _lowerCamelCase				):
           UpperCamelCase_:   Union[str, Any]        =							[]
           for i in self.duals:
             new_duals.append(i // other				)
           return Dual(self.real // other    ,     _lowerCamelCase				)
         raise ValueError





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







def     snake_case   (UpperCAmelCase__      ,       UpperCAmelCase__      ,       UpperCAmelCase__    )			->							int:
  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'    )
  UpperCamelCase_:   Optional[int]        =							Dual(UpperCAmelCase__      ,       1    )
  UpperCamelCase_:   Optional[Any]        =							func(UpperCAmelCase__    )
  if order == 0:
    return result.real
  return result.duals[order - 1] * factorial(UpperCAmelCase__    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   def     snake_case   (UpperCAmelCase__    )			->							Optional[Any]:
     return y**2 * y**4
   print(differentiate(f, 9, 2))





from math import isqrt


def 					_a							(					lowerCAmelCase )->	bool:
		return all(number % divisor != 0 for divisor in range(2    ,						isqrt(lowerCAmelCase ) + 1 ) )


def 					_a							(					lowerCAmelCase = 10**6 )->	int:
		SCREAMING_SNAKE_CASE_					      =							0
		SCREAMING_SNAKE_CASE_					      =							1
		SCREAMING_SNAKE_CASE_					      =							7
		while prime_candidate < max_prime:
				primes_count += is_prime(lowerCAmelCase )

				cube_index += 1
				prime_candidate += 6 * cube_index

		return primes_count


if __name__ == "__main__":
						print(f"""{solution() = }""")