
import math






def        lowerCamelCase__    (    __lowerCAmelCase  :  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(__lowerCAmelCase    ) + 1    )   ,							6    ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True






def        lowerCamelCase__    (    __lowerCAmelCase  :  int = 600851475143    ):




			"""simple docstring"""


			try:
						lowerCAmelCase_      =     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."    )
			lowerCAmelCase_      =     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    ):
												lowerCAmelCase_      =     n // i
												break
									elif is_prime(__lowerCAmelCase    ):
												lowerCAmelCase_      =     i
			return max_number


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





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_A       =					{"configuration_nat": ["NAT_PRETRAINED_CONFIG_ARCHIVE_MAP", "NatConfig"]}


try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			_A       =					[
			    "NAT_PRETRAINED_MODEL_ARCHIVE_LIST",
			    "NatForImageClassification",
			    "NatModel",
			    "NatPreTrainedModel",
			    "NatBackbone",
			]

if TYPE_CHECKING:
			from .configuration_nat import NAT_PRETRAINED_CONFIG_ARCHIVE_MAP, NatConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_nat import (
						    NAT_PRETRAINED_MODEL_ARCHIVE_LIST,
						    NatBackbone,
						    NatForImageClassification,
						    NatModel,
						    NatPreTrainedModel,
						)

else:
			import sys

			_A       =					_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



