





from collections.abc import Callable

_UpperCamelCase    =	Callable[[float], float]  # type alias for a real -> real function







def  lowerCAmelCase__(		lowercase    :      RealFunc				,       lowercase    :      RealFunc				,       lowercase    :      int				,       )	->      float:
  __snake_case				:			Tuple            =    float(lowercase			)
  while True:
    try:
      __snake_case				:			List[Any]            =    prev_guess - function(lowercase			) / derivative(lowercase			)
    except ZeroDivisionError:
      raise ZeroDivisionError("Could not find root"			) from None
    if abs(prev_guess - next_guess			) < 10**-5:
      return next_guess
    __snake_case				:			Optional[int]            =    next_guess







def  lowerCAmelCase__(		lowercase    :      float			)	->      float:
  return (x**3) - (2 * x) - 5







def  lowerCAmelCase__(		lowercase    :      float			)	->      float:
  return 3 * (x**2) - 2


if __name__ == "__main__":
     print(newton(f, fa, 3))








def  lowerCAmelCase__(		lowercase    :      int = 10**6			)	->      int:

  if n <= 0:
    raise ValueError("Please enter an integer greater than 0"			)

  __snake_case				:			List[Any]            =    list(range(n + 1			)			)
  for number in range(2				,       n + 1			):
    if phi[number] == number:
      phi[number] -= 1
      for multiple in range(number * 2				,       n + 1				,       lowercase			):
        __snake_case				:			Optional[int]            =    (phi[multiple] // number) * (number - 1)

  __snake_case				:			List[Any]            =    1
  for number in range(1				,       n + 1			):
    if (answer / phi[answer]) < (number / phi[number]):
      __snake_case				:			List[str]            =    number

  return answer


if __name__ == "__main__":
     print(solution())

