"""simple docstring"""




def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Union[str, Any]  				=					[701, 301, 132, 57, 23, 10, 4, 1]
					for gap in gaps:
										for i in range(_lowercase							, len(_lowercase						)						):
															lowerCamelCase__		:   Union[str, Any]  				=					collection[i]
															lowerCamelCase__		:   Union[str, Any]  				=					i
															while j >= gap and collection[j - gap] > insert_value:
																				lowerCamelCase__		:   Dict  				=					collection[j - gap]
																				j -= gap
															if j != i:
																				lowerCamelCase__		:   Union[str, Any]  				=					insert_value
					return collection


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					UpperCAmelCase       :    List[str]									=			input("Enter numbers separated by a comma:\n").strip()
					UpperCAmelCase       :    Dict									=			[int(item) for item in user_input.split(",")]
					print(shell_sort(unsorted))







"""simple docstring"""




import math
from collections.abc import Generator



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Generator  				=					(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							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Generator  				=					(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__		:   Tuple  				=					int(math.sqrt(_lowercase						)						) + 1
										for j in range(2							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Generator  				=					(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__		:   Union[str, Any]  				=					int(math.sqrt(_lowercase						)						) + 1
										for j in range(3							, _lowercase							, 2						):
															# As we removed the even numbers, we don't need them now
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			):







					"""simple docstring"""





					from timeit import timeit

					lowerCamelCase__		:   Any  				=					'''from __main__ import slow_primes, primes, fast_primes'''
					print(timeit('''slow_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''fast_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)


if __name__ == "__main__":
					UpperCAmelCase       :    Tuple									=			int(input("Calculate primes up to:\n>> ").strip())
					for ret in primes(number):
										print(ret)
					benchmark()






