




from typing import TYPE_CHECKING

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


__UpperCamelCase      : Optional[Any]					      =   {
    "configuration_imagegpt": ["IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP", "ImageGPTConfig", "ImageGPTOnnxConfig"]
}

try:
		if not is_vision_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCamelCase      : str					      =   ["ImageGPTFeatureExtractor"]
		__UpperCamelCase      : int					      =   ["ImageGPTImageProcessor"]

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__UpperCamelCase      : List[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

		__UpperCamelCase      : str					      =   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)







import math





def 	__A	(			__lowerCamelCase					)   -> bool:

	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 	__A	(			__lowerCamelCase = 6008_5147_5143					)   -> int:

	try:
		a		       =							int(__lowerCamelCase					)
	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."""					)
	a		       =							0
	if is_prime(__lowerCamelCase					):
		return n
	while n % 2 == 0:
		n //= 2
	if is_prime(__lowerCamelCase					):
		return n
	for i in range(3							,    int(math.sqrt(__lowerCamelCase					)					) + 1							,    2					):
		if n % i == 0:
			if is_prime(n // i					):
				a		       =							n // i
				break
			elif is_prime(__lowerCamelCase					):
				a		       =							i
	return max_number


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

