import math
from collections.abc import Generator

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

def 	__lowerCamelCase							(				__a    : int		)      ->       Generator[int, None, None]:
	_lowercase   =(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):
		_lowercase   =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 	__lowerCamelCase							(				)      ->       List[Any]:
	from timeit import timeit

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


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





def 	__lowerCamelCase							(				__a    : float		)      ->       float:
	return -num if num < 0 else num

def 	__lowerCamelCase							(				__a    : list[int]		)      ->       int:
	if len(__a		) == 0:
		raise ValueError("abs_min() arg is an empty sequence"		)
	_lowercase   =x[0]
	for i in x:
		if abs_val(__a		) < abs_val(__a		):
			_lowercase   =i
	return j

def 	__lowerCamelCase							(				__a    : list[int]		)      ->       int:
	if len(__a		) == 0:
		raise ValueError("abs_max() arg is an empty sequence"		)
	_lowercase   =x[0]
	for i in x:
		if abs(__a		) > abs(__a		):
			_lowercase   =i
	return j

def 	__lowerCamelCase							(				__a    : list[int]		)      ->       int:
	if len(__a		) == 0:
		raise ValueError("abs_max_sort() arg is an empty sequence"		)
	return sorted(__a      ,							key=__a		)[-1]

def 	__lowerCamelCase							(				)      ->       Optional[Any]:
	assert abs_val(0		) == 0
	assert abs_val(34		) == 34
	assert abs_val(-100_000_000_000		) == 100_000_000_000

	_lowercase   =[-3, -1, 2, -11]
	assert abs_max(__a		) == -11
	assert abs_max_sort(__a		) == -11
	assert abs_min(__a		) == -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						test_abs_val()
						print(abs_val(-3_4))  # --> 34




