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

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