



'''simple docstring'''






def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_						)->						Union[str, Any]:





       '''simple docstring'''


       if n < 0:
              return 0
       # table[i] represents the number of ways to get to amount i
       _UpperCAmelCase    :		Union[str, Any]     	=					[0] * (n + 1)

       # There is exactly 1 way to get to zero(You pick no coins).
       _UpperCAmelCase    :		Optional[int]     	=					1

       # Pick all coins one by one and update table[] values
       # after the index greater than or equal to the value of the
       # picked coin
       for coin_val in s:
              for j in range(lowerCAmelCase_			,  n + 1						):
                     table[j] += table[j - coin_val]

       return table[n]


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()





