




'''simple docstring'''





def UpperCAmelCase    (       UpperCAmelCase_						):
    _a				:							Optional[int]							       =      [True for i in range(n + 1						)]
    _a				:							Any							       =      [i - 1 for i in range(n + 1						)]
    _a				:							Union[str, Any]							       =      []
    for i in range(2   ,	n + 1						):
        if is_prime[i]:
            primes.append(snake_case_						)
        for j in range(0   ,	len(snake_case_						)						):
            if i * primes[j] >= n:
                break
            _a				:							List[str]							       =      False

            if i % primes[j] == 0:
                _a				:							str							       =      totients[i] * primes[j]
                break

            _a				:							Union[str, Any]							       =      totients[i] * (primes[j] - 1)

    return totients


if __name__ == "__main__":
  import doctest

  doctest.testmod()




def      __UpperCAmelCase    (  snake_case_							:		str				):



	'''simple docstring'''



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


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

	testmod()
