util.py

class Vector2:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def dist_sqr(self):
        return self.x*self.x + self.y*self.y

    def dist(self):
        return self.dist_sqr() ** 0.5

    def normalized(self):
        d = self.dist()
        if d == 0:
            return Vector2(0, 0)
        return Vector2(self.x / d, self.y / d)

    def __add__(self, other):
        return Vector2(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Vector2(self.x - other.x, self.y - other.y)

    def __mul__(self, other):
        return Vector2(self.x * other, self.y * other)

    def __truediv__(self, other):
        return Vector2(self.x / other, self.y / other)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __ne__(self, other):
        return self.x != other.x or self.y != other.y

    def __hash__(self):
        return hash((self.x, self.y))

    def __str__(self):
        return f'({self.x}, {self.y})'

    def __repr__(self):
        return f'({self.x}, {self.y})'

    def __iter__(self):
        return iter([self.x, self.y])