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