





from ..utils import DummyObject, requires_backends

class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   Tuple    ,  *UpperCAmelCase						:   str    ,  **UpperCAmelCase						:   Optional[int]			)    ->			List[str]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   Union[str, Any]    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   List[str]			)    ->			int:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   Any    ,  *UpperCAmelCase						:   List[Any]    ,  **UpperCAmelCase						:   Tuple			)    ->			Union[str, Any]:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   List[Any]    ,  *UpperCAmelCase						:   Union[str, Any]    ,  **UpperCAmelCase						:   Dict			)    ->			Any:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   str    ,  *UpperCAmelCase						:   Union[str, Any]    ,  **UpperCAmelCase						:   Union[str, Any]			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   str    ,  **UpperCAmelCase						:   Dict			)    ->			str:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   Dict    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   Dict			)    ->			Optional[int]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   Optional[Any]    ,  *UpperCAmelCase						:   Union[str, Any]    ,  **UpperCAmelCase						:   Any			)    ->			Any:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   List[str]    ,  *UpperCAmelCase						:   Any    ,  **UpperCAmelCase						:   Dict			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   Union[str, Any]    ,  *UpperCAmelCase						:   Optional[int]    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Any:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   int			)    ->			Dict:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   Dict    ,  *UpperCAmelCase						:   Dict    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Optional[int]:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   List[str]    ,  *UpperCAmelCase						:   List[Any]    ,  **UpperCAmelCase						:   List[str]			)    ->			Optional[int]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   Optional[Any]    ,  **UpperCAmelCase						:   Optional[Any]			)    ->			str:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   List[Any]    ,  *UpperCAmelCase						:   Optional[int]    ,  **UpperCAmelCase						:   Any			)    ->			Any:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)


class      lowerCAmelCase							(      metaclass=__UpperCamelCase    ):
 UpperCAmelCase__									=	["""torch""", """transformers""", """onnx"""]
 def __init__(   self						:   List[str]    ,  *UpperCAmelCase						:   Tuple    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Optional[Any]:
     requires_backends(self    ,  ['torch', 'transformers', 'onnx']			)
 @classmethod
 def   A_			(   cls						:   Union[str, Any]    ,  *UpperCAmelCase						:   List[Any]    ,  **UpperCAmelCase						:   Optional[Any]			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)







 @classmethod
 def   A_			(   cls						:   Tuple    ,  *UpperCAmelCase						:   List[str]    ,  **UpperCAmelCase						:   List[str]			)    ->			Tuple:
     requires_backends(cls    ,  ['torch', 'transformers', 'onnx']			)












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())





