For a real number α, let [α] denote the greatest integer less than or equal to α. For a finite set S, let |S| denote the number of elements in the set S. Consider the functions f : (−3, 3) → (−∞, ∞) and g : (−3, 3) → (−∞, ∞) defined by f(x) = [x³] logₑ(1 + sin²(π(x − [x]))) and g(x) = x³ sin²(π logₑ(1 + x − [x])). Let A = {x ∈ (−3, 3) : f is discontinuous at x} and B = {x ∈ (−3, 3) : g is discontinuous at x}. Then the value of |A| + 2|B| − |A ∩ B| is ___________.