



"""simple docstring"""





def 	__lowerCAmelCase						(		__UpperCamelCase      :			int = 1_0_0_0    ):


						'''simple docstring'''






						snake_case_   : int						=			-1
						snake_case_   : Tuple						=			0
						for a in range(1					, n // 3    ):
												# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
												snake_case_   : Optional[Any]						=			(n * n - 2 * a * n) // (2 * n - 2 * a)
												snake_case_   : Dict						=			n - a - b
												if c * c == (a * a + b * b):
																		snake_case_   : Tuple						=			a * b * c
																		if candidate >= product:
																								snake_case_   : Union[str, Any]						=			candidate
						return product


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






"""simple docstring"""





def 	__lowerCAmelCase						(		__UpperCamelCase      :			int					, __UpperCamelCase      :			int    ):


						'''simple docstring'''






						if a < 0 or b < 0:
												raise ValueError("""the value of both inputs must be positive"""    )

						snake_case_   : List[str]						=			str(bin(__UpperCamelCase    )    )[2:]  # remove the leading "0b"
						snake_case_   : Union[str, Any]						=			str(bin(__UpperCamelCase    )    )[2:]  # remove the leading "0b"

						snake_case_   : int						=			max(len(__UpperCamelCase    )					, len(__UpperCamelCase    )    )

						return "0b" + "".join(
						    str(int(char_a != char_b    )    )
						    for char_a, char_b in zip(a_binary.zfill(__UpperCamelCase    )					, b_binary.zfill(__UpperCamelCase    )    )    )


if __name__ == "__main__":
					import doctest

					doctest.testmod()

