
def 		UpperCamelCase    (					_UpperCAmelCase     :      int = 30     )      -> int:






						'''simple docstring'''

						_lowercase					:  Optional[Any]    			=      exponent + 2
						_lowercase					:  Optional[Any]    			=      (1 + 5**0.5) / 2
						_lowercase					:  Optional[int]    			=      (phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

						return int(_UpperCAmelCase     )


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






import math



def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> list:






						'''simple docstring'''

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



def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> int:






						'''simple docstring'''

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



def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> int:






						'''simple docstring'''

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



def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> int:






						'''simple docstring'''

						_lowercase					:  int    			=      n
						for x in set(prime_factors(_UpperCAmelCase     )     ):
												s *= (x - 1) / x
						return int(_UpperCAmelCase     )


if __name__ == "__main__":
							import doctest

							doctest.testmod()




