

def        __UpperCamelCase     (      _A					:							list		)				->list:



							"""simple docstring"""
							lowerCamelCase_								=len(_A		)
							for cycle_start in range(0      ,  array_len - 1		):
														lowerCamelCase_								=array[cycle_start]

														lowerCamelCase_								=cycle_start
														for i in range(cycle_start + 1      ,  _A		):
																					if array[i] < item:
																												pos += 1

														if pos == cycle_start:
																					continue

														while item == array[pos]:
																					pos += 1

														lowerCamelCase_	,   lowerCamelCase_								=item, array[pos]
														while pos != cycle_start:
																					lowerCamelCase_								=cycle_start
																					for i in range(cycle_start + 1      ,  _A		):
																												if array[i] < item:
																																			pos += 1

																					while item == array[pos]:
																												pos += 1

																					lowerCamelCase_	,   lowerCamelCase_								=item, array[pos]

							return array


if __name__ == "__main__":
	assert cycle_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
	assert cycle_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]



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()
