Let [ x ] denotes the greatest integer function and \(\text{f}(\text{x})=\max {1+\text{x}+[\text{x}],2+\text{x},\text{x}…

Let [x] denotes the greatest integer function and \(\text{f}(\text{x})=\max {1+\text{x}+[\text{x}],2+\text{x},\text{x}+2[\text{x}]},\).\(0\leq \text{x}\leq 2\) 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

[JEE Main 2023, 15 Apr (Shift 1)]