Let ℕ denote the set of all positive integers. Consider the sets A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6, 7}. Let S be the set of all functions f : A → B such that f(2) ≠ 2 and f(4) ≠ 4. Consider the set T = {f ∈ S : there exists a function g : B → ℕ such that g(f(x)) = 2x for all x ∈ A}. Then the number of elements in the set T is ___________.