import math


class Vec2:
    def __init__(self, x=0.0, y=0.0):
        self.x = x
        self.y = y

    def __str__(self):
        return "[%s,%s]" % (self.x, self.y)


class Vec3:
    def __init__(self, x=0.0, y=0.0, z=0.0):
        self.x = x
        self.y = y
        self.z = z

    def __add__(self, other):
        return Vec3(self.x + other.x, self.y + other.y, self.z + other.z)

    def __sub__(self, other):
        return self + -other

    def __radd__(self, other):
        return Vec3(self.x + other.x, self.y + other.y, self.z + other.z)

    def __mul__(self, scalar):
        return Vec3(self.x * scalar, self.y * scalar, self.z * scalar)

    def __rmul__(self, scalar):
        return Vec3(self.x * scalar, self.y * scalar, self.z * scalar)

    def __neg__(self):
        return Vec3(-self.x, -self.y, -self.z)

    def __pos__(self):
        return Vec3(self.x, self.y, self.z)

    def __xor__(self, other):
        cx = self.y * other.z - self.z * other.y
        cy = self.z * other.x - self.x * other.z
        cz = self.x * other.y - self.y * other.x
        return Vec3(cx, cy, cz)

    def cross(self, other):
        return self ^ other

    def normalize(self):
        w = math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
        if w == 0:
            return Vec3()
        else:
            return Vec3(self.x / w, self.y / w, self.z / w)

    def __str__(self):
        return "[%s,%s,%s]" % (self.x, self.y, self.z)


class VecRGB:
    def __init__(self, r=0, g=0, b=0):
        self.r = r
        self.g = g
        self.b = b

    def __str__(self):
        return "[%s,%s,%s]" % (self.r, self.g, self.b)


def cross(v1: Vec3, v2: Vec3):
    return v1.cross(v2)