


'''simple docstring'''







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


a__  : str				=	{
    'configuration_imagegpt': ['IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ImageGPTConfig', 'ImageGPTOnnxConfig']
}

try:
  if not is_vision_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  a__  : Union[str, Any]				=	['ImageGPTFeatureExtractor']
  a__  : Dict				=	['ImageGPTImageProcessor']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  a__  : Union[str, Any]				=	[
      'IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST',
      'ImageGPTForCausalImageModeling',
      'ImageGPTForImageClassification',
      'ImageGPTModel',
      'ImageGPTPreTrainedModel',
      'load_tf_weights_in_imagegpt',
  ]


if TYPE_CHECKING:
  from .configuration_imagegpt import IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP, ImageGPTConfig, ImageGPTOnnxConfig

  try:
    if not is_vision_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .feature_extraction_imagegpt import ImageGPTFeatureExtractor
    from .image_processing_imagegpt import ImageGPTImageProcessor

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_imagegpt import (
        IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST,
        ImageGPTForCausalImageModeling,
        ImageGPTForImageClassification,
        ImageGPTModel,
        ImageGPTPreTrainedModel,
        load_tf_weights_in_imagegpt,
    )

else:
  import sys

  a__  : Tuple				=	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)









'''simple docstring'''







import math







def _UpperCamelCase	(					__A   )							->		bool:


      '''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 _UpperCamelCase	(					__A = 1000				,      __A = 1000   )							->		int:


      '''simple docstring'''



      UpperCamelCase__  =    [0, 0, 0]  # length, a, b
      for a in range((a_limit * -1) + 1				,      __A   ):
            for b in range(2				,      __A   ):
                  if is_prime(__A   ):
                        UpperCamelCase__  =    0
                        UpperCamelCase__  =    0
                        while is_prime((n**2) + (a * n) + b   ):
                              count += 1
                              n += 1
                        if count > longest[0]:
                              UpperCamelCase__  =    [count, a, b]
      UpperCamelCase__  =    longest[1] * longest[2]
      return ans


if __name__ == "__main__":
  print(solution(1_0_0_0, 1_0_0_0))





