class Vector
{
public:
  float x, y, z;
  Vector(float x1 = 0, float y1 = 0, float z1 = 0)
  {
    x = x1;
    y = y1;
    z = z1;
  };

  float mag();
};

Vector operator+(Vector v1, Vector v2)
{
  return Vector(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z);
}

Vector operator-(Vector v1, Vector v2)
{
  return Vector(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z);
}

Vector operator*(Vector v1, float f)
{
  return Vector(v1.x * f, v1.y * f, v1.z * f);
}

Vector operator*(float f, Vector v1)
{
  return Vector(v1.x * f, v1.y * f, v1.z * f);
}

Vector operator*(Vector v1, Vector v2)
{
  return Vector(v1.x * v2.x, v1.y * v2.y, v1.z * v2.z);
}

Vector operator/(Vector v1, float f)
{
  return Vector(v1.x / f, v1.y / f, v1.z / f);
}

Vector sign(Vector v)
{
  return Vector(v.x / abs(v.x), v.y / abs(v.y), v.z / abs(v.z));
}

Vector abs(Vector v)
{
  return Vector(fabs(v.x), fabs(v.y), fabs(v.z));
}

float dot(Vector v1, Vector v2)
{
  return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z;
}

float Vector::mag()
{
  return x * x + y * y + z * z;
}