The function $$f(x, y) = xy(1 - 3 x - 6 y)$$ has 4 critical points. List them and select the type of critical point.

Points should be entered as ordered pairs and listed in increasing lexicographic order. By that we mean that $(x, y)$ comes before $(z, w)$ if $x < z$ or if $x = z$ and $y < w$.

First point of type ? Maximum Minimum Saddle
Second point of type ? Maximum Minimum Saddle
Third point of type ? Maximum Minimum Saddle
Fourth point of type ? Maximum Minimum Saddle