



"""simple docstring"""






from functools import lru_cache






def      snake_case__   (		__lowerCamelCase				:    int	):
			"""simple docstring"""
			lowerCamelCase__		:		Optional[Any]			=2
			lowerCamelCase__		:		Optional[int]			=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      snake_case__   (		__lowerCamelCase				:    int	):
			"""simple docstring"""
			return len(unique_prime_factors(__lowerCamelCase	)	)






def      snake_case__   (		__lowerCamelCase				:    list	):
			"""simple docstring"""
			return len(set(__lowerCamelCase	)	) in (0, 1)






def      snake_case__   (		__lowerCamelCase				:    int	):
			"""simple docstring"""
			lowerCamelCase__		:		Tuple			=2

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

						# Run elements through out unique_prime_factors function
						# Append our target number to the end.
						lowerCamelCase__		:		Optional[Any]			=[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      snake_case__   (		__lowerCamelCase				:    int = 4	):
			"""simple docstring"""
			lowerCamelCase__		:		List[Any]			=run(__lowerCamelCase	)
			return results[0] if len(__lowerCamelCase	) else None


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









"""simple docstring"""






class        __SCREAMING_SNAKE_CASE	:


					'''simple docstring'''





					def __init__(       self							:  Dict,  lowerCamelCase							:  list     )->					None:
								lowerCamelCase__		:		Tuple			=set_counts
								lowerCamelCase__		:		Dict			=max(lowerCamelCase     )
								lowerCamelCase__		:		Union[str, Any]			=len(lowerCamelCase     )
								lowerCamelCase__		:		List[str]			=[1] * num_sets
								lowerCamelCase__		:		str			=list(range(lowerCamelCase     )     )



					def 		snake_case       (       self							:  Tuple,  lowerCamelCase							:  int,  lowerCamelCase							:  int     )->					bool:
								lowerCamelCase__		:		List[Any]			=self.get_parent(lowerCamelCase     )
								lowerCamelCase__		:		str			=self.get_parent(lowerCamelCase     )

								if src_parent == dst_parent:
											return False

								if self.ranks[dst_parent] >= self.ranks[src_parent]:
											self.set_counts[dst_parent] += self.set_counts[src_parent]
											lowerCamelCase__		:		Tuple			=0
											lowerCamelCase__		:		int			=dst_parent
											if self.ranks[dst_parent] == self.ranks[src_parent]:
														self.ranks[dst_parent] += 1
											lowerCamelCase__		:		str			=self.set_counts[dst_parent]
								else:
											self.set_counts[src_parent] += self.set_counts[dst_parent]
											lowerCamelCase__		:		List[Any]			=0
											lowerCamelCase__		:		List[str]			=src_parent
											lowerCamelCase__		:		Dict			=self.set_counts[src_parent]

								lowerCamelCase__		:		str			=max(self.max_set,  lowerCamelCase     )
								return True




					def 		snake_case       (       self							:  Union[str, Any],  lowerCamelCase							:  int     )->					int:
								if self.parents[disj_set] == disj_set:
											return disj_set
								lowerCamelCase__		:		Tuple			=self.get_parent(self.parents[disj_set]     )
								return self.parents[disj_set]




