


"""simple docstring"""





from __future__ import annotations


def   _snake_case    (    _snake_case					:      Optional[Any]      ):
      if not list_of_ints:
            return []

      if min(lowercase__      ) < 0:
            raise ValueError('''All numbers must be positive'''      )

      lowerCAmelCase       :						List[str]							= max(len(bin(lowercase__      )[2:]      ) for x in list_of_ints      )
      return _msd_radix_sort(lowercase__			, lowercase__      )


def   _snake_case    (    _snake_case					:      Dict			, _snake_case					:      Union[str, Any]      ):
      if bit_position == 0 or len(lowercase__      ) in [0, 1]:
            return list_of_ints

      lowerCAmelCase       :						Tuple							= []
      lowerCAmelCase       :						Tuple							= []
      # Split numbers based on bit at bit_position from the right
      for number in list_of_ints:
            if (number >> (bit_position - 1)) & 1:
                  # number has a one at bit bit_position
                  ones.append(lowercase__      )
            else:
                  # number has a zero at bit bit_position
                  zeros.append(lowercase__      )

    # recursively split both lists further
      lowerCAmelCase       :						Tuple							= _msd_radix_sort(lowercase__			, bit_position - 1      )
      lowerCAmelCase       :						List[Any]							= _msd_radix_sort(lowercase__			, bit_position - 1      )

      # recombine lists
      lowerCAmelCase       :						Any							= zeros
      res.extend(lowercase__      )

      return res


def   _snake_case    (    _snake_case					:      Dict      ):
      lowerCAmelCase       :						Dict							= len(lowercase__      )
      if not list_of_ints or length == 1:
            return

      if min(lowercase__      ) < 0:
            raise ValueError('''All numbers must be positive'''      )

      lowerCAmelCase       :						Any							= max(len(bin(lowercase__      )[2:]      ) for x in list_of_ints      )
      _msd_radix_sort_inplace(lowercase__			, lowercase__			, 0			, lowercase__      )


def   _snake_case    (    _snake_case					:      List[Any]			, _snake_case					:      Tuple			, _snake_case					:      List[Any]			, _snake_case					:      Optional[Any]      ):
      if bit_position == 0 or end_index - begin_index <= 1:
            return

      bit_position -= 1

      lowerCAmelCase       :						Optional[int]							= begin_index
      lowerCAmelCase       :						Dict							= end_index - 1
      while i <= j:
            lowerCAmelCase       :						Optional[Any]							= False
            if not (list_of_ints[i] >> bit_position) & 1:
                  # found zero at the beginning
                  i += 1
                  lowerCAmelCase       :						List[str]							= True
            if (list_of_ints[j] >> bit_position) & 1:
                  # found one at the end
                  j -= 1
                  lowerCAmelCase       :						List[str]							= True

            if changed:
                  continue

            lowerCAmelCase       :						Union[str, Any]							= list_of_ints[j], list_of_ints[i]
            j -= 1
            if j != i:
                  i += 1

      _msd_radix_sort_inplace(lowercase__			, lowercase__			, lowercase__			, lowercase__      )
      _msd_radix_sort_inplace(lowercase__			, lowercase__			, lowercase__			, lowercase__      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()









'''simple docstring'''






import math
from collections.abc import Generator





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





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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):
												_snake_case: List[str]	       =		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    lowercase_   (		) ->Optional[int]:
						from timeit import timeit

						_snake_case: Dict	       =		'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('fast_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )


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





