




from math import factorial




class       a__	:







     def __init__(     self  ,		A  ,		A			)  ->   Tuple:



          '''simple docstring'''



          a     =				real
          if isinstance(A  ,		A			):
               a     =				[1] * rank
          else:
               a     =				rank







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



          '''simple docstring'''



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







     def       lowerCAmelCase_    (     self			)  ->   int:



          '''simple docstring'''



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







     def __add__(     self  ,		A			)  ->   Any:



          '''simple docstring'''



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

     a		:      Tuple		 =     __add__







     def __sub__(     self  ,		A			)  ->   Optional[Any]:



          '''simple docstring'''



          return self + other * -1







     def __mul__(     self  ,		A			)  ->   int:



          '''simple docstring'''



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

     a		:      int		 =     __mul__







     def __truediv__(     self  ,		A			)  ->   Optional[int]:



          '''simple docstring'''



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







     def __floordiv__(     self  ,		A			)  ->   List[str]:



          '''simple docstring'''



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







     def __pow__(     self  ,		A			)  ->   Optional[Any]:



          '''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
          a     =				self
          for _ in range(n - 1			):
               x *= self
          return x







def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase		, __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")
     a     =				Dual(__UpperCamelCase		, 1)
     a     =				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[Any]:
        return y**2 * y**4





   print(differentiate(f, 9, 2))







from math import isqrt

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

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase = 10**6)      ->					int:
     a     =				0
     a     =				1
     a     =				7
     while prime_candidate < max_prime:
          primes_count += is_prime(__UpperCamelCase)

          cube_index += 1
          prime_candidate += 6 * cube_index

     return primes_count


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

