Find and classify the critical points of the following function. If there are more blanks than critical points, enter NONE. f$($x$,$y$)=$ x$^4-$x$^2-2$xy$+$y$^2+1$ The critical point with the smallest x$-$coordinate.

The point is: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Its classification: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$