
from __future__ import annotations

from pathlib import Path





def 							_lowerCamelCase			(					lowerCamelCase_:  List[Any]				,	lowerCamelCase_:  Dict		):



				'''simple docstring'''







				return pointa[0] * pointa[1] - pointa[1] * pointa[0]





def 							_lowerCamelCase			(					lowerCamelCase_:  List[Any]				,	lowerCamelCase_:  List[str]				,	lowerCamelCase_:  Optional[int]				,	lowerCamelCase_:  List[Any]				,	lowerCamelCase_:  Dict				,	lowerCamelCase_:  Dict		):



				'''simple docstring'''







				A     :  tuple[int, int]   =				(xa, ya)
				A     :  tuple[int, int]   =				(xa - xa, ya - ya)
				A     :  tuple[int, int]   =				(xa - xa, ya - ya)
				A     :  float   =				-vector_product(lowerCamelCase_				,	lowerCamelCase_		) / vector_product(
				    lowerCamelCase_				,	lowerCamelCase_		)
				A     :  float   =				+vector_product(lowerCamelCase_				,	lowerCamelCase_		) / vector_product(
				    lowerCamelCase_				,	lowerCamelCase_		)

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





def 							_lowerCamelCase			(					lowerCamelCase_:  List[str] = "p102_triangles.txt"		):



				'''simple docstring'''







				A     :  str   =				Path(lowerCamelCase_		).parent.joinpath(lowerCamelCase_		).read_text(encoding='''utf-8'''		)

				A     :  list[list[int]]   =				[]
				for line in data.strip().split('''\n'''		):
								triangles.append([int(lowerCamelCase_		) for number in line.split(''','''		)]		)

				A     :  int   =				0
				A     :  list[int]

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

				return ret


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

def 							_lowerCamelCase			(					lowerCamelCase_:  int		):



				'''simple docstring'''







				if not isinstance(lowerCamelCase_				,	lowerCamelCase_		):
								raise ValueError('''double_factorial() only accepts integral values'''		)
				if num < 0:
								raise ValueError('''double_factorial() not defined for negative values'''		)
				A     :  int   =				1
				for i in range(lowerCamelCase_				,	0				,	-2		):
								value *= i
				return value


if __name__ == "__main__":
					import doctest

					doctest.testmod()