from __future__ import annotations

from math import sqrt


class Vec:
    def __init__(self, x: float = 0, y: float = 0) -> None:
        self.x: float = x
        self.y: float = y
    
    def __add__(self, v: Vec) -> Vec:
        return Vec(self.x+v.x, self.y+v.y)
    
    def __sub__(self, v: Vec) -> Vec:
        return Vec(self.x-v.x, self.y-v.y)
    
    def __mul__(self, f: float) -> Vec:
        return Vec(self.x*f, self.y*f)
    
    def __truediv__(self, f: float) -> Vec:
        return Vec(self.x/f, self.y/f)
    
    def mag(self) -> float:
        return sqrt(self.x**2 + self.y**2)
    
    def norm(self) -> Vec:
        mag = self.mag()
        if mag == 0:
            return Vec()
        return self / mag