




'''simple docstring'''






import math
from decimal import Decimal, getcontext




def 		a_(			lowerCamelCase = 400_0000   )					->str:






       '''simple docstring'''




       try:
              lowercase	:		Any    =   int(_lowerCamelCase   )
       except (TypeError, ValueError):
              raise TypeError('''Parameter n must be int or castable to int.'''   )
       if n <= 0:
              raise ValueError('''Parameter n must be greater than or equal to one.'''   )
       lowercase	:		int    =   100
       lowercase	:		Tuple    =   (Decimal(5   ) ** Decimal(0.5   ) + 1) / Decimal(2   )

       lowercase	:		str    =   (math.floor(math.log(n * (phi + 2) ,					_lowerCamelCase   ) - 1   ) // 3) * 3 + 2
       lowercase	:		Optional[int]    =   Decimal(round(phi ** Decimal(index + 1   )   )   ) / (phi + 2)
       lowercase	:		str    =   num // 2
       return int(_lowerCamelCase   )


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









from collections.abc import Callable

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




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     ):
			A				:       int														=    float(_lowerCamelCase     )
			while True:
						try:
									A				:       Optional[int]														=    prev_guess - function(_lowerCamelCase     ) / derivative(_lowerCamelCase     )
						except ZeroDivisionError:
									raise ZeroDivisionError("Could not find root"     ) from None
						if abs(prev_guess - next_guess     ) < 10**-5:
									return next_guess
						A				:       Any														=    next_guess




def 						UpperCAmelCase (    _lowerCamelCase     ):
			return (x**3) - (2 * x) - 5




def 						UpperCAmelCase (    _lowerCamelCase     ):
			return 3 * (x**2) - 2


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