

"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


A_							:     Any     =	{"configuration_nat": ["NAT_PRETRAINED_CONFIG_ARCHIVE_MAP", "NatConfig"]}


try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_							:     str     =	[
						    "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_							:     List[str]     =	_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





"""simple docstring"""




import math

def 		A    (       snake_case__      ):




			'''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(snake_case__      ) + 1      )						,			6      ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True

def 		A    (       snake_case__ = 10_00						,			snake_case__ = 10_00      ):




			'''simple docstring'''


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


if __name__ == "__main__":
						print(solution(1_000, 1_000))


