$37 \cdot 12$ In the Cartesian coordinate system, points with both coordinates being integers are called integer points. The number of integer points $(x, y)$ that satisfy the inequality $(|x|-1)^{2}+(|y|-1)^{2}<2$ is
(A) 16.
(B) 17.
(C) 18.
(D) 25.
(China High School Mathematics League, 1999)
[Solution] From $(|x|-1)^{2}+(|y|-1)^{2}<2$, we can obtain that the integer points satisfying the inequality in $\left.(|x|-1,|y|-1)\right)$ are $(0,0),(0,1),(0,-1),(1,0)$, or $(-1,0)$.

Thus, it is not difficult to find that there are a total of 16 integer points $(x, y)$. Therefore, the answer is (A).