



"""simple docstring"""




from __future__ import annotations

from pathlib import Path



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase):
					return pointa[0] * pointa[1] - pointa[1] * pointa[0]



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
					UpperCamelCase_											=				(xa, ya)
					UpperCamelCase_											=				(xa - xa, ya - ya)
					UpperCamelCase_											=				(xa - xa, ya - ya)
					UpperCamelCase_											=				-vector_product(_lowerCAmelCase				,		_lowerCAmelCase) / vector_product(
					    _lowerCAmelCase				,		_lowerCAmelCase)
					UpperCamelCase_											=				+vector_product(_lowerCAmelCase				,		_lowerCAmelCase) / vector_product(
					    _lowerCAmelCase				,		_lowerCAmelCase)

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



def 				_lowerCAmelCase      (_lowerCAmelCase = "p102_triangles.txt"):
					UpperCamelCase_											=				Path(_lowerCAmelCase).parent.joinpath(_lowerCAmelCase).read_text(encoding="utf-8")

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

					UpperCamelCase_											=				0
					UpperCamelCase_											=				42

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

					return ret


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





def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase):
					UpperCamelCase_											=				0
					for ele in arr:
										total_sum += product_sum(_lowerCAmelCase				,		depth + 1) if isinstance(_lowerCAmelCase				,		_lowerCAmelCase) else ele
					return total_sum * depth



def 				_lowerCAmelCase      (_lowerCAmelCase):
					return product_sum(_lowerCAmelCase				,		1)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
