from math import sqrt


class Vec2:
    def __init__(self, x: float = 0, y: float = 0):
        self.x: float = x
        self.y: float = y

    @property
    def mag(self) -> float:
        return sqrt(self.x ** 2 + self.y ** 2)

    def normalized(self) -> "Vec2":
        mag = self.mag
        if mag == 0:
            return Vec2()
        return self / mag

    def __add__(self, v: "Vec2") -> "Vec2":
        return Vec2(self.x + v.x, self.y + v.y)

    def __sub__(self, v: "Vec2") -> "Vec2":
        return Vec2(self.x - v.x, self.y - v.y)

    def __mul__(self, f: float) -> "Vec2":
        return Vec2(self.x * f, self.y * f)

    def __truediv__(self, f: float) -> "Vec2":
        return Vec2(self.x / f, self.y / f)

    def __neg__(self) -> "Vec2":
        return Vec2(-self.x, -self.y)

    def cross(self, v: "Vec2") -> float:
        return self.x * v.y - self.y * v.x

    def scale(self, v: "Vec2") -> "Vec2":
        return Vec2(self.x * v.x, self.y * v.y)