


'''simple docstring'''


from __future__ import annotations







class        __magic_name__  :

     """simple docstring"""






     def __init__(      self ,    lowerCamelCase		):


          '''simple docstring'''





          __A  :					Any						     =       value
          __A  :					Node | None						     =       None
          __A  :					Node | None						     =       None







class        __magic_name__  :

     """simple docstring"""






     lowerCamelCase__						=							42


     def __init__(      self		):


          '''simple docstring'''





          __A  :					str						     =       0


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase		):


          '''simple docstring'''





          if node is None:
               return

          if path_sum == self.target:
               self.paths += 1

          if node.left:
               self.depth_first_search(node.left ,    path_sum + node.left.value		)
          if node.right:
               self.depth_first_search(node.right ,    path_sum + node.right.value		)


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase = None		):


          '''simple docstring'''





          if node is None:
               return 0
          if target is not None:
               __A  :					Tuple						     =       target

          self.depth_first_search(lowerCamelCase ,    node.value		)
          self.path_sum(node.left		)
          self.path_sum(node.right		)

          return self.paths


if __name__ == "__main__":
      import doctest

      doctest.testmod()





'''simple docstring'''


import math
from collections.abc import Generator


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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					,				SCREAMING_SNAKE_CASE       ):
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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)
          __A  :					Optional[Any]						     =       int(math.sqrt(SCREAMING_SNAKE_CASE       )       ) + 1
          for j in range(2					,				SCREAMING_SNAKE_CASE       ):
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





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


def 		_lowercase   ():




     '''simple docstring'''





     from timeit import timeit

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


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

