"""simple docstring"""
from collections.abc import Callable

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







def 		__a  (      _SCREAMING_SNAKE_CASE						,	_SCREAMING_SNAKE_CASE						,	_SCREAMING_SNAKE_CASE						,	)      ->float:
  a__:	Optional[int]     				=      float(_SCREAMING_SNAKE_CASE  )
  while True:
    try:
      a__:	Optional[int]     				=      prev_guess - function(_SCREAMING_SNAKE_CASE  ) / derivative(_SCREAMING_SNAKE_CASE  )
    except ZeroDivisionError:
      raise ZeroDivisionError('Could not find root'  ) from None
    if abs(prev_guess - next_guess  ) < 10**-5:
      return next_guess
    a__:	Dict     				=      next_guess







def 		__a  (      _SCREAMING_SNAKE_CASE  )      ->float:
  return (x**3) - (2 * x) - 5







def 		__a  (      _SCREAMING_SNAKE_CASE  )      ->float:
  return 3 * (x**2) - 2


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






def   a						(				SCREAMING_SNAKE_CASE_   :		int							):






       """simple docstring"""





       UpperCamelCase     :						Tuple 						=		[True for i in range(n + 1							)]
       UpperCamelCase     :						Tuple 						=		[i - 1 for i in range(n + 1							)]
       UpperCamelCase     :						Optional[Any] 						=		[]
       for i in range(2				,      n + 1							):
              if is_prime[i]:
                     primes.append(SCREAMING_SNAKE_CASE_							)
              for j in range(0				,      len(SCREAMING_SNAKE_CASE_							)							):
                     if i * primes[j] >= n:
                            break
                     UpperCamelCase     :						Any 						=		False

                     if i % primes[j] == 0:
                            UpperCamelCase     :						int 						=		totients[i] * primes[j]
                            break

                     UpperCamelCase     :						Dict 						=		totients[i] * (primes[j] - 1)

       return totients


if __name__ == "__main__":
  import doctest

  doctest.testmod()

