





import pytest

from datasets.utils.sharding import _distribute_shards, _number_of_shards_in_gen_kwargs, _split_gen_kwargs


@pytest.mark.parametrize(
    'kwargs, expected'		,			[
        ({'num_shards': 0, 'max_num_jobs': 1}, []),
        ({'num_shards': 10, 'max_num_jobs': 1}, [range(10				)]),
        ({'num_shards': 10, 'max_num_jobs': 10}, [range(_UpperCAmelCase		,			i + 1				) for i in range(10				)]),
        ({'num_shards': 1, 'max_num_jobs': 10}, [range(1				)]),
        ({'num_shards': 10, 'max_num_jobs': 3}, [range(0		,			4				), range(4		,			7				), range(7		,			10				)]),
        ({'num_shards': 3, 'max_num_jobs': 10}, [range(0		,			1				), range(1		,			2				), range(2		,			3				)]),
    ]		,			)
def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase				)    ->  str:
    lowerCamelCase__					:   str      				=	_distribute_shards(**_UpperCAmelCase				)
    assert out == expected


@pytest.mark.parametrize(
    'gen_kwargs, max_num_jobs, expected'		,			[
        ({'foo': 0}, 10, [{'foo': 0}]),
        ({'shards': [0, 1, 2, 3]}, 1, [{'shards': [0, 1, 2, 3]}]),
        ({'shards': [0, 1, 2, 3]}, 4, [{'shards': [0]}, {'shards': [1]}, {'shards': [2]}, {'shards': [3]}]),
        ({'shards': [0, 1]}, 4, [{'shards': [0]}, {'shards': [1]}]),
        ({'shards': [0, 1, 2, 3]}, 2, [{'shards': [0, 1]}, {'shards': [2, 3]}]),
    ]		,			)
def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase		,			_UpperCAmelCase				)    ->  Any:
    lowerCamelCase__					:   Tuple      				=	_split_gen_kwargs(_UpperCAmelCase		,			_UpperCAmelCase				)
    assert out == expected


@pytest.mark.parametrize(
    'gen_kwargs, expected'		,			[
        ({'foo': 0}, 1),
        ({'shards': [0]}, 1),
        ({'shards': [0, 1, 2, 3]}, 4),
        ({'shards': [0, 1, 2, 3], 'foo': 0}, 4),
        ({'shards': [0, 1, 2, 3], 'other': (0, 1)}, 4),
        ({'shards': [0, 1, 2, 3], 'shards2': [0, 1]}, RuntimeError),
    ]		,			)
def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase				)    ->  int:
    if expected is RuntimeError:
        with pytest.raises(_UpperCAmelCase				):
            _number_of_shards_in_gen_kwargs(_UpperCAmelCase				)
    else:
        lowerCamelCase__					:   Optional[Any]      				=	_number_of_shards_in_gen_kwargs(_UpperCAmelCase				)
        assert out == expected












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())





