code: 
  
  
  
  
  
  '''simple docstring'''
  
  import math
  
  
  
  
  
  def 		UpperCamelCase       (							_lowerCamelCase      :      int ):
  
      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(_lowerCamelCase ) + 1 )		, 6 ):
          if number % i == 0 or number % (i + 2) == 0:
              return False
      return True
  
  
  
  
  
  def 		UpperCamelCase       (							_lowerCamelCase      :      int = 10_00		, _lowerCamelCase      :      int = 10_00 ):
      A__       =    [0, 0, 0]  # length, a, b
      for a in range((a_limit * -1) + 1		, _lowerCamelCase ):
          for b in range(2		, _lowerCamelCase ):
              if is_prime(_lowerCamelCase ):
                  A__       =    0
                  A__       =    0
                  while is_prime((n**2) + (a * n) + b ):
                      count += 1
                      n += 1
                  if count > longest[0]:
                      A__       =    [count, a, b]
      A__       =    longest[1] * longest[2]
      return ans
  
  
  if __name__ == "__main__":
    print(solution(1000, 1000))
  
  
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  import torch
  
  from transformers import AutoTokenizer
  
  
  
  
  
  
  class      UpperCAmelCase			( UpperCamelCase__       ):
   def __init__(       self   :Any		, lowercase_   :Dict							)->							Any:
       A__       =    AutoTokenizer.from_pretrained(lowercase_							)
   def   UpperCAmelCase_							(       self   :Tuple		, lowercase_   :int							)->							Optional[int]:
  
       if isinstance(lowercase_		, lowercase_							) and all(isinstance(_x		, lowercase_							) for _x in x							):
           A__       =    None
           for l in x:
               A__       =    self.tokenizer(
                   lowercase_		, padding="max_length"		, max_length=3_84		, truncation=lowercase_		, return_tensors="pt"		, )
               A__       =    torch.tensor([len(lowercase_							)]							)
               if d is not None:
                   for k in d.keys():
                       A__       =    torch.cat((d[k], t[k])		, 0							)
               else:
                   A__       =    t
  
           A__       =    torch.tensor(self.tokenizer.convert_tokens_to_ids("[E]"							)							)
           A__       =    torch.tensor(self.tokenizer.convert_tokens_to_ids("[/E]"							)							)
  
       elif isinstance(lowercase_		, lowercase_							) and all(isinstance(_x		, lowercase_							) for _x in x							):
           A__       =    self.tokenizer(
               lowercase_		, padding="max_length"		, max_length=3_84		, truncation=lowercase_		, 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   UpperCAmelCase_							(       self   :Union[str, Any]		, lowercase_   :List[str]		, lowercase_   :str		, lowercase_   :str		, lowercase_   :List[Any]		, lowercase_   :Dict=0.7_0							)->							int:
       A__       =    []
       for idx in range(len(W_query["input_ids"]							)							):
           A__       =    A__       =    range(p_start.shape[1]							)
  
           A__       =    []
           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 lowercase_							: (tup[2] * tup[3])		, reverse=lowercase_							)
           A__       =    []
           for k in range(len(lowercase_							)							):
               if output[k][2] * output[k][3] >= thresh:
                   A__,			A__       =    output[k][0], output[k][1]
                   A__       =    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(lowercase_							)
  
       return final_outputs
  
  
  
  