



def 						_UpperCAmelCase							( snake_case     ):





					"""simple docstring"""

					return n * (2 * n - 1)


def 						_UpperCAmelCase							( snake_case     ):





					"""simple docstring"""

					_lowerCAmelCase         =       (1 + 24 * n) ** 0.5
					return ((1 + root) / 6) % 1 == 0


def 						_UpperCAmelCase							( snake_case = 1_44     ):





					"""simple docstring"""

					_lowerCAmelCase         =       start
					_lowerCAmelCase         =       hexagonal_num(snake_case     )
					while not is_pentagonal(snake_case     ):
										n += 1
										_lowerCAmelCase         =       hexagonal_num(snake_case     )
					return num


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








def 						_UpperCAmelCase							( snake_case     ):





					"""simple docstring"""

					_lowerCAmelCase         =       str(snake_case     ).strip()
					if not bin_string:
										raise ValueError("""Empty string was passed to the function"""     )
					_lowerCAmelCase         =       bin_string[0] == """-"""
					if is_negative:
										_lowerCAmelCase         =       bin_string[1:]
					if not all(char in """01""" for char in bin_string     ):
										raise ValueError("""Non-binary value was passed to the function"""     )
					_lowerCAmelCase         =       0
					for char in bin_string:
										_lowerCAmelCase         =       2 * decimal_number + int(snake_case     )
					return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
	from doctest import testmod

	testmod()



