





import torch

from transformers import AutoModel

class      lowerCAmelCase							(      torch.nn.Module    ):
 def __init__(   self						:   Optional[Any]    ,  UpperCAmelCase						:   Tuple="sayef/fsner-bert-base-uncased"			)    ->			Optional[int]:
     super(UpperCAmelCase    ,  self			).__init__()

     lowerCamelCase__					:   int      				=	AutoModel.from_pretrained(UpperCAmelCase    ,  return_dict=UpperCAmelCase			)
     lowerCamelCase__					:   Union[str, Any]      				=	torch.nn.CosineSimilarity(3    ,  1e-08			)
     lowerCamelCase__					:   Dict      				=	torch.nn.Softmax(dim=1			)
 def   A_			(   self						:   int    ,  **UpperCAmelCase						:   Optional[int]			)    ->			Union[str, Any]:
     return self.bert(**UpperCAmelCase			).last_hidden_state
 def   A_			(   self						:   Optional[Any]    ,  UpperCAmelCase						:   Tuple			)    ->			int:
     return token_embeddings.sum(2    ,  keepdim=UpperCAmelCase			)
 def   A_			(   self						:   str    ,  UpperCAmelCase						:   Dict    ,  UpperCAmelCase						:   str    ,  UpperCAmelCase						:   Optional[Any]=1			)    ->			Tuple:
     return self.softmax(T * self.cos(UpperCAmelCase    ,  UpperCAmelCase			)			)







 def   A_			(   self						:   Union[str, Any]    ,  UpperCAmelCase						:   Optional[Any]    ,  UpperCAmelCase						:   int			)    ->			Any:
     lowerCamelCase__					:   int      				=	W_supports['sizes'].tolist()
     lowerCamelCase__					:   str      				=	W_supports['start_token_id'].item()
     lowerCamelCase__					:   int      				=	W_supports['end_token_id'].item()

     del W_supports["sizes"]
     del W_supports["start_token_id"]
     del W_supports["end_token_id"]

     lowerCamelCase__					:   Optional[Any]      				=	self.BERT(**UpperCAmelCase			)
     lowerCamelCase__					:   int      				=	self.BERT(**UpperCAmelCase			)

     lowerCamelCase__					:   Dict      				=	None
     lowerCamelCase__					:   List[str]      				=	None

     lowerCamelCase__					:   Any      				=	W_supports['input_ids'] == start_token_id
     lowerCamelCase__					:   List[Any]      				=	W_supports['input_ids'] == end_token_id

     for i, size in enumerate(UpperCAmelCase			):
         if i == 0:
             lowerCamelCase__					:   str      				=	0
         else:
             lowerCamelCase__					:   List[Any]      				=	support_sizes[i - 1]

         lowerCamelCase__					:   int      				=	S[s : s + size][start_token_masks[s : s + size]]
         lowerCamelCase__					:   Dict      				=	S[s : s + size][end_token_masks[s : s + size]]

         lowerCamelCase__					:   Optional[Any]      				=	torch.matmul(q[i]    ,  s_start.T			).sum(1			).softmax(0			)
         lowerCamelCase__					:   List[str]      				=	torch.matmul(q[i]    ,  s_end.T			).sum(1			).softmax(0			)

         if p_starts is not None:
             lowerCamelCase__					:   int      				=	torch.vstack((p_starts, p_start)			)
             lowerCamelCase__					:   Dict      				=	torch.vstack((p_ends, p_end)			)
         else:
             lowerCamelCase__					:   List[Any]      				=	p_start
             lowerCamelCase__					:   Union[str, Any]      				=	p_end

     return p_starts, p_ends












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())





