Consider the function $f(x, y) = x\sin(y)$.
In the following questions, enter an integer value or type INF for infinity.

(A) How many local minima does $f$ have in $\mathbf{R}^{2}$?

(B) How many local maxima does $f$ have in $\mathbf{R}^{2}$?

(C) How many saddle points does $f$ have in $\mathbf{R}^{2}$?