Mathematics · Continuity and Differentiability

Let [x] denote the greatest integer function and f(x) = max {1 + x + [x], 2 + x, x + 2[x]} for 0 ≤ x ≤ 2. If m is the number of points in [0,2] where f is not continuous and n is the number of points in (0,2) where f is not differentiable, then (m + n)2 + 2 is equal to: