

class 			_SCREAMING_SNAKE_CASE      :







						def __init__(			self     ,						_SCREAMING_SNAKE_CASE							)->							None:
													lowerCamelCase_								=data
													lowerCamelCase_								=42
													lowerCamelCase_								=42




def        __UpperCamelCase     (      _A					:							Node		)				->None:



							"""simple docstring"""
							lowerCamelCase_								=0
							lowerCamelCase_								=x




def        __UpperCamelCase     (      _A					:							Node      ,  _A					:							Node		)				->None:



							"""simple docstring"""
							lowerCamelCase_	,   lowerCamelCase_								=find_set(_A		), find_set(_A		)
							if x == y:
														return

							elif x.rank > y.rank:
														lowerCamelCase_								=x
							else:
														lowerCamelCase_								=y
														if x.rank == y.rank:
																					y.rank += 1




def        __UpperCamelCase     (      _A					:							Node		)				->Node:



							"""simple docstring"""
							if x != x.parent:
														lowerCamelCase_								=find_set(x.parent		)
							return x.parent




def        __UpperCamelCase     (      _A					:							Node		)				->set:



							"""simple docstring"""
							lowerCamelCase_								=({0, 1, 2}, {3, 4, 5})
							for s in sets:
														if node.data in s:
																					return s
							lowerCamelCase_								=f'{node.data} is not in {sets}'
							raise ValueError(_A		)




def        __UpperCamelCase     (      )				->None:



							"""simple docstring"""
							lowerCamelCase_								=[Node(_A		) for i in range(6		)]
							for v in vertex:
														make_set(_A		)

							union_set(vertex[0]      ,  vertex[1]		)
							union_set(vertex[1]      ,  vertex[2]		)
							union_set(vertex[3]      ,  vertex[4]		)
							union_set(vertex[3]      ,  vertex[5]		)

							for nodea in vertex:
														for nodea in vertex:
																					if find_python_set(_A		).isdisjoint(find_python_set(_A		)		):
																												assert find_set(_A		) != find_set(_A		)
																					else:
																												assert find_set(_A		) == find_set(_A		)


if __name__ == "__main__":
	test_disjoint_set()



import math
from collections.abc import Generator




def        __UpperCamelCase     (      _A					:							int		)				->Generator[int, None, None]:



							"""simple docstring"""
							lowerCamelCase_								=(i for i in range(1      ,  (max_n + 1)		))
							for i in (n for n in numbers if n > 1):
														for j in range(2      ,  _A		):
																					if (i % j) == 0:
																												break
														else:
																					yield i




def        __UpperCamelCase     (      _A					:							int		)				->Generator[int, None, None]:



							"""simple docstring"""
							lowerCamelCase_								=(i for i in range(1      ,  (max_n + 1)		))
							for i in (n for n in numbers if n > 1):
														# only need to check for factors up to sqrt(i)
														lowerCamelCase_								=int(math.sqrt(_A		)		) + 1
														for j in range(2      ,  _A		):
																					if (i % j) == 0:
																												break
														else:
																					yield i




def        __UpperCamelCase     (      _A					:							int		)				->Generator[int, None, None]:



							"""simple docstring"""
							lowerCamelCase_								=(i for i in range(1      ,  (max_n + 1)      ,  2		))
							# It's useless to test even numbers as they will not be prime
							if max_n > 2:
														yield 2  # Because 2 will not be tested, it's necessary to yield it now
							for i in (n for n in numbers if n > 1):
														lowerCamelCase_								=int(math.sqrt(_A		)		) + 1
														for j in range(3      ,  _A      ,  2		):
																					# As we removed the even numbers, we don't need them now
																					if (i % j) == 0:
																												break
														else:
																					yield i




def        __UpperCamelCase     (      )				->Dict:



							"""simple docstring"""
							from timeit import timeit

							lowerCamelCase_								="""from __main__ import slow_primes, primes, fast_primes"""
							print(timeit("""slow_primes(1_000_000_000_000)"""      ,  setup=_A      ,  number=1000000		)		)
							print(timeit("""primes(1_000_000_000_000)"""      ,  setup=_A      ,  number=1000000		)		)
							print(timeit("""fast_primes(1_000_000_000_000)"""      ,  setup=_A      ,  number=1000000		)		)


if __name__ == "__main__":
	__A	:   Union[str, Any]	=					int(input('Calculate primes up to:\n>> ').strip())
	for ret in primes(number):
		print(ret)
	benchmark()
