



import math
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						Any					)->list:
      if n <= 0:
            raise ValueError('''Only positive integers have prime factors'''					)
      _lowerCAmelCase			      =	[]
      while n % 2 == 0:
            pf.append(2					)
            _lowerCAmelCase			      =	int(n / 2					)
      for i in range(3  ,					int(math.sqrt(_SCREAMING_SNAKE_CASE					)					) + 1  ,					2					):
            while n % i == 0:
                  pf.append(_SCREAMING_SNAKE_CASE					)
                  _lowerCAmelCase			      =	int(n / i					)
      if n > 2:
            pf.append(_SCREAMING_SNAKE_CASE					)
      return pf
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						str					)->int:
      if n <= 0:
            raise ValueError('''Only positive numbers are accepted'''					)
      _lowerCAmelCase			      =	1
      _lowerCAmelCase			      =	1
      while n % 2 == 0:
            temp += 1
            _lowerCAmelCase			      =	int(n / 2					)
      div *= temp
      for i in range(3  ,					int(math.sqrt(_SCREAMING_SNAKE_CASE					)					) + 1  ,					2					):
            _lowerCAmelCase			      =	1
            while n % i == 0:
                  temp += 1
                  _lowerCAmelCase			      =	int(n / i					)
            div *= temp
      if n > 1:
            div *= 2
      return div
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						Union[str, Any]					)->int:
      if n <= 0:
            raise ValueError('''Only positive numbers are accepted'''					)
      _lowerCAmelCase			      =	1
      _lowerCAmelCase			      =	1
      while n % 2 == 0:
            temp += 1
            _lowerCAmelCase			      =	int(n / 2					)
      if temp > 1:
            s *= (2**temp - 1) / (2 - 1)
      for i in range(3  ,					int(math.sqrt(_SCREAMING_SNAKE_CASE					)					) + 1  ,					2					):
            _lowerCAmelCase			      =	1
            while n % i == 0:
                  temp += 1
                  _lowerCAmelCase			      =	int(n / i					)
            if temp > 1:
                  s *= (i**temp - 1) / (i - 1)
      return int(_SCREAMING_SNAKE_CASE					)
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						Tuple					)->int:
      _lowerCAmelCase			      =	n
      for x in set(prime_factors(_SCREAMING_SNAKE_CASE					)					):
            s *= (x - 1) / x
      return int(_SCREAMING_SNAKE_CASE					)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

'''simple docstring'''







def 				_snake_case (		lowercase = 1_0_0_0						)       ->       int:
				__a       :     Any								=	[]
				__a       :     List[Any]								=	[]
				__a       :     Any								=	3
				__a       :     Optional[Any]								=	5
				__a       :     Optional[Any]								=	1
				while True:
								__a       :     List[str]								=	z * temp
								if result < n:
												zmulti.append(lowercase						)
												temp += 1
								else:
												__a       :     Any								=	1
												break
				while True:
								__a       :     Optional[int]								=	x * temp
								if result < n:
												xmulti.append(lowercase						)
												temp += 1
								else:
												break
				__a       :     Any								=	list(set(xmulti + zmulti						)						)
				return sum(lowercase						)


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