

from __future__ import annotations

from pathlib import Path

def 				A_					(							a   ,				a					):

      """simple docstring"""



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

def 				A_					(							a   ,				a   ,				a   ,				a   ,				a   ,				a					):

      """simple docstring"""



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

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

def 				A_					(							a = "p102_triangles.txt"					):

      """simple docstring"""



      SCREAMING_SNAKE_CASE_			:					str          =       Path(a					).parent.joinpath(a					).read_text(encoding='utf-8'					)

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

      SCREAMING_SNAKE_CASE_			:					int          =       0
      SCREAMING_SNAKE_CASE_			:					list[int]

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

      return ret


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









from math import factorial

def 				A_					(							a   ,				a					):

      """simple docstring"""



      return factorial(a					) / (factorial(a					) * factorial(n - r					))

def 				A_					(							):

      """simple docstring"""



      SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       0

      for i in range(1   ,				1_0_1					):
            for j in range(1   ,				i + 1					):
                  if combinations(a   ,				a					) > 1e6:
                        total += 1
      return total


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






