



"""simple docstring"""







import math


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase	):
		if n <= 0:
				raise ValueError("""Only positive integers have prime factors"""	)
		_lowercase							:      List[Any]			=					[]
		while n % 2 == 0:
				pf.append(2	)
				_lowercase							:      Optional[Any]			=					int(n / 2	)
		for i in range(3					,							int(math.sqrt(__UpperCAmelCase	)	) + 1					,							2	):
				while n % i == 0:
						pf.append(__UpperCAmelCase	)
						_lowercase							:      int			=					int(n / i	)
		if n > 2:
				pf.append(__UpperCAmelCase	)
		return pf


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase	):
		if n <= 0:
				raise ValueError("""Only positive numbers are accepted"""	)
		_lowercase							:      str			=					1
		_lowercase							:      int			=					1
		while n % 2 == 0:
				temp += 1
				_lowercase							:      Union[str, Any]			=					int(n / 2	)
		div *= temp
		for i in range(3					,							int(math.sqrt(__UpperCAmelCase	)	) + 1					,							2	):
				_lowercase							:      Any			=					1
				while n % i == 0:
						temp += 1
						_lowercase							:      Any			=					int(n / i	)
				div *= temp
		if n > 1:
				div *= 2
		return div


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase	):
		if n <= 0:
				raise ValueError("""Only positive numbers are accepted"""	)
		_lowercase							:      Optional[int]			=					1
		_lowercase							:      Optional[Any]			=					1
		while n % 2 == 0:
				temp += 1
				_lowercase							:      Optional[int]			=					int(n / 2	)
		if temp > 1:
				s *= (2**temp - 1) / (2 - 1)
		for i in range(3					,							int(math.sqrt(__UpperCAmelCase	)	) + 1					,							2	):
				_lowercase							:      Optional[Any]			=					1
				while n % i == 0:
						temp += 1
						_lowercase							:      Union[str, Any]			=					int(n / i	)
				if temp > 1:
						s *= (i**temp - 1) / (i - 1)
		return int(__UpperCAmelCase	)


def       __SCREAMING_SNAKE_CASE      (   __UpperCAmelCase	):
		_lowercase							:      Any			=					n
		for x in set(prime_factors(__UpperCAmelCase	)	):
				s *= (x - 1) / x
		return int(__UpperCAmelCase	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()





"""simple docstring"""




def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_			):
					if not isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
										SCREAMING_SNAKE_CASE				=	(
										    'operation can not be conducted on a object of type '
										    f'''{type(SCREAMING_SNAKE_CASE_			).__name__}'''
										)
										raise TypeError(SCREAMING_SNAKE_CASE_			)
					SCREAMING_SNAKE_CASE				=	''
					for _ in range(0,     3_2			):
										bit_string += str(number % 2			)
										SCREAMING_SNAKE_CASE				=	number >> 1
					return bit_string

def   UpperCamelCase_  (		SCREAMING_SNAKE_CASE_			):
					if number < 0:
										raise ValueError('the value of input must be positive'			)
					elif isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
										raise TypeError('Input value must be a \'int\' type'			)
					elif isinstance(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_			):
										raise TypeError('\'<\' not supported between instances of \'str\' and \'int\''			)
					SCREAMING_SNAKE_CASE				=	0
					# iterator over [1 to 32],since we are dealing with 32 bit integer
					for _ in range(1,     3_3			):
										# left shift the bits by unity
										SCREAMING_SNAKE_CASE				=	result << 1
										# get the end bit
										SCREAMING_SNAKE_CASE				=	number % 2
										# right shift the bits by unity
										SCREAMING_SNAKE_CASE				=	number >> 1
										# add that bit to our ans
										SCREAMING_SNAKE_CASE				=	result | end_bit
					return get_reverse_bit_string(SCREAMING_SNAKE_CASE_			)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
