






'''simple docstring'''







import math
from collections.abc import Generator


def 						_UpperCamelCase							(     snake_case__							):
      __A		   =      (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 						_UpperCamelCase							(     snake_case__							):
      __A		   =      (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		   =      int(math.sqrt(snake_case__							)							) + 1
            for j in range(2							,			snake_case__							):
                  if (i % j) == 0:
                        break
            else:
                  yield i


def 						_UpperCamelCase							(     snake_case__							):
      __A		   =      (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		   =      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 						_UpperCamelCase							(     ):
      from timeit import timeit

      __A		   =      "from __main__ import slow_primes, primes, fast_primes"
      print(timeit("slow_primes(1_000_000_000_000)"							,			setup=snake_case__							,			number=1_000_000							)							)
      print(timeit("primes(1_000_000_000_000)"							,			setup=snake_case__							,			number=1_000_000							)							)
      print(timeit("fast_primes(1_000_000_000_000)"							,			setup=snake_case__							,			number=1_000_000							)							)


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










'''simple docstring'''







from __future__ import annotations

from queue import Queue






class 					a__    :
     '''simple docstring'''







     def __init__(self    :	Any					)  ->       None:
           __A		   =      {}






     def     _UpperCamelCase   (self    :	Optional[int]					)  ->       None:
           for i in self.vertices:
                 print(lowercase__				,				" : "				,				" -> ".join([str(lowercase__					) for j in self.vertices[i]]					)					)






     def     _UpperCamelCase   (self    :	Union[str, Any]				,				lowercase__    :	int				,				lowercase__    :	int					)  ->       None:
           if from_vertex in self.vertices:
                 self.vertices[from_vertex].append(lowercase__					)
           else:
                 __A		   =      [to_vertex]






     def     _UpperCamelCase   (self    :	Optional[int]				,				lowercase__    :	int					)  ->       set[int]:
           __A		   =      set()

           # create a first in first out queue to store all the vertices for BFS
           __A		   =      Queue()

           # mark the source node as visited and enqueue it
           visited.add(lowercase__					)
           queue.put(lowercase__					)

           while not queue.empty():
                 __A		   =      queue.get()

                 # loop through all adjacent vertex and enqueue it if not yet visited
                 for adjacent_vertex in self.vertices[vertex]:
                       if adjacent_vertex not in visited:
                             queue.put(lowercase__					)
                             visited.add(lowercase__					)
           return visited


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

       testmod(verbose=True)

       __A      :       Dict      =	Graph()
       g.add_edge(0, 1)
       g.add_edge(0, 2)
       g.add_edge(1, 2)
       g.add_edge(2, 0)
       g.add_edge(2, 3)
       g.add_edge(3, 3)

       g.print_graph()
       # 0  :  1 -> 2
       # 1  :  2
       # 2  :  0 -> 3
       # 3  :  3

       assert sorted(g.bfs(2)) == [0, 1, 2, 3]


