import math
from decimal import Decimal, getcontext

def     lowercase_       (    _lowerCamelCase							: int = 400_0000):

    try:
        lowercase__				:     str					      =       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__				:     Dict					      =       100
    lowercase__				:     Tuple					      =       (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2)

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


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




def     lowercase_       (    _lowerCamelCase							: str	,			_lowerCamelCase							: Optional[int]):
    if len(str(_lowerCamelCase)) == 1 or len(str(_lowerCamelCase)) == 1:
        return a * b

    lowercase__				:     Tuple					      =       max(len(str(_lowerCamelCase))	,			len(str(_lowerCamelCase)))
    lowercase__				:     Union[str, Any]					      =       ma // 2

    lowercase__      ,     lowercase__				:     Union[str, Any]					      =       divmod(_lowerCamelCase	,			10**ma)
    lowercase__      ,     lowercase__				:     Tuple					      =       divmod(_lowerCamelCase	,			10**ma)

    lowercase__				:     int					      =       karatsuba(_lowerCamelCase	,			_lowerCamelCase)
    lowercase__				:     Dict					      =       karatsuba((aa + aa)	,			(ba + ba))
    lowercase__				:     Optional[int]					      =       karatsuba(_lowerCamelCase	,			_lowerCamelCase)

    return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)

def     lowercase_       (    ):
    print(karatsuba(1_5463	,			2_3489))


if __name__ == "__main__":
      main()



