

from __future__ import annotations

from pathlib import Path


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						tuple[int, int]       ,      _SCREAMING_SNAKE_CASE    :						tuple[int, int]				):





    """simple docstring"""


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


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int       ,      _SCREAMING_SNAKE_CASE    :						int				):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_													=  (xa, ya)
    SCREAMING_SNAKE_CASE_													=  (xa - xa, ya - ya)
    SCREAMING_SNAKE_CASE_													=  (xa - xa, ya - ya)
    SCREAMING_SNAKE_CASE_													=  -vector_product(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				) / vector_product(
        _SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				)
    SCREAMING_SNAKE_CASE_													=  +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     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						str = "p102_triangles.txt"				):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_													=  Path(_SCREAMING_SNAKE_CASE				).parent.joinpath(_SCREAMING_SNAKE_CASE				).read_text(encoding='utf-8'				)

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

    SCREAMING_SNAKE_CASE_													=  0
    SCREAMING_SNAKE_CASE_													=  42

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

    return ret


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





from itertools import permutations


def     _UpperCAmelCase				(     ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_													=  list(map(''.join       ,      permutations('0123456789'				)				)				)
    return result[999_999]


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


