






'''simple docstring'''







import torch

from transformers import AutoTokenizer




class 					__UpperCAmelCase (		__snake_case	):

      '''simple docstring'''





      def __init__(					self  ,		_UpperCAmelCase						):
             UpperCAmelCase__	:   int												=	AutoTokenizer.from_pretrained(lowerCamelCase_						)




      def 							lowerCamelCase     (					self  ,		_UpperCAmelCase						):

             if isinstance(lowerCamelCase_  ,		lowerCamelCase_						) and all(isinstance(_x  ,		lowerCamelCase_						) for _x in x						):
                    UpperCAmelCase__	:   Any												=	None
                    for l in x:
                           UpperCAmelCase__	:   Tuple												=	self.tokenizer(
                               lowerCamelCase_  ,		padding='''max_length'''  ,		max_length=384  ,		truncation=lowerCamelCase_  ,		return_tensors='''pt'''  ,		)
                           UpperCAmelCase__	:   Tuple												=	torch.tensor([len(lowerCamelCase_						)]						)
                           if d is not None:
                                  for k in d.keys():
                                         UpperCAmelCase__	:   List[Any]												=	torch.cat((d[k], t[k])  ,		0						)
                           else:
                                  UpperCAmelCase__	:   List[Any]												=	t

                    UpperCAmelCase__	:   Optional[Any]												=	torch.tensor(self.tokenizer.convert_tokens_to_ids('''[E]'''						)						)
                    UpperCAmelCase__	:   List[Any]												=	torch.tensor(self.tokenizer.convert_tokens_to_ids('''[/E]'''						)						)

             elif isinstance(lowerCamelCase_  ,		lowerCamelCase_						) and all(isinstance(_x  ,		lowerCamelCase_						) for _x in x						):
                    UpperCAmelCase__	:   List[Any]												=	self.tokenizer(
                        lowerCamelCase_  ,		padding='''max_length'''  ,		max_length=384  ,		truncation=lowerCamelCase_  ,		return_tensors='''pt'''  ,		)

             else:
                    raise Exception(
                        '''Type of parameter x was not recognized! Only `list of strings` for query or `list of lists of'''
                        ''' strings` for supports are supported.'''						)

             return d




      def 							lowerCamelCase     (					self  ,		_UpperCAmelCase  ,		_UpperCAmelCase  ,		_UpperCAmelCase  ,		_UpperCAmelCase  ,		_UpperCAmelCase=0.70						):
             UpperCAmelCase__	:   Union[str, Any]												=	[]
             for idx in range(len(W_query['''input_ids''']						)						):
                    UpperCAmelCase__	:   List[Any]												=	range(p_start.shape[1]						)

                    UpperCAmelCase__	:   str												=	[]
                    for start_id in start_indexes:
                           for end_id in end_indexes:
                                  if start_id < end_id:
                                         output.append(
                                             (
                                                 start_id,
                                                 end_id,
                                                 p_start[idx][start_id].item(),
                                                 p_end[idx][end_id].item(),
                                             )						)

                    output.sort(key=lambda _UpperCAmelCase						: (tup[2] * tup[3])  ,		reverse=lowerCamelCase_						)
                    UpperCAmelCase__	:   str												=	[]
                    for k in range(len(lowerCamelCase_						)						):
                           if output[k][2] * output[k][3] >= thresh:
                                  UpperCAmelCase__	:   List[str]												=	output[k][0], output[k][1]
                                  UpperCAmelCase__	:   Dict												=	self.tokenizer.decode(W_query['''input_ids'''][idx][c_start_pos:c_end_pos]						)
                                  temp.append((decoded, output[k][2] * output[k][3])						)

                    final_outputs.append(lowerCamelCase_						)

             return final_outputs




import math







def       lowerCamelCase_  (    _a       :						int    ):



    '''simple docstring'''




    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5   ,		int(math.sqrt(_a    ) + 1    )   ,		6    ):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True







def       lowerCamelCase_  (    _a       :						int = 6008_5147_5143    ):



    '''simple docstring'''




    try:
        UpperCAmelCase_     :       str  		=					int(_a    )
    except (TypeError, ValueError):
        raise TypeError("""Parameter n must be int or castable to int."""    )
    if n <= 0:
        raise ValueError("""Parameter n must be greater than or equal to one."""    )
    UpperCAmelCase_     :       Optional[int]  		=					0
    if is_prime(_a    ):
        return n
    while n % 2 == 0:
        n //= 2
    if is_prime(_a    ):
        return n
    for i in range(3   ,		int(math.sqrt(_a    )    ) + 1   ,		2    ):
        if n % i == 0:
            if is_prime(n // i    ):
                UpperCAmelCase_     :       Optional[int]  		=					n // i
                break
            elif is_prime(_a    ):
                UpperCAmelCase_     :       str  		=					i
    return max_number


if __name__ == "__main__":
      print(F"{solution() = }")
