from __future__ import annotations

from math import cos, sin, sqrt


class Vec:
    def __init__(self, x: float = 0, y: float = 0) -> None:
        self.x: float = x
        self.y: float = y

    def __add__(self, other: float | Vec) -> Vec:
        if isinstance(other, Vec):
            return Vec(self.x + other.x, self.y + other.y)
        return Vec(self.x + other, self.y + other)

    def __sub__(self, other: float | Vec) -> Vec:
        if isinstance(other, Vec):
            return Vec(self.x - other.x, self.y - other.y)
        return Vec(self.x - other, self.y - other)

    def __mul__(self, value: float) -> Vec:
        return Vec(self.x * value, self.y * value)

    def __truediv__(self, value: float) -> Vec:
        return Vec(self.x / value, self.y / value)

    def dot(self, other: Vec) -> float:
        return self.x * other.x + self.y * other.y

    def mag(self) -> float:
        return sqrt(self.mag2())

    def mag2(self) -> float:
        return self.dot(self)

    def cross(self, other: Vec) -> float:
        return self.x * other.y - self.y * other.x

    @property
    def normalized(self) -> Vec:
        mag: float = self.mag()
        if mag == 0:
            return Vec()
        return self / mag

    def __len__(self) -> int:
        return 2

    def __getitem__(self, item):
        return [self.x, self.y][item]

    @property
    def perp(self) -> Vec:
        return Vec(-self.y, self.x)

    def __repr__(self) -> str:
        return f"Vec({self.x}, {self.y})"

    def rotate(self, angle: float) -> Vec:
        return Vec(
            cos(angle) * self.x - sin(angle) * self.y,
            sin(angle) * self.x + cos(angle) * self.y,
        )

    def within(self, p1: Vec, p2: Vec) -> bool:
        x1, x2 = min(p1.x, p2.x), max(p1.x, p2.x)
        y1, y2 = min(p1.y, p2.y), max(p1.y, p2.y)
        return (x1 <= self.x <= x2) and (y1 <= self.y <= y2)