



'''simple docstring'''




from functools import lru_cache






def 		_lowerCAmelCase				(_lowercase			):

       """simple docstring"""

       a__								= 2
       a__								= set()
       while i * i <= n:
              if n % i:
                     i += 1
              else:
                     n //= i
                     factors.add(lowerCamelCase__			)
       if n > 1:
              factors.add(lowerCamelCase__			)
       return factors






@lru_cache
def 		_lowerCAmelCase				(_lowercase			):

       """simple docstring"""

       return len(unique_prime_factors(lowerCamelCase__			)			)






def 		_lowerCAmelCase				(_lowercase			):

       """simple docstring"""

       return len(set(lowerCamelCase__			)			) in (0, 1)






def 		_lowerCAmelCase				(_lowercase			):

       """simple docstring"""

       a__								= 2

       while True:
              # Increment each value of a generated range
              a__								= [base + i for i in range(lowerCamelCase__			)]

              # Run elements through out unique_prime_factors function
              # Append our target number to the end.
              a__								= [upf_len(lowerCamelCase__			) for x in group]
              checker.append(lowerCamelCase__			)

              # If all numbers in the list are equal, return the group variable.
              if equality(lowerCamelCase__			):
                     return group

              # Increment our base variable by 1
              base += 1






def 		_lowerCAmelCase				(_lowercase = 4			):

       """simple docstring"""

       a__								= run(lowerCamelCase__			)
       return results[0] if len(lowerCamelCase__			) else None


if __name__ == "__main__":
    print(solution())




from ..utils import DummyObject, requires_backends







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Tuple			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> int:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Optional[Any]			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> Dict:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> List[str]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Dict:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					str			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> Dict:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Union[str, Any]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Optional[int]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					str			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> List[Any]:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Any:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Union[str, Any]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Dict			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> Optional[Any]:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Optional[Any]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Any:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Optional[int]			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> int:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> int:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Union[str, Any]			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> List[Any]:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Tuple:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Optional[int]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Optional[Any]			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> Optional[Any]:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> int:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> int:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Tuple			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> List[Any]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Any			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> List[str]:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> int:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					str			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> Dict:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Optional[int]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Dict:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Optional[int]			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> List[str]:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Any:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Any:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







class        __lowercase       (							metaclass=a_  ):



		"""simple docstring"""

		UpperCamelCase     :					Tuple			       =		["flax"]







		def __init__( self		,      *A		,      **A	)  -> str:







					'''simple docstring'''







					requires_backends(self		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Dict:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)







		@classmethod
		def 					__A   ( cls		,      *A		,      **A	)  -> Union[str, Any]:







					'''simple docstring'''







					requires_backends(cls		,      ["""flax"""]	)

