






from ..utils import DummyObject, requires_backends


class      lowercase__     (			metaclass=_UpperCAmelCase	):
	a_         =["""transformers""", """torch""", """note_seq"""]

	def __init__(							self		,    *__UpperCAmelCase		,    **__UpperCAmelCase       )->					Any:







							'''simple docstring'''





							requires_backends(self		,    ["transformers", "torch", "note_seq"]       )

	@classmethod
	def 		UpperCAmelCase  (							cls		,    *__UpperCAmelCase		,    **__UpperCAmelCase       )->					Optional[Any]:







							'''simple docstring'''





							requires_backends(cls		,    ["transformers", "torch", "note_seq"]       )


	@classmethod
	def 		UpperCAmelCase  (							cls		,    *__UpperCAmelCase		,    **__UpperCAmelCase       )->					Any:







							'''simple docstring'''





							requires_backends(cls		,    ["transformers", "torch", "note_seq"]       )














from __future__ import annotations

from collections.abc import Generator


def        _a  (     ) ->   Generator[int, None, None]:
						"""simple docstring"""







						lowerCAmelCase__       =						{}
						lowerCAmelCase__       =						2
						while True:
												lowerCAmelCase__       =						factor_map.pop(UpperCamelCase_    ,   UpperCamelCase_   )
												if factor:
																		lowerCAmelCase__       =						factor + prime
																		while x in factor_map:
																								x += factor
																		lowerCAmelCase__       =						factor
												else:
																		lowerCAmelCase__       =						prime
																		yield prime
												prime += 1


def        _a  (     UpperCamelCase_					:				float = 1e1_0   ) ->   int:
						"""simple docstring"""







						lowerCAmelCase__       =						sieve()

						lowerCAmelCase__       =						1
						while True:
												lowerCAmelCase__       =						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())






