Greatest Integer Function Continuity Differentiability

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

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