




import math







def       _a (		SCREAMING_SNAKE_CASE_				:							int	):

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







def       _a (		SCREAMING_SNAKE_CASE_				:							int = 10_00 , SCREAMING_SNAKE_CASE_				:							int = 10_00	):
					__lowerCAmelCase							  =			[0, 0, 0]  # length, a, b
					for a in range((a_limit * -1) + 1 , SCREAMING_SNAKE_CASE_	):
										for b in range(2 , SCREAMING_SNAKE_CASE_	):
															if is_prime(SCREAMING_SNAKE_CASE_	):
																				__lowerCAmelCase							  =			0
																				__lowerCAmelCase							  =			0
																				while is_prime((n**2) + (a * n) + b	):
																									count += 1
																									n += 1
																				if count > longest[0]:
																									__lowerCAmelCase							  =			[count, a, b]
					__lowerCAmelCase							  =			longest[1] * longest[2]
					return ans


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










from __future__ import annotations

from pathlib import Path







def       _a (		SCREAMING_SNAKE_CASE_				:							tuple[int, int] , SCREAMING_SNAKE_CASE_				:							tuple[int, int]	):
					return pointa[0] * pointa[1] - pointa[1] * pointa[0]







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					__lowerCAmelCase							  =			(xa, ya)
					__lowerCAmelCase							  =			(xa - xa, ya - ya)
					__lowerCAmelCase							  =			(xa - xa, ya - ya)
					__lowerCAmelCase							  =			-vector_product(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) / vector_product(
					    SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
					__lowerCAmelCase							  =			+vector_product(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) / vector_product(
					    SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)

					return a > 0 and b > 0 and a + b < 1







def       _a (		SCREAMING_SNAKE_CASE_				:							str = "p102_triangles.txt"	):
					__lowerCAmelCase							  =			Path(SCREAMING_SNAKE_CASE_	).parent.joinpath(SCREAMING_SNAKE_CASE_	).read_text(encoding="utf-8"	)

					__lowerCAmelCase							  =			[]
					for line in data.strip().split("\n"	):
										triangles.append([int(SCREAMING_SNAKE_CASE_	) for number in line.split(","	)]	)

					__lowerCAmelCase							  =			0
					__lowerCAmelCase							  =			42

					for triangle in triangles:
										ret += contains_origin(*SCREAMING_SNAKE_CASE_	)

					return ret


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




