


"""simple docstring"""
import math






def 						lowercase				(	_snake_case		: int	)	->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(_snake_case	) + 1	)	,  6	):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True






def 						lowercase				(	_snake_case		: int = 1_000	,  _snake_case		: int = 1_000	)	->int:
	"""simple docstring"""





	__snake_case      :		str         =							[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	):
				__snake_case      :		Tuple         =							0
				__snake_case      :		Optional[int]         =							0
				while is_prime((n**2) + (a * n) + b	):
					count += 1
					n += 1
				if count > longest[0]:
					__snake_case      :		Optional[Any]         =							[count, a, b]
	__snake_case      :		Optional[Any]         =							longest[1] * longest[2]
	return ans


if __name__ == "__main__":
			print(solution(1000, 1000))









"""simple docstring"""
import unittest

from diffusers import __version__
from diffusers.utils import deprecate



class      _UpperCAmelCase					(				unittest.TestCase							):






		'''simple docstring'''

		lowerCamelCase__           ='.'.join([str(int(__version__.split('.'							)[0]							) + 1							)] + __version__.split('.'							)[1:]							)
		lowerCamelCase__           ='0.0.1'



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		int         =							{'''deprecated_arg''': 4}

			with self.assertWarns(a_   ) as warning:
				__snake_case      :		Union[str, Any]         =							deprecate('''deprecated_arg'''							,			self.higher_version							,			'''message'''							,			take_from=a_   )

			assert output == 4
			assert (
			    str(warning.warning   )
			    == f"""The `deprecated_arg` argument is deprecated and will be removed in version {self.higher_version}."""
			    " message"
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		Tuple         =							{'''deprecated_arg''': 4}

			with self.assertWarns(a_   ) as warning:
				__snake_case      :		Dict         =							deprecate(('''deprecated_arg''', self.higher_version, '''message''')							,			take_from=a_   )

			assert output == 4
			assert (
			    str(warning.warning   )
			    == f"""The `deprecated_arg` argument is deprecated and will be removed in version {self.higher_version}."""
			    " message"
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		Union[str, Any]         =							{'''deprecated_arg_1''': 4, '''deprecated_arg_2''': 8}
			with self.assertWarns(a_   ) as warning:
				__snake_case      ,				__snake_case      :		List[Any]         =							deprecate(
				    ('''deprecated_arg_1''', self.higher_version, '''Hey''')							,			('''deprecated_arg_2''', self.higher_version, '''Hey''')							,			take_from=a_							,			)
			assert output_a == 4
			assert output_a == 8
			assert (
			    str(warning.warnings[0].message   )
			    == "The `deprecated_arg_1` argument is deprecated and will be removed in version"
			    f""" {self.higher_version}. Hey"""
			)
			assert (
			    str(warning.warnings[1].message   )
			    == "The `deprecated_arg_2` argument is deprecated and will be removed in version"
			    f""" {self.higher_version}. Hey"""
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		int         =							{'''deprecated_arg''': 4}

			with self.assertRaises(a_   ) as error:
				deprecate(('''wrong_arg''', self.higher_version, '''message''')							,			take_from=a_   )

			assert "test_deprecate_function_incorrect_arg in" in str(error.exception   )
			assert "line" in str(error.exception   )
			assert "got an unexpected keyword argument `deprecated_arg`" in str(error.exception   )



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			with self.assertWarns(a_   ) as warning:
				deprecate(('''deprecated_arg''', self.higher_version, '''message''')   )

			assert (
			    str(warning.warning   )
			    == f"""`deprecated_arg` is deprecated and will be removed in version {self.higher_version}. message"""
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			with self.assertWarns(a_   ) as warning:
				deprecate(
				    ('''deprecated_arg_1''', self.higher_version, '''Hey''')							,			('''deprecated_arg_2''', self.higher_version, '''Hey''')							,			)
			assert (
			    str(warning.warnings[0].message   )
			    == f"""`deprecated_arg_1` is deprecated and will be removed in version {self.higher_version}. Hey"""
			)
			assert (
			    str(warning.warnings[1].message   )
			    == f"""`deprecated_arg_2` is deprecated and will be removed in version {self.higher_version}. Hey"""
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			class      _UpperCAmelCase					:






					'''simple docstring'''

					lowerCamelCase__           =5

			with self.assertWarns(a_   ) as warning:
				__snake_case      :		List[Any]         =							deprecate(('''arg''', self.higher_version, '''message''')							,			take_from=Args()   )

			assert arg == 5
			assert (
			    str(warning.warning   )
			    == f"""The `arg` attribute is deprecated and will be removed in version {self.higher_version}. message"""
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			class      _UpperCAmelCase					:






					'''simple docstring'''

					lowerCamelCase__           =5
					lowerCamelCase__           =7

			with self.assertWarns(a_   ) as warning:
				__snake_case      ,				__snake_case      :		List[str]         =							deprecate(
				    ('''arg''', self.higher_version, '''message''')							,			('''foo''', self.higher_version, '''message''')							,			('''does not exist''', self.higher_version, '''message''')							,			take_from=Args()							,			)

			assert arg_a == 5
			assert arg_a == 7
			assert (
			    str(warning.warning   )
			    == f"""The `arg` attribute is deprecated and will be removed in version {self.higher_version}. message"""
			)
			assert (
			    str(warning.warnings[0].message   )
			    == f"""The `arg` attribute is deprecated and will be removed in version {self.higher_version}. message"""
			)
			assert (
			    str(warning.warnings[1].message   )
			    == f"""The `foo` attribute is deprecated and will be removed in version {self.higher_version}. message"""
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			__snake_case      :		str         =							{'''deprecated_arg''': 4}

			with self.assertRaises(a_   ) as error:
				deprecate(('''wrong_arg''', self.lower_version, '''message''')							,			take_from=a_   )

			assert (
			    str(error.exception   )
			    == "The deprecation tuple ('wrong_arg', '0.0.1', 'message') should be removed since diffusers' version"
			    f""" {__version__} is >= {self.lower_version}"""
			)



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			with self.assertWarns(a_   ) as warning:
				deprecate(('''deprecated_arg''', self.higher_version, '''This message is better!!!''')							,			standard_warn=a_   )

			assert str(warning.warning   ) == "This message is better!!!"



		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

			with self.assertWarns(a_   ) as warning:
				deprecate(('''deprecated_arg''', self.higher_version, '''This message is better!!!''')							,			standard_warn=a_   )
			assert str(warning.warning   ) == "This message is better!!!"
			assert "diffusers/tests/others/test_utils.py" in warning.filename





