
"""simple docstring"""




def   __magic_name__     (				__snake_case    :	Union[str, Any]					,			__snake_case    :	Any					,			__snake_case    :	List[str]					,			__snake_case    :	str  )			->    Optional[Any]:



							if start == end:
														return start if lst[start] > item else start + 1
							if start > end:
														return start

							lowercase   :    Optional[Any]			=							(start + end) // 2
							if lst[mid] < item:
														return binary_search(UpperCamelCase_					,			UpperCamelCase_					,			mid + 1					,			UpperCamelCase_  )
							elif lst[mid] > item:
														return binary_search(UpperCamelCase_					,			UpperCamelCase_					,			UpperCamelCase_					,			mid - 1  )
							else:
														return mid


def   __magic_name__     (				__snake_case    :	int  )			->    Dict:
							lowercase   :    Dict			=							len(UpperCamelCase_  )

							for index in range(1					,			UpperCamelCase_  ):
														lowercase   :    Optional[Any]			=							lst[index]
														lowercase   :    List[str]			=							binary_search(UpperCamelCase_					,			UpperCamelCase_					,			0					,			index - 1  )
														lowercase   :    Dict			=							lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

							return lst


def   __magic_name__     (				__snake_case    :	Any					,			__snake_case    :	str  )			->    Tuple:



							if not left:
														return right

							if not right:
														return left

							if left[0] < right[0]:
														return [left[0], *merge(left[1:]					,			UpperCamelCase_  )]

							return [right[0], *merge(UpperCamelCase_					,			right[1:]  )]


def   __magic_name__     (				__snake_case    :	Dict  )			->    str:
							lowercase   :    List[str]			=							len(UpperCamelCase_  )
							lowercase		,   lowercase   :    Any			=							[], []
							lowercase   :    str			=							[lst[0]]
							lowercase   :    List[Any]			=							[]
							lowercase   :    Union[str, Any]			=							1
							while i < length:
														if lst[i] < lst[i - 1]:
																					runs.append(UpperCamelCase_  )
																					lowercase   :    List[Any]			=							[lst[i]]
														else:
																					new_run.append(lst[i]  )
														i += 1
							runs.append(UpperCamelCase_  )

							for run in runs:
														sorted_runs.append(insertion_sort(UpperCamelCase_  )  )
							for run in sorted_runs:
														lowercase   :    List[str]			=							merge(UpperCamelCase_					,			UpperCamelCase_  )

							return sorted_array


def   __magic_name__     (				)			->    List[str]:
							lowercase   :    Optional[Any]			=							[5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
							lowercase   :    Union[str, Any]			=							tim_sort(UpperCamelCase_  )
							print(UpperCamelCase_  )


if __name__ == "__main__":
			main()




"""simple docstring"""




import math
from collections.abc import Generator


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    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					,			__snake_case  ):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    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)
              lowercase   :    Dict			=							int(math.sqrt(__snake_case  )  ) + 1
              for j in range(2					,			__snake_case  ):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    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):
              lowercase   :    int			=							int(math.sqrt(__snake_case  )  ) + 1
              for j in range(3					,			__snake_case					,			2  ):
                     # As we removed the even numbers, we don't need them now
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				)			->    Tuple:
       from timeit import timeit

       lowercase   :    List[str]			=							"from __main__ import slow_primes, primes, fast_primes"
       print(timeit("slow_primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )
       print(timeit("primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )
       print(timeit("fast_primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )


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


