
import re
def        __lowercase(							__snake_case				:		List[str]					)       ->   Optional[int]:






       def docstring_decorator(__snake_case				:		List[Any]					):
              __snake_case						       =   fn.__doc__
              __snake_case						       =   func_doc.split('\n'					)
              __snake_case						       =   0
              while i < len(__A					) and re.search(r'^\s*Examples?:\s*$'    ,lines[i]					) is None:
                     i += 1
              if i < len(__A					):
                     __snake_case						       =   example_docstring
                     __snake_case						       =   '''\n'''.join(__A					)
              else:
                     raise ValueError(
                         f'''The function {fn} should have an empty \'Examples:\' in its docstring as placeholder, '''
                         f'''current docstring is:\n{func_doc}'''					)
              __snake_case						       =   func_doc
              return fn

       return docstring_decorator






import math
from collections.abc import Generator







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






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







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






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







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					__magic_name__				:						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):
										__magic_name__				:						str     				=				int(math.sqrt(__A					)					) + 1
										for j in range(3				,__A				,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

					__magic_name__				:						Dict     				=				'''from __main__ import slow_primes, primes, fast_primes'''
					print(timeit('''slow_primes(1_000_000_000_000)'''				,setup=__A				,number=1_0_0_0_0_0_0					)					)
					print(timeit('''primes(1_000_000_000_000)'''				,setup=__A				,number=1_0_0_0_0_0_0					)					)
					print(timeit('''fast_primes(1_000_000_000_000)'''				,setup=__A				,number=1_0_0_0_0_0_0					)					)


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



