




from __future__ import annotations

from pathlib import Path




def    __SCREAMING_SNAKE_CASE				(					lowercase_   ,       lowercase_ )    ->		int:

    """simple docstring"""


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




def    __SCREAMING_SNAKE_CASE				(					lowercase_   ,       lowercase_   ,       lowercase_   ,       lowercase_   ,       lowercase_   ,       lowercase_ )    ->		bool:

    """simple docstring"""


    __UpperCamelCase											=  (xa, ya)
    __UpperCamelCase											=  (xa - xa, ya - ya)
    __UpperCamelCase											=  (xa - xa, ya - ya)
    __UpperCamelCase											=  -vector_product(lowercase_   ,       lowercase_ ) / vector_product(
        lowercase_   ,       lowercase_ )
    __UpperCamelCase											=  +vector_product(lowercase_   ,       lowercase_ ) / vector_product(
        lowercase_   ,       lowercase_ )

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




def    __SCREAMING_SNAKE_CASE				(					lowercase_ = "p102_triangles.txt" )    ->		int:

    """simple docstring"""


    __UpperCamelCase											=  Path(lowercase_ ).parent.joinpath(lowercase_ ).read_text(encoding='''utf-8''' )

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

    __UpperCamelCase											=  0
    __UpperCamelCase											=  42

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

    return ret


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












def    __SCREAMING_SNAKE_CASE				(					lowercase_ )    ->		int:

    """simple docstring"""


    if not isinstance(lowercase_   ,       lowercase_ ):
        raise TypeError('''recursive_lucas_number accepts only integer arguments.''' )
    if n_th_number == 0:
        return 2
    if n_th_number == 1:
        return 1

    return recursive_lucas_number(n_th_number - 1 ) + recursive_lucas_number(
        n_th_number - 2 )




def    __SCREAMING_SNAKE_CASE				(					lowercase_ )    ->		int:

    """simple docstring"""


    if not isinstance(lowercase_   ,       lowercase_ ):
        raise TypeError('''dynamic_lucas_number accepts only integer arguments.''' )
    __UpperCamelCase						, __UpperCamelCase											=  2, 1
    for _ in range(lowercase_ ):
        __UpperCamelCase						, __UpperCamelCase											=  b, a + b
    return a


if __name__ == "__main__":
 from doctest import testmod

 testmod()
 a_										=       int(input("Enter the number of terms in lucas series:\n").strip())
 print("Using recursive function to calculate lucas series:")
 print(" ".join(str(recursive_lucas_number(i)) for i in range(n)))
 print("\nUsing dynamic function to calculate lucas series:")
 print(" ".join(str(dynamic_lucas_number(i)) for i in range(n)))






