Is there a cubic polynomial $c(x,y)$ with exactly 3 saddle point critical points?

In other words, can a cubic polynomial in two variables have three critical points, all of which are saddle points? Or could it have the maximum 4 critical points (as per Bézout's theorem), with only one of them being a local extremum?

A broader formulation of the question could be:

What number of saddle points can a cubic polynomial in two variables have without having any local maximum?

Observations:

- By Bézout's Theorem a cubic polynomial (in two variables) has at most 4 critical points.
- It is easy to see that a cubic polynomial has at most one maximum / minimum. Thus every polynomial $c(x,y)$ with 4 critical points has at least 2 saddle points. For example, the polynomial $c(x,y) = x^3-3x + y^3-3y$ has four critical points: Local maximum at $(-1,-1)$; local minimum at $(1,1)$ and saddle points at $(1,-1)$ and $(-1,1)$.
- A quartic polynomial can have all 9 critical points without having any local maximum: Can a real quartic polynomial in two variables have more than 4 isolated local minima?
- As argued in the answer to question https://math.stackexchange.com/q/4620663/1134951, there is an upper bound on the number of $M-s$, where $M$ is the number local extrema (local minima and maxima) and $s$ is the number of saddle points. Here we are interested in the lower bound.