

import math
from collections.abc import Generator




def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	Generator[int, None, None]:



    """simple docstring"""






    UpperCamelCase_      =	(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  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	Generator[int, None, None]:



    """simple docstring"""






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




def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	Generator[int, None, None]:



    """simple docstring"""






    UpperCamelCase_      =	(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):
        UpperCamelCase_      =	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  lowerCAmelCase(			)->	List[str]:



    """simple docstring"""






    from timeit import timeit

    UpperCamelCase_      =	"from __main__ import slow_primes, primes, fast_primes"
    print(timeit("slow_primes(1_000_000_000_000)" ,	setup=SCREAMING_SNAKE_CASE_ ,	number=1_0_0_0_0_0_0 ) )
    print(timeit("primes(1_000_000_000_000)" ,	setup=SCREAMING_SNAKE_CASE_ ,	number=1_0_0_0_0_0_0 ) )
    print(timeit("fast_primes(1_000_000_000_000)" ,	setup=SCREAMING_SNAKE_CASE_ ,	number=1_0_0_0_0_0_0 ) )


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



def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	float:



    """simple docstring"""






    return -num if num < 0 else num




def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	int:



    """simple docstring"""






    if len(SCREAMING_SNAKE_CASE_ ) == 0:
        raise ValueError("abs_min() arg is an empty sequence" )
    UpperCamelCase_      =	x[0]
    for i in x:
        if abs_val(SCREAMING_SNAKE_CASE_ ) < abs_val(SCREAMING_SNAKE_CASE_ ):
            UpperCamelCase_      =	i
    return j




def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	int:



    """simple docstring"""






    if len(SCREAMING_SNAKE_CASE_ ) == 0:
        raise ValueError("abs_max() arg is an empty sequence" )
    UpperCamelCase_      =	x[0]
    for i in x:
        if abs(SCREAMING_SNAKE_CASE_ ) > abs(SCREAMING_SNAKE_CASE_ ):
            UpperCamelCase_      =	i
    return j




def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ )->	int:



    """simple docstring"""






    if len(SCREAMING_SNAKE_CASE_ ) == 0:
        raise ValueError("abs_max_sort() arg is an empty sequence" )
    return sorted(SCREAMING_SNAKE_CASE_ ,	key=SCREAMING_SNAKE_CASE_ )[-1]




def  lowerCAmelCase(			)->	Any:



    """simple docstring"""






    assert abs_val(0 ) == 0
    assert abs_val(3_4 ) == 3_4
    assert abs_val(-1_0_0_0_0_0_0_0_0_0_0_0 ) == 1_0_0_0_0_0_0_0_0_0_0_0

    UpperCamelCase_      =	[-3, -1, 2, -1_1]
    assert abs_max(SCREAMING_SNAKE_CASE_ ) == -1_1
    assert abs_max_sort(SCREAMING_SNAKE_CASE_ ) == -1_1
    assert abs_min(SCREAMING_SNAKE_CASE_ ) == -1


if __name__ == "__main__":
 import doctest

 doctest.testmod()

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