Greatest Integer Function Continuity

Let [x] denote 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