import math
from typing import List


class Pos:
    def __init__(self, x: float = 0, y: float = 0):
        self.x_pos = x
        self.y_pos = y
        pass

    def __add__(self, other: 'Pos') -> 'Pos':
        return Pos(self.x_pos + other.x_pos, self.y_pos + other.y_pos)

    def __sub__(self, other: 'Pos') -> 'Pos':
        return Pos(self.x_pos - other.x_pos, self.y_pos - other.y_pos)

    def __iadd__(self, other: 'Pos') -> 'Pos':
        self.x_pos += other.x_pos
        self.y_pos += other.y_pos
        return self

    def __isub__(self, other: 'Pos') -> 'Pos':
        self.x_pos -= other.x_pos
        self.y_pos -= other.y_pos
        return self

    def __mul__(self, t: float) -> 'Pos':
        return Pos(self.x_pos * t, self.y_pos * t)

    def __imul__(self, t: float) -> 'Pos':
        self.x_pos *= t
        self.y_pos *= t
        return self

    def vec_length(self) -> float:
        return math.sqrt(self.x_pos**2 + self.y_pos**2)

    def normalized(self) -> 'Pos':
        dist = self.vec_length()

        if dist == 0:
            return Pos(0, 0)

        return self * (1/dist)

    def to_text(self) -> str:
        return f"pos<{self.__hash__()}>{{{self.x_pos}, {self.y_pos}}}"

    def make_copy(self) -> 'Pos':
        return Pos(self.x_pos, self.y_pos)


class Point:
    def __init__(self, name:str):
        self.point_name = name
        pass

    def name(self) -> str:
        return self.point_name

    def make_copy(self) -> 'Point':
        return Point(self.point_name)


class PositionalPoint(Point, Pos):
    def __init__(self, name: str, x: float, y: float):
        Point.__init__(self, name)
        Pos.__init__(self, x, y)
        pass

    def make_copy(self) -> 'PositionalPoint':
        return PositionalPoint(self.name(), self.x_pos, self.y_pos)


class Line:
    def __init__(self, p0: Point, p1: Point):
        self.point_set = [p0, p1]
        pass

    def points(self) -> List[Point]:
        return self.point_set

    def make_copy(self) -> 'Line':
        return Line(self.points()[0].make_copy(), self.points()[1].make_copy())


class Arrow(Line):
    def __init__(self, start: Point, end: Point):
        Line.__init__(self, start, end)
        pass

    def start_point(self):
        return self.point_set[0]

    def end_point(self):
        return self.point_set[1]