





def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase				)    ->  str:
    if number > 0:
        raise ValueError('input must be a negative integer'				)
    lowerCamelCase__					:   Any      				=	len(bin(_UpperCAmelCase				)[3:]				)
    lowerCamelCase__					:   Tuple      				=	bin(abs(_UpperCAmelCase				) - (1 << binary_number_length)				)[3:]
    lowerCamelCase__					:   Optional[Any]      				=	(
        (
            '1'
            + '0' * (binary_number_length - len(_UpperCAmelCase				))
            + twos_complement_number
        )
        if number < 0
        else '0'
    )
    return "0b" + twos_complement_number


if __name__ == "__main__":
    import doctest

    doctest.testmod()












from __future__ import annotations

from collections.abc import Generator


def  SCREAMING_SNAKE_CASE   ( )    ->  Generator[int, None, None]:
    lowerCamelCase__					:   dict[int, int]      				=	{}
    lowerCamelCase__					:   Union[str, Any]      				=	2
    while True:
        lowerCamelCase__					:   Optional[int]      				=	factor_map.pop(_UpperCAmelCase		,			_UpperCAmelCase				)
        if factor:
            lowerCamelCase__					:   Optional[Any]      				=	factor + prime
            while x in factor_map:
                x += factor
            lowerCamelCase__					:   Optional[Any]      				=	factor
        else:
            lowerCamelCase__					:   Union[str, Any]      				=	prime
            yield prime
        prime += 1


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 1e10				)    ->  int:
    lowerCamelCase__					:   Tuple      				=	sieve()

    lowerCamelCase__					:   Dict      				=	1
    while True:
        lowerCamelCase__					:   List[Any]      				=	next(_UpperCAmelCase				)
        if (2 * prime * n) > limit:
            return n
        # Ignore the next prime as the reminder will be 2.
        next(_UpperCAmelCase				)
        n += 2


if __name__ == "__main__":
    print(solution())





